Pressure Loss Correlations (NOT MINE)

3/13/2015 Pressure Loss Correlations

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Pressure Loss CorrelationsIntroductionIn the flow of fluids inside pipes, there are three pressure loss components:

FrictionHydrostaticKinetic energy

Of these three, kinetic energy losses are frequently much smaller than the others, and are usually ignored in all practical situations.

All the pressure loss procedures calculate the Hydrostatic Pressure Difference and Friction Pressure Loss components individually, and thenadd (or subtract) them to obtain the total pressure loss. There are many published correlations for calculating pressure losses. These fall intothe two broad categories of "single phase flow" and "multi-phase flow".

Single PhaseThere exist many single-phase correlations that were derived for different operating conditions or from laboratory experiments.Generally speaking, they only account for the friction component, i.e. they are applicable to horizontal flow. Typical examples are :

For Gas : Panhandle, Modified Panhandle, Weymouth and Fanning

For Liquid : Fanning

However, these correlations can also be used for vertical or inclined flow, provided the hydrostatic pressure drop is accounted for,in addition to the friction component. As a result, even though a particular correlation may have been developed for flow in ahorizontal pipe, incorporation of the hydrostatic pressure drop allows that correlation to be used for flow in a vertical pipe. Thisadaptation is rigorous, and has been implemented into all the correlations used in VirtuWell. Nevertheless, for identificationpurposes, the correlations name has been kept unchanged. Thus, as an example Panhandle was originally developed forhorizontal flow, but its implementation in this program allows it to be used for all directions of flow.

Single Phase Friction ComponentThere are two distinct types of correlations for calculating friction pressure loss (Pf). The first type, adopted by theAGA (American Gas Association), includes Panhandle, Modified Panhandle and Weymouth. These correlations arefor single-phase gas only. They incorporate a simplified friction factor and a flow efficiency. They all have a similarformat as follows:

where:

P1,2=upstream and downstream pressures respectively (psia)Q=gas flow rate (ft^3/d @ T,P)E=pipeline efficiency factorP=reference pressure (psia) (14.65 psia)T=reference temperature, (R) (520 R)G=gas gravityD=inside diameter of pipe (inch)Ta=average flowing temperature (R)Za=average gas compressibility factorL=pipe length (miles)

= constants

The other type of correlation is based on the definition of the friction factor (Moody or Fanning) and is given by theFanning equation:

where:

Pf=pressure loss due to friction effects, (lbf/ft2)f=Fanning friction factor (function of Reynolds number)=density, (lbm/ft3)

v=average velocity, (ft/s)



L=length of pipe section, (ft)

gc = conversion factor (32.2 (lbmft)/(lbfs2))

D=inside diameter of pipe, (ft)

This correlation can be used either for single-phase gas (Fanning Gas) or for single-phase liquid (Fanning - Liquid).

Single-Phase friction factor (f)

The single-phase friction factor can be obtained from the Chen (1979) equation, which is representative of the

Fanning friction factor chart.

where:

f = friction factor

k = absolute roughness (in)

k/D = relative roughness (unitless)

Re = Reynolds number

The single-phase friction factor clearly depends on the Reynolds number, which is a function of the fluid density,

viscosity, velocity and pipe diameter. The friction factor is valid for single-phase gas or liquid flow, as their very

different properties are taken into account in the definition of Reynolds number.

where:

= density, lbm/ft3

v = velocity, ft/s

D = diameter, ft

= viscosity, lb/ft*s

Since viscosity is usually measured in "centipoise", and 1 cp = 1488 lb/ft*s, the Reynolds number can be rewritten

for viscosity in centipoise.

Reference:

Chen, N. H., "An Explicit Equation for Friction Factor in Pipe," Ind. Eng. Chem. Fund. (1979).

Single Phase Hydrostatic Component

Hydrostatic pressure difference PHH can be applied to all correlations by simply adding it to the friction

component. The hydrostatic pressure drop ( PHH) is defined, for all situations, as follows:

PHH = gh

where:

=density of the fluid

g=acceleration of gravity

h=vertical elevation (can be positive or negative)

For a liquid, the density ( ) is constant, and the above equation is easily evaluated.

For a gas, the density varies with pressure. Therefore, to evaluate the hydrostatic pressure loss/gain, the pipe (or

wellbore) is subdivided into a sufficient number of segments, such that the density in each segment can be assumed

to be constant. Note that this is equivalent to a multi-step Cullender and Smith calculation.

Single Phase Correlations

Single Phase

Gas Liquid

Correlations Vertical Horizontal Vertical Horizontal

Fanning-Gas * *



Fanning-Liquid

* *

Panhandle * *

Modified Panhandle * *

Weymouth * *

Mechanistic * * * *

Multiphase

Multiphase pressure loss calculations parallel single phase pressure loss calculations. Essentially, each multiphase correlationmakes its own particular modifications to the hydrostatic pressure difference and the friction pressure loss calculations, in order tomake them applicable to multiphase situations.

The friction pressure loss is modified in several ways, by adjusting the friction factor (f), the density ( ) and velocity (v) to accountfor multiphase mixture properties. In the AGA type equations (Panhandle, Modified Panhandle and Weymouth), it is the flowefficiency that is modified.

The hydrostatic pressure difference calculation is modified by defining a mixture density. This is determined by a calculation of in-situ liquid holdup. Some correlations determine holdup based on defined flow patterns. Some correlations (Flanigan) ignore thepressure recovery in downhill flow, in which case, the vertical elevation is defined as the sum of the uphill segments, and not the"net elevation change".

The multiphase pressure loss correlations used in this software are of two types.

The first type (Flanigan, Modified Flaniganand Weymouth (Multiphase)) is based on a combination of the AGA equations for gas flow inpipelines and the Flanigan multiphase corrections. These equations can be used for gas-liquid multiphase flow or for single-phase gasflow. They CANNOT be used for single-phase liquid flow.

Important Note: These three correlations can give erroneous results if the pipe described deviates substantially (more than 10degrees) from the horizontal. For this reason, these correlations are only available on the Pipe and Comparison pages.

The second type (Beggs and Brill, Hagedorn and Brown, Gray) is the set of correlations based on the Fanning friction pressure lossequation. These can be used for either gas-liquid multiphase flow, single-phase gas or single-phase liquid, because in single-phasemode, they revert to the Fanning equation, which is equally applicable to either gas or liquid. Beggs and Brill is a multipurpose correlationderived from laboratory data for vertical, horizontal, inclined uphill and downhill flow of gas-water mixtures. Gray is based on field data forvertical gas wells producing condensate and water. Hagedorn and Brown was derived from field data for flowing vertical oil wells.

Important Note: The Gray and Hagedorn and Brown correlations were derived for vertical wells and may not apply tohorizontal pipes.

Below is a summary of the correlations available in this program and the connection between the single-phase and multiphaseforms. Note that each correlation has been adapted to calculate both a hydrostatic and a friction component.

Procedure

(The phrases "pressure loss," "pressure drop," and "pressure difference" are used by different people but mean the same thing).

In F.A.S.T. VirtuWell, the pressure loss calculations for vertical, inclined or horizontal pipes follow the same procedure:

1. Total Pressure Loss = Hydrostatic Pressure Difference + Friction Pressure Loss. The total pressure loss, as well as each individualcomponent can be either positive or negative, depending on the direction of calculation, the direction of flow and the direction of elevationchange.

2. Subdivide the pipe length into segments so that the total pressure loss per segment is less than twenty (20) psi. Maximum number ofsegments is twenty (20).

3. For each segment assume constant fluid properties appropriate to the pressure and temperature of that segment.

4. Calculate the Total Pressure Loss in that segment as in step #1.

5. Knowing the pressure at the inlet of that segment, add to (or subtract from) it the Total Pressure Loss determined in step #4 to obtain thepressure at the outlet.

6. The outlet pressure from step #5 becomes the inlet pressure for the adjacent segment.

7. Repeat steps #3 to #6 until the full length of the pipe has been traversed.

NOTE: As discussed under Hydrostatic Pressure Difference and Friction Pressure Loss, the hydrostatic pressure difference is positive in thedirection of the earths gravitational pull, whereas the friction pressure loss is always positive in the direction of flow.



Single Phase Flow

The most generally applicable single phase equation for calculating Friction Pressure Loss is the Fanning equation. It utilizes friction factorcharts (Knudsen and Katz, 1958), which are functions of Reynolds number and relative pipe roughness. These charts are also often referred toas the Moody charts. F.A.S.T. VirtuWell uses the equation form of the Fanning friction factor as published by Chen, 1979.

The calculation of Hydrostatic Pressure Difference is different for a gas than for a liquid, because gas is compressible and its density varies withpressure and temperature, whereas for a liquid a constant density can be safely assumed.

Generally it is easier to calculate pressure drops for single-phase flow than it is for multiphase flow. There are several single-phase correlationsthat are available:

Fanning the Fanning correlation is divided into two sub categories Fanning Liquid and Fanning Gas. The Fanning Gas correlation is also known as theMulti-step Cullender and Smith when applied for vertical wellbores.Panhandle the Panhandle correlation was developed originally for single-phase flow of gas through horizontal pipes. In other words, the hydrostaticpressure difference is not taken into account. We have applied the standard hydrostatic head equation to the vertical elevation of the pipe to account forthe vertical component of pressure drop. Thus our implementation of the Panhandle equation includes BOTH horizontal and vertical flow components,and this equation can be used for horizontal, uphill and downhill flow.Modified Panhandle the Modified Panhandle correlation is a variation of the Panhandle correlation that was found to be better suited to sometransportation systems. Thus, it also originally did not account for vertical flow. We have applied the standard hydrostatic head equation to account forthe vertical component of pressure drop. Hence our implementation of the Modified Panhandle equation includes BOTH horizontal and vertical flowcomponents, and this equation can be used for horizontal, uphill and downhill flow.Weymouth the Weymouth correlation is of the same form as the Panhandle and the Modified Panhandle equations. It was originally developed forshort pipelines and gathering systems. As a result, it only accounts for horizontal flow and not for hydrostatic pressure drop. We have applied thestandard hydrostatic head equation to account for the vertical component of pressure drop. Thus, our implementation of the Weymouth equationincludes BOTH horizontal and vertical flow components, and this equation can be used for horizontal, uphill and downhill flow.

In our software, for cases that involve a single phase, the Gray, the Hagedorn and Brown and the Beggs and Brill correlations revert to theFanning single-phase correlations. For example, if the Gray correlation was selected but there was only gas in the system, the Fanning Gascorrelation would be used. For cases where there is a single phase, the Flanigan and Modified Flanigan correlations devolve to the single-phase Panhandle and Modified Panhandle correlations respectively. The Weymouth (Multiphase) correlation devloves to the single-phaseWeymouth correlation.

References

Knudsen, J. G. and D. L. Katz (1958). Fluid Dynamics and Heat Transfer, McGraw-Hill Book Co., Inc., New York.Chen, N. H., "An Explicit Equation for Friction Factor in Pipe," Ind. Eng. Chem. Fund. (1979).

Panhandle Correlation

The original Panhandle correlation (Gas Processors Suppliers Association, 1980) was developed for single-phase gas flow inhorizontal pipes. As such, only the pressure drop due to friction was taken into account by the Panhandle equation. However, wehave applied the standard equation for calculating hydrostatic head to the vertical component of the pipe, and thus our Panhandlecorrelation accounts for horizontal, inclined and vertical pipes. The Panhandle correlation can only be used for single-phase gasflow. The Fanning Liquid correlation should be used for single-phase liquid flow.

Panhandle - Friction Pressure Loss

The Panhandle correlation can be written as follows:

where:

The Panhandle equation incorporates a simplified representation of the friction factor, which is built into theequation. To account for real life situations, the flow efficiency factor, E, was included in the equation. This flowefficiency generally ranges from 0.8 to 0.95. Although we recognize that a common default for the flow efficiency is0.92, our software defaults to E = 0.85, as our experience has shown this to be more appropriate (Mattar and Zaoral,1984).

Panhandle - Hydrostatic Pressure Difference

The original Panhandle equation only accounted for Pf. However, by applying the hydrostatic head calculationsthe Panhandle correlation has been adapted for vertical and inclined pipes. The hydrostatic head is calculated by:

Nomenclature

D = pipe inside diameter (inch)E = Panhandle/Weymouth efficiency factorG = gas gravity



g = gravitational acceleration (32.2 ft/s2)


L = length (mile)

P = reference pressure for standard conditions (psia)

P1 =upstream pressure (psia)

P2 = downstream pressure (psia)

PHH = pressure change due to hydrostatic head (psi)

QG = gas flow rate at standard condition (ft3/d)

T = reference temperature for standard conditions (Rankin)

Ta = average temperature (Rankin)

Za = average compressibility factor

z = elevation change (ft)

G = gas density (lb/ft3)

References

Gas Processors Suppliers Association, Field Engineering Data Book, Vol. 2, 10th ed., Tulsa (1994)

Mattar, L. and Zaoral, K., "Gas Pipeline Efficiencies and Pressure Gradient Curves," JCPT 84-35-93 (1984)

Fanning Correlation

The Fanning friction factor pressure loss ( Pf) can be combined with the hydrostatic pressure difference ( PHH) to give the total

pressure loss. The Fanning Gas Correlation (Multi-step Cullender and Smith) is the name used in this document to refer to the

calculation of the hydrostatic pressure difference ( PHH) and the friction pressure loss ( Pf) for single-phase gas flow, using the

following standard equations.

This formulation for pressure drop is applicable to pipes of all inclinations. When applied to a vertical wellbore it is equivalent to

the Cullender and Smith method. However, it is implemented as a multi-segment procedure instead of a 2 segment calculation.

Fanning Gas - Friction Pressure Loss

The Fanning equation is widely thought to be the most generally applicable single phase equation for calculating

friction pressure loss. It utilizes friction factor charts (Knudsen and Katz, 1958), which are functions of Reynolds

number and relative pipe roughness. These charts are also often referred to as the Moody charts. We use the

equation form of the Fanning friction factor as published by Chen, 1979.

The method for calculating the Fanning Friction factor is the same for single-phase gas or single-phase liquid.

Roughness

Flow Efficiency

Fanning Gas - Hydrostatic Pressure Difference

The calculation of hydrostatic head is different for a gas than for a liquid, because gas is compressible and its

density varies with pressure and temperature, whereas for a liquid a constant density can be safely assumed. Either

way the hydrostatic pressure difference is given by:

Since G varies with pressure, the calculation must be done sequentially in small steps to allow the density to vary

with pressure.

Fanning Liquid Correlation

The Fanning friction factor pressure loss ( Pf) can be combined with the hydrostatic pressure difference ( PHH) to

give the total pressure loss. The Fanning Liquid Correlation is the name used in this program to refer to the

calculation of the hydrostatic pressure difference ( PHH) and the friction pressure loss ( Pf) for single-phase liquid

flow, using the following standard equations.

Fanning Liquid - Friction Pressure Loss

The Fanning equation is widely thought to be the most generally applicable single-phase equation for calculating

friction pressure loss. It utilizes friction factor charts (Knudsen and Katz, 1958), which are functions of Reynolds

number and relative pipe roughness. These charts are also often referred to as the Moody charts. We use the

equation form of the Fanning friction factor as published by Chen (1979).



The method for calculating the Fanning friction factor is the same for single-phase gas or single-phase liquid.

Fanning Liquid - Hydrostatic Pressure Difference

The calculation of hydrostatic head is different for a gas than for a liquid, because gas is compressible and itsdensity varies with pressure and temperature, whereas for a liquid a constant density can be safely assumed. Forliquid, the hydrostatic pressure difference is given by:

Since does not vary with pressure, a constant value can be used for the entire length of the pipe.

Nomenclature

D = pipe inside diameter (inch)f = Fanning friction factorg = gravitational acceleration (32.2 ft/s2)gc = conversion factor (32.2 (lbm*ft)/(lbf*s2))k/D = relative roughness (unitless)L = length (ft)PHH = pressure change due to hydrostatic head (psi)Pf = pressure change due to friciton (psi)

Re = Reynolds numberV = velocity (ft/s)z = elevation changeG = gas density (lb/ft3)

References

Chen, N. H., "An Explicit Equation for Friction Factor in Pipe," Ind. Eng. Chem. Fund. (1979).Cullender, M. H. and R. V. Smith (1956). Practical Solution of Gas-Flow Equations for Wells and Pipelines with LargeTemperature Gradients, Trans., AIME, 207, 281-287.Gas Processors and Suppliers Association, Engineering Data Book. Vol. 2, Sect. 17, 10th ed., 1994.Knudsen, J. G. and D. L. Katz (1958). Fluid Dynamics and Heat Transfer, McGraw-Hill Book Co., Inc., New York.

Weymouth Correlation

This correlation is similar in its form to the Panhandle and the Modified Panhandle correlations. It was designed for single-phasegas flow in pipelines. As such, it calculates only the pressure drop due to friction. However, we have applied the standardequation for calculating hydrostatic head to the vertical component of the pipe, and thus our Weymouth correlation accounts forHORIZONTAL, INCLINED and VERTICAL pipes. The Weymouth equation can only be used for single-phase gas flow. TheFanning Liquid correlation should be used for single-phase liquid flow.

Weymouth Friction Pressure Loss

The pressure drop due to friction is given by:

where:

The Weymouth equation incorporates a simplified representation of the friction factor, which is built into theequation. To account for real life situations, the flow efficiency factor, E, was included in the equation. The flowefficiency generally used is 1. Our software defaults to this value as well (Mattar and Zaoral, 1984).

Weymouth Hydrostatic Pressure Difference

The original Weymouth equation only accounted for Pf . However, by applying the hydrostatic head calculations,the Weymouth equation has been adapted for vertical and inclined pipes. The hydrostatic head is calculated by:



NomenclatureD = pipe inside diameter (inch)E = Panhandle/Weymouth efficiency factorG = gas gravityg = gravitational acceleration (32.2 ft/s2)gc = conversion factor (32.2 (lbmft)/(lbfs2))L = length (mile)P = reference pressure for standard conditions (psia)P1 =upstream pressure (psia)P2 = downstream pressure (psia)PHH = pressure change due to hydrostatic head (psi)

QG = gas flow rate at standard conditions, T,P, ft3/dT = reference temperature for standard conditions (Rankin)Ta = average temperature (Rankin)Za = average compressibility factorz = elevation change (ft)G = gas density (lb/ft3)

ReferencesGas Processors Suppliers Association, Field Engineering Data Book, Vol. 2, 10th ed., Tulsa (1994).Mattar, L. and Zaoral, K., "Gas Pipeline Efficiencies and Pressure gradient Curves." JCPT 84-35-93 (1984).

Multiphase FlowThe presence of multiple phases greatly complicates pressure drop calculations. This is due to the fact that the properties of each fluid presentmust be taken into account. Also, the interactions between each phase have to be considered. Mixture properties must be used, and thereforethe gas and liquid in-situ volume fractions throughout the pipe need to be determined. In general, all multiphase correlations are essentially twophase and not three phase. Accordingly, the oil and water phases are combined, and treated as a pseudo single liquid phase, while gas isconsidered a separate phase. The following is a list of general concepts inherent to multiphase flow. Click on each of them for a brief overview.

Superficial Velocities, Vsl, VsgMixture Velocity, VmLiquid Holdup EffectInput Volume Fraction, CLIn-situ Volume Fraction, ELMixture Viscosity, No Slip Viscosity, Mixture Density, No Slip Density, Surface Tension,

Multiphase Flow CorrelationsMany of the published multiphase flow correlations are applicable for "vertical flow" only, while others apply for "horizontal flow"only. Other than the Beggs and Brill correlation, there are not many correlations that were developed for the whole spectrum offlow situations that can be encountered in oil and gas operations; namely uphill, downhill, horizontal, inclined and vertical flow.However, we have adapted all of the correlations (as appropriate) so that they apply to all flow situations. The following is a list ofthe multiphase flow correlations that are available.

1. Gray: The Gray Correlation (1978) was developed for vertical flow in wet gas wells. We have modified it so that it applies to flow in alldirections by calculating the hydrostatic pressure difference using only the vertical elevation of the pipe segment and the friction pressureloss based on the total pipe length.

2. Hagedorn and Brown: The Hagedorn and Brown Correlation (1964) was developed for vertical flow in oil wells. We have also modified itso that it applies to flow in all directions by calculating the hydrostatic pressure difference using only the vertical elevation of the pipesegment and the friction pressure loss based on the total pipe length.

3. Beggs and Brill: The Beggs and Brill Correlation (1973) is one of the few published correlations capable of handling all of the flowdirections. It was developed using sections of pipe that could be inclined at any angle.

4. Flanigan: The Flanigan Correlation (1958) is an extention of the Panhandle single-phase correlation to multiphase flow. It incorporates acorrection for multiphase Flow Efficiency, and a calculation of hydrostatic pressure difference to account for uphill flow. There is nohydrostatic pressure recovery for downhill flow. In this software, the Flanigan multiphase correlation is also applied to the ModifiedPanhandle and Weymouth correlations. It is recommended that this correlation not be used beyond +/- 10 degrees from the horizontal.

5. Modified-Flanigan: The Modified Flanigan Correlation is an extention of the Modified Panhandle single-phase equation to multiphaseflow. It incorporates the Flanigan correction of the Flow Efficiency for multiphase flow and a calculation of hydrostatic pressure differenceto account for uphill flow. There is no hydrostatic pressure recovery for downhill flow. In this software, the Flanigan multiphase correlationis also applied to the Panhandle and Weymouth correlations. It is recommended that this correlation not be used beyond +/- 10 degreesfrom the horizontal.

6. Weymouth (Multiphase): The Weymouth (Multiphase) is an extension of the Weymouth single-phase equation to multiphase flow. Itincorporates the Flanigan correction of the Flow Efficiency for multiphase flow and a calculation of hydrostatic pressure difference toaccount for uphill flow. There is no hydrostatic pressure recovery for downhill flow. In this software, the Flanigan correlation is alsoapplied to the Panhandle and Modified Panhandle correlations. It is recommended that this correlation not be used beyond +/- 10degrees from the horizontal.

Each of these correlations was developed for its own unique set of experimental conditions, and accordingly, results will varybetween them.

Single Phase Gas



In the case of single-phase gas, the available correlations are the Panhandle, Modified Panhandle, Weymouth and Fanning Gas.

These correlations were developed for horizontal pipes, but have been adapted to vertical and inclined flow by including the

hydrostatic pressure component. In vertical flow situations, the Fanning Gas is equivalent to a multi-step Cullender and Smith

calculation.

Single Phase LiquidIn the case of single-phase liquid, the available correlation is the Fanning Liquid. It has been implemented to apply to horizontal,

inclined and vertical wells.

For multiphase flow in essentially horizontal pipes, the available correlations are Beggs and Brill, Gray, Hagedorn and Brown,

Flanigan, Modified-Flanigan and Weymouth (Multiphase). All of these correlations are accessible on the Pipe page and the

Comparison page.

Multiphase FlowFor multiphase flow in essentially vertical wells, the available correlations are Beggs and Brill, Gray, and Hagedorn and Brown. If

used for single-phase flow, these three correlations devolve to the Fanning Gas or Fanning Liquid correlation.

When switching from multiphase flow to single-phase flow, the correlation will default to the Fanning. When switching from single-

phase flow to multiphase flow, the correlation will default to the Beggs and Brill.

Important Notes

The Flanigan, Modified-Flanigan and Weymouth (Multiphase) correlations can give erroneous results if the pipe described deviates

substantially (more than 10 degrees) from the horizontal. The Gray and Hagedorn and Brown correlations were derived for vertical wells

and may not apply to horizontal pipes.

In our software, the Gray, the Hagedorn and Brown and the Beggs and Brill correlations revert to the appropriate single-phase Fanning

correlation (Fanning Liquid or Fanning Gas. The Flanigan, Modified-Flanigan and Weymouth (Multiphase) revert to the Panhandle,

Modified Panhandle and Weymouth respectively. However, they may not be used for single-phase liquid flow.

Single Phase & Multiphase Correlations

Multiphase

Gas Liquid

Correlations Vertical Horizontal Vertical Horizontal

Fanning-Gas

Fanning-Liquid *

Panhandle

Modified Panhandle

Weymouth

Beggs & Brill * * * *

Gray *

Hagedorn & Brown *

Flanigan *

Modified-Flanigan *

Weymouth

(Multiphase)

*

Mechanistic Model * * * *

Petalas & Aziz Mechanistic ModelDetermine Flow PatternTo determine a flow pattern, we do the following:



Begin with one flow pattern and test for stability.Check the next pattern.Build Flow Pattern Map.

Example Flow Pattern Map

Dispersed Bubble FlowExists if

where

and if

Stratified FlowExists if flow is downward or horizontal ( 0)

Calculate (dimensionless liquid height)

Momentum Balance Equations:

where



and

fG from standard methods where

fL from

where

fsL from standard methods where

fi from

where

Use Lochhart-Martinelli Parameters

where



where

Geometric Variables:

Solve for hL/D iteratively.

Stratified flow exists if

(Note: when cos 0.02 then cos = 0.02)

where



and

(Note: when cos 0.02 then cos = 0.02)

Stratified smooth versus Stratified Wavy

if

where

and

then have Stratified Smooth, else have Stratified Wavy.

Annular Mist FlowCalculate (dimensionless liquid height)

Momentum Balance Equations

where

and



(1)

from standard methods where

from standard methods where

fi from

(2)

Use Lochhart-Martinelli Parameters

where



where

Geometric Variables:

Solve for iteratively.

Annular Mist Flow exists if

where from

Solve iteratively for

Bubble FlowBubble flow exists if

(3)



where:

C1 = 0.5= 1.3db = 7mm

(4)

In addition, transition to bubble flow from intermittent flow occurs when

where:

(see Intermittent flow for additional definitions).

Intermittent FlowIntermittent flow exists if

where:

If EL > 1, EL = CL

and:

where is from standard methods where:

for fm < 1, fm = 1



where is from standard methods where:

if

1. If and then Slug Flow

2. If and then Elongated Bubble Flow

3. Froth Flow

If none of the transition criteria for intermittent flow are met, then the flow pattern is designated as Froth, implying atransitional state between the other flow regimes.

Footnotes

1. , where: G (lb/ft3), L (lb/ft3), VSG (ft/s), L (cP), (dyn/cm)

2. , where: C

(lb/ft3), VC (ft/s), DC (ft), (dyn/cm)

3. , where: L (lb/ft3), G (lb/ft3), (dyn/cm)

4. , where: L (lb/ft3), G (lb/ft3),

(dyn/cm)



5. , where: D (ft), L

(lb/ft3), G (lb/ft3), (dyn/cm)

6. , where: L (lb/ft3), G (lb/ft3),

(dyn/cm)

NomenclatureA = cross sectional areaC0 = velocity distribution coefficientD = pipe internal diameterE = in situ volume fractionFE = liquid fraction entrainedg = acceleration due to gravityhL = height of liquid (stratified flow)L = lengthP = pressureRe = Reynolds numberS = contact perimeterVSG = superficial gas velocityVSL = superficial liquid velocity

= liquid film thickness= pipe roughness= pressure gradient weighting factor (intermittent flow)= Angle of inclination= viscosity= density= interfacial (surface) tension= shear stress= dimensionless quantity

Subscriptsb = relating to the gas bubblec = relating to the gas coreF = relating to the liquid filmdb = relating to dispersed bubblesG = relating to gas phasei = relating to interfaceL = relating to liquid phasem = relating to mixtureSG = based on superficial gas velocitys = relating to liquid slugSL = based on superficial liquid velocitywL = relating to wall-liquid interfacewG = relating to wall-gas interfaceC0 = velocity distribution coefficient

ReferencesPetalas, N., Aziz, K.: "A Mechanistic Model for Multiphase Flow in Pipes," J. Pet. Tech. (June 2000), 43-55.Petalas, N., Aziz, K.: "Development and Testing of a New Mechanistic Model for Multiphase Flow in Pipes," ASME 1996Fluids Engineering Division Conference (1996), FED-Vol 236, 153-159.Gomez, L.E. et al.: "Unified Mechanistic Model for Steady-State Two-Phase Flow," Petalas, N., Aziz, K.: "A MechanisticModel for Multiphase Flow in Pipes," SPE Journal (September 2000), 339-350.

Beggs And Brill CorrelationFor multiphase flow, many of the published correlations are applicable for "vertical flow" only, while others apply for "horizontalflow" only. Not many correlations apply to the whole spectrum of flow situations that may be encountered in oil and gasoperations, namely uphill, downhill, horizontal, inclined and vertical flow. The Beggs and Brill (1973) correlation, is one of the fewpublished correlations capable of handling all these flow directions. It was developed using 1" and 1-1/2" sections of pipe thatcould be inclined at any angle from the horizontal.

The Beggs and Brill multiphase correlation deals with both the friction pressure loss and the hydrostatic pressure difference. Firstthe appropriate flow regime for the particular combination of gas and liquid rates (Segregated, Intermittent or Distributed) isdetermined. The liquid holdup, and hence, the in-situ density of the gas-liquid mixture is then calculated according to theappropriate flow regime, to obtain the hydrostatic pressure difference. A two-phase friction factor is calculated based on the"input" gas-liquid ratio and the Fanning friction factor. From this the friction pressure loss is calculated using "input" gas-liquid



mixture properties.

If only a single-phase fluid is flowing, the Beggs and Brill multi-phase correlation devolves to the Fanning Gas or Fanning Liquidcorrelation.

See Also: Pressure Drop Correlations, Multiphase Flow Correlations

Flow Pattern Map

Unlike the Gray or the Hagedorn and Brown correlations, the Beggs and Brill correlation requires that a flow patternbe determined. Since the original flow pattern map was created, it has been modified. We have used this modifiedflow pattern map for our calculations. The transition lines for the modified correlation are defined as follows:

The flow type can then be readily determined either from a representative flow pattern map or according to thefollowing conditions, where

.

SEGREGATED flow

if

and

Or

and

INTERMITTENT flow

if and

or and

DISTRIBUTED flow

if and

or and

TRANSITION flow

if and

Hydrostatic Pressure Difference

Once the flow type has been determined then the liquid holdup can be calculated. Beggs and Brill divided the liquidholdup calculation into two parts. First the liquid holdup for horizontal flow, EL(0), is determined, and then this holdupis modified for inclined flow. EL(0) must be CL and therefore when EL(0) is smaller than CL, EL(0) is assigned avalue of CL. There is a separate EL(0) for each flow type.

SEGREGATED

INTERMITTENT



DISTRIBUTED

IV.TRANSITION

Where

Once the horizontal in situ liquid volume fraction is determined, the actual liquid volume fraction is obtained bymultiplying EL(0) by an inclination factor, B( ). i.e.

where

is a function of flow type, the direction of inclination of the pipe (uphill flow or downhill flow), the liquid velocitynumber (Nvl), and the mixture Froude Number (Frm). Nvl is defined as:

For UPHILL flow:

SEGREGATED

INTERMITTENT

DISTRIBUTED

For DOWNHILL flow:

I, II, III. ALL flow types

Note: must always be 0. Therefore, if a negative value is calculated for , = 0.

Once the liquid holdup (EL( )) is calculated, it is used to calculate the mixture density ( m). The mixture density is,in turn, used to calculate the pressure change due to the hydrostatic head of the vertical component of the pipe or



well.

Beggs and Brill - Friction Pressure LossThe first step to calculating the pressure drop due to friction is to calculate the empirical parameter S. The value of S

is governed by the following conditions:

if 1 < y < 1.2, then

otherwise,

where:

Note: Severe instabilities have been observed when these equations are used as published. Our implementation

has modified them so that the instabilities have been eliminated.

A ratio of friction factors is then defined as follows:

is the no-slip friction factor. We use the Fanning friction factor, calculated using the Chen equation. The no-slip

Reynolds Number is also used, and it is defined as follows:

Finally, the expression for the pressure loss due to friction is:

NomenclatureCL = liquid input volume fraction

D = inside pipe diameter (ft)

EL(0) = horizontal liquid holdup

EL( ) = inclined liquid holdup

ftp = two phase friction factor

fNS = no-slip friction factor

Frm = Froude Mixture Number


gc = conversion factor (32.2 (lbm*ft)/(lbf*s2))

L = length of pipe (ft)

Nvl = liquid velocity number

Vm = mixture velocity (ft/s)

Vsl = superficial liquid velocity (ft/s)


NS = no-slip viscosity (cp)

= angle of inclination from the horizontal (degrees)

L = liquid density (lb/ft3)

NS = no-slip density (lb/ft3)

m = mixture density (lb/ft3)



= gas/liquid surface tension (dynes/cm)

Reference

Beggs, H. D., and Brill, J.P., "A Study of Two-Phase Flow in Inclined Pipes," JPT, 607-617, May 1973. Source: JPT.

Flanigan Correlation

The Flanigan correlation is an extension of the Panhandle single-phase correlation to multiphase flow. It was developed to

account for the additional pressure loss caused by the presence of liquids. The correlation is empirical and is based on studies of

small amounts of condensate in gas lines. To account for liquids, Flanigan developed a relationship for the Flow Efficiency term of

the Panhandle equation as a function of liquid to gas ratio. Since the Panhandle equation applied to essentially horizontal flow,

Flanigan also developed a liquid holdup factor to account for the hydrostatic pressure difference in upward inclined flow. For

downhill, there is no hydrostatic pressure recovery.

As noted previously, the Flanigan correlation was developed for essentially horizontal flow. Consequently, it is not applicable in

vertical flow situations such as vertical wellbores. Therefore, the Flanigan correlation is only available on the Pipe and

Comparison pages. Care should be taken when applying the Flanigan correlation to situations other than essentially horizontal

flow. The effects of using the Flanigan correlation can be investigated using the Comparison module.

In this program , the Flanigan correlation has been applied to the Panhandle, Modified Panhandle and Weymouth correlations in

the same way, by adjusting the hydrostatic pressure difference using the Flanigan holdup factor and by using the appropriate

efficiency (E) for multiphase flow.

Flanigan - Hydrostatic Pressure Difference

When calculating the pressure losses due to hydrostatic effects the Flanigan correlation ignores downhill flow. The

hydrostatic head caused by the liquid content is calculated as follows:

where:

hi = the vertical "rises" of the individual sections of the pipeline (ft)

EL = Flanigan holdup factor (in-situ liquid volume fraction)

The Flanigan holdup factor is calculated using the following equation.

Flanigan Friction Pressure Loss

In the Flanigan correlation, the friction pressure drop calculation accounts for liquids by adjusting the

Panhandle/Weymouth efficiency (E) according to the following plot.

Notice that when there is mostly gas (the liquid to gas ratio is very small), the Panhandle efficiency is around 0.85

(close to the single-phase default for gas) and as the quantity of liquids increases, the efficiency decreases.

Modified-Flanigan Correlation

The Modified-Flanigan is equivalent to the Flanigan correlation applied to the Modified Panhandle single-phase correlation. The

Flanigan correlation was developed as a method to account for the additional pressure loss caused by the presence of liquids.

The correlation is empirical and is based on studies of small amounts of condensate in gas lines. To account for liquids, Flanigan



developed a relationship for the Flow Efficiency term of the Panhandle equation as a function of liquid to gas ratio. In addition,Flanigan developed a liquid holdup factor to account for the hydrostatic pressure difference in upward inclined flow. For downhill,there is no hydrostatic pressure recovery.

As noted previously, the Flanigan correlation was developed for essentially horizontal flow. Consequently, it is not applicable invertical flow situations such as vertical wellbores. Therefore, the Flanigan correlation, and hence the Modified-Flanigancorrelation, is only available on the Pipe and Comparison pages. Care should be taken when applying the Modified-Flanigancorrelation to situations other than essentially horizontal flow. The effects of using the Modified-Flanigan correlation can beinvestigated using the Comparison module.

In this program , the Flanigan correlation has been applied to the Panhandle, Modified Panhandle and Weymouth correlations inthe same way, by adjusting the hydrostatic pressure difference using the Flanigan holdup factor and by using the appropriateefficiency (E) for multiphase flow.

Modified-Flanigan - Hydrostatic Pressure Difference

When calculating the pressure losses due to hydrostatic effects the Flanigan correlation ignores downhill flow. Thehydrostatic head caused by the liquid content is calculated as follows:

where:

hi = the vertical "rises" of the individual sections of the pipeline (ft)EL = Flanigan holdup factor (in-situ liquid volume fraction)

The Flanigan holdup factor is calculated using the following equation.

Modified-Flanigan Friction Pressure Loss

In the Flanigan correlation, the friction pressure drop calculation accounts for liquids by adjusting thePanhandle/Weymouth efficiency (E) according to the following plot. The plot has been normalized for the Modified-Flanigan correlation, so that when there is mostly gas, the efficiency is around 0.80 (close to the single-phasedefault for gas)

Notice that as the quantity of liquids increases, the efficiency decreases.

Nomenclature

E = Panhandle/Weymouth efficiencyEL = Flanigan holdup factor (in-situ liquid volume fraction)g = gravitational acceleration (32.2 ft/s2)gc = conversion factor (32.2 (lbm*ft)/(lbf*s2))hi = the vertical "rises" of the individual sections of the pipeline (ft)PHH = pressure loss due to hydrostatic head (psi)Pf = pressure change due to friction (psi)

Vsg = superficial gas velocity (ft/s)L = liquid density (lb/ft3)

Reference

Flanigan, O., "Effect of Uphill Flow on Pressure Drop in Design of Two-Phase Gathering Systems", O&GJ, Vol. 56, No. 10, p. 132,March (1958).



Gray Correlation

The Gray correlation was developed by H.E. Gray (Gray, 1978), specifically for wet gas wells. Although this correlation wasdeveloped for vertical flow, we have implemented it in both vertical, and inclined pipe pressure drop calculations. To correct thepressure drop for situations with a horizontal component, the hydrostatic head has only been applied to the vertical component ofthe pipe while friction is applied to the entire length of pipe.

First, the in-situ liquid volume fraction is calculated. The in-situ liquid volume fraction is then used to calculate the mixture density,which is in turn used to calculate the hydrostatic pressure difference. The input gas liquid mixture properties are used to calculatean "effective" roughness of the pipe. This effective roughness is then used in conjunction with a constant Reynolds Number of

to calculate the Fanning friction factor. The pressure difference due to friction is calculated using the Fanning friction pressureloss equation. For a more detailed look at each step, make a selection from the following list:

Gray - Hydrostatic Pressure Difference

The Gray correlation uses three dimensionless numbers, in combination, to predict the in situ liquid volume fraction.These three dimensionless numbers are:

where:

They are then combined as follows:

where:

Once the liquid holdup (EL) is calculated it is used to calculate the mixture density ( m). The mixture density is, inturn, used to calculate the pressure change due to the hydrostatic head of the vertical component of the pipe or well.

Note: For the equations found in the Gray correlation, is given in lbf/s2. We have implemented them using withunits of dynes/cm and have converted the equations by multiplying by 0.00220462. (0.00220462dynes/cm =1lbf/s2)

Gray - Friction Pressure Loss

The Gray Correlation assumes that the effective roughness of the pipe (ke) is dependent on the value of Rv. Theconditions are as follows:

if then

if then



where:

The effective roughness (ke) must be larger than or equal to 2.77 10-5.

The relative roughness of the pipe is then calculated by dividing the effective roughness by the diameter of the pipe.The Fanning friction factor is obtained using the Chen equation and assuming a Reynolds Number (Re) of 107.Finally, the expression for the friction pressure loss is:

Note: The original publication contained a misprint (0.0007 instead of 0.007). Also, the surface tension ( ) is givenin units of lbf/s2. We used a conversion factor of 0.00220462 dynes/cm = 1 lbf/s2.

Nomenclature

CL = liquid input volume fractionD = inside pipe diameter (ft)EL = in-situ liquid volume fraction (liquid holdup)ftp = two-phase friction factorg = gravitational acceleration (32.2 ft/s2)gc = conversion factor (32.2 (lbmft)/(lbfs2))k = absolute roughness of the pipe (in)ke = effective roughness (in)L = length of pipe (ft)PHH = pressure change due to hydrostatic head (psi)Pf = pressure change due to friction (psi)

Vsl = superficial liquid velocity (ft/s)Vsg = superficial gas velocity (ft/s)Vm = mixture velocity (ft/s)z = elevation change (ft)G = gas density (lb/ft3)



m = mixture density (lb/ft3)= gas / liquid surface tension (lbf/s2)

Reference

American Petroleum Institute,API Manual 14B, "Subsurface Controlled Subsurface Safety Valve Sizing Computer Program ",Appendix B, Second Ed., Jan. (1978)

Hagedorn and Brown Correlation

Experimental data obtained from a 1500ft deep, instrumented vertical well was used in the development of the Hagedorn andBrown correlation. Pressures were measured for flow in tubing sizes that ranged from 1 " to 1 " OD. A wide range of liquid ratesand gas/liquid ratios were used. As with the Gray correlation, our software will calculate pressure drops for horizontal and inclinedflow using the Hagedorn and Brown correlation, although the correlation was developed strictly for vertical wells. The softwareuses only the vertical depth to calculate the pressure loss due to hydrostatic head, and the entire pipe length to calculate friction.

The Hagedorn and Brown method has been modified for the Bubble Flow regime (Economides et al, 1994). If bubble flow existsthe Griffith correlation is used to calculate the in-situ volume fraction. In this case the Griffith correlation is also used to calculatethe pressure drop due to friction. If bubble flow does not exist then the original Hagedorn and Brown correlation is used tocalculate the in-situ liquid volume fraction. Once the in-situ volume fraction is determined, it is compared with the input volumefraction. If the in-situ volume fraction is smaller than the input volume fraction, the in-situ fraction is set to equal the input fraction(EL = CL). Next, the mixture density is calculated using the in-situ volume fraction and used to calculate the hydrostatic pressuredifference. The pressure difference due to friction is calculated using a combination of "in-situ" and "input" gas-liquid mixtureproperties. For further details on any of these steps select a topic from the following list:



Hagedorn and Brown - Hydrostatic Pressure Difference

The Hagedorn and Brown correlation uses four dimensionless parameters to correlate liquid holdup. These four

parameters are:

Various combinations of these parameters are then plotted against each other to determine the liquid holdup.

For the purposes of program ming, these curves were converted into equations. The first curve provides a value for

CNL. This CNL value is then used to calculate a dimensionless group, . can then be obtained from a plot of

vs . Finally, the third curve is a plot of vs. another dimensionless group of numbers, . Therefore, the

in-situ liquid volume fraction, which is denoted by EL, is calculated by:

The hydrostatic head is once again calculated by the standard equation:

where:

Hagedorn and Brown - Friction Pressure Loss

The friction factor is calculated using the Chen equation and a Reynolds number equal to:

Note: In the Hagedorn and Brown correlation the mixture viscosity is given by:

The pressure loss due to friction is then given by:

where:

Modifications



We have implemented two modifications to the original Hagedorn and Brown Correlation. The first modification is

simply the replacement of the liquid holdup value with the "no-slip" (input) liquid volume fraction if the calculated

liquid holdup is less than the "no-slip" liquid volume fraction.

if

then

The second modification involves the use of the Griffith correlation (1961) for the bubble flow regime. Bubble flow

exists if where:

If the calculated value of L B is less than 0.13 then L B is set to 0.13. If the flow regime is found to be bubble flow

then the Griffith correlation is applied, otherwise the original Hagedorn and Brown correlation is used.

The Griffith Correlation (Modification to the Hagedorn and Brown Correlation)

In the Griffith correlation the liquid holdup is given by:

where:Vs = 0.8 ft/s

The in-situ liquid velocity is given by:

The hydrostatic head is then calculated the standard way.

The pressure drop due to friction is also affected by the use of the Griffith correlation because EL enters into the

calculation of the Reynolds Number via the in-situ liquid velocity. The Reynolds Number is calculated using the

following format:

The single phase liquid density, in-situ liquid velocity and liquid viscosity are used to calculate the Reynolds Number.

This is unlike the majority of multiphase correlations, which usually define the Reynolds Number in terms of mixture

properties not single phase liquid properties. The Reynolds number is then used to calculate the friction factor using

the Chen equation. Finally, the friction pressure loss is calculated as follows:

The liquid density and the in-situ liquid velocity are used to calculate the pressure drop due to friction.

Nomenclature

CL = input liquid volume fraction

CG = input gas volume fraction

D = inside pipe diameter (ft)

EL = in-situ liquid volume fraction (liquid holdup)

f = Fanning friction factor



L = length of calculation segment (ft)

PHH = pressure change due to hydrostatic head (psi)

Pf = pressure change due to friction (psi)

Vsl = superficial liquid velocity (ft/s)

Vsg = superficial gas velocity (ft/s)

Vm = mixture velocity (ft/s)

VL = in-situ liquid velocity (ft/s)




L= liquid viscosity (cp)m = mixture viscosity (cp)G = gas viscosity (cp)

G = gas density (lb/ft3)



m = mixture density (lb/ft3)

f = (lb/ft3)

= gas / liquid surface tension (dynes/cm)

ReferencesEconomides, M.J. et al, Petroleum Production Systems. New Jersey: Prentice Hall Inc., 1994.Hagedorn, A.R., Brown, K.E., "Experimental Study of Pressure Gradients Occurring During Continuous Two-Phase Flow in SmallDiameter Vertical Conduits", JPT, p.475, April. (1965)

Turner CorrelationR. G. Turner, M. G. Hubbard and A. E Dukler first presented the Turner correlation at the SPE Gas Technology Symposium held in Omaha,Nebraska, September 12 and 13, 1968. The correlation (SPE paper 2198) calculates the minimum gas flow rate required to lift liquids out of awellbore and is often referred to as The Liquid Lift Equation or Critical Flow Rate Calculation for Lifting Liquids. In F.A.S.T. Virtuwell, thiscorrelation is used to test for stable wellbore flow.

Theoretical BackgroundThe Turner correlation assumes free flowing liquid in the wellbore forms droplets suspended in the gas stream. Two forces act onthese droplets. The first is the force of gravity pulling the droplets down and the second is drag force due to flowing gas pushingthe droplets upward. If the velocity of the gas is sufficient, the drops are carried to surface. If not, they fall and accumulate in thewellbore.

The correlation was developed from droplet theory. The theoretical calculations were then compared to field data and a 20%fudge factor was built-in. The correlation is generally very accurate and was formulated using easily obtained oilfield data.Consequently, it has been widely accepted in the petroleum industry. The model was verified to about 130 bbl/MMscf.

The Turner correlation was formulated for free water production and free condensate production in the wellbore. The calculation ofminimum gas velocity for each follows:

From the minimum gas velocity, the minimum gas flow rate required to lift free liquids can then be calculated using:

where:

A = cross-sectional area of flow (ft2)G = gas gravityk = calculation variableP = pressure (psia)qg = gas flow rate (MMscfd)T = temperature (R)vg = minimum gas velocity required to lift liquids (ft/s)Z = compressibility factor (supercompressibility)

Application of the Turner CorrelationThere are two ways to calculate the liquid lift rate in F.A.S.T. Virtuwell. First of all, the Liquid Lift page may be used. Thisrequires the entry of pressure, temperature and tubing IDs to calculate the corresponding gas rates to lift water and condensate.As well, a liquid lift rate is calculated in conjunction with each Tubing Performance Curve on the Gas AOF/TPC page. It isrepresented on the tubing performance curve by a circle listing the number identifying the tubing performance curve. To the rightof the liquid lift rate, the tubing performance curve is a solid green line. To the left, it is a dotted red line. The solid green line



represents stable flow, i.e. the wellbore will lift liquids continuously. The dotted red line represents unstable flow. If the Tubing

Performance Curve is a dotted red line over the entire range of flow rates represented, the circled number is placed in the middle

of the curve solely for identification. The calculated liquid lift rates for each tubing performance curve are tabulated in the Liquid

Lift module.

The Turner correlation incorporates separate equations for water and condensate. The liquid lift rate calculated on the Gas

AOF/TPC pages will be the rate associated with the heaviest liquid in the wellbore. For example, if the flow through the wellbore

includes gas, condensate and water, the liquid lift rate will be calculated for water. If there is no liquid flow in the wellbore, the

liquid lift rate is also calculated for water.

Important Notes

If both condensate and water are present, use the Turner correlation for water to judge behaviour of a system.

It is very important to note that the Turner correlation utilizes the cross-sectional area of the flow path when calculating liquid lift rates.

For example, if the flow path is through the tubing, the minimum gas rate to lift water and condensate will be calculated using the tubing

inside diameter. When the tubing depth is higher in the wellbore than the mid-point of perforations (MPP) in a vertical well, the Turner

correlation does not consider the rate required to lift liquids between the MPP and the end of the tubing. Ultimately, the liquid lift rate

calculations are based on the inside diameter (ID) of the tubing or the area of the annulus and not on the casing ID unless flow is up the

"casing only".

Minimum Gas Rate to Lift CondensateThis is the minimum gas rate at which condensate will be lifted continuously. This rate is calculated based on the Turner

correlation. First the required gas velocity is found:

where:

G = gas gravity

k = calculation variable

P = pressure (psia)

T = temperature (R)

vg = minimum gas velocity required to lift liquids (ft/s)

z = compressibility factor (supercompressibility)

This leads to an expression for the Turner calculated gas rate:

where:

A = cross-sectional area of flow (ft2)

qg = gas flow rate Mcfd (103m3/d)

As pressure increases, so does the minimum gas rate to lift water or condensate. Therefore, to determine the minimum gas rate

to lift water or condensate in a wellbore, it is recommended that the highest pressure in the wellbore be used. This is typically the

flowing sandface pressure. In his original work, Turner (1969) recommends that the wellhead pressure be used. In our research

also supported by Lea Jr. (1983), we have found that generally, if the sandface pressure is known, it and not the wellhead

pressure should be used to calculate the minimum gas rate to lift liquids.

Minimum Gas Rate to Lift WaterThis is the minimum gas rate at which water will be lifted continuously. This rate is calculated based on the Turner correlation.

First the required gas velocity is found:

where:

G = gas gravity

k = calculation variable

P = pressure (psia)

T = temperature (R)

vg = minimum gas velocity required to lift liquids (ft/s)

z = compressibility factor (supercompressibility)



This leads to an expression for the Turner calculated gas rate:

where:

A = cross-sectional area of flow (ft2)qg = gas flow rate (MMscfd)

As pressure increases, so does the minimum gas rate to lift water or condensate. Therefore, to determine the minimum gas rateto lift water or condensate in a wellbore, it is recommended that the highest pressure in the wellbore be used. This is typically theflowing sandface pressure. In his original work, Turner (1969) recommends that the wellhead pressure be used. In our researchalso supported by Lea Jr. (1983), we have found that generally, if the sandface pressure is known, it and not the wellheadpressure should be used to calculate the minimum gas rate to lift liquids.

UNITS: MMcfd (10 3 m 3/d)

DEFAULT: none

ReferencesLea Jr., J.F.and Tighe, R.E., "Gas Well Operation With Liquid Production," SPE Paper No. 11583, presented at the 1983 Production OperationSymposium, Oklahoma City, Oklahoma, February 27 March 1, 1983.Turner, R.G., Hubbard, M.G., and Dukler, A.E.: "Analysis and Prediction of Minimum Flow Rate for the Continuous Removal of Liquids from Gas Wells,"J. Pet. Tech. (Nov. 1969), 1475-1482.

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Pressure Loss Correlations (NOT MINE)