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A Simplified Method for

Determining

Gas Well Deliverability

Robert

W Chase SPE Marietta C

Ted

M

Anthony

SPE, Marathon Oil Co

Summary This paper presents a simplified method for predicting the performance of a gas well. A method for determining the

deliverability

of

an u nfra ctu red gas well by use

of

a single-point flow test and a dimensionless Vogel-type inflow performance

curve was proposed by Mishra and Caudle. Their procedure necessitates the calculation of real-gas pseudopressures for shut-in and

flowing bottomhole pressures BHP) obtained from pressure-buildup and stabilized-flow tests, respectively. This paper offers a

simplification

of

this technique in which a range

of

pressure values is defined over which pressure-squared terms can be substituted

for pseudopressures. A comparison is made between results obtained from analysis of well-test data on several gas wells made with

conventional multipoint test methods, with the Mishra-Caudle technique, and with the simplified method presented in this paper.

The simplified method offers the engineer who might not have access to a pseudopressure computer program

or

pseudopressure

tables a method for estimating gas-well deliverabilities. The method of Mishra and Caudle and the simplified method were both

observed to yield slightly conservative estimates of gas-well deliverabilities compared with the deliverabilities calculated from

multipoint flow-test analyses. The simplified technique was found to be useful for predicting the performance

of

fractured gas wells

as well as unfractured wells.

Introduction

Predicting the performance of gas wells is a process that has relied

almost exclusively on some form

of

multipoint well-testing proce

dure. The conventional backpressure

or

flow-after-flow, 1 the

isochronal,

2

and the modified isochronal tests

3

have been used to

predict the short- and long-term stabilized deliverability

of gas

wells.

In a typical multipoint deliverability test, a well is produced at

a minimum

offour

different flow rates with shut-in periods

ofv r-

ious lengths separating flow periods. Pressure is monitored during

both the flow and shut-in periods throughout the test. Analysis of

the BHP vs. flow rate yields results that, when plotted on log-log

paper as shown in Fig. 1, produce a straight line that reflects the

stabilized deliverability behavior

of

a gas well.

The empirically derived relationship given by Eq.

1

represents

the equation of a stabilized deliverability curve such as the one

shown in Fig.

1.

q=C p1-plt)n

1

The constant C reflects the position

of

the stabilized deliverabil

ity curveon the log-log plot. The value of the exponent,

n,

is equal

to the reciprocal

of

the slope

of

the stabilized deliverability curve

a nd normally has a va lue bet wee n 0 .5 and 1.0 .

The stabilized deliverability curve

or

its equation may be used

to predict the ability

of

a well to produce against a given sandface

backpressure. The absolute open flow AOF)

of

the well is also

frequently calculated. The AOF is the theoretical maximum flow

rate a well can maintain against a zero surface backpressure. The

AOF is used mainly in comparing wells and by regulatory bodies

in establishing production allowables.

Multipoint backpressure tests yield very reliable deliverability

projections when correctly conducted in the field. Frequently, how

ever, these tests require a commitment of manpower, equipment,

and time that may render the tests cost-prohibitive. This is particu

larly true in the case oflow-permeability reservoirs, where testing

times may be very long. The problem is further compounded in

terms of lost revenues

if

gas must be flared throughout the test.

Alternative methods for forecasting gas-well deliverability have

been proposed by several authors.

4

-

6

A replot

of

the stabilized

deliverability curve shown in Fig. o n Cartesian coordinate graph

paper Fig. 2 produces an inflow performance,

or

IPR, curve simi

lar to those observed in the testing

of

oil and gas producing wells.

Russell et

al.

4 showed that IPR curves constructed with Eq.

1

gave

predicted gas-production rates lower than those observed in the field.

Copyright 1988 Society of Petroleum Engineers

1090

Russell

et al.

proposed an equation that depicted gas-inflow per

formance more accurately:

Tsckh p1-p;y.)

q= 2

re 3 )

50.34PscTp. p z p n

- -

s

r

w

4

Greene

5

documented that Neely6 rewrote

Eq.

2 by collecting the

parameters that were constant for a given well in a constant, C1

yielding the gas-well inflow performance equation:

c

p1-p;y.)

q= 3)

p. p z p

The constant C1in Eq. 3 may be determined from a single flow

test

if

the shut-in BHP

is

known. The constant C l will not vary

with flow rate; however, it may change over the life

of

the well

because

of

changes in the producing condition

of

the wellbore

or

formation.

Greene noted that a valid IPR curve could be constructed for a

well from a single C1-factor determination and a known shut-in

BHP. This could be done by assuming values

of Pwf

calculating

corresponding p g and z values, and substituting in Eq. 3 to find

corresponding values

of

BHP could then be plotted vs. flow rate

to obtain the IPR curve.

VogeJ7

extensively studied the inflow performance

of

solution

gas-drive reservoirs. He suggested that the dimensionless IPR curve

shown in Fig . 3 could b e used to generate actual IPR c urves for

wells in which oil and gas were flowing. With Vogel s method,

only a value for shut-in BHP and a single flow-test point are nec

essary to generate an IPR curve for a well completed in a solution

gas-drive reservoir. Brown

8

reported that field experience has

shown that Vogel s dimensionless IPR curve also yields good ap

proximations of flow behavior when the method is applied to wells

producing oil, gas, and water. Vogel suggested that dimensionless

IPR curves could be constructed for wells producing only liquids

or

only gas, as shown in Fig. 3. Ho we ve r, he did not propo se an

actual dimensionless IPR curve that could be used to predict gas

well performance.

Mishra and Caudle

9

presented a method for pre dic ting th e

deliverability

of

a gas well in an unfractured reservoir. The ana

lytic solution to the gas diffusivity equation for flow

of

a real gas

SPE Reservoir Engineering, August 1988

7/26/2019 SPE-14507-PA

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/ / t.... fron i nt J I

I

rrrli

t ~ o ~ ; t l ~ P i C f I D

~ - - - - - - . . J - - - - - - - - - - - J - - - - 7 1 0 : - - - - J . - - - L . . J . - - - - J - - . . . J . . . . ~ 1 0 0

q MMscflD

10000

i=-;;-;

-379

lOJ

p o

i

-

j

- I--

I

j

N

I

1-

- t

Stabili d

T

o

,;,a

1000

O.li

,ability

I

i

I

2

lC

N

Go

I

I

I

I

/

I I '

r- i - --i - , -I-H- H

~ ; ; : : :

? - . : - -

Two-phase Gas

Oil

Flow

=

r

....

oL . . .

.......

L.

J

0 .0

p p 1.0

wE

Fig. 1-Stabllized dellverabllity curve for modified Isochronal

test

(after Ref. 11). Fig.

3-Dimenslonless

IPR curves (after VogeI

7

.

2.00

1.90

1.80

1.70

1.60

1.50

1.40

i

1..30

1.20

1.10

-

1.00

I

0.90

0.80

0.70

0.60

0.50

0.40

0..30

0.20

0.10

0.00

0.00 2.00

4 6

FLOWRATE (MMet/D)

8,00

10,00

12.00

--------

0.

0 .

.7

0

.

,

0.5

.4

-

O.J -

.2

\

.1

\

0.2

0.4 0 .

0.

qlq ,..

Fig. 2-IPR curve generated from stabilized deliverabll lty

curve.

in a porous medium under stabilized or pseudo-steady-state flow

conditions and a broad range

of

rock and fluid properties were used

to generate dimensionless flow rate and pseudopressure data and

to derive the following empirical relationship:

q

5 _

= [1 5 p

p

>< P

p

R - I ] 4

qrnax 4

where

pp r -dp 5

o p z

Eq. 4 is the empirical relationship representing the dimension

less IPR curve shown in Fig. 4. This curve can be used to deter

mine an actual IPR curve for calculating the current deliverability

of an unfractured gas well.

Mishra and Caudle proposed a second empirical equation and

dimensionless IPR curve for calculating the future deliverability

of

an unfractured gas well:

qrnaxf

5 _

= [1 0.4 PpRjPpRi] . (6)

qrnaxi 3

SPE Reservoir Engineering, August 1988

Fig. 4-Dlmenslonless IPR curve for current conditions (af

ter Mishra and Caudle

9

.

Eq. 6 is the empirical relationship representing the dimensionless

IPR curve shown in Fig. 5.

Note that the average reservoir pressure, fiR was used in the

development

of

the dimensionless IPR curves.

In

most testing proce

dures, a well is shut in and BHP is allowed to build up until it ap

proaches some level

of

stabilization. The value for the static BHP

is normally used in lieu of the true average reservoir pressure, which

can be determined only by transient-pressure analysis techniques.

The approximation

of

true average reservoir pressure with static

BHP will introduce some inaccuracy in the prediction of flow rates,

probably on the conservative side.

The dimensionless IPR curves developed by Mishra and Caudle

eliminate the need for multipoint testing and provide a new and

simpler technique for estimating gas-well deliverability. The method

simplifies the process

of

deliverability testing by reducing the

amount

of

well-test data required for analysis to a single shut-in

BHP value and a single stabilized flow-test point. The analysis

of

the data acquired from a field test requires the calculation

of

real

gas pseudopressures, and unfortunately, not all gas producers have

the capability of making pseudopressure calculations.

The purpose

of

this research is two-fold. First, a simplification

of the Mishra-Caudle method is sought in which a range of pres

sures

is

defined over which pseudopressure ratios can be approxi

mated by pressure or pressure-squared terms. This simplification

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0.9

+ - - I - - + - + - - I - - + - - - f - - ~ - + - - + L . . . . j /

Fig. 5-Dlmenslonless PR curve for future conditions after

Mishra and Caudle ).

O.B t - - t - - t -- j - --- , f - - j - - - - -- f --- .L.J----1

0.7 +--I--+--+---I--f--+--I---,..j::V:...-...-I----l

O.B

+--+--+--+--+-+--1--JL/=---f..--l---l

/

I 0.5 t - - - t - - t - - t - - l - - - - - j f - - - j .L-- - - - - - - - - l

0.4 +--IC--+--f--I--::;j.-.:::...../+-f--+--J.-----1

O.J

+---+--+---1/----;;>- L/-+--+-+---+---Il--...l

0.2 t - - - - - - ; 7 f - - f - - - - 1 - - - - - - l - - - I - - ~

/

0.'

- t - - - - f :: ; , .L-+-- t - - l- - f - - - l --+-- - -+-- -+--

/

10

PRESSURE SQUARED

Ix

10' p. . . . )

1

0.9

0.

0.7

III

= t

0.6

co_

co

i l i

a:

0 .

9 ~

0

lll. l

0.3

O.Z

0.1

0

0 Z

6

O.B

.6.4

q-rlci

0.2

1 .

1

1.3

1.Z

1.1

1

III

0.9

= t

o_

o.

o

l l i

0. 7

~ ~

0.6

III

..

0 .

o-

0

0.3

O.Z

0.1

0

0

Z

PRESSURE

x

10'

P .)

Fig.

-Curve of

pseudopressure

VS.

pressure for a O.6-gravlty

gas.

wouldpermit an engineerwho may not have access to pseudopres

sure tables or a pseudopressure computer program to estimate gas

well deliverabilities.

Secondly, the Mishra-Caudle dimensionless IPR curves were de

veloped for real-gas flow in an unfractured reservoir.

It

was desired

to determine whether the method would yield accurate results when

applied to the testing

of

wells that had beenhydraulically

fractured.

udopr

u

pproximation

It

has

been shown that gas flow behavior can

be

most accurately

described using the pseudopressure function,

Pp

which takes into

account the deviation of gas viscosity and the gas deviation factor

with pressure. The pseudopressure function is givenby the integral

expression shown in Eq. 5. .

At

low pressures, the product of viscosity and compressibility

remains essentially constant, and the pseudopressure function can

be

approximated by

Fig. 7-Curve of pseudopressure VS. pressure squared for a

O.6-gravlty gas.

where the combination

of

terms in parentheses also remains essen

tially constant.

As a general guideline, Wattenbarger and RameylO suggested

that for pressures 3,000 psia [> 20.7 MPa], pres

surewill accurately approximate pseudopressure. These guidelines

were developed for application with the diffusivity equation in

transient-pressure analysis.

In

the context

of

the modification to the Mishra-Caudle method

sought in this work, the relationship between pseudopressure and

pressure

or

pressure squared was also examined. A computer pro

gram was used to generate a table

of

data comprising correspond

ing values of pressure, pressure squared, and pseudopressure.

Graphs of pressure squared vs. pseudopressure and pressure vs.

pseudopressure were plotted for 0.60-, 0.65-, 0.70-, and

0.75-gravity gases. Differences between the curves for different

gravity gases were noted, but all basically followed similar trends.

For

this reason, only the results obtained for a O.60-gravity gas

are reproduced in Figs. 6 and 7.

The portions of the curves shown in Figs. 6 and 7 that

are

linear

are

of

particular interest in this research. The curve

of

pseudopres

sure vs. pressure in Fig. 6 was viewed to

be

nearly linear above

about 2,900 psi [20 MPa]. This was confirmed by an incremental

computation of slopes along the line at 50-psi [345-kPa] intervals.

The curve of pseudopressure vs. pressure squared in Fig. 7 was

also viewedto be nearly linearfrom 0 to about 2,000 psi [0 to 13.8

MPa]. This trend was confirmed by calculating slope values at points

50

psi [345 kPa] apart along the curve. Over this pressure range,

the change in slope between any two pressures was less than 1

.

The linear portion of the curve of pseudopressure vs. pressure

squared is of great significance in terms of simplifyingdeliverabil

ity testing procedures for wells with shut-in

BHP s

less than about

2,000 psi [13.8 MPa]. Because the curve shown in Fig. 7 passes

through the origin, the equation describing the linear portion of the

curve can be written as the equation of a straight line having a

y

intercept of zero:

Pp

=

_2_ p

2

. 7)

LiZi

pp=mp2 (9)

Substituting this equation for

Pp

values as they are used in Fig.

4 and Eq. 4 yields the following relationship:

Likewise, at high pressures, the pseudopressure function can

be

approximated

by

pp= 2

P

i

p

2

8

LiZi

Ppwf mpJi.

= = 2

10)

PpR

mpR

A similar relat ionship can be obtained for Fig . 5 and Eq. 6 .

1092

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TABLE

1 MODIFIED

ISOCHRONAL TEST DATA from Ref. 9

Sandface

Pressure Pseudo- Gas Flow

Duration

Pressure Squared

pressure Rate

hours) psia)

psia

2

) psi

2

/cp) McflD)

Initial Shut-in

20 1,948

3 80x

10

6

3 15x10

8

0

Flow 1

12

1,784

3 18x 10

6

2 67x10

8

4,500

Shut-in

12

1,927 3.71 x

10

6

3 08x 10

8

0

Flow 2

12

1,680

2 82x10

6

2.39 x 10

8

5,600

Shut-in

12

1 911

3 65x10

6

3 04x10

8

0

Flow 3 12 1,546

2 39x10

6

2.04 x 10

8

6,850

Shut-in

12 1,887

3 56x 10

6

2.97 x 10

8

0

Flow 4

12 1,355

1 84x

10

6

1 58x

10

8

8,250

Extended flow

81

1,233

1 52x

10

6

1.32 x 10

8

8,000

Final Shut-in

120 1,948

3.80 x 10

6

3 15x 10

8

0

TABLE 2-COMPARISON OF AOF S

FROM

MULTIPOINT

AND SINGLEPOINT TESTS

Because the slope along the curve from 0 to 2,000 psi [0 to 13.8

MPa] is essentially constant, it can readily be seen that the slope

terms in Eq.

1

cancel, leaving a ratio

of

pressure-squared terms

equal to a ratio

of

pseudopressure terms. This key simplification

permits the substitution

of

pressure-squared values for pseudopres

sures in the dimensionless IPR curves

of

Figs. 4 and 5 and in Eqs.

4 and 6, for wells with average reservoir pressures

or

static BHP s

less than about 2,000 psia [13.8 MPa].

Turning to the curve

of

pseudopressure vs. pressure in Fig. 7,

the linear portion

ofthis

curve begins at about 2,900 psi [20 MPa].

This linear trend, however, does not have the origin as an inter

cept, thus prohibiting the substitution of pressure values for pseu

dopressures in the dimensionless IPR expressions. Therefore, it can

be concluded that above about 2,000 psi [13.8 MPa], pseudopres

sure values should be used in working with the dimensionless IPR

expressions proposed by Mishra and Caudle.

12.00.00 10.00

.00

Outflow

Perfonaane. . Cur ve

2.00 4.00

P

19ol8

2.00

-y- - - - - - - - - - - - - - - - - - - - - - - - - - - ,

1.90

1.80

1.70

1.60

1.50

1.40

1.30

1.20

1.10

_

1.00

cr

0.90

I 0.80

0.70

0.60

0.50

0.40

0.30

0.20

0.10

0.00

- - - . - - - - - r - - - r - - - - - - - - r - - - - - - - - - - - r . . - ~ _ _ _ _ _ _ 1

0.00

Fig. 8 Production performance curves constructed for a gas

weil at current conditions with the dimensionless IPR curve.

FLOWRATE MMclID)

dimensionless IPR curve used in the last two techniques being em

pirically derived on the basis

of

curve-fitting a data trend. Mul

tipoint well-test analysis depends on the use

of

actual test data to

determine a unique stabilized deliverability curve and should there

fore still be viewed as the most accurate method for calculating

deliverability. Clearly, a large-scale evaluation

of

test data is needed

to substantiate the use

of

single-point testing methods as a replace

ment for multipoint test methods.

The first three AOF s reported in Table 2 pertain to hydraulical

ly stimulated wells completed in low-permeability reservoirs.

It

can

be seen that the AOF s computed with the Mishra-Caudle method

and the simplified method compare favorably with the AOF s found

with conventionalmethods for the three fractured wells. Addition

al comparisons are needed, however,

to

confirm the validity

of

using

unfractured well dimensionless IPR curves for fractured wells. Fur

ther research has been conducted by Chase and Williams

12

and by

Chase

13

to develop dimensionless IPR curves specifically for pre

dicting the performance

of

fractured gas wells.

Predicting GasWe ellverabUlty

With

imensionless IPR urves

The well-test data appearing in Table 1 were used in conjunction

with the dimensionless IPR curve shown in Fig. 4 to construct the

current deliverability IPR curve shown in Fig. 8. The procedure

for constructing the IPR curve by the simplified pressure-squared

method is detailed in the Appendix.

The IPR curve is used to estimate the ability

of

a porous medium

to flow gas into the wellbore when a given backpressure is main

tained at the sandface. Because deliverability at the wellhead

is

nor

mally desired, either an outflow performance curve or a tubing

performance curve must be constructed. This performance

prediction process is commonly called nodal analysis.

Greene

5

gives several examples

of

the use

of

tubing-pressure

curves in conjunction with IPR curves to analyze gas-well perform

ance. The tubing-head pressure or outflow performance curve is

148

491

692

8,400

8,940

10 341

Pressure-Squared

AOF

MscflD)

149

492

692

8,700

9,080

10,526

Mishra-Caudle

AOF

MscflD)

167

547

696

9,000

9,500

10,988

Multipoint Test

AOF

MscflD)

iscussion of Results

Field-test data were obtained on several gas wells with shut-in aver

age reservoir pressures

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a plotof tubing-headpressure vs. flow rate,

n

represents the ability

of

the gas and l iquid,

if

present, to flow up the tubing.

multiple phases

are

flowing up the tubing, multiphase flow

correlations are necessary to generate outflow performancecurves.

These outflow performance curves normally exhibit a humpbacked

shape.

The

apex of such a curve is designated as the flow point

and represents themaximum flowing tubing-head pressure and the

minimum sustainable flow rate possible for the well.

Any flowing

BHP

algorithm may

be

used to generate the out

flow performance curve fo r a dry gas well. A dry gas well will

have no flow point

or

apex

on

its outflow performance curve.

Outflow performance curves are valid only for the current static

BHP

and

IPR

curve

of

a well.

To

predict future deliverability, fu

ture

IPR

curves must be constructed using Fig. 5 or Eq. 6 Corre

sponding outflow performance curves must then be calculated for

each future IPR curve.

A second type of curve, called the tubing performance curve

or

constant tubinghead pressure curve, can also be constructed with

eithermultiphase flow correlations when multiple phases are flowing

or single-phase flow correlations for dry gas flow. The tubing per

formance curve is a plot of the flowing BHP required to produce

a well at various gas flow rates through a given-size tubing string

at a constant flowing tubinghead pressure. This type of curve is

also shown in Fig. 8.

The

intersection

of

the constant tubinghead

pressure curve with the

IPR

curve yields the stabilized flow rate

that the well can maintain against the specified constant tubinghead

pressure.

As static BHP falls, it is necessary to constructfuture IPR curves

corresponding to the new static

BHP s.

The constant tubinghead

pressure curve, however, applies throughout the flowing life of the

well and need not be recalculated unless tubing size is changed.

onclusions

A simplification

of

a method developed by Mishra and Caudle for

predicting gas-well performancewas proposed in this research. The

procedure requires a value for the shut-in BHP and theflowing BHP

and associated flow rate from a single stabilized flow test for a gas

well. These data

are

used to construct IPR curves for the gas well

by use

of

the dimensionless

IPR

curves developed by Mishra and

Caudle.

1

Pressure-squaredvalues can be substituted for pseudopressutes

in the dimensionless IPR graphs and equations developed by Mis

hra and Caudle

if

the average reservoir pressure

or

static BHP for

a gas well is less than about 2 ,000 psi [13.8 MPa].

2. Above average reservoir pressures of about 2,000 psi [13.8

MPa], pseudopressures must be used in the process of construct

ing

IPR

curves from the dimensionless plots

of

Mishra and Caudle.

3.

The

simplifiedmethod and the Mishra-Caudle technique both

yield reasonable, conservative estimates

of

gas-well deliverabili

ties compared with values obtained with conventional multipoint

test methods.

4.

The

simplified method and theMishra-Caudle technique were

used successfully to predict the deliverabilities

of

several fractured

gas wells completed in low-permeability reservoirs, even though

the dimensionless IPR curves were developed for unfractured wells.

5. A large-scale study of well-test data is needed to determine

whether single-point testing methods can be used as an effective

replacement for conventional deliverability test methods.

6. Further research

on

the development

of

dimensionless IPR

curves for fractured wells is warranted and ongoing.

Nomenclature

C

constant

of

stabilized deliverability equation

C

constant

of

gas inflow performance equation

h

reservoir thickness, ft [m]

k

permeability, md

m

slope

n

exponent

of

stabilized gas deliverability equation

P

average pressure,

[ PR+PMf /2],

psia [kPa]

p real gas pseudopressure evaluated at pressure

psia

2

/cp [kPa

2

/rnPa s]

PR

average reservoir pressure, psia [kPa]

1094

Psc pressure at standard conditions, psia [kPa]

Pth tubinghead pressure, psi [kPa]

f

flowing BHP, psia [kPa]

Pws static BHP, psia [kPa]

q stabilized gas flow rate, Mcf/D [m

3

/d]

r

e

radius of external boundary, ft [m]

r

w

radius of wellbore, ft [m]

s skin factor

T reservoir temperature, OR

]

T

sc

temperature at standard conditions,

OR

[K]

z gas deviation factor

J g gas viscosity, cp [mPa s]

Subscripts

f future conditions

i

initial conditions

P

pseudo

cknowledgements

We

th nk

Paul Hyde (Columbia Natural Resources Inc.), Will Tank

(Marathon Oil Co.), and Jim Murtha (Marietta

C.)

for their input

during the course of this research.

References

1

Rawlins, E.K. and Schellhardt, M.A.: Back-Pressure Dataon Natural

GasWells and theirApplication to Production Practices, Monograph

7, U.S . Bur. Mines (1936).

2. Cullender, M.H.: The Isochronal PerfonnanceMethod ofDetennining

Flow Characteristics of Gas Wells, Trans AIME (1955) 204, 137-42.

3.

Katz, D.L. et al : Handbook ofNatural

as

Engineering McGraw Hill

Book Co. Inc ., New York City (1959) 448.

4.

Russell, D.G. et aI.: ~ t h o d s for Predicti1JB Gas Well Perfonnance,

lP T (Jan. 1966) 99-108, Trans AIME,

237.

5.

Greene, W.R.: Analyzing the Performance of Gas

Wells, lPT uly

1983) 1378-84.

6 Neely, A.B.: The Effect of Compressor InstaIlation On GasWell Per

fonnance,

HAP

Report 65-1, Shell OilCo., Houston (Jan. 1965) 1-13.

7.

Vogel, J.L.: Inflow Perfonnanc Relationships for Solution-Gas Drive

Wells,

lP T (Jan. 1968) 83-92;

Trans

AIME, 243.

8.

Brown, K.E.: The Technology ofArtificialL ift Methods PPC Books,

Tulsa (1977) 13-14.

9 Mishra, S. and Caudle, B.H.:

A

Simplified Procedure forGas Deliver

ability Calculations Using Dimensionless

IPR

Curves, paper SPE

13231 presented at the 1984 SPE Annual Technical Conference and

Exhibition, Houston, Sept. 16-19.

10. Wattenbarger, R.A. and Ramey, H.J. Jr.: Gas Well TestingWith Tur-

bulence, Damage and Wellbore

Storage,

lP T (Aug. 1968)

877-87;

Trans AIME, 243.

i 1

Theory and Practice of the Testing of asWells Energy Resources

Conservation Board, Calgary (1975) 3-25.

12. Chase, R.W. and Williams,

M.A.T.:

Dimensionless IPR Curves for

Predicting the Perfonnance of Fractured Gas Wells, paper SPE 15936

presented at the 1986 SPE Eastern Regional Meeting, Columbus, Nov.

12-14.

13. Chase, R.W.: DimensionlessIPR Curves for PredictingGasWell Per

formance, paper SPE 17062 presented

at

the 1987SPE

Eastern

Region

al Meeting, Pittsburgh, Oct.

21-23.

ppendix Comparison of

Performance

Prediction Methods

The modified isochronal well-test data given in Table 1 were used

in conjunction with the dimensionless IPR curve shown in Fig. 4

to construct the current deliverability IPR curve shown in Fig. 8.

Specifically, the static BHP

of

1,948 psia [13.4MPa] and the flow

ing BHP

of

1,233 psia [8.5 MPa] associated with the extended

or

stabilized flow rate of 8,000 Mcf/D [227 x 10

3

m

3

/d] were used.

Because the static BHP in this well was less than 2,000 psia [13.8

MPa], pressure-squared values were substituted for pseudopressures

in the analysis.

Eq. 4 was used to construct the

IPR

curve shown in Fig. 8. Sub

stituting 8,000 Mcf/D [227x 10

3

m

3

/d] for

q

and the squares

of

PMfequal to 1,233 psia [8.5 MPa]

andPR

equal to 1,948psia [13.4

MPa] for their respective pseudopressures, a value

of

qmax

=

10,341 Mcf/D [293 x

1

3

mJ/d] was obtained. This compares with

SPE Reservoir Engineering, August 1988

7/26/2019 SPE-14507-PA

6/7

TABLE A 1 DATA USED FOR CONSTRUCTION OF

IPR, OUTFLOW PERFORMANCE, AND CONSTANT

TUBINGHEAD PRESSURE CURVES

Fig. A1 Production performance curves constructed

for

a

gas well at future condit ions with

the

dimensionless IPR

curve.

12 00

J utu re TPI. CUl Yl

4 00 6 00 8 00 10 00

FLOW RATE

(MMcI'fD)

2 00

2 00

.

1 90

:: : J : : : = . . . . . r - - - + - - - - - - O : C o n I w > I ~ 1 h . 5 0 0 J * g

1 60

1 50

1 40

1 30

1 20

1 10

1 00

0 90

0 80

0 70

0 60

0 50

0 40

0 30

0 20

0 10

0 00

-- , - - - , - - - , - - , - - , - - - - . - - , - - - - . - - - - - r - - -- , - - - - - - - r - - i

0 00

1,725

1,739

1 781

1,823

1,858

1,884

Constant

tt

=1,500 psig

Curve Data

(psia)

1,679

1 581

1,364

1,128

869

556

334

136

27

Outflow

Performance

Curve Data

(psia)

Calculated

Current Gas

Flow Rate

Mcf/D

o

973

2,709

5,269

6,989

8,164

8,975

9 281

9,414

9,439

9,535

9,914

10,159

10,297

1 341

Flowing

BHP

(psia)

1,948

1,900

1,800

1,600

1,400

1,200

1,000

900

850

840

800

600

400

200

o

a value of 10,988 McflD [311 x 10

3

m

3

d

obtained for the AOF

of

the well from the modified isochronal test analysis and an AOF

of

10,526 McflD [298 x

10

3

m

d found with pseudopressures.

Additional data calculated for constructing the IPR curve are shown

in Table A I

The second step in predicting the performance

of

a gas well re

quires a knowledge

of

flow behavior in the tubing. From Fig. 8,

corresponding values

of

flow rate and flowing BHP were read from

the IPR curve. Tubingheadpressure values were then computed

for each flow rate and BHP for a 0.605-gravity gas producing

through 5,000 ft [1525 m

of

2 -in. [6-cm tubing. These data ap

pear in Table A-I and are plotted in Fig. 8 as the outflow perform

ance

or

tubinghead pressure curve. Note that this curve, like the

IPR curve, is valid only at the current static BHP conditions.

It

is now desired to estimate the current deliverability

of

this well

when producing against a backpressure

of

1,500 psig [10.3 MPa

at the wellhead. Entering Fig. 8 at a tubinghead pressure

of

1,514.7

psia [10.4 MPa , proceeding horizontally to intersect the outflow

performance curve and then vertically downward to the x axis, a

stabilized deliverability of about 3,600 McflD [102 x 10

3

m

d

is

determined. The expected flowing BHP for this well at these produc

ing conditions can be determined by proceeding vertically upward

to intersect the IPR curve, and horizontally across to the y axis to

read a flowing BHP

of

1,750 psia [12.1 MPa .

An alternative method for determining deliverability

of

this well

at a constant tubinghead pressure involves selecting flow rates ar-

bitrarily and calculating BHP for a constant tubinghead pressure

of

1,500 psig [10.3 MPa . This procedure was used, and the resul

tant data also appear in Table A I The corresponding constant

tubinghead pressure curve is plotted in Fig. 8. The intersection

of

this curve with the IPR curve yields a stabilized deliverability

of

3,600

Mcf

[102 x 10

3

m

3

/d at a flowing BHP

of

approximate

ly 1,750 psia [12.1 MPa .

Unlike the outflow performance curve, the constant tubinghead

pressure curve

is

valid for future IPR curves constructed for declin

ing static average reservoir pressures as long as the flow-string con

figuration in the well remains the same.

For

example,

if

the static

reservoir pressure in the well

of

Table 1 declines to 1,800 psia [12.4

MPa , a new IPR curve must be found. Substituting values for the

squares

of

1,800 and 1,948 psia [12.4 and 13.4 MPa], respective

ly, in

PyRflppRi ,

and 10,341 Mcf/D [293 x

10

3

m

3

/d for

qm xi

in Eq. 6 or Fig. 5, a value for the new AOF or qmaxf=9,353

McflD [265x 10

3

m

3

/d is found. The value for

qmaxf

and the new

static reservoir pressure

of

1,800 psia [12.4 MPa are used in con

junctionwith Fig. 4

or

Eq. 4 to construct the new IPR curve shown

in Fig.

A I

Data for this curve appear in Table A-2.

It

can be seen from Fig. A-I that if a 1 5OO-psig [1O.3-MPa

tubinghead pressure is maintained on this well, the stabilized deliver

ability

of

the well will fall from 3,600 to 1,600 McflD [102 to

45 x 10

3

m

3

/

d

as static reservoir pressure falls from 1,948 to

1,800 psia [13.4 to 12.4 MPa .

TABLE A 2 DATA USED FOR CONSTRUCTION

OF

FUTURE PERFORMANCE CURVES

TABLE

A a DATA

FOR CONSTRUCTION OF

PERFORMANCE CURVES FROM MODiFIED ISOCHRONAL

TEST DATA

Constant

tt = 1,500 psig

Curve Data

(psia)

Initial static reservoir pressure, psia

Future static reservoir pressure, psia

Initial j\OF rate, McflD

Future AOF rate,

Mcf/D

1,823

1,797

1,775

1,756

1,742

1,732

1,725

1,724

Flowing

BHP

(psia)

1,800

1,700

1,600

1,400

1,200

1,000

800

600

400

200

o

Gas

Production

Rate

Mcf/D

o

1,866

3 351

5 5 1

6,910

7,849

8,478

8,895

9,159

9,306

9,353

1,948

1,800

1 341

9,353

1,723

1,730

1,747

1,785

1 821

Gas

Flow Rate

(McflD)

10,988

10,000

9,000

8,000

7,000

6,000

5,000

4,000

3,000

2,000

1,000

5

o

P

ws = 1,948 psia

P

ws = 1,800 psia Constant

Flowing Flowing Pth = 1,500 psig

BHP BHP Curve Data

(psia) (psia) (psia)

o 0

743 0

1,036 721

1,249 1,002

1,416 1,204

1,553 1,362

1,665 1,489

1,758 1,592

1,833 1,675

1,890 1,737

1,930 1,780

1,942 1,794

1,948 1,800

SPE Reservoir Engineering, August 1988 1095

7/26/2019 SPE-14507-PA

7/7

Fig.

A Productlon

performance curves constructed for a

gas well at current and future conditions with the stabilized

dellverablllty curve.

5 etrl onveslon actors

cp

x

1.0* E 03

Pa s

ft3 x 2.831 685 E 0 2 m

3

psi

x

6.894 757

E OO

kPa

Eq. A-I was used to compute the data in Table

A 3

and con

struct the IPR curves in Fig. A-2 for static reservoir pressures

of

1,948 and 1,800 psia [13.4 and 12.4 MPa]. Plotting the 1,500-psig

[10.3-MPa] constant tubinghead pressure curve yields expected

stabilized deliverabilities

of

4,000 and 2,000 Mcf/D [113 and

57 x 10

3

m

3

/d] for the respectiveR values.

It

can

be

seen that the values for deliverabilities obtained with

the modified isochronal test analysis were somewhat higher than

the values obtained with the dimensionless IPR curves. One rea

son for the differences may be that pressure-squared values were

used instead

of

pseudopressures in calculating flow rates from the

dimensionless IPR curves.

12.000.00.00 6.00 8.00

FLOW RATE

MWctIOt

2.00

2.00

1.10

1.80

1.70

1.60

1.50

1.40

1.30

1 2 0

1.10

1:00

5

f

0.70

0.60

0.50

0.40

0.30

0.20

0.10

0.00

- - - - - - - . .. . - - - - - . . . . - - - - - .- - r - - - - - - - - - . - - - l

0.00

For comparative purposes, the equation for the stabilized deliver

ability curve resulting from the analysis

of

themodified isochronal

test data in Table 1 was determined to

be

Converslon factor Is exact. SPERE

q=0 00124 p

R2

PMf2 O.60.

.

A-I

Original

SPE

manuscript received for review

Nov. 6, 1985.

Paper accepted for publication

March

16, 1987.

Revised manuscript received

Feb. 11, 1988.

Paper

SPE

14507 first

presented at the 1985 SPE Eastern Regional Meeting held

In

Morgantown WV, Nov. 6-8.

1096

SPE Reservoir Engineering, August 1988