Modeling Asphaltene Phase Behavior in Crude Oil Systems Usingthe Perturbed Chain Form of the Statistical Associating Fluid

Theory (PC-SAFT) Equation of State†

Francisco M. Vargas,‡ Doris L. Gonzalez,§ George J. Hirasaki,‡ and Walter G. Chapman*,‡

Department of Chemical and Biomolecular Engineering, Rice UniVersity, Houston, Texas 77005, and DataQuality Group, Schlumberger, Houston, Texas 77056

ReceiVed August 15, 2008. ReVised Manuscript ReceiVed NoVember 30, 2008

Asphaltene precipitation and deposition can occur at different stages during petroleum production, causingreservoir formation damage and plugging of pipeline and production equipment. Predicting asphaltene flowassurance issues requires the ability to model the phase behavior of asphaltenes as a function of the temperature,pressure, and composition. In this paper, we briefly review some recent approaches to model asphaltene phasebehavior. We also present a method to characterize crude oil, including asphaltenes using the perturbed chainform of the statistical associating fluid theory (PC-SAFT). The theory accurately predicts the crude oil bubblepoint and density as well as asphaltene precipitation conditions. The theory is used to examine the effects ofgas injection, oil-based mud contamination, and asphaltene polydispersity on the phase behavior of asphaltenes.The analysis produces some interesting insights into field and laboratory observations of asphaltene phasebehavior.

Introduction

Asphaltenes constitute a potential problem in oil productionbecause of the tendency of this petroleum fraction to precipitateand deposit because of changes in temperature, pressure, andcomposition. Asphaltene deposition removal is a very expensiveprocedure that includes intervention costs and the loss ofproduction. Better understanding of the mechanisms by whichasphaltenes precipitate and deposit is needed to improve theprediction and avoid associated production and processingproblems.

Asphaltenes are a polydisperse mixture of the heaviest andmost polarizable fraction of the oil. They are defined in termsof their solubility; i.e., asphaltenes are miscible in aromaticsolvents but insoluble in light paraffin solvents. The depositionmechanism and the molecular structure of this solubility classare not completely understood, but it is known that asphaltenephase behavior strongly depends upon pressure, temperature,and composition.

The objective of this paper is to provide some insight intothe effect of pressure, temperature, and composition on asphalt-ene phase behavior using the statistical associating fluid theory(SAFT) equation of state and to offer an explanation of severalfield observations related to asphaltene phase behavior. Theseexamples include oil depressurization, composition changes [gasinjection and oil-based mud (OBM) contamination], and poly-dispersity. The current stage of this research and the future workis also presented.

Previous studies of asphaltenes have relied on Flory-Huggins-based models. Examples of such approaches include theHirschberg model,1 de Boer plot,2 the ASIST method developedby Wang and Buckley,3 and the Yarranton et al. model.4-6 Theadvantage of a Flory-Huggins-based approach is that the modelis simple to apply and interpret in terms of solubility parameters.These methods have been widely applied in the oil industrywith success. However, a limitation of Flory-Huggins-basedmodels is that they do not explicitly include the effect ofcompressibility on phase behavior. This compressibility effectis essential to describe certain types of phase behavior commonlyobserved in systems with large size differences betweenmolecules. In practice, these theories require an equation of stateto predict the effect of compressibility on the solubilityparameter.

Equations of state can be more predictive because theydirectly include the effect of compressibility. Cubic equationsof state (CEOS) are simple models that have been widely appliedin industry. CEOS have also been applied in modeling asphalt-ene phase behavior. Chung et al.7 combined the Flory-Hugginsmodel with the Peng-Robinson CEOS to model asphaltenesolubility in oil. Burk et al.8 obtained the Flory-Huggins modelparameters from the Zudkevitch-Joffe-Redlich-Kwong CEOS.

† Presented at the 9th International Conference on Petroleum PhaseBehavior and Fouling.

* To whom correspondence should be addressed: Department of Chemi-cal and Biomolecular Engineering, Rice University, MS 362, 6100 MainSt., Houston, TX 77005. Telephone: +1 (713) 348-4900. Fax: +1 (713)348-5478. E-mail: wgchap@rice.edu.

‡ Rice University.§ Schlumberger.

(1) Hirschberg, A.; De Jong, L. N. J.; Schipper, B. A.; Meyers, J. G.SPE Tech. Pap. 11202, 1982.

(2) de Boer, R. B.; Leerlooyer, K.; Eigner, M. R. P.; van Bergen, A. R. D.SPE Prod. Facil. 1995.

(3) Wang, J. X.; Buckley, J. S. Energy Fuels 2001, 15, 1004–1012.(4) Alboudwarej, H.; Akbarzadeh, K.; Beck, J.; Svrcek, W. Y.; Yarran-

ton, H. W. AIChE J. 2003, 49, 2948.(5) Mannistu, K. D.; Yarranton, H. W.; Masliyah, J. H. Energy Fuels

1997, 11, 615.(6) Yarranton, H. W.; Masliyah, J. H. AIChE J. 1996, 42, 3533.(7) Chung, F.; Sarathi, P.; Jones, R. Modeling of asphaltene and wax

precipitation. NIPER-498, 1991.(8) Burke, N. E.; Hobbs, R. E.; Kashou, S. F. J. Pet. Technol. 1990, 42,

1440–1446.

Energy & Fuels 2009, 23, 1140–11461140

10.1021/ef8006678 CCC: $40.75 2009 American Chemical SocietyPublished on Web 01/12/2009

In the method proposed by Nghiem et al.,9 the C31+ heavy endof crude oil is first divided into nonprecipitating and precipitatingsubfractions. Different interaction parameters are then assignedto reproduce experimental results. In another example, Ak-barzadeh et al.,10 modified the Soave-Redlich-Kwong CEOSby adding an additional aggregation size parameter to asphalt-enes. More recently, Nikookar, Omidkhah, and Pazuki,11-13 havereported the development and application of a CEOS formodeling the asphaltene precipitation in crude oils.

However, the major limitation of CEOS is that they cannotadequately describe the phase behavior of mixtures of moleculeswith large size differences and that they are unable to accuratelycalculate liquid densities. The reason for their poor predictioncapability is because CEOS are typically fit to the critical point.Accurate modeling of liquid density is essential for an equationof state to predict liquid-liquid equilibria and their correspond-ing parameters, such as the solubility parameter, over a rangeof conditions. It has been found that CEOS that are fit to liquidphase density have a better performance in reproducing phasebehavior data.14 A more modern equation of state is the SAFTfamily of models.15-18 This equation of state can accuratelymodel mixtures of molecules of different sizes. Because it isbased on statistical mechanics, SAFT can accurately predict theeffects of temperature, pressure, and composition on fluid phaseproperties. SAFT-based equations of state have become impor-tant tools in predicting polymer phase behavior to preventfouling in polymer processing.19 We will focus our discussionparticularly on the perturbed chain (PC) version of SAFT,developed by Gross and Sadowski.18 This version of SAFTaccurately predicts the phase behavior of high-molecular-weightfluids similar to the large asphaltene molecules, and it is readilyavailable in commercial simulators, such as Multiflash andVLXE.

Introduction to SAFT

The SAFT theory models a molecule as a chain of bondedspherical segments. The parameters for the model are physical.The model requires the number of segments in a chain molecule,the diameter or volume of a segment, and the van der Waalsattraction between segments. These parameters are fit tosaturated liquid densities and vapor pressures. These segmentscould represent methylene groups on a molecule, but in practice,it is found that the fitted parameters for a segment representabout one and a half methylene groups. As expected, all threepure component parameters correlate with molecular weightwithin a homologous series. For example, the number of

segments in a molecule correlates linearly with the molecularweight within a homologous series, e.g., alkanes and polynucleararomatics. The segment-segment van der Waals attractiondepends upon the molecular weight for small molecules butapproaches a limiting value as the molecular weight increases.In modeling polyethylene, parameters can be estimated byextrapolating the correlations for the chain length, i.e., thenumber of segments, segment diameter, and segment-segmentattraction energy for alkanes, to the molecular weight of thepolymer. Tables of pure component parameters are given byGross and Sadowski,18 and Ting et al.20

The SAFT equation of state can also predict the effect ofassociation between molecules.15-18 The association term inSAFT is widely used to model systems containing alcohols andwater. The association term has been adopted in other models.For example, the association term used in the cubic plusassociation equation of state21 is the SAFT association term.15-17

The association term requires at least two additional parametersfor each associating component. In modeling asphaltene pre-cipitation, we have not needed to include association to matchthe observed phase behavior.

The SAFT model has been applied to a wide range of systemsby numerous academic groups and companies. Systems modeledrange from alcohols to co-polymers, refrigerants to amphiphiles,and even electrolytes and ionic liquids. Although the theory wasdeveloped as a model for small associating molecules, theequation of state has seen its widest application for polymersolutions.

In the area of polymer solutions, we have investigated theeffects of size asymmetry, polydispersity, chain branching, andfunctional groups on phase behavior predictions.19,22-26 One ofthe algorithms that we developed enables the efficient calculationof phase behavior for polydisperse polymer solutions with alarge number of pseudo-components without restriction on thepolymer molecular-weight distribution.27,28

Polymer solutions and solutions containing oligomers areexamples of mixtures with large size asymmetry that showsimilar phase behavior as observed in petroleum systems. Asan example, consider a mixture of polystyrene, cyclohexane,and carbon dioxide shown in Figure 1. You might consider thecyclohexane to be the “oil”, polystyrene to be a large componentsimilar to asphaltenes, and carbon dioxide to be a precipitatingagent. The system has been studied experimentally by de Loos,Bungert, and Arlt, and the results are reported in ref 29. Grossand Sadowski have modeled this system with the PC-SAFTequation of state.29 We perform our own calculations here.

In Figure 1, first consider the mixture with no carbon dioxide.The vapor pressure curve for cyclohexane is shown at thebottom, labeled 0% CO2. The nearly vertical phase boundaryat about 20 °C is an upper critical solution temperature (UCST)-

(9) Nghiem, L. X.; Coombe, D. A. Soc. Pet. Eng. J. 1997, 2, 170–176,SPE 36106.

(10) Akbarzadeh, K.; Ayatollahi, S.; Moshfeghian, M.; Alboudwarej,H.; Yarranton, H. W. J. Can. Pet. Technol. 2004, 43, 31.

(11) Nikookar, M.; Omidkhah, M. R.; Pazuki, G. R. Pet. Sci. Technol.2008, 26, 1904–1912.

(12) Nikookar, M.; Pazuki, G. R.; Omidkhah, M. R.; Sahranavard, L.Fuel 2008, 87, 85.

(13) Pazuki, G. R.; Nikookar, M.; Omidkhah, M. R. Fluid Phase Equilib.2007, 254, 42.

(14) Ting, P. D.; Joyce, P. C.; Jog, P. K.; Chapman, W. G.; Thies, M. C.Fluid Phase Equilib. 2003, 206, 267.

(15) Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. FluidPhase Equilib. 1989, 52, 31.

(16) Chapman, W. G.; Jackson, G.; Gubbins, K. E. Mol. Phys. 1988,65, 1057–1079.

(17) Chapman, W. G.; Jackson, G.; Gubbins, K. E. Ind. Eng. Chem.Res. 1990, 29, 1709–1721.

(18) Gross, J.; Sadowski, G. Ind. Eng. Chem. Res. 2001, 40, 1244–1260.

(19) Jog, P. K.; Chapman, W. G.; Gupta, S. K.; Swindoll, R. D. Ind.Eng. Chem. Res. 2002, 41, 887.

(20) Ting, P. D.; Gonzalez, D. L.; Hirasaki, G. J.; Chapman, W. G. InAsphaltenes, HeaVy Oils, and Petroleomics; Mullins, O. C., Sheu, E. Y.,Hammani, A., Marshall, A. G., Eds.; Springer: New York, 2007.

(21) Yakoumis, L. V.; Kontogeorgis, G. M.; Voutsas, E. C.; Hendriks,E. M.; Tassios, D. P. Ind. Eng. Chem. Res. 1998, 37, 4175.

(22) Dominik, A.; Chapman, W. G. Macromolecules 2005, 38, 10836.(23) Dominik, A.; Chapman, W. G.; Kleiner, M.; Sadowski, G. Ind.

Eng. Chem. Res. 2005, 44, 6928.(24) Dominik, A.; Jain, P.; Chapman, W. G. Mol. Phys. 2005, 103, 1387.(25) Ghosh, A.; Blaesing, J.; Jog, P. K.; Chapman, W. G. Macromol-

ecules 2005, 38, 1025.(26) Jog, P. K.; Garcia-Cuellar, A.; Chapman, W. G. Fluid Phase

Equilib. 1999, 158-160, 321.(27) Ghosh, A.; Ting, P. D.; Chapman, W. G. Ind. Eng. Chem. Res.

2004, 43, 6222.(28) Jog, P. K.; Chapman, W. G. Macromolecules 2002, 35, 1002.(29) Gross, J.; Sadowski, G. Ind. Eng. Chem. Res. 2002, 41, 1084.

Asphaltene Phase BehaVior in Crude Oil Systems Energy & Fuels, Vol. 23, 2009 1141

type boundary. Below this temperature, the system splits intotwo phases. As the temperature rises above this boundary, thesystem moves from a region of two liquid phases to a singleliquid phase. This is typically explained to occur because, atthis phase boundary temperature, the entropy gain from mixingjust overcomes the enthalpically favored phase splitting.

There is another phase boundary as the temperature isincreased at constant pressure. This curve is a lower criticalsolution temperature (LCST)-type phase boundary. As thetemperature is increased at constant pressure, the solventexpands (lowering the solubility parameter of the solvent) andbecomes a poor solvent for the polymer. Prediction of this typeof phase boundary requires an equation of state because it isthe compressibility of the system that causes the phase splitting.The LCST phase boundary usually occurs as you approach thecritical temperature of the mixture because this is where themixture is most compressible.

In Figure 1, considering the results at various amounts ofcarbon dioxide added to the system is like considering a liveoil with an increasing gas/oil ratio or considering the effect ofgas injection on the phase behavior of an oil. With greateramounts of carbon dioxide in the solvent, the bubble point curvefor the solvent increases, thus shifting the LCST-type phaseboundary to higher pressures and lower temperatures. At highenough CO2 content, the LCST-type phase boundary mergeswith the UCST-type phase boundary.

The points in Figure 1 show the experimental results of deLoos,30 Bungert,31 and Saeki et al.32 The curves show ourcalculations using a single set of temperature-independentparameters fit by Gross and Sadowski using PC-SAFT. Agree-ment between the equation of state and the experimental datais noteworthy for this system.

This system shows many qualitative similarities with thephase behavior reported for asphaltenes in crude oil. Similar tothe polystyrene, asphaltenes are said to be stable at reservoirpressure but destabilize on depressurization. Also, interestingly,

temperature changes may result in either asphaltene precipitationor solubilization. For instance, in propane, asphaltenes becomeless soluble as temperature increases.33 However, for titrationswith heavier alkanes, e.g., C5+, asphaltene stability increaseswith increasing temperature.33 At a given temperature andpressure, increasing the gas content can destabilize asphaltenes.Each of these cases is analogous to the polystyrene system inFigure 1. The implication is that, similar to the polystyreneexample, we can understand and predict (given equation of stateparameters) the effect of temperature, pressure, and compositionon asphaltene phase behavior in crude oil.

Oil Characterization Using PC-SAFT

As explained above, the PC-SAFT equation of state has threepure parameters for each non-associating component. Tocharacterize an oil, the three parameters must be determinedfor each pseudo-component. We have developed a methodologyto determine these parameters based on the stock tank oildensity, the bubble point, saturates, aromatics, resins, andasphaltenes (SARA) analysis of the oil, and gas chromatographicanalysis, providing the composition of the mixture. Correlationsfor the three PC-SAFT parameters have been previouslyreported34 as a function of the molecular weight for alkanes,benzene derivatives, and polynuclear aromatics.

This information about the oil is sufficient to fit parametersfor each component, except for the asphaltene component. Wechoose to fit the three PC-SAFT parameters for an asphaltenecomponent to measurements of the asphaltene precipitation onsetconditions. Such precipitation onset has been measured atambient pressure by titrating with n-alkane precipitants or inhigh-pressure measurements at a given gas composition. In theabsence of a molecular-weight distribution, asphaltenes can betreated as a monodisperse pseudo-component. After fittingasphaltene parameters to the precipitation data, the PC-SAFTequation of state can predict the effect of temperature, pressure,and composition on asphaltene phase behavior. If no precipita-

(30) de Loos, T. W. Measurements of 1994. Published in ref 31.(31) Bungert, B. Ph.D. Dissertation, Technische Universitat Berlin,

Berlin, Germany, 1998.(32) Saeki, S.; Kuwahara, N.; Konno, S.; Kaneko, M. Macromolecules

1973, 6, 246–250.

(33) Wu, J. Ph.D. Thesis, University of California at Berkeley, Berkeley,CA, 1998.

(34) Gonzalez, D. L.; Hirasaki, G. J.; Creek, J.; Chapman, W. G. EnergyFuels 2007, 21, 1231–1242.

Figure 1. Cloud-point curves and vapor-liquid equilibrium of the ternary system polystyrene (PS)-cyclohexane-carbon dioxide (PS: Mw ) 101.4kg/mol; Mw/Mn ) 1.09; wPS ) 0.1 at 0% CO2). A comparison of the experimental data to PC-SAFT correlation results. The polymer is modeledas monodisperse (PS-cyclohexane, kij ) 0.0075; PS-CO2, kij ) 0.195; cyclohexane-CO2, kij ) 0.13).

1142 Energy & Fuels, Vol. 23, 2009 Vargas et al.

tion onset data is available for an oil, conditions for asphalteneprecipitation can be predicted using asphaltene parameters fitto another oil. We have found that asphaltenes are well-characterized using parameters for benzene derivatives. Adetailed description of the method to determine pseudo-component parameters is given in ref 34.

Modeling and Analysis of Asphaltene Phase Behavior

Effect of Pressure. Operators have observed in the field thatasphaltenes tend to plug over a range of pressures. For thewellbore, above or below a certain pressure range, no depositionis observed. This behavior can be explained by analyzing thedepressurization of the model oil presented in Figure 2. In thefigure modified from Ting,35 the closed markers are measuredbubble points, the open markers are measured asphalteneprecipitation onset points (asphaltene stability boundary), andthe curves are predictions of the PC-SAFT equation of state.At high pressure, the asphaltenes are soluble in oil. However,during pressure depletion, the oil expands, reducing the oilsolubility parameter, and becomes a poor solvent for asphaltene.At low enough pressure, the asphaltene precipitation onset isreached and asphaltenes begin to precipitate. Upon furtherdepressurization, the system arrives at its bubble point, wherethe light components, which are asphaltene precipitants, escapefrom the liquid phase. As this happens, the solubility parameterof the oil increases until the oil becomes a better asphaltenesolvent and the oil stabilizes again. Because this approachcomprises an equilibrium model, the redissolution kinetics,which may play an important role, is not taken into account.

We can follow the same depressurization in a plot of solubilityparameters1,36 as shown in Figure 3. We see that the solubilityparameter of the oil decreases as the pressure is decreased tothe bubble point. Upon further depressurization, the solubilityparameter of the oil increases. We also find that, along theasphaltene stability boundary, this system shows a nearlyconstant solubility parameter. This indicates, as shown in Figure3, that asphaltenes are unstable below a certain solubility

parameter of the oil as suggested by Buckley and Hirasaki.37

This constant solubility parameter threshold has been used insome models of asphaltene stability.38-40 In further calculationsusing the PC-SAFT equation of state, we have found that thesolubility parameter is not always constant along the asphaltenestability boundary. This result has been shown experimentallyand explained using the Flory-Huggins equation.3,41

Effect of Temperature. We have previously mentioned thatasphaltene solubility can either increase or decrease withincreasing temperature.33 We also stated that the SAFT-basedequations of state are capable of predicting both the lower andupper critical solution temperatures that are present in complexsystems. A lower critical solution temperature-type phasetransition can occur in systems with large size differencesbetween molecules. In this case, an increase in temperature (ata fixed pressure) will result in a decrease in oil density andthus a decrease in solubility parameter, resulting in theprecipitation of asphaltenes. At lower temperatures, we canobserve asphaltene precipitation with a decrease in temperature.

(35) Ting, P. D.; Hirasaki, G. J.; Chapman, W. G. Pet. Sci. Technol.2003, 21, 647–661.

(36) Ting, P. D. Rice University, Houston, TX, 2003.

(37) Buckley, J. S.; Hirasaki, G. J.; Liu, Y.; Von Drasek, S.; Wang,J. X.; Gill, B. S. Pet. Sci. Technol. 1998, 16, 251.

(38) Wiehe, I. A. Prepr. Pap.-Am. Chem. Soc., DiV. Pet. Chem. 1999,44, 166.

(39) Wiehe, I. A. Process Chemistry of Petroleum Macromolecules; CRCPress: Boca Raton, FL, 2008.

(40) Wiehe, I. A.; Kennedy, R. J. Energy Fuels 2000, 14, 56.(41) Wiehe, I. A.; Yarranton, H. W.; Akbarzadeh, K.; Rahimi, P. M.;

Teclemariam, A. Energy Fuels 2005, 19, 1261–1267.

Figure 2. Asphaltene instability onsets (open symbols) and bubble points (filled symbols) for a model oil at two different temperatures. Linesrepresent the simulation results using PC-SAFT. This figure was adapted from Ting.35

Figure 3. Calculated solubility parameter during pressure depletion forthe model live oil at 20.0 °C with 0.143 mass fraction methane abovethe bubble point. Asphaltenes are unstable below the asphalteneinstability line. This figure was adapted from Ting.36

Asphaltene Phase BehaVior in Crude Oil Systems Energy & Fuels, Vol. 23, 2009 1143

Both of these behaviors have been observed experimentally,42

as shown in Figure 4.Furthermore, special temperature effects have been observed

when CO2 is added to oil-containing asphaltenes. We havepreviously reported43 that CO2 can destabilize or stabilizeasphaltenes in an oil depending upon the temperature of thesystem.

We have observed that, at temperatures below a certaincrossover point, CO2 can act as an asphaltene precipitationinhibitor, whereas at temperatures above this point, CO2 behavesas a strong asphaltene precipitant. This dual effect is notobserved with other gases, such as nitrogen or methane. Thephase behavior for a live oil with injection of CO2 is shown inFigure 5. The crossover temperature for this case is about 180°F, which is in good agreement with field observations.44 Anexplanation for this phenomenon is that the solubility parameterof CO2 is greater than the solubility parameter of the oil attemperatures below the crossover point. Thus, adding CO2 tothe oil increases the solubility parameter of the mixture, andbecause of its increasing proximity with the solubility parameterof asphaltenes, the mixture becomes more stable. On the otherhand, at temperatures above the crossover point, the solubilityparameter of CO2 is lower than the solubility parameter of theoil, and therefore, the solubility parameter of the mixturedecreases with an increasing amount of CO2. In this case, theoil becomes unstable and the asphaltenes readily precipitate.

Effect of Composition. The effect of compositional changesin live oils that may result in either asphaltene precipitation orsolubilitization has also been studied. Two examples aresummarized in this paper: the effect of OBM contamination onasphaltene stability and the effect of gas injection.

OBM that is used to increase borehole stability during drillingcan contaminate near wellbore reservoir fluids. An OBM cansignificantly modify the composition and predicted phasebehavior of the asphaltene in the formation fluid, causing wrongdata interpretation.45 Because samples of the reservoir fluid thatare submitted for laboratory analysis may be contaminated withOBMs, the laboratory results must be corrected to remove theeffect of the contamination. The extent of OBM contaminationcan be determined using chromatography. Because the OBMcomposition is known, the OBM-free composition is calculatedmathematically by subtracting the corresponding fraction.Simulations using the PC-SAFT equation of state can beperformed for the clean and contaminated oil to describe theeffect of OBM contamination.34 Because the OBM is aprecipitating agent for asphaltenes, we might expect that OBMcontamination would increase the pressure at which asphaltenesstart precipitating, but this is not necessarily the case. Accordingto the results presented in Figure 6, for a live oil, fluid B, boththe asphaltene precipitation onset and bubble point pressuredecrease when successive amounts of OBM are added to anoriginal high asphaltene content sample. Both the precipitationonset and the bubble point curves estimated by PC-SAFT closelyfollow the experimental findings. Note that the gas-oil ratio(GOR) also decreases by the OBM addition. Although the OBMis a precipitant for asphaltenes, the OBM contamination dilutesthe gaseous components of the oil that are stronger asphalteneprecipitants. As the GOR decreases, the asphaltene precipitationonset pressure and bubble point pressure decrease. The correc-tion for OBM contamination, which can be significant, as inthe case of reservoir fluid C shown in Figure 7, requires anaccurate equation of state model.

The other compositional effect on asphaltene stability thatwe describe in this paper is due to gas injection. Gas injectionhas traditionally played an important role for oil recovery inoil field development. Injection of a gas that dissolves in oilallows for the recovery of oil that would otherwise be trappedin the tight pores of the rock.

The application of enriched or dry natural gas, CO2, or N2

flooding schemes to enhance oil recovery can induce destabi-(42) Jamaluddin, A. K. M.; Joshi, N.; Iwere, F.; Gurnipar, O. SPE 74393,2001.

(43) Gonzalez, D. L.; Vargas, F. M.; Hirasaki, G. J.; Chapman, W. G.Energy Fuels 2008, 22, 757–762.

(44) Creek, J. Personal communication, 2008.

(45) Muhammad, M.; Joshi, N.; Creek, J.; McFadden, J. In the 5thInternational Conference on Petroleum Phase Behavior and Fouling, Banff,Alberta, Canada, 2004; pp 13-17.

Figure 4. Onset of asphaltene precipitation and bubble points forreservoir fluid A. Data were from Jamaluddin et al.42 Curves correspondto simulations using the PC-SAFT equation of state.

Figure 5. Fluid A phase behavior after the addition of CO2, predictedby PC-SAFT.

Figure 6. OBM contamination effect on the asphaltene phase behaviorof fluid B.

1144 Energy & Fuels, Vol. 23, 2009 Vargas et al.

lization and deposition of asphaltenes because of changes incomposition.

The asphaltene stability curve in a recombined oil as afunction of the pressure at different separator gas concentrationswas determined in a previous work.35 The simulated results forthe recombined oil reproduce the experimental data obtainedin a PVT cell by Ting et al.35 from Robinson (Figure 8). InFigure 9, we compare simulation results for nitrogen additionto a recombined oil with experimental depressurization data ata reservoir temperature of 296 °F from Jamaluddin et al.42 Theaddition of 5, 10, and 20 mol % of nitrogen strongly increases

the asphaltene instability onset. The difference between theasphaltene onset pressure and the bubble point pressure (Ponset

- Pbbp) increases with the amount of injected nitrogen. Theagreement between the simulated and experimental data isexcellent.

Effect of Polydispersity. Asphaltenes are a polydisperse classof components in the oil. Polydispersity can have a large affecton the phase behavior as well as (according to our depositionsimulations) the deposition profile. The effect of polydispersitycan be seen by considering the example of a polymer solution.

Consider a plot of the cloud point pressure versus the massfraction of a polymer for a polydisperse polymer in a solvent. Wemodel the polymer molecular-weight distribution using a fewpseudo-components, as illustrated in Figure 10. Using an algorithmdeveloped in our group, the phase behavior of this polydisperse

(46) de Loos, T. W.; de Graaf, L. J.; de Swaan Arons, J. Fluid PhaseEquilib. 1996, 117, 40.

Figure 7. Asphaltene precipitation behavior of reservoir fluid C, calculated with the PC-SAFT equation of state.

Figure 8. SAFT-predicted and measured asphaltene instability onsetand mixture bubble points for the recombined oil at 71 °C.

Figure 9. Addition of successive amounts of N2 to reservoir fluid A.Experimental data were from Jamaluddin et al.42 Curves correspond tosimulation results using the PC-SAFT equation of state.

Figure 10. Cloud-point and shadow curves for poly(ethyleneoctene)+ hexane at 450 K from experimental points and SAFT (curves). Thedotted curve shows the composition of the incipient phase at the cloudpoint. Results for mono- and polydisperse polymers are included.Simulations by Jog et al.,19 and experimental data are taken from deLoos et al.46

Asphaltene Phase BehaVior in Crude Oil Systems Energy & Fuels, Vol. 23, 2009 1145

polymer can efficiently be calculated. Data from de Loos46 forpolyethylene are shown in Figure 10. These data were simulatedassuming a monodisperse polymer as well as a polydispersepolymer. We see that, at higher polymer concentrations, the cloudpoint pressure for a monodisperse polymer and a polydispersepolymer give nearly identical results. For the polydisperse polymerat concentrations above about 5%, the phase that precipitates(shown by the dashed shadow curve) is a light phase (polymer-lean phase). Because the precipitating phase is polymer-lean, thephase boundary primarily depends upon the average molecularweight of the polymer; thus, the monodisperse result is similar tothe polydisperse result. In crude oil systems, precipitation of sucha light phase from a heavy oil has been observed in laboratoryexperiments.47 For polymer concentrations typically less than about5%, polydispersity changes the phase diagram dramatically. Atthese low polymer concentrations, the phase that precipitates, shownby the shadow curve, is a heavy polymer-rich phase. In this case,the phase boundary is determined by the highest polymer molec-ular-weight components. As shown in the figure, a polydispersesystem shows a dramatically higher cloud point pressure at lowpolymer concentrations. The phase behavior of asphaltenes isexpected to be qualitatively similar.

Our preliminary calculations indicate that polydispersity affectsthe shape of the deposition profile. In Figure 11, we have modeledthe asphaltene component as a mixture of three pseudo-componentsthat mimic the incremental amount of asphaltene precipitated on a20:1 dilution of the oil with heptane, undecane, and pentadecane,respectively. From Figure 11, we can see that polydispersity alsoaffects the amount of asphaltene precipitated. The figure showsthe different precipitation profiles obtained for mono- versuspolydisperse asphaltenes upon titration with an alkane precipitant.For a monodisperse asphaltene, the amount of asphaltene thatprecipitates increases quickly upon adding an alkane precipitantbeyond the precipitation onset condition. For polydisperse asphalt-enes, the amount of asphaltene precipitated increases more slowlyupon adding a precipitant. As expected, asphaltene can redissolveat high enough dilution in a precipitant. The amount of dilutionthat is “high enough” depends upon the highest molecular-weightcomponents of the asphaltene fraction.

Conclusions

In this paper, we have described the effect of temperature,pressure, and composition on asphaltene phase behavior.

Examples of each case have been presented on the basis ofexperimental data and modeling using the PC-SAFT equationof state. The emphasis has been to provide a physical explana-tion of the phase behavior and to relate the phase behavior tothat of analogue mixtures with large size asymmetry. In mostcases, asphaltene stability in crude oils can be related to changesin the solubility parameter of the crude oil under changingconditions of temperature, pressure, and composition. The PC-SAFT equation of state has been shown to accurately modelthe phase stability of asphaltenes in crude oil over a wide rangeof conditions and for a variety of cases, including reservoirdepressurization, OBM contamination, and gas addition. Thisenables the model to predict asphaltene behavior at reservoirconditions based on data at ambient conditions. Research iscontinuing to extend the equation of state (including the criticalregion48), to improve characterization of the oil, and to modelpolydisperse asphaltenes.

Although modeling asphaltene phase behavior is related toplugging issues, asphaltene precipitation does not necessarilymean that deposition will occur. It is expected that depositionis related to the properties of the precipitated asphaltene, theamount of asphaltene precipitated, and the flow field in theproduction system. This is a subject of ongoing research, inwhich the thermodynamic description of asphaltene phasebehavior is combined with models for the fluid flow, asphalteneaggregation, and asphaltene deposition.

Acknowledgment. The authors thank DeepStar for financialsupport. The authors also thank Jill Buckley (New Mexico Tech),Jianxing Wang (Chevron ETC), Jeff Creek (Chevron ETC), and P.David Ting (Shell) for fruitful discussions, and VLXE and Infochemfor providing help in accessing their thermodynamic simulators.F.M.V. also thanks the support from Tecnologico de Monterreythrough the Research Chair in Solar Energy and Thermal-FluidSciences (Grant CAT-045).

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(47) Ratulowski, J. Personal communication, 2002.(48) Bymaster, A.; Emborsky, C.; Dominik, A.; Chapman, W. G. Ind.

Eng. Chem. Res. 2008, 47, 6264–6274.

Figure 11. Solubility of mono- and polydisperse asphaltenes in model oil mixed with n-alkanes at 20 °C and 1 bar. Results are by Ting et al.20

1146 Energy & Fuels, Vol. 23, 2009 Vargas et al.