Prediction of Asphaltene Precipitation in Organic Solvents via COSMO

Article pubs.acs.org/EF

Prediction of Asphaltene Precipitation in Organic Solvents via COSMO-SAC Md Rashedul Islam, Yifan Hao, Meng Wang, and Chau-Chyun Chen* Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409-3121, United States ABSTRACT: Asphaltene precipitation is driven by self-association of asphaltene molecules to form nanoaggregates and subsequent formation of clusters from nanoaggregates (Mullins, O. C. Energy Fuels 2010, 24 (4), 2179−2207). Recently, a novel thermodynamic framework was proposed for the onset of asphaltene nanoaggregation in binary solvents with a functional groupbased UNIFAC model (Wang, M., et al. AIChE J. 2016, 62 (4), 1254−1264). In this work, a computational chemistry-based COSMO-SAC model is applied with the aggregation thermodynamics to predict asphaltene precipitation. The predictions are further improved with the use of apparent sigma profiles based on the conceptual segment approach (Islam, M. R., Chen, C.-C. Ind. Eng. Chem. Res. 2015, 54 (16), 4441−4454).

1. INTRODUCTION Sensitive to petroleum composition and processing conditions, asphaltene precipitation is a cause for concern at various levels of petroleum production, transportation, and processing. Pressure depletion during production may induce asphaltene precipitation, which alters rock permeability and plugs the well bore.1 Blending in the crude oil supply chain may prompt asphaltene precipitation if the petroleum fluids are not compatible. Furthermore, asphaltenes may promote solid deposition on unit operations and block catalyst pores through coking2,3 during crude oil processing. To determine fluid compatibility and forecast precipitation conditions, the oil and gas industry has shown a lot of interest in predicting the onset of asphaltene precipitation. Asphaltenes are defined as a solubility class of petroleum, i.e., insoluble in n-alkanes such as n-pentane or n-heptane but soluble in aromatics such as toluene. Chemical identity of asphaltenes has been investigated for decades. Divergent results on asphaltene molecular weight reported by different research groups contributed to the debate over its molecular structure. Yen and co-workers first proposed a hierarchical structure of asphaltenes that would comply with the molecular weight diversity.4 With evolution of advanced characterization techniques, the enigmatic molecular structure of asphaltenes has been unveiled, and it paves the way for the development of a widely accepted model for asphaltene molecular structure, i.e., the Yen−Mullins model.5 According to this model, asphaltenes are composed of polycyclic aromatic hydrocarbon (PAH) molecules with alkyl side chains attached to the periphery of PAH. Heteroatoms, such as sulfur, oxygen, and nitrogen, are commonly present in either part. Mullins and co-workers6 presented a concise account on the molecular weight of asphaltenes measured by different techniques and concluded the molecular weight of petroleum asphaltenes as ∼750 Da (±200 Da). The complex molecular structure was further validated by atomic force microscopy and scanning tunneling microscopy imaging with atomic resolution.7 Concentration potential drives asphaltene molecules to form nanoaggregates through intermolecular forces between PAHs. Nanoaggregates further combine together to form clusters. Evidently, there exist © 2017 American Chemical Society

critical concentrations at which the nanoaggregate formation is seized and the cluster is formed. Modeling of asphaltene precipitation has been extensively pursued for several decades. The obvious effects of temperature, pressure, and solvent composition on asphaltene precipitation and the evidence supporting the reversibility8−11 of the precipitation process have drawn researchers into thermodynamic modeling of asphaltene solubility. Evolution of asphaltene precipitation modeling originated from the utilization of regular solution theory together with Flory− Huggins12,13 (F−H) expression.14,15 At that early stage, asphaltenes were considered as uniform molecules, and their molar volumes and solubility parameters were estimated from experimental precipitation results. In more sophisticated applications of regular solution theory, molar mass distribution of asphaltenes was considered while other fractions of crude oil, i.e., saturates, aromatics, and resins, were represented as single compounds.16 The molar volumes and solubility parameters were further correlated with empirical functions of asphaltene molecular weight. Later, this model was employed to calculate asphaltene precipitation from a wide range of binary organic solvents.17 Apart from empirical correlations, the asphaltene solubility parameters were also calculated from cubic equations of state (EoS) relating the solubility parameters with internal energy of vaporization and molar volume.14,18−21 In crude oil reservoirs, asphaltene solubility greatly depends on the content of lighter components, i.e., gas oil ratio (GOR), and its variation with depth. To account for the effect of depth, regular solution theory was extended to address the effect of gravitational force.22 The gravity term could address the formation of asphaltene dispersion in the oil, i.e., molecules, nanoaggregates, or clusters.23 Additionally, SAFT-based EoS models have been employed for treating asphaltene precipitation as liquid−liquid equilibria (LLE).24−26 Received: April 21, 2017 Revised: June 28, 2017 Published: July 30, 2017 8985

DOI: 10.1021/acs.energyfuels.7b01129 Energy Fuels 2017, 31, 8985−8996

Article

Energy & Fuels ΔGM → C ΔGC → A ΔGM → A = + RT RT RT

Recently, Wang et al. proposed a novel thermodynamic framework for asphaltene precipitation based on aggregation of asphaltene molecules into nanoaggregates.27 The proposed aggregation thermodynamics explicitly accounts for the aggregation driving forces derived from inherent molecular structures of both asphaltenes and nanoaggregates. The authors further applied UNIFAC,28 a widely used activity coefficient model based on functional group interaction contribution, to quantify the aggregation driving forces. The model satisfactorily predicts asphaltene solubility behavior in alkane−toluene binary solvents and shows the correct solubility trend with alkane carbon numbers. However, the model fails to predict asphaltene precipitation in systems containing polar molecules, i.e., acetone, and hydrophilic molecules, i.e., methanol. The underlying reason may be the inadequacy of UNIFAC to predict activity coefficients of large complex molecules such as asphaltenes and nanoaggregates in polar and hydrophilic solvents. This work re-examines the aggregation thermodynamics and applies the state-of-the-art computation chemistry-based activity coefficient model, i.e., COSMO-SAC,29 to predict asphaltene solubility in the 15 binary solvents.17 Here, sigma profiles for asphaltenes and nanoaggregates are generated with the DMol3 module of the Accelrys Material Studio software package.30 In addition, the concept of apparent sigma profiles31,32 is utilized with COSMO-SAC to correlate the available asphaltene solubility data.

(1)

In eq 1, M, C, and A denote asphaltene molecules, nanocrystals, and nanoaggregates in solution, respectively. As depicted in Figure 1, the first step involves formation of highly ordered fictitious nanocrystals from asphaltene molecules, and the Gibbs free energy change for this step, ΔGM→C, can be expressed in terms of a solubility constant, Ks. ΔGM → C = −ln K s = −(ln x Isat + ln γIsat) RT

(2)

Here, xsat and γsat are the concentration and the activity I I coefficient of asphaltene molecules at saturation, respectively. In the subsequent step, the imaginary nanocrystals redissolve in the solution and form colloidal nanoaggregates. The Gibbs free energy change for this second step, ΔGC→A, approximately corresponds to the infinite dilution activity coefficient of nanoaggregates, γ∞ nano, see eq 3. ΔGC → A ∞ ≅ ln γnano RT

(3)

As only alkyl side chains of asphaltene molecules in nanoaggregates are exposed to the solvent molecules in solution, γ∞ nano is determined from the interaction between ∞ alkyl side chains and surrounding solvent molecules. γnano brings the effect of solvent composition into the aggregation thermodynamics. Combining eqs 1−3, the change in Gibbs free energy for the aggregation process is expressed by eq 4. Following the analogy of solubility constant, Kagg represents the formation constant for asphaltene aggregation.

2. AGGREGATION THERMODYNAMICS FOR ASPHALTENE PRECIPITATION Following the Yen−Mullins model,5 Wang et al. examined the transition of asphaltene molecules to nanoaggregates and proposed an aggregation thermodynamics framework to quantify the thermodynamic driving forces in terms of the changes in the Gibbs free energy during this transition.27 The Gibbs free energy calculation follows a path as indicated in Figure 1 which considers asphaltene molecules form

⎛ γIagg ⎞ ΔGM → A agg ⎜ = −ln K agg = −⎜ln x I + ln ∞ ⎟⎟ γnano ⎠ RT ⎝ = −(ln x Iagg + ln γIeff )

(4)

here superscript “agg” denotes asphaltene nanoaggregate formation. xagg I is the mole fraction of asphaltene molecules at the onset of aggregation. γagg is the activity coefficient of I asphaltene molecules. γ∞ nano is the infinite dilution activity coefficient of nanoaggregates. The ratio of γagg and γ∞ I nano is considered as the effective activity coefficient for aggregation, γeff I . At a given temperature and pressure, asphaltene solubility depends on the activity coefficient of asphaltene molecules, the infinite dilution activity coefficient of nanoaggregates, and the nanoaggregate formation constant. In this work, the COSMOSAC model and its variations are used to calculate the activity coefficients.

3. COSMO-SAC ACTIVITY COEFFICIENT MODEL COnductor like Screening MOdels (COSMO) are known as a useful technique of finding solvation free energy. Mathematical correlation of solvation free energy to Gibbs free energy subsequently leads to the computation of activity coefficients of molecules during the solvation process.33 Klamt proposed a novel idea for efficient calculation of solvation free energy for real fluid, i.e., COSMO-RS.34 In this method, the solute molecule is inserted into a perfect conductor, which has infinite dielectric constant, and the charges of the molecule are screened. The perfect conductor is then converted to the real fluid by using the dielectric constant dependent factor.

Figure 1. Transition of asphaltene molecules to nanoaggregates.

nanocrystals en route to nanoaggregates. The change in Gibbs free energy from asphaltene molecules to nanoaggregates is the sum of the changes in Gibbs free energies of asphaltene molecules to nanocrystals and asphaltene nanocrystals to nanoaggregates, see eq 1. 8986


Article

Energy & Fuels

parameters. In COSMO-SAC, the capability of forming a hydrogen bond (H-bond) of a molecule is determined from the sigma profile. A threshold value, σhb, is used to filter hydrogenbond forming segments. This approach of a H-bond forming sigma profile was revised by considering H-bond forming segments to selective atoms, i.e., O, N, and F, and the H atoms that are connected to them.42 The molecular sigma profile is therefore split into a H-bonding sigma profile, phb I (σ), and nonH-bonding sigma profile, pnhb I (σ). COSMO-SAC parameters have been refined on the basis of this new definition of a sigma profile.43 Later, the electrostatic interaction parameter is further correlated with temperature dependent interaction parameters.44 It is claimed that this temperature dependency significantly improves the accuracy of LLE calculation for non-H-bonding compounds. Apart from this, phb I (σ) is further OT OH subdivided into pOH I (σ) and pI (σ). pI (σ) belongs to the surface of the hydroxyl group and pOT I (σ) to all other types of hydrogen-bonding groups. This modification differentiates hydrogen bonding coming from hydroxyl, amine, and nitro groups. In the latest modification of COSMO-SAC, Xiong et al. incorporated the change in Gibbs free energy due to dispersion.45 Additionally, they reported a brief comparison on the accuracy of the activity coefficient calculation for a large data set of 4388 binary mixtures with different versions of COSM-SAC. The comparison showed incremental improvements with the revisions. In this work, we follow the original version of COSMO-SAC29 for asphaltene precipitation calculations.

Recognizing COSMO-RS as a starting point, Lin and Sandler introduced the COSMO-SAC model for the calculation of an activity coefficient that satisfies thermodynamic consistency, i.e., the Gibbs−Duhem equation.29 In this model, the molecular surface is considered as a sum of a number of segments having the same surface area. Therefore, the segment number, nI, of molecule I relates directly to the total surface area of the molecule. Charge distribution over the molecular surface characterizes the segments. For convenience, the charge density is distributed by specified bin size, and the probability of finding segments nI(σ) having charge density σ is reported as pI(σ) = nI(σ)/nI. The surface area distribution over the charge density, pI(σ), is called the “sigma profile,” which is the key model input. COSMO-SAC further assumes that the logarithm of activity coefficient of component I, ln γI, is the sum of a residual contribution term, ln γRI , and a combinatorial contribution term, ln γCI . ln γI = ln γIR + ln γIC

(5)

Accordingly, the residual term of activity coefficient, γRI , is expressed by eq 6. ln γIR = nI ∑ pI (σm)[ln Γs(σm) − ln ΓI(σm)] σm

(6)

here, Γ(σm) is the segment activity coefficient. Subscripts I, s, and m refer to pure component, solution, and segment, respectively. The expressions for segment activity coefficients are available in the literature.29 The size and shape of the solute molecule determine the matrix of cavity formulated inside the solvent. The cavity formation energy is related to the combinatorial contribution of the activity coefficients,35,36 γCI . COSMO-SAC incorporates the Staverman−Guggenheim (SG) expression for the combinatorial contribution to the activity coefficient,37,38 see eqs 7 and 8. Composed of ln γFH and ln I γΔSG , the S-G expression accounts for the effect of surface area I during mixing, and it represents an improvement over the Flory−Huggins (F−H) equation for the entropy of mixing calculation. The first three terms in the S-G expression duplicate the F−H expression, ln γFH I , and the remaining terms are the S-G correction for F−H, ln γΔSG . I ϕI

ϕI

1 − Z xI xI 2 ⎛ ϕ ϕ⎞ qI⎜1 − I + ln I ⎟ = ln γIFH + ln γIΔSG θI θI ⎠ ⎝

ln γIC = ln γISG = 1 −

ϕI =

+ ln

x IqI x IrI and θI = ∑J xJrJ ∑J xJqJ

4. SIGMA PROFILE AND APPARENT SIGMA PROFILE As the key model input to COSMO-SAC, the sigma profile of a given molecule is computed from the molecular structure using quantum chemistry calculations. A number of commercial quantum chemistry software packages are available to generate sigma profiles.30,46−49 Additionally, an open source web-based sigma profile database (www.design.che.vt.edu) stores precalculated sigma profiles of thousands of molecules.41,50,51 However, generation of sigma profiles remains challenging for researchers who have no ready access to such quantum chemistry software packages. Moreover, generation of sigma profiles is impossible for molecules whose chemical identities or molecular configurations are yet unknown. Asphaltenes are an excellent example. As a solubility class of petroleum, asphaltenes are a collective representation of numerous PAH molecules of similar structure with subtle differences in fused aromatic rings, alkyl side chains, functional groups, hetero atoms, etc. The sigma profile of a single representative asphaltene molecule may not reflect the collective nature of that class. Furthermore, due to the built-in empiricism of the COSMO-SAC formulation, sigma profiles generated from the molecular structure may not always yield rational results, and alternative approaches to sigma profile generation become necessary. Islam and Chen proposed a novel approach to generate sigma profiles from experimental phase equilibrium data.31 The idea evolved from the conceptual segment concept of the NRTL-SAC model.52 On the basis of the “like dissolves like” phenomenon, the conceptual segment concept defines molecular surface interaction characteristics as either hydrophobic, polar, or hydrophilic, and each molecule may exhibit various degrees of hydrophobicity, polarity, and hydrophilicity. In NRTL-SAC, molecules are represented by linear combinations of four types of conceptual segment numbers: hydrophobic (X), polar attractive (Y−), polar repulsive (Y+), and

(7)

(8)

Here, ϕI is the volume fraction, θI is the surface area fraction, Z is the coordination number, and rI and qI are normalized volume and surface area parameters, respectively, i.e., rI = VI/r and qI = AI/q. J is component index, r is the standard volume parameter (66.69 Å3), and q is the standard surface area parameter (79.53 Å2).29 VI and AI represent the volume and surface area of the molecule, respectively. Fully parametrized COSMO-RS and COSMO-SAC are predictive with molecular structure as the only required model input. Detailed derivations of COSMO-RS and COSM-SAC are available in the literature.29,34,35,39−41 Over the past decade, the COSMO-SAC model has undergone a number of revisions and refinements of its 8987


Article

Energy & Fuels hydrophilic (Z). Following this concept, Islam and Chen generated molecular sigma profiles from linear combinations of sigma profiles of n-hexane, dimethyl sulfoxide, nitromethane, and water, each representing a reference molecule for hydrophobic, polar attractive, polar repulsive, and hydrophilic conceptual segments, respectively, see eq 9.

⎡X⎤ ⎢ −⎥ Y pI (σ )AI = A ref ⎢⎢ + ⎥⎥ Y ⎢ ⎥ ⎣Z ⎦

(9) Figure 2. Representative molecular structure of asphaltenes.

Here, matrix Aref is composed of reference molecule sigma profile vectors resulting in a dimension of 51 × 4. The conceptual segment vector, [X Y− Y+ Z]T, outlines the contributions of conceptual segments of the molecule. The algebraic operation in eq 9 finds the probability distribution of the molecular surface with respect to charge density, pI(σ), and total surface area of the molecule, AI. The cavity volume is also calculated from AI by considering the molecule a sphere. Estimation of the conceptual segment numbers involves regression of experimental phase equilibrium data, solubility data, or activity coefficient data. Determined from experimental data, this so-called “apparent sigma profile” brings correlative power to COSMO-SAC.

5. PREDICTIONS OF ASPHALTENE PRECIPITATION Three different approaches of applying COSMO-SAC are examined in this study: (1) original COSMO-SAC, (2) COSMO-SAC with a revised S-G expression to improve the COSMO-SAC combinatorial contribution calculation, and (3) COSMO-SAC with the revised S-G expression and apparent sigma profiles to improve both the combinatorial and the residual contribution calculations. Table 1 summarizes the model inputs and their sources with these three approaches.

Figure 3. DMol3 generated sigma profiles of asphaltene molecules (blue), n-C56 (red), n-C120 (green), and apparent sigma profile of asphaltene molecules (black).

Table 1. Sources of Input for Models γRI

well inside the hydrogen bonding cutoff threshold, i.e., −0.0084 ≤ σ ≤ 0.0084 e/Å2. Therefore, the asphaltene molecule exhibits hybrid hydrophobic and polar characteristics as expected from its molecular structure. On the other hand, n-C56 shows a very narrow sigma profile with the charge distribution concentrated around σ = 0, consistent with sigma profiles of hydrophobic molecules. Calculated from the sigma profiles and cavity volumes, the normalized volume and surface area of the representative asphaltene molecule and n-C56 are reported in Table 2. Given the sigma profiles and cavity volumes of asphaltenes and nanoaggregates, COSMO-SAC is then employed to predict asphaltene precipitation for the measurements reported by Mannistu et al. for an Athabasca bitumen sample in 15 different binary solvents at room temperature.17 The initial asphaltene concentration was 8.8 g/l. Experimental results were presented as the mass ratio of precipitation to the total asphaltene samples at different volume ratios of good solvent and poor solvent. A total of 100% of asphaltenes were dissolved in good solvents, while 100% precipitation was observed in poor solvents. The 16 solvents, good and poor, cover a wide spectrum of solvent characteristics: hydrophobic, polar, and hydrophilic. The sigma profiles and cavity volumes of the 16 solvents are retrieved from the VT sigma profile database.51 Normalized volume and surface area parameters of the solvents are reported in Table 2. The experimental data of n-alkane−toluene binary systems are

γCI

model

σ profile

AI

VI

COSMO-SAC COSMO-SAC′ COSMO-ASP

DMol3 DMol3 regression

DMol3 Bondi Bondi

DMol3 Bondi Bondi

5.1. COSMO-SAC for Asphaltenes Precipitation. COSMO-SAC requires molecular structure for the calculations of sigma profile and cavity volume. Following the work of Wang et al.,27 we choose the same representative molecular structure for the asphaltene molecule (MW = 920.4 Da), see Figure 2. Also, a straight chain paraffin molecule is chosen as a surrogate for the nanoaggregates since the aromatic cores inside nanoaggregates are shielded by the alkyl side chains, and these alkyl chains dictate the surface structure of nanoaggregates. After a few trials, n-C56 is found to be the best match that returns a proper experimental trend of slightly increasing asphaltene solubility with increasing carbon number of n-alkane solvents.17 Given the assumed molecular structures of asphaltenes and nanoaggregates, the corresponding sigma profiles and cavity volumes are computed with a standard procedure.41 Figure 3 shows the sigma profiles of asphaltenes and nanoaggregates. The asphaltene molecule has a charge distribution in the range of −0.006 ≤ σ ≤ 0.006 e/Å2, which is 8988


Article

Energy & Fuels

experimental results. Asphaltene precipitation is predicted in nitrobenzene−n-hexane, t-butyl benzene−n-hexane, and dichloromethane−n-hexane binary solvents with fair accuracy, see Figure 5. Figure 5 also reports prediction results for

Table 2. Normalized Volume and Area Parameters DMol3

Bondi

compound

rI

qI

rI

qI

asphaltene n-C56 n-C120 n-pentane n-hexane n-heptane n-octane n-decane i-pentane i-octane c-hexane decalin 1-hexene toluene t-butyl benzene nitrobenzene dichloromethane acetone methanol

17.80 18.50 39.18 1.86 2.19 2.52 2.85 3.50 1.87 2.87 1.95 3.01 2.12 1.98 2.95 2.12 1.24 1.30 0.73

11.54 14.49 28.75 1.73 1.98 2.22 2.48 2.98 1.68 2.26 1.69 2.34 1.92 1.77 2.35 1.88 1.24 1.29 0.85

35.97 38.22 81.38 3.83 4.50 5.17 5.85 7.20 3.82 5.85 3.50 5.66 4.27 3.92 6.17 4.08 2.26 2.57 1.43

25.07 30.86 65.42 3.32 3.86 4.40 4.94 6.02 3.31 5.01 2.43 3.50 3.64 2.97 4.89 3.10 2.00 2.30 1.43

Figure 5. Experimental data,17 in symbols, and COSMO-SAC results, in lines, for asphaltene precipitation in binary solvents. t-butyl benzene−n-hexane (red), nitrobenzene−n-hexane (blue), c-hexane− n-hexane (magenta), decalin−n-hexane (green), and dichloromethane−n-hexane (black).

used to identify the nanoaggregate formation constant. As mentioned previously, the carbon number of the straight chain paraffin surrogate molecule is also adjusted along with the nanoaggregate formation constant in order to best describe quantitatively the experimental data of increasing asphaltene solubility with increasing carbon number of the n-alkane solvents. n-C56 is found to be the best surrogate, and ln Kagg turns out to be −4.85. COSMO-SAC predicts asphaltene precipitation in n-alkane− toluene binaries very well, see Figure 4. The polar nature of toluene favors dissolution of the asphaltene molecule, and the precipitation fraction drops as the toluene content increases in the solution. The calculated precipitation fraction increases with the decrease of carbon number in n-alkanes at the same alkane−toluene volume ratio, an important conformity with the

asphaltene precipitation in naphthenes. Predicted precipitation appears to be independent of the volume ratio of solvents in chexane−n-hexane binary solvent. A similar but slightly better prediction is observed for decalin−n-hexane binary solvent. Asphaltene precipitation is further calculated for i-alkanes, 1hexene, acetone, and methanol and their binary solvents with toluene, see Figure 6. Asphaltene precipitation is predicted well for i-pentane−toluene binary. Underpredictions are observed for i-octane−toluene and 1-hexene−toluene binary systems,

Figure 4. Experimental data,17 in symbols, and COSMO-SAC results, in lines, for asphaltene precipitation in binary solvents. n-pentane− toluene (red), n-hexane−toluene (magenta), n-heptane−toluene (green), n-octane−toluene (blue), and n-decane−toluene (black).

Figure 6. Experimental data,17 in symbols, and COSMO-SAC results, in lines, for asphaltene precipitation in binary solvents. i-pentane− toluene (red), acetone−toluene (magenta), 1-hexene−toluene (green), i-octane−toluene (blue), and methanol−toluene (black). 8989


Article

Energy & Fuels although the predicted trends are consistent with the experimental ones. The model fails to predict asphaltene precipitation in acetone−toluene and methanol−toluene binaries. It transpires that the COSMO-SAC predictions are in fact comparable to those of UNIFAC.27 m

MAD =

ni

∑∑ i

|ln Zij − ln Ziĵ |

j

m

∑i ni

(10)

The goodness of fit of the predictions is expressed in terms of mean absolute deviation (MAD) of the natural logarithm of asphaltene solubility in mole fraction (Table 3), see eq 10. Zij Table 3. Goodness of Fit of the Three Models for Asphaltene Precipitation in the 15 Binary Solvents models

MAD

COSMO-SAC COSMO-SAC′ COSMO-ASP

1.62 2.08 0.96

and Ẑ ij are calculated and measured asphaltene solubility, respectively, for data point j in the binary solvent i. m represents the total number of binary solvents, and ni is the number of data points for the binary solvent i. The MAD calculation considers asphaltene solubility data in the range of asphaltene precipitation yield between 0.1 and 0.9. Precipitation yield is the ratio of precipitated asphaltenes to total asphaltenes. The MAD value for the COSMO-SAC predictions is 1.62. Due to the low solubility of asphaltene molecules in the solutions, a careful examination over the calculated activity coefficients at infinite dilution in the pure solvents should provide valuable insight for the prediction results. As discussed earlier, γeff I captures the solvent composition effects resulting from dissolving asphaltenes in different solvents. Positive ln γeff,∞ suggests poor solvents, while negative ln γeff,∞ suggests I I good solvents. Figure 7a shows that COSMO-SAC predicts positive ln γeff,∞ for asphaltene in the nine alkane solvents and I the alkene and negative ln γeff,∞ for the remaining six solvents: I toluene, t-butyl benzene, nitrobenzene, dichloromethane, acetone, and methanol. The ln γeff,∞ decreases monotonically I with the carbon number in the alkanes and alkenes, suggesting increasing solubility in those solvents with increasing carbon number. An anatomy of ln γeff,∞ should clarify the driving force for I asphaltene aggregation. ln γeff,∞ is the difference between ln γ∞ I I ∞ and ln γnano. Figure 7b shows that, in the 10 poor solvents, ln ∞ γeff,∞ is positive because ln γ∞ I nano is more negative than ln γI . In eff,∞ contrast, in the good solvents, ln γI is negative because ln ∞ γ∞ nano is more positive than ln γI . Figure 7c and d further show the residual contributions and the combinatorial contributions ∞ to both ln γ∞ I and ln γnano. For the 10 poor solvents, the ln ∞,R ∞,R γI ’s and ln γnano’s are relatively constant small positive values ∞ for ln γ∞ I and ln γnano. In other words, the residual contributions ∞,C are relatively small. In contrast, the ln γ∞,C I ’s and ln γnano’s are negative, and the smaller the carbon number of the solvents, the more negative the ln γ∞,C and ln γ∞,C I nano’s become. It suggests the combinatorial term is the dominant contributor to the negative values of ln γ∞ nano and asphaltene precipitation in the poor solvents. ∞,C For the six good solvents, the ln γ∞,C I ’s and ln γnano’s are also negative as they reflect the small molecular size of the solvent molecules in comparison to the larger molecular sizes of

Figure 7. Logarithm of activity coefficients at infinite dilution of asphaltenes (blue) and nanoaggregates (red) in pure solvents as calculated using COSMO-SAC: (a) effective activity coefficient (green), (b) activity coefficient, (c) residual term of activity coefficient, and (d) combinatorial term of activity coefficient.

asphaltenes and nanoaggregates. On the other hand, the ln γ∞,R nano’s are mostly large positive values, suggesting strong repulsive interactions between the solvents and nanoaggregates. It suggests that the residual term is the main contributor to the high barrier for nanoaggregate formation, thus good solvents for asphaltenes. In brief, COSMO-SAC yields good results for asphaltene precipitation in hydrophobic solvents such as n-alkane solvents but inadequate results for polar solvents such as acetone and hydrophilic solvents such as methanol. Two variations of COSMO-SAC are further pursued in this study to address the discrepancies in the asphaltene precipitation predictions. The first variation focuses on a modification of the combinatorial term calculated with the Staverman−Guggenheim entropy of mixing expression. The second variation involves the use of apparent sigma profiles developed with the conceptual segment approach. 8990


Article

Energy & Fuels 5.2. Modification of S-G Expression. The ideal entropy of mixing considers all molecules in the solution having the same size and shape. However, when the size and shape of the molecules are different from one another, the solution entropy deviates from that of ideal mixing. The Flory−Huggins model for excess entropy of mixing, SE, distinguishes molecules by their size but considers them as linear chains. It results in an upper limit in the calculation of SE. Since the presence of bulky molecules should reduce the number of configurations for the mixture, it should thus decrease the excess entropy of mixing. The Staverman−Guggenheim model introduced a correction term to quantify this deviation from the F−H model by considering the shape difference of molecules. Subsequently, it is applied in many activity coefficient models, e.g., UNIQUAC,53 UNIFAC, COSMO-SAC, etc. However, numerous researchers54 observed that the S-G model could yield unrealistic results in some situations, and modifications to the combinatorial expression have been proposed including a recent modification on the combinatorial contribution of COSMO-SAC.55 The author introduced a modified F−H expression56 in which a universal empirical exponent was used to scale down the volume parameter rI, and the surface normalization parameter q was optimized for the S-G correction term. However, although the proposed modification works well for small to moderate size molecules, the S-G correction term would outweigh the F−H term, leading to unrealistic calculation of γCI for large and bulky molecules such as asphaltenes. As shown in eqs 11−13, we propose a modification to the S-G expression by introducing a universal exponent p to scale down both the volume and surface area parameters rI and qI. The proposed expression results in ideal mixing with p = 0 and recovers the original S-G expression with p = 1. The rationale of this exponent p can be traced to the entropy of mixing derivation by the lattice model which assumes unrestricted flexibility of molecules in the lattice. Due to the steric hindrance of molecules restricting the flexibility in real solutions, the number of possible configurations in the lattice should be significantly reduced. Corresponding to the decrease of configuration number due to steric hindrance, the p parameter scales down the entropic contribution due to size and shape difference. ln γISG = 1 −

ϕI′ xI

+ ln

ϕI′ xI

−

Figure 8. Comparison of experimental activity coefficients at infinite dilution, ln γ∞, of alkane molecules in alkane solvents with model results: S-G (red) and modified S-G (blue).

coefficients deviating from the experimental results, while the modified model brings substantial improvement. We replace the combinatorial term of the COSMO-SAC model with the modified S-G expression and name the resultant model COSMO-SAC′. The volume and surface area parameters rI and qI for molecules are calculated with Bondi’s method63 from the van der Waals radii of atoms, then applied with the normalization factors introduced by Abrams and Prausnitz.53 In other words, the COSMO-SAC′ proposed here shares the same rI and qI parameters with UNIQUAC/UNIFAC models. The parameters are available for most compounds from various databanks.64,65 Alternatively, they can be generated from group contribution methods.28,63 The parameters for naphthenic −CH2− and >CH− groups are not distinguishable from those of aliphatic groups in the Bondi method. We identify new parameters for the naphthenic groups from activity coefficient data in mixtures of cyclic alkanes with normal alkanes. COSMO-SAC′ is used to predict asphaltene precipitation from the same set of 15 binary solvents. Due to the modification to the S-G expression, the contribution from the combinatorial term is drastically reduced. Therefore, a larger alkyl chain surrogate molecule is required to represent the nanoaggregates. To capture the observed experimental trend for asphaltene precipitation in n-alkane−toluene systems, n-C120 is identified as the representative molecule for nanoaggregates. The volume and surface area parameters for asphaltenes, nanoaggregates, and solvents are reported in Table 2. Experimental data for asphaltene precipitation in n-alkane− toluene binary systems are used to estimate the nanoaggregate formation constant, and ln Kagg is found to be −5.78. Figure 9 shows the asphaltene precipitation predictions for the five n-alkane−toluene systems with COSMO-SAC′. Compared to the predictions of original COSMO-SAC, the COSMO-SAC′ results show steeper precipitation profiles. Figure 10 shows the precipitation results for five binary solvents with n-hexane as a poor solvent and with either aromatics, c-alkanes, or dichloromethane as a good solvent. The prediction results are comparable to those of the COSMO-SAC results, and no discernible improvement is observed. Figure 11 shows the prediction results for five binary solvents of toluene

ϕ′ ϕ′⎞ 1 ⎛ ZqI′⎜1 − I + ln I ⎟ 2 ⎝ θI′ θI′ ⎠ (11)

ϕI′ =

x IqI′ x IrI′ and θI′ = ∑J xJr′J ∑J xJq′J

rI′ = rIp and qI′ = qIp

(12) (13)

The exponent p is identified against experimental measurements57−62 of the alkane infinite dilution activity coefficient in alkane solutions with a carbon number ranging from 6 to 36. The alkane solutions are treated as athermal here, and the solution nonideality can only come from the entropy contribution. Normal, branched, and cyclic alkanes are studied simultaneously to test the effects of size and shape on the entropy contribution. Figure 8 compares the calculated infinite dilution activity coefficients of various alkanes from the S-G model and the modified S-G model with p identified as 2/3. The original S-G model predicts combinatorial activity 8991


Article

Energy & Fuels

Figure 9. Experimental data,17 in symbols, and COSMO-SAC′ results, in lines, for asphaltene precipitation in binary solvents: n-pentane− toluene (red), n-hexane−toluene (magenta), n-heptane−toluene (green), n-octane−toluene (blue), and n-decane−toluene (black).

Figure 11. Experimental data,17 in symbols, and COSMO-SAC′ results, in lines, for asphaltene precipitation in binary solvents. ipentane−toluene (red), acetone−toluene (magenta), 1-hexene− toluene (green), i-octane−toluene (blue), and methanol−toluene (black). eff,∞ γ∞,R nano is the prime contributor for the negative values of γI in the good solvents. With the larger n-C120 representing nanoaggregates, the augmented sigma profile amplifies γ∞,R nano particularly in polar and hydrophilic solvents. Due to the ∞,R combined effects of reduced ln γ∞,C nano and amplified ln γnano, ln ∞ eff,∞ γnano nets an increment that eventually pulls ln γI toward negative values. Thus, ln γeff,∞ becomes more negative in good I solvents. Consequently, COSMO-SAC′ predicts 1-hexene as a good solvent by finding negative ln γeff,∞ . I In summary, COSMO-SAC′ refines the combinatorial contribution of the COSMO-SAC model and improves the predictions in solvents where the entropic term plays the key role. However, neither COSMO-SAC nor COSMO-SAC′ could properly predict asphaltene solubility in polar and hydrophilic solvents. We then investigate the use of apparent sigma profiles as shown in the next section. 5.3. COSMO-SAC with Apparent Sigma Profiles for Asphaltene Precipitation. On the basis of solubility class definition, the asphaltene fraction is composed of tens of thousands of compounds of similar structure. There is no unique molecular structure for asphaltenes. Rather, several alternative structures have been suggested in the literature.5 Thus, the sigma profile generated from a single molecular structure may not properly reflect the nature of asphaltenes. Therefore, it is appropriate to generate an apparent asphaltene sigma profile that best describes the observed asphaltene aggregation behavior. We follow the apparent sigma profile generation procedure in the literature31 and treat COSMOSAC as a correlation model. The combinatorial contribution is calculated using the modified S-G model, and n-C120 is used to represent the nanoaggregates. ln Kagg is adjusted against the same precipitation data for asphaltenes in n-alkane−toluene binary solvents and found to be −6.11. The conceptual segment numbers of asphaltenes and the nanoaggregate formation constant are estimated from the experimental data of asphaltene precipitation in the 15 binary solvents. The estimated values of conceptual segment numbers are reported in Table 4. Considering the molecular structure of asphaltenes,

Figure 10. Experimental data,17 in symbols, and COSMO-SAC′ results, in lines, for asphaltene precipitation in binary solvents. t-butyl benzene−n-hexane (red), nitrobenzene−n-hexane (blue), c-hexane−nhexane (magenta), decalin−n-hexane (green), and dichloromethane− n-hexane (black).

with i-alkanes, alkenes, acetone, and methanol. Excellent predictions are observed for the binary solvents with i-alkanes. However, opposite of experimental observation, the model predicts asphaltene to be highly soluble in 1-hexene, acetone, and methanol. The MAD value of the COSMO-SAC′ predictions turns out to be 2.08. The difference between the COSMO-SAC′ results and the COSMO-SAC results is due to the reduced contribution of the combinatorial contribution of the activity coefficients. This ∞,C effect is more pronounced in γ∞,C nano than in γI . Even with the ∞,C larger surrogate nanoaggregate molecule (n-C120), ln γnano undergoes substantial reduction in every solvent. The eff,∞ downsized ln γ∞,C ’s in alkane solvents nano’s scale down ln γI and lessen their difference. 8992


Article

Energy & Fuels Table 4. Conceptual Segment Numbers for Asphaltenes conceptual segment

value

X Y− Y+ Z

18.30 2.13 0 0

only the hydrophobic and polar segments are considered. As expected, asphaltene has a very large hydrophobic segment number and a substantial polar attractive segment number corresponding to its hydrocarbon nature and the aromatic core. The resulting asphaltene apparent sigma profile is shown in Figure 3. The use of apparent sigma profile with COSMO-SAC together with the modified S-G model is called COSMO-ASP. For n-alkane−toluene binary systems, the COSMO-ASP results for asphaltene precipitation are much better than those of COSMO-SAC and COSMO-SAC′ with the asphaltene sigma profile generated with DMol3, see Figure 12. The MAD value for the COSMO-ASP results is 0.96, the lowest among the three models.

Figure 13. Experimental data,17 in symbols, and COSMO-ASP results, in lines, for asphaltene precipitation in binary solvents. t-butyl benzene−n-hexane (red), nitrobenzene−n-hexane (blue), c-hexane− n-hexane (magenta), decalin−n-hexane (green), and dichloromethane−n-hexane (black).

Figure 12. Experimental data,17 in symbols, and COSMO-ASP results, in lines, for asphaltene precipitation in binary solvents. n-pentane− toluene (red), n-hexane−toluene (magenta), n-heptane−toluene (green), n-octane−toluene (blue), and n-decane−toluene (black).

Figure 14. Experimental data,17 in symbols, and COSMO-ASP results, in lines, for asphaltene precipitation in binary solvents. i-pentane− toluene (red), acetone−toluene (magenta), 1-hexene−toluene (green), i-octane−toluene (blue), and methanol−toluene (black).

COSMO-ASP predicts proper trends for asphaltene precipitation in n-alkane−toluene binary solvents of different carbon numbers for n-alkane. Shown in Figure 13, COSMOASP predicts asphaltene precipitation in nitrobenzene−nhexane and t-butyl benzene−n-hexane binary solvents with excellent accuracy. Figure 13 also shows that COSMO-ASP predicts nearly constant asphaltene solubility in n-hexane−chexane and n-hexane−decalin binary solvents. COSMO-ASP predictions also match well the experimental trend for dichloromethane−n-hexane binary solvent. Figure 14 shows the COSMO-ASP predictions for asphaltene precipitation in ialkanes, 1-hexene, acetone, and methanol and their binary solvents with toluene. Asphaltene precipitations are predicted for i-pentane−toluene, i-octane−toluene, and methanol− toluene binary solvents with acceptable accuracy. Although they underpredict asphaltene precipitation, or overpredict

asphaltene solubility, in acetone−toluene and 1-hexene− toluene binary solvents, the COSMO-ASP predictions do capture the experimental trends. In short, compared with COSMO-SAC and COSMO-SAC′, COSMO-ASP generates superior predictions for the binary solvents with acetone and methanol. The COSMO-ASP prediction results can be best explained through the predictions for activity coefficient at infinite dilution in pure solvents. Figure 15a presents ln γeff,∞ for I asphaltene in the 16 pure solvents, while Figure 15b shows the ∞ contributing terms of ln γeff,∞ , i.e., ln γ∞ and ln γnano . I I Furthermore, the residual and combinatorial terms of activity coefficients of both asphaltenes and nanoaggregates are reported in Figure 15c and d, respectively. COSMO-ASP calculates negative ln γeff,∞ for asphaltene in the two aromatics I 8993


Article

Energy & Fuels

satisfactorily capture the precipitation data, the predictions miss the “tailing” effect at low fractional precipitation of the precipitation curve. A possible explanation is that the diversity of asphaltene molecules results in a range of concentration for aggregation and thus the “tailing” effect in the precipitation curve. It has been reported that the aggregation process of asphaltene molecules starts at a very low concentration, i.e., at the parts per million level.66,67 For example, there is evidence of forming a dimer of asphaltene at ∼30 mg/L.66 Additionally, there exists a “critical nanoaggregate concentration” (CNAC), at which the asphaltene nanoaggregate is fully developed and further growth is seized. CNAC of asphaltene in toluene is reported in the range of 50−150 mg/L.66,67 Determination of CNAC has been confirmed by different measurement techniques.68 The existence of dimers and nanoaggregates at the parts per million level is consistent with aggregation thermodynamics. Dissolved molecules in liquid solution may exist as a distribution of single molecules, pairs, triplets, or even higher clusters. Likewise, dissolved asphaltenes in liquid may exist as a distribution of monomers, dimers, or even nanoaggregates. The aggregation thermodynamics aim to capture the transition point at which further addition of asphaltene molecules in the solution would exist only as nanoaggregates. Future work will extend aggregation thermodynamics beyond binary solvents to facilitate predictions of asphaltene precipitation in crude oils. Key modeling challenges include (1) molecular representation of crude oils from crude assay data and (2) activity coefficient predictions that properly capture dominant molecular surface interaction characteristics of the diverse crude oil molecules including asphaltenes.

7. CONCLUSION Aggregation thermodynamics successfully predicts asphaltene precipitation in a wide range of binary solvents with variations of the COSMO-SAC model. The efficacy of this model for asphaltene precipitation hinges on a proper description of the combinatorial contribution and the residual contribution to the activity coefficients of asphaltene molecules and nanoaggregates in the solution. Quality predictions of asphaltene precipitation in polar and hydrophilic solvents such as acetone and methanol are achieved with the use of apparent sigma profiles. Future work will extend aggregation thermodynamics beyond binary solvents to allow prediction of the asphaltene precipitation in crude oils.

Figure 15. Logarithm of activity coefficients at infinite dilution of asphaltenes (blue) and nanoaggregates (red) in pure solvents as calculated using COSMO-ASP: (a) effective activity coefficient (green), (b) activity coefficient, (c) residual term of activity coefficient, and (d) combinatorial term of activity coefficient.

and dichloromethane and positive ln γeff,∞ for the remaining 13 I solvents. Of particular interest is that COSMO-ASP predicts a larger positive value of ln γ∞,R for asphaltene in methanol, I resulting in positive ln γeff,∞ and much reduced solubility, see I Figure 15c.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +1 806.834.3098. E-mail: [email protected].

6. DISCUSSION In our approach to simplifying the model, we make the assumption that all asphaltene molecules and the nanoaggregates are identical and the differences in solubility in different solvents are attributed to the activity coefficients of the asphaltene molecules and the nanoaggregates in the solution. Certainly this is a drastic simplification that can be a source of error, and better predictions should be achievable if such an assumption is relaxed. For example, Figure 4 shows the COSMO-SAC predictions for asphaltene precipitation in various binary n-alkane−toluene solvents. While the predictions

ORCID

Chau-Chyun Chen: 0000-0003-0026-9176 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support of the Jack Maddox Distinguished Engineering Chair Professorship in Sustainable Energy sponsored by the J.F Maddox Foundation. 8994


Article

Energy & Fuels

■

(24) Wu, J.; Prausnitz, J. M.; Firoozabadi, A. Molecularthermodynamic framework for asphaltene-oil equilibria. AIChE J. 1998, 44 (5), 1188−1199. (25) Gonzalez, D. L.; Hirasaki, G. J.; Creek, J.; Chapman, W. G. Modeling of asphaltene precipitation due to changes in composition using the perturbed chain statistical associating fluid theory equation of state. Energy Fuels 2007, 21 (3), 1231−1242. (26) Vargas, F. M.; Gonzalez, D. L.; Hirasaki, G. J.; Chapman, W. G. Modeling Asphaltene Phase Behavior in Crude Oil Systems Using the Perturbed Chain Form of the Statistical Associating Fluid Theory (PCSAFT) Equation of State†. Energy Fuels 2009, 23 (3), 1140−1146. (27) Wang, M.; Hao, Y.; Islam, M. R.; Chen, C.-C. Aggregation thermodynamics for asphaltene precipitation. AIChE J. 2016, 62 (4), 1254−1264. (28) Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. Groupcontribution estimation of activity coefficients in nonideal liquid mixtures. AIChE J. 1975, 21 (6), 1086−1099. (29) Lin, S. T.; Sandler, S. I. A priori phase equilibrium prediction from a segment contribution solvation model. Ind. Eng. Chem. Res. 2002, 41 (5), 899−913. (30) DMol3, Material Studio 7.0; Accelrys Software Inc.: San Diego, CA, 2013. (31) Islam, M. R.; Chen, C.-C. COSMO-SAC Sigma Profile Generation with Conceptual Segment Concept. Ind. Eng. Chem. Res. 2015, 54 (16), 4441−4454. (32) Chen, C.-C.; Islam, M. R. Apparatus and computerized method for optimizing or generating a sigma profile for a molecule. US patent application publication, US 2017/0083688 A1; March 23, 2017. (33) Ben-Naim, A. Solvation Thermodynamics; Plenum Press: New York, 1987. (34) Klamt, A. Conductor-like screening model for real solvents: a new approach to the quantitative calculation of solvation phenomena. J. Phys. Chem. 1995, 99 (7), 2224−2235. (35) Lin, S. T.; Sandler, S. I. Infinite dilution activity coefficients from ab initio solvation calculations. AIChE J. 1999, 45 (12), 2606−2618. (36) Lin, S.-T.; Sandler, S. I. Prediction of octanol-water partition coefficients using a group contribution solvation model. Ind. Eng. Chem. Res. 1999, 38 (10), 4081−4091. (37) Staverman, A. The entropy of high polymer solutions. Generalization of formulae. Recueil des Travaux Chimiques des PaysBas 1950, 69 (2), 163−174. (38) Guggenheim, E. A. Mixtures: The Theory of the Equilibrium Properties of Some Simple Classes of Mixtures, Solutions and Alloys; Clarendon Press, 1952. (39) Klamt, A.; Schüürmann, G. COSMO: a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient. J. Chem. Soc., Perkin Trans. 2 1993, No. 5, 799−805. (40) Klamt, A.; Jonas, V.; Burger, T.; Lohrenz, J. C. W. Refinement and parametrization of COSMO-RS. J. Phys. Chem. A 1998, 102 (26), 5074−5085. (41) Mullins, E.; Oldland, R.; Liu, Y.; Wang, S.; Sandler, S. I.; Chen, C.-C.; Zwolak, M.; Seavey, K. C. Sigma-profile database for using COSMO-based thermodynamic methods. Ind. Eng. Chem. Res. 2006, 45 (12), 4389−4415. (42) Lin, S.-T.; Chang, J.; Wang, S.; Goddard, W. A.; Sandler, S. I. Prediction of vapor pressures and enthalpies of vaporization using a COSMO solvation model. J. Phys. Chem. A 2004, 108 (36), 7429− 7439. (43) Wang, S.; Sandler, S. I.; Chen, C.-C. Refinement of COSMOSAC and the applications. Ind. Eng. Chem. Res. 2007, 46 (22), 7275− 7288. (44) Hsieh, C.-M.; Sandler, S. I.; Lin, S.-T. Improvements of COSMO-SAC for vapor−liquid and liquid−liquid equilibrium predictions. Fluid Phase Equilib. 2010, 297 (1), 90−97. (45) Xiong, R.; Sandler, S. I.; Burnett, R. I. An Improvement to COSMO-SAC for Predicting Thermodynamic Properties. Ind. Eng. Chem. Res. 2014, 53 (19), 8265−8278.

REFERENCES

(1) Zanganeh, P.; Ayatollahi, S.; Alamdari, A.; Zolghadr, A.; Dashti, H.; Kord, S. Asphaltene deposition during CO2 injection and pressure depletion: A visual study. Energy Fuels 2012, 26 (2), 1412−1419. (2) Rassamdana, H.; Dabir, B.; Nematy, M.; Farhani, M.; Sahimi, M. Asphalt flocculation and deposition: I. The onset of precipitation. AIChE J. 1996, 42 (1), 10−22. (3) Sheu, E. Y. Petroleum asphaltene properties, characterization, and issues. Energy Fuels 2002, 16 (1), 74−82. (4) Dickie, J. P.; Yen, T. F. Macrostructures of the asphaltic fractions by various instrumental methods. Anal. Chem. 1967, 39 (14), 1847− 1852. (5) Mullins, O. C. The Modified Yen Model†. Energy Fuels 2010, 24 (4), 2179−2207. (6) Mullins, O. C.; Martinez-Haya, B.; Marshall, A. G. Contrasting perspective on asphaltene molecular weight. This comment vs the overview of A. A. Herod, K. D. Bartle, and R. Kandiyoti. Energy Fuels 2008, 22 (3), 1765−1773. (7) Schuler, B.; Meyer, G.; Peña, D.; Mullins, O. C.; Gross, L. Unraveling the Molecular Structures of Asphaltenes by Atomic Force Microscopy. J. Am. Chem. Soc. 2015, 137 (31), 9870−9876. (8) Hammami, A.; Phelps, C. H.; Monger-McClure, T.; Little, T. Asphaltene precipitation from live oils: An experimental investigation of onset conditions and reversibility. Energy Fuels 2000, 14 (1), 14−18. (9) Peramanu, S.; Singh, C.; Agrawala, M.; Yarranton, H. W. Investigation on the reversibility of asphaltene precipitation. Energy Fuels 2001, 15 (4), 910−917. (10) Beck, J.; Svrcek, W.; Yarranton, H. Hysteresis in asphaltene precipitation and redissolution. Energy Fuels 2005, 19 (3), 944−947. (11) Abedini, A.; Ashoori, S.; Torabi, F.; Saki, Y.; Dinarvand, N. Mechanism of the reversibility of asphaltene precipitation in crude oil. J. Pet. Sci. Eng. 2011, 78 (2), 316−320. (12) Flory, P. J. Thermodynamics of High Polymer Solutions. J. Chem. Phys. 1942, 10 (1), 51−61. (13) Huggins, M. L. Some Properties of Solutions of Long-chain Compounds. J. Phys. Chem. 1942, 46 (1), 151−158. (14) Hirschberg, A.; DeJong, L.; Schipper, B.; Meijer, J. Influence of temperature and pressure on asphaltene flocculation. Soc. Pet. Eng. J. 1984, 24 (03), 283−293. (15) Cimino, R.; Correra, S.; Sacomani, P.; Carniani, C. In Thermodynamic Modelling for Prediction of Asphaltene Deposition in Live Oils; SPE International Symposium on Oilfield Chemistry, Society of Petroleum Engineers, 1995. (16) Yarranton, H. W.; Masliyah, J. H. Molar mass distribution and solubility modeling of asphaltenes. AIChE J. 1996, 42 (12), 3533− 3543. (17) Mannistu, K. D.; Yarranton, H. W.; Masliyah, J. H. Solubility modeling of asphaltenes in organic solvents. Energy Fuels 1997, 11 (3), 615−622. (18) Burke, N. E.; Hobbs, R. E.; Kashou, S. F. Measurement and modeling of asphaltene precipitation. J. Pet. Technol. 1990, 42 (11), 1440−1446. (19) Kawanaka, S.; Park, S.; Mansoori, G. Organic deposition from reservoir fluids: a thermodynamic predictive technique. SPE Reservoir Eng. 1991, 6 (02), 185−192. (20) Andersen, S. I.; Speight, J. G. Thermodynamic models for asphaltene solubility and precipitation. J. Pet. Sci. Eng. 1999, 22 (1), 53−66. (21) Kohse, B. F.; Nghiem, L. X.; Maeda, H.; Ohno, K. In Modelling Phase Behaviour Including the Effect of Pressure and Temperature on Asphaltene Precipitation; SPE Asia Pacific Oil and Gas Conference and Exhibition, Society of Petroleum Engineers, 2000. (22) Freed, D. E.; Mullins, O. C.; Zuo, J. Y. Theoretical treatment of asphaltene gradients in the presence of GOR gradients. Energy Fuels 2010, 24 (7), 3942−3949. (23) Zuo, J. Y.; Mullins, O. C.; Freed, D.; Elshahawi, H.; Dong, C.; Seifert, D. J. Advances in the Flory−Huggins−Zuo equation of state for asphaltene gradients and formation evaluation. Energy Fuels 2013, 27 (4), 1722−1735. 8995


Article

Energy & Fuels (46) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. General atomic and molecular electronic structure system. J. Comput. Chem. 1993, 14 (11), 1347−1363. (47) Frisch, M.; Trucks, G.; Schlegel, H.; Scuseria, G.; Robb, M.; Cheeseman, J.; Montgomery, J., Jr.; Vreven, T.; Kudin, K.; Burant, J. Gaussian 03, revision c.02; Gaussian, Inc.: Wallingford, CT, 2008. (48) Jaguar 4.2; Schrödinger Inc.: Portland, OR, 1991. (49) Stewart, J. MOPAC program package; Quantum Chemistry Program Exchange, 1989; 455. (50) Mullins, E.; Liu, Y.; Ghaderi, A.; Fast, S. D. Sigma profile database for predicting solid solubility in pure and mixed solvent mixtures for organic pharmacological compounds with COSMO-based thermodynamic methods. Ind. Eng. Chem. Res. 2008, 47 (5), 1707− 1725. (51) Liu, Y. A. VT Sigma Profile Databases. www.design.che.vt.edu/ VT-Databases.html (accessed Mar. 12, 2017). (52) Chen, C.-C.; Song, Y. Solubility modeling with a nonrandom two-liquid segment activity coefficient model. Ind. Eng. Chem. Res. 2004, 43 (26), 8354−8362. (53) Abrams, D. S.; Prausnitz, J. M. Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems. AIChE J. 1975, 21 (1), 116−128. (54) Sayegh, S.; Vera, J. Lattice-model expressions for the combinatotial entropy of liquid mixtures: A critical discussion. Chemical Engineering Journal 1980, 19 (1), 1−10. (55) Soares, R. D. The Combinatorial Term for COSMO-Based Activity Coefficient Models. Ind. Eng. Chem. Res. 2011, 50 (5), 3060− 3063. (56) Donohue, M. D.; Prausnitz, J. M. Combinatorial Entropy of Mixing Molecules That Differ in Size and Shape - Simple Approximation for Binary and Multicomponent Mixtures. Can. J. Chem. 1975, 53 (11), 1586−1592. (57) Kniaź, K. Influence of size and shape effects on the solubility of hydrocarbons: the role of the combinatorial entropy. Fluid Phase Equilib. 1991, 68, 35−46. (58) Parcher, J. F.; Weiner, P. H.; Hussey, C. L.; Westlake, T. N. Specific retention volumes and limiting activity coefficients of C4-C8 alkane solutes in C22-C36 n-alkane solvents. J. Chem. Eng. Data 1975, 20 (2), 145−151. (59) Kontogeorgis, G. M.; Nikolopoulos, G. I.; Fredenslund, A.; Tassios, D. P. Improved models for the prediction of activity coefficients in nearly athermal mixtures Part II. A theoretically-based G E-model based on the van der Waals partition function. Fluid Phase Equilib. 1997, 127 (1), 103−121. (60) Góral, M.; Oracz, P.; Warycha, S. Vapour-liquid equilibria: VI. The ternary system acetone-hexane-cyclohexane at 313.15 K. Fluid Phase Equilib. 1992, 81, 261−272. (61) Martin, M.; Youings, J. Vapour pressures and excess Gibbs free energies of cyclohexane + n-hexane, + n-heptane and + n-octane at 298. 150 K. Aust. J. Chem. 1980, 33 (10), 2133−2138. (62) Kikic, I.; Alessi, P.; Rasmussen, P.; Fredenslund, A. On the combinatorial part of the UNIFAC and UNIQUAC models. Can. J. Chem. Eng. 1980, 58 (2), 253−258. (63) Bondi, A. A. Physical properties of molecular crystals liquids, and glasses; Wiley: New York, 1968. (64) Gmehling, J. Parameters of the Original UNIFAC Model. www. ddbst.com/published-parameters-unifac.html (accessed Mar. 12, 2017). (65) Aspen Plus, v.8.4; Aspen Technology Inc.: Bedford, MA, 2013. (66) Andreatta, G.; Goncalves, C. C.; Buffin, G.; Bostrom, N.; Quintella, C. M.; Arteaga-Larios, F.; Pérez, E.; Mullins, O. C. Nanoaggregates and Structure−Function Relations in Asphaltenes. Energy Fuels 2005, 19 (4), 1282−1289. (67) Andreatta, G.; Bostrom, N.; Mullins, O. C. High-Q ultrasonic determination of the critical nanoaggregate concentration of asphaltenes and the critical micelle concentration of standard surfactants. Langmuir 2005, 21 (7), 2728−2736.

(68) Goual, L.; Sedghi, M.; Zeng, H.; Mostowfi, F.; McFarlane, R.; Mullins, O. C. On the formation and properties of asphaltene nanoaggregates and clusters by DC-conductivity and centrifugation. Fuel 2011, 90 (7), 2480−2490.

8996


Prediction of Asphaltene Precipitation in Organic Solvents via COSMO

Recommend Documents