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Wellbore CalculationsMultiphase Flow DefinitionsInput Volume FractionThe input volume fractions are defined as:

We can also write this as:

Where:

= gas formation volume factor

= input gas volume fraction

= input liquid volume fraction

= gas flow rate (at standard conditions)

= liquid flow rate (at prevailing pressure and temperature)

= superficial gas velocity

= superficial liquid velocity

= mixture velocity ( + )

Note: is the liquid rate at the prevailing pressure and temperature. Similarly, * is the gas rate at the prevailing pressure and temperature.

The input volume fractions, and , are known quantities, and are often used as correlating variables in empirical multiphase correlations.

In-Situ Volume Fraction (Liquid Holdup)The in-situ volume fraction, (or ), is often the value that is estimated by multiphase correlations. Because

of "slip" between phases, the "holdup" ( ) can be significantly different from the input liquid fraction (

). For example, a single-phase gas can percolate through a wellbore containing water. In this situation = 0 (single-phase gas is being produced), but > 0 (the wellbore contains water). The in-situ volume fraction is defined as follows:

Where:

= cross-sectional area occupied by the liquid phaseA = total cross-sectional area of the pipe

Liquid Holdup EffectWhen two or more phases are present in a pipe, they tend to flow at different in-situ velocities. These in-situ velocities depend on the density and viscosity of the phase. Usually the phase that is less dense will flow faster than the other. This causes a "slip" or holdup effect, which means that the in-situ volume fractions of each phase (under flowing conditions) will differ from the input volume fractions of the pipe.

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

Where:

= in-situ liquid volume fraction (liquid holdup)

= in-situ gas volume fraction

= mixture density= liquid density= gas density

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

density is defined in terms of input volume fractions ( ).

Mixture VelocityMixture Velocity is another parameter often used in multiphase flow correlations. The mixture velocity is given by:

Where:

= mixture velocity



Mixture ViscosityThe mixture viscosity is a measure of the in-situ viscosity of the mixture and can be defined in several different ways. In general, unless otherwise specified, m is defined as follows.

W here:

= in-situ liquid volume fraction (liquid holdup)

= in-situ gas volume fraction= mixture viscosity= liquid viscosity= gas viscosity

Note: The mixture viscosity is defined in terms of in-situ volume fractions ( ), whereas the no-slip

viscosity is defined in terms of input volume fractions ( ).

No-Slip DensityThe "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:



= no-slip density= liquid density= gas density

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

is defined in terms of in-situ volume fractions ( ).

No-Slip ViscosityThe "no-slip" viscosity is the viscosity that is calculated with the assumption that both phases are moving at the same in-situ velocity. There are several definitions of "no-slip" viscosity. In general, unless otherwise specified, is defined as follows.

Where:



= no-slip viscosity= liquid viscosity= gas viscosity

Superficial VelocityThe superficial velocity of each phase is defined as the volumetric flow rate of the phase divided by the cross-sectional area of the pipe (as though that phase alone was flowing through the pipe). Therefore:

and

Where:

= gas formation volume factorD = inside diameter of pipe

= measured gas flow rate (at standard conditions)

= liquid flow rate (at prevailing pressure and temperature)



Since the liquid phase accounts for both oil and water and the gas phase accounts for the solution gas going in and out of the oil as a function of pressure(

), the superficial velocities can be rewritten as:

Where:

= oil flow rate (at stock tank conditions)

= water flow rate in (at stock tank conditions)

= gas flow rate (at standard conditions of 14.65psia and 60F)

= liquid flow rate (oil and water at prevailing pressure and temperature)

= oil formation volume factor

= water formation volume factor

= gas formation volume factor

= solution gas/oil ratioWC = water of condensation (water content of natural gas, Bbl/MMscf)

The oil, water and gas formation volume factors ( , and ) are used to convert the flow rates from standard (or stock tank) conditions to the prevailing pressure and temperature conditions in the pipe.

Since the actual cross-sectional area occupied by each phase is less than the cross-sectional area of the entire pipe the superficial velocity is always less than the true in-situ velocity of each phase.

Surface TensionThe surface tension (interfacial tension) between the gas and liquid phases has very little effect on two-phase pressure drop calculations. However a value is required for use in calculating certain dimensionless numbers used in some of the pressure drop correlations. Empirical relationships for estimating the gas/oil interfacial tension and the gas/water interfacial tension were presented by Baker and Swerdloff, Hough and by Beggs.

Gas/Oil Interfacial TensionThe dead oil interfacial tension at temperatures of 68 F and 100 F is given by:

Where:

= interfacial tension at 68 F (dynes/cm)= interfacial tension at 100 F (dynes/cm)

API = gravity of stock tank oil (API)

If the temperature is greater than 100 F, the value at 100 F is used. If the temperature is less than 68 F, the value at 68 F is used. For intermediate temperatures, linear interpolation is used.

As pressure is increased and gas goes into solution, the gas/oil interfacial tension is reduced. The dead oil interfacial tension is corrected for this by multiplying by a correction factor.

Where:

P = pressure (psia)

The interfacial tension becomes zero at miscibility pressure, and for most systems this will be at any pressure greater than about 5000 psia. Once the correction factor becomes zero (at about 3977 psia), 1 dyne/cm is used for calculations.

Gas/Water Interfacial TensionThe gas/water interfacial tension at temperatures of 74 F and 280 F is given by:

Where:

= interfacial tension at 74 F (dynes/cm)

= interfacial tension at 280 F (dynes/cm)P = pressure (psia)

If the temperature is greater than 280 F, the value at 280 F is used. If the temperature is less than 74 F, the value at 74 F is used. For intermediate temperatures, linear interpolation is used.

Wellbore CorrelationsBeggs 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 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 frictional pressure loss is calculated using "input" gas-liquid mixture properties.

Flow Pattern MapThe 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:

Where:

= liquid input volume fraction

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

.

Where:

D = inside pipe diameter (ft)

= Froude Mixture Number (unitless)

g = acceleration of gravity (32.2 ft/s2)

= mixture velocity (ft/s)

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, , is

determined, and then this holdup is modified for inclined flow. must be greater than or equal to

and therefore when is smaller than , is assigned a value of . There is a

separate for each flow type.

SEGREGATED

INTERMITTENT

DISTRIBUTED

TRANSITION

Where:

Once the horizontal in situ liquid volume fraction is determined, the actual inclined liquid holdup,

,is obtained by multiplying by an inclination factor, .

Where:

= Inclination factor (unitless)

= horizontal liquid holdup (unitless)

= inclined liquid holdup (unitless)

= Beggs and Brill coefficient (unitless)

= angle of inclination from the horizontal (degrees)

is a function of flow type, the direction of inclination of the pipe (uphill flow or downhill flow), the liquid

velocity number ( ), and the Froude Mixture Number ( ) . is defined as:

Where:

= superficial liquid velocity (ft/s)

= liquid velocity number (unitless)

= liquid density (lb/ft3)

= gas/liquid surface tension (dynes/cm)

For UPHILL flow:SEGREGATED

INTERMITTENT

DISTRIBUTED

For DOWNHILL flow:ALL flow types

Note: must always be greater than or equal to 0. Therefore, if a negative value is calculated for , assume = 0.

Once the inclined liquid holdup ( ) is calculated, it is used to calculate the mixture density, . 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.

Where:

gc = conversion factor

= pressure change due to hydrostatic head (psi)

= elevation change (ft)

= mixture density (lb/ft3)

Friction Pressure LossThe first step to calculating the pressure drop due to friction is to calculate the empirical parameter, S. The value of S is governed by the following conditions:

otherwise,

Where:

S = Beggs and Brill coefficient (unitless)

(unitless)

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:

Where:

= no-slip friction factor (unitless)

= two phase friction factor (unitless)

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:

Where:

= no-slip Reynold's Number (unitless)

= no-slip viscosity (cp)

= no-slip density (lb/ft3)

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

Where:

L = length of pipe section (ft)

= frictional pressure loss (psi)

Fanning Gas Correlation (Multi-Step Cullender and Smith)The Fanning Gas Correlation is the name used in this document to refer to the calculation of the hydrostatic pressure difference ( ) and the friction pressure loss ( ) 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.

Friction Pressure LossThe Fanning equation is as follows:

Where:

D = inside diameter of pipe (in)

f = Fanning friction factor (function of Reynolds number)



V = average velocity (ft/s)

= pressure loss due to friction effects (psi)

= density (lb/ft3)

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:

k = absolute roughness (in)

k/D = relative roughness (unitless)

Re = Reynold’s number (unitless)

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:

= 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.

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:

Where:




= gas density (lb/ft3)

Since 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 ( ) can be combined with the hydrostatic pressure difference ( ) 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 ( ) and the frictional pressure loss (

) 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 frictional 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 the Moody charts. We use the equation form of the Fanning friction factor as published by Chen (1979).

Where:

k = absolute roughness (in)

k/D = relative roughness (unitless)

Re = Reynold’s number (unitless)

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

The Fanning equation is as follows:

Where:


f = Fanning friction factor (function of Reynolds number)



V = average velocity (ft/s)

= pressure loss due to friction effects (psi)

= density (lb/ft3)

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

Where:



=elevation change (ft)


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

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 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.

Gray: Hydrostatic Pressure DifferenceThe Gray correlation uses three dimensionless numbers (shown below), in combination, to predict the in situ liquid volume fraction. These three dimensionless numbers are:

And:

Where:


g = gravitational acceleration (32.2 ft/s2)

= Ratio of superificial liquid velocity of superficial gas velocity (unitless)


= superficial gas velocity (ft/s)





= gas / liquid surface tension ( )

They are then combined as follows:

Where:

= input liquid volume fraction (unitless)

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

Once the liquid holdup ( ) is calculated it is used to calculate the mixture density ( ). 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.

Where:





Note: For the equations found in the Gray correlation, is given in . We have implemented them using with units of dynes/cm and have converted the equations by multiplying by 0.00220462.

(0.00220462dynes/cm = 1 )

Gray: Friction Pressure LossThe Gray Correlation assumes that the effective roughness of the pipe ( ) is dependent on the value of

(defined previously). The conditions are as follows:

if then

if then

Where:

k = absolute roughness of the pipe

= effective roughness of the pipe (in)

The effective roughness ( ) 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 of . Finally, the expression for the friction pressure loss is:

Where:

= two-phase friction factor

L = length of pipe (ft)

= pressure change due to friction (psi)

Note: The original publication contained a misprint (0.0007 instead of 0.007). Also, the surface tension (

) is given in units of . We used a conversion factor of 0.00220462 dynes/cm = 1 .

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 ( = ). 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.

Hagedorn and Brown: Hydrostatic Pressure DifferenceThe Hagedorn and Brown correlation uses four dimensionless numbers to correlate liquid holdup. These four numbers are:

Where:

D = inside pipe diameter (ft)


= superficial gas velocity (ft/s)

= liquid viscosity (cp)


= gas / liquid surface tension (dynes/cm)

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

holdup( ).

For the purposes of programming, these curves were converted into equations. The first curve provides a

value for . This 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

, is calculated by:

Where:

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

= Hagedorn and Brown Correctionfactor (unitless)

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

And:

Where:

g = gravitational acceleration (32.2 ft/s2)






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:

Where:


= gas viscosity (cp)

= liquid viscosity (cp)

= mixture viscosity (cp)


The pressure loss due to friction is then given by:

And:

Where:

f = Fanning friction factor

L = length of calculation segment (ft)

= pressure change due to friction (psi)

ModificationsWe 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 =

Where:

= input liquid volume fraction (no-slip liquid hold up)

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

Bubble flow exists if < where:

And:


= Parameter which defines boundary between bubble and slug flow (unitless)

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:

= 0.8 ft/s

The in-situ liquid velocity is given by:

Where:

= in-situ liquid velocity (ft/s)

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.

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

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

Example Flow Pattern Map

Dispersed Bubble FlowExists if

where

and if

Stratified FlowExists if flow is downward or horizontal ( 0)

Calculate (dimensionless liquid height)

Momentum Balance Equations:

where

and

fG from standard methods where

fL from

where

fsL from standard methods where

fi from

where

Use Lochhart-Martinelli Parameters

where

where

Geometric Variables:

Solve for hL/D iteratively.

Stratified flow exists if

(Note: when cos 0.02 then cos = 0.02)

where

and

(Note: when cos 0.02 then cos = 0.02)

Stratified smooth versus Stratified Wavy

if

where

and

then have Stratified Smooth, else have Stratified Wavy.

Annular Mist 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 Flow3. 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)


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


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

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

= dimensionless quantity

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

wG = 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.

Turner CorrelationThe 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 oil field 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:

Where:

G = gas gravity (unitless)

k = calculation variable

= pressure (psia)A

T = temperature (R)

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

Z = compressibility factor (unitless)

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 ( )

= gas flow rate (MMscfd)

Important Notes

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

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".

For each time step:

sorbed gas composition is known, ( ).

initial pressure is known ( )

calculate free gas mole fraction ( )

Given and and using deliverability equation:

calculate total gas production ( ).

calculate component gas production ( , ).

Using component mass balance:

calculate new sorbed gas composition ( )

Using MBE:

calculate new average reservoir pressure, ( ) and average water saturation ( )

Copyright © 2011 Fekete Associates Inc.

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