Energy Fuels 2010, 24, 2956–2963 Published on Web 04/05/2010
: DOI:10.1021/ef9014263
Cubic-Plus-Association Equation of State for Asphaltene Precipitation in Live Oils Zhidong Li and Abbas Firoozabadi* Reservoir Engineering Research Institute (RERI), 385 Sherman Avenue, Suite 5, Palo Alto, California 94306 Received November 22, 2009. Revised Manuscript Received March 8, 2010
We apply a cubic-plus-association equation of state (CPA-EOS) to study the asphaltene precipitation in live oils from temperature, pressure, and composition effects. The live oils are characterized by considering the pure components, the pseudo-hydrocarbon components, and the hydrocarbon residue. The hydrocarbon residue is further divided into the “heavy” component and asphaltenes. The asphaltene precipitation is modeled as liquid-liquid equilibrium between the upper onset and bubble point pressures and as gas-liquid-liquid equilibrium between the bubble point and lower onset pressures. In our work, the selfassociation between asphaltene molecules and the cross-association between asphaltene and “heavy” molecules are taken into account. The EOS parameters are either directly available, from our recent work, or from fitting the bubble point pressure. The cross-association energy between asphaltene and “heavy” molecules depends upon the temperature but is independent of the pressure. We reproduce the experiments of the amount and onset pressures of asphaltene precipitation in several live oils over a broad range of composition, temperature, and pressure conditions.
The lyophilic model includes the solubility theory,2-13 cubic equations of state (EOS),14-23 and perturbed-chain statistical associating fluid theory (PC-SAFT).1,24-28 In this model, asphaltenes and oil constitute a true solution. The molecular size and dispersion attractions dominate asphaltene phase behavior in crude oils. Asphaltene precipitation is due to the reduction of the solvent power of the hydrocarbon fluids. The separation of asphaltenes is described as a traditional liquidliquid or solid-liquid phase equilibrium. The lyophobic model includes the colloidal theory,29 micellization theory,30-33 and McMillan-Mayer-SAFT.34-36 In this model, asphaltenes are insoluble in the crude oil but can be stabilized by resins
1. Introduction Asphaltenes are operationally defined as a group of crude components insoluble in normal alkanes but soluble in aromatics. They represent the heaviest and most polar portion of a petroleum fluid. Asphaltene precipitation from the change of pressure, temperature, and composition may lead to serious plugging problems during the oil production, transportation, storage, and refining. Our knowledge on asphaltenes is limited, and the mechanisms of aggregation and deposition are not completely understood.1 The prevailing theoretical approaches for asphaltene precipitation can be classified into two main categories, lyophilic and lyophobic, corresponding to two different hypotheses on the mechanisms of asphaltene precipitation and stabilization.2
(17) Kohse, B. F.; Nghiem, L. X.; Maeda, H.; Ohno, K. Society of Petroleum Engineers (SPE) Asia Pacific Oil and Gas Conference and Exhibition, Brisbane, Queensland, Australia, Oct 16-18, 2000; SPE 64465. (18) Du, J. L.; Zhang, D. Pet. Sci. Technol. 2004, 22, 1023. (19) Vafaie-Sefti, M.; Mousavi-Dehghani, S. A.; Mohammad-Zadeh, M. Fluid Phase Equilib. 2003, 206, 1. (20) Sabbagh, O.; Akbarzadeh, K.; Badamchi-Zadeh, A.; Svrcek, W. Y.; Yarranton, H. W. Energy Fuels 2006, 20, 625. (21) Behar, E.; Mougin, P.; Pina, A. Oil Gas Sci. Technol. 2003, 58, 637. (22) Szewczyk, V.; Thomas, M.; Behar, E. Rev. Inst. Fr. Pet. 1998, 53, 51. (23) Szewczyk, V.; Behar, E. Fluid Phase Equilib. 1999, 158, 459. (24) Gonzalez, D. L.; Ting, P. D.; Hirasaki, G. J.; Chapman, W. G. Energy Fuels 2005, 19, 1230. (25) Gonzalez, D. L.; Hirasaki, G. J.; Creek, J.; Chapman, W. G. Energy Fuels 2007, 21, 1231. (26) Gonzalez, D. L.; Vargas, F. M.; Hirasaki, G. J.; Chapman, W. G. Energy Fuels 2008, 22, 757. (27) Ting, P. D.; Hirasaki, G. J.; Chapman, W. G. Pet. Sci. Technol. 2003, 21, 647. (28) Vargas, F. M.; Gonzalez, D. L.; Hirasaki, G. J.; Chapman, W. G. Energy Fuels 2009, 23, 1140. (29) Leontaritis, K. J.; Mansoori, G. A. Society of Petroleum Engineers (SPE) International Symposium on Oilfield Chemistry, San Antonio, TX, Feb 4-6, 1987; SPE 16258. (30) Pan, H. Q.; Firoozabadi, A. SPE Prod. Facil. 1998, 13, 118. (31) Pan, H. Q.; Firoozabadi, A. SPE Prod. Facil. 2000, 15, 58. (32) Pan, H. Q.; Firoozabadi, A. AIChE J. 2000, 46, 416. (33) Victorov, A. I.; Firoozabadi, A. AIChE J. 1996, 42, 1753. (34) Wu, J. Z.; Prausnitz, J. M.; Firoozabadi, A. AIChE J. 1998, 44, 1188.
*To whom correspondence should be addressed. Telephone: 650-3269259. Fax: 650-326-9277. E-mail:
[email protected]. (1) Vargas, F. M.; Gonzalez, D. L.; Creek, J. L.; Wang, J. X.; Buckley, J.; Hirasaki, G. J.; Chapman, W. G. Energy Fuels 2009, 23, 1147. (2) Correra, S.; Merino-Garcia, D. Energy Fuels 2007, 21, 1243. (3) Hirschberg, A.; Dejong, L. N. J.; Schipper, B. A.; Meijer, J. G. SPE J. 1984, 24, 283. (4) Wang, J. X.; Buckley, J. S. Energy Fuels 2001, 15, 1004. (5) Jamshidnezhad, M. J. Jpn. Pet. Inst. 2008, 51, 217. (6) Kraiwattanawong, K.; Fogler, H. S.; Gharfeh, S. G.; Singh, P.; Thomason, W. H.; Chavadej, S. Energy Fuels 2007, 21, 1248. (7) Akbarzadeh, K.; Alboudwarej, H.; Svrcek, W. Y.; Yarranton, H. W. Fluid Phase Equilib. 2005, 232, 159. (8) Akbarzadeh, K.; Dhillon, A.; Svrcek, W. Y.; Yarranton, H. W. Energy Fuels 2004, 18, 1434. (9) Mofidi, A. M.; Edalat, M. Fuel 2006, 85, 2616. (10) Nikookar, M.; Pazuki, G. R.; Omidkhah, M. R.; Sahranavard, L. Fuel 2008, 87, 85. (11) Alboudwarej, H.; Akbarzadeh, K.; Beck, J.; Svrcek, W. Y.; Yarranton, H. W. AIChE J. 2003, 49, 2948. (12) Wiehe, I. A.; Yarranton, H. W.; Akbarzadeh, K.; Rahimi, P. M.; Teclemariam, A. Energy Fuels 2005, 19, 1261. (13) Correra, S. Pet. Sci. Technol. 2004, 22, 943. (14) Gupta, A. K. MS Thesis, University of Calgary, Calgary, Alberta, Canada, 1986. (15) James, N. E.; Mehrotra, A. K. Can. J. Chem. Eng. 1988, 66, 870. (16) Godbole, S. P.; Thele, K. J. Society of Petroleum Engineers (SPE) Annual Technical Conference and Exhibition, Washington, D.C., Oct 4-7, 1992; SPE 24936. r 2010 American Chemical Society
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: DOI:10.1021/ef9014263
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peptized on their surface. Resins are considered to be the compounds chemically intermediate between all of the other species in the oil and asphaltenes. Asphaltene precipitation is due to the resin desorption from the surface of asphaltene particles. These two types of models have been used in correlating and predicting the onsets and amount of asphaltene precipitation in various petroleum fluids, with some limitations that may restrict their applications in the petroleum industry. First, in some of the theories, the reservoir fluid is represented by either asphaltene þ resin or asphaltene þ solvent. The two-component model is an oversimplification, and it may not be of value for use in compositional reservoir simulators. Second, most of models cannot describe the gas, oil, and asphaltene phases within a unified framework; i.e., they cannot work independently. Third, some of the methods contain many complex equations and/or adjustable parameters, which may complicate the implementation in the simulation modeling. Finally, some approaches do not account for the polar-polar and polar-induced polar interactions pertinent to asphaltenes and other components (e.g., resins and aromatics), which could also be important for the proper description of the asphaltene phase behavior. In a recent paper, we have proposed a cubic-plus-association equation of state (CPA-EOS) to study asphaltene precipitation in model and real heavy oils from the addition of n-alkanes.37 We have examined the effects of temperature, pressure, and n-alkanes on asphaltene precipitation and demonstrated that our model can reproduce the experiments. This is the first time that CPA-EOS is applied to study the asphaltene problem. Our approach is, in principle, a lyophilic model; i.e., the asphaltene-containing fluid is regarded as a true solution. Differently, besides the molecular size and dispersion attractions, the polar-polar interactions relevant to asphaltenes and other components are taken into consideration. However, different from the lyophobic model, we do not specifically require the species that are polar (e.g., resins) and easy to be polarized (e.g., aromatics) to stabilize asphaltenes in petroleum fluids. They may either inhibit or promote asphaltene precipitation depending upon the composition of the petroleum fluid. Our approach includes the possible intermolecular interactions relevant to asphaltene problems and can partially and in some cases completely overcome the current limitations. In this work, we apply our CPA-EOS to investigate asphaltene precipitation in several live oils from a pressure decrease and mixing with CO2 at high temperature and pressure. Within a unified theoretical framework, we successfully capture the bubble point pressure, asphaltene precipitation amount and onset pressures, and gas-oil-asphaltene threephase coexistence. More importantly, our model can be readily implemented in compositional reservoir simulators. The remainder of this paper is organized as follows: Section 2 describes the modeling and the formulation of our CPA-EOS for asphaltene systems in live oils. Section 3 compares calculations to experiments for asphaltene precipitation in seven live oils induced by a pressure decrease and CO2 mixing. In section 4, the main results and conclusions are summarized.
2. Modeling and Theory In this work, asphaltene precipitation in live oils is modeled as the traditional liquid-liquid or gas-liquid-liquid phase separation. The live oils are complex fluid mixtures of thousands of components. We characterize them by considering the pure components (N2, CO2, H2S, C1, C2, C3, iC4, nC4, iC5, and nC5), the pseudo-hydrocarbon components (C6, C7, C8, etc.), and the hydrocarbon residue (Cnþ). The pseudo-hydrocarbon components are defined by lumping a number of hydrocarbon components within a certain normal boiling point range.38 For instance, C6 includes all of the components with the normal boiling point between those of nC5 and nC6. Full characterization can avoid the extra parameter adjustment because the required EOS parameters are either standard for the pure components or correlated for the pseudo-hydrocarbon components. Thus, our model requires not only the asphaltene precipitation information but also the complete fluid analysis. The hydrocarbon residue is further divided into the “heavy” component and asphaltene. The “heavy” component contains the heavy alkanes, heavy aromatics, and all resins. Here, the heavy alkanes and heavy aromatics are those not included in pure components and pseudohydrocarbon components. The “heavy” component represents the secondary most polar component in petroleum fluids. The higher the molecular weight, the higher the aromatic content and the higher the polarity. Although we coarse-grain the heavy alkanes, heavy aromatics, and resins as only one pseudocomponent, the necessary physical features are essentially presented and well-described in our work. The advantages of our method have been demonstrated in detail in our recent work.37 Specifically, for the asphaltene precipitation in live oils, the additional advantage of our model is that it is based on the existing fluid characterization, which can be readily implemented in the compositional reservoir simulators. In the framework of CPA-EOS, the excess Helmholtz free energy Aex consists of the physical part, which describes the nonassociating molecular interactions, such as short-range repulsions and dispersion attractions, and the association part, which describes the polar-polar interactions (self-association and cross-association) of asphaltene and “heavy” molecules. The physical contribution is represented by the Peng-Robinson (PR)-EOS39 pffiffiffi ! Aex a 1 þ ð1 þ 2ÞbF ph pffiffiffi ¼ - lnð1 - bFÞ - pffiffiffi ln ð1Þ nRT 2 2bRT 1 þ ð1 - 2ÞbF where R is the universal gas constant, T is the absolute temperature, n is the total number of moles, and F is the molar density of the mixture. a and b are the energy and volume parameters of the mixture. They can by applying the van der Waals Pbe estimatedP mixing rules: a = i,jxixjaij, b = ixibi, and aij = (aiaj)1/2(1 - kij), where xi, ai, and bi stand for the mole fraction, energy parameter, and volume parameter of component i, respectively, and kij is the binary interaction coefficient (BIC) between components i and j (kij = 0 if i = j). ai and bi can be determined from the critical properties and acentric factor of an individual component pffiffiffiffiffiffi 2 R2 Tci2 RTci ai ¼ 0:45724 1þci ð1 - Tri Þ , bi ¼ 0:0778 ð2Þ Pci Pci
with ci ¼
0:37464 þ 1:54226ωi - 0:26992ωi 2 , 0:3796 þ 1:485ωi - 0:1644ωi 2 þ 0:01667ωi 3 ,
ωi < 0:5 , ωi > 0:5
where Tri, Tci, Pci, and ωi denote the reduced temperature, critical temperature, critical pressure, and acentric factor of component i, respectively.
(35) Wu, J. Z.; Prausnitz, J. M.; Firoozabadi, A. AIChE J. 2000, 46, 197. (36) Buenrostro-Gonzalez, E.; Lira-Galeana, C.; Gil-Villegas, A.; Wu, J. Z. AIChE J. 2004, 50, 2552. (37) Li, Z. D.; Firoozabadi, A. Energy Fuels 2010, 24, 1106.
(38) Firoozabadi, A. Thermodynamics of Hydrocarbon Reservoirs; McGraw-Hill: New York, 1999. (39) Peng, D. Y.; Robinson, D. B. Ind. Eng. Chem. Fundam. 1976, 15, 59.
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Table 1. Properties of the Seven Live Oils22,23,36,49-51 fluid A
N2 CO2 H2S C1 C2 C3 iC4 nC4 iC5 nC5 C6 C7 C8 C9 C10 C11
fluid C1
fluid Y3
fluid X1
fluid X2
Concentration (mol %) of Pure Components and Pseudo-hydrocarbon Components 0.91 0.47 0.09 0.27 0.38 1.57 1.59 1.02 4.07 4.02 5.39 1.44 0.05 24.02 32.22 42.41 30.53 46.07 10.09 12.42 10.78 7.13 7.72 9.58 10.29 6.92 5.92 5.62 1.83 2.03 1.55 2.43 1.14 4.83 4.87 2.92 1.11 2.35 2.27 2.22 1.47 0.82 0.75 2.74 2.71 1.82 0.79 0.67 4.77 4.12 2.86 1.36 0.82 2.67 1.03 3.82 1.58 4.17 1.91 4.07 0.79
0.49 11.37 3.22 27.36 9.41 6.70 0.81 3.17 1.22 1.98 2.49 2.87 3.14 2.74 2.32 1.90 C12þ mol % = 18.82 MW = 337.94 SG = 0.906
Concentration (mol %), MW, and SG of Hydrocarbon Residue C7þ C7þ C7þ C11þ mol % = 32.00 mol % = 25.62 mol % = 28.11 mol % = 30.83 MW = 334.66 MW = 284.36 MW = 209.50 MW = 302.09 SG = 0.882 SG = 0.805 SG = 0.852 SG = 0.872
1.40
3.80
Concentration (wt %) of Asphaltenes in STO 3.25 0.5 or 0.4 4.35
0.96 0.58 0.3 4.49 2.99 4.75 0.81 1.92 1.27 2.19
C11þ mol % = 25.15 MW = 330.77 SG = 0.881
C6þ mol % = 79.74 MW = 230.00 SG = 0.870
3.40
4.90
3. Results and Discussion In this work, we study the asphaltene precipitation in seven live oils. Table 1 provides the concentration of the pure components and pseudo-hydrocarbon components for these live oils. It also gives the mole fraction, molecular weight (MW), and specific gravity (SG) of the hydrocarbon residue. The asphaltene weight fractions in stock tank oils (STOs) are also included. The physical parameters TC, PC, ω, and MW of the pure components, pseudo-hydrocarbon components, and asphaltene are either directly available or obtained in our recent work.37,48 They are repeated in Table 2 for the sake of completeness. For the reservoir fluids A,49,50 C1,36 Y3,36 X1,49 X2,22 and X3,23 precipitation is from the pressure decrease. For the Weyburn oil, precipitation is induced by CO2 mixing.51 The common association parameters NA = NR = 4, κAA = κAR = 0.01, and εAA/kB = 2000 K are also provided in our recent work for asphaltene precipitation in heavy oils.37 The physical parameters of the “heavy” component are obtained in two steps. First, for the hydrocarbon residue, on the basis of its molecular weight and specific gravity, Cavett’s correlation is used to provide the rough estimation of TC and PC52 and the normal boiling point TB is estimated using the interpolation of the generalized properties of petroleum hexane-plus groups.38 Because the uncertainty in TC estimation is less than that in PC,38 we only adjust PC of the hydrocarbon residue to match the bubble point pressure
ð3Þ The subscripts “A” and “R” represent asphaltenes and the “heavy” component, respectively. χA and χR are the mole fractions of asphaltene and “heavy” molecules not bonded at one of the association sites, respectively. Association bonding occurs between two sites, with one on asphaltene molecule and the other on either asphaltene or a “heavy” molecule. “Heavy” molecules are assumed not to associate with themselves. As a result, χA and χR are given by 1 , χA ¼ AA 1 þ FNA xA χA Δ þ FNR xR χR ΔAR 1 1 þ FNA xA χA ΔAR
Weyburn oil
cross-associations between asphaltene and pseudo-hydrocarbon components are assumed negligible, but they can be included within the same theoretical framework with the introduction of more adjustable parameters.
The contribution to the excess Helmholtz energy because of association is derived from the thermodynamic perturbation theory.40-43 It is the same as that used in the SAFT.44-47 We assume that each asphaltene molecule has NA identical association sites and each “heavy” molecule has NR identical association sites Aex 1 - χA 1 - χR ass ¼ NA xA ln χA þ þ NR xR ln χR þ nRT 2 2
χR ¼
fluid X3
ð4Þ
where Δij = gκijbij[exp(εij/kBT) - 1] (i = A and j = A or R) characterizes the “association strength” with bij = (bi þ bj)/2, kB is the Boltzmann constant, g is the contact value of the radial distribution function of the hard-sphere mixture, and κij and εij are the association volume and energy parameters, respectively. To simplify the calculations, g is approximated by that of the pure hard-sphere fluid as g ≈ (1 - 0.5η)/(1 - η)3, with η = bF/4. The (40) Wertheim, M. S. J. Stat. Phys. 1984, 35, 19. (41) Wertheim, M. S. J. Stat. Phys. 1984, 35, 35. (42) Wertheim, M. S. J. Stat. Phys. 1986, 42, 459. (43) Wertheim, M. S. J. Stat. Phys. 1986, 42, 477. (44) Chapman, W. G.; Jackson, G.; Gubbins, K. E. Mol. Phys. 1988, 65, 1057. (45) Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. Fluid Phase Equilib. 1989, 52, 31. (46) Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. Ind. Eng. Chem. Res. 1990, 29, 1709. (47) Jackson, G.; Chapman, W. G.; Gubbins, K. E. Mol. Phys. 1988, 65, 1.
(48) Database of RERI Flash Computation Software Package. (49) Fahim, M. A. Pet. Sci. Technol. 2007, 25, 949. (50) Jamaluddin, A. K. M.; Joshi, N.; Iwere, F. Society of Petroleum Engineers (SPE) International Petroleum Conference and Exhibition, Villahermosa, Mexico, Feb 10-12, 2002; SPE 74393. (51) Srivastava, R. K.; Huang, S. S.; Dyer, S. B.; Mourits, F. M. J. Can. Pet. Technol. 1995, 34, 31. (52) Cavett, R. H. Proceedings of the American Petroleum Institute (API) 27th Mid-year Meeting, San Francisco, CA, 1962; Vol. 52, p 351.
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Table 2. Common Physical Parameters of Pure Components, Pseudohydrocarbon Components, and Asphaltene37,48 N2 CO2 H2S C1 C2 C3 iC4 nC4 iC5 nC5 C6 C7 C8 C9 C10 C11 asphaltene
TC (K)
PC (bar)
ω
MW
126.21 304.14 373.20 190.56 305.32 369.83 407.80 425.12 460.40 469.70 507.40 556.48 574.76 593.07 617.07 638.24 1474
33.90 73.75 89.40 45.99 48.72 42.48 36.04 37.96 33.80 33.70 30.12 26.75 25.24 23.30 21.55 19.74 6.34
0.039 0.239 0.081 0.011 0.099 0.153 0.183 0.199 0.227 0.251 0.296 0.294 0.418 0.491 0.534 0.566 2
28.0 44.0 34.1 16.0 30.1 44.1 58.1 58.1 72.2 72.2 86.2 100.0 114.0 128.0 142.0 156.0 1800
Table 4. Non-zero Binary Interaction Coefficients for the Seven Live Oils38,53 fluid A fluid C1 fluid Y3 fluid X1 fluid X2 fluid X3 Weyburn oil
TC (K)
PC (bar)
ω
MW
823.2 788.6 689.9 721.3 766.9 786.6 746.2
9.8 11.7 15.7 15.0 10.5 9.9 15.9
1.28 1.28 1.01 0.80 0.99 1.11 1.00
332.9 323.6 276.0 208.5 288.6 320.7 220.1
N2-HC
0.0289 þ 1.633 10-4MW
0.1
CO2-HC
0.15
H2S-HC
0.1
0.071
Table 5. Cross-association Energy between Asphaltene and “Heavy” Molecules εAR for the Seven Live Oils fluid A fluid C1 fluid Y3 fluid X1 fluid X2 fluid X3 Weyburn oil
εAR/kB (K) = 665.82 þ 1.0145T εAR/kB (K) = 1258.85 - 1.2462T εAR/kB (K) = 422.54 þ 2.0125T εAR/kB (K) = 1311.49 - 0.8835T εAR/kB (K) = 1219 (303 K) εAR/kB (K) = 1500 (303 K), 1420 (353 K), 1400 (403 K) εAR/kB (K) = 500 (332 K)
εAR has to be assumed temperature-dependent. Table 5 exhibits εAR as function of the temperature for the seven live oils. For the first four oils (fluids A, C1, X1, and Y3), the coefficients in the correlations are obtained from the measurements of upper onset pressures at the lowest and highest temperatures. The upper onset pressures at the other temperatures and lower onset pressures are then predicted. εAR either increases (fluids A and Y3) or decreases (fluids C1 and X1) with temperature. We are not able to provide a physical interpretation for this behavior within the frame of our work. It is possibly due to the complexity of the asphaltene problems and more likely due to the poor accuracy of the onset measurements. As stated in ref 36, “the onset determination is highly uncertain”. For the other three oils (fluids X2 and X3 and Weyburn oil), εAR is estimated from the fitting of the measured amount of precipitated asphaltenes. Solubility parameter of the oil may explain the asphaltene phase behavior. The solubility parameter of the reservoir fluid decreases as the pressure decreases from the reservoir condition to the bubble point and makes asphaltene less stable because the oil density decreases. Below the bubble point, there is an increase in density and solubility parameter when the pressure decreases because of the release of light hydrocarbons and the oil becomes a better solvent for asphaltene again. During depressurization, when the pressure is higher than the upper onset, the solution is in a single-phase region. Asphaltene precipitation occurs when the pressure is between the upper onset and bubble point and between the bubble point and lower onset. The solution is at oil-asphaltene twophase equilibrium for the former and at gas-oil-asphaltene three-phase equilibrium for the latter. When the pressure is lower than the lower onset, there is no asphaltene precipitation and the solution is in the gas-oil two-phase region. An increase in the temperature decreases the oil density but at the same time increases the solution entropy, resulting in a counter balancing effect; i.e., asphaltene precipitation can be either strengthened or weakened when the temperature increases.54,55 Figure 1 presents the asphaltene precipitation envelop for the reservoir fluid A with the plots of bubble point and upper and lower onset pressures as a function of the temperature.49,50 The STO has a nC7-insoluble asphaltene content of 1.4 wt %.
Table 3. Physical Parameters of the “Heavy” Component for the Seven Live Oils fluid A fluid C1 fluid Y3 fluid X1 fluid X2 fluid X3 Weyburn oil
C1-HC
(without considering asphaltene precipitation). The ω is calculated from38 3 log10 ðPC =1:01325Þ -1 ð5Þ ω ¼ 7 TC =TB - 1 where PC is in bar and TC and TB are in Kelvin. It should be emphasized that we have used the physical parameters of pure components and pseudo-hydrocarbon components (Table 2) and the method of estimating the physical parameters of the hydrocarbon residue in many industrial projects, and they work well for fitting the bubble point pressure at various temperatures. Second, the gas/oil ratio (GOR) and then the asphaltene concentration in live oil can be calculated by flashing the oil at room conditions (293.15 K and 1 bar). The physical parameters of the “heavy” component are then obtained from those of the hydrocarbon residue and asphaltene through molar averaging, as shown in Table 3. Because of the low mole fraction of asphaltene in live oils, the molar averaging does not affect the prediction of the bubble point pressures. We let the hydrocarbons (HCs) include C1, C2, C3, iC4, nC4, iC5, nC5, C6, C7, C8, etc., “heavy” component, and asphaltene. The BICs between C1 and HC (except C1), between N2 and HC, between CO2 and HC, and between H2S and HC can be referred to the previous work and are reproduced in Table 4. Other BICs are set to zero.38,53 It should be mentioned that the BICs between CO2 and HC for the Weyburn oil have to be tuned to fit the bubble point pressures for different CO2/oil mixtures. It should also be emphasized that we have tested the method of estimating the BICs in many industrial projects. For asphaltene precipitation in live oils, to match the available experiments, the crossassociation energy between asphaltene and “heavy” molecules
(54) Ting, P. D. Ph.D. Thesis, Rice University, Houston, TX, 2003. (55) Gonzalez, D. L. Ph.D. Thesis, Rice University, Houston, TX, 2008.
(53) Arbabi, S.; Firoozabadi, A. SPE Adv. Technol., March, 1995, 139-145.
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Figure 1. Pressures of bubble point and asphaltene precipitation upper and lower onsets as function of the temperature for the reservoir fluid A. Symbols are experiments from refs 49 and 50, and lines represent calculations.
It should be noted that our predictions are similar to those in the literature.26 According to our calculations, when the temperature is lower than 400 K, the temperature change dramatically affects the upper onset pressure. When the temperature increases from 300 to 400 K, the upper onset pressure falls by 1300 bar. The low-temperature region is important to evaluate the asphaltene precipitation risk during the production of deep sea reservoirs. When the temperature is higher than 400 K, the effect of the temperature on the upper onset pressure becomes weak. In comparison to the upper onset pressure, the bubble point pressure and lower onset pressure are weakly dependent upon the temperature. With a unified theoretical framework, our model successfully reproduces the asphaltene precipitation envelop. Figure 2 shows the asphaltene precipitation envelop for the reservoir fluid X1 with asphaltene contents in STO of 0.4 and 0.5 wt %. The precipitant used to determine the asphaltene content in STO is not reported.49 It should be emphasized that all of the results in Figure 2b are predictions. For this oil, according to our calculations, the effect of the temperature on the upper onset pressure is much weaker even at low temperatures compared to the reservoir fluid A. A decrease of the asphaltene concentration has essentially no effect on the bubble point pressure but can decrease the upper onset pressure and increase the lower onset pressure; i.e., asphaltene becomes more stable. It is interesting that, when the temperature is higher than 400 K, the asphaltene is less stable as the temperature increases in the gas-oil-asphaltene three-phase region but the trend is opposite in the oil-asphaltene twophase region. For the higher asphaltene content, i.e., Figure 2a, both the upper onset pressure and bubble point pressure are faithfully captured but the lower onset pressure is somewhat overestimated. For the lower asphaltene content, i.e., Figure 2b, the performance for the bubble point pressure is still excellent and, for the lower onset pressure, it is also improved. However, the upper onset pressure is slightly overestimated. We suspect that experiments of onset pressures may have large errors especially for the lower onset. In general, the agreement between the experiments and calculations for the reservoir fluid X1 is satisfactory. In Figures 3 and 4, we examine the effect of the temperature on both upper onset and bubble point pressures for the reservoir fluids C1 and Y3.36 The STO includes nC5-insoluble
Figure 2. Pressures of bubble point and asphaltene precipitation upper and lower onsets as function of the temperature for the reservoir fluid X1 with an asphaltene concentration of (a) 0.5 wt % and (b) 0.4 wt %. Symbols are experiments from ref 49, and lines represent calculations.
Figure 3. Pressures of bubble point and asphaltene precipitation upper onset as function of the temperature for the reservoir fluid C1. Symbols are experiments from ref 36, and lines represent calculations.
asphaltene content of 3.80 wt % for fluid C1 and 3.25 wt % for fluid Y3. The measurements of the lower onset pressure are not reported. For oil Y3, the upper onset pressure also presents strong dependency upon temperature. On the basis of our results, when the temperature increases from 300 to 400 K, the upper onset pressure can drop by 1800 bar. 2960
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: DOI:10.1021/ef9014263
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Figure 4. Pressures of bubble point and asphaltene precipitation upper onset as function of the temperature for the reservoir fluid Y3. Symbols are experiments from ref 36, and lines represent calculations.
Figure 6. (a) Fraction of precipitated asphaltenes and (b) relative volume of the mixture (bubble point is the reference) as function of the pressure for the reservoir fluid X3 at 303, 353, and 403 K. Symbols are experiments from ref 23, and lines represent calculations. In panel a, the calculated bubble point and upper and lower onsets are marked by thin lines.
well with the experiments for both bubble point and upper onset pressures. Our work predicts that the plot of upper onset pressure tends to be parallel to or away from that of the saturation pressure at high temperatures. This is in agreement with the theories in the literature.23-26,28 However, some of the theories predict that these two plots may eventually meet.18,56 The difference is possibly due to different reservoir oils. After a careful literature search, we do not notice any direct experimental evidence to support either of the predictions. For the reservoir fluids X2 and X3, we study the effect of the pressure on the amount of asphaltene precipitation.22,23 The asphaltene content is determined using nC7 titration. The comparison between measurements and calculations is displayed in Figures 5 and 6. The bubble point and upper and lower onset pressures can be readily seen in the plots. As the pressure drops, asphaltene precipitation first increases when the pressure is between the upper onset and bubble point and then decreases when the pressure is between the bubble point and lower onset. The maximum precipitation appears at the bubble point. This behavior can be interpreted from the solubility parameter, which will be presented later. Our model correctly captures the effect of the pressure on the asphaltene
Figure 5. (a) Fraction of precipitated asphaltenes and (b) relative volume of the mixture (bubble point is the reference) as function of the pressure for the reservoir fluid X2 at 303 K. Symbols are experiments from ref 22, and lines represents calculations. In panel a, the calculated bubble point and upper and lower onsets are marked by thin lines.
Our calculation indicates that, in the oil-asphaltene two-phase region when the temperature is above 400 K, the asphaltene precipitation is strengthened as the temperature increases. This phenomenon also weakly appears for the reservoir fluids A and C1 possibly because of the counter effect of the temperature. For the fluids C1 and Y3, our calculations agree
(56) Lopez-Chavez, E.; Pacheco-Sanchez, J. H.; Martinez-Magadan, J. M.; Castillo-Alvarado, F. D.; Soto-Figueroa, C.; Garcia-Cruz, I. Pet. Sci. Technol. 2007, 25, 19.
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Figure 8. Computed solvent solubility parameter and oil phase mass density for the reservoir fluid X2 at 303 K with pressure between upper and lower onsets.
function of the overall concentration of CO2 in the mixture. As expected, as the CO2 overall concentration increases, asphaltene precipitation becomes more pronounced. However, at very high CO2 concentrations, asphaltene precipitation can be inhibited because of the appearance of the gas phase, which is reflected by the slope decrease in Figure 7b. The calculations are in good agreement with the measurements. As mentioned before, the solubility parameter is normally used to explain the asphaltene phase behavior. In Figure 8, we present the solvent solubility parameter and the oil phase density when the pressure decreases from the upper onset to the lower onset for the reservoir fluid X2 at 303 K. Here, the solvent includes all of the components in the oil phase, except asphaltene. Without asphaltene, the CPA-EOS is reduced to the PR-EOS and the solvent solubility parameter can be calculated from5,38 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi ffi 1 da vs þ ð1 þ 2Þb pffiffiffi pffiffiffi δs ¼ a-T ð6Þ ln dT 2 2bvs vs þ ð1 - 2Þb
Figure 7. (a) Bubble point pressure at 332 K and (b) fraction of precipitated asphaltenes at 332 K and 160 bar as function of the CO2 mole fraction for the Weyburn oil. Symbols are experiments from ref 51, and lines represent calculations.
precipitation amount particularly in the oil-asphaltene twophase region. However, for the reservoir fluid X3, our method predicts that the asphaltene precipitation disappears too fast when the pressure is lower than the bubble point; i.e., the lower onset pressure is overestimated, which is similar to Figure 2. This is possibly one limitation of our model. Besides, we also present the comparison between calculations and experiments for the relative volumes (the ratio between the total volume and the bubble point volume) during depressurization. There is a slope change at the bubble point because the vapor phase vanishes when the pressure is higher than the bubble point. Again, the agreement is excellent. For the Weyburn oil, we investigate the asphaltene precipitation from mixing with CO2.51 Saturates, aromatics, resins, and asphaltenes (SARA) analysis of STO was conducted using a modified Syncrude method, but the precipitant is not provided. The asphaltene content of the flashed CO2saturated oils is determined by a photometric technique. A change of 0.1 wt % in asphaltene content in the oil can be estimated with confidence. Weyburn oil contains a very small amount of light components. CO2 injection can potentially improve the oil recovery but may lead to a large amount of asphaltene precipitation. In Figure 7a, the bubble point pressure at 332 K is presented for different CO2/oil mixtures. At a very high CO2 concentration, asphaltene precipitation occurs at the bubble point. In Figure 7b, the fraction of precipitated asphaltenes at 332 K and 160 bar is shown as a
where vs is the molar volume of the solvent. PR-EOS can provide accurate predictions for the solubility parameters (we have tested the solubility parameters of several pure substances, including nC5, nC6, nC8, benzene, and toluene, at 298 K). From Figure 8, as expected, the solvent solubility parameter decreases when the pressure drops from the upper onset to the bubble point because of the decrease of the oil phase density and then increases when the pressure drops further from the bubble point to the lower onset because of evaporation of light components (which causes the increase of the oil phase density). The minimum of both the solvent solubility parameter and oil phase density is at the bubble point where the asphaltene precipitation reaches the maximum. As a representative, in Figure 9, we show the calculated composition of both asphaltene and oil phases for the reservoir fluid X2 at 303 K and 98.1 bar (bubble point). While some of the existing models assume that the precipitated phase is pure asphaltenes and/or the oil phase is pure oil (with no asphaltenes), our method describes the heterogeneity of both asphaltene-rich and asphaltene-lean phases. Even though the asphaltene precipitation reaches the maximum at the bubble point, the precipitated phase still contains a nonnegligible amount of other species (about 12 wt %) and, at the same time, there is also a small amount of asphaltenes remaining in the oil phase (about 1.2 wt %). It can be expected that, at other precipitation conditions, both the asphaltene and oil phases should be even more heterogeneous. 2962
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considering the pure components, the pseudo-hydrocarbon components, and the hydrocarbon residue. The residue is further divided into the “heavy” component and asphaltene. The physical interactions are described by the PR equation. The polar-polar interactions between asphaltene molecules (self-association) and between asphaltene and “heavy” molecules (cross-association) are described by the thermodynamic perturbation theory. The physical parameters of EOS are directly available for the pure components and pseudo-hydrocarbon components, from our recent work for asphaltene, and from the fitting of the bubble point pressures for the “heavy” component. Some common association parameters are also from our recent paper.37 Letting the cross-association energy between asphaltene and “heavy” molecules be temperature-dependent, we successfully reproduce the effect of pressure and temperature on the bubble point, asphaltene precipitation amount and onset pressures, and gas-oilasphaltene three-phase behavior within a unified theoretical framework.
Figure 9. Computed weight fractions of different components in the asphaltene and oil phases for the reservoir fluid X2 at 303 K and 98.1 bar (bubble point).
4. Conclusions We apply the CPA-EOS to study the asphaltene precipitation in several live oils induced by a pressure decrease and CO2 mixing. The live oils are characterized by
Acknowledgment. We are grateful to the financial support from the industrial members of RERI.
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