Choke Sizing & Propiedaes de Los Fluidos

Choke Sizing

Pressure Loss Correlations

Introduction

In 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 ignored in all practical situations.

All the pressure loss procedures calculate the Hydrostatic Pressure Difference and Friction Pressure Loss components 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 Phase

There 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 (Moody)

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, and has been implemented into all the correlations used in VirtuWell. Nevertheless, for identification purposes, the correlations 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 Component

There 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 ( @ T,P)

E=pipeline efficiency factor

P=reference pressure (psia) (14.65 psia)

T=reference temperature, (R) (520 R)

G=gas gravity

D=inside diameter of pipe (inch)

Ta=average flowing temperature (R)

Za=average gas compressibility factor

L=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

f=Fanning friction factor (function of Reynolds number)

=density

v=average velocity

L=length of pipe section

g=acceleration of gravity

D=inside diameter of pipe

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

Single-Phase friction factor ():

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.

References: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 = ghwhere:

=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

GasLiquid

CorrelationsVerticalHorizontalVerticalHorizontal

Fanning-Gas**

Fanning-Liquid **

Panhandle**

Modified Panhandle**

Weymouth**

Mechanistic****

Multiphase

Multiphase 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 defined flow 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 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 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 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 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. 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 accounts for 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 Weymouth equation 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 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-phase Weymouth 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 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 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 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:

Nomenclature

D = pipe inside diameter (inch)

E = Panhandle/Weymouth efficiency factor

G = gas gravity

g = 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, ,, 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 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 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 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.

Nomenclature


f = Fanning friction factor


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

k/D = relative roughness (unitless)

L = length (ft)


Pf = pressure change due to friciton (psi)


V = velocity (ft/s)

z = elevation change


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 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 Correlation

This 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 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 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:

Nomenclature


E = Panhandle/Weymouth efficiency factor

G = gas gravity


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)


QG = gas flow rate at standard conditions, T,P, ft3/d

T = reference temperature for standard conditions (Rankin)

Ta = average temperature (Rankin)

Za = average compressibility factor



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).

Multiphase FlowLa presencia de fases mltiples complica grandemente los clculos de la cada de presin. Esto es debido al hecho de que las propiedades presentes de cada uno elocuente deben ser tomadas en consideracin. Tambin, las interacciones entre cada fase tienen que ser consideradas. Las propiedades de las mezclas deben ser usadas, y por eso las fracciones del gas y las lquidas del volumen in-situ a todo lo largo de la tubera necesitan ser determinados. En general, todas las correlaciones multifsicas son esencialmente de dos fase y no tres fase. Consecuentemente, el petroleo y la fase de agua estn combinados, y son tratados como una sola fase seudoliquida, mientras que el gas es considerado como una una fase separada. Lo siguiente es una lista de conceptos generales inherentes para el flujo multifsicoThe 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 Correlations

Muchas de las correlaciones multifsicas publicadas de flujo multifsicas son aplicables para "el flujo vertical" slo, mientras los otros aplica sola para "flujo horizontal" . Aparte de la correlacin del Beggs y Brill, no hay muchas correlaciones que fueron desarrolladas para el espectro total de situaciones de flujo que pueden ser encontradas en operaciones de petroleo y degas; A saber cuesta arriba, cuesta abajo, el flujo horizontal, inclinado y vertical. Sin embargo, hemos adaptado todas las correlaciones (segn el caso) a fin de que se apliquen a todas las situaciones del flujo. Lo siguiente es una lista de las correlaciones multifsicas de flujo que estn disponibles.Many 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 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: La Correlacin Gray (1978) fue desarrollada para el flujo vertical en fluyo gas humedo. Lo hemos modificado a fin de que se aplice al flujo en todas las direcciones calculando la diferencia hidrosttica de presin usando unicamente la elevacin vertical del segmento de la tubera y la perdida de presin debido a la friccin esta basada en la longitud total de la tubera.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 y Brown: La correlacion Hagedorn y Brown (1964) fue desarrollada para el flujo vertical en pozos de petrleo. Tambin lo hemos modificado a fin de que se aplice al flujo en todas las direcciones para el calculalo de la diferencia hidrosttica de presin usando unicamente la elevacin vertical del segmento de la tubera y la presin de friccin que esta basada en la longitud total de la tubera.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 friction pressure loss based on the total pipe length. 3.- Beggs y Brill: La Beggs y Correlacin Beggs (1973) es uno de los menos publicados correlaciones capaces de manejar en todos los direcciones de flujo. Fue desarrollado usando secciones de tubera que estan inclin en cualquier ngulo.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 Flanigan multiphase 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. There is 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 its own unique set of experimental conditions, and accordingly, results will vary between 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 Liquid

In 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 Flow

For 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

GasLiquid

CorrelationsVerticalHorizontalVerticalHorizontal

Fanning-Gas

Fanning-Liquid *

Panhandle

Modified Panhandle

Weymouth

Beggs & Brill* * * *

Gray*

Hagedorn & Brown *

Flanigan *

Modified-Flanigan *

Weymouth (Multiphase) *

Mechanistic Model* * * *

Mechanistic Model

Determine Flow Pattern

To 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 Flow

Exists if

where

and if

Stratified Flow

Exists 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.

a. 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 Flow

Bubble flow exists if

(3)

where:C1 = 0.5

= 1.3

db = 7mm

(4)

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

where:

(see Intermittent flow for additional definitions).

Intermittent Flow

Intermittent flow exists if

where:

If EL > 1, EL = CLand:

where is from standard methods where:

for fm < 1, fm = 1

where is from standard methods where:

if

a. If and then Slug Flow

b. If and then Elongated Bubble Flow

1. 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), (cP), (dyn/cm)

1. , where: C (lb/ft3), VC (ft/s), DC (ft), (dyn/cm)

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


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


NomenclatureA = cross sectional area

C0 = velocity distribution coefficient

D = pipe internal diameter

E = in situ volume fraction

FE = liquid fraction entrained

g = acceleration due to gravity

hL = height of liquid (stratified flow)

L = length

P = pressure


S = contact perimeter

VSG = superficial gas velocity

VSL = 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

Subscripts

b = relating to the gas bubble

c = relating to the gas core

F = relating to the liquid film

db = relating to dispersed bubbles

G = relating to gas phase

i = relating to interface

L = relating to liquid phase

m = relating to mixture

SG = based on superficial gas velocity

s = relating to liquid slug

SL = based on superficial liquid velocity

wL = relating to wall-liquid interface

wG = relating to wall-gas interface

C0 = 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 Correlation

For 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 of the gas-liquid mixture is then calculated according to the appropriate 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 Liquid correlation.

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 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 Difference

Once 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 Loss

The 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:

Nomenclature

CL = 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



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 () 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 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 () for multiphase flow.

Modified-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.

Modified-Flanigan Friction Pressure Loss

In the Flanigan correlation, the friction pressure drop calculation accounts for liquids by adjusting the Panhandle/Weymouth efficiency () 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.

Nomenclature

E = Panhandle/Weymouth efficiency

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



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)


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 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 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 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 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, 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 Loss

The 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 fraction


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

ftp = two-phase friction factor



k = absolute roughness of the pipe (in)

ke = effective roughness (in)

L = length of pipe (ft)











= 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 and Brown correlation. Pressures were measured for flow in tubing sizes that ranged from 1 " to 1 " 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 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 is less than 0.13 then 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 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


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

f = Fanning friction factor



L = length of calculation segment (ft)






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


= liquid viscosity (cp)

= mixture viscosity (cp)

= gas viscosity (cp)





= (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 Correlation

R. 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 Background

The 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 the second 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 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 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 gravity

k = calculation variable

P = 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 Correlation

There 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. 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


P = pressure (psia)

T = temperature (R)


z = compressibility factor (supercompressibility)

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

where:


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 Water

This 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


P = pressure (psia)

T = temperature (R)


z = compressibility factor (supercompressibility)

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

where:


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 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

Choke Sizing

Single-Phase Flow

Gas Mass Flow

The relationship which describes the mass flow of a single-phase gas through a choke can be generically written as:

where

With the gas density at standard conditions, the gas mass flowrate is readily converted into a daily standard volumetric flowrate.

This equation applies only at the critical pressure ratio, . The critical pressure ratio can be calculated from

Liquid Mass Flow

Single-phase liquids flowing through a restriction almost never reach the critical velocity, which is many times that for single-phase gas. The flowrate can be related to the pressure drop across the restriction with the following relationship:

where

The choke flow coefficient is a function of the Reynolds number in the choke throat and so the solution is necessarily iterative, but convergence is quite rapid.

Rawlins-Schellhardt

Rawlins and Schellhardt give us a form of the equation for gas flow through chokes under critical flow conditions which is dependent only on the upstream pressure. Rawlins and Schellhardt based their equation on ideal gas at a standard pressure of 14.4 psia. Correction for non-ideality and for a standard pressure other than 14.4 psia is included in the following equation:

where

Szilas

Szilas gives us an alternate form of the gas mass flow equation and with constants and conversion factors for field units, as:

where

This equation applies both at and above the critical pressure ratio, .

Multiphase Flow

Ashford-Pierce

Ashford and Pierce developed a correlation specifically describing multiphase flow through safety valves and tested it against field data. Their correlation has the form:

with

and where

This relationship applies both at and above the critical pressure ratio, .

Ashford and Pierce further define the critical pressure ratio, , as

where

As this is implicit in , it must be solved iteratively.

The Ashford-Pierce relationship cannot directly be applied here because oil may or may not be one of the flowing phases. However, their relationship for the fluid velocity downstream of the choke gives rise to an alternative approach which is amenable to solution with gas plus one or more liquid phases present:

where

Assuming critical flow in the choke throat, the downstream pressure and fluid velocity can be calculated, and with the latter plus the produced fluid ratios, the mass flowrate of each phase is obtainable.

Achong

Achong updated Gilberts relationship on the basis of data from oil wells in the Lake Maracaibo field of Venezuela. The rate of multiphase flow through a choke and the upstream pressure are, according to Achong, correlated by the following relationship:

where

Baxendell

Baxendells correlation linking the rate of multiphase flow through a choke and the upstream pressure and fundamentally an update of the Gilbert correlation is:

where

Gilbert

Gilbert developed a generalized correlation based on data from flowing oil wells in the Ten Section field of California. The rate of multiphase flow through a choke and the upstream pressure can be correlated, according to Gilbert, by the following relationship:

where

Omana et al.

Omana et al. carried out field experiments in the Tiger Lagoon field of Louisiana with natural gas and water flowing through restrictions. Carrying out a dimensional analysis, Omana derived the following correlation:

with

and where

Reliable use of Omanas correlation is limited to an upstream pressure range of 400 1000 psig, 800 bbl/d maximum liquid flowrate, and choke sizes from 4/64" to 14/64". It should be applicable for both bottomhole and surface chokes.

Ros

The rate of multiphase flow through a choke and the upstream pressure are, according to Ros on the basis of Gilberts and other prior work, correlated by the following relationship:

where

References

Achong, I., "Revised Bean Performance Formula for Lake Maracaibo Wells", internal co. report, Shell Oil Co., Houston, TX, Oct 1961

Ashford, F.E. and Pierce, P.E., "Determining Multiphase Pressure Drops and Flow Capacities in Down-Hole Safety Valves", SPE Paper No. 5161, J. Pet. Tech., Sep 1975, 1145

Baxendell, P.B., "Bean Performance Lake Maracaibo Wells", internal co. report, Shell Oil Co., Houston, TX, Oct 1967

Gilbert, W.E., "Flowing and Gas-Lift Well Performance", Drill. & Prod. Practice, 1954, 126

Omana, R., Houssiere, C. Jr., Brown, K.E., Brill, J.P., and Thompson, R.E., "Multiphase Flow Through Chokes", SPE Paper No. 2682, paper presented at Annual Fall Meeting of the SPE of AIME, Denver, CO, Sep 28 Oct 1, 1969

Ros, N.C.J., "An Analysis of Critical Simultaneous Gas-Liquid Flow Through a Restriction and Its

Glossary

Absolute Open Flow (AOF)

The Absolute Open Flow potential of a well is the rate at which the well would produce against zero sandface backpressure. Flow into a well depends on both the reservoir characteristics and the wellbore flowing pressure. The relationship of inflow rate to bottomhole flowing pressure is called the IPR (Inflow Performance Relationship). For gas wells, this may also be called the AOF curve. F.A.S.T. VirtuWell presents this relationship in the form of a pressure versus flow rate graph. From this graph, the wells flow potential can be determined at various flowing sandface pressures. As well, the operating point (flow rate and pressure) of a particular wellbore configuration can be determined from the intersection of the AOF curve and the Tubing Performance Curve (TPC).

F.A.S.T. VirtuWell uses the simplified analysis approach to determine AOFs. This approach is based on the following equation:

where

q = flow rate at standard conditions (MMcfd, 103m3/d)

P = shut-in pressure (in the case of a Sandface AOF, this is the static reservoir pressure (psia, kPaA)

Pf = flowing pressure (psia, kPaA)

C = a coefficient which describes the position of the stabilized deliverability line (MMcfd/(psi2)n, 103m3/d/(kPa2)n)

N = an exponent to describe the inverse of the slope of the stabilized deliverability line (n varies between 1.0 for completely laminar flow and 0.5 for fully turbulent flow.)

This equation applies to both sandface and wellhead AOFs. If a sandface AOF is being calculated, all components of the equation refer to the sandface and vice-versa with wellhead AOF calculations. The Gas AOF/TPC page requires sandface AOFs for its calculations. If only a wellhead AOF is known, a sandface AOF may be calculated using the SF/WH AOF page. Care must be taken here when dealing with multi-phase flow as instabilities can occur.

Note: In order to represent a reservoir which is depleting due to pressure loss, several AOF curves may be drawn on the Gas AOF/TPC page. Each successive AOF curve will have a consistent n and c with a declining reservoir pressure. In order to model rate decline caused by wellbore liquid problems, the reservoir pressure and n may be kept constant, and the AOF or C varied to account for the effects of liquids.

For oil wells, there is no AOF, so instead a similar concept is used. AOFP (absolute open flow potential) represents the maximum value of oil flow as the pressure approaches zero. This is analogous to AOF (absolute open flow) with a gas well.

Angle

A calculated angle of the wellbore that is based on entered values of MD and TVD.

AOF Equation Exponent, n

This is the exponent found in the Absolute Open Flow (AOF) equation.

It describes the inverse of the slope of the stabilized deliverability line. "n" varies between 1.0 for completely laminar flow and 0.5 for fully turbulent flow.

It is generally accepted that "n" at wellhead is less than or equal to "n" at sandface. This condition is enforced when the SF/WH AOF module is converting an equation from sandface to wellhead or vice versa in single phase flow. However, in multiphase flow situations, the interaction of friction and hydrostatic pressure effects is much more complicated, and this relationship of wellhead to sandface "n" is not enforced. However, to conform to standard practice, the limits of 1.0 and 0.5 are honoured. Thus in a multiphase flow test, it is possible for the wellhead "n" to be larger than the sandface "n"

The procedure for calculating the wellhead AOF curve, and the wellhead AOF equation, is described below for a multiphase situation:

1. Draw the sandface AOF curve from the given data

2. Divide into 100 equally spaced rate points

3. For each of these, convert the sandface pressure to a wellhead pressure using the specified tubular configuration and fluid properties.

4. Draw the calculated wellhead AOF curve by joining these calculated points. For single phase flow, the curve will look very similar to the sandface curve, but for multiphase flow, the calculated wellhead points could form a curve with a region that represents UNSTABLE rates. This unstable region is characterized by a maximum or discontinuities or the limiting liquid lifting rate determined from the Turner Correlation. Any calculated points to the left of this are considered to be in unstable flow (and the well will eventually kill itself), and the curve is generally drawn as a dashed line to indicate this.

5. From the calculated shut-in wellhead pressure (assuming a static column of gas in the wellbore) and the calculated wellhead pressures in the STABLE portion of the wellhead curve, the wellhead AOF equation (AOF and "n") is determined. These values are copied onto the Option line and plotted as a continuous simplified AOF equation. The user can modify this generic option curve at will.

6. The conversion of a wellhead AOF curve to a sandface AOF curve follows the same procedure, but it is much more prone to irregularities. For example, sometimes the calculated flowing pressure can be higher than the specified reservoir pressure when the combination of specified rates and tubulars is unrealistic. It is very hard to guard against situations like this in a computer program with a wide range of applications. The user is warned to ensure that the calculated AOF curve is meaningful, and if not, to over-ride with a specified curve using the "option" entry.

UNITS: NoneDEFAULT: none LIMITS: 0.5 < n < 1.0

Bubble Point Pressure

The Bubble Point Pressure is defined as the pressure at which the oil is saturated with gas. Above this pressure the oil is undersaturated, and the oil acts as a single phase liquid. At and below this pressure the oil is saturated, and any lowering of the pressure causes gas to be liberated resulting in two phase flow.

The Bubble Point affects the Inflow Performance Relationship Curve (IPR) curve. Above this pressure, the IPR is a straight line, of slope equal to the inverse of productivity index. Below the bubble point pressure, the IPR is a curve based on "Vogels" equation. The straight line and the curve are tangential at the bubble point pressure, where they meet.

UNITS: psia (kPaA)DEFAULT: none

C, Sandface Coefficient

This is the coefficient found in the Absolute Open Flow (AOF) equation.

It describes the position of the stabilized deliverability line. Wellhead and sandface C values for a given system are usually different.

Note: Care must be taken when converting C from field to metric units or vice-versa. This is because the units of C are dependent on n. In order to avoid these problems, both n and C should be entered before changing units.

UNITS: MMcfd/(psia 2 ) n (10 3 m 3 /d/(kPaA 2 ) n)DEFAULT: none

Casing

Casing ID

The Casing ID is the Inside Diameter of the wellbore casing. This value is used to calculate the area of flow when production is through the casing or along with the Tubing OD to calculate the area of flow when production is directed through the annulus. This value will also be required when flow is through the tubing if the Mid-Point of Perforations(MPP) or the Datum is below the End of Tubing Depth (EOT).

For horizontal wellbores, three casing IDs, one for each of the Vertical, Deviated and Horizontal sections of the wellbore are requested.

The casing ID is also used to represent the inside diameter of the wellbore in the event of an openhole completion. There is no differentiation made between flow through openhole and flow through casing.

Note: In the petroleum industry the nominal casing size refers to the outside diameter of the casing. The ID depends on the OD and the weight (linear density) of the casing.

UNITS: Inches (mm)DEFAULT: none

Casing OD

Casing OD is the outside diameter of the casing. This value is not used in any calculations but will appear on printed reports.

Compressibility, Oil (Co)

The compressibility of any substance is the change in volume per unit volume per unit change in pressure. The oil compressibility is a source of energy for fluid flow in a reservoir. In an undersaturated reservoir it is a dominant drive mechanism, but for a saturated reservoir it is over-shadowed by the much larger gas compressibility effects. The oil compressibility is a component in the calculation of total compressibility, which is the value used in the determination of skin effect, dimensionless time and all material balance considerations in the fluid flow calculations.

There is a significant discontinuity at the bubble point pressure. Above this pressure, the oil is a single phase liquid (consisting of oil and dissolved gas). The compressibility of this liquid can be measured in the laboratory, and it is a weak function of pressure. At and below the bubble point pressure, if the pressure is decreased, gas comes out of solution and contributes to the compressibility of the system. This apparent oil compressibility is calculated by including a "dRs / dp" component, to account for the change in solution gas-oil ratio with pressure.

The correlations that can be used to calculate the Oil Compressibility are:

Vazquez and Beggs Generally applicable

Hanafy et al Egyptian oil

Petrosky and Farshad Gulf of Mexico oil

De Ghetto et al Heavy oil (10 22.3 API) and ExtraHeavy oil (API < 10)

UNITS: 1 / psi or 1 / kPa (absolute)DEFAULT: User selectable correlation

Condensate Gas Ratio (CGR)

This is the condensate to gas ratio produced at surface. It is typically known from direct measurements. If the daily condensate rate is known, it must be divided by the daily gas rate to obtain the Condensate-Gas Ratio. The CGR is used to calculate the Recombined Gas Gravity and the Recombined Gas Rate which are used in the wellbore pressure drop calculations.

UNITS: Bbl/MMcf (m3/103m3) DEFAULT: 0

See Also: Condensate Properties

Datum (MD)

The datum is a reference point for calculations. Calculations are either done from the sandface to the datum or from the datum to the wellhead.

This is the user-defined Measured Depth (MD) in a well. In the wellbore, the pressure drop is calculated from the specified Datum to the wellhead. The user may define the Datum to be located at any point in the horizontal section that allows the flexibility to calculate the pressure drop from any desired location.

UNITS: Feet (m)DEFAULT: none

El datum es un punto de referencia para los clculos. Los clculos son efectuados a cualesquier profundidad del sandface para el dato o desde el datum de la cabeza del pozo.

sta es la Profundidad Medida creada por el usuario (MD) en un pozo. En el wellbore, la cada de presin se calcula especificando el Datum desde el WEllhead. El usuario puede definir al Datum para estar localizado en cualquier punto en la seccin horizontal que consiente que la flexibilidad calcule la cada de la presin a cualquier posicin deseada.

Density

Density () as applied to hydrostatic pressure difference calculations:

The method for calculating depends on whether flow is compressible or incompressible (multiphase or single-phase). It follows that:

For a single-phase liquid, calculating the density is easy, and 1 is simply the liquid density.

For a single-phase gas, 1 varies with pressure (since gas is compressible), and the calculation must be done sequentially, in small steps, to allow the density to vary with pressure.

For multiphase flow, the calculations become even more complicated because 1 is calculated from the in-situ mixture density, which in turn is calculated from the "liquid holdup". The liquid holdup, or in-situ liquid volume fraction, is obtained from one of the multiphase flow correlations, and it depends on several parameters including the gas and liquid rates, and the pipe diameter. Note that this is in contrast to the way density is calculated for the friction pressure loss.

Density, Condensate

Condensate Density is the specific gravity in API of condensate at stock tank conditions. It ranges from 60 API to 40 API. The API Gravity is readily obtained from any laboratory oil analysis. It is a fixed property of the condensate.

In F.A.S.T. VirtuWell, this variable is used to calculate the Recombined Gas Gravity and the Recombined Gas Rate which are then used in single-phase pressure drop calculations.

The conversion from API Gravity (field units) to Stock Tank Oil Density (metric units) is:

Stock Tank Density (kg/m3) = 1000 * (141.5 / (API + 131.5))

UNITS: API (kg/m3) DEFAULT: None

Density, Gas

The density of a gas varies with the in-situ conditions of pressure and temperature along a pipe. The gas density is calculated from the "real gas" law :

where:

G = Gas Gravity

P = Pressure (psia)

Z = supercompressibility factor

T = temperature (R)

The gas density is used in calculating the pressure drops caused by friction and by hydrostatic head.

UNITS: lb/ft 3 (kg/m 3 )DEFAULT: Defining Equation

Density, Mixture

The mixture density is a measure of the in-situ density of the mixture, and is defined as follows:

where: EL = in-situ liquid volume fraction (liquid holdup)EG = in-situ gas volume fractionm = mixture densityL = liquid densityG = gas density

Note: The mixture density is defined in terms of in-situ volume fractions (EL), whereas the no-slip density is defined in terms of input volume fractions (CL).

Density, No-Slip

The "no-slip" density is the density that is calculated with the assumption that both phases are moving at the same in-situ velocity. The no-slip density is therefore defined as follows:

where: CL = input liquid volume fractionCG = input gas volume fraction

CL = input liquid volume fractionG = gas density

L = liquid densityNS = no-slip density

Note: The no-slip density is defined in terms of input volume fractions (CL), whereas the mixture density is defined in terms of in-situ volume fractions (EL).

Depth, Total Vertical (TVD)

This is the total vertical depth from the wellhead to a given point. In other words, a depth that is independent of the orientation of tubing in the wellbore. The following picture demonstrates the difference between TVD and MD.

Elevation

This is the elevation of the pipe over which the pressure drop is calculated. A positive elevation represents flow uphill. A negative elevation represents downhill flow. An elevation of zero (0) represents a horizontal pipe.

Erosional Velocity

When fluid flows through a pipe at high velocities, erosion of the pipe can occur. Erosion can occur when the fluid velocity through a pipe is greater than the calculated erosional velocity.

Add New Equation Here

where:

Ve- erosion velocity, ft/s

Ce erosion velocity constant (normal range: 100 300)

NS - no-slip mixture density

where:

CL- input liquid volume fraction

CG - input gas volume fraction

NS - no-slip mixture density

L - liquid density

G - gas density

where:

QL- liquid rate at prevailing pressure and temperature

QGBG- gas rate at prevailing pressure and temperature

VSL - superficial liquid velocity

VSG - superficial gas velocity

Vm - mixture velocity

Flow, %

This is the amount of the total flow that enters a particular set of perforations.

Flow Efficiency

Flow efficiency is a tuning parameter used to match calculated pressures to measured pressures. These two often differ as most calculations involve unknowns, approximations, assumptions, or measurement errors. When measured pressures are available for comparison with calculated values, the Flow Efficiency can be used to obtain a match between the two.

If measured pressures are not available for comparison, then the default value (100%) should be used.

Flow Efficiency adjusts the correlation such that decreasing the flow efficiency increases the pressure loss. Efficiencies greater than 100% are possible. Low efficiencies could be a result of roughness caused by factors such as corrosion, scale, sulfur or calcium deposition and restrictions. Restrictions in a wellbore may be caused by downhole equipment, profiles, etc. Low efficiencies could also be the result of liquid loading. Flow efficiencies less than 50% or greater than 150% should be treated with caution.

The flow efficiency is applied to both the hydrostatic and friction components of the pressure loss equation. Under static (no-flow) conditions the flow efficiency is not applied to the correlations. In this case, a match between measured and calculated pressures may be obtained by adjusting the fluid gravity or temperatures, as appropriate.

F.A.S.T. VirtuWell divides the whole length of pipe into many segments (see Pressure Loss Calculation Procedure). The flow efficiency is applied to each segment and affects the inlet/outlet pressure of that segment, and hence the in situ fluid densities. Therefore, a simple one step application of the flow efficiency to the pressure loss over the whole length of pipe will not produce the same results as those of F.A.S.T. VirtuWell.

UNITS: %DEFAULT: 100%

Formation Volume Factor, Oil (Bo)

This is defined as the ratio of the volume of oil at operating conditions to that at stock tank conditions. This factor is used to convert the flow rate and the density of oil (both normally reported at stock tank conditions) to in-situ conditions. Thus,

Oil Flow Rate (in-situ Barrels) = Oil Flow Rate (Stock Tank Barrels) * Oil Formation Volume Factor

And Oil density (in-situ) = Oil Density (Stock Tank Conditions) * Oil Formation Volume Factor

In the equations used in F.A.S.T. VirtuWell the oil rate and the oil density should be expressed at in-situ conditions, because the equations apply to the pressure and temperature conditions inside the pipe. However, the oil flow rate is generally measured at the surface, in stock tank barrels. Therefore, this rate is multiplied by the oil formation volume factor to convert it to in-situ conditions. Similarly, it is the in-situ density that counts, and that is obtained from the API Gravity (Stock Tank Oil Density) and the Formation Volume Factor

Below the bubble point pressure, the oil formation volume factor increases with pressure. This is because more gas goes into solution as the pressure is increased and this causes the oil to swell. Above the bubble point pressure, the oil formation volume factor decreases as the pressure is increased, because there is no more gas available to go into solution, and the oil is being compressed.

The value of the oil formation volume factor is generally between 1 and 2 RB/STB (m3/m3). It is readily obtained from laboratory PVT measurements, or it may be calculated from correlations such as "Vasquez and Beggs".

In the correlations that are being used to calculate the oil formation volume factor, the Solution Gas-Oil Ratio is the most significant variable.

UNITS: Bbl/Bbl (m 3 /m 3 )DEFAULTS: "Vasquez and Beggs" correlations

Friction Factor (multi-phase)

This is obtained from multi-phase flow correlations (see Beggs and Brill under multi-phase flow). This correlation depends, in part, on the gas and liquid flow rates, but also on the standard Fanning (single phase) friction factor charts. When evaluating the Fanning friction factor, there are many ways of calculating the Reynolds number depending on how the density, viscosity and velocity of the two-phase mixture are defined. For the Beggs and Brill calculation of Reynolds number, these mixture properties are calculated by prorating the property of each individual phase in the ratio of the "input" volume fraction and not of the "in-situ" volume fraction.

Add New Equation Here

For a single phase liquid, equals the liquid density.

For a single phase gas, varies with pressure, and the calculation must be done sequentially in small steps to allow the density to vary with pressure.

For multi-phase flow, is the mixture density, which is calculated by prorating the density of each individual phase in the ratio of the "input" volume fraction and NOT of the "in-situ" volume fraction. Note that this is in contrast to the way the mixture density was defined for the hydrostatic pressure difference.

Friction Factor (single phase)

This is obtained from the Chen (1979) equation which represents the Fanning friction factor chart. It depends on the Reynolds number which is a function of the fluid density, viscosity, velocity and pipe diameter. It is valid for single phase gas or liquid flow, as their very different properties are taken into account in the definition of Reynolds number.

INCLUDEPICTURE "http://www.fekete.com/software/virtuwell/media/webhelp/images/gs-abcamber34.jpg" \* MERGEFORMATINET Friction Pressure Loss

In pipe flow, the friction pressure loss is the component of pressure loss caused by viscous shear effects. The friction pressure loss is ALWAYS p

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