SPE 68666
Analysis of a Non-Volumetric Gas-Condensate Reservoir
L. Vega, Texas A&M University, M.A. Barrufet, Texas A&M University
Copyright 2001, Society of Petroleum Engineers Inc.
This paper was prepared for presentation at the SPE Asia Pacific Oil and Gas Conference and
Exhibition held in Jakarta, Indonesia, 1719 April 2001.
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Abstract
Predicting water encroachment can be of critical importance in
describing and managing a hydrocarbon reservoir.
This study focuses on the use of the generalized material
balance equation (GMBE) proposed by Walsh, et al1,2 along
with the analytical solution to the diffusivity equation for a
constant inner boundary pressure as presented by van
Everdingen and Hurst to determine the size of a water-bearing
formation in contact with a gas-condensate reservoir.
When the hydrocarbon reservoir fluid is a gas-condensate,
it is essential to use the GMBE. Should the conventional
material balance equation (CMBE) be used in lieu of the
GMBE, considerable errors could be introduced as will be
shown.
The main goal of this paper is to illustrate the ability of the
GMBE to determine the size of an aquifer encroaching into a
gas-condensate reservoir. Once this size is obtained, it could
be used as an input parameter to a reservoir simulator to
forecast the future expansion of the aquifer as depletion
proceeds.
When the CMBE is used to describe black oil reservoirs,
certain simplifying assumptions are normally made. Those
include neglecting the effect of the compressibilities of the
connate water and the reservoir rock, in addition to the
volatilized liquid in the gas phase. The effect of these
assumptions in gas-condensate reservoirs will be examined.
Introduction
In 1994, Walsh, et al1, 2 presented the generalized form of
the material balance equation. This equation differs from
previous forms of the material balance equation in that it
includes a term that accounts for the amount of liquid that is
volatilized in the gas phase. These terms are practically zero
when the reservoir fluid is either a black oil or a dry gas.
However, as shown in the discussion below, ignoring this term
when the reservoir fluid is a gas-condensate can lead to
significant errors in the interpretation.
The principal motivation for this study is our current
interest in water coning in horizontal wells. In the 1970s,
Morse, et al3 used numerical reservoir simulation to study the
behavior of vertical wells completed close to a
hydrocarbon/water contact. One method that Morse, et al3
proposed to prevent coning was the completion of the vertical
well both above and below the hydrocarbon/water contact, but
producing both streams through separate tubings. The purpose
of this would be to have an independent control on the
pressure drawdowns above and below the hydrocarbon/water
contact so that coning could be suppressed.
A viable way to apply the same idea to horizontal wells
would be the use of two multilaterals simultaneously
producing above and below the hydrocarbon/water contact.
However, to properly design and operate those wells, it would
be of paramount importance to know how fast the
hydrocarbon/water contact would rise as depletion advances.
The technique illustrated in this paper allows the
determination of the length, or the radius (depending on the
geometry) of the aquifer. Once this is known, it could be used
as an input parameter to a reservoir simulator to make
predictions of the expansion of the aquifer, and thus the rise of
the hydrocarbon/water contact.
Data
During the appraisal stage of a field, scarce information is
usually available to make it viable to use a reservoir simulator
to predict the rise of the hydrocarbon/water contact in a
water/drive hydrocarbon reservoir. This is because such a
prediction not only requires a fairly acceptable description of
the reservoir itself, but also of the encroaching aquifer.
Nonetheless, it is during the appraisal stage, and early
development of the filed, that valuable information can be
obtained about the sizes of both the reservoir and any
neighboring aquifer using material balance techniques. This
information can then be used as input to a reservoir simulator
to predict how fast the neighboring aquifer will encroach into
the reservoir.
In this project, a compositional numerical simulator was
used to generate synthetic data. This synthetic data was then
used as input to the material balance equation.
L. VEGA AND M.A. BARRUFET
As illustrated in Fig. 1, a reservoir model with given
dimensions, properties, fluid composition, and drive
mechanism was assumed. Some of the output of the reservoir
simulator was in the form of cumulative production volumes
and average reservoir pressures.
SPE 68666
depletion (CVD) experiments at 285F were available. The
latter two were used to tune the EOS.
Compare
OGIP,
OOIP, zi,
Aquifer size,
etc.
Zi, ,TR, Pi,
separator
conditions
Compositional
Reservoir
Simulator
Phasebehavior
package
Bo, Bg, Rs, Rv
Gp, Np, Wp,
pav
MBE
OGIP,
OOIP,
Aquifer size.
Fig. 1 - Flow of information to analyze the effectiveness of
the GMBE to back calculate the input to the compositional
reservoir simulator.
On the other hand, the fluid compositions were converted
to PVT parameters using a phase behavior package for a given
reservoir temperature, tuned EOS and separator conditions.
These PVT parameters were then used, along with the
output from the reservoir simulator, as input data to the
material balance equation. The results of the material balance
calculations were then compared to the input to the reservoir
simulator to evaluate the effectiveness of the material balance
equation to determine the sizes of the reservoir, and of the
adjoining aquifer.
Model
As depicted in Fig. 2, the reservoir was modeled using a block
with dimensions 2,639.7 ft by 2,639.7 ft by 120 ft in the
horizontal and vertical directions, respectively.
The numerical grid had nine gridblocks in each horizontal
direction, and four in the vertical direction.
The porosity was assumed constant throughout the
reservoir with a value of 13%. The reservoir temperature was
set equal to 285F (The same as the one reported in the fluid
lab report described below).
Table 1 lists the values of permeability, thickness and
depth assigned to each of the four layers in the reservoir
model.
The initial reservoir pressure was 6,000 psia, and the
dewpoint pressure at 285F was 5,323.3 psia.
The values of relative permeabilities, capillary pressures,
etc., not shown in this paper, are the same as those in the Third
Comparative Solution Project4.
The reservoir fluid composition was that of the Cupiagua
Field, Colombia. A cromatographic report, along with a
constant composition expansion (CCE) and a constant volume
Fig. 2 Geometrical representation of reservoir
Table 1 Reservoir permeabilities, thickness, and depths of
each simulation layer.
Layer
Kx=ky, md
kz, md
Thickness, ft
Depth, ft
1
130
13
30
7,330
2
40
4
30
7,360
3
20
2
50
7,400
4
150
15
50
7,450
The chromatographic analysis includes 36 components. Its
fingerprint, or plot of mole fraction versus molecular weight,
is shown in Fig. 3.
Fig. 3 - Fingerprint of the 36 component mixture
Using this 36-component mixture as input to the
compositional numerical simulator would have slowed it down
dramatically. Consequently, the mixture was lumped into
eight pseudo components as shown in Table 2.
Just like its 36-component counterpart, the 8pseudocomponent mixture was used along with the 3parameter Peng-Robinson equation of state (PR3 EOS). When
either was used to predict the liquid saturation of the CCE at
285F, neither could predict a dew-point fluid (gascondensate). Instead, a bubble-point fluid (volatile oil) was
predicted at this temperature. This conflicted with the lab
observations, as shown in Fig. 4.
SPE 68666
ANALYSIS OF A NON-VOLUMETRIC GAS-CONDENSATE RESERVOIR
Table 2 Pseudo-components after the Cupiagua mixture
was lumped.
Pseudo component
Range
GRP1
CO2
GRP2
N2 and C1
GRP3
C2
GRP4
C3-nC4
GRP5
iC5-Toluene
GRP6
C7-C10
GRP7
C11-C22
GRP8
C23-C30
1.0
0.9
Liquid Saturation, fraction
0.8
Calculated
0.6
Observed
Under both drive mechanisms, the reservoir was produced
by first maintaining a plateau gas production rate of 6,200
Mscf/day. This constant gas production rate would be
maintained for as long as the bottom hole pressure in the
producing well was above 500 psia, after which the gas
production rate would decline while maintaining the bottom
hole pressure constant at 500 psia.
For the case of the water-drive reservoir, the underlying
water-bearing formation was simulated assuming a numerical
linear aquifer. Its dimensions and properties are listed in
Table 3.
Table 3 Aquifer properties used in compositional
reservoir simulator
Type of Aquifer
Linear
k, md
20
13
, %
A, ft3
200,000
L, ft
1,000
Liquid Saturation Before Regression (Peng-Robinson 3p)
0.7
0.5
0.4
0.3
0.2
0.1
0.0
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
Pressure, psia
Fig. 4 - Untuned 3-parameter PR EOS predicts a liquid
instead of a gas.
Therefore, the PR EOS was tuned using the regression
techniques proposed by Whitson5. Fig. 5 compares the liquid
saturation as obtained from the CCE experiment with that
obtained using the tuned PR3 EOS.
In designing the synthetic data set, two issues were taken
into consideration: (1) it is desirable to determine the size of
the encroaching aquifer early in the life of the reservoir, (2)
average reservoir pressure measurements are normally
available on a yearly basis, at best. Consequently, to make the
synthetic data set similar to what is normally available in the
field, eight data points from the first 3 years of the life of the
field were randomly selected from the output of the
compositional numerical simulator. Figs. 6-9 illustrate the
behavior of the average reservoir pressure, cumulative oil
produced, cumulative gas produced, and cumulative water
produced, all as a function of time, for the two assumed drive
mechanisms, and for those randomly selected times.
Average Reservoir Pressure
Cupiagua K5 sample
Lumped into 8 pseudo-components
Liquid saturation after Tuning
6,000
1
0.9
0.8
5,000
0.7
Pressure, psia
Liquid saturation, fraction
5,500
Calculated
Observed
0.6
0.5
0.4
0.3
4,500
4,000
3,500
3,000
0.2
2,500
Water Drive
Volumetric
0.1
2,000
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
200
400
600
800
1,000
1,200
Time, days
Pressure, psia
Fig. 5 Liquid saturation as obtained from the CCE
experiment and as predicted from the tuned PR EOS.
Fig. 6 Average reservoir pressure obtained from
compositional numerical simulator under both assumed
drive-mechanisms
The reservoir was produced assuming two different drive
mechanisms, namely volumetric and water drive.
Notice that, although the assumed aquifer is relatively
small (Table 3), the average reservoir pressure tends to be
L. VEGA AND M.A. BARRUFET
maintained considerably (1,500 psi difference at latest point)
when an aquifer is present, as shown in Fig. 6.
1,400,000
1,200,000
Np, stb
1,000,000
800,000
600,000
W ater Drive
Volum etric
400,000
200,000
0
0
200
400
600
800
1,000
1,200
Tim e, days
Fig. 7 Cumulative oil produced as obtained from
compositional numerical simulator under both assumed
drive-mechanisms
400,000
Water Drive
Volumetric
350,000
300,000
Wp, stb
250,000
200,000
150,000
100,000
50,000
SPE 68666
As illustrated in Fig. 7, the effect of the pressure
maintenance is to increase the amount of produced oil in the
case of the water-drive reservoir. The reason for this is that, at
higher pressures, the fluid will remain in the gaseous phase in
the reservoir, and will be easily produced. By the same token,
in the volumetric depletion case, some liquid dropout will
build up in the reservoir with very small or no mobility at all.
That is why pressure maintenance is so critical in those
reservoirs whose fluid experiences retrograde condensation.
Fig. 8 illustrates the effects of the expansion of the
underlying aquifer, and of water coning. Since the well is
completed only in the top three simulation layers, the
produced water volume is practically identical during the first
200 days in both the depletion and the water-drive cases.
After this time, water production increases substantially in the
water-drive case either because the hydrocarbon/water contact
has risen to the perforations, or because the gravitational
forces have succumbed to the sum of the capillary and viscous
forces.
Fig. 9 shows that the produced gas volume is larger in the
water-drive case. This is basically due to additional amount of
gas dissolved in the liquid that is left in the reservoir in the
volumetric case.
The next step is the determination of the PVT parameters
using the composition of the fluid and the reservoir
temperature.
Fig. 10 shows schematically the algorithm used to
determine Bo, Bg, Rs, and Rv using the 8-pseudo-component
mixture, the PR3 EOS tuned to the CCE and CVD
experiments, and the same separator conditions used in the
compositional numerical simulator.
0
0
200
400
600
800
1,000
1,200
Time, days
Fig. 8 - Cumulative water produced as obtained from
compositional numerical simulator under both assumed
drive-mechanisms
Composition, Reservoir Temperature,
Separator Conditions, and Tuned EOS
8,000,000
Phase Behavior Package
Water Drive
Volumetric
7,000,000
6,000,000
Gp, Mscf
5,000,000
Bo, Bg, Rs, Rv as a function of pressure
4,000,000
3,000,000
Fig. 10 - Procedure to calculate PVT parameters for
hydrocarbon mixture
2,000,000
1,000,000
0
0
200
400
600
800
1,000
1,200
Time, days
Fig. 9 - Cumulative gas produced as obtained from
compositional reservoir simulator under two assumed
drive-mechanisms
Figs. 11-14 are a graphical representation of the PVT
parameters, Bo , B g , Rs and Rv , for the Cupiagua field fluid
obtained in this fashion.
In summary, the average reservoir pressure and cumulative
produced volume data provided in Figs. 6-9, along with the
PVT data supplied in Figs. 11-14 represent the necessary input
to the GMBE as shown in the next section.
SPE 68666
ANALYSIS OF A NON-VOLUMETRIC GAS-CONDENSATE RESERVOIR
Volatilized Oil-Gas Ratio at 285F
Cupiagua Field
Oil FVF at 285F
Cupiagua Field
0.30
3.5
0.25
3.0
Rv, stb/Mscf
Bo, rb/stb
0.20
2.5
2.0
0.15
0.10
0.05
1.5
0.00
0
1.0
0
1,000
2,000
3,000
4,000
5,000
1,000
2,000
3,000
4,000
5,000
6,000
Pressure, psia
6,000
Pressure, psia
Fig. 14 Volatilized oil-gas ratio of the Cupiagua field
fluid at 285F
Fig. 11 Oil FVF for Cupiagua field fluid at 285F
Gas FVF at 285F
Cupiagua Field
Generalized Material Balance Equation
In 1994, Walsh, et al1, 2 presented the generalized material
balance equation (GMBE). Its purpose was to account for the
fraction of the produced liquid that was in the gas phase at
reservoir conditions. Whereas this fraction is practically
negligible in the case of black oil and dry gas, ignoring it
when dealing with gas-condensates may lead to serious errors.
This fraction is expressed as Rv and has units of rb/Mscf.
45
40
35
Bg, rb/Mscf
30
25
20
The GMBE is identical in form to the CMBE, as expressed
by Eq. 1. The difference lies in the definition of its terms.
15
10
F = N foi E o + G fgi E g + We ............................(1)
5
0
0
1,000
2,000
3,000
4,000
5,000
6,000
Pressure, psia
Fig. 12 Gas FVF for Cupiagua field fluid at 285F
Solution Gas-Oil Ratio at 285F
Cupiagua Field
3.5
3.0
Bo (1 Rv R ps ) + B g (R ps Rs )
F = Np
....(2)
(
)
1
R
R
v
s
2.5
Rs, Mscf/stb
Eq. 1 basically states that the underground withdrawal,
F , must be equal to the sum of total expansion of the
hydrocarbon fluids plus the water influx. It assumes that the
expansion of the rock, and that of the interstitial water are
negligible compared to that of the hydrocarbons.
The underground withdrawal, F , is defined by equation
2.
2.0
1.5
Eq. 3 defines the unit expansion of the oil.
1.0
0.5
Eo =
0.0
0
1,000
2,000
3,000
4,000
5,000
6,000
Pressure, psia
Fig. 13 Solution gas-oil ratio for Cupiagua field fluid at
285F
(Bo Boi ) + Bg (Rsi Rs ) + Rv (Boi Rs Bo Rsi )
(1 Rs Rv )
.....................................................................................(3)
The unit expansion of the gas is expressed by Eq. 4.
L. VEGA AND M.A. BARRUFET
Eg =
(B
Bgi )+ Bo (Rvi Rv ) + Rs (Bgi Rv Bg Rvi )
(1 Rv Rs )
Since the reservoir is initially above the dew-pointpressure, then there is initially no liquid. In equation form,
................................................................................(4)
Notice that if the volatilized oil-gas ratio is neglected in
the three definitions above, then the definitions of
underground withdrawal, unit oil expansion, and unit gas
expansion would be modified as expressed by Eq. 5, Eq. 6,
and Eq. 7, respectively.
] ...................... (5)
E0 = B0 Boi + Bg (Rsi Rs )
Diagnosing Drive Mechanism in Volumetric Reservoir
25,000,000
20,000,000
F/Eg, Mscf
F = N p Bo + (R ps Rs )Bg
SPE 68666
15,000,000
10,000,000
5,000,000
..................... (6)
0
0
E g = Bg Bgi
1,000,000
2,000,000
3,000,000
4,000,000
5,000,000
6,000,000
7,000,000
8,000,000
Gp, Mscf
.................................................. (7)
Fig. 15 Plot used to diagnose the drive mechanism
These three definitions correspond to the ones commonly
employed for black oil systems.
In summary, when the definitions in Eq. 2, Eq. 3, and Eq.
4 are used, Eq. 1 will be referred to as the generalized material
balance equation (GMBE). By the same token, when the
definitions in Eq. 5, Eq. 6, and Eq. 7 are utilized, Eq. 1 will be
referred to as the conventional material balance equation
(CMBE).
trend is observed, it basically means that the hydrocarbon pore
volume remains constant throughout the depletion process
no water influx. Fig. 15 displays such a plot obtained using
the output from the numerical simulator for the volumetric
reservoir case.
Notice that the trend is rather flat, but not quite. The
reason for this is that even though there is no water influx,
there are other factors that change the hydrocarbon pore
volume, such as the expansion of the rock and the interstitial
water.
Consequently, for this volumetric depletion case, it can be
stated that
We = 0 .................................................................(8)
Using Eq. 8 and Eq. 9 in Eq. 1, the following is obtained:
F = G fgi E g .........................................................(10)
As initially proposed by Havlena and Odeh6, 7, it can be
concluded from Eq. 10 that a plot of F vs. E g should yield a
straight line with zero intercept and slope
G fgi .
As illustrated in Fig. 16, the effect of using the CMBE
would be to bend the trend away from a straight line. Besides,
if a straight line were forced through the points, an intercept
different from zero (1,877,188 rb) would result.
Plot of F versus E g using CMBE
12,000,000
10,000,000
8,000,000
F = 23,296,330 E g + 1,977,133
F, rb
Effects of Using the Wrong Form of the MBE
The first step in the analysis of the synthetic data obtained
from the numerical simulator will be to investigate how the
answers obtained from MBE techniques are affected by the
mistaken use of the CMBE rather than the GMBE.
To simplify this illustration, the volumetric depletion data
will be used for this analysis.
Conventionally, the procedure to check whether we are
dealing with a volumetric or a water-drive reservoir consists of
making a diagnostic plot of F E g vs. G p . If a horizontal
N foi = 0 ..............................................................(9)
6,000,000
4,000,000
2,000,000
0
0.0
0.1
0.1
0.2
0.2
Eg, rb/Mscf
Fig. 16 Effect of using the CMBE
0.3
0.3
0.4
0.4
SPE 68666
ANALYSIS OF A NON-VOLUMETRIC GAS-CONDENSATE RESERVOIR
From geometric calculations using the numerical model,
the initial volume of free gas at standard conditions, G fgi ,
Drive-Mechanism Diagnosis in Water-Drive Condensate Reservoir
90,000,000
turned out to be equal to 19.1 MMscf. Nevertheless, from the
slope of the straight line in Fig. 16, G fgi was determined to be
Plot of F versus Eg
80,000,000
70,000,000
60,000,000
F/Eg, Mscf
equal to 23.3 MMscf. To put it another way, use of the
CMBE has overestimated G fgi by 22%.
50,000,000
40,000,000
30,000,000
20,000,000
12,000,000
10,000,000
10,000,000
0
0
1,000,000
2,000,000
3,000,000
8,000,000
F,
rb
4,000,000
5,000,000
6,000,000
7,000,000
8,000,000
Gp, Mscf
F = 20,151,809 E g
Fig. 18 Diagnostic plot of the synthetic data for the
water-drive case
6,000,000
4,000,000
2,000,000
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Because of this, determination of the cumulative volume of
water influx, We , requires an independent mathematical
model. From the solution to the diffusivity equation for a
constant inner boundary pressure, the following general
expression is obtained
Eg, rb/Mscf
We = UpW D (t D ) .............................................(12)
Fig. 17 Effect of using the GMBE
By contrast, when the GMBE is used, the
F vs. E g plot
follows a linear trend, as shown in Fig. 17. As predicted by
Eq. 10, the intercept of such a straight line goes through the
origin. In this case, the slope is calculated to be equal to 20.15
MMscf. The slight overestimation (5%) is due to the fact that
the expansion of the rock and the interstitial water are being
neglected in the GMBE (Eq. 1).
Determining the Size of the Aquifer Using the GMBE
The output of the compositional numerical simulator for
the water-drive case was then used as input to the GMBE.
In a similar fashion, a plot of F E g vs. G p was used to
diagnose whether there was water influx or not, as shown in
Fig. 18. From this plot, the apparent non-horizontal trend
confirms the presence of water influx, as anticipated.
Since in this case We 0 (water influx) and
N foi = 0 (the reservoir is initially above the dew point), the
GMBE, Eq. 1, becomes
W
F
= G fgi + e ................................................(11)
Eg
Eg
Eq. 11 has two unknowns, namely
G fgi and We . The
latter term depends on the size and properties of the aquifer,
the pressure drop at the original hydrocarbon-water contact.
To complicate matters even further, it also depends strongly
on time.
For a linear aquifer, like the one used to generate the
synthetic data, the dimensionless cumulative water influx,
WD (t D ) , reaches a maximum plateau value of unity when
t D = 3 2 . Before this dimensionless time, flow is fully
dominated by transient effects. Afterwards, it is called fully
boundary dominated period.
For linear flow, dimensionless time is defined as
t D = 0.00633kt c L2 ..............................(13)
Therefore, the minimum time at which the flow can be
considered as boundary dominated can be obtained by solving
for t from Eq. 13, making t D = 3 2 , and plugging in the
aquifer properties as follows:
( c L ) t
t
2
0.00633 k
Since
data,
L = 1,000 ft was used to generate to synthetic
2
(
0.13)(1)(7 10 6 )(1,000 )
t
(1.5) 10.8 days
(0.00633)(20 )
Therefore, after 10.8 days,
WD (t D ) is equal to unity.
L. VEGA AND M.A. BARRUFET
When the inner boundary pressure is not constant, the
principle of superposition must be used to calculate the
cumulative water influx as
We = Up jWD (t D t D j ) ............................(14)
j =1
where U is a geometrical factor defined as
Conclusions
1. The GMBE can effectively determine the size of a
neighboring water-bearing formation in a gas-condensate
reservoir.
2. Use of the CMBE can seriously overestimate the G fgi in
3.
U = 0 .1781 AL c .............................................(15)
Notice that both U and
t D depend on a previous
knowledge of L . As a result, a trial-and-error procedure is
needed to solve for L from the material balance equation.
From Eq. 11, it can be observed that a plot of F E g vs.
We E g will result in a straight line with intercept equal to
G fgi and unit slope.
The iterative procedure consists of assuming values of
L until a unit slope is obtained.
Determining The Length Of The Water-Bearing Part of the Reservoir
90,000,000
m=2.1
m=1.31
L=1,000ftft
m=1.01
80,000,000
70,000,000
F/E g , Mscf
60,000,000
50,000,000
L=1,000 ft
40,000,000
L=800 ft
30,000,000
L=500 ft
20,000,000
10,000,000
0
0
10,000,000 20,000,000 30,000,000 40,000,000 50,000,000 60,000,000 70,000,000
We/Eg, Mscf
Fig. 19 Iterative procedure to determine length of linear
aquifer
Fig. 19 illustrates the iterative procedure necessary to
determine the length of the linear aquifer used to generate the
synthetic data for the water-drive case.
Notice that if a value of L that is smaller than the actual
one (1,000 ft) is assumed, the slope turns out to be larger than
unity. When the actual length is used, a slope of 1.01 is
obtained. This result illustrates the effectiveness of the
material balance technique to determine the dimensions of the
aquifer.
SPE 68666
a gas-condensate reservoir (22% in the example presented
here).
Neglecting the compressibilities of the rock and the water
in the GMBE has little effect in the determination of the
G fgi (5% in the illustration presented here).
Nomenclature
A
Bg
Aquifer cross-sectional area
Gas FVF
Ft2
rb/Mscf
Bo
c
cf
Oil FVF
rb/stb
Total aquifer compressibility
Formation compressibility
psi-1
psi-1
cw
p
Water compressibility
psi-1
Eg
Gas expansion factor
rb/Mscf
Eo
F
G fgi
Oil expansion factor
rb/stb
Underground withdrawal
Porosity
rb
fraction
Total volume of fluid initially in the gas
phase
permeability
Linear aquifer length
Viscosity
Total volume of fluid initially in the
liquid phase
Solution gas-oil ratio
Mscf
md
ft
cp
stb
Volatilized oil-gas ratio
stb/Mscf
k
L
N foi
Rs
Rv
tD
t
U
WD
We
pi p at original GWC
psi
Mscf/stb
Dimensionless time
Time
Aquifer geometric factor
Dimensionless cumulative water influx
days
bbl/psi
Cumulative water influx
rb
Greek
Difference between two time steps
Subscripts
Pressure level
j
x, y , z
Coordinate directions in permeability tensor
SPE 68666
ANALYSIS OF A NON-VOLUMETRIC GAS-CONDENSATE RESERVOIR
References
1. Walsh, M.P., Ansah, J., Raghavan, R.: The New,
Generalized Material Balance as an Equation of a Straight
Line: Part 1--Applications to Undersaturated, Volumetric
Reservoirs," paper SPE 27684, presented at the 1994 SPE
Permian Basin Oil and Gas Recovery Conference,
Midland, TX.
2. Walsh, M.P., Ansah, J., Raghavan, R.: The New,
Generalized Material Balance as an Equation of a Straight
Line: Part 2--Applications to Saturated and NonVolumetric Reservoirs," paper SPE 27728, presented at
the 1994 SPE Permian Basin Oil and Gas Recovery
Conference, Midland, TX.
3. Morse, R.A., Byrne, W.B.: The Effects of Various
Reservoir and Well Parameters on Water Coning
Performance, paper SPE 4287.
4. Kenyon, D.E., Behie, G.A.: Third SPE Comparative
Solution Project: Gas Cycling of Retrograde Condensate
Reservoirs, Journal of Petroleum Technology (August
1987) 981-997.
5. Whitson, C.H., Fevang, O, Yang, T.: Gas Condensate
PVTWhats Really Important? paper presented at the
1999 IBC Conference Optimization of Gas Condensate
Fields, London, Jan. 28-29.
6. Havlena,D., Odeh, A.S.: The Material Balance as an
Equation of a Straight Line, JPT (August 1963) 896-900.
7. Havlena,D., Odeh, A.S.: The Material Balance as an
Equation of a Straight Line Part II, Field Cases, JPT
(July 1964) 815-822.
