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Predictions of Co2 solubility and CO2 saturated liquid density of heavy oils and bitumens using a cubic equation of state
Fluid Phase Equilibria, 64 (1991) 33-48 Elsevier Science Publishers B.V.. Amsterdam
33
Predictions of CO, solubility and CO, saturated liquid density of heavy oils and bitumens using a cubic equation of state A.K.M. Jamaluddin
‘, N.E. Kalogerakis
and A. Chakma
Department of Chemical and Petroleum Engineering, Alberta T2N lN4 (Canada) (Received
June 29, 1990; accepted
2
The University of Calgary
in final form December
Calgary
5, 1990)
ABSTRACT Jamaluddin, A.K.M., Kalogerakis, N.E. and Chakma, A., 1991. Prediction of CO, solubility and CO, saturated liquid density of heavy oils and bitumens using a cubic equation of state. Fhdd Phase Equilibria, 64: 33-48. This paper presents a method to predict the solubility of CO, in heavy oils and bitumens, as well as the density of CO,-saturated heavy oils and bitumens using a modified threeparameter Martin equation of state. A generalized constant value of the adjusted critical compressibility is suggested in this methodology for the prediction of COz solubility and CO,-saturated liquid density. The CO, solubility in heavy oils and bitumens and their saturated liquid density predictions were compared with several sets of experimental data reported in the literature. The solubility prediction is as accurate as that predicted by the Peng-Robinson equation of state. However, saturated liquid density prediction using the modified Martin equation of state is superior to the Peng-Robinson equation of state.
INTRODUCTION
Attention has centered on the use of carbon dioxide as a tertiary oil recovery agent as the need to recover more original oil in place (OOIP) from reservoirs increases. Carbon dioxide (CO,) is highly soluble in the crude oil at reservoir conditions. The dissolution of CO, greatly reduces the crude oil’s viscosity and also promotes swelling of the crude oil (i.e. the volume of the CO,-crude oil mixture is greater than that of the crude oil alone). Viscosity reduction and swelling of the crude oil results in improved mobility, thereby enhancing its recovery.
i Present address: Noranda Technology Centre, Pointe Claire, Quebec H9R lG5, Canada. ’ Author to whom correspondence should be addressed. 0378-3812/91/$03.50
Q 1991 Elsevier Science Publishers
B.V.
34
Holm (1976) compared the use of carbon dioxide as a miscible solvent for enhanced oil recovery to other solvents, including propane, light-hydrocarbon-enriched gases and solvents that are mutually soluble in both crude oil and water. He concluded that the main advantages of CO, are that it achieves miscible displacement at low pressures in the range 6.89-20.68 MPa, and that it is applicable to reservoirs that have been depleted of their gas and Liquified Petroleum Gas (LPG) components. Design and simulation of enhanced oil recovery field projects involving carbon dioxide injection requires thermodynamic models for accurate prediction of the fluid properties. The solubility of CO, in reservoir crude oils and the swelling of the CO,-saturated crude oils need to be predicted as accurately as possible for such design and simulation. Presently, there are few methods of predicting the CO, solubility and saturated liquid density. Simon and Graue (1965) have correlated CO, solubility, fluid swelling and viscosity data for CO,-oil mixtures obtained from several sources, including their own experimental data. Their correlations are in graphical form and are not suitable for applications in computer simulation studies. Since the correlations are empirical, there is no theoretical basis for extrapolation outside their range or extension to other systems. On the other hand, Katz and Firoozabadi (1978), Firoozabadi et al. (1978) and Baker and Luks (1978) presented equation of state (EOS)-based models to represent the oil-CO, system. They treated the oil as a mixture of lo-40 identifiable species of known properties and composition. For most practical situations, the detailed compositional analysis of an oil might not be available. In such a case, the oil characterization would introduce a lot of uncertainties in the calculations and also require an enormous amount of computer time. Hence, the computation would become costly. Mulliken and Sandler (1980) applied the Peng-Robinson equation of state to predict the solubility and swelling factor for the CO,-oil system. They considered the oil to be a single pseudocomponent and showed a good agreement between their prediction and the reported experimental data. Kokal and Sayegh (1988) applied a volume translation technique (Peneloux et al., 1982) in combination with the Peng-Robinson (PR) EOS to predict gas-saturated liquid densities. They used a two-step procedure. First, they calculated the saturated liquid density using the PR EOS and then corrected the density prediction by the volume translation technique. They showed a very good agreement between their prediction and the reported data. In general, two-parameter EOS, such as the Peng-Robinson and SoaveRedlich-Kwong (SRK) equations of state, have not been successful in accurately predicting liquid densities. However, Joffe (1981) showed that the Martin EOS (Martin, 1979) predicts the vapor-liquid equilibria as good as the SRK (EOS) and at the same time the Martin EOS predicts accurately saturated liquid volumes for light oils. He also introduced a Soave-type temperature function into the Martin EOS.
35
In this work, we have used the Martin EOS with the Soave-type temperature function as proposed by Joffe (1981) to predict the swelling and density of CO,-heavy oil/bitumen mixtures, information that is of extreme significance to the oil industry.
MARTIN EQUATION OF STATE
The original Martin equation of state
To describe the CO,-heavy oil/bitumen mixture we have used the EOS proposed by Martin in 1979. The equation is written as
-p-
Fb-
49 (v+42
where a, b and c are the substance-dependent parameters of the EOS. The equation may also be written in the reduced form as
(2) where B = bP,/RT,, C = cP,/RT,, and A = aPc/R2Tc2. In the above equation, Z, is the experimental critical compressibility factor at the critical point. Martin (1979) proposed that one should use A =
(27/64)T,-”
(3)
B =
0.8572, - 0.1674
(4)
C = 0.1250 - B
(5)
where n is a constant for a given substance, to be determined from the slope of the vapor pressure curve at the critical point. Martin (1979), after comparing his equation, using PVT data for pure substances, with other frequently used equations, such as the Redlich-Kwong (Redlich and Kwong, 1949), Soave-Redlich-Kwong (Soave, 1972) and Peng-Robinson (Peng and Robinson, 1976) equations, concluded that the Martin equation is the simplest and the best of the two-term cubits. Joffe (1981) replaced eqn. (3) with the Soave (1972) temperature function, written as A =
(27/64) (Y
(6)
where “=[l+m(l-fir)]*
(7)
36
The Soave (1972) temperature function, i.e. eqn. (7), was also adopted by Peng and Robinson (1976), and parameter m was expressed as a second-order polynomial of acentric factor o. However, the correlation for m obtained using the Peng-Robinson EOS cannot be used in the Martin EOS. Therefore, Joffe (1981) estimated parameter m for light hydrocarbons to be used in the Martin equation. He used an interaction parameter, S,,, of 0.14 to describe the interaction between CO,--n-butane. He showed very good agreement of solubility and density prediction with the experimental data. In this study, the heavy oil is considered to be a single pseudocomponent. Hence, the CO,-heavy oil mixture is considered to be a binary system. If an EOS is to describe such a system, it should meet the criterion that the fugacities of the saturated vapor and of the saturated liquid are equal along the vapor pressure curve of the mixture. It follows from Martin’s equation that the fugacity coefficient, +, of component 1 in the binary system is given RT ln+,=lnp(V_b)
+
-- b, J/-b
2(x,u,
+ x24
RT(v+c)
UC1 +
RT(Ys-~)~
The classical van der Waals mixing rules (Walas, 1985) were used for calculating the mixture properties, and the mixing rules are given below a =
c
uij =
CXiXj(Uij)
(1 - aij)( uiuj)1’2
(9) (10)
b = Cxibi
(11)
c = cxici
(12)
In eqn. (lo), aij is the interaction parameter between CO, and heavy oil/bitumen. The fugacity coefficient of component 2 is obtained by interchanging subscripts 1 and 2 in eqn. (8). Modification
of the Martin equation of state
The critical compressibility for heavy oil is usually calculated from correlations. This introduces some uncertainty in the calculation of the saturated liquid density. In this study, the experimental critical compressibility in eqn. (4) is replaced by an adjusted critical compressibility l=, and this parameter is estimated by matching the experimental saturated liquid density data. Least-squares estimation is also performed to obtain the interaction parameter Sij and the parameter m of eqn. (7) by matching the solubility data. The least-squares estimation is performed by using a non linear regression routine (ZXSSQ, IMSL library) based on the LevenbergMarquardt algorithm.
37 TABLE 1 Critical properties of CO* (Reid et al., 1987), oil, heavy oils and bitumens PC (MPa)
w
304.1 617.7 870.7 746.5 817.6 871.8 947.9 878.5 851.5 952.6 879.1
7.38 2.12 1.39 1.76 1.09 1.33 0.99 1.61 1.09 1.04 1.27
0.239 0.489 0.925 0.692 0.995 0.952 1.162 0.843 1.023 1.147 0.973
730(20) 951(43) 857(49) 859(49) 945(49) 976(49) 985(49) 894(54) 987(54) 945(63)
935.9
1089.1
0.78
1.363
1074(21)
533.0
870.2
1034.5
1.03
1.184
lOlO(22)
527.5
868.0
1044.6
1.09
1.166
1025(22)
446.5
787.0
960.0
1.127
1.100
1007(22)
Component
MW
Tb (R)
co2
44.01 142.3 350.0 236.0 345.0 358.0 463.0 330.0 373.0 458.0 370.0
447.3 690.7 565.8 665.0 695.7 788.1 683.0 694.7 788.3 705.8
595.0
n-Decane Oil A Oil B Oil C Oil D Oil E Oil F Oil G Oil H Oil I Athabasca bitumen Cold Lake bitumen Peace River bitumen Wabasca bitumen
T, (R)
P (T) (kg.m-3)
In this study, as mentioned previously, the heavy oil is considered to be a single pseudocomponent and the critical properties are calculated by using the Kesler-Lee (Kesler and Lee, 1976) correlation. The critical properties of CO, are given in Table 1, along with the calculated critical properties of all the heavy oils and bitumens used in this study.
RESULTS AND DISCUSSION
Several sets of CO,-heavy oil/bitumen experimental solubility and density data were regressed and the regressed parameters are given in Table 2. In Fig. 1, the regressed parameter m is plotted as a function of the heavy oil acentric factor. The regressed parameter m is also fitted with a second-order polynomial. In this correlation, the parameter m for the light hydrocarbon components as estimated by Joffe (1981) is also included. The polynomial is given below m = 0.4394 + 2.16450 - 1.0333~~
(13)
The regressed parameter m for oil C, oil E, Peace River bitumen Athabasca bitumen were slightly scattered and they were not taken account in the correlation.
and into
38 TABLE 2 Regressed parameters m, {, and Sii a Parameter m
Component lc = Z .(Joffe, 1981) CH, C,H, C,Hs n C,H,, &Hi, CO,
0.6465 0.7335 0.8064 0.8856 0.8456
0.2874 0.2847 0.2803 0.2741 0.2627 0.2742
_. _
0.8456 1.3285 1.5238 1.6319 1.0150 1.6660 2.4919 1.5044 1.6987 1.5373 1.4649 1.5128 1.5334 1.0527 1.4238
0.2558 0.2772 0.2633 0.2590 0.2549 0.2629 0.2616 0.2648 0.2524 0.2648 0.2549 0.2657 0.2638 0.2657 0.2633
0.1149 0.1345 0.1229 0.1842 0.1247 0.0757 0.1405 0.1336 0.1357 0.1419 0.1479 0.1453 0.1638 0.1397
03059
{c # Z, (This work)
co2 G,H,,
Oil A Oil B Oil C Oil D Oil E Oil F Oil G Oil H Oil I Athabasca bitumen Cold Lake bitumen Peace River bitumen Wabasca bitumen
a Suggested values: m = 0.4394+2.16450
-
- 1.03330~; 5, = 0.2640; aij = 0.1336.
In Fig. 2,
the estimated interaction parameter for CO, and several heavy oils/bitumens are plotted as a function of acentric factor. This figure indicates that a constant value of 0.1336 can be used to represent the interaction of CO, and several heavy oils/bitumens that have been tested. The regressed interaction parameters, Sij, were also slightly scattered for oil
3.00 l
2.25
Regressed Gxrelated
.
-
E i 1.i
///-.-.yy
E B 0.75
-,*,.."' .
0.04
1 0.0
0.5
1.0
1.5
Acenfric factor, u
Fig. 1. Regressed parameter m as a function of o.
39
*)
:=
i P)
B
0.3
-
E
e g e .o t e
bii = 0.1336 0.2 -
. \
0.1 -
.
.
c.+*
.
l
l
.
3 E
0.01
0.4
’
I
0.6
0.6
I 1.0
I 1.2
J
1.4
Acentric factor, o
Fig. 2. Regressed interaction
parameter as a function of o.
C, oil E, Peace River bitumen and Athabasca bitumen. Similarly, the estimated adjusted critical compressibility, cc, for all the heavy oils can be represented by a constant value of 0.2640, as shown in Fig. 3. Having obtained these parameters, the modified Martin EOS was then used to predict the CO, solubility and density of the CO,-saturated n-decane system. The critical compressibility of CO, was adjusted to 0.2558 using the CO,-nC,, system and kept constant for subsequent use of CO, in combination with other oils and bitumens. The data of Reamer and Sage (1963) for the CO,-nC,, system are compared with the model predictions in Figs. 4 and 5. As seen, the predictions are in excellent agreement with the experimental data. In these and later figures the data points are presented as dots and the predictions are presented as solid lines. This method was then extended to predict the CO, solubility and CO,saturated liquid density for nine different heavy oils (A-I). The experimental data were reported by Simon and Graue (1965). The comparisons showing good agreement between predicted and experimental data for selective oils are illustrated in Figs. 6-11.
1c g
0.5
0.4
-
cc =
0.264
e :: iE
0.3 -
4
0.2
.g .-
0.1 -
i .Z %
\
.
.-.-..*-_-m*-.*.-.
-
0.0 0.4
0.6
0.6
1.0
1.2
1.4
Acentric factor, o
Fig. 3. Regressed adjusted critical compressibility
as a function of o.
16.0 Data
[Reamer
& Sage, 19631
CO, - nC, 0.0
20.0
40.0
MI.0
CO, Solubility,
Fig. 4 . CO, solubility
rx
60.0
100.0
Mole %
in n-decane.
Dots are the data points and the solid lines are predicted.
0
k z
System
0
0
0
c
410 K
600.0
500.0 0.0
4.0
6.0
12.0
Pressure,
Fig. 5. CO,-saturated predicted.
16.0
MPa
n-decane
density.
Dots
are the data
points
and the solid lines are
The comparisons of model predictions with the experimental data for different bitumens are presented graphically in Figs. 12-19. The experimental data for bitumens were reported by Mehrotra and Svrcek (1985, 1988b, 1989b) and Svrcek and Mehrotra (1982). The prediction of CO, solubility and CO,-saturated bitumen density agrees well with the experimental data except for Athabasca bitumen. As seen in Fig. 18, the predicted solubility of
20.0
Oil A [Simon
& Graue, 19651 7
15.0 B I e 2
10.0
f!
5.0
<, = 0.2640
/--’ 0.0 0.0
20.0
40.0
CO, Sdubility,
Fig. 6. CO, solubility
641.0
60.0
100.0
Mole %
in oil A. Dots are the data points and the solid lines are predicted.
41 1200.0
7
Oil A [Simon & Graue, 19651
z 82
.I! 8 3
1100.0 -
I
316
1000.0
K
.-.-.
900.0
.
.
366 K.
5.0
0.0
10.0 Pressure,
Fig. 7. CO,-saturated
15.0
20.0
MPa
oil A density.
Dots are the data points and the solid lines are predicted.
20.0
Oil B [Simon % Graue, 19651 0
15.0
.
P e! a !
344 K 10.0
.i /
5.0
dii = 0.1336 (, = 0.2640
0.01
’
’
20.0
0.0
’
/
60.0
40.0
80.0
100.0
CO, Solubility, Mole %
Fig. 8. CO, solubility
in oil B. Dots are the data points and the solid line is predicted.
Oil B [Simon & Graue, 19651
.
.
l
’
344 K
dii = 0.1336 cc = 0.2640 I/?
600.0
’ 0.0
5.0
I 10.0
Pressure, Fig. 9. CO,-saturated
15.0
20.0
MPa
oil B density.
Dots are the data points
and the solid line is predicted.
Athabasca bitumen does not agree well with the experimental data with the generalized interaction parameter of 0.1336. The predictions can be improved if an interaction parameter of 0.1479 is used. Similarly, the prediction of CO,-saturated bitumen density also deviates substantially if the generalized adjusted critical compressibility of 0.264 is used, as shown in Fig. 19. An adjusted critical compressibility of 0.2656 provides a better match of the experimental density data. Hence, for Athabasca bitumen one CO,
in
42 Oil C [Simon & Graue, 19651 .
1 322 K
.
.
$ = 0.1336
(, = 0.2640
20.0
0.0
40.0
60.0
80.0
100.0
CO, Solubility, Mole %
Fig. 10. CO, solubility in oil C. Dots are the data points and the solid line is predicted.
1100.0 . a
Oil C [Simon & Gaue, 19651
1000.0 -
z e B 9 s 3
j
900.0
-
800.0
-
700.0
-
.
l
.
.
322K 6,, =
0.1336
(. = 0.2640 IF+
600.0 __ 0.0
5.0
10.0
15.0
20.0
Pressure, MPa
Fig. 11. COT-saturated oil C density. Dots are the data points and the solid line is predicted.
10.0
Wabaska Bitumen [Mehrotra & Svrcek 19851 7.5
-
2 I
e 2
371 K 5.0
296 K
-
%
0.0
20.0
40.0
60.0
80.0
CO, Solubility, Mole %
Fig. 12. CO, solubility in Wabasca bitumen. Dots are the data points and the solid lines are predicted.
should use S, = 0.2656 to calculate CO,-saturated density and use an interaction parameter of 0.1479 for solubility calculations. As seen in these figures, the modified Martin EOS predicts the CO, solubilities and the CO,-saturated liquid densities very close to the experimental data. The overall average absolute per cent deviation (%AAD) for all the sets of data points for the solubility prediction is less than 5% and for
43
Wabaska Bitumen [Mehratra & Svrcek 19851
i
c
1100.0
E $
2 g ?
ii
5
.
.
.
.
.
dii = 0.1336 CE = 0.2640
t 600.0
296 K . 371 K
900.0
2
8
.
.
1000.0
1
1
Presrii,
2.0
0.0
6.0
8.0
MPa
Fig. 13. CO,-saturated are predicted.
Wabasca
bitumen
density.
Dots are the data points and the solid lines
Cold Lake Bitumen [Mehrotra & Svrcek 1988b]
0.0
1
I
0.0
40.0
20.0
60.0
80.0
CO, Solubility, Mole %
Fig. 14. CO2 solubility predicted.
in Cold Lake bitumen.
1200.0
.
Dots are the data points and the solid lines are
Cold Lake Bitumen [Mehrotra & Svrcek 1988b]
2
1100.0
f:
d 0 g zi
1000.0
I
*-.A*_..
299K
.
m-*350
K
dii = 0.1336 (, = 0.2640
iii
800.0
’ 0.0
0 3.0
I 6.0 Pressure,
Fig. 15. CO,-saturated lines are predicted.
’
0 9.0
12.0
1
15.0
MPo
Cold Lake bitumen
density.
Dots are the data points
and the solid
the saturated liquid densities is less than 7%. The predicted results using the modified Martin EOS are compared with the results of the Peng-Robinson EOS as reported in the literature and the comparison is tabulated in Table 3. As seen in the table, the CO, solubility prediction with a constant value of ajj for all the heavy oils of Simon and Graue (1965) were very good and the
44
12.0 Peace River Bitumen [Mehrotra et al. 1989b] 9.0 a0 I
s D E a
328 K 6.0 /I
/’
2g6 K
//*
3.0 -
bii =
0.1336
(, = 0.2640 0.0 40.0
20.0
0.0
60.0
80.0
CO, Solubility, Mole %
Fig. 16. CO2 solubility in Peace River bitumen. Dots are the data points and the solid lines are predicted.
1100.0
Peace River Bitumen [Mehrotra et al. 1989b] P 2
E
10M.O
-
8 .z & f
328 K
: 1000.0
296K
.
-.
5
.
.
-
m e!
e 1 cx
0.1336
cSii=
(, = 0.2640 950.0
I 0.0
2.0
4.0
6.0
8.0
Pressure, MPa
Fig. 17. CO,-saturated lines are predicted.
Peace River bitumen density. Dots are the data points and the solid
._._ Athabasca Bitumen [Svrcek % Mehrotra, 19821 8.0
369 K
314 K
6.0
t 20.0
40.0
CO, Solubility, Mole %
Fig. 18. CO, solubility in Athabasca bitumen. Dots are the data points and the solid lines are predicted.
AAD from the experimental data was less than 5%. The CO,-saturated density of heavy oils with a constant value excellent (AAD < 5%) except for oils E, G and I. This difference in the used and the regressed c,. Similarly, as seen
prediction of of 5, was also is due to the in Table 3, the
45
prediction of CO, solubility in bitumens using the modified Martin EOS is as good as those predicted by the Peng-Robinson EOS. However, the prediction of CO,-saturated bitumen density using the modified Martin EOS is superior to those predicted by the Peng-Robinson EOS.
CONCLUSIONS
A modified Martin EOS is proposed to predict the CO, solubility in heavy oils and bitumens and their saturated liquid densities. A constant
TABLE 3 Comparison
of prediction
Hydrocarbon
Method
a
of CO* solubilities S,,
{,
and CO,-saturated
liquid densities
AAD( X) b AAD (p)
Reference
(W)
_
Oil B
PREOS MM EOS PREOS
0.1336 -
0.2640 _
1.85 -
Oil C
MM EOS PREOS
0.1336 -
0.2640 _
2.07 -
Oil D
MM EOS PREOS
0.1336 -
0.2640 _
5.36 -
0.1336 0.1336 -
0.2640 0.2640 _
2.11 -
Oil F
MM EOS PREOS MM EOS PREOS
Oil G
MM EOS PREOS
0.1336 -
0.2640 _
0.77 _
Oil H
MM EOS PREOS
0.1336 -
0.2640 _
5.18 -
MM EOS PREOS MM EOS PR EOS PREOS MM EOS PR EOS PREOS MM EOS PR EOS PREOS MM EOS PR EOS PREOS
0.1336 0.1336 0.109 0.1336 0.119 0.1336 0.101 0.1336 0.111 -
0.2640 0.2640 0.2640 0.2640 0.2640 _
1.04 -
6.86 8.70 -
MM EOS MM EOS
0.1336 0.1479
0.2640 0.2656
16.57 7.19
Oil A
Oil E
Oil I Peace River bitumen Cold Lake bitumen Wabasca bitumen Athabasca bitumen
a PR = Peng-Robinson; b ‘%AAD = (l/N)Z(
MM = modified
3.25 -
1.83 7.65 8.91 1.90 7.85 8.80 -
Martin.
l(Xexr - X,,) I x,,,)-1of).
(%) 20.83 1.96 15.85 4.94 25.95 5.06 20.58 1.21 23.44 7.68 1.31 26.44 14.32 22.66 1.08 22.70 9.45 19.08 2.21 _ 19.77 0.814 17.77 1.10 _ 19.01 19.86 1.15
Kokal & Sayegh (1988) This work Kokal & Sayegh (1988) This work Kokal & Sayegh (1988) This work Kokal & Sayegh (1988) This work Kokal & Sayegh (1988) This work Kokal & Sayegh (1988) This work Kokal & Sayegh (1988) This work Kokal & Sayegh (1988) This work Kokal & Sayegh (1988) This work Mehrotra et al. (1989b) Kokal & Sayegh (1988) This work Mehrotra & Svrcek (1988b) Kokal& Sayegh (1988) This work Mehrotra et al. (1989a) Kokal & Sayegh (1988) This work Mehrotra & Svrcek (1988a) Kokal & Sayegh (1988) This work This work
46 x
1200.0 Athabasca Bitumen [Svrcek & Mehrotra, 19821
B .z e
looo.o :
8 0
3s
-0 a 3e
z
33%;
. Y’L::.:‘P
.tirbT.+ C
800.0-
‘:~‘~Y’::‘:~“~’ ::‘::::,3l4
K 369 K
t, = 0.2640 600.0
I 0.0
2.0
4.0
1
1
6.0
6.0
Pressure. MPa
Fig. 19. CO,-saturated lines are predicted.
Athabasca
bitumen density. Dots are the data points and the solid
interaction parameter ( Sjj = 0.1336) and a constant adjusted critical compressibility (cc = 0.2640) are suggested in this work for the prediction of CO, solubility and CO,-saturated liquid density. CO, solubility prediction is as accurate as that predicted by the Peng-Robinson EOS. However, in terms of density prediction, the modified Martin EOS is superior to the Peng-Robinson EOS.
ACKNOWLEDGMENTS
The financial assistance provided by the Natural Sciences and Engineering Research Council of Canada and Energy, Mines and Resources Canada in partial support of this work is gratefully acknowledged.
LIST OF SYMBOLS
a, b, c A, B, C m P
P, P, R T
Tb T, T, V
Xi Yi
zc
parameters in the Martin equation parameters in the Martin equation characteristic constant of Soave-type temperature absolute pressure critical pressure reduced pressure ideal gas constant absolute temperature boiling point temperature critical temperature reduced temperature volume mole fraction of component i in liquid phase mole fraction of component i in vapor phase experimental critical compressibility factor
function
47
Greek letters
temperature function binary interaction parameter density at temperature T adjusted critical compressibility acentric factor
factor
REFERENCES Baker, L.E. and Luks, K.D., 1978. Critical point and saturation pressure calculations for multipoint systems. Paper SPE 7478, presented at the 53rd Annual Fall Technical Conference of the Society of Petroleum Engineers, Houston, October 1-3, 1978. SPE, Richardson, TX. Firoozabadi, A., Hekim, Y. and Katz, D.L., 1978. Reservoir depletion calculations for gas condensates using extended analyses in the Peng-Robinson equation of state. Can. J. Chem. Eng., 56: 610-615. Holm, L.W., 1976. Status of COz and hydrocarbon miscible oil recovery methods. J. Pet. Technol., 28: 76-84. Joffe, J., 1981. Vapor-liquid equilibria and densities with the Martin equation of state. Ind. Eng. Chem. Process Des. Dev., 20: 168-172. Katz, D.L. and Firoozabadi, A., 1978. Predicting phase behavior of condensate/crude-oil system using methane interaction coefficient. J. Pet. Technol., 30: 1649-1655. Kesler, M.G. and Lee, B.I., 1976. Improve prediction of enthalpy of fractions. Hydrocarbon Process., 55: 153-158. Kokal, S.L. and Sayegh, S.G., 1988. Gas-saturated bitumen density prediction using the volume-translated Peng-Robinson equation of state. Report 1988-14, Petroleum Recovery Institute, Calgary, Canada. Martin, J.J., 1979. Cubic equation of state - which? Ind. Eng. Chem. Fundam., 18(2): 81-97. Mehrotra, A.K. and Svrcek, W.Y., 1985. Viscosity, density and gas solubility data for oil-sand bitumens. Part III. Wabasca bitumen saturated with N,, CO, COz, CH, and C,H,. AOSTRA J. Res., 2(2): 83-93. Mehrotra, A.K. and Svrcek, W.Y., 1988a. Characterization of Athabasca bitumen for gas solubility calculations. J. Pet. Technol., 27(6): 107-110. Mehrotra, A.K. and Svrcek, W.Y., 1988b. Correlation and prediction of gas solubility in Cold Lake bitumen. Can. J. Chem. Eng., 66: 666-670. Mehrotra, A.K., Patience, G.S. and Svrcek, W.Y., 1989a. Calculation of gas solubility in Wabasca bitumen. J. Can. Pet. Technol., 28(3): 81-83. Mehrotra, A.K., Nighswander, J.A. and Kalogerakis, N., 1989b. Data and correlation for CO,-Peace River bitumen phase behavior at 22-200 o C. AOSTRA J. Res., 5(4): 351-358. Mulliken, C.A. and Sandler, S.I., 1980. The prediction of CO2 solubility and swelling factors for enhanced oil recovery. Ind. Eng. Chem. Process Des. Dev., 19: 709-711. Peneloux, A., Rauzy, E. and Freze, R., 1982. A consistent correlation for Redlich-KwongSoave volumes. Fluid Phase Equilibria, 8: 7-23. Peng, D. and Robinson, D.B., 1976. A new two-constant equation of state. Ind. Eng. Chem. Fundam., 15: 59-64. Reamer, H.H. and Sage, B.H., 1963. Phase equilibria in hydrocarbon systems. Volumetric and phase behavior of n-decane-CO2 system. J. Chem. Eng. Data, 8(4): 508-513. Reid, R.G., Prausnitz, J.M. and Poling, B.E., 1987. The properties of gases and Liquids, 4th edn. McGraw Hill, New York.
Redlich, O., and Kwong, J.N.S., 1949. On the thermodynamics of solutions. V. An equation of state. Fugacities of gaseous solutions. Chem. Rev., 44: 233-244. Simon, S.L. and Graue, D.J., 1965. Generalized correlations for predicting solubility, swelling and viscosity behavior of CO1-crude oil systems. J. Pet. Technol., 13: 102-106. Soave, G., 1972. Equilibrium constants from a mddified Redlich-Kwong equation of state. Chem. Eng. Sci., 27: 1197-1203. Svrcek, W.Y. and Mehrotra, A.K., 1982. Gas solubility, viscosity and density measurements for Athabasca bitumen. J. Can. Pet. Technol., 21(4): 31-38. Walas, S.M., 1985. Phase Equilibria in Chemical Engineering. Butterworths, Boston.
33
Predictions of CO, solubility and CO, saturated liquid density of heavy oils and bitumens using a cubic equation of state A.K.M. Jamaluddin
‘, N.E. Kalogerakis
and A. Chakma
Department of Chemical and Petroleum Engineering, Alberta T2N lN4 (Canada) (Received
June 29, 1990; accepted
2
The University of Calgary
in final form December
Calgary
5, 1990)
ABSTRACT Jamaluddin, A.K.M., Kalogerakis, N.E. and Chakma, A., 1991. Prediction of CO, solubility and CO, saturated liquid density of heavy oils and bitumens using a cubic equation of state. Fhdd Phase Equilibria, 64: 33-48. This paper presents a method to predict the solubility of CO, in heavy oils and bitumens, as well as the density of CO,-saturated heavy oils and bitumens using a modified threeparameter Martin equation of state. A generalized constant value of the adjusted critical compressibility is suggested in this methodology for the prediction of COz solubility and CO,-saturated liquid density. The CO, solubility in heavy oils and bitumens and their saturated liquid density predictions were compared with several sets of experimental data reported in the literature. The solubility prediction is as accurate as that predicted by the Peng-Robinson equation of state. However, saturated liquid density prediction using the modified Martin equation of state is superior to the Peng-Robinson equation of state.
INTRODUCTION
Attention has centered on the use of carbon dioxide as a tertiary oil recovery agent as the need to recover more original oil in place (OOIP) from reservoirs increases. Carbon dioxide (CO,) is highly soluble in the crude oil at reservoir conditions. The dissolution of CO, greatly reduces the crude oil’s viscosity and also promotes swelling of the crude oil (i.e. the volume of the CO,-crude oil mixture is greater than that of the crude oil alone). Viscosity reduction and swelling of the crude oil results in improved mobility, thereby enhancing its recovery.
i Present address: Noranda Technology Centre, Pointe Claire, Quebec H9R lG5, Canada. ’ Author to whom correspondence should be addressed. 0378-3812/91/$03.50
Q 1991 Elsevier Science Publishers
B.V.
34
Holm (1976) compared the use of carbon dioxide as a miscible solvent for enhanced oil recovery to other solvents, including propane, light-hydrocarbon-enriched gases and solvents that are mutually soluble in both crude oil and water. He concluded that the main advantages of CO, are that it achieves miscible displacement at low pressures in the range 6.89-20.68 MPa, and that it is applicable to reservoirs that have been depleted of their gas and Liquified Petroleum Gas (LPG) components. Design and simulation of enhanced oil recovery field projects involving carbon dioxide injection requires thermodynamic models for accurate prediction of the fluid properties. The solubility of CO, in reservoir crude oils and the swelling of the CO,-saturated crude oils need to be predicted as accurately as possible for such design and simulation. Presently, there are few methods of predicting the CO, solubility and saturated liquid density. Simon and Graue (1965) have correlated CO, solubility, fluid swelling and viscosity data for CO,-oil mixtures obtained from several sources, including their own experimental data. Their correlations are in graphical form and are not suitable for applications in computer simulation studies. Since the correlations are empirical, there is no theoretical basis for extrapolation outside their range or extension to other systems. On the other hand, Katz and Firoozabadi (1978), Firoozabadi et al. (1978) and Baker and Luks (1978) presented equation of state (EOS)-based models to represent the oil-CO, system. They treated the oil as a mixture of lo-40 identifiable species of known properties and composition. For most practical situations, the detailed compositional analysis of an oil might not be available. In such a case, the oil characterization would introduce a lot of uncertainties in the calculations and also require an enormous amount of computer time. Hence, the computation would become costly. Mulliken and Sandler (1980) applied the Peng-Robinson equation of state to predict the solubility and swelling factor for the CO,-oil system. They considered the oil to be a single pseudocomponent and showed a good agreement between their prediction and the reported experimental data. Kokal and Sayegh (1988) applied a volume translation technique (Peneloux et al., 1982) in combination with the Peng-Robinson (PR) EOS to predict gas-saturated liquid densities. They used a two-step procedure. First, they calculated the saturated liquid density using the PR EOS and then corrected the density prediction by the volume translation technique. They showed a very good agreement between their prediction and the reported data. In general, two-parameter EOS, such as the Peng-Robinson and SoaveRedlich-Kwong (SRK) equations of state, have not been successful in accurately predicting liquid densities. However, Joffe (1981) showed that the Martin EOS (Martin, 1979) predicts the vapor-liquid equilibria as good as the SRK (EOS) and at the same time the Martin EOS predicts accurately saturated liquid volumes for light oils. He also introduced a Soave-type temperature function into the Martin EOS.
35
In this work, we have used the Martin EOS with the Soave-type temperature function as proposed by Joffe (1981) to predict the swelling and density of CO,-heavy oil/bitumen mixtures, information that is of extreme significance to the oil industry.
MARTIN EQUATION OF STATE
The original Martin equation of state
To describe the CO,-heavy oil/bitumen mixture we have used the EOS proposed by Martin in 1979. The equation is written as
-p-
Fb-
49 (v+42
where a, b and c are the substance-dependent parameters of the EOS. The equation may also be written in the reduced form as
(2) where B = bP,/RT,, C = cP,/RT,, and A = aPc/R2Tc2. In the above equation, Z, is the experimental critical compressibility factor at the critical point. Martin (1979) proposed that one should use A =
(27/64)T,-”
(3)
B =
0.8572, - 0.1674
(4)
C = 0.1250 - B
(5)
where n is a constant for a given substance, to be determined from the slope of the vapor pressure curve at the critical point. Martin (1979), after comparing his equation, using PVT data for pure substances, with other frequently used equations, such as the Redlich-Kwong (Redlich and Kwong, 1949), Soave-Redlich-Kwong (Soave, 1972) and Peng-Robinson (Peng and Robinson, 1976) equations, concluded that the Martin equation is the simplest and the best of the two-term cubits. Joffe (1981) replaced eqn. (3) with the Soave (1972) temperature function, written as A =
(27/64) (Y
(6)
where “=[l+m(l-fir)]*
(7)
36
The Soave (1972) temperature function, i.e. eqn. (7), was also adopted by Peng and Robinson (1976), and parameter m was expressed as a second-order polynomial of acentric factor o. However, the correlation for m obtained using the Peng-Robinson EOS cannot be used in the Martin EOS. Therefore, Joffe (1981) estimated parameter m for light hydrocarbons to be used in the Martin equation. He used an interaction parameter, S,,, of 0.14 to describe the interaction between CO,--n-butane. He showed very good agreement of solubility and density prediction with the experimental data. In this study, the heavy oil is considered to be a single pseudocomponent. Hence, the CO,-heavy oil mixture is considered to be a binary system. If an EOS is to describe such a system, it should meet the criterion that the fugacities of the saturated vapor and of the saturated liquid are equal along the vapor pressure curve of the mixture. It follows from Martin’s equation that the fugacity coefficient, +, of component 1 in the binary system is given RT ln+,=lnp(V_b)
+
-- b, J/-b
2(x,u,
+ x24
RT(v+c)
UC1 +
RT(Ys-~)~
The classical van der Waals mixing rules (Walas, 1985) were used for calculating the mixture properties, and the mixing rules are given below a =
c
uij =
CXiXj(Uij)
(1 - aij)( uiuj)1’2
(9) (10)
b = Cxibi
(11)
c = cxici
(12)
In eqn. (lo), aij is the interaction parameter between CO, and heavy oil/bitumen. The fugacity coefficient of component 2 is obtained by interchanging subscripts 1 and 2 in eqn. (8). Modification
of the Martin equation of state
The critical compressibility for heavy oil is usually calculated from correlations. This introduces some uncertainty in the calculation of the saturated liquid density. In this study, the experimental critical compressibility in eqn. (4) is replaced by an adjusted critical compressibility l=, and this parameter is estimated by matching the experimental saturated liquid density data. Least-squares estimation is also performed to obtain the interaction parameter Sij and the parameter m of eqn. (7) by matching the solubility data. The least-squares estimation is performed by using a non linear regression routine (ZXSSQ, IMSL library) based on the LevenbergMarquardt algorithm.
37 TABLE 1 Critical properties of CO* (Reid et al., 1987), oil, heavy oils and bitumens PC (MPa)
w
304.1 617.7 870.7 746.5 817.6 871.8 947.9 878.5 851.5 952.6 879.1
7.38 2.12 1.39 1.76 1.09 1.33 0.99 1.61 1.09 1.04 1.27
0.239 0.489 0.925 0.692 0.995 0.952 1.162 0.843 1.023 1.147 0.973
730(20) 951(43) 857(49) 859(49) 945(49) 976(49) 985(49) 894(54) 987(54) 945(63)
935.9
1089.1
0.78
1.363
1074(21)
533.0
870.2
1034.5
1.03
1.184
lOlO(22)
527.5
868.0
1044.6
1.09
1.166
1025(22)
446.5
787.0
960.0
1.127
1.100
1007(22)
Component
MW
Tb (R)
co2
44.01 142.3 350.0 236.0 345.0 358.0 463.0 330.0 373.0 458.0 370.0
447.3 690.7 565.8 665.0 695.7 788.1 683.0 694.7 788.3 705.8
595.0
n-Decane Oil A Oil B Oil C Oil D Oil E Oil F Oil G Oil H Oil I Athabasca bitumen Cold Lake bitumen Peace River bitumen Wabasca bitumen
T, (R)
P (T) (kg.m-3)
In this study, as mentioned previously, the heavy oil is considered to be a single pseudocomponent and the critical properties are calculated by using the Kesler-Lee (Kesler and Lee, 1976) correlation. The critical properties of CO, are given in Table 1, along with the calculated critical properties of all the heavy oils and bitumens used in this study.
RESULTS AND DISCUSSION
Several sets of CO,-heavy oil/bitumen experimental solubility and density data were regressed and the regressed parameters are given in Table 2. In Fig. 1, the regressed parameter m is plotted as a function of the heavy oil acentric factor. The regressed parameter m is also fitted with a second-order polynomial. In this correlation, the parameter m for the light hydrocarbon components as estimated by Joffe (1981) is also included. The polynomial is given below m = 0.4394 + 2.16450 - 1.0333~~
(13)
The regressed parameter m for oil C, oil E, Peace River bitumen Athabasca bitumen were slightly scattered and they were not taken account in the correlation.
and into
38 TABLE 2 Regressed parameters m, {, and Sii a Parameter m
Component lc = Z .(Joffe, 1981) CH, C,H, C,Hs n C,H,, &Hi, CO,
0.6465 0.7335 0.8064 0.8856 0.8456
0.2874 0.2847 0.2803 0.2741 0.2627 0.2742
_. _
0.8456 1.3285 1.5238 1.6319 1.0150 1.6660 2.4919 1.5044 1.6987 1.5373 1.4649 1.5128 1.5334 1.0527 1.4238
0.2558 0.2772 0.2633 0.2590 0.2549 0.2629 0.2616 0.2648 0.2524 0.2648 0.2549 0.2657 0.2638 0.2657 0.2633
0.1149 0.1345 0.1229 0.1842 0.1247 0.0757 0.1405 0.1336 0.1357 0.1419 0.1479 0.1453 0.1638 0.1397
03059
{c # Z, (This work)
co2 G,H,,
Oil A Oil B Oil C Oil D Oil E Oil F Oil G Oil H Oil I Athabasca bitumen Cold Lake bitumen Peace River bitumen Wabasca bitumen
a Suggested values: m = 0.4394+2.16450
-
- 1.03330~; 5, = 0.2640; aij = 0.1336.
In Fig. 2,
the estimated interaction parameter for CO, and several heavy oils/bitumens are plotted as a function of acentric factor. This figure indicates that a constant value of 0.1336 can be used to represent the interaction of CO, and several heavy oils/bitumens that have been tested. The regressed interaction parameters, Sij, were also slightly scattered for oil
3.00 l
2.25
Regressed Gxrelated
.
-
E i 1.i
///-.-.yy
E B 0.75
-,*,.."' .
0.04
1 0.0
0.5
1.0
1.5
Acenfric factor, u
Fig. 1. Regressed parameter m as a function of o.
39
*)
:=
i P)
B
0.3
-
E
e g e .o t e
bii = 0.1336 0.2 -
. \
0.1 -
.
.
c.+*
.
l
l
.
3 E
0.01
0.4
’
I
0.6
0.6
I 1.0
I 1.2
J
1.4
Acentric factor, o
Fig. 2. Regressed interaction
parameter as a function of o.
C, oil E, Peace River bitumen and Athabasca bitumen. Similarly, the estimated adjusted critical compressibility, cc, for all the heavy oils can be represented by a constant value of 0.2640, as shown in Fig. 3. Having obtained these parameters, the modified Martin EOS was then used to predict the CO, solubility and density of the CO,-saturated n-decane system. The critical compressibility of CO, was adjusted to 0.2558 using the CO,-nC,, system and kept constant for subsequent use of CO, in combination with other oils and bitumens. The data of Reamer and Sage (1963) for the CO,-nC,, system are compared with the model predictions in Figs. 4 and 5. As seen, the predictions are in excellent agreement with the experimental data. In these and later figures the data points are presented as dots and the predictions are presented as solid lines. This method was then extended to predict the CO, solubility and CO,saturated liquid density for nine different heavy oils (A-I). The experimental data were reported by Simon and Graue (1965). The comparisons showing good agreement between predicted and experimental data for selective oils are illustrated in Figs. 6-11.
1c g
0.5
0.4
-
cc =
0.264
e :: iE
0.3 -
4
0.2
.g .-
0.1 -
i .Z %
\
.
.-.-..*-_-m*-.*.-.
-
0.0 0.4
0.6
0.6
1.0
1.2
1.4
Acentric factor, o
Fig. 3. Regressed adjusted critical compressibility
as a function of o.
16.0 Data
[Reamer
& Sage, 19631
CO, - nC, 0.0
20.0
40.0
MI.0
CO, Solubility,
Fig. 4 . CO, solubility
rx
60.0
100.0
Mole %
in n-decane.
Dots are the data points and the solid lines are predicted.
0
k z
System
0
0
0
c
410 K
600.0
500.0 0.0
4.0
6.0
12.0
Pressure,
Fig. 5. CO,-saturated predicted.
16.0
MPa
n-decane
density.
Dots
are the data
points
and the solid lines are
The comparisons of model predictions with the experimental data for different bitumens are presented graphically in Figs. 12-19. The experimental data for bitumens were reported by Mehrotra and Svrcek (1985, 1988b, 1989b) and Svrcek and Mehrotra (1982). The prediction of CO, solubility and CO,-saturated bitumen density agrees well with the experimental data except for Athabasca bitumen. As seen in Fig. 18, the predicted solubility of
20.0
Oil A [Simon
& Graue, 19651 7
15.0 B I e 2
10.0
f!
5.0
<, = 0.2640
/--’ 0.0 0.0
20.0
40.0
CO, Sdubility,
Fig. 6. CO, solubility
641.0
60.0
100.0
Mole %
in oil A. Dots are the data points and the solid lines are predicted.
41 1200.0
7
Oil A [Simon & Graue, 19651
z 82
.I! 8 3
1100.0 -
I
316
1000.0
K
.-.-.
900.0
.
.
366 K.
5.0
0.0
10.0 Pressure,
Fig. 7. CO,-saturated
15.0
20.0
MPa
oil A density.
Dots are the data points and the solid lines are predicted.
20.0
Oil B [Simon % Graue, 19651 0
15.0
.
P e! a !
344 K 10.0
.i /
5.0
dii = 0.1336 (, = 0.2640
0.01
’
’
20.0
0.0
’
/
60.0
40.0
80.0
100.0
CO, Solubility, Mole %
Fig. 8. CO, solubility
in oil B. Dots are the data points and the solid line is predicted.
Oil B [Simon & Graue, 19651
.
.
l
’
344 K
dii = 0.1336 cc = 0.2640 I/?
600.0
’ 0.0
5.0
I 10.0
Pressure, Fig. 9. CO,-saturated
15.0
20.0
MPa
oil B density.
Dots are the data points
and the solid line is predicted.
Athabasca bitumen does not agree well with the experimental data with the generalized interaction parameter of 0.1336. The predictions can be improved if an interaction parameter of 0.1479 is used. Similarly, the prediction of CO,-saturated bitumen density also deviates substantially if the generalized adjusted critical compressibility of 0.264 is used, as shown in Fig. 19. An adjusted critical compressibility of 0.2656 provides a better match of the experimental density data. Hence, for Athabasca bitumen one CO,
in
42 Oil C [Simon & Graue, 19651 .
1 322 K
.
.
$ = 0.1336
(, = 0.2640
20.0
0.0
40.0
60.0
80.0
100.0
CO, Solubility, Mole %
Fig. 10. CO, solubility in oil C. Dots are the data points and the solid line is predicted.
1100.0 . a
Oil C [Simon & Gaue, 19651
1000.0 -
z e B 9 s 3
j
900.0
-
800.0
-
700.0
-
.
l
.
.
322K 6,, =
0.1336
(. = 0.2640 IF+
600.0 __ 0.0
5.0
10.0
15.0
20.0
Pressure, MPa
Fig. 11. COT-saturated oil C density. Dots are the data points and the solid line is predicted.
10.0
Wabaska Bitumen [Mehrotra & Svrcek 19851 7.5
-
2 I
e 2
371 K 5.0
296 K
-
%
0.0
20.0
40.0
60.0
80.0
CO, Solubility, Mole %
Fig. 12. CO, solubility in Wabasca bitumen. Dots are the data points and the solid lines are predicted.
should use S, = 0.2656 to calculate CO,-saturated density and use an interaction parameter of 0.1479 for solubility calculations. As seen in these figures, the modified Martin EOS predicts the CO, solubilities and the CO,-saturated liquid densities very close to the experimental data. The overall average absolute per cent deviation (%AAD) for all the sets of data points for the solubility prediction is less than 5% and for
43
Wabaska Bitumen [Mehratra & Svrcek 19851
i
c
1100.0
E $
2 g ?
ii
5
.
.
.
.
.
dii = 0.1336 CE = 0.2640
t 600.0
296 K . 371 K
900.0
2
8
.
.
1000.0
1
1
Presrii,
2.0
0.0
6.0
8.0
MPa
Fig. 13. CO,-saturated are predicted.
Wabasca
bitumen
density.
Dots are the data points and the solid lines
Cold Lake Bitumen [Mehrotra & Svrcek 1988b]
0.0
1
I
0.0
40.0
20.0
60.0
80.0
CO, Solubility, Mole %
Fig. 14. CO2 solubility predicted.
in Cold Lake bitumen.
1200.0
.
Dots are the data points and the solid lines are
Cold Lake Bitumen [Mehrotra & Svrcek 1988b]
2
1100.0
f:
d 0 g zi
1000.0
I
*-.A*_..
299K
.
m-*350
K
dii = 0.1336 (, = 0.2640
iii
800.0
’ 0.0
0 3.0
I 6.0 Pressure,
Fig. 15. CO,-saturated lines are predicted.
’
0 9.0
12.0
1
15.0
MPo
Cold Lake bitumen
density.
Dots are the data points
and the solid
the saturated liquid densities is less than 7%. The predicted results using the modified Martin EOS are compared with the results of the Peng-Robinson EOS as reported in the literature and the comparison is tabulated in Table 3. As seen in the table, the CO, solubility prediction with a constant value of ajj for all the heavy oils of Simon and Graue (1965) were very good and the
44
12.0 Peace River Bitumen [Mehrotra et al. 1989b] 9.0 a0 I
s D E a
328 K 6.0 /I
/’
2g6 K
//*
3.0 -
bii =
0.1336
(, = 0.2640 0.0 40.0
20.0
0.0
60.0
80.0
CO, Solubility, Mole %
Fig. 16. CO2 solubility in Peace River bitumen. Dots are the data points and the solid lines are predicted.
1100.0
Peace River Bitumen [Mehrotra et al. 1989b] P 2
E
10M.O
-
8 .z & f
328 K
: 1000.0
296K
.
-.
5
.
.
-
m e!
e 1 cx
0.1336
cSii=
(, = 0.2640 950.0
I 0.0
2.0
4.0
6.0
8.0
Pressure, MPa
Fig. 17. CO,-saturated lines are predicted.
Peace River bitumen density. Dots are the data points and the solid
._._ Athabasca Bitumen [Svrcek % Mehrotra, 19821 8.0
369 K
314 K
6.0
t 20.0
40.0
CO, Solubility, Mole %
Fig. 18. CO, solubility in Athabasca bitumen. Dots are the data points and the solid lines are predicted.
AAD from the experimental data was less than 5%. The CO,-saturated density of heavy oils with a constant value excellent (AAD < 5%) except for oils E, G and I. This difference in the used and the regressed c,. Similarly, as seen
prediction of of 5, was also is due to the in Table 3, the
45
prediction of CO, solubility in bitumens using the modified Martin EOS is as good as those predicted by the Peng-Robinson EOS. However, the prediction of CO,-saturated bitumen density using the modified Martin EOS is superior to those predicted by the Peng-Robinson EOS.
CONCLUSIONS
A modified Martin EOS is proposed to predict the CO, solubility in heavy oils and bitumens and their saturated liquid densities. A constant
TABLE 3 Comparison
of prediction
Hydrocarbon
Method
a
of CO* solubilities S,,
{,
and CO,-saturated
liquid densities
AAD( X) b AAD (p)
Reference
(W)
_
Oil B
PREOS MM EOS PREOS
0.1336 -
0.2640 _
1.85 -
Oil C
MM EOS PREOS
0.1336 -
0.2640 _
2.07 -
Oil D
MM EOS PREOS
0.1336 -
0.2640 _
5.36 -
0.1336 0.1336 -
0.2640 0.2640 _
2.11 -
Oil F
MM EOS PREOS MM EOS PREOS
Oil G
MM EOS PREOS
0.1336 -
0.2640 _
0.77 _
Oil H
MM EOS PREOS
0.1336 -
0.2640 _
5.18 -
MM EOS PREOS MM EOS PR EOS PREOS MM EOS PR EOS PREOS MM EOS PR EOS PREOS MM EOS PR EOS PREOS
0.1336 0.1336 0.109 0.1336 0.119 0.1336 0.101 0.1336 0.111 -
0.2640 0.2640 0.2640 0.2640 0.2640 _
1.04 -
6.86 8.70 -
MM EOS MM EOS
0.1336 0.1479
0.2640 0.2656
16.57 7.19
Oil A
Oil E
Oil I Peace River bitumen Cold Lake bitumen Wabasca bitumen Athabasca bitumen
a PR = Peng-Robinson; b ‘%AAD = (l/N)Z(
MM = modified
3.25 -
1.83 7.65 8.91 1.90 7.85 8.80 -
Martin.
l(Xexr - X,,) I x,,,)-1of).
(%) 20.83 1.96 15.85 4.94 25.95 5.06 20.58 1.21 23.44 7.68 1.31 26.44 14.32 22.66 1.08 22.70 9.45 19.08 2.21 _ 19.77 0.814 17.77 1.10 _ 19.01 19.86 1.15
Kokal & Sayegh (1988) This work Kokal & Sayegh (1988) This work Kokal & Sayegh (1988) This work Kokal & Sayegh (1988) This work Kokal & Sayegh (1988) This work Kokal & Sayegh (1988) This work Kokal & Sayegh (1988) This work Kokal & Sayegh (1988) This work Kokal & Sayegh (1988) This work Mehrotra et al. (1989b) Kokal & Sayegh (1988) This work Mehrotra & Svrcek (1988b) Kokal& Sayegh (1988) This work Mehrotra et al. (1989a) Kokal & Sayegh (1988) This work Mehrotra & Svrcek (1988a) Kokal & Sayegh (1988) This work This work
46 x
1200.0 Athabasca Bitumen [Svrcek & Mehrotra, 19821
B .z e
looo.o :
8 0
3s
-0 a 3e
z
33%;
. Y’L::.:‘P
.tirbT.+ C
800.0-
‘:~‘~Y’::‘:~“~’ ::‘::::,3l4
K 369 K
t, = 0.2640 600.0
I 0.0
2.0
4.0
1
1
6.0
6.0
Pressure. MPa
Fig. 19. CO,-saturated lines are predicted.
Athabasca
bitumen density. Dots are the data points and the solid
interaction parameter ( Sjj = 0.1336) and a constant adjusted critical compressibility (cc = 0.2640) are suggested in this work for the prediction of CO, solubility and CO,-saturated liquid density. CO, solubility prediction is as accurate as that predicted by the Peng-Robinson EOS. However, in terms of density prediction, the modified Martin EOS is superior to the Peng-Robinson EOS.
ACKNOWLEDGMENTS
The financial assistance provided by the Natural Sciences and Engineering Research Council of Canada and Energy, Mines and Resources Canada in partial support of this work is gratefully acknowledged.
LIST OF SYMBOLS
a, b, c A, B, C m P
P, P, R T
Tb T, T, V
Xi Yi
zc
parameters in the Martin equation parameters in the Martin equation characteristic constant of Soave-type temperature absolute pressure critical pressure reduced pressure ideal gas constant absolute temperature boiling point temperature critical temperature reduced temperature volume mole fraction of component i in liquid phase mole fraction of component i in vapor phase experimental critical compressibility factor
function
47
Greek letters
temperature function binary interaction parameter density at temperature T adjusted critical compressibility acentric factor
factor
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