SPE

SPE 24352
Analysis of lnflow Performance Simulation of Solution-Gas Drive
for Horizontal/Slant/Vertical Wells
Ming-Ming Chang, NlPER
SPE Member

This paper was prepared for presentation at the SPE Rocky Mountain Regional Meeting held in Casper, Wyoming, May 18-21, 1992.
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ABSTRACT
The inflow performance relationship (IPR) developed through
numerical simulation of vertical, horizontal, and slant wells in
solution-gas drive reservoirs was analyzed. The IPR is essential
to optimize production design; however, little information is
available for interpreting the change of IPR with wellbore
geometry and depletion stages. Gas saturation, PVT properties,
and formation pressure close to a wellbore were investigated to
interpret the shape of IPR curves at various flowing bottomhole
pressures and stages of depletion. The effect of oil gravities on
IPR curves was studied, and newly developed IPR curves for
slant wells were compared to those for horizontal and vertical
wells.
Horizontal well IPR curves fall on both sides of Vogel's
reference IPR curve for a vertical well. Horizontal wells show a
better productivity improvement with additional pressure
drawdown than vertical wells at the early stage of depletion.
Horizontal well IPR curves increase their curvature with
depletion up to 8%then slightly decrease in curvature at later
stages of oil recovery. This trend, different than that found for
vertical wells, is due to a high gas production rate from
horizontal wells at low bottomhole pressures before oil recovery
reaches 8%. The decrease in curvature of IPR curves for a
vertical well with depletion is due to a slightly higher formation
pressure around the wellbore at lower flowing bottomhole
pressures at later stages of depletion.
INTRODUCTION
Reliable estimates of well production allow operators to optimize
production design and predict recovery for project planning. In
two-phase flow of oil and gas, the relationship between the oil
production rate and the wellbore pressure drawdown is not
linear as it in single-phase flow. The equation that describes this
relationship is known as the inflow performance relationship
References and illustratons at end of paper.

(IPR) of a well. Vogel's numerically-derived IPR of a vertical

well for solution-gas drive reservoirs has received wide
acceptance since it was proposed in 1%2.1 Various studies
have been conducted to investigate effects of wellbore skin2 and
fluid parameters3 on IPR and methods to predict well
performance from test data.4-5
Inflow performance relationship curves for horizontal wells have
also been devel0ped6-~recently due to the interest in production
from horizontal wells. The IPR's of horizontal wells are
different from those of vertical wells; however, little information
is available to explain the difference. The objective of this study
are to interpret the IPR's of vertical, horizontal, and slant wells
producing from solution-gas drive reservoirs using a
mathematical simulation method.
A black oil reservoir simulator (BEST-VHS) was used in this
study for developing IPR curves of a single-well in a 20-acre
drainage area. BEST-VHS was modified from BOAST-VHS,
which was developed to simulate the performance of
verticallhorizontallslant wellslo for U.S. Department of
Energy. 11 This numerical simulator was first validated by
comparing its IPR simulations of a vertical well with a Vogel
curve. The simulator was then used to generate the IPR for a
horizontal well and the IPR for a slant well. The behavior of
horizontal well IPR curves was analyzed, and the difference of
IPR results between horizontal and vertical wells was
interpreted. Finally, the IPR for oil of 25" API gravity was
developed for horizontal and vertical wells, respectively, and the
effect of oil gravity on IPR was studied.
IPR SIMULATIONS
Numerical simulations were conducted to develop IPR curves
for vertical, horizontal, and slant wells, respectively, from a
solution-gas drive reservoir. The pressure-volume-temperature
(PVT) (Table 1) and relative permeability values were
reproduced from Figs. 9(a) and 10(a), respectively, in Vogel's
paper.1 The wellbore radius was assumed to be 3 in. and no
slun factor was assigned on the wellbore. Constant bottomhole

ANALYSIS O F INFLOW PERFORMANCE SIMULATIONS OF SOLUTION-GAS DRIVE

FOR HORIZONTAUSUNTIVERTICAL WELLS
algorithm employed in the simulator, small time steps (0.02 day)
were used in simulations for generating IPR curves.

Vertical well Simulator Validation. IPR curves of a

vertical well were generated from mathematical simulations
using reservoir and fluid-rock data provided by vogell in his
base case. This 20-acre and 23.5-ft-thick reservoir was
dimensioned at l7* l7* 1 in the simulation. The vertical well is
located in the middle (9,9,1) of the reservoir. The size of the
reservoir grid increases gradually from the well block to the
boundary block of the reservoir in both x and y directions as:
10, 10, 15, 25, 50, 75, 89.2, 100, and 100 ft (Fig. 1). The
wellblock size of 10 ft makes the equivalent wellblock radius,
which corresponds to the radius of wellblock pressure in the
simulation, to be 2 ft.

Figure 2 shows results of IPR simulation runs at various

depletion stages: 0.1, 2, 4, and 6%, together with Vogel's
reference curve. The 0.1% IPR curve shows the largest
curvature among the four curves. IPR curves shift slightly to
the left-hand side with depletion. The close agreement between
simulation results and Vogel's curve indicates that BEST-VHS
has worked properly for generating the IPR for a vertical well
from a solution-gas drive reservoir.
Horizontal well. The same reservoir and fluid-rock data
employed in previous vertical well IPR simulations were used in
developing horizontal well IPR curves. But the reservoir model
was dimensioned at 17*3*5 with a horizontal well located in the
middle of the x-direction and parallel to the y-direction (Fig. 1).
The horizontal well was assumed to penetrate the reservoir in the
middle layer. Sizes of reservoir grids in the x-direction were the
same as those in vertical well IPR simulations. The reservoir
length in the y-direction and thickness in the z-direction were
equally divided into three and five grids, respectively.

Simulation results of horizontal well IPR runs at different

depletion stages are shown in Fig. 3. Vogel's reference curve of
the vertical well is included for comparison. Horizontal well
IPR curves fall about evenly on both sides of Vogel's reference
curve. The IPR curve at an early depletion stage (such as 2%) is
close to a straight line. As the depletion proceeds, IPR curves
shift to the right-hand side with a larger curvature until it reaches
8%depletion. When the depletion exceeds 8%, the IPR curve
reverses the shift to the left-hand side.
These horizontal well IPR curves were compared to those
developed by Bendakhlia and Aziz at Stanford university.6 An
identical trend of the IPR shift with reservoir depletion was
observed by Bendakhlia and Aziz. For comparison,
Bendakhlia's horizontal well IPR curves were reproduced using
Eq. 6 and V and n values from Fig. 16 in reference 6. V values
of 0.150 and 0.164 and n values of 1.10 and 0.98 were used for
reproducing Stanford's IPR curves at 2 and 8% depletion
stages, respectively.
Figure 4 shows a comparison of the IPR from this study to that
of Stanford's at depletion stages of 8 % and 2%, respectively.
At the depletion of 8%, where IPR shows the greatest curvature,
the IPR of this study matches well with Stanford's curve. At the
early depletion of 2%, Stanford's 2% IPR curve shows larger
curvature than that of this study when the dimensionless
pressure is greater than 0.5. This disagreement at the early
depletion stage is considered to be minor, and the overall
comparison is favorable.
Slant Well. IPR curves were developed for a solution-gas
drive slant well using the same rock and fluid properties as those
used in generating IPR's for vertical and horizontal wells. A

SPE 24352

slant well of 221 ft was located in the middle of a reservoir

model dimensioned at 17*10*5 (Fig. 5). Generally, slant wells
are longer than vertical wells but shorter than horizontal wells.
Therefore, slant wells have higher productivity than vertical
wells and lower productivity than horizontal wells. IPR curves
developed from simulations for a slant well are shown in Fig. 6.
Discussions of IPR Curves of Horizontal, Vertical,
and Slant Wells

The shape of IPR curves of solution-gas drive reservoirs was

investigated for vertical, horizontal, and slant wells. Fluid
properties, gas saturations, and pressure variations near the
wellbore were analyzed during various depletion stages.
Vertical Well. The decrease of flowing bottomhole pressure
(BHP) reduces the formation pressure close to the wellbore, or
the wellblock pressure, as shown in Fig. 7. The wellblock
pressure in this study was equivalent to the formation pressure 2
ft away from the wellbore. The near-well formation pressure
(NWFP), or the wellblock pressure, dictates PVT properties of
fluids flowing into the wellbore. The low NWFP decreases the
gas viscosity and increases the oil viscosity (Table 1). This
increase of gas mobility and decrease of oil mobility reduce the
wellbore productivity for oil at low NWFP. It therefore creates
in IPR a curvature shifting to the right-hand side in Fig. 2.
Although the produced gas-oil ratio (GOR) at the surface stays
approximately the same value at different BHP's (Fig. 8), more
reservoir volume of gas is produced under a lower BHP when a
higher gas formation volume factor (Table 1) is taken into
account. A slightly higher gas saturation near the wellbore at a
lower BHP reduces oil relative permeability and contributes to
additional curvature in IPR curves.

Because of the relatively low productivity of a vertical well, the

NWFP and wellblock bubble point pressure decline slowly with
reservoir depletion (Fig. 9). The sharp pressure gradient near
the wellbore (Fig. 10) helps replace the produced oil in the nearwell region by oil from the reservoir boundary. Therefore the
near-well gas saturation and producing GOR increase slowly
with the depletion (Fig. 9).
In addition to fluid mobility, the effective pressure drawdown
near the wellbore also affects the oil production rate. The total
pressure drawdown, or the difference between formation
pressure and BHP, can be divided into two components:
pressure drawdown away from the well (PDAW) and pressure
drawdown near the well (PDNW). PDAW is defined as the
pressure difference between boundary and wellblock, and
PDNW is the pressure difference between wellblock and
flowing bottomhole pressure. PDAW determines the oil
replacement rate from reservoir boundary to the near-well
region, and PDNW determines the oil and total fluid production
rate into the wellbore. Figure 11 shows plots of BHP vs.
PDNW at various depletion stages. At the early depletion stage
(0.1%) a nearly straight line was observed between BHP and
PDNW. As the depletion proceeds, the lines in Fig. 11 exhibit
curvature shifting to the left-hand side of the graph. For the case
of a lower BHP during the later depletion stage, this indicates a
higher ratio of PDNW over total pressure drawdown. Since
PDNW dictates the well rate, it produces a higher rate of oil or
total fluid under lower BHP at the later depletion stage. This
results in a reduction of curvature in IPR with depletion.
Horizontal Well. Figure 12 shows pressure profiles of a
horizontal well at various depletion stages. Compared to a
vertical well, the horizontal well creates a less sharp pressure
profile near the wellbore (Fig. 13) after 2% depletion. This is
due to high productivity and nearby formation boundaries in the
vertical direction for the horizontal well. This results in a lower

1'

SPE 24352

M. M. Chang
I

oil saturation (or a higher gas saturation) near the horizontal

wellbore than that in a vertical wellbore (Fig. 14). As the
depletion continues, the producing GOR, the near-well gas
saturation, and the declination of near-well pressure of a
horizontal well increase at a faster rate (Fig. 15) than that of a
vertical well (Fig. 9).

that of Vogel's reference curve. The IPR's curvature then

decreases after 2% depletion. The small amount of dissolved
gas in 25" API gravity oil reduces the curvature of IPR curves
compared to those of volatile oil.

For the same reason as that for the vertical well case, the
horizontal well exhibits a curvature in its IPR curves (Fig. 3).
Figure 16 shows the NWFP versus depletion at various BHP's
for a horizontal well. Compared to that of a vertical well, the
lower NWFP of the horizontal well after 0.1% depletion results
in a higher producing GOR's for the horizontal well (Figs. 8 and
17). At the very early recovery stage (0.1%)- the approximately
equal amount of gas production at various BHP's (Fig. 17) from
a nearly undisturbed reservoir results in a nearly straight line in
its IPR. As the depletion continues, as shown in Fig. 17, the
producing GOR increases faster under a lower BHP than it does
under a higher BHP until 8% depletion. This increases the
curvature by shifting IPR curves to the right-hand side. When
the recovery exceeds 8%, a higher GOR is produced from a
higher BHP. This causes a reduction of IPR curvature and
shifts curves slightly back to the left-hand side. Figure 18
shows the plot of BHP versus PDNW for the horizontal well.
The PDNW during the period of 2 to 10% depletion helps
reduce the curvature in IPR curves. The horizontal well IPR
curves would exhibit even larger curvatures without the high
PDNW at low BHP.

The following conclusions were drawn from this IPR simulation

study:

Slant Well. Similar to IPR's of a vertical well at the early

depletion stage (0.1%) the IPR of a slant well reaches a
curvature of Vogel's reference curve (Fig. 6). This is due to a
limited exposure of the slant wellbore to the reservoir. A
significant pressure drawdown near the well helps to produce
more gas than oil and, therefore, establishes the IPR curvature.
As the depletion continues up to 4%, the IPR increases its
curvature by shifting to the right-hand side which is similar to
the trend in horizontal well IPR's. The large gas saturation near
the slant wellbore is responsible for this IPR shift. No
significant shift of IPR curves was found during depletion
between 4 and 10% in this study.

CONCLUSIONS

1. The black oil simulator BEST-VHS was validated for its

capability for generating IPR's for vertical and horizontal wells.
Good agreements of IPRts developed in this study with those of
published curves for vertical and horizontal wells were obtained.

2. IPR curves were developed for one case of a slant well.

3. The horizontal well IPR curves increase in curvature with
depletion up to 8% then slightly decrease in curvature at later
stages of oil recovery. This is due to the high gas production
rate from horizontal wells at low bottomhole pressure before oil
recovery reaches 8%.
4. The decrease in curvature of vertical well IPR curves with
depletion is due to a slightly higher formation pressure around
the wellbore at a lower flowing bottomhole pressure at the later
depletion stage.

5. The decrease of solution gas-oil ratio in oil of low API gravity

accelerates the decrease of IPR's curvature with the reservoir
depletion for vertical wells as well as horizontal wells.
NOMENCLATURE
BHP
GOR
NplN
NWFP
PDAW
PDNW
Pwf1P
QlQmax

Effect of Oil Gravity on IPR

Since the oil rate is directly determined by the PVT of oil near
the well, effects of oil gravity on IPR were studied. The oil PVT
used in the above IPR simulations obtained from Vogel's base
case matches that of volatile oil with gravity equivalent to or
above 40" API. PVT values (Table 2) derived f r o m
correlatiosl2-13 for oil of 25" API gravity were used to generate
a new set of IPR's for vertical and horizontal wells. Other fluid,
rock, and reservoir properties were kept the same in the model
as those in previous simulations.
The IPR of 25" API gravity oil for a vertical well is shown in
Fig. 19. At a depletion of 0.1%, the vertical well's IPR
matches well with Vogel's reference curve. This indicates no
effect of oil gravity on IPR at the early depletion stage.
However, the decrease rate of IPR's curvature with depletion is
much higher for 25" API gravity oil (Fig. 19) in contrast to that
of the volatile oil. The little dissolved gas in the 25" API gravity
oil after depletion of 1% makes the production close to a singlephase depletion at the wellbore. Therefore a straight line of IPR
was obtained after depletion of 1%.
Similar to that of vertical wells, no oil gravity effect was
observed on IPR of horizontal wells (Fig. 20) at the early
depletion stage. The IPR curve shifts to the right-hand side with
depletion as shown in IPR's for volatile oil produced from
horizontal wells. But at 2% depletion, the IPR of 25" API
gravity oil reaches its maximum curvature, which is less than

= bottomhole pressure, psi

= gas-oil ratio, SCFISTB
= oil depletion
= near-well flowing pressure or wellblock
pressure, psi
= pressure drawdown away from well
= pressure drawdown near well
= ratio of BHP over average reservoir pressure
= ratio of oil rate at BHP over maximum oil
rate when BHP = 0

ACKNOWLEDGEMENT
The author thanks Dr. Thomas E. Burchfield, Dr. Michael P.
Madden, Dr. Min K. Tham, and Bill Linville, all of NIPER, for
their encouragement in the course of this work and for their
reviews of this paper.

REFERENCES
1.

Vogel, J. V.: "Inflow Performance Relationships for

Solution-Gas Drive Wells," JPT (Jan. 1968) 83-92.

2.

Camacho-V., R. G. and R. Raghavan.: "Inflow

Performance Relationships for Solution-Gas-Drive
Reservoirs," JPT (May 1989) 541-550.

3.

Wiggins, M. L., J. E. Russell, and J. W. Jennings:

"Analytical Development of Vogel-type Inflow
Performance Relationships," unsolicited paper S P E
23580.

4.

Standing, M. B.: "Concerning the Calculation of Inflow

Performance of Wells Producing from Solution Gas
Reservoirs," JFT (Sept. 1971) 1141-1142.

SPE 24352

ANALYSIS OF INFLOW PERFORMANCE SIMULATIONS OF SOLUTION-GAS DRIVE

FOR HONZONTAUSLANTIVERTICAL WELLS

Fetkovich, M. J.: "The Isochronal Testing of Oil Wells,"

paper SPE 4529 presented at the 1973 SPE Annual
Technical Conference and Exhibition, Las Vegas, Sept. 30
- Oct. 3.
Bendakhlia, H. and K. Aziz: "Inflow Performance
Relationships for Solution-Gas Drive Horizontal Wells,"
paper SPE 19823 presented at the 1989 SPE Annual
Technical Conference and Exhibition, San Antonio, Oct.
8-11.

Table 2. - PVT of 25" API gravity oil

Pressure,
psi

Viscosity,
CP

Formation
Volume
Factor

Solution
Gas-Oil Ratio,
SCFISTB

Cheng, A. M.: "Inflow Performance Relationships for

Solution-Gas Drive SlantedlHorizontal Wells," paper SPE
19823 presented at the 1990 SPE Annual Technical
Conference and Exhibition, New Orleans, Sept. 23-26.
Cheng, A. M.: "Development of an Inflow Performance
Relationship (IPR) for a SlantedlHorizontal Well," U.S
Dept. of Energy Report No. NIPER-458, Jan. 1990.
Cheng, A. M.: "Development of General Inflow
Performance Relationship (IPR's) for Slanted and
Horizontal Well Producing Heterogeneous Solution-Gas
Drive Reservoirs," U.S Dept. of Energy Report No.
NIPER-573, Feb. 1992.
Chang, M-M., L. Tomusa, and M. Tham: "Predicting
HorizontallSlanted Well Production by Mathematical
Modeling," paper SPE 18854 presented at the 1989 SPE
Production Operations Symposium, Oklahoma City, Mar.
13-14.
Chang, M-M., P. Sarathi, R. Heemstra, A. Cheng, and J.
Pautz: "User's Guide and Documentation Manual for
"BOAST-VHS for the PC"," U.S Dept. of Energy Report
No. NIPER-542, July 1991.
Beggs, H. D. and J. R. Robinson: "Estimating the
Viscosity of Crude Oil Systems," JPT (Sept. 1975) 11401141.
Vasquez, M. E. and H. D. Beggs: "Correlations for Fluid
Property Prediction," JPT, June 1980,968-970.

Table 1. - Oil PVT obtained from Vogel's base case

Pressure,
psi

Viscosity,

CP

Formation
Volume
Factor

Solution
Gas-Oil Ratio,
SCFISTB

Fig. 1-Reservoir models of IPR simulations for (a)

vertical well and (b) horizontal well productions. Grid sizes are marked in feet.

0.1%
2%

6%

Vogel
0
0

0.2

0.4

0.6

0.8

Q I Qmax

0.2

0.4

0.6

0.8

Q I Qmax

Fig. 2-IPR curves of a vertical well generated by using BESTVHS as compared with Vogel's data.

Fig. 3-IPR curves of a horizontal well generated using BESTVHS compared with Vogel's data for a vertical well.

Y-Direction

0.4 -

@O

-.

Np/N =
2%0,NlPER
8% NlPER
0.2
0 2%, Stanford
8%, Stanford

0.2

0.

SLANT WELL

8".
.cO-

0.4

0.6

0.8

QIQmax

4.7
4.7
4.7
4.7
4.7

Fig. 4-Comparison of horizontal well IPR curves.

SLANT WELL
(0)

Fig. 5-Reservoir models of IPR simulations for slant

well production: (a) areal model and (b) crosssectional model. Grid sizes are marked in feet.

2000

3
L

1;:

0.2

BHP, pCi =

I-+

50

0
A@

o +

Depletion:

El

1%

*P
,

0.4

0.6

,*A!

8'10
10%
Vogel
0.2

0.8

Q 1 Qmax

10

12

Fig. 7-Wellblock pressure profiles at various depletion stages and flowing bottomhole pressures of a vertical well.

Fig. 6-IPR curves of a slant well generated using BEST-VHS

compared with Vogel's data for a vertical well.

6
8
DEPLETION,%

500

1000

1500

2000

WELLBLOCK PRESSURE, psia

Fig. 8-Gasloil ratios at various flowing bottomhole pressures and depletion
stages of a vertical well.

2000

400

ds g

: Bubble Point Press.

A
Wellblock Press.

20

RC,

X
3

12

DEPLETION, %

WELL DISTANCE, ft

Fig. 9-Profiles of gas saturation, producing gasloil ratio, wellblock pressure, and bubblepoint pressure with depletion from a vertical well under BHP of 500 psi.

200

400

Fig. 10-Reservoir pressure profiles at various depletion stages from a vertical well under BHP of 500 psi.

600

800

1000

WELLBLOCK PRESSURE DRAWDOWN, psi

Fig. 1l-Variations of near-well pressure drawdown with bottomhole pressure of a vertical well at various depletion stages.

2500

__---/

Np/N =

0.1%, H
2%, H
8%,H
- -0-0.1%, v
- - 0 -2%, v
4- 8% V
-+

,'o..--.D-.-*--

-3-- ---=--

100

200

300

400

500

500
0

600

200

300

100

Fig. 12-Reservoir pressure profiles at various depletion stages from a horizontal well
under BHP of 500 psi.

500

600

Fig. 13-Comparison of reservoir pressure profiles between vertical and horizontal

wells at various depletion stages under BHP of 500 psi.

H: Horizontal well
6
- 0-

H: Horizontal well
V; Vertical well

400
WELL DISTANCE, ft

WELL DISTANCE, ft

--

100

200

300

V; Vertical well

400

500

-I

600

WELL DISTANCE, ft
Fig. 14-Comparison of oil saturation profiles between vertical and horizontal wells
at various depletion stages under BHP of 500 psi.

2000

--+Bubble Point Press.

--A-

2000

*sg
-a-GOR

Wellblock Press.

!-b-+

400 1
0

10

12

BHP, psi =

a
$1500

4
15
-E 250
- + 500
--X- 750
-.+. 1000

16

DEPLETION, %
Fig. 15-Profiles of gas saturation, producing gasloil ratio, wellblock pressure, and
bubblepoint pressure with depletion from a horizontal well under BHP of
500 psi.

Fig. 16-Wellblock pressure profiles at various depletion

stages and flowing bottomhole pressures of a
horizontal well.

0
0

300

600

900

1200

1500

WELLBLOCK PRESSURE, psia

Fig. 17-Gasloil ratio at various flowing bottomhole pressures and depletion
stages of a horizontal well.

a
\

3
a
OS4

200

400

600

800

1000

0-

WELLBLOCK PRESSURE DRAWDOWN, psi

Depletion:

Fig. 19-IPR

.c

a 0.4

1-

A0

Depletion:

+
0

..

4%
Vogel
I

X,
I

+I

Q I Qmax
Fig. 20-IPR

a
+

Vogel

Fig. 18-Variations of near-well pressure drawdown with bottomhole pressure of

a horizontal well at various depletion stages.

0
6l

curves of 25O API gravlty oil for a horizontal well.

0.2

r!
0.4
0.6
Q I Qmax

0.8

curves of 25' API gravity oil for a vertical well.