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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

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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:

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Requesting Signature

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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.”

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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:

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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

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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:

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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

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100 Introduction Abstract This section describes the scope of the Fluid Flow Manual and discusses its basic approach to fluid flow problems.

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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

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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.

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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

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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.

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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).

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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.

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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).

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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.

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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.

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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)

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400 Friction Pressure Drop

Fluid Flow Manual

Fig. 400-14 Flow Pattern Map for Horizontal Two-Phase Flow

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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

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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:

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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

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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).

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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

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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.

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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)

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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

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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

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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)

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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.

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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.

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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.

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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

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400 Friction Pressure Drop

Fluid Flow Manual

Fig. 400-29 Design Charts for Gas Flow at High Pressure Drop (2 of 2)

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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.

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400 Friction Pressure Drop

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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.

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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

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500-8

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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

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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

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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)

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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

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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

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Fluid Flow Manual

Fig. 800-1

800 Surge Pressure

Average Bulk Modulus for Crude Oil, Fuel Oil, Gas Oil, and Gasoline

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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

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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

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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

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900 Pipeline Flow

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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

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900-2

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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

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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

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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.

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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

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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

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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

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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

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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.

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900-11

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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

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1000 Fluid Properties

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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

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1000-2

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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.

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Fig. 1000-1 Conversion Factors for Absolute Viscosity

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Fluid Flow Manual

1000 Fluid Properties

Fig. 1000-2 Viscosity Conversion—From Various Terms to Saybolt Universal (1 of 2) Courtesy of Hydraulic Institute

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Fluid Flow Manual

Fig. 1000-2 Viscosity Conversion—From Various Terms to Saybolt Universal (2 of 2) Courtesy of Hydraulic Institute

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1000-6

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1000 Fluid Properties

Fig. 1000-3 Viscosity of Common Liquids (1 of 4) Courtesy of Hydraulic Institute

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1000 Fluid Properties

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Fig. 1000-3 Viscosity of Common Liquids (2 of 4) Courtesy of Hydraulic Institute

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1000-8

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1000 Fluid Properties

Fig. 1000-3 Viscosity of Common Liquids (3 of 4) Courtesy of Hydraulic Institute

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1000-9

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1000 Fluid Properties

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Fig. 1000-3 Viscosity of Common Liquids (4 of 4) Courtesy of Hydraulic Institute

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1000-10

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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

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1000-11

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1000 Fluid Properties

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Fig. 1000-5 Viscosity Conversion—Centistokes to Saybolt Universal or Saybolt Furol

March 1997

1000-12

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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.

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1000-13

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1000 Fluid Properties

1000-14

Fig. 1000-6 Viscosity Data—Average San Joaquin Valley Crudes

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1000-15

Fig. 1000-7 Viscosity Data—Los Angeles Basin Crudes

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1000 Fluid Properties

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1000-16

Fig. 1000-8 Viscosity Data—San Joaquin Valley and Coastal Crudes

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Fig. 1000-9 Viscosity Data—Miscellaneous Crudes

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Fig. 1000-10 Viscosity vs. Temperature, Refined Products—Light Products

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1000-18

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1000-19

Fig. 1000-11 Viscosity vs. Temperature, Refined Products—Asphalts & Fuel Oils

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1000 Fluid Properties

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Fig. 1000-12 Viscosity vs. Temperature, Refined Products—Lubricating Oils

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1000-20

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1000 Fluid Properties

Fig. 1000-13 Viscosity of Liquid Ethane, Propane, and N-Butane

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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.

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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.

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Fig. 1000-14 Viscosities of Hydrocarbon Liquids

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Fig. 1000-15 Approximate Viscosity-Temperature Relations for Liquid Petroleum Fractions

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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.

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Fig. 1000-16 Viscosity Blending Chart (2 of 2)

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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.

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Fig. 1000-17 Viscosity of Brine-In-Oil Emulsions (2 of 2) VISCOSITY OF BRINE-IN-OIL EMULSIONS

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Fig. 1000-18 Viscosity of Gases

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Fig. 1000-19 Weights of Petroleum Products

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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.

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Fig. 1000-20 Gravity Conversion Chart

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Fig. 1000-21 Gravity Blending Chart

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Fig. 1000-22 Thermal Expansion of Petroleum Fractions (1 of 2)

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Fig. 1000-22 Thermal Expansion of Petroleum Fractions (2 of 2)

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Fig. 1000-23 API and Baumé Gravity Tables Courtesy of Goulds Pumps

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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

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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.

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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.

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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:

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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)

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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)

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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

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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.

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Fig. 1000-27 Laboratory Data

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Fig. 1000-28 Flow Curve at T1

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Fig. 1000-29 Flow Parameters

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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)

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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

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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.

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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:

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(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.

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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.

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1100 Computer Programs Abstract This section discusses several computer programs that are useful for fluid flow calculations. Contents

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1110 Introduction

1100-2

1120 Description of Programs

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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

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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.

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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

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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.

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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.

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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).

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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

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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.

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Appendix A. Conversion Tables

Contents

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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.

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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

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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.

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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.

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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

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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

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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

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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

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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

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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: •

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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

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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

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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

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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 !;

" --'.,

/0000

304 56/0 9/ :40 89 450 1666 13:5 ! 639:

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 56/0 150: 608 1596 13/5 17/4 15737 ! 3703

7/ 74 /8 /: <

8#5 9#5 :#: 63#8

956 /5/ 843 6675

5#9 6#9 5#3 7#0

600000

304 56/0 1673 1666 1308 150:0 1874 16387 ! /764

7/ 77 73 74 <

/#: /#5 3#9 5/#7

5949 5070 5:95 37:8

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

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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:

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•

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)

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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

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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

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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

View more...
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

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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

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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

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M.I.

Current Owner:

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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.”

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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:

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Document Control, Room 50-4328 Chevron Research and Technology Company 100 Chevron Way (P.O.Box 1627) Richmond, CA 94802 Comments

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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

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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

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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:

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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

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100 Introduction Abstract This section describes the scope of the Fluid Flow Manual and discusses its basic approach to fluid flow problems.

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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.

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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

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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.

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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).

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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

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Fig. 400-12 10-Inch Pipe—1/4-Inch Wall (2 of 2)

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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

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400 Friction Pressure Drop

Fig. 400-13 12-Inch Pipe—1/4-Inch Wall (2 of 2)

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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.

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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.

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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).

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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.

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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.

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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)

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Fluid Flow Manual

Fig. 400-14 Flow Pattern Map for Horizontal Two-Phase Flow

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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

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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:

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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

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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).

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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

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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)

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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.

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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)

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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

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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)

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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

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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)

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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.

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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.

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400-59

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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.

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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

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Fluid Flow Manual

Fig. 400-29 Design Charts for Gas Flow at High Pressure Drop (2 of 2)

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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.

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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.

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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.

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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

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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

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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

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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.

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500-5

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500-6

Equivalent Length of Valves and Fittings in Feet

500 Fitting Pressure Drop

Fig. 500-3

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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

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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

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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

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500 Fitting Pressure Drop

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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

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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

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Fig. 1000-5 Viscosity Conversion—Centistokes to Saybolt Universal or Saybolt Furol

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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.

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Fig. 1000-6 Viscosity Data—Average San Joaquin Valley Crudes

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Fig. 1000-7 Viscosity Data—Los Angeles Basin Crudes

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Fig. 1000-8 Viscosity Data—San Joaquin Valley and Coastal Crudes

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Fig. 1000-9 Viscosity Data—Miscellaneous Crudes

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Fig. 1000-10 Viscosity vs. Temperature, Refined Products—Light Products

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Fig. 1000-11 Viscosity vs. Temperature, Refined Products—Asphalts & Fuel Oils

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Fig. 1000-12 Viscosity vs. Temperature, Refined Products—Lubricating Oils

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Fig. 1000-13 Viscosity of Liquid Ethane, Propane, and N-Butane

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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.

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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.

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Fig. 1000-14 Viscosities of Hydrocarbon Liquids

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Fig. 1000-15 Approximate Viscosity-Temperature Relations for Liquid Petroleum Fractions

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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.

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Fig. 1000-16 Viscosity Blending Chart (2 of 2)

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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.

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Fig. 1000-17 Viscosity of Brine-In-Oil Emulsions (2 of 2) VISCOSITY OF BRINE-IN-OIL EMULSIONS

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Fig. 1000-18 Viscosity of Gases

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Fig. 1000-19 Weights of Petroleum Products

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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.

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Fig. 1000-20 Gravity Conversion Chart

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Fig. 1000-21 Gravity Blending Chart

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Fig. 1000-22 Thermal Expansion of Petroleum Fractions (1 of 2)

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Fig. 1000-22 Thermal Expansion of Petroleum Fractions (2 of 2)

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Fig. 1000-23 API and Baumé Gravity Tables Courtesy of Goulds Pumps

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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

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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.

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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.

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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:

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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)

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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)

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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

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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.

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Fig. 1000-27 Laboratory Data

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Fig. 1000-28 Flow Curve at T1

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Fig. 1000-29 Flow Parameters

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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)

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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

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(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.

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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:

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(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.

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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.

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Woelfin, Wm. Viscosity of Crude Oil Emulsions. California Oil World and Petroleum Industry, March, 1962.

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1100 Computer Programs Abstract This section discusses several computer programs that are useful for fluid flow calculations. Contents

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1110 Introduction

1100-2

1120 Description of Programs

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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

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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.

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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

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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.

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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.

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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).

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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:

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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

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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.

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Appendix A. Conversion Tables

Contents

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A1.0

Conversion Factors

A1.1

International System (SI)

A-1

A-2

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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.

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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

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Fluid Flow Manual

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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

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Appendix B. Properties of Water

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B-1

January 1990

Appendix B

January 1990

Fluid Flow Manual

B-2

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Fluid Flow Manual

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Appendix B

B-3

January 1990

Appendix B

January 1990

Fluid Flow Manual

B-4

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Fluid Flow Manual

Chevron Corporation

Appendix B

B-5

January 1990

Appendix C. Design Properties of Pipe

Bulletin TT 330

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C-1

January 1990

Appendix C

January 1990

Fluid Flow Manual

C-2

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Fluid Flow Manual

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Appendix C

C-3

January 1990

Appendix C

January 1990

Fluid Flow Manual

C-4

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Fluid Flow Manual

Chevron Corporation

Appendix C

C-5

January 1990

Appendix C

January 1990

Fluid Flow Manual

C-6

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Fluid Flow Manual

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Appendix C

C-7

January 1990

Appendix C

January 1990

Fluid Flow Manual

C-8

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Fluid Flow Manual

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Appendix C

C-9

January 1990

Appendix C

January 1990

Fluid Flow Manual

C-10

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Fluid Flow Manual

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Appendix C

C-11

January 1990

Appendix C

January 1990

Fluid Flow Manual

C-12

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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

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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.

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D-2

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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.

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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.

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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

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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

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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

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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

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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

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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 !;

" --'.,

/0000

304 56/0 9/ :40 89 450 1666 13:5 ! 639:

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 56/0 150: 608 1596 13/5 17/4 15737 ! 3703

7/ 74 /8 /: <

8#5 9#5 :#: 63#8

956 /5/ 843 6675

5#9 6#9 5#3 7#0

600000

304 56/0 1673 1666 1308 150:0 1874 16387 ! /764

7/ 77 73 74 <

/#: /#5 3#9 5/#7

5949 5070 5:95 37:8

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): •

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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

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