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GUIDELINE FOR FIELD TESTING OF RECIPROCATING COMPRESSOR PERFORMANCE

RELEASE 1.0

November 2009 Gas Machinery Research Council Southwest Research Institute®

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GUIDELINE FOR FIELD TESTING OF RECIPROCATING COMPRESSOR PERFORMANCE

RELEASE 1.0

Authors: Melissa Wilcox, SwRI Klaus Brun, Ph.D., SwRI

Industry Advisory Committee: David Krenek, Caterpillar – Principal Rainer Kurz, Solar Turbines – Principal Bob Webber, Dynalco William Elston, Compressor Systems, Inc. Martin Hinchliff, Dresser-Rand Everette Johnson, Cameron Warren Laible, Windrock Greg Lortie, Ariel Corporation Randall Raymer, El Paso Corporation Norm Shade, ACI Services, Inc.

This document contains information resulting from a cooperative study effort and is intended to be of beneficial use to those interested. However, the contents hereof are only guidelines for the subject matter to which the document ® pertains. Neither Southwest Research Institute Southern Gas Association, nor the Gas Machinery Research Council make any warranty or representation, express or implied, (1) with respect to the accuracy or completeness of the information contained in this document, or (2) that the use of any method, suggestion, technology, information, or guidelines disclosed herein may not infringe on rights owned or claimed by others and further disclaim any liability for the use of any methods, suggestions, technology, guidelines or other information disclosed herein.

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Guideline for Field Testing Reciprocating Compressor Performance RELEASE 1.0 Foreword Field testing of reciprocating compressors has become increasingly common due to the need to verify efficiency, power, and capacity of the compressor package upon delivery. The performance test of the reciprocating compressor in the field is often necessary to assure that the manufacturer meets performance predictions and guarantees a customer’s return on investment. Economic considerations demand that the performance and efficiency of a reciprocating compressor package be verified at the actual field site. Since the field environment is not ideal, an assessment of measurement uncertainties is necessary to characterize the validity of a performance test. As the working field environments shift further from the ideal case, the uncertainties increase. Previous field tests have shown that the compressor efficiency uncertainty can be unacceptably high when some basic rules for proper test procedures and standards are violated. This guideline applies to a typical reciprocating compressor or compressor package. The motivation for conducting a field test is based on at least one of the following objectives: •

The manufacturer is required to supply the customer with the expected performance of the reciprocating compressor. To the manufacturer, the field test provides a baseline for the compressor at the site of delivery to compare to expected performance, which is based on predicted performance. In addition, the field performance test is the final verification of the guaranteed performance.

•

The user needs to verify performance of the reciprocating compressor. Baseline performance data is obtained from the initial field performance test. The baseline test can be used for comparing and monitoring the health of compressor package in the future.

•

The user or manufacturer needs to assess performance of the reciprocating compressor or compressor package because of degradation concerns. Based on the field test results, a performance recovery program may be initiated.

•

The user requires calibration of an installed historical trend monitoring system. The field test is used to provide initial calibration of the system based on the first performance of the reciprocating compressor or compressor package.

•

The user needs to compare the performance of different units at the station or compare the performance of different stations to guide sequential dispatch of the “best” performing units/stations which are available first.

•

Incorrect pressures may have been used during compressor selection process if pulsation design was not considered. If a field performance test was not originally required during installation, the user needs to conduct a test to determine the compressor’s operation at the actual conditions experienced at the installation sight.

•

The user needs to measure the degradation (or improvement) of the system due to pulsation attenuation devices installed based on the pulsation analysis and subsequent “as-built” fabrication of the system.

The following guideline is a suggested best practice for field testing of reciprocating compressors. Specific considerations at a field site may require deviation from this guideline in order to meet safety requirements, improve testing efficiency, or comply with station operating philosophy.

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Guideline for Field Testing of Reciprocating Compressor Performance RELEASE 1.0 TABLE OF CONTENTS 1. 2. 3.

4.

5.

6.

7.

8.

9.

PURPOSE AND APPLICATION .........................................................................................1 PACKAGE AND COMPRESSOR PERFORMANCE ..........................................................1 PERFORMANCE PARAMETERS ......................................................................................2 3.1 Reciprocating Compressor Flow/Capacity .................................................................2 3.2 Compressor Efficiency ...............................................................................................3 3.3 Indicated Cylinder Horsepower (ICHP) and Brake Horsepower (BHP).......................6 3.4 Differential Indicated Power (DIP) ..............................................................................7 3.5 Suction and Discharge Volumetric Efficiency .............................................................7 3.6 Driver Power and System Efficiency ..........................................................................8 3.7 Equations of State .....................................................................................................9 DATA COLLECTION PROCEDURES ..............................................................................11 4.1 PV Card Method ......................................................................................................11 4.2 Enthalpy Rise Method ..............................................................................................20 4.3 PV Card and Enthalpy Rise Method ........................................................................24 TEST PREPARATION......................................................................................................24 5.1 Pre-Test Meeting .....................................................................................................25 5.2 Pre-Test Operation and Instrumentation Checkout ..................................................25 5.3 Pre-Test Equipment Checkout .................................................................................27 5.4 Pre-Test Information ................................................................................................27 5.5 Test Stability ............................................................................................................29 5.6 Safety Considerations..............................................................................................31 MEASUREMENT AND INSTRUMENTATION ..................................................................31 6.1 Measurement of Pressure........................................................................................32 6.2 Measurement of Temperature .................................................................................36 6.3 Measurement of Flow ..............................................................................................38 6.4 Measurement of Gas Composition...........................................................................40 6.5 Measurement of Crank Position ...............................................................................42 TEST UNCERTAINTY ......................................................................................................47 7.1 Ideal Field Test Conditions for Reducing Uncertainties ............................................ 49 7.2 Effects of Non-Ideal Installations on Uncertainty ......................................................52 INTERPRETATION OF TEST DATA ................................................................................55 8.1 Data Reduction and Checking Uncertainties ............................................................55 8.2 Use and Comparison of Data ...................................................................................55 8.3 Using Redundancy to Check Test Measurement and Uncertainty ........................... 57 8.4 Analysis of Measured Results ..................................................................................57 REFERENCES .................................................................................................................59

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APPENDICES APPENDIX A – General Performance Testing Procedure .........................................................62 APPENDIX B – Calculation of Theoretical PV Diagram.............................................................68 APPENDIX C – Equation of State Models .................................................................................77 APPENDIX D – Equation of State Model Comparison of Predicted Performance Data ............. 85 APPENDIX E – Uncertainty Analysis for Independent Variable Measurements......................... 91 APPENDIX F – Compressor Performance Diagnostics with PV Diagrams .............................. 105 APPENDIX G – Polytropic Efficiency ......................................................................................112 APPENDIX H – Heat Loss Estimations ...................................................................................116 APPENDIX I – Example PV Card Calculations........................................................................ 128 APPENDIX J – Data Sheets for Reciprocating Compressor Performance Testing .................. 145

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LIST OF FIGURES Figure 3-1.

Figure 8-3.

Enthalpy/Pressure Change During Compression and Expansion Process (Edmister and Lee, 1984).....................................................................................5 Typical PV Diagram .............................................................................................6 PV Diagram with Pressure Also Measured in Nozzles .........................................7 Typical PV Diagram ...........................................................................................12 Location of Test Instrumentation for PV Card Method ........................................ 13 Pressure Transducer Installed on Compressor Cylinder with Indicator Valve ..... 14 PV Diagram with Channel Resonance Present – Uncorrected High-Speed Compressor (950 RPM) .....................................................................................15 PV Diagram with Channel Resonance Present – Corrected High-Speed Compressor (950 RPM) .....................................................................................15 PV Diagram with Channel Resonance Present – Uncorrected Low-Speed Compressor (330 RPM) .....................................................................................16 PV Diagram with Channel Resonance Present – Corrected Low-Speed Compressor (330 RPM) .....................................................................................16 PV Diagram with Varying ODC Measurements ..................................................18 Location of Test Instrumentation for Enthalpy Rise Method ............................... 21 Example of Drift and Fluctuations in a Temperature Measurement .................... 31 ASME PTC 10 Recommended Installation Configuration for Pressure and Temperature Measurement ................................................................................34 Sampling Method with Pigtail as Recommended in API MPMS Chapter 14.1....................................................................................................................41 Encoder Installed on a Slow-Speed Reciprocating Compressor on Flywheel ..... 43 Encoder and Adapter Installed on a High-Speed Reciprocating Compressor ..... 43 Rotation of PV diagram to Correctly Reference ODC ......................................... 44 Example of Set-up for Dial Indicator Method ......................................................45 Hard Stop Placed Between Cylinder Head and Piston Through Valve Pocket................................................................................................................46 Placement of ODC Mark Between Two Initial Marks .......................................... 46 Comparison of Tests with Different Levels of Uncertainty .................................. 50 Actual and Theoretical PV Diagrams for Performance Test at 450 RPM ............ 51 Example of Compressor Performance Curves for High-Speed Transmission Compressor .......................................................................................................56 Comparison of Theoretical Predicted Performance and Measured Performance Test Point .....................................................................................57 Example of Test Uncertainty Range ...................................................................58

Figure B-1. Figure B-2. Figure B-3. Figure B-4.

Theoretical PV Diagram with Start of Expansion Stroke Indicated ..................... 71 Theoretical PV Diagram with Start of Compression Stroke Indicated ................. 71 Theoretical PV Diagram with Multiple Points Plotted on Expansion Line ............ 72 Theoretical PV Diagram with Multiple Points on Compression Line ................... 73

Figure 3-2. Figure 3-3. Figure 4-1. Figure 4-2. Figure 4-3. Figure 4-4. Figure 4-5. Figure 4-6. Figure 4-7. Figure 4-8. Figure 4-9. Figure 5-1. Figure 6-1. Figure 6-2. Figure 6-3. Figure 6-4. Figure 6-5. Figure 6-6. Figure 6-7. Figure 6-8. Figure 7-1. Figure 7-2. Figure 8-1. Figure 8-2.

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Figure B-5.

Complete Theoretical PV Diagram ..................................................................... 73

Figure C-1.

Calculation Path for Equations of State .............................................................. 81

Figure D-1.

Compression T-S Diagram................................................................................. 88

Figure E-1. Figure E-2. Figure E-3.

Determination of Uncertainty Using Differential Methods ................................... 94 Determination of Uncertainty Using Perturbation Methods ................................. 95 Example of Change in Theoretical PV Diagram with Pressure Uncertainty ...... 101

Figure F-1. Figure F-2. Figure F-3.

Diagram Illustrating the Effects of Suction Valve Leaks ................................... 107 Diagram Illustrating the Effects of Discharge Valve Leaks ............................... 108 Diagram Illustrating the Effects of Piston Ring Leaks ....................................... 109

Figure H-1. Figure H-2. Figure H-3.

Figure H-7.

Schematic of Energy Exchange in Reciprocating Compressor ......................... 118 Radiation Heat Transfer Coefficient with Emissivity and Mean Temperature.... 120 Natural Convection Heat Transfer Coefficient with X and Mean Temperature .................................................................................................... 121 Forced Convection Heat Transfer Coefficient with Y and Mean Temperature .................................................................................................... 122 Natural Convection Heat Transfer Coefficient for Vertical Pipes with ∆T and Length.............................................................................................................. 124 Natural Convection Heat Transfer Coefficient for Horizontal Pipes with ∆T and Diameter ................................................................................................... 124 Forced Convection Heat Transfer Coefficient with Z and Mean Temperature .. 126

Figure I-1. Figure I-2. Figure I-3. Figure I-4. Figure I-5. Figure I-6.

Constructed Measured PV Diagram ................................................................. 131 PV Diagram with Channel Resonance Removed through Filtering ................... 132 Graphical Representation of Integration of PV Diagram ................................... 133 Where Suction and Discharge Valves Open on PV Diagram ........................... 134 Theoretical PV Diagram with Correct PV Diagram ........................................... 135 Variation in PV Diagram with Piston Position Uncertainty ................................ 138

Figure H-4. Figure H-5. Figure H-6.

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LIST OF TABLES Table 3-1. Table 5-1. Table 5-2. Table 5-3. Table 6-1. Table 6-2. Table 6-3. Table 6-4. Table 7-1. Table 7-2. Table 7-3. Table 7-4. Table 7-5. Table 7-6. Table D-1. Table D-2. Table D-3. Table D-4. Table D-5.

Table I-1. Table I-2. Table I-3. Table I-4. Table I-5.

Suggested Applications for Equation of State Usage ......................................... 10 Maximum Deviations from Specified Values and Fluctuations from Average Readings ........................................................................................................... 28 Additional Assessment of Stability of Compressor During Pre-Test ................... 30 Assessment of Stability of Compressor Driver During Pre-Test.......................... 30 Typical Uncertainties in Pressure Measurement (shown as percent of full scale) ................................................................................................................. 36 Recommended Depth of Thermowells ............................................................... 37 Typical Uncertainties in Temperature Measurement (shown as percent of full scale) ........................................................................................................... 38 Achievable Uncertainties in Flow Measurement with No Pulsating Flow ............ 40 In-Practice Achievable Uncertainty for Measured Test Parameters .................... 49 Compressor Geometry ....................................................................................... 50 Summarization of Uncertainty for Performance Test at 450 RPM ...................... 51 Example of Total Uncertainty Calculation for Compressor in "Near Ideal" Case .................................................................................................................. 52 Non-Ideal Installation Effects on Compressor Uncertainty.................................. 53 Effects of Non-Ideal Encoder and Cylinder Pressure Measurements ................. 54 Gas Mixtures Used in EOS Model Comparison .................................................. 87 Assumed Measured Conditions; PR = 1.3.......................................................... 87 Assumed Measured Conditions; PR = 2.2.......................................................... 88 Horsepower and Efficiency Calculations for EOS Models at Pressure Ratio of 1.3.................................................................................................................. 89 Horsepower and Efficiency Calculations for EOS Models at Pressure Ratio of 2.2.................................................................................................................. 89 Calculation of Total Uncertainty of Measured ICHP for Cylinder End ............... 139 Defined and Calculated Values for Theoretical ICHP Uncertainty Due to Pressure Uncertainty ....................................................................................... 140 Defined and Calculated Values for Theoretical ICHP Uncertainty Due to Isentropic Constant Uncertainty ....................................................................... 141 Defined and Calculated Values for Theoretical ICHP Uncertainty Due to Clearance Volume Uncertainty......................................................................... 141 Calculation of Total Uncertainty of Measured ICHP for Cylinder End ............... 142

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DEFINITION OF SYMBOLS Symbols and Units: cp cv e f h i k l m n p q r s x y

= = = = = = = = = = = = = = = =

Specific heat at constant pressure (Btu/lbm-R) Specific heat at constant volume (Btu/lbm-R) Voltage (volts) Schultz factor for polytropic efficiency calculation or function elsewhere Enthalpy of gas at suction, discharge or isentropic conditions (Btu/lbm) Current (amps) Isentropic exponent Connecting Rod Length (in) Mass (lbm) Exponent or ending counting value Total (stagnation) pressure of gas at suction or discharge side (psia) Heat transferred (Btu/lbm) Piston rod diameter (if not present r = 0) (inches) Entropy at specified pressure and temperature (Btu/lbm-R) Represents a parameter or calculated value Mole fractions

A B BDC BHP BWR BWRS C*

= = = = = = =

CL% CQ*

= =

DF DIP EOS EVs EVd F FFT H ICHP IDC K1 K2 L LHV LKP MW N ODC

= = = = = = = = = = = = = = = = = =

Cross-sectional area of pipe (ft2) Cylinder bore (inches) Bottom Dead Center (see IDC definition) Brake Horsepower of Compressor (HP) Benedict-Webb-Rubin Benedict-Webb-Rubin-Starling Factor to convert capacity using defined units for other symbols, to MMSCFD (0.6397) or SCFM (444.25) Percent clearance of cylinder (%) Factor to convert capacity using defined units for other symbols, to MMSCFD (0.2314 x 10-6) or SCFM (1.607 x 10-4) Degrees of Freedom Differential Indicated Power (HP) Equation of State Suction volumetric efficiency (%) Discharge volumetric efficiency (%) Represents a calculated function, F Fast Fourier Transform Enthalpy rise for compressor, either actual or ideal (Btu/lbm) Actual Indicated Compressor Horsepower from measured PV Diagram (HP) Inner Dead Center (see definitions) Expansion line constant used for theoretical PV diagram generation Compression line constant used for theoretical PV diagram generation Loss factor Fuel gas lower heating value, as determined through thermodynamic analysis (Btu/lbm) Lee-Kesler-Plocker Molecular Weight Unit Speed (RPM) Outer Dead Center (see definitions)

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P Pf PR PV Q R RK RTD S SG SRK T TDC U V W Z

= = = = = = = = = = = = = = = = =

Power (HP) Power factor Peng-Robinson Pressure-Volume Capacity (MMSCFD or SCFM) or volumetric flow rate Gas constant Redlich-Kwong Resistance Temperature Detector Stroke (inches) Specific gravity of gas (referenced to air) Soave-Redlich-Kwong Absolute temperature (°R) Top Dead Center (see ODC definition) Flow velocity in pipe (ft/min) Volume (in3) Work performed by compressor end (area of PV diagram) (in-lbs) Gas compressibility

Δ ζ η θ v ρ ω

= = = = = = =

Finite change in value or uncertainty Damping Ratio Efficiency (%) Position of shaft as reported by encoder (degrees) Specific volume of gas at suction, discharge or isentropic conditions (ft3/lbm) Density (lbm/ft3) Resonance frequency

Subscripts: a comp components cool cyl cl d e fuel gas ho i in isen m min max mo mol% p s stat stroke

= = = = = = = = = = = = = = = = = = = = = = =

Actual Full compressor Components Cooling Individual cylinder end Clearance Discharge Engine Fuel Gas Heat removed through cooling jackets, conduction, and convection Placeholder for later assigned number Input condition Isentropic Mechanical Minimum Maximum Motor Fractional mol % for gas composition Polytropic Suction Static Stroke

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sys swept th universal

= = = =

System Swept volume Thermal Universal gas constant

P STD

= =

Polytropic condition Standard conditions (14.7 psia and 60 °F)

•

= = =

Rate (ex. m is mass flow rate) Numbers used to represent individual cylinders or cylinder ends Function of theta or rotational position

•

1,2,… θ

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DEFINITIONS 1.

Absolute Pressure: The pressure measured above a perfect vacuum.

2.

Absolute Temperature: The temperature above absolute zero stated in degrees Rankine or Kelvin. Rankine temperature is the Fahrenheit temperature plus 459.67 degrees; Kelvin is the Celsius temperature plus 273.15 degrees.

3.

Brake Horsepower (BHP): Brake horsepower refers to the power required of the driver to supply power to the compressor, or compressor cylinder, and must include compressor mechanical (bearings and seals) and compression losses. In the evaluation of a compressor package, the BHP will need to also consider other parasitic loads, such as cooling fans driven off the front end of the engine.

4.

Brake Specific Fuel Consumption: Brake Specific Fuel Consumption is the fuel flow rate in standard cubic feet per hour multiplied by the net dry heating value (LHV) of the fuel at standard conditions in British thermal units per cubic foot divided by the total brake horsepower measured at the engine flywheel. This term is applicable to engine driven packages and integral compressors.

5.

Brake Thermal Efficiency: Brake Thermal Efficiency is the overall efficiency of an engine. It is the BHP or useful work delivered by the engine divided by the power input of the fuel.

6.

Capacity: The rate of flow, determined by the mass flow divided by density of the gas under standard conditions (SCFM or MMSCFD).

7.

Clearance: Clearance refers to the actual volume in cubic inches trapped in the cylinder when the piston is at outer dead center (including pocket and valve dead volumes).

8.

Compression and Expansion Effective Exponents: These are the isentropic exponents for compression and expansion of the gas. These can be determined from the expansion and compression lines on the PV diagram.

9.

Crank End: The crank end of the compressor cylinder is the end which is closest to the crank shaft.

10. Cylinder Displaced Volume: Cylinder displaced volume refers to the total volume displaced by the piston, including the total cylinder end clearance volume. 11. Density: The mass of gas per unit volume, equal to the reciprocal of the specific volume. The density is a thermodynamic property determined from the total pressure and temperature at a point in the fluid. 12. DIP (Differential Indicated Power): DIP represents the difference between the indicated power for some portion or zone of the PV diagram with one boundary of that zone being a reference pressure line, which may be constant or varying. 13. Differential Pressure: The difference between any two pressures measured with respect to a common reference (i.e., the difference between two gage pressures). 14. Discharge Volumetric Efficiency (EVd or VEd): This is defined as the ratio of the volume of gas discharged from the cylinder (at discharge pressure and temperature) to the swept volume of the cylinder end. 15. Electric Motor Efficiency: The electric motor efficiency is the ratio between the output or delivered power to the measured electrical input power.

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16. Engine Fuel Flow: The engine fuel flow is the mass flow rate of fuel to the engine for operation. 17. Gage Pressure: The pressure measured directly with the existing barometric pressure as the zero base reference. 18. Head End: The head end of the compressor cylinder is the end which is furthest from the crankshaft. 19. Indicated Compressor Horsepower (ICHP): This is the total rate at which the piston faces of all cylinder ends do work on the gas, based on measured cylinder pressure, expressed in HP. 20. Inner Dead Center (IDC): Inner dead center refers to the condition where the piston is closest to the crankshaft (also referred to as bottom dead center (BDC)). 21. Isentropic Compression: A reversible, adiabatic compression process. 22. Isentropic Efficiency: This is the ratio of isentropic power (IP) to measured power (ICHP for PV Cards or P for Enthalpy Rise). This efficiency assumes that all heat transfer is accounted for in the actual or measured power. If all the heat transfer is not accounted for, then the efficiency should be referred to as a “modified” isentropic efficiency. 23. Isentropic Power: This is the ideal power required to isentropically compress and deliver the capacity from suction to discharge conditions. 24. Mean Cylinder Effective Exponent: compression in the cylinder.

This is the polytropic exponent for expansion and

25. Mechanical Efficiency: This is the ratio of the total measured compressor power (ICHP or P) to total shaft horsepower (BHP). This is often assumed to be in the range of 92-97% for lowspeed and high-speed compressors. 26. Mechanical Losses: The total power consumed by frictional losses in integral gearing, bearings, seals, packing, rider bands, and piston rings. 27. Outer Dead Center (ODC): Outer Dead Center refers to the condition where the piston is at point of travel furthest from the crankshaft (also referred to as top dead center (TDC)). 28. Polytropic Compression: A reversible compression process between the total suction pressure and temperature and the total discharge pressure and temperature. The polytropic compression process follows a path such that the polytropic exponent, nP, is constant during the process. 29. Pressure Ratio: The ratio of absolute total discharge pressure to absolute total suction pressure. 30. Shaft Power: The power delivered to the compressor shaft by the driver, also known as brake power. Shaft power is equal to gas power plus mechanical losses. 31. Stage: A single, or number of parallel piston-cylinders and associated stationary flow passages. 32. Standard Volume Flow: The flow rate expressed in volume flow units at either of the standard conditions outlined: a. SI flow units are typically i. Normal cubic meters per hour (Nm3/h) or Normal cubic meters per minute (Nm3/min) ii. At ISO standard conditions of: Absolute Pressure: 1.013 bar, Temperature 0 deg C

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b. US customary flow units are typically i. Standard cubic feet per minute (SCFM), or Million standard cubic feet per day (MMSCFD) ii. At customary standard conditions of: Absolute pressure: 14.7 psia, Temperature: 60 deg F 33. Static Pressure: The pressure measured in such a manner that no effect is produced by the velocity of the flowing fluid. 34. Static Temperature: The temperature determined in such a way that no effect is produced by the velocity of the flowing fluid. 35. Suction Volumetric Efficiency (EVs or VEs): This is defined as the ratio of the volume of gas drawn into the cylinder (at suction pressure and temperature) to the swept volume of the cylinder end. 36. Swept Volume: Swept volume refers to the total volume displaced by the piston not including the total cylinder end clearance volume. 37. Total (Stagnation) Pressure: An absolute or gage pressure that would exist when a moving fluid is brought to rest, and its kinetic energy is converted to an enthalpy rise by an isentropic process from the flow condition to the stagnation condition. In a stationary body of fluid, the static and total pressures are equal. 38. Total (Stagnation) Temperature: The temperature that would exist when a moving fluid is brought to rest and its kinetic energy is converted to an enthalpy rise by an isentropic process from the flow condition to the stagnation condition. In a stationary body of fluid, the static and total temperatures are equal. 39. Valve Losses: Valve losses refer to the pressure losses across the suction and discharge valves. These are due to valve geometry flow losses. The flow through the valve is affected by pulsations.

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Guideline for Field Testing of Reciprocating Compressor Performance FINAL VERSION 1.0 1.

PURPOSE AND APPLICATION

The following guideline is intended to serve as a reference for field testing of reciprocating compressor performance. This guideline applies to any party conducting a field test of a reciprocating compressor or compressor package (manufacturer, user company, or third-party). It is intended to provide a technically sound, yet practical procedure for all aspects of conducting field performance tests of reciprocating compressors. Specific requirements of a particular test may dictate that the test procedure deviates from this guideline or the ideal installation described. However, when a particular test deviates from the installation requirements or other test procedures, the deviation will affect the uncertainty of the test and should be accounted for in the uncertainty analysis, as recommended in this guideline. The development of this guideline was initiated by the ever growing presence of high-speed reciprocating compressors in the industry. However, there are several low-speed reciprocating compressors operating that also need performance tests. This guideline addresses items that should be considered for both highand low-speed compressors when conducting performance tests. The standards that are used as references for this guideline are ASME PTC 10-1997, “Performance Test Code on Compressors and Exhausters,” and API 618, “Reciprocating Compressors for Petroleum, Chemical, and Gas Industry Service,” and ISO 1217, “Displacement Compressors – Acceptance Tests.” 2.

PACKAGE AND COMPRESSOR PERFORMANCE

The performance testing of a reciprocating compressor can be completed in various fashions. This is dependent upon the intent of the testing. There are two main methodologies that are used for testing: the Enthalpy Rise method and the Pressure-Volume (PV) Card method (these methods are discussed in detail in later sections of this guideline). These two methodologies can be used individually or in combination with one another. Again, this is dependent upon the objectives of the performance test. There is much debate as to whether the compressor performance can adequately be assessed by looking at the compressor individually, flange-to-flange, or the compressor package as a whole, lateral-to-lateral. All of these tests have their benefits depending upon the objective of the testing. If the user intends to conduct a performance test with the intent of verifying the manufacturer’s ratings, then the compressor would need to be tested individually. The compressor performance encompasses the machinery located between the suction and discharge nozzle of each compressor cylinder. It would not necessarily include the effects of pulsation bottles and piping and other equipment outside the nozzles. These could be included, if these effects are deemed important in the performance test. A combination of the Enthalpy Rise and PV Card methods can provide more information. If testing to verify the manufacturer’s ratings is desired, then the tests should be conducted using a methodology as close to that used during the manufacturer’s performance tests as possible, if practical. Compressor package performance is used when the performance test mandates that the losses associated with piping, bottles, and other auxiliary equipment be included in the assessment. This approach may be

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used to validate the package design or to develop performance maps relative to the process parameters that are being monitored for capacity/load control or reporting purposes. For example, if routine load control is based on suction pressure observed at the inlet of the suction scrubber, the compressor performance test should allow for performance to be correlated to this measurement point regardless of cylinder flange measurements. It also can include the performance of compressor drivers. The package performance requires more measurements than the ones detailed below for the PV Card and Enthalpy Rise method. It may also require a fuel flow rate measurement for engine driven compressors or electrical usage measurement for electric motor driven compressors. The package performance is lacking in the sense that the losses may not be directly identified. This is one way a combination of the PV Card and Enthalpy Rise method is useful. Losses can easily be placed on the suction or discharge of particular cylinders using the PV Card method and overall performance can be found with the Enthalpy Rise method. The losses are a combination of valve losses, gas passage losses, and pulsations. Further testing would be needed to identify losses associated with equipment external to the compressor. All side streams or exchanges of mass need to be considered in the package performance test. This guideline focuses on the details for compressor performance tests. It covers the Enthalpy Rise method and PV Card method. It does not cover all the aspects of package performance testing, such as acoustical and mechanical responses and parasitic loads on the compressor or engine, but the information presented here is useful and can be used in completing a compressor package performance test. 3.

PERFORMANCE PARAMETERS

The following six performance parameters generally describe the performance of a reciprocating compressor. These parameters are commonly used in acceptance testing, testing to determine degradation of the machine, and operational range testing. The primary measurements required in order to calculate these parameters are discussed in Section 6. The uncertainty calculations are discussed in Section 7. Accounting for the effect of non-ideal installations on uncertainty is also discussed in Section 7. Performance Parameters:

3.1

1.

Capacity

2.

Compressor Efficiency

3.

Indicated Cylinder Horsepower and Brake Horsepower

4.

Differential Indicated Power

5.

Suction and Discharge Volumetric Efficiency

6.

Driver Power and System Efficiency

Reciprocating Compressor Flow/Capacity

Capacity of a compressor cylinder is the gas flow rate in standard cubic feet per minute (SCFM) or in million standard cubic feet per day (MMSCFD) at standard conditions of 14.696 psia pressure and 519.67 R temperature. There are many ways to determine this value. It can be measured directly with a flow meter or calculated given other measured parameters. Due to significant effects of pulsations on flow measurements, it is necessary to check the flow measurement. This can be done by completing one of the calculations below to compare the results. For adiabatic compression (no heat transfer, no valve losses, or leaks) of either

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ideal or real gases, flow may be properly predicted by the methods given below. In reality, heat transfer, valve losses, and finite valve and ring leaks are always present to some degree. Each of these effects tends to reduce the actual capacity from that predicted by equations. Industry experience has shown that on “healthy” cylinders, the capacity can be calculated within 2-3% of the actual value. For low ratio compressors, such as pipeline compressors, the capacity can be calculated within 1% of the measured value. The deviation will be greater on non-cooled or unhealthy cylinders. Capacity from Enthalpy This method can only be used when pressure and temperature measurements are taken at the suction and discharge of the compressor and when the PV diagram is constructed from measurements on each cylinder end. These measurements are used with the appropriate Equation of State (EOS) to calculate the enthalpy values (hd and hs). The variable C* is a factor used to convert the capacity into MMSCFD or SCFM. For MMSCFD use 0.6397 and for SCFM use 444.25. These factors apply when the units of the variables in the equations are the same as defined in the nomenclature of this document. The variable ICHP is the full compressor horsepower. This is the area of the PV diagram for the cylinder end being tested.

C * * ICHP Q= (hd − hs ) * SG

(3-1)

Capacity from Cylinder Parameters Capacity for a cylinder end may also be calculated from cylinder parameters using the following equations. The variable CQ* is used to convert the final capacity into MMSCFD or SCFM. The value for MMSCFD is 0.2314x10-6 and for SCFM is 1.607x10-4. These factors apply when the units of the variables in the equations are the same as defined in the nomenclature of this document. The volumetric efficiencies, EVs and EVd, can be calculated using Equations 3-14 and 3-15. The piston rod diameter (r) equals zero for capacity calculations for the head end of the compressor:

(CQ )* (B Q= *

2

(CQ ) * (B Q= *

2

2

)

− r 2 * S * N * EVs * p s * Z STD Ts * Z s

(3-2)

EV * p s EVd * pd − r 2 * S * N * Z STD * s + Td * Z d Ts * Z s

(3-3)

)

These equations tend to overestimate the actual capacity because they do not account for gas preheating. As the gas enters the cylinder, it gets hotter from heat transfer with the cylinder walls and from mixing with residual gas in the cylinder bore. 3.2

Compressor Efficiency

Compressor efficiency is commonly defined based on either isentropic or polytropic ideal processes (see Appendix G for polytropic efficiency). Both definitions are appropriate for performance comparison as they provide a ratio of the ideal (isentropic or polytropic) enthalpy difference across the compressor to the actual enthalpy difference (head). The isentropic process assumes a reversible adiabatic process without losses (i.e., no change in entropy). This process is an ideal reference process.

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The compressor actual enthalpy rise (H) and isentropic enthalpy rise (Hisen) are determined from the measurement of pressure and temperature on the suction and discharge and the calculation of enthalpy using an EOS model. The enthalpy rises are calculated from the enthalpies associated with each state from the EOS as follows: Isentropic Enthalpy Rise

H isen = hd ,isen − hs = h( pd , ss ) − h( ps , Ts )

(3-4)

Actual Enthalpy Rise

H = hd − hs = h( pd , Td ) − h( ps , Ts )

(3-5) * Note that hd,isen is the enthalpy associated with the discharge pressure at the suction entropy, ss, because the entropy change is zero in an isentropic process. All enthalpies should be directly determined from the EOS. Isentropic enthalpy difference can also be determined for estimation purposes (assuming ideal gas behavior):

∆h = hd ,isen

k −1 pd k − hs = −c pTs 1 − ps

(3-6)

The isentropic exponent, k, is defined as:

ln k= ln

pd ps

νs

(3-7)

ν d ,isen

Isentropic Efficiency Below are three equations to calculate isentropic efficiency. As mentioned above, the isentropic process is adiabatic and reversible. In order to calculate a true isentropic efficiency, all heat losses in the system should be accounted for. This is extremely difficult to do since many of these losses are due to friction. If a reciprocating compressor has low or negligible overall heat losses (this would be true on a low pressure ratio machine with no jacket cooling), then the efficiency calculated from Equations 3-8 through 3-10 can be considered to be an isentropic efficiency. However, if heat transfer is present, then the efficiency can be considered a “modified isentropic efficiency” instead, since it does not represent a purely isentropic process. Some examples of where heat transfer would be present are cylinders with jacket cooling and when the surface temperature of the compressor is significantly different than the ambient temperature (more than 20 degrees). The criterion discussed here applies for any mention of isentropic efficiency throughout this guideline.

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Equation 3-8 would be used with the Enthalpy Rise method where the enthalpy values will be calculated from pressure and temperature on the suction and discharge of the compressor. The isentropic efficiency is calculated from the isentropic and actual enthalpy rise. This can also be used to calculate the efficiency of an individual cylinder with pressure and temperature measurements at the suction and discharge nozzles. Equation 3-9 is used with the PV Card method. This equation is used to determine the individual cylinder end efficiency. The indicated compressor horsepower (ICHP) is determined from the measured PV diagram and the isentropic power (Pisen) is from the theoretical isentropic PV diagram. Equation 3-10 is used with the PV Card method to calculate the efficiency of the full compressor. The top of the equation is the summation of all calculated theoretical powers which are divided by the summation of all measured powers.

η isen ,comp = η isen ,cyl =

hd ,isen − hs

(3-8)

hd − hs

Pisen ICHP

η isen ,comp =

(3-9)

Pisen ,1, HE + Pisen ,1,CE + Pisen , 2, HE + ...

(3-10)

ICHP1, HE + ICHP1,CE + ICHP2, HE + ...

The compression process for a typical reciprocating compressor and the associated enthalpy change are shown on a P-h diagram in Figure 3-1 for 100% methane gas mixture. At the start of the compression process the pressure and enthalpy are at ps and hs. An isentropic compression would follow the top dashed line until it reaches pd and hd,isen. The actual compression process follows the bottom solid line until it reaches pd and hd. The difference in enthalpy across these two lines gives the efficiency (Equation 3-8).

pd, hd,isen pd, hd ps, hs

Figure 3-1. Enthalpy/Pressure Change During Compression and Expansion Process (Edmister and Lee, 1984)

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3.3

Indicated Cylinder Horsepower (ICHP) and Brake Horsepower (BHP)

The Indicated Cylinder Horsepower term is characteristic of a performance test conducted using the PV Card method. In that particular method, a pressure-volume curve is generated from the pressure and volume changes within the compressor cylinder. The area within the PV curve represents the work performed by the cylinder end and can be used to derive Indicated Cylinder Horsepower (ICHP), which is directly related to the speed of the compressor. The equation below shows the calculation of ICHP from the area of the PV diagram. The ICHP is, in turn, used with a theoretical horsepower to determine the individual cylinder end’s efficiency. Figure 3-2 shows a representation of an actual PV diagram. The area enclosed within the compression and expansions lines, as well as the discharge and suction lines, is the ICHP.

ICHP =

W *N 396000

(3-11)

The BHP includes the effects of seals, bearings, rider bands, and piston rings. The BHP can be measured with a torque meter on separable compressors, but usually the mechanical efficiency is assumed to be 9297% for both low- and high-speed compressors. Once the BHP for each individual cylinder end is calculated, these values can be summed to obtain the compressor BHP. Equation 3-12 below shows the calculation of cylinder end BHP with indicated compressor cylinder end horsepower and mechanical efficiency. Equation 3-13 shows the calculation of the full compressor BHP by adding the individual cylinder end values. More information on shaft power measurements with a torque meter can be found in the American Society of Mechanical Engineers (ASME) Performance Test Code (PTC) 19.7, “Measurement of Shaft Power.”

BHPcyl =

ICHP

(3-12)

ηm

BHPcomp = BHP1 + BHP2 + ...

(3-13)

Figure 3-2. Typical PV Diagram

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3.4

Differential Indicated Power (DIP)

Differential Indicated Power (DIP) is a term used with the PV Card method. DIP represents the difference between the indicated power for some portion or zone of the diagram with one boundary of that zone being a reference pressure line, which may be constant or varying. Figure 3-2 illustrates the Discharge Differential Indicated Power (DIPd) and Suction Differential Indicated Power (DIPs) relative to assumed constant suction pressure (ps) and discharge pressure (pd), for this case, taken as the Inner Dead Center (IDC) and Outer Dead Center (ODC) diagram pressure points. DIPd and DIPs, using the IDC and ODC pressure values, reflect the effects of valve and internal passage flow losses and pulsation effects. Nozzle or bottle pressures are often used as references for obtaining DIPd and DIPs values in an effort to account for the influence of pulsations; however, this should be approached with caution since pressures at these locations may not be representative of the dynamic pressure just outside the valves. Figure 3-3 shows an example of a PV diagram where the pressures inside the suction and discharge nozzles were used to determine the DIP.

Figure 3-3. PV Diagram with Pressure Also Measured in Nozzles

3.5

Suction and Discharge Volumetric Efficiency

The effective suction volume is the amount of gas drawn into the cylinder during the expansion stroke. The effective discharge volume is the amount of gas expelled during the compression stroke. These values are characterized by the Volumetric Efficiency. Volumetric Efficiency (EV or VE) is defined as the ratio of the volume of gas drawn into or expelled from the cylinder (at suction or discharge pressure and temperature) to the swept volume of the piston. Theoretical or ideal EVs (suction) and EVd (discharge) may be calculated using the equations below. The calculated EVs has an implicit assumption that gas is induced at suction temperature. The temperature actually rises during the suction intake, due to heat transfer from the cylinder and mixing of the suction gas with the residual gas remaining in the

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clearance of the cylinder. The temperature effects, as well as effects due to piston rings, packing rings, and valve leaks, are accounted for in the theoretical calculation with a loss factor (L). The losses can only be determined empirically (measured in test). For transmission compressors or low pressure ratio compressors, the losses usually range from 1-3%. At high pressure ratios, these losses are from 5-10%.

p EVs = 100 - CL% * d p s

EVd =

p 100 - CL% * d p s pd ps

1 k

- 1 − L 1 k

1 k − 1

−L

(3-14)

(3-15)

The measured volumetric efficiency is defined by the valve opening events, toe pressure, or measured nozzle pressure. The valve openings can be determined from the measured PV diagram. Valve openings are assumed to occur when the cylinder pressure crosses the pressure just outside the valve (pressure in the suction or discharge nozzles). The suction and discharge valve openings are labeled in Figure 3-3. For example, if the suction valve opens at 25% volume (ODC is 0% volume) on the expansion stroke, then the suction volumetric efficiency is 75%. Also, if the discharge valves open at 60% volume on the compression stroke, then the discharge volumetric efficiency is 60%. 3.6

Driver Power and System Efficiency

If the overall performance is being evaluated (including the driver and compressor), it is important to determine the driver power during performance testing. Engine During performance testing of reciprocating compressors with gas engines, the flow rate of the fuel is measured with a flow meter. Also, the gas composition of fuel is measured. From the gas composition, the Low Heating Value (LHV) of the fuel can be calculated using EOS. The equations below are used to calculate the input power from the fuel and the engine brake thermal efficiency. The BHP is determined from the compressor ICHP using a calculated, measured, or assumed mechanical efficiency of the compressor. If the compressor is separable (usually high speeds), then the power can be measured with a torque meter at the coupling. The power input to an integral engine (slow speed) would have to be determined with the ICHP. More details on performance test of engines can be found in PTC 17, “Reciprocating Internal – Combustion Engines.” •

Pin = m fuel * LHV

ηe =

BHP Pin

Guideline for Field Testing of Reciprocating Compressor Performance

(3-16) (3-17)

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BHP =

ICHP

ηm

(3-18)

Electric Motor If an electric motor is driving the compressor, then the applied voltage and phase currents must be measured to determine the absorbed power. Typically an ammeter will measure the current draw of the motor. If these values are measured, then the power can be determined from the first equation below for each phase. The power factor should be measured at the conditions that the performance test will be conducted. The power factor provided in the manufacturer literature was determined for a steady state load. Electric motors driving reciprocating compressors will experience a pulsating load, which causes a shift in the power factor. The total power is determined by summing the power of the phases. The motor efficiency, ηmo, can be calculated using Equation 3-17 and substituting the input power to the engine with input power to the motor. Methods of determining motor absorbed power can be found in a relevant standard, such as IEEE 112, “Test Procedure for Polyphase Induction Motors and Generators” and IEEE 115, “Test Procedures for Synchronous Machines.”

Pin = 0.001341* i * e * Pf

(3-19)

System Efficiency The system efficiency can be estimated from the ratio of the compressor gas power (power transmitted from compressor to gas through compression) and the power input into the compressor driver, as shown in the equation below. For the PV Card method, compressor power is calculated by adding the ICHP of each cylinder end together. For the Enthalpy Rise method, if the power is measured across the compressor, then the power is calculated with the mass flow rate of the gas and the enthalpy difference. If each individual cylinder is tested, the power for each cylinder will be added together to obtain the total power. The system efficiency will be lower than the compressor efficiency since it also takes into account the engine efficiency.

η sys = 3.7

Pcomp P in

η isenη mη e

(3-20)

Equations of State

In the field performance test of the compressor, the correct determination of the thermodynamic properties of the gas (such as enthalpy, entropy, and density) plays a critical role. The measured quantities (such as pressure, temperature, and composition) are used as inputs to an EOS to determine thermodynamic properties. The enthalpy change is used to determine the head and the isentropic or polytropic efficiency of a compressor. The choice of the EOS used in calculating enthalpy and density affects the accuracy of the results and needs to be considered in the uncertainty calculation. The possible equations of state commonly used in the gas industry are: Redlich-Kwong (RK), SoaveRedlich-Kwong (SRK), Peng-Robinson (PR), Benedict-Webb-Rubin (BWR), Benedict-Webb-RubinStarling (BWRS), Lee-Kesler-Plocker (LKP), and AGA-10. The final selection of the EOS to be used in the field test should depend on the applicability of the particular EOS model to the gas and temperatures encountered along with the process of interest. EOS model accuracy may depend upon the application range and the gas mixture at the site (Sandberg, 2005; Kumar et al., 1999).

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The consistent application of the EOS throughout the planning, testing, and analysis phases of the field test is imperative. The choice of which EOS to use must be agreed upon before the test. It is recommended to use the EOS for test data reduction that was also used for the performance prediction. The selection of a particular EOS can have an important effect on the apparent efficiency and absorbed gas power. An added uncertainty of 1 to 2% can be incurred on the performance results if the EOS is inconsistently applied (Kumar et al., 1999). The formulation of the various EOS is given in Appendix C. 3.7.1

Application of Equation of State

Generally, it is not possible to select a “most accurate” EOS to predict gas properties, since there is generally no “calibration norm” to test against for typical hydrocarbon mixtures. All the frequently used EOS models (RK, BWR, BWRS, LKP, SRK, and PR) can predict the properties of hydrocarbon mixtures accurately below 20 MPa for common natural gas mixtures. Outside this pressure range, deviations between the EOS models of 0.5 to 2.5% in compressibility factor Z are common, especially if the natural gas contains significant amounts of diluents. Because derivatives of the compressibility factor (Z) must be used to calculate the enthalpy rise, the enthalpy rise deviations can be larger than the compressibility factor for different EOS. Table 3-1 provides usage suggestions for the various EOS models based on application. For normal hydrocarbon gas mixtures (such as pipeline quality gas) with diluent content (combined CO2 and N2) below 10%, all equations of state shown in Table 3-1 provide accurate results. Beyond this range, Table 3-1 provides some general recommendations on the most applicable EOS. Table 3-1. Suggested Applications for Equation of State Usage Type of Application

Typically Used EOS Model

Typical hydrocarbon gas mixture, standard pressures and temperatures, low CO2 and N2 diluents (< 6% total). Air mixtures.

All EOS Models may be used for this application: Redlich-Kwong (RK), Soave-Redlich-Kwong (SRK), Peng Robinson (PR), Benedict-Webb-Rubin-Starling (BWRS), Benedict-Webb-Rubin (BWR), Lee-KeslerPlocker (LKP), AGA-10

High-pressure applications (>3000 psi).

BWRS, BWR, AGA-10, LKP

Some CO2 and N2 diluents (6-10%).

BWRS, BWR, AGA-10, LKP

High CO2 and N2 diluents (10-30%) and/or high hydrogen content gases.

BWRS, BWR, AGA-10, LKP

High hydrogen content gases (>80% H2)

PR, LKP, SRK

Non-hydrocarbon mixtures: ethylenes, glycols, carbon dioxide mixtures, refrigerants, hydrocarbon vapors, etc.

Specific EOS model designed for chemical mixture will result in greater accuracy. The literature should be consulted for the particular gas and application.

A further comparison of the various EOS models is provided in Appendix D. The calculated enthalpies for various EOS models at different states are used to calculate isentropic efficiency and compressor power for two compressor operating cases.

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4.

DATA COLLECTION PROCEDURES

In reciprocating compressor performance testing, the most common method used is the PV Card method. This method utilizes a pressure measurement inside the cylinder along with a piston position measurement to develop a pressure-volume curve for each cylinder end. From this, the compressor cylinder end’s indicated horsepower can be calculated. The isentropic efficiency can be calculated with the measured horsepower and calculated theoretical or isentropic horsepower. The second method is the Enthalpy Rise method. This is mostly used with centrifugal compressors but can be useful with reciprocating compressors as well. This method takes temperature and pressure measurements on the suction and discharge sides of the compressor. Using EOS relationships, the enthalpy is calculated at each location. With a mass flow rate measurement, the total power can be calculated with the measured enthalpy difference. This method can also be used to measure each cylinder’s efficiency. The pressure and temperature measurements would be made at the suction and discharge nozzles. Both methods are beneficial, depending upon the objectives of the performance measurement. For example, if the objective of the test is to obtain an overall estimate of the efficiency of the compressor package, the Enthalpy Rise method would be beneficial. In this case, it would require the minimum number of measurements (suction and discharge line pressure and temperature) to obtain the efficiency. If the user wanted to complete a diagnostics type performance test, studying each individual cylinder, the PV Card method would be more useful. These two methods can also be utilized in conjunction with one another. Discussed below are the details that should be considered with each method. 4.1

PV Card Method

The PV Card method is commonly used for reciprocating compressor performance testing. In general, this method is used to assess the performance of individual cylinder ends. The results can then be used to evaluate the performance of the compressor as a whole. 4.1.1

Description of PV Diagram

With the use of the PV Card method, it is essential to have a clear understanding of the PV diagram. This section discusses the physical operation of the compressor in relation to the PV diagram. Figure 4-1 shows a typical PV diagram with labels indicating different important parameters. Some of these parameters are discussed below. Line 4-1: The suction valve opens at Point 4, as the piston travels toward IDC (for the crank, or frame end of a compressor cylinder), the volume in the cylinder increases, and gas flows into the cylinder. The pressure inside the cylinder is slightly less than the pressure outside the cylinder. This small differential pressure holds the suction valve open. The suction valve closes as the piston reaches IDC and changes direction at Point 1. The differential pressure across the suction valve decreases to zero as the piston reaches IDC. The pressure force holding the valve open becomes less than the spring force of the valves and the suction valve closes. Line 1-2: The piston reverses directions and the volume inside the cylinder starts to decrease. As the volume of the contained gas continues to decrease toward Point 2, the pressure increases. The shape of the compression line (Line 1-2) is determined by the many different factors. In a measured PV diagram, the shape is affected primarily by the clearance volume, the pressure ratio, and the gas composition. A theoretical curve is determined with clearance volume, pressure ratio, and calculated constant compression exponent. For an ideal gas and adiabatic process (no flow of heat to or from the gas being

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operated on), the compression exponent is the isentropic (constant entropy) exponent, which is equal to the ratio of specific heats of the gas being compressed.

Figure 4-1. Typical PV Diagram

Line 2-3: At Point 2, the pressure inside the cylinder has become slightly greater than the pressure outside the cylinder. The resulting differential pressure across the discharge valve causes the valve to open, allowing gas to flow out of the cylinder. The volume continues to decrease toward Point 3, maintaining sufficient pressure differential across the discharge valve to hold it open. At Point 3, the piston reaches ODC (for the crank, or frame end of a compressor cylinder) and reverses direction. The differential pressure across the discharge valve decreases to zero as the piston reaches ODC. The pressure force holding the valve open becomes less than the spring force of the valves and the discharge valve closes. Line 3-4: The gas trapped in the cylinder expands as the volume increases toward Point 4. At Point 4, the gas pressure inside the cylinder becomes less than the pressure outside the cylinder, creating a differential pressure which opens the suction valves. The cycle then starts over again. The shape of the expansion line (Line 3-4) is dependent on the same factors as the compression line. 4.1.2

Measurements

The PV Card method requires the measurements listed below, and shown in Figure 4-2, to calculate the compressor power and efficiency. Depending upon the requirements set for the performance test, not all of the measurement locations shown in Figure 4-2 are required. 1.

Cylinder pressure

2.

Piston position (crank-shaft rotational position)

3.

Suction and discharge temperatures

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4.

Gas composition

5.

Barometric Pressure

6.

Compressor geometry (ex. Bore diameter, clearance, etc.)

7.

Engine fuel gas flow rate or electric motor power consumption (for overall system efficiency)

8.

Fuel gas composition (for overall system efficiency)

The cylinder pressure and piston position are used to form the pressure-volume curve. The area inside of this curve, which is determined by numerical integration, gives the indicated power for the cylinder end. The total brake horsepower consumed by the compressor can be estimated by summing the individual cylinder end indicated horsepower and by applying an assumed mechanical efficiency from cylinder to crankshaft. The suction and discharge temperature, gas composition, and toe pressures from the measured PV diagram are utilized to calculate the theoretical isentropic power for the cylinders. This theoretical power is then used to calculate the isentropic efficiency of each cylinder as well as the compressor. Barometric pressure should be measured in order to correctly calculate absolute pressure from measured gage pressure. Compressor geometry will be reported in manufacturer literature, but it is possible that over the life of the compressor changes will have been made. Current changes in compressor dimensions, such as bore diameter (especially on older compressors) and if additional clearance has been added, should be documented and possibly measured. The engine fuel gas flow, electric motor power consumption, and fuel gas composition are required, if the overall system efficiency is being evaluated.

Figure 4-2. Location of Test Instrumentation for PV Card Method

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4.1.2.1 Cylinder Pressure The cylinder pressure is a time varying cylinder end pressure that is a function of the piston’s positions in the cylinder. It is measured with a pressure transducer, which has a high enough frequency of response to track the dynamic pressure in the cylinder without phase delay. Optimal cylinder pressure measurement is accomplished with a pressure transducer mounted flush with the inside of the cylinder wall, so that the transducer diaphragm will sense the pressure directly in the cylinder chamber without the distorting effects cause by indicator passages. Typically, ports are drilled in the side of the compressor cylinder for pressure transducers. These are referred to as indicator ports. Pressure transducers that fit into larger indicator passageways are available. This would allow the transducer to be flush-mounted to the cylinder bore. When the transducers are not flush-mounted, the ports will usually have an indicator valve (example shown in Figure 4-3), such that the pressure transducers can be installed without shutting down the compressor. Externally-mounted pressure transducers are an effective method for moving transducers during testing, but this also can lead to pressure variations at the transducer that are not representative of the pressure in the cylinder. These are referred to as channel resonances and channel attenuations.

Figure 4-3. Pressure Transducer Installed on Compressor Cylinder with Indicator Valve

Channel Resonance Installation of pressure transducers to monitor cylinder conditions on reciprocating compressors can give rise to an acoustic resonance phenomenon known as Helmholtz or channel resonance. The channel resonance is a function of the geometry of the indicator port and valve, and it occurs due to an excitation of the quarter-wave acoustic length resonance of the gas passage between the cylinder interior and the pressure transducer. This effect can superimpose a large amplitude, periodic pressure wave on the true cylinder pressure and can result in a distorted pressure-volume diagram. This resonance will typically show up on the expansion and compression lines, as well as when the suction or discharge valves are

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open. In high-speed compressor cylinders, this may significantly add to the peak differential pressure measured in the cylinder, which can affect the accuracy of rod load and pin reversal calculations. The resonance or waves will not be as apparent on high-speed compressor expansion and compression lines as on a low-speed compressor PV diagram. However, the resonance is still present, if the sensors are not flush-mounted. Since the resonance is sinusoidal in nature, it can be removed without significantly affecting the measured indicated horsepower. This is assuming that it can be deleted without causing a phase shift in the original PV diagram. Figure 4-4 and Figure 4-5 show examples of PV diagrams taken with the presence of channel resonance on a high-speed compressor. Figure 4-6 and Figure 4-7 show channel resonance on a low-speed compressor.

Figure 4-4. PV Diagram with Channel Resonance Present – Uncorrected High-Speed Compressor (950 RPM)

Figure 4-5. PV Diagram with Channel Resonance Present – Corrected High-Speed Compressor (950 RPM)

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Figure 4-6. PV Diagram with Channel Resonance Present – Uncorrected Low-Speed Compressor (330 RPM)

Figure 4-7. PV Diagram with Channel Resonance Present – Corrected Low-Speed Compressor (330 RPM)

There are several ways to mitigate the effects of channel resonance. One method is to flush-mount the transducer in the cylinder. This is not always practical since it eliminates the use of a valve. Without the valve, the transducer cannot be moved while the compressor is in operation, and it cannot be isolated to check the transducer calibration. Pinching the transducer cutoff valve is not an acceptable method, because it will introduce an unacceptable horsepower measurement error. During the selection and purchase of the compressor, the user should consider the indicator port geometry. The port should be made as short as possible, with a large diameter and a straight through ball valve for the indicator valve. The volume of the gas in the indicator port to the transducer should be minimized. Following these recommendations will ensure that the resonance frequency is as high as possible for the channel.

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A practical method of eliminating the channel resonance after the measurement has been taken is through mathematical filtering. Mathematical filtering techniques can be effective, if the channel resonance frequency can be identified. Once the frequency is determined, then the application of a non-phase shifting low pass filter is recommended. This will improve the accuracy of the suction and discharge toe pressure picks and the identification of the suction and discharge volumetric efficiencies while not detrimentally affecting the indicated horsepower measurement. Another method for removing the resonance is with a linear acoustic transfer function developed under GMRC funding. This transfer function was developed specifically for removing channel resonance on low speed, low ratio compressors. The transfer function and phase is determined with Equations 4-1 and 4-2 below. The frequency and damping factors can be determined with an FFT (Fast Fourier Transform) analysis or computing the log decrement. This transfer function is only applicable to low speed/low ratio compressors. High-speed/high ratio compressors have a greater phase lag during the compressor process due to high channel restrictions, which makes the linear transfer function inadequate. A non-linear transfer function developed under GMRC research funding is proposed by Harris and Edmund in their paper titled, “Performance Measurements of High-Speed/High Ratio Reciprocating Compressors” (1998).

ω ∑ i =3, 5, 7 ,... i n

TRF = TRF +

2 1−ω

(

)

2

2

2 1/ 2

ω + 2ζ i

ω ζ 2 n i −1 i φ (ω ) = φ (ω ) + ∑ tan ω 2 i =3, 5, 7 ,... 1 − i

(4-1)

(4-2)

Experience has indicated that effective channel resonance elimination can be made with less than -1% indicated change in the measured horsepower on a high-speed compressor cylinder and less than -0.5% change in the measured horsepower on a low-speed compressor cylinder. The change in measured horsepower refers to the difference between ICHP before and after the channel resonance has been removed. Horsepower changes larger than this would indicate that more than channel resonance is being eliminated or the method has introduced a phase shift into the raw data. Filtering is generally incorporated into digital compressor performance analyzers. Channel Attenuation Channel attenuation develops in environments with rapid (real) changes in pressure. It is common with high-speed compressors, heavy gases, and small diameter measurement channels. It is directly related to the resistance of the channel to pressure changes. A high resistance or restrictive channel will prevent the gas density from changing fast enough in the channel to match the real transient conditions. The resulting pressure measurements will be distorted. Typically, this error is identified by distortions on the compression and expansion lines on the PV diagram. The most effective method of avoiding this phenomenon is to have large diameter indicator ports or to flush mount the transducers. More information on calibration, installation, and use of pressure transducers is in Section 6.1.

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4.1.2.2 Piston Position The piston position is needed for calculation of the instantaneous cylinder volume. There are many factors that can affect this measurement. Encoders attached to the crankshaft are typically used to make this measurement. Encoders with higher resolution may provide less uncertainty. The use of an encoder is based on ideal kinematic relationships to crankshaft rotation. The effects of crankshaft twisting and deflection in the crankpin and crosshead bearings can cause deviations from this ideal relationship. In some instances, a key phasor may be used to indicate the position of all pistons. This can have a very high uncertainty due to variations in rotational speeds during each revolution. The pressure measurement may not correlate with the volume measurement correctly with the use of a once per turn device, such as a key phasor, optical, or magnetic pick-up. The best practice is to use an encoder with resolution of 360 or greater. Because of this, the use of a once per turn device is not discussed in the power, efficiency, or uncertainty calculations. ODC Determination In order to have the correct reference of pressure to piston position, the location of ODC must be found and synchronized with the encoder. If the ODC determination is off, the horsepower will not be correct and it will appear as if the valves are opening and closing at the wrong time. A 1-3 degree inaccuracy in ODC determination can cause a 3-5% error in horsepower. Figure 4-8 shows the difference in a PV diagram with different ODC errors. In this example, a 4.9 deg error leads to approximately an 8% error in the horsepower. More information on the use of encoders and determination of ODC is in Section 6.5. 90 Original 8.73 HP 1.4 deg 8.54 HP (-2.2%)

80

4.9 deg 8.04 HP (-7.9%)

Pressure (psig)

70

60

50

40

30 0

50

100

150

200

250

300

Volume (in^3)

Figure 4-8. PV Diagram with Varying ODC Measurements

4.1.2.3 Suction and Discharge Temperature and Gas Composition The suction and discharge temperature and gas composition are needed for calculating the theoretical PV diagram from the EOS. The temperature is usually measured outside the cylinder (in the nozzle). This temperature will be different than the actual temperature inside the cylinder during suction and discharge due to several factors: in most cases (some exceptions are Helium or Hydrogen) the pressure drop across the valves causes a decrease in temperature, heat is transferred from the cylinder to the incoming gas, and the suction gas mixes with the residual gas in the cylinder. The heat transfer is typically small for low compression ratios, but can be significant for higher compression ratios and non-cooled cylinders. The

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factor that has the most significant effect is the mixing of the suction gas with the residual gas. The resulting suction temperature due to this effect can be calculated using simple thermodynamic relationships. Temperature measurements in the nozzles will have high variations due to pulsating flow. The measurement device should be installed in a thermowell to damp out the pulsation effects. More information on temperature measurements can be found in Section 6.2. 4.1.2.4 Driver Fuel Gas Composition, Fuel Gas Flow Rate, and Motor Power These measurements are required to determine the power developed by the gas engine or electric motor to meet the compressor demand. The gas composition will be measured with a gas chromatograph to determine the composition of the fuel gas. It will also serve to verify that the gas composition does not change significantly during the performance tests. The gas composition will be used with EOS to determine the fuel gas properties. The fuel flow rate will be used to determine the amount of energy being supplied to the driver. This is measured with a typical flow meter such as an orifice meter. With this value, the overall efficiency of the driver/compressor system can be determined as shown in Section 3.6. This efficiency will include the efficiency of the driver, compressor, and mechanical losses. The motor power is found with a measured voltage and current. Typically, an ammeter will measure the current draw of the motor. This, along with the power factor and efficiency of the motor, can be used to calculate the power absorbed. As with the gas engine, the overall efficiency of the driver/compressor system can be determined, as shown in Section 3.6. 4.1.3

Capacity and Volumetric Efficiency Calculation

Theoretical equations are presented in Section 3.1 for the calculation of capacity. Several considerations should be taken when completing these calculations to ensure that the error is minimized. Several of the parameters in the equations presented are found in manufacturer literature, directly measured, or calculated from EOS with the measured values. The suction and discharge volumetric efficiency is a variable that needs to be calculated from ideal equations or determined from the PV diagram. The theoretical EV may be used for operation or control, so it is important that the theoretical and measured EV are close. The theoretical EV may be different from the measured EV due to an unhealthy cylinder, restrictive flow, variations in gas composition, etc. It is important that any performance issues, such as leaks, be corrected before taking performance data. However, if the difference between the theoretical and measured EV are due to permanent physical phenomena, such as flow restrictions through valves or gas passages, then the losses can be accounted for with a loss factor in the theoretical equations as shown in Equations 3-14 and 3-15. As shown in Section 3.4, the percent clearance (%CL) is used within the calculations of both suction and discharge volumetric efficiency. Percent clearance is a value usually reported in manufacturer literature. The actual %CL may be different due to manufacturing tolerances or aftermarket capacity control device installation. The manufacturer’s stated %CL will usually be within 2-3% of the actual value without aftermarket devices. The %CL needs to be determined for each cylinder end either based on manufacturer nameplate values and aftermarket devices or measured values. Clearance pocket geometry may cause a variation between actual and effective clearance volume. For example, if there is a small throat to the clearance pocket, the full pocket volume may not achieve discharge pressure during the compression stroke. The variation in volumetric efficiency gives the appearance of an effective clearance that varies from the measured or stated clearance. The effective

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clearance can be determined from the PV diagram. Analyzers are available that determine the effective clearance value. Incorrect clearance will lead to error in the volumetric efficiency, horsepower, and flow calculations. 4.1.4

Uncertainty

Listed below are the potential sources of uncertainty in the PV Card method. The effect of these individual uncertainties on the results of the performance measurements will be discussed in Sections 6 and 7.

4.1.5

•

Pulsations

•

AC or Electrical Noise

•

Sensor Accuracy

•

Sensor Calibration

•

Channel/Helmholtz Resonance and Attenuation for Pressure Transducers

•

Temperature Effects on Pressure Measurement

•

Valve Effects

•

ODC Determination

•

Unsteady Operation Conditions

•

Theoretical Calculations/EOS

Compressor Efficiency

The actual measurement of the PV diagram provides a curve from which the indicated compressor horsepower can be calculated. In order to use this data to calculate an isentropic efficiency of the compressor cylinder, the theoretical PV diagram must be generated. This is done using the results of the measurements, compressor geometry, and EOS calculations. The process of calculating the PV diagram is described in more detail in Appendix B. Once the theoretical PV diagram is generated, then the isentropic efficiency of the compressor cylinder end can be calculated using the equations detailed in Section 3.2. Commercial analyzers automatically develop the theoretical PV diagram and calculate the isentropic ICHP. 4.2

Enthalpy Rise Method

The Enthalpy Rise method is based on a relationship of the energy contained in the gas at the suction and discharge of the compressor. This method uses temperature and pressure measurements at the suction and discharge to calculate the enthalpy. The enthalpy difference multiplied by mass flow rate gives the power consumed by the compressor and can be used with theoretical calculations to obtain the isentropic efficiency. This method is good at assessing the overall performance of the compressor. It can also be used to determine the performance of individual cylinders. 4.2.1

Measurements

The Enthalpy Rise method requires the measurements listed below to calculate the power and efficiency of the compressor and as shown in Figure 4-9.

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1.

Suction and discharge pressures

2.

Suction and discharge temperatures

3.

Gas flow rate

4.

Gas composition

5.

Driver fuel gas flow rate or electric motor power (for overall system efficiency)

6.

Fuel gas composition (for overall system efficiency)

The suction and discharge pressures and temperatures are used with the Equations of State (EOS) to calculate the enthalpies. The gas composition is required for the EOS calculations. The suction pressure and temperature are used to calculate the entropy at the suction condition. This entropy with the discharge pressure is used in the EOS to calculate the isentropic enthalpy at the discharge. The enthalpy difference at the suction and discharge conditions is used to calculate power and efficiency. The flow rate of the gas is used with the enthalpy difference to calculate total power. In the Enthalpy Rise method, the driver fuel gas flow, electric motor power, and fuel gas composition for determination of overall efficiency will have the same considerations as the PV Card method (refer to Section 4.1.2.4).

Figure 4-9. Location of Test Instrumentation for Enthalpy Rise Method

4.2.1.1 Suction and Discharge Temperatures The suction and discharge temperatures are required to calculate the enthalpy from the EOS. This is measured with either a thermocouple or RTD. There are several locations that can be used for measuring the temperature. Consideration should be given to the fact that both the temperature and pressure should be measured for this method. It may not be feasible to measure each of these in the same location due to space constraints. The optimal temperature measurement location is on the nozzles near the cylinders as shown in Figure 4-9. When determining an isentropic efficiency, it is important to place the pressure and temperature measurements in locations that will best represent isentropic compression. Since an isentropic process does not have any heat transfer (adiabatic), placing the sensors before or after vessels

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where heat transfer could occur should be avoided. However, the desired measurement location is often not accessible. The temperature measurements may end up being made outside of the suction and discharge bottles. If this is the case, then the heat losses should be accounted for in the efficiency calculation. A methodology is presented in Appendix H that can be used to determine heat transfer effects. In order to avoid this extra computation, it is easiest to place the temperature sensors in the nozzles. The nozzle region has pulsations, which causes an unsteady temperature measurement. The temperature sensor should be placed in a thermowell to damp out the effects of pulsations. If a thermowell is used, adequate time needs to be allowed during the test for the thermowell to properly heat soak. More information is presented in Section 6.2 on temperature measurements. The heat losses due to water cooling of the compressor cylinder should be considered in the isentropic efficiency calculation. The equations below show in general how these are accounted for in the compressor power and isentropic efficiency where the component energy includes the bottles, nozzles, and piping and the cooling energy includes cylinder cooling through a water jacket. Further information is provided in Appendix H on methods to account for these losses.

P = m(hd − hs + q components + q cool ) •

η isen =

hd ,isen − hs hd − hs + q components + q cool

(4-3)

(4-4)

4.2.1.2 Suction and Discharge Pressures The suction and discharge pressures are also required for the enthalpy calculation with the EOS. The objective of the tests dictates where the transducer should be installed. If the goal is to analyze the compressor package, then the transducers would need to be placed outside the bottles. If individual cylinders are the subject of interest, then the pressure needs to be measured in the nozzles. The location of measurement affects the type of pressure transducer that should be used. Before the first set of bottles, the flow may be steady enough for the use of a static pressure transducer. If the pressure is measured on the nozzles right before the cylinder, a dynamic pressure transducer would be needed due to the pulsating flow. With regards to instrument drift, dynamic pressure transducers have a higher inaccuracy over time compared to static pressure transducers. However, by calibrating dynamic transducers just prior to the performance test they can achieve sufficient accuracy during the test. If compressor cylinder (as opposed to package) performance is being analyzed and the pressure measurements are taken either before or after the bottles, then the pressure losses for each pulsation control chamber needs to be taken into account. If pressure measurements are taken in the nozzles, or in an area of high pulsating flow, then the resulting pressures need to be time averaged. An average pressure needs to be obtained before the pressure is used with the EOS to determine the enthalpy. Further details on pressure measurements are presented in Section 6.1. 4.2.1.3 Gas Flow Rate Accurate gas flows are required to assure accurate power calculations. There are multiple types of flow meters that can measure the flow rate. The accuracy of the flow measurement is dependent upon the level

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of pulsations. Pulsations adversely affect the flow measurement. The flow meter should be placed in a location with minimal pulsations. This is usually at a location far upstream or downstream from the compressor, typically before the suction bottles or after the discharge bottles. The bottles on the reciprocating compressors are acoustic filters which decrease the pulsation levels. The effects of pulsations and selection of the flow meter are discussed in more detail in Section 6 of this guideline. Custody transfer meters may be available for flow measurement. These can only be used if the compressor being tested is the only one running and no gas is being consumed or lost at the station by any other equipment. The flow rate may also be obtained from calculations if the PV Card and Enthalpy Rise methods are being used in conjunction with one another. 4.2.1.4 Gas Composition The process gas composition is needed for the calculation of the enthalpy from the EOS. The gas composition is directly used to determine the properties of the gas, such as the isentropic exponent, compressibility, density, and speed of sound. The gas composition should be measured continuously during the test. The sample rate of the gas composition will depend upon the cycle time of the gas chromatograph. Gas chromatographs are available with four-minute cycle times for an analysis up to C6+. This will give the most accurate composition for the EOS calculations and also the multiple composition measurements will be used to analyze the steadiness of the gas composition during the test. A large variation in gas composition could make the test invalid. All components contributing 0.1 mol percent or greater to the composition should be measured and recorded. 4.2.2

Uncertainty

Listed below are the potential sources of uncertainty in the Enthalpy Rise method. The effect of these individual uncertainties on the results of the performance measurements will be discussed in Section 7.

4.2.3

•

Pulsations

•

AC or Electrical Noise

•

Sensor Accuracy

•

Sensor Calibration

•

Number of Sensors

•

Calculation of Enthalpy from EOS

•

Heat Loss on Bottles, Nozzle, Piping

•

Cooling of Compressor Cylinders

•

Mass Flow Measurement

•

Unsteady Operating Conditions

•

Theoretical Calculations/EOS

Compressor Efficiency

For the Enthalpy Rise method, the isentropic efficiency is calculated with the enthalpy differences from experimental measurements and calculated isentropic relationships. Terms to account for heat losses and cooling are included depending on where the measurements are taken. The equation used to calculate the isentropic efficiency is shown above in Section 4.2.1.1.

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4.3

PV Card and Enthalpy Rise Method

Depending on what the objectives of the performance tests are, either of the methods described above can be used. In some instances, both methods may be needed in combination with each other. The Enthalpy Rise method provides a good overall assessment of the compressor or the station. The PV Card method could be used with this to focus in on the performance of individual cylinder ends of a compressor (if the performance of not all of the individual cylinder ends is desired). The Enthalpy Rise method can also be used to assess individual cylinders. For example, a user would like to measure the overall efficiency of the compressor, but also test a few cylinders of interest for diagnostics. In this case, the PV Card method would be used to diagnose the cylinders of interest, but the Enthalpy Rise method could be used to assess the overall compressor efficiency. This would prevent the user from having to instrument every cylinder with pressure transducers. 5.

TEST PREPARATION

A general procedure for a field test is outlined in Appendix A. Many of the individual tasks are discussed below. A field test agenda or plan should be prepared prior to the test as this is an essential part of test preparation. The optimum time to start planning for field testing is prior to the design of the compressor packages and compressor station. The first step in the planning process is to determine the scope of the field test and what level of uncertainty is desired for the measurements relative to budget constraints and any contractual performance guarantees. Based upon the targeted uncertainty, temperature, pressure, and flow measurement points, methodologies can be defined for the package and station design that will ensure that the desired results can be achieved. If a field test is going to be performed to validate the performance of a new installation, the purchaser should specify where in the process stream that the design pressures and temperatures will be measured for validation purposes—as well as the EOS that will be used. For example, the locations could be at the inlet and outlet flanges of a compressor cylinder or at the inlet and outlet flanges of the compressor package piping. Specifying this requirement is important for two reasons. One is to ensure that the package and station design includes the necessary connection points for mounting test instrumentation without having to replace or rely on package instruments. The second is more of an application design issue than it is a test issue. Nevertheless, it is an issue that, if overlooked, could result in the compressor not meeting the purchaser’s requirements. If the design and validation points are going to be in locations other than the compressor cylinder flanges (such as package limits), then the pressure losses predicted from any acoustical study need to be included in the compressor performance calculations. While this may appear to be a trivial point, there have been industry cases where erroneous pressures losses were used during compressor/driver selection and the expected performance was not achieved. The test plan should include field conditions and equipment layout, instruments to be used and their location, method of operation, test safety considerations, and the pressure, temperature and flow limits of the facility. Piping and station layouts should be made available. Any deviations from normal operation that may be necessary to conduct the test should also be provided. The field test agenda should include a discussion of the following: 1.

The method of data reduction.

2.

The selected approach for determining the test uncertainty.

3.

The acceptance criteria (specified in terms of maximal uncertainty allowable).

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4.

The EOS to be used for all calculations in the test.

Test preparations should also include a discussion on possible operating conditions and operational limitations. In many cases, a specified operating point can only be maintained for a limited period of time (for example, because the pipeline operation depends upon the tested package) or at fixed ambient conditions. The requirements for installation of test instrumentation need to be communicated early (even during construction of the station), because instrumentation is part of the overall station design. The selection and calibration of the test instrumentation is important. Generally, the instruments supplied for monitoring and protection of the packages are not accurate enough to meet the stringent requirements necessary for a field test (redundant measurement requirements, small uncertainty margins, detailed sensor location placement, and proper flow measurement). Whenever possible, calibrated laboratory quality instrumentation should be installed for the tests (refer to Section 6). The accuracy of the instruments and the calibration procedure should be such that the measurement uncertainty is reduced to the best attainable uncertainty under ideal conditions (see Section 7). 5.1

Pre-Test Meeting

A meeting between the test engineer, the parties involved (supplier, operator, etc.) and the customer to discuss test procedures and the situation on-site should be conducted in advance of the performance test. The site P&ID, Site Layout, and Mechanical Installation Drawing diagrams should be obtained (if available) and used in preparation for the performance test. During the pre-test meeting, the parties should reach an agreement on the test purposes, test procedures, safety requirements, the availability of full bore shut-off valves on compressor cylinders, responsibilities during the test (including who has authority to make quick decisions if problems arise during testing), availability of necessary operating conditions, and acceptance conditions. 5.2

Pre-Test Operation and Instrumentation Checkout

The following items should be checked during the pre-test checkout: •

The test engineer should verify that the unit has been proven suitable for continuous operation and in good mechanical condition.

•

A mechanical assessment should be performed on the compressor before the performance test is conducted. This should include inspection of suction and discharge valves, piston rings, and packings. If these are found to have wear, they need to be replaced before the performance test. If the valves cannot be replaced for any reason, the valves should be evaluated for degradation. An estimation should be made of their affect on the performance of the compressor. Compressor valves that have high wear will affect the power and efficiency of the compressor. A mechanical condition analysis using an engine/compressor analyzer, performed at a highest achievable compression ratio, could be substituted for a physical inspection.

•

If the driver performance will be measured during the test, then a mechanical assessment of the driver is needed as well. The user should ensure that the engine is in good working order and tuned before the performance test is conducted.

•

Sufficient gas should be available for the anticipated flow and conditions for the duration of the test.

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•

If an online system is installed with cylinder pressure measurements, some planning, discussion, and agreement should be reached on how the field test instruments will be installed with the existing instrumentation. Consideration should be given as to how the installation of the instrumentation will affect the operation. Will new vibrations result from the installation of the instruments or new fittings and valves?

•

All instrumentation should be calibrated in the range in which it will be operated during the test. Check all instrument readings (temperature, pressure, flow, and speed) to assure that the sensors are functioning properly. Verify data acquisition system operation prior to starting the field performance test.

•

All RTD’s or thermocouples used in the test should use spring load type fittings, or when necessary, the thermowells will be serviced with oil or other approved heat transfer material. Accuracy must be within ±0.1 deg F.

•

If thermowells are used during the test and a large portion of the thermowell is exposed to the atmosphere, the area around the exposed portion should be insulated to preclude the ambient air from affecting the temperature reading.

•

Check insertion depth of thermowells (see Table 6-2).

•

Where pressure taps involve tubing runs, the tubing should be checked for leaks.

•

The proper number of capable personnel should be on site to ensure that all the data can be recorded in a reasonable amount of time.

•

Check the fixed clearance. If testing a new compressor in the field, the manufacturer’s supplied value for fixed clearance may be used, but if testing an existing compressor, then this value needs to be checked. The effective fixed clearance can vary from the design fixed clearance because of the influence of cylinder operational problems, compressor valve leakage, piston ring leakage, pulsation effects, valve losses, ineffective cylinder pockets, etc. In addition, the measured clearances may vary from design clearances if the pocket shutoff valves are partially opened or closed. ♦ There are several methods that can be used to measure the compressor cylinder clearance. The first is by filling the cylinder with a metered volume of liquid. This method can be very difficult in the field due to leaks past piston rings and out of discharge valves. It usually involves filling the entire cylinder bore and using valve blanks. Another method is using the effective volume calculated by the PV analyzer. However, this method is subject to error due to valve leaks, piston ring leaks, heat exchange within the cylinder, error in ODC position, and restrictive flow paths to clearance pockets. The actual and effective clearances are not equal due to error effects mentioned above. This method can be effectively used if the uncertainty in the measurement is accounted for.

•

Prepare data acquisition system by installing any required programs or generating data collection protocols. If possible, use a data acquisition system that will automatically calculate the results of the field data such as PV diagrams, ICHP, efficiency, and flow, so that they can be quickly reviewed in the field for any discrepancies.

•

Communicate with the station operators where access to the compressor will be required (indicator ports, flywheel for ODC, removal of compressor valve, etc.) so that the proper work permits can be generated for the tasks.

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5.3

•

Ensure that the instrumentation and data acquisition system used for testing meets the required hazardous classifications for temporary work or local safety requirements at the compressor site (e.g., IEEE Class 1 Div 2 rating).

•

Ensure that all safety and contractual documents are in place before mobilizing to the test site.

Pre-Test Equipment Checkout

Prior to running the field performance test, the following should be performed:

5.4

•

Verify fuel and site load to assure continuous operation of the unit at full-load conditions as required at the time of the test.

•

Perform a visual walk-through of the compressor package to eliminate any sources of hot air ingestion or recirculation.

•

Consult with gas control on station operation and verify the compressor can be run at the guarantee point or testing condition (specific gas, speed, pressure, and temperatures). If the test is not run at the guarantee point, then consult with the compressor manufacturer to obtain performance predictions for the conditions that will be tested.

•

If the test is going to be conducted on a closed loop, check if gas cooling is available and if recirculation of gas is an option during the field test. Notify all parties of the time frame for the test.

•

Determine how load steps will be maintained constant during a test point and how they will be changed for different test points.

•

Consult with station operators about the gas samples or compositional analyses that will be required for the performance test.

Pre-Test Information

The following information should be obtained from the test preparation and pre-test meeting: •

General ♦ Predicted performance curves for compressor (or existing test curves).

If a guarantee point is being tested, the manufacturer of the compressor or the packager needs to be involved with the performance predictions for the test conditions. If the test conditions follow closely with the original performance specified for the compressor, then these can be used for the comparison. If the test conditions vary greatly from the original performance predictions, then the manufacturer needs to be contacted in order to obtain performance predictions that will be in line with the performance test results. Table 5-1 details maximum permissible deviations from the manufacturer’s specified performance. This table has been adapted from ISO 1217.

♦

Piping geometry between compressor and test instrumentation.

♦

Compressor configuration for testing: deactivated valves, pocket clearances, and suction valve loading.

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Table 5-1. Maximum Deviations from Specified Values and Fluctuations from Average Readings

Measured Variable

Maximum Permissible Deviations from Manufacturer Specified Performance

Maximum Permissible Fluctuations During Performance Test

Suction Pressure Discharge Pressure Pressure Ratio Suction Temperature Isentropic Constant Gas Constant x Compressibility Factor, RZ Shaft Speed

± 10 % Not specified ±5% Not specified ±3% ±5% ±4%

±1% ±1% Not specified ±2K Not specified Not specified ±1%

Difference between suction temperature of external coolant and gas suction temperature

± 10 K for coolant air ± 5 K for coolant water

±2K ±2K

External coolant flow Temperature at the nozzle or orifice plate Differential pressure over nozzle or orifice plate NOTES

± 10 % Not specified Not specified

± 10 % ±2K ±2%

1. The test can be performed if the deviations from the specified conditions are equal to or less than the deviation tolerances. 2. If the deviation from test conditions results in a deviation in absorbed power higher than ± 10 % then the test is not within the limits. 3. A test at a shaft speed different from the specified value is not accepted if unpermitted resonant pressure pulsations occur. 4. For the test of a gas compressor with a gas different from that specified, a bigger variation in gas properties often occurs. This should be agreed upon by both parties.

•

PV Card Method ♦ Compressor Geometry: Bore diameter, stroke length, connecting rod diameter, connecting rod length, clearance volume, pressure transducer port geometry (length and diameter), pocket volumes, load step definitions, valve types (poppet, plate, ring, reed, or channel), and unloader mechanisms.

•

Enthalpy Rise Method ♦ Flow meter information: Pipe ID, orifice bore or beta ratio (for orifice meter), K-factor (for turbine or vortex shedding meter), flow coefficient (for annubar or nozzle) scaling frequency, configuration log (for ultrasonic meter or to adjust turbine or mass flow meters).

Before conducting the performance test, a test matrix should be developed to include all operating conditions to be tested and how they are to be achieved. This should consider the objective of the test. The test planner should examine what performance curves are needed for the compressor. Parameters, such as suction pressure, compressor speed, and clearance, should be considered. The test planner should discuss the test matrix with the compressor operator to ensure that all the operating conditions can be met. If testing requires more than one test day, have a plan in place on how to leave the compressor in an operational state overnight. This will allow the station to operate as needed when testing is not occurring. The plan may include removal of some instrumentation or plugging various ports.

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5.5

Test Stability

In order to obtain steady state conditions, the compressor should be started prior to the initiation of the test (compressors require at least 30 minutes of heat soak time and engines require 1-2 hours of soak time). The field test should be performed when the compressor operating conditions have reached steady state. Also, the operating conditions should stay constant during each test point. To determine if the compressor has reached steady state, estimate how long it will take to collect all the required measurements either through experience or a trial collection run. This collection time will be the length of time between each check for test stability. For example, if it takes 10 minutes to collect all the test data, then the stability parameters, such as pressure and temperature values, should be checked at 10minute intervals to verify whether or not the compressor operation is steady. The compressor stability should be determined from the criteria discussed below. Power fluctuations should not occur during the performance testing. As it is very difficult to determine fuel gas composition variations during the short test intervals, it is important to ensure that the fuel and process gas compositions will remain unchanged for the duration of the testing period for each test point. Multiple or continuous gas samples should be taken during the test to ensure that the compressor remains at a steady state during one test point. Also, multiple gas samples of the process gas and fuel gas must be taken for each test point if the gas composition significantly changes (heating value change of more than 1.0%) in between test points. Temperature measurements will especially be affected by any instability during the test. Temperature probes reach equilibrium through relatively slow heat transfer and heat soaking, while the system operating conditions vary at much faster rates. The heat storing capacity of the compressor and system piping will need adequate time to reach equilibrium after any operating conditions have changed. It is, thus, critical to maintain extended stable operating conditions prior to beginning the test in order to reach thermal equilibrium and measure accurate gas temperatures. When using the PV Card method, pressure measurements on cylinder ends may be made one at a time, depending upon the number of pressure transducers on hand. If the pressure measurements are made consecutively (one or two at a time) then the stability of the test needs to be maintained throughout the full set of pressure measurements. Any stability changes during these measurements should be considered in the uncertainty. The stability of the compressor can be monitored by considering other continuous measurements, such as compressor speed, temperature, and gas composition. Cylinder load steps should be maintained through a test point. Regardless of the assumption of steady state test operation, any variation in measured parameters during the test interval should be accounted for in the uncertainty calculation. Note that an increase in pressure ratio due to drift during the test will cause an increase in the temperature as well, though the temperature change will lag behind the pressure change. Refer to Section 7 on uncertainty for more discussion of unsteady conditions and drifting conditions during a test. These added uncertainties due to drift during the test interval are in addition to non-ideal effects discussed in Section 7. 5.5.1

Compressor Steady State

The compressor should be operated for at least 30 minutes prior to the test. Steady state is achieved if the compressor measurements listed in Table 5-1 (in the maximum permissible fluctuations during performance test column) applies during a test interval. Also, the following performance conditions shown in Table 5-2 should be satisfied:

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Table 5-2. Additional Assessment of Stability of Compressor During Pre-Test

5.5.2

Test Reading

Maximum Allowable Variation During Test Interval

Efficiency

Fluctuations < + 1% of Average

Enthalpy Rise

+ 1% of Average Value

Compressor Flow

+ 1% of Average Value

Engine Steady State

Before readings are taken for any individual test point, engine steady state operating conditions must be achieved. The engine must be heat soaked according to manufacturer specifications. If manufacturer specifications are not available, the engine should be heat soaked for at least 1 hour. To verify stability of the engine, the parameters given in Table 5-3 should be checked. Table 5-3. Assessment of Stability of Compressor Driver During Pre-Test

5.5.3

Test Reading

Maximum Allowable Variation During Test Interval

Driver Speed

+ 1% Average Speed

Fuel Flow

+ 2% Average Flow

Motor Current

+ 2% Average Current

Unsteady Operations

If unsteady operations cannot be avoided during the test interval, measurements may still be valid, but the fluctuations have to be accounted for in the uncertainty calculations of the results. Also, if this is a factory performance test, the purchaser can specify criterion for fluctuations. If fluctuations during the test exceed quasi-steady conditions, as given in Table 5-1 through Table 5-3, the test may need to be performed again. For measurement cases where there is a simple drift in the average operating condition, the criteria listed above should be employed to determine whether a data point is steady. If the drift in any of the instrument readings exceeds the steady state conditions (as defined in Table 5-1 through Table 5-3), it is difficult to determine any valid performance results from this measured data because of the high degree of interdependence of all measured parameters and the system as a whole. Namely, as the validity of the data depends on the rate of drift, heat storage capacity of the pipe and measurement system, and the frequency response of the transducers, a total uncertainty cannot be determined. On the other hand, if the fluctuations in the data can be determined to be varying around a mean value, without the average drifting significantly, the resultant measurement error is primarily due to a time lag of the temperature transducers. Namely, while the pressure and flow transducers generally measure at a high frequency and, thus, capture rapid operating changes accurately, the temperature transducers lag due to the requirement of complete heat soaking of the piping and measurement system. Thus, if the fluctuations produce a mean performance value, the criteria for acceptance of unsteady operation can be extended to allow up to twice (i.e., factor-of-two range) the fluctuations listed in Table 5-1 and Table 5-2 for compressor steady state testing. In these cases, the fluctuations must be accounted for in the uncertainty calculation. The uncertainty of the measurement then becomes the fluctuation instead of the instrument uncertainty due to calibration, installation, data acquisition, and the device itself. As this can generally result in very high total uncertainties for efficiency and power, one should carefully evaluate whether to accept this test data. Also, once this factor-of-two range is exceeded, the non-linear behavior of the system as a whole makes it unrealistic to determine accurate performance results from experimental

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data. Figure 5-1 shows examples of a measurement that has a drift or fluctuations around the mean value. The graph does not show actual measurements. The fluctuation and drift in the figures are exaggerated. 121 Average Drift

Temperature (deg F)

120.8

Fluctuating

120.6

120.4

120.2

120

119.8 0

10

20

30

40

50

60

Time (minutes)

Figure 5-1. Example of Drift and Fluctuations in a Temperature Measurement

5.6

Safety Considerations

Safety considerations should remain a priority during the pre-test phase, as well as the actual testing of the compressor. Abnormal operating conditions should be discussed with station personnel prior to running the test. If possible, a schematic of the yard piping should be given to all test personnel. Unit vibration equipment operation should be verified. When cables are run to test instrumentation, the cables should be covered with mats or correctly taped down (if possible) to reduce trip hazards. Cable connections should be secured. Site specific hazardous location requirements for instrumentation, cables, and devices should be followed. Aviation type headsets can be useful during the testing for quick communication and can help the testers maintain a safe testing environment. Finally, the requirements of the field test should not be given priority over station safety precautions in order to reduce measurement uncertainty or meet test schedules. 6.

MEASUREMENT AND INSTRUMENTATION

The reciprocating compressor cylinders, pulsation bottles, and piping must be equipped to measure the test variables shown in Figure 4-2 and Figure 4-9, depending on which data collection procedure is used and the objective of the test. All pressure test points must have appropriate test taps in the proper place to record pressure and temperatures. This is the responsibility of the design engineers and constructors. All test taps should utilize dampers for accurate results. For testing purposes, a dedicated set of laboratory quality instrumentation should be utilized. This dedicated set of test instrumentation should be maintained and calibrated before each test using acceptable reference standards. A valid calibration certificate for all measurement instrumentation is recommended. An end-to-end calibration of the data acquisition system, wiring, and instrumentation is also recommended prior to the field test but may not always be practical.

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If possible, all measurement instrumentation should be installed inside the branch piping to the compressor’s recirculation or bypass flow loop, such that the measured values represent the true flow through the compressor. The bypass loop should not offer undue restriction to flow. Ideally, the bypass uses a full open type valve and a line size not more than one size smaller than the discharge line. If the test instrumentation is located outside the recycle loop for the compressor, the recycle valve must be fully closed during the tests for the results to be valid. If the recycle is part of the normally active flow control system, then this system may need to be disabled or the recycle may need to be actively controlled to achieve certain test conditions. A piping configuration using a closed loop through the compressor or station recycle line may also be utilized for the performance testing of the compressor. In this case, a process gas cooler on the discharge of the compressor will generally be required to maintain the gas temperature stable in the closed loop piping system which results from this configuration. Also, for this test scenario, the effects of gas lean out must be considered as the heavier components in the test gas may liquefy and drop out due to sequential compression and cooling. If the test is run on a closed loop, then prior to the performance test, the compressor should be run in the closed loop configuration while monitoring the gas using an online gas chromatograph until there is no significant change in the gas composition. 6.1

Measurement of Pressure

6.1.1

Recommended Best Practice

Pressure transducers are selected and installed depending upon the objective and methodology of the performance test. If the PV Card method is used, a pressure transducer which can detect the dynamic change in pressure is required for the cylinder pressure measurement. The Enthalpy Rise method requires a more steady pressure measurement upstream and downstream of the compressor. If this measurement is made at the cylinder nozzles, the pressure has strong variations due to pulsations. In this case, a pressure transducer with dynamic capabilities is required. If the pressure measurements are made upstream or downstream of the bottles, the pressure variation may be low enough where a static pressure transducer may be used. Static pressure transducers typically have a much lower drift than dynamic pressure transducers. If the transducers are calibrated for the performance test, the drift of the instrumentation may not be a concern. The ambient pressure also needs to be measured. The cylinder pressure will be a gage pressure and needs to be made absolute before completing any calculations. The ambient pressure can often be obtained from a local airport weather station, but in some cases this is not sufficient. In areas with significant elevation changes or a varying landscape, such as in the mountains, the ambient pressure will not be consistent from one location to the next. An accurate atmospheric pressure measurement is also important in applications with low suction pressure (< 50 psig, typically gas gathering applications) or low pressure ratios. Below, the details of compressor pressure measurements for each performance test methodology are discussed. PV Card Method For the PV Card method, a pressure measurement inside the cylinder is required. The pressure inside the cylinder is constantly changing during the compression and expansion cycles and relatively steady state during the suction and discharge events on a healthy cylinder. A strain gauge pressure transducer is required due to the pressure variation. This transducer must be a DC coupled transducer with a high frequency of response. On the compressor cylinder, there is an indicator port for the pressure transducer. If the compressor does not have indicator ports, then the user will need to drill and tap a port for the transducer if they choose to install the transducer on the bore of the cylinder.

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Dynamic pressure transducers have a frequency of response. When testing high-speed compressors, this is an important consideration when selecting the transducer. The transducer should be able to accurately track the pressure changes without a phase delay in the frequency range of interest. Quality pressure transducers can be found with frequency response ranges around 2,000 Hz. This frequency of response is adequate for the reciprocating compressor performance testing as discussed in the guideline. Enthalpy Rise Method The Enthalpy Rise method requires strain gauge pressure measurements. Pulsations may be present depending on where the transducers are installed. The sensor should have a high enough frequency of response to track these pulsations without a phase delay. Total (stagnation) pressure must always be used for performance calculations. However, it is often more convenient to measure static pressures (Pstat) and then convert static to total pressure (P) using:

p = p stat + 3 x10 −8 U 2

(6-1)

In Equation 6-1, the flow velocities can be calculated using the measured actual flow rate (referenced to actual temperature and pressure conditions) and the pipe cross-sectional area (U=Q/A). Whenever feasible, it is recommended to use four pressure taps and four temperature taps at the pressure and temperature locations indicated in Figure 6-1, consistent with ASME PTC 10 recommendations. The accuracy of the static pressure or temperature measurement is dependent upon the selected location. Four pressure and temperature sensors assure that the average measurement of pressure or temperature will be accurate, even in a non-uniform flow field. Additional pressure and temperature measurements can be employed, if four sensors are not sufficient. Two different approaches are appropriate for locating the suction and discharge pressure and temperature taps. The first approach is to place measurement taps at locations relatively far upstream and downstream from the compressor in the longest available straight pipe segment to assure a uniform flow field at the transducer taps. These locations may be relatively far away from the compressor, so the pressure measurement values must be corrected using empirical loss factors (i.e., pressure losses) for the straight pipe, elbows, tees, reducer, pulsations bottles, and orifice plates that lie in between the measurement location and the compressor inlet/discharge. The second approach is recommended for field testing, if possible. The approach is to measure the pressure and temperature as close as possible to the compressor, using multiple temperature and pressuretaps at suction and discharge. Generally, the flow field near the compressor will be highly non-uniform and, thus, at least four pressure and temperature taps should be used on both suction and discharge. Nonuniformity of the flow field affects the uncertainty of the measurement data. If less than four transmitters or test taps (for pressure or temperature) are available, the first measurement approach is recommended. Using less than four pressure or temperature sensors will result in an increase in the total uncertainty for pressure or temperature, as discussed in Section 7. 6.1.2

Installation

PV Card Method Indicator ports on cylinder bores are used for installing pressure transducers. The transducer will be installed on a valve attached to the port. If possible, avoid using additional connectors or adaptors between the compressor and pressure transducers. This can be avoided by contacting the station in

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advance and determining what type of transducer connections are available or installed. Any valves, connectors, or fittings should be the straight through type in order to avoid having varying diameters or gas volumes in the channel to the transducer. Installation of the sensor in this configuration tends to produce other influences on the measurement, such as channel resonance and attenuation. It is not advisable to leave these effects on the measurement. Channel resonance can be corrected after the measurement is taken through data filtration. Channel resonance and attenuation are discussed in more detail in Section 4.1.2.1.

Figure 6-1. ASME PTC 10 Recommended Installation Configuration for Pressure and Temperature Measurement

Pressure transducers are subject to the temperature variations due to the compression and expansion of the gas. The transducers may require heating depending on the type of transducer to maintain the transducer at a constant temperature. If not, temperature compensation curves should be applied to the measured values. It is best to calibrate the transducers after they have been allowed to heat soak when installed on the machine. This will reduce the deviation of the signal due to temperature effects. Pressure measurements in the cylinder nozzles should be made after the orifice plate or inside the cylinder flange when possible. If the measurements are made before the orifice plate, then the pressure drop across the orifice plate needs to be accounted for. Pulsations will be present in this location of the compressor. Dynamic pressure transducers should be used for this measurement. Some compressors will have taps on the cylinder passages which can be used for this measurement. If these are not present, then a pressure tap should be installed on the cylinder nozzle.

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Enthalpy Rise Method The installation of the pressure measurement device, pressure tap size, and symmetry is critical to the measurement accuracy. ASME PTC 10 provides specific guidelines for correct installation and location of pressure probes. The pressure tapping should be inspected prior to installation of the pressure measurement device. The tube and static tapping used to make the pressure measurement should have a constant length to diameter ratio and must be greater than 2. The ratio between the pressure tubing and the pipe diameter should be as small as possible to prevent the pressure measurement from altering the flow pattern. In addition, the wall taps should be exactly perpendicular and flush to the surface. Burrs or slag in the taps are not acceptable and will influence measurement accuracy. 6.1.3

Calibration

Prior to performing the field test, the transmitter or transducer should be calibrated, such that the maximum device error is less than or equal to 0.1% of the actual value. However, this is only achievable if the pressure transducer being used has accuracy to this level. The calibration procedure should contain at least two points. One of the calibration points should be near the maximum pressure that will be measured. The other point can be ambient pressure or another reference pressure. Due to the fact that pressure transducers have linear responses, only two calibration points are required, but it is beneficial to check the pressure on a third or more points. This will ensure the linearity of the transducer. The calibration process will not eliminate all measurement errors, since the calibration process itself is subject to non-linearities, hysteresis, and reference condition error. Transducers should be recalibrated frequently. If possible, calibration at the test site is recommended. If the sensors are calibrated at the test site, then they should be calibrated at least once a day. Some common methods of calibration at the test site are with a pressurized manifold or with dead weights. Ambient, suction or discharge pressure can be supplied to the manifold from the compressor. Calibration at the test site is also convenient if transducers need to be replaced during or before testing. In the PV Card method, the pressure measurement in the cylinder is subject to dynamic temperatures. This can distort the pressure measurement. These sensors will be installed with temperature stabilizers (either heaters or coolers) or have a temperature compensation curve (provided by sensor manufacturer). If the sensors have temperature stabilizers, then the transducer needs to be calibrated at the temperature at which it will operate. If not, then the zero reference of the transducer may shift during testing. 6.1.4

Accuracy Achieved in Practice

The precision uncertainty in pressure measurement will depend upon the uniformity of the flow field. For static pressure measurements, if piping vibration or flow-induced pulsations are high, the measurement of pressure will show a significantly higher random uncertainty. Non-uniformities, location, installation, and calibration errors will affect the pressure measurement. The signal from the transmitter should be transformed into a digital signal by means of a portable data acquisition system (DAQ). The data acquisition system should have an instrumentation accuracy of better than 0.01 to 0.05% of reading. For static pressure measurement, the main source of pressure measurement error is incorrect installation and location of pressure probes. Table 6-1 provides typical values for sources of pressure measurement errors encountered during field tests. All values are percent full scale. For cases of multiple static transmitters, it is assumed that the transmitters are installed at equal angular intervals in the pipe and the flow field is uniform. Table 6-1 assumes that the static transmitter installation meets the upstream and downstream requirements of ASME PTC 10. Installation configurations, which do not meet ASME PTC 10, will have significantly higher location uncertainties in pressure measurement. Table 6-1 shows

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the uncertainty for two and four static transmitters to be the same. This can be true in an even flow field with installations following ASME PTC 10. The four transmitters become valuable when ASME PTC 10 installation requirements cannot be met or the flow field is uneven. In this case, the four static transducers will give a more accurate pressure measurement than the two transmitters (see Figure 6-1 for ASME PTC 10 recommended installation). Table 6-1. Typical Uncertainties in Pressure Measurement (shown as percent of full scale) Sensor Type

Location

1

Installation

Calibration

Device

Acquisition

Pulsations

One Static Transmitter

0.15

0.02

0.10

0.10

0.005

0 - 10

Two Static Transmitters

0.10

0.02

0.10

0.10

0.005

0 - 10

Four Static Transmitters

0.10

0.02

0.10

0.10

0.005

0 - 10

One Dynamic Transmitter

0.15

0.02

0.10

0.10

0.005

0

2,3

1

Errors in location will largely be dependent on uniformity of flow field at measuring location and the number of pressure measurement devices used at a single location. Wall static error will cause high uncertainty if wall taps are not correct. Wall taps should be exactly perpendicular to the surface and flush (with no burrs or slag). For dynamic measurements in the compressor cylinder, the location errors are associated with channel resonance and attenuation. 2 The error due to pulsation depends on the level of pulsation present. If pulsations are present, then a dynamic transmitter should be used. 3 The error in the dynamic transmitter assumes that the sensor has a high enough frequency of response to detect any changes in pressure.

6.2

Measurement of Temperature

6.2.1

Recommended Best Practice

The approach to measurement of temperature is dependent upon whether the PV Card or Enthalpy Rise method is used. In the PV Card method, a suction and discharge temperature is recorded either in the nozzles or outside of the bottles. The temperature in this testing serves two purposes. The first is to verify that steady state has been reached. The second is to provide a temperature for generation of theoretical PV diagram and calculation of the flow through the cylinder end. Typically, only one temperature sensor, usually an RTD, is installed at each measurement location. The actual power measurement is independent of the measured temperature, but the flow and efficiency are not. In the Enthalpy Rise method, the calculated power and efficiency are dependent upon the measured temperature. The temperature can be measured in the nozzles or outside the bottles. If the temperature is measured outside the bottles, then any heat losses through the vessel walls should be accounted for. For this method, it is best to use four temperature sensors in order to identify any inconsistent measurements due to varying flow field. The temperature should be measured downstream of the pressure, if possible. The pressure and temperature sensors should not be installed in the same line of sight. Thermocouples, thermistors, and resistance temperature devices (RTDs) are typically used to measure temperature. RTD’s are recommended for measurement of temperature in the flow stream over a broad temperature range. Thermocouples can be used for high temperature measurements, but below 200°F the resolution will be reduced. Also, thermocouples tend to drift more than RTDs and, thus, require more frequent recalibration. At low temperatures, thermistors are useful but should be carefully calibrated because of inherent non-linearities.

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6.2.2

Installation

These devices should be inserted into a thermowell, though RTD sensors may be used as direct insert devices. Direct insert RTD’s will provide a faster response time. The RTD-thermowell configuration should have the highest recovery factor possible to accurately measure stagnation temperature. The temperature sensor should be instrumented to a temperature transmitter that is connected to the field test data acquisition system. The measurement location should assure that the temperature sensor will be relatively insensitive to radiation, convection, and conduction between the temperature sensor and all external bodies. The insertion depth can produce a large error in the temperature measurement if the sensor is placed too deep or too shallow in the flow stream (see Table 6-2). The manufacturer’s safety guideline should be consulted for insertion depth of RTD’s without thermowells and extra long thermowells to ensure the pipe velocity meets acceptable safety levels. The ASME PTC 10 standard provides specific guidelines for proper installation and location of temperature sensors. Though the field test constraints may make ideal measurement locations impossible, it is important to be aware of the required specifications to assess measurement error and the propagation of additional measurement uncertainty (see Section 7.2 on uncertainty in non-ideal installations). Table 6-2. Recommended Depth of Thermowells Pipe Diameter (inches) 6 8 10 12 14 16 18 >18

Thermowell Depth (inches) 2.0 2.5-3.0 3.0-3.5 4.0 4.5-5.0 5.0-5.5 6.0 7.5 minimum

Note: Above 18-inch diameter, a minimum depth of 7.5 inches from the inner wall is enough to avoid pipe influence and breakage.

6.2.3

Calibration

The temperature sensor shall be calibrated, such that the maximum measurement uncertainty for each sensor is less than or equal to 0.1ºF. Transmitters used in acquiring data from the temperature sensor should be calibrated in tandem (i.e., the transmitter used to read the signal from the RTD should be calibrated with the RTD as a single measurement chain). The calibration procedure should involve at least three points. The calibration process can introduce errors into the temperature measurement, primarily through non-linear response, instrument drift, cold junction, and reference temperature error. 6.2.4

Accuracy Achieved in Practice

Table 6-3 provides typical uncertainty values for the five main sources of temperature measurement errors encountered during field tests. Uncertainties in the temperature originate from the following five major sources of error: (1) location: incorrect position of the thermal sensor in the gas stream; (2) installation: wall conduction heat transfer to and from the sensor due to inadequate insulation; (3) calibration: instrument drift, non-linearities, cold junction, and reference temperature errors; (4) device: inherent accuracy limitations of the sensor device; and (5) acquisition: amplifier, transmission, noise, read, and analog-digital conversion errors.

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Location, installation, and calibration errors may be minimized easily in production or laboratory test facilities. However, for field testing, this is more difficult because time and cost constraints can force the test engineer to accept field test arrangements with improperly located, installed, and calibrated instruments. While it is often impossible to correct these problems during the short field test duration, it is imperative to recognize them and account for them in the uncertainty analysis. Table 6-3 shows that the location, installation, and calibration errors are the dominant factors, while the device and acquisition errors are a smaller contribution to the total temperature error. Also, note that field test device and acquisition errors are significantly larger than values quoted by instrument manufacturers (>0.005 percent full scale). Again, the circumstances and limitations encountered in the field test may not always allow for ideal handling of the sensitive measurement instruments. Table 6-3 assumes that the installation meets the upstream and downstream requirements of ASME PTC 10 for temperature sensor installation. Installation configurations, which do not meet ASME PTC 10, will have significantly higher location uncertainties in temperature measurement. Table 6-3. Typical Uncertainties in Temperature Measurement (shown as percent of full scale) Sensor Type Hg Thermometer Thermistor Thermocouple RTD Infrared Sensor

Location

1

0.10 0.10 0.10 0.10 0.40

Installation

Calibration

Device

Acquisition

0.20 0.20 0.20 0.20 0.20

0.03 0.10 0.10 0.05 0.10

0.03 0.05 0.10 0.05 0.25

0.10 0.05 0.05 0.05 0.05

1

Location error is based on having four (4) equally spaced sensors in the pipe and assumes uniform flow in the pipe. For a single sensor installation, the location uncertainty should be multiplied by four (4). For two (2) sensors, the location uncertainty should be multiplied by two (2). For highly non-uniform flow or pulsating flow fields these values may be larger.

6.3

Measurement of Flow

An accurate measurement or calculation of the gas flow through a compressor is essential for proper determination of the performance and is necessary to identify degradation in the performance of a compressor. The most common meter type installed at gas compressor field sites is orifice meters. Other meters that are available at some times are full bore turbine meters, ultrasonic meters, flow nozzles, and a range of insertion type meters, such as vortex shedding meters, insertion turbine meter, and multi-port pitot probes. Fuel gas flow rates are also measured with these common meters, including orifice, turbine, insertion, and Coriolis mass flow meters. The proper sizing, installation, maintenance, adjustments, and calibrations are necessary for any of these meters to achieve the desired level of precision and repeatability in flow measurement. 6.3.1

Recommended Best Practice

Orifice, ultrasonic, and turbine flow meters are typically employed to measure pipeline flow at a high level of accuracy. However, proper installation, maintenance, and calibration are critical to achieve a desired level of precision and repeatability. All three meter types have upstream length requirements, which may be mitigated through the use of a flow conditioner. When installed correctly with a properly calibrated differential pressure transducer, an orifice flow meter may be used to measure flow over a 3:1 range with an accuracy of 1.5%. Turbine meters have a greater flow range than orifice meters. Turbine meters are very repeatable in both high and low flow situations

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and can provide accuracies better than 1.0% depending upon the quality of calibration. A calibrated ultrasonic meter will provide flow measurement accuracy better than 1.0%. 6.3.2

Installation and Calibration

The upstream piping configurations at field compressor installation are normally not ideal and result in distorted velocity profiles at the meter. Non-ideal meter piping will result in errors in the flow measurement unless something is done to correct the metering configuration. AGA Report No. 3, ISO 5167, AGA Report No. 7, and AGA Report No. 9 should be referenced for the installation and calibration of various flow meters. 6.3.3

Accuracy Achieved in Practice

Pulsation adversely affects most types of meters and, therefore, must be avoided during reciprocating compressor performance testing. However, as most flow measurement instruments provide a low frequency output response, it is often difficult to determine pulsation magnitudes and frequencies. RMS output variation on the flow meter can be used to estimate pulsation amplitudes, but flow turbulence also contributes to RMS flow velocity and pressure variations. AGA Report No. 3 defines that when the pressure differential or the velocity fluctuations across the measurement device exceed 10% RMS value, the flow meter results cannot be considered valid. In order to calculate flow accurately for an orifice meter, the temperature, pressure, gas composition, and differential pressure must be measured accurately. Properly sized orifice meters are suitable for testing reciprocating compressors over a normal operating range. Orifice meters are highly susceptible to installation-effects resulting from improperly conditioned flow, insufficient upstream length, upstream bends, elbows or valves, or extreme beta ratios (>0.65). If installed correctly with a beta ratio less than 0.65, orifice meters will provide a flow measurement accuracy of 1.5% or better. Turbine meters can be calibrated to obtain a measurement uncertainty of 1.0% or better. If the gas pressure or flow rate is outside the calibration curve, the measurement will contain a bias error, which can be as large as 1.5 to 2.0% additional measurement uncertainty. If a turbine meter is over-ranged by exceeding its maximum velocity, permanent damage to the rotor may cause the measurement uncertainty of the meter to exceed 2.0%. The accuracy of an ultrasonic meter decreases at flow velocities of less than 5 to 7 feet per second and at high flow velocities, above 70 to 90 feet per second. Therefore, ultrasonic meters should only be used for compressor testing, if the flow range in the pipe is between 5 to 70 ft/sec. Ultrasonic meters should not be oversized, such that low flow velocities routinely occur, or undersized, such that high velocities are experienced. The field accuracy of ultrasonic meters is normally in the range of 0.5 to 1.0% and is based on the meter’s calibration and having a suitable piping configuration. Other differential pressure devices (annubar, v-cone, etc.) and Venturi meters (sonic nozzles) may also be used to measure gas flow through the compressor. These meter types typically have a lower pressure loss than an orifice meter, but the flow measurement error is highly sensitive to the measurement of differential pressure across the device. Typical meter accuracy is 0.5 to 1.5% if the differential pressure sensor is calibrated and operating well within its range. Venturi meters and differential pressure (DP) type meters are similar to an orifice meter, in that large installation errors can occur (1 to 5%) if installed incorrectly. Installation guidelines for Venturi meters are provided in ISO 5167, Measurement of Fluid Flow by Means of Orifice Plates, Nozzles and Venturi Tubes, and ASME MFC-3M-1989, Measurement of Fluid Flow in Pipes Using Orifice, Nozzle and Venturi Tubes. All differential pressure flow devices must meet a test protocol standard specified in American Petroleum Institute Manual of Petroleum

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Measurement Standards (API MPMS) Chapter 5.7, Testing Protocol for Differential Pressure Flow Measurement Devices. Specific installation requirements for DP type meters should be provided by the meter manufacturer and should assure that the meter conforms to API MPMS Chapter 5.7. Table 6-4 summarizes the achievable accuracies of the various flow meters. Table 6-4. Achievable Uncertainties in Flow Measurement with No Pulsating Flow Type of Flow Meter Orifice Plate Turbine Meter Ultrasonic Meter Annubar Hot Wire Anemometer Tracer Gas

6.4

Measurement of Gas Composition

6.4.1

Recommended Best Practice

Achievable Measurement Uncertainty (%) 1.0 - 1.5 1.0 0.5 - 1.0 0.5 - 1.5 1.0 - 2.0 2.0

Both the engine fuel gas and compressor process gas composition should be evaluated at regular intervals throughout the field test, either through automatic gas chromatograph sampling or by taking regular gas samples. This is particularly true in applications where the gas composition can vary significantly within the course of one day such as in gas gathering applications. Depending on which method is used for the test, the varying gas composition can affect the power, efficiency, and capacity calculations. At a minimum, a gas sample should be taken before and after the test. Multiple sampling methods are defined in GPA Standard 2166 and the American Petroleum Institute Manual of Petroleum Measurement Standards (API MPMS) Chapter 14.1. These include both spot methods and composite sampling (on-line methods). If possible, the gas sample should be taken near the compressor to ensure that it is representative of the gas flowing through the compressor. A gas sample downstream from the gas plant can be more or less meaningless for testing a field gathering unit, although this is often what customers provide. If an automatic sampling probe is used (such as a gas chromatograph probe regulator), the probe should be properly sized to draw samples from the center one-third of the pipe, so that liquids that may appear in the flow cannot be easily ingested into the probes and sample lines. Velocities in the location where samples are taken should not exceed 150 ft/sec in order to avoid possible probe vibration and failure. To properly determine the gas properties from the gas samples, the gas composition should evaluate all components that contribute at least 0.1 mol percent to the composition. Namely, as a minimum, the gas samples should be analyzed for all hydrogen, oxygen, water, sulfur compounds, carbon dioxide, nitrogen, nitrous oxides, other inert gasses, and all hydrocarbon gasses or vapors between C1 and C6. If the hydrocarbon dewpoint of the gas mixture is within 0 to 20ºC of the temperature of the sampling equipment or above the temperature of the sampling equipment (ambient temperature), then additional precautions must be taken. The hydrocarbon dewpoint will vary with different gas mixtures and primarily be influenced by the presence of heavier hydrocarbons, above C6. The best practice in this case is to preheat the sample line and sampling containers prior to taking the gas sample. If pre-heating is not practical, “dead-end” spot sampling methods may be used in combination with re-heating the sample

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above the mixture dewpoint during the analysis process. In addition, if the dewpoint is close to the operating temperature, the compressor should be run for a minimum of two hours after start-up to make sure the gas temperature and composition are relatively stable to expect consistent and reliable data. “Dead-end” spot sampling methods include the water or glycol displacement method, the piston displacement method, the evacuated cylinder methods (evacuated, reduced pressure, or helium pop), and the fill and empty method. These methods work best because the depleted gas is not convected out of the cylinder in the sampling process. If condensate is formed on the wall of the sampling cylinder, re-heating the sample will cause the condensate to re-vaporize as part of the sampled gas mixture. 6.4.2

Installation

All sampling lines and equipment that come in contact with the sample streams should be made of stainless steel or other materials that are inert, compatible with the gas and minimize adsorption of heavy hydrocarbons from the gas stream. Polyethylene, Nylon, and Teflon will cause sample distortion because of these materials’ preferential absorption of specific hydrocarbon components. The probes and lines should be insulated to avoid condensation of the heavier hydrocarbon constituents or water vapor in the sample. The probes and sample lines should also be arranged above the pipeline. As stated in API MPMS Chapter 14.1, the sampling bottle should have a pigtail line connected to its outlet to assure that the process gas is kept above the hydrocarbon dewpoint (see Figure 6-4 below). Prior to sampling the gas, the gas sampling equipment should be cleaned, preferably by steam cleaning or using acetone or liquid propane. Filters in the sample lines are required in most cases. All fittings, tubing, and pressure regulators should be rated for the appropriate operating pressure of the station.

Figure 6-2. Sampling Method with Pigtail as Recommended in API MPMS Chapter 14.1

6.4.3

Calibration

Gas chromatographs are almost exclusively used to determine the gas chemical composition, in order to determine gas density, compressibility, and energy content. A gas chromatograph should not be regarded as an infallible device. A calibration gas standard should be used to calibrate the gas chromatograph regularly. The gas chromatograph should be calibrated at the beginning of each test day. The calibration

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standard should have a composition and heating value comparable to the process gas. This calibration gas should have a certified accuracy of at least 2% or better. The calibration gas should be blended in a procedure traceable to NIST. 6.4.4

Accuracy Achieved in Practice

The test gas composition will almost always differ from the gas composition used in the baseline or factory test. Errors in the determination of the gas composition will affect the density, compressibility, and the energy content determination. Density errors will propagate in the flow measurement when converting between mass and volume flow. Online gas chromatographs must be calibrated regularly (at least once per day during performance testing) to ensure accurate gas composition with a calibration gas that is similar in composition to the processed gas being measured. 6.5

Measurement of Crank Position

6.5.1

Recommended Best Practice

In the PV Card method, the crank position should be measured in order to know what the instantaneous cylinder position is. Knowing the geometry of the compressor, the volume at that instant can be calculated. With the pressure measurement, the PV diagram can be constructed. Two types of sensors are used for the crank position measurement: encoders and once-per-revolution sensors (key phasor, tachometer, magnetic pick-up, etc.). Caution should be taken when using a onceper-revolution sensor. During a full rotation of the crankshaft, there are velocity variations, which would not be accounted for in a single revolution type sensor. If angular velocity and acceleration variations are present with a key phasor in use, this can result in an incorrect reference to ODC. If the once-per-rev signal does not trigger at ODC, then the ODC can be occurring at a different location each time. Also, the data acquisition system will collect pressure transducer signals at specified time intervals. Because of the variations, the calculated volumes and pressures may be not be properly matched. Small errors in position measurement can have significant effects on the power calculation. An encoder should be used, if at all possible. An encoder typically has a metallic disc with multiple slots. The encoder employs a detection mechanism that registers the position of the shaft at each of these slots. A 360 encoder will have 360 slots such that its resolution is 1 deg. Higher count encoders can be used, such as 512, 720, etc. It is recommended to use at least a 360 encoder. The volume of the cylinder at the reported encoder position is calculated with Equation 6-2. Theta (θ) is the position of the shaft as reported by the encoder. When theta equals zero, the referenced cylinder end is at ODC; and when theta equal 180 degrees, the referenced cylinder end is at IDC. The angle reported by the encoder may need to have a phase shift applied if the zero angle is not referencing ODC on the cylinder end being evaluated. For example, the ODC of the encoder may be referenced to the ODC for the first cylinder in the compressor. Cylinder or throw 2 may be at IDC when cylinder 1 is at ODC. Cylinder 2 would then have a 180 degree phase shift. 2 S π S 2 V = (1 − cos θ ) − l − sin θ + l * B 2 + Vcl 2 4 2

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6.5.2

Installation

The encoder is typically installed on the flywheel of the crankshaft for a slow speed integral driver/compressor package. In high-speed separable compressor packages, the encoder may be installed on the compressor frame opposite from the flywheel usually with some type of adapter. There is typically an access point for the encoder installation. Figure 6-3 shows an example of an encoder installation on a flywheel in a slow-speed compressor, and Figure 6-4 shows an encoder installation on a high-speed unit with an adapter. It is necessary to ensure that there is no slippage between the flywheel and encoder. If this occurs, then the results will be invalid. The encoder should be mounted to the flywheel with some type of flexible coupling to avoid mechanical damage due to misalignment. Also, no misalignment can be tolerated with a mechanical drive, as the instantaneous angular velocity of the encoder can be significantly affected.

Figure 6-3. Encoder Installed on a Slow-Speed Reciprocating Compressor on Flywheel

Figure 6-4. Encoder and Adapter Installed on a High-Speed Reciprocating Compressor

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Avoid using multiple fittings on the shaft from the encoder to the compressor since this could lead to alignment issues. It is recommended that multiple encoder shafts of varying length be taken to the test site, due to the fact that the length required will not be known until the tester is at the test site. Every effort should be made to ensure that the encoder rotation is representative of the compressor crankshaft rotation. Avoid placing the encoder close to the opening on the compressor frame (usually on high speed units), because oil vapors escaping from the opening can cause the encoder to malfunction. 6.5.3

Calibration

The encoder itself does not require calibration. The calibration for positional measurement is completed through the determination of Outer Dead Center (ODC) and synchronization of the encoder. ODC refers to the condition where the piston is at a point of travel furthest from the crankshaft (also referred to as top dead center (TDC)). This is a critical step that determines how accurate your positional measurements will be. Once ODC position is known, this can be related to the position of the encoder wheel, otherwise known as synchronization. Determination of ODC requires the compressor to be shut down for access to the flywheel (if there is one). In some cases, such as process compressors, this is not possible. Usually an ODC mark will be placed on the machine during installation and start-up or an initial performance test. This can be used as a reference. In situations where there is no ODC mark and the compressor cannot be shutdown, the PV diagram can be shifted during post-processing, such that the start of the expansion line is set at the minimum clearance. This is not an exact science and the possible error of this should be accounted for in the uncertainty. Note the effect this can have on the PV diagram, shown in Figure 6-5.

Figure 6-5. Rotation of PV diagram to Correctly Reference ODC

The universal approach to determine ODC is to mechanically position a reference piston to its ODC position and mark the flywheel to a match mark on some member fixed to the frame. In principle, this seems a simple procedure; however, in practice, it is the most frustrating task. This can be appreciated when one considers that a 1-degree angular displacement about ODC amounts to only 0.0014 inch linear displacement of a piston on an 18-inch stroke compressor, but the cumulative total of clearances in main bearing journals, crank pin journals, and connecting rod bearings may be 0.015 or more. When marking ODC, it is important to approach ODC from both rotational directions. This will cancel out the effects of the clearances on the position of ODC. When marking ODC, there are several considerations that could affect the reference. The first is where ODC is marked. The most common approach is to mark ODC on the flywheel; however, this cannot or should not always be done. In high-speed compressors, the flywheel is often installed between the

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compressor and driver next to the coupling. If the flywheel is on the driver side of the coupling, then consideration should be given to the type of coupling installed. With highly flexible couplings, such as elastomeric couplings, there could be as much as 10 to 20 degrees of wind up during normal operation. If a rigid coupling, such as a disk pack type is installed, then ODC can be measured on the flywheel on the driver side. The same consideration should be given for couplings on a compressor without a flywheel, such as an electric motor driven compressor. If a highly flexible coupling is installed, then ODC should be marked on the compressor side of the coupling. The section below describes a few methodologies commonly used to determine ODC. Dial Indicator Method Rotate the compressor crankshaft until cylinder #1 is approximately at ODC (other cylinders can be used). Install a dial indicator on the crosshead or crosshead guide of cylinder #1 (whichever is more practical). Position the dial indicator, such that the probe is touching the crosshead or crosshead guide. Rotate the compressor until the cylinder is approximately at ODC (the dial indicator will stop moving). Zero the dial indicator.

Dial Indicator on Crosshead

ODC Mark

Figure 6-6. Example of Set-up for Dial Indicator Method

Rotate the crankshaft in the opposite direction until it reaches 0.03”. Rotate the crankshaft back in the other direction until the dial indicator reads 0.015”. Mark this location on the flywheel. Rotate the crankshaft in the same direction until the dial indicator reads 0.03” (the compressor will progress through ODC and pass it, so the dial indicator will read 0 and then go back to 0.03”). Rotate the crankshaft back the other direction until the dial indicator reads 0.015”. Mark this location on the flywheel. Using an accurate distance measurement, make the center between these two marks on the flywheel. This is the location of ODC. Rotate the crankshaft back to the marks made (using the procedure above) and check the locations of the marks. If the locations are repeatable, then the ODC marking is satisfactory. If not, repeat the process again. Positive Stop Method Another method of locating ODC is known as the positive stop method. No dial indicator is required for this procedure; however, the cylinder head or valve cap must be removed so the unit must be blown down. The basis of this method is that ODC can be determined from the midpoint of two piston positions marked on the flywheel. These piston positions are determined by the placement of the piston at a fixed distance from ODC. This fixed distance is determined by the hard stop used.

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The first step in this process is to obtain the hard stop. The stop can be inserted into the cylinder by removing the valve assembly or the cylinder head. If the cylinder head is removed, obtain a stiff 1/4-inch rod or similar material and sharpen one end to form a pointer. The length of the rod should be set, such that the piston stops at 2 to 10 degrees below ODC. Attach this pointer to a stout strip of steel and drill the appropriate mounting holes in it. Be sure that the strip of steel is rigid enough so that it will not be deflected when the piston contacts the center bolt stop. This strip is placed across the center of the cylinder bore and bolted on each end to secure it to the block. If the valve assembly is removed, place the stop between the cylinder head and piston instead (Figure 6-7).

Figure 6-7. Hard Stop Placed Between Cylinder Head and Piston Through Valve Pocket

Once the positive stop mechanism is installed manually, rotate the crankshaft around in the clockwise direction until the piston end comes in contact with the stop. Mark this position (to a reference) on the flywheel. Rotate the crankshaft in the counterclockwise direction until the piston end comes in contact with the stop. Mark this position on the flywheel. Using highly accurate measurement devices, determine the middle between the two marks (Figure 6-8). This is the location of ODC. Synchronization There are several methods that can be used for synchronizing the encoder with the location of ODC. One method is to drill a hole or install a pin at the location of ODC on the flywheel. A magnetic pick-up can then be used to detect ODC and synchronize the ODC reference with the encoder. Synchronization can also be achieved by using a strobo-scope to detect the ODC location. This requires a special strobo-scope that is linked to the encoder. The scope will have buttons on it that will allow the operator to vary the timing of the scope such that it will flash when ODC passes by. This scope’s link to the encoder software will send a signal to change the ODC reference point for the encoder to the timing of the flash set by the operator.

Figure 6-8. Placement of ODC Mark Between Two Initial Marks

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6.5.4

Accuracy Achieved in Practice

If ODC is determined correctly, then the accuracy of the positional measurement will be directly related to the resolution of the encoder. If a 360 encoder is used, then the resolution will be 1 degree or 0.3%. Higher resolution can be achieved with higher count encoders if the ODC is determined correctly and synchronization is completed accurately. One must weigh the advantages and cost of using a higher resolution encoder. If ODC is not determined correctly, then the accuracy of the positional measurement will be related to the estimated error in ODC, the resolution of the encoder, and synchronization. Regardless of the method used, ODC determination should be repeated at least once in order to verify that the first marking was correct. A 1-3 deg error in the positional measurement can lead to 3-5% error in the calculated power from the PV diagram. This is a significant error and indicates the high importance of correctly determining ODC. On reciprocating compressors that have six or more throws, wind-up along the shaft may introduce error to ODC reference. ODC is marked when the compressor is in a static position. During operation, the loads on the compressor pistons cause the shaft to deflect torsionally, which produces the wind-up. The further away the throw is from the ODC reference cylinder, the greater the wind-up may be. This error is approximately a maximum of 2 degrees for a six-throw machine. Therefore, wind-up should only be a concern if the compressor has six or more throws. 7.

TEST UNCERTAINTY

Test uncertainty must be calculated to determine the accuracy or quality of the test and the bounds of any measured quantity. Without doing this, the tester cannot be sure if the results are valid or within an acceptable range. The effects of the uncertainty of instrumentation, data acquisition, installation, steadiness of operation, and calculations of performance parameters must be considered. There are two primary components to uncertainty of any physical measurement: random (precision) uncertainty and bias (fixed) uncertainty. A larger test uncertainty could increase the risk of failing the test, if the compressor is actually performing better than the acceptance level, and could reduce the risk of failing if the compressor is performing below the acceptance level. Test uncertainties need to be clearly distinguished from machine building tolerances. Building tolerances cover the inevitable manufacturing variance and the subsequent variation in performance predictions. The actual machine that is installed on the test stand will differ in its actual performance from the predicted performance by the machine building tolerances. Building tolerances are entirely the responsibility of the manufacturer and must be excluded in any uncertainty calculation. In addition, the test uncertainty is not equivalent to the contractual test tolerance. The contractually agreed upon test tolerance might be influenced by consideration of how accurate a test can be performed or by more commercial considerations, such as the amount of risk the parties are willing to accept. Because it is normal practice to use a lower performance than predicted as an acceptance criterion, it is in the interest of the manufacturer, as well as the user, to test as accurately as possible. The following definitions should be applied to the discussion of uncertainty: Precision (Random) Error: The error due to random fluctuations of the measured quantity. The true value of the measurement should lie within the scatter of the data points, if no bias error exists. This error is reduced by taking more measurements of the test quantity.

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Bias (Fixed) Error: A systematic deviation of an instrument’s output from a fixed input. Bias can be a complex functional form over the instrument’s operational range, but in most cases, it is just the consistent over- or under-reading of input data. It is often due to installation effects or calibration errors. Bias errors must be estimated in the uncertainty analysis. Note: In a field site test, the bias error and precision error may not be distinguishable. These two components of the uncertainty are often treated as a single combined uncertainty. Linearity: Compares the deviation of a system’s output to a straight-line assumption. Clearly, few physical systems behave linearly over a wide range and, thus, linearity must always be stated with an upper and lower limit. Hysteresis: Refers to the system or instrument output dependency on directionality of the input. Hysteresis has nothing to do with an instrument’s accuracy degradation over time. In most cases, it is defined as the maximum difference in instrument reading for a given input value when the value is approached first with increasing, and then with decreasing, input signals. Hysteresis is often caused by energy absorption in the elements of the measuring instrument or system. All of the above are factors that contribute to, but are fundamentally different than the definition of measurement uncertainty. Uncertainty does not refer to a single instrument’s accuracy, but evaluates the complete range of possible test results given a singular test condition. The field test cannot be performed with all variables fixed. Consequently, the measured performance calculations and test results must also be a range rather than a point and must account for all possible input combinations of all input variables. It is important to understand that if the input ranges to the system are defined as statistical bounds, such as 95% confidence intervals, then the output from the uncertainty analysis will also present the same 95% confidence interval statistical bounds. Similarly, if the inputs are absolute errors of measurements, then the uncertainty analysis will also yield absolute errors (i.e., whatever is the type of uncertainty range for the input variables will be the type of uncertainty range for the result). Consistent application and definitions of the input variable’s uncertainty ranges is, thus, critically important in any uncertainty analysis. Furthermore, prior to determining a test uncertainty, it is important to know whether the measured variables in the test are independent or dependent, as this determines the method of uncertainty calculation that must be employed. For almost all real measurement scenarios, there is some physical dependency between the input variables and, thus, unless one is absolutely certain that all measured and given system inputs are independent; it is safer to opt for the more conservative assumption of measurement dependence. Thus, as the determination whether an experiment’s measured variables are interdependent directly establishes the uncertainty analysis method that must be employed, a thorough physical understanding of the measured system is imperative. The test uncertainty calculation should be performed using one of the three methods described in Appendix E. To evaluate the test data, the uncertainty of the test must be calculated correctly, and the required uncertainty limits must be understood prior to the test. For example, data with an uncertainty of 3.0% cannot yield conclusions requiring an accuracy of 1.0% and, thus, if 1% accuracy is required, the test preparation, instrumentation, and planning must reflect this requirement. In addition, if a measurement of pressure is made with a value of 100 psi and an uncertainty of ±3%, then the pressure measurement will actually be in the range of 97 to 103 psi. Also, in comparing the field test data to any

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other set of data of the same machine (such as historical data or the factory test data), the uncertainties in both tests must be considered in the comparison. If an uncertainty analysis is performed before testing begins, it could be useful in determining what the most influential test parameters are. The determination of influential test parameters should be used to assess the measurement parameters in order to improve the accuracy of the field test. The terms in the total uncertainty equation can be compared at different operating conditions. If the comparison reveals that a certain term becomes more significant to the overall uncertainty, then extra efforts to improve this measurement will be worthwhile. The test uncertainty tolerances are recommended in Table 7-1 for the primary measurement parameters in the performance test. This table was assembled from current practices, recommendations from industry experts, and what type of instrumentation is commercially available. Table 7-1. In-Practice Achievable Uncertainty for Measured Test Parameters Measurement

Recommended Uncertainty

Pressure

0.3 – 1.0% Full Scale

Temperature

0.5 – 7.0 ºF

Flow

0.5 – 2.0% of value

Gas composition (Density, compressibility, gas constant, specific heat, energy content)

0.2 – 3.0% of value

Piston Position (encoder)

0.1 – 0.3% of 360 degrees

For all parameters derived from an EOS (such as compressibility, heating value, isentropic coefficient, density, specific heat, and gas constants), there is an added inherent uncertainty, since the EOS is an empirical model. Unless direct experimental data for comparison is available for the gas composition used in the performance test, it is difficult to quantify the added EOS model uncertainty. However, a consistent application of the selected EOS between the factory test, field test, and predictions will minimize any potential performance analysis differences and, thus, reduce the contribution of the EOS model uncertainty to a negligible contribution. The effect of typical “near ideal” measurement uncertainties on the total compressor uncertainty for both the PV Card and Enthalpy Rise method is provided in Section 7.1. Non-ideal installation effects on uncertainty are provided in Section 7.2 below. 7.1

Ideal Field Test Conditions for Reducing Uncertainties

In an ideal field installation, the uncertainty in measured power and efficiency for the reciprocating compressor is at a minimum. Departures from the ideal installation will increase these uncertainties. Uncertainties should be calculated using the methods described in Appendix E and instrument uncertainty values listed in the preceding sections. This section describes an example of a near ideal field test installation and provides a typical baseline uncertainty in power and efficiency for this case. The effects of non-ideal measurement conditions on the total performance uncertainties are discussed and compared in Section 7.2. In the example, uncertainty calculations given in Sections 7.1 and in the non-ideal installations shown in Section 7.2, the perturbation method was used to determine the total performance uncertainty, as described in Appendix E.

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7.1.1

Compressor Uncertainty Examples

The validity of a compressor performance field test depends on the level of uncertainty of measured efficiency and power. Also, the test uncertainty can be used to determine if the test is worthwhile. If the test uncertainty bands cross over the theoretical predictions of compressor performance power, then the test cannot prove or disprove the theoretical predictions. The theoretical predictions would then provide adequate information on the performance of the compressor. Figure 7-1 shows two examples: one where the test would not provide worthwhile data due to high uncertainty (left side) and one with an uncertainty which provides useful test data (right side). Power and efficiency uncertainties should be calculated from the individual measurement uncertainties (temperature, pressure, piston position, flow rate, and gas properties). Below are examples of the PV Card and Enthalpy Rise methods uncertainty analyses. Test Point and Respective Uncertainty Ellipse

Test Point and Respective Uncertainty Ellipse

Theoretical Prediction Uncertainty Bands

Theoretical Performance Curve

BHP

BHP

Theoretical Performance Curve

Theoretical Prediction Uncertainty Bands

ps

ps

Figure 7-1. Comparison of Tests with Different Levels of Uncertainty

PV Card Method An example of uncertainty calculation of a performance test conducted using the PV Card method is described below. This was conducted on a medium speed unit with air being compressed. The pressure transducer was installed on the head end of the cylinder with the transducer flush-mounted. The compressor was run at various speeds from 450-900 RPM. The test data analyzed below is for the 450 RPM test. Table 7-2 details the geometry of the compressor. The uncertainty of the clearance was assumed to be 1%. This is considered to be a best case scenario. There is an uncertainty associated with the clearance volume regardless if it is from manufacturer literature, measured, or an effective clearance. An isentropic constant for air was assumed to be 1.4. This is a standard value at 14.7 psia and 60ºF. An uncertainty of 0.01% was assumed for this value based on expected uncertainties in suction temperature and pressure and gas composition measurements in field performance tests at steady state. Figure 7-2 shows the actual PV diagram plotted with the theoretical PV diagram for 450 RPM and a suction pressure of 35 psia. Table 7-2. Compressor Geometry Component Bore Diameter (in) Stroke (in) Rod Diameter (in) Rod Length (in) Clearance (%)

Guideline for Field Testing of Reciprocating Compressor Performance

Value 7.5 6 2.25 14.5 17.83

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The data from the test was evaluated for its uncertainty related to clearance volume measurement, isentropic constant calculation (from EOS with suction pressure, suction temperature, and gas composition measurements), piston position, and cylinder pressure. The results for each variable are shown in Table 7-3. The total resulting uncertainty from the performance test at 450 RPM was 2.03% for power and 2.06% for efficiency. As shown in Table 7-3, the main influential values on the uncertainty are the pressure and cylinder position measurements. These measurements should be targeted to have the lowest uncertainty allowable based on budgetary, field testing, and installation constraints. 100

Measured Theoretical 90

Pressure (psia)

80

70

60

50

40 0

50

100

150

200

250

300

350

Volume (in^3)

Figure 7-2. Actual and Theoretical PV Diagrams for Performance Test at 450 RPM Table 7-3. Summarization of Uncertainty for Performance Test at 450 RPM Variable Clearance Volume Isentropic Constant (Suction Temperature and Pressure & Gas Composition) Piston Position Cylinder Pressure Total Uncertainty

Variable Uncertainty (+/- %) 1

Power Uncertainty (+/- %) 0

Efficiency Uncertainty (+/- %) 0.007

0.01

0

0.02

0.2 0.25

1.09 1.71 2.03

1.1 1.74 2.06

Enthalpy Rise Method An example uncertainty calculation for a reciprocating compressor test using the Enthalpy Rise method is given in Table 7-4. The values of the measured variables shown in Table 7-4 represent a typical reciprocating compressor application in pipeline (low compression ratio) service. Operating conditions are shown in Table 7-4. A representative gas composition was used to compute the gas properties, consisting of the following components: 90.0% methane 5.37% ethane 1.7% propane 0.274% isobutene 0.331% n-butane

0.055% isopentane 0.09% n-pentane 0.07% n-hexane 1.06% carbon dioxide 1.05% nitrogen

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The Benedict-Webb-Rubin (BWR) EOS model was used to compute the compressibility, specific heat, and molecular weight. Table 7-4. Example of Total Uncertainty Calculation for Compressor in "Near Ideal" Case Input Parameter

Value

Input Δ(%)3

ΔPower

Δη

Measured properties: ps (psia) 159.5 0.3 26.11 0.006 Ts (deg F) 80.3 0.1 73.98 0.005 pd (psia) 224.8 0.3 26.18 0.006 Td (deg F) 152.3 0.1 65.44 0.005 3 1 Q (ft /min) 19345 0.5 43.52 0.000 Calculated properties based on gas composition at suction conditions 2 Z 0.9763 0.05 4.36 0.000 cp (Btu/lbm-deg F) 0.52 0.3 26.11 0.000 K 1.31 0.08 0 0.003 R (Btu/lbm-deg F) 0.11 0.3 26.11 0.000 Performance Parameter Pcomp (HP) Efficiency, ηisen (%)

Value

Total ΔPower (%)

Total Δη (%)

8703 0.636

1.35

1.81

1

Q is actual flow rate at suction conditions, v = 3937 ft/min in a 30" diameter pipe. Z, cp, k, and R represent a typical hydrocarbon transmission grade gas. 3 Typical values of uncertainty represent ideal pressure and temperature measurement using four sensors on suction and discharge, recommended flow meter installation and gas property calculation made with consistent EOS model and accurate gas sample. 2

The measurement uncertainties calculated in Table 7-4 assume near-ideal test conditions, procedures, and efficiencies. These uncertainties are based on proper installation, application, and acquisition of the test instrumentation, as recommended previously. The calculated property uncertainties (Z, cp, k, R) are based on typical variations in a sampled gas composition due to sample variation and uncertainty introduced by the gas sampling process (∆ = +0.3% for methane and ethane, ∆ = +0.1% for propane, ∆ = -0.3% for carbon dioxide, ∆ = -0.4% for nitrogen). The calculated property uncertainties include the uncertainty due to gas chromatograph analysis for a calibrated gas chromatograph. Based on all the input uncertainties, the resulting uncertainty in compressor power is 1.35%. The resulting uncertainty in compressor efficiency is 1.81%. These values of measurement uncertainty for the compressor are close to the minimum attainable test uncertainty for this case. 7.2

Effects of Non-Ideal Installations on Uncertainty

Deviations in the ideal test conditions or procedures (as recommended previously) will increase the individual measurement uncertainties and result in a higher total performance measurement uncertainty for the compressor. Depending upon the effect of the non-ideal installation on the measurement, the resulting increase in uncertainty can range from a small increase of 0.20% in some cases to above 5.0%. This uncertainty can affect the measured accuracy of the efficiency and the power. Some typical nonideal effects are instrumentation uncertainty, channel resonance and attenuation, heat losses, and the

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pulsating flow field. Table 7-5 details some of the non-ideal uncertainties experienced with instrumentation installations. The majority of these uncertainties are targeted for the Enthalpy Rise method, but some can also be used with the PV Card method such as use of thermocouple instead of RTD and error in gas sampling. Table 7-5. Non-Ideal Installation Effects on Compressor Uncertainty

Non-Ideal Installation Single elbow 1 to 3 pipe diameters upstream of flow measurement point (no flow conditioner) Double elbow in-plane, second elbow 1 to 3 pipe diameters upstream of flow measurement point (no flow conditioner) Double elbow out of plane, second elbow 1 to 3 pipe diameters upstream of flow measurement point (no flow conditioner) Partially closed gate or ball valve within 1 to 3 pipe diameters upstream of flow measurement point (no flow conditioner) Single elbow within 1 to 3 pipe diameters of temperature and pressure sensors Double elbows in-plane, second elbow within 1 to 3 pipe diameters of temperature and pressure sensors Double elbows out of plane, second elbow within 1 to 3 pipe diameters of temperature and pressure sensors RTD not fully inserted into flow stream Use of thermocouple instead of RTD Error in gas sampling (no pigtail used) with heavy hydrocarbons

Total ΔPower (%)

Deviation from Baseline Δpower

Total Δη (%)

Deviation from Baseline Δη

1.73

0.38

1.81

0

1.95

0.6

1.81

0

2.79

1.44

1.81

0

3.72

2.37

1.81

0

2.39

1.04

2.85

1.04

3.19

1.84

3.66

1.85

4.84

3.49

5.37

3.56

2.37 3.15

1.02 1.8

2.66 3.38

0.85 1.57

1.38

0.03

2.01

0.2

*Note: This table assumes that the measurements are taken outside of the bottles with a minimal pulsating flow (less than 2-3%). If measurements are taken in a pulsating flow, then additional uncertainty should be added. Table 7-6 details the increase in performance uncertainty using an encoder and cylinder pressure measurement with the PV Card method. There are many factors that play into the accuracy of an encoder. Outer dead center (ODC) must be determined and synchronized correctly in the data acquisition system to yield accurate results. Also, misalignment with a mechanical drive will introduce high error, as the instantaneous angular velocity of the encoder can be significantly affected. Every effort should be made to ensure that the encoder rotation is representative of the compressor rotation. Encoders can be installed and calibrated to achieve accuracies of 1 degree. As shown in Table 7-6, a near-ideal uncertainty of 0.28% yields an overall uncertainty in power and efficiency of 1.54% and 1.57%, respectively. The cylinder pressure measurement is influenced by instrumentation characteristics and proper installation. The installation of the dynamic pressure sensor should be designed to avoid channel resonance and attenuation. Channel resonance is a function of the geometry of the port (diameter and length of the channel). It occurs due to an excitation of the quarter-wave acoustic length resonance of the

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gas passage between the cylinder interior and the pressure transducer. The channel resonance and attenuation error is not related to the machine’s efficiency, but the effect is a common phenomenon with high-speed compressors. Channel attenuation can cause errors in the actual power calculation up to 40%. High errors will be seen in high speed units with heavy gases such as propane or CO2 and long, small diameter indicator passages. The measured ICHP is not normally affected by pure channel resonance since it is a sinusoidal phenomenon. Table 7-6. Effects of Non-Ideal Encoder and Cylinder Pressure Measurements Variable

Encoder

Cylinder Pressure

Variable Uncertainty (+/- %) 0.28 0.42 0.56 0.25 0.50 1.00 1.50

Power Uncertainty (+/- %) 1.54 2.33 3.11 1.71 3.42 6.84 10.25

Efficiency Uncertainty (+/- %) 1.57 2.38 3.21 1.74 3.54 7.34 11.43

If channel resonance is present, it can be removed by filtering techniques. However, the user is cautioned in doing this. If the data is not properly filtered, the calculated power and efficiencies will be incorrect. There is also uncertainty associated with temperature measurements. This effect manifests itself in the theoretical PV diagram construction. This calculation is based on EOS results. It is difficult to summarize the effects of EOS on uncertainty. If the proper EOS is utilized consistently throughout the performance test, the uncertainty of the theoretical ICHP will mainly be due to the uncertainties in the temperature, pressure, gas composition, and piston position measurements. If the test is conducted at steady state, the effect on the variation of the theoretical power and efficiency will be minimal (less than 0.01%). This uncertainty only needs to be considered if the test has highly fluctuating conditions. A large number of reciprocating compressors utilize some type of cylinder cooling system. This is true on high-speed and low-speed compressors. Removing heat from the compressor cylinder is essentially removing some of the energy applied by the compressor to the gas. This heat removed needs to be considered when determining an isentropic efficiency. If it is not accounted for, the calculated isentropic efficiency will be optimistic. The cylinder cooling effects are already included in the measured PV diagram. This is due to the fact that the work applied to the gas is directly measured. Equation 4-4 shows how the heat removal is included in the Enthalpy Rise method calculation. The uncertainty of the heat losses estimations directly affects the uncertainty of the total power measurement and efficiency in the Enthalpy Rise method. Care should be taken to obtain an accurate estimate for heat removed from the compressor cylinders. Pulsations are always present in a reciprocating compressor. It is important to understand their effects in order to account for their influence during performance test. The capacity of the compressor can be calculated from a PV diagram, but sometimes the capacity is measured. Flow measurement is highly influenced by pulsations. A flow meter must be installed in an area of low pulsations (much less than 10% and preferably under 2%) in order to obtain a valid reading. This must be outside the suction or discharge pulsation bottles in virtually all cases. Beyond the flow measurement, the pressure and temperature measurement can be affected by large pulsations and introduce higher than 3% uncertainties.

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Pulsations can also have a direct effect on both the actual and the calculated power and efficiency. While the suction and discharge valves are open, the acoustic pulsation present in the system is reflected into the compressor cylinder. Should the pulsation levels be of sufficient amplitude, the valve opening and closing times can be affected, and the average inlet and/or discharge pressures of the cylinder can be different than the design pressures, the net result being horsepower and capacity values which are different than the design values. These values may be greater or smaller, depending on the pulsation characteristics. Variations of operating conditions during testing will affect the uncertainty of the performance measurements and calculations. The requirements for test stability were shown in Table 5-1 through Table 5-3. If the measured and calculated values deviate outside these ranges, then the uncertainty of the test will increase. Every effort should be taken to ensure that test stability is achieved. If this is not possible, then the uncertainty of the deviations must be considered in the test results. 8.

INTERPRETATION OF TEST DATA

8.1

Data Reduction and Checking Uncertainties

Test points taken at different points in time should not be averaged. If this is done, the non-linear effects will not be averaged correctly. Instead, the performance parameter should be calculated for each data point. The resulting parameters can then be averaged. Data reduction procedures should be aimed at minimizing time and cost in the determination of performance. If the test data from the field test deviates more than the level of test uncertainty, the source of the deviation should be explored further. For example, two test points, which were taken at the same condition, may show vastly different calculated flows. Further investigation may reveal that a clearance volume pocket was open at one test point, but not the other. Repeating the performance test is not recommended by this guideline unless the data is clearly un-usable. It is advised to have a performance calculation program set-up in the field such that the results can be calculated automatically. Any significant deviations in the data can be investigated in the field. Then it will be quick and easy to repeat tests as necessary. The results should be monitored throughout the test. For the reciprocating compressor, there are many ways to determine what could possibly influence the test results. For the PV Card method, the structure of the PV diagram can indicate whether there are leaks in the valves or seals. Also, if a shift is seen in the compression and expansion lines of the PV diagram, the gas composition may have not been stable during the test. Compressor performance diagnostics with PV diagrams is discussed in more detail in Appendix F. Effects such as suction valve leakage, discharge valve leakage, piston ring leakage, pulsation effects, and valve and cylinder gas passage losses can be identified with the geometry of the diagram. For the Enthalpy Rise method, if the enthalpy difference versus flow curve has shifted horizontally, the flow may have been measured incorrectly or contain a bias error. If some of the points on the curve match predictions and others do not, the gas composition (or another influential parameter) may not have been stable during the test. 8.2

Use and Comparison of Data

There are many different objectives to performance tests. A company may be conducting a manufacturer verification performance test or they may be generating a set of performance curves for the operational control of the system. Each data point recorded during the field test should be evaluated individually. The average of all data points at a particular condition should be used to compute the average power,

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enthalpy difference, flow, and efficiency. This should only be done after the results have been calculated for each data point. For a manufacturer performance verification test, these final data point averages should be compared to the performance curves for the compressor. The performance curves are provided by the manufacturer of the compressor. There are multiple performance curves that can be supplied with the compressor. Some of these include: BHP/MMSCFD verses suction pressure, discharge pressure or pressure ratio, capacity verses suction pressure, discharge pressure or pressure ratio, and discharge pressure verses suction pressure. The performance results can be compared to the various curves depending upon what parameters were measured during the performance test. When comparing the measured data points to the manufacturer stated performance, the uncertainty must be considered. If the performance test is conducted in order to characterize the performance of the compressor at various conditions and development of curves, each individual point should still be evaluated individually and then averaged. The developed curves should include uncertainty curves. The uncertainty curves will provide the user with the range of possible values for the plotted values. An example of a compressor performance curve is shown below in Figure 8-1 for a high-speed transmission compressor. 2600 2400 2200

Driver HP

Power (BHP)

2000 1800 Step 1

1600 Step 2

1400

Step 3 Step 4 Step 5

1200 1000 800

250

200

Step 1

Flow (MMSCFD)

Step 2

150

Step 3 Step 4 Step 5

100

Reg Flow 50

0 500

550

600

650

700

750

800

850

900

Ps (psig)

Figure 8-1. Example of Compressor Performance Curves for High-Speed Transmission Compressor

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8.3

Using Redundancy to Check Test Measurement and Uncertainty

Redundant calculations should be performed, if possible, to check test measurements. The compressor driver power may be measured as discussed in previous sections. The shaft power output (or engine BHP) from the engine can be calculated with the fuel flow, lower heating value of the fuel, and efficiency of the engine. The compressor BHP measured during the field test should match the engine BHP. If the flow rate is measured during the performance test, this can be compared to the capacity calculated from the volumetric efficiencies measured. There may be some variation in these numbers due to the uncertainty associated with each type of measurement, but the values should be fairly close. The calculated values, or if available factory test (manufacturer supplied) values, should match the measured values within the associated uncertainty for both values. The uncertainty on any measured value obtained in the field test should be calculated (or estimated as accurately as possible). This uncertainty will be a plus or minus value. It should overlap with the uncertainty band (also a plus or minus) on the calculated/factory test value. This analysis will determine if the redundant measurement is statistically equal to the measured value. This method of comparison should always be used in order to practically determine if measured values are correct. A graphical example of this is shown in Figure 8-2. Test Point and Respective Uncertainty Ellipse

ps

Performance Statistically Equal

BHP

Theoretical Performance Curve

BHP

BHP

Theoretical Prediction Uncertainty Bands

ps

ps

Performance Statistically Equal

Performance Not Statistically Equal

Figure 8-2. Comparison of Theoretical Predicted Performance and Measured Performance Test Point

8.4

Analysis of Measured Results

The true value of the compressor performance parameters (capacity, efficiency, and power) lies within the measured data points, assuming the data has been recorded correctly without a significant bias error. The measured data points should be viewed as a representation of the bracket surrounding the true value. If two measured parameter data points are plotted on a horizontal- and vertical-axis, an uncertainty band on each measured variable exists. An ellipse surrounds the measured data point (see Figure 8-3). The predicted performance test point, or manufacturer factory test curve, may lie within the uncertainty band produced from the field test, though the exact values from the field test do not exactly match the manufacturer suggested curve. This example (shown in Figure 8-3) shows good performance of the compressor during the field test. The compressor performance in the field test is statistically equal to the factory test in this example.

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Test Points and Respective Uncertainty Ellipse

BHP

Performance Curves

ps Figure 8-3. Example of Test Uncertainty Range

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9.

REFERENCES

1.

AGA Report No. 7, “Measurement of Natural Gas by Turbine Meter,” 2006.

2.

API 618, “Reciprocating Compressors for Petroleum, Chemical and Gas Industry Services,” 1995.

3.

Deffenbaugh, D. M., Smalley, A. J., Harris, R. E., Brun, K., Moore, J. J., McKee, R. J., et al., “Advanced Reciprocating Compression Technology,” Southwest Research Institute Final Report for DOE-NETL, December 2005.

4.

ASME PTC 10, “Performance Test Code on Compressors and Exhausters,” 1997.

5.

ASME PTC 19.1, “Measurement Uncertainties,” American Society of Mechanical Engineers, New York, New York, 1985.

6.

Boutin, B. and Webber, B., “Basic Reciprocating Engine and Compressor Analysis Techniques,” Proceedings of the Gas Machinery Conference, Albuquerque, New Mexico, 2004.

7.

Brun, K. and Nored, M. G., “Guideline for Field Testing of Gas Turbine and Centrifugal Compressor Performance,” Gas Machinery Research Council, August 2006.

8.

Casey, M.V., Fesich, T.M., “On the Efficiency of Compressors with Diabatic Flows,” GT200959015, Proceedings of ASME TurboExpo 2009: Power for Land, Sea and Air, Orlando, FL, 2009.

9.

Durke, R. G. and McKee, R. J., “Orifice Meter Gage Line Distortions,” Southwest Research Institute.

10.

Edmister, W. C. and Lee, B. I., Applied Hydrocarbon Thermodynamics – Volume 1, Second Edition, Gulf Publishing Company, Houston, Texas, 1984.

11.

Ely, C. and Messick, T., “Performance Measures for Gas Compression and Transportation,” Proceedings of Gas Machinery Conference, Salt Lake City, Utah, 2003.

12.

“Field Measurement Guidelines Compressor Cylinder Performance Summary,” GMRC Technical Report No. 84-10a, May 1984.

13.

Gehri, C. and Harris, R. E., “Technology for the Design and Evaluation of High-Speed Reciprocating Compressor Installations,” Proceedings of the European Forum for Reciprocating Compressors, Dresden, Germany, November 1999.

14.

Harris, R., E. and Edlund, C., “Performance Measurements of High Speed/High Ratio Reciprocating Compressors,” GMRC, 1998.

15.

Howard, B., “Channel Resonance in Reciprocating Compressor Cylinder Pressure Measurements,” GE Energy, 2006.

16.

IEEE 515, “Standard for the Testing, Design, Installation, and Maintenance of Electrical Resistance Heat Tracing for Industrial Applications,” 2004.

17.

ISO 1217, “Displacement Compressors – Acceptance Test,” 1996.

18.

ISO 5167, “Measurement of Fluid Flow by Means of Pressure Differential Devices Inserted in Circular Cross-Section Conduits Running Full,” 2003.

19.

Kumar, S. K., Kurz, R., and O’Connell, J. P. “Equations of State for Compressor Design and Testing,” ASME Paper No. 99-GT-12, 1999.

20.

Kurz, R. and Brun, K. “Site Performance Test Evaluation for Gas Turbine and Electric Motor Driven Compressors,” Proceedings of the Thirty-Fourth Turbomachinery Symposium, Houston, Texas, 2005.

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21.

Kurz, R. and Brun, K. “Degradation in Gas Turbine Systems,” Journal of Engineering for Gas Turbines and Power, Transactions of the ASME, Vol. 123, pp. 70-77, January 2001.

22.

Kurz, R. and Brun, K., “Efficiency Definition and Load Management for Reciprocation and Centrifugal Compressors,” Proceedings of 6th Conference of the EFRC, Dusseldorf, Germany, October 2008.

23.

Mathews, H., “Compressor Performance Analysis,” Proceedings of Gas Machinery Conference, 2000.

24.

McKee, R. J., “Pulsation Mitigation in Gas Flow Measurement,” Southwest Research Institute.

25.

Moffat, R., “Describing the Uncertainties in Experimental Results,” Experimental Thermal and Fluid Science, Vol. 1, 13-17, 1988.

26.

Nimitz, W., “Evaluation and Optimization of Reciprocating Compressor Performance,” Proceedings of the AGA Transmission/Distribution Conference, 1985.

27.

Ransom, D., Brun, K., and Kurz, R., “Enthalpy Determination Methods for Compressor Performance Calculations,” Proceedings of ASME TurboExpo, Montreal, Canada, 2007.

28.

Sandberg, M. R. “Equation of State Influences on Compressor Performance Determination,” Proceedings of the 34th Turbomachinery Symposium, Houston, Texas, 2005.

29.

Schultheis, S., Lickteig, C., and Parchewsky, R., “Reciprocating Compressor Condition Monitoring,” Proceedings of the 36th Turbomachinery Symposium, 2007.

30.

Smalley, A., Lagus, P., Kothari, K., Wang, J., and Clowney, S., “Reciprocating Compressor Flow by Tracer Dilution and Cylinder Pressure Measurement,” Proceedings of the International Gas Research Conference, 1992.

31.

Soave, G., “Equilibrium Constants from a Modified Redlich-Kwong Equation of State,” Chemical Engineering Science, Vol. 27, Issue 6, 1972.

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APPENDIX A GENERAL PERFORMANCE TESTING PROCEDURE

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APPENDIX A This section outlines the steps that should be followed to complete a reciprocating compressor performance test. Differences in the PV Card and Enthalpy Rise method will be noted in the appropriate steps. References to certain sections of the guideline (that provide more details) will be in parentheses. 1. Determine test objectives (Forward and Section 2) 2. Develop Field Test Agenda (Section 5) a. Select calculation methodology i. Chose method of data reduction: PV Card or Enthalpy Rise method (Section 4) ii. Select EOS of state for all calculations (Section 3.7 and Appendix C) iii. Select approach for determining uncertainty (Section 7 and Appendix E) iv. Set test results acceptance criteria (specified in terms of maximum uncertainty allowed) b. Review site specific details i. Review field conditions and equipment, pipe, and station layout ii. Determine if any deviation from normal operation may be necessary to achieve test objectives iii. Identify operating conditions and operational limits of compressor including pressure, temperature and flow limits of facility 1. Obtain manufacturer performance curves for compressor 2. Review capacity control and load steps of compressor 3. Determine operation matrix for testing based on typical operating conditions and test objectives a. If possible test guarantee points and then additional desired points iv. Review test safety considerations (Section 5.6) v. Select instruments to be used, their location, method of operation, calibration, requirements for installation (Sections 4 and 6) 1. Determine how these instruments will be installed with existing instrumentation 3. Pre-test meeting: Meeting between test engineer, customer, and all parties involved to discuss the details of the test (Section 5.1) a. Review field test agenda b. Agreement should be reached on… i. Test objectives ii. Test procedures iii. Safety requirements iv. Responsibilities during test v. Availability of necessary operating conditions 1. Review contractual guarantee points and what operating conditions they could be reached at 2. If cannot operate at guarantee points then consult with manufacturer to determine alternate guarantee points vi. Acceptance conditions 4. Pre-test operation and instrumentation check-out (Section 5.2) a. Unit preparation i. Have operator take the unit offline if it is running

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b. c. d.

e.

f.

g. h.

i. j. k.

1. If unit cannot be taken offline all items below except e can be completed with the unit online. The unit must be shutdown in order to complete ODC determination. ii. Blow down the unit iii. Lockout Tagout the unit Verify compressor is in good mechanical condition (complete a mechanical assessment) and conduct appropriate maintenance If driver performance will be measured during the test, verify the mechanical condition of the driver and conduct appropriate maintenance Instrumentation (Section 6) i. Calibrate instruments in the range which they will operate in ii. Install instruments 1. Check insertion depth of thermowells. 2. Verify that thermowells are service with appropriate oil or heat transfer material 3. If large area of thermowell is exposed, insulate this area 4. Where pressure taps involve tubing runs, the tubing should be checked for leaks. iii. Check all instrument readings to assure that they are functioning properly iv. Verify data acquisition system (DAQ) operation prior to starting the test ODC Determination (Section 6.5) i. Prepare compressor for ODC determination 1. Before starting ODC determination open all indicator valves on compressor cylinders and power cylinders to relive any excess gas ii. Complete ODC determination with selected method (two methodologies described in Section 6.5) iii. Repeat ODC determination for verification iv. Synchronize encoder with ODC position Check fixed clearance (Section 5.2 and Section 4.1.3) i. Compare the calculated clearance from the PV analyzer to the manufacturer stated clearance. Take into considerations what capacity control devices are being used (ex. valve unloaders, clearance pockets). If these values are within 1 to 2% of the manufactures stated fixed or variable clearances then the manufacturer clearance can be used for the performance test. If they are not close then further investigation should be conducted to determine what is causing the variability or the fixed clearance should be measured. Ensure sufficient gas is available for the anticipated flow and operating conditions of the test If the test is going to be conducted on a closed loop, check if gas cooling is available and if recirculation of gas is an option during field test. Notify all parties of time frame for test. Determine how load steps will be maintained constant during a test point and how they will be changed for different test points. Identify and document what orifice plates are installed Check the position of the recycle or bypass valve. Both of these values should be in operable conditions and not leak when closed. Check if in line strainers are plugged or not

l. 5. Testing a. Start compressor and allow system to reach thermal equilibrium (at least 30 minutes for the compressor) b. Adjust compressor to reach desired operating conditions for first test point on test matrix.

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c. If using the PV Card method, verify that PV diagram is as expected and that no channel resonance or attenuation is present. (Section 4.1) d. Estimate the amount of time required to collect all data during a test. Assure that compressor is stable over this amount of time before each test (Section 5.5, Table 5-2) e. Capture test data by obtaining an average of several data points over a short time span. i. The test data should not fluctuate more than the requirements listed in the guideline (Table 5-1 through Table 5-3). ii. If the test data variations does not fall within the limits specified in the guideline perform the test again once the compressor is stable iii. If the test data variations do not fall within the limits after several attempts then take the test data as is. An additional uncertainty should be added to the results due to the instability of the test. (Section 5.5.3) f. Measure surface temperature of bottles and pipe for heat loss estimations during each test (Appendix H) g. Record wind speed (only on units not housed in a building), ambient temperature, and ambient pressure once during each test if not measure continuously and recorded by DAQ system h. Repeat steps b through g for all test points in test matrix i. After all tests are complete, ensure that all data has been captured and stored in the test computer 6. Post-test operation a. Have operator shut compressor down b. Bleed gas pressure out of compressor c. Remove all instrumentation and return compressor back to original condition (pre-test condition) 7. Test Data Processing a. Retrieve test data from test computer b. Process data to calculated desired performance parameters in accordance with the data reduction method and EOS selected prior to testing (Section 3, Section 4, Section 8, Appendix B, Appendix C, Appendix H) i. Determine compressor efficiency and power at each test point (Section 3.2, Section 3.3, and Appendix B) ii. Calculate heat losses for each test point when using the Enthalpy Rise method (Appendix H) c. Calculate uncertainty for each test parameter (Section 7 and Appendix E) d. Plot test data and uncertainty ellipse with manufacturer performance curves. (Section 8) e. Document details of test including operation conditions tested, compressor configuration, test data and results and uncertainty in a test report

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APPENDIX B CALCULATION OF THEORETICAL PV DIAGRAM

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APPENDIX B The following are two general procedures for construction of the theoretical PV diagram. With this diagram, the theoretical ICHP can be calculated. This will be used to find the isentropic efficiency of a compressor cylinder. The first method is the method most commonly used in testing. It is based on ideal gas relationships for isentropic compression. It should be noted that in natural gas service, assuming ideal gas relationships is not necessarily correct. The second method is more rigorous and requires the use of an EOS solver. The EOS solver is used to generate a constant entropy PV diagram without the assumptions of an ideal gas. This method is perhaps more accurate than the first since it does not assume ideal gas relationships. Commercial PV analyzers will automatically calculate the theoretical PV diagram and use it to calculate the theoretical ICHP. These procedures are presented here for completeness of the guideline. Ideal Gas and Isentropic Relationships There are several pieces of information that need to be known before construction of the PV diagram can begin. These are listed below. •

Gas Composition

•

Absolute Suction Pressure (from toe pressure on PV diagram or measured in nozzle)

•

Absolute Discharge Pressure (from toe pressure on PV diagram or measured in nozzle)

•

Suction Temperature (measured in nozzle)

•

Clearance Volume (or Minimum Volume)

•

Maximum Volume

The theoretical PV diagram consists of four sides. The left side is an isentropic expansion line, the bottom a constant suction pressure line, the right side an isentropic compression line, and the top a constant discharge pressure line. The items listed below give step-by-step instructions on how to generate the theoretical PV diagram. 1. Determine the isentropic exponent, k. a. The isentropic constant calculated from a ratio of specific heats (Equation B-1). The constant pressure and constant volume specific heats are found using the gas composition, suction pressure, and suction temperature with an EOS solver. There are many programs available that can complete this calculation. Also, Equation 3-7 can be used to calculate this.

k=

cp cv

(B-1)

2. Determine the discharge pressure and minimum volume (clearance volume). a. This will be the start point of the expansion line and the end point of the constant discharge pressure line as shown in Figure B-1.

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90

pd 80

70

Pressure (psia)

60

50

ps

40

30

20

10

Vmin

Vmax

0 0

50

100

150

200

250

300

350

400

Volume (in^3)

Figure B-1. Theoretical PV Diagram with Start of Expansion Stroke Indicated

3. Determine the suction pressure and maximum volume. a. This will be the start point of the compression line and the end point of the constant suction pressure line as shown in Figure B-2. 90

pd 80

70

Pressure (psia)

60

50

ps

40

30

20

10

Vmin

Vmax

0 0

50

100

150

200

250

300

350

400

Volume (in^3)

Figure B-2. Theoretical PV Diagram with Start of Compression Stroke Indicated

4. Calculate the expansion line constant, K1.

K1 = pd * Vmin

k

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5. Calculate the volume at the suction pressure on the expansion line.

K Vs = 1 ps

1 k

(B-3)

6. Calculate several other points on the expansion line using the equation in step 5 and plot the expansion line (see Figure B-3). 90

pd 80

70

Pressure (psia)

60

50

ps

40

30

20

10

Vmin

Vmax

0 0

50

100

150

200

250

300

350

400

Volume (in^3)

Figure B-3. Theoretical PV Diagram with Multiple Points Plotted on Expansion Line

7. Calculate the compression line constant, K2.

K 2 = ps * Vmax

k

(B-4)

8. Calculate the volume at the discharge pressure on the compression line.

K Vd = 2 pd

1 k

(B-5)

9. Calculate several other points on the compression line using the equation in step 8 and plot the compression line (see Figure B-4).

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90

pd 80

70

Pressure (psia)

60

50

ps

40

30

20

10

Vmin

Vmax

0 0

50

100

150

200

250

300

350

400

Volume (in^3)

Figure B-4. Theoretical PV Diagram with Multiple Points on Compression Line

10. Connect the expansion and compression lines with the suction and discharge pressure lines (see Figure B-5). 90

pd 80

70

Pressure (psia)

60

50

ps

40

30

20

10

Vmin

Vmax

0 0

50

100

150

200

250

300

350

400

Volume (in^3)

Figure B-5. Complete Theoretical PV Diagram

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Constant Entropy with EOS Solver For the procedure using the EOS Solver and using constant entropy, the parameters obtained for the first method are also used for this method. This method also requires the use of the discharge temperature. •

Gas Composition

•

Absolute Suction Pressure (from toe pressure on PV diagram or measured in nozzle)

•

Absolute Discharge Pressure (from toe pressure on PV diagram or measured in nozzle)

•

Suction Temperature (measured in nozzle)

•

Discharge Temperature (measured in nozzle)

•

Clearance Volume (or Minimum Volume)

•

Maximum Volume

The items listed below give step-by-step instructions on how to generate the theoretical PV diagram. 1. Determine the discharge pressure and minimum volume (clearance volume). a. This will be the start point of the expansion line and the end point of the constant discharge pressure line as shown in Figure B-1. 2. Determine the suction pressure and maximum volume. a. This will be the start point of the compression line and the end point of the constant suction pressure line as shown in Figure B-2. 3. Expansion Line a. Calculate the mass present in the cylinder at the start of the expansion. i. This can be done by knowing the properties of the gas (calculated with gas composition and EOS), discharge temperature, discharge pressure, and volume in the cylinder (clearance volume). b. Calculate the entropy at discharge temperature and discharge pressure with the EOS. i. The expansion on the theoretical PV diagram is an isentropic process. This assumes constant entropy throughout the process. c. Calculate the end point of the expansion line and plot. i. This is done by determining the density of the gas with the EOS from the suction pressure and entropy determined in step 3b. ii. Use this density to calculate the volume at the suction pressure with the mass calculated in step 3a. d. Calculate a few other points along the expansion line with the various densities (calculate from mass and volume in the cylinder) and the entropy previously determined. e. Plot these on the graph and complete a curve fit to obtain the full expansion line (see Figure B-3).

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4. Compression Line a. Complete the same process described above for the expansion line but use the start point (location for entropy and mass calculation) with the suction pressure and suction temperature. b. Use the discharge pressure and start entropy for the end point of the compression line (see Figure B-4). 5. Connect the expansion and compression lines with the suction and discharge pressure lines (see Figure B-5).

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APPENDIX C EQUATIONS OF STATE

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APPENDIX C The following explanation of the EOS models is taken from Equations of State for Gas Compressor Design and Testing by Kumar, Kurz and O’Connell, 2003. While the operating conditions for gas compressors are typically defined in terms of pressures, temperatures, and mass or standard flows, the relevant data that describe the behavior of a compressor are the head (H), which is related to the work input, the volumetric flow (Q) and efficiency (η), which compares the real process to an isentropic process between the same inlet state and outlet pressure. The head, or specific enthalpy difference between two states (e.g., inlet and discharge side of the compressor), is defined by:

H = h( p d , Td , {y}) − h( p s , Ts , {y})

(C-1)

The enthalpy (h) is a function of pressure, temperature, and gas composition defined through a set of mole •

fractions {y}. The actual absorbed power (Pgas) involves the mass flow rate ( m ): •

Pgas = m H

(C-2)

The mass flow rate is obtained from the actual or volumetric flow rate (Q) and the gas density (ρ): •

m = ρQ

(C-3)

The density is found from the temperature (T) and pressure (p) with the compressibility factor (Z). When Z differs from unity, the gas is not ideal and its value is a function of T, p, and gas composition. ρ = p/ZRT

(C-4)

The result of these definitions is that Pgas is found from:

Pgas = ρQH =

p QH ZRT

(C-5)

In order to define the quality of the compression process, H is usually compared to the head for an ideal compression process, which is defined as compression between the same inlet Ts and ps and outlet pd, with the outlet temperature being fictitious Td,isen:

∆s = s ( p d , Td ,isen , {y}) − s ( p s , Ts {y}) = 0

(C-6)

This isentropic change of state defines an isentropic head, Hisen, such that:

H isen = h( p d , Td ,isen , {y}) − h( p s , Ts {y})

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The quality or efficiency of the compression is defined by:

η=

H isen H

(C-8)

Compressor characteristics, in terms of head versus flow and efficiency versus flow, are found by comparing test data, taken with test gases such as Nitrogen, with results obtained from the thermodynamic calculations above. The characteristics can later be used to calculate the performance of the compressor under arbitrary conditions of pressures, temperatures, and gas compositions. As long as the same EOS is used for obtaining compressor performance predictions and data reduction, errors are minimized. An EOS is a relation among variables of a fully specified system: T, p, ρ and the N-1 component mole fractions yi (Alberty and Silbey, 1997). This is usually expressed in the form: Z = Z (ρ, T, {y})

(C-9)

since in a multiphase region, multiple values of ρ give the same value of p. Thermodynamics gives rigorous relations for enthalpy and entropy differences from derivatives and integrals of Z from any EOS and ideal gas specific heat, c 0p . A gas is said to be in a specified state if it has zero degrees of freedom. The degrees of freedom are the number of properties that can be arbitrarily set before all other properties become specified. The formula for the degrees of freedom of N nonreacting gases is: DF = N – # phases + 2

(C-10)

In gas compressor design calculations, only one phase exists, and the gas composition is usually specified, so two more degrees of freedom must be chosen. Generally, p and T are specified and the number of phases is always one. Then, all other thermodynamic properties are fixed and calculated via an EOS. Since real gas behavior commonly plays a role in gas compressors, knowledge of the relationships between pressures and temperatures, on one hand, and enthalpies, entropies and densities, on the other hand, is of great importance in compressor design, their performance under arbitrary operating conditions, and test data reduction. Especially during gas compressor performance tests, the selection of a particular EOS can have an important effect on the apparent efficiency and absorbed gas power. Thermodynamic Approach In order to decide on the most appropriate (EOS) to be used for designing and testing gas compressors for natural gas applications, five frequently applied EOS were studied: original Redlich-Kwong, RedlichKwong-Soave, Peng-Robinson (Reid et al., 1986), Lee-Kesler-Ploecker (Ploecker et al., 1978) and Starling version of the Benedict-Webb-Rubin model (Starling, 1973). The variation in entropy or enthalpy between two states of a gas or mixture, each defined by a temperature and pressure, is independent from the path chosen from one state to the other (Reid et al., 1986). A convenient path involving three steps of changing the real gas to an ideal gas at T1, changing the ideal gas from T1 to T2 and changing the ideal gas back to the real gas at T2 (Figure C-1).

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T2 Isotherms

Pressure

T1

Zero pressure

Enthalpy Figure C-1. Calculation Path for Equations of State

h = f ( p, T ) dh = (∂h / ∂p )T dp + (∂h / ∂T ) p dT p2

h2 − h1 =

T2

∫ (∂h / ∂p )T + ∫ (∂h / ∂T ) p DT

p1

(

h2 − h1 = h 0 − h p1

T1

)

T1

T2

(

+ ∫ c 0p dT − h 0 − h p 2

)

T2

T1

(C-11)

The terms in the parentheses of Equation C-11 are called departure functions, real gas contributions, or residual properties, which relate the enthalpy at some p and T to that at an ideal gas reference state at T, H0. These departure functions can be calculated solely from the EOS. The same approach can be used for the entropy. The ideal gas law is based on the assumption that the molecules of the gas do not interact with each other or that there is no attractive or repulsive forces between two molecules. The heat capacity of a gas is the amount of energy, which the gas needs to absorb before its temperature increases one unit. For an ideal gas, the heat capacity c 0p is a function only of T. An empirical equation for the ideal gas heat capacity can be stated as a polynomial, e.g., third order polynomial:

c 0p = A + BT + CT2 + DT3

(C-12)

A, B, C, and D are empirical parameters or constants based on the type of gas being analyzed. Once an equation for c 0p is found, the ideal gas enthalpy change, which is the change in total energy in the gas as it goes from state one to state two, can be found by:

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T2

∆h 0 = ∫ c p dT T1

(C-13)

Even for an ideal gas, the entropy change depends upon the initial and final temperatures and pressures. The entropy change is expressed by:

∆s 0 = ∫

T2

T1

p dT − R ln 2 T p1

cp

(C-14)

When calculating the enthalpy or entropy of a given state, an arbitrary reference state must be selected whose enthalpy and entropy are set to zero. The enthalpy and entropy for a given state is calculated relative to this reference. Therefore, any absolute value of the enthalpy or entropy of a gas at a given state has no real meaning, given its dependence on the reference state. However, when the enthalpy difference between two states is calculated, the reference state cancels out, so an enthalpy or entropy difference is an actual value that does not depend on the reference state. Functionality of Equations of State The departure functions for enthalpy and entropy for each of the five EOS can be found in the literature (Reid et al., 1986; Peng and Robinson, 1976; Ploecker et al., 1978; and Starling, 1973). Herein, the RK, RKS, and PR EOS are referred to as cubics. In Equation C-15, Z represents the compressibility factor of the gas, defined as:

Z=

pv RT

(C-15)

The quantities X and Y are two other types of compressibility factors used in compressor design. The formulas for each:

Y = 1−

X=

p ∂Z Z ∂p T

T ∂Z × Z ∂T

(C-16)

(C-17)

The calculation of the molecular weight and the heat capacity at given temperatures of the gas mixture is completed by using the following mixing rules:

~ MW = ∑ y i MWi c~ = yc p

∑

i

pi

(C-18)

MWi and y are the molecular weight and mole fraction of each component in the mixture. The heat capacities are divided by R to make them dimensionless, so when the linear function is found at a given

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temperature, the result should be multiplied by R in the desired units to get the heat capacity in those units. The linear function for ideal cp0/R is calculated using the cp0/R values at 10 and 149°C (50 and 300°F). These two points are used to find the slope of a straight line on a cp0/R versus temperature plot. This slope is used to solve for the y intercept of the following simple linear equation:

c 0p R

= CT + B (C-19)

Finally, the specific gravity (sg) and the real gas parameter (RG) are calculated; sg is calculated relative to the molecular weight of air:

~ MW sg = 28.964

(C-20)

The RG parameter is given by:

RG =

0.287 kJ / kgK sg

(C-21)

The Redlich-Kwong and Peng-Robinson models are cubic equations of state. The LKP equation is like the BWRS, a modification of the original BWR EOS. The LKP EOS has mixing rules that are very different from the cubics. The Starling version (BWRS) of the original BWR EOS added three extra parameters for improving the temperature dependence of the eight parameter forms. These parameters must be found for each pure gas. There also are mixing rules for the 11 parameters (Starling, 1973). For the cubic EOS, an analytical method can be used to solve for the three roots of ρ, thus, yielding Z. There are three roots to any cubic equation; however, when Tr >1 only the largest real root has any physical significance. After Z is calculated, the X and Y compressibility factors, along with specific heat, are calculated. For the LKP and BWRS models, Z is found by an iterative method.

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APPENDIX D EQUATION OF STATE MODEL COMPARISON OF PREDICTED PERFORMANCE DATA

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APPENDIX D The following comparison of the EOS models relies on results presented in Enthalpy Determination Methods for Compressor Performance Calculations by David Ransom, Rainer Kurz, and Klaus Brun. This comparison was completed for centrifugal compressors as described below. However, the comparison of EOS can be directly applied to reciprocating compressor performance testing. Approach for EOS Model Comparison For this comparison, a matrix of three gas compositions and two pressure ratios are considered. Enthalpy values are calculated using various EOS models and used to calculate compression power and isentropic efficiency. The three gas compositions (Table D-1) are intended to represent a variety of typical compression products including natural gas, high hydrogen, and high diluent compositions. (Note that gas mixture 1 is the same composition used in the uncertainty analysis in Section 7.) The two pressure ratios included in this comparison (PR = 1.3 and 2.2) are consistent with typical two- and six-stage machines, although neither value represents any specific application. In all cases, inlet conditions of 1,000 psia and 80°F are assumed. For each analysis configuration (gas mix and pressure ratio), both the isentropic and actual gas horsepower are determined, followed then by the isentropic efficiency. Gas power is a function of mass flow (assumed to be measured) and the change in enthalpy of the working fluid. Table D-1. Gas Mixtures Used in EOS Model Comparison

Component Methane Ethane Propane Iso-Butane N-Butane Iso-Pentane N-Pentane Hexane Carbon Dioxide Nitrogen Hydrogen Hydrogen Suflide Total

Mix 1 90.00 5.37 1.70 0.27 0.33 0.06 0.09 0.07 1.06 1.05 0.00 0.00 100.00

Mix 2 80.00 5.37 1.70 0.27 0.33 0.06 0.09 0.07 6.06 6.05 0.00 0.00 100.00

Mix 3 7.65 1.06 0.20 0.00 0.00 0.00 0.00 0.00 0.85 3.85 86.34 0.05 100.00

Table D-2. Assumed Measured Conditions; PR = 1.3

Parameter ps (psia) Ts (°F) pd (psia) Td (°F)

Mix 1 1000 80 1295 119

Mix 2 1000 80 1295 117

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Table D-3. Assumed Measured Conditions; PR = 2.2

Parameter ps (psia) Ts (°F) pd (psia) Td (°F)

Mix 1 1000 80 2200 201

Mix 2 1000 80 2200 199

Mix 3 1000 80 2200 235

Temperature

Five EOS models are included in this comparison: Redlich-Kwong (1948), Redlich-Kwong-Soave (Soave, 1972), Peng-Robinson (1976), Lee-Kesler-Ploecker (Ploeker et al., 1978), and Benedict-WebbRubin-Starling (Starling, 1973). Using the appropriate EOS, three enthalpy values are determined as follows: determine the inlet enthalpy (hs) and entropy (ss) as a function of the inlet conditions (ps, Ts); determine the isentropic discharge enthalpy (hd,isen) as a function of isentropic discharge conditions (pd, ss); and determine the actual discharge enthalpy (hd) as a function of the actual discharge conditions (pd, Td). A graphic representation of this process is provided below on a generic T-s diagram (Figure D-1).

(hd) = f(pd, Td)

(hd,isen) = f(pd, ss)

(hs,ss) = f(ps, Ts)

Entropy Figure D-1. Compression T-S Diagram

Once these values are determined, it is a very simple calculation to determine the isentropic and actual gas horsepower values (Equations D-1 and D-2).

P = m (hd − hs )

(D-1)

(hd ,isen − hs ) Pisen = m

(D-2)

Isentropic efficiency is calculated using Equation D-3.

η=

hd ,isen − hs hd − hs

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(D-3)

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Enthalpy Determination Results The results for gas horsepower and isentropic efficiency for each of the EOS models are shown in Table D-4 and Table D-5. For the sake of comparison, the mass flow for Mix 3 (high hydrogen gas) is adjusted to provide a similar horsepower as the natural gas compositions. Note that results are not shown for BWRS for the High H2 gas composition (Mix 3) since BWRS does not contain hydrogen data. These results demonstrate the relative agreement between the five EOS methods applied in this study. At the lower pressure ratio, for the first two gas mixtures, the standard deviation is about 30 HP, or 1.2% of the average value. In the case of the high hydrogen gas (Mix 3), the standard deviation is approximately 140 HP, or 1.7% of the average value at the same pressure ratio. For the higher pressure ratio, the deviation in the first two mixtures between the EOS models is approximately the same as the lower pressure ratio. The deviation increases to 1.8% at the higher pressure ratio for the high hydrogen gas (Mix 3). It should also be noted that the Peng-Robinson model consistently predicts slightly lower horsepower for all three gas mixtures, while the SRK model predicts higher horsepower within the deviations stated above. The isentropic efficiencies calculated using the various EOS models show relatively close agreement as well. However, the standard deviation among the five methods used in this study is as high as 2%, which can be significant when evaluating compressor performance against the promised performance, usually specified within 1%. In the extreme case, the isentropic efficiency between one particular EOS model and another can be as high as 3.8%. These results underscore the importance of applying the same EOS model throughout the performance analysis. Table D-4. Horsepower and Efficiency Calculations for EOS Models at Pressure Ratio of 1.3 EOS Model LKP BWRS SRK SRK-API PR Stdev Avg Stdev - %avg

Mix1 Hp-Act Eff-is 2530 68.2% 2522 64.6% 2528 65.6% 2530 65.6% 2460 65.0% 30.21 1.395% 2514 0.658 1.20% 2.12%

Mix2 Hp-Act Eff-is 2249 63.6% 2262 64.7% 2261 66.2% 2263 66.2% 2200 65.6% 26.63 1.098% 2247 0.652 1.19% 1.68%

Mix3 Hp-Act Eff-is 8400 87.9% 8368 8554 8213 139.74 8384 1.67%

88.2% 87.6% 88.2% 0.294% 0.880 0.33%

Table D-5. Horsepower and Efficiency Calculations for EOS Models at Pressure Ratio of 2.2 EOS Model LKP BWRS SRK SRK-API PR Stdev Avg Stdev - %avg

Mix1 Hp-Act Eff-is 8840 61.3% 8843 60.9% 8940 61.7% 8949 61.7% 8695 60.8% 102.48 0.387% 8853 0.613 1.16% 0.63%

Mix2 Hp-Act Eff-is 7879 60.3% 7922 61.2% 7986 62.3% 7994 62.3% 7767 61.5% 92.56 0.839% 7910 0.615 1.17% 1.36%

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Mix3 Hp-Act Eff-is 28169 87.3% 28046 28689 27462 503.75 28091 1.79%

87.7% 87.1% 87.8% 0.321% 0.875 0.37%

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APPENDIX E UNCERTAINTY ANALYSIS OF INDEPENDENT VARIABLE MEASUREMENTS

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APPENDIX E Prior to determining a test uncertainty, it is important to know whether the measured variables in the test are independent or dependent, as this determines the method of uncertainty calculation that must be employed. For almost all real measurement scenarios, there is some physical dependency between the input variables and, thus, unless one is absolutely certain that all measured and given system inputs are independent, it is safer to opt for the more conservative assumption of measurement dependence. If the measured variables in an experiment are truly found to be independent, then the method to determine total uncertainty is simply an addition of all individual measurement uncertainties. This is mathematically expressed as: n

∆F = ∆x1 + ∆x2 + ∆x3 + ... ∆xn = ∑ ∆xi i =1

(E-1)

where ΔF is the total result uncertainty and Δx are the individual measurement uncertainty ranges. This is the absolute value method rather than square root of the sum of squares method, which is more commonly utilized (as shown in E-2). The absolute value addition presents a true superposition of individual uncertainties rather than a blended sum. This method yields more conservative uncertainty results than the square-root-sum method, but both approaches are generally acceptable for uncertainty analyses.

∆V = ∆x12 + ∆x 22 + ∆x32 + ...∆x n2

(E-2)

Uncertainty Analysis for Dependent Variable Measurements If the measured variables in an experiment are dependent, which is usually the case, then the analysis becomes more complex. Specifically, the individual measurement uncertainties, Δx, are now functionally related and this must be accounted for in the analysis. There are three methods that are commonly used by engineers for this type of uncertainty analysis: •

Partial Derivative Method

•

Coefficient Method

•

Perturbation Method

All three methods are based on a functional transfer from input to output variable but employ a different approach to the determination of the proper transfer function. The Partial Derivative Method The most traditional method for uncertainty calculations is based on determining the transfer function using a partial derivative and adding the individual uncertainty transformations. Namely:

∆F = ∆F (∆x1 ) + ∆F (∆x2 ) + ∆F (∆x3 ) + ...∆F (∆xn ) = ∆x1 ⋅

n ∂F ∂F ∂F ∂F ∂F + ∆x2 ⋅ + ∆x3 ⋅ + ... ∆xn ⋅ = ∑ ∆xi ⋅ ∂x1 ∂x2 ∂x3 ∂xn i =1 ∂xi

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(E-3)

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To understand this method, one must analyze the principal term ∆xi ⋅

∂F and derive some basic ∂xi

physical understanding. Figure E-1 shows a graphical interpretation of the functional transformation from range Δx to ΔF using this term. Effectively, the input range Δx is multiplied by the slope of the function F at the measurement point x1, x2, x3, etc., to determine the ΔF output range. This assumes that the function F is linear over the interval Δx from the specified measurement point, which is a reasonable assumption for small Δx and any linear functional form. However, few physical laws are linear over a wide range and, thus, this method will be inaccurate for steeply sloped functions combined with large individual measurement uncertainties. Also, this method assumes that the function F is in an algebraic form that can be readily differentiated. This is obviously not always the case as many physical governing equations include ordinary and partial differential terms.

Figure E-1. Determination of Uncertainty Using Differential Methods

Coefficient Method

∂F can be determined numerically using a simple forward ∂x1 difference approach. This is commonly called the coefficient method and is shown below.

Clearly, the above partial differential

ci =

∂Fi F ( xi ) − F ( xi + ∆xi ) = ∂xi ∆xi

(E-4)

and n

∆F = c1 ⋅ ∆x1 + c 2 ⋅ ∆x 2 + c3 ⋅ ∆x3 + ... c n ⋅ ∆x n = ∑ ci ⋅ ∆xi i =1

(E-5)

Both the partial derivative and coefficient method should yield identical answers when properly applied. Again, as long as Δx is small and the slope of the function F is moderate, this approach will yield

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reasonably accurate uncertainties. A slight variation of this approach centers the numerical derivative around x, specifically:

ci =

∂F F ( x − 0.5∆x) − F ( x + 0.5∆x) = ∂x ∆x

(E-6)

This modified method often provides an improved determination of the uncertainty for measurements centered distributions. Unfortunately, for convenience, the coefficient method is often misapplied by assuming fixed coefficients for a standard analysis. A number of well established engineering codes and specifications publish fixed numbers for uncertainty coefficients of standard engineering analysis problems. This approach can only be valid if the actual physical equation is strictly linear, which is seldom the case. Also, unless all units of measurement are identical to those of the published coefficients, largely incorrect uncertainty results will be obtained. Perturbation Method The most accurate analysis to determine total uncertainty of dependent variable measurement systems is the perturbation method, as it is based on the actual function F and does not require any linearity assumptions. It is simply expressed as:

∆F = ∆F (∆x1 ) + ∆F (∆x2 ) + ∆F (∆x3 ) + ...∆F (∆xn ) = F ( x1 ) − F ( x1 + ∆x1 ) + F ( x2 ) − F ( x2 + ∆x2 ) + F ( x3 ) − F ( x3 + ∆x3 ) + ... F ( xn ) − F ( xn + ∆xn ) n

= ∑ F ( xi ) − F ( xi + ∆xi ) i =1

(E-7)

The term F ( x1 ) − F ( x1 + ∆x1 ) is graphically reviewed in Figure E-2 and demonstrates that the ΔF uncertainty obtained using this method is the actual transformation of Δx.

Figure E-2. Determination of Uncertainty Using Perturbation Methods

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The variation of parameters method is implemented by sequentially perturbing the input values (temperature, pressure, etc.) by their respective uncertainties and recording the effects on the calculated output quantity (i.e., efficiency, power, etc.). Assuming the uncertainty perturbation is fairly small, any term in Equation E-8 can be determined in this manner:

∆u1 ×

∂f ≅ f (u1 + ∆u1 ) − f (u1 ) ∂u1

(E-8)

The contribution of the variable u1 towards the overall uncertainty can be determined by calculating f twice—at the observed value at u1 and at the perturbed value of u1 + ∆u1. For several variables, the results for each term should be summed using the square-root-sum or absolute value of the individual terms. The benefits of this approach are that it does not matter if the uncertainty is an absolute or relative number, the procedure can be implemented using any spreadsheet program, and the values in the spreadsheet can be the results of complex, iterative relationships. Implementation of the Partial Derivative Method for Compressors (Enthalpy Rise Method) The partial derivative method was described in detail by Brun and Kurz [ASME Journal of Engineering for Gas Turbines and Power, 2001]. The implementation for the reciprocating compressor with the Enthalpy Rise method is briefly described herein: For the specific heat uncertainty, ∆cp is obtained:

⋅Z ⋅Z R R R + ∆MW Universal 2 ∆Z Universal + ∆L Universal 2 L ⋅ MW 2 L ⋅ MW L ⋅ MW 2

2

(E-9)

The above Equation E-9 is valid if the physical gas properties, specific heat ratio, compressibility factor, and molecular weight are directly determined from testing. A physical property uncertainty, due to the effect of applying uncertainties in T and p to the non-ideal gas state equation has to be included (i.e., since there is a measurement error in T and p, there will be an added error in determining cp from the gas equation). This uncertainty is most conveniently obtained numerically by varying temperatures and pressures parametrically in the gas equation and, thus, determining the gradients dγ/dT, dγ/dp, dZ/dT, and dZ/dp indirectly. Recognizing that dγ/dT = dL/dT and dγ/dp = dL/dp, one can easily determine corrections for ∆Z and ∆L: 2

∂γ ∂γ ∆Z = ∆T ⋅ + ∆p ⋅ ∂T ∂p 2

∂Z ∂Z ∆Z = ∆T ⋅ + ∆p ⋅ ∂T ∂p

2

(E-10) 2

(E-11)

The uncertainty in cp, is also affected by the variation of the gas properties during the duration of the test. This effect is again mathematically difficult to describe but can be easily handled numerically using a procedure similar to the one shown above for the variations in T and p. It is beyond the scope of this paper to list all possible gas composition variations; however, it is important to realize that they can strongly affect Z, L, and MW.

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The uncertainty of the compressor enthalpy rise is determined using Equation E-12. Since the enthalpy rise uncertainty is not dependent on the absolute temperatures, but rather on the temperature difference (Td – Ts), and since the specific heats (cp) for the discharge and suction are functionally related, the temperature difference (Td – Ts) should be employed for the derivation rather than the absolute temperature values (Td, Ts).

∆H =

(∆c p ⋅ (Td − Ts ))2 + (∆Td ⋅ c pTd )2 + (∆Ts ⋅ c pTs )2

(E-12)

The uncertainty for the isentropic (ideal) compressor outlet temperature is obtained using Equation E-13. Isentropic Temperature 2

∆Td ,isen

2 L p d LTs p dL −1 LTs p dL p + ∆ ⋅ + ∆p d ⋅ = ∆Ts ⋅ s p sL p sL +1 p s

2

(E-13)

The uncertainty of the compressor efficiency is given in Equation E-15. The temperature difference should be used rather than the absolute temperature values for the derivation of the isentropic enthalpy given in Equation E-14. Isentropic Enthalpy

∆hisen =

(∆c ⋅ (T p

d , isen

− Ts

)) + (∆T 2

d , isen

⋅ c p , d ,isen

) + (∆T ⋅ c ) 2

2

s

p,s

(E-14)

Isentropic Efficiency

h ∆h ∆η isen = isen + ∆H ⋅ isen2 H H 2

2

(E-15)

Mass Flow

MW ⋅ Q ∆ m = ∆p s ⋅ RUniversal ZTs • 2

2

ps Q + ∆MW ⋅ RUniversal ZTs

p s ⋅ MW + ∆Q ⋅ RUniversal ZTs

2

2

p ⋅ MW ⋅ Q + ∆Z ⋅ s RUniversal Z 2Ts

p ⋅ MW ⋅ Q + ∆Ts ⋅ s RUniversal ZTs2

2

2

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(E-16)

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Power • m ∆P = ∆H ⋅ ηm

2

• H + ∆ m⋅ η m

• 2 H ⋅m + ∆η m ⋅ 2 η m

2

(E-17)

The flow rate uncertainty, ∆Q, depends strongly on the device type employed for the measurements. A detailed discussion of flow measurement uncertainty is provided in ASME PTC 19.1 and is, thus, not further discussed herein. By evaluating Equations E-14 through E-17, estimates of the total measurement uncertainties for the compressor efficiency, enthalpy rise, and required driver power can be obtained. However, one source of measurement uncertainty that is often overlooked is the uncertainty due to a finite sample size. The above uncertainty statistics are valid only for mean parameters with an assumed Gaussian normal distribution. This is a good assumption for measurements where sample sizes are larger than 30. But for field tests, it is sometimes difficult to maintain a steady state system operating condition for a time period adequate to collect 30 or more samples. Implementation of the Partial Derivative Method for Compressor Package To complete the above field test measurement uncertainty evaluation, one also needs to look at the complete compressor package (engine and compressor efficiency) performance. The engine output power has to equal the compressor required power (PGT = P). Thus, the following two equations can be used to define the engine thermal efficiency, ηth, and the total package efficiency, ηsys: Thermal Efficiency

η th =

Pin •

m fuel ⋅ LHV

(E-18)

Package Efficiency

ηsys =

Pcomp Pin

ηisenηmηe

(E-19)

•

Here m fuel is the fuel flow into the engine and LHV is the fuel heating value. The fuel flow is typically measured using an orifice plate in a metering run and the heating value is determined from the chemical composition of the fuel. Based on the above equations, the corresponding driver uncertainty, ∆ηth, and package uncertainty, ∆ηsys, are given by:

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Thermal Efficiency

1 ∆η th = ∆Pin • m fuel LHV

2 • Pin + ∆ m fuel 2 • m LHV fuel

2

Pin + ∆LHV • 2 m fuel LHV

2

(E-20)

Package Efficiency

∆η sys

Pcomp = η isenη mη e P in

∆Pcomp P comp

2

+ ∆η isen η isen

2

∆P + in Pin

2

∆η m + ηm

2

∆η e + ηe

2

(E-21)

To complete the above Equations E-20 and E-21, the only additional information needed is the fuel flow uncertainty and the fuel heating value uncertainty. Since the fuel flow is measured in the same way as the flow through the gas compressor, uncertainty values in Equation E-16 can be used. Also, since the heating value is obtained directly from gas composition, the same percent uncertainty as was obtained for the specific heat Equation E-9 can be used, namely:

∆LHV ∆c p = LHV cp

(E-22)

By introducing the uncertainty experience values from those suggested in this guideline, the measurement uncertainty for a field test can be predicted prior to the test. Consequently, the above method allows the manufacturer and the end-user to determine reasonable test uncertainties, as well as necessary requirements for the test instrumentation prior to the test. This method can also be employed to resolve observed variations of field test performance results from theoretically predicted and/or factory test results. The different EOS models will provide different values of enthalpy rise, isentropic enthalpy rise, and compressibility for the compressor based on the differences in calculated enthalpy and compressibility. Implementation of the Perturbation Method for Compressors (PV Card Method) Described above were the uncertainty calculations for the Enthalpy Rise method. perturbation method with the PV Card analysis is discussed here.

The use of the

In this method the individual uncertainties must be found for each measured parameter used in power and efficiency calculations. For efficiency calculations, the uncertainties must be considered for the calculation of actual (ICHP) and theoretical power due to the fact that the efficiency is dependent upon both of these calculations. The measured parameters in a performance test where uncertainty should be considered are listed below: •

Piston position (∆θ)

•

Compressor Speed (∆N)

•

Pressure measurement (∆P)

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•

Temperature measurement (∆T)

•

Gas Composition (∆mol%)

•

Clearance volume (∆Vcl)

•

Steady state of test (if the test data is acquired when the conditions are not steady then additional uncertainty should be included in the pressure and temperature results to account for this)

Piston Position To calculate the uncertainty of the power and efficiency with piston position, a phase shift equal to the total positional uncertainty should be applied to the piston position on the measured PV diagram. This should be done for plus (Equation E-23) and minus (Equation E-24) the positional uncertainty. Once the shifted ICHP are calculated, the efficiencies can be found for that shift. The theoretical power should be calculated with the measured toe pressures (not shifted values) in this step. This isolates the uncertainty just to the effect of positional measurement variation on the measured power and calculated efficiency with that power. The difference between the maximum and minimum ICHP (Equation E-25) and efficiencies (Equation E-26) are the total uncertainty (∆ICHPθ and ∆ηθ) for the piston position measurement. θ i , plus = θ i + ∆ θ θ

i , min us

∆ ICHP

= θ

θ

i

(E-23)

− ∆θ

= ICHP

(E-24) max

− ICHP

min

∆ η θ = η max − η min

(E-25) (E-26)

The process described above should be repeated for the theoretical PV diagram. From this the position uncertainty on the theoretical ICHP can be found. This can be used with the measured ICHP to determine the uncertainty effect on the efficiency calculation. Speed The uncertainty due to speed variation should be calculated for both the measured and theoretical ICHP. The speed is used to calculate the power from the area of the PV diagram or work. Equations E-27 and (E-28) below detail how the maximum and minimum ICHP’s are calculated. The uncertainty in the speed measurement is the difference between these two values as shown in Equation E-25.

ICHPmax = ICHPmin =

W * (N + ∆N) 396000

(E-27)

W * (N − ∆N ) 396000

(E-28)

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Pressure The calculation of the uncertainty of power and efficiency due to pressure is not completely intuitive. One would think that the pressure uncertainty could just be added to the measured pressure and obtain the maximum ICHP and efficiency. However, this does not work. The end result is the exact same ICHP and efficiency calculated directly from the measured data. This is due to the fact that adding or subtracting the pressure to the full PV diagram will only shift the diagram up or down. It will not change the area within the diagram. In order to obtain the maximum possible ICHP from the diagram, a positive increase in pressure should be applied to the compression and discharge event lines and a negative decrease in pressure should be applied to the expansion and suction event lines. This will make the diagram grow outward and a maximum ICHP can be calculated. To obtain a minimum ICHP, the opposite should be applied: a negative decrease in pressure on the compression and discharge event lines and a positive increase in pressure on the expansion and suction event lines. Figure E-3 shows an example of maximum ICHP PV diagram with a 2 psig pressure uncertainty. From the pressure uncertainty PV diagrams, the maximum and minimum ICHP can be calculated. With this, the maximum and minimum efficiencies will be found. Again, the theoretical ICHP should be calculated with the measured values in order to isolate the error to the variation in pressure on the actual PV diagram power and efficiency. The total change in ICHP and efficiency due to pressure uncertainty is then found with Equations E-25 and E-26. This process should be repeated for the theoretical PV diagram. The measured PV diagram should be developed with the measured values in order to isolate the uncertainty effects to the theoretical calculation. In many performance tests, especially with high-speed units, channel resonance will be present in the pressure signal. This resonance is removed in order to complete flow calculations. Removing this resonance can affect the ICHP calculated value. If the ICHP is reported from the corrected PV diagram, then this ICHP should be compared to the ICHP of the uncorrected diagram. Any difference between these two ICHPs should be included as uncertainty in the power and efficiency. 90 80

Maximum ICHP 70

Original ICHP

Pressure (psig)

60 50 40 30 20 10 0 0

50

100

150

200

250

300

350

Volume (in3)

Figure E-3. Example of Change in Theoretical PV Diagram with Pressure Uncertainty

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Temperature and Gas Composition The temperature and gas composition are used in the PV Card method to generate the theoretical diagram. These values have no effects on the actual ICHP calculation. They do influence the uncertainty of the efficiency through the theoretical or isentropic power. The development of the theoretical PV diagram should be done with one of the methods discussed in Appendix B. The uncertainty is found by varying the temperature and gas composition with their specific uncertainties. For example, the theoretical ICHP should be found for a maximum temperature (Toriginal + ∆T) and for a minimum temperature. The same will be done for the gas composition. The difference between the maximum and minimum ICHP and efficiency will be the uncertainty due to temperature measurements and gas composition (Equation E-25). When determining this uncertainty, the actual ICHP should be calculated with the measured values, in order to isolate the effect of the uncertainty to the generation of the theoretical PV diagram. If the compressor operates at steady state during the performance test, then this uncertainty will be minimal (less than 0.01%) and perhaps negligible. However, tests that are performed at unsteady conditions should account for this uncertainty. Clearance Volume Uncertainty in the clearance volume will affect the theoretical ICHP and flow calculations. For the theoretical ICHP, the uncertainty in clearance volume affects the expansion and compression curves of the PV diagram. A positive increase and negative decrease in clearance volume should be applied to the PV diagrams separately in order to obtain the maximum and minimum ICHP and efficiencies. The differences in these maxima and minima are the uncertainty of the ICHP and efficiency due to the uncertainty in the clearance volume (Equation E-25). Total ICHP Uncertainty Up to this point, only the determination of uncertainty for individual measurements has been explained. To determine the overall compressor uncertainty, first, the individual uncertainties for each cylinder end should be combined with a root mean sum (Equation E-29). Once the uncertainty of each cylinder end is known, then these can be summed to determine the total deviation for the measured ICHP (Equation E30). The equations below also apply to the theoretical ICHP uncertainty calculation. ∆ ICHP cyl ∆ ICHP

1 − HE

comp

=

(∆ ICHP

= ∆ ICHP

) + (∆ ICHP 2

i , cyl 1 − HE

cyl 1 − HE

+ ∆ ICHP

cyl 1 − CE

)

2

i + 1 , cyl 1 − HE

+ ∆ ICHP

cyl

+ ...

2 − HE

(E-29) + ...

(E-30)

Total Efficiency Uncertainty Efficiency uncertainties can be calculated for each individual cylinder end as discussed above. This gives insight into the error in the efficiency for each cylinder end, but these values are not used to calculate the overall efficiency uncertainty. Due to the method which efficiencies are calculated, they cannot be averaged or summed like the power value can to obtain an overall efficiency uncertainty. Therefore, the overall efficiency uncertainty is calculated using the overall deviations found for the measured and theoretical ICHPs. Equations E-31 and E-32 below detail how the minimum and maximum efficiencies should be calculated. The difference in these two values (Equation E-33) gives the overall uncertainty in the efficiency of the compressor.

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η comp ,max =

η comp ,min = ∆η

comp

= η

Pcomp ,isen + ∆Pcomp ,isen ICHPcomp − ∆ICHPcomp

(E-31)

Pcomp ,isen − ∆Pcomp ,isen ICHPcomp + ∆ICHPcomp comp

, max

−η

comp

, min

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(E-32) (E-33)

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APPENDIX F COMPRESSOR PERFORMANCE DIAGNOSTICS WITH PV DIAGRAMS

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APPENDIX F The following is a discussion of the different effects that can be observed and diagnosed with a PV diagram. Each of the effects is discussed individually. It should be noted that in practice typically the PV diagram will have multiple influences. The effects discussed below are suction valve leakage, compressor rod pressure package leakage, discharge valve leakage, piston ring leakage, pulsation effects, and valve and cylinder gas passage losses. Suction Valve Leaks Figure F-1 illustrates the P-V diagram of a typical compressor cylinder with suction valve leakage. The difference between the theoretical P-V diagram and the “actual” P-V diagram will depend on the severity of leakage through the suction valves. Following is a step-by-step analysis of the P-V diagram in Figure F-1.

Figure F-1. Diagram Illustrating the Effects of Suction Valve Leaks

Line 1-2A: During the compression portion of the cycle, gas leaks out of the cylinder through the suction valves. Since less gas remains in the cylinder than the cylinder is designed for, more piston travel is required than the design piston travel to reach the discharge valve opening pressure. The cylinder volume at Point 2A is smaller than the volume at Point 2, resulting in the actual EVd being smaller than the design EVd. Line 2A-3B: During this portion of the cycle, gas is exiting the cylinder through the discharge valves and continues to leak through the suction valves. Should the leakage be great enough, the discharge valve will close prematurely at Point 3B. The actual EVd will be smaller than the design EVd. Line 3B-3A: The discharge valve has closed prematurely. The cylinder volume continues to grow smaller, causing gas to leak through the suction valves. The internal pressure at Point 3A is less than the design pressure at Point 3. This effect may not be noticeable except in cases of major valve failure. Line 3A-4A: During the expansion portion of the cycle, gas continues to leak through the suction valves. Less gas is present in the cylinder than the cylinder is designed for, resulting in a premature opening of the suction valves at the Point 4A. Line 4A-1: The premature opening of the suction valves causes the actual EVs to be greater than the design EVs. Detailed below are some of the symptoms that will be observed if there are suction valve leaks in the compressor. •

The externally measured cylinder capacity will be less than the design cylinder capacity.

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•

The gas temperature at the cylinder inlet will be greater than that measured during normal operation.

•

The discharge gas temperature will be greater than that observed during normal operation.

•

The actual compression and expansion lines will not match the design compression and expansion lines.

•

Capacity calculations based on EVs will be greater than capacity calculations based on EVd.

Compressor Rod Pressure Package Leaks The characteristics of the PV diagram for compressor rod pressure package leaks will be the same as suction valve leakage; however, there will be no temperature rise noticed at the suction and discharge cavities. Discharge Valve Leaks Figure F-2 illustrates the P-V diagram of a typical compressor cylinder which is experiencing discharge valve leakage. The difference between the “actual” P-V diagram and the “design” P-V diagram will depend on the severity of leakage through the discharge valves. Following is a step-by-step analysis of the P-V diagram in Figure F-2.

Figure F-2. Diagram Illustrating the Effects of Discharge Valve Leaks

Line 3-4A: In the expansion portion of the cycle, the trapped gas in the cylinder is expanding and gas is leaking into the cylinder through the discharge valves. The suction valve opens at a cylinder volume corresponding to the volume at point 4A which is greater than the design volume at point 4. This causes the actual EVs to be smaller than the design EVs. Line 4A-1B: During the intake portion of the cycle, gas is entering the cylinder through the suction valves and gas is leaking into the cylinder through the discharge valves. The internal pressure of the cylinder will rise to the point which will cause premature closure of the suction valves at Point 1B. This results in smaller EVs than design. Line 1B-1A: The suction valve has closed, cylinder volume is increasing and the internal cylinder pressure is rising, resulting in a higher pressure at Point 1A than design Point 1. Line 1A-2A: The actual compression line will not match the design compression line since the pressure at 1A is not the same as the pressure at 1. Gas is leaking into the cylinder through the discharge valves throughout the compression portion of the cycle. The discharge valve opens prematurely at 2A because the pressure at 1A was higher than design and gas continued to leak into the cylinder during the compression stroke.

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Line 2A-3: The actual EVd is larger than the design EVd due to the premature opening of the discharge valve. Detailed below are some of the symptoms that will be observed if there are discharge valve leaks in the compressor. •

The actual discharge temperature will be higher than the discharge temperature observed in normal operation.

•

The measured cylinder capacity will be less than the design cylinder capacity.

•

Capacity calculations based on EVd will be greater than capacity calculations based on EVs.

•

The actual compression and expansion lines will differ from the design compression and expansion lines. The value of the compression line exponent will be greater than normal, while the expansion line exponent will be less than normal.

Piston Ring Leaks Figure F-3 illustrates the P-V diagram of a typical compressor cylinder which is experiencing piston ring leakage. The shape of the “actual” P-V diagram will depend on the severity of the piston ring leakage. Following is a step-by-step analysis of Figure F-3.

Figure F-3. Diagram Illustrating the Effects of Piston Ring Leaks

Line 1A-2A: As the pressure in the cylinder increases, an increasing amount of gas escapes from the cylinder past the piston rings. Greater piston travel (smaller cylinder volume) is required to bring the internal pressure of the cylinder to the discharge valve opening pressure than design. If the discharge valve opening is delayed, occurring at Point 2A instead of Point 2, the actual EVd will be smaller than design. Line 2A-3B: During the discharge portion of the cycle, gas is exiting the cylinder through the discharge valves and leaking out of the cylinder past the piston rings. Should the leakage be severe enough, premature closing of the discharge valve can occur at Point 3B. Line 3B-3A: The discharge valves have closed, the cylinder volume continues to decrease, and gas continues to leak from the cylinder past the piston rings. The pressure at Point 3A is lower than design pressure (Point 3). Line 3A-4A: The actual expansion line will not be the same as the design expansion line since it begins at a lower pressure (Point 3A). Gas continues to leak out of the cylinder for a portion of the expansion

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cycle. The lower design pressure at Point 3A and the additional gas leakage result in the premature opening of the suction valves (in double-acting cylinders this can vary depending on gas state point in the opposite end). Line 4A-1B: Gas is entering the cylinder through the suction valves and is leaking into the cylinder past the piston rings. The leakage results in the premature closing of the suction valves at Point 1B (doubleacting cylinder). Line 1B-1A: The suction valves have closed, the cylinder volume is increasing, and the pressure in the cylinder is increasing due to continued piston ring leakage. The pressure at Point 1A is higher than design pressure (Point 1). Detailed below are some of the symptoms that will be observed if there are piston ring leaks in the compressor. •

The externally measured capacity will be lower than the design capacity.

•

The discharge temperature observed in normal operation will be higher than the design discharge temperature (double- acting cylinder).

•

Capacity calculations based on EVs will not agree with capacity calculations based on EVd.

•

The measured compression and expansion lines will not match the design compression and expansion lines.

Pulsation Effects While the suction and discharge valves are open, the acoustic pulsation present in the system is reflected into the compressor cylinder. Should the pulsation levels be of sufficient amplitude, the valve opening and closing times can be affected, and the average inlet and/or discharge pressures of the cylinder can be different than the design pressures. The net result being horsepower and capacity values, which are different than the design values. These values may be greater or smaller, depending on the pulsation characteristics. The change in horsepower and flow may be proportional, resulting in actual BHP/MMSCFD figures that are the same as design; however, the predicted loading curves will no longer be accurate. Valve and Cylinder Gas Passage Losses Valve loss is the pressure drop through the compressor valve. Cylinder gas passage loss is pressure drop between the cylinder flange and the compressor valve. Should these losses exceed the allowances which were made for them in the cylinder design; the actual flow will be less than the design flow. (Note that these losses are also affected by the gas pulsations.) Compressor performance problems are generally due to the “cylinder effects,” if it has been determined that: •

All compressor cylinder design parameters have been met (bore, stroke, fixed clearance, clearance pocket volumes, compressor speed, Ts, Zs, ps, pd).

•

No cylinder operational problems are present (compressor valve leakage and/or piston ring leakage).

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APPENDIX G POLYTROPIC EFFICIENCY

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APPENDIX G The polytropic process is also a reversible process like the isentropic process, but it is not adiabatic. It is defined by an infinite number of small isentropic steps followed by heat exchange. The heat exchange is necessary for constant polytropic efficiency. Both isentropic and polytropic processes are ideal, reference processes. Polytropic enthalpy rise is determined from: n −1 n pd n P P H = P ⋅ − 1 ⋅ f ⋅ p Sν S n − 1 p S P

P

(G-1)

The polytropic exponent, nP, is found with Equation G-2. This exponent should be based on the same conditions used to find hs and hd.

ln nP = ln

pd ps

νS νd

(G-2)

The polytropic efficiency is calculated based upon the polytropic enthalpy rise and the polytropic exponent, nP, as defined in the equation below: n −1 n p d n P − 1 ⋅ f ⋅ p sν s P ⋅ (n − 1) p s P

P

hdP − hs η = = hd − hs P

hd − hs

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(G-3)

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APPENDIX H HEAT LOSS ESTIMATIONS

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APPENDIX H Heat loss estimations are necessary in order to have accurate compressor performance predictions. This is true for the Enthalpy Rise method. Energy lost due to temperature differences or cooling has a direct effect on the efficiency of the compressor. Loss estimates are needed when the compressor has cylinder cooling systems, the instrumentation is installed such that the losses must be accounted for, or the compressor is being operated in an environment where the ambient temperature is largely different from the surface temperature of the compressor. However, in many cases, the heat losses are very small and can be considered negligible. If this is thought to be the case, then the tester may want to complete order of magnitude calculations to verify that more detailed calculations are not necessary. Figure H-1 shows a schematic of the energy exchange in a compressor. The potential heat losses for the compressor are shown as energy leaving on the bottom of the figure. If the components of the compressor are cooler than the ambient temperature, which is often true for the suction bottle, then the energy could be entering instead of leaving. Any further discussions on heat losses will include reference to heat energy, both entering and leaving the compressor. The direction will be dictated by the thermal gradient. Power In Compression

Gas In

Suction Bottle

Pipe Heat Losses

Discharge Bottle

Compressor

Pipe Heat Losses Bottle Heat Losses

Pipe Heat Losses Cylinder Cooling – Heat Removal

Gas Out

Pipe Heat Losses Bottle Heat Losses

Figure H-1. Schematic of Energy Exchange in Reciprocating Compressor

Computer programs are available that can be used to perform thermal or heat loss analysis on machines of complex geometry. Basic methods for calculating heat losses are discussed below. This method is based on calculated heat loss curves for typical compressor bottle geometries with the equations discussed in Appendices B and C of IEEE 515, “Standard for the Testing, Design, Installation, and Maintenance of Electrical Resistance Heat Tracing for Industrial Applications.” Estimation of Bottle or Piping Losses The total losses are calculated by adding the losses calculated for the bottle and for the pipe as shown in Equation H-1. The calculation of the individual losses for bottles and pipes are discussed below.

Q = Qb + Q p Q Qb Qp

= = =

(H-1) Total heat loss (Btu/hr) Bottle heat loss (Btu/hr) Pipe heat loss (Btu/hr)

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In all the cases discussed below, natural convection refers to the condition where the wind velocity is less than 1 mph. If the wind velocity (V) exceeds 1 mph, then the heat transfer coefficients should be found using the forced convection coefficients. Bottle Losses Total Bottle Losses The total heat loss (Q) from the bottle is determined from the convective heat transfer (Qc) and radiation heat transfer (Qr). These two values are calculated as discussed in the following sections. The convective heat transfer is either calculated as natural or forced convection depending on the wind velocity (V).

Q = Qc + Q r Q Qc Qr

= = =

(H-2) Total heat loss (Btu/hr) Convective heat transfer (Btu/hr) Radiation heat transfer (Btu/hr)

Radiation (Qr) The steps to determine the radiation heat transfer are detailed below. 1. Measure the surface temperature of the bottle (Ts), the ambient temperature of the air (T∞), diameter of the bottle (D), and length of the bottle (L). 2. Determine the emissivity (ε) of the surface of the bottle. Common emissivity values are shown in Figure H-2. 3. Calculate the mean temperature (Tm) using the Equation H-3.

Tm =

Ts + T∞ 2

Tm Ts T∞

= = =

(H-3) Mean temperature (deg F) Bottle surface temperature (deg F) Ambient temperature (deg F)

4. Determine the value of the radiation heat transfer coefficient (hr) from Figure H-2 with the mean temperature (Tm) and emissivity of the bottle (ε). 5. Calculate the surface area of the bottle (A) with the Equation H-4.

D2 A = 3.14 D * L + 2 A D L

= = =

(H-4)

Surface area of bottle (ft2) Diameter of bottle (ft) Length of bottle (ft)

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6. Calculate the radiation heat loss of the bottle (Qr) with the Equation H-5.

Qr = hr A(Ts − T∞ ) Qr hr A Ts T∞

= = = = =

(H-5)

Radiation heat transfer (Btu/hr) Radiation heat transfer coefficient (Btu/hr-ft2-deg F) Surface area of bottle (ft2) Surface temperature of bottle (deg F) Ambient temperature (deg F)

1.6 1.4 1.2 1.0

2

hr (Btu/h-ft -degF)

Tm = 10 Tm = 30 Tm = 50 Tm = 70 Tm = 90 Tm = 110 Tm = 130 Tm = 150

Common Emissivity Values Stainless Steel: 0.21-0.6 Plated metals: 0.08-0.09 Concrete: 0.88 Black Paint: 0.97 White Paint: 0.93

0.8 0.6 0.4 0.2 0.0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ε

Figure H-2. Radiation Heat Transfer Coefficient with Emissivity and Mean Temperature

Natural Convection (Qc - V < 1 mph) The steps to determine the convective heat transfer from natural convection are detailed below. These steps apply when the wind velocity is less than 1 mph. 1. Measure the surface temperature of the bottle (Ts), the ambient temperature of the air (T∞), diameter of the bottle (D), and length of the bottle (L). (These are the same values measured for the radiation heat loss.) 2. Calculate the mean temperature (Tm) using the Equation H-3. 3. Calculate the parameter X using Equation H-6.

X =

Ts − T∞ Ts + T∞ + 920

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(H-6)

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X Ts T∞

= = =

Parameter used in Figure H-3 Surface temperature of bottle (deg F) Ambient temperature (deg F)

4. Using the mean temperature (Tm) and the parameter X, find the value of the natural convection heat transfer coefficient (hn) from Figure H-3. 5. Calculate the surface area of the bottle (A) with the Equation H-4. 6. Calculate the natural convection heat loss of the bottle (Qc) with the Equation H-7.

Qc = hn A(Ts − T∞ ) Qc hn A Ts T∞

= = = = =

(H-7)

Natural convection heat transfer (Btu/hr) Natural convection heat transfer coefficient (Btu/hr-ft2-deg F) Surface area of bottle (ft2) Surface temperature of bottle (deg F) Ambient temperature (deg F)

1.1

1

0.8

2

hn (Btu/h-ft -degF)

0.9

0.7 Tm = 10 Tm = 30 Tm = 50 Tm = 70 Tm = 90 Tm = 110 Tm = 130 Tm = 150

0.6

0.5

0.4 0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Figure H-3. Natural Convection Heat Transfer Coefficient with X and Mean Temperature

Forced Convection (Qc - V > 1 mph) The steps to determine the convective heat transfer from forced convection are detailed below. These steps apply when the wind velocity is greater than 1 mph. 1. Measure the surface temperature of the bottle (Ts), the ambient temperature of the air (T∞), diameter of the bottle (D), length of the bottle (L), and the wind velocity (V). (Many of these are the same values measured for the radiation heat loss.) 2. Calculate the mean temperature (Tm) using the Equation H-3.

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3. Calculate the parameter Y using Equation H-8.

Y = (V * L )

0.8

Y V L

= = =

(H-8) Parameter used in Figure H-4 Wind velocity (mph) Length of Bottle (ft)

4. Using the mean temperature (Tm) and the parameter Y, find the value of the forced convection heat transfer coefficient (Hf) from Figure H-4. 5. Calculate the surface area of the bottle (A) with the Equation H-4. 6. Calculate the forced convection heat loss of the bottle (Qc) with the Equation H-9.

Qc =

H f A(Ts − T∞ ) L

Qc Hf A L Ts T∞

= = = = = =

(H-9)

Forced convection heat transfer (Btu/hr) Forced convection heat transfer coefficient (Btu/hr-ft2-deg F) Surface area of bottle (ft2) Length of Bottle (ft) Surface temperature of bottle (deg F) Ambient temperature (deg F)

250 225 200

Hf (Btu/h-ft-degF)

175 150 125 100

Tm = 10 Tm = 30 Tm = 50 Tm = 70 Tm = 90 Tm = 110 Tm = 130 Tm = 150

75 50 25 0 20

40

60

80

100

120

140

160

(V*L)0.8 (mph*ft)

Figure H-4. Forced Convection Heat Transfer Coefficient with Y and Mean Temperature

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Pipe Losses Total Pipe Losses Heat losses occur on non-insulated pipe. These may be significant if the instrumentation is installed far away from the compressor. If the instruments are installed close to the compressor being tested, then these losses do not have to be considered since they will be minimal ( 1 mph) The steps to determine the convective heat transfer from forced convection are detailed below. These steps apply when the wind velocity is greater than 1 mph. 1. Measure the surface temperature of the pipe (Ts), the ambient temperature of the air (T∞), diameter of the pipe (D), length of the pipe (L), and the wind velocity (V). (Many of these are the same values measured for the radiation heat loss.) 2. Calculate the mean temperature (Tm) using the Equation H-3. 3. Calculate the parameter Z using Equation H-14.

Z=

(V * D )0.805

Z V L

D = = =

(H-14) Parameter used in Figure H-7 Wind velocity (mph) Diameter of pipe (in)

4. Using the mean temperature (Tm) and the parameter Z, find the value of the forced convection heat transfer coefficient (hf) from Figure H-7. 5. Calculate the surface area of the pipe (A) with the Equation H-11. 6. Calculate the forced convection heat loss of the pipe (Qc) with the Equation H-15.

Qc = h f A(Ts − T∞ ) Qc hf A Ts T∞

= = = = =

(H-15)

Forced convection heat transfer (Btu/hr) Forced convection heat transfer coefficient (Btu/hr-ft2-deg F) Surface area of pipe (ft2) Surface temperature of pipe (deg F) Ambient temperature (deg F)

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7

6

4

2

hf (Btu/h-ft -degF)

5

3 Tm = 10 Tm = 30 Tm = 50 Tm = 70 Tm = 90 Tm = 110 Tm = 130 Tm = 150

2

1

0 1

2

3

4

5

6

7

Figure H-7. Forced Convection Heat Transfer Coefficient with Z and Mean Temperature

Estimation of Heat Transfer in Cylinder Cooling Some reciprocating compressor cylinders will have cooling jackets to be removed heat during compression. This is especially true for process compressors. The heat removed from cylinder cooling needs to be considered in the performance test in order to obtain an accurate efficiency calculation. The steps detailed below will give a sufficient estimate of the energy removed with cylinder cooling. The method detailed below assumes the energy change in the cooling medium will be representative of the energy change in the gas due to cooling. There will be some energy change difference due to heat transfer through the housing of the cylinder and cooling passages, but the analysis below assumes this to be negligible. The rate of heat transfer is calculated using Equation H-16. •

Q = m C p (T2 − T1 ) Q

(H-16)

Heat removed for cylinder cooling (Btu/hr)

•

m Cp T2 T1

Tm =

Mass flow rate of cooling medium (lbm/hr) Specific heat of cooling medium (Btu/lbm-deg F) at mean temperature Tm (deg F), see Equation H-17 (for water it is 1 Btu/lbm-deg F and ethylene glycol 0.678 Btu/lbm-deg F) Exit temperature of cooling medium (deg F) Inlet temperature of cooling medium (deg F)

T2 + T1 2

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(H-17)

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APPENDIX I EXAMPLE PV CARD CALCULATIONS

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APPENDIX I This appendix reviews example calculations for an individual cylinder end performance test conducted with the PV Card method. It covers the calculation of cylinder volume from compressor geometry, construction of measured PV diagram, calculation of ICHP from the measured PV diagram, development of theoretical PV diagram, calculation of cylinder end efficiency, calculation of cylinder end flow, and calculation of uncertainty of power and efficiency. The calculations completed here are for a transmission compressor. Data for Calculations The first step in this process is to assemble the data required for the calculations that need to be performed for this test. This data is listed below for the example. Cylinder End: Head End Process Fluid = Natural Gas Gas Composition Methane (C1) = 90.315% Ethane (C2) = 6.006% Propane (C3) = 1.018% Iso-Butane (IC4) = 0.113% N-Butane (NC4) = 0.141% Iso-Pentane (IC5) = 0.04% N-Pentane (NC5) = 0.04% Heavies (C6+) = 0.025% Nitrogen = 0.509% Carbon Dioxide = 1.803% Equation of State = BWRS Isentropic Constant (k) = 1.36 Cylinder Bore (B) = 10.875 in Piston Stroke (S) = 5.5 in Piston Rod Diameter (d) = 2.5 in Connecting Rod Length (l) = 17 in Piston Phase = 0 deg Cylinder Area = 92.88 in2 Volume of Stroke (Vstroke) = 510.87 in3 % Clearance (CL%) = 58.9% Clearance Volume (Vcl) = 301.11 in3 Suction Pressure (ps) = 754.80 psia Discharge Pressure (pd) = 992.66 psia Suction Temperature (Ts) = 61.56 deg F Discharge Temperature (Td) =102.82 deg F Compressor Speed (N) = 998.5 RPM Encoder Resolution = 512

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Construction of Measured PV Diagram During testing, each time the encoder triggered, pressure data was collected. Since the encoder used for the test was a 512 encoder, 512 pressure points were recorded for the test. The encoder provided the rotational position (in degrees) of the shaft at each pressure measurement. From this rotational position, the gas volume in the cylinder is calculated for each point. This is done with Equation I-1 below. An example of this calculation is shown below when theta equals 30 degrees. This volume matches with a pressure of 846.55 psia. Once all the volumes are calculated, the PV diagram can be constructed as shown in Figure I-1. 2 S π S 2 (1 − cos θ ) − l − sin θ + l * B 2 + Vcl V= 2 4 2

(I-1)

Example

5.5in 1 − cos 30 o − V30 deg = 2 V30 deg = 340.5in 3

(

) (17in)

2

2 π 5.5in 2 − sin 30 o + 17in * (10.875in ) + 301.11in 3 4 2

1200

1100

Pressure (psig)

1000

900

800

700

600 0

100

200

300

400

500

600

700

800

900

Volume (in^3)

Figure I-1. Constructed Measured PV Diagram

Removal of Channel Resonance As can be seen, the PV diagram in Figure I-1 has channel resonance present. Calculation of the ICHP is not affected by the channel resonance since it is a sinusoidal phenomenon, but the other calculations such as volumetric efficiency and flow are affected by it. Therefore, channel resonance needs to be removed before proceeding further. The channel resonance is removed with filtering techniques and the result is shown below in Figure I-2.

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1200 HE HE - Corrected 1100

Pressure (psig)

1000

900

800

700

600 0

100

200

300

400

500

600

700

800

900

Volume (in^3)

Figure I-2. PV Diagram with Channel Resonance Removed through Filtering

Calculation Measured ICHP Once the PV diagram is constructed, the ICHP can be calculated. During this process the pressure volume diagram is integrated to determine the area inside of the card, which is the work applied to the gas. The area below the expansion and constant suction pressure line will be subtracted from the area below the compression and constant discharge pressure line as shown in Figure I-3. This integration can be performed with any typical integration algorithm; Trapezoidal rule, Simpson’s rule, and others. In this example, a variation of the Trapezoidal rule was used. The basic equation for the integration is Equation I-2. V represents volume, i indicates which step is being integrated, p is the pressure, and n is maximum number of steps. The maximum number of steps would typically correspond to the resolution of the encoder used for the performance test.

Work = ∫ pdV =

n −1 1 ( pn + p1 )Vn − V1 + 1 ∑ ( pi + pi +1 )Vi − Vi +1 2 2 i =1, 2,3, 4,...

(I-2)

The integration of the pressure-volume diagram as shown in Figure I-3 gave a value of 123,719 in-lbs. ICHP is calculated from the work with Equation I-3. The resulting ICHP of the PV diagram is 312.0 HP.

ICHP =

W *N 396000

(I-3)

Example

123,719in − lbs * 998.5 RPM 396000 ICHP= 312.0 HP ICHP =

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1000

1000

900

900

Pressure (psig)

1100

Pressure (psig)

1100

800

700

800

700

600 200

300

400

600

500

700

800

600 200

900

300

400

500

Volume (in^3)

600

700

800

900

Volume (in^3)

Integration of Compression and Constant Discharge Pressure Lines

Integration of Expansion and Constant Suction Pressure Lines

1100

1000

Pressure (psig)

900

800

700

600 200

300

400

500

600

700

800

900

Volume (in^3)

Subtraction of Integrated Areas Resulting in Area Inside Pressure-Volume Trace

Figure I-3. Graphical Representation of Integration of PV Diagram

Determination of Suction and Discharge Volumetric Efficiency The suction and discharge volumetric efficiency can be calculated using Equations 3-14 and 3-15, but it can also be determined from the PV diagram. First, the PV diagram is observed for where the suction valve opens on the cycle and where the discharge valve closes on the cycle. These locations with corresponding gas volumes are indicated on the PV diagram in Figure I-4. The suction volumetric efficiency is calculated with the ratio of volume differences as shown in Equation I-4. The discharge volumetric efficiency is calculated under the same premise with Equation I-5. In both of these equations, the volume when the valve opens is the total volume minus the clearance volume. In the example shown below, the clearance volume is subtracted from the volumes listed on Figure I-4. The suction and discharge volumetric efficiencies for this example are 88.3% and 72.1%, respectively.

EVs =

Vstroke − Vsuction _ valve _ open Vstroke

*100%

V stroke − Vdisch arg e _ valve _ open EVd = 1 − V stroke

(I-4)

* 100%

(I-5)

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Example

510.87in 3 − (360.9in 3 − 301.11in 3 ) *100% 510.87in 3 EVs = 88.3% EVs =

1100

1000

Discharge Valve Opens V = 669.3 in3

Pressure (psig)

900

Suction Valve Opens V = 360.9 in3

800

700

600 200

300

400

500

600

700

800

900

Volume (in^3)

Figure I-4. Where Suction and Discharge Valves Open on PV Diagram

Construction of Theoretical PV Diagram Procedures for the construction of the theoretical PV diagram are discussed in detail in Appendix B, so it will not be repeated here. The toe pressures and volumes used for the construction are listed below. The theoretical PV diagram is shown plotted in Figure I-5 with the corrected PV diagram previously generated. •

Start of Expansion Line ♦ Pressure = 992.66 psia ♦ Volume = 301.11 in3

•

Start of Compression Line ♦ Pressure = 754.80 psia ♦ Volume = 811.98 in3

The isentropic constant was determined to be 1.36, with an EOS solver using the suction temperature and pressure. The K1 and K2 factors were calculated to be 2,332,742 and 6,836,181, respectively. The volumes and pressures at the end of the expansion and compression lines were found to be the values listed below.

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•

End of Expansion Line ♦ Pressure = 754.80 psia ♦ Volume = 368.3 in3

•

End of Compression Line ♦ Pressure = 992.66 psia ♦ Volume = 663.8 in3 1100 HE - Corrected Theoretical 1000

Pressure (psig)

900

800

700

600 200

300

400

500

600

700

800

900

Volume (in^3)

Figure I-5. Theoretical PV Diagram with Correct PV Diagram

After the theoretical PV diagram is constructed the isentropic ICHP can be calculated following the same integration procedure described above for the measured ICHP. The ICHP for the theoretical PV diagram shown in Figure I-5 is 239.85 HP. Calculation of Efficiency The efficiency of the compressor is calculated from the ratio of the measured ICHP and the theoretical ICHP as shown in Equation I-6.

η isen,cyl =

Pisen *100% ICHP

(I-6)

Example

η isen ,cyl =

239.85 HP *100% 312.0 HP

η isen ,cyl = 76.9%

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Calculation of Capacity The capacity can be calculated with any of the equations shown in the guideline. For this example, Equation I-7 is used as shown below.

(CQ )* (B Q= *

2

)

− r 2 * S * N * EVs * p s * Z STD Ts * Z s

(I-7)

The compressibility must be calculated for the standard conditions (14.7 psia and 60 deg F) and for the suction conditions for the gas being compressed. There are ways to calculate these values analytically as discussed in Appendix C, but perhaps the easiest method for calculating this is to use an EOS solver. With the solver, the appropriate EOS can be selected and the compressibility can be determined for the standard and suction conditions. Using a BWRS EOS solver, the compressibilites at the standard and suction conditions were found to be 0.9949 and 0.8694, respectively. The rest of the values included in Equation I-7 are known from cylinder geometry or measured and calculated parameters. The flow through the cylinder end is calculated as shown below. Example

Q=

(0.2314 *10 )* ((10.875 in ) −6

)

− 0 2 * 5.5 in * 998.5 RPM * 88.3 * 754.80 psia * 0.9949 (61.56 deg F + 460 R )* 0.8694 2

Q = 21.98 MMSCFD The rod diameter in this calculation is set to zero since the cylinder end is on the head end. The flow through this cylinder end is 21.98 MMSCFD. Calculation of Measured ICHP Uncertainty There are several different methods that can be used to calculate uncertainty. This example will use the perturbation method as described in Appendix E of the guideline. The measured ICHP has uncertainty due to four variables: pressure, piston position, speed, and channel resonance. The pressure and position uncertainty are important, since these are the properties measured in order to generate the PV diagram during a single cycle. The speed uncertainty is included, since the compressor speed is used to calculate the power from the work from the PV diagram. Channel resonance is included, because the data is filtered before calculations are completed. It was mentioned before that channel resonance is a sinusoidal phenomenon and does not affect the power. However, when the resonance is removed with filtering, there is a possibility that other valuable data could be lost. The uncertainty for this parameter is the difference between the ICHP calculated before and after the channel resonance has been removed. To calculate the uncertainty in the ICHP, each parameter is varied independently while the other parameters are held constant. The difference between ICHP with the positive and negative changes in the parameter is the total uncertainty for that parameter. The calculation of the uncertainty in ICHP for each of the four parameters mentioned above is discussed below.

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Pressure The first step in calculating the uncertainty of the ICHP due to pressure is to determine the uncertainty in the pressure measurement itself. In this example, the pressure uncertainty was calculated from the accuracy of the pressure transducer, calibration uncertainty, and data acquisition uncertainty. These uncertainty values are listed below. Pressure Transducer Uncertainty Calibration Uncertainty Data Acquisition Uncertainty Total Uncertainty

= = = =

1.5 psi 0.5 psi 0.05 psi 2.05 psi

Once the pressure measurement uncertainty is known, the uncertainty of the ICHP due to pressure can be calculated. The uncertainty due to pressure in the ICHP is slightly different than the process described above. Applying only a positive change in pressure or only a negative change in pressure will just shift the PV diagram up or down. It will not cause any change in the ICHP. Therefore the positive and negative variations are used in conjunction. For the maximum ICHP change, a positive pressure change is applied to the compression line and constant discharge line and a negative pressure change is applied to the expansion line and constant suction line. The opposite is done for the minimum ICHP. An example of the maximum ICHP variation is show in Figure E-4. The work is then calculated from these maximum and minimum PV diagrams using the integration discussed above and the ICHP is calculated with the compressor speed. The maximum and minimum ICHP are 317.3 and 306.8 HP, respectively, resulting in an uncertainty in the ICHP from pressure of 10.5 HP. Piston Position The piston position uncertainty is due to the resolution of the encoder, ODC marking and synchronization, and the data acquisition uncertainty. These values of these uncertainties are outlined below. Encoder Uncertainty ODC Determination Synchronization Uncertainty Data Acquisition Uncertainty Total Uncertainty

= = = = =

0.703 deg 0.1 deg 0.1 deg 0.01 deg 0.913 deg

The uncertainty is added and subtracted from the measured position of the shaft. Figure I-6 shows the PV diagrams with the positive and negative change in piston position. The ICHP calculated from the positive and negative changes in piston position are 309.4 and 314.7 HP for a total uncertainty of 5.3 HP. Speed The speed can be measured by an encoder or with a one-per-revolution device. In this example, a magnetic pick-up was used to measure the speed of rotation. This device had an uncertainty of 0.1% of the measured value which correlated to an absolute uncertainty of approximately 1 RPM. The uncertainty calculation for speed is shown below.

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1200 Plus Minus

1100

Pressure (psia)

1000

900

800

700

600 200

300

400

500 600 Volume (in^3)

700

800

900

Figure I-6. Variation in PV Diagram with Piston Position Uncertainty

Example Maximum ICHP

123,719in − lbs * (998.5 RPM + 1 RPM ) 396000 ICHPmax = 312.3HP

ICHPmax =

Minimum ICHP

123,719in − lbs * (998.5 RPM − 1 RPM ) 396000 ICHPmin = 311.6 HP ICHPmin =

Total Uncertainty

∆ICHP = ICHPmax − ICHPmin ∆ICHP = 312.3 HP − 311.6 HP ∆ICHP = 0.7 HP Channel Resonance The uncertainty from channel resonance is actually the uncertainty of the filtering process. It is calculated from the difference between ICHP calculated from the measured PV diagram and the corrected PV diagram. The ICHP from the corrected PV diagram was found above to be 312.0 HP. The ICHP from the uncorrected PV diagram is 310.8 HP which results in a total uncertainty of 1.2 HP due to the filtering process.

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Total Measured ICHP Uncertainty Once the uncertainty due to each measured parameter is determined, the total uncertainty for the measured ICHP can be determined. This value is found by calculating the root mean sum of all the uncertainties (Equation I-8). This calculation is shown in Table I-1. This shows the total uncertainty for the measured ICHP for this cylinder end is 11.8 HP or 3.78% of measured ICHP.

∆ICHPcyl 1− HE =

(∆ICHP

) + (∆ICHP 2

i ,cyl 1− HE

)

2

i +1,cyl 1− HE

+ ...

(I-8)

Table I-1. Calculation of Total Uncertainty of Measured ICHP for Cylinder End

Parameter Pressure Piston Position Speed Channel Resonance

Uncertainty (HP) 10.5 5.3 0.7 1.2 Sum of Squares Square Root of Sum

Square of Uncertainty (HP2) 110.25 28.09 0.49 1.44 140.27 11.8 HP

Calculation of Theoretical ICHP Uncertainty The theoretical ICHP uncertainty is calculated in the same manner that the measured ICHP uncertainty is: a combination of uncertainties from various parameters. However, there is a difference in the parameters which must be included in the uncertainty analysis. For the theoretical ICHP uncertainty, the parameters which must be considered are pressure, isentropic constant, speed, and clearance volume. Pressure The toe pressures obtained from the measured PV diagram are used to construct the theoretical PV diagram. The uncertainty in the pressure measurement is applied to the toe pressures to obtain the uncertainty in the theoretical ICHP from pressure. The pressure measurement uncertainty of 2.05 psi was used to determine the toe pressures. From these toe pressures and with an isentropic constant of 1.36, the end points of both the compression and expansion lines were calculated. The calculated values, along with the maximum and minimum theoretical ICHP, are shown in Table I-2. The uncertainty of the theoretical ICHP is calculated from the difference between the maximum and minimum theoretical ICHP which equals to 6 HP. Isentropic Constant The uncertainty of the isentropic constant is due to the uncertainty of the pressure, temperature, and gas composition measurement. The best method to determine the maximum and minimum possible variation in the isentropic constant is to vary each of these parameters with each test point and determine the isentropic constant for that particular condition. However, this can be very time consuming. Instead, determine which test point had the highest uncertainty in the pressure, temperature, and gas composition, and determine the maximum and minimum isentropic constants for this scenario. Calculate a percentage

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of variation for this condition and apply it to the rest of the uncertainty calculations with isentropic constants. This method will reduce the computations needed and yield a conservative uncertainty.

K2

Start

End

Expansion Line

K1

Compression Line

Start

Table I-2. Defined and Calculated Values for Theoretical ICHP Uncertainty Due to Pressure Uncertainty

Discharge Pressure (psia) Volume (in^3) Suction Pressure (psia) Volume (in^3) Suction Pressure (psia) Volume (in^3)

Measured ICHP 992.66 301.11

Minimum ICHP 994.71 301.11

Maximum ICHP 990.61 301.11

2332742

2313772

2323348

754.80 368.30 754.80 811.98

752.75 367.10 752.75 811.98

756.85 369.66 756.85 811.98

6836181

6805796

6768928

End

Discharge Pressure (psia) 992.66 994.71 Volume (in^3) 663.80 666.10 Theoretical ICHP (HP) 239.85 236.80 NOTE: Bolded values were defined, and shaded values are calculated.

990.61 661.41 242.80

For this example, varying the pressure, temperature and gas composition yielded a maximum and minimum isentropic constant of 1.3672 and 1.3539, respectively. This is a +0.53% and -0.45% variation. Therefore, 0.5% will be used for the uncertainty of the isentropic constant. The defined and calculated values for the theoretical ICHP due to variation in isentropic constant are shown in Table I-3. The difference between the maximum and minimum theoretical ICHP’s is 0.021 HP. This is less than 0.01% of the theoretical horsepower and can be considered negligible. Unless there is a significant deviation in pressure, temperature, or gas composition then the uncertainty due the isentropic constant can be ignored. Speed The uncertainty of the theoretical ICHP due to the uncertainty in the speed measurement is calculated using the same methodology describe above in the “Calculation of Measured ICHP Uncertainty” section. The work calculated from the integration of the theoretical ICHP diagram is 95,124 in-lbs. With a speed uncertainty of 1 RPM, this gives a total uncertainty of 0.5 HP for the calculation of the theoretical ICHP. Clearance Volume The uncertainty of the clearance volume affects the start and end volumes for the PV diagram. Changing these values will affect the curvature and end points of the expansion and compression lines. The clearance volume is obtained from the manufacturer information on the compressor, a volume measurement, or the effective clearance volume from the measured PV diagram. For this example, we assume we have used the value from the manufacturer and that there is a 2% uncertainty. The defined and calculated values for the theoretical ICHP due to uncertainty in clearance volume are shown in Table I-4. The difference between the maximum and minimum theoretical ICHP’s is 1.45 HP.

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Expansion Line

Start

Measured k 1.36 992.66 301.11

K1

2332742

Compression Line

Table I-3. Defined and Calculated Values for Theoretical ICHP Uncertainty Due to Isentropic Constant Uncertainty

K2

Start

End

Isentropic Constant Discharge Pressure (psia) Volume (in^3) Suction Pressure (psia) Volume (in^3) Suction Pressure (psia) Volume (in^3)

Maximum k 1.3668 992.66 301.11

Minimum k 1.3532 992.66 301.11

2410241

2230367

754.80 368.30 754.80 811.98

754.80 367.99 754.80 811.98

754.80 368.74 754.80 811.98

6836181

7103467

6485324

End

Discharge Pressure (psia) 992.66 992.66 Volume (in^3) 663.80 664.41 Theoretical ICHP (HP) 239.85 239.864 NOTE: Bolded values were defined, and shaded values are calculated

992.66 663.07 239.843

Table I-4. Defined and Calculated Values for Theoretical ICHP Uncertainty Due to Clearance Volume Uncertainty

K2

Start

End

Expansion Line

K1

Compression Line

Start

Clearance Volume (in^3) Discharge Pressure (psia) Volume (in^3) Suction Pressure (psia) Volume (in^3) Suction Pressure (psia) Volume (in^3)

Measured CL% 301.11 992.66 301.11

Maximum CL% 307.1322 992.66 307.13

Minimum CL% 295.0878 992.66 295.09

2332742

2381801

2255772

754.80 368.30 754.80 811.98

754.80 375.73 754.80 818.00

754.80 360.99 754.80 805.96

6836181

6855861

6719045

End

Discharge Pressure (psia) 992.66 992.66 Volume (in^3) 663.80 668.67 Theoretical ICHP (HP) 239.85 239.13 NOTE: Bolded values were defined, and shaded values are calculated

992.66 658.82 240.58

Total Measured ICHP Uncertainty Once the uncertainty due to each measured parameter is determined, the total uncertainty for the theoretical ICHP can be determined. This value is found by calculating the root mean sum of all the uncertainties (Equation I-8). This calculation is shown in Table I-5. This shows the total uncertainty for the theoretical ICHP for this cylinder end is 6.19 HP or 2.58%.

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Table I-5. Calculation of Total Uncertainty of Measured ICHP for Cylinder End

Parameter Pressure Isentropic Constant Speed Clearance Volume

Uncertainty (HP) 6 0.021 0.5 1.45 Sum of Squares Square Root of Sum

Square of Uncertainty (HP2) 36 0.000441 0.25 2.1025 38.35 6.19 HP

Calculation of Efficiency Uncertainty The uncertainty of the efficiency can be calculated for each parameter (pressure, piston position, etc.) as completed above for the ICHP; however, the tester is more interested in an overall uncertainty of the efficiency for the cylinder end. In order to reduce the effort required to find the efficiency uncertainty, the equations listed below (also shown in Appendix E) can be used to calculate it with the measured and theoretical ICHP uncertainties calculated above.

η cyl ,max =

η cyl ,min =

Pcyl ,isen + ∆Pcyl ,isen ICHPcyl − ∆ICHPcyl

(I-9)

Pcyl ,isen − ∆Pcyl ,isen ICHPcyl + ∆ICHPcyl

∆η cyl = η cyl ,max − η cyl ,min

(I-10) (I-11)

The uncertainty of the efficiency for the cylinder end being evaluated in this example is calculated below. The total uncertainty of the calculated efficiency is 9.5 efficiency points or 12.4% of the efficiency (76.9%). Example

Pcyl ,isen = 229.85 HP ∆Pcyl ,isen = 6.19 HP ICHPcyl = 312.0 HP ∆ICHPcyl = 11.8 HP

229.85 HP + 6.19 HP 312.0 HP − 11.8 HP = 78.6%

η cyl ,max = η cyl ,max

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η cyl ,min =

229.85 HP − 6.19 HP 312.0 HP + 11.8 HP

η cyl ,min = 69.1% ∆η cyl = 78.6% − 69.1% ∆η cyl = 9.5%

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APPENDIX J DATASHEETS FOR RECIPROCATING COMPRESSOR PERFORMANCE TESTING

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APPENDIX J Datasheets are shown on the next pages. They are labeled as General, PV Card, and Enthalpy Rise. The sheets labeled as general apply to both the PV Card and Enthalpy Rise methods. The other datasheets only apply to either the PV Card or Enthalpy Rise methods.

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Datasheet for Compressor Performance Test - General 1 Date: _____________________ Time Cylinder ID Service or Stage HE Pocket Number(s)*Open HE Valve(s) Lifted (Yes or No) CE Pocket Number(s)*Open CE Valve(s) Lifted (Yes or No) Suction Gas Pressure Suction Gas Temperature Suction Nozzle Pressure Suction Nozzle Temperature Discharge Nozzle Pressure Discharge Nozzle Temperature Discharge Gas Pressure Discharge Gas Temperature Compressor RPM

Test No:

Units

Gas Flow Meter Static Pressure Temperature Static ΔP Dynamic ΔP Orifice Coefficient Barometric Pressure Volume Flow Fuel Meter Static Pressure Temperature Static ΔP Dynamic ΔP Orifice Coefficient Barometric Pressure Volume Flow

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Datasheet for Compressor Performance Test - General 2 Date: _____________________ Time: _____________________

Test No:

Driver Current Voltage Power Factor Motor Mechanical Efficiency Gas Composition (mol %) Oxygen Hydrogen Water Hydrogen Sulfide Nitrogen Ammonia Carbon Monoxide Carbon Dioxide Methane Ethane Propane N-Butane Iso-Butane N-Pentane Iso-Pentane Neo-Pentane N-Hexane Iso - Hexane Other: ___________________ Other: ___________________ Other: ___________________ Other: ___________________ Other: ___________________ Other: ___________________ Other: ___________________

Units

Gas

Fuel

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Datasheet for Compressor Performance Test - General 3 Date: _____________________

Test No:

Cylinder Cooling Flow Meter Static Pressure Temperature Static ΔP Dynamic ΔP Orifice Coefficient Barometric Pressure Volume Flow Inlet Temperature Outlet Temperature

Units

Calculated Values Cylinder Cooling Mass Flow Rate (mcool) Heat Flux (qcool) Driver Low Heating Value of Fuel (LHV) Fuel Mass Flow Rate (mfuel) Power Input (Pin) Efficiencies Driver Efficiency (η e) System Efficiency (η sys)

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Datasheet for Compressor Performance Test - PV Card 1 Date: __________________________ Cylinder ID Bore Diameter Stroke Rod Diameter Rod Length

Test No:

RPM: Units

Head End (HE) Fixed Clearance Volume Pocket 1 Volume Pocket 2 Volume Pocket 3 Volume Pocket 4 Volume Valve Lifters (Number) Crank End (CE) Fixed Clearance Volume Pocket 1 Volume Pocket 2 Volume Pocket 3 Volume Pocket 4 Volume Valve Lifters (Number) Compressor Indicator Passage Length Diameter Maximum Rod Loading Compression Tension Single Acting HE (CE Valve Lifted) Single Acting CE (HE Valve Lifted)

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Datasheet for Compressor Performance Test - PV Card 2 Date: _____________________ Cylinder ID Calculated Values Head End Indicated Compressor Horsepower (ICHP) Brake Horsepower (BHP) Suction Volumetric Efficiency (EVs)

Test No: Units

Discharge Volumetric Efficiency (EVd) Suction Gas Compressibility (Zs) Discharge Gas Compressibility (Zd) Capacity (Q) Isentropic Power (from theoretical PV diagram)(Pisen) Isentropic Efficiency (η isen) Crank End Indicated Compressor Horsepower (ICHP) Brake Horsepower (BHP) Suction Volumetric Efficiency (EVs) Discharge Volumetric Efficiency (EVd) Suction Gas Compressibility (Zs) Discharge Gas Compressibility (Zd) Capacity (Q) Isentropic Power (from theoretical PV diagram)(Pisen) Isentropic Efficiency (η isen) Full Compressor Indicated Compressor Horsepower (ICHP) Isentropic Efficiency (η isen) Capacity (Q)

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Datasheet for Compressor Performance Test - Enthalpy Rise 1 Date: _____________________ Cylinder ID

Test No: Units

Calculated Values Cylinders Actual Suction Enthalpy (hs) Actual Discharge Enthalpy (hd) Theoretical Suction Enthalpy (hs) Theoretical Discharge Enthalpy (hd,isen) Actual Enthalpy Difference (H) Theoretical Enthalpy Difference (Hisen) Isentropic Efficiency (η isen,cyl) Capacity (Q) Mass Flow Rate (mcyl) Actual Power (Pcyl) Full Compressor Actual Suction Enthalpy (hs) Actual Discharge Enthalpy (hd) Theoretical Suction Enthalpy (hs) Theoretical Discharge Enthalpy (hd,isen) Actual Enthalpy Difference (H) Theoretical Enthalpy Difference (Hisen) Isentropic Efficiency (η isen,cyl) Capacity (Q) Mass Flow Rate (mcyl) Actual Power (Pcyl)

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View more...
RELEASE 1.0

November 2009 Gas Machinery Research Council Southwest Research Institute®

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GUIDELINE FOR FIELD TESTING OF RECIPROCATING COMPRESSOR PERFORMANCE

RELEASE 1.0

Authors: Melissa Wilcox, SwRI Klaus Brun, Ph.D., SwRI

Industry Advisory Committee: David Krenek, Caterpillar – Principal Rainer Kurz, Solar Turbines – Principal Bob Webber, Dynalco William Elston, Compressor Systems, Inc. Martin Hinchliff, Dresser-Rand Everette Johnson, Cameron Warren Laible, Windrock Greg Lortie, Ariel Corporation Randall Raymer, El Paso Corporation Norm Shade, ACI Services, Inc.

This document contains information resulting from a cooperative study effort and is intended to be of beneficial use to those interested. However, the contents hereof are only guidelines for the subject matter to which the document ® pertains. Neither Southwest Research Institute Southern Gas Association, nor the Gas Machinery Research Council make any warranty or representation, express or implied, (1) with respect to the accuracy or completeness of the information contained in this document, or (2) that the use of any method, suggestion, technology, information, or guidelines disclosed herein may not infringe on rights owned or claimed by others and further disclaim any liability for the use of any methods, suggestions, technology, guidelines or other information disclosed herein.

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Guideline for Field Testing Reciprocating Compressor Performance RELEASE 1.0 Foreword Field testing of reciprocating compressors has become increasingly common due to the need to verify efficiency, power, and capacity of the compressor package upon delivery. The performance test of the reciprocating compressor in the field is often necessary to assure that the manufacturer meets performance predictions and guarantees a customer’s return on investment. Economic considerations demand that the performance and efficiency of a reciprocating compressor package be verified at the actual field site. Since the field environment is not ideal, an assessment of measurement uncertainties is necessary to characterize the validity of a performance test. As the working field environments shift further from the ideal case, the uncertainties increase. Previous field tests have shown that the compressor efficiency uncertainty can be unacceptably high when some basic rules for proper test procedures and standards are violated. This guideline applies to a typical reciprocating compressor or compressor package. The motivation for conducting a field test is based on at least one of the following objectives: •

The manufacturer is required to supply the customer with the expected performance of the reciprocating compressor. To the manufacturer, the field test provides a baseline for the compressor at the site of delivery to compare to expected performance, which is based on predicted performance. In addition, the field performance test is the final verification of the guaranteed performance.

•

The user needs to verify performance of the reciprocating compressor. Baseline performance data is obtained from the initial field performance test. The baseline test can be used for comparing and monitoring the health of compressor package in the future.

•

The user or manufacturer needs to assess performance of the reciprocating compressor or compressor package because of degradation concerns. Based on the field test results, a performance recovery program may be initiated.

•

The user requires calibration of an installed historical trend monitoring system. The field test is used to provide initial calibration of the system based on the first performance of the reciprocating compressor or compressor package.

•

The user needs to compare the performance of different units at the station or compare the performance of different stations to guide sequential dispatch of the “best” performing units/stations which are available first.

•

Incorrect pressures may have been used during compressor selection process if pulsation design was not considered. If a field performance test was not originally required during installation, the user needs to conduct a test to determine the compressor’s operation at the actual conditions experienced at the installation sight.

•

The user needs to measure the degradation (or improvement) of the system due to pulsation attenuation devices installed based on the pulsation analysis and subsequent “as-built” fabrication of the system.

The following guideline is a suggested best practice for field testing of reciprocating compressors. Specific considerations at a field site may require deviation from this guideline in order to meet safety requirements, improve testing efficiency, or comply with station operating philosophy.

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Guideline for Field Testing of Reciprocating Compressor Performance RELEASE 1.0 TABLE OF CONTENTS 1. 2. 3.

4.

5.

6.

7.

8.

9.

PURPOSE AND APPLICATION .........................................................................................1 PACKAGE AND COMPRESSOR PERFORMANCE ..........................................................1 PERFORMANCE PARAMETERS ......................................................................................2 3.1 Reciprocating Compressor Flow/Capacity .................................................................2 3.2 Compressor Efficiency ...............................................................................................3 3.3 Indicated Cylinder Horsepower (ICHP) and Brake Horsepower (BHP).......................6 3.4 Differential Indicated Power (DIP) ..............................................................................7 3.5 Suction and Discharge Volumetric Efficiency .............................................................7 3.6 Driver Power and System Efficiency ..........................................................................8 3.7 Equations of State .....................................................................................................9 DATA COLLECTION PROCEDURES ..............................................................................11 4.1 PV Card Method ......................................................................................................11 4.2 Enthalpy Rise Method ..............................................................................................20 4.3 PV Card and Enthalpy Rise Method ........................................................................24 TEST PREPARATION......................................................................................................24 5.1 Pre-Test Meeting .....................................................................................................25 5.2 Pre-Test Operation and Instrumentation Checkout ..................................................25 5.3 Pre-Test Equipment Checkout .................................................................................27 5.4 Pre-Test Information ................................................................................................27 5.5 Test Stability ............................................................................................................29 5.6 Safety Considerations..............................................................................................31 MEASUREMENT AND INSTRUMENTATION ..................................................................31 6.1 Measurement of Pressure........................................................................................32 6.2 Measurement of Temperature .................................................................................36 6.3 Measurement of Flow ..............................................................................................38 6.4 Measurement of Gas Composition...........................................................................40 6.5 Measurement of Crank Position ...............................................................................42 TEST UNCERTAINTY ......................................................................................................47 7.1 Ideal Field Test Conditions for Reducing Uncertainties ............................................ 49 7.2 Effects of Non-Ideal Installations on Uncertainty ......................................................52 INTERPRETATION OF TEST DATA ................................................................................55 8.1 Data Reduction and Checking Uncertainties ............................................................55 8.2 Use and Comparison of Data ...................................................................................55 8.3 Using Redundancy to Check Test Measurement and Uncertainty ........................... 57 8.4 Analysis of Measured Results ..................................................................................57 REFERENCES .................................................................................................................59

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APPENDICES APPENDIX A – General Performance Testing Procedure .........................................................62 APPENDIX B – Calculation of Theoretical PV Diagram.............................................................68 APPENDIX C – Equation of State Models .................................................................................77 APPENDIX D – Equation of State Model Comparison of Predicted Performance Data ............. 85 APPENDIX E – Uncertainty Analysis for Independent Variable Measurements......................... 91 APPENDIX F – Compressor Performance Diagnostics with PV Diagrams .............................. 105 APPENDIX G – Polytropic Efficiency ......................................................................................112 APPENDIX H – Heat Loss Estimations ...................................................................................116 APPENDIX I – Example PV Card Calculations........................................................................ 128 APPENDIX J – Data Sheets for Reciprocating Compressor Performance Testing .................. 145

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LIST OF FIGURES Figure 3-1.

Figure 8-3.

Enthalpy/Pressure Change During Compression and Expansion Process (Edmister and Lee, 1984).....................................................................................5 Typical PV Diagram .............................................................................................6 PV Diagram with Pressure Also Measured in Nozzles .........................................7 Typical PV Diagram ...........................................................................................12 Location of Test Instrumentation for PV Card Method ........................................ 13 Pressure Transducer Installed on Compressor Cylinder with Indicator Valve ..... 14 PV Diagram with Channel Resonance Present – Uncorrected High-Speed Compressor (950 RPM) .....................................................................................15 PV Diagram with Channel Resonance Present – Corrected High-Speed Compressor (950 RPM) .....................................................................................15 PV Diagram with Channel Resonance Present – Uncorrected Low-Speed Compressor (330 RPM) .....................................................................................16 PV Diagram with Channel Resonance Present – Corrected Low-Speed Compressor (330 RPM) .....................................................................................16 PV Diagram with Varying ODC Measurements ..................................................18 Location of Test Instrumentation for Enthalpy Rise Method ............................... 21 Example of Drift and Fluctuations in a Temperature Measurement .................... 31 ASME PTC 10 Recommended Installation Configuration for Pressure and Temperature Measurement ................................................................................34 Sampling Method with Pigtail as Recommended in API MPMS Chapter 14.1....................................................................................................................41 Encoder Installed on a Slow-Speed Reciprocating Compressor on Flywheel ..... 43 Encoder and Adapter Installed on a High-Speed Reciprocating Compressor ..... 43 Rotation of PV diagram to Correctly Reference ODC ......................................... 44 Example of Set-up for Dial Indicator Method ......................................................45 Hard Stop Placed Between Cylinder Head and Piston Through Valve Pocket................................................................................................................46 Placement of ODC Mark Between Two Initial Marks .......................................... 46 Comparison of Tests with Different Levels of Uncertainty .................................. 50 Actual and Theoretical PV Diagrams for Performance Test at 450 RPM ............ 51 Example of Compressor Performance Curves for High-Speed Transmission Compressor .......................................................................................................56 Comparison of Theoretical Predicted Performance and Measured Performance Test Point .....................................................................................57 Example of Test Uncertainty Range ...................................................................58

Figure B-1. Figure B-2. Figure B-3. Figure B-4.

Theoretical PV Diagram with Start of Expansion Stroke Indicated ..................... 71 Theoretical PV Diagram with Start of Compression Stroke Indicated ................. 71 Theoretical PV Diagram with Multiple Points Plotted on Expansion Line ............ 72 Theoretical PV Diagram with Multiple Points on Compression Line ................... 73

Figure 3-2. Figure 3-3. Figure 4-1. Figure 4-2. Figure 4-3. Figure 4-4. Figure 4-5. Figure 4-6. Figure 4-7. Figure 4-8. Figure 4-9. Figure 5-1. Figure 6-1. Figure 6-2. Figure 6-3. Figure 6-4. Figure 6-5. Figure 6-6. Figure 6-7. Figure 6-8. Figure 7-1. Figure 7-2. Figure 8-1. Figure 8-2.

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Figure B-5.

Complete Theoretical PV Diagram ..................................................................... 73

Figure C-1.

Calculation Path for Equations of State .............................................................. 81

Figure D-1.

Compression T-S Diagram................................................................................. 88

Figure E-1. Figure E-2. Figure E-3.

Determination of Uncertainty Using Differential Methods ................................... 94 Determination of Uncertainty Using Perturbation Methods ................................. 95 Example of Change in Theoretical PV Diagram with Pressure Uncertainty ...... 101

Figure F-1. Figure F-2. Figure F-3.

Diagram Illustrating the Effects of Suction Valve Leaks ................................... 107 Diagram Illustrating the Effects of Discharge Valve Leaks ............................... 108 Diagram Illustrating the Effects of Piston Ring Leaks ....................................... 109

Figure H-1. Figure H-2. Figure H-3.

Figure H-7.

Schematic of Energy Exchange in Reciprocating Compressor ......................... 118 Radiation Heat Transfer Coefficient with Emissivity and Mean Temperature.... 120 Natural Convection Heat Transfer Coefficient with X and Mean Temperature .................................................................................................... 121 Forced Convection Heat Transfer Coefficient with Y and Mean Temperature .................................................................................................... 122 Natural Convection Heat Transfer Coefficient for Vertical Pipes with ∆T and Length.............................................................................................................. 124 Natural Convection Heat Transfer Coefficient for Horizontal Pipes with ∆T and Diameter ................................................................................................... 124 Forced Convection Heat Transfer Coefficient with Z and Mean Temperature .. 126

Figure I-1. Figure I-2. Figure I-3. Figure I-4. Figure I-5. Figure I-6.

Constructed Measured PV Diagram ................................................................. 131 PV Diagram with Channel Resonance Removed through Filtering ................... 132 Graphical Representation of Integration of PV Diagram ................................... 133 Where Suction and Discharge Valves Open on PV Diagram ........................... 134 Theoretical PV Diagram with Correct PV Diagram ........................................... 135 Variation in PV Diagram with Piston Position Uncertainty ................................ 138

Figure H-4. Figure H-5. Figure H-6.

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LIST OF TABLES Table 3-1. Table 5-1. Table 5-2. Table 5-3. Table 6-1. Table 6-2. Table 6-3. Table 6-4. Table 7-1. Table 7-2. Table 7-3. Table 7-4. Table 7-5. Table 7-6. Table D-1. Table D-2. Table D-3. Table D-4. Table D-5.

Table I-1. Table I-2. Table I-3. Table I-4. Table I-5.

Suggested Applications for Equation of State Usage ......................................... 10 Maximum Deviations from Specified Values and Fluctuations from Average Readings ........................................................................................................... 28 Additional Assessment of Stability of Compressor During Pre-Test ................... 30 Assessment of Stability of Compressor Driver During Pre-Test.......................... 30 Typical Uncertainties in Pressure Measurement (shown as percent of full scale) ................................................................................................................. 36 Recommended Depth of Thermowells ............................................................... 37 Typical Uncertainties in Temperature Measurement (shown as percent of full scale) ........................................................................................................... 38 Achievable Uncertainties in Flow Measurement with No Pulsating Flow ............ 40 In-Practice Achievable Uncertainty for Measured Test Parameters .................... 49 Compressor Geometry ....................................................................................... 50 Summarization of Uncertainty for Performance Test at 450 RPM ...................... 51 Example of Total Uncertainty Calculation for Compressor in "Near Ideal" Case .................................................................................................................. 52 Non-Ideal Installation Effects on Compressor Uncertainty.................................. 53 Effects of Non-Ideal Encoder and Cylinder Pressure Measurements ................. 54 Gas Mixtures Used in EOS Model Comparison .................................................. 87 Assumed Measured Conditions; PR = 1.3.......................................................... 87 Assumed Measured Conditions; PR = 2.2.......................................................... 88 Horsepower and Efficiency Calculations for EOS Models at Pressure Ratio of 1.3.................................................................................................................. 89 Horsepower and Efficiency Calculations for EOS Models at Pressure Ratio of 2.2.................................................................................................................. 89 Calculation of Total Uncertainty of Measured ICHP for Cylinder End ............... 139 Defined and Calculated Values for Theoretical ICHP Uncertainty Due to Pressure Uncertainty ....................................................................................... 140 Defined and Calculated Values for Theoretical ICHP Uncertainty Due to Isentropic Constant Uncertainty ....................................................................... 141 Defined and Calculated Values for Theoretical ICHP Uncertainty Due to Clearance Volume Uncertainty......................................................................... 141 Calculation of Total Uncertainty of Measured ICHP for Cylinder End ............... 142

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DEFINITION OF SYMBOLS Symbols and Units: cp cv e f h i k l m n p q r s x y

= = = = = = = = = = = = = = = =

Specific heat at constant pressure (Btu/lbm-R) Specific heat at constant volume (Btu/lbm-R) Voltage (volts) Schultz factor for polytropic efficiency calculation or function elsewhere Enthalpy of gas at suction, discharge or isentropic conditions (Btu/lbm) Current (amps) Isentropic exponent Connecting Rod Length (in) Mass (lbm) Exponent or ending counting value Total (stagnation) pressure of gas at suction or discharge side (psia) Heat transferred (Btu/lbm) Piston rod diameter (if not present r = 0) (inches) Entropy at specified pressure and temperature (Btu/lbm-R) Represents a parameter or calculated value Mole fractions

A B BDC BHP BWR BWRS C*

= = = = = = =

CL% CQ*

= =

DF DIP EOS EVs EVd F FFT H ICHP IDC K1 K2 L LHV LKP MW N ODC

= = = = = = = = = = = = = = = = = =

Cross-sectional area of pipe (ft2) Cylinder bore (inches) Bottom Dead Center (see IDC definition) Brake Horsepower of Compressor (HP) Benedict-Webb-Rubin Benedict-Webb-Rubin-Starling Factor to convert capacity using defined units for other symbols, to MMSCFD (0.6397) or SCFM (444.25) Percent clearance of cylinder (%) Factor to convert capacity using defined units for other symbols, to MMSCFD (0.2314 x 10-6) or SCFM (1.607 x 10-4) Degrees of Freedom Differential Indicated Power (HP) Equation of State Suction volumetric efficiency (%) Discharge volumetric efficiency (%) Represents a calculated function, F Fast Fourier Transform Enthalpy rise for compressor, either actual or ideal (Btu/lbm) Actual Indicated Compressor Horsepower from measured PV Diagram (HP) Inner Dead Center (see definitions) Expansion line constant used for theoretical PV diagram generation Compression line constant used for theoretical PV diagram generation Loss factor Fuel gas lower heating value, as determined through thermodynamic analysis (Btu/lbm) Lee-Kesler-Plocker Molecular Weight Unit Speed (RPM) Outer Dead Center (see definitions)

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P Pf PR PV Q R RK RTD S SG SRK T TDC U V W Z

= = = = = = = = = = = = = = = = =

Power (HP) Power factor Peng-Robinson Pressure-Volume Capacity (MMSCFD or SCFM) or volumetric flow rate Gas constant Redlich-Kwong Resistance Temperature Detector Stroke (inches) Specific gravity of gas (referenced to air) Soave-Redlich-Kwong Absolute temperature (°R) Top Dead Center (see ODC definition) Flow velocity in pipe (ft/min) Volume (in3) Work performed by compressor end (area of PV diagram) (in-lbs) Gas compressibility

Δ ζ η θ v ρ ω

= = = = = = =

Finite change in value or uncertainty Damping Ratio Efficiency (%) Position of shaft as reported by encoder (degrees) Specific volume of gas at suction, discharge or isentropic conditions (ft3/lbm) Density (lbm/ft3) Resonance frequency

Subscripts: a comp components cool cyl cl d e fuel gas ho i in isen m min max mo mol% p s stat stroke

= = = = = = = = = = = = = = = = = = = = = = =

Actual Full compressor Components Cooling Individual cylinder end Clearance Discharge Engine Fuel Gas Heat removed through cooling jackets, conduction, and convection Placeholder for later assigned number Input condition Isentropic Mechanical Minimum Maximum Motor Fractional mol % for gas composition Polytropic Suction Static Stroke

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sys swept th universal

= = = =

System Swept volume Thermal Universal gas constant

P STD

= =

Polytropic condition Standard conditions (14.7 psia and 60 °F)

•

= = =

Rate (ex. m is mass flow rate) Numbers used to represent individual cylinders or cylinder ends Function of theta or rotational position

•

1,2,… θ

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DEFINITIONS 1.

Absolute Pressure: The pressure measured above a perfect vacuum.

2.

Absolute Temperature: The temperature above absolute zero stated in degrees Rankine or Kelvin. Rankine temperature is the Fahrenheit temperature plus 459.67 degrees; Kelvin is the Celsius temperature plus 273.15 degrees.

3.

Brake Horsepower (BHP): Brake horsepower refers to the power required of the driver to supply power to the compressor, or compressor cylinder, and must include compressor mechanical (bearings and seals) and compression losses. In the evaluation of a compressor package, the BHP will need to also consider other parasitic loads, such as cooling fans driven off the front end of the engine.

4.

Brake Specific Fuel Consumption: Brake Specific Fuel Consumption is the fuel flow rate in standard cubic feet per hour multiplied by the net dry heating value (LHV) of the fuel at standard conditions in British thermal units per cubic foot divided by the total brake horsepower measured at the engine flywheel. This term is applicable to engine driven packages and integral compressors.

5.

Brake Thermal Efficiency: Brake Thermal Efficiency is the overall efficiency of an engine. It is the BHP or useful work delivered by the engine divided by the power input of the fuel.

6.

Capacity: The rate of flow, determined by the mass flow divided by density of the gas under standard conditions (SCFM or MMSCFD).

7.

Clearance: Clearance refers to the actual volume in cubic inches trapped in the cylinder when the piston is at outer dead center (including pocket and valve dead volumes).

8.

Compression and Expansion Effective Exponents: These are the isentropic exponents for compression and expansion of the gas. These can be determined from the expansion and compression lines on the PV diagram.

9.

Crank End: The crank end of the compressor cylinder is the end which is closest to the crank shaft.

10. Cylinder Displaced Volume: Cylinder displaced volume refers to the total volume displaced by the piston, including the total cylinder end clearance volume. 11. Density: The mass of gas per unit volume, equal to the reciprocal of the specific volume. The density is a thermodynamic property determined from the total pressure and temperature at a point in the fluid. 12. DIP (Differential Indicated Power): DIP represents the difference between the indicated power for some portion or zone of the PV diagram with one boundary of that zone being a reference pressure line, which may be constant or varying. 13. Differential Pressure: The difference between any two pressures measured with respect to a common reference (i.e., the difference between two gage pressures). 14. Discharge Volumetric Efficiency (EVd or VEd): This is defined as the ratio of the volume of gas discharged from the cylinder (at discharge pressure and temperature) to the swept volume of the cylinder end. 15. Electric Motor Efficiency: The electric motor efficiency is the ratio between the output or delivered power to the measured electrical input power.

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16. Engine Fuel Flow: The engine fuel flow is the mass flow rate of fuel to the engine for operation. 17. Gage Pressure: The pressure measured directly with the existing barometric pressure as the zero base reference. 18. Head End: The head end of the compressor cylinder is the end which is furthest from the crankshaft. 19. Indicated Compressor Horsepower (ICHP): This is the total rate at which the piston faces of all cylinder ends do work on the gas, based on measured cylinder pressure, expressed in HP. 20. Inner Dead Center (IDC): Inner dead center refers to the condition where the piston is closest to the crankshaft (also referred to as bottom dead center (BDC)). 21. Isentropic Compression: A reversible, adiabatic compression process. 22. Isentropic Efficiency: This is the ratio of isentropic power (IP) to measured power (ICHP for PV Cards or P for Enthalpy Rise). This efficiency assumes that all heat transfer is accounted for in the actual or measured power. If all the heat transfer is not accounted for, then the efficiency should be referred to as a “modified” isentropic efficiency. 23. Isentropic Power: This is the ideal power required to isentropically compress and deliver the capacity from suction to discharge conditions. 24. Mean Cylinder Effective Exponent: compression in the cylinder.

This is the polytropic exponent for expansion and

25. Mechanical Efficiency: This is the ratio of the total measured compressor power (ICHP or P) to total shaft horsepower (BHP). This is often assumed to be in the range of 92-97% for lowspeed and high-speed compressors. 26. Mechanical Losses: The total power consumed by frictional losses in integral gearing, bearings, seals, packing, rider bands, and piston rings. 27. Outer Dead Center (ODC): Outer Dead Center refers to the condition where the piston is at point of travel furthest from the crankshaft (also referred to as top dead center (TDC)). 28. Polytropic Compression: A reversible compression process between the total suction pressure and temperature and the total discharge pressure and temperature. The polytropic compression process follows a path such that the polytropic exponent, nP, is constant during the process. 29. Pressure Ratio: The ratio of absolute total discharge pressure to absolute total suction pressure. 30. Shaft Power: The power delivered to the compressor shaft by the driver, also known as brake power. Shaft power is equal to gas power plus mechanical losses. 31. Stage: A single, or number of parallel piston-cylinders and associated stationary flow passages. 32. Standard Volume Flow: The flow rate expressed in volume flow units at either of the standard conditions outlined: a. SI flow units are typically i. Normal cubic meters per hour (Nm3/h) or Normal cubic meters per minute (Nm3/min) ii. At ISO standard conditions of: Absolute Pressure: 1.013 bar, Temperature 0 deg C

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b. US customary flow units are typically i. Standard cubic feet per minute (SCFM), or Million standard cubic feet per day (MMSCFD) ii. At customary standard conditions of: Absolute pressure: 14.7 psia, Temperature: 60 deg F 33. Static Pressure: The pressure measured in such a manner that no effect is produced by the velocity of the flowing fluid. 34. Static Temperature: The temperature determined in such a way that no effect is produced by the velocity of the flowing fluid. 35. Suction Volumetric Efficiency (EVs or VEs): This is defined as the ratio of the volume of gas drawn into the cylinder (at suction pressure and temperature) to the swept volume of the cylinder end. 36. Swept Volume: Swept volume refers to the total volume displaced by the piston not including the total cylinder end clearance volume. 37. Total (Stagnation) Pressure: An absolute or gage pressure that would exist when a moving fluid is brought to rest, and its kinetic energy is converted to an enthalpy rise by an isentropic process from the flow condition to the stagnation condition. In a stationary body of fluid, the static and total pressures are equal. 38. Total (Stagnation) Temperature: The temperature that would exist when a moving fluid is brought to rest and its kinetic energy is converted to an enthalpy rise by an isentropic process from the flow condition to the stagnation condition. In a stationary body of fluid, the static and total temperatures are equal. 39. Valve Losses: Valve losses refer to the pressure losses across the suction and discharge valves. These are due to valve geometry flow losses. The flow through the valve is affected by pulsations.

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Guideline for Field Testing of Reciprocating Compressor Performance FINAL VERSION 1.0 1.

PURPOSE AND APPLICATION

The following guideline is intended to serve as a reference for field testing of reciprocating compressor performance. This guideline applies to any party conducting a field test of a reciprocating compressor or compressor package (manufacturer, user company, or third-party). It is intended to provide a technically sound, yet practical procedure for all aspects of conducting field performance tests of reciprocating compressors. Specific requirements of a particular test may dictate that the test procedure deviates from this guideline or the ideal installation described. However, when a particular test deviates from the installation requirements or other test procedures, the deviation will affect the uncertainty of the test and should be accounted for in the uncertainty analysis, as recommended in this guideline. The development of this guideline was initiated by the ever growing presence of high-speed reciprocating compressors in the industry. However, there are several low-speed reciprocating compressors operating that also need performance tests. This guideline addresses items that should be considered for both highand low-speed compressors when conducting performance tests. The standards that are used as references for this guideline are ASME PTC 10-1997, “Performance Test Code on Compressors and Exhausters,” and API 618, “Reciprocating Compressors for Petroleum, Chemical, and Gas Industry Service,” and ISO 1217, “Displacement Compressors – Acceptance Tests.” 2.

PACKAGE AND COMPRESSOR PERFORMANCE

The performance testing of a reciprocating compressor can be completed in various fashions. This is dependent upon the intent of the testing. There are two main methodologies that are used for testing: the Enthalpy Rise method and the Pressure-Volume (PV) Card method (these methods are discussed in detail in later sections of this guideline). These two methodologies can be used individually or in combination with one another. Again, this is dependent upon the objectives of the performance test. There is much debate as to whether the compressor performance can adequately be assessed by looking at the compressor individually, flange-to-flange, or the compressor package as a whole, lateral-to-lateral. All of these tests have their benefits depending upon the objective of the testing. If the user intends to conduct a performance test with the intent of verifying the manufacturer’s ratings, then the compressor would need to be tested individually. The compressor performance encompasses the machinery located between the suction and discharge nozzle of each compressor cylinder. It would not necessarily include the effects of pulsation bottles and piping and other equipment outside the nozzles. These could be included, if these effects are deemed important in the performance test. A combination of the Enthalpy Rise and PV Card methods can provide more information. If testing to verify the manufacturer’s ratings is desired, then the tests should be conducted using a methodology as close to that used during the manufacturer’s performance tests as possible, if practical. Compressor package performance is used when the performance test mandates that the losses associated with piping, bottles, and other auxiliary equipment be included in the assessment. This approach may be

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used to validate the package design or to develop performance maps relative to the process parameters that are being monitored for capacity/load control or reporting purposes. For example, if routine load control is based on suction pressure observed at the inlet of the suction scrubber, the compressor performance test should allow for performance to be correlated to this measurement point regardless of cylinder flange measurements. It also can include the performance of compressor drivers. The package performance requires more measurements than the ones detailed below for the PV Card and Enthalpy Rise method. It may also require a fuel flow rate measurement for engine driven compressors or electrical usage measurement for electric motor driven compressors. The package performance is lacking in the sense that the losses may not be directly identified. This is one way a combination of the PV Card and Enthalpy Rise method is useful. Losses can easily be placed on the suction or discharge of particular cylinders using the PV Card method and overall performance can be found with the Enthalpy Rise method. The losses are a combination of valve losses, gas passage losses, and pulsations. Further testing would be needed to identify losses associated with equipment external to the compressor. All side streams or exchanges of mass need to be considered in the package performance test. This guideline focuses on the details for compressor performance tests. It covers the Enthalpy Rise method and PV Card method. It does not cover all the aspects of package performance testing, such as acoustical and mechanical responses and parasitic loads on the compressor or engine, but the information presented here is useful and can be used in completing a compressor package performance test. 3.

PERFORMANCE PARAMETERS

The following six performance parameters generally describe the performance of a reciprocating compressor. These parameters are commonly used in acceptance testing, testing to determine degradation of the machine, and operational range testing. The primary measurements required in order to calculate these parameters are discussed in Section 6. The uncertainty calculations are discussed in Section 7. Accounting for the effect of non-ideal installations on uncertainty is also discussed in Section 7. Performance Parameters:

3.1

1.

Capacity

2.

Compressor Efficiency

3.

Indicated Cylinder Horsepower and Brake Horsepower

4.

Differential Indicated Power

5.

Suction and Discharge Volumetric Efficiency

6.

Driver Power and System Efficiency

Reciprocating Compressor Flow/Capacity

Capacity of a compressor cylinder is the gas flow rate in standard cubic feet per minute (SCFM) or in million standard cubic feet per day (MMSCFD) at standard conditions of 14.696 psia pressure and 519.67 R temperature. There are many ways to determine this value. It can be measured directly with a flow meter or calculated given other measured parameters. Due to significant effects of pulsations on flow measurements, it is necessary to check the flow measurement. This can be done by completing one of the calculations below to compare the results. For adiabatic compression (no heat transfer, no valve losses, or leaks) of either

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ideal or real gases, flow may be properly predicted by the methods given below. In reality, heat transfer, valve losses, and finite valve and ring leaks are always present to some degree. Each of these effects tends to reduce the actual capacity from that predicted by equations. Industry experience has shown that on “healthy” cylinders, the capacity can be calculated within 2-3% of the actual value. For low ratio compressors, such as pipeline compressors, the capacity can be calculated within 1% of the measured value. The deviation will be greater on non-cooled or unhealthy cylinders. Capacity from Enthalpy This method can only be used when pressure and temperature measurements are taken at the suction and discharge of the compressor and when the PV diagram is constructed from measurements on each cylinder end. These measurements are used with the appropriate Equation of State (EOS) to calculate the enthalpy values (hd and hs). The variable C* is a factor used to convert the capacity into MMSCFD or SCFM. For MMSCFD use 0.6397 and for SCFM use 444.25. These factors apply when the units of the variables in the equations are the same as defined in the nomenclature of this document. The variable ICHP is the full compressor horsepower. This is the area of the PV diagram for the cylinder end being tested.

C * * ICHP Q= (hd − hs ) * SG

(3-1)

Capacity from Cylinder Parameters Capacity for a cylinder end may also be calculated from cylinder parameters using the following equations. The variable CQ* is used to convert the final capacity into MMSCFD or SCFM. The value for MMSCFD is 0.2314x10-6 and for SCFM is 1.607x10-4. These factors apply when the units of the variables in the equations are the same as defined in the nomenclature of this document. The volumetric efficiencies, EVs and EVd, can be calculated using Equations 3-14 and 3-15. The piston rod diameter (r) equals zero for capacity calculations for the head end of the compressor:

(CQ )* (B Q= *

2

(CQ ) * (B Q= *

2

2

)

− r 2 * S * N * EVs * p s * Z STD Ts * Z s

(3-2)

EV * p s EVd * pd − r 2 * S * N * Z STD * s + Td * Z d Ts * Z s

(3-3)

)

These equations tend to overestimate the actual capacity because they do not account for gas preheating. As the gas enters the cylinder, it gets hotter from heat transfer with the cylinder walls and from mixing with residual gas in the cylinder bore. 3.2

Compressor Efficiency

Compressor efficiency is commonly defined based on either isentropic or polytropic ideal processes (see Appendix G for polytropic efficiency). Both definitions are appropriate for performance comparison as they provide a ratio of the ideal (isentropic or polytropic) enthalpy difference across the compressor to the actual enthalpy difference (head). The isentropic process assumes a reversible adiabatic process without losses (i.e., no change in entropy). This process is an ideal reference process.

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The compressor actual enthalpy rise (H) and isentropic enthalpy rise (Hisen) are determined from the measurement of pressure and temperature on the suction and discharge and the calculation of enthalpy using an EOS model. The enthalpy rises are calculated from the enthalpies associated with each state from the EOS as follows: Isentropic Enthalpy Rise

H isen = hd ,isen − hs = h( pd , ss ) − h( ps , Ts )

(3-4)

Actual Enthalpy Rise

H = hd − hs = h( pd , Td ) − h( ps , Ts )

(3-5) * Note that hd,isen is the enthalpy associated with the discharge pressure at the suction entropy, ss, because the entropy change is zero in an isentropic process. All enthalpies should be directly determined from the EOS. Isentropic enthalpy difference can also be determined for estimation purposes (assuming ideal gas behavior):

∆h = hd ,isen

k −1 pd k − hs = −c pTs 1 − ps

(3-6)

The isentropic exponent, k, is defined as:

ln k= ln

pd ps

νs

(3-7)

ν d ,isen

Isentropic Efficiency Below are three equations to calculate isentropic efficiency. As mentioned above, the isentropic process is adiabatic and reversible. In order to calculate a true isentropic efficiency, all heat losses in the system should be accounted for. This is extremely difficult to do since many of these losses are due to friction. If a reciprocating compressor has low or negligible overall heat losses (this would be true on a low pressure ratio machine with no jacket cooling), then the efficiency calculated from Equations 3-8 through 3-10 can be considered to be an isentropic efficiency. However, if heat transfer is present, then the efficiency can be considered a “modified isentropic efficiency” instead, since it does not represent a purely isentropic process. Some examples of where heat transfer would be present are cylinders with jacket cooling and when the surface temperature of the compressor is significantly different than the ambient temperature (more than 20 degrees). The criterion discussed here applies for any mention of isentropic efficiency throughout this guideline.

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Equation 3-8 would be used with the Enthalpy Rise method where the enthalpy values will be calculated from pressure and temperature on the suction and discharge of the compressor. The isentropic efficiency is calculated from the isentropic and actual enthalpy rise. This can also be used to calculate the efficiency of an individual cylinder with pressure and temperature measurements at the suction and discharge nozzles. Equation 3-9 is used with the PV Card method. This equation is used to determine the individual cylinder end efficiency. The indicated compressor horsepower (ICHP) is determined from the measured PV diagram and the isentropic power (Pisen) is from the theoretical isentropic PV diagram. Equation 3-10 is used with the PV Card method to calculate the efficiency of the full compressor. The top of the equation is the summation of all calculated theoretical powers which are divided by the summation of all measured powers.

η isen ,comp = η isen ,cyl =

hd ,isen − hs

(3-8)

hd − hs

Pisen ICHP

η isen ,comp =

(3-9)

Pisen ,1, HE + Pisen ,1,CE + Pisen , 2, HE + ...

(3-10)

ICHP1, HE + ICHP1,CE + ICHP2, HE + ...

The compression process for a typical reciprocating compressor and the associated enthalpy change are shown on a P-h diagram in Figure 3-1 for 100% methane gas mixture. At the start of the compression process the pressure and enthalpy are at ps and hs. An isentropic compression would follow the top dashed line until it reaches pd and hd,isen. The actual compression process follows the bottom solid line until it reaches pd and hd. The difference in enthalpy across these two lines gives the efficiency (Equation 3-8).

pd, hd,isen pd, hd ps, hs

Figure 3-1. Enthalpy/Pressure Change During Compression and Expansion Process (Edmister and Lee, 1984)

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3.3

Indicated Cylinder Horsepower (ICHP) and Brake Horsepower (BHP)

The Indicated Cylinder Horsepower term is characteristic of a performance test conducted using the PV Card method. In that particular method, a pressure-volume curve is generated from the pressure and volume changes within the compressor cylinder. The area within the PV curve represents the work performed by the cylinder end and can be used to derive Indicated Cylinder Horsepower (ICHP), which is directly related to the speed of the compressor. The equation below shows the calculation of ICHP from the area of the PV diagram. The ICHP is, in turn, used with a theoretical horsepower to determine the individual cylinder end’s efficiency. Figure 3-2 shows a representation of an actual PV diagram. The area enclosed within the compression and expansions lines, as well as the discharge and suction lines, is the ICHP.

ICHP =

W *N 396000

(3-11)

The BHP includes the effects of seals, bearings, rider bands, and piston rings. The BHP can be measured with a torque meter on separable compressors, but usually the mechanical efficiency is assumed to be 9297% for both low- and high-speed compressors. Once the BHP for each individual cylinder end is calculated, these values can be summed to obtain the compressor BHP. Equation 3-12 below shows the calculation of cylinder end BHP with indicated compressor cylinder end horsepower and mechanical efficiency. Equation 3-13 shows the calculation of the full compressor BHP by adding the individual cylinder end values. More information on shaft power measurements with a torque meter can be found in the American Society of Mechanical Engineers (ASME) Performance Test Code (PTC) 19.7, “Measurement of Shaft Power.”

BHPcyl =

ICHP

(3-12)

ηm

BHPcomp = BHP1 + BHP2 + ...

(3-13)

Figure 3-2. Typical PV Diagram

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3.4

Differential Indicated Power (DIP)

Differential Indicated Power (DIP) is a term used with the PV Card method. DIP represents the difference between the indicated power for some portion or zone of the diagram with one boundary of that zone being a reference pressure line, which may be constant or varying. Figure 3-2 illustrates the Discharge Differential Indicated Power (DIPd) and Suction Differential Indicated Power (DIPs) relative to assumed constant suction pressure (ps) and discharge pressure (pd), for this case, taken as the Inner Dead Center (IDC) and Outer Dead Center (ODC) diagram pressure points. DIPd and DIPs, using the IDC and ODC pressure values, reflect the effects of valve and internal passage flow losses and pulsation effects. Nozzle or bottle pressures are often used as references for obtaining DIPd and DIPs values in an effort to account for the influence of pulsations; however, this should be approached with caution since pressures at these locations may not be representative of the dynamic pressure just outside the valves. Figure 3-3 shows an example of a PV diagram where the pressures inside the suction and discharge nozzles were used to determine the DIP.

Figure 3-3. PV Diagram with Pressure Also Measured in Nozzles

3.5

Suction and Discharge Volumetric Efficiency

The effective suction volume is the amount of gas drawn into the cylinder during the expansion stroke. The effective discharge volume is the amount of gas expelled during the compression stroke. These values are characterized by the Volumetric Efficiency. Volumetric Efficiency (EV or VE) is defined as the ratio of the volume of gas drawn into or expelled from the cylinder (at suction or discharge pressure and temperature) to the swept volume of the piston. Theoretical or ideal EVs (suction) and EVd (discharge) may be calculated using the equations below. The calculated EVs has an implicit assumption that gas is induced at suction temperature. The temperature actually rises during the suction intake, due to heat transfer from the cylinder and mixing of the suction gas with the residual gas remaining in the

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clearance of the cylinder. The temperature effects, as well as effects due to piston rings, packing rings, and valve leaks, are accounted for in the theoretical calculation with a loss factor (L). The losses can only be determined empirically (measured in test). For transmission compressors or low pressure ratio compressors, the losses usually range from 1-3%. At high pressure ratios, these losses are from 5-10%.

p EVs = 100 - CL% * d p s

EVd =

p 100 - CL% * d p s pd ps

1 k

- 1 − L 1 k

1 k − 1

−L

(3-14)

(3-15)

The measured volumetric efficiency is defined by the valve opening events, toe pressure, or measured nozzle pressure. The valve openings can be determined from the measured PV diagram. Valve openings are assumed to occur when the cylinder pressure crosses the pressure just outside the valve (pressure in the suction or discharge nozzles). The suction and discharge valve openings are labeled in Figure 3-3. For example, if the suction valve opens at 25% volume (ODC is 0% volume) on the expansion stroke, then the suction volumetric efficiency is 75%. Also, if the discharge valves open at 60% volume on the compression stroke, then the discharge volumetric efficiency is 60%. 3.6

Driver Power and System Efficiency

If the overall performance is being evaluated (including the driver and compressor), it is important to determine the driver power during performance testing. Engine During performance testing of reciprocating compressors with gas engines, the flow rate of the fuel is measured with a flow meter. Also, the gas composition of fuel is measured. From the gas composition, the Low Heating Value (LHV) of the fuel can be calculated using EOS. The equations below are used to calculate the input power from the fuel and the engine brake thermal efficiency. The BHP is determined from the compressor ICHP using a calculated, measured, or assumed mechanical efficiency of the compressor. If the compressor is separable (usually high speeds), then the power can be measured with a torque meter at the coupling. The power input to an integral engine (slow speed) would have to be determined with the ICHP. More details on performance test of engines can be found in PTC 17, “Reciprocating Internal – Combustion Engines.” •

Pin = m fuel * LHV

ηe =

BHP Pin

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(3-16) (3-17)

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BHP =

ICHP

ηm

(3-18)

Electric Motor If an electric motor is driving the compressor, then the applied voltage and phase currents must be measured to determine the absorbed power. Typically an ammeter will measure the current draw of the motor. If these values are measured, then the power can be determined from the first equation below for each phase. The power factor should be measured at the conditions that the performance test will be conducted. The power factor provided in the manufacturer literature was determined for a steady state load. Electric motors driving reciprocating compressors will experience a pulsating load, which causes a shift in the power factor. The total power is determined by summing the power of the phases. The motor efficiency, ηmo, can be calculated using Equation 3-17 and substituting the input power to the engine with input power to the motor. Methods of determining motor absorbed power can be found in a relevant standard, such as IEEE 112, “Test Procedure for Polyphase Induction Motors and Generators” and IEEE 115, “Test Procedures for Synchronous Machines.”

Pin = 0.001341* i * e * Pf

(3-19)

System Efficiency The system efficiency can be estimated from the ratio of the compressor gas power (power transmitted from compressor to gas through compression) and the power input into the compressor driver, as shown in the equation below. For the PV Card method, compressor power is calculated by adding the ICHP of each cylinder end together. For the Enthalpy Rise method, if the power is measured across the compressor, then the power is calculated with the mass flow rate of the gas and the enthalpy difference. If each individual cylinder is tested, the power for each cylinder will be added together to obtain the total power. The system efficiency will be lower than the compressor efficiency since it also takes into account the engine efficiency.

η sys = 3.7

Pcomp P in

η isenη mη e

(3-20)

Equations of State

In the field performance test of the compressor, the correct determination of the thermodynamic properties of the gas (such as enthalpy, entropy, and density) plays a critical role. The measured quantities (such as pressure, temperature, and composition) are used as inputs to an EOS to determine thermodynamic properties. The enthalpy change is used to determine the head and the isentropic or polytropic efficiency of a compressor. The choice of the EOS used in calculating enthalpy and density affects the accuracy of the results and needs to be considered in the uncertainty calculation. The possible equations of state commonly used in the gas industry are: Redlich-Kwong (RK), SoaveRedlich-Kwong (SRK), Peng-Robinson (PR), Benedict-Webb-Rubin (BWR), Benedict-Webb-RubinStarling (BWRS), Lee-Kesler-Plocker (LKP), and AGA-10. The final selection of the EOS to be used in the field test should depend on the applicability of the particular EOS model to the gas and temperatures encountered along with the process of interest. EOS model accuracy may depend upon the application range and the gas mixture at the site (Sandberg, 2005; Kumar et al., 1999).

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The consistent application of the EOS throughout the planning, testing, and analysis phases of the field test is imperative. The choice of which EOS to use must be agreed upon before the test. It is recommended to use the EOS for test data reduction that was also used for the performance prediction. The selection of a particular EOS can have an important effect on the apparent efficiency and absorbed gas power. An added uncertainty of 1 to 2% can be incurred on the performance results if the EOS is inconsistently applied (Kumar et al., 1999). The formulation of the various EOS is given in Appendix C. 3.7.1

Application of Equation of State

Generally, it is not possible to select a “most accurate” EOS to predict gas properties, since there is generally no “calibration norm” to test against for typical hydrocarbon mixtures. All the frequently used EOS models (RK, BWR, BWRS, LKP, SRK, and PR) can predict the properties of hydrocarbon mixtures accurately below 20 MPa for common natural gas mixtures. Outside this pressure range, deviations between the EOS models of 0.5 to 2.5% in compressibility factor Z are common, especially if the natural gas contains significant amounts of diluents. Because derivatives of the compressibility factor (Z) must be used to calculate the enthalpy rise, the enthalpy rise deviations can be larger than the compressibility factor for different EOS. Table 3-1 provides usage suggestions for the various EOS models based on application. For normal hydrocarbon gas mixtures (such as pipeline quality gas) with diluent content (combined CO2 and N2) below 10%, all equations of state shown in Table 3-1 provide accurate results. Beyond this range, Table 3-1 provides some general recommendations on the most applicable EOS. Table 3-1. Suggested Applications for Equation of State Usage Type of Application

Typically Used EOS Model

Typical hydrocarbon gas mixture, standard pressures and temperatures, low CO2 and N2 diluents (< 6% total). Air mixtures.

All EOS Models may be used for this application: Redlich-Kwong (RK), Soave-Redlich-Kwong (SRK), Peng Robinson (PR), Benedict-Webb-Rubin-Starling (BWRS), Benedict-Webb-Rubin (BWR), Lee-KeslerPlocker (LKP), AGA-10

High-pressure applications (>3000 psi).

BWRS, BWR, AGA-10, LKP

Some CO2 and N2 diluents (6-10%).

BWRS, BWR, AGA-10, LKP

High CO2 and N2 diluents (10-30%) and/or high hydrogen content gases.

BWRS, BWR, AGA-10, LKP

High hydrogen content gases (>80% H2)

PR, LKP, SRK

Non-hydrocarbon mixtures: ethylenes, glycols, carbon dioxide mixtures, refrigerants, hydrocarbon vapors, etc.

Specific EOS model designed for chemical mixture will result in greater accuracy. The literature should be consulted for the particular gas and application.

A further comparison of the various EOS models is provided in Appendix D. The calculated enthalpies for various EOS models at different states are used to calculate isentropic efficiency and compressor power for two compressor operating cases.

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4.

DATA COLLECTION PROCEDURES

In reciprocating compressor performance testing, the most common method used is the PV Card method. This method utilizes a pressure measurement inside the cylinder along with a piston position measurement to develop a pressure-volume curve for each cylinder end. From this, the compressor cylinder end’s indicated horsepower can be calculated. The isentropic efficiency can be calculated with the measured horsepower and calculated theoretical or isentropic horsepower. The second method is the Enthalpy Rise method. This is mostly used with centrifugal compressors but can be useful with reciprocating compressors as well. This method takes temperature and pressure measurements on the suction and discharge sides of the compressor. Using EOS relationships, the enthalpy is calculated at each location. With a mass flow rate measurement, the total power can be calculated with the measured enthalpy difference. This method can also be used to measure each cylinder’s efficiency. The pressure and temperature measurements would be made at the suction and discharge nozzles. Both methods are beneficial, depending upon the objectives of the performance measurement. For example, if the objective of the test is to obtain an overall estimate of the efficiency of the compressor package, the Enthalpy Rise method would be beneficial. In this case, it would require the minimum number of measurements (suction and discharge line pressure and temperature) to obtain the efficiency. If the user wanted to complete a diagnostics type performance test, studying each individual cylinder, the PV Card method would be more useful. These two methods can also be utilized in conjunction with one another. Discussed below are the details that should be considered with each method. 4.1

PV Card Method

The PV Card method is commonly used for reciprocating compressor performance testing. In general, this method is used to assess the performance of individual cylinder ends. The results can then be used to evaluate the performance of the compressor as a whole. 4.1.1

Description of PV Diagram

With the use of the PV Card method, it is essential to have a clear understanding of the PV diagram. This section discusses the physical operation of the compressor in relation to the PV diagram. Figure 4-1 shows a typical PV diagram with labels indicating different important parameters. Some of these parameters are discussed below. Line 4-1: The suction valve opens at Point 4, as the piston travels toward IDC (for the crank, or frame end of a compressor cylinder), the volume in the cylinder increases, and gas flows into the cylinder. The pressure inside the cylinder is slightly less than the pressure outside the cylinder. This small differential pressure holds the suction valve open. The suction valve closes as the piston reaches IDC and changes direction at Point 1. The differential pressure across the suction valve decreases to zero as the piston reaches IDC. The pressure force holding the valve open becomes less than the spring force of the valves and the suction valve closes. Line 1-2: The piston reverses directions and the volume inside the cylinder starts to decrease. As the volume of the contained gas continues to decrease toward Point 2, the pressure increases. The shape of the compression line (Line 1-2) is determined by the many different factors. In a measured PV diagram, the shape is affected primarily by the clearance volume, the pressure ratio, and the gas composition. A theoretical curve is determined with clearance volume, pressure ratio, and calculated constant compression exponent. For an ideal gas and adiabatic process (no flow of heat to or from the gas being

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operated on), the compression exponent is the isentropic (constant entropy) exponent, which is equal to the ratio of specific heats of the gas being compressed.

Figure 4-1. Typical PV Diagram

Line 2-3: At Point 2, the pressure inside the cylinder has become slightly greater than the pressure outside the cylinder. The resulting differential pressure across the discharge valve causes the valve to open, allowing gas to flow out of the cylinder. The volume continues to decrease toward Point 3, maintaining sufficient pressure differential across the discharge valve to hold it open. At Point 3, the piston reaches ODC (for the crank, or frame end of a compressor cylinder) and reverses direction. The differential pressure across the discharge valve decreases to zero as the piston reaches ODC. The pressure force holding the valve open becomes less than the spring force of the valves and the discharge valve closes. Line 3-4: The gas trapped in the cylinder expands as the volume increases toward Point 4. At Point 4, the gas pressure inside the cylinder becomes less than the pressure outside the cylinder, creating a differential pressure which opens the suction valves. The cycle then starts over again. The shape of the expansion line (Line 3-4) is dependent on the same factors as the compression line. 4.1.2

Measurements

The PV Card method requires the measurements listed below, and shown in Figure 4-2, to calculate the compressor power and efficiency. Depending upon the requirements set for the performance test, not all of the measurement locations shown in Figure 4-2 are required. 1.

Cylinder pressure

2.

Piston position (crank-shaft rotational position)

3.

Suction and discharge temperatures

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4.

Gas composition

5.

Barometric Pressure

6.

Compressor geometry (ex. Bore diameter, clearance, etc.)

7.

Engine fuel gas flow rate or electric motor power consumption (for overall system efficiency)

8.

Fuel gas composition (for overall system efficiency)

The cylinder pressure and piston position are used to form the pressure-volume curve. The area inside of this curve, which is determined by numerical integration, gives the indicated power for the cylinder end. The total brake horsepower consumed by the compressor can be estimated by summing the individual cylinder end indicated horsepower and by applying an assumed mechanical efficiency from cylinder to crankshaft. The suction and discharge temperature, gas composition, and toe pressures from the measured PV diagram are utilized to calculate the theoretical isentropic power for the cylinders. This theoretical power is then used to calculate the isentropic efficiency of each cylinder as well as the compressor. Barometric pressure should be measured in order to correctly calculate absolute pressure from measured gage pressure. Compressor geometry will be reported in manufacturer literature, but it is possible that over the life of the compressor changes will have been made. Current changes in compressor dimensions, such as bore diameter (especially on older compressors) and if additional clearance has been added, should be documented and possibly measured. The engine fuel gas flow, electric motor power consumption, and fuel gas composition are required, if the overall system efficiency is being evaluated.

Figure 4-2. Location of Test Instrumentation for PV Card Method

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4.1.2.1 Cylinder Pressure The cylinder pressure is a time varying cylinder end pressure that is a function of the piston’s positions in the cylinder. It is measured with a pressure transducer, which has a high enough frequency of response to track the dynamic pressure in the cylinder without phase delay. Optimal cylinder pressure measurement is accomplished with a pressure transducer mounted flush with the inside of the cylinder wall, so that the transducer diaphragm will sense the pressure directly in the cylinder chamber without the distorting effects cause by indicator passages. Typically, ports are drilled in the side of the compressor cylinder for pressure transducers. These are referred to as indicator ports. Pressure transducers that fit into larger indicator passageways are available. This would allow the transducer to be flush-mounted to the cylinder bore. When the transducers are not flush-mounted, the ports will usually have an indicator valve (example shown in Figure 4-3), such that the pressure transducers can be installed without shutting down the compressor. Externally-mounted pressure transducers are an effective method for moving transducers during testing, but this also can lead to pressure variations at the transducer that are not representative of the pressure in the cylinder. These are referred to as channel resonances and channel attenuations.

Figure 4-3. Pressure Transducer Installed on Compressor Cylinder with Indicator Valve

Channel Resonance Installation of pressure transducers to monitor cylinder conditions on reciprocating compressors can give rise to an acoustic resonance phenomenon known as Helmholtz or channel resonance. The channel resonance is a function of the geometry of the indicator port and valve, and it occurs due to an excitation of the quarter-wave acoustic length resonance of the gas passage between the cylinder interior and the pressure transducer. This effect can superimpose a large amplitude, periodic pressure wave on the true cylinder pressure and can result in a distorted pressure-volume diagram. This resonance will typically show up on the expansion and compression lines, as well as when the suction or discharge valves are

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open. In high-speed compressor cylinders, this may significantly add to the peak differential pressure measured in the cylinder, which can affect the accuracy of rod load and pin reversal calculations. The resonance or waves will not be as apparent on high-speed compressor expansion and compression lines as on a low-speed compressor PV diagram. However, the resonance is still present, if the sensors are not flush-mounted. Since the resonance is sinusoidal in nature, it can be removed without significantly affecting the measured indicated horsepower. This is assuming that it can be deleted without causing a phase shift in the original PV diagram. Figure 4-4 and Figure 4-5 show examples of PV diagrams taken with the presence of channel resonance on a high-speed compressor. Figure 4-6 and Figure 4-7 show channel resonance on a low-speed compressor.

Figure 4-4. PV Diagram with Channel Resonance Present – Uncorrected High-Speed Compressor (950 RPM)

Figure 4-5. PV Diagram with Channel Resonance Present – Corrected High-Speed Compressor (950 RPM)

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Figure 4-6. PV Diagram with Channel Resonance Present – Uncorrected Low-Speed Compressor (330 RPM)

Figure 4-7. PV Diagram with Channel Resonance Present – Corrected Low-Speed Compressor (330 RPM)

There are several ways to mitigate the effects of channel resonance. One method is to flush-mount the transducer in the cylinder. This is not always practical since it eliminates the use of a valve. Without the valve, the transducer cannot be moved while the compressor is in operation, and it cannot be isolated to check the transducer calibration. Pinching the transducer cutoff valve is not an acceptable method, because it will introduce an unacceptable horsepower measurement error. During the selection and purchase of the compressor, the user should consider the indicator port geometry. The port should be made as short as possible, with a large diameter and a straight through ball valve for the indicator valve. The volume of the gas in the indicator port to the transducer should be minimized. Following these recommendations will ensure that the resonance frequency is as high as possible for the channel.

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A practical method of eliminating the channel resonance after the measurement has been taken is through mathematical filtering. Mathematical filtering techniques can be effective, if the channel resonance frequency can be identified. Once the frequency is determined, then the application of a non-phase shifting low pass filter is recommended. This will improve the accuracy of the suction and discharge toe pressure picks and the identification of the suction and discharge volumetric efficiencies while not detrimentally affecting the indicated horsepower measurement. Another method for removing the resonance is with a linear acoustic transfer function developed under GMRC funding. This transfer function was developed specifically for removing channel resonance on low speed, low ratio compressors. The transfer function and phase is determined with Equations 4-1 and 4-2 below. The frequency and damping factors can be determined with an FFT (Fast Fourier Transform) analysis or computing the log decrement. This transfer function is only applicable to low speed/low ratio compressors. High-speed/high ratio compressors have a greater phase lag during the compressor process due to high channel restrictions, which makes the linear transfer function inadequate. A non-linear transfer function developed under GMRC research funding is proposed by Harris and Edmund in their paper titled, “Performance Measurements of High-Speed/High Ratio Reciprocating Compressors” (1998).

ω ∑ i =3, 5, 7 ,... i n

TRF = TRF +

2 1−ω

(

)

2

2

2 1/ 2

ω + 2ζ i

ω ζ 2 n i −1 i φ (ω ) = φ (ω ) + ∑ tan ω 2 i =3, 5, 7 ,... 1 − i

(4-1)

(4-2)

Experience has indicated that effective channel resonance elimination can be made with less than -1% indicated change in the measured horsepower on a high-speed compressor cylinder and less than -0.5% change in the measured horsepower on a low-speed compressor cylinder. The change in measured horsepower refers to the difference between ICHP before and after the channel resonance has been removed. Horsepower changes larger than this would indicate that more than channel resonance is being eliminated or the method has introduced a phase shift into the raw data. Filtering is generally incorporated into digital compressor performance analyzers. Channel Attenuation Channel attenuation develops in environments with rapid (real) changes in pressure. It is common with high-speed compressors, heavy gases, and small diameter measurement channels. It is directly related to the resistance of the channel to pressure changes. A high resistance or restrictive channel will prevent the gas density from changing fast enough in the channel to match the real transient conditions. The resulting pressure measurements will be distorted. Typically, this error is identified by distortions on the compression and expansion lines on the PV diagram. The most effective method of avoiding this phenomenon is to have large diameter indicator ports or to flush mount the transducers. More information on calibration, installation, and use of pressure transducers is in Section 6.1.

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4.1.2.2 Piston Position The piston position is needed for calculation of the instantaneous cylinder volume. There are many factors that can affect this measurement. Encoders attached to the crankshaft are typically used to make this measurement. Encoders with higher resolution may provide less uncertainty. The use of an encoder is based on ideal kinematic relationships to crankshaft rotation. The effects of crankshaft twisting and deflection in the crankpin and crosshead bearings can cause deviations from this ideal relationship. In some instances, a key phasor may be used to indicate the position of all pistons. This can have a very high uncertainty due to variations in rotational speeds during each revolution. The pressure measurement may not correlate with the volume measurement correctly with the use of a once per turn device, such as a key phasor, optical, or magnetic pick-up. The best practice is to use an encoder with resolution of 360 or greater. Because of this, the use of a once per turn device is not discussed in the power, efficiency, or uncertainty calculations. ODC Determination In order to have the correct reference of pressure to piston position, the location of ODC must be found and synchronized with the encoder. If the ODC determination is off, the horsepower will not be correct and it will appear as if the valves are opening and closing at the wrong time. A 1-3 degree inaccuracy in ODC determination can cause a 3-5% error in horsepower. Figure 4-8 shows the difference in a PV diagram with different ODC errors. In this example, a 4.9 deg error leads to approximately an 8% error in the horsepower. More information on the use of encoders and determination of ODC is in Section 6.5. 90 Original 8.73 HP 1.4 deg 8.54 HP (-2.2%)

80

4.9 deg 8.04 HP (-7.9%)

Pressure (psig)

70

60

50

40

30 0

50

100

150

200

250

300

Volume (in^3)

Figure 4-8. PV Diagram with Varying ODC Measurements

4.1.2.3 Suction and Discharge Temperature and Gas Composition The suction and discharge temperature and gas composition are needed for calculating the theoretical PV diagram from the EOS. The temperature is usually measured outside the cylinder (in the nozzle). This temperature will be different than the actual temperature inside the cylinder during suction and discharge due to several factors: in most cases (some exceptions are Helium or Hydrogen) the pressure drop across the valves causes a decrease in temperature, heat is transferred from the cylinder to the incoming gas, and the suction gas mixes with the residual gas in the cylinder. The heat transfer is typically small for low compression ratios, but can be significant for higher compression ratios and non-cooled cylinders. The

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factor that has the most significant effect is the mixing of the suction gas with the residual gas. The resulting suction temperature due to this effect can be calculated using simple thermodynamic relationships. Temperature measurements in the nozzles will have high variations due to pulsating flow. The measurement device should be installed in a thermowell to damp out the pulsation effects. More information on temperature measurements can be found in Section 6.2. 4.1.2.4 Driver Fuel Gas Composition, Fuel Gas Flow Rate, and Motor Power These measurements are required to determine the power developed by the gas engine or electric motor to meet the compressor demand. The gas composition will be measured with a gas chromatograph to determine the composition of the fuel gas. It will also serve to verify that the gas composition does not change significantly during the performance tests. The gas composition will be used with EOS to determine the fuel gas properties. The fuel flow rate will be used to determine the amount of energy being supplied to the driver. This is measured with a typical flow meter such as an orifice meter. With this value, the overall efficiency of the driver/compressor system can be determined as shown in Section 3.6. This efficiency will include the efficiency of the driver, compressor, and mechanical losses. The motor power is found with a measured voltage and current. Typically, an ammeter will measure the current draw of the motor. This, along with the power factor and efficiency of the motor, can be used to calculate the power absorbed. As with the gas engine, the overall efficiency of the driver/compressor system can be determined, as shown in Section 3.6. 4.1.3

Capacity and Volumetric Efficiency Calculation

Theoretical equations are presented in Section 3.1 for the calculation of capacity. Several considerations should be taken when completing these calculations to ensure that the error is minimized. Several of the parameters in the equations presented are found in manufacturer literature, directly measured, or calculated from EOS with the measured values. The suction and discharge volumetric efficiency is a variable that needs to be calculated from ideal equations or determined from the PV diagram. The theoretical EV may be used for operation or control, so it is important that the theoretical and measured EV are close. The theoretical EV may be different from the measured EV due to an unhealthy cylinder, restrictive flow, variations in gas composition, etc. It is important that any performance issues, such as leaks, be corrected before taking performance data. However, if the difference between the theoretical and measured EV are due to permanent physical phenomena, such as flow restrictions through valves or gas passages, then the losses can be accounted for with a loss factor in the theoretical equations as shown in Equations 3-14 and 3-15. As shown in Section 3.4, the percent clearance (%CL) is used within the calculations of both suction and discharge volumetric efficiency. Percent clearance is a value usually reported in manufacturer literature. The actual %CL may be different due to manufacturing tolerances or aftermarket capacity control device installation. The manufacturer’s stated %CL will usually be within 2-3% of the actual value without aftermarket devices. The %CL needs to be determined for each cylinder end either based on manufacturer nameplate values and aftermarket devices or measured values. Clearance pocket geometry may cause a variation between actual and effective clearance volume. For example, if there is a small throat to the clearance pocket, the full pocket volume may not achieve discharge pressure during the compression stroke. The variation in volumetric efficiency gives the appearance of an effective clearance that varies from the measured or stated clearance. The effective

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clearance can be determined from the PV diagram. Analyzers are available that determine the effective clearance value. Incorrect clearance will lead to error in the volumetric efficiency, horsepower, and flow calculations. 4.1.4

Uncertainty

Listed below are the potential sources of uncertainty in the PV Card method. The effect of these individual uncertainties on the results of the performance measurements will be discussed in Sections 6 and 7.

4.1.5

•

Pulsations

•

AC or Electrical Noise

•

Sensor Accuracy

•

Sensor Calibration

•

Channel/Helmholtz Resonance and Attenuation for Pressure Transducers

•

Temperature Effects on Pressure Measurement

•

Valve Effects

•

ODC Determination

•

Unsteady Operation Conditions

•

Theoretical Calculations/EOS

Compressor Efficiency

The actual measurement of the PV diagram provides a curve from which the indicated compressor horsepower can be calculated. In order to use this data to calculate an isentropic efficiency of the compressor cylinder, the theoretical PV diagram must be generated. This is done using the results of the measurements, compressor geometry, and EOS calculations. The process of calculating the PV diagram is described in more detail in Appendix B. Once the theoretical PV diagram is generated, then the isentropic efficiency of the compressor cylinder end can be calculated using the equations detailed in Section 3.2. Commercial analyzers automatically develop the theoretical PV diagram and calculate the isentropic ICHP. 4.2

Enthalpy Rise Method

The Enthalpy Rise method is based on a relationship of the energy contained in the gas at the suction and discharge of the compressor. This method uses temperature and pressure measurements at the suction and discharge to calculate the enthalpy. The enthalpy difference multiplied by mass flow rate gives the power consumed by the compressor and can be used with theoretical calculations to obtain the isentropic efficiency. This method is good at assessing the overall performance of the compressor. It can also be used to determine the performance of individual cylinders. 4.2.1

Measurements

The Enthalpy Rise method requires the measurements listed below to calculate the power and efficiency of the compressor and as shown in Figure 4-9.

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1.

Suction and discharge pressures

2.

Suction and discharge temperatures

3.

Gas flow rate

4.

Gas composition

5.

Driver fuel gas flow rate or electric motor power (for overall system efficiency)

6.

Fuel gas composition (for overall system efficiency)

The suction and discharge pressures and temperatures are used with the Equations of State (EOS) to calculate the enthalpies. The gas composition is required for the EOS calculations. The suction pressure and temperature are used to calculate the entropy at the suction condition. This entropy with the discharge pressure is used in the EOS to calculate the isentropic enthalpy at the discharge. The enthalpy difference at the suction and discharge conditions is used to calculate power and efficiency. The flow rate of the gas is used with the enthalpy difference to calculate total power. In the Enthalpy Rise method, the driver fuel gas flow, electric motor power, and fuel gas composition for determination of overall efficiency will have the same considerations as the PV Card method (refer to Section 4.1.2.4).

Figure 4-9. Location of Test Instrumentation for Enthalpy Rise Method

4.2.1.1 Suction and Discharge Temperatures The suction and discharge temperatures are required to calculate the enthalpy from the EOS. This is measured with either a thermocouple or RTD. There are several locations that can be used for measuring the temperature. Consideration should be given to the fact that both the temperature and pressure should be measured for this method. It may not be feasible to measure each of these in the same location due to space constraints. The optimal temperature measurement location is on the nozzles near the cylinders as shown in Figure 4-9. When determining an isentropic efficiency, it is important to place the pressure and temperature measurements in locations that will best represent isentropic compression. Since an isentropic process does not have any heat transfer (adiabatic), placing the sensors before or after vessels

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where heat transfer could occur should be avoided. However, the desired measurement location is often not accessible. The temperature measurements may end up being made outside of the suction and discharge bottles. If this is the case, then the heat losses should be accounted for in the efficiency calculation. A methodology is presented in Appendix H that can be used to determine heat transfer effects. In order to avoid this extra computation, it is easiest to place the temperature sensors in the nozzles. The nozzle region has pulsations, which causes an unsteady temperature measurement. The temperature sensor should be placed in a thermowell to damp out the effects of pulsations. If a thermowell is used, adequate time needs to be allowed during the test for the thermowell to properly heat soak. More information is presented in Section 6.2 on temperature measurements. The heat losses due to water cooling of the compressor cylinder should be considered in the isentropic efficiency calculation. The equations below show in general how these are accounted for in the compressor power and isentropic efficiency where the component energy includes the bottles, nozzles, and piping and the cooling energy includes cylinder cooling through a water jacket. Further information is provided in Appendix H on methods to account for these losses.

P = m(hd − hs + q components + q cool ) •

η isen =

hd ,isen − hs hd − hs + q components + q cool

(4-3)

(4-4)

4.2.1.2 Suction and Discharge Pressures The suction and discharge pressures are also required for the enthalpy calculation with the EOS. The objective of the tests dictates where the transducer should be installed. If the goal is to analyze the compressor package, then the transducers would need to be placed outside the bottles. If individual cylinders are the subject of interest, then the pressure needs to be measured in the nozzles. The location of measurement affects the type of pressure transducer that should be used. Before the first set of bottles, the flow may be steady enough for the use of a static pressure transducer. If the pressure is measured on the nozzles right before the cylinder, a dynamic pressure transducer would be needed due to the pulsating flow. With regards to instrument drift, dynamic pressure transducers have a higher inaccuracy over time compared to static pressure transducers. However, by calibrating dynamic transducers just prior to the performance test they can achieve sufficient accuracy during the test. If compressor cylinder (as opposed to package) performance is being analyzed and the pressure measurements are taken either before or after the bottles, then the pressure losses for each pulsation control chamber needs to be taken into account. If pressure measurements are taken in the nozzles, or in an area of high pulsating flow, then the resulting pressures need to be time averaged. An average pressure needs to be obtained before the pressure is used with the EOS to determine the enthalpy. Further details on pressure measurements are presented in Section 6.1. 4.2.1.3 Gas Flow Rate Accurate gas flows are required to assure accurate power calculations. There are multiple types of flow meters that can measure the flow rate. The accuracy of the flow measurement is dependent upon the level

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of pulsations. Pulsations adversely affect the flow measurement. The flow meter should be placed in a location with minimal pulsations. This is usually at a location far upstream or downstream from the compressor, typically before the suction bottles or after the discharge bottles. The bottles on the reciprocating compressors are acoustic filters which decrease the pulsation levels. The effects of pulsations and selection of the flow meter are discussed in more detail in Section 6 of this guideline. Custody transfer meters may be available for flow measurement. These can only be used if the compressor being tested is the only one running and no gas is being consumed or lost at the station by any other equipment. The flow rate may also be obtained from calculations if the PV Card and Enthalpy Rise methods are being used in conjunction with one another. 4.2.1.4 Gas Composition The process gas composition is needed for the calculation of the enthalpy from the EOS. The gas composition is directly used to determine the properties of the gas, such as the isentropic exponent, compressibility, density, and speed of sound. The gas composition should be measured continuously during the test. The sample rate of the gas composition will depend upon the cycle time of the gas chromatograph. Gas chromatographs are available with four-minute cycle times for an analysis up to C6+. This will give the most accurate composition for the EOS calculations and also the multiple composition measurements will be used to analyze the steadiness of the gas composition during the test. A large variation in gas composition could make the test invalid. All components contributing 0.1 mol percent or greater to the composition should be measured and recorded. 4.2.2

Uncertainty

Listed below are the potential sources of uncertainty in the Enthalpy Rise method. The effect of these individual uncertainties on the results of the performance measurements will be discussed in Section 7.

4.2.3

•

Pulsations

•

AC or Electrical Noise

•

Sensor Accuracy

•

Sensor Calibration

•

Number of Sensors

•

Calculation of Enthalpy from EOS

•

Heat Loss on Bottles, Nozzle, Piping

•

Cooling of Compressor Cylinders

•

Mass Flow Measurement

•

Unsteady Operating Conditions

•

Theoretical Calculations/EOS

Compressor Efficiency

For the Enthalpy Rise method, the isentropic efficiency is calculated with the enthalpy differences from experimental measurements and calculated isentropic relationships. Terms to account for heat losses and cooling are included depending on where the measurements are taken. The equation used to calculate the isentropic efficiency is shown above in Section 4.2.1.1.

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4.3

PV Card and Enthalpy Rise Method

Depending on what the objectives of the performance tests are, either of the methods described above can be used. In some instances, both methods may be needed in combination with each other. The Enthalpy Rise method provides a good overall assessment of the compressor or the station. The PV Card method could be used with this to focus in on the performance of individual cylinder ends of a compressor (if the performance of not all of the individual cylinder ends is desired). The Enthalpy Rise method can also be used to assess individual cylinders. For example, a user would like to measure the overall efficiency of the compressor, but also test a few cylinders of interest for diagnostics. In this case, the PV Card method would be used to diagnose the cylinders of interest, but the Enthalpy Rise method could be used to assess the overall compressor efficiency. This would prevent the user from having to instrument every cylinder with pressure transducers. 5.

TEST PREPARATION

A general procedure for a field test is outlined in Appendix A. Many of the individual tasks are discussed below. A field test agenda or plan should be prepared prior to the test as this is an essential part of test preparation. The optimum time to start planning for field testing is prior to the design of the compressor packages and compressor station. The first step in the planning process is to determine the scope of the field test and what level of uncertainty is desired for the measurements relative to budget constraints and any contractual performance guarantees. Based upon the targeted uncertainty, temperature, pressure, and flow measurement points, methodologies can be defined for the package and station design that will ensure that the desired results can be achieved. If a field test is going to be performed to validate the performance of a new installation, the purchaser should specify where in the process stream that the design pressures and temperatures will be measured for validation purposes—as well as the EOS that will be used. For example, the locations could be at the inlet and outlet flanges of a compressor cylinder or at the inlet and outlet flanges of the compressor package piping. Specifying this requirement is important for two reasons. One is to ensure that the package and station design includes the necessary connection points for mounting test instrumentation without having to replace or rely on package instruments. The second is more of an application design issue than it is a test issue. Nevertheless, it is an issue that, if overlooked, could result in the compressor not meeting the purchaser’s requirements. If the design and validation points are going to be in locations other than the compressor cylinder flanges (such as package limits), then the pressure losses predicted from any acoustical study need to be included in the compressor performance calculations. While this may appear to be a trivial point, there have been industry cases where erroneous pressures losses were used during compressor/driver selection and the expected performance was not achieved. The test plan should include field conditions and equipment layout, instruments to be used and their location, method of operation, test safety considerations, and the pressure, temperature and flow limits of the facility. Piping and station layouts should be made available. Any deviations from normal operation that may be necessary to conduct the test should also be provided. The field test agenda should include a discussion of the following: 1.

The method of data reduction.

2.

The selected approach for determining the test uncertainty.

3.

The acceptance criteria (specified in terms of maximal uncertainty allowable).

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4.

The EOS to be used for all calculations in the test.

Test preparations should also include a discussion on possible operating conditions and operational limitations. In many cases, a specified operating point can only be maintained for a limited period of time (for example, because the pipeline operation depends upon the tested package) or at fixed ambient conditions. The requirements for installation of test instrumentation need to be communicated early (even during construction of the station), because instrumentation is part of the overall station design. The selection and calibration of the test instrumentation is important. Generally, the instruments supplied for monitoring and protection of the packages are not accurate enough to meet the stringent requirements necessary for a field test (redundant measurement requirements, small uncertainty margins, detailed sensor location placement, and proper flow measurement). Whenever possible, calibrated laboratory quality instrumentation should be installed for the tests (refer to Section 6). The accuracy of the instruments and the calibration procedure should be such that the measurement uncertainty is reduced to the best attainable uncertainty under ideal conditions (see Section 7). 5.1

Pre-Test Meeting

A meeting between the test engineer, the parties involved (supplier, operator, etc.) and the customer to discuss test procedures and the situation on-site should be conducted in advance of the performance test. The site P&ID, Site Layout, and Mechanical Installation Drawing diagrams should be obtained (if available) and used in preparation for the performance test. During the pre-test meeting, the parties should reach an agreement on the test purposes, test procedures, safety requirements, the availability of full bore shut-off valves on compressor cylinders, responsibilities during the test (including who has authority to make quick decisions if problems arise during testing), availability of necessary operating conditions, and acceptance conditions. 5.2

Pre-Test Operation and Instrumentation Checkout

The following items should be checked during the pre-test checkout: •

The test engineer should verify that the unit has been proven suitable for continuous operation and in good mechanical condition.

•

A mechanical assessment should be performed on the compressor before the performance test is conducted. This should include inspection of suction and discharge valves, piston rings, and packings. If these are found to have wear, they need to be replaced before the performance test. If the valves cannot be replaced for any reason, the valves should be evaluated for degradation. An estimation should be made of their affect on the performance of the compressor. Compressor valves that have high wear will affect the power and efficiency of the compressor. A mechanical condition analysis using an engine/compressor analyzer, performed at a highest achievable compression ratio, could be substituted for a physical inspection.

•

If the driver performance will be measured during the test, then a mechanical assessment of the driver is needed as well. The user should ensure that the engine is in good working order and tuned before the performance test is conducted.

•

Sufficient gas should be available for the anticipated flow and conditions for the duration of the test.

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•

If an online system is installed with cylinder pressure measurements, some planning, discussion, and agreement should be reached on how the field test instruments will be installed with the existing instrumentation. Consideration should be given as to how the installation of the instrumentation will affect the operation. Will new vibrations result from the installation of the instruments or new fittings and valves?

•

All instrumentation should be calibrated in the range in which it will be operated during the test. Check all instrument readings (temperature, pressure, flow, and speed) to assure that the sensors are functioning properly. Verify data acquisition system operation prior to starting the field performance test.

•

All RTD’s or thermocouples used in the test should use spring load type fittings, or when necessary, the thermowells will be serviced with oil or other approved heat transfer material. Accuracy must be within ±0.1 deg F.

•

If thermowells are used during the test and a large portion of the thermowell is exposed to the atmosphere, the area around the exposed portion should be insulated to preclude the ambient air from affecting the temperature reading.

•

Check insertion depth of thermowells (see Table 6-2).

•

Where pressure taps involve tubing runs, the tubing should be checked for leaks.

•

The proper number of capable personnel should be on site to ensure that all the data can be recorded in a reasonable amount of time.

•

Check the fixed clearance. If testing a new compressor in the field, the manufacturer’s supplied value for fixed clearance may be used, but if testing an existing compressor, then this value needs to be checked. The effective fixed clearance can vary from the design fixed clearance because of the influence of cylinder operational problems, compressor valve leakage, piston ring leakage, pulsation effects, valve losses, ineffective cylinder pockets, etc. In addition, the measured clearances may vary from design clearances if the pocket shutoff valves are partially opened or closed. ♦ There are several methods that can be used to measure the compressor cylinder clearance. The first is by filling the cylinder with a metered volume of liquid. This method can be very difficult in the field due to leaks past piston rings and out of discharge valves. It usually involves filling the entire cylinder bore and using valve blanks. Another method is using the effective volume calculated by the PV analyzer. However, this method is subject to error due to valve leaks, piston ring leaks, heat exchange within the cylinder, error in ODC position, and restrictive flow paths to clearance pockets. The actual and effective clearances are not equal due to error effects mentioned above. This method can be effectively used if the uncertainty in the measurement is accounted for.

•

Prepare data acquisition system by installing any required programs or generating data collection protocols. If possible, use a data acquisition system that will automatically calculate the results of the field data such as PV diagrams, ICHP, efficiency, and flow, so that they can be quickly reviewed in the field for any discrepancies.

•

Communicate with the station operators where access to the compressor will be required (indicator ports, flywheel for ODC, removal of compressor valve, etc.) so that the proper work permits can be generated for the tasks.

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5.3

•

Ensure that the instrumentation and data acquisition system used for testing meets the required hazardous classifications for temporary work or local safety requirements at the compressor site (e.g., IEEE Class 1 Div 2 rating).

•

Ensure that all safety and contractual documents are in place before mobilizing to the test site.

Pre-Test Equipment Checkout

Prior to running the field performance test, the following should be performed:

5.4

•

Verify fuel and site load to assure continuous operation of the unit at full-load conditions as required at the time of the test.

•

Perform a visual walk-through of the compressor package to eliminate any sources of hot air ingestion or recirculation.

•

Consult with gas control on station operation and verify the compressor can be run at the guarantee point or testing condition (specific gas, speed, pressure, and temperatures). If the test is not run at the guarantee point, then consult with the compressor manufacturer to obtain performance predictions for the conditions that will be tested.

•

If the test is going to be conducted on a closed loop, check if gas cooling is available and if recirculation of gas is an option during the field test. Notify all parties of the time frame for the test.

•

Determine how load steps will be maintained constant during a test point and how they will be changed for different test points.

•

Consult with station operators about the gas samples or compositional analyses that will be required for the performance test.

Pre-Test Information

The following information should be obtained from the test preparation and pre-test meeting: •

General ♦ Predicted performance curves for compressor (or existing test curves).

If a guarantee point is being tested, the manufacturer of the compressor or the packager needs to be involved with the performance predictions for the test conditions. If the test conditions follow closely with the original performance specified for the compressor, then these can be used for the comparison. If the test conditions vary greatly from the original performance predictions, then the manufacturer needs to be contacted in order to obtain performance predictions that will be in line with the performance test results. Table 5-1 details maximum permissible deviations from the manufacturer’s specified performance. This table has been adapted from ISO 1217.

♦

Piping geometry between compressor and test instrumentation.

♦

Compressor configuration for testing: deactivated valves, pocket clearances, and suction valve loading.

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Table 5-1. Maximum Deviations from Specified Values and Fluctuations from Average Readings

Measured Variable

Maximum Permissible Deviations from Manufacturer Specified Performance

Maximum Permissible Fluctuations During Performance Test

Suction Pressure Discharge Pressure Pressure Ratio Suction Temperature Isentropic Constant Gas Constant x Compressibility Factor, RZ Shaft Speed

± 10 % Not specified ±5% Not specified ±3% ±5% ±4%

±1% ±1% Not specified ±2K Not specified Not specified ±1%

Difference between suction temperature of external coolant and gas suction temperature

± 10 K for coolant air ± 5 K for coolant water

±2K ±2K

External coolant flow Temperature at the nozzle or orifice plate Differential pressure over nozzle or orifice plate NOTES

± 10 % Not specified Not specified

± 10 % ±2K ±2%

1. The test can be performed if the deviations from the specified conditions are equal to or less than the deviation tolerances. 2. If the deviation from test conditions results in a deviation in absorbed power higher than ± 10 % then the test is not within the limits. 3. A test at a shaft speed different from the specified value is not accepted if unpermitted resonant pressure pulsations occur. 4. For the test of a gas compressor with a gas different from that specified, a bigger variation in gas properties often occurs. This should be agreed upon by both parties.

•

PV Card Method ♦ Compressor Geometry: Bore diameter, stroke length, connecting rod diameter, connecting rod length, clearance volume, pressure transducer port geometry (length and diameter), pocket volumes, load step definitions, valve types (poppet, plate, ring, reed, or channel), and unloader mechanisms.

•

Enthalpy Rise Method ♦ Flow meter information: Pipe ID, orifice bore or beta ratio (for orifice meter), K-factor (for turbine or vortex shedding meter), flow coefficient (for annubar or nozzle) scaling frequency, configuration log (for ultrasonic meter or to adjust turbine or mass flow meters).

Before conducting the performance test, a test matrix should be developed to include all operating conditions to be tested and how they are to be achieved. This should consider the objective of the test. The test planner should examine what performance curves are needed for the compressor. Parameters, such as suction pressure, compressor speed, and clearance, should be considered. The test planner should discuss the test matrix with the compressor operator to ensure that all the operating conditions can be met. If testing requires more than one test day, have a plan in place on how to leave the compressor in an operational state overnight. This will allow the station to operate as needed when testing is not occurring. The plan may include removal of some instrumentation or plugging various ports.

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5.5

Test Stability

In order to obtain steady state conditions, the compressor should be started prior to the initiation of the test (compressors require at least 30 minutes of heat soak time and engines require 1-2 hours of soak time). The field test should be performed when the compressor operating conditions have reached steady state. Also, the operating conditions should stay constant during each test point. To determine if the compressor has reached steady state, estimate how long it will take to collect all the required measurements either through experience or a trial collection run. This collection time will be the length of time between each check for test stability. For example, if it takes 10 minutes to collect all the test data, then the stability parameters, such as pressure and temperature values, should be checked at 10minute intervals to verify whether or not the compressor operation is steady. The compressor stability should be determined from the criteria discussed below. Power fluctuations should not occur during the performance testing. As it is very difficult to determine fuel gas composition variations during the short test intervals, it is important to ensure that the fuel and process gas compositions will remain unchanged for the duration of the testing period for each test point. Multiple or continuous gas samples should be taken during the test to ensure that the compressor remains at a steady state during one test point. Also, multiple gas samples of the process gas and fuel gas must be taken for each test point if the gas composition significantly changes (heating value change of more than 1.0%) in between test points. Temperature measurements will especially be affected by any instability during the test. Temperature probes reach equilibrium through relatively slow heat transfer and heat soaking, while the system operating conditions vary at much faster rates. The heat storing capacity of the compressor and system piping will need adequate time to reach equilibrium after any operating conditions have changed. It is, thus, critical to maintain extended stable operating conditions prior to beginning the test in order to reach thermal equilibrium and measure accurate gas temperatures. When using the PV Card method, pressure measurements on cylinder ends may be made one at a time, depending upon the number of pressure transducers on hand. If the pressure measurements are made consecutively (one or two at a time) then the stability of the test needs to be maintained throughout the full set of pressure measurements. Any stability changes during these measurements should be considered in the uncertainty. The stability of the compressor can be monitored by considering other continuous measurements, such as compressor speed, temperature, and gas composition. Cylinder load steps should be maintained through a test point. Regardless of the assumption of steady state test operation, any variation in measured parameters during the test interval should be accounted for in the uncertainty calculation. Note that an increase in pressure ratio due to drift during the test will cause an increase in the temperature as well, though the temperature change will lag behind the pressure change. Refer to Section 7 on uncertainty for more discussion of unsteady conditions and drifting conditions during a test. These added uncertainties due to drift during the test interval are in addition to non-ideal effects discussed in Section 7. 5.5.1

Compressor Steady State

The compressor should be operated for at least 30 minutes prior to the test. Steady state is achieved if the compressor measurements listed in Table 5-1 (in the maximum permissible fluctuations during performance test column) applies during a test interval. Also, the following performance conditions shown in Table 5-2 should be satisfied:

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Table 5-2. Additional Assessment of Stability of Compressor During Pre-Test

5.5.2

Test Reading

Maximum Allowable Variation During Test Interval

Efficiency

Fluctuations < + 1% of Average

Enthalpy Rise

+ 1% of Average Value

Compressor Flow

+ 1% of Average Value

Engine Steady State

Before readings are taken for any individual test point, engine steady state operating conditions must be achieved. The engine must be heat soaked according to manufacturer specifications. If manufacturer specifications are not available, the engine should be heat soaked for at least 1 hour. To verify stability of the engine, the parameters given in Table 5-3 should be checked. Table 5-3. Assessment of Stability of Compressor Driver During Pre-Test

5.5.3

Test Reading

Maximum Allowable Variation During Test Interval

Driver Speed

+ 1% Average Speed

Fuel Flow

+ 2% Average Flow

Motor Current

+ 2% Average Current

Unsteady Operations

If unsteady operations cannot be avoided during the test interval, measurements may still be valid, but the fluctuations have to be accounted for in the uncertainty calculations of the results. Also, if this is a factory performance test, the purchaser can specify criterion for fluctuations. If fluctuations during the test exceed quasi-steady conditions, as given in Table 5-1 through Table 5-3, the test may need to be performed again. For measurement cases where there is a simple drift in the average operating condition, the criteria listed above should be employed to determine whether a data point is steady. If the drift in any of the instrument readings exceeds the steady state conditions (as defined in Table 5-1 through Table 5-3), it is difficult to determine any valid performance results from this measured data because of the high degree of interdependence of all measured parameters and the system as a whole. Namely, as the validity of the data depends on the rate of drift, heat storage capacity of the pipe and measurement system, and the frequency response of the transducers, a total uncertainty cannot be determined. On the other hand, if the fluctuations in the data can be determined to be varying around a mean value, without the average drifting significantly, the resultant measurement error is primarily due to a time lag of the temperature transducers. Namely, while the pressure and flow transducers generally measure at a high frequency and, thus, capture rapid operating changes accurately, the temperature transducers lag due to the requirement of complete heat soaking of the piping and measurement system. Thus, if the fluctuations produce a mean performance value, the criteria for acceptance of unsteady operation can be extended to allow up to twice (i.e., factor-of-two range) the fluctuations listed in Table 5-1 and Table 5-2 for compressor steady state testing. In these cases, the fluctuations must be accounted for in the uncertainty calculation. The uncertainty of the measurement then becomes the fluctuation instead of the instrument uncertainty due to calibration, installation, data acquisition, and the device itself. As this can generally result in very high total uncertainties for efficiency and power, one should carefully evaluate whether to accept this test data. Also, once this factor-of-two range is exceeded, the non-linear behavior of the system as a whole makes it unrealistic to determine accurate performance results from experimental

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data. Figure 5-1 shows examples of a measurement that has a drift or fluctuations around the mean value. The graph does not show actual measurements. The fluctuation and drift in the figures are exaggerated. 121 Average Drift

Temperature (deg F)

120.8

Fluctuating

120.6

120.4

120.2

120

119.8 0

10

20

30

40

50

60

Time (minutes)

Figure 5-1. Example of Drift and Fluctuations in a Temperature Measurement

5.6

Safety Considerations

Safety considerations should remain a priority during the pre-test phase, as well as the actual testing of the compressor. Abnormal operating conditions should be discussed with station personnel prior to running the test. If possible, a schematic of the yard piping should be given to all test personnel. Unit vibration equipment operation should be verified. When cables are run to test instrumentation, the cables should be covered with mats or correctly taped down (if possible) to reduce trip hazards. Cable connections should be secured. Site specific hazardous location requirements for instrumentation, cables, and devices should be followed. Aviation type headsets can be useful during the testing for quick communication and can help the testers maintain a safe testing environment. Finally, the requirements of the field test should not be given priority over station safety precautions in order to reduce measurement uncertainty or meet test schedules. 6.

MEASUREMENT AND INSTRUMENTATION

The reciprocating compressor cylinders, pulsation bottles, and piping must be equipped to measure the test variables shown in Figure 4-2 and Figure 4-9, depending on which data collection procedure is used and the objective of the test. All pressure test points must have appropriate test taps in the proper place to record pressure and temperatures. This is the responsibility of the design engineers and constructors. All test taps should utilize dampers for accurate results. For testing purposes, a dedicated set of laboratory quality instrumentation should be utilized. This dedicated set of test instrumentation should be maintained and calibrated before each test using acceptable reference standards. A valid calibration certificate for all measurement instrumentation is recommended. An end-to-end calibration of the data acquisition system, wiring, and instrumentation is also recommended prior to the field test but may not always be practical.

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If possible, all measurement instrumentation should be installed inside the branch piping to the compressor’s recirculation or bypass flow loop, such that the measured values represent the true flow through the compressor. The bypass loop should not offer undue restriction to flow. Ideally, the bypass uses a full open type valve and a line size not more than one size smaller than the discharge line. If the test instrumentation is located outside the recycle loop for the compressor, the recycle valve must be fully closed during the tests for the results to be valid. If the recycle is part of the normally active flow control system, then this system may need to be disabled or the recycle may need to be actively controlled to achieve certain test conditions. A piping configuration using a closed loop through the compressor or station recycle line may also be utilized for the performance testing of the compressor. In this case, a process gas cooler on the discharge of the compressor will generally be required to maintain the gas temperature stable in the closed loop piping system which results from this configuration. Also, for this test scenario, the effects of gas lean out must be considered as the heavier components in the test gas may liquefy and drop out due to sequential compression and cooling. If the test is run on a closed loop, then prior to the performance test, the compressor should be run in the closed loop configuration while monitoring the gas using an online gas chromatograph until there is no significant change in the gas composition. 6.1

Measurement of Pressure

6.1.1

Recommended Best Practice

Pressure transducers are selected and installed depending upon the objective and methodology of the performance test. If the PV Card method is used, a pressure transducer which can detect the dynamic change in pressure is required for the cylinder pressure measurement. The Enthalpy Rise method requires a more steady pressure measurement upstream and downstream of the compressor. If this measurement is made at the cylinder nozzles, the pressure has strong variations due to pulsations. In this case, a pressure transducer with dynamic capabilities is required. If the pressure measurements are made upstream or downstream of the bottles, the pressure variation may be low enough where a static pressure transducer may be used. Static pressure transducers typically have a much lower drift than dynamic pressure transducers. If the transducers are calibrated for the performance test, the drift of the instrumentation may not be a concern. The ambient pressure also needs to be measured. The cylinder pressure will be a gage pressure and needs to be made absolute before completing any calculations. The ambient pressure can often be obtained from a local airport weather station, but in some cases this is not sufficient. In areas with significant elevation changes or a varying landscape, such as in the mountains, the ambient pressure will not be consistent from one location to the next. An accurate atmospheric pressure measurement is also important in applications with low suction pressure (< 50 psig, typically gas gathering applications) or low pressure ratios. Below, the details of compressor pressure measurements for each performance test methodology are discussed. PV Card Method For the PV Card method, a pressure measurement inside the cylinder is required. The pressure inside the cylinder is constantly changing during the compression and expansion cycles and relatively steady state during the suction and discharge events on a healthy cylinder. A strain gauge pressure transducer is required due to the pressure variation. This transducer must be a DC coupled transducer with a high frequency of response. On the compressor cylinder, there is an indicator port for the pressure transducer. If the compressor does not have indicator ports, then the user will need to drill and tap a port for the transducer if they choose to install the transducer on the bore of the cylinder.

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Dynamic pressure transducers have a frequency of response. When testing high-speed compressors, this is an important consideration when selecting the transducer. The transducer should be able to accurately track the pressure changes without a phase delay in the frequency range of interest. Quality pressure transducers can be found with frequency response ranges around 2,000 Hz. This frequency of response is adequate for the reciprocating compressor performance testing as discussed in the guideline. Enthalpy Rise Method The Enthalpy Rise method requires strain gauge pressure measurements. Pulsations may be present depending on where the transducers are installed. The sensor should have a high enough frequency of response to track these pulsations without a phase delay. Total (stagnation) pressure must always be used for performance calculations. However, it is often more convenient to measure static pressures (Pstat) and then convert static to total pressure (P) using:

p = p stat + 3 x10 −8 U 2

(6-1)

In Equation 6-1, the flow velocities can be calculated using the measured actual flow rate (referenced to actual temperature and pressure conditions) and the pipe cross-sectional area (U=Q/A). Whenever feasible, it is recommended to use four pressure taps and four temperature taps at the pressure and temperature locations indicated in Figure 6-1, consistent with ASME PTC 10 recommendations. The accuracy of the static pressure or temperature measurement is dependent upon the selected location. Four pressure and temperature sensors assure that the average measurement of pressure or temperature will be accurate, even in a non-uniform flow field. Additional pressure and temperature measurements can be employed, if four sensors are not sufficient. Two different approaches are appropriate for locating the suction and discharge pressure and temperature taps. The first approach is to place measurement taps at locations relatively far upstream and downstream from the compressor in the longest available straight pipe segment to assure a uniform flow field at the transducer taps. These locations may be relatively far away from the compressor, so the pressure measurement values must be corrected using empirical loss factors (i.e., pressure losses) for the straight pipe, elbows, tees, reducer, pulsations bottles, and orifice plates that lie in between the measurement location and the compressor inlet/discharge. The second approach is recommended for field testing, if possible. The approach is to measure the pressure and temperature as close as possible to the compressor, using multiple temperature and pressuretaps at suction and discharge. Generally, the flow field near the compressor will be highly non-uniform and, thus, at least four pressure and temperature taps should be used on both suction and discharge. Nonuniformity of the flow field affects the uncertainty of the measurement data. If less than four transmitters or test taps (for pressure or temperature) are available, the first measurement approach is recommended. Using less than four pressure or temperature sensors will result in an increase in the total uncertainty for pressure or temperature, as discussed in Section 7. 6.1.2

Installation

PV Card Method Indicator ports on cylinder bores are used for installing pressure transducers. The transducer will be installed on a valve attached to the port. If possible, avoid using additional connectors or adaptors between the compressor and pressure transducers. This can be avoided by contacting the station in

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advance and determining what type of transducer connections are available or installed. Any valves, connectors, or fittings should be the straight through type in order to avoid having varying diameters or gas volumes in the channel to the transducer. Installation of the sensor in this configuration tends to produce other influences on the measurement, such as channel resonance and attenuation. It is not advisable to leave these effects on the measurement. Channel resonance can be corrected after the measurement is taken through data filtration. Channel resonance and attenuation are discussed in more detail in Section 4.1.2.1.

Figure 6-1. ASME PTC 10 Recommended Installation Configuration for Pressure and Temperature Measurement

Pressure transducers are subject to the temperature variations due to the compression and expansion of the gas. The transducers may require heating depending on the type of transducer to maintain the transducer at a constant temperature. If not, temperature compensation curves should be applied to the measured values. It is best to calibrate the transducers after they have been allowed to heat soak when installed on the machine. This will reduce the deviation of the signal due to temperature effects. Pressure measurements in the cylinder nozzles should be made after the orifice plate or inside the cylinder flange when possible. If the measurements are made before the orifice plate, then the pressure drop across the orifice plate needs to be accounted for. Pulsations will be present in this location of the compressor. Dynamic pressure transducers should be used for this measurement. Some compressors will have taps on the cylinder passages which can be used for this measurement. If these are not present, then a pressure tap should be installed on the cylinder nozzle.

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Enthalpy Rise Method The installation of the pressure measurement device, pressure tap size, and symmetry is critical to the measurement accuracy. ASME PTC 10 provides specific guidelines for correct installation and location of pressure probes. The pressure tapping should be inspected prior to installation of the pressure measurement device. The tube and static tapping used to make the pressure measurement should have a constant length to diameter ratio and must be greater than 2. The ratio between the pressure tubing and the pipe diameter should be as small as possible to prevent the pressure measurement from altering the flow pattern. In addition, the wall taps should be exactly perpendicular and flush to the surface. Burrs or slag in the taps are not acceptable and will influence measurement accuracy. 6.1.3

Calibration

Prior to performing the field test, the transmitter or transducer should be calibrated, such that the maximum device error is less than or equal to 0.1% of the actual value. However, this is only achievable if the pressure transducer being used has accuracy to this level. The calibration procedure should contain at least two points. One of the calibration points should be near the maximum pressure that will be measured. The other point can be ambient pressure or another reference pressure. Due to the fact that pressure transducers have linear responses, only two calibration points are required, but it is beneficial to check the pressure on a third or more points. This will ensure the linearity of the transducer. The calibration process will not eliminate all measurement errors, since the calibration process itself is subject to non-linearities, hysteresis, and reference condition error. Transducers should be recalibrated frequently. If possible, calibration at the test site is recommended. If the sensors are calibrated at the test site, then they should be calibrated at least once a day. Some common methods of calibration at the test site are with a pressurized manifold or with dead weights. Ambient, suction or discharge pressure can be supplied to the manifold from the compressor. Calibration at the test site is also convenient if transducers need to be replaced during or before testing. In the PV Card method, the pressure measurement in the cylinder is subject to dynamic temperatures. This can distort the pressure measurement. These sensors will be installed with temperature stabilizers (either heaters or coolers) or have a temperature compensation curve (provided by sensor manufacturer). If the sensors have temperature stabilizers, then the transducer needs to be calibrated at the temperature at which it will operate. If not, then the zero reference of the transducer may shift during testing. 6.1.4

Accuracy Achieved in Practice

The precision uncertainty in pressure measurement will depend upon the uniformity of the flow field. For static pressure measurements, if piping vibration or flow-induced pulsations are high, the measurement of pressure will show a significantly higher random uncertainty. Non-uniformities, location, installation, and calibration errors will affect the pressure measurement. The signal from the transmitter should be transformed into a digital signal by means of a portable data acquisition system (DAQ). The data acquisition system should have an instrumentation accuracy of better than 0.01 to 0.05% of reading. For static pressure measurement, the main source of pressure measurement error is incorrect installation and location of pressure probes. Table 6-1 provides typical values for sources of pressure measurement errors encountered during field tests. All values are percent full scale. For cases of multiple static transmitters, it is assumed that the transmitters are installed at equal angular intervals in the pipe and the flow field is uniform. Table 6-1 assumes that the static transmitter installation meets the upstream and downstream requirements of ASME PTC 10. Installation configurations, which do not meet ASME PTC 10, will have significantly higher location uncertainties in pressure measurement. Table 6-1 shows

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the uncertainty for two and four static transmitters to be the same. This can be true in an even flow field with installations following ASME PTC 10. The four transmitters become valuable when ASME PTC 10 installation requirements cannot be met or the flow field is uneven. In this case, the four static transducers will give a more accurate pressure measurement than the two transmitters (see Figure 6-1 for ASME PTC 10 recommended installation). Table 6-1. Typical Uncertainties in Pressure Measurement (shown as percent of full scale) Sensor Type

Location

1

Installation

Calibration

Device

Acquisition

Pulsations

One Static Transmitter

0.15

0.02

0.10

0.10

0.005

0 - 10

Two Static Transmitters

0.10

0.02

0.10

0.10

0.005

0 - 10

Four Static Transmitters

0.10

0.02

0.10

0.10

0.005

0 - 10

One Dynamic Transmitter

0.15

0.02

0.10

0.10

0.005

0

2,3

1

Errors in location will largely be dependent on uniformity of flow field at measuring location and the number of pressure measurement devices used at a single location. Wall static error will cause high uncertainty if wall taps are not correct. Wall taps should be exactly perpendicular to the surface and flush (with no burrs or slag). For dynamic measurements in the compressor cylinder, the location errors are associated with channel resonance and attenuation. 2 The error due to pulsation depends on the level of pulsation present. If pulsations are present, then a dynamic transmitter should be used. 3 The error in the dynamic transmitter assumes that the sensor has a high enough frequency of response to detect any changes in pressure.

6.2

Measurement of Temperature

6.2.1

Recommended Best Practice

The approach to measurement of temperature is dependent upon whether the PV Card or Enthalpy Rise method is used. In the PV Card method, a suction and discharge temperature is recorded either in the nozzles or outside of the bottles. The temperature in this testing serves two purposes. The first is to verify that steady state has been reached. The second is to provide a temperature for generation of theoretical PV diagram and calculation of the flow through the cylinder end. Typically, only one temperature sensor, usually an RTD, is installed at each measurement location. The actual power measurement is independent of the measured temperature, but the flow and efficiency are not. In the Enthalpy Rise method, the calculated power and efficiency are dependent upon the measured temperature. The temperature can be measured in the nozzles or outside the bottles. If the temperature is measured outside the bottles, then any heat losses through the vessel walls should be accounted for. For this method, it is best to use four temperature sensors in order to identify any inconsistent measurements due to varying flow field. The temperature should be measured downstream of the pressure, if possible. The pressure and temperature sensors should not be installed in the same line of sight. Thermocouples, thermistors, and resistance temperature devices (RTDs) are typically used to measure temperature. RTD’s are recommended for measurement of temperature in the flow stream over a broad temperature range. Thermocouples can be used for high temperature measurements, but below 200°F the resolution will be reduced. Also, thermocouples tend to drift more than RTDs and, thus, require more frequent recalibration. At low temperatures, thermistors are useful but should be carefully calibrated because of inherent non-linearities.

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6.2.2

Installation

These devices should be inserted into a thermowell, though RTD sensors may be used as direct insert devices. Direct insert RTD’s will provide a faster response time. The RTD-thermowell configuration should have the highest recovery factor possible to accurately measure stagnation temperature. The temperature sensor should be instrumented to a temperature transmitter that is connected to the field test data acquisition system. The measurement location should assure that the temperature sensor will be relatively insensitive to radiation, convection, and conduction between the temperature sensor and all external bodies. The insertion depth can produce a large error in the temperature measurement if the sensor is placed too deep or too shallow in the flow stream (see Table 6-2). The manufacturer’s safety guideline should be consulted for insertion depth of RTD’s without thermowells and extra long thermowells to ensure the pipe velocity meets acceptable safety levels. The ASME PTC 10 standard provides specific guidelines for proper installation and location of temperature sensors. Though the field test constraints may make ideal measurement locations impossible, it is important to be aware of the required specifications to assess measurement error and the propagation of additional measurement uncertainty (see Section 7.2 on uncertainty in non-ideal installations). Table 6-2. Recommended Depth of Thermowells Pipe Diameter (inches) 6 8 10 12 14 16 18 >18

Thermowell Depth (inches) 2.0 2.5-3.0 3.0-3.5 4.0 4.5-5.0 5.0-5.5 6.0 7.5 minimum

Note: Above 18-inch diameter, a minimum depth of 7.5 inches from the inner wall is enough to avoid pipe influence and breakage.

6.2.3

Calibration

The temperature sensor shall be calibrated, such that the maximum measurement uncertainty for each sensor is less than or equal to 0.1ºF. Transmitters used in acquiring data from the temperature sensor should be calibrated in tandem (i.e., the transmitter used to read the signal from the RTD should be calibrated with the RTD as a single measurement chain). The calibration procedure should involve at least three points. The calibration process can introduce errors into the temperature measurement, primarily through non-linear response, instrument drift, cold junction, and reference temperature error. 6.2.4

Accuracy Achieved in Practice

Table 6-3 provides typical uncertainty values for the five main sources of temperature measurement errors encountered during field tests. Uncertainties in the temperature originate from the following five major sources of error: (1) location: incorrect position of the thermal sensor in the gas stream; (2) installation: wall conduction heat transfer to and from the sensor due to inadequate insulation; (3) calibration: instrument drift, non-linearities, cold junction, and reference temperature errors; (4) device: inherent accuracy limitations of the sensor device; and (5) acquisition: amplifier, transmission, noise, read, and analog-digital conversion errors.

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Location, installation, and calibration errors may be minimized easily in production or laboratory test facilities. However, for field testing, this is more difficult because time and cost constraints can force the test engineer to accept field test arrangements with improperly located, installed, and calibrated instruments. While it is often impossible to correct these problems during the short field test duration, it is imperative to recognize them and account for them in the uncertainty analysis. Table 6-3 shows that the location, installation, and calibration errors are the dominant factors, while the device and acquisition errors are a smaller contribution to the total temperature error. Also, note that field test device and acquisition errors are significantly larger than values quoted by instrument manufacturers (>0.005 percent full scale). Again, the circumstances and limitations encountered in the field test may not always allow for ideal handling of the sensitive measurement instruments. Table 6-3 assumes that the installation meets the upstream and downstream requirements of ASME PTC 10 for temperature sensor installation. Installation configurations, which do not meet ASME PTC 10, will have significantly higher location uncertainties in temperature measurement. Table 6-3. Typical Uncertainties in Temperature Measurement (shown as percent of full scale) Sensor Type Hg Thermometer Thermistor Thermocouple RTD Infrared Sensor

Location

1

0.10 0.10 0.10 0.10 0.40

Installation

Calibration

Device

Acquisition

0.20 0.20 0.20 0.20 0.20

0.03 0.10 0.10 0.05 0.10

0.03 0.05 0.10 0.05 0.25

0.10 0.05 0.05 0.05 0.05

1

Location error is based on having four (4) equally spaced sensors in the pipe and assumes uniform flow in the pipe. For a single sensor installation, the location uncertainty should be multiplied by four (4). For two (2) sensors, the location uncertainty should be multiplied by two (2). For highly non-uniform flow or pulsating flow fields these values may be larger.

6.3

Measurement of Flow

An accurate measurement or calculation of the gas flow through a compressor is essential for proper determination of the performance and is necessary to identify degradation in the performance of a compressor. The most common meter type installed at gas compressor field sites is orifice meters. Other meters that are available at some times are full bore turbine meters, ultrasonic meters, flow nozzles, and a range of insertion type meters, such as vortex shedding meters, insertion turbine meter, and multi-port pitot probes. Fuel gas flow rates are also measured with these common meters, including orifice, turbine, insertion, and Coriolis mass flow meters. The proper sizing, installation, maintenance, adjustments, and calibrations are necessary for any of these meters to achieve the desired level of precision and repeatability in flow measurement. 6.3.1

Recommended Best Practice

Orifice, ultrasonic, and turbine flow meters are typically employed to measure pipeline flow at a high level of accuracy. However, proper installation, maintenance, and calibration are critical to achieve a desired level of precision and repeatability. All three meter types have upstream length requirements, which may be mitigated through the use of a flow conditioner. When installed correctly with a properly calibrated differential pressure transducer, an orifice flow meter may be used to measure flow over a 3:1 range with an accuracy of 1.5%. Turbine meters have a greater flow range than orifice meters. Turbine meters are very repeatable in both high and low flow situations

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and can provide accuracies better than 1.0% depending upon the quality of calibration. A calibrated ultrasonic meter will provide flow measurement accuracy better than 1.0%. 6.3.2

Installation and Calibration

The upstream piping configurations at field compressor installation are normally not ideal and result in distorted velocity profiles at the meter. Non-ideal meter piping will result in errors in the flow measurement unless something is done to correct the metering configuration. AGA Report No. 3, ISO 5167, AGA Report No. 7, and AGA Report No. 9 should be referenced for the installation and calibration of various flow meters. 6.3.3

Accuracy Achieved in Practice

Pulsation adversely affects most types of meters and, therefore, must be avoided during reciprocating compressor performance testing. However, as most flow measurement instruments provide a low frequency output response, it is often difficult to determine pulsation magnitudes and frequencies. RMS output variation on the flow meter can be used to estimate pulsation amplitudes, but flow turbulence also contributes to RMS flow velocity and pressure variations. AGA Report No. 3 defines that when the pressure differential or the velocity fluctuations across the measurement device exceed 10% RMS value, the flow meter results cannot be considered valid. In order to calculate flow accurately for an orifice meter, the temperature, pressure, gas composition, and differential pressure must be measured accurately. Properly sized orifice meters are suitable for testing reciprocating compressors over a normal operating range. Orifice meters are highly susceptible to installation-effects resulting from improperly conditioned flow, insufficient upstream length, upstream bends, elbows or valves, or extreme beta ratios (>0.65). If installed correctly with a beta ratio less than 0.65, orifice meters will provide a flow measurement accuracy of 1.5% or better. Turbine meters can be calibrated to obtain a measurement uncertainty of 1.0% or better. If the gas pressure or flow rate is outside the calibration curve, the measurement will contain a bias error, which can be as large as 1.5 to 2.0% additional measurement uncertainty. If a turbine meter is over-ranged by exceeding its maximum velocity, permanent damage to the rotor may cause the measurement uncertainty of the meter to exceed 2.0%. The accuracy of an ultrasonic meter decreases at flow velocities of less than 5 to 7 feet per second and at high flow velocities, above 70 to 90 feet per second. Therefore, ultrasonic meters should only be used for compressor testing, if the flow range in the pipe is between 5 to 70 ft/sec. Ultrasonic meters should not be oversized, such that low flow velocities routinely occur, or undersized, such that high velocities are experienced. The field accuracy of ultrasonic meters is normally in the range of 0.5 to 1.0% and is based on the meter’s calibration and having a suitable piping configuration. Other differential pressure devices (annubar, v-cone, etc.) and Venturi meters (sonic nozzles) may also be used to measure gas flow through the compressor. These meter types typically have a lower pressure loss than an orifice meter, but the flow measurement error is highly sensitive to the measurement of differential pressure across the device. Typical meter accuracy is 0.5 to 1.5% if the differential pressure sensor is calibrated and operating well within its range. Venturi meters and differential pressure (DP) type meters are similar to an orifice meter, in that large installation errors can occur (1 to 5%) if installed incorrectly. Installation guidelines for Venturi meters are provided in ISO 5167, Measurement of Fluid Flow by Means of Orifice Plates, Nozzles and Venturi Tubes, and ASME MFC-3M-1989, Measurement of Fluid Flow in Pipes Using Orifice, Nozzle and Venturi Tubes. All differential pressure flow devices must meet a test protocol standard specified in American Petroleum Institute Manual of Petroleum

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Measurement Standards (API MPMS) Chapter 5.7, Testing Protocol for Differential Pressure Flow Measurement Devices. Specific installation requirements for DP type meters should be provided by the meter manufacturer and should assure that the meter conforms to API MPMS Chapter 5.7. Table 6-4 summarizes the achievable accuracies of the various flow meters. Table 6-4. Achievable Uncertainties in Flow Measurement with No Pulsating Flow Type of Flow Meter Orifice Plate Turbine Meter Ultrasonic Meter Annubar Hot Wire Anemometer Tracer Gas

6.4

Measurement of Gas Composition

6.4.1

Recommended Best Practice

Achievable Measurement Uncertainty (%) 1.0 - 1.5 1.0 0.5 - 1.0 0.5 - 1.5 1.0 - 2.0 2.0

Both the engine fuel gas and compressor process gas composition should be evaluated at regular intervals throughout the field test, either through automatic gas chromatograph sampling or by taking regular gas samples. This is particularly true in applications where the gas composition can vary significantly within the course of one day such as in gas gathering applications. Depending on which method is used for the test, the varying gas composition can affect the power, efficiency, and capacity calculations. At a minimum, a gas sample should be taken before and after the test. Multiple sampling methods are defined in GPA Standard 2166 and the American Petroleum Institute Manual of Petroleum Measurement Standards (API MPMS) Chapter 14.1. These include both spot methods and composite sampling (on-line methods). If possible, the gas sample should be taken near the compressor to ensure that it is representative of the gas flowing through the compressor. A gas sample downstream from the gas plant can be more or less meaningless for testing a field gathering unit, although this is often what customers provide. If an automatic sampling probe is used (such as a gas chromatograph probe regulator), the probe should be properly sized to draw samples from the center one-third of the pipe, so that liquids that may appear in the flow cannot be easily ingested into the probes and sample lines. Velocities in the location where samples are taken should not exceed 150 ft/sec in order to avoid possible probe vibration and failure. To properly determine the gas properties from the gas samples, the gas composition should evaluate all components that contribute at least 0.1 mol percent to the composition. Namely, as a minimum, the gas samples should be analyzed for all hydrogen, oxygen, water, sulfur compounds, carbon dioxide, nitrogen, nitrous oxides, other inert gasses, and all hydrocarbon gasses or vapors between C1 and C6. If the hydrocarbon dewpoint of the gas mixture is within 0 to 20ºC of the temperature of the sampling equipment or above the temperature of the sampling equipment (ambient temperature), then additional precautions must be taken. The hydrocarbon dewpoint will vary with different gas mixtures and primarily be influenced by the presence of heavier hydrocarbons, above C6. The best practice in this case is to preheat the sample line and sampling containers prior to taking the gas sample. If pre-heating is not practical, “dead-end” spot sampling methods may be used in combination with re-heating the sample

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above the mixture dewpoint during the analysis process. In addition, if the dewpoint is close to the operating temperature, the compressor should be run for a minimum of two hours after start-up to make sure the gas temperature and composition are relatively stable to expect consistent and reliable data. “Dead-end” spot sampling methods include the water or glycol displacement method, the piston displacement method, the evacuated cylinder methods (evacuated, reduced pressure, or helium pop), and the fill and empty method. These methods work best because the depleted gas is not convected out of the cylinder in the sampling process. If condensate is formed on the wall of the sampling cylinder, re-heating the sample will cause the condensate to re-vaporize as part of the sampled gas mixture. 6.4.2

Installation

All sampling lines and equipment that come in contact with the sample streams should be made of stainless steel or other materials that are inert, compatible with the gas and minimize adsorption of heavy hydrocarbons from the gas stream. Polyethylene, Nylon, and Teflon will cause sample distortion because of these materials’ preferential absorption of specific hydrocarbon components. The probes and lines should be insulated to avoid condensation of the heavier hydrocarbon constituents or water vapor in the sample. The probes and sample lines should also be arranged above the pipeline. As stated in API MPMS Chapter 14.1, the sampling bottle should have a pigtail line connected to its outlet to assure that the process gas is kept above the hydrocarbon dewpoint (see Figure 6-4 below). Prior to sampling the gas, the gas sampling equipment should be cleaned, preferably by steam cleaning or using acetone or liquid propane. Filters in the sample lines are required in most cases. All fittings, tubing, and pressure regulators should be rated for the appropriate operating pressure of the station.

Figure 6-2. Sampling Method with Pigtail as Recommended in API MPMS Chapter 14.1

6.4.3

Calibration

Gas chromatographs are almost exclusively used to determine the gas chemical composition, in order to determine gas density, compressibility, and energy content. A gas chromatograph should not be regarded as an infallible device. A calibration gas standard should be used to calibrate the gas chromatograph regularly. The gas chromatograph should be calibrated at the beginning of each test day. The calibration

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standard should have a composition and heating value comparable to the process gas. This calibration gas should have a certified accuracy of at least 2% or better. The calibration gas should be blended in a procedure traceable to NIST. 6.4.4

Accuracy Achieved in Practice

The test gas composition will almost always differ from the gas composition used in the baseline or factory test. Errors in the determination of the gas composition will affect the density, compressibility, and the energy content determination. Density errors will propagate in the flow measurement when converting between mass and volume flow. Online gas chromatographs must be calibrated regularly (at least once per day during performance testing) to ensure accurate gas composition with a calibration gas that is similar in composition to the processed gas being measured. 6.5

Measurement of Crank Position

6.5.1

Recommended Best Practice

In the PV Card method, the crank position should be measured in order to know what the instantaneous cylinder position is. Knowing the geometry of the compressor, the volume at that instant can be calculated. With the pressure measurement, the PV diagram can be constructed. Two types of sensors are used for the crank position measurement: encoders and once-per-revolution sensors (key phasor, tachometer, magnetic pick-up, etc.). Caution should be taken when using a onceper-revolution sensor. During a full rotation of the crankshaft, there are velocity variations, which would not be accounted for in a single revolution type sensor. If angular velocity and acceleration variations are present with a key phasor in use, this can result in an incorrect reference to ODC. If the once-per-rev signal does not trigger at ODC, then the ODC can be occurring at a different location each time. Also, the data acquisition system will collect pressure transducer signals at specified time intervals. Because of the variations, the calculated volumes and pressures may be not be properly matched. Small errors in position measurement can have significant effects on the power calculation. An encoder should be used, if at all possible. An encoder typically has a metallic disc with multiple slots. The encoder employs a detection mechanism that registers the position of the shaft at each of these slots. A 360 encoder will have 360 slots such that its resolution is 1 deg. Higher count encoders can be used, such as 512, 720, etc. It is recommended to use at least a 360 encoder. The volume of the cylinder at the reported encoder position is calculated with Equation 6-2. Theta (θ) is the position of the shaft as reported by the encoder. When theta equals zero, the referenced cylinder end is at ODC; and when theta equal 180 degrees, the referenced cylinder end is at IDC. The angle reported by the encoder may need to have a phase shift applied if the zero angle is not referencing ODC on the cylinder end being evaluated. For example, the ODC of the encoder may be referenced to the ODC for the first cylinder in the compressor. Cylinder or throw 2 may be at IDC when cylinder 1 is at ODC. Cylinder 2 would then have a 180 degree phase shift. 2 S π S 2 V = (1 − cos θ ) − l − sin θ + l * B 2 + Vcl 2 4 2

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6.5.2

Installation

The encoder is typically installed on the flywheel of the crankshaft for a slow speed integral driver/compressor package. In high-speed separable compressor packages, the encoder may be installed on the compressor frame opposite from the flywheel usually with some type of adapter. There is typically an access point for the encoder installation. Figure 6-3 shows an example of an encoder installation on a flywheel in a slow-speed compressor, and Figure 6-4 shows an encoder installation on a high-speed unit with an adapter. It is necessary to ensure that there is no slippage between the flywheel and encoder. If this occurs, then the results will be invalid. The encoder should be mounted to the flywheel with some type of flexible coupling to avoid mechanical damage due to misalignment. Also, no misalignment can be tolerated with a mechanical drive, as the instantaneous angular velocity of the encoder can be significantly affected.

Figure 6-3. Encoder Installed on a Slow-Speed Reciprocating Compressor on Flywheel

Figure 6-4. Encoder and Adapter Installed on a High-Speed Reciprocating Compressor

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Avoid using multiple fittings on the shaft from the encoder to the compressor since this could lead to alignment issues. It is recommended that multiple encoder shafts of varying length be taken to the test site, due to the fact that the length required will not be known until the tester is at the test site. Every effort should be made to ensure that the encoder rotation is representative of the compressor crankshaft rotation. Avoid placing the encoder close to the opening on the compressor frame (usually on high speed units), because oil vapors escaping from the opening can cause the encoder to malfunction. 6.5.3

Calibration

The encoder itself does not require calibration. The calibration for positional measurement is completed through the determination of Outer Dead Center (ODC) and synchronization of the encoder. ODC refers to the condition where the piston is at a point of travel furthest from the crankshaft (also referred to as top dead center (TDC)). This is a critical step that determines how accurate your positional measurements will be. Once ODC position is known, this can be related to the position of the encoder wheel, otherwise known as synchronization. Determination of ODC requires the compressor to be shut down for access to the flywheel (if there is one). In some cases, such as process compressors, this is not possible. Usually an ODC mark will be placed on the machine during installation and start-up or an initial performance test. This can be used as a reference. In situations where there is no ODC mark and the compressor cannot be shutdown, the PV diagram can be shifted during post-processing, such that the start of the expansion line is set at the minimum clearance. This is not an exact science and the possible error of this should be accounted for in the uncertainty. Note the effect this can have on the PV diagram, shown in Figure 6-5.

Figure 6-5. Rotation of PV diagram to Correctly Reference ODC

The universal approach to determine ODC is to mechanically position a reference piston to its ODC position and mark the flywheel to a match mark on some member fixed to the frame. In principle, this seems a simple procedure; however, in practice, it is the most frustrating task. This can be appreciated when one considers that a 1-degree angular displacement about ODC amounts to only 0.0014 inch linear displacement of a piston on an 18-inch stroke compressor, but the cumulative total of clearances in main bearing journals, crank pin journals, and connecting rod bearings may be 0.015 or more. When marking ODC, it is important to approach ODC from both rotational directions. This will cancel out the effects of the clearances on the position of ODC. When marking ODC, there are several considerations that could affect the reference. The first is where ODC is marked. The most common approach is to mark ODC on the flywheel; however, this cannot or should not always be done. In high-speed compressors, the flywheel is often installed between the

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compressor and driver next to the coupling. If the flywheel is on the driver side of the coupling, then consideration should be given to the type of coupling installed. With highly flexible couplings, such as elastomeric couplings, there could be as much as 10 to 20 degrees of wind up during normal operation. If a rigid coupling, such as a disk pack type is installed, then ODC can be measured on the flywheel on the driver side. The same consideration should be given for couplings on a compressor without a flywheel, such as an electric motor driven compressor. If a highly flexible coupling is installed, then ODC should be marked on the compressor side of the coupling. The section below describes a few methodologies commonly used to determine ODC. Dial Indicator Method Rotate the compressor crankshaft until cylinder #1 is approximately at ODC (other cylinders can be used). Install a dial indicator on the crosshead or crosshead guide of cylinder #1 (whichever is more practical). Position the dial indicator, such that the probe is touching the crosshead or crosshead guide. Rotate the compressor until the cylinder is approximately at ODC (the dial indicator will stop moving). Zero the dial indicator.

Dial Indicator on Crosshead

ODC Mark

Figure 6-6. Example of Set-up for Dial Indicator Method

Rotate the crankshaft in the opposite direction until it reaches 0.03”. Rotate the crankshaft back in the other direction until the dial indicator reads 0.015”. Mark this location on the flywheel. Rotate the crankshaft in the same direction until the dial indicator reads 0.03” (the compressor will progress through ODC and pass it, so the dial indicator will read 0 and then go back to 0.03”). Rotate the crankshaft back the other direction until the dial indicator reads 0.015”. Mark this location on the flywheel. Using an accurate distance measurement, make the center between these two marks on the flywheel. This is the location of ODC. Rotate the crankshaft back to the marks made (using the procedure above) and check the locations of the marks. If the locations are repeatable, then the ODC marking is satisfactory. If not, repeat the process again. Positive Stop Method Another method of locating ODC is known as the positive stop method. No dial indicator is required for this procedure; however, the cylinder head or valve cap must be removed so the unit must be blown down. The basis of this method is that ODC can be determined from the midpoint of two piston positions marked on the flywheel. These piston positions are determined by the placement of the piston at a fixed distance from ODC. This fixed distance is determined by the hard stop used.

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The first step in this process is to obtain the hard stop. The stop can be inserted into the cylinder by removing the valve assembly or the cylinder head. If the cylinder head is removed, obtain a stiff 1/4-inch rod or similar material and sharpen one end to form a pointer. The length of the rod should be set, such that the piston stops at 2 to 10 degrees below ODC. Attach this pointer to a stout strip of steel and drill the appropriate mounting holes in it. Be sure that the strip of steel is rigid enough so that it will not be deflected when the piston contacts the center bolt stop. This strip is placed across the center of the cylinder bore and bolted on each end to secure it to the block. If the valve assembly is removed, place the stop between the cylinder head and piston instead (Figure 6-7).

Figure 6-7. Hard Stop Placed Between Cylinder Head and Piston Through Valve Pocket

Once the positive stop mechanism is installed manually, rotate the crankshaft around in the clockwise direction until the piston end comes in contact with the stop. Mark this position (to a reference) on the flywheel. Rotate the crankshaft in the counterclockwise direction until the piston end comes in contact with the stop. Mark this position on the flywheel. Using highly accurate measurement devices, determine the middle between the two marks (Figure 6-8). This is the location of ODC. Synchronization There are several methods that can be used for synchronizing the encoder with the location of ODC. One method is to drill a hole or install a pin at the location of ODC on the flywheel. A magnetic pick-up can then be used to detect ODC and synchronize the ODC reference with the encoder. Synchronization can also be achieved by using a strobo-scope to detect the ODC location. This requires a special strobo-scope that is linked to the encoder. The scope will have buttons on it that will allow the operator to vary the timing of the scope such that it will flash when ODC passes by. This scope’s link to the encoder software will send a signal to change the ODC reference point for the encoder to the timing of the flash set by the operator.

Figure 6-8. Placement of ODC Mark Between Two Initial Marks

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6.5.4

Accuracy Achieved in Practice

If ODC is determined correctly, then the accuracy of the positional measurement will be directly related to the resolution of the encoder. If a 360 encoder is used, then the resolution will be 1 degree or 0.3%. Higher resolution can be achieved with higher count encoders if the ODC is determined correctly and synchronization is completed accurately. One must weigh the advantages and cost of using a higher resolution encoder. If ODC is not determined correctly, then the accuracy of the positional measurement will be related to the estimated error in ODC, the resolution of the encoder, and synchronization. Regardless of the method used, ODC determination should be repeated at least once in order to verify that the first marking was correct. A 1-3 deg error in the positional measurement can lead to 3-5% error in the calculated power from the PV diagram. This is a significant error and indicates the high importance of correctly determining ODC. On reciprocating compressors that have six or more throws, wind-up along the shaft may introduce error to ODC reference. ODC is marked when the compressor is in a static position. During operation, the loads on the compressor pistons cause the shaft to deflect torsionally, which produces the wind-up. The further away the throw is from the ODC reference cylinder, the greater the wind-up may be. This error is approximately a maximum of 2 degrees for a six-throw machine. Therefore, wind-up should only be a concern if the compressor has six or more throws. 7.

TEST UNCERTAINTY

Test uncertainty must be calculated to determine the accuracy or quality of the test and the bounds of any measured quantity. Without doing this, the tester cannot be sure if the results are valid or within an acceptable range. The effects of the uncertainty of instrumentation, data acquisition, installation, steadiness of operation, and calculations of performance parameters must be considered. There are two primary components to uncertainty of any physical measurement: random (precision) uncertainty and bias (fixed) uncertainty. A larger test uncertainty could increase the risk of failing the test, if the compressor is actually performing better than the acceptance level, and could reduce the risk of failing if the compressor is performing below the acceptance level. Test uncertainties need to be clearly distinguished from machine building tolerances. Building tolerances cover the inevitable manufacturing variance and the subsequent variation in performance predictions. The actual machine that is installed on the test stand will differ in its actual performance from the predicted performance by the machine building tolerances. Building tolerances are entirely the responsibility of the manufacturer and must be excluded in any uncertainty calculation. In addition, the test uncertainty is not equivalent to the contractual test tolerance. The contractually agreed upon test tolerance might be influenced by consideration of how accurate a test can be performed or by more commercial considerations, such as the amount of risk the parties are willing to accept. Because it is normal practice to use a lower performance than predicted as an acceptance criterion, it is in the interest of the manufacturer, as well as the user, to test as accurately as possible. The following definitions should be applied to the discussion of uncertainty: Precision (Random) Error: The error due to random fluctuations of the measured quantity. The true value of the measurement should lie within the scatter of the data points, if no bias error exists. This error is reduced by taking more measurements of the test quantity.

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Bias (Fixed) Error: A systematic deviation of an instrument’s output from a fixed input. Bias can be a complex functional form over the instrument’s operational range, but in most cases, it is just the consistent over- or under-reading of input data. It is often due to installation effects or calibration errors. Bias errors must be estimated in the uncertainty analysis. Note: In a field site test, the bias error and precision error may not be distinguishable. These two components of the uncertainty are often treated as a single combined uncertainty. Linearity: Compares the deviation of a system’s output to a straight-line assumption. Clearly, few physical systems behave linearly over a wide range and, thus, linearity must always be stated with an upper and lower limit. Hysteresis: Refers to the system or instrument output dependency on directionality of the input. Hysteresis has nothing to do with an instrument’s accuracy degradation over time. In most cases, it is defined as the maximum difference in instrument reading for a given input value when the value is approached first with increasing, and then with decreasing, input signals. Hysteresis is often caused by energy absorption in the elements of the measuring instrument or system. All of the above are factors that contribute to, but are fundamentally different than the definition of measurement uncertainty. Uncertainty does not refer to a single instrument’s accuracy, but evaluates the complete range of possible test results given a singular test condition. The field test cannot be performed with all variables fixed. Consequently, the measured performance calculations and test results must also be a range rather than a point and must account for all possible input combinations of all input variables. It is important to understand that if the input ranges to the system are defined as statistical bounds, such as 95% confidence intervals, then the output from the uncertainty analysis will also present the same 95% confidence interval statistical bounds. Similarly, if the inputs are absolute errors of measurements, then the uncertainty analysis will also yield absolute errors (i.e., whatever is the type of uncertainty range for the input variables will be the type of uncertainty range for the result). Consistent application and definitions of the input variable’s uncertainty ranges is, thus, critically important in any uncertainty analysis. Furthermore, prior to determining a test uncertainty, it is important to know whether the measured variables in the test are independent or dependent, as this determines the method of uncertainty calculation that must be employed. For almost all real measurement scenarios, there is some physical dependency between the input variables and, thus, unless one is absolutely certain that all measured and given system inputs are independent; it is safer to opt for the more conservative assumption of measurement dependence. Thus, as the determination whether an experiment’s measured variables are interdependent directly establishes the uncertainty analysis method that must be employed, a thorough physical understanding of the measured system is imperative. The test uncertainty calculation should be performed using one of the three methods described in Appendix E. To evaluate the test data, the uncertainty of the test must be calculated correctly, and the required uncertainty limits must be understood prior to the test. For example, data with an uncertainty of 3.0% cannot yield conclusions requiring an accuracy of 1.0% and, thus, if 1% accuracy is required, the test preparation, instrumentation, and planning must reflect this requirement. In addition, if a measurement of pressure is made with a value of 100 psi and an uncertainty of ±3%, then the pressure measurement will actually be in the range of 97 to 103 psi. Also, in comparing the field test data to any

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other set of data of the same machine (such as historical data or the factory test data), the uncertainties in both tests must be considered in the comparison. If an uncertainty analysis is performed before testing begins, it could be useful in determining what the most influential test parameters are. The determination of influential test parameters should be used to assess the measurement parameters in order to improve the accuracy of the field test. The terms in the total uncertainty equation can be compared at different operating conditions. If the comparison reveals that a certain term becomes more significant to the overall uncertainty, then extra efforts to improve this measurement will be worthwhile. The test uncertainty tolerances are recommended in Table 7-1 for the primary measurement parameters in the performance test. This table was assembled from current practices, recommendations from industry experts, and what type of instrumentation is commercially available. Table 7-1. In-Practice Achievable Uncertainty for Measured Test Parameters Measurement

Recommended Uncertainty

Pressure

0.3 – 1.0% Full Scale

Temperature

0.5 – 7.0 ºF

Flow

0.5 – 2.0% of value

Gas composition (Density, compressibility, gas constant, specific heat, energy content)

0.2 – 3.0% of value

Piston Position (encoder)

0.1 – 0.3% of 360 degrees

For all parameters derived from an EOS (such as compressibility, heating value, isentropic coefficient, density, specific heat, and gas constants), there is an added inherent uncertainty, since the EOS is an empirical model. Unless direct experimental data for comparison is available for the gas composition used in the performance test, it is difficult to quantify the added EOS model uncertainty. However, a consistent application of the selected EOS between the factory test, field test, and predictions will minimize any potential performance analysis differences and, thus, reduce the contribution of the EOS model uncertainty to a negligible contribution. The effect of typical “near ideal” measurement uncertainties on the total compressor uncertainty for both the PV Card and Enthalpy Rise method is provided in Section 7.1. Non-ideal installation effects on uncertainty are provided in Section 7.2 below. 7.1

Ideal Field Test Conditions for Reducing Uncertainties

In an ideal field installation, the uncertainty in measured power and efficiency for the reciprocating compressor is at a minimum. Departures from the ideal installation will increase these uncertainties. Uncertainties should be calculated using the methods described in Appendix E and instrument uncertainty values listed in the preceding sections. This section describes an example of a near ideal field test installation and provides a typical baseline uncertainty in power and efficiency for this case. The effects of non-ideal measurement conditions on the total performance uncertainties are discussed and compared in Section 7.2. In the example, uncertainty calculations given in Sections 7.1 and in the non-ideal installations shown in Section 7.2, the perturbation method was used to determine the total performance uncertainty, as described in Appendix E.

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7.1.1

Compressor Uncertainty Examples

The validity of a compressor performance field test depends on the level of uncertainty of measured efficiency and power. Also, the test uncertainty can be used to determine if the test is worthwhile. If the test uncertainty bands cross over the theoretical predictions of compressor performance power, then the test cannot prove or disprove the theoretical predictions. The theoretical predictions would then provide adequate information on the performance of the compressor. Figure 7-1 shows two examples: one where the test would not provide worthwhile data due to high uncertainty (left side) and one with an uncertainty which provides useful test data (right side). Power and efficiency uncertainties should be calculated from the individual measurement uncertainties (temperature, pressure, piston position, flow rate, and gas properties). Below are examples of the PV Card and Enthalpy Rise methods uncertainty analyses. Test Point and Respective Uncertainty Ellipse

Test Point and Respective Uncertainty Ellipse

Theoretical Prediction Uncertainty Bands

Theoretical Performance Curve

BHP

BHP

Theoretical Performance Curve

Theoretical Prediction Uncertainty Bands

ps

ps

Figure 7-1. Comparison of Tests with Different Levels of Uncertainty

PV Card Method An example of uncertainty calculation of a performance test conducted using the PV Card method is described below. This was conducted on a medium speed unit with air being compressed. The pressure transducer was installed on the head end of the cylinder with the transducer flush-mounted. The compressor was run at various speeds from 450-900 RPM. The test data analyzed below is for the 450 RPM test. Table 7-2 details the geometry of the compressor. The uncertainty of the clearance was assumed to be 1%. This is considered to be a best case scenario. There is an uncertainty associated with the clearance volume regardless if it is from manufacturer literature, measured, or an effective clearance. An isentropic constant for air was assumed to be 1.4. This is a standard value at 14.7 psia and 60ºF. An uncertainty of 0.01% was assumed for this value based on expected uncertainties in suction temperature and pressure and gas composition measurements in field performance tests at steady state. Figure 7-2 shows the actual PV diagram plotted with the theoretical PV diagram for 450 RPM and a suction pressure of 35 psia. Table 7-2. Compressor Geometry Component Bore Diameter (in) Stroke (in) Rod Diameter (in) Rod Length (in) Clearance (%)

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Value 7.5 6 2.25 14.5 17.83

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The data from the test was evaluated for its uncertainty related to clearance volume measurement, isentropic constant calculation (from EOS with suction pressure, suction temperature, and gas composition measurements), piston position, and cylinder pressure. The results for each variable are shown in Table 7-3. The total resulting uncertainty from the performance test at 450 RPM was 2.03% for power and 2.06% for efficiency. As shown in Table 7-3, the main influential values on the uncertainty are the pressure and cylinder position measurements. These measurements should be targeted to have the lowest uncertainty allowable based on budgetary, field testing, and installation constraints. 100

Measured Theoretical 90

Pressure (psia)

80

70

60

50

40 0

50

100

150

200

250

300

350

Volume (in^3)

Figure 7-2. Actual and Theoretical PV Diagrams for Performance Test at 450 RPM Table 7-3. Summarization of Uncertainty for Performance Test at 450 RPM Variable Clearance Volume Isentropic Constant (Suction Temperature and Pressure & Gas Composition) Piston Position Cylinder Pressure Total Uncertainty

Variable Uncertainty (+/- %) 1

Power Uncertainty (+/- %) 0

Efficiency Uncertainty (+/- %) 0.007

0.01

0

0.02

0.2 0.25

1.09 1.71 2.03

1.1 1.74 2.06

Enthalpy Rise Method An example uncertainty calculation for a reciprocating compressor test using the Enthalpy Rise method is given in Table 7-4. The values of the measured variables shown in Table 7-4 represent a typical reciprocating compressor application in pipeline (low compression ratio) service. Operating conditions are shown in Table 7-4. A representative gas composition was used to compute the gas properties, consisting of the following components: 90.0% methane 5.37% ethane 1.7% propane 0.274% isobutene 0.331% n-butane

0.055% isopentane 0.09% n-pentane 0.07% n-hexane 1.06% carbon dioxide 1.05% nitrogen

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The Benedict-Webb-Rubin (BWR) EOS model was used to compute the compressibility, specific heat, and molecular weight. Table 7-4. Example of Total Uncertainty Calculation for Compressor in "Near Ideal" Case Input Parameter

Value

Input Δ(%)3

ΔPower

Δη

Measured properties: ps (psia) 159.5 0.3 26.11 0.006 Ts (deg F) 80.3 0.1 73.98 0.005 pd (psia) 224.8 0.3 26.18 0.006 Td (deg F) 152.3 0.1 65.44 0.005 3 1 Q (ft /min) 19345 0.5 43.52 0.000 Calculated properties based on gas composition at suction conditions 2 Z 0.9763 0.05 4.36 0.000 cp (Btu/lbm-deg F) 0.52 0.3 26.11 0.000 K 1.31 0.08 0 0.003 R (Btu/lbm-deg F) 0.11 0.3 26.11 0.000 Performance Parameter Pcomp (HP) Efficiency, ηisen (%)

Value

Total ΔPower (%)

Total Δη (%)

8703 0.636

1.35

1.81

1

Q is actual flow rate at suction conditions, v = 3937 ft/min in a 30" diameter pipe. Z, cp, k, and R represent a typical hydrocarbon transmission grade gas. 3 Typical values of uncertainty represent ideal pressure and temperature measurement using four sensors on suction and discharge, recommended flow meter installation and gas property calculation made with consistent EOS model and accurate gas sample. 2

The measurement uncertainties calculated in Table 7-4 assume near-ideal test conditions, procedures, and efficiencies. These uncertainties are based on proper installation, application, and acquisition of the test instrumentation, as recommended previously. The calculated property uncertainties (Z, cp, k, R) are based on typical variations in a sampled gas composition due to sample variation and uncertainty introduced by the gas sampling process (∆ = +0.3% for methane and ethane, ∆ = +0.1% for propane, ∆ = -0.3% for carbon dioxide, ∆ = -0.4% for nitrogen). The calculated property uncertainties include the uncertainty due to gas chromatograph analysis for a calibrated gas chromatograph. Based on all the input uncertainties, the resulting uncertainty in compressor power is 1.35%. The resulting uncertainty in compressor efficiency is 1.81%. These values of measurement uncertainty for the compressor are close to the minimum attainable test uncertainty for this case. 7.2

Effects of Non-Ideal Installations on Uncertainty

Deviations in the ideal test conditions or procedures (as recommended previously) will increase the individual measurement uncertainties and result in a higher total performance measurement uncertainty for the compressor. Depending upon the effect of the non-ideal installation on the measurement, the resulting increase in uncertainty can range from a small increase of 0.20% in some cases to above 5.0%. This uncertainty can affect the measured accuracy of the efficiency and the power. Some typical nonideal effects are instrumentation uncertainty, channel resonance and attenuation, heat losses, and the

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pulsating flow field. Table 7-5 details some of the non-ideal uncertainties experienced with instrumentation installations. The majority of these uncertainties are targeted for the Enthalpy Rise method, but some can also be used with the PV Card method such as use of thermocouple instead of RTD and error in gas sampling. Table 7-5. Non-Ideal Installation Effects on Compressor Uncertainty

Non-Ideal Installation Single elbow 1 to 3 pipe diameters upstream of flow measurement point (no flow conditioner) Double elbow in-plane, second elbow 1 to 3 pipe diameters upstream of flow measurement point (no flow conditioner) Double elbow out of plane, second elbow 1 to 3 pipe diameters upstream of flow measurement point (no flow conditioner) Partially closed gate or ball valve within 1 to 3 pipe diameters upstream of flow measurement point (no flow conditioner) Single elbow within 1 to 3 pipe diameters of temperature and pressure sensors Double elbows in-plane, second elbow within 1 to 3 pipe diameters of temperature and pressure sensors Double elbows out of plane, second elbow within 1 to 3 pipe diameters of temperature and pressure sensors RTD not fully inserted into flow stream Use of thermocouple instead of RTD Error in gas sampling (no pigtail used) with heavy hydrocarbons

Total ΔPower (%)

Deviation from Baseline Δpower

Total Δη (%)

Deviation from Baseline Δη

1.73

0.38

1.81

0

1.95

0.6

1.81

0

2.79

1.44

1.81

0

3.72

2.37

1.81

0

2.39

1.04

2.85

1.04

3.19

1.84

3.66

1.85

4.84

3.49

5.37

3.56

2.37 3.15

1.02 1.8

2.66 3.38

0.85 1.57

1.38

0.03

2.01

0.2

*Note: This table assumes that the measurements are taken outside of the bottles with a minimal pulsating flow (less than 2-3%). If measurements are taken in a pulsating flow, then additional uncertainty should be added. Table 7-6 details the increase in performance uncertainty using an encoder and cylinder pressure measurement with the PV Card method. There are many factors that play into the accuracy of an encoder. Outer dead center (ODC) must be determined and synchronized correctly in the data acquisition system to yield accurate results. Also, misalignment with a mechanical drive will introduce high error, as the instantaneous angular velocity of the encoder can be significantly affected. Every effort should be made to ensure that the encoder rotation is representative of the compressor rotation. Encoders can be installed and calibrated to achieve accuracies of 1 degree. As shown in Table 7-6, a near-ideal uncertainty of 0.28% yields an overall uncertainty in power and efficiency of 1.54% and 1.57%, respectively. The cylinder pressure measurement is influenced by instrumentation characteristics and proper installation. The installation of the dynamic pressure sensor should be designed to avoid channel resonance and attenuation. Channel resonance is a function of the geometry of the port (diameter and length of the channel). It occurs due to an excitation of the quarter-wave acoustic length resonance of the

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gas passage between the cylinder interior and the pressure transducer. The channel resonance and attenuation error is not related to the machine’s efficiency, but the effect is a common phenomenon with high-speed compressors. Channel attenuation can cause errors in the actual power calculation up to 40%. High errors will be seen in high speed units with heavy gases such as propane or CO2 and long, small diameter indicator passages. The measured ICHP is not normally affected by pure channel resonance since it is a sinusoidal phenomenon. Table 7-6. Effects of Non-Ideal Encoder and Cylinder Pressure Measurements Variable

Encoder

Cylinder Pressure

Variable Uncertainty (+/- %) 0.28 0.42 0.56 0.25 0.50 1.00 1.50

Power Uncertainty (+/- %) 1.54 2.33 3.11 1.71 3.42 6.84 10.25

Efficiency Uncertainty (+/- %) 1.57 2.38 3.21 1.74 3.54 7.34 11.43

If channel resonance is present, it can be removed by filtering techniques. However, the user is cautioned in doing this. If the data is not properly filtered, the calculated power and efficiencies will be incorrect. There is also uncertainty associated with temperature measurements. This effect manifests itself in the theoretical PV diagram construction. This calculation is based on EOS results. It is difficult to summarize the effects of EOS on uncertainty. If the proper EOS is utilized consistently throughout the performance test, the uncertainty of the theoretical ICHP will mainly be due to the uncertainties in the temperature, pressure, gas composition, and piston position measurements. If the test is conducted at steady state, the effect on the variation of the theoretical power and efficiency will be minimal (less than 0.01%). This uncertainty only needs to be considered if the test has highly fluctuating conditions. A large number of reciprocating compressors utilize some type of cylinder cooling system. This is true on high-speed and low-speed compressors. Removing heat from the compressor cylinder is essentially removing some of the energy applied by the compressor to the gas. This heat removed needs to be considered when determining an isentropic efficiency. If it is not accounted for, the calculated isentropic efficiency will be optimistic. The cylinder cooling effects are already included in the measured PV diagram. This is due to the fact that the work applied to the gas is directly measured. Equation 4-4 shows how the heat removal is included in the Enthalpy Rise method calculation. The uncertainty of the heat losses estimations directly affects the uncertainty of the total power measurement and efficiency in the Enthalpy Rise method. Care should be taken to obtain an accurate estimate for heat removed from the compressor cylinders. Pulsations are always present in a reciprocating compressor. It is important to understand their effects in order to account for their influence during performance test. The capacity of the compressor can be calculated from a PV diagram, but sometimes the capacity is measured. Flow measurement is highly influenced by pulsations. A flow meter must be installed in an area of low pulsations (much less than 10% and preferably under 2%) in order to obtain a valid reading. This must be outside the suction or discharge pulsation bottles in virtually all cases. Beyond the flow measurement, the pressure and temperature measurement can be affected by large pulsations and introduce higher than 3% uncertainties.

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Pulsations can also have a direct effect on both the actual and the calculated power and efficiency. While the suction and discharge valves are open, the acoustic pulsation present in the system is reflected into the compressor cylinder. Should the pulsation levels be of sufficient amplitude, the valve opening and closing times can be affected, and the average inlet and/or discharge pressures of the cylinder can be different than the design pressures, the net result being horsepower and capacity values which are different than the design values. These values may be greater or smaller, depending on the pulsation characteristics. Variations of operating conditions during testing will affect the uncertainty of the performance measurements and calculations. The requirements for test stability were shown in Table 5-1 through Table 5-3. If the measured and calculated values deviate outside these ranges, then the uncertainty of the test will increase. Every effort should be taken to ensure that test stability is achieved. If this is not possible, then the uncertainty of the deviations must be considered in the test results. 8.

INTERPRETATION OF TEST DATA

8.1

Data Reduction and Checking Uncertainties

Test points taken at different points in time should not be averaged. If this is done, the non-linear effects will not be averaged correctly. Instead, the performance parameter should be calculated for each data point. The resulting parameters can then be averaged. Data reduction procedures should be aimed at minimizing time and cost in the determination of performance. If the test data from the field test deviates more than the level of test uncertainty, the source of the deviation should be explored further. For example, two test points, which were taken at the same condition, may show vastly different calculated flows. Further investigation may reveal that a clearance volume pocket was open at one test point, but not the other. Repeating the performance test is not recommended by this guideline unless the data is clearly un-usable. It is advised to have a performance calculation program set-up in the field such that the results can be calculated automatically. Any significant deviations in the data can be investigated in the field. Then it will be quick and easy to repeat tests as necessary. The results should be monitored throughout the test. For the reciprocating compressor, there are many ways to determine what could possibly influence the test results. For the PV Card method, the structure of the PV diagram can indicate whether there are leaks in the valves or seals. Also, if a shift is seen in the compression and expansion lines of the PV diagram, the gas composition may have not been stable during the test. Compressor performance diagnostics with PV diagrams is discussed in more detail in Appendix F. Effects such as suction valve leakage, discharge valve leakage, piston ring leakage, pulsation effects, and valve and cylinder gas passage losses can be identified with the geometry of the diagram. For the Enthalpy Rise method, if the enthalpy difference versus flow curve has shifted horizontally, the flow may have been measured incorrectly or contain a bias error. If some of the points on the curve match predictions and others do not, the gas composition (or another influential parameter) may not have been stable during the test. 8.2

Use and Comparison of Data

There are many different objectives to performance tests. A company may be conducting a manufacturer verification performance test or they may be generating a set of performance curves for the operational control of the system. Each data point recorded during the field test should be evaluated individually. The average of all data points at a particular condition should be used to compute the average power,

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enthalpy difference, flow, and efficiency. This should only be done after the results have been calculated for each data point. For a manufacturer performance verification test, these final data point averages should be compared to the performance curves for the compressor. The performance curves are provided by the manufacturer of the compressor. There are multiple performance curves that can be supplied with the compressor. Some of these include: BHP/MMSCFD verses suction pressure, discharge pressure or pressure ratio, capacity verses suction pressure, discharge pressure or pressure ratio, and discharge pressure verses suction pressure. The performance results can be compared to the various curves depending upon what parameters were measured during the performance test. When comparing the measured data points to the manufacturer stated performance, the uncertainty must be considered. If the performance test is conducted in order to characterize the performance of the compressor at various conditions and development of curves, each individual point should still be evaluated individually and then averaged. The developed curves should include uncertainty curves. The uncertainty curves will provide the user with the range of possible values for the plotted values. An example of a compressor performance curve is shown below in Figure 8-1 for a high-speed transmission compressor. 2600 2400 2200

Driver HP

Power (BHP)

2000 1800 Step 1

1600 Step 2

1400

Step 3 Step 4 Step 5

1200 1000 800

250

200

Step 1

Flow (MMSCFD)

Step 2

150

Step 3 Step 4 Step 5

100

Reg Flow 50

0 500

550

600

650

700

750

800

850

900

Ps (psig)

Figure 8-1. Example of Compressor Performance Curves for High-Speed Transmission Compressor

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8.3

Using Redundancy to Check Test Measurement and Uncertainty

Redundant calculations should be performed, if possible, to check test measurements. The compressor driver power may be measured as discussed in previous sections. The shaft power output (or engine BHP) from the engine can be calculated with the fuel flow, lower heating value of the fuel, and efficiency of the engine. The compressor BHP measured during the field test should match the engine BHP. If the flow rate is measured during the performance test, this can be compared to the capacity calculated from the volumetric efficiencies measured. There may be some variation in these numbers due to the uncertainty associated with each type of measurement, but the values should be fairly close. The calculated values, or if available factory test (manufacturer supplied) values, should match the measured values within the associated uncertainty for both values. The uncertainty on any measured value obtained in the field test should be calculated (or estimated as accurately as possible). This uncertainty will be a plus or minus value. It should overlap with the uncertainty band (also a plus or minus) on the calculated/factory test value. This analysis will determine if the redundant measurement is statistically equal to the measured value. This method of comparison should always be used in order to practically determine if measured values are correct. A graphical example of this is shown in Figure 8-2. Test Point and Respective Uncertainty Ellipse

ps

Performance Statistically Equal

BHP

Theoretical Performance Curve

BHP

BHP

Theoretical Prediction Uncertainty Bands

ps

ps

Performance Statistically Equal

Performance Not Statistically Equal

Figure 8-2. Comparison of Theoretical Predicted Performance and Measured Performance Test Point

8.4

Analysis of Measured Results

The true value of the compressor performance parameters (capacity, efficiency, and power) lies within the measured data points, assuming the data has been recorded correctly without a significant bias error. The measured data points should be viewed as a representation of the bracket surrounding the true value. If two measured parameter data points are plotted on a horizontal- and vertical-axis, an uncertainty band on each measured variable exists. An ellipse surrounds the measured data point (see Figure 8-3). The predicted performance test point, or manufacturer factory test curve, may lie within the uncertainty band produced from the field test, though the exact values from the field test do not exactly match the manufacturer suggested curve. This example (shown in Figure 8-3) shows good performance of the compressor during the field test. The compressor performance in the field test is statistically equal to the factory test in this example.

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Test Points and Respective Uncertainty Ellipse

BHP

Performance Curves

ps Figure 8-3. Example of Test Uncertainty Range

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9.

REFERENCES

1.

AGA Report No. 7, “Measurement of Natural Gas by Turbine Meter,” 2006.

2.

API 618, “Reciprocating Compressors for Petroleum, Chemical and Gas Industry Services,” 1995.

3.

Deffenbaugh, D. M., Smalley, A. J., Harris, R. E., Brun, K., Moore, J. J., McKee, R. J., et al., “Advanced Reciprocating Compression Technology,” Southwest Research Institute Final Report for DOE-NETL, December 2005.

4.

ASME PTC 10, “Performance Test Code on Compressors and Exhausters,” 1997.

5.

ASME PTC 19.1, “Measurement Uncertainties,” American Society of Mechanical Engineers, New York, New York, 1985.

6.

Boutin, B. and Webber, B., “Basic Reciprocating Engine and Compressor Analysis Techniques,” Proceedings of the Gas Machinery Conference, Albuquerque, New Mexico, 2004.

7.

Brun, K. and Nored, M. G., “Guideline for Field Testing of Gas Turbine and Centrifugal Compressor Performance,” Gas Machinery Research Council, August 2006.

8.

Casey, M.V., Fesich, T.M., “On the Efficiency of Compressors with Diabatic Flows,” GT200959015, Proceedings of ASME TurboExpo 2009: Power for Land, Sea and Air, Orlando, FL, 2009.

9.

Durke, R. G. and McKee, R. J., “Orifice Meter Gage Line Distortions,” Southwest Research Institute.

10.

Edmister, W. C. and Lee, B. I., Applied Hydrocarbon Thermodynamics – Volume 1, Second Edition, Gulf Publishing Company, Houston, Texas, 1984.

11.

Ely, C. and Messick, T., “Performance Measures for Gas Compression and Transportation,” Proceedings of Gas Machinery Conference, Salt Lake City, Utah, 2003.

12.

“Field Measurement Guidelines Compressor Cylinder Performance Summary,” GMRC Technical Report No. 84-10a, May 1984.

13.

Gehri, C. and Harris, R. E., “Technology for the Design and Evaluation of High-Speed Reciprocating Compressor Installations,” Proceedings of the European Forum for Reciprocating Compressors, Dresden, Germany, November 1999.

14.

Harris, R., E. and Edlund, C., “Performance Measurements of High Speed/High Ratio Reciprocating Compressors,” GMRC, 1998.

15.

Howard, B., “Channel Resonance in Reciprocating Compressor Cylinder Pressure Measurements,” GE Energy, 2006.

16.

IEEE 515, “Standard for the Testing, Design, Installation, and Maintenance of Electrical Resistance Heat Tracing for Industrial Applications,” 2004.

17.

ISO 1217, “Displacement Compressors – Acceptance Test,” 1996.

18.

ISO 5167, “Measurement of Fluid Flow by Means of Pressure Differential Devices Inserted in Circular Cross-Section Conduits Running Full,” 2003.

19.

Kumar, S. K., Kurz, R., and O’Connell, J. P. “Equations of State for Compressor Design and Testing,” ASME Paper No. 99-GT-12, 1999.

20.

Kurz, R. and Brun, K. “Site Performance Test Evaluation for Gas Turbine and Electric Motor Driven Compressors,” Proceedings of the Thirty-Fourth Turbomachinery Symposium, Houston, Texas, 2005.

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21.

Kurz, R. and Brun, K. “Degradation in Gas Turbine Systems,” Journal of Engineering for Gas Turbines and Power, Transactions of the ASME, Vol. 123, pp. 70-77, January 2001.

22.

Kurz, R. and Brun, K., “Efficiency Definition and Load Management for Reciprocation and Centrifugal Compressors,” Proceedings of 6th Conference of the EFRC, Dusseldorf, Germany, October 2008.

23.

Mathews, H., “Compressor Performance Analysis,” Proceedings of Gas Machinery Conference, 2000.

24.

McKee, R. J., “Pulsation Mitigation in Gas Flow Measurement,” Southwest Research Institute.

25.

Moffat, R., “Describing the Uncertainties in Experimental Results,” Experimental Thermal and Fluid Science, Vol. 1, 13-17, 1988.

26.

Nimitz, W., “Evaluation and Optimization of Reciprocating Compressor Performance,” Proceedings of the AGA Transmission/Distribution Conference, 1985.

27.

Ransom, D., Brun, K., and Kurz, R., “Enthalpy Determination Methods for Compressor Performance Calculations,” Proceedings of ASME TurboExpo, Montreal, Canada, 2007.

28.

Sandberg, M. R. “Equation of State Influences on Compressor Performance Determination,” Proceedings of the 34th Turbomachinery Symposium, Houston, Texas, 2005.

29.

Schultheis, S., Lickteig, C., and Parchewsky, R., “Reciprocating Compressor Condition Monitoring,” Proceedings of the 36th Turbomachinery Symposium, 2007.

30.

Smalley, A., Lagus, P., Kothari, K., Wang, J., and Clowney, S., “Reciprocating Compressor Flow by Tracer Dilution and Cylinder Pressure Measurement,” Proceedings of the International Gas Research Conference, 1992.

31.

Soave, G., “Equilibrium Constants from a Modified Redlich-Kwong Equation of State,” Chemical Engineering Science, Vol. 27, Issue 6, 1972.

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APPENDIX A GENERAL PERFORMANCE TESTING PROCEDURE

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APPENDIX A This section outlines the steps that should be followed to complete a reciprocating compressor performance test. Differences in the PV Card and Enthalpy Rise method will be noted in the appropriate steps. References to certain sections of the guideline (that provide more details) will be in parentheses. 1. Determine test objectives (Forward and Section 2) 2. Develop Field Test Agenda (Section 5) a. Select calculation methodology i. Chose method of data reduction: PV Card or Enthalpy Rise method (Section 4) ii. Select EOS of state for all calculations (Section 3.7 and Appendix C) iii. Select approach for determining uncertainty (Section 7 and Appendix E) iv. Set test results acceptance criteria (specified in terms of maximum uncertainty allowed) b. Review site specific details i. Review field conditions and equipment, pipe, and station layout ii. Determine if any deviation from normal operation may be necessary to achieve test objectives iii. Identify operating conditions and operational limits of compressor including pressure, temperature and flow limits of facility 1. Obtain manufacturer performance curves for compressor 2. Review capacity control and load steps of compressor 3. Determine operation matrix for testing based on typical operating conditions and test objectives a. If possible test guarantee points and then additional desired points iv. Review test safety considerations (Section 5.6) v. Select instruments to be used, their location, method of operation, calibration, requirements for installation (Sections 4 and 6) 1. Determine how these instruments will be installed with existing instrumentation 3. Pre-test meeting: Meeting between test engineer, customer, and all parties involved to discuss the details of the test (Section 5.1) a. Review field test agenda b. Agreement should be reached on… i. Test objectives ii. Test procedures iii. Safety requirements iv. Responsibilities during test v. Availability of necessary operating conditions 1. Review contractual guarantee points and what operating conditions they could be reached at 2. If cannot operate at guarantee points then consult with manufacturer to determine alternate guarantee points vi. Acceptance conditions 4. Pre-test operation and instrumentation check-out (Section 5.2) a. Unit preparation i. Have operator take the unit offline if it is running

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b. c. d.

e.

f.

g. h.

i. j. k.

1. If unit cannot be taken offline all items below except e can be completed with the unit online. The unit must be shutdown in order to complete ODC determination. ii. Blow down the unit iii. Lockout Tagout the unit Verify compressor is in good mechanical condition (complete a mechanical assessment) and conduct appropriate maintenance If driver performance will be measured during the test, verify the mechanical condition of the driver and conduct appropriate maintenance Instrumentation (Section 6) i. Calibrate instruments in the range which they will operate in ii. Install instruments 1. Check insertion depth of thermowells. 2. Verify that thermowells are service with appropriate oil or heat transfer material 3. If large area of thermowell is exposed, insulate this area 4. Where pressure taps involve tubing runs, the tubing should be checked for leaks. iii. Check all instrument readings to assure that they are functioning properly iv. Verify data acquisition system (DAQ) operation prior to starting the test ODC Determination (Section 6.5) i. Prepare compressor for ODC determination 1. Before starting ODC determination open all indicator valves on compressor cylinders and power cylinders to relive any excess gas ii. Complete ODC determination with selected method (two methodologies described in Section 6.5) iii. Repeat ODC determination for verification iv. Synchronize encoder with ODC position Check fixed clearance (Section 5.2 and Section 4.1.3) i. Compare the calculated clearance from the PV analyzer to the manufacturer stated clearance. Take into considerations what capacity control devices are being used (ex. valve unloaders, clearance pockets). If these values are within 1 to 2% of the manufactures stated fixed or variable clearances then the manufacturer clearance can be used for the performance test. If they are not close then further investigation should be conducted to determine what is causing the variability or the fixed clearance should be measured. Ensure sufficient gas is available for the anticipated flow and operating conditions of the test If the test is going to be conducted on a closed loop, check if gas cooling is available and if recirculation of gas is an option during field test. Notify all parties of time frame for test. Determine how load steps will be maintained constant during a test point and how they will be changed for different test points. Identify and document what orifice plates are installed Check the position of the recycle or bypass valve. Both of these values should be in operable conditions and not leak when closed. Check if in line strainers are plugged or not

l. 5. Testing a. Start compressor and allow system to reach thermal equilibrium (at least 30 minutes for the compressor) b. Adjust compressor to reach desired operating conditions for first test point on test matrix.

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c. If using the PV Card method, verify that PV diagram is as expected and that no channel resonance or attenuation is present. (Section 4.1) d. Estimate the amount of time required to collect all data during a test. Assure that compressor is stable over this amount of time before each test (Section 5.5, Table 5-2) e. Capture test data by obtaining an average of several data points over a short time span. i. The test data should not fluctuate more than the requirements listed in the guideline (Table 5-1 through Table 5-3). ii. If the test data variations does not fall within the limits specified in the guideline perform the test again once the compressor is stable iii. If the test data variations do not fall within the limits after several attempts then take the test data as is. An additional uncertainty should be added to the results due to the instability of the test. (Section 5.5.3) f. Measure surface temperature of bottles and pipe for heat loss estimations during each test (Appendix H) g. Record wind speed (only on units not housed in a building), ambient temperature, and ambient pressure once during each test if not measure continuously and recorded by DAQ system h. Repeat steps b through g for all test points in test matrix i. After all tests are complete, ensure that all data has been captured and stored in the test computer 6. Post-test operation a. Have operator shut compressor down b. Bleed gas pressure out of compressor c. Remove all instrumentation and return compressor back to original condition (pre-test condition) 7. Test Data Processing a. Retrieve test data from test computer b. Process data to calculated desired performance parameters in accordance with the data reduction method and EOS selected prior to testing (Section 3, Section 4, Section 8, Appendix B, Appendix C, Appendix H) i. Determine compressor efficiency and power at each test point (Section 3.2, Section 3.3, and Appendix B) ii. Calculate heat losses for each test point when using the Enthalpy Rise method (Appendix H) c. Calculate uncertainty for each test parameter (Section 7 and Appendix E) d. Plot test data and uncertainty ellipse with manufacturer performance curves. (Section 8) e. Document details of test including operation conditions tested, compressor configuration, test data and results and uncertainty in a test report

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APPENDIX B CALCULATION OF THEORETICAL PV DIAGRAM

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APPENDIX B The following are two general procedures for construction of the theoretical PV diagram. With this diagram, the theoretical ICHP can be calculated. This will be used to find the isentropic efficiency of a compressor cylinder. The first method is the method most commonly used in testing. It is based on ideal gas relationships for isentropic compression. It should be noted that in natural gas service, assuming ideal gas relationships is not necessarily correct. The second method is more rigorous and requires the use of an EOS solver. The EOS solver is used to generate a constant entropy PV diagram without the assumptions of an ideal gas. This method is perhaps more accurate than the first since it does not assume ideal gas relationships. Commercial PV analyzers will automatically calculate the theoretical PV diagram and use it to calculate the theoretical ICHP. These procedures are presented here for completeness of the guideline. Ideal Gas and Isentropic Relationships There are several pieces of information that need to be known before construction of the PV diagram can begin. These are listed below. •

Gas Composition

•

Absolute Suction Pressure (from toe pressure on PV diagram or measured in nozzle)

•

Absolute Discharge Pressure (from toe pressure on PV diagram or measured in nozzle)

•

Suction Temperature (measured in nozzle)

•

Clearance Volume (or Minimum Volume)

•

Maximum Volume

The theoretical PV diagram consists of four sides. The left side is an isentropic expansion line, the bottom a constant suction pressure line, the right side an isentropic compression line, and the top a constant discharge pressure line. The items listed below give step-by-step instructions on how to generate the theoretical PV diagram. 1. Determine the isentropic exponent, k. a. The isentropic constant calculated from a ratio of specific heats (Equation B-1). The constant pressure and constant volume specific heats are found using the gas composition, suction pressure, and suction temperature with an EOS solver. There are many programs available that can complete this calculation. Also, Equation 3-7 can be used to calculate this.

k=

cp cv

(B-1)

2. Determine the discharge pressure and minimum volume (clearance volume). a. This will be the start point of the expansion line and the end point of the constant discharge pressure line as shown in Figure B-1.

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90

pd 80

70

Pressure (psia)

60

50

ps

40

30

20

10

Vmin

Vmax

0 0

50

100

150

200

250

300

350

400

Volume (in^3)

Figure B-1. Theoretical PV Diagram with Start of Expansion Stroke Indicated

3. Determine the suction pressure and maximum volume. a. This will be the start point of the compression line and the end point of the constant suction pressure line as shown in Figure B-2. 90

pd 80

70

Pressure (psia)

60

50

ps

40

30

20

10

Vmin

Vmax

0 0

50

100

150

200

250

300

350

400

Volume (in^3)

Figure B-2. Theoretical PV Diagram with Start of Compression Stroke Indicated

4. Calculate the expansion line constant, K1.

K1 = pd * Vmin

k

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(B-2)

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5. Calculate the volume at the suction pressure on the expansion line.

K Vs = 1 ps

1 k

(B-3)

6. Calculate several other points on the expansion line using the equation in step 5 and plot the expansion line (see Figure B-3). 90

pd 80

70

Pressure (psia)

60

50

ps

40

30

20

10

Vmin

Vmax

0 0

50

100

150

200

250

300

350

400

Volume (in^3)

Figure B-3. Theoretical PV Diagram with Multiple Points Plotted on Expansion Line

7. Calculate the compression line constant, K2.

K 2 = ps * Vmax

k

(B-4)

8. Calculate the volume at the discharge pressure on the compression line.

K Vd = 2 pd

1 k

(B-5)

9. Calculate several other points on the compression line using the equation in step 8 and plot the compression line (see Figure B-4).

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90

pd 80

70

Pressure (psia)

60

50

ps

40

30

20

10

Vmin

Vmax

0 0

50

100

150

200

250

300

350

400

Volume (in^3)

Figure B-4. Theoretical PV Diagram with Multiple Points on Compression Line

10. Connect the expansion and compression lines with the suction and discharge pressure lines (see Figure B-5). 90

pd 80

70

Pressure (psia)

60

50

ps

40

30

20

10

Vmin

Vmax

0 0

50

100

150

200

250

300

350

400

Volume (in^3)

Figure B-5. Complete Theoretical PV Diagram

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Constant Entropy with EOS Solver For the procedure using the EOS Solver and using constant entropy, the parameters obtained for the first method are also used for this method. This method also requires the use of the discharge temperature. •

Gas Composition

•

Absolute Suction Pressure (from toe pressure on PV diagram or measured in nozzle)

•

Absolute Discharge Pressure (from toe pressure on PV diagram or measured in nozzle)

•

Suction Temperature (measured in nozzle)

•

Discharge Temperature (measured in nozzle)

•

Clearance Volume (or Minimum Volume)

•

Maximum Volume

The items listed below give step-by-step instructions on how to generate the theoretical PV diagram. 1. Determine the discharge pressure and minimum volume (clearance volume). a. This will be the start point of the expansion line and the end point of the constant discharge pressure line as shown in Figure B-1. 2. Determine the suction pressure and maximum volume. a. This will be the start point of the compression line and the end point of the constant suction pressure line as shown in Figure B-2. 3. Expansion Line a. Calculate the mass present in the cylinder at the start of the expansion. i. This can be done by knowing the properties of the gas (calculated with gas composition and EOS), discharge temperature, discharge pressure, and volume in the cylinder (clearance volume). b. Calculate the entropy at discharge temperature and discharge pressure with the EOS. i. The expansion on the theoretical PV diagram is an isentropic process. This assumes constant entropy throughout the process. c. Calculate the end point of the expansion line and plot. i. This is done by determining the density of the gas with the EOS from the suction pressure and entropy determined in step 3b. ii. Use this density to calculate the volume at the suction pressure with the mass calculated in step 3a. d. Calculate a few other points along the expansion line with the various densities (calculate from mass and volume in the cylinder) and the entropy previously determined. e. Plot these on the graph and complete a curve fit to obtain the full expansion line (see Figure B-3).

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4. Compression Line a. Complete the same process described above for the expansion line but use the start point (location for entropy and mass calculation) with the suction pressure and suction temperature. b. Use the discharge pressure and start entropy for the end point of the compression line (see Figure B-4). 5. Connect the expansion and compression lines with the suction and discharge pressure lines (see Figure B-5).

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APPENDIX C EQUATIONS OF STATE

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APPENDIX C The following explanation of the EOS models is taken from Equations of State for Gas Compressor Design and Testing by Kumar, Kurz and O’Connell, 2003. While the operating conditions for gas compressors are typically defined in terms of pressures, temperatures, and mass or standard flows, the relevant data that describe the behavior of a compressor are the head (H), which is related to the work input, the volumetric flow (Q) and efficiency (η), which compares the real process to an isentropic process between the same inlet state and outlet pressure. The head, or specific enthalpy difference between two states (e.g., inlet and discharge side of the compressor), is defined by:

H = h( p d , Td , {y}) − h( p s , Ts , {y})

(C-1)

The enthalpy (h) is a function of pressure, temperature, and gas composition defined through a set of mole •

fractions {y}. The actual absorbed power (Pgas) involves the mass flow rate ( m ): •

Pgas = m H

(C-2)

The mass flow rate is obtained from the actual or volumetric flow rate (Q) and the gas density (ρ): •

m = ρQ

(C-3)

The density is found from the temperature (T) and pressure (p) with the compressibility factor (Z). When Z differs from unity, the gas is not ideal and its value is a function of T, p, and gas composition. ρ = p/ZRT

(C-4)

The result of these definitions is that Pgas is found from:

Pgas = ρQH =

p QH ZRT

(C-5)

In order to define the quality of the compression process, H is usually compared to the head for an ideal compression process, which is defined as compression between the same inlet Ts and ps and outlet pd, with the outlet temperature being fictitious Td,isen:

∆s = s ( p d , Td ,isen , {y}) − s ( p s , Ts {y}) = 0

(C-6)

This isentropic change of state defines an isentropic head, Hisen, such that:

H isen = h( p d , Td ,isen , {y}) − h( p s , Ts {y})

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(C-7)

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The quality or efficiency of the compression is defined by:

η=

H isen H

(C-8)

Compressor characteristics, in terms of head versus flow and efficiency versus flow, are found by comparing test data, taken with test gases such as Nitrogen, with results obtained from the thermodynamic calculations above. The characteristics can later be used to calculate the performance of the compressor under arbitrary conditions of pressures, temperatures, and gas compositions. As long as the same EOS is used for obtaining compressor performance predictions and data reduction, errors are minimized. An EOS is a relation among variables of a fully specified system: T, p, ρ and the N-1 component mole fractions yi (Alberty and Silbey, 1997). This is usually expressed in the form: Z = Z (ρ, T, {y})

(C-9)

since in a multiphase region, multiple values of ρ give the same value of p. Thermodynamics gives rigorous relations for enthalpy and entropy differences from derivatives and integrals of Z from any EOS and ideal gas specific heat, c 0p . A gas is said to be in a specified state if it has zero degrees of freedom. The degrees of freedom are the number of properties that can be arbitrarily set before all other properties become specified. The formula for the degrees of freedom of N nonreacting gases is: DF = N – # phases + 2

(C-10)

In gas compressor design calculations, only one phase exists, and the gas composition is usually specified, so two more degrees of freedom must be chosen. Generally, p and T are specified and the number of phases is always one. Then, all other thermodynamic properties are fixed and calculated via an EOS. Since real gas behavior commonly plays a role in gas compressors, knowledge of the relationships between pressures and temperatures, on one hand, and enthalpies, entropies and densities, on the other hand, is of great importance in compressor design, their performance under arbitrary operating conditions, and test data reduction. Especially during gas compressor performance tests, the selection of a particular EOS can have an important effect on the apparent efficiency and absorbed gas power. Thermodynamic Approach In order to decide on the most appropriate (EOS) to be used for designing and testing gas compressors for natural gas applications, five frequently applied EOS were studied: original Redlich-Kwong, RedlichKwong-Soave, Peng-Robinson (Reid et al., 1986), Lee-Kesler-Ploecker (Ploecker et al., 1978) and Starling version of the Benedict-Webb-Rubin model (Starling, 1973). The variation in entropy or enthalpy between two states of a gas or mixture, each defined by a temperature and pressure, is independent from the path chosen from one state to the other (Reid et al., 1986). A convenient path involving three steps of changing the real gas to an ideal gas at T1, changing the ideal gas from T1 to T2 and changing the ideal gas back to the real gas at T2 (Figure C-1).

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T2 Isotherms

Pressure

T1

Zero pressure

Enthalpy Figure C-1. Calculation Path for Equations of State

h = f ( p, T ) dh = (∂h / ∂p )T dp + (∂h / ∂T ) p dT p2

h2 − h1 =

T2

∫ (∂h / ∂p )T + ∫ (∂h / ∂T ) p DT

p1

(

h2 − h1 = h 0 − h p1

T1

)

T1

T2

(

+ ∫ c 0p dT − h 0 − h p 2

)

T2

T1

(C-11)

The terms in the parentheses of Equation C-11 are called departure functions, real gas contributions, or residual properties, which relate the enthalpy at some p and T to that at an ideal gas reference state at T, H0. These departure functions can be calculated solely from the EOS. The same approach can be used for the entropy. The ideal gas law is based on the assumption that the molecules of the gas do not interact with each other or that there is no attractive or repulsive forces between two molecules. The heat capacity of a gas is the amount of energy, which the gas needs to absorb before its temperature increases one unit. For an ideal gas, the heat capacity c 0p is a function only of T. An empirical equation for the ideal gas heat capacity can be stated as a polynomial, e.g., third order polynomial:

c 0p = A + BT + CT2 + DT3

(C-12)

A, B, C, and D are empirical parameters or constants based on the type of gas being analyzed. Once an equation for c 0p is found, the ideal gas enthalpy change, which is the change in total energy in the gas as it goes from state one to state two, can be found by:

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T2

∆h 0 = ∫ c p dT T1

(C-13)

Even for an ideal gas, the entropy change depends upon the initial and final temperatures and pressures. The entropy change is expressed by:

∆s 0 = ∫

T2

T1

p dT − R ln 2 T p1

cp

(C-14)

When calculating the enthalpy or entropy of a given state, an arbitrary reference state must be selected whose enthalpy and entropy are set to zero. The enthalpy and entropy for a given state is calculated relative to this reference. Therefore, any absolute value of the enthalpy or entropy of a gas at a given state has no real meaning, given its dependence on the reference state. However, when the enthalpy difference between two states is calculated, the reference state cancels out, so an enthalpy or entropy difference is an actual value that does not depend on the reference state. Functionality of Equations of State The departure functions for enthalpy and entropy for each of the five EOS can be found in the literature (Reid et al., 1986; Peng and Robinson, 1976; Ploecker et al., 1978; and Starling, 1973). Herein, the RK, RKS, and PR EOS are referred to as cubics. In Equation C-15, Z represents the compressibility factor of the gas, defined as:

Z=

pv RT

(C-15)

The quantities X and Y are two other types of compressibility factors used in compressor design. The formulas for each:

Y = 1−

X=

p ∂Z Z ∂p T

T ∂Z × Z ∂T

(C-16)

(C-17)

The calculation of the molecular weight and the heat capacity at given temperatures of the gas mixture is completed by using the following mixing rules:

~ MW = ∑ y i MWi c~ = yc p

∑

i

pi

(C-18)

MWi and y are the molecular weight and mole fraction of each component in the mixture. The heat capacities are divided by R to make them dimensionless, so when the linear function is found at a given

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temperature, the result should be multiplied by R in the desired units to get the heat capacity in those units. The linear function for ideal cp0/R is calculated using the cp0/R values at 10 and 149°C (50 and 300°F). These two points are used to find the slope of a straight line on a cp0/R versus temperature plot. This slope is used to solve for the y intercept of the following simple linear equation:

c 0p R

= CT + B (C-19)

Finally, the specific gravity (sg) and the real gas parameter (RG) are calculated; sg is calculated relative to the molecular weight of air:

~ MW sg = 28.964

(C-20)

The RG parameter is given by:

RG =

0.287 kJ / kgK sg

(C-21)

The Redlich-Kwong and Peng-Robinson models are cubic equations of state. The LKP equation is like the BWRS, a modification of the original BWR EOS. The LKP EOS has mixing rules that are very different from the cubics. The Starling version (BWRS) of the original BWR EOS added three extra parameters for improving the temperature dependence of the eight parameter forms. These parameters must be found for each pure gas. There also are mixing rules for the 11 parameters (Starling, 1973). For the cubic EOS, an analytical method can be used to solve for the three roots of ρ, thus, yielding Z. There are three roots to any cubic equation; however, when Tr >1 only the largest real root has any physical significance. After Z is calculated, the X and Y compressibility factors, along with specific heat, are calculated. For the LKP and BWRS models, Z is found by an iterative method.

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APPENDIX D EQUATION OF STATE MODEL COMPARISON OF PREDICTED PERFORMANCE DATA

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APPENDIX D The following comparison of the EOS models relies on results presented in Enthalpy Determination Methods for Compressor Performance Calculations by David Ransom, Rainer Kurz, and Klaus Brun. This comparison was completed for centrifugal compressors as described below. However, the comparison of EOS can be directly applied to reciprocating compressor performance testing. Approach for EOS Model Comparison For this comparison, a matrix of three gas compositions and two pressure ratios are considered. Enthalpy values are calculated using various EOS models and used to calculate compression power and isentropic efficiency. The three gas compositions (Table D-1) are intended to represent a variety of typical compression products including natural gas, high hydrogen, and high diluent compositions. (Note that gas mixture 1 is the same composition used in the uncertainty analysis in Section 7.) The two pressure ratios included in this comparison (PR = 1.3 and 2.2) are consistent with typical two- and six-stage machines, although neither value represents any specific application. In all cases, inlet conditions of 1,000 psia and 80°F are assumed. For each analysis configuration (gas mix and pressure ratio), both the isentropic and actual gas horsepower are determined, followed then by the isentropic efficiency. Gas power is a function of mass flow (assumed to be measured) and the change in enthalpy of the working fluid. Table D-1. Gas Mixtures Used in EOS Model Comparison

Component Methane Ethane Propane Iso-Butane N-Butane Iso-Pentane N-Pentane Hexane Carbon Dioxide Nitrogen Hydrogen Hydrogen Suflide Total

Mix 1 90.00 5.37 1.70 0.27 0.33 0.06 0.09 0.07 1.06 1.05 0.00 0.00 100.00

Mix 2 80.00 5.37 1.70 0.27 0.33 0.06 0.09 0.07 6.06 6.05 0.00 0.00 100.00

Mix 3 7.65 1.06 0.20 0.00 0.00 0.00 0.00 0.00 0.85 3.85 86.34 0.05 100.00

Table D-2. Assumed Measured Conditions; PR = 1.3

Parameter ps (psia) Ts (°F) pd (psia) Td (°F)

Mix 1 1000 80 1295 119

Mix 2 1000 80 1295 117

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Mix 3 1000 80 1295 127

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Table D-3. Assumed Measured Conditions; PR = 2.2

Parameter ps (psia) Ts (°F) pd (psia) Td (°F)

Mix 1 1000 80 2200 201

Mix 2 1000 80 2200 199

Mix 3 1000 80 2200 235

Temperature

Five EOS models are included in this comparison: Redlich-Kwong (1948), Redlich-Kwong-Soave (Soave, 1972), Peng-Robinson (1976), Lee-Kesler-Ploecker (Ploeker et al., 1978), and Benedict-WebbRubin-Starling (Starling, 1973). Using the appropriate EOS, three enthalpy values are determined as follows: determine the inlet enthalpy (hs) and entropy (ss) as a function of the inlet conditions (ps, Ts); determine the isentropic discharge enthalpy (hd,isen) as a function of isentropic discharge conditions (pd, ss); and determine the actual discharge enthalpy (hd) as a function of the actual discharge conditions (pd, Td). A graphic representation of this process is provided below on a generic T-s diagram (Figure D-1).

(hd) = f(pd, Td)

(hd,isen) = f(pd, ss)

(hs,ss) = f(ps, Ts)

Entropy Figure D-1. Compression T-S Diagram

Once these values are determined, it is a very simple calculation to determine the isentropic and actual gas horsepower values (Equations D-1 and D-2).

P = m (hd − hs )

(D-1)

(hd ,isen − hs ) Pisen = m

(D-2)

Isentropic efficiency is calculated using Equation D-3.

η=

hd ,isen − hs hd − hs

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(D-3)

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Enthalpy Determination Results The results for gas horsepower and isentropic efficiency for each of the EOS models are shown in Table D-4 and Table D-5. For the sake of comparison, the mass flow for Mix 3 (high hydrogen gas) is adjusted to provide a similar horsepower as the natural gas compositions. Note that results are not shown for BWRS for the High H2 gas composition (Mix 3) since BWRS does not contain hydrogen data. These results demonstrate the relative agreement between the five EOS methods applied in this study. At the lower pressure ratio, for the first two gas mixtures, the standard deviation is about 30 HP, or 1.2% of the average value. In the case of the high hydrogen gas (Mix 3), the standard deviation is approximately 140 HP, or 1.7% of the average value at the same pressure ratio. For the higher pressure ratio, the deviation in the first two mixtures between the EOS models is approximately the same as the lower pressure ratio. The deviation increases to 1.8% at the higher pressure ratio for the high hydrogen gas (Mix 3). It should also be noted that the Peng-Robinson model consistently predicts slightly lower horsepower for all three gas mixtures, while the SRK model predicts higher horsepower within the deviations stated above. The isentropic efficiencies calculated using the various EOS models show relatively close agreement as well. However, the standard deviation among the five methods used in this study is as high as 2%, which can be significant when evaluating compressor performance against the promised performance, usually specified within 1%. In the extreme case, the isentropic efficiency between one particular EOS model and another can be as high as 3.8%. These results underscore the importance of applying the same EOS model throughout the performance analysis. Table D-4. Horsepower and Efficiency Calculations for EOS Models at Pressure Ratio of 1.3 EOS Model LKP BWRS SRK SRK-API PR Stdev Avg Stdev - %avg

Mix1 Hp-Act Eff-is 2530 68.2% 2522 64.6% 2528 65.6% 2530 65.6% 2460 65.0% 30.21 1.395% 2514 0.658 1.20% 2.12%

Mix2 Hp-Act Eff-is 2249 63.6% 2262 64.7% 2261 66.2% 2263 66.2% 2200 65.6% 26.63 1.098% 2247 0.652 1.19% 1.68%

Mix3 Hp-Act Eff-is 8400 87.9% 8368 8554 8213 139.74 8384 1.67%

88.2% 87.6% 88.2% 0.294% 0.880 0.33%

Table D-5. Horsepower and Efficiency Calculations for EOS Models at Pressure Ratio of 2.2 EOS Model LKP BWRS SRK SRK-API PR Stdev Avg Stdev - %avg

Mix1 Hp-Act Eff-is 8840 61.3% 8843 60.9% 8940 61.7% 8949 61.7% 8695 60.8% 102.48 0.387% 8853 0.613 1.16% 0.63%

Mix2 Hp-Act Eff-is 7879 60.3% 7922 61.2% 7986 62.3% 7994 62.3% 7767 61.5% 92.56 0.839% 7910 0.615 1.17% 1.36%

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Mix3 Hp-Act Eff-is 28169 87.3% 28046 28689 27462 503.75 28091 1.79%

87.7% 87.1% 87.8% 0.321% 0.875 0.37%

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APPENDIX E UNCERTAINTY ANALYSIS OF INDEPENDENT VARIABLE MEASUREMENTS

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APPENDIX E Prior to determining a test uncertainty, it is important to know whether the measured variables in the test are independent or dependent, as this determines the method of uncertainty calculation that must be employed. For almost all real measurement scenarios, there is some physical dependency between the input variables and, thus, unless one is absolutely certain that all measured and given system inputs are independent, it is safer to opt for the more conservative assumption of measurement dependence. If the measured variables in an experiment are truly found to be independent, then the method to determine total uncertainty is simply an addition of all individual measurement uncertainties. This is mathematically expressed as: n

∆F = ∆x1 + ∆x2 + ∆x3 + ... ∆xn = ∑ ∆xi i =1

(E-1)

where ΔF is the total result uncertainty and Δx are the individual measurement uncertainty ranges. This is the absolute value method rather than square root of the sum of squares method, which is more commonly utilized (as shown in E-2). The absolute value addition presents a true superposition of individual uncertainties rather than a blended sum. This method yields more conservative uncertainty results than the square-root-sum method, but both approaches are generally acceptable for uncertainty analyses.

∆V = ∆x12 + ∆x 22 + ∆x32 + ...∆x n2

(E-2)

Uncertainty Analysis for Dependent Variable Measurements If the measured variables in an experiment are dependent, which is usually the case, then the analysis becomes more complex. Specifically, the individual measurement uncertainties, Δx, are now functionally related and this must be accounted for in the analysis. There are three methods that are commonly used by engineers for this type of uncertainty analysis: •

Partial Derivative Method

•

Coefficient Method

•

Perturbation Method

All three methods are based on a functional transfer from input to output variable but employ a different approach to the determination of the proper transfer function. The Partial Derivative Method The most traditional method for uncertainty calculations is based on determining the transfer function using a partial derivative and adding the individual uncertainty transformations. Namely:

∆F = ∆F (∆x1 ) + ∆F (∆x2 ) + ∆F (∆x3 ) + ...∆F (∆xn ) = ∆x1 ⋅

n ∂F ∂F ∂F ∂F ∂F + ∆x2 ⋅ + ∆x3 ⋅ + ... ∆xn ⋅ = ∑ ∆xi ⋅ ∂x1 ∂x2 ∂x3 ∂xn i =1 ∂xi

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(E-3)

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To understand this method, one must analyze the principal term ∆xi ⋅

∂F and derive some basic ∂xi

physical understanding. Figure E-1 shows a graphical interpretation of the functional transformation from range Δx to ΔF using this term. Effectively, the input range Δx is multiplied by the slope of the function F at the measurement point x1, x2, x3, etc., to determine the ΔF output range. This assumes that the function F is linear over the interval Δx from the specified measurement point, which is a reasonable assumption for small Δx and any linear functional form. However, few physical laws are linear over a wide range and, thus, this method will be inaccurate for steeply sloped functions combined with large individual measurement uncertainties. Also, this method assumes that the function F is in an algebraic form that can be readily differentiated. This is obviously not always the case as many physical governing equations include ordinary and partial differential terms.

Figure E-1. Determination of Uncertainty Using Differential Methods

Coefficient Method

∂F can be determined numerically using a simple forward ∂x1 difference approach. This is commonly called the coefficient method and is shown below.

Clearly, the above partial differential

ci =

∂Fi F ( xi ) − F ( xi + ∆xi ) = ∂xi ∆xi

(E-4)

and n

∆F = c1 ⋅ ∆x1 + c 2 ⋅ ∆x 2 + c3 ⋅ ∆x3 + ... c n ⋅ ∆x n = ∑ ci ⋅ ∆xi i =1

(E-5)

Both the partial derivative and coefficient method should yield identical answers when properly applied. Again, as long as Δx is small and the slope of the function F is moderate, this approach will yield

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reasonably accurate uncertainties. A slight variation of this approach centers the numerical derivative around x, specifically:

ci =

∂F F ( x − 0.5∆x) − F ( x + 0.5∆x) = ∂x ∆x

(E-6)

This modified method often provides an improved determination of the uncertainty for measurements centered distributions. Unfortunately, for convenience, the coefficient method is often misapplied by assuming fixed coefficients for a standard analysis. A number of well established engineering codes and specifications publish fixed numbers for uncertainty coefficients of standard engineering analysis problems. This approach can only be valid if the actual physical equation is strictly linear, which is seldom the case. Also, unless all units of measurement are identical to those of the published coefficients, largely incorrect uncertainty results will be obtained. Perturbation Method The most accurate analysis to determine total uncertainty of dependent variable measurement systems is the perturbation method, as it is based on the actual function F and does not require any linearity assumptions. It is simply expressed as:

∆F = ∆F (∆x1 ) + ∆F (∆x2 ) + ∆F (∆x3 ) + ...∆F (∆xn ) = F ( x1 ) − F ( x1 + ∆x1 ) + F ( x2 ) − F ( x2 + ∆x2 ) + F ( x3 ) − F ( x3 + ∆x3 ) + ... F ( xn ) − F ( xn + ∆xn ) n

= ∑ F ( xi ) − F ( xi + ∆xi ) i =1

(E-7)

The term F ( x1 ) − F ( x1 + ∆x1 ) is graphically reviewed in Figure E-2 and demonstrates that the ΔF uncertainty obtained using this method is the actual transformation of Δx.

Figure E-2. Determination of Uncertainty Using Perturbation Methods

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The variation of parameters method is implemented by sequentially perturbing the input values (temperature, pressure, etc.) by their respective uncertainties and recording the effects on the calculated output quantity (i.e., efficiency, power, etc.). Assuming the uncertainty perturbation is fairly small, any term in Equation E-8 can be determined in this manner:

∆u1 ×

∂f ≅ f (u1 + ∆u1 ) − f (u1 ) ∂u1

(E-8)

The contribution of the variable u1 towards the overall uncertainty can be determined by calculating f twice—at the observed value at u1 and at the perturbed value of u1 + ∆u1. For several variables, the results for each term should be summed using the square-root-sum or absolute value of the individual terms. The benefits of this approach are that it does not matter if the uncertainty is an absolute or relative number, the procedure can be implemented using any spreadsheet program, and the values in the spreadsheet can be the results of complex, iterative relationships. Implementation of the Partial Derivative Method for Compressors (Enthalpy Rise Method) The partial derivative method was described in detail by Brun and Kurz [ASME Journal of Engineering for Gas Turbines and Power, 2001]. The implementation for the reciprocating compressor with the Enthalpy Rise method is briefly described herein: For the specific heat uncertainty, ∆cp is obtained:

⋅Z ⋅Z R R R + ∆MW Universal 2 ∆Z Universal + ∆L Universal 2 L ⋅ MW 2 L ⋅ MW L ⋅ MW 2

2

(E-9)

The above Equation E-9 is valid if the physical gas properties, specific heat ratio, compressibility factor, and molecular weight are directly determined from testing. A physical property uncertainty, due to the effect of applying uncertainties in T and p to the non-ideal gas state equation has to be included (i.e., since there is a measurement error in T and p, there will be an added error in determining cp from the gas equation). This uncertainty is most conveniently obtained numerically by varying temperatures and pressures parametrically in the gas equation and, thus, determining the gradients dγ/dT, dγ/dp, dZ/dT, and dZ/dp indirectly. Recognizing that dγ/dT = dL/dT and dγ/dp = dL/dp, one can easily determine corrections for ∆Z and ∆L: 2

∂γ ∂γ ∆Z = ∆T ⋅ + ∆p ⋅ ∂T ∂p 2

∂Z ∂Z ∆Z = ∆T ⋅ + ∆p ⋅ ∂T ∂p

2

(E-10) 2

(E-11)

The uncertainty in cp, is also affected by the variation of the gas properties during the duration of the test. This effect is again mathematically difficult to describe but can be easily handled numerically using a procedure similar to the one shown above for the variations in T and p. It is beyond the scope of this paper to list all possible gas composition variations; however, it is important to realize that they can strongly affect Z, L, and MW.

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The uncertainty of the compressor enthalpy rise is determined using Equation E-12. Since the enthalpy rise uncertainty is not dependent on the absolute temperatures, but rather on the temperature difference (Td – Ts), and since the specific heats (cp) for the discharge and suction are functionally related, the temperature difference (Td – Ts) should be employed for the derivation rather than the absolute temperature values (Td, Ts).

∆H =

(∆c p ⋅ (Td − Ts ))2 + (∆Td ⋅ c pTd )2 + (∆Ts ⋅ c pTs )2

(E-12)

The uncertainty for the isentropic (ideal) compressor outlet temperature is obtained using Equation E-13. Isentropic Temperature 2

∆Td ,isen

2 L p d LTs p dL −1 LTs p dL p + ∆ ⋅ + ∆p d ⋅ = ∆Ts ⋅ s p sL p sL +1 p s

2

(E-13)

The uncertainty of the compressor efficiency is given in Equation E-15. The temperature difference should be used rather than the absolute temperature values for the derivation of the isentropic enthalpy given in Equation E-14. Isentropic Enthalpy

∆hisen =

(∆c ⋅ (T p

d , isen

− Ts

)) + (∆T 2

d , isen

⋅ c p , d ,isen

) + (∆T ⋅ c ) 2

2

s

p,s

(E-14)

Isentropic Efficiency

h ∆h ∆η isen = isen + ∆H ⋅ isen2 H H 2

2

(E-15)

Mass Flow

MW ⋅ Q ∆ m = ∆p s ⋅ RUniversal ZTs • 2

2

ps Q + ∆MW ⋅ RUniversal ZTs

p s ⋅ MW + ∆Q ⋅ RUniversal ZTs

2

2

p ⋅ MW ⋅ Q + ∆Z ⋅ s RUniversal Z 2Ts

p ⋅ MW ⋅ Q + ∆Ts ⋅ s RUniversal ZTs2

2

2

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(E-16)

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Power • m ∆P = ∆H ⋅ ηm

2

• H + ∆ m⋅ η m

• 2 H ⋅m + ∆η m ⋅ 2 η m

2

(E-17)

The flow rate uncertainty, ∆Q, depends strongly on the device type employed for the measurements. A detailed discussion of flow measurement uncertainty is provided in ASME PTC 19.1 and is, thus, not further discussed herein. By evaluating Equations E-14 through E-17, estimates of the total measurement uncertainties for the compressor efficiency, enthalpy rise, and required driver power can be obtained. However, one source of measurement uncertainty that is often overlooked is the uncertainty due to a finite sample size. The above uncertainty statistics are valid only for mean parameters with an assumed Gaussian normal distribution. This is a good assumption for measurements where sample sizes are larger than 30. But for field tests, it is sometimes difficult to maintain a steady state system operating condition for a time period adequate to collect 30 or more samples. Implementation of the Partial Derivative Method for Compressor Package To complete the above field test measurement uncertainty evaluation, one also needs to look at the complete compressor package (engine and compressor efficiency) performance. The engine output power has to equal the compressor required power (PGT = P). Thus, the following two equations can be used to define the engine thermal efficiency, ηth, and the total package efficiency, ηsys: Thermal Efficiency

η th =

Pin •

m fuel ⋅ LHV

(E-18)

Package Efficiency

ηsys =

Pcomp Pin

ηisenηmηe

(E-19)

•

Here m fuel is the fuel flow into the engine and LHV is the fuel heating value. The fuel flow is typically measured using an orifice plate in a metering run and the heating value is determined from the chemical composition of the fuel. Based on the above equations, the corresponding driver uncertainty, ∆ηth, and package uncertainty, ∆ηsys, are given by:

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Thermal Efficiency

1 ∆η th = ∆Pin • m fuel LHV

2 • Pin + ∆ m fuel 2 • m LHV fuel

2

Pin + ∆LHV • 2 m fuel LHV

2

(E-20)

Package Efficiency

∆η sys

Pcomp = η isenη mη e P in

∆Pcomp P comp

2

+ ∆η isen η isen

2

∆P + in Pin

2

∆η m + ηm

2

∆η e + ηe

2

(E-21)

To complete the above Equations E-20 and E-21, the only additional information needed is the fuel flow uncertainty and the fuel heating value uncertainty. Since the fuel flow is measured in the same way as the flow through the gas compressor, uncertainty values in Equation E-16 can be used. Also, since the heating value is obtained directly from gas composition, the same percent uncertainty as was obtained for the specific heat Equation E-9 can be used, namely:

∆LHV ∆c p = LHV cp

(E-22)

By introducing the uncertainty experience values from those suggested in this guideline, the measurement uncertainty for a field test can be predicted prior to the test. Consequently, the above method allows the manufacturer and the end-user to determine reasonable test uncertainties, as well as necessary requirements for the test instrumentation prior to the test. This method can also be employed to resolve observed variations of field test performance results from theoretically predicted and/or factory test results. The different EOS models will provide different values of enthalpy rise, isentropic enthalpy rise, and compressibility for the compressor based on the differences in calculated enthalpy and compressibility. Implementation of the Perturbation Method for Compressors (PV Card Method) Described above were the uncertainty calculations for the Enthalpy Rise method. perturbation method with the PV Card analysis is discussed here.

The use of the

In this method the individual uncertainties must be found for each measured parameter used in power and efficiency calculations. For efficiency calculations, the uncertainties must be considered for the calculation of actual (ICHP) and theoretical power due to the fact that the efficiency is dependent upon both of these calculations. The measured parameters in a performance test where uncertainty should be considered are listed below: •

Piston position (∆θ)

•

Compressor Speed (∆N)

•

Pressure measurement (∆P)

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•

Temperature measurement (∆T)

•

Gas Composition (∆mol%)

•

Clearance volume (∆Vcl)

•

Steady state of test (if the test data is acquired when the conditions are not steady then additional uncertainty should be included in the pressure and temperature results to account for this)

Piston Position To calculate the uncertainty of the power and efficiency with piston position, a phase shift equal to the total positional uncertainty should be applied to the piston position on the measured PV diagram. This should be done for plus (Equation E-23) and minus (Equation E-24) the positional uncertainty. Once the shifted ICHP are calculated, the efficiencies can be found for that shift. The theoretical power should be calculated with the measured toe pressures (not shifted values) in this step. This isolates the uncertainty just to the effect of positional measurement variation on the measured power and calculated efficiency with that power. The difference between the maximum and minimum ICHP (Equation E-25) and efficiencies (Equation E-26) are the total uncertainty (∆ICHPθ and ∆ηθ) for the piston position measurement. θ i , plus = θ i + ∆ θ θ

i , min us

∆ ICHP

= θ

θ

i

(E-23)

− ∆θ

= ICHP

(E-24) max

− ICHP

min

∆ η θ = η max − η min

(E-25) (E-26)

The process described above should be repeated for the theoretical PV diagram. From this the position uncertainty on the theoretical ICHP can be found. This can be used with the measured ICHP to determine the uncertainty effect on the efficiency calculation. Speed The uncertainty due to speed variation should be calculated for both the measured and theoretical ICHP. The speed is used to calculate the power from the area of the PV diagram or work. Equations E-27 and (E-28) below detail how the maximum and minimum ICHP’s are calculated. The uncertainty in the speed measurement is the difference between these two values as shown in Equation E-25.

ICHPmax = ICHPmin =

W * (N + ∆N) 396000

(E-27)

W * (N − ∆N ) 396000

(E-28)

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Pressure The calculation of the uncertainty of power and efficiency due to pressure is not completely intuitive. One would think that the pressure uncertainty could just be added to the measured pressure and obtain the maximum ICHP and efficiency. However, this does not work. The end result is the exact same ICHP and efficiency calculated directly from the measured data. This is due to the fact that adding or subtracting the pressure to the full PV diagram will only shift the diagram up or down. It will not change the area within the diagram. In order to obtain the maximum possible ICHP from the diagram, a positive increase in pressure should be applied to the compression and discharge event lines and a negative decrease in pressure should be applied to the expansion and suction event lines. This will make the diagram grow outward and a maximum ICHP can be calculated. To obtain a minimum ICHP, the opposite should be applied: a negative decrease in pressure on the compression and discharge event lines and a positive increase in pressure on the expansion and suction event lines. Figure E-3 shows an example of maximum ICHP PV diagram with a 2 psig pressure uncertainty. From the pressure uncertainty PV diagrams, the maximum and minimum ICHP can be calculated. With this, the maximum and minimum efficiencies will be found. Again, the theoretical ICHP should be calculated with the measured values in order to isolate the error to the variation in pressure on the actual PV diagram power and efficiency. The total change in ICHP and efficiency due to pressure uncertainty is then found with Equations E-25 and E-26. This process should be repeated for the theoretical PV diagram. The measured PV diagram should be developed with the measured values in order to isolate the uncertainty effects to the theoretical calculation. In many performance tests, especially with high-speed units, channel resonance will be present in the pressure signal. This resonance is removed in order to complete flow calculations. Removing this resonance can affect the ICHP calculated value. If the ICHP is reported from the corrected PV diagram, then this ICHP should be compared to the ICHP of the uncorrected diagram. Any difference between these two ICHPs should be included as uncertainty in the power and efficiency. 90 80

Maximum ICHP 70

Original ICHP

Pressure (psig)

60 50 40 30 20 10 0 0

50

100

150

200

250

300

350

Volume (in3)

Figure E-3. Example of Change in Theoretical PV Diagram with Pressure Uncertainty

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Temperature and Gas Composition The temperature and gas composition are used in the PV Card method to generate the theoretical diagram. These values have no effects on the actual ICHP calculation. They do influence the uncertainty of the efficiency through the theoretical or isentropic power. The development of the theoretical PV diagram should be done with one of the methods discussed in Appendix B. The uncertainty is found by varying the temperature and gas composition with their specific uncertainties. For example, the theoretical ICHP should be found for a maximum temperature (Toriginal + ∆T) and for a minimum temperature. The same will be done for the gas composition. The difference between the maximum and minimum ICHP and efficiency will be the uncertainty due to temperature measurements and gas composition (Equation E-25). When determining this uncertainty, the actual ICHP should be calculated with the measured values, in order to isolate the effect of the uncertainty to the generation of the theoretical PV diagram. If the compressor operates at steady state during the performance test, then this uncertainty will be minimal (less than 0.01%) and perhaps negligible. However, tests that are performed at unsteady conditions should account for this uncertainty. Clearance Volume Uncertainty in the clearance volume will affect the theoretical ICHP and flow calculations. For the theoretical ICHP, the uncertainty in clearance volume affects the expansion and compression curves of the PV diagram. A positive increase and negative decrease in clearance volume should be applied to the PV diagrams separately in order to obtain the maximum and minimum ICHP and efficiencies. The differences in these maxima and minima are the uncertainty of the ICHP and efficiency due to the uncertainty in the clearance volume (Equation E-25). Total ICHP Uncertainty Up to this point, only the determination of uncertainty for individual measurements has been explained. To determine the overall compressor uncertainty, first, the individual uncertainties for each cylinder end should be combined with a root mean sum (Equation E-29). Once the uncertainty of each cylinder end is known, then these can be summed to determine the total deviation for the measured ICHP (Equation E30). The equations below also apply to the theoretical ICHP uncertainty calculation. ∆ ICHP cyl ∆ ICHP

1 − HE

comp

=

(∆ ICHP

= ∆ ICHP

) + (∆ ICHP 2

i , cyl 1 − HE

cyl 1 − HE

+ ∆ ICHP

cyl 1 − CE

)

2

i + 1 , cyl 1 − HE

+ ∆ ICHP

cyl

+ ...

2 − HE

(E-29) + ...

(E-30)

Total Efficiency Uncertainty Efficiency uncertainties can be calculated for each individual cylinder end as discussed above. This gives insight into the error in the efficiency for each cylinder end, but these values are not used to calculate the overall efficiency uncertainty. Due to the method which efficiencies are calculated, they cannot be averaged or summed like the power value can to obtain an overall efficiency uncertainty. Therefore, the overall efficiency uncertainty is calculated using the overall deviations found for the measured and theoretical ICHPs. Equations E-31 and E-32 below detail how the minimum and maximum efficiencies should be calculated. The difference in these two values (Equation E-33) gives the overall uncertainty in the efficiency of the compressor.

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η comp ,max =

η comp ,min = ∆η

comp

= η

Pcomp ,isen + ∆Pcomp ,isen ICHPcomp − ∆ICHPcomp

(E-31)

Pcomp ,isen − ∆Pcomp ,isen ICHPcomp + ∆ICHPcomp comp

, max

−η

comp

, min

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(E-32) (E-33)

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APPENDIX F COMPRESSOR PERFORMANCE DIAGNOSTICS WITH PV DIAGRAMS

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APPENDIX F The following is a discussion of the different effects that can be observed and diagnosed with a PV diagram. Each of the effects is discussed individually. It should be noted that in practice typically the PV diagram will have multiple influences. The effects discussed below are suction valve leakage, compressor rod pressure package leakage, discharge valve leakage, piston ring leakage, pulsation effects, and valve and cylinder gas passage losses. Suction Valve Leaks Figure F-1 illustrates the P-V diagram of a typical compressor cylinder with suction valve leakage. The difference between the theoretical P-V diagram and the “actual” P-V diagram will depend on the severity of leakage through the suction valves. Following is a step-by-step analysis of the P-V diagram in Figure F-1.

Figure F-1. Diagram Illustrating the Effects of Suction Valve Leaks

Line 1-2A: During the compression portion of the cycle, gas leaks out of the cylinder through the suction valves. Since less gas remains in the cylinder than the cylinder is designed for, more piston travel is required than the design piston travel to reach the discharge valve opening pressure. The cylinder volume at Point 2A is smaller than the volume at Point 2, resulting in the actual EVd being smaller than the design EVd. Line 2A-3B: During this portion of the cycle, gas is exiting the cylinder through the discharge valves and continues to leak through the suction valves. Should the leakage be great enough, the discharge valve will close prematurely at Point 3B. The actual EVd will be smaller than the design EVd. Line 3B-3A: The discharge valve has closed prematurely. The cylinder volume continues to grow smaller, causing gas to leak through the suction valves. The internal pressure at Point 3A is less than the design pressure at Point 3. This effect may not be noticeable except in cases of major valve failure. Line 3A-4A: During the expansion portion of the cycle, gas continues to leak through the suction valves. Less gas is present in the cylinder than the cylinder is designed for, resulting in a premature opening of the suction valves at the Point 4A. Line 4A-1: The premature opening of the suction valves causes the actual EVs to be greater than the design EVs. Detailed below are some of the symptoms that will be observed if there are suction valve leaks in the compressor. •

The externally measured cylinder capacity will be less than the design cylinder capacity.

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•

The gas temperature at the cylinder inlet will be greater than that measured during normal operation.

•

The discharge gas temperature will be greater than that observed during normal operation.

•

The actual compression and expansion lines will not match the design compression and expansion lines.

•

Capacity calculations based on EVs will be greater than capacity calculations based on EVd.

Compressor Rod Pressure Package Leaks The characteristics of the PV diagram for compressor rod pressure package leaks will be the same as suction valve leakage; however, there will be no temperature rise noticed at the suction and discharge cavities. Discharge Valve Leaks Figure F-2 illustrates the P-V diagram of a typical compressor cylinder which is experiencing discharge valve leakage. The difference between the “actual” P-V diagram and the “design” P-V diagram will depend on the severity of leakage through the discharge valves. Following is a step-by-step analysis of the P-V diagram in Figure F-2.

Figure F-2. Diagram Illustrating the Effects of Discharge Valve Leaks

Line 3-4A: In the expansion portion of the cycle, the trapped gas in the cylinder is expanding and gas is leaking into the cylinder through the discharge valves. The suction valve opens at a cylinder volume corresponding to the volume at point 4A which is greater than the design volume at point 4. This causes the actual EVs to be smaller than the design EVs. Line 4A-1B: During the intake portion of the cycle, gas is entering the cylinder through the suction valves and gas is leaking into the cylinder through the discharge valves. The internal pressure of the cylinder will rise to the point which will cause premature closure of the suction valves at Point 1B. This results in smaller EVs than design. Line 1B-1A: The suction valve has closed, cylinder volume is increasing and the internal cylinder pressure is rising, resulting in a higher pressure at Point 1A than design Point 1. Line 1A-2A: The actual compression line will not match the design compression line since the pressure at 1A is not the same as the pressure at 1. Gas is leaking into the cylinder through the discharge valves throughout the compression portion of the cycle. The discharge valve opens prematurely at 2A because the pressure at 1A was higher than design and gas continued to leak into the cylinder during the compression stroke.

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Line 2A-3: The actual EVd is larger than the design EVd due to the premature opening of the discharge valve. Detailed below are some of the symptoms that will be observed if there are discharge valve leaks in the compressor. •

The actual discharge temperature will be higher than the discharge temperature observed in normal operation.

•

The measured cylinder capacity will be less than the design cylinder capacity.

•

Capacity calculations based on EVd will be greater than capacity calculations based on EVs.

•

The actual compression and expansion lines will differ from the design compression and expansion lines. The value of the compression line exponent will be greater than normal, while the expansion line exponent will be less than normal.

Piston Ring Leaks Figure F-3 illustrates the P-V diagram of a typical compressor cylinder which is experiencing piston ring leakage. The shape of the “actual” P-V diagram will depend on the severity of the piston ring leakage. Following is a step-by-step analysis of Figure F-3.

Figure F-3. Diagram Illustrating the Effects of Piston Ring Leaks

Line 1A-2A: As the pressure in the cylinder increases, an increasing amount of gas escapes from the cylinder past the piston rings. Greater piston travel (smaller cylinder volume) is required to bring the internal pressure of the cylinder to the discharge valve opening pressure than design. If the discharge valve opening is delayed, occurring at Point 2A instead of Point 2, the actual EVd will be smaller than design. Line 2A-3B: During the discharge portion of the cycle, gas is exiting the cylinder through the discharge valves and leaking out of the cylinder past the piston rings. Should the leakage be severe enough, premature closing of the discharge valve can occur at Point 3B. Line 3B-3A: The discharge valves have closed, the cylinder volume continues to decrease, and gas continues to leak from the cylinder past the piston rings. The pressure at Point 3A is lower than design pressure (Point 3). Line 3A-4A: The actual expansion line will not be the same as the design expansion line since it begins at a lower pressure (Point 3A). Gas continues to leak out of the cylinder for a portion of the expansion

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cycle. The lower design pressure at Point 3A and the additional gas leakage result in the premature opening of the suction valves (in double-acting cylinders this can vary depending on gas state point in the opposite end). Line 4A-1B: Gas is entering the cylinder through the suction valves and is leaking into the cylinder past the piston rings. The leakage results in the premature closing of the suction valves at Point 1B (doubleacting cylinder). Line 1B-1A: The suction valves have closed, the cylinder volume is increasing, and the pressure in the cylinder is increasing due to continued piston ring leakage. The pressure at Point 1A is higher than design pressure (Point 1). Detailed below are some of the symptoms that will be observed if there are piston ring leaks in the compressor. •

The externally measured capacity will be lower than the design capacity.

•

The discharge temperature observed in normal operation will be higher than the design discharge temperature (double- acting cylinder).

•

Capacity calculations based on EVs will not agree with capacity calculations based on EVd.

•

The measured compression and expansion lines will not match the design compression and expansion lines.

Pulsation Effects While the suction and discharge valves are open, the acoustic pulsation present in the system is reflected into the compressor cylinder. Should the pulsation levels be of sufficient amplitude, the valve opening and closing times can be affected, and the average inlet and/or discharge pressures of the cylinder can be different than the design pressures. The net result being horsepower and capacity values, which are different than the design values. These values may be greater or smaller, depending on the pulsation characteristics. The change in horsepower and flow may be proportional, resulting in actual BHP/MMSCFD figures that are the same as design; however, the predicted loading curves will no longer be accurate. Valve and Cylinder Gas Passage Losses Valve loss is the pressure drop through the compressor valve. Cylinder gas passage loss is pressure drop between the cylinder flange and the compressor valve. Should these losses exceed the allowances which were made for them in the cylinder design; the actual flow will be less than the design flow. (Note that these losses are also affected by the gas pulsations.) Compressor performance problems are generally due to the “cylinder effects,” if it has been determined that: •

All compressor cylinder design parameters have been met (bore, stroke, fixed clearance, clearance pocket volumes, compressor speed, Ts, Zs, ps, pd).

•

No cylinder operational problems are present (compressor valve leakage and/or piston ring leakage).

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APPENDIX G POLYTROPIC EFFICIENCY

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APPENDIX G The polytropic process is also a reversible process like the isentropic process, but it is not adiabatic. It is defined by an infinite number of small isentropic steps followed by heat exchange. The heat exchange is necessary for constant polytropic efficiency. Both isentropic and polytropic processes are ideal, reference processes. Polytropic enthalpy rise is determined from: n −1 n pd n P P H = P ⋅ − 1 ⋅ f ⋅ p Sν S n − 1 p S P

P

(G-1)

The polytropic exponent, nP, is found with Equation G-2. This exponent should be based on the same conditions used to find hs and hd.

ln nP = ln

pd ps

νS νd

(G-2)

The polytropic efficiency is calculated based upon the polytropic enthalpy rise and the polytropic exponent, nP, as defined in the equation below: n −1 n p d n P − 1 ⋅ f ⋅ p sν s P ⋅ (n − 1) p s P

P

hdP − hs η = = hd − hs P

hd − hs

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APPENDIX H HEAT LOSS ESTIMATIONS

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APPENDIX H Heat loss estimations are necessary in order to have accurate compressor performance predictions. This is true for the Enthalpy Rise method. Energy lost due to temperature differences or cooling has a direct effect on the efficiency of the compressor. Loss estimates are needed when the compressor has cylinder cooling systems, the instrumentation is installed such that the losses must be accounted for, or the compressor is being operated in an environment where the ambient temperature is largely different from the surface temperature of the compressor. However, in many cases, the heat losses are very small and can be considered negligible. If this is thought to be the case, then the tester may want to complete order of magnitude calculations to verify that more detailed calculations are not necessary. Figure H-1 shows a schematic of the energy exchange in a compressor. The potential heat losses for the compressor are shown as energy leaving on the bottom of the figure. If the components of the compressor are cooler than the ambient temperature, which is often true for the suction bottle, then the energy could be entering instead of leaving. Any further discussions on heat losses will include reference to heat energy, both entering and leaving the compressor. The direction will be dictated by the thermal gradient. Power In Compression

Gas In

Suction Bottle

Pipe Heat Losses

Discharge Bottle

Compressor

Pipe Heat Losses Bottle Heat Losses

Pipe Heat Losses Cylinder Cooling – Heat Removal

Gas Out

Pipe Heat Losses Bottle Heat Losses

Figure H-1. Schematic of Energy Exchange in Reciprocating Compressor

Computer programs are available that can be used to perform thermal or heat loss analysis on machines of complex geometry. Basic methods for calculating heat losses are discussed below. This method is based on calculated heat loss curves for typical compressor bottle geometries with the equations discussed in Appendices B and C of IEEE 515, “Standard for the Testing, Design, Installation, and Maintenance of Electrical Resistance Heat Tracing for Industrial Applications.” Estimation of Bottle or Piping Losses The total losses are calculated by adding the losses calculated for the bottle and for the pipe as shown in Equation H-1. The calculation of the individual losses for bottles and pipes are discussed below.

Q = Qb + Q p Q Qb Qp

= = =

(H-1) Total heat loss (Btu/hr) Bottle heat loss (Btu/hr) Pipe heat loss (Btu/hr)

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In all the cases discussed below, natural convection refers to the condition where the wind velocity is less than 1 mph. If the wind velocity (V) exceeds 1 mph, then the heat transfer coefficients should be found using the forced convection coefficients. Bottle Losses Total Bottle Losses The total heat loss (Q) from the bottle is determined from the convective heat transfer (Qc) and radiation heat transfer (Qr). These two values are calculated as discussed in the following sections. The convective heat transfer is either calculated as natural or forced convection depending on the wind velocity (V).

Q = Qc + Q r Q Qc Qr

= = =

(H-2) Total heat loss (Btu/hr) Convective heat transfer (Btu/hr) Radiation heat transfer (Btu/hr)

Radiation (Qr) The steps to determine the radiation heat transfer are detailed below. 1. Measure the surface temperature of the bottle (Ts), the ambient temperature of the air (T∞), diameter of the bottle (D), and length of the bottle (L). 2. Determine the emissivity (ε) of the surface of the bottle. Common emissivity values are shown in Figure H-2. 3. Calculate the mean temperature (Tm) using the Equation H-3.

Tm =

Ts + T∞ 2

Tm Ts T∞

= = =

(H-3) Mean temperature (deg F) Bottle surface temperature (deg F) Ambient temperature (deg F)

4. Determine the value of the radiation heat transfer coefficient (hr) from Figure H-2 with the mean temperature (Tm) and emissivity of the bottle (ε). 5. Calculate the surface area of the bottle (A) with the Equation H-4.

D2 A = 3.14 D * L + 2 A D L

= = =

(H-4)

Surface area of bottle (ft2) Diameter of bottle (ft) Length of bottle (ft)

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6. Calculate the radiation heat loss of the bottle (Qr) with the Equation H-5.

Qr = hr A(Ts − T∞ ) Qr hr A Ts T∞

= = = = =

(H-5)

Radiation heat transfer (Btu/hr) Radiation heat transfer coefficient (Btu/hr-ft2-deg F) Surface area of bottle (ft2) Surface temperature of bottle (deg F) Ambient temperature (deg F)

1.6 1.4 1.2 1.0

2

hr (Btu/h-ft -degF)

Tm = 10 Tm = 30 Tm = 50 Tm = 70 Tm = 90 Tm = 110 Tm = 130 Tm = 150

Common Emissivity Values Stainless Steel: 0.21-0.6 Plated metals: 0.08-0.09 Concrete: 0.88 Black Paint: 0.97 White Paint: 0.93

0.8 0.6 0.4 0.2 0.0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ε

Figure H-2. Radiation Heat Transfer Coefficient with Emissivity and Mean Temperature

Natural Convection (Qc - V < 1 mph) The steps to determine the convective heat transfer from natural convection are detailed below. These steps apply when the wind velocity is less than 1 mph. 1. Measure the surface temperature of the bottle (Ts), the ambient temperature of the air (T∞), diameter of the bottle (D), and length of the bottle (L). (These are the same values measured for the radiation heat loss.) 2. Calculate the mean temperature (Tm) using the Equation H-3. 3. Calculate the parameter X using Equation H-6.

X =

Ts − T∞ Ts + T∞ + 920

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X Ts T∞

= = =

Parameter used in Figure H-3 Surface temperature of bottle (deg F) Ambient temperature (deg F)

4. Using the mean temperature (Tm) and the parameter X, find the value of the natural convection heat transfer coefficient (hn) from Figure H-3. 5. Calculate the surface area of the bottle (A) with the Equation H-4. 6. Calculate the natural convection heat loss of the bottle (Qc) with the Equation H-7.

Qc = hn A(Ts − T∞ ) Qc hn A Ts T∞

= = = = =

(H-7)

Natural convection heat transfer (Btu/hr) Natural convection heat transfer coefficient (Btu/hr-ft2-deg F) Surface area of bottle (ft2) Surface temperature of bottle (deg F) Ambient temperature (deg F)

1.1

1

0.8

2

hn (Btu/h-ft -degF)

0.9

0.7 Tm = 10 Tm = 30 Tm = 50 Tm = 70 Tm = 90 Tm = 110 Tm = 130 Tm = 150

0.6

0.5

0.4 0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Figure H-3. Natural Convection Heat Transfer Coefficient with X and Mean Temperature

Forced Convection (Qc - V > 1 mph) The steps to determine the convective heat transfer from forced convection are detailed below. These steps apply when the wind velocity is greater than 1 mph. 1. Measure the surface temperature of the bottle (Ts), the ambient temperature of the air (T∞), diameter of the bottle (D), length of the bottle (L), and the wind velocity (V). (Many of these are the same values measured for the radiation heat loss.) 2. Calculate the mean temperature (Tm) using the Equation H-3.

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3. Calculate the parameter Y using Equation H-8.

Y = (V * L )

0.8

Y V L

= = =

(H-8) Parameter used in Figure H-4 Wind velocity (mph) Length of Bottle (ft)

4. Using the mean temperature (Tm) and the parameter Y, find the value of the forced convection heat transfer coefficient (Hf) from Figure H-4. 5. Calculate the surface area of the bottle (A) with the Equation H-4. 6. Calculate the forced convection heat loss of the bottle (Qc) with the Equation H-9.

Qc =

H f A(Ts − T∞ ) L

Qc Hf A L Ts T∞

= = = = = =

(H-9)

Forced convection heat transfer (Btu/hr) Forced convection heat transfer coefficient (Btu/hr-ft2-deg F) Surface area of bottle (ft2) Length of Bottle (ft) Surface temperature of bottle (deg F) Ambient temperature (deg F)

250 225 200

Hf (Btu/h-ft-degF)

175 150 125 100

Tm = 10 Tm = 30 Tm = 50 Tm = 70 Tm = 90 Tm = 110 Tm = 130 Tm = 150

75 50 25 0 20

40

60

80

100

120

140

160

(V*L)0.8 (mph*ft)

Figure H-4. Forced Convection Heat Transfer Coefficient with Y and Mean Temperature

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Pipe Losses Total Pipe Losses Heat losses occur on non-insulated pipe. These may be significant if the instrumentation is installed far away from the compressor. If the instruments are installed close to the compressor being tested, then these losses do not have to be considered since they will be minimal ( 1 mph) The steps to determine the convective heat transfer from forced convection are detailed below. These steps apply when the wind velocity is greater than 1 mph. 1. Measure the surface temperature of the pipe (Ts), the ambient temperature of the air (T∞), diameter of the pipe (D), length of the pipe (L), and the wind velocity (V). (Many of these are the same values measured for the radiation heat loss.) 2. Calculate the mean temperature (Tm) using the Equation H-3. 3. Calculate the parameter Z using Equation H-14.

Z=

(V * D )0.805

Z V L

D = = =

(H-14) Parameter used in Figure H-7 Wind velocity (mph) Diameter of pipe (in)

4. Using the mean temperature (Tm) and the parameter Z, find the value of the forced convection heat transfer coefficient (hf) from Figure H-7. 5. Calculate the surface area of the pipe (A) with the Equation H-11. 6. Calculate the forced convection heat loss of the pipe (Qc) with the Equation H-15.

Qc = h f A(Ts − T∞ ) Qc hf A Ts T∞

= = = = =

(H-15)

Forced convection heat transfer (Btu/hr) Forced convection heat transfer coefficient (Btu/hr-ft2-deg F) Surface area of pipe (ft2) Surface temperature of pipe (deg F) Ambient temperature (deg F)

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7

6

4

2

hf (Btu/h-ft -degF)

5

3 Tm = 10 Tm = 30 Tm = 50 Tm = 70 Tm = 90 Tm = 110 Tm = 130 Tm = 150

2

1

0 1

2

3

4

5

6

7

Figure H-7. Forced Convection Heat Transfer Coefficient with Z and Mean Temperature

Estimation of Heat Transfer in Cylinder Cooling Some reciprocating compressor cylinders will have cooling jackets to be removed heat during compression. This is especially true for process compressors. The heat removed from cylinder cooling needs to be considered in the performance test in order to obtain an accurate efficiency calculation. The steps detailed below will give a sufficient estimate of the energy removed with cylinder cooling. The method detailed below assumes the energy change in the cooling medium will be representative of the energy change in the gas due to cooling. There will be some energy change difference due to heat transfer through the housing of the cylinder and cooling passages, but the analysis below assumes this to be negligible. The rate of heat transfer is calculated using Equation H-16. •

Q = m C p (T2 − T1 ) Q

(H-16)

Heat removed for cylinder cooling (Btu/hr)

•

m Cp T2 T1

Tm =

Mass flow rate of cooling medium (lbm/hr) Specific heat of cooling medium (Btu/lbm-deg F) at mean temperature Tm (deg F), see Equation H-17 (for water it is 1 Btu/lbm-deg F and ethylene glycol 0.678 Btu/lbm-deg F) Exit temperature of cooling medium (deg F) Inlet temperature of cooling medium (deg F)

T2 + T1 2

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APPENDIX I EXAMPLE PV CARD CALCULATIONS

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APPENDIX I This appendix reviews example calculations for an individual cylinder end performance test conducted with the PV Card method. It covers the calculation of cylinder volume from compressor geometry, construction of measured PV diagram, calculation of ICHP from the measured PV diagram, development of theoretical PV diagram, calculation of cylinder end efficiency, calculation of cylinder end flow, and calculation of uncertainty of power and efficiency. The calculations completed here are for a transmission compressor. Data for Calculations The first step in this process is to assemble the data required for the calculations that need to be performed for this test. This data is listed below for the example. Cylinder End: Head End Process Fluid = Natural Gas Gas Composition Methane (C1) = 90.315% Ethane (C2) = 6.006% Propane (C3) = 1.018% Iso-Butane (IC4) = 0.113% N-Butane (NC4) = 0.141% Iso-Pentane (IC5) = 0.04% N-Pentane (NC5) = 0.04% Heavies (C6+) = 0.025% Nitrogen = 0.509% Carbon Dioxide = 1.803% Equation of State = BWRS Isentropic Constant (k) = 1.36 Cylinder Bore (B) = 10.875 in Piston Stroke (S) = 5.5 in Piston Rod Diameter (d) = 2.5 in Connecting Rod Length (l) = 17 in Piston Phase = 0 deg Cylinder Area = 92.88 in2 Volume of Stroke (Vstroke) = 510.87 in3 % Clearance (CL%) = 58.9% Clearance Volume (Vcl) = 301.11 in3 Suction Pressure (ps) = 754.80 psia Discharge Pressure (pd) = 992.66 psia Suction Temperature (Ts) = 61.56 deg F Discharge Temperature (Td) =102.82 deg F Compressor Speed (N) = 998.5 RPM Encoder Resolution = 512

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Construction of Measured PV Diagram During testing, each time the encoder triggered, pressure data was collected. Since the encoder used for the test was a 512 encoder, 512 pressure points were recorded for the test. The encoder provided the rotational position (in degrees) of the shaft at each pressure measurement. From this rotational position, the gas volume in the cylinder is calculated for each point. This is done with Equation I-1 below. An example of this calculation is shown below when theta equals 30 degrees. This volume matches with a pressure of 846.55 psia. Once all the volumes are calculated, the PV diagram can be constructed as shown in Figure I-1. 2 S π S 2 (1 − cos θ ) − l − sin θ + l * B 2 + Vcl V= 2 4 2

(I-1)

Example

5.5in 1 − cos 30 o − V30 deg = 2 V30 deg = 340.5in 3

(

) (17in)

2

2 π 5.5in 2 − sin 30 o + 17in * (10.875in ) + 301.11in 3 4 2

1200

1100

Pressure (psig)

1000

900

800

700

600 0

100

200

300

400

500

600

700

800

900

Volume (in^3)

Figure I-1. Constructed Measured PV Diagram

Removal of Channel Resonance As can be seen, the PV diagram in Figure I-1 has channel resonance present. Calculation of the ICHP is not affected by the channel resonance since it is a sinusoidal phenomenon, but the other calculations such as volumetric efficiency and flow are affected by it. Therefore, channel resonance needs to be removed before proceeding further. The channel resonance is removed with filtering techniques and the result is shown below in Figure I-2.

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1200 HE HE - Corrected 1100

Pressure (psig)

1000

900

800

700

600 0

100

200

300

400

500

600

700

800

900

Volume (in^3)

Figure I-2. PV Diagram with Channel Resonance Removed through Filtering

Calculation Measured ICHP Once the PV diagram is constructed, the ICHP can be calculated. During this process the pressure volume diagram is integrated to determine the area inside of the card, which is the work applied to the gas. The area below the expansion and constant suction pressure line will be subtracted from the area below the compression and constant discharge pressure line as shown in Figure I-3. This integration can be performed with any typical integration algorithm; Trapezoidal rule, Simpson’s rule, and others. In this example, a variation of the Trapezoidal rule was used. The basic equation for the integration is Equation I-2. V represents volume, i indicates which step is being integrated, p is the pressure, and n is maximum number of steps. The maximum number of steps would typically correspond to the resolution of the encoder used for the performance test.

Work = ∫ pdV =

n −1 1 ( pn + p1 )Vn − V1 + 1 ∑ ( pi + pi +1 )Vi − Vi +1 2 2 i =1, 2,3, 4,...

(I-2)

The integration of the pressure-volume diagram as shown in Figure I-3 gave a value of 123,719 in-lbs. ICHP is calculated from the work with Equation I-3. The resulting ICHP of the PV diagram is 312.0 HP.

ICHP =

W *N 396000

(I-3)

Example

123,719in − lbs * 998.5 RPM 396000 ICHP= 312.0 HP ICHP =

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1000

1000

900

900

Pressure (psig)

1100

Pressure (psig)

1100

800

700

800

700

600 200

300

400

600

500

700

800

600 200

900

300

400

500

Volume (in^3)

600

700

800

900

Volume (in^3)

Integration of Compression and Constant Discharge Pressure Lines

Integration of Expansion and Constant Suction Pressure Lines

1100

1000

Pressure (psig)

900

800

700

600 200

300

400

500

600

700

800

900

Volume (in^3)

Subtraction of Integrated Areas Resulting in Area Inside Pressure-Volume Trace

Figure I-3. Graphical Representation of Integration of PV Diagram

Determination of Suction and Discharge Volumetric Efficiency The suction and discharge volumetric efficiency can be calculated using Equations 3-14 and 3-15, but it can also be determined from the PV diagram. First, the PV diagram is observed for where the suction valve opens on the cycle and where the discharge valve closes on the cycle. These locations with corresponding gas volumes are indicated on the PV diagram in Figure I-4. The suction volumetric efficiency is calculated with the ratio of volume differences as shown in Equation I-4. The discharge volumetric efficiency is calculated under the same premise with Equation I-5. In both of these equations, the volume when the valve opens is the total volume minus the clearance volume. In the example shown below, the clearance volume is subtracted from the volumes listed on Figure I-4. The suction and discharge volumetric efficiencies for this example are 88.3% and 72.1%, respectively.

EVs =

Vstroke − Vsuction _ valve _ open Vstroke

*100%

V stroke − Vdisch arg e _ valve _ open EVd = 1 − V stroke

(I-4)

* 100%

(I-5)

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Example

510.87in 3 − (360.9in 3 − 301.11in 3 ) *100% 510.87in 3 EVs = 88.3% EVs =

1100

1000

Discharge Valve Opens V = 669.3 in3

Pressure (psig)

900

Suction Valve Opens V = 360.9 in3

800

700

600 200

300

400

500

600

700

800

900

Volume (in^3)

Figure I-4. Where Suction and Discharge Valves Open on PV Diagram

Construction of Theoretical PV Diagram Procedures for the construction of the theoretical PV diagram are discussed in detail in Appendix B, so it will not be repeated here. The toe pressures and volumes used for the construction are listed below. The theoretical PV diagram is shown plotted in Figure I-5 with the corrected PV diagram previously generated. •

Start of Expansion Line ♦ Pressure = 992.66 psia ♦ Volume = 301.11 in3

•

Start of Compression Line ♦ Pressure = 754.80 psia ♦ Volume = 811.98 in3

The isentropic constant was determined to be 1.36, with an EOS solver using the suction temperature and pressure. The K1 and K2 factors were calculated to be 2,332,742 and 6,836,181, respectively. The volumes and pressures at the end of the expansion and compression lines were found to be the values listed below.

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•

End of Expansion Line ♦ Pressure = 754.80 psia ♦ Volume = 368.3 in3

•

End of Compression Line ♦ Pressure = 992.66 psia ♦ Volume = 663.8 in3 1100 HE - Corrected Theoretical 1000

Pressure (psig)

900

800

700

600 200

300

400

500

600

700

800

900

Volume (in^3)

Figure I-5. Theoretical PV Diagram with Correct PV Diagram

After the theoretical PV diagram is constructed the isentropic ICHP can be calculated following the same integration procedure described above for the measured ICHP. The ICHP for the theoretical PV diagram shown in Figure I-5 is 239.85 HP. Calculation of Efficiency The efficiency of the compressor is calculated from the ratio of the measured ICHP and the theoretical ICHP as shown in Equation I-6.

η isen,cyl =

Pisen *100% ICHP

(I-6)

Example

η isen ,cyl =

239.85 HP *100% 312.0 HP

η isen ,cyl = 76.9%

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Calculation of Capacity The capacity can be calculated with any of the equations shown in the guideline. For this example, Equation I-7 is used as shown below.

(CQ )* (B Q= *

2

)

− r 2 * S * N * EVs * p s * Z STD Ts * Z s

(I-7)

The compressibility must be calculated for the standard conditions (14.7 psia and 60 deg F) and for the suction conditions for the gas being compressed. There are ways to calculate these values analytically as discussed in Appendix C, but perhaps the easiest method for calculating this is to use an EOS solver. With the solver, the appropriate EOS can be selected and the compressibility can be determined for the standard and suction conditions. Using a BWRS EOS solver, the compressibilites at the standard and suction conditions were found to be 0.9949 and 0.8694, respectively. The rest of the values included in Equation I-7 are known from cylinder geometry or measured and calculated parameters. The flow through the cylinder end is calculated as shown below. Example

Q=

(0.2314 *10 )* ((10.875 in ) −6

)

− 0 2 * 5.5 in * 998.5 RPM * 88.3 * 754.80 psia * 0.9949 (61.56 deg F + 460 R )* 0.8694 2

Q = 21.98 MMSCFD The rod diameter in this calculation is set to zero since the cylinder end is on the head end. The flow through this cylinder end is 21.98 MMSCFD. Calculation of Measured ICHP Uncertainty There are several different methods that can be used to calculate uncertainty. This example will use the perturbation method as described in Appendix E of the guideline. The measured ICHP has uncertainty due to four variables: pressure, piston position, speed, and channel resonance. The pressure and position uncertainty are important, since these are the properties measured in order to generate the PV diagram during a single cycle. The speed uncertainty is included, since the compressor speed is used to calculate the power from the work from the PV diagram. Channel resonance is included, because the data is filtered before calculations are completed. It was mentioned before that channel resonance is a sinusoidal phenomenon and does not affect the power. However, when the resonance is removed with filtering, there is a possibility that other valuable data could be lost. The uncertainty for this parameter is the difference between the ICHP calculated before and after the channel resonance has been removed. To calculate the uncertainty in the ICHP, each parameter is varied independently while the other parameters are held constant. The difference between ICHP with the positive and negative changes in the parameter is the total uncertainty for that parameter. The calculation of the uncertainty in ICHP for each of the four parameters mentioned above is discussed below.

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Pressure The first step in calculating the uncertainty of the ICHP due to pressure is to determine the uncertainty in the pressure measurement itself. In this example, the pressure uncertainty was calculated from the accuracy of the pressure transducer, calibration uncertainty, and data acquisition uncertainty. These uncertainty values are listed below. Pressure Transducer Uncertainty Calibration Uncertainty Data Acquisition Uncertainty Total Uncertainty

= = = =

1.5 psi 0.5 psi 0.05 psi 2.05 psi

Once the pressure measurement uncertainty is known, the uncertainty of the ICHP due to pressure can be calculated. The uncertainty due to pressure in the ICHP is slightly different than the process described above. Applying only a positive change in pressure or only a negative change in pressure will just shift the PV diagram up or down. It will not cause any change in the ICHP. Therefore the positive and negative variations are used in conjunction. For the maximum ICHP change, a positive pressure change is applied to the compression line and constant discharge line and a negative pressure change is applied to the expansion line and constant suction line. The opposite is done for the minimum ICHP. An example of the maximum ICHP variation is show in Figure E-4. The work is then calculated from these maximum and minimum PV diagrams using the integration discussed above and the ICHP is calculated with the compressor speed. The maximum and minimum ICHP are 317.3 and 306.8 HP, respectively, resulting in an uncertainty in the ICHP from pressure of 10.5 HP. Piston Position The piston position uncertainty is due to the resolution of the encoder, ODC marking and synchronization, and the data acquisition uncertainty. These values of these uncertainties are outlined below. Encoder Uncertainty ODC Determination Synchronization Uncertainty Data Acquisition Uncertainty Total Uncertainty

= = = = =

0.703 deg 0.1 deg 0.1 deg 0.01 deg 0.913 deg

The uncertainty is added and subtracted from the measured position of the shaft. Figure I-6 shows the PV diagrams with the positive and negative change in piston position. The ICHP calculated from the positive and negative changes in piston position are 309.4 and 314.7 HP for a total uncertainty of 5.3 HP. Speed The speed can be measured by an encoder or with a one-per-revolution device. In this example, a magnetic pick-up was used to measure the speed of rotation. This device had an uncertainty of 0.1% of the measured value which correlated to an absolute uncertainty of approximately 1 RPM. The uncertainty calculation for speed is shown below.

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1200 Plus Minus

1100

Pressure (psia)

1000

900

800

700

600 200

300

400

500 600 Volume (in^3)

700

800

900

Figure I-6. Variation in PV Diagram with Piston Position Uncertainty

Example Maximum ICHP

123,719in − lbs * (998.5 RPM + 1 RPM ) 396000 ICHPmax = 312.3HP

ICHPmax =

Minimum ICHP

123,719in − lbs * (998.5 RPM − 1 RPM ) 396000 ICHPmin = 311.6 HP ICHPmin =

Total Uncertainty

∆ICHP = ICHPmax − ICHPmin ∆ICHP = 312.3 HP − 311.6 HP ∆ICHP = 0.7 HP Channel Resonance The uncertainty from channel resonance is actually the uncertainty of the filtering process. It is calculated from the difference between ICHP calculated from the measured PV diagram and the corrected PV diagram. The ICHP from the corrected PV diagram was found above to be 312.0 HP. The ICHP from the uncorrected PV diagram is 310.8 HP which results in a total uncertainty of 1.2 HP due to the filtering process.

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Total Measured ICHP Uncertainty Once the uncertainty due to each measured parameter is determined, the total uncertainty for the measured ICHP can be determined. This value is found by calculating the root mean sum of all the uncertainties (Equation I-8). This calculation is shown in Table I-1. This shows the total uncertainty for the measured ICHP for this cylinder end is 11.8 HP or 3.78% of measured ICHP.

∆ICHPcyl 1− HE =

(∆ICHP

) + (∆ICHP 2

i ,cyl 1− HE

)

2

i +1,cyl 1− HE

+ ...

(I-8)

Table I-1. Calculation of Total Uncertainty of Measured ICHP for Cylinder End

Parameter Pressure Piston Position Speed Channel Resonance

Uncertainty (HP) 10.5 5.3 0.7 1.2 Sum of Squares Square Root of Sum

Square of Uncertainty (HP2) 110.25 28.09 0.49 1.44 140.27 11.8 HP

Calculation of Theoretical ICHP Uncertainty The theoretical ICHP uncertainty is calculated in the same manner that the measured ICHP uncertainty is: a combination of uncertainties from various parameters. However, there is a difference in the parameters which must be included in the uncertainty analysis. For the theoretical ICHP uncertainty, the parameters which must be considered are pressure, isentropic constant, speed, and clearance volume. Pressure The toe pressures obtained from the measured PV diagram are used to construct the theoretical PV diagram. The uncertainty in the pressure measurement is applied to the toe pressures to obtain the uncertainty in the theoretical ICHP from pressure. The pressure measurement uncertainty of 2.05 psi was used to determine the toe pressures. From these toe pressures and with an isentropic constant of 1.36, the end points of both the compression and expansion lines were calculated. The calculated values, along with the maximum and minimum theoretical ICHP, are shown in Table I-2. The uncertainty of the theoretical ICHP is calculated from the difference between the maximum and minimum theoretical ICHP which equals to 6 HP. Isentropic Constant The uncertainty of the isentropic constant is due to the uncertainty of the pressure, temperature, and gas composition measurement. The best method to determine the maximum and minimum possible variation in the isentropic constant is to vary each of these parameters with each test point and determine the isentropic constant for that particular condition. However, this can be very time consuming. Instead, determine which test point had the highest uncertainty in the pressure, temperature, and gas composition, and determine the maximum and minimum isentropic constants for this scenario. Calculate a percentage

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of variation for this condition and apply it to the rest of the uncertainty calculations with isentropic constants. This method will reduce the computations needed and yield a conservative uncertainty.

K2

Start

End

Expansion Line

K1

Compression Line

Start

Table I-2. Defined and Calculated Values for Theoretical ICHP Uncertainty Due to Pressure Uncertainty

Discharge Pressure (psia) Volume (in^3) Suction Pressure (psia) Volume (in^3) Suction Pressure (psia) Volume (in^3)

Measured ICHP 992.66 301.11

Minimum ICHP 994.71 301.11

Maximum ICHP 990.61 301.11

2332742

2313772

2323348

754.80 368.30 754.80 811.98

752.75 367.10 752.75 811.98

756.85 369.66 756.85 811.98

6836181

6805796

6768928

End

Discharge Pressure (psia) 992.66 994.71 Volume (in^3) 663.80 666.10 Theoretical ICHP (HP) 239.85 236.80 NOTE: Bolded values were defined, and shaded values are calculated.

990.61 661.41 242.80

For this example, varying the pressure, temperature and gas composition yielded a maximum and minimum isentropic constant of 1.3672 and 1.3539, respectively. This is a +0.53% and -0.45% variation. Therefore, 0.5% will be used for the uncertainty of the isentropic constant. The defined and calculated values for the theoretical ICHP due to variation in isentropic constant are shown in Table I-3. The difference between the maximum and minimum theoretical ICHP’s is 0.021 HP. This is less than 0.01% of the theoretical horsepower and can be considered negligible. Unless there is a significant deviation in pressure, temperature, or gas composition then the uncertainty due the isentropic constant can be ignored. Speed The uncertainty of the theoretical ICHP due to the uncertainty in the speed measurement is calculated using the same methodology describe above in the “Calculation of Measured ICHP Uncertainty” section. The work calculated from the integration of the theoretical ICHP diagram is 95,124 in-lbs. With a speed uncertainty of 1 RPM, this gives a total uncertainty of 0.5 HP for the calculation of the theoretical ICHP. Clearance Volume The uncertainty of the clearance volume affects the start and end volumes for the PV diagram. Changing these values will affect the curvature and end points of the expansion and compression lines. The clearance volume is obtained from the manufacturer information on the compressor, a volume measurement, or the effective clearance volume from the measured PV diagram. For this example, we assume we have used the value from the manufacturer and that there is a 2% uncertainty. The defined and calculated values for the theoretical ICHP due to uncertainty in clearance volume are shown in Table I-4. The difference between the maximum and minimum theoretical ICHP’s is 1.45 HP.

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Expansion Line

Start

Measured k 1.36 992.66 301.11

K1

2332742

Compression Line

Table I-3. Defined and Calculated Values for Theoretical ICHP Uncertainty Due to Isentropic Constant Uncertainty

K2

Start

End

Isentropic Constant Discharge Pressure (psia) Volume (in^3) Suction Pressure (psia) Volume (in^3) Suction Pressure (psia) Volume (in^3)

Maximum k 1.3668 992.66 301.11

Minimum k 1.3532 992.66 301.11

2410241

2230367

754.80 368.30 754.80 811.98

754.80 367.99 754.80 811.98

754.80 368.74 754.80 811.98

6836181

7103467

6485324

End

Discharge Pressure (psia) 992.66 992.66 Volume (in^3) 663.80 664.41 Theoretical ICHP (HP) 239.85 239.864 NOTE: Bolded values were defined, and shaded values are calculated

992.66 663.07 239.843

Table I-4. Defined and Calculated Values for Theoretical ICHP Uncertainty Due to Clearance Volume Uncertainty

K2

Start

End

Expansion Line

K1

Compression Line

Start

Clearance Volume (in^3) Discharge Pressure (psia) Volume (in^3) Suction Pressure (psia) Volume (in^3) Suction Pressure (psia) Volume (in^3)

Measured CL% 301.11 992.66 301.11

Maximum CL% 307.1322 992.66 307.13

Minimum CL% 295.0878 992.66 295.09

2332742

2381801

2255772

754.80 368.30 754.80 811.98

754.80 375.73 754.80 818.00

754.80 360.99 754.80 805.96

6836181

6855861

6719045

End

Discharge Pressure (psia) 992.66 992.66 Volume (in^3) 663.80 668.67 Theoretical ICHP (HP) 239.85 239.13 NOTE: Bolded values were defined, and shaded values are calculated

992.66 658.82 240.58

Total Measured ICHP Uncertainty Once the uncertainty due to each measured parameter is determined, the total uncertainty for the theoretical ICHP can be determined. This value is found by calculating the root mean sum of all the uncertainties (Equation I-8). This calculation is shown in Table I-5. This shows the total uncertainty for the theoretical ICHP for this cylinder end is 6.19 HP or 2.58%.

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Table I-5. Calculation of Total Uncertainty of Measured ICHP for Cylinder End

Parameter Pressure Isentropic Constant Speed Clearance Volume

Uncertainty (HP) 6 0.021 0.5 1.45 Sum of Squares Square Root of Sum

Square of Uncertainty (HP2) 36 0.000441 0.25 2.1025 38.35 6.19 HP

Calculation of Efficiency Uncertainty The uncertainty of the efficiency can be calculated for each parameter (pressure, piston position, etc.) as completed above for the ICHP; however, the tester is more interested in an overall uncertainty of the efficiency for the cylinder end. In order to reduce the effort required to find the efficiency uncertainty, the equations listed below (also shown in Appendix E) can be used to calculate it with the measured and theoretical ICHP uncertainties calculated above.

η cyl ,max =

η cyl ,min =

Pcyl ,isen + ∆Pcyl ,isen ICHPcyl − ∆ICHPcyl

(I-9)

Pcyl ,isen − ∆Pcyl ,isen ICHPcyl + ∆ICHPcyl

∆η cyl = η cyl ,max − η cyl ,min

(I-10) (I-11)

The uncertainty of the efficiency for the cylinder end being evaluated in this example is calculated below. The total uncertainty of the calculated efficiency is 9.5 efficiency points or 12.4% of the efficiency (76.9%). Example

Pcyl ,isen = 229.85 HP ∆Pcyl ,isen = 6.19 HP ICHPcyl = 312.0 HP ∆ICHPcyl = 11.8 HP

229.85 HP + 6.19 HP 312.0 HP − 11.8 HP = 78.6%

η cyl ,max = η cyl ,max

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η cyl ,min =

229.85 HP − 6.19 HP 312.0 HP + 11.8 HP

η cyl ,min = 69.1% ∆η cyl = 78.6% − 69.1% ∆η cyl = 9.5%

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APPENDIX J DATASHEETS FOR RECIPROCATING COMPRESSOR PERFORMANCE TESTING

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APPENDIX J Datasheets are shown on the next pages. They are labeled as General, PV Card, and Enthalpy Rise. The sheets labeled as general apply to both the PV Card and Enthalpy Rise methods. The other datasheets only apply to either the PV Card or Enthalpy Rise methods.

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Datasheet for Compressor Performance Test - General 1 Date: _____________________ Time Cylinder ID Service or Stage HE Pocket Number(s)*Open HE Valve(s) Lifted (Yes or No) CE Pocket Number(s)*Open CE Valve(s) Lifted (Yes or No) Suction Gas Pressure Suction Gas Temperature Suction Nozzle Pressure Suction Nozzle Temperature Discharge Nozzle Pressure Discharge Nozzle Temperature Discharge Gas Pressure Discharge Gas Temperature Compressor RPM

Test No:

Units

Gas Flow Meter Static Pressure Temperature Static ΔP Dynamic ΔP Orifice Coefficient Barometric Pressure Volume Flow Fuel Meter Static Pressure Temperature Static ΔP Dynamic ΔP Orifice Coefficient Barometric Pressure Volume Flow

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Datasheet for Compressor Performance Test - General 2 Date: _____________________ Time: _____________________

Test No:

Driver Current Voltage Power Factor Motor Mechanical Efficiency Gas Composition (mol %) Oxygen Hydrogen Water Hydrogen Sulfide Nitrogen Ammonia Carbon Monoxide Carbon Dioxide Methane Ethane Propane N-Butane Iso-Butane N-Pentane Iso-Pentane Neo-Pentane N-Hexane Iso - Hexane Other: ___________________ Other: ___________________ Other: ___________________ Other: ___________________ Other: ___________________ Other: ___________________ Other: ___________________

Units

Gas

Fuel

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Datasheet for Compressor Performance Test - General 3 Date: _____________________

Test No:

Cylinder Cooling Flow Meter Static Pressure Temperature Static ΔP Dynamic ΔP Orifice Coefficient Barometric Pressure Volume Flow Inlet Temperature Outlet Temperature

Units

Calculated Values Cylinder Cooling Mass Flow Rate (mcool) Heat Flux (qcool) Driver Low Heating Value of Fuel (LHV) Fuel Mass Flow Rate (mfuel) Power Input (Pin) Efficiencies Driver Efficiency (η e) System Efficiency (η sys)

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Datasheet for Compressor Performance Test - PV Card 1 Date: __________________________ Cylinder ID Bore Diameter Stroke Rod Diameter Rod Length

Test No:

RPM: Units

Head End (HE) Fixed Clearance Volume Pocket 1 Volume Pocket 2 Volume Pocket 3 Volume Pocket 4 Volume Valve Lifters (Number) Crank End (CE) Fixed Clearance Volume Pocket 1 Volume Pocket 2 Volume Pocket 3 Volume Pocket 4 Volume Valve Lifters (Number) Compressor Indicator Passage Length Diameter Maximum Rod Loading Compression Tension Single Acting HE (CE Valve Lifted) Single Acting CE (HE Valve Lifted)

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Datasheet for Compressor Performance Test - PV Card 2 Date: _____________________ Cylinder ID Calculated Values Head End Indicated Compressor Horsepower (ICHP) Brake Horsepower (BHP) Suction Volumetric Efficiency (EVs)

Test No: Units

Discharge Volumetric Efficiency (EVd) Suction Gas Compressibility (Zs) Discharge Gas Compressibility (Zd) Capacity (Q) Isentropic Power (from theoretical PV diagram)(Pisen) Isentropic Efficiency (η isen) Crank End Indicated Compressor Horsepower (ICHP) Brake Horsepower (BHP) Suction Volumetric Efficiency (EVs) Discharge Volumetric Efficiency (EVd) Suction Gas Compressibility (Zs) Discharge Gas Compressibility (Zd) Capacity (Q) Isentropic Power (from theoretical PV diagram)(Pisen) Isentropic Efficiency (η isen) Full Compressor Indicated Compressor Horsepower (ICHP) Isentropic Efficiency (η isen) Capacity (Q)

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Datasheet for Compressor Performance Test - Enthalpy Rise 1 Date: _____________________ Cylinder ID

Test No: Units

Calculated Values Cylinders Actual Suction Enthalpy (hs) Actual Discharge Enthalpy (hd) Theoretical Suction Enthalpy (hs) Theoretical Discharge Enthalpy (hd,isen) Actual Enthalpy Difference (H) Theoretical Enthalpy Difference (Hisen) Isentropic Efficiency (η isen,cyl) Capacity (Q) Mass Flow Rate (mcyl) Actual Power (Pcyl) Full Compressor Actual Suction Enthalpy (hs) Actual Discharge Enthalpy (hd) Theoretical Suction Enthalpy (hs) Theoretical Discharge Enthalpy (hd,isen) Actual Enthalpy Difference (H) Theoretical Enthalpy Difference (Hisen) Isentropic Efficiency (η isen,cyl) Capacity (Q) Mass Flow Rate (mcyl) Actual Power (Pcyl)

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