Znd. Eng. Chem. Res. 1993,32, 1196-1203
1196
Characterization of Heavy Oils Evelyne Neau' a n d Jean-No41 J a u b e r t Laboratoire de Chimie Physique, Facultd des Sciences de Luminy, 13288 Marseille Cedex 9, France
Marek Rogalski Laboratoire de Thermodynamique Chimique et AppliquOe, ZNPL-ENSZC, 54042 Nancy Cedex, France
The PVT properties of petroleum oils were studied using a modified Peng-Robinson equation of state and a characterization procedure developed for this purpose. Experimental data on constant mass expansion and differential vaporization of petroleum fluids from different fields were used. It was shown that currently available experimental properties of petroleum cuts (densities, molecular weights and normal boiling temperatures) can be used to obtain satisfactory predictions of the PVT properties of crude oils. The present results were compared with those obtained by using the method proposed by Pedersen. Both methods gave good predictions of the liquid shrinkage curve and saturation pressures. The tank oil density was also predicted satifactorily with the present model.
Introduction Petroleum fluid modeling mainly consists of describing phase equilibria during depletion experiments performed, on the reservoir fluid, at constant temperature. For practical purposes, a pseudoization technique is used to model a fluid with a small number of pseudocomponents. Flash calculations are performed using a simple (usually cubic) equation of state. Once the number of pseudocomponents has been selected, their physical properties (the critical parameters, the acentric factor and the Rackett compressibility factor) have to be estimated, in order to establish equation of state parameters. This description in pseudocomponents is difficult for two reasons: First, the fluid is represented by components, which are not all very accurately defined. Second, petroleum mixtures contain a limited number of light components, the mole fraction of which can be determined, and very numerous heavy components, which cannot be precisely quantified and identified. In addition, the physical properties of these heavy components are usually unknown. In most cases, the components which are heavier than n-decane do not amount to more than a few percent of the total mole number of the fluid; but their accurate modeling is crucial for obtaining a good idea of the PVT properties of petroleum mixtures. This is particularly true in the case of gas condensate mixtures and, to a lesser extent, in the case of crude oils. The main difference between the two is that heavy cuts are in smaller amounts in gas condensate mixtures; however their modeling is more difficult. This is mainly due to the fact that the errors on the liquid mole number introduced by an equation of state are relatively greater in the case of condensategases, which produce a smaller amount of liquid during depletion. Heavy cuts contain large number of components, but they can be represented with a limited number of functional groups. Recent studies (including those by, Rousseau, 1987, and Dosseh, 1990) have shown that the relative amounts of these groups can be determined with NMR analysis. This is one possible way of describing heavy cut compositions. In order to make it applicable to petroleum calculations, an equation of state, with parameters established in terms of functional group composition, is needed. A modified Peng-Robinson equation of state (EOS), suitable for this purpose, was proposed
recently (Carrier et al., 1988, Rogalski and Neau, 1990, and Abdoul et al., 1992). Utilization of NMR characterization is still being studied at our laboratory and results will be soon published. In our opinion, this approach makes it possible to preserve the physical significance of the equation of state parameters, what is necessary for prediction and extrapolation purposes. Traditional methods based on empirical correlations are not completely reliable. In this paper, it is proposed to model the PVT and VLE properties of petroleum fluids. Two approaches to the fluid modeling are considered: The first one is a simplified version of the method described above (detailed analysis of light components and functional group contents of heavy single carbon number (SCN) cuts). In this study, heavy cuts are modeled with representative molecules, the choice and amounts of which are established on the basis of the experimental molar weights and densities of these cuts. The second one, which has long been traditional in petroleum industry calculations, consists in calculating physical properties of SCN cuts using empirical correlations. Recently, Pedersen et al. (1989a, 1989b) have proposed a similar method based on experimental molar weights and densities. In principle, both of these methods could be applied to gas condensates, but the prediction of PVT properties is not completely satisfactory. Though, this paper will be restricted to reservoir oils. Depletion experimentswere carried out on reservoir oils and the results were predicted with the two methods. The influence of heavy cut characterization on the quality of results obtained was investigated. Various compositional models of fluids were studied in order to establish the minimal number of components necessary to model the properties of crude oils.
Experimental Data To determine the VLE behavior of petroleum fluids, two kinds of depletion experiments are usually performed at constant temperature: constant mass expansion (CM) and differential vaporization (DV). In the first case, the composition of the fluid is kept constant during the
Q888-5885/93/2632-1196$Q4.QQ/Q0 1993 American Chemical Society
Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993 1197 Table I. Experimental Analysis of the Oils Investigated in This Study molecular density SCN cute comDosition weight (15 O C , 1atm) C, (4 I n 1 6 ) isoalkane C, n-alkane C, c, (7 I n I 10) isoalkane C, naphthene Cna aromatic C1, n-alkane C, c, (11I n I20+)
makes it possible to describe the liquid volumes more accurately (PBneloux et al., 1982) (Appendix I). For mixtures, classical mixing rules were used P
6 = C"Xi
~
a
Not available for C ~ cut. O
expansion and at each pressure, the experimental liquid shrinkage, D, also called the relative volume is calculated as follows
D
= VbdI Vmt
Vliquid/Vref
(2)
where Vfiquid is the liquid volume and Vref is the liquid volume at the final pressure, measured under atmospheric conditions (15 "C, 1 atm). The density of the tank oil is also measured, usually under atmospheric conditions. This oil is obtained after flashing the separator oil, which is itself obtained by flashing the reservoir fluid. For the lightest cuts (until Clo), the composition of the reservoir fluid is obtained from chromatographic analysis. The composition of the other cuts is calculated from the results of the TBP (true boiling point) distillation. The compositions of light components (Nz, COz, methane, ethane, propane) and following SCN cuts are specified as shown in Table I. The cut C, includes components, the boiling points of which are equal or lower than the one of the normal n-alkane. A more detailed analysis is performed by means of TBP distillation: the molecular weights and densities of the cuts, from C7 to C ~ O +are , measured. Twenty-six depletion results (14 CM and 1 2 DV) obtained, with 14 oils, from five different fields, were used in this study. The experimental characteristics of these oils (noted Oill, ..., Oill4) are given in Table 11.
Equation of State Both of the methods used in this study involve the use of cubic equations of state. The general form can be expressed in the way proposed by Rauzy (1982) P = RT/(B - 6) - a(T)/[B(B + y6)]
(3)
where y characterizes the equation of state, as shown in Appendix I. B is the pseudovolume, which is related to the molar volume u as follows u=B-c
c=co+cl
P
c = &Xi
(7)
i=l
In this work, parameters kij were calculated using the formalism of excess functions (PBneloux et al., 1989). In this case, parameters kij were expressed by means of binary interaction parameters Eij:
(1)
where Vbd is the total volume of the fluid and V,, is the liquid volume at saturation pressure. In the second case, all the gas produced is removed at each step of the depletion. The liquid shrinkage, also called the oil formation volume factor can be expressed as =
ill
(4)
where co is the volume correction which makes it possible to obtain the original equation of state (CO = 0 with the Redlich-Kwong equation, co = -0.03222RTJPc with the Peng-Robinson equation). The volume translation c1
The parameters Eij were estimated using a group contribution method (Abdoul, 1992).
Oil Modeling Pedersen'sMethod. Thismethod utilizes the RedlichKwong-Soaveequation of state; the general and particular characteristics are given in Appendix I. (a) Oil Characterization. The authors use a C7+ characterization. The heavy oil is described with anumber of components which may exceed 90. The experimental TBP residue, &+, is modeled by SCN cuts (usually until Cw) the molar weight, the density, and the molar fraction of which are determined by extrapolation of the corresponding properties, measured for lighter cuts. SCN cuts from C, are grouped into three pseudocomponents which have slightly the same weight. The final compositional model noted (8-C7+) considers eight components or pseudocomponents (8-C7+): N,, coz,CH4, Cz-C3, c4-c6, c7+(1),c7+(2), c,+(3) (b) Equation of State Parameters. Parameters of the EOS are established using relations given in Appendices I and 11. The critical parameters and acentric factor of SCN cuts from C7, necessary for this calculation, are obtained with correlations based on the experimental values of molar weight and density of each SCN cut (Pedersen et al., 1989a, 1989b). The volume correction c (eq 4) of light components and SCN cuts is estimated with general correlations given in Appendix I (eqs A6A8). Properties and volume correction of pseudocomponents (Cz-C3, C4-C6, C7+(1), C7+(2), C7+(3)) are estimated by correlations given in Appendix I11 (eqs A21-A24). Zero binary interaction parameters kij (eq 6) are used for hydrocarbon-hydrocarbon interactions, while the values recommended by Reid et al. (1977) are used for interactions with nonhydrocarbons. Proposed Method. With the present method, the Peng-Robinson equation of state is used as described in Appendix I. (a)Oil Characterization. In the case of gas condensate mixtures, it was previously shown by Carrier et al. (1989a, 1989b), that there exists an optimal way of grouping
1198 Ind. Eng. Chem. Rea., Vol. 32,No. 6,1993 Table 11. Characteristicr of Invertigated Oil6 oil1 oil2 Oils 0i4 molwt density molwt density molwt density molwt density of ofthe reservoir of ofthe reservoir of ofthe reservoir of ofthe reservoir Oil the cuts Oil the cuts oil the cuts oil the cuts (molar 5%) cuts (g/cma) (molar %) cuts (8/cm3) (molar %) cuts (g/cm3) (molar %) cuts (g/cms)
compounds HIS N;
O.OO0
O.OO0
O.OO0
0.000
methane ethane propane isobutane n-butane isopentane n-pentane
1.348 3.239 45.817 5.171 3.462 0.639 1.632 0.764 0.898
0.392 2.437 46.371 10.013 6.999 0.910 3.079 0.960 1.641
0.670 0.860 46.630 6.830 6.210 0.920 3.330 1.200 1.930
0.735 2.007 51.301 10.674 7.122 0.837 2.772 0.838 1.364
alkane C6 n-hexane
0.821 0.653
86.0
0.6956
1.111 1.233
86.0
0.6807
1.240 1.240
86.0
0.6748
0.881 0.951
86.0
0.6855
alkane CI aromatic C6 naphthene CI n-heptane
0.317 0.636 1.568 0.514
89.0
0.7429
0.800 0.436 1.600 0.870
92.0
0.7334
1.080 0.250 0.950 1.750
96.0
0.7338
0.635 0.526 1.461 0.755
91.0
0.7387
alkane CS aromatic CI naphthene Ca n-octane
0.464 0.795 1.389 0.356
103.0
0.7657
0.639 1.002 1.309 0.685
102.0
0.7584
1.160 0.760 0.950 1.150
108.0
0.7542
0.415 0.919 1.239 0.575
103.0
0.7629
alkane Ce aromatic Ce naphthene CS n-nonane
0.579 1.105 0.258 0.359
116.0
0.7829
0.541 0.836
118.0
0.7755
0.730 1.OO0 0.420 0.700
119.0
0.7777
0.379 0.956 0.391 0.415
117.0
0.7801
alkane CIO aromatic CS n-decane
0.679 0.510 0.296
134.0
0.7909
0.767 0.372 0.261
136.0
0.7836
0.830 0.530 0.430
135.0
0.7904
0.721 0.386 0.297
136.0
0.7884
12.363
194.3
0.8420
8.788
186.3
0.8278
9.700
199.9
0.8376
6.951
187.1
0.8253
13.368
410.0
0.9071
5.051
443.0
0.8973
6.550
450.0
0.9270
3.497
425.0
0.8979
c02
depletion temperature saturation pressure at Tdrp
compounds H2S N2 COa methane ethane
propane isobutane n-butane isopentane n-pentane alkane c6 n-hexane
0.546
0.451
Tdrp
365.95 K
Tdrp
P,= 263.4 bar
3
380.35 K
Tdep
373.75 K
P8 = 245.7 bar
P,= 251.0 bar
oils Oils molwt density molwt density reservoir of ofthe reservoir of ofthe reservoir Oil the cuts oil the cuts Oil (molar %) cuts (g/cms) (molar %) cuts (g/cmg) (molar 5%)
Tdrp
405.65 K
P, 305.9 bar 5
Oile
oil1
molwt density molwt density of ofthe reservoir of ofthe the cuts Oil the cuts cuts (g/Cma) b o l a r %) cuts (B/CmS)
O.OO0
O.OO0
O.OO0
O.OO0
0.534 2.442 54.916 9.016 6.037 0.739 2.472 0.818 1.326 0.801 0.906
0.438 2.161 55.927 10.831 6.563 0.818 2.514 0.747 1.170
0.597 2.457 59.117 8.179 5.496 0.661 2.094 0.661 1.085
0.555 1.796 60.215 10.349 6.049 0.762 2.364 0.716 1.129
86.0
0.6800
0.716 0.715
86.0
0.6771
0.692 0.795
86.0
0.6799
0.957 0.500
86.0
alkane CI aromatic Ce naphthene CI n-heptane
0.588 0.501 1.374 0.683
91.0
0.7397
0.425 0.412 1.153 0.543
90.0
0.7331
0.397 0.494 1.594 0.692
91.0
0.7379
0.400 0.391 1.512 0.523
90.0
0.7336
alkane Ce
aromatic CI naphthene CS n-octane
0.455 0.819 1.143 0.544
103.0
0.7595
0.422 0.746 0.932 0.447
101.0
0.7619
0.264 0.816 1.182 0.489
102.0
0.7808
0.236 0.629 1.056 0.446
103.0
0.7676
alkane Ce aromatic Ce naphthene Ce n-nonane
0.280 0.797 0.594 0.359
119.0
0.7823
0.509 0.803 0.334 0.372
119.0
0.7838
0.339 0.789 0.381 0.375
117.0
0.7740
0.299 0.716 0.348 0.306
118.0
0.7764
Ind. Eng. Chem. Res., Vol. 32, No. 6,1993 1199 Table I1 (Continued) 0%
0% ~~~
compounds alkane CIO aromatic Cg n-decane
Cll-ClS Clo+ depletion temperature saturation pressure at T h
cornpounds
coz
methane ethane propane isobutane n-butane bopentane n-pentane alkane Ce
0.8310
6.050
186.3
0.8268
5.864
192.3
0.8263
4.120
193.0
0.8228
3.993
450.0
0.9087
2.834
461.0
0.8967
3.410
440.0
0.9035
2.548
405.0
0.8912
T h = 382.05 K
Tdp
P. = 331.4 bar
= 401.55 K
P. = 355.2 bar
P,= 374.2 bar
P,= 381.5 bar
1.814 60.420 10.371 6.003 0.732 2.209 0.678 1.099
O.OO0
0.000
1.814 0.234 60.554 8.164 4.208
0.588 1.886 60.986 10.375 5.748 0.724 2.267 0.671 1.134
0.611 1.732 61.373 9.850 5.998 0.792 2.361 0.732 1.082
0.850
2.093 0.679 1.129
alkane CI aromatic Ce naphthene CI n-heptane
0.338 0.423 1.338 0.534
90.0
e Ce
0.293 0.613 0.995 0.375
104.0
aromatic C8 naphthene CS n-nonane
0.292 0.665 0.400 0.292
118.0
alkane CIO aromatic Cg n-decane
0.393 0.285 0.287
136.0
0.7843
1.124 0.413 0.495
136.0
Cll-ClS Clot
4.307
184.2
0.8220
6.628
2.521
400.0
0.8909
3.544
depletion temperature saturation pressure at T h
T h 398.15 K
O.OO0
86.0
alkane&
Tdq = 380.95 K
oil9 oil10 oil11 oilla molwt density molwt density molwt density molwt density of ofthe reservoir of ofthe reservoir of ofthe reservoir of ofthe reservoir Oil the cuts Oil the cuts Oil the cuts Oil the cuts (molar %) cuts (g/cm*) (molar %) cuts (g/cms) (molar %) cuts (g/cm8) (molar %) cuts (a/cm*)
0.867 0.616
h
~
193.5
n-hexane
aromatic CI naphthene C8 n-octane
~
6.641
O.OO0 0.840
HaS Na
~
molwt density molwt density molwt density molwt density reservoir of ofthe reservoir of ofthe reservoir of ofthe reservoir of ofthe Oil the cuts Oil the cuts Oil the cuts Oil the cuts (molar %) cuts @/an*) (molar%) cuts (g/cm*) (molar%) cuts (&ma) (molar %) cuts (g/cm*) 0.723 0.740 0.551 0.613 0.250 137.0 0.7841 0.373 136.0 0.7886 0.286 136.0 0.7838 0.270 136.0 0.7843 0.249 0.315 0.243 0.195
0.802 1.031
86.0
0.6724
0.663 0.705
86.0
0.6813
0.662 0.760
86.0
0.895 0.413 0.206 0.796
96.0
0.7092
0.256 0.372 1.076 0.487
90.0
0.7312
0.531 0.341
92.0
0.7310
0.7576
0.902 0.188 0.370 0.604
112.0
0.7340
0.390 0.578 0.861 0.338
104.0
0.7616
104.0
0.7550
0.7758
0.796 0.536
122.0
0.7484
0.324 0.673 0.171 0.266
117.0
0.7783
119.0
0.7762
0.7625
0.341 0.313 0.192
134.0
0.7834
0.539 0.293 0.185
136.0
0.7830
194.2
0.8081
4.724
186.1
0.8255
4.388
193.5
0.8232
431.0
0.8871
2.891
375.0
0.8929
2.376
435.0
0.8918
0.7389
O.OO0
0.532
Tdq 3 398.15K
Tbp= 358.15K
P,= 398.8 bar
P, = 379.0 bar
~~~
0.968 0.560
0.238
Tdap
400.95 K
compounds
HzS Na
COa
methane ethane propane isobutane n-butane isopentane n-pentane
Tdp = 396.15 K
P,= 380.0 bar ~
mol w t of the cuts
0.560
0.535 0.233
P. = 381.0 bar
~~~~~~~
Oil18
reservoir oil (molar %)
0.291 0.627 0.984 0.408
oil14
density of the cuts (g/cm*)
reservoir oil (molar %)
O.OO0
O.OO0
0.986 0.873 61.629 9.351 5.801 0.914 2.349 0.635 1.061
0.575 1.801 63.003 10.377 5.588 0.685 2.141 0.633 1.028
mol wt of the cuts
density of the cuts (g/cms)
1200 Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993 Table I1 (Continued) reservoir oil (molar %)
compounds
oil13 mol w t of the cuts 86.0
density of the cuts (g/cm3)
reservoir oil (molar % )
0.6810
0.610 0.660
91.0
0.7369
105.0
0.7474
119.0
0.7673
oil,, mol w t of the cuts
density of the cuts (g/cm*)
86.0
0.6856
89.0
0.7406
103.0
0.7594
116.0
0.7790
alkane c6 n-hexane
0.596 0.763
alkane CI aromatic C6 naphthene C7 n-heptane
0.497 0.556 0.853 0.603
alkane Ca aromatic C, naphthene Ce n-octane
0.417 0.416 0.799 0.455
alkane Cg aromatic Ce naphthene Cg n-nonane
0.307 0.487 0.330 0.352
alkane Clo aromatic Cg n-decane
0.483 0.215 0.231
137.0
0.7747
0.346 0.234 0.164
135.0
0.7845
Cll-cle
5.305
191.1
0.8189
4.304
189.8
0.8270
CaO+ depletion temperature saturation pressure at Tdep
2.736
0.8941
2.320
2.2
415.0 = 392.15 K P,= 375.4 bar
Tdsp
,
I
t
Experimental d a t a
---
Pedersen's method
W 7 t )
- This
1.2 1.0
s t u d y (9-CZot)
L l P/Bar
0.
100.
200.
300.
400.
500.
Figure 1. Differential vaporization at T/K = 380.35 of an oil containing 46.4 mol % of methane. 1.10
1.05
t
Experimental d a t a
---
Pederren's method
W 7 + )
1.00
- This
s t u d y (9-CZot)
0.95
0.90 350.
400.
450.
500.
550.
Figure 2. Constant mass depletion at T/K = 400.95 on an oil containing 61.0 mol 7% of methane.
appropriate components into a minimal number of pseudocomponents; it is thus possible to calculate PVT properties close to those obtained with nonregrouped components. The same procedure, using a CZO+or a C11+ characterization, was considered in this study. For a CZO+ characterization, the fluid is described as a mixture of the nine following components and pseudocomponents: N,, CO,, CH,, C,H,, C,H,, butanes, (9-c20+): C6--ClO, Cll-cl91 c20+ In order to reduce the number of components, a C11+ characterization may be considered also, using three
0.231 0.342 1.023 0.437 0.346 0.620 0.848 0.337 0.313 0.651 0.130 0.253
410.0 = 399.85 K P,= 384.3 bar
0.8932
Tdep
Table 111. Molecules Used To Model the Different SCN Cuts or Pseudocomponents cuts representative molecules 3-methyl hexane, cyclohexane, benzene, n-heptane c7 4-methyl heptane, methylcyclohexane, toluene, n-octane CS c9 4-methyl octane, ethylcyclohexane, ethylbenzene, n-nonane CIO 4-methyl nonane, propylbenzene, n-decane C11-Clg dicyclohexylmethane, 2-ethylnaphthalene, n-alkane (11I n I 19) Cm+ 'Aromatic CZO+",~ n-alkane (24 5 n I 70) C11+ dicyclohexylmethane, 'Aromatic C ~ O + "n-alkane ,~ (11I n I 45) OGroup structure and physical properties of the component hued w, "Aromatic Cm+": (10 Cmmtic, 4 CBu,ubstit,,tedMmtic, 2 C-ti, 4 CH3,4 CH2,2 CH) Tc = 850 K,Pc = 18 bar, zra = 0.245, w = 0.74, p = 1.24 g/cm3 at 288.15 K.
different compositional models (8-C11+): N,, CO,, CH4, C2H6,C&, butanes, C5-Cl0, CI1+ (6-C11+):
N2, C o p CH4, C244, C5-Ci0, C11+
(4-C1,+): (N2, C o p CH,), C,-C4, C6-C10, C11+ (b) Modeling of Pseudocomponents. Paraffinic, naphthenic, and aromatic molecules chosen to describe the SCN cuts or pseudocomponents from C, to C20+ are given in Table 111. For the Cll-Clg, CZO+,or CII+ cuts the experimental molar fractions of the representative molecules are not known (Table I);they were determined from the experimental molar weight and densities of the cuts using the following method. (1) CLI-CI~ Modeling. The Cll-C19 is represented by a mixture of three molecules: an aromatic, a naphthenic, and a n-paraffin, the composition of which is respectively XA, XN, xp. Assuming a n-paraffin chosen between n-C11 and n-CI9 and a given value of the N/P ratio (XN = 0.3xp, X A + 1.3xp = l), the composition of the cut (XA, XN, xp) is established by matching the calculated molar density of the cut to the experimental value. The choice of the n-paraffin corresponds to the one which allows reproducing
Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993 1201 the molar weight of the cut as close as possible. The value N/P = 0.3 is an average value obtained from experimental PNA analysis with a few oils. (2) Cm+ Modeling. The Cm+ cut is particularly complex and it probably contains some nonhydrocarbon compounds. This is suggested by ita very high density, which cannot be matched simultaneously with its molar weight when using hydrocarbon molecules only. For this reason, the C ~ O +is considered to be a mixture of a n-paraffin and an aromatic molecule “Aromatic Cm+”, the physical properties of which are given in Table 111. The composition of this mixture and the carbon number of the n-alkane are calculated as previously described for the C11-Cls cut, assuming XN = 0. (3)C11+ Modeling. The C11+ cut is represented by a mixture of a n-paraffin, a naphthene, and the “Aromatic Cm+” molecule. The same procedure as for the C11-Cl9 cut is used to determine the composition of this mixture. (c) Equation of State Parameters. The critical parameters, acentric factor, and Rackett factor of light components and selected molecules of the SCN cuts up to C ~are O known; parameters a, 6, and c can be calculated directly. The physical parameters of heavier pure components are estimated using a predictive method described in Appendix I1 (eqs AlFA20). The properties of correspondingpseudocomponents are estimated using the regrouping method proposed by Carrier et al. (1989a, 1989b) (Appendix 111,eqs A25-A28). The binary interaction parameters Eij (eq 8) are estimated using a group contribution method (Abdoul, 1992).
Rssults The results obtained with Pedersen’s method (C,+ characterization) and the proposed Cm+ characterization method are compared in Table IV for 26 depletion experiments performed at the reservoir temperature. In columns I and 11, the percentage of methane and the depletion type are specified. In further columns, the mean absolute percent deviation on the liquid shrinkage (AD %) and percent deviation on saturation pressure (AP,7% ) are given for both methods. The percent deviation on the tank oil density (Ap %) is given only in the case of the present study; as stated previously, liquid volumes were fitted to the experimental data with Pedersen’s method. Results obtained with the two methods can be compared significantly since they involve nearly the same number of components. They call for several comments: The liquid shrinkage predictions obtained by the two methods are reasonably accurate and of the same magnitude. It can be observed, however, that the proposed method provides more accurate predictions of the saturation pressure. The predictions are in better agreement with constant mass depletion data, than with those obtained by using the differential vaporization technique. The resulting errors do not seem to be correlated with the methane content of the reservoir oil. The tank oil density predicted, using the present method, is fairly satisfactory. The agreement could be improved using the procedure proposed by Pedersen et al. (1989a, 1989b). Typical patterns of experimental data obtained by constant mass depletion and differential vaporization techniques are presented in Figures 1 and 2. Curves predicted by the two methods have also been plotted.
Table IV. Results of Predictions Performed with Two Characterization Methods. Pedersen’s % of method (8-C7+) this study (9-Cm+) methane depletion AD 9% AP8 % AD % AP, % Ap % -5.1 -1.8 45.8 CM 0.5 0.3 2.2 DV 1.8 0.3 1.0 46.4 CM 0.7 0.2 4.6 7.8 DV 1.7 1.3 46.6 CM 0.8 -1.9 -3.6 -4.2 0.9 DV 2.2 2.2 0.2 2.5 -0.6 1.2 51.3 CM 0.3 DV 8.3 5.4 54.9 CM 0.2 -2.1 4.7 0.0 0.8 DV 2.3 1.4 CM 0.6 55.9 0.8 3.0 2.5 8.6 DV 5.9 1.6 CM 0.1 0.1 0.4 0.4 59.1 1.6 DV 2.0 1.6 5.1 CM 0.2 60.2 0.6 3.0 5.0 DV 6.8 5.4 CM 0.3 60.4 1.9 7.8 6.9 3.9 DV 18.2 14.7 CM 2.2 11.2 1.8 60.6 4.9 0.5 CM 0.4 0.5 61.0 2.6 0.3 4.2 DV 10.0 9.3 0.8 CM 0.4 61.4 -1.7 -1.0 3.2 DV 6.5 3.6 1.2 CM 0.3 61.6 -0.2 -2.4 3.0 5.5 DV 3.5 2.4 CM 0.7 63.0 -6.5 -5.4 3.2 Overall deviations CM 0.7 5.0 0.9 2.9 2.4 DV 6.1 4.0 4.3 2.5 2.5 CM+DV 3.2 4.5 2.5 2.7 2.5
I, ALI % is the mean absolute percent deviation on the liquid shrinkage, AP, % and Ap % are the percent deviationson saturation pressure and on tank oil density at atmospheric conditions. Table V. Prediction Results Obtained with 26 Depletion Experiments Using Different Compositional Models. comDositionalmode1 N AD % AP.% AD % 2.6 2.7 (8-Cii+) Nz, COz, Ci, Cz, Cs, C4, 8 2.6 CS-ClO, Cll+ 3.3 2.9 (6-Cii+) Nz,COz, Ci, C d 4 , 6 2.7 CS-ClO, c11+ (4-cii+) (Nz,COz, Ci), C d 4 , 4 3.0 5.2 2.9 CSclO, c11+ (9-Cm+) Nz,COz, C1, Cz, Cs, C4, 9 2.5 2.7 2.5 CSclO, Cll-ClS, cm+ (8-C7+) Pedersen’smethod 8 3.2 4.5 0 N is the component number corresponding to a given compositional model. AD %, AP, %, and Ap %, are the mean absolute percent deviationson the liquid shrinkage, saturation pression, and tank oil density under atmospheric conditions.
As mentioned above, heavy oil PVT properties may be accurately described using a C11+ characterization. The initial nine-component pseudoization was rearranged into eight-, six-, and four-component pseudoizations (8-C11+, 6-C11+, 4-Cll+). In Table V, the mean values obtained with the 26 depletions, using these compositional models, are given. Results obtained with Pedersen’s method and the proposed Cm+ characterization are recalled. The effects of the component number reduction are illustrated also in Figure 3. In Figure 4, the proposed (4-c11+) pseudoization is compared with Pedersen’s method. The liquid shrinkage and tank oil density results are practically the same for all the regroupings considered. The saturation pressure results are deteriorated, but even with four pseudocomponents, the agreement is still reasonable. The latter compositional model (4-C11+) is particularly useful, since it allows reduction of flash
1202 Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993
I
3.5
1-
*
---
I
2.5 2.0
1.0
1
1 /"
I
I
t
Experlmental data
- This
study (8-Cllt)
- - This ~ study (4-Cllt)
t 0.
study was sponsored by TOTAL-Compagnie Francaise des PBtroles.
P l i q u i d l "ref
y=l 6 = O.08664RTJPc
I3 100.
200.
300. 400.
'!:.. ---
Pedersen's method
- This
2.0
(8-C7*) study (4-C11t)
1.5
100. 200.
300.
400.
P/Bar
500. 600._ _ j
Figure 4. Comparison between results obtained with Pedersen's method and the (4-C11+) characterization. The oil considered is the same as in Figure 3.
calculation time by a factor of 2 as compared with Pedersen's method (8-C7+).
(AI) (A2)
+ m(1- T,'/2)12
a(T) = a,[l
500. 600.
Figure 3. Differential vaporization at T / K = 401.55 of an oil containing 55.9 mol % of methane. Comparison between results obtainedwith the C11+ characterization, using several compositional models.
1 .o 0 .
Appendix I. Equation of State Parameters Parameters of both equations of state (eq 3) used in this study were established as described below. Redlich-Kwong-Soave Equation.
T, = TIT, (A3)
with a, = 0.42740R2T~/P,
+
m = 0.480 1.574~- 0.1760~ (A51 where w is the acentric factor. Pedersen et al. (1989a, 198913) calculated the volume correction as follows: for light components and pseudocomponents up to c6 c = O.4O768RTJPC(O.29441- zra)
(A6) where the parameter of the Rackett equation, zra, is given as z,, = 0.29056 - 0.087750
(A7) For higher cuts, parameter c was fitted to the experimental liquid volume of the cut under atmospheric conditions (15 "C, 1 atm) c = 0- p P
(A81
Peng-Robinson Equation. y = 4.a2a3
Conclusion A method has been developed for predicting PVT properties of heavy oils with a restrictive number of components or pseudocomponents (between four and nine). SCN cuts or pseudocomponents were modeled with representative molecules. Beyond C10, the molar fractions of these moleculeswere obtained from experimental molar weight and densities and their thermodynamical properties were estimated by group contribution methods. The proposed method, used witha Cm+ characterization and nine pseudocomponents, yields comparable results as those obtained withpedersen's method, which estimates properties of cuts with empirical correlations. Predictions obtained with a C11+ characterization and only four components are of the same accuracy as with Pedersen's method but using eight components. This result seems to be very interesting since reservoir simulation programs used usually in petroleum companies describe the fluids with a maximum of four pseudocomponenta. In the case of heavy oils, the phase behavior is little affected by the light component regrouping. The successful results obtained using (N2, C02, CHd regrouping are probably partly due to the method of estimating properties of pseudocomponents, which takes into account internal binary interactions. Acknowledgment The authors wish to gratefully thank Professor A. PBneloux for helpful discussions during this research. This
(A4)
(A91
6 = 0.04557RTJPC a ( T ) = a,[l
+ m(1- T,")I2
(AW a!
= 0.445 ( A l l )
with a, = 0.45724R2T,2/Pc
(A121
m = 6.81256[(1.12754 + 0.51725~- 0.00374~~)'/~ - 11 (A131 The volume correction, eq 4, is given by the relation proposed by Rauzy (1982) c = RT,/P,(0.08315
- 0.44064~~~) (A141
Appendix 11. Properties of Heavy Components The critical parameters of the pure components chosen for modeling C11-cl9, CU+, and Cm+ cuts (see Table 111) are usually unknown. In this study, they were estimated using group contribution methods (Rogalski and Neau, 1990) based on the knowledge of the molecular structure and the normal boiling point Tb. The critical temperature and volume were calculated as follows: TdT, = 0.6685 + s - 0.1772S2- (0.1490 x 1 0 4 ) ~ -p 0.4368m1.' with 13
Ticj
S= I-].
and
Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993 1203 4
ujGj
u, =
+ 19.122 - (0.5474 X 10-2)Tb1.76- 5.8831Vst
proposed by Carrier et al. (1989a, 198913)
1'1
where Gj is the number of groups j and Tj and vj are the values of group parametersj. Vatis a structural parameter characterizing effects exerted by different types of molecules. The critical compressibility factor zc and the critical pressure P,were calculated using the following relations:
=
+ Z~T;*'+ ~
~ (A17) . ~ P,= ZpTJU, (A181 with where m was estimated by a group contribution method (Carrier et al., 1988) and Z,
z1=
0.51273 0.34763 0.34268
z2
= 0.81309 X 1V -0.10032 X 1od -0.12249 X 106
~
m
= -0.38431 for n-alkanes -0.10115 aromatics -0.08321 cyclanes
zg
The Rackett factor z, and the acentric factor w were given as z,, = 0.3098 - 0.006325~,'/~for n-alkanes
- 0.006583~,'/~aromatics - 0.006060~,'/~cyclanes Ln w = 4.62301 - 4.91329m-'/3
(A191 (A20)
Appendix 111. Pseudocomponent Properties Pedersen et al. The critical properties and volume correction of a pseudocomponent i (containing p components) are calculated as follows (Pedersen et al., 1985) P
P
Tci= [ x x j M W j T c j l / ~ x j M W j 11 '
1'1
P
P
(A211
Pci= ~ ~ x j M W , . P c j l / ~ x j M W j (A22) 14
1'1
P
Gi
P
[ ~ X ~ M W ~ W ~ ] / C " ~ M(A231 W~ 11 '
1-1
P
Ei = c x j c j
(A241
J'1
where MWj is the molar weight of the component j . Proposed Method. The parameters of the equation of state for pseudocomponents were estimated as follows: let Nk be the number of components i in one pseudocomponent c k and p the total number of Components in the fluid; xk is the molar fraction of the pseudocomponent c k in the fluid and Zi are the internal molar fractions of components i in this pseudocomponent. The properties of pseudocomponents were estimated using the method
Literature Cited Abdoul, W.; Rauzy, E.; PBneloux, 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. 1992,68,47-102. Carrier, B.; Rogalski, M.; PBneloux, A. Correlation and prediction of physical properties of hydrocarbons with the modified PengRobinson equation of state. Znd. Eng. Chem. Res. 1988,27,1714. Carrier, B.; Rogalski, M.; PBneloux, A. Choice of pseudo-components for flash calculation of petroleum fluids. C+ fraction c b a c terization; Chorn, L. G., Mansoori, G. A., Eds.; Taylor and Francis: New York, 1989a, pp 123-136. Carrier, B. Modelisation dea couples lourdes des fluidea pholiera. Thesis, Marseille, 198913. Dosseh, G. D. Caracterisation structurale d'un fluide de gisement par RBsonance MagnBtique NuclBaire B une et deux dimensions. Thesis, Paris, 1990. Pedersen, K. S.; Thomassen, P.; Fredenslund, Aa. Thermodynamics of petroleum mixtures containing heavy hydrocarbons. 3. Efficient flash calculationproceduresusing the SRK equation of state. Ind. Eng. Chem. Process Des. Deu. 1986,24,948-954. Pedersen, K. S.; Thomassen, P.; Fredenslund, Aa. Characterization of gascondensatemixtures. C+ fraction characterization. Chorn, L. G., Mansoori,G. A., Eds.; Taylor and Francis: New York, 1989a, pp 137-152. Pedersen, K. S.; Thomassen, P.; Fredenslund, Aa. Contribution in petroleum geology and engineering. Properties ofoils and natural gases; Gulf Publishing Company: Houston, 1989b, Vol. 5. PBneloux,A.; Rauzy, E.; Freze, R. Aconsistent correctionfor Redlick Kwong-Soave volumes. Fluid Phase Equilib. 1982,8,7-23. PBneloux, A,; Abdoul, W.;Rauzy, E. Excess functions and equations of state. Fluid Phase Equilib. 1989,47,115-132. Rauzy, E. Les mbthodes simples de calcul des 6quilibres liquidevapeur sous pression. Thesis, Marseille, 1982. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The properties of gases and liquids; McGraw-Hilk New York, 1977. Rogalski, M.; Neau, E. A group contribution method for prediction of hydrocarbon saturated liquid volumes. Fluid Phase Equilib. 1990, 56,59-69. Rousseau, B. Contribution Bl'Btude structuralede fluidea de giaement par RLonance MagnBtique NuclBaire. Thesis, Paris, 1987. Received for review September 23, 1992 Accepted March 5, 1993
