Ind. Eng. Chem. Res. 1995,34, 4016-4032
4016
Characterization of Heavy Oils. 3. Prediction of Gas Injection Behavior: Swelling Test, Multicontact Test, Multiple-Contact Minimum Miscibility Pressure, and Multiple-ContactMinimum Miscibility Enrichment Jean-NoGl Jaubert’ Laboratoire de Thermodynamique Chimique et Appliquee, Znstitut National Polytechnique de Lorraine, Ecole Nationale Superieure des Industries Chimiques, 1 Rue Grandville, B.P. 451, 54001 Nancy Cedex, France
Evelyne Neaut and Laurent Avaullket Laboratoire de Chimie Physique, Facult4 des Sciences de Luminy, 163, Avenue de Luminy, 13288 Marseille Cedex 9, France
Georges Zaborowski Compagnie Pitroli2re TOTAL, Centre Scientifique et Technique, Domaine de Beauplan, Route de Versailles, France 78470 Saint-Remy-l2s-Chevreuse,
The modeling of miscible gas injection into reservoir crude oils was performed using a cubic equation of state coupled with a predictive procedure for characterizing the heavy fractions. It is shown t h a t experimental data on the swelling test, multicontact test, slim tube minimum miscibility pressure (MMP), and minimum miscibility enrichment (MME) for 10 different crude oils from different fields are satisfactorily calculated using the predictive characterization. However, in the case of MMP and MME calculations, a significant deviation may appear between predicted and experimental values. Reasons for this discrepancy are discussed. The influence of tuning the equation of state parameters in the estimation of results for the swelling test is also discussed.
Introduction After their discovery, most oil reservoirs typically undergo a period of production called “primary recovery” in which natural energy is used to recover a portion of the oil. Primary recovery efficiency varies from reservoir to reservoir, but a typical range for recovery efficiency is 5-20%. Gas injection is nowadays a very important enhanced oil recovery (EOR) process, i.e., a method for increasing oil recovery. It has become a common practice even though very complex technology is required. Although gas injection has been the subject of important research and development for more than 40 years, there is still some disagreement in the interpretation of several laboratory data, and much progress still needs to be made to improve the estimation of the experimental data. Gas injection is a very expensive process, and a high degree of accuracy is required for predicting the outcome of the process. For instance, if an unrealistically low oil recovery is predicted, a potential project may look unattractive and the petroleum company may decide against continuing with the project and lose money. On the other hand, much more money is lost if an unrealistically high oil recovery is predicted since the field will never become profitable. In this paper, the predictive method recently developed by Jaubert (1993) and by Neau et al. (1993) is used to predict the results of various gas injection tests on different reservoir crude oils. Background on the Predictive Method (a) Equation of State. To perform a flash calculation, the predictive method developed by Neau et al.
* FAX:
’ FAX:
(33) 83.35.08.11. (33) 91.26.93.04.
0888-588519512634-4016$09.00/0
(1993) uses the modified Peng-Robinson equation of state initially proposed by Rauzy (1982):
with y = 2&
+2
RZ
4.828 427
6 = 0.045 572-RTC PC
(1)
8 is the pseudovolume related to the molar volume and to the volume correction c (PBneloux et al., 1982) by
u
8=u+c
with
RTC
c = -(0.083
PC
150 - 0.440 6422,)
(2)
In eq 2, ,2 is the Rackett compressibility factor appearing in Spencer and Danner’s modification (1973) of the Rackett equation. The u(T) function used is u(T)= 0.457 236-
[1+ m(1
with
0 1995 American Chemical Society
-
(E)0.445075)]2 (3)
Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 4017
m= 6.8126[.J1.127 539
+ 0.517 2 5 2 ~- 0.003 7 3 7 ~ ’- 11 (4)
For a mixture containing p compounds of mole fraction xi, classical mixing rules were used: P
6,
= c,,6, i=l
P
c, = &Ci i=l
with
The binary interaction parameters Eij were estimated using the group contribution method developed by Abdoul et al. (1992). These authors proposed the following relationship:
where ng is the total number of different groups present in the mixture. To perform phase equilibrium calculations on a petroleum fluid, the 12 groups in Chart 1(ng Chart 1 aromatic special alkane naphthene groups POUPS groups groups g r 0 ~ p 8 :CHI group 1: CH3 group 4: CHz group 6: CH,, (cyclic) (methane) group2: CHz g r o u p 5 CH g r 0 ~ p 7 :Carom group9: CzH6 (ethane) (cyclic) group10: c02 group3: CH gr0up11: Nz (nitrogen) group 12: HzS
= 12) must be used. In eq 7, aik is the fraction occupied by group ir, in molecule i. It is calculated by nik
where ngi is the number of different groups present in molecule i (ngi < 12) and nik the number of groups k present in molecule i. ALI(T) is a temperature-dependent function:
(b)C11+ Characterization. For economic reasons (gas injection experiments are very expensive), a true boiling point (TBP) distillation was not performed on the C7+ fraction of the different crude oils used in this study. The composition of the crude oils was thus roughly determined by chromatography up to Clo. In this case, Neau et al. (1993) have shown that the best PVT predictions are obtained by describing the crude oil as a mixture of the following eight components and pseudocomponents: Nz, COZ, CH4, C2H6, C3H8, “butanes”, ‘C5-C10n, and ‘CII+”. Nz, COZ,CH4, C2H6, and C3H8 are pure components for which the mole fractions and physical properties are accurately knOWn. ‘Butanes” is a grouping of n-butane and isobutane. The mole percent of these two pure compounds is determined by chromatography. The procedure for lumping these two components, into the pseudocomponent butanes, is described in the next section. In this study, no data are available on the internal composition of the paraffinic, naphthenic, and aromatic compounds from the cuts of C5-clO. Instead C5-clO is represented by only seven pure alkanes which are found in the cuts of C5-ClO: isopentane, n-pentane, nhexane, n-heptane, n-octane, n-nonane, and n-decane. Their mole fractions were determined by chromatography, and their physical properties were taken from the literature (Reid et al., 1987). The procedure for lumping these seven pure components into the pseudocomponent called “C5-C10n is explained in the next section. ‘Cll+” is the residue containing all the components whose boiling points are higher than the n-decane normal boiling point. Neau et al. (1993) have shown that good PVT predictions can be obtained if this residue is represented as a grouping of only three compounds: an aromatic compound, a naphthenic compound, and an n-alkane. The predictive method stipulates that the naphthenic compound is dicyclohexylmethane and its mole fraction in the residue, its molar weight, and its density are noted respectively as XN, M N , and p ~ The . aromatic molecule is not a real molecule but is defined by the structure 1OCaromatio 4Csubed arom, 2Carom fused ring, 4CH3,4CH2, and 2CH. Its internal mole fraction in the residue, its molar weight, and its density are respectively noted as XA, MA, and PA. The alkane compound is an n-alkane which is chosen to be between n-C11 and n-C45. Its internal mole fraction in the residue, its molar weight, and its density are respectively noted as xp, M p , and pp. For a given n-alkane, chosen between n-C11 and n-C45, the three mole fractions (XN, XA, and xp) are determined by assuming that X N = 0 . 3 ~and ~ by equating the calculated standard molar density of the residue to the experimental value ( p z + ) . The following equation can therefore be solved:
QN
with
QA
QP
with
Ail and Bil are constants determined by Abdoul et al. (1992) for the 12 groups appearing in the petroleum fluids. These values are recalled in Table 1.
In eq 9, the standard density (15 “C, 1 atm) of the three compounds ( p ~ PA, , and pp) is calculated using the Rackett equation which has been modified by
4018 Ind. Eng. Chem. Res., Vol. 34,No. 11, 1995 Table 1. A!,har and B h a r Values Necessary To Estimate the Binary Interaction Parameters
1 2 3 4 5 6
1
2
3
4
5
6
7
8
9
10
11
12
0.0
779.7 0.0
326.8 77.0 0.0
494.8 284.6 222.1 0.0
356.7 149.3 18.4 36.2 0.0
1890.1 857.8 1132.6 870.4 727.3 0.0
6293.1 1778.3 2912.5 3827.2 2816.5 2503.9 0.0
458.7 974.4 443.8 1125.6 287.0 1492.7 6433.9 0.0
22.1 670.8 1.2 307.9 55.6 1209.2 5093.9 78.6 0.0
4382.1 4082.1 4092.4 1733.0 3688.3 2775.7 5909.4 3915.6 3979.8 0.0
3143.5 2303.5 2311.0 0.0 3075.3 6985.2 7269.2 1300.0 2847.7 3688.0 0.0
5216.2 4380.2 3939.1 0.0 4019.7 3243.5 -315.6 5441.0 4875.2 4193.3 10176.4 0.0
7 8 9 10 11
12
1 2 3 4 5 6
1
2
3
4
5
6
7
8
9
10
11
12
0.0
1343.6 0.0
499.8 187.5 0.0
1293.0 457.4 310.7 0.0
1129.1 38.4 167.8 -66.9 0.0
3961.5 1341.1 1880.9 1905.4 1480.4 0.0
6347.9 1277.6 3695.0 4236.3 3278.8 3102.3 0.0
-1306.3 1836.2 -1319.4 498.3 5181.1 -622.3 35137.6 0.0
430.6 313.0 -3.6 -149.8 -416.0 1304.6 12829.9 247.1 0.0
5130.5 7890.8 6245.4 863.7 10714.1 2001.6 28472.5 5654.1 6909.5 0.0
-330.9 3800.6 3560.4 0.0 4724.9 12426.6 6542.2 1089.8 -417.4 5238.0 0.0
367.0 8852.1 4932.9 0.0 10820.4 36582.6 -631.2 722.2 5676.6 6179.5 13595.2 0.0
oil 7
oil 8
oil 9
oil 10
0.383 0.450 2.070 26.576 7.894 6.730 1.485 3.899 1.937 2.505 3.351 4.311 4.133 3.051 2.033 29.192
0.00 0.45 1.64 45.85 7.15 6.74 0.84 3.11 1.03 1.65 2.52 3.77 4.28 2.70 1.69 16.58
0.355 0.400 2.548 47.244 6.937 4.805 1.190 3.063 1.441 1.964 2.877 3.001 2.919 2.454 1.973 16.829
1.40 0.15 5.40 56.21 5.99 3.93 0.94 2.23 0.90 1.05 1.59 1.88 1.79 1.60 1.41 13.53
0.900 0.083 3.463 36.459 10.993 6.822 1.215 3.716 1.576 2.546 3.488 3.649 3.377 2.869 2.211 16.633
0.9113 308.0 394.25 145.8
0.8835 288.0 387.45 255.6
0.8758 277.6 394.25 245.7
0.8759 291.0 394.25 328.6
0.8820 278.5 369.24 187.4
7 8 9 10 11 12
Table 2. Composition and Physical Properties of the Crude Oils Investigated reservoir, mol % compd oil 1 oil 2 oil 3 oil 4 oil 5 oil 6 HzS Nz
coz
methane ethane propane isobutane n-butane isopentane n-pentane n-hexane n-heptane n-octane n-nonane n-decane (211- (residue)
0.00 0.12 0.07 0.64 0.56 1.44 0.55 2.34 1.79 2.74 5.34 8.51 8.40 6.65 5.17 55.68
0.36 0.33 0.54 9.82 5.93 6.84 1.49 4.78 2.26 3.46 5.12 5.51 5.25 4.88 3.72 39.71
0.00 0.08 2.28 32.39 6.58 6.23 1.51 3.96 1.88 2.63 3.88 4.23 3.89 3.45 2.87 24.14
0.8843 345.0 338.15 5.5
0.9108 320.0 366.15 46.5
0.8623 258.0 394.25 167.1
0.00 0.07 0.72 34.84 12.72 6.69 0.54 2.48 1.04 1.65 2.75 4.30 4.78 3.63 2.37 21.42
0.00 0.34 0.00 59.95 8.36 4.29 0.75 1.03 0.70 0.74 1.74 2.16 3.85 2.99 2.07 11.03
Residue Characteristics Q;:+,
gicm3
flc*
Tdep, K bubble pt a t Tdep,bar
0.8860 312.0 405.15 181.0
Spencer and Danner (1973):
The n-alkane is chosen so as to reproduce the experimental molar weight of the C l l f residue, i.e., t o solve eq 11 as precisely as possible:
For these three molecules, the different physical parameters necessary t o solve the equation of state (EOS) or eq 10, i.e., T,, P,, V,, a,Zm,are estimated by the group contribution methods developed by Rogalski and Neau (1990).
0.8732 275.0 366.45 366.3
The great advantage of this C11+ characterization is due t o the fact that the only experimental values necessary to apply it are the experimental molar weight and density of the C11+ residue. (c) Grouping Method. As previously mentioned, three pseudocomponents (C4, C~-CIO,and C11+) can be defined to describe a crude oil. Each pseudocomponent is represented by two, seven, and three pure compounds, respectively. The equation_of state parameters for each pseudocomponent ( n k and bk) were estimated as follows. Let Nk be the number of components i in one pseudocomponent ck andp the total number of components in the fluid, x k is the mole fraction of the pseudocomponent c k in the fluid, and Z i is the internal mole fraction of component i in this pseudocomponent. The properties of the pseudocomponents were estimated using the
Ind. Eng. Chem. Res., Vol. 34,No. 11, 1995 4019 I.'
7
1
fV4
h 'lbu.
0.8 0.0
Oil1 (q30 = 0.62)
100.0
400.0
Oil2 ( 9 3 0 = 0.69)
1.1.
1.2
fVd
Oil3 (930 = 0.81)
-
+ 1.0.
1.0.
+ \
pmpr.
0.8 i
pmpr.
0.8 7
0.0
Oil4 ( 9 3 0 = 0.80)
Oil5 ( 4 3 0 = 1-01)
I
100.0
600.0
Oil6 (q30 = 0.72) ..-
0.0
300.0
t
400.0
Oil8 (q30 = 0.89)
Oil7 ( 4 3 0 = 0.85)
Oil9 ( 9 3 0 = 1.05)
e
L 0.0
200.0
Oil10 (q30 = 0.88) Figure 1. Prediction of the variation of the relative volume vs pressure during a constant mass expansion for the 10 crude oils selected in this study.
method proposed by Carrier (1989) and Carrier et al. (1989). Nh
6k =
Z6izi i=l
Nk
E , = ccizi i=l
(12) with
(d) Results. When it is used with a well-defined composition for the reservoir fluid, this predictive method (Neau et al., 1993) can predict the variation of the relative volume vs pressure during a constant mass expansion with an average overall deviation of less than 1%,the variation of the relative volume vs pressure during a differential vaporization with an average
4020 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 Table 4. Prediction of the Bubble Point and of the Swollen Volume during a Swelling Test Using the Predictive Method of Neau et al. (1993)
cndeoildon?ain
gasmnders& dolnain
w domain
oil 1
G1
oil 1
G2
oil 2
G3
Figure 2. Phase envelope of an undersaturated crude oil. = ?!.I
P
I
?it
m i
T
-
7“.
oil 3
7
7.7-
-
T”,
Figure 3. Schematic illustration of an experimental swelling test. 300.0
G1
0.00 0.18 0.20 0.29 0.36 0.00 0.32 0.50 0.64 0.79 0.00 0.15 0.26 0.34 0.41 0.46 0.50 0.00 0.19 0.34 0.42 0.49 0.54 0.58 0.60
5.5 104.2 122.9 184.7 248.6 5.5 57.6 107.7 159.7 230.0 46.5 92.7 135.0 177.9 218.4 253.8 285.8 167.1 240.8 304.3 355.4 402.5 442.9 485.3 502.8
3.6 97.4 111.9 166.2 222.0 3.6 67.4 117.1 164.3 232.8 44.8 94.3 138.8 181.2 219.7 252.3 280.3 151.6 225.2 294.9 337.2 375.4 408.2 434.8 448.7
1.000 1.047 1.056 1.082 1.112 1.000 1.115 1.230 1.402 1.904 1.000 1.045 1.085 1.126 1.165 1.200 1.232 1.000 1.092 1.200 1.271 1.345 1.420 1.483 1.524
1.000 1.049 1.057 1.088 1.122 1.000 1.118 1.255 1.449 1.983 1.000
1.046 1.091 1.136 1.180 1.220 1.255 1.000 1.093 1.200 1.277 1.359 1.441 1.518 1.563
Amount of injected gas. Experimental bubble point. Calculated bubble point. Experimental swollen volume. e Calculated swollen volume.
obtained using a very detailed composition of the cuts (up to C45) measured by nuclear magnetic resonance.
I ~
Experimental Data Bank
\
X,=032
P 500.0
3,
700.0
Figure 4. Phase envelopes of the different fluids successively present in the cell during a swelling test. Table 3. Composition of the Lean Gases Used To Swell the Crude Oils Oil 1, Oil 2, and Oil 3 G2, mol % G3, mol % compd G1, mol % 2.06 0.00 0.00 H2S 3.27 0.00 0.00 N2 2.77 0.00 0.00 coz 60.37 85.33 methane 100.00 5.27 4.24 0.00 ethane 1.21 0.00 14.02 propane 0.25 0.00 8.65 isobutane 0.40 0.00 11.38 n-butane 0.00 0.00 0.16 isopentane 0.12 0.31 0.00 n-pentane 0.12 n-hexane 0.00 0.00 0.00 0.07 0.00 n-heptane ~~
overall deviation of 4.3%,and the saturation pressure and the tank oil density with an average overall deviation of 2.7% and 2.5%, respectively. Moreover, Jaubert et al. (1995) have shown that this predictive method could lead t o results as accurate as those
In this study, 10 crude oils from different fields were used in various gas injection experiments. Data on the experimental composition of these oils noted as oil 1t o oil 10 are listed in Table 2. Initially, the predictive method of Neau et al. (1993) was used to check the accuracy between experimental and calculated relative volumes during a constant mass expansion. In this kind of experiment, the composition of the fluid is kept constant during the depletion, and at each pressure, the relative volume is calculated by Vrel = VtotalWsat, where Vtotal and Vsat are respectively the total volufne and the liquid volume at saturation pressure. The curves obtained are illustrated in Figure 1. This figure shows that a good prediction of the experimental PVT data for the different crude oils is obtained. It should be noted that the predictive method should be used in conjunction with the detailed composition of the cuts from CF, to (210, Le., their internal composition in paraffinic, naphthenic, and aromatic compounds. In this study, however, because of the absence of a TBP distillation, the cuts from C5 to CIOwere modeled with the corresponding n-alkane only. This remark explains why the relative volumes during depletion of oils 5 and 9 are not very accurately predicted. The q 3 0 parameter shown for each oil in Figure 1 refers to the parameter recently defined by Jaubert and Neau (1995). This parameter permits the classification of a crude oil as either “classical” or “critical-like”. For all of the selected crude oils, the 4 3 0 parameter is less than 1.3, and thus, all of these oils can be described as classical. In this case, it is not surprising that, even with limited compositional data, the predictive method
Ind. Eng. Chem. Res., Vol. 34,No. 11, 1995 4021 I
I
T=T,, 5.0
'
cp
+ -
pA,,,
-
relative volume vs pressure.
leads to accurate results. It is recalled that the definition of this parameter is q30
=
0.3Ps Ps - P(~=0.3)
(14)
where Pa is the bubble point at the depletion temperature and P(u = 0.3) is the diphasic pressure corresponding to a vaporization rate ( u ) of 0.3 a t the same temperature. It is important to note that oils 5 and 9, the relative volumes of which are not accurately predicted, have the highest values of this parameter. Oils 1, 2, and 6 have the lowest values of 430 and the most accurate predicted relative volumes. In this last case, the bubble points corresponding to the breakover point in the relative volume curve are also accurately predicted.
Swelling Test (a) Introduction. Let us consider an undersaturated crude oil, i.e., a crude oil the bubble point of which (Psat) a t the reservoir temperature (Z'res) is lower than the reservoir pressure (Pres). The phase envelope typical for such a crude oil is illustrated in the (P,T) diagram shown in Figure 2.
When a gas is injected into such a crude oil, it may dissolve completely into solution. This has the effect of "swelling" the oil, i.e., increasing its volume. The purpose of this laboratory experiment is t o determine the degree t o which the injection gas will dissolve into the crude oil at the reservoir conditions (Tres and Pres). The greatest quantity of gas which may be dissolved will lead to a saturated crude oil whose bubble point is equal to the reservoir pressure (Pres). (b) Experimental Procedure Discussion. The experimental procedure used by the French petroleum company TOTAL is schematically represented in Figure 3 and may be summarized by the following steps. Step 1. A sample of the crude oil is introduced into a visual PVT cell thermostated at the reservoir temperature. A constant mass expansion is then performed in order t o define the bubble point (Pfat).The volume at the saturation pressure is recorded and noted as Step 2. A predetermined amount of gas is introduced into the PVT cell. The pressure is increased until only one phase is present. In practice, a constant mass expansion is performed to determine the bubble point of the new mixture which corresponds t o the breakover point in the plot of the relative volume vs pressure. During a swelling test, the relative volume is simply
Cat.
4022 Ind. Eng. Chem. Res., Vol. 34,No. 11, 1995 300.0 I
+ % 0.50
0.00
1.00
0.50
0.00
Oil1 - G1 (TJK = 338.15) 800.0 I
1
1
1.oo
Oil1 - G2 (T,JK = 338.15) 'I 4
I Phar
1
600.0
400.0 7
5 0.00
0.50
1.oo
0.0 0.00
0.50
Oil2 - G3 (T,JK = 366.15)
1.oo
Oil3 - G1 (T,JK = 394.25)
Figure 6. Variation of the bubble point vs quantity of injected gas during a swelling test.
defined as v s y
=
total volume in the cell (at P and TreJ
(15)
t a t
Step 3. Step 2 is repeated until the bubble point of the mixture (initial crude oil dissolved gas) reaches the reservoir pressure, i.e., the mixture keeps single phase under reservoir conditions. The amount of dissolved gas may be 4 times higher than the initial number of moles of crude oil. After each gas injection, the following data are obtained: the bubble point Psat(k); the density of the saturated oil present in the cell, p z t ( k ) = p$t(Psat(k),Tres); the swollen volume defined as VS,&) = V s a t ( k ) e a t , where Vsat(k) is the volume of the saturated oil at P = P s a t ( k ) after the injection of k predetermined amounts of gas. We have plotted in Figure 4 the phase envelopes of the different fluids obtained after the injection of determined amounts of gas into a specified crude oil. This figure shows that the bubble point of the fluid can increase considerably after it is injected with gas. Moreover, this figure shows that the critical point of the newly formed fluid approaches the reservoir tempera-
+
ture, which means that the larger the quantity of gas injection, the more critical the newly formed oil becomes. If the critical temperature of the fluid becomes lower than the reservoir temperature, this fluid becomes a gas condensate (see Figure 2). In Figure 4,the amount of injected gas, noted as Xgas, is defined by
X,,, = no. of moles of dissolved gas/(no. of moles of dissolved gas + no. of moles of oil initially in the cell (step 1)) This definition allows us to consider the injection gas and the crude oil as a pseudobinary mixture, the mole fractions of which are Xgas and 1 - Xgas, respectively. As illustrated in Figure 5, the experimental curves giving the variation of the relative volume TF1'(see step 2) vs pressure allow us to plot the variation of the swollen volume and the variation of the bubble point vs Xga,. The curve giving the variation of the swollen volume vs pressure stops experimentally when the bubble point of the newly formed crude oil (original crude oil dissolved gas) reaches the reservoir pressure. However, in theory, this curve stops when the critical composition (XCP) is reached, Le., when the new fluid is a gas condensate.
+
'
7.0
"
"
"
' ~vsvmn
7.0
4-
5.0
-
5 .o
3.0 -
3 .O
1.o
1.o
0.5
0.0
1.0-
1
-
1
1
~
I
I
Q
I
T
!
1
b + )
I
-
Oil1 G1 (T& = 338.15) 0
I-
Oil1 G2 (TJK = 338.15) l
1
I
I
I
1
I
I
I
1
I
3.0 2.0
2.0
1.o
0.0
0.5
-
Oil2 G3 (T& = 366.15)
0.5
0.0
-
Oil3 G1 (T& = 394.25)
Figure 7. Variation of the swollen volume vs quantity of injected gas during a swelling test. Table 5. Calculation of the First Contact Minimum Miscibility Pressure oil considered injected gas calcd FCMP,bar oil 1 G1 893.10 281.77 oil 1 G2 739.19 oil 2 G3 604.10 oil 3 G1
The P-X curve (see Figure 5c) obtained has the same appearance as that obtained for a mixture of two pure compounds, although several fundamental differences must be noted. The critical point is, in general, not at the top of the curve; that is, it may be located on either side of the stationary point of the curve. ForXgas= 0.0, we have two pressures corresponding to the bubble point and to the dew point of the crude oil (obviously for a mixture of two pure compounds, these two pressures are identical and are equal to the saturation pressure of the less volatile pure compound). For X,,, = 1.0,the curve may be closed or opened, depending only on the relative values of the gas maxcondentherm MT,,, and of the reservoir temperature (Tre,). Note that MTga, is the maximum value of the temperature at which it is possible to obtain a diphasic mixture, i.e., the highest temperature of the phase envelope in a (P,T) diagram (see Figure 2). If MTga, < Tre,, it is obvious that, for
XFa, = 1.0 the gas is monophasic and the P-X curve wlll close at a given value of X,,, such that Xga, < 1.0. This situation occurs with a mixture of two pure compounds when the more volatile compound is supercritical (T> Tc). If MT,,, > T,,,, then fOrXgas= 1.0,it is possible t o define for the gas a t the reservoir temperature an upper dew point and a lower dew point. The curve will then be opened, exhibiting two distinguished parts. For a mixture of two pure compounds, these two dew points are identical and represent the saturation pressure of the more volatile compound a t the considered temperature. The top of the P-X curve is very important for petroleum companies since it represents the first contact minimum miscibility pressure (FCMP). This means that, a t a pressure higher or equal t o the FCMP, all possible mixtures of the two fluids (the crude oil and the injected gas) are single-phase fluids at the considered temperature. This pressure is scarcely determined experimentally but may be easily calculated. (c) Results. Predictive Method. Swelling tests were performed on three oils (oil 1,oil 2,and oil 3)with three different lean gases denoted as G1,G2, and G3. G1 is pure methane, whereas G2 and G3 are lean gases whose composition is given in Table 3.
4024 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995
14
1
400 0 -
200 0
1
I/,;
00 0 00
1 %
0 50
1 00
Figure 8. Calculation of the bubble points during a swelling test performed on oil 3 using tuned EOS parameters for the Cii+ fraction. Starting parameters (predictive method): TJK = 762.96, PJbar = 15.57, w = 0.7300, and Z u = 0.2469. Tuned TJK = 780.09, PJbar = 17.25, o = 0.7300, Zm = 0.2469. q-4 rh
1
TNI
T-1,
T-T,
1-1,
Figure 9. Schematic illustration of the backward MCT experiment. A
1
4
1
\
'
k P * I
'
P i
Figure 10. Phase envelopes of the different liquid phases present in the cell during a backward MCT experiment.
The predictive method of Neau et al. (1993) was used to predict the variation of the bubble point and of the swollen volume vs amount of injected gas. The results are shown in Table 4 and in Figures 6 and 7. Figure 7 shows that the swollen volume is accurately predicted using the predictive method of Neau et al. (19931, even when the quantity of the injected gas is very significant. For example, X g a , = 0.8 corresponds t o a system in which 4 g-mol of gas have been injected per g-mol of crude oil. The same conclusion can be made for the prediction of the bubble point (see Figure 6) except for oil 3, where the values of the bubble points are overestimated when the quantity of gas injected becomes significant Ur,, > 0.5). On closer examination of the predicted bubble points, it appears that the very heavy oils, i.e., those that have less than 10% methane, are better predicted than the oils whose methane content is higher than 30%. Our program is also capable of determining the FCMP between the oil and
Figure 11. Ternary diagram giving an approximate representation of a backward MCT. Table 6. Composition of the Lean Gases Used during Backward MCT Experiments compd G1, mol % G4, mol % Nz methane ethane propane isobutane n-butane isopentane n-pentane n-hexane n-heptane n-octane n-nonane n-decane
0.00 100.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.28 85.06 6.77 3.21 0.53 0.61 0.31 0.30 0.61 0.56 0.82 0.61 0.33
the gas considered. These values are summarized in Table 5, but no experimental data are available for comparison. Tuning of Equation of State Parameters. The tuning process recently described by Jaubert and Neau (1995) was used to improve the calculation of the bubble points for oil 3. In this study the equation of state parameters for the C11+fraction were tuned. This tuning process consists of first tuning the critical pressure and the critical temperature of the Cll+ fraction; the acentric factor and the Rackett compressibility factor are those given by the predictive method. In the second step, the acentric factor and the Rackett compressibility factor are also fitted. The experimental data included in the tuning process are the relative volume during a constant mass expansion performed on the reservoir crude oil, its bubble point, and the tank oil density. The swelling data are not taken into account a t any stage of the tuning process but are instead calculated using the fitted parameters. The improvement obtained is clearly demonstrated in Figure 8. In conclusion, we advice tuning the EOS parameters using the experimental relative volume data before performing a swelling test calculation when the crude oil methane content is higher than 30%. For heavy crude oils, i.e., those that have less than 10%methane, this tuning process, taking PVT data into account, does not improve the results of the swelling test and may in some cases lead to worse results.
Multicontact Test (a)Introduction. The procedure for a multicontact test is as follows. At constant temperature (usually at the reservoir temperature, T,,,)and pressure, a gas
Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 4025 Table 7. Comparison of Experimental and Calculated Compositions of the Phases in Equilibrium When Gas G1 Was Injected into Oil 4 during a Backward MCT Experiment exptl comp, mol % compd Nz
coz
methane ethane propane isobutane n-butane isopentane n-pentane n-hexane n-heptane n-octane n-nonane n-decane C11- (residue)
Nz
coz
methane ethane propane isobutane n-butane isopentane n-pentane n-hexane n-heptane n-octane n-nonane n-decane C11- (residue)
Nz
con
methane ethane propane isobutane n-butane isopentane n-pentane n-hexane n-heptane n-octane n-nonane n-decane C11- (residue)
NZ
coz
methane ethane propane isobutane n-butane isopentane n-pentane n-hexane n-heptane n-octane n-nonane n-decane C11- (residue)
contact no.
Table 8. Comparison of Experimental and Calculated Compositions of the Phases in Equilibrium When Gas G4 Was Injected into Oil 5 during a Backward MCT Experiment
calcd comp, mol %
liquid phase
gas phase
liquid phase
gas phase
0.07 0.01 44.24 3.64 2.94 0.28 1.33 0.68 1.01 2.21 3.92 4.85 4.02 2.82 27.97 0.07 0.01 43.92 1.48 1.55 0.16 0.68 0.45 0.65 1.81 3.41 4.90 4.06 3.21 33.64 0.03 0.00 45.11 0.49 0.62 0.05 0.27 0.22 0.20 1.22 2.40 4.49 4.20 3.27 37.41 0.00 0.00 42.23 0.04 0.07 0.01 0.11 0.12 0.23 0.79 2.04 4.87 4.48 3.43 41.58
0.01 0.29 90.37 4.12 1.85 0.14 0.61 0.22 0.36 0.45 0.56 0.47 0.25 0.11 0.19 0.01 0.00 96.06 0.95 0.65 0.06 0.30 0.12 0.19 0.28 0.45 0.34 0.28 0.08 0.23 0.01 0.00 98.32 0.23 0.22 0.03 0.10 0.06 0.11 0.16 0.29 0.21 0.08 0.07 0.11 0.01 0.00 99.11 0.11 0.13 0.01 0.04 0.03 0.00 0.12 0.14 0.04 0.06 0.06 0.14
0.01 0.17 39.50 3.50 2.78 0.29 1.40 0.72 1.17 2.34 4.21 5.20 4.29 2.98 31.44 0.00 0.03 40.81 0.85 1.03 0.14 0.71 0.44 0.74 1.76 3.60 4.89 4.32 3.16 37.52 0.00 0.00 41.04 0.13 0.26 0.05 0.26 0.20 0.36 1.05 2.57 3.98 3.89 3.06 43.16 0.00 0.00 40.97 0.02 0.07 0.02 0.09 0.10 0.17 0.63 1.82 3.17 3.40 2.85 46.69
0.03 0.24 90.35 4.14 1.92 0.14 0.61 0.22 0.34 0.46 0.58 0.50 0.29 0.14 0.03 0.00 0.05 96.06 1.00 0.69 0.06 0.29 0.12 0.20 0.31 0.43 0.40 0.24 0.12 0.02 0.00 0.01 98.32 0.15 0.17 0.02 0.10 0.05 0.09 0.18 0.29 0.30 0.20 0.11 0.02 0.00 0.00 99.01 0.02 0.04 0.01 0.04 0.03 0.04 0.10 0.20 0.23 0.17 0.09 0.02
(fresh gas) is injected into a sample of crude oil (fresh oil) in order to form a diphasic fluid. Either the equilibrium gas or the equilibrium oil is then removed from the cell, and the remaining saturated fluid is recontacted with either fresh gas or fresh oil. The repeated contacts may lead to a system remaining single phase. The goal of this study is to determine whether after several contacts, a t the chosen pressure, the
exptl comp, mol % compd
NZ methane ethane propane isobutane n-butane isopentane n-pentane n-hexane n-heptane n-octane n-nonane n-decane C11+ (residue)
Nz methane ethane propane isobutane n-butane isopentane n-pentane n-hexane n-heptane n-octane n-nonane n-decane C11- (residue)
Nz methane ethane propane isobutane n-butane isopentane n-pentane n-hexane n-heptane n-octane n-nonane n-decane CU+ (residue)
NZ methane ethane propane isobutane n-butane isopentane n-pentane n-hexane n-heptane n-octane n-nonane n-decane C11- (residue)
contact no.
liquid phase
gas phase
0.27 57.51 7.99 4.10 0.71 1.01 0.63 0.81 1.90 2.28 4.06 3.38 2.29 13.08 0.30 55.93 7.69 4.05 0.72 1.04 0.64 0.87 2.03 2.34 4.02 3.39 2.35 14.61 0.20 54.89 7.17 3.99 0.77 1.15 0.65 0.89 2.23 2.54 4.26 3.46 2.42 15.38 0.10 56.47 6.65 3.91 0.78 1.17 0.60 0.75 1.83 2.14 4.03 3.42 2.51 15.64
0.32 81.45 7.22 3.49 0.59 0.70 0.41 0.35 0.75 0.80 1.29 0.89 0.56 1.19 0.27 82.56 7.01 3.33 0.54 0.64 0.34 0.33 0.71 0.73 1.19 0.91 0.52 0.92 0.31 83.37 6.99 3.28 0.53 0.61 0.33 0.33 0.65 0.62 0.97 0.78 0.45 0.78 0.30 83.30 6.92 3.27 0.54 0.63 0.34 0.36 0.78 0.75 1.03 0.75 0.40 0.62
calcd comp, mol % liquid gas phase phase 0.20 60.35 7.56 4.39 0.82 1.06 0.69 0.72 1.74 2.11 3.79 3.07 2.11 11.39 0.16 60.45 7.20 4.44 0.86 1.08 0.68 0.71 1.73 2.07 3.73 3.12 2.14 11.63 0.15 60.45 7.04 4.47 0.89 1.09 0.68 0.70 1.73 2.03 3.68 3.16 2.15 11.78 0.15 60.42 6.99 4.49 0.90 1.10 0.68 0.69 1.72 2.00 3.63 3.18 2.16 11.89
0.37 83.23 7.38 3.22 0.50 0.62 0.34 0.34 0.68 0.69 1.05 0.71 0.41 0.47 0.30 83.71 7.02 3.24 0.52 0.62 0.33 0.33 0.67 0.67 1.01 0.71 0.41 0.46 0.28 83.92 6.87 3.25 0.53 0.63 0.33 0.32 0.66 0.65 0.98 0.71 0.41 0.45 0.28 84.02 6.81 3.26 0.54 0.63 0.33 0.32 0.66 0.64 0.97 0.71 0.40 0.45
system will remain monophasic regardless of the quantity of injected fluid. If after each contact the remaining saturated fluid becomes more critical, i.e., its critical temperature it is approaches the experimental temperature (T,,,), possible to determine whether during a gas injection the miscibility develops a t the front (the remaining gas phase becomes more critical) or at the injection point (the remaining liquid phase becomes more critical). (b)Backward MCT. Experimental Procedure. The procedure is schematically represented in Figure 9 and may be summarized by the following steps.
4026 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 ,
,
,
,
,
,
,
!
,
,
4
I
7
,
+ experimental liquid composition 4.0
~
x calculated liquid comporition 0o calculated ~ gas~composition l ~
a
s
c
R
~
o
2.0
0.0 N I C G C I CI Cj iC4
G iC3 CJ Cs C7 CCCg Clo (
First contact (T" = 405.15 K,PeV= 181 bar)
Second contact (TE8= 405.15 K,Pexp= 18 1 bar)
7"""""""' 4.0
2.0
0.0 NICQCI CI Ci iG C4 iC5 CJ c6 C7 Ca C9 CioCii+
NICQCI CI CJ iC4 G iCJ CJ Cg C7 Ce C9 CIOCil+
Third contact (T" = 405.15 K,PeV = 181 bar)
Fourth contact (T" = 405.15 K,PeV = 181 bar)
Figure 12. Comparison of experimental and calculated compositions of the phases in equilibrium when gas G1 was injected into oil 4 during a backward MCT experiment.
Step 1. A sample of the crude oil is introduced into a visual PVT cell thennostated at reservoir temperature (Tres); the pressure is kept constant at a value higher than the bubble point of the crude oil (P,,t) in order to have a single-phase fluid. The pressure and temperature are kept constant during the experiment. Step 2. A predetermined amount of gas is introduced into the PVT cell in order to obtain a diphasic fluid. When the thermodynamic equilibrium has been obtained, all the saturated gas phase is removed from the cell and analyzed by gas chromatography. The composition of the liquid phase is determined by a mass balance. Step 3. Step 2 is usually repeated 3 or 4 times. If it is impossible to obtain a diphasic mixture, the two fluids (crude oil and injected gas) are defined as being miscible. Discussion. After each contact between the lean gas and the crude oil, a saturated oil, Le., whose bubble point is equal to the experimental pressure, is present in the cell. The evolution of the phase envelopes of these saturated liquid phases are plotted in Figure 10 for a selected crude oil. In this example, the pressure of the cell was Pexp = 271 bar > Psat and the temperature was T = 377.55 K. It is possible to check in this case
that the critical temperature of the different liquid phases (CP1, ..., CP4) approaches the reservoir temperature (Tres);i.e., they become more critical. This gas could be used to develop miscibility at the injection point. To better understand what is happening, it is useful to describe the fluid with only three pseudocomponents: the light components (HzS, N2, COz, CI), the intermediate components (Cz-Cs), and the heavy components (C7+). With the temperature and pressure constant, it becomes possible to plot the phase envelope in a ternary diagram (see Figure 11). In this figure, the point Ores represents the reservoir crude oil initially introduced in the cell and the point Go,the injected gas. As expected, the different liquid phases (LI, L2, L3, and L4) move toward the critical point
(CP). ( c ) Forward MCT. The experimental procedure is identical to that for a backward MCT, but initially the cell is filled with the lean gas to which different amounts of crude oil are added. At each step, the liquid phase is removed from the cell. In this case, the different saturated gas phases successively present in the cell have the same dew point, i.e., the experimental pressure, at the reservoir temperature.
Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 4027 + cxparjrmosltrlliquid composition x
calcullJtcdliquid conporition
o expaimartrl gm comportion
4.0
4.0
0 calculated gas compooition
A:
2.0
2.0
(T" = 363.45 K, Pap = 366 bar)
4.0
4.0
2.0
2.0
0.0
0.0
NZCI Ca 6 i G G iCs Cs C6 C7 CB C9 CIOCII+
Third contact (T* = 363.45 K, Pexp= 366 bar)
Fourth contact (T* = 363.45 K, POxp= 366 bar)
Figure 13. Comparison of experimental and calculated compositions of the phases in equilibrium when gas G4 was injected into oil 5 during a backward MCT experiment. H2S + N2+ CO>+C,
component i in the liquid phase or in the gas phase. These figures show that the predictive method of Neau et al. (1993) allows us to calculate, with a good accuracy, the composition of phases in equilibrium during a backward MCT. The last contacts are, in general, predicted with less accuracy. This may be explained by the fact that the errors are accumulating as the number of contacts increases.
MMP Calculations
Figure 14. Condensing gas drive mechanism.
(d) Results. Backward MCT's were performed on two different crude oils (oil 4 and oil 5) with two different lean gases (G1 and G4). G1 is pure methane, and the composition of G4 is given in Table 6. The predictive method was used t o calculate the compositions of the different phases in equilibrium, and these values were compared to the experimental ones. Each time four contacts were performed, and the results are summarized in Tables 7 and 8. In Figures 12 and 13 are shown the variations of the neperian logarithm of the sum 1 x i , where xi stands for the mole percent of
+
(a) Theoretical Background. When a gas is injected into a reservoir crude oil, miscibility may develop at the front or at the well bore. These effects are most commonly explained by the condensing or the vaporizing gas drive mechanisms (Stalkup, 1983). Condensing Gas Drive Mechanism. This mechanism occurs when a rich injection gas displaces an oil that is relatively lean in the intermediate components. In this process, the oil near the injection point (at the rear) is enriched in intermediate components by repeated contacts with the injection gas. As illustrated in Figure 14, the intermediate components of the gas condense into the oil, moving the composition of the oil toward the critical point on the phase envelope. The oil may become so enriched with the intermediate
4028 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 Light
Heavy
Intermediate
Figure 15. Vaporizing gas drive mechanism.
I
-l--I (1) washing fluid cell (21 Constant temperature reservoir cell (31Constant temperature injection gas cell (41 Thermostated slim tube 151 Atmospheric separator 6)Gasometer (7) High accuracy automatic balance
Figure 16. Slim tube apparatus used by the French petroleum company TOTAL.
components that it may become miscible with the gas; i.e., any mixture of the newly formed oil and the injected gas remains monophasic (this is the case for Goand L3 in Figure 14). Vaporizing Gas Drive Mechanism. This mechanism takes place when a lean gas, e.g., nitrogen, is injected into a crude oil containing a high percentage of intermediate components. In this process, the gas (at the front) is enriched in intermediate components by repeated contacts with the original crude oil, moving the composition of the gas on the dew point curve of the phase envelope toward the critical point. The gas may become so enriched with the intermediate components that it may become miscible with the oil (see Figure 15). (b)Experimental Determination. In the laboratory, the MMP experiments are performed on a synthetic porous medium (slim tube filled with glass beads) which reproduces multiple-contact equilibria between the reservoir oil and the injected gas at the reservoir temperature. A schematic diagram of the apparatus is shown in Figure 16, and its main characteristics are as follows: tube length, 8-12 m; internal diameter, 0.635 x m; porosity, 38%; injection rate, (10-13) x m3h; glass bead diameter, 63 x m; working temperature range, 20-180 “C;working pressure range, 0-600 bar. The reservoir oil to be tested is placed in a PVT cell (2 in Figure 16). Two liters of reservoir oil is usually required per MMP determination. The injection gas can be prepared by recombination of field samples or by synthesis from pure components. Before each displacement, the slim tube is cleaned by injection of specific
solvents. The displacement pressure is then selected, and the pore volume of the slim tube is measured at that pressure by injecting a heavy refined oil at the reservoir temperature. The reservoir oil is then injected into the tube at the displacement pressure so as t o displace the refined oil. The gas-oil ratio (GOR) of the produced oil is checked to be sure that a representative reservoir fluid is in the tube. Injection gas is then introduced at the same conditions, and production parameters are recorded (volume of gas produced and weight of oil produced) as well as volume of gas injected. The instantaneous GOR and cumulative oil production are plotted as a function of injected gas (expressed as pore volume fraction) for each displacement pressure (see Figure 17a and b). For each displacement pressure, two characteristic recovery values are defined: oil recovery (% IOIP, i.e., weight percent of initial oil in place) at gas breakthrough and oil recovery (% IOIP) at one pore volume (1 PV) of injected gas. As illustrated in Figure 17, b and c, when the displacement pressure is higher than the minimum miscibility pressure (MMP),the miscible front has been created, and therefore, the pressure has little influence on the recovery factor at gas breakthrough (or at 1PV of injected gas). As shown in Figure 17b, in such cases, the recovery factor reaches value close t o 100%. This is not the case if the displacement pressure is below the MMP (see Figure 17a). Therefore, the plot of these oil recovery factors with respect to pressure allows us to determine the MMP as shown in Figure 17c. (c) Results. Five slim tube tests were performed on five different crude oils with five different natural gases noted as G5-G9. The compositions of these gases are given in Table 9. A computer program was developed t o determine which gas drive mechanism takes place (condensing or vaporizing) and to determine the MMP (Neau et al., 1995). The experimental values and the calculated values for the MMP are listed in Table 10. As can be seen, the calculated MMP values are, on average, around 20% greater than the experimentally determined values. The discrepancy between the experimental and calculated MMP’s is probably due to the PengRobinson EOS parameters which were not adjusted for conditions in the critical region. It is well known that this EOS is not able to predict correctly the critical point of the complex mixtures. Another possible explanation is given by Orr et al. (19811, who explain that a breakover point in the oil recovery curve may not always signify a change from immiscible displacement to a displacement that attains dynamic miscibility in the strict thermodynamical sense as used in this paper. These authors mention a “near miscible” displacement. A few more recent papers (Zick, 1986; Johns et al., 1992) explain that a condensing-vaporizing mechanism could take place in the slim tube instead of the pure condensing mechanism. The fundamental question is thus “does the slim tube experiment always lead to the thermodynamic MMP as calculated in this paper?”. It appears that this is not often the case, and under these conditions, the uncertainty of 20% may be regarded as acceptable.
M M E Calculations (a) Introduction. If, for a given injection gas and crude oil, the MMP is higher than the reservoir pressure, miscibility will not be achieved in the reservoir. The only way t o obtain miscibility, then, is to change
Ind. Eng. Chem. Res., Vol. 34, No. 11,1995 4029
Oil 7re-V
PhIU
100.0 .O
50.0
0.0 0.0
50.0
100.0
Figure 17. Experimental MMP determination. (a) The pressure is lower than the MMP, and the oil recovery factor remains low at gas breakthrough (or at 1PV of injected gas). (b) The pressure is higher than the MMP, and the oil recovery is close to 100% (at breakthrough or at 1 PV of injected gas). (c) Plot of the oil recovery with respect to pressure, allowing for the location of the experimental MMP. Table 9. Composition of the Injected Gases for M M P Determination compd
HzS Nz
coz
methane ethane propane isobutane n-butane isopentane n-pentane n-hexane n-heptane n-octane
G5,
G6,
G7,
G8,
G9,
mol %
mol %
mol %
mol %
mol %
0.02 0.55 5.29 81.84 8.94 2.72 0.21 0.31 0.04 0.04 0.04 0.00 0.00
1.07 1.01 4.24 56.47 15.15 10.76 1.92 4.23 1.44 1.53 1.14 0.75 0.29
0.00 0.49 1.82 81.39 9.15 4.67 0.50 1.24 0.20 0.26 0.09 0.06 0.13
2.72 0.22 4.43 66.10 6.41 12.04 0.50 6.93 0.24 0.23 0.12 0.03 0.03
2.74 0.60 5.47 74.41 10.38 4.40 0.54 1.02 0.20 0.19 0.05 0.00 0.00
the composition of the injected gas. In MME calculations, the temperature and pressure are kept constant and equal to the reservoir temperature and pressure, respectively. Different amounts of LPG (liquified petroleum gas), also called solvent, are added to the injection gas in order to change its composition. The lowest quantity of solvent required to achieve miscibility between the gas and the crude oil is called the minimum miscibility enrichment (MME). This definition is illustrated in Figure 18. In this example, injection of Go into Lo (crude oil) leads to, after several contacts, a
Table 10. Comparison between Calculated and Experimental (Slim Tube Test) MMP's MMP, bar oil gas exptl calcd % dev mechanism 396 3 G5 318 -24.5 vaporizing 318 -24.2 condensing 6 G6 256 7 G7 429 376 -14.1 vaporizing 8 G8 287 349 -21.6 condensing 9 G9 483 378 -27.8 vaporizing av -22.4
partial miscibility of both fluids by a vaporizing gas drive mechanism. Adding a significant amount of solvent So into Gocreates a new injection gas GI, which leads to a complete miscibility with Loby a condensing gas drive mechanism. It is thus easy to see that, in this case, the mechanism taking place is a function of the amount of solvent. (b)Experimental Determination. In the laboratory, the M M E is determined with the same apparatus used for the MMP determination (see Figure 16). In this case, the pressure is kept constant and equal to the reservoir pressure. Different gases formed by the combination of the initial injection gas (Go)and different amounts of solvents displace the reservoir crude oil. The instantaneous GOR and cumulative oil production (oil recovery) are plotted as a function of the injected gas,
4030 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995
than the MME. The comparison of these oil recovery factors allows us to determine the MME as shown in Figure 19c. ( c ) Results. Two slim tube tests were performed on oil 10 with two different natural gases noted as G10 and G11 but with the same solvent noted as So. The compositions of these fluids are given in Table 11. The subroutine used to calculate the MMP was slightly modified in order to estimate the MME. The calculated values, obtained using the characterizing procedure developed by Neau et al. (19931, and experimental values are listed in Table 12. The discrepancy between the experimental and calculated MME values may be explained in the same way as that observed for MMP calculations.
Light
*Lojl/ Intermediate
Heavy
Figure 18. Illustration of the MME definition.
expressed as pore volume fraction, for each enrichment (percentage of solvent added). When the enrichment is higher than the MME (Figure 19b),the miscible front has been created, and therefore, the enrichment has little influence on the oil recovery factor. The opposite case (Figure 19a) appears when the enrichment is lower 150.0
I -
0.0R
Conclusion This paper is the last of three papers in a series described as “characterization of heavy oils”. The first paper (Neau et al., 1993) described a procedure for characterizing the heavy fractions. It was shown that this predictive method was able to successfully predict the variation of the relative volume during a constant mass expansion or a differential vaporization. Com-
U
Oil recovery
Figure 19. Experimental MME determination. (a) The enrichment of the injection gas with the LPG is lower than the MME. The oil recovery at gas breakthrough remains low. (b) The enrichment of the injection gas with the LPG is higher than the MME. (c) Plot of the oil recovery with respect to pressure, allowing for the location of the MME.
Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 4031 Table 11. Composition of the Different Gases Used for MME Determination compd
G10, mol %
G11, mol %
So, mol %
H2S Nz CO2 methane ethane propane isobutane n-butane isopentane n-pentane n-hexane n-heptane
1.16 0.74 4.57 73.18 12.25 4.77 0.54 1.49 0.39 0.50 0.30 0.11
0.45 3.66 1.98 89.27 4.59 0.05 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 60.00 0.00 40.00 0.00 0.00 0.00 0.00
Table 12. Comparison between Calculated and Experimental (Slim Tube Test) MME’sa MME, % of solvent oil ~~~
eas
solvent
exptl
calcd
% dev
mechanism
So So
28.5 40.5
34.9 44.6
-22.5 -10.1
condensingb condensingb
~
OillO G10 OillO G11
In this example, T,,, = 369.25 K and P,, = 186.3 bar. Initially, gases G10 and G11 lead to a partial miscibility when they are injected into oil 10 by a vaporizing gas drive mechanism. b
parisons were made with other well-known predictive methods available in the literature. The second paper (Jaubert and Neau, 1995) defined a new parameter, noted as q 3 0 , which can indicate in advance the accuracy of the calculations performed with the predictive method. This parameter also leads to a new classification of crude oils. In the case where the crude oil is classified as “critical-like”, i.e., when the Peng-Robinson equation of state leads to significant deviations compared with experimental values for the relative volume during a differential vaporization, a tuning process coupled with variance analysis theory allows us to considerably improve the correlation of experimental data. In addition, Jaubert et al. (1995) have shown that this very simple characterizing method yields better results than those obtained from a complete analysis of a crude oil (up to C45)using NMR. This last paper shows that this predictive method (Neau et al., 1993) is also capable of satisfactorily predicting the gas injection behavior of a crude oil as indicated by the swelling test, multicontact test, MMP, and MME. However, in the case of MMP and MME calculations, significant deviations may appear between calculated and experimental values. The deviations are partly due to the deficiency of the Peng-Robinson EOS but are mainly due to the assumptions made in our program. In this work, our program assumes that either a condensing or a vaporizing gas drive mechanism is taking place during the gas injection. However, new mechanisms, different from the condensing and vaporizing gas drive mechanisms, have been recently evidenced and may explain the deviations observed. A new paper taking into account these new mechanisms will soon be published by us.
Nomenclature a = equation of state parameter 6 = equation of state parameter c = volume correction C P = critical point
E ~= J binary interaction energy kij = binary interaction parameter
m = equation of state parameter = molar weight MT = maxcondentherm p = number of components P = pressure PxP= experimental pressure Pres= reservoir pressure P , = critical pressure Ps = bubble point of a crude oil at the depletion temperature 430 = parameter allowing us to classify a crude oil as “classical”or as “critical-like” T = Temperature T , = Critical temperature Tdep= depletion temperature (reservoir temperature) T,,, = reservoir temperature u = vaporization rate or molar volume 8 = pseudomolar volume uc = critical molar volume Vrel = relative volume during an isothermal depletion v“?” = relative volume during a swelling test = reference volume Vswell= swollen volume 3c = mole fraction 2 = internal mole fraction ZRA = Rackett compressibility factor
M
Greek Symbols = saturated oil density
o = acentric factor a0 = fraction occupied by group j in molecule i y = equation of state parameter
Literature Cited Abdoul, W.; Rauzy, E.; Peneloux, A. A group contribution equation of state for correlating and predicting thermodynamic properties of weakly polar and nonassociating mixtures. I. Binary and multicomponent systems. Fluid Phase Equilib. 1992,68, 47102.
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Received for review December 27, 1994 Revised manuscript received J u n e 21, 1995 Accepted July 3, 1995@ IE940764L
@
Abstract published in Advance ACS Abstracts, September
15, 1995.
