A comparison of two phase inflow perform. SPE Paper

1. A Comparison of Two-Phase Inflow
Performance Relationships
Frederic Gallice,* SPE, and Michael L. Wiggins, SPE, U. of Oklahoma
Summary
Petroleum engineers are routinely required to predict the pressure/
production behavior of individual oil wells. These well-perfor-
mance estimates assist the engineer in evaluating various operating
conditions, determining the optimum production scheme, and de-
signing production equipment and artificial-lift systems.
In this paper, commonly used empirical, inflow performance
relationships for estimating the pressure/production behavior dur-
ing two-phase flow are investigated. Relationships studied include
those proposed by Vogel; Fetkovich; Jones, Blount, and Glaze;
Klins and Majcher; and Sukarno and Wisnogroho. Each method is
described briefly, and the methods used to develop the relationship
are discussed.
On the basis of actual vertical-well data, the relationships are
used to predict performance for 26 cases. The predicted perfor-
mance is then compared to the actual measured rate and pressure
data. The variation between the predicted and measured data is
analyzed, and from this analysis, an assessment is made on the use
of inflow performance relationships and of the quality of the per-
formance estimates.
Introduction
When considering the performance of oil wells, it is often assumed
that production rates are proportional to pressure drawdown. This
straight-line relationship can be derived from Darcy’s law for
steady-state flow of a single, incompressible fluid and is called the
productivity index (PI).
Evinger and Muskat1
were some of the earliest investigators to
look at oilwell performance. They pointed out that a straight-line
relationship should not be expected when two fluid phases are
flowing in the reservoir. They presented evidence, based on mul-
tiphase flow equations, that a curved relationship existed between
flow rate and pressure.
This work led to the development of several empirical inflow
performance relationships (IPRs) to predict the pressure/
production behavior of oil wells producing under two-phase flow
conditions. These estimates assist the engineer in evaluating various
operating conditions, determining the optimum production scheme,
and designing production equipment and artificial-lift systems.
This paper reviews and compares five IPRs proposed in the
literature for predicting individual-vertical-well performance in so-
lution-gas-drive reservoirs. The IPRs studied are Vogel2
; Fetkov-
ich3
; Jones, Blount, and Glaze4
; Klins and Majcher5
; and Sukarno
and Wisnogroho.6
Each IPR was developed for various conditions
but essentially represents vertical wells producing from a single
solution-gas-drive reservoir under boundary-dominated flow con-
ditions. A homogeneous reservoir is assumed in all the methods
except for Fetkovich’s; however, Wiggins et al.7
have shown that
this assumption does not restrict the applicability of an IPR
method. Using data from 26 field cases, the five IPR methods are
used to predict the pressure/production behavior for the individual
cases, and the predictions are compared to the actual well perfor-
mance and to the other methods’ predictions to develop an under-
standing of their reliability.
Deliverability Methods
Vogel developed one of the earliest IPRs based on simulation data
for 21 reservoir data sets representing a wide range of reservoir
rock and fluid properties. Vogel noticed that the shapes of the
pressure/production curve for these cases were very similar. He
made the curves dimensionless by dividing the pressure at each
point by the reservoir pressure and by dividing the flow rate by the
maximum flow rate to obtain the dimensionless inflow perfor-
mance curve. He observed that all the points fell within a narrow
range and developed the following relationship to describe the
dimensionless behavior.
qo
qo,max
= 1 − 0.2ͩpwf
pR
ͪ− 0.8ͩpwf
pR
ͪ2
. . . . . . . . . . . . . . . . . . . . . . . (1)
Fetkovich3
proposed the isochronal testing of oil wells to esti-
mate their productivity. This relationship is based on the empirical
gas-well-deliverability equation proposed by Rawlins and Schell-
hardt.8
Using data from multirate tests on 40 different oil wells in
six fields, Fetkovich showed that the following approach was suit-
able for predicting performance:
qo = C͑pR
2
− pwf
2
͒n
, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)
which can be expressed in a form similar to Vogel’s IPR, as follows:
qo
qo,max
= ͫ1 − ͩpwf
pR
ͪ2
ͬn
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)
This method requires that a multirate test be conducted to obtain
the values of C and n. A log-log plot of the pressure-squared
difference vs. flow rate is expected to plot as a straight line, where
the inverse of the slope of the curve yields the deliverability ex-
ponent n required in Eq. 3.
Using Forchheimer’s9
model to describe non-Darcy flow, Jones
et al.4
proposed the following relationship between pressure and rate.
pR − pwf
qo
= A + Bqo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4)
This method requires that a multirate test be conducted to deter-
mine the coefficients, A and B, in which A is the laminar-flow
coefficient and B is the turbulence coefficient. From Eq. 4, it is
evident that a Cartesian plot of the ratio of the pressure difference
to the flow rate vs. the flow rate yields a straight line, with the
y-intercept being A and the slope, B. Once the coefficients are
estimated, the flow rate at any flowing pressure can be determined
with Eq. 5.
qo =
− A + ͌A2
+ 4B͑pR − pwf͒
2B
. . . . . . . . . . . . . . . . . . . . . . . . (5)
On the basis of Vogel’s work, Klins and Majcher5
developed an
IPR that incorporated the bubblepoint pressure. The authors simulated
21 wells using Vogel’s data and developed 1,344 IPR curves. Using
nonlinear regression analysis, they presented the following IPR.
qo
qo,max
= 1 − 0.295ͩpwf
pR
ͪ− 0.705ͩpwf
pR
ͪd
, . . . . . . . . . . . . . . . . . . (6)
in which
d = ͩ0.28 + 0.72
pR
pb
ͪ͑1.235 + 0.001pb͒ . . . . . . . . . . . . . . . . . . (7)
* Now with Kerr-McGee, Houston.
Copyright © 2004 Society of Petroleum Engineers
This paper (SPE 88445) was revised for publication from paper SPE 52171, first presented
at the 1999 SPE Mid-Continent Operations Symposium, Oklahoma City, Oklahoma, 28–31
March. Original manuscript received for review 1 July 1999. Revised manuscript received 5
March 2004. Paper peer approved 6 March 2004.
100 May 2004 SPE Production & Facilities

2. Sukarno and Wisnogroho6
developed an IPR based on simula-
tion results that attempts to account for the flow-efficiency varia-
tion caused by rate-dependent skin as the flowing bottomhole pres-
sure changes. The authors developed the following relationship
using nonlinear regression analysis.
qo,actual
qo,max,r=0
= FEͫ1 − 0.1489
pwf
pR
− 0.4416ͩpwf
pR
ͪ2
− 0.4093ͩpwf
pR
ͪ3
ͬ,
. . . . . . . . . . . . . . . . . . . . . . . . . . . (8)
in which
FE = a0 + a1ͩpwf
pR
ͪ+ a2ͩpwf
pR
ͪ2
+ a3ͩpwf
pR
ͪ3
, . . . . . . . . . . . . . . . (9)
and
aR = bo + b1s + b2s2
+ b3s3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . (10)
In Eq. 10, s is the skin factor, and a and b are the fitting coeffi-
cients shown in Table 1.
IPR Comparison
To compare the various IPRs, data from 26 cases presented in the
literature are analyzed. Each case uses actual field data represent-
ing different producing conditions. Data from each case are used to
select rate and pressure information for test points, and these points
are used to predict well performance with each IPR method. The
predictions are then compared to the actual measured production
data at drawdowns greater than the test data. Several cases are used
to demonstrate the analysis and to provide insight into the behavior
of the various predictive models. Complete details of the analysis
are presented by Gallice,10
while the cases analyzed are summa-
rized in Table 2.
Case 1. Millikan and Sidewell11
presented multirate-test data for a
well producing from the Hunton Lime in the Carry City Field,
Oklahoma. The test was conducted in approximately 2 weeks, with
the well producing at random rates rather than in an increasing or
decreasing rate sequence. The average reservoir pressure was
1,600 psi, with an estimated bubblepoint pressure of 2,530 psi
and an assumed skin value of zero. The field data are summarized
in Table 3.
Table 4 presents the performance predictions for test informa-
tion at a flowing bottomhole pressure of 1,267 psi, representing a
21% pressure drawdown. As can be seen, the maximum well de-
liverability varies from 2,562 to 3,706 STB/D. The largest flow
rate was calculated with Vogel’s IPR, while the smallest rate was
obtained using Fetkovich’s method.
Fig. 1 shows the various IPR curves generated from the test
data. Visual inspection indicates that the methods of Fetkovich and
Jones, Blount, and Glaze estimate the actual well performance
more accurately. The other methods capture the general shape of
the data but overestimate actual performance. If the straight-line
PI is used in this case, a maximum flow rate of 6,054 STB/D
would have been predicted from the test point. This estimate is
more than 60% greater than the highest rate predicted by the IPR
methods and shows the importance of using a multiphase flow
relationship to evaluate well performance when multiphase flow
occurs in the reservoir.
Table 5 shows the percent difference between the recorded
flow-rate data and the computed rate for the five IPR methods. The
multirate methods have differences of less than 10%. The average
absolute difference for Fetkovich’s method is 4%, while Jones
et al.’s is 7%. The single-point methods have an absolute average
difference ranging from 18 to 31% for Klins and Majcher and
Vogel, respectively. In general, the difference tends to increase
with increasing pressure drawdown. This increased difference in
predicted vs. actual performance is expected. Because each IPR is
actually used to extrapolate performance behavior at drawdowns
greater than the test point, one would expect these estimates to
increase in error as one moves further from the known data point.
Because the test data cover a wide range of pressure draw-
downs, they allow an investigation of the effect of drawdown on
performance estimates. Table 6 presents a summary of the average
absolute differences for each method based on drawdown percent-
ages (8, 21, 38, 51, and 78%) of the test point. As shown, the average
101May 2004 SPE Production & Facilities

3. absolute differences in the performance predictions for all the
methods decrease as the test-point drawdown percentage increases.
For example, Vogel’s method predicted a maximum flow rate
of 5,108 STB/D at an 8% pressure drawdown, compared with
2,564 STB/D at a drawdown of 78%. This is almost a 100%
reduction in the maximum well deliverability. In addition, the
average differences in the performance estimates decrease from
72% at an 8% drawdown to 1.7% at a 78% drawdown.
All the methods show that the average absolute differences
decrease similarly in the predicted performance. By increasing
the pressure drawdown of the test point from 8 to 21%, the av-
erage absolute differences were decreased by more than 100%
for each method. For this particular case, a 20% pressure draw-
down appears sufficient to predict the well performance. This
is consistent with the observations of Wiggins12
who recom-
mended, on the basis of simulation results, that a minimum pres-
sure drawdown of 20% be used for all well testing used to predict
oilwell performance.
In summary, Fetkovich’s relation provided the best estimates of
well performance for this case’s entire range of interest. In general,
the difference in performance predictions increased as the pressure
drawdown increased from the test pressure. Also, the average ab-
solute difference in the predictions decreased as the test pressure
drawdown increased.
Cases 2 and 3. The next cases represent one well located in the
Keokuk pool, Seminole County, Oklahoma, where test data were
collected 8 months apart at two different reservoir pressures.13
The
reservoir pressure decreased from 1,734 to 1,609 psi, or 7%, be-
tween tests. These cases were selected to demonstrate the effect of
depletion on the IPR methods.
Owing to limited test data, performance predictions were made
from test information at pressure drawdowns of 13 and 12% for
reservoir pressures of 1,734 and 1,609 psi, respectively. As antic-
ipated, the various methods provide a range of performance esti-
mates for both reservoir pressures. Table 7 summarizes the abso-
lute differences in the IPR estimates. When the data were plotted,
there was little to distinguish the multipoint methods from single-
point ones for the first case. However, the second case clearly
showed a definite difference between the multipoint and single-
point methods. The average absolute difference in the performance
estimates also changed between the two cases, indicating that the
reliability of the various performance methods may change during
the life of a well.
Summary. The additional cases and their analysis are presented in
detail in Ref. 10. Table 8 presents a summary of the average
absolute difference for each method for all cases examined. As
indicated, no one method always provided the most reliable esti-
mates of the actual well data analyzed. However, some general
comments can be made on the basis of this table and all the cases
analyzed in this study.
The multipoint methods of Fetkovich and Jones et al. tend to do
a better job of predicting well performance than the single-point
methods. As a matter of fact, the total average absolute difference
is almost twice as great for the single-point methods as compared
to Fetkovich’s multipoint method—15 compared to 8%. The
method of Jones et al. had an average difference of 12%. Overall,
the single-point methods of Vogel, Klins and Majcher, and
Sukarno provided similar average differences in the cases exam-
ined—14 to 15%.
Case 5 demonstrates the variation in the predicted performance.
In this case, Fetkovich’s method performed the poorest in estimat-
ing actual performance, while Vogel’s IPR did the best. This case
clearly shows that one should not depend on a single IPR method
to make reliable performance predictions in all reservoirs.
Case 9 provides another anomaly in this analysis. Each method
provides very similar estimates, except for Jones et al. In this
case, Vogel’s method provides a somewhat better estimate than
Fetkovich. However, the multipoint method of Jones et al. pre-
dicted rates that are significantly different from the actual perfor-
mance. For this case, this method estimated performance with an
average absolute difference of 58%, compared with 16 to 18% for
the other methods.
As a final note, the available data or costs of obtaining data will
influence selecting an IPR method to predict performance. Overall,
multipoint methods will provide more information and are recom-
mended to estimate well performance; however, it costs more to
obtain the data compared to single-point methods. In the end, the
Fig. 1—Predicted inflow performance curves compared to ac-
tual field data for Case 1.
102 May 2004 SPE Production & Facilities

4. benefit of multipoint methods must be carefully considered in
relation to the expense of obtaining the information.
Conclusions
In this study, five different methods to predict the pressure/
production performance of oil wells producing from solution-gas-
drive reservoirs have been presented. These are the methods of
Vogel; Fetkovich; Jones, Blount, and Glaze; Klins and Majcher;
and Sukarno and Wisngroho. Each method requires parameters
that are normally available from a production test. The methods
can be separated into multipoint and single-point methods. The
primary concern of this study was to evaluate the reliability of the
IPR methods on the basis of actual production-test data. Detailed
analysis and comparisons for 26 different cases were performed.
From this study, the following conclusions were drawn.
1. There is no one method that is the most suitable for every test.
It has been observed that in one case, one method will provide
the most reliable estimates, while providing the worst estimates
in the next case. From this observation, consideration should be
given to using more than one method in predicting performance
to provide a range of possible outcomes.
2. Of the well-performance methods evaluated in this study and the
field data analyzed, Fetkovich’s multipoint method tended to be
the most reliable. It has been shown, on the basis of the test data,
that the overall absolute difference for Fetkovich’s method was
less than for the others. Also, Fetkovich’s method provided
consistent performance predictions throughout the pressure-
drawdown range, while the single-point methods appeared to be
more sensitive to the drawdown pressure of the test point.
3. The selection of a drawdown pressure for testing purposes is an
important parameter related to the reliability of the IPR meth-
ods. It appears that a minimum drawdown pressure of 20% of
the average reservoir pressure is required to obtain reliable es-
timates of well performance for any IPR method. In general, it
is recommended that test information be obtained as near to
operating conditions as possible.
4. Because of depletion effects, one IPR method may be reliable at
one reservoir pressure but unreliable at another. This may be
caused by changes in reservoir parameters with time that can
lead to changes in reservoir flow properties. Once again, this
suggests the use of multiple IPR methods to estimate well per-
formance.
Nomenclature
a ‫ס‬ fitting parameter defined in Eq. 10, dimensionless
A ‫ס‬ laminar-flow coefficient, mL4
/t, psia/STB/D
b ‫ס‬ constant in Eq. 10, dimensionless
B ‫ס‬ turbulence coefficient, mL7
, psia/(STB/D)2
C ‫ס‬ flow coefficient, L3+2n
t4n−1
/m2n
, STB/D/psia2n
d ‫ס‬ exponent defined in Eq. 7, dimensionless
FE ‫ס‬ Sukarno and Wisnogroho flow efficiency, defined in
Eq. 9, dimensionless
n ‫ס‬ deliverability exponent, dimensionless
pb ‫ס‬ bubblepoint pressure, m/Lt2
, psia
pR ‫ס‬ average reservoir pressure, m/Lt2
, psia
pwf ‫ס‬ flowing bottomhole pressure, m/Lt2
, psia
qo ‫ס‬ oil flow rate, L3
/t, STB/D
qo,max ‫ס‬ maximum oil flow rate, L3
/t, STB/D
s ‫ס‬ skin factor, dimensionless
References
1. Evinger, H.H. and Muskat, M.: “Calculation of Theoretical Productiv-
ity Factors,” Trans., AIME (1942) 146, 126.
2. Vogel, J.V.: “Inflow Performance Relationships for Solution-Gas Drive
Wells,” JPT (January 1968) 83; Trans., AIME, 243.
3. Fetkovich, M.J.: “The Isochronal Testing of Oil Wells,” paper SPE
4529 presented at the 1973 SPE Annual Fall Meeting, Las Vegas,
Nevada, 30 September–3 October.
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tiple Rate Flow Tests To Predict Performance of Wells Having Tur-
bulence,” paper SPE 6133 presented at the 1976 SPE Annual Technical
Conference and Exhibition, New Orleans, 3–6 October.
103May 2004 SPE Production & Facilities

5. 5. Klins, M.A. and Majcher, M.W.: “Inflow Performance Relationships
for Damaged or Improved Wells Producing Under Solution-Gas
Drive,” JPT (December 1992) 1357.
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140–157.
SI Metric Conversion Factors
bbl × 1.589 873 E-01 ‫ס‬ m3
psi × 6.894 757 E+00 ‫ס‬ kPa
psi2
× 4.753 8 E+01 ‫ס‬ kPa2
Frederic Gallice is a geoscientist at Kerr-McGee Corp., Hous-
ton. e-mail: fgallice@kmg.com. Gallice holds a BS degree in
physics from the U. of Blaise Pascal and an MS degree in pe-
troleum engineering from the U. of Oklahoma (OU). Michael L.
Wiggins is a professor of petroleum and geological engineer-
ing at OU. e-mail: mwiggins@ou.edu. He has industry experi-
ence with major and independent exploration and produc-
tion companies. His teaching and research interests include
production operations, well performance, stimulation, artificial
lift, and production optimization. Wiggins holds BS, MEng, and
PhD degrees in petroleum engineering from Texas A&M U. He
is a Distinguished Member of SPE and currently serves on the
Editorial Review Committee as Executive Editor of SPE Produc-
tion & Facilities. He has been a member of the Production and
Operations Symposium (POS) technical program committee
since 1992 and served as the General Chairman for the 2003
POS. He was a Director of the Oklahoma City Section from
1999 to 2001. He has served as a member of the Engineering
Registration Committee, as the Faculty Adviser for the OU SPE
Student Chapter, and as a committee member for the Petro-
leum Computer Conference.
104 May 2004 SPE Production & Facilities