FLUID FLOW MANUAL
CHEVRON RESEARCH AND TECHNOLOGY COMPANY RICHMOND, CA
March 1997
Manual sponsor:
For information or help regarding this manual, contact R.P. (Rob) Hohmann 242-2216
Printing History Fluid Flow Manual Second Edition First Revision Second Edition
January 1990 October 1992 March 1997
Restricted Material Technical Memorandum This material is transmitted subject to the Export Control Laws of the United States Department of Commerce for technical data. Furthermore, you hereby assure us that the material transmitted herewith shall not be exported or re-exported by you in violation of these export controls.
The information in this Manual has been jointly developed by Chevron Corporation and its Operating Companies. The Manual has been written to assist Chevron personnel in their work; as such, it may be interpreted and used as seen fit by operating management. Copyright 1990, 1992, 1997 CHEVRON CORPORATION. All rights reserved. This document contains proprietary information for use by Chevron Corporation, its subsidiaries, and affiliates. All other uses require written permission.
March 1997
Chevron Corporation
List of Current Pages Fluid Flow Manual The following list shows publication or revision dates for the contents of this manual. To verify that your manual contains current material, check the sections in question with the list below. If your copy is not current, contact the Technical Standards Team, Chevron Research and Technology Company, Richmond, CA (510) 242-7232.
Section Front Matter Table of Contents 50 100 200 300 400 500 600 700 800 900 1000 1100 Appendix A Appendix B Appendix C Appendix D Appendix E Appendix F Appendix G Appendix H Appendix I Index PC Disks Page
Chevron Corporation
Date March 1997 March 1997 March 1997 January 1990 January 1990 October 1992 March 1997 March 1997 January 1990 January 1990 January 1990 January 1990 March 1997 March 1997 January 1990 January 1990 January 1990 March 1997 October 1992 March 1997 January 1990 January 1990 March 1997 March 1997 March 1997
March 1997
Maintaining This Manual Fluid Flow Manual If you have moved or you want to change the distribution of this manual, use the form below. Once you have completed the information, fold, staple, and send by company mail. You can also FAX your change to (510) 242-2157. ❑ Change addressee as shown below. ❑ Replace manual owner with name below. ❑ Remove the name shown below. Previous Owner:
Title: Last
First
M.I.
Current Owner:
Title: Last
First
M.I.
Company:
Dept/Div:
Street:
P.O. Box:
City:
State:
Requesting Signature
Zip:
Date
Send this completed form to: Document Control, Room 50-4328 Chevron Research and Technology Company 100 Chevron Way (P.O. Box 1627) Richmond, CA 94802
CRTC Consultants Card The Chevron Research and Technology Company (CRTC) is a full-service, in-house engineering organization. CRTC periodically publishes a Consultants Card listing primary contacts in the CRTC specialty divisions. To order a Consultants Card, contact Ken Wasilchin of the CRTC Technical Standards Team at (510) 242-7241, or email him at “KWAS.”
Chevron Corporation
March 1997
Reader Response Form Fluid Flow Manual We are very interested in comments and suggestions for improving this manual and keeping it up to date. Please use this form to suggest changes; notify us of errors or inaccuracies; provide information that reflects changing technology; or submit material (drawings, specifications, procedures, etc.) that should be considered for inclusion. Feel free to include photocopies of page(s) you have comments about. All suggestions will be reviewed as part of the update cycle for the next revision of this manual. Send your comments to:
Page or Section Number
Document Control, Room 50-4328 Chevron Research and Technology Company 100 Chevron Way (P.O.Box 1627) Richmond, CA 94802 Comments
Name Address
Phone
Chevron Corporation
March 1997
Fluid Flow Manual Sponsor: R.P. Hohmann / Phone: (510) 242-2216 / E-mail :
[email protected] This document contains extensive hyperlinks to figures and cross-referenced sections. The pointer will change to a pointing finger when positioned over text which contains a link.
List of Current Pages 50
Using This Manual
50-1
100
Introduction
100-1
200
Static Pressure
200-1
300
Acceleration Pressure Drop
300-1
400
Friction Pressure Drop
400-1
500
Fitting Pressure Drop
500-1
600
Noncircular Conduits
600-1
700
Open Channel Flow (Section not developed)
800
Surge Pressure
800-1
900
Pipeline Flow
900-1
1000
Fluid Properties
1000-1
1100
Computer Programs
1100-1
Appendices Appendix A Appendix B Appendix C Appendix D Appendix E Appendix F Appendix G Appendix H Appendix I
Chevron Corporation
Conversion Tables Properties of Water Design Properties of Pipe PCFLOW Program PIPEFLOW-2 Program HOTOIL Program HOTOL* Program SURGE Program PCSURGE Program
June 1993
50
Using This Manual Abstract This section summarizes the contents and explains the organization of the Fluid Flow Manual. This manual is in one volume that includes engineering guidelines with accompanying appendices. The manual has a table of contents and a complete index to aid you in finding specific subjects.
Chevron Corporation
50-1
March 1997
50 Using This Manual
Fluid Flow Manual
Scope and Application The Fluid Flow Manual provides basic fluid flow theory, calculational methods, and physical data for use in piping design. It is directed both to entry-level personnel and nonspecialists regardless of experience. This manual should not be used as a substitute for sound engineering judgment. The intent is to provide practical, useful information based on Company experience. Therefore, forms have been included in the front of the manual for your convenience in suggesting changes. Your input and experience are important for improving subsequent printings and keeping this manual up to date.
Organization This manual comprises Engineering Guidelines and appendices that address such concerns as: (1) designing piping to efficiently carry fluids, (2) determining open channel flow, (3) calculating surge pressures, (4) handling special pipeline problems, (5) fluid and pipe properties, (6) available computer programs.
Tabs The colored tabs in the manual will help you find information quickly.
March 1997
•
White tabs are for table of contents, introduction, appendices, PC disks, index, and general purpose topics
•
Blue tabs denote Engineering Guidelines
•
Red tab marks a place for you to keep documents that are developed at your facility
50-2
Chevron Corporation
Fluid Flow Manual
50 Using This Manual
Other Company Manuals The text sometimes refers to documents in other Company manuals. These documents carry the prefix of that manual. The prefixes are defined here:
Chevron Corporation
Prefix
Company Manual
CIV
Civil and Structural
CMP
Compressor
COM
Coatings
CPM
Corrosion Prevention
DRI
Driver
ELC
Electrical
EXH
Heat Exchanger and Cooling Tower
FFM
Fluid Flow
FPM
Fire Protection
HTR
Fired Heater and Waste Heat Recovery
ICM
Instrumentation and Control
IRM
Insulation and Refractory
MAC
General Machinery
NCM
Noise Control in Designs
PIM
Piping
PMP
Pump
PPL
Pipeline
PVM
Pressure Vessel
TAM
Tank
UTL
Utilities
WEM
Welding
50-3
March 1997
50 Using This Manual
Fluid Flow Manual
Fig. 50-1
Fluid Flow Manual Quick-Reference Guide Task
Fluid Flow Manual Sections
Learning Background Information •
Pressure drop calculations
100, 200, 300, 400, 500
•
Pipeline friction heating
900
•
Surge
800
•
Open channel flow
700
•
Computer programs
1100, Appendices D, E, F, G, H, I
Selecting the Best Computer Program •
Selection guide
1100
•
Detailed operation
Appendices D, E, F, G, H, I
Calculating Flow Rates •
By PCFLOW program
1100, Appendix D
•
With flow charts
400
•
With sophisticated programs
1100, Appendices D, E, F, G, H, I
Finding Engineering Data
March 1997
•
Pipe dimensions
Appendix C
•
Fluid properties
1000
•
Heat transfer properties
900
50-4
Chevron Corporation
100 Introduction Abstract This section describes the scope of the Fluid Flow Manual and discusses its basic approach to fluid flow problems.
Chevron Corporation
Contents
Page
110
Scope of the Fluid Flow Manual
100-2
120
Basic Elements of Pressure Drop
100-2
130
Importance of the Darcy-Weisbach Equation
100-2
140
Nomenclature
100-3
150
References
100-3
100-1
January 1990
100 Introduction
Fluid Flow Manual
110 Scope of the Fluid Flow Manual The Fluid Flow Manual presents the equations that model basic fluid flow phenomena. Most of the equations and discussions are oriented toward solving for pressure drop given well defined fluids, flow rates, and geometry in simple hydraulic systems. In general the manual treats isothermal flow. The exception to this is that some of the computer programs referenced in Section 1100 perform heat transfer calculations and appropriately adjust fluid properties and pressure drop along the flow path.
120 Basic Elements of Pressure Drop The total pressure drop in a fluid flow system can be accurately defined if all of the following components of that pressure drop are found: • • •
Pressure change due to elevation change Pressure drop due to acceleration losses Pressure drop due to frictional losses
The relationship between the three components of pressure drop may be expressed as follows: ∆Psystem = ∆Pelevation + ∆Pacceleration + ∆Pfriction (Eq. 100-1)
These components of total system pressure drop are treated in Sections 200, 300, and 400, respectively, for simple cases. Special considerations are treated in the remaining sections. For example, Section 500 presents a method for approximating the combination of both acceleration and friction losses that occurs in valves, fittings, and pipe entrances.
130 Importance of the Darcy-Weisbach Equation The dominant effect in most fluid flow systems is friction pressure drop. The DarcyWeisbach equation solves for friction pressure drop for any fluid, in any pipe, over any length for which the fluid properties remain relatively constant. This equation is presented here because of its importance. It is discussed more fully in Section 410: 2
fL V h = ------ ⋅ ------D 2g
(Eq. 100-2)
where: h = head loss, ft f = friction factor L = pipe length, ft
January 1990
100-2
Chevron Corporation
Fluid Flow Manual
100 Introduction
D = pipe internal diameter, ft V = fluid velocity, ft/sec g = gravitational constant (32.17 ft/sec2) The Darcy-Weisbach equation defines the friction factor, f. Whenever possible the reader is encouraged to use this equation instead of the flow charts in Section 400. This equation is automated in the “Incompressible Flow” section of the PCFLOW program, which is provided on disk at the end of this manual.
140 Nomenclature This manual does not contain a master list of nomenclature. Equation variables are defined following each equation.
150 References The following selection of general references is supplemented by specific references in the applicable sections of the manual.
Chevron Corporation
1.
Fox, R. W., A. T. McDonald. Introduction to Fluid Mechanics. John Wiley & Sons, New York: 1978.
2.
Perry, R. H., C. H. Chilton. Chemical Engineers’ Handbook, Section 5. McGraw-Hill, New York: 1973.
3.
Streeter, V. L., E. B. Wylie. Fluid Mechanics. McGraw-Hill, New York.
4.
Engineering Data Book, Section 17. Gas Processors Association, Tulsa: 1987.
5.
Cameron Hydraulic Data. Ingersoll-Rand, Woodcliff Lake, N.J.: 1979.
100-3
January 1990
200 Static Pressure Abstract This section discusses the equations for calculating static pressure and head.
Chevron Corporation
Contents
Page
210
Definition of Static Pressure
200-2
220
Equations for Static Pressure and Head
200-2
200-1
January 1990
200 Static Pressure
Fluid Flow Manual
210 Definition of Static Pressure The pressure generated by the height of a column of liquid (see Figure 200-1) is expressed as static pressure, or, alternatively, static head or elevation head. Pressures other than static pressure are often expressed in terms of the column of liquid required to generate an equivalent static pressure, such as feet of water or inches of mercury. Similarly head (H), expressed in feet, often describes pressures that are not static. Units of static pressure and head can be converted to one another using the following equations. Fig. 200-1
Static Pressure
220 Equations for Static Pressure and Head Equation 200-1 expresses the static pressure in psi generated by a column of liquid: ρh P s = --------144 (Eq. 200-1)
where: Ps = static pressure, psi h = height of liquid column, ft ρ = fluid density, lbm/cu ft
January 1990
200-2
Chevron Corporation
Fluid Flow Manual
200 Static Pressure
Equation 200-2 expresses head, in feet, equivalent to an arbitrary pressure, in psi: 144 H = P --------ρ (Eq. 200-2)
where: H = head, ft P = pressure, psi ρ = fluid density, lbm/cu ft The conversion of head in feet to pressure in pounds per square inch for water at 60°F is as follows: Ps = 0.433 h h = 2.31 Ps
Chevron Corporation
200-3
January 1990
300 Acceleration Pressure Drop Abstract This section presents the equations for calculating pressure drop due to fluid acceleration and discusses the phenomenon in terms of changes in pipe geometry and change of phase.
Chevron Corporation
Contents
Page
310
Definition of Acceleration Pressure Drop
300-2
320
Equations for Acceleration Pressure Drop
300-2
330
Discussion
300-2
300-1
October 1992
300 Acceleration Pressure Drop
Fluid Flow Manual
310 Definition of Acceleration Pressure Drop An increase in velocity (i.e., acceleration) of a fluid is accompanied by a decrease in its static pressure. This decrease is called acceleration pressure drop. It occurs at pipe entrances and reducers, and where a phase change from liquid to gas occurs, to give two common examples. Acceleration pressure drop is usually expressed in pounds per square inch (psi) or in units of velocity head (in feet). One velocity head is the acceleration head loss of a fluid accelerated from rest in a reservoir to a specific velocity in a pipe.
320 Equations for Acceleration Pressure Drop Velocity head is calculated using the following equation: 2
V h = ------2g
(Eq. 300-1)
where: h = velocity head in feet of liquid, ft V = fluid velocity, ft/sec g = gravitational constant (32.17 ft/sec2) Acceleration pressure drop across an entrance or reducer, expressed in terms of static pressure drop (in psi), is: 2
2
ρ( V2 – V1 ) ∆P = --------------------------------2g ⋅ 144 (Eq. 300-2)
where: ∆P = static pressure drop, psi ρ = fluid density, lbm/cu ft V1 = upstream fluid velocity, ft/sec V2 = downstream fluid velocity, ft/sec Determination of acceleration pressure drop is particularly important when calculating the NPSHA of reciprocating pumps, to avoid cavitation. See Section 100 of the Pump Manual.
330 Discussion Equations 300-1 and 300-2 describe acceleration loss at pipe entrances and reducers. Frictional losses (see Section 500) must be added to get the total loss for
October 1992
300-2
Chevron Corporation
Fluid Flow Manual
300 Acceleration Pressure Drop
this geometry. The fitting loss coefficients given in Section 500 for other types of valves and fittings (besides pipe entrances and reducers) take into account both acceleration and friction effects. During changes of phase (evaporation, flashing, and boiling), the velocity of a fluid must increase as the gas phase increases its mass flow rate. The pressure required to produce that acceleration is accurately described by Equations 300-1 and 300-2. The total pressure drop is the sum of the acceleration pressure drop and the flowing friction pressure drop. This friction loss can be difficult to calculate because the flow rates of the two phases are changing and, therefore, the friction pressure drop is changing as the fluid moves downstream. The static pressure that is converted to kinetic energy through the acceleration of a flowing fluid is theoretically recoverable as static pressure when the flow decelerates. However, since even carefully designed diffusers can recover only a fraction of the original static pressure, this recovery is not attempted in normal piping situations. In standard piping systems the kinetic energy of a flowing fluid is dissipated as turbulence at pipe exits and enlargements. Confusion on this point can arise because some authors attribute acceleration pressure loss not to the pipe entrance or reducer, but to the pipe exit or enlargement, where the potentially recoverable energy is finally lost. This gives some readers the false impression that there is a static pressure drop across pipe exits and enlargements. Static pressure drop— produced by acceleration and friction effects—occurs across pipe entrances and reducers, not their exits and enlargements.
Chevron Corporation
300-3
October 1992
400 Friction Pressure Drop Abstract This section presents equations for calculating the relationship between flow rate and pressure drop for incompressible flow, two-phase flow, compressible flow, and gas flow at high pressure drop (choked flow).
Chevron Corporation
Contents
Page
410
Incompressible Flow
400-3
411
Fitting Loss Coefficients
412
Pipe and Tube Friction Losses
413
Flow Charts
414
Correction Factor for Internal Roughness for Use With Flow Charts
420
Two-phase Flow
421
Pressure Drop Calculations
422
Friction Pressure Drop Correlations
423
Fitting and Bend Losses
424
Acceleration Pressure Loss
425
Elevation Losses
426
Flow Patterns
427
Accuracy of Friction Pressure Drop Calculation
428
Liquid Holdup Correlation
430
Compressible Flow
400-41
440
Gas Flow At High Pressure Drop (Choked Flow)
400-59
441
Assumptions
442
Use of Design Charts
443
Sonic Flow
444
Choked Flow
445
Temperature Variations
400-30
400-1
March 1997
400 Friction Pressure Drop
March 1997
Fluid Flow Manual
446
Effects of Valves and Fittings
447
Deviation from Assumptions
450
References
400-64
400-2
Chevron Corporation
Fluid Flow Manual
400 Friction Pressure Drop
410 Incompressible Flow The Darcy-Weisbach Equation (Equation 400-1) expresses the relationship between flow rate and friction pressure drop for incompressible flow in pipes and tubes. It is accurate for both liquids and gases, and for any length of pipe over which fluid properties are relatively constant. 2
fL V h = ------ ⋅ ------D 2g
(Eq. 400-1)
where: h = head loss, ft f = Darcy friction factor L = pipe length, ft D = pipe inside diameter, ft V = fluid velocity, ft/sec g = gravitational constant (32.17 ft/sec2) The Darcy-Weisbach Equation can be rewritten in terms of pressure drop in psi, flow rate in pounds per hour, and a constant that combines all the unit conversions, as in Equation 400-2. 2
fL W P = ------ ⋅ -------------------------------------4 D ρD ( 7.4 ⋅ 10 10 ) (Eq. 400-2)
where: P = pressure drop, psi W = mass flow rate, lbm/hr ρ = fluid density, lbm/ft3
411 Fitting Loss Coefficients Fitting loss coefficients (see Section 500) are dimensionally equivalent to the term fL/D and can be added to pipe friction losses using Equation 400-3. Fitting loss coefficients include both friction and acceleration effects. 2
W fL P = K + ------ ⋅ ------------------------------------- D ρD 4 ( 7.4 ⋅ 10 10 ) (Eq. 400-3)
Chevron Corporation
400-3
March 1997
400 Friction Pressure Drop
Fluid Flow Manual
where: K = fitting loss coefficient (from Section 500)
412 Pipe and Tube Friction Losses For pipe and tube flow, the friction factor is a function of the Reynolds number and the flow regime. In the turbulent flow regime it is also a function of pipe roughness. Reynolds number can be written using units consistent with Equation 400-3, as follows: 0.526W Re = ------------------Dµ (Eq. 400-4)
where: Re = Reynolds number µ = absolute viscosity, cp There are no sharp divisions between the laminar, transition, and turbulent flow regimes. For design purposes, the recommended boundary between laminar and transition flow is Re = 1600. The recommended boundary between transition and turbulent flow is Re = 3400. These values provide relatively smooth transitions between regimes for calculated friction factors, and produce conservative results (tend to overpredict pressure drop) around the laminar-to-transition flow boundary. The friction factor for laminar flow (Re < 1600) can be derived analytically (without experimental components) to give: f = 64/Re (Eq. 400-5)
The friction factor for transition flow (1600 < Re < 3400) cannot be predicted accurately. The following conservative value (overprediction) is recommended for most cases: f = 0.04 (Eq. 400-6)
The Moody Diagram (Figure 400-1) presents experimentally derived friction factors for turbulent flow (Re ≥ 3400). In turbulent flow the friction factor is a function of pipe roughness as well as the Reynolds number. At high Reynolds numbers the friction factor is a function of only relative roughness (absolute roughness/diameter). Figure 400-2 gives the relative roughness for various diameters and types of pipe.
March 1997
400-4
Chevron Corporation
Fluid Flow Manual
Fig. 400-1
400 Friction Pressure Drop
Moody Diagram
Chevron Corporation
400-5
March 1997
400 Friction Pressure Drop
Fig. 400-2
March 1997
Fluid Flow Manual
Relative Pipe Roughness (ε/D) and Friction Factors (f) for Complete Turbulence
400-6
Chevron Corporation
Fluid Flow Manual
400 Friction Pressure Drop
Many equations have been proposed to approximate the Moody Diagram friction factors. One of these is the Chen Equation (Equation 400-7), which is simple, accurate, and stable when used on small computers: 2 2 f = ------------------------------------------- – 4 log 10 (A1-A2)
(Eq. 400-7)
where: ε ---D A1 = ---------------3.7065 5.0452 A2 = ---------------- ⋅ log 10 ( A3 ) Re ε --D 7.149 0.8981 A3 = ----------------------- + ------------- Re 2.8257 ε = absolute pipe roughness, ft 1.1098
D = pipe diameter, ft ε ---- = relative roughness D
413 Flow Charts The relationship between pressure drop and flow rate can also be found graphically using the nomographs in Figures 400-4 through 400-13. All of these charts are derived from the Darcy-Weisbach Equation. Be sure to apply the appropriate corrections in Figures 400-3 through 400-13.
414 Correction Factor for Internal Roughness for Use With Flow Charts Figures 400-4 through 400-13 are based on new steel pipe having an absolute roughness of 0.0018 inches. The effect of other values of roughness can be estimated by multiplying the pressure drop by a correction factor from Figure 400-3. Typical values of roughness, E, are as follows:
Chevron Corporation
Pipe
Absolute Roughness, ε
Plastic
0.000005 ft
Smooth Steel, New
0.00015 ft
Galvanized Steel
0.00042 ft
400-7
March 1997
400 Friction Pressure Drop
Fluid Flow Manual
Pipe
Absolute Roughness, ε
Cast Iron, Asphalted
0.00042 ft
Transite
0.00042 ft
Cast Iron, Uncoated, New
0.00083 ft
Steel, Concrete Lined
0.00083 ft
Concrete
0.0083 ft
Riveted Steel
0.025 ft
Correction factors in Figure 400-3 for 1 centistoke (cs) are typical of water or petroleum products ranging from 0.5 to 2.0 cs viscosity. Correction factors in Figure 400-3 for 10 centistoke (cs) are typical of crude oils or other liquids in the viscosity range from 5 to 20 cs. Correction factors are applicable for turbulent flow. No correction is required for laminar flow. The uncertainties in the transition range increase with roughness. The correction factors are the ratio fc / fo where: fc = friction factor from the Colebrook formula (Equation 400-12) fo = friction factor on which Figures 400-4 to 400-13 are based Where accurate performance data are required, pressure losses should be determined by test. If test measurements are not possible, the friction factor can be found with the Moody Diagram or calculated with the Chen Equation (Equation 400-7). Fig. 400-3
Correction Factors for Internal Roughness (1 of 2) Use for Viscosity = 1 Centistoke and Turbulent flow. No correction for laminar flow. Absolute Roughness, in.
ID, in.
Velocity, ft/sec
0.0010
0.0018
0.0050
0.0100
0.0300
2
3
0.95
0.99
1.15
1.34
1.85
5
0.98
1.05
1.24
1.47
2.06
10
1.01
1.10
1.35
1.62
2.30
3
0.99
1.04
1.17
1.33
1.76
2.62
5
1.03
1.09
1.27
1.47
1.96
2.94
10
1.02
1.10
1.31
1.54
2.08
3.14
3
1.06
1.10
1.22
1.38
1.77
2.52
3.78
5
1.11
1.16
1.33
1.51
1.97
2.82
4.25
10
1.02
1.09
1.29
1.49
1.96
2.83
4.26
5
10
March 1997
400-8
0.1000
0.3000
Chevron Corporation
Fluid Flow Manual
400 Friction Pressure Drop
Correction Factors for Internal Roughness (2 of 2)
Fig. 400-3
Use for Viscosity = 1 Centistoke and Turbulent flow. No correction for laminar flow (cont.). Absolute Roughness, in. ID, in.
Velocity, ft/sec
0.0010
0.0018
0.0050
0.0100
0.0300
0.1000
0.3000
20
3
1.08
1.12
1.23
1.37
1.72
2.37
3.39
5
1.11
1.16
1.31
1.48
1.88
2.60
3.73
10
1.03
1.09
1.27
1.45
1.86
2.59
3.72
3
1.13
1.16
1.27
1.39
1.70
2.25
3.08
5
1.11
1.16
1.29
1.43
1.77
2.36
3.23
10
1.03
1.09
1.25
1.41
1.76
2.36
3.23
0.3000
50
Use for Viscosity = 10 centistoke and turbulent flow. Absolute Roughness, in. ID, in.
Velocity, ft/sec
0.0010
0.0018
0.0050
0.0100
0.0300
0.1000
2
3
0.97
0.98
1.02
1.08
1.30
1.91
5
0.93
0.94
1.00
1.08
1.34
2.04
10
0.92
0.94
1.03
1.14
1.50
2.35
3
0.95
0.96
0.99
1.03
1.20
1.63
2.52
5
0.94
0.95
1.00
1.06
1.28
1.79
2.81
10
0.95
0.97
1.04
1.13
1.42
2.07
3.27
3
0.98
0.99
1.01
1.06
1.20
1.57
2.27
5
0.98
0.99
1.03
1.09
1.28
1.72
2.53
10
1.00
1.01
1.08
1.17
1.43
1.98
2.95
3
0.97
0.98
1.01
1.04
1.16
1.47
2.04
5
0.98
0.99
1.03
1.08
1.24
1.62
2.27
10
1.01
1.03
1.08
1.16
1.39
1.86
2.64
3
0.99
.99
1.01
1.04
1.15
1.40
1.85
5
1.01
1.01
1.04
1.09
1.22
1.54
2.06
10
1.04
1.06
1.11
1.17
1.37
1.77
2.40
5
10
20
50
Chevron Corporation
400-9
March 1997
400 Friction Pressure Drop
Fig. 400-4
Fluid Flow Manual
1-Inch Pipe—Schedule 40 (1 of 2) Correction Factor Table for 1 in. Pipe of Various Thicknesses
Schedule
Inside Diameter, in.
5S
1.185
0.56
1.39
0.61
1.63
10S
1.097
0.81
1.13
0.84
1.20
Fp
Fq
Fp
Fq
Transition & Turbulent Flow
Laminar Flow
40
1.049
1.00
1.00
1.00
1.00
80
0.957
1.55
0.78
1.44
0.69
160
0.815
3.33
0.51
2.74
0.36
Fp = Pressure loss correction factor Fq = Flow rate correction factor NOTES: 1. Multiply pressure loss from flow chart by Fp for pressure loss with pipe walls other than Schedule 40. 2. Multiply flow rate from flow chart by Fq to obtain flow rate with pipe walls other than Schedule 40. 3. For SG≠1.0, multiply pressure loss at SG 1.0 by actual SG to obtain pressure loss. For known pressure loss, divide by SG, then enter chart at SG 1.0 to determine flow rate. 4. In laminar range, pressure loss is directly proportional to viscosity. To determine pressure losses for viscosities not shown, the ratio of a known viscosity to pressure loss at desired flow rate is applied to the actual viscosity.
EXAMPLE 1: Given:
Flow rate = 5 BPH; viscosity = 20 cs; specific gravity = 0.9; line size = 1 in. schedule 10S (ID = 1.097 in.)
Determine:
Pressure loss (psi/1000 ft)
Solution:
Enter flow chart at 5 BPH. Move across to viscosity of 20 cs. Move vertically to SG 0.9. Move diagonally to pressure loss of 14.3 psi/1000 ft. for 1.049-in. ID pipe. From correction table, for 1.097-in. ID pipe and laminar flow, Fp = 0.84 Pressure loss = (14.3) (0.84) = 12 psi/1000 feet
EXAMPLE 2: Given:
Pressure loss = 16.0 psi/1000 ft; viscosity = 2 cs; specific gravity = 0.9; line size = 1 in. schedule 80 (ID = 0.957 in.)
Determine:
Flow rate (BPH)
Solution:
Enter flow chart at 16 psi/1000 feet. Move diagonally to SG 0.9. Move vertically to viscosity of 2.0 cs in turbulent range. Move horizontally to flow rate of 10 BPH for 1.049-in. ID pipe. From correction table, for 0.957-in. ID pipe and turbulent flow, Fq = 0.78. Flow rate = (10) (0.78) = 7.8 BPH
March 1997
400-10
Chevron Corporation
Fluid Flow Manual
Fig. 400-4
400 Friction Pressure Drop
1-Inch Pipe—Schedule 40 (2 of 2)
Chevron Corporation
400-11
March 1997
400 Friction Pressure Drop
Fig. 400-5
Fluid Flow Manual
1-1/2-Inch Pipe—Schedule 40 (1 of 2) Correction Factor Table for 1-1/2 in. Pipe of Various Thicknesses
Schedule
Inside Diameter, in.
Transition & Turbulent Flow
Laminar Flow
Fp
Fq
Fp
Fq
5S
1.770
0.64
1.29
0.68
1.46
10S
1.682
0.81
1.13
0.84
1.19
40
1.610
1.00
1.00
1.00
1.00
80
1.500
1.40
0.83
1.33
0.75
160
1.337
2.43
0.61
2.10
0.48
Fp = Pressure loss correction factor Fq = Flow rate correction factor NOTES: 1. Multiply pressure loss from flow chart by Fp for pressure loss with pipe walls other than Schedule 40. 2. Multiply flow rate from flow chart by Fq to obtain flow rate with pipe walls other than Schedule 40. 3. For SG≠1.0, multiply pressure loss at SG 1.0 by actual SG to obtain pressure loss. For known pressure loss, divide by SG, then enter chart at SG 1.0 to determine flow rate. 4. In laminar range, pressure loss is directly proportional to viscosity. To determine pressure losses for viscosities not shown, the ratio of a known viscosity to pressure loss at desired flow rate is applied to the actual viscosity. EXAMPLE 1: Given:
Flow rate 12 BPH; viscosity = 20 cs; specific gravity = 0.9; line size = 1-1/2 in. schedule 10S (ID = 1.682 in.)
Determine:
Pressure loss (psi/1000 ft)
Solution:
Enter flow chart at 12 BPH. Move across to viscosity of 20 cs. Move vertically to SG 0.9. Move diagonally to pressure loss of 6.1 psi/1000 ft. for 1.610-in. ID pipe. From correction table, for 1.682-in. ID pipe and laminar flow, Fp = 0.84 Pressure loss = (6.1) (0.84) = 5.1 psi/1000 feet
EXAMPLE 2: Given:
Pressure loss = 15.7 psi/1000 ft; viscosity = 5 cs; specific gravity = 0.9; line size = 1-1/2 in. schedule 80 (ID = 1.500 in.)
Determine:
Flow rate (BPH)
Solution:
Enter flow chart at 15.7 psi/1000 feet. Move diagonally to SG 0.9. Move vertically to viscosity of 5.0 cs in turbulent range. Move horizontally to flow rate of 28 BPH for 1.610-in. ID pipe. From correction table, for 1.500-in. ID pipe and turbulent flow, Fq = 0.83. Flow rate = (28) (0.83) = 23.2 BPH
March 1997
400-12
Chevron Corporation
Fluid Flow Manual
Fig. 400-5
400 Friction Pressure Drop
1-1/2-Inch Pipe—Schedule 40 (2 of 2)
Chevron Corporation
400-13
March 1997
400 Friction Pressure Drop
Fig. 400-6
Fluid Flow Manual
2-Inch Pipe—Schedule 40 (1 of 2) Correction Factor Table for 2 in. Pipe of Various Thicknesses
Schedule
Inside Diameter, in.
Transition & Turbulent Flow
Laminar Flow
Fp
Fq
Fp
Fq
5S
2.245
0.67
1.25
0.72
1.39
10S
2.157
0.82
1.12
0.84
1.19
40
2.067
1.00
1.00
1.00
1.00
80
1.939
1.36
0.84
1.29
0.77
160
1.689
2.62
0.58
2.24
0.45
Fp = Pressure loss correction factor Fq = Flow rate correction factor NOTES: 1. Multiply pressure loss from flow chart by Fp for pressure loss with pipe walls other than Schedule 40. 2. Multiply flow rate from flow chart by Fq to obtain flow rate with pipe walls other than Schedule 40. 3. For SG≠1.0, multiply pressure loss at SG 1.0 by actual SG to obtain pressure loss. For known pressure loss, divide by SG, then enter chart at SG 1.0 to determine flow rate. 4. In laminar range, pressure loss is directly proportional to viscosity. To determine pressure losses for viscosities not shown, the ratio of a known viscosity to pressure loss at desired flow rate is applied to the actual viscosity. EXAMPLE 1: Given:
Flow rate = 24 BPH; viscosity = 60 cs; specific gravity = 0.9; line size = 2 in. schedule 10S (ID = 2.157 in.)
Determine:
Pressure loss (psi/1000 ft)
Solution:
Enter flow chart at 24 BPH. Move across to viscosity of 60 cs. Move vertically to SG 0.9. Move diagonally to pressure loss of 13.8 psi/1000 ft. for 2.067-in. ID pipe. From correction table, for 2.157-in. ID pipe and laminar flow, Fp = 0.84 Pressure loss = (13.8) (0.84) = 11.6 psi/1000 feet
EXAMPLE 2: Given:
Pressure loss = 12.4 psi/1000 ft; viscosity = 5 cs; specific gravity = 0.9; line size = 2 in. Schedule 80 (ID = 1.939 in.)
Determine:
Flow rate (BPH)
Solution:
Enter flow chart at 12.4 psi/1000 feet. Move diagonally to SG 0.9. Move vertically to viscosity of 5.0 cs in turbulent range. Move horizontally to flow rate of 48 BPH for 2.067-in. ID pipe. From correction table, for 1.939-in. ID pipe and turbulent flow, Fq = 0.84. Flow rate = (48) (0.84) = 40.3 BPH
March 1997
400-14
Chevron Corporation
Fluid Flow Manual
Fig. 400-6
400 Friction Pressure Drop
2-Inch Pipe—Schedule 40 (2 of 2)
Chevron Corporation
400-15
March 1997
400 Friction Pressure Drop
Fig. 400-7
Fluid Flow Manual
2-1/2-Inch Pipe—Schedule 40 (1 of 2) Correction Factor Table for 2-1/2 in. Pipe of Various Thicknesses
Schedule
Inside Diameter, in.
Transition & Turbulent Flow
Laminar Flow
Fp
Fq
Fp
Fq
5S
2.709
0.64
1.28
0.69
1.45
10S
2.635
0.73
1.19
0.77
1.30
40
2.469
1.00
1.00
1.00
1.00
80
2.323
1.34
0.85
1.29
0.78
160
2.125
2.05
0.67
1.82
0.55
Fp = Pressure loss correction factor Fq = Flow rate correction factor NOTES: 1. Multiply pressure loss from flow chart by Fp for pressure loss with pipe walls other than Schedule 40. 2. Multiply flow rate from flow chart by Fq to obtain flow rate with pipe walls other than Schedule 40. 3. For SG≠1.0, multiply pressure loss at SG 1.0 by actual SG to obtain pressure loss. For known pressure loss, divide by SG, then enter chart at SG 1.0 to determine flow rate. 4. In laminar range, pressure loss is directly proportional to viscosity. To determine pressure losses for viscosities not shown, the ratio of a known viscosity to pressure loss at desired flow rate is applied to the actual viscosity. EXAMPLE 1: Given:
Flow rate = 40 BPH; viscosity = 60 cs; specific gravity = 0.9; line size = 2-1/2 in. schedule 10S (ID = 2.635 in.)
Determine:
Pressure loss (psi/1000 ft)
Solution:
Enter flow chart at 40 BPH. Move across to viscosity of 60 cs. Move vertically to SG 0.9. Move diagonally to pressure loss of 11.2 psi/1000 ft. for 2.469-in. ID pipe. From correction table, for 2.635-in. ID pipe and laminar flow, Fp = 0.77 Pressure loss = (11.2) (0.77) = 8.6 psi/1000 feet
EXAMPLE 2: Given:
Pressure loss = 12.8 psi/1000 ft; viscosity = 10 cs; specific gravity = 0.9; line size = 2-1/2 in. schedule 80 (ID = 2.323 in.)
Determine:
Flow rate (BPH)
Solution:
Enter flow chart at 12.8 psi/1000 feet. Move diagonally to SG 0.9. Move vertically to viscosity of 10 cs in turbulent range. Move horizontally to flow rate of 74 BPH for 2.469-in. ID pipe. From correction table, for 2.323-in. ID pipe and turbulent flow, Fq = 0.85. Flow rate = (74) (0.85) = 63 BPH
March 1997
400-16
Chevron Corporation
Fluid Flow Manual
Fig. 400-7
400 Friction Pressure Drop
2-1/2-Inch Pipe—Schedule 40 (2 of 2)
Chevron Corporation
400-17
March 1997
400 Friction Pressure Drop
Fig. 400-8
Fluid Flow Manual
3-Inch Pipe—Schedule 40 (1 of 2) Correction Factor Table for 3 in. Pipe of Various Thicknesses
Schedule
Inside Diameter, in.
Transition & Turbulent Flow
Laminar Flow
Fp
Fq
Fp
Fq
5S
3.334
0.67
1.25
0.72
1.39
10S
3.260
0.75
1.18
0.78
1.27
40
3.068
1.00
1.00
1.00
1.00
80
2.900
1.31
0.86
1.25
0.80
160
2.624
2.11
0.66
1.87
0.54
Fp = Pressure loss correction factor Fq = Flow rate correction factor NOTES: 1. Multiply pressure loss from flow chart by Fp for pressure loss with pipe walls other than Schedule 40. 2. Multiply flow rate from flow chart by Fq to obtain flow rate with pipe walls other than Schedule 40. 3. For SG≠1.0, multiply pressure loss at SG 1.0 by actual SG to obtain pressure loss. For known pressure loss, divide by SG, then enter chart at SG 1.0 to determine flow rate. 4. In laminar range, pressure loss is directly proportional to viscosity. To determine pressure losses for viscosities not shown, the ratio of a known viscosity to pressure loss at desired flow rate is applied to the actual viscosity. EXAMPLE 1: Given:
Flow rate = 65 BPH; viscosity = 70 cs; specific gravity = 0.9; line size = 3 in. schedule 10S (ID = 3.260 in.)
Determine:
Pressure loss (psi/1000 ft)
Solution:
Enter flow chart at 65 BPH. Move across to viscosity of 70 cs. Move vertically to SG 0.9. Move diagonally to pressure loss of 8.8 psi/1000 ft. for 3.068-in. ID pipe. From correction table, for 3.260-in. ID pipe and laminar flow, Fp = 0.78 Pressure loss = (8.8) (0.78) = 6.9 psi/1000 feet
EXAMPLE 2: Given:
Pressure loss = 10.7 psi/1000 ft; viscosity = 10 cs; specific gravity = 0.9; line size = 3 in. schedule 80 (ID = 2.900 in.)
Determine:
Flow rate (BPH)
Solution:
Enter flow chart at 10.7 psi/1000 feet. Move diagonally to SG 0.9. Move vertically to viscosity of 10 cs in turbulent range. Move horizontally to flow rate of 120 BPH for 3.068-in. ID pipe. From correction table, for 2.900-in. ID pipe and turbulent flow, Fq = 0.86. Flow rate = (120) (0.86) = 103 BPH
March 1997
400-18
Chevron Corporation
Fluid Flow Manual
Fig. 400-8
400 Friction Pressure Drop
3-Inch Pipe—Schedule 40 (2 of 2)
Chevron Corporation
400-19
March 1997
400 Friction Pressure Drop
Fig. 400-9
Fluid Flow Manual
4-Inch Pipe—Schedule 40 (1 of 2) Correction Factor Table for 4 in. Pipe of Various Thicknesses
Schedule
Inside Diameter, in.
Transition & Turbulent Flow
Laminar Flow
Fp
Fq
Fp
Fq
5S
4.334
0.70
1.22
0.74
1.34
10S
4.260
0.76
1.16
0.80
1.25
40
4.026
1.00
1.00
1.00
1.00
80
3.826
1.28
0.87
1.23
0.82
120
3.624
1.65
0.75
1.52
0.66
160
3.438
2.12
0.65
1.88
0.53
Fp = Pressure loss correction factor Fq = Flow rate correction factor NOTES: 1. Multiply pressure loss from flow chart by Fp for pressure loss with pipe walls other than Schedule 40. 2. Multiply flow rate from flow chart by Fq to obtain flow rate with pipe walls other than Schedule 40. 3. For SG≠1.0, multiply pressure loss at SG 1.0 by actual SG to obtain pressure loss. For known pressure loss, divide by SG, then enter chart at SG 1.0 to determine flow rate. 4. In laminar range, pressure loss is directly proportional to viscosity. To determine pressure losses for viscosities not shown, the ratio of a known viscosity to pressure loss at desired flow rate is applied to the actual viscosity. EXAMPLE 1: Given:
Flow rate = 96 BPH; viscosity = 80 cs; specific gravity = 0.9; line size = 4 in. schedule 10S (ID = 4.260 in.)
Determine:
Pressure loss (psi/1000 ft)
Solution:
Enter flow chart at 96 BPH. Move across to viscosity of 80 cs. Move vertically to SG 0.9. Move diagonally to pressure loss of 5.05 psi/1000 ft. for 4.026-in. ID pipe. From correction table, for 4.260-in. ID pipe and laminar flow, Fp = 0.80 Pressure loss = (5.05) (0.80) = 4.04 psi/1000 feet
EXAMPLE 2: Given:
Pressure loss = 7.9 psi/1000 ft; viscosity = 10 cs; specific gravity = 0.9; line size = 4 in. schedule 80 (ID = 3.826 in.)
Determine:
Flow rate (BPH)
Solution:
Enter flow chart at 7.9 psi/1000 feet. Move diagonally to SG 0.9. Move vertically to viscosity of 10 cs in turbulent range. Move horizontally to flow rate of 210 BPH for 4.026-in. ID pipe. From correction table, for 3.826-in. ID pipe and turbulent flow, Fq = 0.87.
Flow rate = (210) (0.87) = 183 BPH
March 1997
400-20
Chevron Corporation
Fluid Flow Manual
Fig. 400-9
400 Friction Pressure Drop
4-Inch Pipe—Schedule 40 (2 of 2)
Chevron Corporation
400-21
March 1997
400 Friction Pressure Drop
Fluid Flow Manual
Fig. 400-10 6-Inch Pipe—1/4-Inch Wall (1 of 2) Correction Factor Table for 6 in. Pipe of Various Thicknesses Schedule
Inside Diameter, in.
Transition & Turbulent Flow
Laminar Flow
Fp
Fq
Fp
Fq
5S
6.407
.81
1.13
.84
1.20
10S
6.357
.84
1.11
.86
1.16
1/4 in. wall
6.125
1.00
1.00
1.00
1.00
40
6.065
1.05
.97
1.04
.96
80
5.761
1.34
.85
1.28
.78
120
5.501
1.67
.75
1.54
.65
160
5.189
2.21
.64
1.94
.52
Fp = Pressure loss correction factor Fq = Flow rate correction factor NOTES: 1. Multiply pressure loss from flow chart by Fp for pressure loss with pipe walls other than 1/4-inch. 2. Multiply flow rate from flow chart by Fq to obtain flow rate with pipe walls other than 1/4-inch. 3. For SG≠1.0, multiply pressure loss at SG 1.0 by actual SG to obtain pressure loss. For known pressure loss, divide by SG, then enter chart at SG 1.0 to determine flow rate. 4. In laminar range, pressure loss is directly proportional to viscosity. To determine pressure losses for viscosities not shown, the ratio of a known viscosity to pressure loss at desired flow rate is applied to the actual viscosity. EXAMPLE 1: Given:
Flow rate = 400 BPH; viscosity = 150 cs; specific gravity = 0.9; line size = 6 in. schedule 40 (ID = 6.065 in.)
Determine:
Pressure loss (psi/1000 ft)
Solution:
Enter flow chart at 400 BPH. Move across to viscosity of 150 cs. Move vertically to SG 0.9. Move diagonally to pressure loss of 7.3 psi/1000 ft. for 6.125-in. ID pipe. From correction table, for 6.065-in. ID pipe and laminar flow, Fp = 1.04 Pressure loss = (7.3) (1.04) = 7.6 psi/1000 feet
EXAMPLE 2: Given:
Pressure loss = 5.9 psi/1000 ft; viscosity = 20 cs; specific gravity = 0.9; line size = 6 in. schedule 80 (ID = 5.761 in.)
Determine:
Flow rate (BPH)
Solution:
Enter flow chart at 5.9 psi/1000 feet. Move diagonally to SG 0.9. Move vertically to viscosity of 20 cs in turbulent range. Move horizontally to flow rate of 520 BPH for 6.125-in. ID pipe. From correction table, for 5.761-in. ID pipe and turbulent flow, Fq = 0.85.
Flow rate = (520) (0.85) = 441 BPH
March 1997
400-22
Chevron Corporation
Fluid Flow Manual
400 Friction Pressure Drop
Fig. 400-10 6-Inch Pipe—1/4-Inch Wall (2 of 2)
Chevron Corporation
400-23
March 1997
400 Friction Pressure Drop
Fluid Flow Manual
Fig. 400-11 8-Inch Pipe—1/4-Inch Wall (1 of 2) Correction Factor Table for 8 in. Pipe of Various Thicknesses Schedule
Inside Diameter, in.
Transition & Turbulent Flow
Laminar Flow
Fp
Fq
Fp
Fq
10S
8.329
0.89
1.07
0.91
1.10
20
8.125
1.00
1.00
1.00
1.00
40
7.981
1.09
0.95
1.07
0.93
60
7.813
1.21
0.90
1.17
0.86
80
7.625
1.35
0.84
1.29
0.78
120
7.189
1.79
0.72
1.63
0.61
160
6.813
2.32
0.62
2.02
0.49
Fp = Pressure loss correction factor Fq = Flow rate correction factor NOTES: 1. Multiply pressure loss from flow chart by Fp for pressure loss with pipe walls other than Schedule 20. 2. Multiply flow rate from flow chart by Fq to obtain flow rate with pipe walls other than Schedule 20. 3. For SG≠1.0, multiply pressure loss at SG 1.0 by actual SG to obtain pressure loss. For known pressure loss, divide by SG, then enter chart at SG 1.0 to determine flow rate. 4. In laminar range, pressure loss is directly proportional to viscosity. To determine pressure losses for viscosities not shown, the ratio of a known viscosity to pressure loss at desired flow rate is applied to the actual viscosity. EXAMPLE 1: Given:
Flow rate = 840 BPH; viscosity = 250 cs; specific gravity = 0.9; line size = 8 in. schedule 40 (ID = 7.981 in.)
Determine:
Pressure loss (psi/1000 ft)
Solution:
Enter flow chart at 840 BPH. Move across to viscosity of 250 cs. Move vertically to SG 0.9. Move diagonally to pressure loss of 8.3 psi/1000 ft. for 8.125-in. ID pipe. From correction table, for 7.981-in. ID pipe and laminar flow, Fp = 1.07 Pressure loss = (8.3) (1.07) = 8.9 psi/1000 feet
EXAMPLE 2: Given:
Pressure loss = 4.15 psi/1000 ft; viscosity = 20 cs; specific gravity = 0.9; line size = 8 in. schedule 80 (ID = 7.625 in.)
Determine:
Flow rate (BPH)
Solution:
Enter flow chart at 4.15 psi/1000 feet. Move diagonally to SG 0.9. Move vertically to viscosity of 20 cs in turbulent range. Move horizontally to flow rate of 910 BPH for 8.125-in. ID pipe. From correction table, for 7.625-in. ID pipe and turbulent flow, Fq = 0.84.
Flow rate = (910) (0.84) = 764 BPH
March 1997
400-24
Chevron Corporation
Fluid Flow Manual
400 Friction Pressure Drop
Fig. 400-11 8-Inch Pipe—1/4-Inch Wall (2 of 2)
Chevron Corporation
400-25
March 1997
400 Friction Pressure Drop
Fluid Flow Manual
Fig. 400-12 10-Inch Pipe—1/4-Inch Wall (1 of 2) Correction Factor Table for 10 in. Pipe of Various Thicknesses Schedule
Inside Diameter, in.
Transition & Turbulent Flow
Laminar Flow
Fp
Fq
Fp
Fq
10S
10.420
0.92
1.05
0.94
1.07
20S
10.250
1.00
1.00
1.00
1.00
40
10.020
1.11
0.94
1.10
0.91
60
9.750
1.27
0.87
1.22
0.82
80
9.564
1.39
0.83
1.32
0.76
120
9.064
1.80
0.72
1.64
0.61
160
8.500
2.44
0.60
2.11
0.47
Fp = Pressure loss correction factor Fq = Flow rate correction factor NOTES: 1. Multiply pressure loss from flow chart by Fp for pressure loss with pipe walls other than Schedule 20S. 2. Multiply flow rate from flow chart by Fq to obtain flow rate with pipe walls other than Schedule 20S. 3. For SG≠1.0, multiply pressure loss at SG 1.0 by actual SG to obtain pressure loss. For known pressure loss, divide by SG, then enter chart at SG 1.0 to determine flow rate. 4. In laminar range, pressure loss is directly proportional to viscosity. To determine pressure losses for viscosities not shown, the ratio of a known viscosity to pressure loss at desired flow rate is applied to the actual viscosity. EXAMPLE 1: Given:
Flow rate = 1100 BPH; viscosity = 300 cs; specific gravity = 0.9; line size = 10 in. schedule 40 (ID = 10.020 in.)
Determine:
Pressure loss (psi/1000 ft)
Solution:
Enter flow chart at 1100 BPH. Move across to viscosity of 300 cs. Move vertically to SG 0.9. Move diagonally to pressure loss of 5.15 psi/1000 ft. for 10.250-in. ID pipe. From correction table, for 10.020-in. ID pipe and laminar flow, Fp = 1.10 Pressure loss = (5.15) (1.10) = 5.7 psi/1000 feet
EXAMPLE 2: Given:
Pressure loss = 3.70 psi/1000 ft; viscosity = 20 cs; specific gravity = 0.9; line size = 10 in. schedule 80 (ID = 9.564 in.)
Determine:
Flow rate (BPH)
Solution:
Enter flow chart at 3.70 psi/1000 feet. Move diagonally to SG 0.9. Move vertically to viscosity of 20 cs in turbulent range. Move horizontally to flow rate of 1600 BPH for 10.250-in. ID pipe. From correction table, for 9.564-in. ID pipe and turbulent flow, Fq = 0.83.
Flow rate = (1600) (0.83) = 1330 BPH
March 1997
400-26
Chevron Corporation
Fluid Flow Manual
400 Friction Pressure Drop
Fig. 400-12 10-Inch Pipe—1/4-Inch Wall (2 of 2)
Chevron Corporation
400-27
March 1997
400 Friction Pressure Drop
Fluid Flow Manual
Fig. 400-13 12-Inch Pipe—1/4-Inch Wall (1 of 2) Correction Factor Table for 12 in. Pipe of Various Thicknesses Schedule
Inside Diameter, in.
Transition & Turbulent Flow
Laminar Flow
Fp
Fq
Fp
Fq
10S
12.390
0.95
1.03
0.96
1.05
20S
12.250
1.00
1.00
1.00
1.00
40
11.938
1.13
0.93
1.11
0.90
80
11.376
1.42
0.82
1.34
0.74
120
10.750
1.86
0.70
1.69
0.59
160
10.126
2.48
0.60
2.14
0.47
Fp = Pressure loss correction factor Fq = Flow rate correction factor NOTES: 1. Multiply pressure loss from flow chart by Fp for pressure loss with pipe walls other than Schedule 20S. 2. Multiply flow rate from flow chart by Fq to obtain flow rate with pipe walls other than Schedule 20S. 3. For SG≠1.0, multiply pressure loss at SG 1.0 by actual SG to obtain pressure loss. For known pressure loss, divide by SG, then enter chart at SG 1.0 to determine flow rate. 4. In laminar range, pressure loss is directly proportional to viscosity. To determine pressure losses for viscosities not shown, the ratio of a known viscosity to pressure loss at desired flow rate is applied to the actual viscosity. EXAMPLE 1: Given:
Flow rate = 1500 BPH; viscosity = 400 cs; specific gravity = 0.9; line size = 12 in. schedule 40 (ID = 11.938 in.)
Determine:
Pressure loss (psi/1000 ft)
Solution:
Enter flow chart at 1500 BPH. Move across to viscosity of 400 cs. Move vertically to SG 0.9. Move diagonally to pressure loss of 4.55 psi/1000 ft. for 12.250-in. ID pipe. From correction table, for 11.938-in. ID pipe and laminar flow, Fp = 1.11 Pressure loss = (4.55) (1.11) = 5.05 psi/1000 feet
EXAMPLE 2: Given:
Pressure loss = 3.49 psi/1000 ft; viscosity = 20 cs; specific gravity = 0.9; line size = 12 in. schedule 80 (ID = 11.376 in.)
Determine:
Flow rate (BPH)
Solution:
Enter flow chart at 3.49 psi/1000 feet. Move diagonally to SG 0.9. Move vertically to viscosity of 20 cs in turbulent range. Move horizontally to flow rate of 2500 BPH for 12.250-in. ID pipe. From correction table, for 11.376-in. ID pipe and turbulent flow, Fq = 0.82.
Flow rate = (2500) (0.82) = 2050 BPH
March 1997
400-28
Chevron Corporation
Fluid Flow Manual
400 Friction Pressure Drop
Fig. 400-13 12-Inch Pipe—1/4-Inch Wall (2 of 2)
Chevron Corporation
400-29
March 1997
400 Friction Pressure Drop
Fluid Flow Manual
420 Two-phase Flow This section presents a method for calculating gas-liquid two-phase flow pressure drop. Lines carrying flashing mixtures, solid-liquid mixtures, or gas-solid mixtures must be analyzed more thoroughly than this method allows. The special cases of (1) mixture flow in column and furnace transfer lines, and (2) flashing water are covered in the Fired Heater and Waste Heat Recovery Manual and Utilities Manual, respectively.
Limitations The method described here applies to isothermal gas-liquid flow, not to situations in which a phase change occurs; that is, constant gas-liquid ratios (by weight) are assumed. This method has not been verified for very long vertical piping (such as in oil wells) nor has the accuracy been established for horizontal piping more than 5-1/2 inches in diameter. In these cases the method should be used with caution, for vertical piping, PIPEFLOW-2 will yield better results. In addition, the limited experimental data available indicate that when the mixture velocity is less than 3 ft/sec the accuracy of the friction pressure drop calculations is very poor. This method is not fully applicable to flow of water-oil-gas (WOG) mixtures (socalled three-phase flow). This case requires the more powerful calculation methods of PIPEFLOW-2.
General References Reference 1 (see Section 450) contains a more detailed discussion of two-phase flow. Reference 2 contains an extensive bibliography of two-phase literature.
421 Pressure Drop Calculations As in single-phase flow, pressure drop in two-phase flow consists of several components, as shown in Equation 400-8. ∆Ptotal = ∆Pfriction + ∆Pfittings + ∆Pacceleration + ∆Pelevation (Eq. 400-8)
The components of this equation, ∆Pfriction, ∆Pfittings, ∆Pacceleration, and ∆Pelevation are discussed in the following sections. The total pressure drop is calculated by evaluating each component individually and summing.
422 Friction Pressure Drop Correlations More than 25 correlations for two-phase friction pressure drop have appeared in print. Because these correlations contain empirical factors obtained from limited experimental data, they cannot be applied with confidence beyond their particular experimental bases.
March 1997
400-30
Chevron Corporation
Fluid Flow Manual
400 Friction Pressure Drop
The five most widely used correlations are compared in Reference 3 using experimental data from a number of investigators. The data were carefully screened to eliminate unreliable measurements. The screened data, about 2600 points in all, cover pipe diameters from 1 to 5-1/2 inches and liquid viscosities from 1 to 20 centipoise. Of the five the most reliable correlation over this range of experimental conditions was the Lockhart-Martinelli correlation (see Reference 4). Another somewhat better correlation with the screened experimental data was achieved using similarity analysis (see Reference 5). This method is based on calculating a two-phase density, ρtp, and viscosity, µtp, evaluated at the pipe entrance pressure and temperature and assumed constant for the friction and fitting pressure drop calculation, as follows: ρtp = ρl (λ) + ρg (1.0 - λ) (Eq. 400-9)
µtp = µl (λ) + µg (1.0 - λ) (Eq. 400-10)
where: ρ = fluid density, lbm/ft3 µ = absolute viscosity, cp tp
= two-phase
l
= liquid phase
g
= gas phase
λ = liquid volume fraction at pipe entrance Equations 400-9 and 400-10 assume that both phases flow at the same velocity. The two-phase Reynolds number Retp is expressed as follows: 0.527W t V m Dρ tp Re tp = --------------------- = --------------------Dµ tp µ tp ----------- 1490 (Eq. 400-11)
where: Vm = velocity of mixture, ft/sec D = pipe inside diameter, ft Wt = mass flow rate of total fluid, lbm/hr For new steel pipe, two-phase Reynolds numbers should be used with the Moody diagram (Figure 400-1) to determine the friction factor f. If different pipe conditions exist or a more accurate determination is desired, the Colebrook formula (Equation 400-12) may be used.
Chevron Corporation
400-31
March 1997
400 Friction Pressure Drop
Fluid Flow Manual
ε 2.51 1 ------ = – 2 log 10 ------------ + ----------------- 3.7D Re tp f f (Eq. 400-12)
where: ε = absolute pipe wall roughness, ft The need to proceed by trial and error is an inconvenience when using this equation for hand calculation, but a computer or Moody chart eliminates this problem. The equation reduces to the smooth tube equation when the wall roughness (left term in bracket) approaches zero or to Nikuradse’s Formula at high Reynolds numbers (when the right term in bracket approaches zero). The same absolute wall roughness, ε, should be used for both single-phase and two-phase flow calculations. The pressure drop due to friction may then be calculated as follows: 2
L ρ tp V m ∆P friction = f ---- --------- ⋅ ----------D 144 2g o 2
= 1.35 ⋅ 10
– 11
L Wt f ------5- --------D ρ tp (Eq. 400-13)
where: ∆P = pressure drop, psi f = friction factor L = pipe length, ft go = gravitational constant (32.174 lbm ft/lbf sec2) Wl = flow rate of liquid, lbm/hr Wg = flow rate of gas, lbm/hr W t = Wl + W g This method of calculating friction pressure drop has the following characteristics:
March 1997
•
It reduces to the single-phase flow equations if the flow rate of either phase is zero.
•
Except for the assumptions concerning two-phase density and viscosity (Equations 400-9 and 400-10), no empirical factors from two-phase flow data have been used.
•
It is reasonably accurate for all flow patterns (see Section 427).
400-32
Chevron Corporation
Fluid Flow Manual
400 Friction Pressure Drop
423 Fitting and Bend Losses For two-phase flow, as for single-phase flow, pressure drop due to bends and fittings can be expressed in terms of velocity head loss. However, for two-phase flow, the velocity head is based on the pipe inlet mixture density, rtp, from Equation 400-9, as follows: 2
2
Kρ tp V m – 11 KW t ⋅ -------------∆P fittings = ------------ ⋅ ----------- = 1.35 ⋅ 10 4 144 2g o D ρ
tp
(Eq. 400-14)
where: K = single phase velocity head loss
424 Acceleration Pressure Loss Acceleration losses also contribute to the total pressure drop. In most cases this loss is relatively small, and may be neglected if only a rough estimate is required. However, when the total pressure drop along the line is large, the acceleration losses can be significant and should be calculated. In this case, the gas expands and the mixture occupies a larger volume at a lower pressure. This causes the mixture to be accelerated to a higher velocity in order to maintain the same mass flow. The expression for acceleration pressure drop, as given in Reference 5, is as follows: – 13
1.87 ⋅ 10 W t W g ZRT - ⋅ ∆P tp ∆P acceleration = -------------------------------------------------------4 D P1 P2 (Eq. 400-15)
where: Z = compressibility factor T = temperature, °R R = gas constant P1 = upstream pressure, psi P2 = downstream pressure, psi D = pipe inside diameter, ft
425 Elevation Losses The calculation of two-phase density using Equation 400-9 is an approximation that assumes the velocities of the liquid and gas phases are equal. However, the actual density of the gas-liquid mixture is needed to calculate the elevation pressure drop for upwards flow. One cannot assume that the velocities of the two phases are equal.
Chevron Corporation
400-33
March 1997
400 Friction Pressure Drop
Fluid Flow Manual
The actual flow density depends on how the liquid and gas are distributed in the pipe. The flow density in a short section of pipe of length L is given by Equation 400-16: LA g ρ g + LA 1 ρ 1 ρ′ tp = ----------------------------------------- = R g ρ g + R 1 ρ 1 LA (Eq. 400-16)
where: ρ´ = actual density in pipe section Ag = area gas Al = area liquid Rg = gas volume fraction Rl = liquid holdup Rg is the fractional volume of the pipe filled with gas and Rl is the fractional volume of the pipe filled with liquid. Rl is called liquid holdup (see Equation 400-22). Because of the difference in velocity of the two phases, liquid holdup is greater downstream than at the entrance. Therefore, to calculate the actual flow density, the liquid holdup Rl has to be known along the pipe. The available correlations for liquid holdup were checked against experimental data from Reference 3. The correlation developed by Hughmark (see Reference 7, and below in this section, “Liquid Holdup Correlation”) was the best. The effects of bends and fittings on liquid holdup and, therefore, the flow density cannot be predicted at this time. Therefore, it is assumed that the same holdup correlation can be used even if the pipe contains bends and fittings. In two-phase flow, as in single-phase flow, the elevation head loss is expressed as follows: ρ′ tp ∆P elevation = --------- ⋅ h 144 (Eq. 400-17)
where: h = static elevation, ft The flow density is calculated using Equation 400-16, where the gas density is evaluated at the average pressure. The elevation pressure drop term is included only in vertical upward flow. A conservative evaluation of acceleration pressure loss for vertical downward flow cannot take credit for the elevation pressure component in the downward section. Therefore, sections where the flow is downward should be treated as horizontal piping. No provisions have been made to handle inclined piping.
March 1997
400-34
Chevron Corporation
Fluid Flow Manual
400 Friction Pressure Drop
426 Flow Patterns Horizontal Flow. When gas and liquid fluids flow in a pipe together, the two phases can be distributed in a number of ways. The distribution is described according to visually observed flow patterns, which depend on the gas and liquid mass velocity as well as on the physical properties of the fluids. Figure 400-14 is a flow map devised by Baker (Reference 8), to predict flow patterns and indicate the physical appearance of the flow. A detailed description of the flow patterns is given in the review of two-phase flow in Reference 1. The pressure drop calculation method presented in this section does not depend on flow patterns. However, the comparison of calculated pressure drop with experimental data has been grouped according to flow patterns (see the next section below, “Accuracy of Friction Pressure Drop Calculation,” and Figure 400-16). Figure 400-14 can help in predicting the calculated pressure drop. The boundaries separating the flow regimes in Figure 400-14 are not distinct, but represent regions of transition. A band of ± 20% of the ordinate as shown by the dashed lines was chosen to represent the region of uncertainty. Vertical Flow. Figure 400-15 is a flow pattern map for vertical upwards flow (see Reference 9). The slug flow region of the map was determined by plotting points where slug flow has been observed experimentally. The boundaries between the flow patterns are transition regions, represented by a band ± 20% wide.
427 Accuracy of Friction Pressure Drop Calculation The friction pressure drop calculation was checked against carefully screened experimental data from a number of investigators. Partial results of the comparison are shown in Figure 400-16. A more extensive discussion of the calculations and a statistical analysis of the errors are available in References 3 and 5. The values shown in Figure 400-16 represent the percent deviation between the calculated pressure drop and experimental data, as shown in Equation 400-18. ∆P calc – ∆P exp %dev = ------------------------------------- ⋅ 100 ∆P exp (Eq. 400-18)
Figure 400-17 can be used to estimate the accuracy of a calculated friction pressure drop for any flow regime. For example, the calculated friction pressure drop for horizontal slug flow is within -18.0 to +12.0 percent of the actual value. Equation 400-18 may be restated as follows: ∆P calc ∆P exp = -----------------------% dev 1 + --------------100 (Eq. 400-19)
Chevron Corporation
400-35
March 1997
400 Friction Pressure Drop
Fluid Flow Manual
Fig. 400-14 Flow Pattern Map for Horizontal Two-Phase Flow
March 1997
400-36
Chevron Corporation
Fluid Flow Manual
400 Friction Pressure Drop
Fig. 400-15 Flow Pattern Map for Vertical Two-Phase Flow From Two Phase Slug Flow by Griffith & Wallis. Journal of Heat Transfer, Transactions of ASME Series C83 (Aug., 1961). Courtesy of ASME
Chevron Corporation
400-37
March 1997
400 Friction Pressure Drop
Fluid Flow Manual
Fig. 400-16 Calculated vs. Experimental Frictional Pressure Drop—Horizontal Flow Flow Regime
Range of Deviation (%)
Plug
-22.3 to -2.3
Stratified
-25.3 to +24.7
Wave
-21.0 to +39.0
Slug
-17.9 to +12.1
Annular
-59.2 to +15.8
Dispersed
-24.4 to +30.6
Bubble
not given
Based on the range of deviation for horizontal slug flow, the actual value of a calculated pressure drop of 10 psi would be (approximately) between the following values: 10 ∆P = --------------------------- = 12.2 psi 1 + ( – 0.18 ) (Eq. 400-20)
and 10 ∆P = ------------------- = 8.9 psi 1 + 0.12 (Eq. 400-21)
A comparison between calculated and experimental friction pressure drop for vertical flow is not available.
428 Liquid Holdup Correlation The density of two-phase mixtures at any section in the pipe may be calculated if the liquid holdup–the fractional volume of the pipe occupied by the liquid–is known. Correlations have been developed to predict the holdup as it changes along the pipe. That developed by Hughmark (Reference 7) is the most accurate. This correlation relates the flow parameter Y to the variable X as shown in Figure 400-17. The relationship between the flow parameter Y and the gas volume fraction Rg assumes that Rg is distributed radially across the pipe, with the largest value at the center. The relationship is expressed in terms of the gas volume fraction Rg and liquid holdup Rl, as follows:
March 1997
400-38
Chevron Corporation
Fluid Flow Manual
400 Friction Pressure Drop
Fig. 400-17 Correlation for the Flow Pattern Y From “Holdup in Gas-Liquid Flow” by G.A. Hughmark, Chemical Engineering Progress, Vol. 58, April, 1962, p. 62
Y R g = 1 – R 1 = ---------------------------------ρg 1 ----- ---- – 1 + 1 ρ1 X (Eq. 400-22)
The variable X in Equation 400-22 is defined as follows: 1 --6
1 --8
Re ⋅ Fr X = ---------------------1 λ
--4
(Eq. 400-23)
where: Fr = Froude number = V2/Dg λ = liquid volume fraction at pipe entrance
Chevron Corporation
400-39
March 1997
400 Friction Pressure Drop
Fluid Flow Manual
D = diameter, ft g = gravitational constant (32.174 ft/sec2) The dimensionless numbers used in the variable X are shown in Equations 400-24 and 400-25. D ⋅ Gm ------------------------------------( R1µ1 + Rg µg ) Re = ------------------------------------1490 (Eq. 400-24)
where: Gm = ρtpVm = mass velocity mixture (lbm/ft2-sec) Re ≠ Retp (from Equation 400-11) 2
2
Vm ( ( Q1 + Q g ) ⁄ A ) F r = ----------- = ----------------------------------------gD gD
(Eq. 400-25)
Q1 W1 υ1 λ = ------------------------------------ = -------------------W1 υ1 + Wg υg Q 1 + Qg (Eq. 400-26)
where: υ = specific volume The calculation procedure is to evaluate Re, Fr, and λ using Equations 400-24, 400-25, and 400-26. The variable X is then evaluated using Equation 400-23, and the flow parameter Y is determined from Figure 400-16. Using the flow parameter Y, the liquid holdup is found from Equation 400-22. An iterative calculation is required since the gas density used in Equation 400-22 is evaluated at the average pressure. The gas volume flow rate Qg used in Equations 400-25 and 400-26 is the inlet value evaluated using the inlet density. The actual flow density calculated using Equation 400-16 is then used to determine the elevation pressure drop in upwards vertical flow. The deviation between the calculated (Figure 400-17) and experimental (Reference 3) values of the liquid holdup varies by ± 25%. For vertical flow not as much experimental data are available. For the available data the deviation between experimental and calculated liquid holdup does not exceed ± 10 percent (see Section 450, Reference 7).
March 1997
400-40
Chevron Corporation
Fluid Flow Manual
400 Friction Pressure Drop
430 Compressible Flow Pressure drop in gas transmission lines can be calculated in five ways, as follows: •
Using the PIPEFLOW-2 program, discussed in Section 1100
•
Using the gas flow charts, Figures 400-18 through Figure 400-25. These give reasonable engineering accuracy.
•
Applying the widely used Weymouth and Panhandle fundamental flow equations (see Figure 400-26 on page 400-58)
•
Using the PCFLOW program, discussed in Section 1100
•
Using COMFLOW, a computer program developed for Chevron Pipeline Company by CRTC. COMFLOW solves for pressure drop in branched gas pipeline systems. See Section 1100 for further discussion.
Of these options only COMFLOW and PIPEFLOW-2 consider heat transfer, and only PIPEFLOW-2 considers condensation. Condensation due to heat transfer is common in hot gas transmission and can significantly affect the friction pressure drop. Section 420 discusses two-phase flow pressure drop.
Weymouth and Panhandle Equations The general formula for compressible flow has the following form:
(Eq. 400-27)
where: Q = flow rate, SCFD To = standard absolute temperature, °R Po = standard pressure, psia D = pipe ID, in. P1 = upstream pressure, psia P2 = downstream pressure, psia S = fluid specific gravity (air = 1) T = fluid absolute temperature, °R L = length of pipeline, miles C1 through C7 = constants as shown in Figure 400-26
Chevron Corporation
400-41
March 1997
Flow of Any Fluid (Gas, Vapor, Liquid) Nomenclature: M Mass flow rate, lb/hr P
Average line pressure, psia
P1 & P2
Initial and final pressure, psia
P′
Rate of pressure drop, psi/1000 ft
T
Absolute temperature, °F + 460
µ
Viscosity, cp
V
Specific volume of fluid, cu ft/sec
G
Specific gravity of gas referred to dry air at standard conditions
L
Line length, thousands of feet
2. Fluid, carbon dioxide gas; temperature = 70°F; viscosity = 0.015 cp; inlet pressure = 25 psig; outlet pressure = 20 psig; line length = 600 ft; line size = 2 in. sch 40 = 2.067 in. ID. Average flowing pressure = 22.5 psig.
400 Friction Pressure Drop
March 1997
Fig. 400-18 Flow of Any Fluid—1/2 to 6-Inch Pipe (1 of 2)
400-42
Examples: 1. Fluid, carbon dioxide gas; flow rate = 2500 lb/hr; temperature = 70°F; viscosity = 0.015 cp; inlet pressure 15 psig; pipe size = 3 in. sch 40 = 3.068 in. ID. Assume average line pressure = 12 psig. Determine pressure loss. Miscellaneous Data: Specific volume of a perfect gas, V = 10.72 T / P(MOL. WT) 1 cubic foot per minute of gas at standard conditions = 4.58G pounds per hour 1 inch of water = 0.0361 pounds per square inch
2. Standard conditions = 60°F and 14.73 psia
Fluid Flow Manual
Chevron Corporation
Notes: 1. The chart, strictly speaking, gives rate of pressure drop at a point in the pipe, but for a perfect gas will give the average rate of pressure drop if the specific volume at the average pressure is used.
Fluid Flow Manual
Chevron Corporation
Fig. 400-18 Flow of Any Fluid—1/2 to 6-Inch Pipe (2 of 2)
400-43
400 Friction Pressure Drop
March 1997
Flow of Any Fluid (Gas, Vapor, Liquid) Nomenclature: M Mass flow rate, lb/hr P
Average line pressure, psia
P1 & P2
Initial and final pressure, psia
P′
Rate of pressure drop, psi/1000 ft
T
Absolute temperature, °F + 460
µ
Viscosity, cp
V
Specific volume of fluid, cu ft/sec
G
Specific gravity of gas referred to dry air at standard conditions
L
Line length, thousands of feet
2. Fluid, carbon dioxide gas; temperature = 70°F; viscosity = 0.015 cp; inlet pressure = 25 psig; outlet pressure = 20 psig; line length = 600 ft; line size = 2 in. sch 40 = 2.067 in. ID. Average flowing pressure = 22.5 psig.
400 Friction Pressure Drop
March 1997
Fig. 400-19 Flow of Any Fluid—2 to 48-Inch Pipe (1 of 2)
400-44
Examples: 1. Fluid, carbon dioxide gas; flow rate = 50 lb/hr; temperature = 70°F; viscosity = 0.015 cp; inlet pressure 15 psig; pipe size = 3/4 in. sch 40 = 0.824 in. ID. Assume average line pressure = 12 psig. Determine pressure loss. Miscellaneous Data: Specific volume of a perfect gas, V = 10.72 T / P(MOL. WT) 1 cubic foot per minute of gas at standard conditions = 4.58G pounds per hour 1 inch of water = 0.0361 pounds per square inch
2. Standard conditions = 60°F and 14.73 psia
Fluid Flow Manual
Chevron Corporation
Notes: 1. The chart, strictly speaking, gives rate of pressure drop at a point in the pipe, but for a perfect gas will give the average rate of pressure drop if the specific volume at the average pressure is used.
Fluid Flow Manual
Chevron Corporation
Fig. 400-19 Flow of Any Fluid—2 to 48-Inch Pipe (2 of 2)
400-45
400 Friction Pressure Drop
March 1997
Flow of Natural Gas Nomenclature: Q Flow rate, millions of standard cubic feet per day P
Average line pressure, psia
P1 & P2
Initial and final pressure, psia
P′
Rate of pressure drop, psi/1000 ft
L
Length of line, thousands of feet
T
Temperature absolute degrees, °F + 460
D
Internal diameter of pipe, in.
G
Specific gravity of gas referred to dry air at standard conditions
µ
Viscosity, cp
Z
Supercompressibility factor
400-46
Examples: 1. Flow quantity = 1.3 million cu ft/day; specific gravity = 0.70; viscosity = 0.012 cp; temperature = 200°F; inlet pressure 2050 psia; pipe size = 2 in. sch 40; line length = 3000 ft. Find pressure drop. From GPSA (see Section 450, reference 14), supercompressibility factor = 0.882. Assume average pressure = 2000 psia.
2. Line size = 4 in. sch 40 = 4.026 in. ID; inlet pressure = 100 psia; outlet pressure = 80 psia; specific gravity = 0.70.; viscosity = 0.012 cp; line length = 10,000 ft; temperature = 60°F. Assume a perfect gas. Find flow rate.
400 Friction Pressure Drop
March 1997
Fig. 400-20 Flow of Natural Gas—1/2 to 6-Inch Pipe (1 of 2)
Notes: 1. The chart, strictly speaking, gives rate of pressure drop at a point in the pipe, but will give the average rate of pressure drop if the specific volume at the average pressure is used. 2. Standard conditions = 60°F and 14.73 psia
Fluid Flow Manual
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Fig. 400-20 Flow of Natural Gas—1/2 to 6-Inch Pipe (2 of 2)
400-47
400 Friction Pressure Drop
March 1997
Flow of Natural Gas Nomenclature: Q Flow rate, millions of standard cubic feet per day P
Average line pressure, psia
P1 & P2
Initial and final pressure, psia
P′
Rate of pressure drop, psi/1000 ft
L
Length of line, thousands of feet
T
Temperature absolute degrees, °F + 460
D
Internal diameter of pipe, in.
G
Specific gravity of gas referred to dry air at standard conditions
µ
Viscosity, cp
Z
Supercompressibility factor
400-48
Examples: 1. Flow quantity = 1.3 million cu ft/day; specific gravity = 0.70; viscosity = 0.012 cp; temperature = 200°F; inlet pressure 2050 psia; pipe size = 2 in. sch 40; line length = 3000 ft. Find pressure drop. From GPSA (see Section 450, reference 14), supercompressibility factor = 0.882. Assume average pressure = 2000 psia.
2. Line size = 4 in. sch 40 = 4.026 in. ID; inlet pressure = 100 psia; outlet pressure = 80 psia; specific gravity = 0.70; viscosity = 0.012 cp; line length = 10,000 ft; temperature = 60°F. Assume a perfect gas. Find flow rate.
400 Friction Pressure Drop
March 1997
Fig. 400-21 Flow of Natural Gas—2 to 48-Inch Pipe (1 of 2)
Notes: 1. The chart, strictly speaking, gives rate of pressure drop at a point in the pipe, but will give the average rate of pressure drop if the specific volume at the average pressure is used. 2. Standard conditions = 60°F and 14.73 psia.
Fluid Flow Manual
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Fig. 400-21 Flow of Natural Gas—2 to 48-Inch Pipe (2 of 2)
400-49
400 Friction Pressure Drop
March 1997
Flow of Air Nomenclature: Q Flow rate, standard cubic feet per minute P
Average line pressure, psia
P1 & P2
Initial and final pressure, psia
P′
Rate of pressure drop, psi/1000 ft
L
Length of line, thousands of feet
T
Absolute temperature, °F + 460
D
Internal diameter, in.
Examples: 1. Line size = 1 in. sch 40 = 1.049 in. ID. Flow rate = 78 scfm, inlet pressure = 100 psia, temperature = 60°F. Line length = 400 ft. Assume average pressure = 95 psia. From the chart.
2. Line size = 4 in. sch 40 = 4.026 in. ID. Length of line = 300 ft, inlet pressure = 100 psia, outlet pressure = 90 psia, temperature = 60 °F.
400 Friction Pressure Drop
March 1997
Fig. 400-22 Flow of Air—1/2 to 6-Inch Pipe (1 of 2)
Miscellaneous Data: 1 inch of water = 0.0361 psi 1 lb per hour = 13.2 cu ft of air per hour at standard conditions
400-50
Notes: 1. The chart, strictly speaking, gives rate of pressure drop at a point in the pipe, but will give the average rate of pressure drop if the specific volume at the average pressure is used. 2. Standard conditions = 60°F and 14.73 psia
Fluid Flow Manual
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Fig. 400-22 Flow of Air—1/2 to 6-Inch Pipe (2 of 2)
400-51
400 Friction Pressure Drop
March 1997
Flow of Air Nomenclature: Q Flow rate, standard cubic feet per minute P
Average line pressure, psia
P1 & P2
Initial and final pressure, psia
P′
Rate of pressure drop, psi/1000 ft
L
Length of line, thousands of feet
T
Absolute temperature, °F + 460
D
Internal Diameter, in.
Examples: 1. Line size = 4 in. sch 40 = 4.026 in. ID. Flow rate = 2650 scfm, inlet pressure = 100 psia, temperature = 60°F. Line length = 400 ft. Assume average pressure = 95 psia. From the chart.
2. Line size = 4 in. sch 40 = 4.026 in. ID. Length of line = 300 ft, inlet pressure = 100 psia, outlet pressure = 90 psia, temperature = 60 °F.
400 Friction Pressure Drop
March 1997
Fig. 400-23 Flow of Air—2 to 48-Inch Pipe (1 of 2)
Miscellaneous Data: 1 inch of water = 0.0361 psi 1 lb per hour = 13.2 cu ft of air per hour at standard conditions
400-52
Notes: 1. The chart, strictly speaking, gives rate of pressure drop at a point in the pipe, but will give the average rate of pressure drop if the specific volume at the average pressure is used. 2. Standard conditions = 60°F and 14.73 psia
Fluid Flow Manual
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Fig. 400-23 Flow of Air—2 to 48-Inch Pipe (2 of 2)
400-53
400 Friction Pressure Drop
March 1997
Flow of Steam
Specific Volume (V)
400-54
SAT. TEMP, °F 79.1 91.8 101.2 108.7 115.1 126.1 141.5 212.0 228.0 250.3 267.2 281.0 292.7 302.9 312.0 320.3 327.8 334.8 341.3 347.3 353.0 358.4 381.8 401.0 417.3 444.6 467.0 486.2 503.0 518.2 532.0 544.6 596.1 635.6
SAT. STEAM 653 445 340 275 232 174.0 118.9 26.8 20.1 13.74 10.50 8.51 7.17 6.20 5.47 4.89 4.43 4.04 3.72 3.45 3.22 3.01 2.28 1.841 1.541 1.160 .926 .768 .653 .565 .497 .442 .274 .1875
300°F 922 615 461 369 308 226 150.5 30.5 22.4 14.82 11.04 8.78 7.26 -
400°F 1142 695 521 417 348 256 170.4 34.6 25.4 16.89 12.62 10.06 8.35 7.13 6.22 5.50 4.93 4.47 4.08 3.75 3.46 3.22 2.36 -
500°F 1163 776 582 466 388 286 190.3 38.8 28.4 18.92 14.16 11.30 9.40 8.04 7.02 6.22 5.58 5.06 4.63 4.26 3.95 3.68 2.72 2.15 1.765 1.283 .990 .792 -
600°F 1287 857 844 515 430 315 210 42.8 31.5 20.9 15.68 12.53 10.42 8.92 7.79 6.92 6.22 5.64 5.16 4.76 4.41 4.11 3.06 2.42 2.00 1.474 1.156 .943 .790 .675 .584 .511 .279 -
700°F 1408 939 705 563 470 345 230 46.9 34.5 22.9 17.19 13.74 11.44 9.79 8.56 7.60 6.83 6.20 5.68 5.24 4.86 4.53 3.38 2.68 2.22 1.647 1.301 1.069 .904 .779 .682 .604 .368 .247
800°F 1530 1020 765 611 510 375 250 51.0 37.4 24.9 18.69 14.93 12.44 10.65 9.31 8.27 7.44 6.76 6.19 5.71 5.30 4.94 3.69 2.94 2.44 1.812 1.436 1.186 1.006 .872 .768 .684 .432 .305
Nomenclature: M Mass rate of flow, lbm/hr P
Average Line pressure, psia
P1 & P2
Inlet and outlet pressures, psia
P’
Rate of pressure drop, psi/1000 ft
V
Specific volume, cu ft/lbm
L
Line length, thousands of feet
Notes: This chart, strictly speaking, gives rate of pressure drop at a point in the pipe, but for relatively small changes in pressure through the pipe will give the average rate of pressure drop if the specific volume at the average pressure is used. Example: Pipe size = 1 1/2 in. sch 40; inlet pressure = 151 psia; outlet pressure = 149 psia; pipe length = 487 ft; temperature = 500°F. Find mass flow rate. Average pressure, P = (P1 + P2)/2 = 150 psia. From the table V = 3.68 cu ft per lbm. P= (P1 - P2)/L = (151 -149)/0.487 = 4.1 psi per 1000 ft from the chart, M = 405 lbm per hr.
Fluid Flow Manual
Chevron Corporation
ABS PRESS. 1 in. Hg 1-1/2 2 2-1/2 3 2 psia 3 14.7 20 30 40 50 60 70 80 90 100 110 120 130 140 150 200 250 300 400 500 600 700 800 900 1000 1500 2000
400 Friction Pressure Drop
March 1997
Fig. 400-24 Flow of Steam—1/2 to 6-Inch Pipe (1 of 2) Table of Specific Volumes For Steam
Fluid Flow Manual
Chevron Corporation
Fig. 400-24 Flow of Steam—1/2 to 6-Inch Pipe (2 of 2)
400-55
400 Friction Pressure Drop
March 1997
Flow of Steam
Specific Volume (V)
400-56
SAT. TEMP, °F 79.1 91.8 101.2 108.7 115.1 126.1 141.5 212.0 228.0 250.3 267.2 281.0 292.7 302.9 312.0 320.3 327.8 334.8 341.3 347.3 353.0 358.4 381.8 401.0 417.3 444.6 467.0 486.2 503.0 518.2 532.0 544.6 596.1 635.6
SAT. STEAM 653 445 340 275 232 174.0 118.9 26.8 20.1 13.74 10.50 8.51 7.17 6.20 5.47 4.89 4.43 4.04 3.72 3.45 3.22 3.01 2.28 1.841 1.541 1.160 .926 .768 .653 .565 .497 .442 .274 .1875
300°F 922 615 461 369 308 226 150.5 30.5 22.4 14.82 11.04 8.78 7.26 -
400°F 1142 695 521 417 348 256 170.4 34.6 25.4 16.89 12.62 10.06 8.35 7.13 6.22 5.50 4.93 4.47 4.08 3.75 3.46 3.22 2.36 -
500°F 1163 776 582 466 388 286 190.3 38.8 28.4 18.92 14.16 11.30 9.40 8.04 7.02 6.22 5.58 5.06 4.63 4.26 3.95 3.68 2.72 2.15 1.765 1.283 .990 .792 -
600°F 1287 857 844 515 430 315 210 42.8 31.5 20.9 15.68 12.53 10.42 8.92 7.79 6.92 6.22 5.64 5.16 4.76 4.41 4.11 3.06 2.42 2.00 1.474 1.156 .943 .790 .675 .584 .511 .279 -
700°F 1408 939 705 563 470 345 230 46.9 34.5 22.9 17.19 13.74 11.44 9.79 8.56 7.60 6.83 6.20 5.68 5.24 4.86 4.53 3.38 2.68 2.22 1.647 1.301 1.069 .904 .779 .682 .604 .368 .247
800°F 1530 1020 765 611 510 375 250 51.0 37.4 24.9 18.69 14.93 12.44 10.65 9.31 8.27 7.44 6.76 6.19 5.71 5.30 4.94 3.69 2.94 2.44 1.812 1.436 1.186 1.006 .872 .768 .684 .432 .305
Nomenclature: M Mass rate of flow, lbm/hr P
Average Line pressure, psia
P1 & P2
Inlet and outlet pressures, psia
P’
Rate of pressure drop, psi/1000 ft
V
Specific volume, cu ft/lbm
L
Line length, thousands of feet
Notes: This chart, strictly speaking, gives rate of pressure drop at a point in the pipe, but for relatively small changes in pressure through the pipe will give the average rate of pressure drop if the specific volume at the average pressure is used. Example: Pipe size = 6 in. 1/4 in. wall; inlet pressure = 151 psia; outlet pressure = 149 psia; pipe length = 487 ft; temperature = 500°F. Find mass flow rate. Average pressure, P = (P1 + P2)/2 = 150 psia. From the table V = 3.68 cu ft per lbm. P= (P1 - P2)/L = (151 -149)/0.487 = 4.1 psi per 1000 ft from the chart, M = 13,800 lbm per hr.
Fluid Flow Manual
Chevron Corporation
ABS PRESS. 1 in. Hg 1-1/2 2 2-1/2 3 2 psia 3 14.7 20 30 40 50 60 70 80 90 100 110 120 130 140 150 200 250 300 400 500 600 700 800 900 1000 1500 2000
400 Friction Pressure Drop
March 1997
Fig. 400-25 Flow of Steam—2 to 48-Inch Pipe (1 of 2) Table of Specific Volumes for Steam
Fluid Flow Manual
Chevron Corporation
Fig. 400-25 Flow of Steam—2 to 48-Inch Pipe (2 of 2)
400-57
400 Friction Pressure Drop
March 1997
400 Friction Pressure Drop
Fluid Flow Manual
This equation can be derived from basic pressure drop relations, but in the literature it is often presented in simplified form with certain empirical components. The two most widely accepted forms are the Weymouth Equation and the Panhandle Equation. The Weymouth Equation, in which friction is a function of the diameter, applies at high Reynolds numbers. The Panhandle Equation, in which friction is a function of the Reynolds number, applies at lower Reynolds numbers. The break point is defined as follows: Re = 9031D2.449 (Eq. 400-28)
where: D = inside diameter, in. The constants (C1 through C7) for the Weymouth and Panhandle equations are shown in Figure 400-25 both as presented in the literature and as derived without empirical components. Fig. 400-26 Weymouth and Panhandle Equation Constant Equation
C1
C2
C3
C4
C5
C6
C7
Source
Weymouth
433.45
Z
1
2.667
1
1
0.5
1
Weymouth
433.50
1
1
2.667
Z
1
0.5
2
Panhandle
435.87
E
1.0788
2.6182
1
0.8539
0.5394
3
Panhandle
503.30
1
1
2.695
1
0.77
0.565
2
where E Z
= = =
A = Tr = Tc = T = Pr = Pc = P = Sources:
pipeline efficiency, ranging from 0.94 (new pipe) to 0.88 (old rough pipe) compressibility 0.41P r A 8 1 – --------------- + ( 0.29 ) P r (From Source 4.) 4.04 Accurate within 10% if Pr1.0 T r or if Pr>0.8 and Tr>1.1 Tr16 T/Tc critical temperature, °R operating temperature,°R P/Pc critical pressure, psia operating pressure, psia
1. Natural Gas Processors Suppliers Association, Engineering Data Book, 1972. 2. Derived by W.A. Ebert, Chevron Engineering Department, 1984. 3. Baumeister and Marks, eds., Standard Handbook for Mechanical Engineers, McGraw-Hill, 1967. 4. Heat Transfer Research Inc., Computer Program Support Volume, pg. E1-47, 1976.
March 1997
400-58
Chevron Corporation
Fluid Flow Manual
400 Friction Pressure Drop
440 Gas Flow At High Pressure Drop (Choked Flow) A compressible fluid flowing through a pipe at high pressure drop approaches maximum velocity at a critical value of downstream pressure. Reduction of pressure below this value will not increase velocity. This maximum gas velocity—in a pipe of constant cross-sectional area—is limited to the velocity of pressure wave propagation in the fluid (the speed of sound). This section presents a method for determining pressure drop and flow rate in such situations. Some applications for this method include design of gas pipelines, pressure reduction lines, and relief lines. Theoretical methods for calculating high pressure drop are available, but are usually long and complex. However, C. E. Lapple (Section 450, Reference 15) has developed a graphical solution, which is the basis for Figure 400-29.
441 Assumptions The charts in Figure 400-29 (and Lapple’s analysis) are based on the following assumptions: •
The friction factor (f) is constant along the length of the pipe.
•
For the entire range of each chart, either the Perfect Gas Law applies or the compressibility factor (Z) and the ratio of specific heats (K) of the gases are constant.
•
The charts are based on horizontal flow through constant cross-sectional area.
442 Use of Design Charts The design charts in Figure 400-29 are for gases with values of K (the ratio of specific heats cp/cv) equal to 1.0 (isothermal flow of any gas) and 1.4 (flow of air and diatomic gases, H2, O2, N2). For the other gases with K values between 1.0 and 1.4, a visual interpolation between the charts may be made. Figure 400-27 gives approximate values of K for various gases. Fig. 400-27 Ratios of Specific Heats (cp/cv) Low Pressure Gas
K-value
C2H6
1.2
CO2, SO2, H2O, H2S, NH3, Cl2, CH4, C2H2, C2H4
1.3
Air, H2, O2, N2, NO, HCl
1.4
The design charts in Figure 400-29 are used when upstream conditions (usually static conditions within a vessel or reservoir) are known and either the discharge rate or downstream pressure are required for a given pipe size. In Figure 400-28, the typical problem is to determine mass flow rate G or pressure P2, given P0, T0, P3, L, and D. The velocity at Section “0” is assumed to be zero.
Chevron Corporation
400-59
March 1997
400 Friction Pressure Drop
Fluid Flow Manual
Fig. 400-28 Flow Conditions High Pressure Gas
In Figure 400-29, flow rates are expressed as a ratio of the actual mass velocity, G, to a hypothetical maximum isothermal mass velocity through a nozzle, Gmax. Thus, it is first necessary to calculate Gmax from known conditions:
(Eq. 400-29)
where: G = mass velocity, lbm/ft2⋅sec gc = conversion factor (32.17 lbm ft/lbf sec2) MW = molecular weight, lbm/mole e = base of natural logarithm (2.718) R = gas constant, 1546 ft⋅lbf/lb⋅mole⋅°R T = absolute temperature, °R, at location designated by subscript P = absolute pressure, lbf/ft2, at location designated by subscript V = specific volume, ft3/lbm, at location designated by subscript The friction factor (f) must also be established (see Section 410) prior to using the charts, although variations in f affect the answer very little. The initial value of f is usually assumed to be 0.0143 for gas flow.
March 1997
400-60
Chevron Corporation
Fluid Flow Manual
400 Friction Pressure Drop
Fig. 400-29 Design Charts for Gas Flow at High Pressure Drop (1 of 2) 1. To use design charts in Figure 400-29: a. Calculate an overall effective length L of straight pipe of diameter D, including equivalent length for valve and fitting losses (see Section 500). b. Assume a friction factor f for gas flow (usually assumed 0.0143) and calculate fL/D parameter. c. Calculate the hypothetical maximum mass velocity, Gmax, from g c P o 0.5 g c MW 0.5 lb m G max = ------------= P o ----------------------------------ev eRT 2 o o ft ⋅ sec d. Estimate K (ratio of specific heats) from Figure 400-27. e. Enter appropriate chart to determine P2/P0 or G/Gmax and solve for pressure P2 or mass flow. 2. Values for P2/P0 are valid only above the critical pressure ratio line which defines the point of sonic flow and maximum mass flow. Ratio P3/P0 is, however, valid over the entire range shown. Examples: Given: Air within a reservoir at 80°F and 200 psig is discharging to the atmosphere through 20 feet of three-inch, schedule 40 pipe which includes two standard 90° long radius elbows. Determine: Discharge rate to the atmosphere Solution: 1. Calculate fL/D parameter (use consistent units) f = 0.0143; assumed D=3.068 in. = 0.256 ft L = 20 + L’ = 20 + (2)(0.256)(23) = 31.8 ft (see Section 500) 2. Calculate maximum mass velocity, Gmax To = 460 + 80 = 540°R Po = (200 + 14.7)(144) = 30,900 lbf/ft2 MW = 29 lbm/mole lbm 0.5 ( 32.17 ) ( 29 ) G max = 30, 900 --------------------------------------------= 627 ------------------------( 2.718 ) ( 1546 ) ( 540 ) 2 ( sec ) ( ft ) 3. Find Flow Rate P3 = (14.7)(144) = 2120 lbf/ft2 P3/Po = 2120/30,900 = 0.0685 G/Gmax = 0.76 (K=1.4) G = (627)(0.76) = 476 lbm/(sec)(ft)2 A = (0.256)2/4 = 0.0515 ft2 Flow Rate = (G)(A) = (476)(0.515) = 24.6 lbm/sec
Chevron Corporation
400-61
March 1997
400 Friction Pressure Drop
Fluid Flow Manual
Fig. 400-29 Design Charts for Gas Flow at High Pressure Drop (2 of 2)
March 1997
400-62
Chevron Corporation
Fluid Flow Manual
400 Friction Pressure Drop
443 Sonic Flow After considering these preliminaries, use of the charts is generally self-explanatory. However, caution is advised concerning the area on each chart below the diagonal line labeled critical pressure ratio. This line defines the minimum possible pressure within the pipe at the exit for a particular fL/D flow parameter. That is, P2 will remain constant at this minimum despite further decrease in discharge reservoir pressure, P3. A sonic flow condition is said to exist at the pipe exit, since the exit gas velocity equals the velocity of sound in the fluid. Therefore, any further reduction in P3 cannot be transmitted back to the pipe exit to result in further pressure reduction within the pipe. The excess pressure energy in such a case (P2 - P3) is dissipated in turbulence from the rapid lateral expansion of gases leaving the pipe.
444 Choked Flow For the same reasons, the flow rate is at its maximum under critical pressure ratio conditions and will remain so regardless of any further decrease in P3. This limiting phenomenon can result in choking of a vent relief or pressure reduction line. A relief valve might be sized to handle the required flow only to have an inadequate vent line choke or limit the discharge rate at the critical pressure ratio.
445 Temperature Variations In the case of adiabatic flow, a drop in gas temperature from T0 to T2 may also be estimated from the design chart (for K = 1.4). Temperature ratios T2/T0 are shown as diagonal lines intersecting the fL/D parameter curves. For known reservoir temperature T0 and flow rate or pressure drop, the gas temperature T2 at the pipe exit may easily be calculated.
446 Effects of Valves and Fittings The increased pressure drop through valves and fittings should be taken into account by the equivalent length method of Section 500. The equivalent length L´, of the valve or fitting is added to the actual length of straight pipe to yield the effective overall length used to calculate the fL/D parameter.
447 Deviation from Assumptions Various deviations from the assumptions in Lapple’s analysis (listed previously) will affect the accuracy of the design charts. One such deviation is the variation from the perfect gas laws under high pressure. Allowance for such variation may be made by multiplying the gas constant R by the compressibility factor Z (a measure of variation from perfect gas properties) before calculating the hypothetical maximum discharge mass velocity, Gmax. Since the compressibility factor Z will vary along the length of the pipe, calculations should be made at stepped intervals and the results added together. Further discussion and techniques for handling such deviations are included in the references.
Chevron Corporation
400-63
March 1997
400 Friction Pressure Drop
Fluid Flow Manual
450 References 1.
Scott, D. S. Properties of Concurrent Gas-Liquid Flow. Advances in Chemical Engineering, Vol. 4, p.199. New York: Academic Press, 1963.
2.
Gouse, W. S., Jr. An Index to the Two-Phase Gas-Liquid Flow Literature. MIT Report No. 9. MIT Press, 1966.
3.
Dukler, A. E., M. Wicks III, and R. G. Cleveland. Frictional Pressure Drop in Two-Phase Flow: A. A Comparison of Existing Correlations for Pressure Loss and Holdup. AIChE Journal 10 (1964), p. 38.
4.
Lockhart, R. W., and R. C. Martinelli. Proposed Correlation of Data for Isothermal Two-Phase, Two-Component Flow in Pipes. Chemical Engineering Progress, 45 (1949), p. 39.
5.
Dukler, A. E., M. Wicks III, and R. G. Cleveland. Frictional Pressure Drop in Two-Phase Flow: B. An Approach Through Similarity Analysis. AIChE Journal 10 (1964), p. 44.
6.
Streeter, V. L. Fluid Mechanics. 2nd Edition. New York: McGraw-Hill, 1958.
7.
Hughmark, G. A. Holdup in Gas-Liquid Flow. Chemical Engineering Progress Vol. 58 (April 1962), p. 62.
8.
Baker, O. Multiphase Flow in Pipelines. Oil and Gas Journal, 10 (Nov, 1958).
9.
Griffith, P., and G. B. Wallis. Two-Phase Slug Flow. Journal of Heat Transfer, Transactions of ASME Series C 83 (Aug 1961), p. 307.
10. California Research Corporation Standard Technical Books. California Research Corporation, Richmond, California, 1960. 11. Mark’s Mechanical Engineers Handbook. 6th Edition. New York: McGrawHill, 1958. 12. Perry’s Chemical Engineers Handbook. 4th Edition. New York: McGraw-Hill, 1963. 13. Technical Data Book - Petroleum Refining. New York: American Petroleum Institute, Division of Refining, 1966. 14. S I Engineering Data Book. Tulsa: Gas Processors Suppliers Association, 1987. 15. Lapple, C.E. Isothermal and Adiabatic Flow of Compressible Fluids. Transactions of AIChE, Vol. 39 (1943), pp. 385-432. 16. Loeb, M. B. Graphical Solution of Compressible Fluid Flow Problems. NASA/Kennedy Space Center Document TR-256D, 1965. 17. Loeb, M. B. New Graphics for Solving Compressible Flow Problems. Chemical Engineering, Vol. 76, No. 11 (May 19, 1969). 18. Shapiro, A. H. The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. I. New York: The Ronald Press Company, 1953.
March 1997
400-64
Chevron Corporation
500 Fitting Pressure Drop Abstract This section discusses energy loss at changes in pipe section. Two methods for calculating pressure drop in fittings are presented, the velocity head loss method and equivalent length method, and example calculations are given.
Chevron Corporation
Contents
Page
510
Introduction
500-2
520
Velocity Head Loss Method
500-2
530
Equivalent Length Method
500-5
540
Transition and Laminar Flow Conditions
500-7
550
Examples
500-7
551
Example 1—Velocity Head Loss Method
552
Example 2—Equivalent Length Method
560
References
500-10
500-1
March 1997
500 Fitting Pressure Drop
Fluid Flow Manual
510 Introduction Valves and fittings cause more energy loss than pipe of equal axial length. This loss may be relatively insignificant in long lines but, within process plants, it can be a major contributor to system losses. Losses at a change in section take two distinct forms, pressure loss and energy loss. At a well-rounded pipe entrance, there is a pressure loss due to the increase in velocity, but a negligible energy loss. At a pipe exit, pressure change is usually nominal and velocity energy is dissipated as turbulence. Head loss through a valve or fitting can be expressed in two ways: •
As the number of velocity heads lost
•
As a length of straight pipe with a diameter and pressure drop equal to those of the valve or fitting
520 Velocity Head Loss Method In the turbulent flow range, the resistance to flow through a fitting is roughly a constant times the square of the average line velocity at the fitting. This can be expressed as follows: 2
V h f = K ------- 2g (Eq. 500-1)
where: hf = head loss through the fitting, ft V = average velocity in the line, ft/sec K = constant for the fitting type g = gravitational constant (32.2 ft/sec2) Since V2/2g is the velocity head of the fluid, K is the number of velocity heads lost through the fitting. The average values of K for various valves and fittings are shown in Figure 500-2. K values for various entrance losses are given in Figure 500-1.
March 1997
500-2
Chevron Corporation
Fluid Flow Manual
Fig. 500-1
500 Fitting Pressure Drop
Losses Through Entrances and Changes in Section Courtesy of Tube Turns Technologies
Chevron Corporation
500-3
March 1997
Valve and Fitting Loss Data
500 Fitting Pressure Drop
Fig. 500-2
March 1997
500-4
Fluid Flow Manual
Chevron Corporation
Fluid Flow Manual
500 Fitting Pressure Drop
530 Equivalent Length Method The equivalent length method is a convenient but less accurate way to estimate pressure drop through valves and fittings. This method may be understood by looking at the Darcy-Weisbach equation for friction head loss, which can be expressed as follows: 2
L V h = f ---- ------- D 2g (Eq. 500-2)
where: h = friction head loss, ft f = friction factor L = length of fitting, ft D = diameter of fitting, ft Thus K equals f(L/D). By expressing this relation in terms of L, the loss through the fitting may be expressed as an equivalent length (L′) of straight pipe (of the same diameter as the fitting). That is, ′
K L K L′ = D ---- or ----- = ---D f f (Eq. 500-3)
Figure 500-3 gives equivalent length of various sizes of valves and fittings. The L′/D ratio provides equivalent length values in terms of diameters of straight pipe, so that one value can be applied to varying diameters of a valve or fitting. The equivalent length ratios shown in Figure 500-2 were calculated from the fittings’ K values (assumed constant for each type fitting) and a friction factor of 0.025 for liquids and 0.0143 for gases. Because the actual friction factor may differ appreciably, the equivalent length method should be used only for rough estimates or when the total equivalent length for valves and fittings is small compared to the length of straight pipe.
Chevron Corporation
500-5
March 1997
500-6
Equivalent Length of Valves and Fittings in Feet
500 Fitting Pressure Drop
Fig. 500-3
March 1997
Fluid Flow Manual
Chevron Corporation
Fluid Flow Manual
500 Fitting Pressure Drop
540 Transition and Laminar Flow Conditions Under transition and most laminar flow conditions, the velocity head loss method, using turbulent range K values, is accurate enough for normal estimating. However, the K values increase rapidly for Reynolds numbers below 500. Additional data and discussion can be found in the references cited in Section 560 (for Re < 500 see Reference 6).
550 Examples Consult Figures 500-1 and 500-2 for the K and L′/D values to be used in the following examples. In practice, manufacturers’ proprietary fitting loss data should be used whenever available. For elbows under three inches in diameter, increase loss by 30 percent. Add appropriate reducer losses to fitting losses for total loss through a reducing fitting, such as a tee with a reducing branch or a venturi pattern valve.
551 Example 1—Velocity Head Loss Method Given the following, determine the pressure loss through the fittings: •
Flowing liquid: gasoline (gravity = 0.75) with a flow rate of 150,000 lb per hour.
•
Fittings: 6-inch Schedule 40 size; one globe valve; one check valve; three 90degree elbows (R/D = 1.5); one 6-inch to 3-inch ANSI reducer.
Solution Calculate the pressure drops separately for each diameter. Diameter Ratio: DS/DL = 3.068 in./6.065 in. = 0.51 From Figure 500-1:
Chevron Corporation
Fitting
K
Reducer (friction)
0.16
Reducer (acceleration)
0.56
TOTAL
0.72
500-7
March 1997
500 Fitting Pressure Drop
Fluid Flow Manual
From Figure 500-2: Fitting
K
Globe Valve
10.0
Check Valve
2.3
Elbows (3 x .33) TOTAL
0.99 13.29
Pipe Area = A = πr2 2
1ft 6.065 2 2 A 1 = 3.14 ------------- in. ⋅ -------------------2 2 144 in. = 0.201 ft2 3
1ft 3.068 2 2 A 2 = 3.14 ------------- in. ⋅ -------------------2 2 144 in. = .051 ft2 Flow rate = Q 3
lb 1 hr ft = 150, 000 ----- ⋅ -------------------- ⋅ --------------- ⋅ ------hr 3600sec 62.4lb .75 = 0.89 ft3/sec Q Velocity = V = ---A 3
Q 0.89ft ⁄ sec V 1 = ------- = ---------------------------2 A1 0.201ft = 4.44 ft/sec 3
Q 0.89ft ⁄ sec V 2 = ------- = ---------------------------2 A2 0.051ft =17.45 ft/sec
March 1997
500-8
Chevron Corporation
Fluid Flow Manual
500 Fitting Pressure Drop
2
V One Velocity Head = ------2g 2
2 2
2
V1 4.44 ft ⁄ sec --------- = -------------------------------------22g 2 × 32.2 ft ⁄ sec = 0.306 ft 2
2
2
V2 17.45 sq ft ⁄ sec --------- = ----------------------------------------2 2g 2 × 32.2 ft ⁄ sec = 4.73 ft Total pressure drop:
62.4 × 0.75 ∆P 1 = ( 13.29 ) ( 0.306 ) --------------------------- = 1.322psi 144 62.4 × 0.75 ∆P 2 = ( 0.72 ) ( 4.73 ) --------------------------- = 1.107psi 144 Total = 2.429 psi (Eq. 500-4)
552 Example 2—Equivalent Length Method Given the following, determine the estimated total equivalent length of straight 6inch pipe:
Chevron Corporation
•
Flowing liquid: gasoline (gravity = 0.75) at a flow rate of 150,000 lb per hour
•
Total line length (including fittings): 800 ft
•
Pipe and fitting size: 6 inch, schedule 40 = 6.065 in. ID
•
Fittings: one gate valve (open), six 90° elbows (R/D = 1.5), one square edged entry, one exit
500-9
March 1997
500 Fitting Pressure Drop
Fluid Flow Manual
Solution From Figures 500-1 and 500-2: L′/D
Fitting Gate Valve
8
Elbows (6 x 13)
78
Square Edged Entry (friction)
20
Square Edged Entry (acceleration)
40
TOTAL
146
Equivalent length L′ = (L′/D) (D) = (146) (6.065) = 855 in. = 71.2 ft Total equivalent line length 800 + L′ = 871.2 ft
560 References
March 1997
1.
Flow of Fluids Through Valves, Fittings, and Pipe. Crane Co., Crane Technical Paper No. 410-C, 1984.
2.
King, R.C., and S. Crocker. Piping Handbook, 5th Edition, McGraw-Hill, pp 167-181, 1967.
3.
Piping Engineering - Fluid Flow in Pipe. Tube Turns Bulletin No. 301, 1951.
4.
Simpson, L.L. “Process Piping: Functional Design.” Chemical Engineering, Vol. 76, No. 8, 1969.
5.
Perry’s Chemical Engineers Handbook. 4th Edition, McGraw-Hill, New York, 1963.
6.
Beck, C. “Laminar Flow Friction Losses Through Fittings, Bends, and Valves.” Journal American Society Naval Engineers, vol. 56, p. 235-271, 1944.
7.
Kittredge, C.P., and D.S. Rowley. “Resistance Coefficients for Laminar and Turbulent Flow Through One-Half-Inch Valves and Fittings.” ASME Transactions, Vol. 79, pp 1759-1766, 1957.
500-10
Chevron Corporation
600 Noncircular Conduits Abstract This section presents methods for approximating pressure drop for turbulent and laminar flow in noncircular conduits. These conduits are assumed to be closed and filled with fluid.
Chevron Corporation
Contents
Page
610
Introduction
600-2
620
Turbulent Flow (Re > 2000)
600-2
630
Laminar Flow (Re ≤ 2000)
600-3
640
References
600-4
600-1
January 1990
600 Noncircular Conduits
Fluid Flow Manual
610 Introduction The calculation of pressure drop in noncircular conduits is handled differently for laminar and turbulent flow. Turbulent flow boundary layers are thin and relatively unaffected by proximity to the conduit walls. Laminar boundary layers, however, are thick, and the boundary layers from opposite walls often interact. Pressure drop for turbulent flow can be closely approximated based on the calculation of the conduit’s hydraulic diameter given in Section 620. For laminar flow, empirical data is needed to arrive at a reasonable approximation of the pressure drop for a specific case. Section 630 provides empirical correlations for the friction factor for rectangular and concentric annulus geometry. For this analysis, the transition between laminar and turbulent flow can be assumed to be at a Reynolds number of 2000.
620 Turbulent Flow (Re > 2000) The hydraulic diameter (Dh) is derived from the flow area and the wetted perimeter length of the noncircular conduit. It is used in determining the Reynolds number, which, in turn, is used to find a friction factor appropriate for the noncircular conduit flow. Ax D h = 4 ------- Pw (Eq. 600-1)
VρD h VD h Re = --------------- = ----------µ ν (Eq. 600-2) 2
V dh = fL ----------------D h ⋅ 2g (Eq. 600-3)
where: f = friction factor from Figure 400-1, Moody Chart Dh = hydraulic diameter, ft Ax = cross-sectional flow area, ft2 Pw = wetted perimeter of channel, ft Re = Reynolds number ρ = density, lbm/ft3 V = velocity, ft/sec
January 1990
600-2
Chevron Corporation
Fluid Flow Manual
600 Noncircular Conduits
ν = kinematic viscosity, ft2/sec µ = viscosity, lb ⋅ sec/ft2 f = friction factor dh = pressure drop in head loss, ft L = conduit length, ft g = gravitational constant, 32.17 ft/sec2
630 Laminar Flow (Re ≤ 2000) Pressure drop for laminar flow in noncircular conduits can be calculated using the standard pressure drop equation (Eq. 600-3) and the hydraulic diameter (Eq.600-1). The friction factor (f) is a function of the Reynolds number (Eq. 600-2) and the constants as shown in Figure 600-1 and Equations 600-4 and 600-5. For rectangular conduit geometry choose C1 such that: a = short side of rectangle b = long side of rectangle Calculate the friction factor as follows: C1 f = ------Re (Eq. 600-4)
For concentric tube annulus choose C2 such that: a = radius of inner tube b = radius of outer tube Calculate the friction factor as follows: C2 f = ------Re (Eq. 600-5)
Chevron Corporation
600-3
January 1990
600 Noncircular Conduits
Fluid Flow Manual
Fig. 600-1
Laminar Flow Pressure Drop Constants
a/b(1)
C1(1)
C2(1)
0.0
96.0
64.0
0.025
94.0
81.2
0.05
90.0
86.0
0.1
85.2
89.2
0.2
76.8
92.4
0.3
70.4
93.6
0.4
65.6
94.8
0.5
62.8
95.2
0.6
60.0
95.6
0.7
58.8
96.0
0.8
57.6
96.0
0.9
57.2
96.0
1.0
56.8
96.0
Source: See Section 640. (1) See Eq. 600-4, 600-5
640 References Kays and Crawford, Convective Heat and Mass Transfer, McGraw- Hill, 1980.
January 1990
600-4
Chevron Corporation
800 Surge Pressure Abstract This section presents the basic physical principles involved in surge and a method for approximating surge pressure in simple cases. In addition, it identifies two computer programs available within the Company for analysis of complex fluid pressure transients.
Chevron Corporation
Contents
Page
810
Introduction
800-2
820
Maximum Surge Pressure in a Simple Case
800-2
830
Surge Computer Programs
800-7
840
References
800-7
800-1
January 1990
800 Surge Pressure
Fluid Flow Manual
810 Introduction If a valve is closed rapidly in a line containing flowing liquid, the inertia of the flowing liquid will increase the pressure at the valve. This effect is called surge, and the increase in pressure is called surge pressure. Surge can cause extremely rapid changes in pressure—rapid enough to cause the metallic percussions commonly called water hammer. The surge pressure wave will then propagate back up the line, and may cause mechanical damage. Water flowing at 10 ft/sec can generate a surge pressure rise of about 500 psi. Bulk modulus values for hydrocarbons are generally lower than for water, but surge pressures are still significant considerations in designing hydrocarbon piping systems. See Figures 800-1 through 800-3. This section provides a method for approximating the maximum surge pressure in a simple system. Because of nonlinear elements in the analysis, a more thorough calculation of surge pressure can be a complex problem. See Section 840 for sources providing more general solution techniques.
820 Maximum Surge Pressure in a Simple Case The simplest case is of flow through a line starting at a vessel and ending at a valve (see Figure 800-4). When the valve is closed, the kinetic energy of the flowing liquid is converted to surge pressure as the liquid compresses and the pipe wall stretches. The conversion of kinetic energy to surge pressure propagates in a wave upstream to the vessel at the velocity of sound in the liquid, followed by a return “negative” pressure wave back to the valve. This cycle repeats with diminishing intensity until damped completely. To a first approximation, the magnitude of the surge pressure is directly proportional to the change in velocity. It follows that maximum surge pressure occurs when the flow is stopped completely and quickly. To calculate surge pressure, the velocity of sound in the liquid must be calculated using Equation 800-1.
January 1990
800-2
Chevron Corporation
Fluid Flow Manual
Fig. 800-1
800 Surge Pressure
Average Bulk Modulus for Crude Oil, Fuel Oil, Gas Oil, and Gasoline
Chevron Corporation
800-3
January 1990
800 Surge Pressure
Fig. 800-2
Fluid Flow Manual
Average Bulk Modulus for Lubricating Oils
January 1990
800-4
Chevron Corporation
Fluid Flow Manual
Fig. 800-3
Bulk Modulus of Water
Fig. 800-4
Surge—Simple Case
Chevron Corporation
800 Surge Pressure
800-5
January 1990
800 Surge Pressure
Fluid Flow Manual
α =
144Kg ------------------------------KDC ρ 1 + ------------- Et (Eq. 800-1)
where: α = speed of sound through liquid in pipe, ft/sec K = bulk modulus of liquid, psi. For hydrocarbon liquids, see Figures 800-2 and 800-3; for water, see Figure 800-4. ρ = density of liquid, lbm/ft3 g = 32.2 ft ⋅ lbm/sec2 ⋅ lbf D = inside diameter of pipe, inches t = wall thickness of pipe, inches E = modulus of elasticity of pipe material, psi C = constant which depends on pipe fixity = 0.91 for line anchored against axial movement = 0.95 for unrestrained line A pressure disturbance generated at the valve will propagate back to the vessel and return to the valve in a propagation time equal to 2L/α (where L = line length between vessel and valve in feet). If the valve closing time (T) is less than 2L/α, the surge pressure can be approximated by αρ∆V 2L P = ---------------- for T < ------α 144g (Eq. 800-2)
where: P = surge pressure, psi ∆V = total change in velocity, ft/sec T = valve closing time, sec 2L/α = propagation time, sec This solution is only an approximation tailored to this simple case. For example, this equation is not valid if the valve closing time is greater than 2L/α. Section 840, references 1, 2, and 3, presents general techniques for calculating surge pressure accurately and in more complex situations.
January 1990
800-6
Chevron Corporation
Fluid Flow Manual
800 Surge Pressure
830 Surge Computer Programs The SURGE computer program available on the VM mainframe engineering program library (HOVMA) is described in Section 1100 and Appendix H of this manual. This software performs a rigorous analysis of pressure transients for common applications. The HYDRESS computer program calculates fluid transients in small-diameter flexible conduits (instrument control and subsea lines) and is available on VM Houston (OELIB).
840 References
Chevron Corporation
1.
“Symposium on Surges in Pipelines,” The Institution of Mechanical Engineers, Proceedings 1965-66, Vol. 180, Part 3E.
2.
Hydraulic Transients, Rich, G. R., Dover Publications, Inc., New York, 1963.
3.
Hydraulic Transients, Streeter, V. L., Wylie, E. B., McGraw-Hill, 1967.
800-7
January 1990
900 Pipeline Flow Abstract This section discusses the flow effects of increased temperature and pressure in above-ground, buried, and subsea oil pipelines. Basic equations are given for calculating friction heating in viscous flow, pressure correction to viscosity, and external heat transfer coefficients. Computer programs for calculating effects of temperature changes on large segments of pipeline are identified and briefly discussed. Tables for external heat transfer coefficients and soil conductivities are included.
Chevron Corporation
Contents
Page
910
Introduction
900-2
920
Pipeline Temperature Limits
900-2
930
Friction Heating In Viscous Flow
900-2
940
Pressure Correction to Viscosity
900-3
950
Applicable Computer Programs
900-4
960
External Heat Transfer Coefficients
900-5
970
References
900-7
900-1
January 1990
900 Pipeline Flow
Fluid Flow Manual
910 Introduction Section 900 addresses pipeline flow situations in which large temperature changes significantly affect fluid properties and flow characteristics. Other situations, involving typical liquids and gases at close to ambient temperatures or with small temperature changes, can be adequately addressed using the methods of Section 400. For long pipelines carrying fluids that require high pumping energy, the effects of friction heating should be investigated. Section 930 defines the relationship of temperature change to pumping energy for viscous fluids. Similarly, at high pressures, a pressure correction to viscosity may be necessary, as discussed in Section 940. Section 960 discusses heat transfer between the pipeline and its surroundings, including calculation of external heat transfer coefficients for pipelines in various ambient conditions. Section 950 identifies computer programs available for solving difficult temperature/flow problems over the length of a pipeline.
920 Pipeline Temperature Limits The allowable coating or insulation temperature normally limits pipeline temperature. Coating temperature (for buried pipelines) is normally limited to less than about 150°F. Special fusion bonded epoxy coatings of extra thickness are limited to about 200°F. Polyurethane foam insulation temperature limits are about 200°F. Some forms of insulation may resist higher temperatures, but Chevron has no experience with them.
930 Friction Heating In Viscous Flow In a flowing fluid, pressure dissipated by friction becomes heat. This heat has historically been ignored in flow calculations because it is often insignificant. However, with some oils friction heating significantly decreases the pumping energy required. The temperature increase from friction heating accumulates over the length of the pipeline. In a perfectly insulated pipeline, the outlet temperature would be higher than the inlet temperature. This change in temperature can be related to the hydraulic horsepower (friction component) and flow rate by the following expression:
(Eq. 900-1)
where: ∆T = temperature increase, °F HP = hydraulic (friction) horsepower, hp
January 1990
900-2
Chevron Corporation
Fluid Flow Manual
900 Pipeline Flow
BPD = oil flow rate, BPD r = oil density, lbm/ft3 Cp = oil specific heat, BTU/lbm °F When Cp = 0.5 and ρ = 58 the expression becomes:
High viscosities increase the ratio of HP to BPD and therefore increase the temperature change due to friction. How well the pipeline is insulated determines how much of the added heat will actually stay in the oil. The following factors determine the decrease in required pumping power: •
How much the viscosity is decreased by the increased temperature
•
How sensitive the flow regime is to decreases in viscosity. Pressure drop in laminar flow is a stronger function of viscosity than in turbulent flow. Pressure drop in transition flow is not a function of viscosity
The effect of friction heating generally increases with: • • • •
Flow rate Viscosity Insulation Line length
940 Pressure Correction to Viscosity The viscosity of a liquid increases with pressure, but, as with friction heating, this effect is often ignored in pressure drop calculations. At high pressures and viscosities the average viscosity increase in a pipeline can be 20% or more. Equation 900-2 gives the increased viscosity due to pressure for high molecular weight hydrocarbons (source: see Section 970, reference 1). V = Vo ⋅ 10A (Eq. 900-2)
where:
(Eq. 900-3)
V = viscosity corrected for pressure, cp Vo = viscosity at standard pressure, cp
Chevron Corporation
900-3
January 1990
900 Pipeline Flow
Fluid Flow Manual
P = pressure, psig As with friction heating, the effect of increased viscosity on pumping energy requirements depends on the flow regime’s sensitivity to viscosity. Since some pipelines have more than one flow regime (laminar, transition, or turbulent), the change in pumping requirements can be difficult to calculate without a computer program.
950 Applicable Computer Programs Over the length of a pipeline, temperature changes and resulting fluid property changes make it difficult to calculate pipeline hydraulics by hand. Fortunately, computer programs make hand calculations unnecessary. Several computer programs are briefly discussed here in terms of how they handle pipeline considerations. This is not intended to be a complete description of these programs or to be an exhaustive list of the programs that could be used for pipeline calculations. Section 1100 contains more information on fluid flow computer programs. HOTOL* calculates pressure drop and heat transfer for hydrocarbon liquids in pipelines where fluid properties change significantly with temperature. The program’s heat transfer routines assume the fluid is at or above ambient temperature. HOTOL* does not consider friction heating or pressure correction to viscosity. The program is available on the mainframe engineering disk. For details on the use of the program see Appendix G. HOTPIPE2 is a modification of HOTOL*. It retains the rigorous fluid property correlations and heat transfer routines of HOTOL*, and also accepts elevation profiles. It can automatically place pump stations and heater stations along the pipeline, and it considers friction heating and pressure correction of viscosity. HOTPIPE2 runs on an IBM compatible personal computer. It is available from the Engineering Analysis Division of Chevron Research and Technology Company (CRTC). HOTOIL is an IBM compatible personal computer program that handles both Newtonian and non-Newtonian flow. As rigorous as HOTOL* in its heat transfer and Newtonian fluid property correlations, HOTOIL also considers friction heating, pressure correction to viscosity and elevation profiles. It is available from the Engineering Analysis Division of CRTC. For details on the use of the program see Appendix F. PIPEFLOW-2 is the only program considered here that solves piping network and multiphase flow problems. It handles elevation profiles and detects and handles change of phase. Its reference manual does not mention friction heating. Although it does not automatically handle pressure correction to viscosity, viscosity can be entered in tabular form as a function of temperature and pressure. PIPEFLOW-2 resides on the Houston VM mainframe computer. For details on the use of the program see Appendix E.
January 1990
900-4
Chevron Corporation
Fluid Flow Manual
900 Pipeline Flow
960 External Heat Transfer Coefficients All the computer programs mentioned in Section 950 require the user to input an external heat transfer coefficient and the ambient air or water temperature. This value is factored in with the computer-derived internal heat transfer coefficient to find the overall heat transfer coefficient. The external heat transfer coefficient value (ho) should include all heat transfer resistances between the pipe wall and the ambient fluid. These include, first, insulating pipeline coverings such as insulation, soil, concrete liners, and pipe coatings of significant thickness, and, second, the area between the outside of the pipe or pipe covering and the ambient fluid. The following sections present equations for calculating external heat transfer coefficients for buried, above-ground, and subsea pipe.
Buried Pipelines The appropriate ambient temperature value for a buried line is the yearly average air temperature. The external heat transfer coefficient for buried pipe can be calculated as follows:
(Eq. 900-4)
where: ho = external heat transfer coefficient, Btu/hr ft2 °F k = soil thermal conductivity, Btu/hr ft °F D = pipe outside diameter, inches d = virtual pipe burial depth, inches = da + 12 k/ha where: da = actual pipe depth to center line, inches ha = ground to air heat transfer coefficient, Btu/hr ft2 °F Ground-to-air heat transfer coefficients are typically 1 to 3 Btu/hr sq ft °F for low to moderate winds. Soil thermal conductivity is mainly a function of moisture content. Typical values are between 0.2 and 1 Btu/ hr ft °F. Figure 900-2 gives conductivity values for some soil, sand, and rock types, and other related materials. It also shows the relationship between soil density and thermal conductivity.
Chevron Corporation
900-5
January 1990
900 Pipeline Flow
Fluid Flow Manual
Ground moisture tends to migrate away from heated objects. Therefore, the actual soil conductivity around a buried hot (or warm) pipeline may vary with time and with distance from the line.
Above-Ground and Subsea Pipelines The appropriate ambient temperature value for above-ground lines is the yearly average air temperature. The cases for high summer and low winter temperatures should also be checked. For subsea lines, use the average bottom water temperature. The external heat transfer coefficient (ho) for above-ground and subsea pipelines can be approximated using Equation 900-5. This equation can accommodate thermal resistance values for an arbitrary number of coverings on the pipeline (R1, R2, etc.). For an above-ground pipeline, these coverings might include insulation and pipe coatings. Subsea lines are likely to have an outside concrete liner. For bare lines, the layer terms (R1, R2, etc.) equal zero and are dropped from the equation.
(Eq. 900-5)
where: ho = external heat transfer coefficient, Btu/hr ft2 °F ha = ambient fluid heat transfer coefficient, Btu/hr ft2 °F R1 = thermal resistance of layer 1, hr ft2 °F/Btu R2 = thermal resistance of layer 2, hr ft2 °F/Btu rop = outside radius of outermost layer on pipe, ft ro1 = outside radius of layer 1, ft ro2 = outside radius of layer 2, ft ri1 = inside radius of layer 1, ft ri2 = inside radius of layer 2, ft k1 = thermal conductivity of layer 1, Btu/hr ft °F
January 1990
900-6
Chevron Corporation
Fluid Flow Manual
900 Pipeline Flow
k2 = thermal conductivity of layer 2, Btu/hr ft °F ln = natural logarithm Thermal conductivity for subsea concrete (k1) coatings is about 0.5 Btu/hr ft °F. Subsea ambient heat transfer coefficients (ha) are in the low one-hundreds for moderate currents. Using ha equal to 150 Btu/hr sq ft °F should give acceptable accuracy. Figure 900-1 shows approximate ambient heat transfer coefficients for air.
970 References 1.
Fig. 900-1
Petroleum Refining, Technical Data Book. Washington, D.C.: American Petroleum Institute, 1970, pp 11-47.
Heat Loss from Hot Surfaces to Air
Chevron Corporation
900-7
January 1990
900 Pipeline Flow
Fig. 900-2
Fluid Flow Manual
Soil Conductivity Chart (1 of 4)
Material
Conductivity, Btu/hr ft °F
Source
————————— Moisture Content————————
(dry density where reported)
dry
Soil
0.2
Soil (80 lb/cu ft)
0.24
0.40
0.50
0.58
2
Soil (90 lb/cu ft)
0.31
0.51
0.59
0.72
2
Soil (100 lb/cu ft)
0.61
0.73
Soil (110 lb/cu ft)
0.72
Sandy soil
0.16
Sand
0.20
White sand, clean
0.14
Yellow sand, clean
0.17
Yellow sand and clay Clay
2%
4%
6%
8%
10%
12%
14%
20%
30% 1
2 2 2
0.60
1 2
0.20
0.28
0.40
0.56
0.16
0.17
0.20
0.26
2 0.35
0.74
0.51
0.79
2 3
Fine crushed quartz (100 lb/cu ft)
1.00
4
(110 lb/cu ft)
1.33
4
(100 lb/cu ft)
0.96
4
(110 lb/cu ft)
1.33
4
(120 lb/cu ft)
1.83
4
(100 lb/cu ft)
0.83
4
(110 lb/cu ft)
1.17
4
(100 lb/cu ft)
0.71
4
(110 lb/cu ft)
0.87
(120 lb/cu ft)
1.12
Crushed quartz
Graded Ottawa sand
Fairbanks sand
January 1990
1.25
4 4
900-8
Chevron Corporation
Fluid Flow Manual
Fig. 900-2
900 Pipeline Flow
Soil Conductivity Chart (2 of 4)
Material (dry density where reported)
Conductivity, Btu/hr ft °F
Source
————————— Moisture Content———————— dry
2%
4%
6%
8%
10%
12%
14%
20%
30%
Lowell sand (100 lb/cu ft)
0.71
(110 lb/cu ft)
0.87
4 1.12
4
Chena river gravel (110 lb/cu ft)
0.75
4
(120 lb/cu ft)
1.08
4
(100 lb/cu ft)
0.50
4
(110 lb/cu ft)
0.62
4
(120 lb/cu ft)
0.79
4
(100 lb/cu ft)
0.46
4
(110 lb/cu ft)
0.62
4
(120 lb/cu ft)
0.79
4
(110 lb/cu ft)
0.54
4
(120 lb/cu ft)
0.79
Crushed feldspar
Crushed granite
Dakota sandy loam
1.08
4
Crushed trap rock (100 lb/cu ft)
0.42
4
(110 lb/cu ft)
0.50
4
(120 lb/cu ft)
0.58
4
(100 lb/cu ft)
0.37
4
(110 lb/cu ft)
0.54
Ramsey sandy loam
Chevron Corporation
0.83
900-9
4
January 1990
900 Pipeline Flow
Fig. 900-2
Fluid Flow Manual
Soil Conductivity Chart (3 of 4)
Material (dry density where reported)
Conductivity, Btu/hr ft °F
Source
————————— Moisture Content———————— dry
2%
4%
6%
8%
10%
12%
14%
20%
30%
Northway fine sand (100 lb/cu ft)
0.37
(110 lb/cu ft)
0.46
4 0.71
4
Northway sand (100 lb/cu ft)
0.37
(110 lb/cu ft)
0.50
4 0.62
4
Healy clay (90 lb/cu ft)
0.46
(100 lb/cu ft)
0.33
(110 lb/cu ft)
0.67
4
0.83
4
0.75
4
Fairbanks silt loam (90 lb/cu ft)
0.42
(100 lb/cu ft) (110 lb/cu ft)
0.62
4
0.83
4
0.75
4
Fairbanks silty clay loam (90 lb/cu ft)
0.42
(100 lb/cu ft) (110 lb/cu ft)
0.62
4
0.79
4
0.75
4
Northway silt loam (90 lb/cu ft)
0.33
(100 lb/cu ft) (110 lb/cu ft)
0.58
0.50
4
0.58
4 4
Iraq Desert Steppe
0.27
5
Iraq Desert Sand
0.49
5
January 1990
900-10
Chevron Corporation
Fluid Flow Manual
Fig. 900-2
900 Pipeline Flow
Soil Conductivity Chart (4 of 4)
Material
Conductivity, Btu/hr ft °F
Source
————————— Moisture Content————————
(dry density where reported)
dry
Abqaiq sand
1.06
5
Earth, coarse gravelly
0.30
3
Concrete
0.54
Common red brick
0.36
2%
4%
6%
8%
10%
12%
14%
20%
30%
(in a limestone trench)
0.70
1 2
Granite
1.73-3.98
6
Limestone
1.26-1.33
6
Marble
2.07-2.94
6
Sandstone
1.83
Material
6 Conductivity, Btu/hr ft °F
Source
Soil (fairly dry, avg. California summer)
0.25
7
Soil (wet weather, some drainage)
0.35
7
Soil (heavy rains, but ground not flooded)
0.65
7
Soil (marshy or constantly soaked)
1.00
7
Sources 1. Krieth, F. Principles of Heat Transfer. New York: Harper & Row, 1973. 2. Flow of Hot Oil in Pipelines. Various sources. Chevron: discontinued. 3. Eckert, E. R. G., and R. M. Drake, Jr. Heat and Mass Transfer. New York: McGraw-Hill, 1959. 4. McAdams, W. H. Heat Transmission, 3rd ed. New York: McGraw-Hill, 1954. 5.
Journal of the Institute of Petroleum, Vol. 36, No. 321, September, 1950.
6.
Holman, J. P. Heat Transfer, 5th ed. New York: McGraw-Hill, 1981.
7. Flow of Hot Oil in Pipelines. Chevron experience. Chevron: discontinued.
Chevron Corporation
900-11
January 1990
1000 Fluid Properties Abstract This section discusses the viscosity and gravity properties of Newtonian and nonNewtonian fluids as they relate to the characterization of hydrocarbon liquids and gases. It presents graphs and equations for estimating or calculating viscosity versus temperature, gravity versus temperature, viscosity of blends and brine-in-oil emulsions, etc. Relationships of pressure and flow rate to viscosity are also discussed. Conversion tables are included. A general discussion of non-Newtonian waxy crude viscosity includes basic equations and analytical correlations. It covers practical aspects, principles, and equations related to the measurement of viscosity as well as the design and use of viscometers. Laboratory measurement of non-Newtonian flow properties and gel strength is discussed. An overview of computer program HOTOIL is included. Contents
Page
1010 Viscosity
1000-3
1011 Absolute Viscosity 1012 Kinematic Viscosity 1013 Temperature and Viscosity 1014 Viscosity Index 1015 Pressure and Viscosity 1016 Flow Rate and Viscosity 1017 Measurement of Viscosity 1018 Viscosity of Blends 1019 Viscosity of Brine-in-Oil Emulsions 1020 Gravity
1000-32
1021 Example 1030 Non-Newtonian Fluids
1000-38
1031 Laboratory Measurement of Flow Properties 1032 Laboratory Measurement of Gel Strength
Chevron Corporation
1000-1
March 1997
1000 Fluid Properties
Fluid Flow Manual
1033 Constitutive Relationships 1034 Calculation of Flow Parameters 1035 Hydraulics Equations 1036 Computer Program HOTOIL 1037 Estimating Pipeline Restart Pressure Gradient 1038 Wax Deposition 1040 References
1000-54
1041 Viscosity Conversion 1042 Viscosity Data 1043 Brine-in-Oil Emulsions
March 1997
1000-2
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
1010 Viscosity Viscosity is a measure of the internal friction or resistance of a fluid to the relative motion of its parts. It may be regarded as the relationship between the force applied to a fluid and the rate of deformation produced in the fluid.
1011 Absolute Viscosity The force F required to move a fluid layer with surface area A located a distance D from a stationary surface, at a velocity V, can be expressed by:
(Eq. 1000-1)
The coefficient µ is defined as the absolute, or dynamic, viscosity. Its metric system dimensions are as follows:
(Eq. 1000-2)
where: F = shearing force, dynes (dyne = gram cm/sec2) V/D = velocity gradient, sec-1 A = area of shear, cm2 Since the poise is a relatively large number, absolute viscosity is normally expressed in centipoise (0.01 poise). The English system expression for absolute viscosity is as follows:
(Eq. 1000-3)
or (Eq. 1000-4)
Conversion factors for absolute viscosities are included as Figures 1000-1 through 1000-5.
Chevron Corporation
1000-3
March 1997
1000 Fluid Properties
Fig. 1000-1 Conversion Factors for Absolute Viscosity
March 1997
1000-4
Fluid Flow Manual
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
Fig. 1000-2 Viscosity Conversion—From Various Terms to Saybolt Universal (1 of 2) Courtesy of Hydraulic Institute
Chevron Corporation
1000-5
March 1997
1000 Fluid Properties
Fluid Flow Manual
Fig. 1000-2 Viscosity Conversion—From Various Terms to Saybolt Universal (2 of 2) Courtesy of Hydraulic Institute
March 1997
1000-6
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
Fig. 1000-3 Viscosity of Common Liquids (1 of 4) Courtesy of Hydraulic Institute
Chevron Corporation
1000-7
March 1997
1000 Fluid Properties
Fluid Flow Manual
Fig. 1000-3 Viscosity of Common Liquids (2 of 4) Courtesy of Hydraulic Institute
March 1997
1000-8
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
Fig. 1000-3 Viscosity of Common Liquids (3 of 4) Courtesy of Hydraulic Institute
Chevron Corporation
1000-9
March 1997
1000 Fluid Properties
Fluid Flow Manual
Fig. 1000-3 Viscosity of Common Liquids (4 of 4) Courtesy of Hydraulic Institute
March 1997
1000-10
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
Fig. 1000-4 Viscosity Conversion Equations Equation for Converting Kinematic Viscosity to Flow Times(1) where: T = flow time, seconds (or Engler degrees) V = kinematic viscosity, centistokes (CS) D,E,F,G,H,I = constants given below
1 + EV T = DV + ---------------------------------------------2 3 F + GV + HV + IV Unit
D
E
F
G
H
I
Range (CS)
Saybolt Universal(2) seconds at 100 °F
4.6324
0.03264
0.039302
0.02627
0.002397
0.0000164 6
>1.8
Saybolt Universal(2) seconds at 210 °F
4.6635
0.00677
0.039911
0.000938
0.000280
0.0000027 4
>1.8
Saybolt Furol seconds at 122 °F
0.47170
0.0
0.4895
-0.005213
0.0000718
0.0
>48
Saybolt Furol seconds at 210 °F
0.47916
0.0
0.3797
0.0
0.0001783
0.0
>48
Redwood No. 1 seconds at 140 °F
4.0984
0.0
0.038014
0.001919
0.0000278
0.0000052 1
>40
Redwood No. 2 seconds
0.40984
0.0
0.38014
0.01919
0.000278
0.000521
>73
Engler degrees
0.13158
0.0
1.1326
0.01040
0.00656
0.0
>1.0
Equation for Converting Flow Times to Kinematic Viscosity(1) where: V T A,B,C
BT V = AT – --------------3 T +C
= kinematic viscosity, centistokes (CS) = flow time, seconds (or Engler degrees) = constants given below
Unit
A
B
C
Range
Saybolt Universal seconds at 100 °F
0.21587
11,069
37,003
SUS >32
Saybolt Universal seconds at 210 °F
0.21443
11,219
37,755
SUS >32
Saybolt Furol seconds at 122 °F
2.120
8,920
27,100
SFS >25
Saybolt Furol seconds at 210 °F
2.087
2,460
8,670
SFS >25
Redwood No. 1 seconds at 140 °F
0.244
8,000
12,500
R1 >35
Redwood No. 2 seconds
2.44
3,410
9,550
R2 >31
Engler degrees
7.60
18.0
1.7273
E >1.000
(1) Figure 1000-5 is based on these equations and should provide equal accuracy. (2) The following correction for Saybolt Universal seconds at other temperatures, is small and usually unnecessary:
SUS100°F SUS = CS [ 1 + 0.000061 ( t – 100°F ) ] ------------------------- CS100°F
Chevron Corporation
1000-11
March 1997
1000 Fluid Properties
Fluid Flow Manual
Fig. 1000-5 Viscosity Conversion—Centistokes to Saybolt Universal or Saybolt Furol
March 1997
1000-12
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
1012 Kinematic Viscosity Kinematic viscosity, ν, is defined as the absolute viscosity of a fluid divided by its density. In the metric system, the unit of kinematic viscosity is the stoke and is expressed as follows: ν=µ/ρ (Eq. 1000-5)
where: ν = kinematic viscosity, stokes µ = absolute viscosity, poises ρ = density, grams/cm3 The most commonly used unit of kinematic viscosity is the centistoke (cs = 0.01 stoke). The corresponding unit in English units is ft2/sec. To convert centistokes to English units, multiply by 1.08 x 10-5 to obtain ft2/sec.
1013 Temperature and Viscosity In liquids, an increase in temperature increases the kinetic energy of molecules and thus reduces viscosity. In gases, on the other hand, an increase in temperature increases interaction between molecules, which increases viscosity. Viscosity versus temperature curves for a number of petroleum products and crude oils are included as Figures 1000-6 through 1000-12. These “curves” are plotted on a special graph paper which, for most oils, produces a straight line. This graph paper is described in American Society for Testing Materials (ASTM) Standard D341-43 and may be obtained from ASTM. If the viscosity of an oil is known at a given temperature, its viscosity at other temperatures may be estimated by plotting the known point on this graph paper and drawing a line parallel to one for a similar oil. The viscosity versus temperature curves for a number of gases are given in Figure 1000-18. Under most flow conditions, the viscosity of gases is so low that, for fluid flow problems, it may be assumed to be constant at all ordinary temperatures and pressures. This assumption has been made in plotting the curves for gas and steam flow. The error attributable to assuming constant viscosity in flow calculations will usually be smaller than experimental errors. For most flow problems, the data plotted in the viscosity-temperature charts is sufficiently accurate. This is particularly true in the turbulent flow region. However, when pumping high viscosity liquids under laminar flow conditions the pressure drop is directly proportional to viscosity, and viscosity data must be as accurate as possible. Under these conditions, there is no substitute for a test of the actual material to be pumped.
Chevron Corporation
1000-13
March 1997
1000 Fluid Properties
1000-14
Fig. 1000-6 Viscosity Data—Average San Joaquin Valley Crudes
March 1997
Fluid Flow Manual
Chevron Corporation
Fluid Flow Manual
1000-15
Fig. 1000-7 Viscosity Data—Los Angeles Basin Crudes
Chevron Corporation
1000 Fluid Properties
March 1997
1000 Fluid Properties
1000-16
Fig. 1000-8 Viscosity Data—San Joaquin Valley and Coastal Crudes
March 1997
Fluid Flow Manual
Chevron Corporation
Fluid Flow Manual
Fig. 1000-9 Viscosity Data—Miscellaneous Crudes
Chevron Corporation
1000-17
1000 Fluid Properties
March 1997
1000 Fluid Properties
Fluid Flow Manual
Fig. 1000-10 Viscosity vs. Temperature, Refined Products—Light Products
March 1997
1000-18
Chevron Corporation
Fluid Flow Manual
1000-19
Fig. 1000-11 Viscosity vs. Temperature, Refined Products—Asphalts & Fuel Oils
Chevron Corporation
1000 Fluid Properties
March 1997
1000 Fluid Properties
Fluid Flow Manual
Fig. 1000-12 Viscosity vs. Temperature, Refined Products—Lubricating Oils
March 1997
1000-20
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
Fig. 1000-13 Viscosity of Liquid Ethane, Propane, and N-Butane
Chevron Corporation
1000-21
March 1997
1000 Fluid Properties
Fluid Flow Manual
1014 Viscosity Index The viscosity index is an empirical number indicating the effect of a change of temperature on the viscosity of an oil. A low viscosity index signifies a relatively large change of viscosity. The viscosity index is calculated by comparing the viscosity-temperature relationship of the oil under test with those of two standard oils, one of which is assumed to have a 0 viscosity index and the other a 100 viscosity index. The procedure for calculating the viscosity index is given in ASTM Standard D2270-64.
1015 Pressure and Viscosity Below the critical pressure the viscosity of liquids is essentially constant with respect to changes in pressure. Above the critical pressure, however, viscosity may increase substantially with an increase in pressure. Variation of liquid and gaseous viscosity at high pressures is covered in the American Petroleum Institute (API) Technical Data Book - Petroleum Refining, Chapter 11, Viscosity.
1016 Flow Rate and Viscosity At constant temperature and pressure, the viscosity of most fluids is independent of flow rate. These fluids are called Newtonian fluids. Most petroleum crude oils and products can be considered Newtonian fluids at temperatures above their pour points. For some non-Newtonian fluids, viscosity is a function of flow rate or time. These fluids are further categorized as pseudoplastic, semiplastic or thixotropic. See also Section 1030. At constant temperature, the viscosity of a pseudoplastic fluid decreases as the rate of shear increases. Asphalts, glues, and molasses are pseudoplastic fluids. A semiplastic fluid is a material that will sustain a certain shear stress without flowing. Once this shear stress has been exceeded, the material will behave like a normal fluid, and may have a relatively low viscosity. An example of such a material is a clay slurry such as drilling mud. At constant temperature and shear rate, the viscosity of a thixotropic fluid decreases with time to a minimum value. When the shearing stress is removed, the viscosity increases with time to the value at zero shear. Examples include paints, ketchup, crude oil emulsions and oils near or below their pour points. Finally, the viscosity of a dilatant fluid increases as the rate of shear increases. Certain colloidal solutions are dilatant.
1017 Measurement of Viscosity Liquid viscosity is usually determined by timing the efflux of a given volume of liquid through a standard aperture or capillary tube under specified conditions. The aperture or capillary, together with a heating bath and other necessary parts, forms a viscometer.
March 1997
1000-22
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
The viscosities of petroleum products are generally specified in terms of time, and using one of the following viscometers: •
Saybolt Universal for lubricating oils, gas oils, and crude oils. Saybolt Universal viscosity is the time in seconds needed for the delivery of 60 cc of liquid from the Saybolt viscometer. Temperatures usually employed are 70°F, 130°F, and 210°F.
•
Saybolt Furol for crude residuum and heavy fuel oils. Saybolt Furol viscosity is the time in seconds needed for the delivery of 60 cc of liquid from the Saybolt viscometer equipped with a Furol outlet tube. The test is usually run at a temperature of 122°F. The outflow time of the Furol instrument is approximately one-tenth that of the Universal.
Although Saybolt viscometers are used in petroleum product specification, capillary instruments are more widely used in making viscosity measurements. Capillary instruments give more precise and reproducible results which can be converted to centistokes or Saybolt seconds with the appropriate charts. Test procedures for kinematic viscosities and descriptions of several commercially available viscometers are given in ASTM Standard D-445-65. Equations and tables for converting kinematic viscosity to Saybolt Universal viscosity and Saybolt Furol viscosity are given in Figures 1000-4 and 1000-5.
1018 Viscosity of Blends Figure 1000-16 provides a convenient means of estimating the viscosity of blends of petroleum liquids at a given temperature. Reasonably accurate results can be expected if the two oils being blended are of the same or similar type. If more accurate data are required the blend should be tested.
1019 Viscosity of Brine-in-Oil Emulsions Flow from many producing wells consists of an emulsion in which globules of brine are dispersed in crude oil. The viscosity of such an emulsion can have a direct influence on pumping pressures and line sizes. No theoretical means of estimating a brine-in-oil emulsion’s viscosity over the range of possible brine content is available. However, experimental data compiled by William Woelfin (see Section 1040, reference 9) allows approximation of emulsion viscosity if the clean oil viscosity is known. Given the degree of emulsification (tight, medium, loose) and the percent brine content, the viscosity of the emulsion can be calculated from the viscosity ratio and clean oil viscosity (see Figure 1000-17). Emulsions with higher brine contents (about 60 to 70%), develop a very high viscosity and may show plastic-solid qualities. At an inversion point (usually 70 to 80%) the brine-in-oil emulsion inverts to oil-in-brine and the viscosity drops to roughly that of the brine.
Chevron Corporation
1000-23
March 1997
1000 Fluid Properties
Fig. 1000-14 Viscosities of Hydrocarbon Liquids
March 1997
1000-24
Fluid Flow Manual
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
Fig. 1000-15 Approximate Viscosity-Temperature Relations for Liquid Petroleum Fractions
Chevron Corporation
1000-25
March 1997
1000 Fluid Properties
Fluid Flow Manual
Fig. 1000-16 Viscosity Blending Chart (1 of 2) VISCOSITY BLENDING CHART
1. This chart can be used to estimate the viscosity of a blend of two oils where their viscosities and volume fractions for a given temperature are known. 2. Reasonably accurate answers can be expected only where the two oils being blended are of the same type. 3. Viscosity scales on the chart are based on Chevron Research Company’s blending factor method in which the viscosity scale is drawn proportional to: ln [ l + ln (2ν)] Where ν equals kinematic viscosity in centistokes. Example: Given:
A blend is to be made with 80% consisting of an oil with a 10,000 centistoke viscosity and 20% of an oil with a 100 centistoke viscosity.
Problem:
Determine the viscosity of the blend.
Solution:
1. Connect the point for the higher viscosity oil (10,000 cs) on the left-hand scale with the point for the lower viscosity oil (100 cs) on the right hand-scale with a straight edge. 2. Read the viscosity of the blend at the percentage composition of the blend.
For this example, the viscosity of the blend is 3,200 cs.
March 1997
1000-26
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
Fig. 1000-16 Viscosity Blending Chart (2 of 2)
Chevron Corporation
1000-27
March 1997
1000 Fluid Properties
Fluid Flow Manual
Fig. 1000-17 Viscosity of Brine-In-Oil Emulsions (1 of 2) VISCOSITY OF BRINE-IN-OIL EMULSIONS
1. This chart may be used to estimate the order of magnitude of the effective viscosity of a brine-in-oil emulsion at a given temperature if the viscosity of the clean oil at that temperature and the percent brine in the emulsion are known. 2. To estimate an emulsion viscosity: •
Classify the emulsion as follows: – Tight. Small brine particle size—might occur in a wet well where a high gas-oil ratio results in extremely agitated flow. – Medium. Brine particle size between that of tight and loose emulsions—might occur if a pump is in poor condition or under moderate gas agitation. – Loose. Large brine particle size—might occur in production from a pumping well in which mechanical equipment is in good condition.
•
Find the point on the appropriate curve for percent brine in emulsion and read the corresponding viscosity ratio.
•
Calculate the viscosity of the emulsion by multiplying the viscosity of the clean oil by the viscosity ratio.
3. In general, emulsions are thixotropic fluids with appreciable shear strength. As the percent brine approaches the inversion point (often about 79%) the shear strength of the emulsion may be very high and the emulsion may take on a plastic-solid quality. 4. At the inversion point a brine-in-oil emulsion will invert to an oil-in-brine emulsion. Viscosity of the oil-inbrine emulsion will be approximately that of the brine. Example: Given:
A tight emulsion of 40% brine in 12.3° API Inglewood crude is flowing at 100°F.
Problem:
Determine the viscosity of the emulsion.
Solution:
From Figure 1000-17, viscosity ratio = 5.
From chart on Figure 1000-8, viscosity of clean oil = 34 cs. Viscosity of emulsion = (viscosity of clean) (viscosity ratio). Viscosity of emulsion = (34 cs) (5) = 170 cs.
March 1997
1000-28
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
Fig. 1000-17 Viscosity of Brine-In-Oil Emulsions (2 of 2) VISCOSITY OF BRINE-IN-OIL EMULSIONS
Chevron Corporation
1000-29
March 1997
1000 Fluid Properties
Fluid Flow Manual
Fig. 1000-18 Viscosity of Gases
March 1997
1000-30
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
Fig. 1000-19 Weights of Petroleum Products
Chevron Corporation
1000-31
March 1997
1000 Fluid Properties
Fluid Flow Manual
1020 Gravity In the petroleum industry the mass-volume relationship most commonly used for gases and liquids is gravity. Gravity can be expressed in several ways, for instance, specific gravity and degrees API. The density of a fluid, ρ, is defined as its mass per unit volume. ρ=m/v (Eq. 1000-6)
The density of water at standard conditions of 14.7 psia and 39.4°F (4°C) is 62.43 1bm/cu ft or 1000 kg/m3. The standard conditions for defining water are not equivalent to the more commonly used, which are 14.696 psia and 60°F. The specific weight, γ, of a unit volume of a material depends on its location in the earth’s gravity field. Thus: γ=ρg (Eq. 1000-7)
Specific gravity (SG) is the ratio of the weight of a substance to the weight of an equal volume of water (or air, density 0.0763 lbm/cu ft) at standard conditions. Since specific gravity is related to standard conditions it does not change with location. Specific gravity may also be expressed as a ratio of density. API gravity is expressed in degrees and is related to specific gravity by the equation shown in Figure 1000-23. Other gravity scales exist and conversion tables are available. Since specific gravity is based on water at a standard temperature, substances which change volume with temperature have varying specific gravities. Figure 1000-20 shows the temperature relationship for oils. In Figure 1000-20: •
Specific gravities are referred to water at 60°F
•
The temperature correction to specific gravity is based on the ASTM-IP Petroleum Measurement Tables, Table 24
Figure 1000-19 gives API gravities and corresponding volume measurements for various refined petroleum products. Figures 1000-21 and 1000-22 show the thermal expansion of petroleum fractions. Figure 1000-21 provides a fast means of solving for resultant gravity after blending two oils of different gravities. The graph reproduces the equation on Figure 1000-23. Values obtained from Figure 1000-21 are approximate since no allowance has been made for shrinkage of the blend. Where more accurate data is required, a test should be made of the stocks in question. Specific gravities in Figure 1000-21 are referred to water at 60°F. For use of the chart all gravity data should be at the same temperature.
March 1997
1000-32
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
Fig. 1000-20 Gravity Conversion Chart
Chevron Corporation
1000-33
March 1997
1000 Fluid Properties
Fluid Flow Manual
Fig. 1000-21 Gravity Blending Chart
March 1997
1000-34
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
Fig. 1000-22 Thermal Expansion of Petroleum Fractions (1 of 2)
Chevron Corporation
1000-35
March 1997
1000 Fluid Properties
Fluid Flow Manual
Fig. 1000-22 Thermal Expansion of Petroleum Fractions (2 of 2)
March 1997
1000-36
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
Fig. 1000-23 API and Baumé Gravity Tables Courtesy of Goulds Pumps
Chevron Corporation
1000-37
March 1997
1000 Fluid Properties
Fluid Flow Manual
1021 Example Find the gravity of a blend consisting of 21-1/2% 42°API gravity oil and 78-1/2% 23.50°API gravity oil. On Figure 1000-21, lay a straightedge connecting the specific gravity of the heavier oil at the top of the page (0.913) with the specific gravity of the lighter oil at the bottom (0.815). The intersection of this line with the composition of the blend gives the gravity of the blend: 0.892 specific gravity, or 27.1°API gravity.
1030 Non-Newtonian Fluids It is normal for waxy crude oils to flow from producing wells at elevated temperatures. At these temperatures, the properties of waxy crudes are much like those of normal crude oils. However, when the temperature of a waxy crude approaches the pour point, its consistency and behavior deviate significantly from those of normal crude oils. Waxy crudes’ anomalous characteristics impose special design considerations on facilities that handle them. This section describes the equipment and techniques Chevron Research has developed to measure the properties of waxy crudes, and the procedures and computer programs that the Chevron Research and Technology Company has used to design facilities for handling waxy crudes.
The Sources of Anomalous Behavior Deviations from normal crude oil behavior are caused by precipitation or crystallization of wax from the crude oil as it cools. The wax forms a structure within the oil that changes the consistency, and can develop into a gel —resembling shoe polish— that sets up a “solid” plug requiring significant pressures to move. An added complication with waxy crudes is their history-dependence. The rates at which the wax components crystallize and the nature of the structure that is developed depend on the cooling rate and the amount of stirring or shearing of the oil as it cools. Therefore, the properties measured in the laboratory —specifically near or below the pour point—depend on the temperature profile (thermal history) and shearing profile (mechanical history) of the oil sample before the test. This historydependence is not observed in normal crude oils.
The Importance of Sample Collection and Handling Since the measured properties depend on the concentration and distribution of wax components in the sample and the blend of other non-waxy components, the sample collection procedure must ensure that the sample is truly representative of the oil that will be produced. Sample distortion during drill stem tests may result from deposition of wax in the tubing (and its loss from the sample), dilution by the diesel cushion, wax deposition on cold surfaces in the separator or storage tank, and contamination by other oils left over in the test separator. These sources of error cannot be eliminated, but their effects can be minimized by running a longer drill stem test to increase the wellhead temperature, filling and emptying the separator and storage tanks with the produced crude several times
March 1997
1000-38
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
during the drill stem test, keeping the separator and storage facilities hot, and taking the samples as late in the drill stem test as possible. Sample drums should be clean, preferably epoxy-coated, and (if possible) filled from flowing lines rather than from storage tanks. After the residual gas has been allowed to boil off, the drums should be sealed tightly for shipment to prevent loss of light ends and intrusion of water. In the Chevron Research laboratory the drums are heated and stirred to melt any wax that may have precipitated and deposited on the drum surfaces. This is done in a way that minimizes the loss of light ends. The crude is then put in smaller containers for ease of handling. The collection and handling process imposes a different history on the crude sample than would the production process. Before any testing is done, this history is “erased,” usually just before the test, by heating the sample enough to ensure that all the wax is back in solution. This temperature is often close to the reservoir temperature.
Characterization of Crude Standard laboratory tests are normally used to characterize a crude sample. These tests usually include gravity, pour point, viscosity (in a capillary viscometer at higher temperatures), and water content. If the water content is higher than that expected from the production separators it is removed before the testing begins, because water can have a significant effect on the crude properties. Additional testing includes wax content, microscopic cloud point, specific heat capacity, distillation, and toluene and pentane insolubles. These tests are only done if required for a specific purpose.
1031 Laboratory Measurement of Flow Properties The primary tests for waxy crudes include consistency measurements with a concentric cylinder viscometer, and gel yield strength measurements with a long 1/4-inch diameter tube. This equipment will now be discussed in more detail. For any given project the laboratory testing program must suit the planned or existing facilities. The thermal and mechanical histories of the oil flowing through the producing facilities must be estimated and these estimates used to design the test program. The program design includes a definition of the initial oil temperature (history erasing temperature), temperature profile in time, and shearing profile in time.
Chevron Corporation
1000-39
March 1997
1000 Fluid Properties
Fluid Flow Manual
The temperature profile, T(t), is usually defined by the initial temperature, Ti, ambient temperature, Ta, and cooling parameter, α, where T(t) = Ta + (Ti - Ta) e-αt (Eq. 1000-8)
If the time, t, is in hours then the parameter, α, is in hours-1. As oil flowing in a pipeline cools, the shearing profile changes, increasing from the inlet to the outlet. This shearing (or turbulence) can be characterized by the power dissipation density (in horsepower/cubic foot). Although this change can be simulated in the laboratory, fluid properties are usually not very dependent on the amount of turbulence, and this parameter usually remains fixed in a test. In a typical test of consistency, an oil sample heated to Ti is placed in a device that simulates the shear. This device is immersed in a temperature-controlled bath and cooled according to the predefined temperature profile (Eq.1000-8) while being subjected to shear at a specified rate. When the oil temperature reaches the range of interest, the oil sample is transferred to a concentric cylinder viscometer that is also immersed in the temperature-controlled bath. Cooling continues while the sample is sheared in the viscometer. The temperature in the bath is controlled to within a fraction of a degree. This is an important feature of the laboratory procedure. Concentric cylinder viscometers come in various styles. The Ferranti model favored by Chevron Research is shown in Figure 1000-24. The oil sample is contained in the annular gap between the two cylinders. The outer cylinder is rotated at a controlled speed and the inner one is fixed to a torsion balance. The cylinder diameters, the annular gap between the cylinders, and the rotation speed of the outer cylinder define the shear strain rate imposed on the oil in the gap. The cylindrical area of the inner cylinder and the torque on the torsion balance define the resulting shear stress on the oil. The air bubble under the inner cylinder eliminates end effects. At various temperatures along the cooling profile, the rotational speed of the outer cup is varied to measure shear stress/shear strain rate pairs over a range of shear strain rates. In the Ferranti viscometer this is done at three shear strain rates. In other viscometers pairs can be measured at up to eight shear strain rates. During these shear scans the shear strain rate is held constant long enough to let transient or thixotropic effects decay. The resulting pairs are called equilibrium values. Chevron has found that these measurements can be quite misleading if the thixotropic effects often associated with waxy crude oils are not permitted to decay before the test values are recorded. The temperature range for these consistency tests is usually from the neighborhood of the pour point down to the lowest temperature of interest or to the point where the viscometer goes off scale. The use of the shear stress, shear strain rate pairs produced by these tests is discussed in the section on calculation of flow parameters.
March 1997
1000-40
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
Fig. 1000-24 Ferranti Viscometer
1032 Laboratory Measurement of Gel Strength In many pipelines the crude oil temperature at the inlet is higher than the ambient temperature. In these cases there is a temperature distribution in the oil along the pipeline. If the pipeline is long enough, the oil cools to the ambient temperature. If the flow is stopped, all of the oil in the pipeline will eventually cool to the ambient temperature. The oil near the inlet will cool the most. The oil near the outlet may already have cooled to the ambient temperature under dynamic (flowing) conditions. This oil will have a different cooling history than the oil cooled under static conditions; that is, without shear. The measurement of gel strength must simulate these dynamic and static cooling histories. To test gel strength, the oil sample is heated, placed in the (dynamic) shearing device, immersed in a temperature-controlled bath, and cooled to a transfer temperature, Tt (the oil temperature at a given point in the pipeline when flow stops). The oil is then transferred to a coiled tube (Figure 1000-25) and cooled statically to the test temperature (usually the pipeline ambient temperature) along the defined profile. The coil is carefully crafted to prevent formation of unvented gas pockets during filling. After several hours at the test temperature, the oil is subjected to a pressure difference which is slowly increased until the oil yields or starts to flow. The pressure difference at yielding is used to calculate the breakaway yield strength (BAYS), τb, as follows: tb = Dδp/4L (Eq. 1000-9)
where:
Chevron Corporation
1000-41
March 1997
1000 Fluid Properties
Fluid Flow Manual
D = inside diameter of coil δp = pressure difference across the coil L = length of the coil In general, the BAYS at any temperature Ta depends on the amount of static cooling δT = Tt - Ta. A test program usually includes measuring the BAYS as a function of δT. For many crudes, there is a value for δT that gives a maximum value for BAYS.
1033 Constitutive Relationships The relationship between the load exerted on and deformation of a material is called a constitutive relationship. The familiar relationship between load and deformation (or stress and strain) for steels is linear over a range of stress called the elastic range. The slope of the stress-strain curve is the modulus of elasticity. Beyond the elastic limit (above the yield strength) the curve is not straight. For liquids, there is a similar constitutive relationship. However, instead of stress and strain, the relationship is between shear stress and shear strain rate. Several relationships, or “flow models,” for different liquids are shown in Figure 1000-26. Fig. 1000-25 BAYS Pipe Rig
Fig. 1000-26 Flow Models
Newtonian liquids have a certain constitutive relationship: the shear stress is proportional to the shear strain rate. The proportionality constant (or slope) of the Newtonian relationship is the absolute viscosity µ, a function of temperature—the lower the temperature, the higher the slope. For Newtonian liquids we can express the relationship between shear stress, τ, and shear strain rate, s, as τ = µs (Eq. 1000-10)
March 1997
1000-42
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
If the shear strain rate and the corresponding shear stress are known, then the absolute viscosity is µ = τ/s (Eq. 1000-11)
The absolute viscosity of Newtonian fluids is a function of temperature only. Furthermore, Newtonian liquids will flow even when a very small shear stress is applied. In general, there is no reason for the constitutive relationship for liquids to be straight and to go through the origin. There are many such non-Newtonian relationships or flow models. In Figure 1000-26 the Power Law (or Pseudoplastic) Model goes through the origin but is curved. The Bingham Model is straight but does not go through the origin. The Herschel-Bulkley Model is neither straight nor does it go through the origin. The equations describing the relationship between shear stress, τ, and shear strain rate, s, for these models are as follows: •
Power Law Model: τ = µsn (Eq. 1000-12)
•
Bingham Model: τ = τy + µs (Eq. 1000-13)
•
Herschel-Bulkley Model: τ = τy + µsn (Eq. 1000-14)
For Equations 1000-13 and 1000-14 the parameter τy is the intercept of the curve with the vertical axis. This intercept yield strength is not the same as the BAYS, and one cannot be estimated from the other. Often the BAYS, τb, is larger than τy. In addition, power law liquids have no intercept yield strength but can have a BAYS. Equations 1000-12 and 1000-13 are two-parameter models; to define the flow model one needs either (µ, n) or (µ, τy). Equation 1000-14 requires three parameters to define the flow, (µ, n, and τy). The Herschel-Bulkley model becomes the power law model when τy = 0 and the Bingham model when n = 1. All three become the Newtonian model when τy = 0 and n = 1. Heat loss and pressure drop can be calculated for any of these models. All of the flow parameters just discussed depend upon temperature. With nonNewtonian liquids one can also talk about the apparent viscosity, µa = τ/s (Eq. 1000-15)
Chevron Corporation
1000-43
March 1997
1000 Fluid Properties
Fluid Flow Manual
Apparent viscosity is a function both of temperature and shear strain rate; as the shear strain rate increases, the apparent viscosity decreases. This leads to the notion of shear thinning liquids. In contrast to the Newtonian and power law models, Bingham and Herschel-Bulkley liquids will not flow when a small shear stress is applied, but only when the applied shear stress exceeds the intercept value τy. The study of flow models and the measurement of flow properties is the science of rheology. Often the flow properties and flow model for a liquid are called the rheology of the liquid. As we shall see, the selection of the flow model comes from an analysis of the laboratory data. When plotted as shear stress versus shear strain rate, the laboratory data suggest a model that gives the best fit of the data.
1034 Calculation of Flow Parameters As discussed earlier, the laboratory work measures the equilibrium shear stresses τ associated with shear rates, s, at a uniform temperature. The equipment used dictates the number of (τ,s) pairs measured at each temperature. Some devices, such as the Ferranti viscometer, measure three; others measure up to eight. At higher temperatures, crude oils demonstrate Newtonian behavior. At these temperatures, conventional capillary viscometers can be used to measure the viscosity. The task at this stage of the analysis is to develop a set of curves that shows the variation in flow properties as a function of temperature. There should be a continuous relationship from the Newtonian behavior at higher temperatures to the non-Newtonian behavior at lower temperatures. The viscosity term will be the continuous thread. At higher temperatures, where the liquid is Newtonian, τy will be zero and n will be unity. There are many ways to accomplish this data reduction; we will discuss the method, employing hand calculations and the computer program HOTOIL (see following and Appendix D), that the Company has found most useful. The first step is to generate a plot of shear stress versus temperature with shear strain rate as a parameter as shown in Figure 1000-27. On the right side of the figure the curves are developed from the Newtonian viscosity measurements. Such measurements can normally be represented as a straight line using special graph paper (discussed in Section 1010) that plots kinematic viscosity versus temperature (see Figures 1000-6 through 1000-12). Lower temperature data that deviate from a straight line may indicate the onset of non-Newtonian behavior. At any temperature T, the kinematic viscosity, ν, can be read from this plot and converted to absolute viscosity, µ, with the following equation: µ(T) = ν(T) SG(T) (Eq. 1000-16)
where: SG(T) = specific gravity of the liquid at T
March 1997
1000-44
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
The Newtonian curves on the right side of Figure 1000-27 are calculated with Equation 1000-10, s being the parameter of each curve. The circled points are typical data from a laboratory viscometer. The task is to draw smooth curves for each shear strain rate through these circled points, blending into the Newtonian curves on the right. These curves are also shown. Using the curves in Figure 1000-27, (τ,s) pairs can be read for any temperature. These pairs can be plotted on either linear or log-log graph paper. On linear graph paper, Bingham liquids will appear as a straight line. On log-log graph paper, Power Law liquids will appear as a straight line. The flow model selected should give the best representation of the data over the shear strain rate range of interest. Pairs from Figure 1000-27 at T = T1 are plotted in Figure 1000-28. Using least squares regression techniques, the parameters for Bingham and Power Law equations can be calculated. The resulting equations are •
Power Law: τ = 14.09s0.355 r2 = 0.998
•
Bingham: τ = 20.49 + .837s r2 = 0.973
The term r2 is a measure of how well the curve fits the data; the closer the value is to unity, the better the fit. For these points, the Power Law is a better fit. The same process can be applied at several temperatures. Using Figure 1000-27, three data pairs can be selected at any temperature and the parameters calculated for the selected flow model. These parameters can then be plotted against temperature as shown in Figure 1000-29. For this plot, the absolute viscosity-like term, µ, is converted to a kinematic viscosity-like term, ν, using the inversion of Equation 1000-16: ν(T) = µ (T)/SG(T) (Eq. 1000-17)
Equation 1000-17 relates the data more easily to the higher temperature Newtonian measurements and is easier to use with HOTOIL. The term “viscosity-like” is used because, in the non-Newtonian range, the factor µ is not always given in units of viscosity. For the same reason the units of ν in Figure 1000-29 are stokes. The variable n in Figure 1000-29 is the second parameter for the selected flow model. See also Figure 1000-31. The curves in Figure 1000-29 characterize the constitutive relationship for the liquid over the temperature range of interest. These curves, in tabular form, will be used as input data for HOTOIL. Before discussing this program, we must discuss the equations needed for the hydraulics calculations.
Chevron Corporation
1000-45
March 1997
1000 Fluid Properties
Fluid Flow Manual
Fig. 1000-27 Laboratory Data
March 1997
1000-46
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
Fig. 1000-28 Flow Curve at T1
Chevron Corporation
1000-47
March 1997
1000 Fluid Properties
Fluid Flow Manual
Fig. 1000-29 Flow Parameters
March 1997
1000-48
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
1035 Hydraulics Equations The equations for relating flow rate, Q, to pressure drop, δp, in circular pipes for the four flow models discussed above are known explicitly only for the laminar flow range. These equations can be found in any text on non-Newtonian fluid mechanics. To permit the calculation of Q(δp) or δp(Q) for any flow regime and for any flow model, the generalized non-Newtonian equations can be used. In the laminar range, the generalized equations yield the same results as the modelspecific equations. The generalized non-Newtonian hydraulics equations are shown with the corresponding Newtonian equations in Figure 1000-30. Instead of the flow rate, Q, the equations are expressed in terms of the flow velocity, where
(Eq. 1000-18)
In Figure 1000-30, the two δp(V) equations are identical, using the Fanning friction factor, f, to relate the δp term to the V term. For the laminar flow range, the relationship between f and the Reynolds number is also identical for Newtonian and NonNewtonian. The only difference is in the definition of the generalized Reynolds number which, for non-Newtonian, is expressed in terms of the generalized flow parameters, K’ and n’. For the turbulent flow range, Figure 1000-30 shows the relationship between the friction factor and the Reynolds number. Note that the generalized non-Newtonian equation collapses to the Newtonian equation when n’ = 1 (When n’ = 1, K’ = µ). Similarly, the generalized Reynolds number collapses to the Newtonian Reynolds number when n’ = 1. The equations in Figure 1000-30 for the turbulent flow range friction factor are for smooth tubes. A correlation relating f to Reg for rough tubes has not been published. To estimate the non-Newtonian rough tube turbulent friction factor, HOTOIL uses an approximation:
(Eq. 1000-19)
Chevron Corporation
1000-49
March 1997
1000 Fluid Properties
Fluid Flow Manual
Fig. 1000-30 Hydraulics Equations Newtonian
Generalized Non-Newtonian
δp - V:
Laminar f: Turbulent f: (smooth tube)
Reynolds No.:
δp
=
pressure drop
d
=
liquid density
L
=
pipeline length
gc
=
gravity conversion factor
D
=
pipeline inside diameter
µ
=
liquid viscosity
V
=
liquid velocity
K´, n´
=
generalized flow parameters (see Figure 1000-31)
f
=
friction factor
where: fr = rough-tube friction factor at Reg fs = smooth-tube friction factor at Reg from equation in Figure 1000-30 fnr = rough-tube friction factor for Newtonian liquids at Re = Reg fns = smooth-tube friction factor for Newtonian liquids at Re Newtonian friction factors are calculated with the Colebrook equation. The final element needed to make Figure 1000-30 complete is a criterion for establishing the transition from laminar to turbulent flow. This is provided in a paper by Dodge and Metzner and is reproduced in texts on non-Newtonian flow. The minimum Reynolds number for the turbulent flow regime can be approximated as follows: Ret = 4000 (1 - 0.25 n´) (Eq. 1000-20)
In the computer program the friction factor in the critical range between laminar and turbulent flow is assumed to be constant at fcr, where fcr is the turbulent friction factor at Ret. The laminar range is assumed to stop at Rel where
March 1997
1000-50
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
(Eq. 1000-21)
This is the Reynolds number at the intersection of the laminar friction factor curve and the horizontal line f = fcr. The equations in Figure 1000-30 are valid for any liquid model. The liquid properties enter the equations through the terms K´ and n´. For each of the models discussed above, the relationships between the generalized parameters K´ and n´ and the model-specific flow parameters µ, n, and τy are shown in Figure 1000-31. The equations for the Herschel-Bulkley Model become the equations for the Power Law Model when τy = 0 and for the Bingham Model when n = 1. Finally, the equations in Figure 1000-31 for the Bingham and Herschel-Bulkley models involve the term
(Eq. 1000-22)
where: tw = Dδp/4L, the shear stress at the wall This presents some computational difficulties in that δp is needed to calculate δp. In the computer program this is done in iterative fashion, a value for τw is assumed and then τw is calculated. This process is repeated until the assumed value equals the calculated value.
1036 Computer Program HOTOIL The equations presented in this section are used in the HOTOIL computer program. This program can be used to calculate the non-isothermal pressure drop in a pipeline containing non-Newtonian liquids. HOTOIL makes this calculation by breaking the pipeline into shorter segments, each with a temperature drop of no more than 2°F. Each segment is treated as isothermal. The total pressure drop equals the sum of the pressure drops in individual segments. The program also calculates the internal film heat transfer coefficient used in the temperature drop calculations. Correlations are included for the laminar and turbulent heat transfer coefficients for both Newtonian and generalized non-Newtonian liquids. The effects of friction heating and of pressure on viscosity are optional. HOTOIL assumes that pressure affects only the viscosity-like parameter of nonNewtonian liquids.
Chevron Corporation
1000-51
March 1997
1000 Fluid Properties
Fluid Flow Manual
Fig. 1000-31 Generalized Flow Parameters Constitutive Equation
Generalized Flow Parameters
Power law τ = µsn
Bingham τ = τy + µs
Herschel-Bulkley τ = τy + µsn
1037 Estimating Pipeline Restart Pressure Gradient The BAYS (breakaway yield strength) can be used to estimate the pressure gradient required to restart a gelled pipeline. The estimate is made by inverting Equation 1000-9:
March 1997
1000-52
Chevron Corporation
Fluid Flow Manual
1000 Fluid Properties
(Eq. 1000-23)
where: τb = BAYS Designs usually include a safety factor over this estimate. This model assumes that all of the gelled oil in the section will yield instantaneously at the pipe wall as a rigid body. This is rarely so. For instance, thermal shrinkage may result in autodestruction of the gel. Voids may be present that permit some flow before general yielding. Temperature gradients across the pipe radius may leave a slower cooling, liquid core in large diameter pipelines. Finally, pressure waves may generate much higher local pressure gradients as the wave moves down the pipeline. None of several attempts to model these mitigating effects has been successful. Fortunately, Equation 1000-23 usually overpredicts the pressure gradient needed. The peak value mentioned above may be used for the BAYS. If the design is capable of generating shear stresses significantly larger than this peak value, then the pipeline can be considered restartable. If more accurate estimates are needed, the plot of τb versus δT, along with the estimated temperature distribution along the pipeline, can be used to calculate the required pressure gradient distribution. After the initial yielding, the waxy structure continues to break down and, for a constant applied pressure gradient, the flow rate continues to increase. Estimates can be made of this breakdown process but the laboratory work needed to generate the flow properties and the engineering work needed to do the calculations are very time consuming. These estimates are not done routinely.
1038 Wax Deposition Several attempts have been made to measure wax deposition tendencies in the laboratory. There are, however, no widely accepted ways of measuring wax deposition and no useful models for relating the measurements to field experience. If wax deposition in pipelines is possible, the normal response is to install scraper launchers and traps. Scraping frequency is decided from operating experience.
Mitigating Actions There are several mitigating actions available if the handling of waxy crudes becomes troublesome. Lines can be kept hot with insulation or heaters. Non-waxy crudes, lighter oils (diluents or solvents), and flow-improving additives may be added. Additives can be effective, but are very crude-specific.
Chevron Corporation
1000-53
March 1997
1000 Fluid Properties
Fluid Flow Manual
One should not generalize about the behavior of waxy crudes. Each seems to be different, if not idiosyncratic, and must be considered a unique material. The design features selected and mitigating actions used will, consequently, be site specific.
1040 References 1041 Viscosity Conversion 1.
O’Donnell, R. J. Equations for Converting Different Viscosity Units. American Society for Testing and Materials, Materials Research and Standards, Vol. 9, No. 5. May, 1969.
2.
Standard Method for Conversion of Kinematic Viscosity to Saybolt Universal Viscosity or to Saybolt Furol Viscosity. American Society for Testing and Materials, ASTM Designation D2161-66, ASTM Standards, Vol. 17, 1969.
1042 Viscosity Data 3.
API - Technical Data Book - Petroleum Refining. American Petroleum Institute, 1966.
4.
Standards of Tubular Exchanger Manufacturers Association, Section 10, 1968.
5.
Gallant, R. W. Physical Properties of Hydrocarbons. Houston: Gulf Publishing Co., Houston, 1969.
6.
Sage, B. H., W. D. Yale, and W. N. Lacey. Effect of Pressure on Viscosity of N - Butane and Isobutane. Industrial and Engineering Chemistry, Vol. 31, 1939, p. 223.
7.
Lipkin, M. R., J. A. Davison, and S. S. Kurtz. Viscosity of Propane, Butane and Isobutane. Industrial and Engineering Chemistry, Vol. 34, 1942, p. 976.
8.
Swift, G. W., J. Lorenz, and F. Kurata. Liquid Viscosities Above the Normal Boiling Point for Methane, Ethane, Propane, and N-Butane. AIChE Journal, Vol. 6, No. 3, 1960.
1043 Brine-in-Oil Emulsions 9.
March 1997
Woelfin, Wm. Viscosity of Crude Oil Emulsions. California Oil World and Petroleum Industry, March, 1962.
1000-54
Chevron Corporation
1100 Computer Programs Abstract This section discusses several computer programs that are useful for fluid flow calculations. Contents
Chevron Corporation
Page
1110 Introduction
1100-2
1120 Description of Programs
1100-2
1100-1
March 1997
1100 Computer Programs
Fluid Flow Manual
1110 Introduction Recently, PC-based fluid flow programs have proliferated, and this section does not attempt to cover them all or limit the user to those that are covered. Each program discussed below tends to be strongest in a particular area and best suited for a certain type of calculation. Users are encouraged to find the most productive program for the calculations they are doing, even if it is not mentioned in this manual. In addition to the brief discussions contained in this section, more extended treatment is provided for PCFLOW, PIPEFLOW-2, HOTOIL, HOTOL*, SURGE, and PCSURGE in Appendices D, E, F, G, H, and I respectively.
1120 Description of Programs PCFLOW PCFLOW was written by the proprietors of the Fluid Flow Manual. The program automates equations from selected sections of the manual. Incompressible flow calculations using PCFLOW give more accurate results than are possible using the flow charts in Section 400. Inputs include flow rate, pipe ID, length and roughness, and fluid density and viscosity. Outputs are pressure drop, friction factor, Reynolds number, and velocity. See Appendix D for details on PCFLOW program operation and ways to obtain a copy of the program.
PIPEFLOW-2 PIPEFLOW-2 is a full featured, steady state pressure and flow simulation program. It handles single and multiphase piping systems and networks. It will model complex systems of pipelines, production and injection wells (including reservoir inflow to and from well-boxes), and surface facilities such as compressors and separators. Pressures, temperatures, flow rates, and fluid compositions can be calculated at any point in a network. The program is recommended for problems involving a network, multiphase flow, flashing liquids, or vertical flow, or for compositional modeling during flow calculations. For details on PIPEFLOW-2 program operation see Appendix E.
HOTOIL HOTOIL is a PC based program that handles the full range of non-Newtonian fluid flow models as well as Newtonian flow. HOTOIL is as rigorous as HOTOL* in its heat transfer and Newtonian fluid property correlations. Friction heating and pressure correction to viscosity can be turned on or off during a run. Elevation profiles are accommodated. HOTOIL is very flexible, allowing inputs to be defined in English units, SI units, or any combination thereof. HOTOIL lets the user specify either the upstream or the downstream pressure in either psi or head. See
March 1997
1100-2
Chevron Corporation
Fluid Flow Manual
1100 Computer Programs
Appendix F for details on HOTOIL program operation and ways to obtain a copy of the program.
HOTOL* HOTOL* is useful for calculating pressure drop and heat transfer in pipelines where fluid temperature changes cause significant changes in fluid properties. The program’s fluid property correlations assume the fluid is liquid phase hydrocarbon. The heat transfer routines assume the fluid is at or above ambient temperature. HOTOL* does not consider friction heating or pressure correction to viscosity, nor does it accommodate elevation profiles. HOTOL* is available on the mainframe engineering disk. Details on the use of the program are given in Appendix G. See also Section , “HOTPIPE2.”
SURGE The SURGE program models surges (water hammer) for systems of considerable complexity in which the user may specify valves, pumps, and surge chambers in any arrangement. It can accommodate multiple inlets, outlets, loops, and dead ends, and simulate the normal function of relief valves and check valves. Other types of valves with specified characteristics may be opened or closed at specified times. Pumps may be started or stopped at specified times, or tripped if calculated pressure transients exceed a specified value. Discharge-pressure-controlled relief to pump suction can be simulated, including off-control operation (spill back valve closed or wide open). Initial flow in various branches may be finite or zero. Steel pipe, plastic pipe, concrete lined pipe, hoses, and combinations thereof can be modeled. SURGE does not model pressure pulsations from reciprocating pumps. SURGE is in the Chevron Research and Technology Company computer program library. Gaining access to it is explained in Appendix H. (SURGE was previously available only on Chevron’s VM mainframe computer.) The program is also available on floppy disks from Rob Hohmann, CRTC Richmond, CTN 242-2216 for use on IBM compatible PC’s. See also Section , “PCSURGE” and Section , “HYDRESS.”
PCSURGE PCSURGE is a menu driven input and output system built around the original SURGE program. PCSURGE will run on an IBM compatible PC with a math coprocessor. The math co-processor is necessary because the SURGE calculations are performed in FORTRAN. PCSURGE allows quick, interactive creation and manipulation of SURGE input data files. It allows a user to load an input data file, edit and save the new data file, run SURGE calculations, and view the output on the screen or send the output to a file. The menu system was designed to be self-explanatory. Most users who are familiar with the SURGE program should be able to use PCSURGE with minimal reference to SURGE or PCSURGE documentation.
Chevron Corporation
1100-3
March 1997
1100 Computer Programs
Fluid Flow Manual
For all but the simplest systems, it is important that the user start with a good sketch of the system to be modeled, with all branches and nodes numbered. The sketch should include geometry, elevations, initial flow rates, pressures, etc. Users of PCSURGE should refer to Appendix I for an thorough explanation of the program’s operation, capabilities, inputs, and outputs and for instructions on obtaining a copy of the program.
HOTPIPE2 HOTPIPE2 is a modification of HOTOL*. It retains the rigorous fluid property correlations and heat transfer routines of HOTOL*, but also accommodates elevation profiles. The user can place pump stations and heater stations along the length of the pipeline, or instruct the program to automatically place pumps or heaters when specified pressures and temperatures are reached. Friction heating and pressure correction to viscosity can be turned on and off during a run, allowing results to be compared to programs which do not have those features. HOTPIPE2 runs on an IBM compatible personal computer. It is available from Rob Hohmann, CRTC Richmond, CTN 242-2216.
CPAS The Chevron Production Analysis Simulator (CPAS), is a general-purpose multiphase simulator designed to analyze producing systems from the outer boundary of a reservoir to the outlet of a producing system. It can analyze flows across completions, up tubing strings, and through gas-lift valves and submersible pumps. CPAS is available on Houston VM HOVMB. To run CPAS type CPAS at the VM prompt. Contact Rob Hohmann, CRTC Richmond, CTN 242-2216, for current CPAS support information. CPAS was designed primarily to help engineers in producing organizations to evaluate and locate deficiencies in oil and gas producing systems, and to design production systems. A nodal analysis approach similar to the one used for analyzing centrifugal pump performance is used to evaluate pressure and rate relationships in oil and gas producing systems. With CPAS nodal analysis, engineers can determine the causes of low flow rates, evaluate the relative magnitude of pressure drops through completion zones and strings, identify bottlenecks, decide if a well needs an artificial-lift system, and determine incremental production rates. CPAS has proven to be a valuable tool in the design of more efficient, cost-effective production systems. The simulator can provide additional information, enabling engineers to make more informed decisions, and thereby increase production. Producing systems which can be evaluated by CPAS are: • • • •
Reservoir Perforations Tubing, with all restrictions and artificial lift equipment Flowlines with all production facilities
The performances of reservoir, completion, well, and surface devices can be combined to calculate the operating point for naturally flowing or artificial-lift
March 1997
1100-4
Chevron Corporation
Fluid Flow Manual
1100 Computer Programs
wells. Also, the effects of changing tubing size, flow-line size, submersible pump horsepower, or gas-lift gas rate in a production system can be evaluated and operating points calculated. Analysis Options. The primary analysis options in CPAS are: •
Production system performance (for tubing, flowline, gas lift, and submersible pump)
•
Reservoir vs. production system performance (Inflow performance relationship (IPR) vs. tubing-surface intake)
•
Surface vs. subsurface production system performance (tubing performance vs. flowline intake)
•
Well completion performance
•
Gas lift design
The first four options can be used for oil and gas single or multiphase producing systems. Production System Performance. This option provides pressure-flow rate relationships for a given production system. The effects of changes in one parameter on the system can be evaluated. For example, the effect of changing the tubing diameter on the pressure-flow rate relationship can be shown. A production system, as defined by the simulator, consists of one or a combination of the following devices: •
Surface devices – – –
•
Pipe Pumps Risers
Subsurface devices – – –
Tubing Pumps Gas-lift valves
The behavior of the production system is determined by calculating pressure losses for each device based on multiphase fluid-flow techniques. The total pressure loss is calculated from the wellbore to the outlet of the production system. The effect of each device on total pressure losses in the system can be evaluated with this option.
Chevron Corporation
1100-5
March 1997
1100 Computer Programs
Fluid Flow Manual
The following device parameters can be varied within the same run: Device
Parameter
Tubing
Tubing inner diameter
Pipe
Pipe inner diameter
Pumps
Pump horsepower
Gas-lift valves
Gas-lift rate
The simulator contains various fluid flow correlations and fluid property calculations. The pressure loss for each device is calculated based on user-specified correlations. Reservoir vs. Production System Performance. A producing system consists of a reservoir and a production system. In this option, the effect of changes in one parameter in the producing system can be evaluated to determine whether the system is limited by the reservoir or by the production system (from wellbore to the outlet point). Reservoir performance can be described by an inflow performance curve (IPR) which is constructed from a well’s productively index (PI). The following methods are available to construct an IPR curve: •
For oil – Straight-line PI method (Muskat) – Vogel method – Fetkovich radial method (solution gas and water-drive reservoirs) – Well test method
•
For gas – J method for known C and n – Multipoint backpressure test
This option is also used to evaluate the behavior of a device in a production system (such as tubing intake, flowline intake, pump horsepower, and gas-lift rate). An operating point is calculated for every reservoir and production system curve. Surface vs. Subsurface Production System Performance. This option divides the production system into surface and subsurface production systems and calculates whether the entire production system is limited at the surface or subsurface. For example, a flowline that is too large or tubing that is too small can retard the production rate. This option is effective for evaluating bottlenecks in existing production systems. Well Completion Performance. This option determines the pressure drop across the completion interval for gravel-packed and open-hole completions. The effects of shot density, perforation diameter, and gravel-pack permeability on the production system can be evaluated.
March 1997
1100-6
Chevron Corporation
Fluid Flow Manual
1100 Computer Programs
Gas Lift Design. The CPAS gas-lift option applies a universal design and spacing approach for all types of continuous flow gas-lift valves. It is used to design gas-lift strings based on user specified desired production rate, wellhead pressure, bottomhole conditions, etc. It calculates valve locations by depth with corresponding casing pressure and generates a plot of pressure and gas-lift valve locations by depth. Primary calculations include point of injection, gas-lift valve depths, fluid gradient, and design tubing wellhead pressure. Data Entry and Retrieval. The simulator features user-friendly input menus and an interactive output graphics system, and can be accessed with one command. The menus help users prepare their input files and run the program. The simulator is easy to use and can be successfully run by users with minimal computer knowledge. Output consists of a variety of reports and plots. Standard output includes a onepage summary report and a plot of the results. The following plots represent the available graphics: • • • •
Production system curves (such as tubing intake) IPR vs. production system curves Subsurface vs. surface device curves Completion performance curves
Each plot contains a summary of input and output data and can be displayed on a terminal or routed to a printer.
HYDRESS HYDRESS is a modification of the SURGE program. It was designed to handle fluid transients (surge pressures) in long flexible conduits. Its specific use is to model the time it takes high pressure and low pressure waves to travel from offshore platforms to subsea controls through rubber hose and stainless steel hydraulic control lines. HYDRESS is a mainframe FORTRAN program which resides on OELIB (Offshore Engineering Library) on HOVMB. To access HYDRESS type OELIB at the VM prompt.
ORIFICE ORIFICE is a stand-alone flow meter design and analysis program. It is available on the VM system in the CRTC Technical Library. The full description and operating manual for ORIFICE are contained in Appendix A of the Instrumentation and Control Manual. The orifice design calculations performed by the program are suitable for flow meters in process plants and producing facilities where the orifice meters do not require accuracy better than plus or minus 2 percent. It is not suitable for custody transfer applications, where flow rate calculations must conform to American Gas Association Report No. 3 (AGA-3) Orifice Metering of Natural Gas (ANSI/API 2530).
Chevron Corporation
1100-7
March 1997
1100 Computer Programs
Fluid Flow Manual
ORIFICE performs three kinds of calculations, as follows: •
Sizing new orifices given standard differential pressure and full scale flow rate
•
Reranging existing orifices given orifice diameter and full-scale flow rate
•
Calculating flow rate given differential pressure and orifice diameter
Three kinds of orifice plates are included in the program, as follows: •
Square edge orifice plates for clean liquid, gas, and low-velocity vapor (steam) flows in 2-inch or larger pipe
•
ASME small bore orifice plates (for liquid vapor or gas) usually with 1/2 to 11/2-inch (nominal) pipe size, depending on the type of taps used
•
Quadrant edge orifice (or “quarter circle”) plates for viscous liquids only; often used where the pipe Reynolds number is low (usually below 10,000)
Conic edge and integral orifices are not covered in the ORIFICE program. The program covers four types of pressure taps: •
Flange taps. One inch upstream and 1 inch downstream of the orifice plate
•
Radius taps. One D (pipe inside diameter) upstream and 1/2 D downstream
•
Corner taps. Front and rear face of orifice plate
•
Pipe taps. Two-and-one-half D upstream and 8 D downstream
ORIFICE handles single phase flow for three kinds of fluid flows and their engineering units: •
Liquid. Flow rate units can be in barrels per day (bpd), barrels per hour (bph), gallons per minute (gpm) or gallons per hour (gph), all corrected to 60°F
•
Vapor (steam). Flow rate unit should be in pounds per hour (pph)
•
Gas. Flow rate units should be in standard cubic feet per hour (scfh), i.e., at 60°F and 14.73 psia, which are the base conditions used by AGA-3
The calculations in ORIFICE are based on the latest applicable industry standards and technical reports which contain certain limits. These limits are generalized to be incorporated in the program. ORIFICE may be accessed on the VM system as follows:
March 1997
1.
Log on to HOVMA, HOVMB, or HOVMC
2.
Type in ATT T9ENGR
3.
Type in ORIFICE when you see the first menu for program choice in the Technical Library (ORIFICE is listed under VM programs)
4.
Select screen version desired
1100-8
Chevron Corporation
Fluid Flow Manual
1100 Computer Programs
COMFLOW COMFLOW solves gas pipeline network flow problems using compressible flow equations. The network may consist of any number of upstream locations feeding one downstream location. The program accounts for heat transfer effects. Compressors and let-down valves may be specified. The program is written in FORTRAN and runs on the VM mainframe. To obtain a copy of the program contact Rob Hohmann, CRTC Richmond, CTN 242-2216.
Chevron Corporation
1100-9
March 1997
Appendix A. Conversion Tables
Contents
Chevron Corporation
Page
A1.0
Conversion Factors
A1.1
International System (SI)
A-1
A-2
January 1990
Appendix A
A1.0
Fluid Flow Manual
Conversion Factors The table of conversion factors is based on the Gould Pump Manual table, with some additions. They are not meant to include all possible units or conversions. The exact conversion factors may in some cases disagree with other authorities. English measures—unless otherwise designated, are those used in the United States, and the units of weight and mass are avoirdupois units. Gallon—designates the U.S. gallon. To convert into the imperial gallon, multiply the U.S. gallon by 0.83267. Likewise, the word ton designates a short ton, 2,000 pounds. Properties of water—it freezes at 32°F, and is at its maximum density at 39.2°F. In the multipliers using the properties of water, calculations are based on water at 39.2°F in a vacuum, weighing 62.427 pounds per cubic foot, or 8.345 pounds per U.S. gallon.
A1.1
International System (SI) The governments of many countries have adopted or are converting to the use of the International System of Units. In the United States, the Metric Conversion Act of 1975 declared the coordination and planning of increasing use of the metric system to be government policy. In Canada, the SI system has been fully implemented. Those wishing definitions of SI units and definitive listings of SI conversions between metric and customary (English) units should refer to: API Publication 2564, Manual of Petroleum, Measurement Standards, Chapter 15—Guidelines for the use of the International System of Units (SI) in the Petroleum and Allied Industries.
January 1990
A-2
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Appendix A
Multiply
By
To Obtain
Acres
43,560
Square feet
Acres
4047
Square meters
Acres
1.562 x 103
Square miles
Acres
4840
Square yards
Acre-feet
43,560
Cubic feet
Acre-feet
325,851
Gallons
Acre-feet
1233.48
Cubic meters
Atmospheres
76.0
Cm of mercury
Atmospheres
29.92
Inches of mercury
Atmospheres
33.90
Feet of water
Atmospheres
10.332
Kg/sq meter
Atmospheres
14.70
Lb/sq inch
Atmospheres
1.058
Tons/sq ft
Barrels-oil
42
Gallons-oil
Barrels-Beer
31
Gallons-Beer
Barrels-Whiskey
45
Gallons-Whiskey
Barrels/Day-oil
0.02917
Gallons/Min-oil
Bags or sacks-cement
94
Pounds-cement
Board feet
144 sq in. x 1 in.
Cubic inches
British thermal units
0.2520
Kilogram-calories
British thermal units
777.6
Foot-lb
British thermal units
3.927 x 104
Horsepower-hr
British thermal units
107.5
Kilogram-meters
British thermal units
2.928 x 104
Kilowatt-hr
British thermal units
1.0551 x 103
Joules
Btu/min
12.96
Foot-lb/sec
Btu/min
0.02356
Horsepower
Btu/min
0.01757
Kilowatts
Btu/min
17.57
Watts
Centares (Centiares)
1
Square meters
Centigrams
0.01
Grams
Centiliters
0.01
Liters
A-3
January 1990
Appendix A
January 1990
Fluid Flow Manual
Multiply
By
To Obtain
Centimeters
0.3937
Inches
Centimeters
0.01
Meters
Centimeters
10
Millimeters
Centimeters of Mercury
0.01316
Atmospheres
Centimeters of Mercury
0.4461
Feet of water
Centimeters of Mercury
136.0
Kg/sq meter
Centimeters of Mercury
27.85
Lb/sq ft
Centimeters of Mercury
0.1934
Lb/sq inch
Centimeters/sec
1.969
Feet/min
Centimeters/sec
0.03281
Feet/sec
Centimeters/sec
0.036
Kilometers/hr
Centimeters/sec
0.6
Meters/min
Centimeters/sec
0.02237
Miles/hr
Centimeters/sec
3.728 x 10-4
Miles/min
Cm/sec/sec
0.03281
Feet/sec/sec
Cubic centimeters
3.531 x 10-5
Cubic feet
Cubic centimeters
6.102 x 10-2
Cubic inches
Cubic centimeters
10-4
Cubic meters
Cubic centimeters
1.308 x 10-4
Cubic yards
Cubic centimeters
2.642 x 10-4
Gallons
Cubic centimeters
9.999 x 10-4
Liters
Cubic centimeters
2.113 x 10-3
Pints (liq)
Cubic centimeters
1.057 x 10-3
Quarts (liq)
Cubic feet
2.832 x 10-4
Cubic cm
Cubic feet
1728
Cubic inches
Cubic feet
0.02832
Cubic meters
Cubic feet
0.03704
Cubic yards
Cubic feet
7.48052
Gallons
Cubic feet
28.32
Liters
Cubic feet
59.84
Pints (liq)
Cubic feet
29.92
Quarts (liq)
Cubic feet/min
472.0
Cubic cm/sec
Cubic feet/min
0.1247
Gallons/sec
Cubic feet/min
0.4719
Liters/sec
A-4
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Appendix A
Multiply
By
To Obtain
Cubic feet/min
62.43
Pounds of water/min
Cubic feet/sec
0.646317
Millions gals/day
Cubic feet/sec
448.831
Gallons/min
Cubic inches
16.39
Cubic centimeters
Cubic inches
5.787 x 10-4
Cubic feet
Cubic inches
1.639 x 10-5
Cubic meters
Cubic inches
2.143 x 10-5
Cubic yards
Cubic inches
4.329 x 10-3
Gallons
Cubic inches
1.639 x 10-2
Liters
Cubic inches
0.03463
Pints (liq)
Cubic inches
0.01732
Quarts (liq)
Cubic meters
106
Cubic centimeters
Cubic meters
35.31
Cubic feet
Cubic meters
61023
Cubic inches
Cubic meters
1.308
Cubic yards
Cubic meters
264.2
Gallons
Cubic meters
999.97
Liters
Cubic meters
2113
Pints (liq)
Cubic meters
1057
Quarts (liq)
Cubic meters/hr
4.40
Gallons/min
Cubic yards
764,554.86
Cubic centimeters
Cubic yards
27
Cubic feet
Cubic yards
46.656
Cubic inches
Cubic yards
0.7646
Cubic meters
Cubic yards
202.0
Gallons
Cubic yards
764.5
Liters
Cubic yards
1616
Pints (liq)
Cubic yards
807.9
Quarts (liq)
Cubic yards/min
0.45
Cubic feet/sec
Cubic yards/min
3.366
Gallons/sec
Cubic yards/min
12.74
Liters/sec
Decigrams
0.1
Grams
Deciliters
0.1
Liters
A-5
January 1990
Appendix A
January 1990
Fluid Flow Manual
Multiply
By
To Obtain
Decimeters
0.1
Meters
Degrees (angle)
60
Minutes
Degrees (angle)
0.01745
Radians
Degrees (angle)
3600
Seconds
Degrees/sec
0.01745
Radians/sec
Degrees/sec
0.1667
Revolutions/min
Degrees/sec
0.002778
Revolutions/sec
Dekagrams
10
Grams
Dekaliters
10
Liters
Dekameters
10
Meters
Drams
27.34375
Grains
Drams
0.0625
Ounces
Drams
1.771845
Grams
Dynes
1 x 105
Newtons
Fathoms
6
Feet
Feet
30.48
Centimeters
Feet
12
Inches
Feet
0.3048
Meters
Feet
1/3
Yards
Feet of water
0.0295
Atmospheres
Feet of water
0.8826
Inches of mercury
Feet of water
304.8
Kg/sq meter
Feet of water
62.43
Lb/sq ft
Feet of water
0.4335
Lb/sq inch
Feet/min
0.5080
Centimeters/sec
Feet/min
0.01667
Feet/sec
Feet/min
0.01829
Kilometers/hr
Feet/min
0.3048
Meters/min
Feet/min
0.01136
Miles/hr
Feet/sec
30.48
Centimeters/sec
Feet/sec
1.097
Kilometers/hr
Feet/sec
0.5924
Knots
Feet/sec
18.29
Meters/min
A-6
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Appendix A
Multiply
By
To Obtain
Feet/sec
0.6818
Miles/hr
Feet/sec
0.01136
Miles/min
Feet/sec/sec
30.48
Cm/sec/sec
Feet/sec/sec
0.3048
Meters/sec/sec
Foot-pounds
1.286 x 10-3
British thermal units
Foot-pounds
5.050 x 10-7
Horsepower-hr
Foot-pounds
3.240 x 10-4
Kilogram-calories
Foot-pounds
0.1383
Kilogram-meters
Foot-pounds
3.766 x 10-7
Kilowatt-hours
Foot-pounds/min
2.140 x 10-5
Btu/sec
Foot-pounds/min
0.01667
Foot-pounds/sec
Foot-pounds/min
3.030 x 10-5
Horsepower
Foot-pounds/min
5.393 x 10-3
Gm-calories/sec
Foot-pounds/min
2.280 x 10-5
Kilowatts
Foot-pounds/sec
7.704 x 10-2
Btu/min
Foot-pounds/sec
1.818 x 10-3
Horsepower
Foot-pounds/sec
1.941 x 10-2
Kg-calories/min
Foot-pounds/sec
1.356 x 10-3
Kilowatts
Gallons
3785
Cubic centimeters
Gallons
0.1337
Cubic feet
Gallons
231
Cubic inches
Gallons
3.785 x 10-3
Cubic meters
Gallons
4.951 x 10-3
Cubic yards
Gallons
3.785
Liters
Gallons
8
Pints (liq)
Gallons
4
Quarts (liq)
Gallons-Imperial
1.20095
U.S. gallons
Gallons-U.S.
0.83267
Imperial Gallons
Gallons water
8.345
Pounds of water
Gallons/min
2.228 x 10-3
Cubic feet/sec
Gallons/min
0.06308
Liters/sec
Gallons/min
8.0208
Cu ft/hr
Grains (troy)
0.06480
Grams
A-7
January 1990
Appendix A
January 1990
Fluid Flow Manual
Multiply
By
To Obtain
Grains (troy)
0.04167
Pennyweights (troy)
Grains (troy)
2.0833 x 10-3
Ounces (troy)
Grains/U.S. gal
17.118
Parts/million
Grains/U.S. gal
142.86
Lb/million gal
Grains/Imp gal
14.254
Parts/million
Grams
980.7
Dynes
Grams
15.43
Grains
Grams
.001
Kilograms
Grams
1000
Milligrams
Grams
0.03527
Ounces
Grams
0.03215
Ounces (troy)
Grams
2.205 x 10-3
Pounds
Grams/cm
5.600 x 10-3
Pounds/inch
Grams/cu cm
62.43
Pounds/cubic foot
Grams/cu cm
0.03613
Pounds/cubic inch
Grams/liter
58.416
Grains/gal
Grams/liter
8.345
Pounds/1000 gals
Grams/liter
0.06242
Pounds/cubic foot
Grams/liter
1000
Parts/million
Hectares
2.471
Acres
Hectares
1.076 x 105
Square feet
Hectograms
100
Grams
Hectoliters
100
Liters
Hectometers
100
Meters
Hectowatts
100
Watts
Horsepower
42.44
Btu/min
Horsepower
33,000
Foot-lb/min
Horsepower
550
Foot-lb/sec
Horsepower
1.014
Horsepower (metric)
Horsepower
10.547
Kg-calories/min
Horsepower
0.7457
Kilowatts
Horsepower
745.7
Watts
Horsepower (boiler)
33,493
Btu/hr
A-8
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Appendix A
Multiply
By
To Obtain
Horsepower (boiler)
9.809
Kilowatts
Horsepower-hours
2546
Btu
Horsepower-hours
1.98 x 106
Foot-lb
Horsepower-hours
641.6
Kilogram-calories
Horsepower-hours
2.737 x 105
Kilogram-meters
Horsepower-hours
0.7457
Kilowatt-hours
Inches
2.540
Centimeters
Inches of mercury
0.03342
Atmospheres
Inches of mercury
1.133
Feet of water
Inches of mercury
345.3
Kg/sq meter
Inches of mercury
70.73
Lb/sq foot
Inches of mercury (32°F)
0.491
Lb/sq inch
Inches of water
0.002458
Atmospheres
Inches of water
0.07355
Inches of mercury
Inches of water
25.40
Kg/sq meter
Inches of water
0.578
Ounces/sq inch
Inches of water
5.202
Lb/sq foot
Inches of water
0.03613
Lb/sq inch
Joules
0.9478 x 10-3
Btu
Kilograms
980.665
Dynes
Kilograms
2.205
Pounds
Kilograms
1.102 x 10-3
Tons (short)
Kilograms
103
Grams
Kilograms (force)
9.80665
Newtons
Kilograms-cal/sec
3.968
Btu/sec
Kilograms-cal/sec
3086
Foot-lb/sec
Kilograms-cal/sec
5.6145
Horsepower
Kilograms-cal/sec
4186.7
Watts
Kilogram-cal/min
3085.9
Foot-lb/min
Kilogram-cal/min
0.09351
Horsepower
Kilogram-cal/min
69.733
Watts
A-9
January 1990
Appendix A
January 1990
Fluid Flow Manual
Multiply
By
To Obtain
Kg/meter
0.6720
Lb/foot
Kg/sq meter
9.678 x 10-5
Atmospheres
Kg/sq meter
3.281 x 10-3
Feet of water
Kg/sq meter
2.896 x 10-3
Inches of mercury
Kg/sq meter
0.2048
Lb/sq foot
Kg/sq meter
1.422 x 10-3
Lb/sq inch
Kg/sq millimeter
106
Kg/sq meter
Kiloliters
103
Liters
Kilometers
105
Centimeters
Kilometers
3281
Feet
Kilometers
103
Meters
Kilometers
0.6214
Miles
Kilometers
1094
Yards
Kilometers/hr
27.78
Centimeters/sec
Kilometers/hr
54.68
Feet/min
Kilometers/hr
0.9113
Feet/sec
Kilometers/hr
.5399
Knots
Kilometers/hr
16.67
Meters/min
Kilometers/hr
0.6214
Miles/hr
Km/hr/sec
27.78
Cm/sec/sec
Km/hr/sec
0.9113
Ft/sec/sec
Km/hr/sec
0.2778
Meters/sec/sec
Kilopascals
6.895
Pounds/sq inch
Kilowatts
56.907
Btu/min
Kilowatts
4.425 x 104
Foot-lb/min
Kilowatts
737.6
Foot-lb/sec
Kilowatts
1.341
Horsepower
Kilowatts
14.34
Kg-calories/min
Kilowatts
103
Watts
Kilowatt-hours
3414.4
Btu
Kilowatt-hours
2.655 x 106
Foot-lb
Kilowatt-hours
1.341
Horsepower-hr
Kilowatt-hours
860.4
Kilogram-calories
Kilowatt-hours
3.671 x 105
Kilogram-meters
A-10
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Appendix A
Multiply
By
To Obtain
Liters
103
Cubic centimeters
Liters
0.03531
Cubic feet
Liters
61.02
Cubic inches
Liters
10-3
Cubic meters
Liters
1.308 x 10-3
Cubic yards
Liters
0.2642
Gallons
Liters
2.113
Pints (liq)
Liters
1.057
Quarts (liq)
Liters/min
5.886 x 10-4
Cubic ft/sec
Liters/min
4.403 x 10-3
Gal/sec
Lumber Width (in.) x Thickness (in.)/12
Length (ft.)
Board feet
Meters
100
Centimeters
Meters
3.281
Feet
Meters
39.37
Inches
Meters
10-3
Kilometers
Meters
103
Millimeters
Meters
1.094
Yards
Meters/min
1.667
Centimeters/sec
Meters/min
3.281
Feet/min
Meters/min
0.05468
Feet/sec
Meters/min
0.06
Kilometers/hr
Meters/min
0.03728
Miles/hr
Meters/sec
196.8
Feet/min
Meters/sec
3.281
Feet/sec
Meters/sec
3.6
Kilometers/hr
Meters/sec
0.06
Kilometers/min
Meters/sec
2.287
Miles/hr
Meters/sec
0.03728
Miles/min
Microns
10-6
Meters
Miles
1.609 x 105
Centimeters
Miles
5280
Feet
A-11
January 1990
Appendix A
January 1990
Fluid Flow Manual
Multiply
By
To Obtain
Miles
1.609
Kilometers
Miles
1760
Yards
Miles/hr
44.70
Centimeters/sec
Miles/hr
88
Feet/min
Miles/hr
1.467
Feet/sec
Miles/hr
1.609
Kilometers/hr
Miles/hr
0.8689
Knots
Miles/hr
26.82
Meters/min
Miles/min
2682
Centimeters/sec
Miles/min
88
Feet/sec
Miles/min
1.609
Kilometers/min
Miles/min
60
Miles/hr
Milliers
103
Kilograms
Milligrams
10-3
Grams
Milliliters
10-3
Liters
Millimeters
0.1
Centimeters
Millimeters
0.03937
Inches
Milligrams/liter
1
Parts/million
Million gals/day
1.54723
Cubic ft/sec
Miner’s inches
1.5
Cubic ft/min
Minutes (angle)
2.909 x 10-4
Radians
Newtons
1 x 10-5
Dynes
Newtons
0.22481
Pounds (force)
Newtons
0.10197
Kilograms (force)
Ounces
16
Drams
Ounces
437.5
Grains
Ounces
0.0625
Pounds
Ounces
28.3495
Grams
Ounces
0.9115
Ounces (troy)
Ounces
2.790 x 10-5
Tons (long)
Ounces
2.835 x 10-5
Tons (metric)
Ounces (troy)
480
Grains
A-12
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Appendix A
Multiply
By
To Obtain
Ounces (troy)
20
Pennyweights (troy)
Ounces (troy)
0.08333
Pounds (troy)
Ounces (troy)
31.10348
Grams
Ounces (troy)
1.09714
Ounces (avoir)
Ounces (fluid)
1.805
Cubic inches
Ounces (fluid)
0.02957
Liters
Ounces/sq inch
0.0625
Lb/sq inch
Parts/million
0.0584
Grains/U.S. gal
Parts/million
0.07015
Grains/Imp gal
Parts/million
8.345
Lb/million gal
Pennyweights (troy)
24
Grains
Pennyweights (troy)
1.55517
Grams
Pennyweights (troy)
0.05
Ounces (troy)
Pennyweights (troy)
4.1667 x 10-3
Pounds (troy)
Pounds
16
Ounces
Pounds
256
Drams
Pounds
7000
Grains
Pounds
0.0005
Tons (short)
Pounds
453.5924
Grams
Pounds
1.21528
Pounds (troy)
Pounds
14.5833
Ounces (troy)
Pounds (troy)
5760
Grains
Pounds (troy)
240
Pennyweights (troy)
Pounds (troy)
12
Ounces (troy)
Pounds (troy)
373.2417
Grams
Pounds (troy)
0.822857
Pounds (avoir)
Pounds (troy)
13.1657
Ounces (avoir)
Pounds (troy)
3.6735 x 10-4
Tons (long)
Pounds (troy)
4.1143 x 10-4
Tons (short)
Pounds (troy)
3.7324 x 10-4
Tons (metric)
Pounds of water
0.01602
Cubic feet
Pounds of water
27.68
Cubic inches
Pounds of water
0.1198
Gallons
A-13
January 1990
Appendix A
January 1990
Fluid Flow Manual
Multiply
By
To Obtain
Pounds of water/min
2.670 x 10-4
Cubic ft/sec
Pounds/cubic foot
0.01602
Grams/cubic cm
Pounds/cubic foot
16.02
Kg/cubic meters
Pounds/cubic foot
5.787 x 10-4
Lb/cubic inch
Pounds/cubic inch
27.68
Grams/cubic cm
Pounds/cubic inch
2.768 x 104
Kg/cubic meter
Pounds/cubic inch
1728
Lb/cubic foot
Pounds/foot
1.488
Kg/meter
Pounds/inch
1152
Grams/cm
Pounds (force)
4.44822
Newtons
Pounds/sq foot
0.01602
Feet of water
Pounds/sq foot
4.882
Kg/sq meter
Pounds/sq foot
6.944 x 10-3
Pounds/sq inch
Pounds/sq inch
0.06804
Atmospheres
Pounds/sq inch
2.307
Feet of water
Pounds/sq inch
2.036
Inches of mercury
Pounds/sq inch
703.1
Kg/sq meter
Pounds/sq inch
0.146
Kilopascals
Quadrants (angle)
90
Degrees
Quadrants (angle)
5400
Minutes
Quadrants (angle)
1.571
Radians
Quarts (dry)
67.20
Cubic inches
Quarts (liq)
57.75
Cubic inches
Quintal, Argentine
101.28
Pounds
Quintal, Brazil
129.54
Pounds
Quintal, Castile, Peru
101.43
Pounds
Quintal, Chile
101.41
Pounds
Quintal, Mexico
101.47
Pounds
Quintal, metric
220.46
Pounds
Quires
25
Sheets
Radians
57.30
Degrees
Radians
3438
Minutes
A-14
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Appendix A
Multiply
By
To Obtain
Radians
0.637
Quadrants
Radians/sec
57.30
Degrees/sec
Radians/sec
0.1592
Revolutions/sec
Radians/sec
9.549
Revolutions/min
Radians/sec/sec
573.0
Rev/min/min
Radians/sec/sec
0.1592
Rev/sec/sec
Reams
500
Sheets
Revolutions
360
Degrees
Revolutions
4
Quadrants
Revolutions
6.283
Radians
Revolutions/min
6
Degrees/sec
Revolutions/min
0.1047
Radians/sec
Revolutions/min
0.01667
Revolutions/sec
Revolutions/min/min
1.745 x 10-3
Rads/sec/sec
Revolutions/min/min
2.778 x 10-4
Revs/sec/sec
Revolutions/sec
360
Degrees/sec
Revolutions/sec
6.283
Radians/sec
Revolutions/sec
60
Revolutions/min
Revolutions/sec/sec
6.283
Radians/sec/sec
Revolutions/sec/sec
3600
Revs/min/min
Seconds (angle)
4.848 x 10-4
Radians
Square centimeters
1.076 x 10-3
Square feet
Square centimeters
0.1550
Square inches
Square centimeters
10-4
Square meters
Square centimeters
100
Square millimeters
Square feet
2.296 x 10-5
Acres
Square feet
929.0
Square centimeters
Square feet
144
Square inches
Square feet
0.09290
Square meters
Square feet
3.587 x 10-4
Square miles
Square feet
1/9
Square yards
1/Sq ft/gal/min
8.0208
Overflow rate (ft/hr)
Square inches
6.452
Square centimeters
A-15
January 1990
Appendix A
January 1990
Fluid Flow Manual
Multiply
By
To Obtain
Square inches
6.944 x 10-3
Square feet
Square inches
645.2
Square millimeters
Square kilometers
247.1
Acres
Square kilometers
10.76 x 106
Square feet
Square kilometers
106
Square meters
Square kilometers
0.3861
Square miles
Square kilometers
1.196 x 106
Square yards
Square meters
2.471 x 10-4
Acres
Square meters
10.76
Square feet
Square meters
3.861 x 10-7
Square miles
Square meters
1.196
Square yards
Square miles
640
Acres
Square miles
27.88 x 106
Square feet
Square miles
2.590
Square kilometers
Square miles
3.098 x 106
Square yards
Square millimeters
0.01
Square centimeters
Square millimeters
1.550 x 10-3
Square inches
Square yards
2.066 x 10-4
Acres
Square yards
9
Square feet
Square yards
0.8361
Square meters
Square yards
3.228 x 10-7
Square miles
Temp (°C) + 273
1
Abs. temp (°C)
Temp (°C) + 17.78
1.8
Temp (°F)
Temp (°F) + 460
1
Abs. temp (°F)
Temp (°F) - 32
5/9
Temp (°C)
Tons (long)
1016
Kilograms
Tons (long)
2240
Pounds
Tons (long)
1.12000
Tons (short)
Tons (metric)
103
Kilograms
Tons (metric)
2205
Pounds
Tons (short)
2000
Pounds
Tons (short)
32,000
Ounces
Tons (short)
907.1843
Kilograms
A-16
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Appendix A
Multiply
By
To Obtain
Tons (short)
2430.56
Pounds (troy)
Tons (short)
0.89287
Tons (long)
Tons (short)
29166.66
Ounces (troy)
Tons (short)
0.90718
Tons (metric)
Tons of water/24 hrs
83.333
Pounds water/hr
Tons of water/24 hrs
0.16643
Gallons/min
Tons of water/24 hrs
1.3349
Cu ft/hr
Watts
0.05686
Btu/min
Watts
44.25
Foot-lb/min
Watts
0.7376
Foot-lb/sec
Watts
1.341 x 10-3
Horsepower
Watts
0.01434
Kg-calories/min
Watts
10-3
Kilowatts
Watt-hours
3.414
Btu
Watt-hours
2655
Foot-lb
Watt-hours
1.341 x 10-3
Horsepower-hours
Watt-hours
0.8604
Kilogram-calories
Watt-hours
367.1
Kilogram-meters
Watt-hours
10-3
Kilowatt-hours
Yards
91.44
Centimeters
Yards
3
Feet
Yards
36
Inches
Yards
0.9144
Meters
A-17
January 1990
Appendix A
January 1990
Fluid Flow Manual
A-18
Chevron Corporation
Appendix B. Properties of Water
Chevron Corporation
B-1
January 1990
Appendix B
January 1990
Fluid Flow Manual
B-2
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Appendix B
B-3
January 1990
Appendix B
January 1990
Fluid Flow Manual
B-4
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Appendix B
B-5
January 1990
Appendix C. Design Properties of Pipe
Bulletin TT 330
Chevron Corporation
C-1
January 1990
Appendix C
January 1990
Fluid Flow Manual
C-2
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Appendix C
C-3
January 1990
Appendix C
January 1990
Fluid Flow Manual
C-4
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Appendix C
C-5
January 1990
Appendix C
January 1990
Fluid Flow Manual
C-6
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Appendix C
C-7
January 1990
Appendix C
January 1990
Fluid Flow Manual
C-8
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Appendix C
C-9
January 1990
Appendix C
January 1990
Fluid Flow Manual
C-10
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Appendix C
C-11
January 1990
Appendix C
January 1990
Fluid Flow Manual
C-12
Chevron Corporation
Fluid Flow Manual
Chevron Corporation
Appendix C
C-13
January 1990
Appendix D. PCFLOW Program
Abstract This section discusses the computer program PCFLOW. The program automates many of the equations of fluid flow found in this manual. Contents
Chevron Corporation
Page
D1.0
Description Of PCFLOW
D-2
D2.0
Programming Philosophy
D-2
D3.0
PCFLOW Limitations
D-2
D4.0
Accessing PCFLOW
D-3
D5.0
Installing PCFLOW on Your Computer
D-3
D5.1
Installing PCFLOW from the Technical Standards Website
D5.2
Installing PCFLOW from a Floppy Disk
D6.0
Running PCFLOW
D-4
D7.0
Program Support
D-4
D-1
March 1997
Appendix D
D1.0
Fluid Flow Manual
Description Of PCFLOW PCFLOW is a Windows program that runs in both Windows 3.1 and Windows 95. This new version of PCFLOW was created by converting the original BASIC language menu-driven program to an easy to use Visual BASIC compiled program. The PCFLOW program files include executable files, sample data, text files, and message files. PCFLOW automates the equations presented in the following sections of this manual: • • • • • • •
D2.0
Section 410, “Incompressible Flow” Section 420, “Two-phase Flow” Section 430, “Compressible Flow” Section 440, “Gas Flow At High Pressure Drop (Choked Flow)” Section 500, “Fitting Pressure Drop” Section 600, “Noncircular Conduits” Section 820, “Maximum Surge Pressure in a Simple Case”
Programming Philosophy PCFLOW is easy to use. Its menu-driven screens are self-explanatory, and the equations used for calculations are the same as the ones presented in this manual. There is no user manual for PCFLOW. The user is as responsible for the input values when using PCFLOW as when using a calculator. No data checking is done by the program to constrain the user’s inputs to preconceived values. The only limit on user inputs is the inherent stability of the equations themselves in the Visual BASIC programming environment.
D3.0
PCFLOW Limitations PCFLOW is not intended to replace, compete with, or discourage the use of commercially available piping design and fluid flow programs, which are often more useful in specific design cases. PCFLOW is not an all-purpose piping design program; it simply automates the equations for common fluid flow problems. PCFLOW is not designed to be a data base for fluid properties or piping data. Although PCFLOW provides typical input values in the help-screens and sample data files, the user should refer to this manual or other sources for input data. Fluid properties in the sample data files are from the VM mainframe program PPROP, which is also available in PC version.
March 1997
D-2
Chevron Corporation
Fluid Flow Manual
D4.0
Appendix D
Accessing PCFLOW PCFLOW is available three ways:
D5.0
1.
By accessing the Technical Standards Web site at http://techstds.rrc.chevron.com/tech_standards/ and downloading the program to your hard disk per the instructions given.
2.
By calling, e-mailing, or faxing Technical Standards customer service to request a disk from which the program can be installed to your hard disk. E-MAIL: TECHSTDS (use global address list) CTN: 242-7241 Fax CTN: 242-2157
3.
By purchasing the Chevron Process Simulation Suite, a CD-ROM available from the Process Simulation Team at CRTC.
Installing PCFLOW on Your Computer D5.1
D5.2
Installing PCFLOW from the Technical Standards Website 1.
Create a directory on your hard disk called “PCFLOW”.
2.
Use your web browser to access the Technical Standards Website; click the “Engineering Guidelines Software” link.
3.
Click the “PCFlow” link.
4.
Save the file called “pcflw.exe” to the PCFLOW directory you just created. “pcflw.exe” is a compressed file containing the PCFLOW program files.
5.
After you have saved “pcflw.exe” to your hard disk, double-click the filename from Windows Explorer (Windows 95) or File Manager (Windows 3.x) to decompress the program files.
6.
After the program files have been decompressed, double-click on the file called “pcflow1.exe” to run the program.
Installing PCFLOW from a Floppy Disk You must install the program on your hard disk while you are in the Windows environment. Installation is as follows: Windows 3.1. Insert Disk 1 in your A: or B: floppy drive and go to Program Manager. Click FILE and then select RUN. In the command line, type “a:install.exe” or “b:install.exe”, depending on where Disk 1 was inserted. Then follow the instructions on the screen. Windows 95. Insert Disk 1 in your A: or B: floppy drive. Click START and then select RUN. Type “a:install.exe” or “b:install.exe”, depending on where Disk 1 was inserted and open the file. Then follow the instructions on the screen.
Chevron Corporation
D-3
March 1997
Appendix D
D6.0
Fluid Flow Manual
Running PCFLOW To run PCFLOW, click the icon or the file called “pcflow1.exe”. A menu will appear on the screen and allow you to select the type of calculations you wish to perform. From this point, the program should be self-explanatory. Questions should be directed to the PCFLOW support contact (see Section D7.0) The following suggestions will help you make efficient use of PCFLOW:
D7.0
•
Modify sample data files rather than building input data from scratch.
•
Use the HELP button to access help-screens that will assist in defining input data.
•
Name your data files something other than “DATA1” through “DATA20” to preserve the sample data filenames.
Program Support If you have trouble running PCFLOW on your system or have questions about the program, please contact Yen Chen, CRTC, Richmond, CA, CTN-242-3437. If you have questions regarding the technical aspects of the program (i.e., correlations used, etc.), contact the Fluid Flow Manual sponsor Rob Hohmann, CTN 242-2216. Comments, questions, and suggestions concerning PCFLOW are welcome.
March 1997
D-4
Chevron Corporation
Appendix E. PIPEFLOW-2 Program
Contents
Chevron Corporation
Page
E1.0
Introduction
E-2
E2.0
Data Preparation
E-3
E3.0
Using the Input Menu System
E-3
E4.0
Fluid Types
E-5
E5.0
Calculation Options
E-5
E6.0
General Input Requirements
E-6
E7.0
Pressure Loss Correlations
E-7
E8.0
Friction Calculations
E-8
E9.0
Flow Devices
E-8
E10.0
Fluid Property Correlations
E-9
E11.0
PVT Tables
E-9
E12.0
Output Reports
E-9
E13.0
Calibration Using PIPEFLOW-2
E-1
E-10
October 1992
Appendix E
E1.0
Fluid Flow Manual
Introduction PIPEFLOW-2 is available on Houston VM HOVMB. Contact Rob Hohmann, CRTC Richmond, CTN 242-2216 for current support information. PIPEFLOW-2 includes a generalized, steady state pressure and flow simulator for single phase or multiphase fluid piping systems, and a computerized, mathematical description of fluid flow laws for producing and injection systems. Pressure and temperature losses and flow rates can be calculated at any point in the network for any combination of reservoir deliverability, fluid type, water cut and gas-oil ratio (GOR). PIPEFLOW-2 can also calculate two-phase steam flow behavior. The following discussion is only a brief introduction to the program’s capabilities. A complete three-volume user manual is available from Chevron Exploration and Production Services Company. A multiday hands-on course is also available. PIPEFLOW-2 can handle problems ranging from a single pipe link to a highly complex network with hundreds of junction points. It can also link dynamically with Chevron’s CRS-3D numerical reservoir simulator to simulate an entire oilfield system. Figure E-1 shows facilities that can be modeled using PIPEFLOW-2.
Fig. E-1
Facilities Modeled by PIPEFLOW-2
Optional output reports vary from concise summaries to detailed pressure profiles. A plotting postprocessor can display any calculated result. Most widely used pressure-flow correlations and fluid property techniques are included. New ones can easily be added. The program is dynamically dimensioned. It adjusts itself to the smallest possible increment of computer memory necessary for the given problem. This means that
October 1992
E-2
Chevron Corporation
Fluid Flow Manual
Appendix E
the user with a small problem need not be aware that he is using a large, sophisticated system or pay a premium for more core than is necessary. It also means that problem sizes are limited only by available core.
E2.0
Data Preparation The input menu system is recommended. It uses interactive, full screen forms to guide the user through problem setup. The system then automatically creates an input file and stores it on the user’s permanent disk. Each menu screen has a help function. Alternatively, the input forms guide the user in manually creating a dataset. Alternative approaches to preparing input to PIPEFLOW-2 are illustrated in Figure E-2.
Fig. E-2
E3.0
Input Options, PIPEFLOW-2
Using the Input Menu System The PIPEFLOW-2 input menu system (see Figure E-3) is an interactive computer program that assists in preparing input data for the PIPEFLOW-2 simulator. Its userfriendly features allow modeling of a wide range of problems with minimal knowledge of the simulator. There is extensive logic-checking of input. All major calculation methods contained in PIPEFLOW-2 can be defined through the input menu system. These include single flow stream, network, gas lift analysis, well bore analysis, and PVT table generation. The input menu system allows you to create an input file, edit or browse a file, run the simulator, send notes to user support, obtain the latest changes, enter CMS commands, list available manuals, and view a tutorial. To run the PIPEFLOW-2
Chevron Corporation
E-3
October 1992
Appendix E
Fig. E-3
Fluid Flow Manual
General System Flow
input menu system on the Houston VM, enter the command PIPEFLOW from the VM/CMS environment on HOVMB. After this command is entered a system identification logo appears, followed by the primary option menu. You may then create an input file or use any other feature (see Figure E-4). Fig. E-4
Primary Options
October 1992
E-4
Chevron Corporation
Fluid Flow Manual
E4.0
Appendix E
Fluid Types Any fluid type currently available in PIPEFLOW-2 can be represented by the input menu system. These include the following: • • • • • •
E5.0
Black oil (multiphase oil, water, and gas) Condensate (multiphase condensate, water, and gas) Single phase gas Single phase liquid Steam (multiphase water and water vapor) Compositionally modeled fluids
Calculation Options The system has two primary options, single flow stream calculations and network calculations. A single flow stream is a combination of flow devices connected in a series. This combination makes up a flow link. The single stream option handles only one link at a time. A network consists of any branched or parallel combination of flow links.
Single Flow Stream Calculations For a single liquid flow stream, the program can calculate the pressure drop for a given flow rate or the flow rate for a given pressure drop. Typical single stream applications are: • • • • • • • • •
Calculating the pressure drop over a length of pipe Calculating flow rate for a known pressure drop Finding the capacity of a well, given wellhead or flowline outlet pressure Casing and tubing sizing Pipeline sizing Calculation of well productivity indices Single well production forecasting Submersible pump design analysis Gas life design and analysis
Network Calculations PIPEFLOW-2 network options solve for pressure and flow rates throughout a producing (or injecting) network, including both surface and wellbore flow devices. Some typical network applications are:
Chevron Corporation
•
Modeling an existing gathering system to help locate system bottlenecks
•
Determining the effect of separator conditions on system capacity
•
Determining the overall effect of planned system modifications
•
Improving the design of new systems by rapidly evaluating responses under various conditions
E-5
October 1992
Appendix E
Fluid Flow Manual
•
Determining the combined effect of wellbore and surface facilities on reservoir performance using the PIPEFLOW-2/CRS interface
•
Allocating known total system production to individual wells
Two network solution methods are available, the Newton-Raphson technique and a successive approximation method called DYNER (Dynamic Network Reduction). The Newton-Raphson method is normally used for networks with complex loops and crossovers. It solves a set of nonlinear differential equations that represents balanced flow conditions throughout the system using Newton’s method of successive linear approximations. The DYNER network solution method is more straightforward (and generally faster) than Newton-Raphson. However, it is not capable of handling crossovers or loops and is best suited to tree-branched networks. DYNER calculates flow through each link on successive forward passes and pressure loss on corresponding backward passes through the network until the entire system is balanced.
Flow Tables Solution time for multiphase network problems can often be reduced by first generating a set of pressure-flow tables for all flow links as functions of varying gas and water ratios. PIPEFLOW-2 can do this automatically. The program then interpolates among these tables to get finite-difference pressure-flow derivatives to use in balancing the network. The flow tables can be saved for additional runs, a significant saving on large studies.
E6.0
General Input Requirements To use PIPEFLOW-2, an input data file must be prepared using the menu system or the input forms. This data file consists of the following: •
Basic system information and solution control parameters, such as flow tolerances, pressure limits, and program options.
•
Fluid property data. This may consist of relatively simple correlations that are functions of liquid gravity, curve fits, tables of actual data, simulated compositional calculations, etc.
•
Flow device parameters, such as pipe lengths and diameters, pump horsepower, regulator set pressures, etc. The user can choose the pressure drop correlation (or combination of correlations) to use for each individual device.
•
Parameters such as pressure, flow, temperature, fluid property region, etc. For a well, these include well test flow rates, GOR, water cut, tubing pressure, etc.
Since PIPEFLOW-2 network solution techniques are built around the concept of nodes and links, it will be helpful to define them. •
October 1992
Node. A reference point for system pressures and fluid properties where links meet, begin, or end, or where flow can enter or leave the system
E-6
Chevron Corporation
Fluid Flow Manual
Appendix E
•
Link. A continuous-flow conduit between nodes. A link can be made up of any number of flow devices
•
Device. An individual component of a link. A flow device is a segment of tubing or pipe of constant diameter. Several such devices might make up a tubing string for a well
Each link has a “from” and “to” node. PIPEFLOW-2 assumes the flow direction through the link to be positive from the “from” node to the “to” node. This, however, does not restrict the final solution of flow to that direction. It is helpful to think of nodes where flow enters or leaves the system as boundary nodes, and others as interior nodes. “Node flow” at interior nodes is zero by definition; node flow refers only to flow entering or leaving the system at that point and could be more precisely termed “flow imbalance.”
E7.0
Pressure Loss Correlations For single-phase flow, the pressure loss calculations are straightforward. PIPEFLOW-2 offers the most widely used methods: •
•
Single phase gas – Fundamental flow (recommended) – Panhandle B – Weymouth Single phase liquid – Darcy-Weisbach (recommended) – Hazen and Williams
Multiphase pressure drop calculations are very complex. They require prediction of liquid holdup and flow regime using complicated correlations and iterative calculations that move through each device in small increments. The most widely used pressure-loss-versus-flow-rate relationships are available in PIPEFLOW-2, as follows: •
Chevron Corporation
Multiphase Vertical – Orkiszewski – Duns-Ros – Hagedorn-Brown – Beggs-Brill – Beggs-Brill with Moody friction (recommended for initial trial run) – Beggs-Brill no-slip – Gray (gas condensate) – Gray with Moody friction – Aziz (friction)-Flanigan – Angel-Welchon-Ross (water and free gas)
E-7
October 1992
Appendix E
Fluid Flow Manual
•
•
E8.0
Multiphase chokes – Fortunati (subcritical flow) – Ashford (critical flow) Multiphase Horizontal – Eaton – Eaton-Flanigan – Lockhart-Martinelli – Beggs-Brill – Beggs-Brill with Moody friction (recommended for initial trial run) – Beggs-Brill no-slip – Dukler – Dukler-Flanigan – Eaton (holdup)-Dukler
Friction Calculations Basic friction factor components for liquids and gases are calculated using a modified Wood-Colebrook iterative solution of the Moody diagram. The various pressure loss correlations combine the components in different ways. Some correlations have their own built-in friction calculations. For those that do not, PIPEFLOW-2 provides both the standard version and a modified version which substitutes the Moody-derived friction factors.
E9.0
Flow Devices PIPEFLOW-2 can model the following devices: • • • • • • • • • • • •
October 1992
Well tubing Well annulus Surface pipelines Compressors Pumps Risers Chokes Well productivity and injectivity functions Gas lift valves Regulators User-defined P versus Q functions Check valves
E-8
Chevron Corporation
Fluid Flow Manual
Appendix E
E10.0 Fluid Property Correlations PIPEFLOW-2 calculates hydrocarbon fluid properties such as formation volume factor, solution GOR, viscosity, density, and Z-factor as functions of temperature and pressure from: •
Correlations based primarily on fluid gravities such as Standing, Lasater, Katz, and others
•
Standing’s correlations adjusted to measured data
•
PVT polynomials fitted to laboratory data as functions of temperature and pressure
•
Detailed tables of measured PVT data as functions of temperature and pressure
Steam properties are calculated by subroutines that duplicate the Keenan and Keyes and ASME steam tables.
E11.0 PVT Tables For any of the methods of specifying PVT properties listed above, PIPEFLOW-2 can generate a report showing values of key fluid properties as functions of pressure and temperature. This report can be used to verify that PVT information supplied to the program will result in a sufficiently accurate prediction of fluid behavior in the flow simulation. If fluid composition is known, PIPEFLOW-2 can also pregenerate a table of PVT data that can be inserted in a dataset for a simulation run. This table is constructed by running a set of flash calculations over user-specified ranges of pressure and temperature. Since this section of PIPEFLOW-2 makes use of program components purchased from sources outside the Company, the compositional table generation feature is currently not available to users outside the Company. Detailed documentation of this feature is available as a separate user’s manual.
E12.0 Output Reports The user may choose from a variety of reports. Network calculation results can be reported as tables of pressures, flow rates, and other parameters for each node or link in the model. A separate report for wells can also be requested. For single-stream calculations, or for individual links in a network, a range of pressure profile reports can be requested that: (1) report only inlet and outlet conditions for the entire link, (2) report inlet and outlet conditions for each device, and (3) report conditions at the smallest increments of distance that the program uses for its calculations. Other special reports are available for specific calculation options such as gas lift analysis and flow table generation. Special “debug” reports can sometimes be helpful in finding data problems. Many of the reports may be accompanied by printer plots (sometimes automatically, other times when requested) in the input
Chevron Corporation
E-9
October 1992
Appendix E
Fluid Flow Manual
data. Examples are pressure and temperature profiles, gas lift analysis results, flow table generation results, and PVT property reports.
E13.0 Calibration Using PIPEFLOW-2 Calibration involves adjusting the input model (not the simulator) to match pressure and flow data observed on an existing system. For a single phase network, this can be done analytically by adjusting the single phase flow efficiency factor in each link. In multiphase networks, the problem is more complex. Since there is no direct analytical method of obtaining the relationship of flow to pressure loss in multiphase flow, there is no straightforward way to automatically calculate adjustment factors for an entire network. However, there are several techniques that can be used to match an existing system, including the following:
October 1992
•
Selection of the best pressure loss correlation. PIPEFLOW-2 has options which allow an experienced user to select various correlations and determine the best combination for a given problem
•
Selective adjustment of certain fluid property parameters
•
Use of equivalent lengths and diameters
•
Adjustment of friction components
•
Selective adjustment of external heat transfer coefficient
•
An overall linear pressure loss efficiency factor can be used to adjust calculated pressure losses. PIPEFLOW-2 can automatically calculate this factor to match pressure drops for individual links. In using this approach, the user should recognize that the calibrated model may only be accurate over a narrow range of flow rates and pressure conditions. Extension of the model beyond this range should be checked against additional measurements.
E-10
Chevron Corporation
Appendix F. HOTOIL Program
Abstract This section discusses the computer program HOTOIL. The program calculates pressure drop and heat transfer in hydrocarbon pipelines and pipes where fluid temperature changes cause significant changes in fluid properties. HOTOIL is one of the few tools available that can perform pressure drop calculations for non-Newtonian fluids such as waxy crudes. Contents
Chevron Corporation
Page
F1.0
Description Of HOTOIL
F-2
F2.0
Programming Philosophy
F-2
F3.0
HOTOIL Limitations
F-2
F4.0
Accessing HOTOIL
F-3
F5.0
Installing HOTOIL on Your Computer
F-3
F5.1
Installing HOTOIL from the Technical Standards Website
F5.2
Running HOTOIL from a Floppy Disk
F6.0
Running HOTOIL
F-4
F7.0
Sample Input and Output
F-4
F8.0
Program Support
F-5
F-1
March 1997
Appendix F
F1.0
Fluid Flow Manual
Description Of HOTOIL HOTOIL is a compiled, Microsoft Quick Basic language program. It should run on any IBM-compatible personal computer. The HOTOIL files include the main program file, HOTOIL.EXE, and the following three sample data files: SAMPLEN.HOD - Sample data file for Newtonian fluid. SAMPLEP.HOD - Sample data file for the Power model of a non-Newtonian fluid. SAMPLEB.HOB - Sample data file for the Bingham model of a non-Newtonian fluid.
F2.0
Programming Philosophy HOTOIL’s user interface is designed to be self explanatory and easy to use. This user’s guide is provided for completeness, but the instructions on the HOTOIL screen should be sufficient to lead users through the steps of creating a data file and running the HOTOIL calculations for most pipeline systems. HOTOIL uses the equations presented in Section 400, Friction Pressure Drop, of this manual for normal (Newtonian) fluids. The equations used by HOTOIL for modeling non-Newtonian fluids are presented in Section 1030 of this manual. HOTOIL breaks a pipeline into short calculation segments, each with a temperature drop of no more than 2 degrees F. Each segment is treated as isothermal. The total pressure drop equals the sum of the pressure drops in the individual segments. The program also calculates the internal film heat transfer coefficient used in the temperature drop calculations. Correlations are included for the laminar and turbulent heat transfer coefficients for both Newtonian and generalized non-Newtonian liquids. The effects of friction heating and of pressure on viscosity are optional and can be switched on and off when editing the data. HOTOIL assumes that pressure affects only the viscosity-like parameter of non-Newtonian liquids.
F3.0
HOTOIL Limitations As its name implies, HOTOIL is useful only for single-phase liquid hydrocarbon cases. Several internal fluid property correlations for liquid hydrocarbons would introduce errors for systems with non-hydrocarbon fluids. HOTOIL will accept up to 15 sections of line with different geometry, elevations, external heat transfer coefficients, etc. However, these sections must be connected in series. The program cannot handle piping systems with parallel lines or branching networks. HOTOIL is a steady-state program. It does not address fluid transients associated with opening and closing valves, or starting and stopping pumps.
March 1997
F-2
Chevron Corporation
Fluid Flow Manual
F4.0
Appendix F
Accessing HOTOIL HOTOIL is available three ways:
F5.0
1.
By accessing the Technical Standards Web site at http://techstds.rrc.chevron.com/tech_standards/ and downloading the program to your hard disk per the instructions given.
2.
By calling, e-mailing, or faxing Technical Standards customer service to request a floppy disk from which the program can be installed to your hard disk. E-MAIL: TECHSTDS (use global address list) CTN: 242-7241 Fax CTN: 242-2157
3.
By purchasing the Chevron Process Simulation Suite, a CD-ROM available from the Process Simulation Team at CRTC.
Installing HOTOIL on Your Computer F5.1
F5.2
Installing HOTOIL from the Technical Standards Website 1.
Create a directory on your hard disk called “HOTOIL”.
2.
Use your web browser to access the Technical Standards Website; click the “Engineering Guidelines Software” link.
3.
Click the “HotOil” link.
4.
Save the file called “ho_files.exe” to the HOTOIL directory you just created. “ho_files.exe” is a compressed file containing the HOTOIL program files.
5.
After you have saved “ho_files.exe” to your hard disk, double-click the filename from Windows Explorer (Windows 95) or File Manager (Windows 3.x) to decompress the program files.
6.
After the program files have been decompressed, double-click on the file called “hotoil.exe” to run the program.
Running HOTOIL from a Floppy Disk Windows 3.1. Insert the floppy disk in your A: or B: floppy drive and go to Program Manager. Click FILE and then select RUN. In the command line, type “a:hotoil” or “b:hotoil” depending on where the floppy disk was inserted. Windows 95. Insert the floppy disk in your A: or B: floppy drive. Click START and then select RUN. Type “a:hotoil” or “b:hotoil”, depending on where the floppy disk was inserted, and open the file. Then follow the instructions on the screen.
Chevron Corporation
F-3
March 1997
Appendix F
F6.0
Fluid Flow Manual
Running HOTOIL The following suggestions will help you make efficient use of HOTOIL: Modify sample data files rather than building input data from scratch. Use the F9 key to access help-screens that will provide explanations for the topics where the cursor is currently placed. Give your data files new names to preserve the sample data files. Questions should be directed to the HOTOIL support contact (see Section F8.0) HOTOIL is operated from a single screen. This screen displays all the data necessary to define a flowing pipeline. Large tables are handled by scrolling sections of the screen. One scrolling section displays three lines of a pipeline geometry data table. The other scrolling section displays three lines of fluid properties as a function of temperature. The user controls the operation of HOTOIL with function keys. These keys are defined at the bottom of the screen. The functions that are available at any moment are shown with a dark background. The function key definitions are shown below. F1 - LOAD a data file. You will be asked to point to the file name. F2 - SAVE the current data file. You will be asked to give the file name. F3 - EDIT or change the loaded data file. F4 - ZERO or erase the values in the loaded data file to start afresh. F5 - Run the program with the data shown. F6 - STOP running the program. (This will not exit from HOTOIL.) F7 - INSert a new line into Configuration or Viscosity table. F8 - DELete a line from Configuration or Viscosity table or DELete a file. F9 - HELP information on using HOTOIL. The help is context sensitive. Alt-F9 - HELP information on HOTOIL output. F10 - EXIT the program and return to DOS Alt-F10 - Changes the monitor display to color or monochrome as needed. Monochrome may give better results on some color monitors.
F7.0
Sample Input and Output The input screen for the data file SAMPLEN.HOD is shown below in Figure F-1. This data file is for a Newtonian fluid. The HOTOIL output screen corresponding to the above data is shown in Figure F-2.
March 1997
F-4
Chevron Corporation
Fluid Flow Manual
Appendix F
Fig. F-1
Input Screen for the Sample data file SAMPLEN.HOD
Fig. F-2
Output Screen for the Sample Data File SAMPLEN.HOD !" '
# $ % # (
! 12 5 585 6 43/ 4 743 ! ;
" --'.,
/0 000
304 5 6/0 9/ :40 89 450 1666 13:5 ! 6 39:
7/ /7 38 39 <
66#9 60#3 58#3 76#7
576 545 633 /4:
6#: 6#0 0#4 /#0
56/ 000
304 5 6/0 150: 608 1596 13/5 17/4 15 737 ! 3 703
7/ 74 /8 /: <
8#5 9#5 :#: 63#8
956 /5/ 843 6 675
5#9 6#9 5#3 7#0
600 000
304 5 6/0 1673 1666 1308 15 0:0 1874 16 387 ! / 764
7/ 77 73 74 <
/#: /#5 3#9 5/#7
5 949 5 070 5 :95 3 7:8
10#: 6#6 0#8 6#3
, ! $( , . = 51 61 > 41 31? /1 71 :1
91
! 12 5 495 6 764 4 5074 ! ; ! 12 5 /48 6 9/0 4 54:6 ! ;
F8.0
&&&&&&&&&&!&&&&&&&&&&& !" ( )% $(* +$ $,
81 501@
Program Support If you have trouble running HOTOIL on your system or have questions about the program inputs or outputs, please contact Rob Hohmann, CRTC Richmond, CTN-242-2216. Comments and suggestions concerning the HOTOIL program are also welcomed.
Chevron Corporation
F-5
March 1997
Appendix G. HOTOL* Program
Abstract This section explains the use of the Chevron Research and Technology Company computer program HOTOL*. This program calculates pressure drop, outlet temperature, and heat loss vs. flow rate in a hot oil pipeline. Contents
Chevron Corporation
Page
G1.0
Introduction
G-2
G2.0
Method of Calculation
G-2
G2.1
Establishing Zones
G2.2
Calculating Pressure Drop
G3.0
Input Data Format
G3.1
Number of Sections in Series (Line 1)
G3.2
Section Variables (Line 1+n)
G4.0
Data Input and Program Execution
G-5
G5.0
Program Output
G-5
G6.0
Limitations
G-7
G7.0
Revision History
G-7
G8.0
Equations Used In HOTOL*
G-7
G8.1
Basic Relations
G8.2
Property Variations
G8.3
Flow Regime Boundaries and Friction Factors
G8.4
Derivation of Iteration Equations
G8.5
Corrections to Isothermal Pressure Drop
G9.0
References
G-3
G-17
G-1
January 1990
Appendix G
G1.0
Fluid Flow Manual
Introduction If fluid temperature is constant along a pipe, then pressure drop is a function of the liquid properties, flow rate, and line size (see Section 410). In a hot oil pipeline, however, the temperature of the liquid is higher than the ambient temperature, and is not constant, but decreases as the oil flows through the pipe. As the temperature of the oil changes, its liquid properties change, particularly the viscosity. The HOTOL* computer program evaluates these temperature changes and accounts for changes in the following liquid properties of the oil: specific gravity, density, bulk modulus, specific heat, thermal conductivity, and kinematic viscosity. HOTOL* does not consider friction heating, or pressure correction to viscosity, nor does it accommodate elevation profiles. To be analyzed by HOTOL* a pipeline must consist either of one section or of sections connected in series. Each section is described by its length, outside diameter, wall thickness, internal roughness, ambient temperature, external heat transfer coefficient, number of identical parallel lines, and whether or not the fluid is mixed at the section inlet (see Section G3.0).
G2.0
Method of Calculation HOTOL* defines each relevant liquid property as a function of temperature. These correlations are shown in Section G8.2. This makes it possible to express the Reynolds number as a function of temperature and pipeline geometry for any given flow rate. The program can then define the following flow regimes in terms of the Reynolds numbers at the boundaries of the regimes: • • • •
Laminar flow Transition flow Turbulent flow Hyperturbulent flow
Both the Reynolds number for the turbulent/hyperturbulent boundary and the friction factor in the hyperturbulent regime are functions of internal roughness and inside diameter. Flow regime boundaries and friction factors are defined in Section G8.3. Given the pipeline data, the system inlet temperature and flow rate, and using the flow regime boundaries defined in Section G8.3, HOTOL* begins the calculation. The following terms are used in this discussion:
January 1990
•
Section. A length of pipe over which all relevant geometrical and heat transfer variables are constant. Sections are described thoroughly by the input data
•
Zone. A subdivision of a section—made by the program—that has a single flow regime
G-2
Chevron Corporation
Fluid Flow Manual
G2.1
Appendix G
Establishing Zones First, HOTOL* computes the temperature at each flow regime boundary within each section. It then divides the pipeline into a number of zones. HOTOL* establishes the end of one zone and the beginning of the next where either of the following occurs: •
The temperature of the liquid decreases enough to cause a change in the flow regime
•
The end of the current section is reached
Within each zone the pipeline section variables remain constant; the Reynolds number changes, but the flow regime remains the same. Once established, the pipeline zones are the basic subdivisions on which all subsequent calculations are performed. When a pipeline zone is terminated by a change in flow regime, an iterative heat balance (see Section G8.4) is used to generate the length of the zone. A similar iteration is used to calculate the zone outlet temperature when the end of the zone is also the end of the section. In both cases the outlet temperature for one zone is the inlet temperature for the next.
G2.2
Calculating Pressure Drop Once the pipeline has been divided into zones, the Darcy-Weisbach equation (see Section G8.1) is applied to each zone to calculate an isothermal pressure drop across the zone, based on zone inlet temperature. The isothermal friction factor is selected from the correlations in Section G8.3. These isothermal pressure drops are then corrected for: • • •
Radial property variation Natural convection Axial property variation
An appropriate correction factor for each effect is described in Section G8.5.
G3.0
Input Data Format The data necessary to define the pipeline geometry, flow rates, liquid properties and temperature conditions are entered by means of statements in a data file. Temperature and viscosity are related by a set of data pairs. Figure G-1 is an example of a data file. The line-by-line layout of this file is as follows: •
Line 1. Number of sections (4) connected in series in the pipeline system
This is followed by one line for each section (n = total number of sections): •
Chevron Corporation
Lines 1+n; (n=1 to 4). Number of lines in parallel (1, 1, 1, 1); flow is mixed at the inlet of this section? ('yes', 'no', 'no', 'no'); length in feet (4000, 18600, 18600, 4000); outside diameter in inches (21, 21, 21, 21); wall thickness in
G-3
January 1990
Appendix G
Fluid Flow Manual
Fig. G-1
Example Data File
inches (0.375, 0.375, 0.375, 0.375); roughness in inches (0.0018, 0.0018, 0.0018, 0.0018); external heat transfer coefficient in Btu/hr/sq. ft./F (0.25, 13.3, 0.432, 0.25); ambient temperature in degrees F (60, 48, 48, 60) This is followed by one line for the entire pipeline (n = total number of sections): •
Line 2+n; (n=4). Name of fluid (18-character maximum)('FUTURE A-960'), gravity (15.9), UOP characterization factor (11.7), number of temperature/viscosity data pairs(2)
This is followed by one line for each data pair (m = number of data pairs): •
Line 2+n+m; (n=4, m=1 to 2). Temperature (100, 210), kinematic viscosity (centistokes)(854, 35.5)
This is followed by one line for the entire pipeline:
G3.1
•
Line 3+n+m; (n=4, m=2). Temperature of fluid at inlet (100)
•
Line 4+n+m. First flow rate (60°F bbl/hr) (500), last flow rate (2000), increment (1500)
Number of Sections in Series (Line 1) Enter the number of series-connected sections on this line. Each section is defined by a set of data lines. See Section G6.0 for limitations.
G3.2
Section Variables (Line 1+n) This line gives the values of the relevant section variables for each pipeline section. Sections are connected in series in the order listed, starting at the inlet. •
January 1990
Number of lines in parallel. Enter the number of identical lines in parallel. HOTOL* cannot handle a general looped-line case or network systems
G-4
Chevron Corporation
Fluid Flow Manual
Appendix G
•
Flow is mixed at the inlet of this section (yes/no). Consider the flow to be mixed at: – – – –
G4.0
The entrance to the first section A division into parallel lines A junction of parallel lines An increase or decrease of inside diameter by a factor of 1.2 or more
•
Internal roughness. A value of 0.0018 inches (0.00015 feet) is common for steel pipe
•
External Heat Transfer Coefficient. For buried and submarine lines, refer to Section 900.
Data Input and Program Execution HOTOL* is on the Engineering Department computer program library, ENGR, on COVMA. To access ENGR type “ATT T9ENGR”. When prompted for a program name type “HOTOL*”. To use HOTOL*, a user data file must be created or edited either before attaching ENGR or in the course of using ENGR. If the user data file is created independently of ENGR, a filetype of DATA must be specified. HOTOL* program operation is menu-driven. The user may choose either to see a sample data file or run the program. After program execution he may either see the output on the terminal or save it in a file. The saved file name will be HOTOL OUTPUT. If a file by that name already exists on the user’s disk the output cannot be saved and the program will have to be rerun to generate the output again.
G5.0
Program Output HOTOL* output (see Figure G-2) includes a summary of some of the input data. The results of the computer calculations are appropriately labeled. For each flow rate, the program prints out the following:
Chevron Corporation
•
Liquid temperature at the outlet of each section
•
Pressure drop (psi) and heat loss rate (million Btu/Hr) for each individual section
•
Cumulative pressure drop and heat loss rate for the pipeline, up to the outlet of the section in question
G-5
January 1990
Appendix G
Fig. G-2
Fluid Flow Manual
HOTOL* Sample Output
January 1990
G-6
Chevron Corporation
Fluid Flow Manual
G6.0
G7.0
Appendix G
Limitations •
HOTOL* applies only to liquid phase hydrocarbon pipelines because of the fluid property vs. temperature correlations used
•
HOTOL* uses internal heat transfer coefficient correlations that are valid for liquid cooling only. If the inlet temperature to the pipeline system is below the ambient temperature the program will not run. If the liquid should cool to below the ambient temperature at any point in the pipeline, the program will preemptively assume that the liquid temperature and ambient temperature are equal, and continue the calculations on an isothermal basis for as long as necessary. The pressure drops calculated on this basis will be too low. In this case, a warning to this effect will appear in the output (see sample output)
•
HOTOL* is capable of handling pipelines consisting of fifty series sections or less in its standard form. If the number input is greater than fifty, the program will print an error message. HOTOL* can be extended to handle any number of series sections. If greater capacity is needed contact CRTC’s computer systems analyst
•
HOTOL* cannot handle branch lines or loop lines other than multiple identical parallel lines
•
The HOTOL* analysis is valid only for Newtonian fluids. It is not applicable if the fluid in question is cooled below its pour point temperature
Revision History HOTOL* was originally prepared by J. C. Sebastian (May 1968). The program logic was revised and expanded by W. A. Ebert (September 1976). G. H. Horne subsequently modified the program for multiple sections in series (November, 1977). The documentation (Design Practice A-871-3) was rewritten by G. W. Williams (October 1978) and revised by G. H. Horne (February 1979). Design Practice A-871-3 was republished as Appendix G of the Fluid Flow Manual in October 1988.
G8.0
Equations Used In HOTOL* G8.1
Basic Relations Darcy-Weisbach Equation
(Eq. G-1)
Chevron Corporation
G-7
January 1990
Appendix G
Fluid Flow Manual
where: L = length of zone, ft f = friction factor ρ = liquid density, lbm/ft3 Di = inside diameter, ft V = average liquid, velocity ft/sec ∆P = pressure drop, lbf/ft2 g = conversion factor, ft lbm/sec2 lbf
Heat Loss Rate ∆Q = w ⋅ Cp ⋅ ∆T (Eq. G-2)
where: ∆Q = rate of heat loss, Btu/sec w = mass flow rate, lbm/sec Cp = specific heat at average section bulk temperature, Btu/lbm/°F ∆T = change in bulk temperature from inlet to outlet, °F
G8.2
Property Variations The variations of fluid properties with temperature are calculated as follows:
Specific Gravity at 60°F
(Eq. G-3)
Density Per Section G9.0, reference 1. ρ = D1 + D2(T - 60) + D3(T - 60)2 (Eq. G-4)
where: ρ = density, lbm/ft3 T = temperature, °F D1 = 62.4 SG60
January 1990
G-8
Chevron Corporation
Fluid Flow Manual
Appendix G
D2 = 62.4 [(8 x 10-4)SG60 - (1.05 x 10-3)] D3 = 62.4 [(6 x 10-7)SG60 - (4.9 x 10-7)]
Bulk Modulus
(Eq. G-5)
Specific Heat Per Section G9.0, reference 1. Cp = Co (C1 + C2T) (Eq. G-6)
where: Cp = specific heat, Btu/lbm/°F T = temperature, °F Co = 0.055 Kw + 0.35 C1 = 0.681 - 0.308 SG60 C2 = 0.000815 - 0.000306 SG60 Kw = Watson (or UOP) characterization factor=(Tb)1/3/SG60 Tb = normal (average) boiling point, °R SG60 =
specific gravity at 60°
Thermal Conductivity k = K1 + K 2 T (Eq. G-7)
where: k = thermal conductivity, Btu/Hr °F ⋅ ft T = temperature, °F K1 = 0.08934 - (6.7407 x 10-4) (°API) + (5.77 x 10-6) (°API)2 K2 = -2.976 x 10-5 + (1.104 x 10-6)(°API) - (2.201 x 10-8) (°API)2
Chevron Corporation
G-9
January 1990
Appendix G
Fluid Flow Manual
Kinematic Viscosity Input pairs of kinematic viscosity and temperature, (ν, T), are fitted to a curve of the form: ln[1 + ln(2ν)] = A - B ln(T + 460) (Eq. G-8)
where: ν = kinematic viscosity, cs T = temperature, °F
(Eq. G-9)
(Eq. G-10)
G8.3
Flow Regime Boundaries and Friction Factors For inside diameters ≤2 inches (per Section G9.0, reference 1):
January 1990
Flow Regime
Reynolds Number Range
Friction Factor
Laminar
0
