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a

ARRAA

KAPMWG

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Fluid Phase Equilibria 369 (2014) 86–94

Contents lists available at ScienceDirect

Fluid Phase Equilibria

journa l h om epage: www.elsev ier .com/ locate / f lu id

C-SAFT modeling of asphaltene phase behavior in the presence ofonionic dispersants

ohammad Sedghi, Lamia Goual ∗

epartment of Chemical and Petroleum Engineering, University of Wyoming, 1000 East University Avenue, Laramie, WY 82071, USA

r t i c l e i n f o

rticle history:eceived 11 November 2013eceived in revised form 14 February 2014ccepted 17 February 2014vailable online 27 February 2014

eywords:sphaltene dispersantC-SAFT thermodynamic modelolecular dynamicsertheim association theory

ibbs energy of association

a b s t r a c t

This study introduced a new method to characterize asphaltenes in PC-SAFT equation of state (EOS)and correctly model the effect of nonionic dispersants on the thermodynamic behavior of asphaltenes.Our approach is to combine microscale parameters from Molecular Dynamics (MD) simulations withPerturbed Chain Statistical Associating Fluid Theory (PC-SAFT) to develop a comprehensive model thatenables the prediction of macroscopic behavior such as the amount and onset of asphaltene precipitationat various pressures, temperatures, and fluid compositions. More specifically, association parameterswere considered for asphaltene molecules and determined by equating the Gibbs energy of associa-tion calculated by PC-SAFT EOS to the one obtained from MD simulations. A correlation was derivedto relate the association energy parameter (εAB) of asphaltenes to the molar weight of their aromaticcores. Our model showed that asphaltene association energy is affected by temperature and solventtype and is inversely proportional to the solubility parameter of the medium. The hetero-segmentapproach in PC-SAFT EOS was adopted to accurately characterize asphaltene molecules and their non-association parameters in PC-SAFT were determined based on the molecular weight and aromaticity

factor of asphaltenes. Moreover, the average aggregation number of asphaltene nanoaggregates wascalculated using the Wertheim association theory. This model was applied to predict asphaltene precipita-tion envelopes for three different live crude oils and showed excellent agreement with experimental datain the literature. Additionally, the model could correctly predict the amount of asphaltene precipitationupon addition of nonionic dispersants.

© 2014 Elsevier B.V. All rights reserved.

. Introduction

Asphaltene precipitation and subsequent deposition in produc-ion tubings and topside facilities present a significant challengeo the petroleum industry because they reduce well productivitynd limit fluid flow. The main factors that promote precipitationre pressure, temperature and composition variations due to gasnjection, phase separation, and mixing of fluid streams. Paradoxi-ally, asphaltene precipitation is often observed in light crude oilshat contain very low asphaltene content. This is because light oilsontain large amounts of light alkanes in which asphaltenes haveimited solubility. In order to limit the costs associated with asphal-ene remediation in the field, it is necessary to accurately predict

heir thermodynamic phase behavior.

There are currently two prevalent schools of thought regardingow asphaltenes are stabilized in crude oil: colloidal theory and

∗ Corresponding author. Tel.: +1 3077663278.E-mail address: lgoual@uwyo.edu (L. Goual).

ttp://dx.doi.org/10.1016/j.fluid.2014.02.021378-3812/© 2014 Elsevier B.V. All rights reserved.

solubility theory. In the colloidal theory, asphaltenes are describedas insoluble solid particles stabilized in crude oil by steric stabi-lization layers formed by resins adsorbed on their surface [1–5].Precipitation is believed to occur when resin molecules are strippedaway from asphaltene particles leading to further aggregation andflocculation of asphaltene colloids [1]. Examples of this theory canbe found in the steric-stabilization model of Leontarities and Man-soori [2] and the thermodynamic micellization model proposed byFiroozabadi and co-workers [3–5]. However recent studies indi-cated that resins may not have a significant impact on asphaltenestability in petroleum fluids [6].

In the solubility theory, asphaltene molecules are solublein crude oil [7–9] and their precipitation can be modeled asliquid–liquid or solid–liquid phase equilibrium. Two main types ofmodels have emerged from this theory: (1) regular solution mod-els that use Flory–Huggins theory [10,11], and (2) equations of state

(EOS) models. Hirschberg [12] was the first to use Flory–Hugginsequation, originally developed for polymers, to model asphal-tene precipitation. Due to the simplicity of the model, it becamewidely popular in the oil industry and many works have been

hase E

ppitoarwcdawtHuicac[pelP(oatt

nopstcsststa(ttcsd

uatasmngHmono[hMd

M. Sedghi, L. Goual / Fluid P

erformed to improve its accuracy ever since [13–19]. For exam-le, the Flory–Huggins EOS was recently modified by Zuo et al. to

nclude a gravitational potential term for asphaltene particles. Inhis model, the size of asphaltene particles was determined basedn the Yen–Mullins model [7,8,19,20]. However, the Flory–Hugginspproach ignores the association of asphaltene molecules andequires new solubility parameter and molar volume calculationshenever oil composition is changed. To explicitly account for the

omposition of crude oil, EOS models have been applied to pre-ict asphaltene phase behavior. A cubic EOS combined with thessociation term of the Statistical Association Fluid Theory (SAFT)as used by Li and Firoozabadi [21,22] to calculate the asphal-

ene precipitation envelope (APE) and the amount of precipitation.owever, the association parameters of asphaltene molecules weresed as fitting parameters. To avoid this problem, Ting et al. [23]

ntroduced a new model based on Perturbed-Chain Statistical Asso-iating Fluid Theory (PC-SAFT) EOS [24] that considers asphalteness monodispersed nanoaggregates. This model assumes that pre-ipitation is mainly governed by van der Waals dispersion forces25]. However, since the size of nanoaggregates is not known ariori, the PC-SAFT parameters for asphaltenes had to be fitted toxperimental data. Recently, Pannuganti et al. [26] used the corre-ations developed by Gonzalez et al. [27,28] to calculate asphalteneC-SAFT parameters based on molar weight and aromaticity factor�) of asphaltene nanoaggregates in order to reduce the numberf fitting parameters. The agreement between model predictionnd experimental data was excellent; although fitted values ofhe aromaticity factor did not agree very well with the litera-ure.

To the best of our knowledge, there are currently no thermody-amic models that can accurately predict the effect of dispersantsn asphaltene precipitation. The difference between nonionic dis-ersants and aromatic solvents is that dispersants can reduce theize of asphaltene aggregates as opposed to aromatic solvents,herefore they can effectively delay the onset of asphaltene pre-ipitation even at very low concentrations without changing theolvent quality. In order to predict the effect of nonionic disper-ants, we introduce in this paper a new model that can calculatehe aggregation size of asphaltene nanoaggregates based on thetatistical association theory and use the PC-SAFT EOS to predicthe phase behavior of asphaltene nanoaggregates. New relationsre proposed between the molecular weight (Mw) and aromaticity�) of asphaltene molecules and asphaltene association parame-ers in PC-SAFT EOS. The advantage of working with Mw and � iswo-fold: (1) these quantities have a more physical meaning andan be measured in laboratories, and (2) unlike nanoaggregates, thetructure of molecules does not change in the presence of chemicalispersants.

Our approach is to combine microscale parameters from Molec-lar Dynamics (MD) simulations such as the Gibbs energy ofssociation with PC-SAFT EOS to develop a comprehensive modelhat enables the prediction of macroscopic behavior such as themount and onset of asphaltene precipitation at various pres-ures, temperatures, and fluid compositions. To determine theacroscopic phase behavior of asphaltene, we only need the

on-association PC-SAFT EOS parameters for asphaltene nanoag-regates, as proposed by Chapman’s research group [23,26–33].owever in this study, we introduce a new method to deter-ine these parameters based on the average aggregation number

f asphaltene nanoaggregates. In order to find this aggregationumber, it is essential to have the SAFT association parametersf asphaltene molecules. In a recent study by Ferrando et al.

34], PC-SAFT association parameters were calculated for someydrogen-bonding molecules such as alkanols. For each alkanol,onte Carlo simulation was run in the NVT Gibbs ensemble at

ifferent temperatures and the monomer fraction was obtained

quilibria 369 (2014) 86–94 87

from each simulation. Knowing the monomer fraction and theassociation scheme (number of association sites for each molecule),they were able to calculate the association parameters in theWertheim association theory. Although this is an elegant methodto find association parameters of pure liquid alcohols; however,applying this approach to characterize asphaltene association inorganic liquids at nanoaggregate concentrations (<0.1 wt%) wouldbe computationally expensive. For example, if one wants to con-sider the association behavior of only 30 asphaltene moleculesat 0.1 wt% concentration in heptane, it would require runningMD simulations for a box of ∼1 million particles for more than100 ns (to ensure that equilibrium is reached) which is only fea-sible on powerful supercomputers. Therefore, in this work weadopted an alternative method to find the association parametersof asphaltenes from MD simulations. The free energy of associationwas first computed for 8 asphaltene molecular structures in dif-ferent solvents from Umbrella Sampling simulations. By equatingthe free energy of association computed from the MD simula-tions with the one calculated by PC-SAFT EOS, we obtained theassociation parameters for these molecular structures and intro-duced a new correlation relating the association energy parametersin PC-SAFT EOS to the molecular structure of asphaltenes. Withthis approach, the PC-SAFT model is able to correctly predictthe phase behavior of asphaltenes upon addition of nonionicdispersants.

2. Methods

2.1. Molecular dynamics simulations

In this section, we used the free energy of association reportedin our previous work [35] for eight asphaltene structures in hep-tane or toluene through Umbrella Sampling simulations by usingGROMACS 4.5.5 simulation package. The asphaltene structures forA01–A08 are shown in Fig. 1. We performed three additional MDsimulations to find the Gibbs energy of association for asphalteneA01 in pyridine and acetone at room temperature and in heptaneat a temperature of 373 K. Details of these simulations are providedelsewhere [35].

2.2. Thermodynamic modeling with PC-SAFT EOS

2.2.1. Non-association PC-SAFT parameters of asphaltenemolecules

The PC-SAFT theory was developed by Gross and Sadowskito improve the performance of the original SAFT EOS for largemolecules and polymers [24]. SAFT EOS was derived based on theWertheim’s thermodynamic perturbation theory of the first orderTPT1 [36–39], which enables the thermodynamic model to calcu-late the dispersion, association and other energy terms from theproperties of the reference system (hard spheres (HS) in SAFT andhard chains (HC) in PC-SAFT). The hetero-segment approach in PC-SAFT EOS was introduced by Gross and Sadowski [40] to model thethermodynamics behavior of co-polymers composed of differentmonomers. The detailed formulation of hetero-segment PC-SAFTis presented elsewhere [40].

Since asphaltene molecules consist of an aromatic core andaliphatic side chains, which have different characteristics, weemployed the two-segment approach in PC-SAFT to representasphaltene molecules. The non-association parameters of satu-

rate and aromatic segments were calculated using the correlationsdeveloped by Gonzalez et al. [27,28] for saturate and polynucleararomatic molecules as presented in Table 1. The units of � and u/kare Angstrom and Kelvin, respectively.

88 M. Sedghi, L. Goual / Fluid Phase Equilibria 369 (2014) 86–94

Fig. 1. Asphaltene molecular structures used in MD simulations.

Table 1Correlations derived by Gonzalez et al. [27,28] to calculate the non-associatingparameters of PC-SAFT for saturate and polynuclear aromatic molecules.

Saturates PNA (poly nuclear aromatics)

m = 0.0257*Mw + 0.844 m = 0.0101*Mw + 1.7298

a

M

M

waa

cst7b

Table 2Bonding fractions for asphaltene molecules.

B�� B��

� = 4.047 − 4.8013 ∗ ln(Mw)Mw � = 4.6169 − 93.98

Mw

ln(uk

)= 5.5769 − 9.523

Mwuk

= 508 − 234100Mw1.5

The molecular weight of the aromatic and saturate parts ofsphaltenes are given by,

war = Mwasph ∗ � (1)

wsat = Mwasph ∗ (1 − �) (2)

here Mwasph, Mwar, and Mwsat are the molecular weights ofsphaltene, aromatic core and the aliphatic chains, respectively,nd � is the aromaticity factor.

In the one-dimensional view, asphaltene molecules are linearhains that have aromatic segments in the center and aliphatic

egments on the sides. With this simplification, the bonding frac-ions (B��) for an asphaltene molecule with a molecular weight of50 g/mol can be approximated as shown in Table 2. We used theseonding fractions for other asphaltenes in this paper.

0.425 0.150

2.2.2. Association PC-SAFT parameters for asphaltene aromaticcores

Finding reliable association parameters for asphaltenemolecules was the main challenge in this work. In order toobtain these parameters, we need to have the free energies ofasphaltene association. In a recent study by Sedghi and Goual, theGibbs free energies of dimerization were obtained for 8 modelmolecules (see Fig. 1) in heptane from MD simulations [35].Equating the association energy from MD simulations and PC-SAFTEOS, we can find the association parameters for the asphaltenemolecules as described in the following.

In PC-SAFT EOS, the Helmholtz energy of association for a mix-ture of n components with s association sites is given by,

aassoc =n∑i=1

xi

s∑j=1

Sji

[ln Xj

i+ 1

2(

1 − Xij)]

(3)

hase Equilibria 369 (2014) 86–94 89

w

a

o

X

wtii

�

wws

M

it

�

wmita

G

g

wstaidwhmdScaaditbe

aE

X

mfb

Table 3Gibbs energy of association calculated from MD simulations and the associationparameters in PC-SAFT EOS are shown for the 8 model molecules in Fig. 1.

Asphaltene Gassoc (kJ/mole) ε/k (K) �

A01 −14.0 2836.7 0.1A02 −19.4 3513.7 0.1A03 −13.0 2698.4 0.1A04 −19.1 3509.9 0.1A05 −15.0 2975.7 0.1A06 −17.7 3330.8 0.1

molecule in Fig. 1) in different solvents from MD simulations. TheGibbs energy of association and the calculated ε/k are presented inTable 4.

M. Sedghi, L. Goual / Fluid P

here xi is the mole fraction of component i, Sjiis the total number of

ssociation site j in component i and Xji

is the non-bonded fraction

f site j of component i. Xji

can be calculated from this equation,

ji= 1

1 + �∑n

k=1xk ∗∑s

l=1,l /= 1SlkXlk�ljki

(4)

here � is the number density of the system and �ljki

is the associa-ion strength between site l of component k and site j of component. In the first order thermodynamic perturbation theory (TPT1), �lj

kis defined as,

ljki

=∫f ljki

(r, T)grefki (r)4�r2dr (5)

here gref(r) is the radial distribution function (RDF) for a systemith the reference potential interaction between the segments. For

implicity, the hard sphere potential is being used. f ljki

(r, T) is the

ayer f-function defined as f ljki

(r, T) = exp(

− (r)kˇT

)− 1. By assum-

ng the square wall potential model (SW) for the association sites,he association strength can be approximated by,

ljki

= �ljki

∗ �2kig

hski ( �ki)

(exp

(εljki

kˇT

)− 1

)(6)

here k� in the denominator of the exponential term is the Boltz-ann constant, �i is the diameter of the segments of component

, � is the association volume meaning that � * �3 is a measure ofhe volume available for association bond and ε is the energy ofssociation.

From the Helmholtz energy (see Eq. (3)), we can calculate theibbs energy of association using the following relation,

˜assoc = aassoc − ZR (7)

here ZR is the change of residual compressibility factor of theystem due to association of components. It should be mentionedhat for asphaltene association in heptane, ZR is significantly smallnd hence negligible since heptane liquid is almost incompress-ble at room conditions and hence the volume remains the sameuring the association. For example during the MD simulations,e separated two A01 asphaltenes molecules from each other ineptane and found that the maximum change in the PV (pressureultiplied by volume) energy of the system was around 1% of the

imerization energy and therefore could be safely ignored. In theAFT model, asphaltenes have two association sites. However in thealculation of the dimerization energy of asphaltenes, we assumed

hypothetical condition where the aromatic core has only onessociation site so that asphaltene molecules are only able to formimers. In this case the association energy is equal to the dimer-

zation energy. If the non-bonded fraction of association site is X,hen the energy of association calculated by MD simulations woulde equal togassoc

MD(1−X)

2 . Equating this energy with the Helmholtznergy of association calculated from Eq. (3), we would have,

gassocMD = 2nRT

(1 − X)∗[

ln X + 12(1 − X)

](8)

nd since we have only one component and one association site,q. (4) can be simplified to,

=√

1 + 4�� − 1

2��(9)

Due to the fact that asphaltenes associate through their aro-atic cores, the volume available for association should be larger

or asphaltenes than other components that associate through H-onding. Therefore we fixed the � parameters of all asphaltene

A07 −8.3 2052 0.1A08 −10.0 2086.4 0.1

molecules to 0.1 (almost the upper limit of the � values that havebeen reported in literature for PC-SAFT EOS) and calculated the εform Eqs. (6), (8) and (9). The calculated ε for the 8 asphaltene modelmolecules in Fig. 1 are tabulated in Table 3.

The calculated ε’s were in the range of values reported in theliterature. Since the main mechanism of asphaltene association isthe interactions between asphaltene aromatic cores; we used thearomatic core size to correlate the asphaltene ε with their molecu-lar structure. Fig. 2 shows the ε/k values for asphaltene versus theiraromatic core size (Mw*�).

The correlation for estimating the association energy can beobtained by linear regression,

ε

k= 9.8203 ∗ (Mw ∗ Ar) − 807.71 (10)

The unit of εk in the above equation is Kelvin (K). This is the firsttime that the association energy (ε) of asphaltene molecules can becalculated in PC-SAFT EOS.

It has been shown before that the strength of asphaltene asso-ciation could change depending on the solution medium [35]. Ifthe solution becomes more aliphatic, the energy of dimerizationwill increase. To investigate this effect, we have calculated theGibbs energy of association for an asphaltene model molecule (A01

Fig. 2. Association energies over Boltzmann constant (ε/k) for asphaltenes versusthe molar weight of their aromatic cores (Mw*�).

90 M. Sedghi, L. Goual / Fluid Phase Equilibria 369 (2014) 86–94

Table 4Gibbs energy of association and calculated ε/k for A01 asphaltene in differentsolvents.

Solvent Temperature (K) Gassoc (kJ/mol) ε/k (K)

Pyridine 300 −2.7 388.7Acetone 300 −9.9 2300Toluene 300 −11.4 2526Heptane 300 −14.0 2894Heptane 373 −16.4 3535

Fig. 3. (ε/k) calculated from Eq. (12) versus (ε/k) obtained from MD simulations. Thep

aTdimi

ı

wiwa(

dasiesd

Fig. 4. Asphaltene phase envelopes calculated by our model when (a) the averageaggregation number is variable at each temperature and pressure, (b) the averageaggregation number is constant during the simulation (gray line: bubble point pres-sure, black line: onset of asphaltene precipitation calculated from our model, anddata points from [26]).

oint off the straight line represents pyridine.

As shown in Table 4, the association between asphaltenes can beffected by the intermolecular forces between solvent molecules.he general trend is that the energy of asphaltene associationecreases as the intermolecular forces between solvent molecules

ncrease. One of the quantities that represent the strength of inter-olecular forces is the Hildebrand solubility parameter (ı), which

s defined as the square root of the cohesive energy density,

=√uvap

vm(11)

here uvap is the latent internal energy of vaporization and vm

s the molar volume of the system. Based on the data in Table 4e suggest an inverse relation between the association energy of

sphaltene and the solubility parameter of the solution,

ε

k

)2

=(ε

k

)1

∗ ı1

ı2(12)

We have tested the validity of this correlation with theata presented in Table 4 by considering heptane at T = 300 Ks solvent 1 and calculating the association energies for otherolvents or temperatures. The results are shown in Fig. 3 andndicate that Eq. (12) can provide good estimates for ε at differ-

nt solution conditions. The energy of association in pyridine isignificantly lower than in other solvents, which suggests that pyri-ine might form strong aromatic interactions with the aromatic

core of asphaltenes and should be investigated in future stud-ies.

2.2.3. Calculation of the aggregation number of asphaltenenanoaggregates

After asphaltenes form nanoaggregates, they stop aggregating.At this stage, some of the asphaltene association sites (i.e. aro-matic cores) are not involved in any association and are callednon-bonded sites, noted by X in our formulation. For example XA

iis the non-bonded fraction of (association) site A in componenti. For a component that has two sites, A and B, the probabilityof finding a monomer after aggregation is equal to finding bothsites A and B in non-bonded state, which is equal to P1 = XA * XB.Following the same logic, the probability of finding aggregate of gmonomers is,

Pg = (XA)2 ∗ (1 − XA)

g−1(13)

Since we have only two sites, XB is equal to XA. The proba-bility Pg is equal to the mole fraction of aggregates (Yg). Fromthe mole fraction distribution of aggregates, the number-average

M. Sedghi, L. Goual / Fluid Phase Equilibria 369 (2014) 86–94 91

Fig. 5. Asphaltene phase envelopes predicted by our model for crude A at various rates of gas injection (gray line: bubble point pressure, black line: onset of asphaltenep

ao

g

2

agTooccdoqd

recipitation calculated from our model, and data points from [26]).

ggregation number (gn) of asphaltene nanoaggregates can bebtained from this relation,

n = ˙Yg ∗ g

˙Yg(14)

.2.4. Effect of nonionic dispersants on asphaltene aggregationNonionic dispersants are molecules that can associate with

sphaltenes from their head group and hinder asphaltene aggre-ation due to the steric repulsion of their aliphatic tails.herefore, dispersants can reduce asphaltene precipitation with-ut significantly affecting the bulk properties of solutions, aspposed to aromatic solvents. In our model, asphaltenes areonsidered as associating molecules and hence they can formross-association with dispersants. Having cross-association with

ispersants increases the non-bonded fraction of association sitesf asphaltenes that are associating with each other and conse-uently, from Eqs. (13) and (14), the average aggregation numberecreases. To find the cross-association parameters, Wolbach and

Sandler [41] suggested the following mixing rules for associatingcomponents k and i,

εljki

= 0.5(εljkk

+ εljii) (15)

�ljki�2ki =

√�ljkk�2k�ljii�2i

(16)

We considered the coefficient 0.5 in Eq. (15) as an adjustableparameter due to the fact that association between dispersantsand asphaltenes can change based on their chemistry and differ-ent nonionic dispersants have different mechanisms of associationwith asphaltenes. Also we should bear in mind that the methodused to determine the association parameters of asphaltenes (seeSection 2.2.2) could only provide estimates for these parameters.

2.2.5. Non-association parameters of asphaltene nanoaggregates

In the previous sections, we showed how to calculate the asso-

ciation and non-association parameters of PC-SAFT for asphaltenemolecules from their Mw and aromaticity factors. Having the asso-ciation parameters, the average aggregation number of asphaltene

92 M. Sedghi, L. Goual / Fluid Phase Equilibria 369 (2014) 86–94

Frp

noea

m

g(bpttcti

Fig. 7. Asphaltene phase envelopes calculated by our model for crude oil C (gray

ig. 6. Asphaltene phase envelopes predicted by our model for crude B at variousates of gas injection (gray line: bubble point pressure, black line: onset of asphaltenerecipitation calculated from our model, and data points from [26]).

anoaggregates can be calculated from Eq. (14). For nanoaggregatesf asphaltene, it is assumed that the volume (�) and the dispersionnergy (u) of molecule’s segments do not change upon aggregationnd therefore, only the total number of segments will increase.

aggregate = mmonomer ∗ gn (17)

Having all three non-bonding parameters of asphaltene nanoag-regates, we can use PC-SAFT EOS for non-associative componentssimilar to the work of Ting et al. [23]) to predict asphaltene phaseehavior. Thus, our thermodynamic model requires only two inputarameters: the average molecular weight and aromaticity fac-or of asphaltene molecules. By providing the model with these

wo parameters, the average aggregation number of asphaltenesan be calculated from Eqs. (10)–(17) and the PC-SAFT parame-ers of asphaltenes can be obtained from the correlations providedn Table 1. Considering that the molecular weight and aromaticity

line: bubble point pressure, black line: onset of asphaltene precipitation calculatedfrom our model, and data points from [26]).

factor of asphaltene molecules can readily be measured in the lab-oratory, this model is able to predict asphaltene phase behaviorentirely based on physically based characteristics of the molecules.We have tested our methodology to predict asphaltene precipita-tion for three crude oils reported in [26]. The results are shown inthe next section.

3. Results

3.1. Asphaltene precipitation envelope at high pressures andtemperatures

Our model was applied to predict the onset of asphaltene pre-cipitation for three live crude oils (A, B and C) at high temperaturesand pressures and under various gas injection rates. PC-SAFT EOShas been previously applied to model asphaltene precipitation byPunnapala et al. [26] for these crude oils and the details of oil com-positions and characterizations are shown in their work [26]. In ourcalculations, we used the binary interaction parameters (kij’s) thatwere reported in [26] and, for simplicity, we used the same valuesfor binary interactions parameters of aromatic and saturate seg-ments of asphaltenes with other components. The kij between thesetwo segments was set to 0.02. The PC-SAFT parameters of compo-nents other than asphaltenes were also adopted from Punnapalaet al.’s paper [26].

The calculated asphaltene precipitation envelope (APE) is shownin Figs. 4–7. For crude oil A and B, we matched the asphaltenemolecular parameters (Mw and �) to the experimental data for10 mole% gas injection and APE was predicted for live oil and othergas injection rates. For crude oil C, the molecular parameters werematched to the precipitation data of the live oil.

One of the limitations of our model is that it underestimatesthe aggregation number for asphaltenes at temperatures that arenoticeably higher than ambient temperature. The reason is that

in Eq. (6), temperature is in the denominator of the exponentialpart. Therefore, as temperature increases, the association strength(�AB

ij) starts to decrease significantly. To overcome this problem,

the aggregation number for each crude oil was calculated at the

M. Sedghi, L. Goual / Fluid Phase Equilibria 369 (2014) 86–94 93

F tions with and without OP dispersant. Lines represent modeling results and points showe

ecFa(ucams

pFaHti[

ima

3p

epwdaa

nPia

Table 5Asphaltene Mw and aromaticity factors obtained as fitting parameters from ourmodel.

Asphaltenes Mw (g/mol) �

Crude oil A 905 0.575Crude oil B 1050 0.486Crude oil C 600 0.616

ig. 8. Amount of asphaltene precipitation upon addition of heptane to toluene soluxperimental data.

xperimental data point with the lowest temperature and keptonstant for other temperatures, pressures and gas injection rates.ig. 4 compares the results of our modeling as we change the aver-ge aggregation number (AN) at each temperature and pressureFig. 4a) with the case where AN is kept constant during the sim-lation (Fig. 4b). The calculated average aggregation number forrude oils A, B and C are 3.47, 3.68 and 2.34, respectively, whichre in the range of values obtained from conductivity measure-ents for asphaltene solutions in toluene at the nanoaggregation

tate [6].The performance of our model to predict the asphaltene onset

ressure (AOP) at high temperature and pressure (as shown inigs. 4–7) is similar to Punnapala et al.’s work [26] since the aver-ge aggregation number is kept constant during each simulation.owever, the Mw and aromaticity factor of asphaltenes obtained

hrough matching our model results to the experimental data falln the ranges of values that are reported for asphaltene molecules42–45].

Asphaltene molecular parameters from our model are shownn Table 5. The experimental values for molecular weight and aro-

aticity of asphaltene are reported in the range of 500–1000 g/molnd 0.40–0.65, respectively [7,9,42–45].

.2. Asphaltene precipitation at room temperature in theresence of dispersants

One of the main goals of our model is to be able to predict theffect of chemical dispersants on asphaltene precipitation. For thisurpose, we used experimental data of asphaltene precipitationith and without the presence of dispersants at ambient con-itions, provided by Wang [46]. The model oil was 5 mg/mlsphaltenes in toluene and the dispersant was octylphenol (OP)t two concentrations of 5 and 10 mg/ml in heptane.

The OP dispersant was modeled as a two-segment compo-

ent to account for the phenol head and the octane tail. TheC-SAFT parameters for phenol and octane have been reportedn the literature [40–47]. The density of OP was calculated atmbient conditions and a value of 0.955 g/ml was obtained,

which is in good agreement with the experimental value of0.961 g/ml.

We applied our method to predict the amount of asphalteneprecipitation as heptane was added to asphaltene-in-toluene solu-tions. The results of our model are shown in Fig. 8 and comparedto precipitation data measured in our laboratory [46]. The cross-association parameters were calculated from Eqs. (15) and (16)with an adjusted coefficient of 0.39 instead of 0.5 in Eq. (15).This coefficient was found by fitting the modeling results to theexperimental data with 5 mg/ml OP in heptol. We then used thesame coefficient to predict asphaltene precipitation with otherOP concentrations such as 10 mg/ml in heptol. Fig. 8 shows thatour method can predict fairly well the effect of OP on asphal-tene precipitation behavior. The fitted values for molecular weightand aromaticity factor of asphaltene molecules are 840 g/mol and0.6343, respectively, and fall in the range of values expected forasphaltenes.

The correct prediction of asphaltene thermodynamic behaviorin the presence of dispersants can be a challenging task since dis-persants can be effective even at low concentrations where they donot change the macroscopic properties of the solvent. For example,the addition of 10 mg/ml of OP to our model oil has a notice-able impact on the amount of asphaltene precipitation, although itcan only change the solubility parameter of toluene from 18.18 to18.19 MPa1/2. Hence, when a thermodynamic model relies solely onthe macroscopic properties of the medium to calculate asphaltene

precipitation, it may not be able to fully account for the presenceof dispersants.

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[45] H.H. Ibrahim, R.O. Idem, Energy Fuels 18 (2004) 1354–1369.

4 M. Sedghi, L. Goual / Fluid P

. Conclusions

A new approach was introduced in this paper to predict asphal-ene phase behavior by calculating the aggregation number ofsphaltenes based on the statistical association fluid theory (PC-AFT). For the first time, the association energy parameters inC-SAFT formulations were calculated for asphaltenes by usinghe free energies of dimerization obtained from MD simulations.

correlation was suggested to relate the association energy ofsphaltene molecules to the size of their aromatic cores. Ourodel showed that asphaltene association energy is affected by

emperature and solvent type and is inversely related to the sol-bility parameter of the medium. The hetero-segment approach

n PC-SAFT EOS was adopted to accurately characterize asphalteneolecules and their non-association parameters in PC-SAFT were

etermined based on the molecular weight and aromaticity factorf asphaltenes and the average aggregation number of asphalteneanoaggregates.

This model was applied to predict asphaltene phase envelopor three crude oils and showed excellent agreement with exper-mental data. The fitted molecular weight and aromaticity factorf asphaltenes are in the range suggested in the literature, indi-ating that the underlying assumptions are physically valid. Forhe first time, the effect of dispersants on asphaltene precipita-ion was predicted and the results show qualitative agreement withxperimental data.

cknowledgements

The authors would like to thank the School of Energy Resourcest the University of Wyoming for their financial support. Theuthors are also grateful to Professor Maciej Radosz and Dr. Sugataan for providing PC-SAFT source codes and for valuable discus-ions.

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