Chevron Fluid Flow

ffm50___.pdfffm100__.pdfffm200__.pdfffm300__.pdfffm400__.pdfffm500__.pdfffm600__.pdfffm800__.pdfffm900__.pdfffm1000_.pdfffm1100_.pdfffmappa_.pdfffmappb_.pdfffmappc_.pdfffmappd_.pdfffmappe_.pdfffmappf_.pdfffmappg_.pdfffmapph_.pdfffmappi_.pdf

50 Using This Manual

AbstractThis 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 ManualScope and ApplicationThe 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 experi-ence. 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.

OrganizationThis 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 prob-lems, (5) fluid and pipe properties, (6) available computer programs.

TabsThe colored tabs in the manual will help you find information quickly.

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 facilityMarch 1997 50-2 Chevron Corporation

Fluid Flow Manual 50 Using This ManualOther Company ManualsThe text sometimes refers to documents in other Company manuals. These docu-ments carry the prefix of that manual. The prefixes are defined here:

Prefix Company ManualCIV Civil and StructuralCMP CompressorCOM CoatingsCPM Corrosion PreventionDRI DriverELC ElectricalEXH Heat Exchanger and Cooling

TowerFFM Fluid FlowFPM Fire ProtectionHTR Fired Heater and Waste Heat

RecoveryICM Instrumentation and ControlIRM Insulation and RefractoryMAC General MachineryNCM Noise Control in DesignsPIM PipingPMP PumpPPL PipelinePVM Pressure VesselTAM TankUTL UtilitiesWEM WeldingChevron Corporation 50-3 March 1997

50 Using This Manual Fluid Flow ManualFig. 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

Pipe dimensions Appendix C

Fluid properties 1000

Heat transfer properties 900March 1997 50-4 Chevron Corporation

100 Introduction

AbstractThis section describes the scope of the Fluid Flow Manual and discusses its basic approach to fluid flow problems.

Contents Page

110 Scope of the Fluid Flow Manual 100-2120 Basic Elements of Pressure Drop 100-2130 Importance of the Darcy-Weisbach Equation 100-2140 Nomenclature 100-3150 References 100-3Chevron Corporation 100-1 January 1990

100 Introduction Fluid Flow Manual110 Scope of the Fluid Flow ManualThe 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 DropThe 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 EquationThe dominant effect in most fluid flow systems is friction pressure drop. The Darcy-Weisbach 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:

(Eq. 100-2)where:

h = head loss, ft

f = friction factor

L = pipe length, ft

h fLD------V2

2g-------=January 1990 100-2 Chevron Corporation

Fluid Flow Manual 100 IntroductionD = 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 NomenclatureThis manual does not contain a master list of nomenclature. Equation variables are defined following each equation.

150 ReferencesThe following selection of general references is supplemented by specific refer-ences in the applicable sections of the manual.

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.Chevron Corporation 100-3 January 1990

200 Static Pressure

AbstractThis section discusses the equations for calculating static pressure and head.

Contents Page

210 Definition of Static Pressure 200-2220 Equations for Static Pressure and Head 200-2Chevron Corporation 200-1 January 1990

200 Static Pressure Fluid Flow Manual210 Definition of Static PressureThe 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. Pres-sures 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.

220 Equations for Static Pressure and HeadEquation 200-1 expresses the static pressure in psi generated by a column of liquid:

(Eq. 200-1)

where:Ps = static pressure, psi

h = height of liquid column, ft

= fluid density, lbm/cu ft

Fig. 200-1 Static Pressure

Psh144---------=January 1990 200-2 Chevron Corporation

Fluid Flow Manual 200 Static PressureEquation 200-2 expresses head, in feet, equivalent to an arbitrary pressure, in psi:

(Eq. 200-2)

where:H = head, ft

P = pressure, psi


The conversion of head in feet to pressure in pounds per square inch for water at 60F is as follows:

Ps = 0.433 h

h = 2.31 Ps

H P144---------=Chevron Corporation 200-3 January 1990

300 Acceleration Pressure Drop

AbstractThis section presents the equations for calculating pressure drop due to fluid accel-eration and discusses the phenomenon in terms of changes in pipe geometry and change of phase.

Contents Page

310 Definition of Acceleration Pressure Drop 300-2320 Equations for Acceleration Pressure Drop 300-2330 Discussion 300-2Chevron Corporation 300-1 October 1992

300 Acceleration Pressure Drop Fluid Flow Manual310 Definition of Acceleration Pressure DropAn 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 DropVelocity head is calculated using the following equation:

(Eq. 300-1)where:

h = velocity head in feet of liquid, ft


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:

(Eq. 300-2)where:

P = static pressure drop, psi


V1 = upstream fluid velocity, ft/sec

V2 = downstream fluid velocity, ft/sec

Determination of acceleration pressure drop is particularly important when calcu-lating the NPSHA of reciprocating pumps, to avoid cavitation. See Section 100 of the Pump Manual.

330 DiscussionEquations 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

h V2

2g-------=

P V2

2 V12

( )2g 144---------------------------------=October 1992 300-2 Chevron Corporation

Fluid Flow Manual 300 Acceleration Pressure Dropthis 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 deceler-ates. However, since even carefully designed diffusers can recover only a fraction of the original static pressure, this recovery is not attempted in normal piping situa-tions. 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 dropproduced by acceleration and friction effectsoccurs across pipe entrances and reducers, not their exits and enlargements.Chevron Corporation 300-3 October 1992

400 Friction Pressure Drop

AbstractThis 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).

Contents Page

410 Incompressible Flow 400-2411 Fitting Loss Coefficients

412 Pipe and Tube Friction Losses

420 Two-phase Flow 400-7421 Pressure Drop Calculations

422 Friction Pressure Drop Correlations

423 Fitting and Bend Losses

424 Acceleration Pressure Loss

425 Elevation Losses426 Accuracy of Friction Pressure Drop Calculation427 Liquid Holdup Correlation

430 Compressible Flow 400-17440 Gas Flow At High Pressure Drop (Choked Flow) 400-19441 Assumptions

442 Use of Design Charts

443 Sonic Flow

444 Choked Flow

445 Temperature Variations446 Effects of Valves and FittingsChevron Corporation 400-1 March 2001

447 Deviation from Assumptions

450 References 400-24

400 Friction Pressure Drop Fluid Flow Manual410 Incompressible FlowThe 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.

(Eq. 400-1)where:

h = head loss, ft

f = Darcy friction factor

L = pipe length, ft

D = pipe inside diameter, ft


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.

(Eq. 400-2)where:

P = pressure drop, psi

W = mass flow rate, lbm/hr

= fluid density, lbm/ft3

411 Fitting Loss CoefficientsFitting 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.

(Eq. 400-3)

h fLD------

V2

2g-------=

P fLD------

W2

D4 7.4 1010( )---------------------------------------=

P K fLD------+ W

2

D4 7.4 1010( )---------------------------------------=March 2001 400-2 Chevron Corporation

Fluid Flow Manual 400 Friction Pressure Dropwhere:K = fitting loss coefficient (from Section 500)

412 Pipe and Tube Friction LossesFor 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:

(Eq. 400-4)where:

Re = Reynolds number

= 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 accu-rately. 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 func-tion 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/diam-eter). Figure 400-2 gives the relative roughness for various diameters and types of pipe.

Re 0.526WD-------------------=Chevron Corporation 400-3 March 2001

400 Friction Pressure Drop Fluid Flow ManualFig. 400-1 Moody Diagram Crane Technical Paper 410-C, 1984, Flow of Fluids. Courtesy of Crane ValvesMarch 2001 400-4 Chevron Corporation

Fluid Flow Manual 400 Friction Pressure DropFig. 400-2 Relative Pipe Roughness (/D) and Friction Factors (f) for Complete Turbulence Crane Technical Paper 410-C, 1984, Flow of Fluids. Courtesy of Crane ValvesChevron Corporation 400-5 March 2001

400 Friction Pressure Drop Fluid Flow ManualMany equations have been proposed to approximate the Moody Diagram friction factors. One of these is the Chen Equation (Equation 400-7), which is simple, accu-rate, and stable when used on small computers:

(Eq. 400-7)where:

= absolute pipe roughness, ft

D = pipe diameter, ft

= relative roughness

Typical values of roughness, , are as follows:

f 24 log10 (A1-A2)-------------------------------------------

2=

A1

D----

3.7065----------------=

A2 5.0452Re---------------- log10 A3( )=

A3

D----

1.1098

2.8257-----------------------

7.149Re

------------- 0.8981

+=

D----

Pipe Absolute Roughness,

Plastic 0.000005 ftSmooth Steel, New 0.00015 ftGalvanized Steel 0.00042 ft

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 ftMarch 2001 400-6 Chevron Corporation

Fluid Flow Manual 400 Friction Pressure DropWhere accurate performance data are required, pressure losses should be deter-mined 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).

420 Two-phase FlowThis 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.

LimitationsThe 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, PIPEPHASE will yield better results. In addition, the limited experimental data available indicate that when the mixture velocity is less than 3 ft/sec the accu-racy of the friction pressure drop calculations is very poor.

This method is not fully applicable to flow of water-oil-gas (WOG) mixtures (so-called three-phase flow). This case requires the more powerful calculation methods of PIPEPHASE.

General ReferencesReference 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 CalculationsAs in single-phase flow, pressure drop in two-phase flow consists of several compo-nents, 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.Chevron Corporation 400-7 March 2001

400 Friction Pressure Drop Fluid Flow Manual422 Friction Pressure Drop CorrelationsMore 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.

The five most widely used correlations are compared in Reference 3 using experi-mental 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 calcu-lating a two-phase density, tp, and viscosity, tp, evaluated at the pipe entrance pressure and temperature and assumed constant for the friction and fitting pressure drop calculation, as follows:

tp = l () + g (1.0 - )(Eq. 400-9)

tp = l () + g (1.0 - )(Eq. 400-10)

where: = fluid density, lbm/ft3

= absolute viscosity, cp

tp = two-phase

l = liquid phase

g = gas phase

= 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:

(Eq. 400-11)where:

Vm = velocity of mixture, ft/sec


RetpVmDtp

tp1490------------

---------------------

0.527WtDtp

---------------------= =March 2001 400-8 Chevron Corporation

Fluid Flow Manual 400 Friction Pressure DropWt = 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 condi-tions exist or a more accurate determination is desired, the Colebrook formula (Equation 400-12) may be used.

(Eq. 400-12)where:

= 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 Nikuradses Formula at high Reynolds numbers (when the right term in bracket approaches zero). The same absolute wall rough-ness, , should be used for both single-phase and two-phase flow calculations. The pressure drop due to friction may then be calculated as follows:

(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

Wt = Wl + WgThis method of calculating friction pressure drop has the following characteristics:

It reduces to the single-phase flow equations if the flow rate of either phase is zero.

1f

------ 2 log10

3.7D------------

2.51Retp f-----------------+

=

Pfriction fLD----

tp144---------

Vm2

2go-----------=

1.35 10 11 f LD5-------

Wt2

tp---------=Chevron Corporation 400-9 March 2001

400 Friction Pressure Drop Fluid Flow Manual Except for the assumptions concerning two-phase density and viscosity (Equa-tions 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 426).

423 Fitting and Bend LossesFor 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:

(Eq. 400-14)where:

K = single phase velocity head loss

424 Acceleration Pressure LossAcceleration 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:

(Eq. 400-15)where:

Z = compressibility factor

T = temperature, R

R = gas constant

P1 = upstream pressure, psi

P2 = downstream pressure, psi


PfittingsKtp144

------------

Vm2

2go----------- 1.35 10 11

KW t2

D4tp--------------- = =

Pacceleration1.87 10 13 WtWgZRT

D4P1P2--------------------------------------------------------- Ptp=March 2001 400-10 Chevron Corporation

Fluid Flow Manual 400 Friction Pressure Drop425 Elevation LossesThe 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.

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:

(Eq. 400-16)where:

= 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 corre-lation 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 corre-lation 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:

(Eq. 400-17)where:

h = static elevation, ft

tpLAgg LA11+

LA----------------------------------------- Rgg R11+= =

Pelevationtp144--------- h=Chevron Corporation 400-11 March 2001

400 Friction Pressure Drop Fluid Flow ManualThe flow density is calculated using Equation 400-16, where the gas density is eval-uated 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.

426 Accuracy of Friction Pressure Drop CalculationThe friction pressure drop calculation was checked against carefully screened exper-imental data from a number of investigators. Partial results of the comparison are shown in Figure 400-5. A more extensive discussion of the calculations and a statis-tical analysis of the errors are available in References 3 and 5.

The values shown in Figure 400-5 represent the percent deviation between the calculated pressure drop and experimental data, as shown in Equation 400-18.

(Eq. 400-18)Figure 400-6 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:

(Eq. 400-19)Based on the range of deviation for horizontal slug flow, the actual value of a calcu-lated pressure drop of 10 psi would be (approximately) between the following values:

(Eq. 400-20)and

(Eq. 400-21)

%devPcalc Pexp

Pexp------------------------------------- 100=

PexpPcalc

1 % dev100---------------+

------------------------=

P 101 0.18( )+--------------------------- 12.2 psi= =

P 101 0.12+------------------- 8.9 psi= =March 2001 400-12 Chevron Corporation

Fluid Flow M

anual400 Friction Pressure Drop

Chevron Corporation400-13

March 2001

F of the Oil and Gas Journalig. 400-3 Flow Pattern Map for Horizontal Two-Phase Flow O. Baker: Multiphase Flow in Pipelines Nov. 1958. Courtesy

400 Friction Pressure DropFluid Flow

Manual

March 2001

400-14Chevron Corporation

Fig. 400-4 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

Fluid Flow Manual 400 Friction Pressure DropA comparison between calculated and experimental friction pressure drop for vertical flow is not available.

427 Liquid Holdup CorrelationThe density of two-phase mixtures at any section in the pipe may be calculated if the liquid holdupthe fractional volume of the pipe occupied by the liquidis 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 400-6.

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:

(Eq. 400-22)The variable X in Equation 400-22 is defined as follows:

(Eq. 400-23)where:

Fr = Froude number = V2/Dg

Fig. 400-5 Calculated vs. Experimental Frictional Pressure DropHorizontal Flow Dukler, Wicks and Cleveland, Frictional Pressure Drop in Two-Phase Flow: A Compar-ison of Existing Correlations for Pressure Loss and Hold-up. From AlChE Journal Vol. 10, #1m 1964. Used by permission.

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

Rg 1 R1Y

g1-----

1X---- 1 1+

-----------------------------------= =

X Re16---

Fr18---

14---

----------------------=Chevron Corporation 400-15 March 2001

400 Friction Pressure Drop Fluid Flow Manual = liquid volume fraction at pipe entrance

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.

(Eq. 400-24)where:

Gm = tpVm

= mass velocity mixture (lbm/ft2-sec)

Fig. 400-6 Correlation for the Flow Pattern Y From Holdup in Gas-Liquid Flow by G.A. Hughmark, Chemical Engi-neering Progress, Vol. 58, April, 1962, p. 62

Re

D GmR11 Rgg+( )

-------------------------------------

1490-------------------------------------=March 2001 400-16 Chevron Corporation

Fluid Flow Manual 400 Friction Pressure DropRe Retp (from Equation 400-11)

(Eq. 400-25)

(Eq. 400-26)where:

= specific volume

The calculation procedure is to evaluate Re, Fr, and 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 400-5. 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 400-6) and experimental (Reference 3) values of the liquid holdup varies by 25%. For vertical flow not as much exper-imental data are available. For the available data the deviation between experi-mental and calculated liquid holdup does not exceed 10 percent (see Section 450, Reference 7).

430 Compressible FlowPressure drop in gas transmission lines can be calculated in four ways, as follows:

Using the PIPEPHASE program, discussed in Section 1100

Applying the widely used Weymouth and Panhandle fundamental flow equa-tions (see Figure 400-7 on page 400-19)

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 PIPEPHASE consider heat transfer, and only PIPEPHASE 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.

FrVm

2

gD-----------

Q1 Qg+( ) A( )2

gD-----------------------------------------= =

W11

W11 Wgg+------------------------------------

Q1Q1 Qg+--------------------= =Chevron Corporation 400-17 March 2001

400 Friction Pressure Drop Fluid Flow ManualWeymouth and Panhandle EquationsThe general formula for compressible flow has the following form:

(Eq. 400-27)where:

Q = flow rate, SCFDTo = 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 400-7

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 Equa-tion.

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 400-7 both as presented in the literature and as derived without empirical components.March 2001 400-18 Chevron Corporation

Fluid Flow Manual 400 Friction Pressure Drop440 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 pres-sure below this value will not increase velocity. This maximum gas velocityin a pipe of constant cross-sectional areais 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, pres-sure 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 devel-oped a graphical solution, which is the basis for Figure 400-10.

Fig. 400-7 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 = pipeline efficiency, ranging from 0.94 (new pipe) to 0.88 (old rough pipe)Z = compressibility

= (From Source 4.) Accurate within 10% if Pr1.0

or if Pr>0.8 and Tr>1.1

A = Tr16

Tr = T/TcTc = critical temperature, RT = operating temperature,RPr = P/PcPc = critical pressure, psiaP = operating pressure, psiaSources:

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.

10.41Pr

Tr4.04

--------------- 0.29( )APr8

+Chevron Corporation 400-19 March 2001

400 Friction Pressure Drop Fluid Flow Manual441 AssumptionsThe charts in Figure 400-10 (and Lapples 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 ChartsThe design charts in Figure 400-10 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 400-8 gives approximate values of K for various gases.

The design charts in Figure 400-10 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 400-9, 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.

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)

Fig. 400-8 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 1.4March 2001 400-20 Chevron Corporation

Fluid Flow Manual 400 Friction Pressure Dropwhere:G = mass velocity, lbm/ft2sec

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 ftlbf/lbmoleR

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.

443 Sonic FlowAfter considering these preliminaries, use of the charts is generally self-explana-tory. However, caution is advised concerning the area on each chart below the diag-onal 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 reser-voir 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

Fig. 400-9 Flow Conditions High Pressure GasChevron Corporation 400-21 March 2001

400 Friction Pressure Drop Fluid Flow ManualFig. 400-10 Design Charts for Gas Flow at High Pressure Drop (1 of 2) Perry and Chilton, Engineers Handbook, 5th Ed. Used by permission of The McGraw-Hill Companies.

1. To use design charts in Figure 400-10:

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

d. Estimate K (ratio of specific heats) from Figure 400-8.

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 80F 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 ftL = 20 + L = 20 + (2)(0.256)(23) = 31.8 ft (see Section 500)

2. Calculate maximum mass velocity, GmaxTo = 460 + 80 = 540RPo = (200 + 14.7)(144) = 30,900 lbf/ft

2

MW = 29 lbm/mole

3. Find Flow RateP3 = (14.7)(144) = 2120 lbf/ft

2

P3/Po = 2120/30,900 = 0.0685G/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

Gmax

gcPoevo

-------------0.5

Po

gcMW

eRTo-----------------

0.5 lbm

ft2

sec-------------------= =

Gmax 30 90032.17( ) 29( )

2.718( ) 1546( ) 540( )---------------------------------------------0.5

, 627lbm

sec( ) ft( )2-------------------------= =March 2001 400-22 Chevron Corporation

Fluid Flow Manual 400 Friction Pressure DropFig. 400-10 Design Charts for Gas Flow at High Pressure Drop (2 of 2) Perry and Chilton, Engineers Handbook, 5th Ed. Used by permission of The McGraw-Hill Companies.Chevron Corporation 400-23 March 2001

400 Friction Pressure Drop Fluid Flow Manualreduction in P3 cannot be transmitted back to the pipe exit to result in further pres-sure 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 FlowFor 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 VariationsIn 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 FittingsThe 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 effec-tive overall length used to calculate the fL/D parameter.

447 Deviation from AssumptionsVarious deviations from the assumptions in Lapples 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 varia-tion 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 devia-tions are included in the references.

450 References1. 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.March 2001 400-24 Chevron Corporation

Fluid Flow Manual 400 Friction Pressure Drop3. 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. Marks Mechanical Engineers Handbook. 6th Edition. New York: McGraw-Hill, 1958.

12. Perrys 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. Transac-tions 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. Chem-ical 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.Chevron Corporation 400-25 March 2001

500 Fitting Pressure Drop

AbstractThis 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.

Contents Page

510 Introduction 500-2520 Velocity Head Loss Method 500-2530 Equivalent Length Method 500-5540 Transition and Laminar Flow Conditions 500-7550 Examples 500-7551 Example 1Velocity Head Loss Method552 Example 2Equivalent Length Method560 References 500-10Chevron Corporation 500-1 March 1997

500 Fitting Pressure Drop Fluid Flow Manual510 IntroductionValves 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 MethodIn 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:

(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.

hf KV2

2g------- =March 1997 500-2 Chevron Corporation

Fluid Flow Manual 500 Fitting Pressure DropFig. 500-1 Losses Through Entrances and Changes in Section Courtesy of Tube Turns TechnologiesChevron Corporation 500-3 March 1997

500 Fitting Pressure DropFluid Flow

Manual

March 1997


Fig. 500-2 Valve and Fitting Loss Data Crane Technical Paper 410-C, 1984, Flow of Fluids. Courtesy of Crane Valves

Fluid Flow Manual 500 Fitting Pressure Drop530 Equivalent Length MethodThe equivalent length method is a convenient but less accurate way to estimate pres-sure 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:

(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,

(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 appre-ciably, 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.

h f LD----V2

2g------- =

L DKf---- or

L

D-----Kf----= =Chevron Corporation 500-5 March 1997

500 Fitting Pressure DropFluid Flow

Manual

March 1997


Fig. 500-3 Equivalent Length of Valves and Fittings in Feet From Engineering Data Book, 9th Ed. 1972. Courtesy of GPSA.

Fluid Flow Manual 500 Fitting Pressure Drop540 Transition and Laminar Flow ConditionsUnder 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 ExamplesConsult 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 appro-priate 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 1Velocity Head Loss MethodGiven 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 90-degree elbows (R/D = 1.5); one 6-inch to 3-inch ANSI reducer.

SolutionCalculate the pressure drops separately for each diameter.

Diameter Ratio: DS/DL = 3.068 in./6.065 in. = 0.51

From Figure 500-1:

Fitting K

Reducer (friction) 0.16

Reducer (acceleration) 0.56

TOTAL 0.72Chevron Corporation 500-7 March 1997

500 Fitting Pressure Drop Fluid Flow ManualFrom Figure 500-2:

Pipe Area = A = pir2

= 0.201 ft2

= .051 ft2Flow rate = Q

= 0.89 ft3/sec

= 4.44 ft/sec

=17.45 ft/sec

Fitting K

Globe Valve 10.0

Check Valve 2.3

Elbows (3 x .33) 0.99

TOTAL 13.29

A1 3.146.065

2------------- 2in.2 1ft

2

144 in.2--------------------=

A2 3.143.068

2------------- 2in.2 1ft

3

144 in.2--------------------=

150 000lbhr-----,hr

3600sec--------------------ft3

62.4lb---------------1

.75------- =

Velocity V QA----= =

V1QA1-------

0.89ft3 sec0.201ft2

-----------------------------= =

V2QA2-------

0.89ft3 sec0.051ft2

-----------------------------= =March 1997 500-8 Chevron Corporation

Fluid Flow Manual 500 Fitting Pressure Drop= 0.306 ft

= 4.73 ftTotal pressure drop:

(Eq. 500-4)

552 Example 2Equivalent Length MethodGiven the following, determine the estimated total equivalent length of straight 6-inch pipe:

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

One Velocity Head V2

2g-------=

V212g---------

4.442ft2 sec22 32.2 ft sec2--------------------------------------=

V222g---------

17.452sq ft sec22 32.2 ft sec2------------------------------------------=

P1 13.29( ) 0.306( )62.4 0.75

144--------------------------- 1.322psi= =

P2 0.72( ) 4.73( )62.4 0.75

144--------------------------- 1.107psi= =

Total 2.429 psi=Chevron Corporation 500-9 March 1997

500 Fitting Pressure Drop Fluid Flow ManualSolutionFrom Figures 500-1 and 500-2:

Equivalent length L = (L/D) (D) = (146) (6.065)= 855 in. = 71.2 ft

Total equivalent line length 800 + L = 871.2 ft

560 References1. 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. Perrys 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 Transac-tions, Vol. 79, pp 1759-1766, 1957.

Fitting L/D

Gate Valve 8

Elbows (6 x 13) 78

Square Edged Entry (friction) 20

Square Edged Entry (acceleration) 40

TOTAL 146March 1997 500-10 Chevron Corporation

600 Noncircular Conduits

AbstractThis 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.

Contents Page

610 Introduction 600-2620 Turbulent Flow (Re > 2000) 600-2630 Laminar Flow (Re 2000) 600-3640 References 600-4Chevron Corporation 600-1 January 1990

600 Noncircular Conduits Fluid Flow Manual610 IntroductionThe 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 calcula-tion of the conduits 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 transi-tion 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.

(Eq. 600-1)

(Eq. 600-2)

(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

= density, lbm/ft3

V = velocity, ft/sec

Dh 4AxPw-------

=

ReVDh

---------------VDh

-----------= =

dh fL V2

Dh 2g-----------------=January 1990 600-2 Chevron Corporation

Fluid Flow Manual 600 Noncircular Conduits = kinematic viscosity, ft2/sec

= 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:

(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:

(Eq. 600-5)

f C1Re-------=

f C2Re-------=Chevron Corporation 600-3 January 1990

600 Noncircular Conduits Fluid Flow Manual640 ReferencesKays and Crawford, Convective Heat and Mass Transfer, McGraw- Hill, 1980.

Fig. 600-1 Laminar Flow Pressure Drop Constants Kays & Crawford, Convective Heat and Mass Transfer, 1980. Used by permission of The McGraw-Hill Companies.

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, 600-5January 1990 600-4 Chevron Corporation

800 Surge Pressure

AbstractThis 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.

Contents Page

810 Introduction 800-2820 Maximum Surge Pressure in a Simple Case 800-2830 Surge Computer Programs 800-7840 References 800-7Chevron Corporation 800-1 January 1990

800 Surge Pressure Fluid Flow Manual810 IntroductionIf 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 pressurerapid 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 pres-sures 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 CaseThe 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 propor-tional 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 800 Surge PressureFig. 800-1 Average Bulk Modulus for Crude Oil, Fuel Oil, Gas Oil, and GasolineChevron Corporation 800-3 January 1990

800 Surge Pressure Fluid Flow ManualFig. 800-2 Average Bulk Modulus for Lubricating OilsJanuary 1990 800-4 Chevron Corporation

Fluid Flow Manual 800 Surge PressureFig. 800-3 Bulk Modulus of Water

Fig. 800-4 SurgeSimple CaseChevron Corporation 800-5 January 1990

800 Surge Pressure Fluid Flow Manual(Eq. 800-1)where:

= 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.

= density of liquid, lbm/ft3

g = 32.2 ft lbm/sec2 lbfD = 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/ (where L = line length between vessel and valve in feet). If the valve closing time (T) is less than 2L/, the surge pressure can be approximated by

(Eq. 800-2)where:

P = surge pressure, psi

V = total change in velocity, ft/sec

T = valve closing time, sec

2L/ = 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/. Section 840, references 1, 2, and 3, presents general techniques for calculating surge pressure accurately and in more complex situations.

144Kg

1 KDCEt-------------+ -------------------------------=

P V144g---------------- for T2L

-------

Fluid Flow Manual 800 Surge Pressure830 Surge Computer ProgramsThe 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 flex-ible conduits (instrument control and subsea lines) and is available on VM Houston (OELIB).

840 References1. 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.Chevron Corporation 800-7 January 1990

900 Pipeline Flow

AbstractThis section discusses the flow effects of increased temperature and pressure in above-ground, buried, and subsea oil pipelines. Basic equations are given for calcu-lating 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.

Contents Page

910 Introduction 900-2920 Pipeline Temperature Limits 900-2930 Friction Heating In Viscous Flow 900-2940 Pressure Correction to Viscosity 900-3950 Applicable Computer Programs 900-4960 External Heat Transfer Coefficients 900-5970 References 900-7Chevron Corporation 900-1 January 1990

900 Pipeline Flow Fluid Flow Manual910 IntroductionSection 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 pres-sures, 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 LimitsThe allowable coating or insulation temperature normally limits pipeline tempera-ture. Coating temperature (for buried pipelines) is normally limited to less than about 150F. Special fusion bonded epoxy coatings of extra thickness are limited to about 200F. Polyurethane foam insulation temperature limits are about 200F. Some forms of insulation may resist higher temperatures, but Chevron has no expe-rience with them.

930 Friction Heating In Viscous FlowIn a flowing fluid, pressure dissipated by friction becomes heat. This heat has histor-ically 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 expres-sion:

(Eq. 900-1)where:

T = temperature increase, F

HP = hydraulic (friction) horsepower, hpJanuary 1990 900-2 Chevron Corporation

Fluid Flow Manual 900 Pipeline FlowBPD = oil flow rate, BPD

r = oil density, lbm/ft3

Cp = oil specific heat, BTU/lbm F

When Cp = 0.5 and = 58 the expression becomes:

High viscosities increase the ratio of HP to BPD and therefore increase the tempera-ture 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 ViscosityThe 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 viscosi-ties 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, cpChevron Corporation 900-3 January 1990

900 Pipeline Flow Fluid Flow ManualP = pressure, psig

As with friction heating, the effect of increased viscosity on pumping energy requirements depends on the flow regimes sensitivity to viscosity. Since some pipe-lines 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 ProgramsOver 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 pipe-lines where fluid properties change significantly with temperature. The programs 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 pipe-line, 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 Flow960 External Heat Transfer CoefficientsAll 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, insu-lating 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 coef-ficients for buried, above-ground, and subsea pipe.

Buried PipelinesThe appropriate ambient temperature value for a buried line is the yearly average air temperature. The external heat transfer coefficient for buried pipe can be calcu-lated 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/hawhere:

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 ManualGround 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 PipelinesThe 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 FJanuary 1990 900-6 Chevron Corporation

Fluid Flow Manual 900 Pipeline Flowk2 = 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 References1. Petroleum Refining, Technical Data Book. Washington, D.C.: American Petro-

leum Institute, 1970, pp 11-47.

Fig. 900-1 Heat Loss from Hot Surfaces to AirChevron Corporation 900-7 January 1990

900 Pipeline Flow Fluid Flow ManualFig. 900-2 Soil Conductivity Chart (1 of 4)

Material Conductivity, Btu/hr ft F Source

(dry density where reported)

Moisture Content

dry 2% 4% 6% 8% 10% 12% 14% 20% 30%

Soil 0.2 1

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 2

Soil (110 lb/cu ft) 0.72 2

Sandy soil 0.16 2

Sand 0.20 0.60 1

White sand, clean 0.14 2

Yellow sand, clean 0.17 0.20 0.28 0.40 0.56 2

Yellow sand and clay 0.16 0.17 0.20 0.26 0.35 0.51 0.79 2

Clay 0.74 3

Fine crushed quartz

(100 lb/cu ft) 1.00 4

(110 lb/cu ft) 1.33 4

Crushed quartz

(100 lb/cu ft) 0.96 4

(110 lb/cu ft) 1.33 4

(120 lb/cu ft) 1.83 4

Graded Ottawa sand

(100 lb/cu ft) 0.83 4

(110 lb/cu ft) 1.17 4

Fairbanks sand

(100 lb/cu ft) 0.71 4

(110 lb/cu ft) 0.87 1.25 4

(120 lb/cu ft) 1.12 4January 1990 900-8 Chevron Corporation

Fluid Flow Manual 900 Pipeline FlowLowell sand

(100 lb/cu ft) 0.71 4

(110 lb/cu ft) 0.87 1.12 4

Chena river gravel

(110 lb/cu ft) 0.75 4

(120 lb/cu ft) 1.08 4

Crushed feldspar

(100 lb/cu ft) 0.50 4

(110 lb/cu ft) 0.62 4

(120 lb/cu ft) 0.79 4

Crushed granite

(100 lb/cu ft) 0.46 4

(110 lb/cu ft) 0.62 4

(120 lb/cu ft) 0.79 4

Dakota sandy loam

(110 lb/cu ft) 0.54 4

(120 lb/cu ft) 0.79 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

Ramsey sandy loam

(100 lb/cu ft) 0.37 4

(110 lb/cu ft) 0.54 0.83 4

Fig. 900-2 Soil Conductivity Chart (2 of 4)



Moisture Content

dry 2% 4% 6% 8% 10% 12% 14% 20% 30%Chevron Corporation 900-9 January 1990

900 Pipeline Flow Fluid Flow ManualNorthway fine sand

(100 lb/cu ft) 0.37 4

(110 lb/cu ft) 0.46 0.71 4

Northway sand

(100 lb/cu ft) 0.37 4

(110 lb/cu ft) 0.50 0.62 4

Healy clay

(90 lb/cu ft) 0.46 0.67 4

(100 lb/cu ft) 0.33 0.83 4

(110 lb/cu ft) 0.75 4

Fairbanks silt loam

(90 lb/cu ft) 0.42 0.62 4

(100 lb/cu ft) 0.83 4

(110 lb/cu ft) 0.75 4

Fairbanks silty clay loam

(90 lb/cu ft) 0.42 0.62 4

(100 lb/cu ft) 0.79 4

(110 lb/cu ft) 0.75 4

Northway silt loam

(90 lb/cu ft) 0.33 0.50 4

(100 lb/cu ft) 0.58 4

(110 lb/cu ft) 0.58 4

Iraq Desert Steppe 0.27 5

Iraq Desert Sand 0.49 5




Moisture Content

dry 2% 4% 6% 8% 10% 12% 14% 20% 30%January 1990 900-10 Chevron Corporation

Fluid Flow Manual 900 Pipeline FlowAbqaiq sand 1.06 5

(in a limestone trench)

Earth, coarse gravelly 0.30 3

Concrete 0.54 0.70 1

Common red brick 0.36 2

Granite 1.73-3.98 6

Limestone 1.26-1.33 6

Marble 2.07-2.94 6

Sandstone 1.83 6


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.




Moisture Content

dry 2% 4% 6% 8% 10% 12% 14% 20% 30%Chevron Corporation 900-11 January 1990

1000 Fluid Properties

AbstractThis section discusses the viscosity and gravity properties of Newtonian and non-Newtonian 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 equa-tions and analytical correlations. It covers practical aspects, principles, and equa-tions 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 1000-31011 Absolute Viscosity

1012 Kinematic Viscosity

1013 Temperature and Viscosity

1014 Viscosity Index

1015 Pressure and Viscosity1016 Flow Rate and Viscosity1017 Measurement of Viscosity

1018 Viscosity of Blends

1019 Viscosity of Brine-in-Oil Emulsions1020 Gravity 1000-321021 Example

1030 Non-Newtonian Fluids 1000-38Chevron Corporation 1000-1 March 1997

1031 Laboratory Measurement of Flow Properties

1032 Laboratory Measurement of Gel Strength

1000 Fluid Properties Fluid Flow Manual1033 Constitutive Relationships

1034 Calculation of Flow Parameters

1035 Hydraulics Equations1036 Computer Program HOTOIL1037 Estimating Pipeline Restart Pressure Gradient

1038 Wax Deposition

1040 References 1000-541041 Viscosity Conversion

1042 Viscosity Data

1043 Brine-in-Oil EmulsionsMarch 1997 1000-2 Chevron Corporation

Fluid Flow Manual 1000 Fluid Properties1010 ViscosityViscosity 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 ViscosityThe 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 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 PropertiesFluid Flow

Manual

March 1997


Fig. 1000-1Conversion Factors for Absolute Viscosity

Fluid Flow Manual 1000 Fluid PropertiesFig. 1000-2 Viscosity ConversionFrom Various Terms to Saybolt Universal (1 of 2) Courtesy of Hydraulic InstituteChevron Corporation 1000-5 March 1997

1000 Fluid Properties Fluid Flow ManualFig. 1000-2 Viscosity ConversionFrom Various Terms to Saybolt Universal (2 of 2) Courtesy of Hydraulic InstituteMarch 1997 1000-6 Chevron Corporation

Fluid Flow Manual 1000 Fluid PropertiesFig. 1000-3 Viscosity of Common Liquids (1 of 4) Courtesy of Hydraulic InstituteChevron Corporation 1000-7 March 1997

1000 Fluid Properties Fluid Flow ManualFig. 1000-3 Viscosity of Common Liquids (2 of 4) Courtesy of Hydraulic InstituteMarch 1997 1000-8 Chevron Corporation

Fluid Flow Manual 1000 Fluid PropertiesFig. 1000-3 Viscosity of Common Liquids (3 of 4) Courtesy of Hydraulic InstituteChevron Corporation 1000-9 March 1997

1000 Fluid Properties Fluid Flow ManualFig. 1000-3 Viscosity of Common Liquids (4 of 4) Courtesy of Hydraulic InstituteMarch 1997 1000-10 Chevron Corporation

Fluid Flow Manual 1000 Fluid Properties(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:

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

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 0.00001646

>1.8

Saybolt Universal(2) seconds at 210 F

4.6635 0.00677 0.039911 0.000938 0.000280 0.00000274

>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 0.00000521

>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 = kinematic viscosity, centistokes (CS)T = flow time, seconds (or Engler degrees)A,B,C = 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

T DV1 EV+

F GV HV2

IV3

+ + +----------------------------------------------+=

V ATBT

T3

C+---------------=

SUS CS 1 0.000061 t 100F( )+[ ] SUS100FCS100F------------------------- =Chevron Corporation 1000-11 March 1997

1000 Fluid Properties Fluid Flow ManualFig. 1000-5 Viscosity ConversionCentistokes to Saybolt Universal or Saybolt FurolMarch 1997 1000-12 Chev

Chevron Fluid Flow

Documents

Transcript of Chevron Fluid Flow