Pressure Loss Correlations -...

Pressure Loss Correlations

IntroductionIn the flow of fluids inside pipes, there are three pressure loss components:

Friction

Hydrostatic

Kinetic energy

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

All the pressure loss procedures calculate the Hydrostatic Pressure Difference and Friction Pressure Losscomponents individually, and then add (or subtract) them to obtain the total pressure loss. There are many published correlations for calculating pressure losses. These fall into the 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 a horizontal pipe, incorporation of the hydrostatic pressure drop allows that correlation to be used for flow in a vertical pipe. This adaptation is rigorous, andhas been implemented into all the correlations used in VirtuWell. Nevertheless, for identification purposes,the correlation’s name has been kept unchanged. Thus, as an example Panhandle was originally developed for horizontal 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 the AGA (American Gas Association), includes Panhandle, Modified Panhandle and Weymouth. These correlations are for single-phase gas only. They incorporate a simplified friction factor and a flow efficiency. They all have a similar format 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 the Fanning 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 ofthe Fanning friction factor chart.

where:

f = friction factork = absolute roughness (in)k/D = relative roughness (unitless)Re = Reynold’s number

The single-phase friction factor clearly depends on the Reynold’s 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 Reynold’s number.

where:

= density, lbm/ft3v = velocity, ft/sD = 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 fluidg=acceleration of gravityh=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 * * * *

MultiphaseMultiphase pressure loss calculations parallel single phase pressure loss calculations. Essentially, each multiphase correlation makes its own particular modifications to the hydrostatic pressure difference and the friction pressure loss calculations, in order to make 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 account for multiphase mixture properties. In the AGA type equations (Panhandle, Modified Panhandle and Weymouth), it is the flow efficiency 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 definedflow patterns. Some correlations (Flanigan) ignore the pressure 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 in pipelines and the Flanigan multiphase corrections. These equations can be used for gas-liquid multiphase flow or for single-phase gas flow. 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 10 degrees) 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 loss equation. These can be used for either gas-liquid multiphase flow, single-phase gas or single-phase liquid, because in single-phase mode, they revert to the Fanning equation, which is equally applicable to either gas or liquid. Beggs and Brill is a multipurpose correlation derived from laboratory data for vertical, horizontal, inclined uphill and downhill flow of gas-water mixtures. Gray is based on field data for vertical 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 to horizontal pipes.

Below is a summary of the correlations available in this program and the connection between the single-phase and multiphase forms. 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 individual component can be either positive or negative, depending on the direction of calculation, the direction of flow and the direction of elevation change.

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

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

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 the pressure 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 the direction of the earth’s gravitational pull, whereas the friction pressure loss is always positive in the direction of flow.

Single Phase FlowThe most generally applicable single phase equation for calculating Friction Pressure Loss is the Fanning equation. It utilizes friction factor charts (Knudsen and Katz, 1958), which are functions of Reynold’s number and relative pipe roughness. These charts are also often referred to as 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 with pressure 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 correlations that 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 the Multi-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 hydrostatic pressure difference is not taken into account. We have applied the standard hydrostatic head equation to the vertical elevation of the pipe to account for the 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 some transportation systems. Thus, it also originally did not account for vertical flow. We have applied the standard hydrostatic head equation to account for the vertical component of pressure drop. Hence our implementation of the Modified Panhandle equation includes BOTH horizontal and vertical flow components, 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 for short pipelines and gathering systems. As a result, it only accountsfor horizontal flow and not for hydrostatic pressure drop. We have applied the standard hydrostatic head equation to account for the vertical component of pressure drop. Thus, our implementation of the Weymouthequation includes 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 the Fanning single-phase correlations. For example, if the Gray correlation was selected but there was only gas in the system, the Fanning Gas correlation would be used. For caseswhere 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-phase Weymouth correlation.

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

Panhandle - Friction Pressure LossThe Panhandle correlation can be written as follows:

where:

The Panhandle equation incorporates a simplified representation of the friction factor, which is built into the equation. To account for real life situations, the flow efficiency factor, E, was included in the equation. This flow efficiency generally ranges from 0.8 to 0.95. Although we recognize that a common default for the flow efficiency is 0.92, 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 calculations the Panhandle correlation 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 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)

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)

Fanning CorrelationThe 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 thename 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 LossThe 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 Reynold’s number and relative pipe roughness. These charts are also often referred to as theMoody 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 DifferenceThe 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 CorrelationThe 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 LossThe 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 Reynold’s number and relative pipe roughness. These charts are also often referred to as theMoody 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 DifferenceThe 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. For liquid, 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.

NomenclatureD = 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 = Reynold’s numberV = velocity (ft/s)

z = elevation change


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

Weymouth – Friction Pressure LossThe pressure drop due to friction is given by:

where:

The Weymouth equation incorporates a simplified representation of the friction factor, which is built into the equation. To account for real life situations, the flow efficiency factor, E, was included in the equation. The flow efficiency 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 factor



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 present must be taken into account. Also, the interactions between each phase have to be considered. Mixture properties must be used, and therefore the gas and liquid in-situ volume fractions throughout the pipe need to be determined. In general, all multiphase correlations are essentially two phase and not three phase. Accordingly, the oil and water phases are combined, and treated as a pseudo single liquid phase, while gas is considered 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, Vsg

Mixture Velocity, Vm

Liquid Holdup Effect

Input Volume Fraction, CL

In-situ Volume Fraction, EL

Mixture 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 correlationsthat were developed for the whole spectrum of flow 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 of the 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 all directions by calculating the hydrostatic pressure difference using only the vertical elevation of the pipe segment and the friction pressure loss 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 it so that it applies to flow in all directions by calculating the hydrostatic pressure difference using only the vertical elevation of the pipe segment and the frictionpressure 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 flow directions. 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 a correction for multiphase Flow Efficiency, and a calculation of hydrostatic pressure difference to account for uphill flow. There is no hydrostatic pressure recovery for downhill flow. In this software, the Flanigan multiphase correlation is also applied to the Modified Panhandle 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 multiphase flow. It incorporates the Flanigan correction of the Flow

Efficiency for multiphase flow and a calculation of hydrostatic pressure difference to account for uphill flow. There is no hydrostatic pressure recovery for downhill flow. In this software, the Flaniganmultiphase correlation is also applied to the Panhandle and Weymouth correlations. It is recommended that this correlation not be used beyond +/- 10 degrees from the horizontal.

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

Each of these correlations was developed for it’s own unique set of experimental conditions, and accordingly, results will vary between them.

Single Phase GasIn 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 implementedto 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 Model

Determine 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 Flow

Calculate (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 a transitional 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:


5.

, where: D (ft), L (lb/ft3), G (lb/ft3), (dyn/cm)

6. , where:


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 number

S = 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

References

Petalas, 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 1996 Fluids 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 Mechanistic Model 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 "horizontal flow" only. Not many correlations apply to the whole spectrum of flow situations that may be encountered in oil and gas operations, namely uphill, downhill, horizontal, inclined and vertical flow. The Beggs and Brill (1973) correlation, is one of the few published correlations capable of handling all these flow directions. It was developed using 1" and 1-1/2" sections of pipe that could 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. First the appropriate flow regime for the particular combination of gas and liquid rates(Segregated, Intermittent or Distributed) is determined. The liquid holdup, and hence, the in-situ density ofthe gas-liquid mixture is then calculated according to the appropriate flow regime, to obtain the hydrostaticpressure 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 Liquid correlation.

See Also: Pressure Drop Correlations, Multiphase Flow Correlations

Flow Pattern MapUnlike the Gray or the Hagedorn and Brown correlations, the Beggs and Brill correlation requires that a flow pattern be determined. Since the original flow pattern map was created, it has been modified. We have used this modified flow 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 the following 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 DifferenceOnce the flow type has been determined then the liquid holdup can be calculated. Beggs and Brill divided the liquid holdup calculation into two parts. First the liquid holdup for horizontal flow, EL(0), is determined, and then this holdup is modified for inclined flow. EL(0) must be CL and therefore when EL(0) is smaller than CL, EL(0) is assigned a value 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 by multiplying 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 velocity number (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. Thevalue 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:

Nomenclature

CL = liquid input volume fractionD = inside pipe diameter (ft)EL(0) = horizontal liquid holdupEL( ) = inclined liquid holdupftp = two phase friction factor

fNS = no-slip friction factorFrm = Froude Mixture Numberg = gravitational acceleration (32.2 ft/s2)gc = conversion factor (32.2 (lbm*ft)/(lbf*s2))L = length of pipe (ft)Nvl = liquid velocity numberVm = 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)

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

Flanigan CorrelationThe 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 correlationis 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 correlationcan 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 DifferenceWhen 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 LossIn 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 CorrelationThe 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 in vertical flow situations such as vertical wellbores. Therefore, the Flanigan correlation, and hence the Modified-Flanigan correlation, is only available on the Pipe and Comparison pages. Care should be taken when applying the Modified-Flanigan correlation to situations other than essentially horizontal flow. The effects of using the Modified-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.

Modified-Flanigan - Hydrostatic Pressure DifferenceWhen 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.

Modified-Flanigan – Friction Pressure LossIn the Flanigan correlation, the friction pressure drop calculation accounts for liquids by adjusting the Panhandle/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-phase default for gas)

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

NomenclatureE = 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)


ReferenceFlanigan, 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 CorrelationThe Gray correlation was developed by H.E. Gray (Gray, 1978), specifically for wet gas wells. Although this correlation was developed for vertical flow, we have implemented it in both vertical, and inclined pipe pressure drop calculations. To correct the pressure drop for situations with a horizontal component, the hydrostatic head has only been applied to the vertical component of the pipe while friction is applied to theentire 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 calculate an "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 pressure loss equation. For a more detailed look at each step, make a selection from the following list:

Gray - Hydrostatic Pressure DifferenceThe 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, in turn, 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 with units of dynes/cm and have converted the equations by multiplying by 0.00220462. (0.00220462dynes/cm = 1lbf/s2)

Gray - Friction Pressure LossThe Gray Correlation assumes that the effective roughness of the pipe (ke) is dependent on the value of Rv. The conditions 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 given in 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)





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

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

Hagedorn and Brown CorrelationExperimental data obtained from a 1500ft deep, instrumented vertical well was used in the development of the Hagedorn and Brown correlation. Pressures were measured for flow in tubing sizes that ranged from 1 " to 1 ½" OD. A wide range of liquid rates and gas/liquid ratios were used. As with the Gray correlation, our software will calculate pressure drops for horizontal and inclined flow using the Hagedorn

and Brown correlation, although the correlation was developed strictly for vertical wells. The software uses 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 exists the Griffith correlation is used to calculate the in-situ volume fraction. In this case the Griffith correlation is also used to calculate the pressure drop due to friction. If bubble flow does not exist then the original Hagedorn and Brown correlation is used to calculate the in-situ liquid volume fraction. Once the in-situ volume fraction is determined, it is compared with the input volume fraction. 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 pressure difference. The pressure difference due to friction is calculated using a combination of "in-situ" and "input" gas-liquid mixture properties. For further details on any of these steps select a topic from the following list:

Hagedorn and Brown - Hydrostatic Pressure DifferenceThe 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 LossThe 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 fractionCG = input gas volume fractionD = inside pipe diameter (ft)EL = in-situ liquid volume fraction (liquid holdup)f = Fanning friction factorg = gravitational acceleration (32.2 ft/s2)gc = conversion factor (32.2 (lbmft)/(lbfs2))

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)

z = elevation change (ft)L= liquid viscosity (cp)

m = mixture viscosity (cp)

G = gas viscosity (cp)




m = mixture density (lb/ft3)

f = (lb/ft3)= gas / liquid surface tension (dynes/cm)

References

Economides, 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 Small Diameter 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 a wellbore and is often referred to as The Liquid Lift Equation or Critical Flow Rate Calculation for Lifting Liquids. In F.A.S.T. Virtuwell™, this correlation 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 on these droplets. The first is the force of gravity pulling the droplets down and thesecond is drag force due to flowing gas pushing the droplets upward. If the velocity of the gas is sufficient,the drops are carried to surface. If not, they fall and accumulate in the wellbore.

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 petroleumindustry. 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 of minimum 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. This requires 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 is represented on the tubing performance curve by a circle listing the number identifying the tubing performance curve. To the right of 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. Thecalculated 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 becalculated 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 ofa 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 basedon the Turner correlation. First the required gas velocity is found:

where:

G = gas gravityk = calculation variableP = 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 determinethe 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 gravityk = calculation variableP = 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 determinethe 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.

UNITS: MMcfd (10 3 m 3 /d)

DEFAULT: none

References

Lea Jr., J.F.and Tighe, R.E., "Gas Well Operation With Liquid Production," SPE Paper No. 11583, presented at the 1983 Production Operation Symposium, 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.

Copyright © 2013 Fekete Associa

Pressure Loss Correlations -...

Documents

Transcript of Pressure Loss Correlations -...