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2956r 2010 American Chemical Society pubs.acs.org/EF

Energy Fuels 2010, 24, 2956–2963 : DOI:10.1021/ef9014263Published on Web 04/05/2010

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 inlive oils from temperature, pressure, and composition effects. The live oils are characterized by consideringthe pure components, the pseudo-hydrocarbon components, and the hydrocarbon residue. The hydro-carbon residue is further divided into the “heavy” component and asphaltenes. The asphaltene precipita-tion is modeled as liquid-liquid equilibrium between the upper onset and bubble point pressures and asgas-liquid-liquid equilibrium between the bubble point and lower onset pressures. In our work, the self-association 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 experimentsof the amount and onset pressures of asphaltene precipitation in several live oils over a broad range ofcomposition, temperature, and pressure conditions.

1. Introduction

Asphaltenes are operationally defined as a group of crudecomponents insoluble in normal alkanes but soluble in aro-matics. They represent the heaviest and most polar portion ofa petroleum fluid. Asphaltene precipitation from the changeof pressure, temperature, and compositionmay lead to seriousplugging problems during the oil production, transportation,storage, and refining. Our knowledge on asphaltenes is limi-ted, and the mechanisms of aggregation and deposition arenot completely understood.1

The prevailing theoretical approaches for asphaltene pre-cipitation can be classified into two main categories, lyophilicand lyophobic, corresponding to two different hypotheses onthemechanismsof asphalteneprecipitationand stabilization.2

The lyophilic model includes the solubility theory,2-13 cubicequations of state (EOS),14-23 and perturbed-chain statisticalassociating fluid theory (PC-SAFT).1,24-28 In this model,asphaltenes and oil constitute a true solution. The molecularsize and dispersion attractions dominate asphaltene phasebehavior in crude oils. Asphaltene precipitation is due to thereduction of the solvent power of the hydrocarbon fluids. Theseparation of asphaltenes is described as a traditional liquid-liquid or solid-liquid phase equilibrium. The lyophobicmodel includes the colloidal theory,29 micellization theory,30-33

andMcMillan-Mayer-SAFT.34-36 In this model, asphaltenesare insoluble in the crude oil but can be stabilized by resins

*Towhomcorrespondence should be addressed.Telephone: 650-326-9259. 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.MSThesis, 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 PetroleumEngineers (SPE)

Annual Technical Conference and Exhibition, Washington, D.C., Oct4-7, 1992; SPE 24936.

(17) Kohse, B. F.; Nghiem, L. X.; Maeda, H.; Ohno, K. Society ofPetroleum Engineers (SPE) Asia Pacific Oil and Gas Conference andExhibition, Brisbane, Queensland, Australia, Oct 16-18, 2000; SPE64465.

(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 En-

gineers (SPE) International Symposium on Oilfield Chemistry, SanAntonio, 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.

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Energy Fuels 2010, 24, 2956–2963 : DOI:10.1021/ef9014263 Li and Firoozabadi

peptized on their surface. Resins are considered to be thecompounds chemically intermediate between all of the otherspecies in the oil and asphaltenes. Asphaltene precipitation isdue to the resin desorption from the surface of asphalteneparticles.

These two types ofmodels havebeenused in correlatingandpredicting the onsets and amount of asphaltene precipitationin various petroleum fluids, with some limitations that mayrestrict their applications in the petroleum industry. First, insomeof the theories, the reservoir fluid is represented by eitherasphaltene þ resin or asphaltene þ solvent. The two-compo-nentmodel is an oversimplification, and itmay not be of valuefor use in compositional reservoir simulators. Second,most ofmodels cannot describe the gas, oil, and asphaltene phaseswithin a unified framework; i.e., they cannot work indepen-dently. Third, some of the methods contain many complexequations and/or adjustable parameters, which may compli-cate the implementation in the simulation modeling. Finally,some approaches do not account for the polar-polar andpolar-induced polar interactions pertinent to asphaltenes andother components (e.g., resins and aromatics), which couldalso be important for the proper description of the asphaltenephase behavior.

In a recent paper, we have proposed a cubic-plus-asso-ciation equation of state (CPA-EOS) to study asphalteneprecipitation in model and real heavy oils from the additionof n-alkanes.37 We have examined the effects of tempera-ture, pressure, and n-alkanes on asphaltene precipitationand demonstrated that our model can reproduce the experi-ments. This is the first time that CPA-EOS is applied tostudy the asphaltene problem. Our approach is, in princi-ple, a lyophilic model; i.e., the asphaltene-containing fluidis regarded as a true solution. Differently, besides themolecular size and dispersion attractions, the polar-polarinteractions relevant to asphaltenes and other componentsare taken into consideration. However, different from thelyophobic model, we do not specifically require the speciesthat 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 precipita-tion depending upon the composition of the petroleumfluid. Our approach includes the possible intermolecularinteractions relevant to asphaltene problems and can par-tially and in some cases completely overcome the currentlimitations.

In this work, we apply our CPA-EOS to investigate asphal-tene precipitation in several live oils from a pressure decreaseand mixing with CO2 at high temperature and pressure.Within a unified theoretical framework, we successfullycapture the bubble point pressure, asphaltene precipitationamount and onset pressures, and gas-oil-asphaltene three-phase coexistence. More importantly, our model can be read-ily implemented in compositional reservoir simulators. Theremainder of this paper is organized as follows: Section 2describes the modeling and the formulation of our CPA-EOSfor asphaltene systems in live oils. Section 3 compares calcula-tions to experiments for asphaltene precipitation in seven liveoils induced by a pressure decrease andCO2mixing. In section4, the main results and conclusions are summarized.

2. Modeling and Theory

In this work, asphaltene precipitation in live oils is modeled asthe traditional liquid-liquid or gas-liquid-liquid phase separa-tion. The live oils are complex fluid mixtures of thousands ofcomponents. We characterize them by considering the purecomponents (N2, CO2, H2S, C1, C2, C3, iC4, nC4, iC5, and nC5),the pseudo-hydrocarbon components (C6, C7, C8, etc.), and thehydrocarbon residue (Cnþ). The pseudo-hydrocarbon compo-nents are defined by lumping a number of hydrocarbon compo-nents within a certain normal boiling point range.38 For instance,C6 includes all of the components with the normal boiling pointbetween those of nC5 and nC6.Full characterization canavoid theextra parameter adjustment because the required EOS para-meters are either standard for the pure components or correlatedfor the pseudo-hydrocarbon components. Thus, our modelrequires not only the asphaltene precipitation information butalso the complete fluid analysis. The hydrocarbon residue isfurther divided into the “heavy” component and asphaltene.The “heavy” component contains the heavy alkanes, heavyaromatics, and all resins. Here, the heavy alkanes and heavyaromatics are those not included inpure components andpseudo-hydrocarbon components. The “heavy” component representsthe secondary most polar component in petroleum fluids. Thehigher the molecular weight, the higher the aromatic contentand the higher the polarity. Although we coarse-grain theheavy alkanes, heavy aromatics, and resins as only one pseudo-component, the necessary physical features are essentially pre-sented and well-described in our work. The advantages of ourmethod have been demonstrated in detail in our recent work.37

Specifically, for the asphaltene precipitation in live oils, theadditional advantage of our model is that it is based on theexisting fluid characterization, which can be readily implementedin the compositional reservoir simulators.

In the framework of CPA-EOS, the excess Helmholtz freeenergy Aex consists of the physical part, which describes the non-associatingmolecular interactions, such as short-range repulsionsand dispersion attractions, and the association part, whichdescribes the polar-polar interactions (self-association andcross-association) of asphaltene and “heavy” molecules.

The physical contribution is represented by the Peng-Robinson(PR)-EOS39

Aexph

nRT¼ - lnð1- bFÞ- a

2ffiffiffi2

pbRT

ln1þð1þ ffiffiffi

2p ÞbF

1þð1- ffiffiffi2

p ÞbF

!ð1Þ

where R is the universal gas constant, T is the absolute tempera-ture, n is the total number of moles, and F is the molar density ofthe mixture. a and b are the energy and volume parameters of themixture. They can be estimated by applying the van der Waalsmixing rules: a=

Pi,jxixjaij, b=

Pixibi, and aij=(aiaj)

1/2(1- kij),where xi, ai, and bi stand for the mole fraction, energy para-meter, and volume parameter of component i, respectively,and kij is the binary interaction coefficient (BIC) betweencomponents i and j (kij=0 if i= j). ai and bi can be determinedfrom the critical properties and acentric factor of an individualcomponent

ai ¼ 0:45724R2T2

ci

Pci

�1þcið1-

ffiffiffiffiffiffiTri

pÞ�2, bi ¼ 0:0778

RTci

Pcið2Þ

with ci ¼ 0:37464þ 1:54226ωi - 0:26992ωi2, ωi < 0:5

0:3796þ 1:485ωi - 0:1644ωi2 þ 0:01667ωi

3, ωi > 0:5

�,

whereTri,Tci,Pci, andωi denote the reduced temperature, criticaltemperature, 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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The contribution to the excess Helmholtz energy because ofassociation is derived from the thermodynamic perturbationtheory.40-43 It is the same as that used in the SAFT.44-47 Weassume that each asphaltene molecule has NA identical associa-tion sites and each “heavy”molecule hasNR identical associationsites

Aexass

nRT¼ NAxA ln χA þ 1- χA

2

� �þNRxR ln χR þ 1- χR

2

� �ð3Þ

The subscripts “A” and “R” represent asphaltenes and the“heavy” component, respectively. χA and χR are the mole frac-tions of asphaltene and “heavy” molecules not bonded at one ofthe association sites, respectively. Association bonding occursbetween two sites, with one on asphaltenemolecule and the otheron either asphaltene or a “heavy” molecule. “Heavy” moleculesare assumed not to associate with themselves. As a result, χA andχR are given by

χA ¼ 1

1þ FNAxAχAΔAAþ FNRxRχRΔ

AR,

χR ¼ 1

1þ FNAxAχAΔAR

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, kBis the Boltzmann constant, g is the contact value of the radialdistribution function of the hard-sphere mixture, and κij and εijare the association volume and energy parameters, respectively.To simplify the calculations, g is approximated by that of the purehard-sphere fluid as g ≈ (1 - 0.5η)/(1 - η)3, with η= bF/4. The

cross-associations between asphaltene and pseudo-hydrocarboncomponents are assumed negligible, but they can be includedwithin the same theoretical framework with the introduction ofmore adjustable parameters.

3. Results and Discussion

In this work, we study the asphaltene precipitation in sevenlive oils. Table 1 provides the concentration of the purecomponents and pseudo-hydrocarbon components for theselive 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) arealso included. The physical parametersTC, PC,ω, andMW ofthe pure components, pseudo-hydrocarbon components, andasphaltene are either directly available or obtained in ourrecent work.37,48 They are repeated in Table 2 for the sake ofcompleteness. For the reservoir fluidsA,49,50 C1,36Y3,36X1,49

X2,22 and X3,23 precipitation is from the pressure decrease.For the Weyburn oil, precipitation is induced by CO2 mix-ing.51 The common association parameters NA=NR= 4,κAA= κAR=0.01, and εAA/kB=2000Kare also provided inour recent work for asphaltene precipitation in heavy oils.37

The physical parameters of the “heavy” component areobtained in two steps. First, for the hydrocarbon residue, onthe basis of its molecular weight and specific gravity, Cavett’scorrelation 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 petroleumhexane-plus groups.38 Because the uncertainty in TC estima-tion is less than that in PC,

38 we only adjust PC of thehydrocarbon residue to match the bubble point pressure

Table 1. Properties of the Seven Live Oils22,23,36,49-51

fluid A fluid C1 fluid Y3 fluid X1 fluid X2 fluid X3 Weyburn oil

Concentration (mol %) of Pure Components and Pseudo-hydrocarbon ComponentsN2 0.49 0.91 0.47 0.09 0.27 0.38 0.96CO2 11.37 1.57 1.59 1.02 4.07 4.02 0.58H2S 3.22 5.39 1.44 0.05 0.3C1 27.36 24.02 32.22 42.41 30.53 46.07 4.49C2 9.41 10.09 12.42 10.78 7.13 7.72 2.99C3 6.70 9.58 10.29 6.92 5.92 5.62 4.75iC4 0.81 1.83 2.03 1.55 2.43 1.14 0.81nC4 3.17 4.83 4.87 2.92 1.11 2.35 1.92iC5 1.22 2.27 2.22 1.47 0.82 0.75 1.27nC5 1.98 2.74 2.71 1.82 0.79 0.67 2.19C6 2.49 4.77 4.12 2.86 1.36 0.82C7 2.87 2.67 1.03C8 3.14 3.82 1.58C9 2.74 4.17 1.91C10 2.32 4.07 0.79C11 1.90

Concentration (mol %), MW, and SG of Hydrocarbon ResidueC12þ C7þ C7þ C7þ C11þ C11þ C6þmol % = 18.82 mol % = 32.00 mol % = 25.62 mol % = 28.11 mol % = 30.83 mol % = 25.15 mol % = 79.74MW = 337.94 MW = 334.66 MW = 284.36 MW = 209.50 MW = 302.09 MW = 330.77 MW = 230.00SG = 0.906 SG = 0.882 SG = 0.805 SG = 0.852 SG = 0.872 SG = 0.881 SG = 0.870

Concentration (wt %) of Asphaltenes in STO1.40 3.80 3.25 0.5 or 0.4 4.35 3.40 4.90

(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.

2959


(without considering asphaltene precipitation). The ω iscalculated from38

ω ¼ 3

7

log10ðPC=1:01325ÞTC=TB - 1

� - 1 ð5Þ

where PC is in bar and TC and TB are in Kelvin. It should beemphasized that we have used the physical parameters of purecomponents and pseudo-hydrocarbon components (Table 2)and the method of estimating the physical parameters of thehydrocarbon residue in many industrial projects, and theywork well for fitting the bubble point pressure at varioustemperatures. Second, the gas/oil ratio (GOR) and then theasphaltene concentration in live oil can be calculated byflashing the oil at room conditions (293.15 K and 1 bar).The physical parameters of the “heavy” component are thenobtained from those of the hydrocarbon residue and asphal-tene throughmolar averaging, as shown inTable 3.Because ofthe low mole fraction of asphaltene in live oils, the molaraveraging does not affect the prediction of the bubble pointpressures. We let the hydrocarbons (HCs) include C1, C2, C3,iC4, nC4, iC5, nC5, C6, C7, C8, etc., “heavy” component, andasphaltene. The BICs between C1 and HC (except C1),between N2 and HC, between CO2 and HC, and betweenH2S and HC can be referred to the previous work and arereproduced in Table 4. Other BICs are set to zero.38,53 Itshould be mentioned that the BICs between CO2 and HC forthe Weyburn oil have to be tuned to fit the bubble pointpressures for different CO2/oil mixtures. It should also beemphasized that we have tested the method of estimating theBICs inmany industrial projects. For asphaltene precipitationin live oils, to match the available experiments, the cross-association energybetween asphaltene and“heavy”molecules

εAR has to be assumed temperature-dependent. Table 5 ex-hibits εAR as function of the temperature for the seven live oils.For the first four oils (fluids A, C1, X1, and Y3), thecoefficients in the correlations are obtained from themeasure-ments of upper onset pressures at the lowest and highesttemperatures. The upper onset pressures at the other tem-peratures and lower onset pressures are then predicted. εAR

either increases (fluids A and Y3) or decreases (fluids C1 andX1) with temperature. We are not able to provide a physicalinterpretation for this behavior within the frame of our work.It is possibly due to the complexity of the asphaltene problemsand more likely due to the poor accuracy of the onsetmeasurements. As stated in ref 36, “the onset determinationis highly uncertain”. For the other three oils (fluidsX2 andX3and Weyburn oil), εAR is estimated from the fitting of themeasured amount of precipitated asphaltenes.

Solubility parameter of the oil may explain the asphaltenephase behavior. The solubility parameter of the reservoir fluiddecreases as the pressure decreases from the reservoir condi-tion to the bubble point and makes asphaltene less stablebecause the oil density decreases. Below the bubble point,there is an increase in density and solubility parameter whenthe pressure decreases because of the release of light hydro-carbons and the oil becomes a better solvent for asphalteneagain. During depressurization, when the pressure is higherthan the upper onset, the solution is in a single-phase region.Asphaltene precipitation occurs when the pressure is betweenthe upper onset and bubble point and between the bubblepoint and lower onset. The solution is at oil-asphaltene two-phase equilibrium for the former and at gas-oil-asphaltenethree-phase equilibrium for the latter. When the pressure islower than the lower onset, there is no asphaltene precipita-tion and the solution is in the gas-oil two-phase region. Anincrease in the temperature decreases the oil density but at thesame time increases the solution entropy, resulting in acounter balancing effect; i.e., asphaltene precipitation can beeither strengthened or weakened when the temperature in-creases.54,55

Figure 1 presents the asphaltene precipitation envelop forthe reservoir fluid A with the plots of bubble point and upperand lower onset pressures as a function of the temperature.49,50

The STO has a nC7-insoluble asphaltene content of 1.4 wt%.

Table 2. CommonPhysical Parameters of Pure Components, Pseudo-

hydrocarbon Components, and Asphaltene37,48

TC (K) PC (bar) ω MW

N2 126.21 33.90 0.039 28.0CO2 304.14 73.75 0.239 44.0H2S 373.20 89.40 0.081 34.1C1 190.56 45.99 0.011 16.0C2 305.32 48.72 0.099 30.1C3 369.83 42.48 0.153 44.1iC4 407.80 36.04 0.183 58.1nC4 425.12 37.96 0.199 58.1iC5 460.40 33.80 0.227 72.2nC5 469.70 33.70 0.251 72.2C6 507.40 30.12 0.296 86.2C7 556.48 26.75 0.294 100.0C8 574.76 25.24 0.418 114.0C9 593.07 23.30 0.491 128.0C10 617.07 21.55 0.534 142.0C11 638.24 19.74 0.566 156.0asphaltene 1474 6.34 2 1800

Table 3. Physical Parameters of the “Heavy” Component for the

Seven Live Oils

TC (K) PC (bar) ω MW

fluid A 823.2 9.8 1.28 332.9fluid C1 788.6 11.7 1.28 323.6fluid Y3 689.9 15.7 1.01 276.0fluid X1 721.3 15.0 0.80 208.5fluid X2 766.9 10.5 0.99 288.6fluid X3 786.6 9.9 1.11 320.7Weyburn oil 746.2 15.9 1.00 220.1

Table 4. Non-zero Binary Interaction Coefficients for the Seven Live

Oils38,53

C1-HC N2-HC CO2-HC H2S-HC

fluid A

0.0289 þ 1.633 �10-4MW

0.10.15

0.1

fluid C1fluid Y3fluid X1fluid X2fluid X3Weyburn oil 0.071

Table 5. Cross-association Energy between Asphaltene and “Heavy”

Molecules εAR for the Seven Live Oils

fluid A εAR/kB (K) = 665.82 þ 1.0145Tfluid C1 εAR/kB (K) = 1258.85 - 1.2462Tfluid Y3 εAR/kB (K) = 422.54 þ 2.0125Tfluid X1 εAR/kB (K) = 1311.49 - 0.8835Tfluid X2 εAR/kB (K) = 1219 (303 K)fluid X3 εAR/kB (K) = 1500 (303 K), 1420 (353 K), 1400 (403 K)Weyburn oil εAR/kB (K) = 500 (332 K)

(53) Arbabi, S.; Firoozabadi, A. SPE Adv. Technol., March, 1995,139-145.

(54) Ting, P. D. Ph.D. Thesis, Rice University, Houston, TX, 2003.(55) Gonzalez, D. L. Ph.D. Thesis, Rice University, Houston, TX,

2008.

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It should be noted that our predictions are similar to those inthe literature.26 According to our calculations, when thetemperature is lower than 400 K, the temperature changedramatically affects the upper onset pressure. When thetemperature increases from 300 to 400 K, the upper onsetpressure falls by 1300 bar. The low-temperature region isimportant to evaluate the asphaltene precipitation risk duringtheproductionofdeep sea reservoirs.When the temperature ishigher than 400 K, the effect of the temperature on the upperonset pressure becomes weak. In comparison to the upperonset pressure, the bubble point pressure and lower onsetpressure are weakly dependent upon the temperature. With aunified theoretical framework, our model successfully repro-duces the asphaltene precipitation envelop.

Figure 2 shows the asphaltene precipitation envelop for thereservoir fluid X1 with asphaltene contents in STO of 0.4 and0.5 wt %. The precipitant used to determine the asphaltenecontent in STO is not reported.49 It should be emphasized thatall of the results in Figure 2b are predictions. For this oil,according to our calculations, the effect of the temperature onthe upper onset pressure is much weaker even at low tempera-tures compared to the reservoir fluid A. A decrease of theasphaltene concentration has essentially no effect on thebubble point pressure but can decrease the upper onsetpressure and increase the lower onset pressure; i.e., asphaltenebecomes more stable. It is interesting that, when the tempera-ture is higher than 400 K, the asphaltene is less stable as thetemperature increases in the gas-oil-asphaltene three-phaseregion but the trend is opposite in the oil-asphaltene two-phase region. For the higher asphaltene content, i.e.,Figure 2a, both the upper onset pressure and bubble pointpressure are faithfully captured but the lower onset pressure issomewhat overestimated. For the lower asphaltene content,i.e., Figure 2b, the performance for the bubble point pressureis still excellent and, for the lower onset pressure, it is alsoimproved. However, the upper onset pressure is slightly over-estimated. We suspect that experiments of onset pressuresmay have large errors especially for the lower onset. Ingeneral, the agreement between the experiments and calcula-tions for the reservoir fluid X1 is satisfactory.

InFigures 3 and 4,we examine the effect of the temperatureon both upper onset and bubble point pressures for thereservoir fluids C1 andY3.36 The STO includes nC5-insoluble

asphaltene content of 3.80wt%for fluidC1and3.25wt%forfluid Y3. The measurements of the lower onset pressure arenot reported. For oil Y3, the upper onset pressure alsopresents strong dependency upon temperature. On the basisof our results, when the temperature increases from 300to 400 K, the upper onset pressure can drop by 1800 bar.

Figure 1. Pressures of bubble point and asphaltene precipitationupper and lower onsets as function of the temperature for thereservoir fluid A. Symbols are experiments from refs 49 and 50,and lines represent calculations.

Figure 2. Pressures of bubble point and asphaltene precipitationupper and lower onsets as function of the temperature for thereservoir fluid X1 with an asphaltene concentration of (a) 0.5 wt% and (b) 0.4 wt%. Symbols are experiments from ref 49, and linesrepresent calculations.

Figure 3. Pressures of bubble point and asphaltene precipitationupper onset as function of the temperature for the reservoir fluidC1. Symbols are experiments from ref 36, and lines representcalculations.

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Our calculation indicates that, in the oil-asphaltene two-phaseregion when the temperature is above 400 K, the asphalteneprecipitation is strengthened as the temperature increases.This phenomenon also weakly appears for the reservoir fluidsA and C1 possibly because of the counter effect of thetemperature. For the fluids C1 andY3, our calculations agree

well with the experiments for both bubble point and upperonset pressures.

Our work predicts that the plot of upper onset pressuretends to be parallel to or away from that of the saturationpressure at high temperatures. This is in agreement with thetheories in the literature.23-26,28 However, some of the the-ories predict that these two plots may eventually meet.18,56

The difference is possibly due to different reservoir oils. Aftera careful literature search, we do not notice any direct experi-mental evidence to support either of the predictions.

For the reservoir fluidsX2andX3,we study the effect of thepressure on the amount of asphaltene precipitation.22,23 Theasphaltene content is determined using nC7 titration. Thecomparison between measurements and calculations is dis-played in Figures 5 and 6. The bubble point and upper andlower onset pressures can be readily seen in the plots. As thepressure drops, asphaltene precipitation first increases whenthe pressure is between the upper onset and bubble point andthen decreases when the pressure is between the bubble pointand lower onset. The maximum precipitation appears at thebubble point. This behavior can be interpreted from thesolubility parameter, whichwill be presented later. Ourmodelcorrectly captures the effect of the pressure on the asphaltene

Figure 4. Pressures of bubble point and asphaltene precipitationupper onset as function of the temperature for the reservoir fluidY3. Symbols are experiments from ref 36, and lines representcalculations.

Figure 5. (a) Fraction of precipitated asphaltenes and (b) relativevolume of the mixture (bubble point is the reference) as function ofthe pressure for the reservoir fluid X2 at 303 K. Symbols areexperiments from ref 22, and lines represents calculations. In panela, the calculated bubble point and upper and lower onsets aremarked by thin lines.

Figure 6. (a) Fraction of precipitated asphaltenes and (b) relativevolume of the mixture (bubble point is the reference) as function ofthe pressure for the reservoir fluid X3 at 303, 353, and 403 K.Symbols are experiments from ref 23, and lines represent calcula-tions. In panel a, the calculated bubble point and upper and loweronsets are marked by thin lines.

(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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precipitation amount particularly in the oil-asphaltene two-phase region.However, for the reservoir fluidX3, ourmethodpredicts that the asphaltene precipitation disappears too fastwhen thepressure is lower than thebubblepoint; i.e., the loweronset pressure is overestimated, which is similar to Figure 2.This is possibly one limitation of our model. Besides, we alsopresent the comparison between calculations and experimentsfor the relative volumes (the ratio between the total volumeand the bubble point volume) during depressurization. Thereis a slope change at the bubble point because the vapor phasevanishes when the pressure is higher than the bubble point.Again, the agreement is excellent.

For the Weyburn oil, we investigate the asphaltene pre-cipitation from mixing with CO2.

51 Saturates, aromatics,resins, and asphaltenes (SARA) analysis of STO was con-ducted using amodified Syncrudemethod, but the precipitantis not provided. The asphaltene content of the flashed CO2-saturated oils is determined by a photometric technique. Achange of 0.1 wt % in asphaltene content in the oil can beestimated with confidence. Weyburn oil contains a very smallamount of light components. CO2 injection can potentiallyimprove the oil recovery but may lead to a large amount ofasphaltene precipitation. In Figure 7a, the bubble pointpressure at 332 K is presented for different CO2/oil mixtures.At a very high CO2 concentration, asphaltene precipitationoccurs at the bubble point. In Figure 7b, the fraction ofprecipitated asphaltenes at 332 K and 160 bar is shown as a

function of the overall concentration ofCO2 in themixture. Asexpected, as the CO2 overall concentration increases, asphal-tene precipitation becomes more pronounced. However, atvery high CO2 concentrations, asphaltene precipitation can beinhibited because of the appearance of the gas phase, which isreflected by the slope decrease in Figure 7b. The calculationsare in good agreement with the measurements.

As mentioned before, the solubility parameter is normallyused to explain the asphaltene phase behavior. In Figure 8, wepresent the solvent solubility parameter and the oil phasedensity when the pressure decreases from the upper onset tothe lower onset for the reservoir fluid X2 at 303 K. Here, thesolvent includes all of the components in the oil phase, exceptasphaltene. Without asphaltene, the CPA-EOS is reduced tothe PR-EOS and the solvent solubility parameter can becalculated from5,38

δs ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

2ffiffiffi2

pbvs

a-Tda

dT

� �ln

vs þð1þ ffiffiffi2

p Þbvs þð1- ffiffiffi

2p Þb

sð6Þ

where vs is the molar volume of the solvent. PR-EOS canprovide accurate predictions for the solubility parameters (wehave tested the solubility parameters of several pure sub-stances, including nC5, nC6, nC8, benzene, and toluene, at298 K). From Figure 8, as expected, the solvent solubilityparameter decreases when the pressure drops from the upperonset to the bubble point because of the decrease of the oilphase density and then increases when the pressure dropsfurther from the bubble point to the lower onset because ofevaporation of light components (which causes the increase ofthe oil phase density). The minimum of both the solventsolubility parameter and oil phase density is at the bubblepointwhere the asphalteneprecipitation reaches themaximum.

As a representative, in Figure 9, we show the calculatedcomposition of both asphaltene and oil phases for the reser-voir fluidX2at 303Kand98.1 bar (bubble point).While someof the existing models assume that the precipitated phase ispure asphaltenes and/or the oil phase is pure oil (with noasphaltenes), our method describes the heterogeneity of bothasphaltene-rich and asphaltene-lean phases. Even thoughthe asphaltene precipitation reaches the maximum at thebubble point, the precipitated phase still contains a non-negligible amount of other species (about 12 wt %) and, atthe same time, there is also a small amount of asphaltenesremaining in the oil phase (about 1.2wt%). It can be expectedthat, at other precipitation conditions, both the asphalteneand oil phases should be even more heterogeneous.

Figure 7. (a) Bubble point pressure at 332 K and (b) fraction ofprecipitated asphaltenes at 332 K and 160 bar as function of theCO2 mole fraction for the Weyburn oil. Symbols are experimentsfrom ref 51, and lines represent calculations.

Figure 8.Computed solvent solubility parameter and oil phasemassdensity for the reservoir fluid X2 at 303 K with pressure betweenupper and lower onsets.

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4. Conclusions

We apply the CPA-EOS to study the asphaltene pre-cipitation in several live oils induced by a pressure decreaseand CO2 mixing. The live oils are characterized by

considering the pure components, the pseudo-hydrocarboncomponents, and the hydrocarbon residue. The residueis further divided into the “heavy” component and asphal-tene. The physical interactions are described by the PRequation. The polar-polar interactions between asphal-tene molecules (self-association) and between asphalteneand “heavy” molecules (cross-association) are describedby the thermodynamic perturbation theory. The physi-cal parameters of EOS are directly available for thepure components and pseudo-hydrocarbon components,from our recent work for asphaltene, and from the fittingof the bubble point pressures for the “heavy” component.Some common association parameters are also fromour recent paper.37 Letting the cross-association energybetween asphaltene and “heavy” molecules be temp-erature-dependent, we successfully reproduce the effectof pressure and temperature on the bubble point, asphalteneprecipitation amount and onset pressures, and gas-oil-asphaltene three-phase behavior within a unified theoreticalframework.

Acknowledgment. We are grateful to the financial supportfrom the industrial members of RERI.

Figure 9.Computed weight fractions of different components in theasphaltene andoil phases for the reservoir fluidX2 at 303Kand98.1bar (bubble point).

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