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Copyright 2006, Society of Petroleum Engineers
This paper was prepared for presentation at the 2006 SPE Annual Technical Conference and
Exhibition held in San Antonio, Texas, U.S.A., 24–27 September 2006.
This paper was selected for presentation by an SPE Program Committee following review of
information contained in an abstract submitted by the author(s). Contents of the paper, as
presented, have not been reviewed by the Society of Petroleum Engineers and are subject to
correction by the author(s). The material, as presented, does not necessarily reflect any
position of the Society of Petroleum Engineers, its officers, or members. Papers presented at
SPE meetings are subject to publication review by Editorial Committees of the Society of
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acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.
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Abstract
Several authors have shown the applicability of modified
black oil (MBO) approach for modeling gas condensate and
volatile oil reservoirs. It was shown before that MBO could
adequately replace compositional simulation in many
applications. In this work, a new set of MBO PVT correlations
was developed. The four PVT functions (oil-gas ratio, Rv,
solution gas-oil ratio, Rs, oil formation volume factor, Bo, and
gas formation volume factor, Bg) were investigated. According
to our knowledge, no other correlation for calculating oil-gas
ratio exists in the petroleum literature. Alternatively, oil-gas
ratio (needed for material balance and reservoir simulation
calculations of gas condensate and volatile oil reservoirs) had
to be generated from a combination of laboratory experiments
and elaborate calculation procedures using EOS models. In
previous work, we found that Whitson and Torp method for
generating Modified Black Oil (MBO) PVT properties yielded
best results when compared with compositional simulation.
This method (and the others available in the literature such as
Coats’ and Walsh’s) requires the use of data from PVT
laboratory experiments and proper construction of EOS
models. We used Whitson and Torp’s method to generate our
database of the MBO PVT curves used in developing our
correlations after matching the PVT experimental results with
an EOS model. For each one of the four PVT parameters, we
used 1850 values obtained from PVT analysis of eight gas
condensate fluid samples and 1180 values obtained from PVT
analysis of five volatile oil fluid samples. The samples were
selected to cover a wide range of fluid composition,
condensate yield, reservoir temperature, and pressure. The
data points were generated by extracting the PVT properties of
each sample at six different separator conditions. We then
used multi-variable regression techniques to calculate our
correlation constants.
The new correlations were validated using the generalized
material balance equation calculations with data generated
from a compositional reservoir simulator.
These new correlations depend only on readily available
parameters in the field and can have wide applications when
representative fluid samples are not available.
Introduction
In 1973, Spivak and Dixon1
introduced the Modified Black Oil
(MBO) simulation approach. The MBO simulation considers
three components (dry gas, oil, and water). The main
difference between the conventional black-oil simulation and
the MBO simulation (also called Extended Black-Oil) lies in
the treatment of the liquid in the gas phase. The MBO
approach assumes that stock-tank liquid component can exist
in both liquid and gas phases under reservoir conditions. It
also assumes that the liquid content of the gas phase can be
defined as a sole function of pressure called vaporized oil-gas
ratio, Rv (also referred to as rs
2
). This function is similar to the
solution gas-oil ratio, Rs, normally used to describe the amount
of gas-in-solution in the liquid phase.
Whitson and Torp3
presented a procedure to calculate
MBO properties from PVT experimental data of gas
condensate. Coats2
also presented a different procedure for gas
condensate fluids. Coats procedure was extended by McVay4
for volatile oil fluids. Walsh and Towler5
also presented a
procedure to calculate MBO PVT properties from the CVD
experiment data. Abdel Fattah et al.6
showed that both
Whitson and Torp and Coats procedures provide excellent
match with compositional simulation results when PVT
experimental data are matched with an EOS model and then
used to output the MBO PVT properties.
El-Banbi et al.7
presented a field case where they used
MBO PVT properties and the MBO approach to speed us a
field development plan study. They presented convincing
evidence that MBO approach is adequate in simulation of gas
condensate fluids above and below the dew point and with
water influx. Other authors also presented different
comparisons between the MBO and compositional
approaches2,3,6
. In a more recent work, Fevang et al.8
presented
guidelines to help engineers choose between MBO and
compositional approaches.
In this paper, we show new correlations to develop MBO
PVT properties when fluid samples are not available.
SPE 102240
New Modified Black-Oil Correlations for Gas Condensate and Volatile Oil Fluids
A.H. El-Banbi, Schlumberger, and K.A. Fattah and M.H. Sayyouh, Cairo U.
2 SPE 102240
Fluid Samples
Thirteen reservoir fluid samples were used in this study [eight
gas condensates, (GC), and five volatile oils, (VO)]. The
samples were obtained from reservoirs representing different
locations and depth, and were selected to cover a wide range
of oil and gas fluid characteristics. Table 1 presents a
description of the major properties of the thirteen fluid
samples. The PVT experiments for all these samples were
presented in Ref. 9. Some samples represent near critical
fluids (VO 2, VO 5, GC 1, and GC 2) as explained by McCain
and Bridges10
.
Approach
For every sample in Table 1, we constructed an EOS model
that matched as best as possible the experimental results of all
available PVT laboratory experiments (CCE, DL, CVD, and
separator tests). For consistency, we developed all EOS
models using Peng and Robinson11
EOS with volume shift
correction (3-parameter EOS). We followed the procedure
suggested by Coats and Smart12
to match the laboratory
results.
We then used the developed EOS model for each sample to
output MBO PVT properties at different separator conditions
using Whitson and Torp3
procedure. The MBO PVT
properties include the four functions required for MBO
simulation (oil-gas ratio, Rv, solution gas-oil ratio, Rs, oil
formation volume factor, Bo, and gas formation volume factor,
Bg). For each property of the four, we generated six curves,
representing six different separator conditions, for each
sample. Our database of PVT properties consisted of 1850
points from 8 different gas condensate samples and 1180
points from 5 volatile oil samples. We used PVTi program of
Eclipse13
to generate the curves for the MBO PVT properties.
For the three parameters that are commonly used for black
oil material balance and simulation (Rs, Bo, and Bg), we tested
some of the commonly known correlations to see which one
fits our database and to see if we need to modify the
correlation’ constants. For the fourth parameter (Rv), we had to
develop a completely new correlation, since we think that the
petroleum literature lacks one. Our approach here was to start
from a similar form to Rs correlations, then modify the
correlation parameters using regression methods until we
obtain the best fit to Rv data.
MBO PVT Correlations
The following discussion shows which correlations were used
for each PVT parameter of the four required for MBO material
balance and simulation calculations. We also report the
average error which we calculated using Eq. 1.
∑=
−
=
N
i Data
ModelData
N
error
1
1
................................... (1)
Solution Gas Oil Ratio, Rs. Several correlations were used to
test the data base for both volatile oil and gas condensate
samples. We found that the forms suggested by Standing14
and
Vasques and Beggs15
gave the best results after modifying the
correlation constants. We noticed that the average absolute
error for both gas condensates and volatile oil samples was as
high as 50% if the original correlation parameters were used.
This is probably justified since the original Standing and
Vasques and Beggs correlations were developed for black-
oils16
. The modified Standing correlation has the form
suggested by Eqs. 2 and 3 and Vasques and Beggs correlation
has the form given in Eqs. 4 and 5. The five parameters for
modified Standing correlation, obtained from regression
analysis for both gas condensate and volatile oil samples, are
given in Table 2. The new parameters for modified Vasques
and Beggs are given in Table 3, also for gas condensates and
volatile oils.
3
102
1
A
X
gs A
A
p
R ⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
+= γ ........................................(2)
( )46054 −−×= TAAPIAX ....................................(3)
⎥⎦
⎤
⎢⎣
⎡ ×
×××=
T
APIA
EXPpAR A
gsS
3
1 2
γ ...............(3)
( )( )( ) ⎥
⎦
⎤
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
−
+=
7.114
log460
5
10912.51
sepp
sepTAPIggs γγ ....(4)
The average error calculated using Eq. 1 was 20.5% for
gas condensates, and 23.2% for volatile oils using modified
Standing correlation. Modified Vasques and Beggs showed
higher errors (27.7% for gas condensates and 29.2% for
volatile oils). For volatile oil above the bubble point, Rs, value
is taken as the same of the bubble point value.
Oil-Gas Ratio, Rv. A completely new form was suggested for
the oil-gas ratio correlation after trying different forms and
combination of parameters. For the correlation to be useful
and to have wide application, all parameters selected in the
correlation have to be readily available without the need for
fluid samples or elaborate calculation procedures using EOS
models. The form given by Eq. 5 was suggested. The absolute
average error using this form is 10.4% with a standard
deviation of 0.0308 for gas condensates and 15.0% with
0.1271 standard deviation for volatile oils.
( )
⎥
⎦
⎤
⎢
⎣
⎡
××
××
×
+×+×××
=
scosc
sc
s
gsc
V
PT
TCGRA
EXP
p
ApApAA
R
ρ
ρ 54321 2
.......(5)
The correlation constants (A1 through A5) are shown in
Table 4. Fig. 1 is a cross plot for all gas condensate points and
shows the 45 degrees line, as an indication of the goodness of
fit for calculated results with the experimental results. Notice
that initial condensate yield (which can be obtained from
production data) depends on separator conditions in the field.
Saturation pressure can be determined from a pressure versus
cumulative production plot (saturation pressure is observed by
change in slope in this plot due to difference in depletion
SPE 102240 3
above and below the saturation pressure), or from constant
composition expansion on a representative sample. The Rv
value is constant above the dew points for gas condensate
samples.
Oil Formation Volume Factor, Bo. Several correlations were
tested against the database of Bo points for both the gas
condensate and volatile oil samples below the saturation
pressure. It was found that both Standing correlation and
Vasques and Beggs correlation can be used adequately
(absolute average errors around 4%) without modifications.
However, the error percentage can be improved for Bo if we
use the form suggested by Standing with the constants
presented in Table 5. The modified Standing correlation is
given as Eq. 6.
( )
4
460*3*21
A
SO TARAAB osc
gsc
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−++= γ
γ
................ (6)
The above form gives average absolute error of 2.7% for
gas condensate samples, and error of 1.6% for volatile oils.
Further testing of the modified Bo correlation showed that it
was not significantly affected by the degree of accuracy of Rs
values used.
Gas Formation Volume Factor, Bg. Gas formation volume
factor can be calculated from z factor. We tested the use of
Sutton17
correlation to calculate pseudo-critical properties then
Standing z-factor correlation using the calculation procedure
suggested by Dranchuk and Abou-Kassem18
. We found this
procedure for calculating Bg adequate for both the gas
condensate and volatile oil samples (absolute average error
less than 8%). However the correlation can be significantly
improved for the gas condensate and volatile oil samples with
the use of different Sutton’s parameters in Eqs. 7 and 8. The
values for the modified Sutton equation are given in Table 6
for both gas condensate and volatile oil samples. Those
parameters were obtained by minimizing the error given by
Eq. 1.
2
321 gsgspc AAAp γγ ×+×+= ...................................... (7)
2
321 gsgspc BBBT γγ ×+×+= ....................................... (8)
The pseudo critical properties given by Eqs. 7 and 8 are used
to calculate z-factor, and then Bg is calculated from Eq. 9.
p
Tz
Bg
××
=
04.5
............................................................ (9)
Average absolute error in Bg, using this procedure, is 3.8% for
gas condensate and 1.65% for volatile oil samples. Notice that
the gas specific used in modified Sutton correlation is the
value corrected for separator conditions using Eq. 4.
Validation of MBO PVT Correlations
In addition to cross-plots (e.g. Fig. 1) to see how the new
correlation values compared to the values obtained from the
EOS model, we also used both reservoir simulation and
material balance calculations to validate the new correlations.
We used the generalized material balance equation
suggested by Walsh19,20
to validate the new Rv correlations (for
both gas condensate and volatile oil samples) by performing
the material balance calculations using the PVT properties
from the new correlations to calculate original hydrocarbon in
place. These values were compared to original hydrocarbon in
place values obtained from compositional reservoir simulation
for a tank model. For simplicity, the original fluid in place was
normalized to 1.0 BSTB for oil cases and 1 Bscf for gas cases.
Fig. 2 shows a plot of F versus the expansion term, Eg, for a
gas condensate sample (GC 1), as suggested by Walsh
procedure. The slope of the line passing through the calculated
points gives the original fluid in place volume. The plot shows
that the slope of the line is 1.038, i.e. the error in gas in place
calculation is approximately 1.4%.
Fig. 3 is a similar plot for a volatile oil sample (VO 1).
The plot shows a line slope of 0.9948 which is equivalent to
error in the oil in place calculation of approximately 0.5%. We
calculated the error in fluid in place calculations for most of
the fluid samples in our database and reported the error
percentages in Table 7. The reported error values show high
accuracy and prove the validity of the new correlation.
Discussion
The petroleum literature has reported many cases where MBO
approach was used to replace the more expensive
compositional simulation. To generate MBO PVT properties,
one has to have a representative fluid sample that undergone
enough laboratory experiments. Then, one usually constructs
EOS models to match the laboratory experimental results,
although other less accurate techniques are available6
. Then,
one can output the MBO properties at appropriate separator
conditions using one of the procedures suggested in the
literature. This process requires the availability of a
representative fluid sample in addition to the skills of EOS
modeling.
The set of correlations presented in this work can be used
to generate MBO PVT properties without the need for fluid
samples or elaborate procedure for EOS calculations. The
application of these correlations is of particular importance
especially when a representative sample is not available.
Conclusions
1. New correlations are presented for oil-gas ratio of gas
condensates and volatile oils. The correlation can be
used in generalized material balance calculations and
MBO simulation. The new correlations match the
fluid properties of the database selected for
computations. They were also validated using
generalized material balance calculations.
4 SPE 102240
2. The new oil-gas ratio correlation is accurate within
10.4% for gas condensate and 15% for volatile oil
samples used in this study.
3. Existing solution gas oil ratio, oil formation volume
factor, and gas formation volume factor correlations
were modified to increase their accuracy when used
with gas condensates and volatile oils.
Acknowledgements
We would like to thank Schlumberger Egypt for donating
Eclipse suite of software, which was used in this investigation,
to the Petroleum Engineering Department of Cairo University.
The first author would also like to thank Prof. Dr. Bill McCain
for many valuable discussions that led to this research idea.
Nomenclature
Bg = gas formation volume factor, bbl/Mscf
Bo = oil formation volume factor, bbl/STB
CCE = constant Composition Experiment
CVD= constant Volume Depletion Test
DL = differential Liberation Test
EOS = equation of state
MBO= Modified Black Oil
N = number of points or values
p = pressure, psia
ps = saturation pressure, psia
psc = standard pressure, psia
psep = separator pressure, psia
PVT = pressure-Volume-Temperature
Rs = initial solution gas oil-ratio, SCF/STB
Rv = volatile oil-gas ratio, STB/Mcf
T = reservoir temperature, o
R
Tsc = standard temperature, o
R
Tsep = separator temperature, o
R
z = gas compressibility factor, fraction
ρgsc = gas density at standard conditions, lb/cc
ρosc = oil density at standard conditions, lb/cc
γg = gas gravity at the actual separator conditions of psep
and Tsep
γgs = gas gravity at reference separator pressure
γgsc = specific gravity of gas at standard conditions
γosc = specific gravity of oil at standard conditions
References
1. Spivak, A. and Dixon, T.N.: “Simulation of Gas Condensate
Reservoirs,” paper SPE 4271 presented at the 3rd
Numerical
Simulation of Reservoir Performance Symposium, Houston, Jan.
10-12, 1973.
2. Coats, K.H.: “Simulation of Gas Condensate Reservoir
Performance,” JPT (Oct. 1985) 1870-1886.
3. Whitson, C.H. and Torp, S.B.: “Evaluating Constant-Volume
Depletion Data,” JPT (March 1983) 610-620.
4. McVay, D. A.: Generation of PVT Properties For Modified
Black-Oil Simulation of Volatile Oil and Gas Condensate
Reservoirs, Ph.D. Thesis, Texas A&M University, TX 1994.
5. Walsh, M.P., Towler, B.F.: "Method Computes PVT Properties
for Gas Condensate," OGJ, July 31, 1994, pp. 83-86.Coats, K.H.
and Smart, G.T.: “Application of a Regression-Based EOS PVT
Program to Laboratory Data,” SPERE (May 1986) 277-299.
6. Abdel Fattah, K. El-Banbi, Ahmed H., and Sayyouh, M.H.:
“Study Compares PVT Calculation Methods for Non Black Oil
Fluids,” Oil & Gas Journal, March 27, 2006.
7. El-Banbi, Ahmed H., Forrest, J.K., Fan, L., and McCain, W.D.,
Jr.: “Producing Rich-Gas-Condensate Reservoirs--Case History
and Comparison Between Compositional and Modified Black-
Oil Approaches,” paper SPE 58988 presented at the SPE Fourth
International Petroleum Conference and Exhibition,
Villahermosa, Mexico. Feb. 1-3, 2000.
8. Fevang, O., Singh, K., and Whitson, C.H.: “Guidelines for
Choosing Compositional and Black-Oil Models for Volatile Oil
and Gas-Condensate Reservoirs,” paper SPE 63087 presented at
the 2000 SPE Annual Technical Conference and Exhibition,
Dallas, TX. Oct. 1-4, 2000.
9. Khaled A. El-Fattah: Volatile Oil and Gas Condensate Fluid
Behavior for Material Balance Calculations and Reservoir
Simulation, Ph.D. Thesis, Cairo University, Egypt 2005.
10. McCain, W.D., Jr. and Bridges, B.: “Volatile Oils and
Retrograde Gases-What’s the Difference?” Petroleum Engineer
International (Jan. 1994) 35-36.
11. Peng, D.Y. and Robinson, D.B. "A New Two-Constant Equation
of State" Ind. and Eng. Chem. Fund. (1976) 15, 59.
12. Coats, K.H. and Smart, G.T.: “Application of a Regression-
Based EOS PVT Program to Laboratory Data,” SPERE (May
1986) 277-299.
13. ECLIPSE suite of programs (Schlumberger, 2005).
14. Standing, M. B., "A Pressure-Volume-Temperature Correlation
for Mixture of California Oils and Gases," Drilling and
Production Practice, API, 1957, pp. 275-287.
15. Vasques, M. and Beggs, H. D.: "Correlation for Fluid Physical
Property Prediction," JPT, June 1980.
16. Ahmed, T.: Hydrocarbon Phase Behavior, Gulf Publishing
Company, Houston, 1989.
17. Sutton, R.P.: “Compressibility Factors for High-Molecular-
Weight Reservoir Gases,” paper SPE 14265 presented at the
1985 SPE Annual Technical Meeting and Exhibition, Las
Vegas, Sept. 22-25.
18. Dranchuk, P.M. and Abou-Kassem, J.H.: “Calculation of Z
Factors for Natural Gases Using Equations of State,” J. Cdn.
Pet. Tech. (July-Sept. 1975) 34-36.
19. Walsh, M.P.: "A Generalized Approach to Reservoir Material
Balance calculations,” JCPT, 1994.
20. Walsh, M.P., Ansah, J., and Raghavan, R.: " The New
Generalized Material Balance As an equation of a Straight-Line:
Part 1- Application to undersaturated and Volumetric
Reservoirs," SPE 27684, presented at the 1994 SPE Permian
Basin Oil and Gas recovery Conference, March 16-18, 1994,
Midland TX.
SPE 102240 5
TABLE 1 - CHARACTERISTICS OF FLUID SAMPLES
Property VO 1 VO 2 VO 3 VO 4 VO 5 GC 1 GC 2 GC 3 GC 4 GC 5 GC 6 GC 7 GC 8
Reservoir
Temperature (o
F)
249 246 260 190 197 312 286 238 256 186 312 300 233
Initial Reservoir
Pressure (psig)
NA 5055 5270 NA 13668 14216 NA 6000 7000 5728 14216 5985 17335
Initial Producing
Gas-Oil ratio
(SCF/STB)
1991 2000 2032 2424 2416 3413 4278 NA 4697 5987 8280 6500 6665
Stock Oil
gravity (o
API)
45.5 51.2 NA 36.8 34.1 45.6 NA NA 46.5 58.5 50.7 45.6 43
Saturation
Pressure (psig) 4527 4821 4987 7437 9074 5210 5410 4815 6010 4000 5465 5800 11475
Components Composition (Mole %)
CO2 2.14 2.18 2.4 0.1 0.34 2.66 4.48 0.14 0.01 0.18 2.79 6.98 0.36
N2 0.11 1.67 0.31 0.16 0 0.17 0.70 1.62 0.11 0.13 0.14 1.07 0.31
C1 55.59 60.51 56.94 69.84 72.47 59.96 66.24 63.06 68.93 61.72 66.73 65.25 81.23
C2 8.7 7.52 9.21 5.37 4.57 7.72 7.21 11.35 8.63 14.1 10.22 8.92 5.54
C3 5.89 4.74 5.84 3.22 2.79 6.50 4.00 6.01 5.34 8.37 5.90 4.81 2.66
iC4 1.36 4.12 1.44 0.87 0.67 1.93 0.84 1.37 1.15 0.98 1.88 0.85 0.62
nC4 2.69 0 2.73 1.7 1.33 3.00 1.76 1.94 2.33 3.45 2.10 1.75 1.06
iC5 1.17 2.97 1.03 0.79 0.69 1.64 0.74 0.84 0.93 0.91 1.37 0.65 0.47
nC5 1.36 0 1.22 0.88 0.82 1.35 0.87 0.97 0.85 1.52 0.83 0.69 0.52
C6 1.97 1.38 1.96 1.41 1.52 2.38 0.96 1.02 1.73 1.79 1.56 0.83 0.84
C7+ 19.02 14.91 16.92 15.66 14.8 12.69 12.2 11.68 9.99 6.85 6.48 8.2 6.39
TABLE 2 – Modified Standing Correlation Parameters for Gas
Condensates and Volatile Oil Fluids (Eqs. 2 and 3).
Constant Gas Condensate Volatile Oil
A1 0.19408473 47.23306
A2 -3709.4214 -8.833514
A3 1.06052098 1.3251534
A4 -0.05022324 0.0091756
A5 -0.003771627 -0.000385524
TABLE 3 – Modified Vasques and Beggs Correlation Parameters
for Gas Condensates and Volatile Oil Fluids (Eqs. 4 and 5).
Constant Gas Condensate Volatile Oil
A1 12.5849757 0.0005473
A2 1.343554054 1.607758566
A3 -105.486585 20.35993884
TABLE 4 – Oil-Gas Ratio Correlation Constants for Gas
Condensates and Volatile Oil Fluids (Eq. 5).
Constant Gas Condensate Volatile Oil
A1 3.45841109 1.225537042
A2 6.89461E-05 0.000107257
A3 - 0.03169875 - 0.194226755
A4 251.0827307 240.549909
A5 4.174003053 8.32137351
TABLE 5 – Oil Formation Volume Factor Correlation Constants
for Gas Condensates and Volatile Oil Fluids (Eq. 6).
Constant Gas Condensate Volatile Oil
A1 0.965109778 0.839614826
A2 0.000342547 0.000460621
A3 1.303305644 2.013137024
A4 1.053171234 1.015821025
TABLE 6 – Modified Sutton Correlation Parameters for Gas
Condensates and Volatile Oil Fluids (Eqs. 7 and 8).
Constant Gas Condensate Volatile Oil
A1 670.958 608.520
A2 -188.078 -45.8495
A3 -3.7882 27.71169
B1 480.1142 29.70495
B2 -94.2128 871.57199
B3 9.398696 -502.6044
6 SPE 102240
TABLE 7 – Error in Fluid In Place Calculation from Generalized
Material Balance Calculations Using the New Rv Correlation.
Fluid Sample Original Fluid In
Place
Error
(%)
VO 1 0.9948 0.52
VO 2 1.0027 0.27
GC 1 1.0138 1.38
GC 2 0.9451 5.49
GC 3 1.0154 1.54
GC 4 1.0092 0.92
GC 5 1.1526 15.26
GC 6 1.0319 3.19
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.1 0.2 0.3 0.4 0.5
Rv (Obser), STB/Mscf
Rv(Cal),STB/Mscf
Fig. 1 - Cross-plot for RV (New Correlation) vs. RV (Driven
from the EOS Model) for gas Condensate samples.
y = 1.0138x
0
0.04
0.08
0.12
0.16
0.2
0 0.05 0.1 0.15 0.2
E o, Rb/stb
F,Rb
GMB C Linear (GMB C )
Fig. 2 – Material Balance as Straight Line Calculations for
a Gas Condensate Sample (GC 1).
y = 0.9948x
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.2 0.4 0.6 0.8
Eo, Rb/stb
F,Rb
GMBC Linear (GMBC)
Fig. 3 – Material Balance as Straight Line Calculations for
a Volatile Oil Sample (VO 1).

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SPE-102240-MS y SPE-164712-MS

  • 1. Copyright 2006, Society of Petroleum Engineers This paper was prepared for presentation at the 2006 SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, U.S.A., 24–27 September 2006. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435. Abstract Several authors have shown the applicability of modified black oil (MBO) approach for modeling gas condensate and volatile oil reservoirs. It was shown before that MBO could adequately replace compositional simulation in many applications. In this work, a new set of MBO PVT correlations was developed. The four PVT functions (oil-gas ratio, Rv, solution gas-oil ratio, Rs, oil formation volume factor, Bo, and gas formation volume factor, Bg) were investigated. According to our knowledge, no other correlation for calculating oil-gas ratio exists in the petroleum literature. Alternatively, oil-gas ratio (needed for material balance and reservoir simulation calculations of gas condensate and volatile oil reservoirs) had to be generated from a combination of laboratory experiments and elaborate calculation procedures using EOS models. In previous work, we found that Whitson and Torp method for generating Modified Black Oil (MBO) PVT properties yielded best results when compared with compositional simulation. This method (and the others available in the literature such as Coats’ and Walsh’s) requires the use of data from PVT laboratory experiments and proper construction of EOS models. We used Whitson and Torp’s method to generate our database of the MBO PVT curves used in developing our correlations after matching the PVT experimental results with an EOS model. For each one of the four PVT parameters, we used 1850 values obtained from PVT analysis of eight gas condensate fluid samples and 1180 values obtained from PVT analysis of five volatile oil fluid samples. The samples were selected to cover a wide range of fluid composition, condensate yield, reservoir temperature, and pressure. The data points were generated by extracting the PVT properties of each sample at six different separator conditions. We then used multi-variable regression techniques to calculate our correlation constants. The new correlations were validated using the generalized material balance equation calculations with data generated from a compositional reservoir simulator. These new correlations depend only on readily available parameters in the field and can have wide applications when representative fluid samples are not available. Introduction In 1973, Spivak and Dixon1 introduced the Modified Black Oil (MBO) simulation approach. The MBO simulation considers three components (dry gas, oil, and water). The main difference between the conventional black-oil simulation and the MBO simulation (also called Extended Black-Oil) lies in the treatment of the liquid in the gas phase. The MBO approach assumes that stock-tank liquid component can exist in both liquid and gas phases under reservoir conditions. It also assumes that the liquid content of the gas phase can be defined as a sole function of pressure called vaporized oil-gas ratio, Rv (also referred to as rs 2 ). This function is similar to the solution gas-oil ratio, Rs, normally used to describe the amount of gas-in-solution in the liquid phase. Whitson and Torp3 presented a procedure to calculate MBO properties from PVT experimental data of gas condensate. Coats2 also presented a different procedure for gas condensate fluids. Coats procedure was extended by McVay4 for volatile oil fluids. Walsh and Towler5 also presented a procedure to calculate MBO PVT properties from the CVD experiment data. Abdel Fattah et al.6 showed that both Whitson and Torp and Coats procedures provide excellent match with compositional simulation results when PVT experimental data are matched with an EOS model and then used to output the MBO PVT properties. El-Banbi et al.7 presented a field case where they used MBO PVT properties and the MBO approach to speed us a field development plan study. They presented convincing evidence that MBO approach is adequate in simulation of gas condensate fluids above and below the dew point and with water influx. Other authors also presented different comparisons between the MBO and compositional approaches2,3,6 . In a more recent work, Fevang et al.8 presented guidelines to help engineers choose between MBO and compositional approaches. In this paper, we show new correlations to develop MBO PVT properties when fluid samples are not available. SPE 102240 New Modified Black-Oil Correlations for Gas Condensate and Volatile Oil Fluids A.H. El-Banbi, Schlumberger, and K.A. Fattah and M.H. Sayyouh, Cairo U.
  • 2. 2 SPE 102240 Fluid Samples Thirteen reservoir fluid samples were used in this study [eight gas condensates, (GC), and five volatile oils, (VO)]. The samples were obtained from reservoirs representing different locations and depth, and were selected to cover a wide range of oil and gas fluid characteristics. Table 1 presents a description of the major properties of the thirteen fluid samples. The PVT experiments for all these samples were presented in Ref. 9. Some samples represent near critical fluids (VO 2, VO 5, GC 1, and GC 2) as explained by McCain and Bridges10 . Approach For every sample in Table 1, we constructed an EOS model that matched as best as possible the experimental results of all available PVT laboratory experiments (CCE, DL, CVD, and separator tests). For consistency, we developed all EOS models using Peng and Robinson11 EOS with volume shift correction (3-parameter EOS). We followed the procedure suggested by Coats and Smart12 to match the laboratory results. We then used the developed EOS model for each sample to output MBO PVT properties at different separator conditions using Whitson and Torp3 procedure. The MBO PVT properties include the four functions required for MBO simulation (oil-gas ratio, Rv, solution gas-oil ratio, Rs, oil formation volume factor, Bo, and gas formation volume factor, Bg). For each property of the four, we generated six curves, representing six different separator conditions, for each sample. Our database of PVT properties consisted of 1850 points from 8 different gas condensate samples and 1180 points from 5 volatile oil samples. We used PVTi program of Eclipse13 to generate the curves for the MBO PVT properties. For the three parameters that are commonly used for black oil material balance and simulation (Rs, Bo, and Bg), we tested some of the commonly known correlations to see which one fits our database and to see if we need to modify the correlation’ constants. For the fourth parameter (Rv), we had to develop a completely new correlation, since we think that the petroleum literature lacks one. Our approach here was to start from a similar form to Rs correlations, then modify the correlation parameters using regression methods until we obtain the best fit to Rv data. MBO PVT Correlations The following discussion shows which correlations were used for each PVT parameter of the four required for MBO material balance and simulation calculations. We also report the average error which we calculated using Eq. 1. ∑= − = N i Data ModelData N error 1 1 ................................... (1) Solution Gas Oil Ratio, Rs. Several correlations were used to test the data base for both volatile oil and gas condensate samples. We found that the forms suggested by Standing14 and Vasques and Beggs15 gave the best results after modifying the correlation constants. We noticed that the average absolute error for both gas condensates and volatile oil samples was as high as 50% if the original correlation parameters were used. This is probably justified since the original Standing and Vasques and Beggs correlations were developed for black- oils16 . The modified Standing correlation has the form suggested by Eqs. 2 and 3 and Vasques and Beggs correlation has the form given in Eqs. 4 and 5. The five parameters for modified Standing correlation, obtained from regression analysis for both gas condensate and volatile oil samples, are given in Table 2. The new parameters for modified Vasques and Beggs are given in Table 3, also for gas condensates and volatile oils. 3 102 1 A X gs A A p R ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ += γ ........................................(2) ( )46054 −−×= TAAPIAX ....................................(3) ⎥⎦ ⎤ ⎢⎣ ⎡ × ×××= T APIA EXPpAR A gsS 3 1 2 γ ...............(3) ( )( )( ) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − − += 7.114 log460 5 10912.51 sepp sepTAPIggs γγ ....(4) The average error calculated using Eq. 1 was 20.5% for gas condensates, and 23.2% for volatile oils using modified Standing correlation. Modified Vasques and Beggs showed higher errors (27.7% for gas condensates and 29.2% for volatile oils). For volatile oil above the bubble point, Rs, value is taken as the same of the bubble point value. Oil-Gas Ratio, Rv. A completely new form was suggested for the oil-gas ratio correlation after trying different forms and combination of parameters. For the correlation to be useful and to have wide application, all parameters selected in the correlation have to be readily available without the need for fluid samples or elaborate calculation procedures using EOS models. The form given by Eq. 5 was suggested. The absolute average error using this form is 10.4% with a standard deviation of 0.0308 for gas condensates and 15.0% with 0.1271 standard deviation for volatile oils. ( ) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ×× ×× × +×+××× = scosc sc s gsc V PT TCGRA EXP p ApApAA R ρ ρ 54321 2 .......(5) The correlation constants (A1 through A5) are shown in Table 4. Fig. 1 is a cross plot for all gas condensate points and shows the 45 degrees line, as an indication of the goodness of fit for calculated results with the experimental results. Notice that initial condensate yield (which can be obtained from production data) depends on separator conditions in the field. Saturation pressure can be determined from a pressure versus cumulative production plot (saturation pressure is observed by change in slope in this plot due to difference in depletion
  • 3. SPE 102240 3 above and below the saturation pressure), or from constant composition expansion on a representative sample. The Rv value is constant above the dew points for gas condensate samples. Oil Formation Volume Factor, Bo. Several correlations were tested against the database of Bo points for both the gas condensate and volatile oil samples below the saturation pressure. It was found that both Standing correlation and Vasques and Beggs correlation can be used adequately (absolute average errors around 4%) without modifications. However, the error percentage can be improved for Bo if we use the form suggested by Standing with the constants presented in Table 5. The modified Standing correlation is given as Eq. 6. ( ) 4 460*3*21 A SO TARAAB osc gsc ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ −++= γ γ ................ (6) The above form gives average absolute error of 2.7% for gas condensate samples, and error of 1.6% for volatile oils. Further testing of the modified Bo correlation showed that it was not significantly affected by the degree of accuracy of Rs values used. Gas Formation Volume Factor, Bg. Gas formation volume factor can be calculated from z factor. We tested the use of Sutton17 correlation to calculate pseudo-critical properties then Standing z-factor correlation using the calculation procedure suggested by Dranchuk and Abou-Kassem18 . We found this procedure for calculating Bg adequate for both the gas condensate and volatile oil samples (absolute average error less than 8%). However the correlation can be significantly improved for the gas condensate and volatile oil samples with the use of different Sutton’s parameters in Eqs. 7 and 8. The values for the modified Sutton equation are given in Table 6 for both gas condensate and volatile oil samples. Those parameters were obtained by minimizing the error given by Eq. 1. 2 321 gsgspc AAAp γγ ×+×+= ...................................... (7) 2 321 gsgspc BBBT γγ ×+×+= ....................................... (8) The pseudo critical properties given by Eqs. 7 and 8 are used to calculate z-factor, and then Bg is calculated from Eq. 9. p Tz Bg ×× = 04.5 ............................................................ (9) Average absolute error in Bg, using this procedure, is 3.8% for gas condensate and 1.65% for volatile oil samples. Notice that the gas specific used in modified Sutton correlation is the value corrected for separator conditions using Eq. 4. Validation of MBO PVT Correlations In addition to cross-plots (e.g. Fig. 1) to see how the new correlation values compared to the values obtained from the EOS model, we also used both reservoir simulation and material balance calculations to validate the new correlations. We used the generalized material balance equation suggested by Walsh19,20 to validate the new Rv correlations (for both gas condensate and volatile oil samples) by performing the material balance calculations using the PVT properties from the new correlations to calculate original hydrocarbon in place. These values were compared to original hydrocarbon in place values obtained from compositional reservoir simulation for a tank model. For simplicity, the original fluid in place was normalized to 1.0 BSTB for oil cases and 1 Bscf for gas cases. Fig. 2 shows a plot of F versus the expansion term, Eg, for a gas condensate sample (GC 1), as suggested by Walsh procedure. The slope of the line passing through the calculated points gives the original fluid in place volume. The plot shows that the slope of the line is 1.038, i.e. the error in gas in place calculation is approximately 1.4%. Fig. 3 is a similar plot for a volatile oil sample (VO 1). The plot shows a line slope of 0.9948 which is equivalent to error in the oil in place calculation of approximately 0.5%. We calculated the error in fluid in place calculations for most of the fluid samples in our database and reported the error percentages in Table 7. The reported error values show high accuracy and prove the validity of the new correlation. Discussion The petroleum literature has reported many cases where MBO approach was used to replace the more expensive compositional simulation. To generate MBO PVT properties, one has to have a representative fluid sample that undergone enough laboratory experiments. Then, one usually constructs EOS models to match the laboratory experimental results, although other less accurate techniques are available6 . Then, one can output the MBO properties at appropriate separator conditions using one of the procedures suggested in the literature. This process requires the availability of a representative fluid sample in addition to the skills of EOS modeling. The set of correlations presented in this work can be used to generate MBO PVT properties without the need for fluid samples or elaborate procedure for EOS calculations. The application of these correlations is of particular importance especially when a representative sample is not available. Conclusions 1. New correlations are presented for oil-gas ratio of gas condensates and volatile oils. The correlation can be used in generalized material balance calculations and MBO simulation. The new correlations match the fluid properties of the database selected for computations. They were also validated using generalized material balance calculations.
  • 4. 4 SPE 102240 2. The new oil-gas ratio correlation is accurate within 10.4% for gas condensate and 15% for volatile oil samples used in this study. 3. Existing solution gas oil ratio, oil formation volume factor, and gas formation volume factor correlations were modified to increase their accuracy when used with gas condensates and volatile oils. Acknowledgements We would like to thank Schlumberger Egypt for donating Eclipse suite of software, which was used in this investigation, to the Petroleum Engineering Department of Cairo University. The first author would also like to thank Prof. Dr. Bill McCain for many valuable discussions that led to this research idea. Nomenclature Bg = gas formation volume factor, bbl/Mscf Bo = oil formation volume factor, bbl/STB CCE = constant Composition Experiment CVD= constant Volume Depletion Test DL = differential Liberation Test EOS = equation of state MBO= Modified Black Oil N = number of points or values p = pressure, psia ps = saturation pressure, psia psc = standard pressure, psia psep = separator pressure, psia PVT = pressure-Volume-Temperature Rs = initial solution gas oil-ratio, SCF/STB Rv = volatile oil-gas ratio, STB/Mcf T = reservoir temperature, o R Tsc = standard temperature, o R Tsep = separator temperature, o R z = gas compressibility factor, fraction ρgsc = gas density at standard conditions, lb/cc ρosc = oil density at standard conditions, lb/cc γg = gas gravity at the actual separator conditions of psep and Tsep γgs = gas gravity at reference separator pressure γgsc = specific gravity of gas at standard conditions γosc = specific gravity of oil at standard conditions References 1. Spivak, A. and Dixon, T.N.: “Simulation of Gas Condensate Reservoirs,” paper SPE 4271 presented at the 3rd Numerical Simulation of Reservoir Performance Symposium, Houston, Jan. 10-12, 1973. 2. Coats, K.H.: “Simulation of Gas Condensate Reservoir Performance,” JPT (Oct. 1985) 1870-1886. 3. Whitson, C.H. and Torp, S.B.: “Evaluating Constant-Volume Depletion Data,” JPT (March 1983) 610-620. 4. McVay, D. A.: Generation of PVT Properties For Modified Black-Oil Simulation of Volatile Oil and Gas Condensate Reservoirs, Ph.D. Thesis, Texas A&M University, TX 1994. 5. Walsh, M.P., Towler, B.F.: "Method Computes PVT Properties for Gas Condensate," OGJ, July 31, 1994, pp. 83-86.Coats, K.H. and Smart, G.T.: “Application of a Regression-Based EOS PVT Program to Laboratory Data,” SPERE (May 1986) 277-299. 6. Abdel Fattah, K. El-Banbi, Ahmed H., and Sayyouh, M.H.: “Study Compares PVT Calculation Methods for Non Black Oil Fluids,” Oil & Gas Journal, March 27, 2006. 7. El-Banbi, Ahmed H., Forrest, J.K., Fan, L., and McCain, W.D., Jr.: “Producing Rich-Gas-Condensate Reservoirs--Case History and Comparison Between Compositional and Modified Black- Oil Approaches,” paper SPE 58988 presented at the SPE Fourth International Petroleum Conference and Exhibition, Villahermosa, Mexico. Feb. 1-3, 2000. 8. Fevang, O., Singh, K., and Whitson, C.H.: “Guidelines for Choosing Compositional and Black-Oil Models for Volatile Oil and Gas-Condensate Reservoirs,” paper SPE 63087 presented at the 2000 SPE Annual Technical Conference and Exhibition, Dallas, TX. Oct. 1-4, 2000. 9. Khaled A. El-Fattah: Volatile Oil and Gas Condensate Fluid Behavior for Material Balance Calculations and Reservoir Simulation, Ph.D. Thesis, Cairo University, Egypt 2005. 10. McCain, W.D., Jr. and Bridges, B.: “Volatile Oils and Retrograde Gases-What’s the Difference?” Petroleum Engineer International (Jan. 1994) 35-36. 11. Peng, D.Y. and Robinson, D.B. "A New Two-Constant Equation of State" Ind. and Eng. Chem. Fund. (1976) 15, 59. 12. Coats, K.H. and Smart, G.T.: “Application of a Regression- Based EOS PVT Program to Laboratory Data,” SPERE (May 1986) 277-299. 13. ECLIPSE suite of programs (Schlumberger, 2005). 14. Standing, M. B., "A Pressure-Volume-Temperature Correlation for Mixture of California Oils and Gases," Drilling and Production Practice, API, 1957, pp. 275-287. 15. Vasques, M. and Beggs, H. D.: "Correlation for Fluid Physical Property Prediction," JPT, June 1980. 16. Ahmed, T.: Hydrocarbon Phase Behavior, Gulf Publishing Company, Houston, 1989. 17. Sutton, R.P.: “Compressibility Factors for High-Molecular- Weight Reservoir Gases,” paper SPE 14265 presented at the 1985 SPE Annual Technical Meeting and Exhibition, Las Vegas, Sept. 22-25. 18. Dranchuk, P.M. and Abou-Kassem, J.H.: “Calculation of Z Factors for Natural Gases Using Equations of State,” J. Cdn. Pet. Tech. (July-Sept. 1975) 34-36. 19. Walsh, M.P.: "A Generalized Approach to Reservoir Material Balance calculations,” JCPT, 1994. 20. Walsh, M.P., Ansah, J., and Raghavan, R.: " The New Generalized Material Balance As an equation of a Straight-Line: Part 1- Application to undersaturated and Volumetric Reservoirs," SPE 27684, presented at the 1994 SPE Permian Basin Oil and Gas recovery Conference, March 16-18, 1994, Midland TX.
  • 5. SPE 102240 5 TABLE 1 - CHARACTERISTICS OF FLUID SAMPLES Property VO 1 VO 2 VO 3 VO 4 VO 5 GC 1 GC 2 GC 3 GC 4 GC 5 GC 6 GC 7 GC 8 Reservoir Temperature (o F) 249 246 260 190 197 312 286 238 256 186 312 300 233 Initial Reservoir Pressure (psig) NA 5055 5270 NA 13668 14216 NA 6000 7000 5728 14216 5985 17335 Initial Producing Gas-Oil ratio (SCF/STB) 1991 2000 2032 2424 2416 3413 4278 NA 4697 5987 8280 6500 6665 Stock Oil gravity (o API) 45.5 51.2 NA 36.8 34.1 45.6 NA NA 46.5 58.5 50.7 45.6 43 Saturation Pressure (psig) 4527 4821 4987 7437 9074 5210 5410 4815 6010 4000 5465 5800 11475 Components Composition (Mole %) CO2 2.14 2.18 2.4 0.1 0.34 2.66 4.48 0.14 0.01 0.18 2.79 6.98 0.36 N2 0.11 1.67 0.31 0.16 0 0.17 0.70 1.62 0.11 0.13 0.14 1.07 0.31 C1 55.59 60.51 56.94 69.84 72.47 59.96 66.24 63.06 68.93 61.72 66.73 65.25 81.23 C2 8.7 7.52 9.21 5.37 4.57 7.72 7.21 11.35 8.63 14.1 10.22 8.92 5.54 C3 5.89 4.74 5.84 3.22 2.79 6.50 4.00 6.01 5.34 8.37 5.90 4.81 2.66 iC4 1.36 4.12 1.44 0.87 0.67 1.93 0.84 1.37 1.15 0.98 1.88 0.85 0.62 nC4 2.69 0 2.73 1.7 1.33 3.00 1.76 1.94 2.33 3.45 2.10 1.75 1.06 iC5 1.17 2.97 1.03 0.79 0.69 1.64 0.74 0.84 0.93 0.91 1.37 0.65 0.47 nC5 1.36 0 1.22 0.88 0.82 1.35 0.87 0.97 0.85 1.52 0.83 0.69 0.52 C6 1.97 1.38 1.96 1.41 1.52 2.38 0.96 1.02 1.73 1.79 1.56 0.83 0.84 C7+ 19.02 14.91 16.92 15.66 14.8 12.69 12.2 11.68 9.99 6.85 6.48 8.2 6.39 TABLE 2 – Modified Standing Correlation Parameters for Gas Condensates and Volatile Oil Fluids (Eqs. 2 and 3). Constant Gas Condensate Volatile Oil A1 0.19408473 47.23306 A2 -3709.4214 -8.833514 A3 1.06052098 1.3251534 A4 -0.05022324 0.0091756 A5 -0.003771627 -0.000385524 TABLE 3 – Modified Vasques and Beggs Correlation Parameters for Gas Condensates and Volatile Oil Fluids (Eqs. 4 and 5). Constant Gas Condensate Volatile Oil A1 12.5849757 0.0005473 A2 1.343554054 1.607758566 A3 -105.486585 20.35993884 TABLE 4 – Oil-Gas Ratio Correlation Constants for Gas Condensates and Volatile Oil Fluids (Eq. 5). Constant Gas Condensate Volatile Oil A1 3.45841109 1.225537042 A2 6.89461E-05 0.000107257 A3 - 0.03169875 - 0.194226755 A4 251.0827307 240.549909 A5 4.174003053 8.32137351 TABLE 5 – Oil Formation Volume Factor Correlation Constants for Gas Condensates and Volatile Oil Fluids (Eq. 6). Constant Gas Condensate Volatile Oil A1 0.965109778 0.839614826 A2 0.000342547 0.000460621 A3 1.303305644 2.013137024 A4 1.053171234 1.015821025 TABLE 6 – Modified Sutton Correlation Parameters for Gas Condensates and Volatile Oil Fluids (Eqs. 7 and 8). Constant Gas Condensate Volatile Oil A1 670.958 608.520 A2 -188.078 -45.8495 A3 -3.7882 27.71169 B1 480.1142 29.70495 B2 -94.2128 871.57199 B3 9.398696 -502.6044
  • 6. 6 SPE 102240 TABLE 7 – Error in Fluid In Place Calculation from Generalized Material Balance Calculations Using the New Rv Correlation. Fluid Sample Original Fluid In Place Error (%) VO 1 0.9948 0.52 VO 2 1.0027 0.27 GC 1 1.0138 1.38 GC 2 0.9451 5.49 GC 3 1.0154 1.54 GC 4 1.0092 0.92 GC 5 1.1526 15.26 GC 6 1.0319 3.19 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 Rv (Obser), STB/Mscf Rv(Cal),STB/Mscf Fig. 1 - Cross-plot for RV (New Correlation) vs. RV (Driven from the EOS Model) for gas Condensate samples. y = 1.0138x 0 0.04 0.08 0.12 0.16 0.2 0 0.05 0.1 0.15 0.2 E o, Rb/stb F,Rb GMB C Linear (GMB C ) Fig. 2 – Material Balance as Straight Line Calculations for a Gas Condensate Sample (GC 1). y = 0.9948x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.2 0.4 0.6 0.8 Eo, Rb/stb F,Rb GMBC Linear (GMBC) Fig. 3 – Material Balance as Straight Line Calculations for a Volatile Oil Sample (VO 1).