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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
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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