Application of the Conduct-like Screening Models ... - ACS Publications

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Application of the Conduct-like Screening Models for Real Solvent and Segment Activity Coefficient for the Predictions of Partition Coefficients and Vapor−Liquid and Liquid−Liquid Equilibria of Biooil-Related Mixtures Jinlong Li†,‡ and Patrice Paricaud*,† Unité d’enseignement et de recherche de Chimie et Procédés (UCP), École Nationale Supérieure de Techniques Avancées (ENSTA), 75739 Paris, cedex 15, France ‡ State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, People’s Republic of China †

S Supporting Information *

ABSTRACT: The 1-octanol/water partition coefficients (log P) at 298.15 K and the vapor−liquid and liquid−liquid equilibria (VLE and LLE) of biofuel-related mixtures have been predicted with four different thermodynamic models: conduct-like screening models for real solvent (COSMO-RS), conduct-like screening models for segment activity coefficient (COSMO-SAC) (2002 version), modified COSMO-SAC (2006 version), and universal functional activity coefficient (UNIFAC). The 2002 version of COSMO-SAC gives more reasonable predictions for log P for most investigated mixtures than the other two approaches when appropriate molecular geometries are chosen for the computation of the σ profiles. However, the COSMO-RS model gives better predictions for VLE pressures and vapor-phase compositions for biofuel-related mixtures, as well as for the LLE of the 1-octanol + water and furfural + water mixtures. The accuracy of the models for the predictions of the partition coefficients and VLE may be improved by changing the molecular conformations used to generate the σ profiles. Generally, the three COSMO-based models give better predictions than UNIFAC for log P and VLE of the investigated systems and can be applied to predict the thermodynamic properties of the biofuel-related mixtures especially when no experimental data are available.

1. INTRODUCTION Bio-oils are liquid biofuels produced from the flash pyrolysis of lignocellulosic biomass. They are obtained from the partial condensation of the gas mixture produced from the fast heating of biomass in the absence of oxygen. The amount of bio-oil produced and its composition depend upon the type of biomass and the production conditions: a high-temperature pyrolysis leads to a smaller proportion of bio-oil and more incondensable gases, while a slower pyrolysis leads to a larger amount of coke. Several reviews on the pyrolysis process and the applications of bio-oils can be found in the literature.1−4 The reader is also directed to extensive reviews on biofuels.5−8 In contrast to petroleum fluids, bio-oils contain large amounts of oxygenated molecules. Bio-oils are complex mixtures that contain several hundreds of compounds:9 carboxylic acids, esters, alcohols, ketones, furans, sugars, water, etc. Some of these compounds are very useful molecules that can be used as raw products for the production of fine chemicals. The design of the separation units for the extraction of organic compounds from bio-oils requires a very good knowledge of the phase equilibria of binary and multicomponent mixtures of organic molecules + solvents. Different activity coefficient models and equations of state have been used to model the phase behavior of biofuel-related mixtures.10−13 However, few experimental data are available for these systems. Thus, predictive thermodynamic models that do not require any adjustment of parameters on experimental data are of crucial importance. Predictive models can be based on a © 2012 American Chemical Society

group contribution (GC) method, which consists in relating the parameters of a thermodynamic model to the number of the chemical groups constituting the investigated molecules. GC approaches have been developed for both activity coefficient models14−16 and equations of state.17−25 These approaches can provide very accurate predictions of phase equilibria and mixing properties, as long as the group parameters of the molecules are available. A refreshing approach based on quantum mechanical calculation and called conduct-like screening model for real solvent (COSMO-RS) was proposed by Klamt and coworkers.26−29 A COSMO calculation consists in performing a density functional theory (DFT) ab initio calculation on an isolated molecule surrounded by an ideal conductor. The cavity surrounding the molecule and defining the conductor boundary and molecular surface is constructed as atom-centered spheres and is divided into surface segments. The COSMO calculation determines the polarization (screening) charges on the surface segments of the cavity. After a local averaging of the surface charges was performed, one can determine the so-called σ profile for each molecule, which is the distribution of the surface charges. Each molecule is then characterized by its surface, its volume, and its σ profile. Assuming that the surface Received: January 30, 2012 Revised: April 10, 2012 Published: April 12, 2012 3756

dx.doi.org/10.1021/ef300181j | Energy Fuels 2012, 26, 3756−3768

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following procedure of Mullins et al.33 The paper is organized as follows: the three COSMO-like models used in the current work are briefly discussed in section 2. The calculation methods for VLE, LLE, and log P are explained in section 3. In section 4, the predictions of log P, VLE, and LLE for biofuel-related mixtures obtained with the different approaches are compared. A conclusion is finally made in section 5.

segments independently interact by pair, the expressions for the chemical potentials can be derived (COSMOSPACE equations), leading to the COSMO-RS activity coefficient model.30 Later, Lin et al.31 re-derived another COSMO-based model, called conduct-like screening model for segment activity coefficient (COSMO-SAC), based on the COSMO-RS approach, because of a confusion of indistinguishability and distinguishability for identical segments, as stated by Lin et al.32 Several versions of COSMO-SAC were then proposed.31,33−36 Another version called COSMO-RS(ol) and based on the COSMO-RS and universal functional activity coefficient (UNIFAC)(Do) approaches was developed by Gmehling and co-workers.37,38 All of these approaches are predictive models that use ab initio calculations as inputs to characterize the studied molecules. They all have a restricted number of universal parameters that were determined by adjusting a large set of experimental vapor−liquid equilibrium (VLE) and/or liquid−liquid equilibrium (LLE) data. The COSMO-based thermodynamic models have extensively been applied for the prediction of macroscopic thermodynamic properties in many different fields. Macroscopic thermodynamic properties, such as heat of mixing, VLE, LLE, and partition coefficients (log P), can be predicted. The COSMO-RS solvation model was first used to predict VLE and LLE of some common systems.27 Then, it has been extended to predict a broad range of systems: associating fluids, drugs, ionic liquids, proteins, polymers, etc. The reader is directed to detailed reviews30,39,40 of the applications of COSMO-RS in different fields. The COSMORS model has been implemented into the COSMOthermX software package,41 which can be used to predict many thermodynamic properties, such as vapor pressures, boiling points, activity coefficients, mixing enthalpies, Henry’s constant, solubility, log P, VLE, LLE, solid−liquid equilibrium (SLE), density, etc. In this package,41 the authors also provided four different databases of ab initio calculation data for different special requirements, such as macromolecules, ionic solutes, etc. Similarly, the COSMO-SAC approach has a wide application in representation of phase behavior properties as well. For example, Lee and Lin42 employed the COSMO-SAC and Peng−Robinson (PR) models to predict VLE of some mixtures at elevated pressures. Athès et al.43 and Yang et al.44 extended COSMO-SAC to predict the phase behavior of mixtures containing aroma compounds and polymers, respectively. In the present work, we focus on the predictions of octanol− water partition coefficients and the phase equilibria of biofuelrelated mixtures, in which the biofuel-related compounds were selected on the basis of various studies on the valorization of lignocellulosic biomass. The chosen compounds are molecules with high added value, because they can be used as reaction intermediates for the production of important chemicals.45−47 Three different versions of COSMO-like approaches, namely, the last version of COSMO-RS,39,41 the original version of COSMO-SAC,31 and a modified version of COSMO-SAC33 that we denote as mCOSMO-SAC, are applied to model these properties. The effect of the molecular geometry on the prediction of octanol−water partition coefficients and phase equilibria has been studied. Most COSMO-RS calculations were obtained with the COSMOthermX-C21-0110 molecular modeling package41 based on the BP-TZVP database. The results obtained with COSMO-SAC and mCOSMO-SAC approaches are based on the VT-2005 database33,48 and our own ab initio calculation. All new ab initio data (i.e., COSMO files) are produced with the Dmol3 software package49 by

2. THERMODYNAMIC MODELS Here, we only provided the main working equations of the different COSMO-like models. The reader is directed to studies by Klamt and co-workers,26−30,39 Lin and Sandler,31 and Mullins et al.33 for further details. Both COSMO-RS and COSMO-SAC models are excess Gibbs thermodynamic models providing pressure-independent activity coefficients as a function of the temperature and composition. In the COSMO-RS approach,28,30 the chemical potential μi/S of component i in the solution at temperature T is given by μi /S =

∫ Aipi (σ )μS(σ )dσ + μiC/S + kT ln xi

(1)

μCi/S

is the combinatorial where Ai is the surface area of molecule i, contribution to the chemical potential of component i, and xi is the mole fraction of component i. pi(σ) is the normalized σ profile of component i. μS(σ) is called the σ potential of the solution. It is a segment chemical potential defined in kilojoules per unit area. By applying the COSMOSPACE equation,28 one can show that

⎛ ⎛ aeff (μ (σ ′) − e(σ , σ ′)) ⎞⎞ S ⎟⎟⎟dσ′ μS (σ ) = − kT ln⎜⎜ pS (σ ′)exp⎜ kT ⎝ ⎠⎠ ⎝

∫

(2) 2

where aeff = 6.15 Å is the effective contact surface. pS(σ′) is the normalized σ profile of the solution and defined as pS (σ ) =

∑i xiAi pi (σ ) ∑i xiAi

(3)

In eq 2, the term e(σ,σ′) denotes the interaction energy between segments of charge densities σ and σ′, which includes a charge−charge (misfit) Emf and a hydrogen-bonding Ehb interaction contribution. It was defined by28

e(σ , σ ′) = Emf (σ , σ ′) + E hb(σ , σ ′) =

α′ (σ + σ ′)2 + chb min(0; σdonor + σhb)max(0; σaccep − σhb) 2 (4)

where α′ = 6636 kJ mol−1 Å−2, chb = 33 800 kJ mol−1 Å−2 at T = 298 K, and σhb = 0.0084 e/Å2 are universal parameters and were determined on large sets of experimental thermodynamic properties. In addition, the van der Waals (vdW) interactions between surface segments EvdW = aeff(τvdW + τ′vdW) with the element-specific adjustable parameter τ, which is only dependent upon the element type of the atoms while independent of any neighborhood relations, are taken into account in COSMO-RS. In the model, the vdW energy is only an additional contribution to the energy of the reference state in solution and not to liquid activities, so that they do not appear in eq 4. Note that temperature dependence was used for the hydrogen bonding and vdW energy constants.28 The activity coefficient of component i in the solution can then be determined from

⎛ μi /S − μi / i ⎞ ⎟ γi /S = exp⎜ ⎝ ⎠ kT

(5)

where μi/i is the chemical potential of solute i in its pure state. In the COSMO-SAC approach,31 the activity coefficient of component i is given by 3757


Energy & Fuels ln γi /S =

∑

Article

Ai pi (σm) aeff

σm

[ln ΓS(σm) − ln Γi(σm)] + ln γiSG /S

where the superscripts “α” and “β” denote the coexistence phases of the mixture. For a non-ideal solution, the chemical potential of each component i in a liquid mixture can be expressed as

(6)

where the summation is over all possible discrete charge densities σm and aeff = 7.5 Å2. γSG i/S is combinatorial contribution to the activity coefficient, which is determined from Staverman−Guggenheim as

⎛θ ⎞ ⎛ϕ⎞ ϕ z ln γiSG = ln⎜ i ⎟ + qi ln⎜⎜ i ⎟⎟ + li − i /S xi ⎝ xi ⎠ 2 ⎝ ϕi ⎠

μi = μi* + RT ln(xiγi)

where xi and γi are the mole fractions and activity coefficient of component i, respectively, and μ*i is the chemical potential of pure component i at temperature T and pressure P. When eqs 12 and 13 are combined, one can express the condition for LLE as

∑ xjlj j

(7)

xiαγiα = xiβγi β

where z = 10 and li = z(ri − qi)/2 − (ri − 1). θi = xiqi/∑jxjqj, and ϕi = xiqi/∑jxjqj are the surface area fraction and volume fraction of component i, respectively. ri = Vi/r and qi = Ai/q are the normalized molecular volume and surface area of component i, respectively. Vi and Ai are the cavity volume and cavity surface area determined from the COSMO calculation, respectively. r = 66.69 Å3, and q = 79.53 Å2. The surface segment activity coefficients of component i, Γi(σm), and the solution, ΓS(σm) are determined by solving

⎛ ⎛ −ΔW (σm , σn) ⎞⎞ ln Γl(σm) = − ln⎜⎜∑ pl (σn)Γl(σn)exp⎜ ⎟⎟⎟ ⎝ ⎠⎠ kT ⎝ σn

σv =

ru 2reff 2 2

∑u

( exp(− f

ru 2 + reff 2

ru reff

2

ru 2 + reff 2

exp − fdecay

duv 2

yp = xip0 γi i

) )

duv decay ru 2 + reff 2

(8)

log10 Pi = log10 Cαi

(9)

Ciα Ciβ

∑u σu* σv =

2

∑u

( exp(−

ru 2 + rav 2

ru rav

2

ru 2 + rav 2

exp −

duv 2

) )

duv

ru 2 + rav 2

xiα xiβ

xiβv α

(17)

β

=

γi β γiα

(18)

(19)

Because the COSMO-like models are activity coefficient models, they cannot predict molar volumes of liquid phases at fixed T, p, and composition. The molar volume ratio can be calculated from β ρα ∑j xj Mj vβ = β α vα ρ ∑j xj Mj

(20) α

β

where Mj is the molecular weight of component j and ρ and ρ are the densities in g cm−3 of the coexistent phases. Because the solute is at infinite dilution, its mole fraction is negligible compared the solvent mole fractions; therefore, the presence of the solute does not affect the densities of the coexistent phases. As a result, the ratio vβ/vα can be determined from the experimental densities and compositions of the coexistent octanol-rich and water-rich phases for the octanol + water binary system,50 which are summarized in Table 1. Equation 20 leads to vβ/vα = 0.1402. Thus, the term log10(vβ/vα) is not negligible and equal to −0.853. Moreover, the prediction of log P for a given solute i requires the determination of the activity coefficients of solute i at ∞,β ∞,α and γ∞,β are predicted infinite dilution (γ∞,α i , γi ) in both phases: γi i with the COSMO-RS and COSMO-SAC models using the

(11)

The equilibrium conditions for a mixture are given by μiα = μi β

xiαv β

⎛ γ βv β ⎞ log Pi = log10⎜⎜ i α α ⎟⎟ ⎝ γi v ⎠

3. PHASE EQUILIBRIA AND PARTITION COEFFICIENTS pα = p β ,

=

When eqs 16−18 are combined, one can express the partition coefficient as

(10)

where rav = 0.817 64 Å.

T α = Tβ,

(16)

where v and v are the molar volumes of phases α and β. When the LLE condition is applied for solute i (eq 14), the mole fraction ratio is expressed as

ru 2 + rav 2 2

Ciβ

Cβi

α

where α′ = 16 465.98 kcal Å4 e−2 mol−1 is the misfit energy constant, chb = 85 580.0 kcal Å4 mol−1 e−2 is the hydrogen-bonding energy constant, and σhb = 0.0084 e/Å2 is a cutoff value for the hydrogenbonding interaction. The parameters σacc and σdon are the largest and smallest values of σm and σn, respectively. In COSMO-SAC and COSMO-RS, different adjustable parameters for the interactions of “misfit” and hydrogen-bonding energy between surface segments were employed, although both models were based on very similar expressions for the interaction energy. The main difference between COSMO-SAC31 and mCOSMOSAC33 is the way the charge density is locally averaged. Mullins et al.33 proposed a slightly different procedure given by ru 2rav 2

Ciα

and are the molarities (mol/L) in the coexistent octanolwhere rich and water-rich phases, respectively, at T = 298.15 K and p = 1.01 bar. The octanol−water partition coefficient is measured using a small amount of solute i. Thus, one can assume that the solute is at infinite dilution in both phases. The molarity ratio in eq 16 can be expressed in terms of a mole fraction ratio as

where σv is the average surface charge density on segment v, reff = (aeff/ π)0.5 is the effective radius (an adjustable parameter), duv the distance between segments u and v, ru = (au/π)0.5 is the radius of segment u, and fdecay = 3.57 is an empirical parameter used to balance the unit. The exchange energy ΔW(σm, σn) between the surface segments σm and σn is given by

α′ ΔW (σm , σn) = (σm + σn)2 + chb max[0, σacc − σhb] 2 min[0, σdon + σhb]

(15)

Here, xi and yi are the molar fractions of component i in liquid and vapor phases, respectively. p0i is the vapor pressure of component i at temperature T. Equation 15 is only valid at low pressure because it is based on the assumptions that the vapor phase is considered as an ideal mixture and that the properties of the liquid phase are pressureindependent. The octanol−water partition coefficient log Pi of solute i is defined as

ru 2 + reff 2 2

(14)

The equilibrium condition for VLE is given by

where the index l stands for all pure compounds i and the solution. The renormalized σ profile pi(σn) of each component i of the mixture is determined for charge densities ranging from −0.025 to 0.025 e/Å2. Before this histogram is determined, the screening charge density on each surface segment of molecule i is locally averaged using the following procedure:

∑u σu*

(13)

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Table 1. Experimental Compositions and Densities of the Coexistent Liquid Phases for the 1-Octanol (1) + Water (2) Binary System, at 298.15 K and 1 atm50 1-octanol (1)/water (2)

x1

x2

density (kg/m3)

organic phase aqueous phase

0.793 0.703 × 10−4

0.207 0.9999297

829.7 996.7

experimental 1-octanol and water mole fractions in the coexistent phases (Table 1).

4. RESULTS AND DISCUSSION 4.1. Partition Coefficients. The octanol−water partition coefficients (log P) of 10 biofuel-related compounds (solutes) have been predicted at 298.15 K and 1.01 bar with the COSMO-RS approach combined with the BP-TZVP database and with the COSMO-SAC and mCOSMO-SAC models combined with the VT-2005 database. For predictions at infinite dilution, the mole fraction of a solute was set to 10−8 in both coexistent liquid phases. The experimental log P values,51−53 the predicted values, the average absolute deviations (AADs), and the correlation coefficients are reported in Table 2. One can see from the average deviations that the COSMO-RS model gives more accurate predictions of log P for the investigated compounds in comparison to the COSMOSAC and mCOSMO-SAC models combined with the VT-2005 database. However, the correlation coefficients are closer to 1 for the COSMO-SAC and mCOSMO-SAC models than for COSMO-RS. This is due to the fact that the relative deviations between the experimental values and the COSMO-RS predictions are large for some specific compounds: for example, the experimental log P value of sorbitol is −2.20, while the value predicted by COSMO-RS is only −0.6512. The experimental data51−53 and the predicted values of log P are compared in Figure 1. It can be seen that the COSMO-RS model generally gives better predictions than the other approaches, except for some specific compounds, such as sorbitol and glycerol. One can note that the deviations are very large for some compounds for both COSMO-RS and COSMO-SAC. For

Figure 1. Octanol−water partition coefficients at 298.15 K predicted with (□) COSMO-RS, (△) COSMO-SAC, and (○) mCOSMO-SAC compared to experimental data (or pseudo-experimental data generated with GC methods).51−53 () Log10 Piexp = log10 Pical.

example, for furfural, COSMO-RS underestimates log P by a factor of 2, while the predictions of COSMO-SAC and mCOSMO-SAC are of opposite signs. These deviations can be explained by the fact that the predictions of COSMO-like models dramatically depend upon the COSMO ab initio calculation, in particular on the molecular geometries used to determine the σ profiles. The effect of the molecular geometry on the predicted thermodynamic properties has already been observed by several authors.30,35,43,54 Therefore, we have performed new ab initio calculations for some compounds using the Dmol3 package49 and following the procedure proposed by Mullins et al.33 The new geometries and σ profiles for the 10 biofuel compounds listed in Table 2 were given in the Supporting Information. The predictions of log P obtained with the new ab initio calculation are also reported in Table 2 for both the COSMO-SAC and mCOSMO-SAC models. Note that the COSMO files of water and 1-octanol used in these new predictions were still taken from the VT-2005 database. It can be seen that the accuracy of both COSMO-SAC and mCOSMO-SAC can be dramatically improved using the new geometries instead of those from the VT-2005 database: the

Table 2. Octanol−Water Partition Coefficients (Log P) for Some Biofuel-Related Compounds at 298.15 K COSMORS system fumaric acid itaconic acid levulinic acid glycerol sorbitol furfural anisole m-cresol vanillin quinone AADc Rd

CAS number

experimental (or estimated) values of log P51−53

110-17-8 97-65-4 123-76-2 56-81-5 50-70-4 98-01-1 100-66-3 108-39-4 121-33-5 106-51-4

0.46 −0.34 (EST)b −0.49 −1.76 −2.20 0.41 2.11 1.96 1.21 0.20

COSMO-SAC

mCOSMO-SAC

BP-TZVP

VT-2005

new geometrya

VT-2005

new geometrya

0.4078 0.0623 −0.3795 −1.1474 −0.6512 0.2059 2.2183 1.9731 1.1670 0.3072 0.3202 0.9525

0.0718 0.1785 −0.1547 −1.4731 −1.7864 −0.1232 1.6020 1.5838 1.0430 0.0561 0.3671 0.9753

0.4788 −0.1276 −0.3300 −1.6434 −2.2037 0.2928 1.8245 1.7948 1.2017 0.0733 0.1214 0.9961

−0.0551 0.0671 −0.1693 −1.4233 −1.7053 −0.1777 1.4998 1.4431 0.9486 0.0439 0.4207 0.9744

0.3847 −0.2342 −0.3511 −1.6024 −1.9763 0.2611 1.7135 1.6454 1.0914 0.0622 0.1818 0.9983

UNIFAC −0.5220 −0.1153 −0.5477 −1.5473 −3.2105 0.7132 2.1970 2.7259 1.1247 0.4143 0.9587

The new ab initio COSMO files obtained with newly optimized geometries were used only for the solutes, while the ab initio files used for water and 1-octanol are still taken from VT-2005 database. b“EST” means that the value was estimated from the software KOWWIN, version 1.67 (pseudod exp cal NP cal − log10 Pcal − ∑i =NP1 log10 Pexp experimental data). cAAD = ∑i =NP1 (|log10 Pexp i i |)/NP. R = (∑(log10 Pi i /NP)(log10 Pi − ∑i = 1 log10 Pi /NP))/ exp NP exp cal NP cal 2 2 1/2 ((∑(log10 Pi − ∑i = 1 log10 Pi /NP) ∑(log10 Pi − ∑i = 1 log10 Pi /NP) ) ). a

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is broader than the σ profile of the cis conformation. This result is consistent with the fact that the trans conformation has a larger dipole than the cis conformation. The fact the trans conformation gives rise to better predictions can be explained by the fact that the universal parameters of the COSMO-SAC model were determined by always trying to use the optimal geometries of the molecules in the gas phase.31 We have compared the prediction capabilities of COSMOlike models to those of UNIFAC. The predicted partition coefficients from UNIFAC were listed in Table 2 as well. No result is given for quinone because no suitable subgroups in UNIFAC can be used. Note that the 2003 version of UNIFAC and its corresponding group parameters was employed to carry out the partition coefficient calculation here. One can see that its AAD is comparable to those of mCOSMO-SAC + VT-2005 database but worse than those of COSMO-RS and COSMOSAC, especially when the COSMO files from new geometries are used in COSMO-SAC. The COSMO-based models are more versatile compared to UNIFAC in application because the former type of models is only dependent upon the σ profile, while UNIFAC is strongly related to the group database, which is difficult to extrapolate for a molecule contained in new subgroups, for example, for quinone in the current work. 4.2. VLE and LLE. The VLE of 32 binary mixtures related to biofuels have been predicted using COSMO-RS + BP-TZVP, COSMO-SAC + VT-2005 database, mCOSMO-SAC + VT2005 database, and UNIFAC. The temperature and pressure ranges, the average deviations for the saturated temperatures, pressures, and vapor-phase compositions, the number of data points, and the reference for each system are reported in Table 3. In Table 4, the experimental and theoretical temperature, pressure, and composition for four azeotropic mixtures at the azeotropic point were listed and compared. For the determination of VLE, the Antoine equation has been used to compute the saturated vapor pressure of the pure compounds. The parameters of the Antoine equation are reported in Table 5. In general, both COSMO-SAC models give similar predictions of binary VLE for biofuel-related mixtures, and both give slightly better predictions of the equilibrium temperature for isobaric systems than predictions from COSMO-RS. However, the COSMO-RS model gives slightly better predictions of equilibrium pressures and vaporphase compositions for the investigated isothermal systems. The predictions of UNIFAC are worse than those of COSMObased models. The AADs for the equilibrium temperatures are 9.43, 7.16, 7.18, and 10.7 K. The AADs for the equilibrium pressures are 3.29, 3.95, 4.04, and 4.60 kPa. The AADs for the vapor compositions are 0.0290, 0.0388, 0.0329, and,0.0341 for COSMO-RS, COSMO-SAC, mCOSMO-SAC, and UNIFAC, respectively. Note that the original Soave−Redlich−Kwong (SRK) equation of state was employed to describe the fugacity of the component in vapor phase in UNIFAC calculations, except for systems containing guaiacol because of the lack of experimental values for the critical temperature and pressure. The AADs calculated here did not include those for glycecol + methanol and glycecol + ethanol mixtures at elevated pressures. These results show that the three COSMO models are comparable in terms of accuracy, while UNIFAC is worse for the investigated systems. In addition, the COSMO-RS model generally gives the best predictions for mixtures containing furfural. Meanwhile, the predicted azeotropic properties for the investigated mixtures (except for furfural + 1-octanol) from each model (including UNIFAC) are in good agreement with

overall average deviations are decreased from 0.3671 to 0.1214 and from 0.4207 to 0.1818 for the COSMO-SAC and mCOSMO-SAC models, respectively. One can see in Figure 2a that the predicted log P with COSMO-SAC based on the

Figure 2. (a) Octanol−water partition coefficients at 298.15 K predicted with COSMO-SAC + VT-2005 database and COSMO-SAC + new ab initio COSMO files and compared to experimental data.51−53 The numbers from 1 to 10 on the x axis correspond to the compounds listed from the top to the bottom in Table 2. (b) Comparison of molecular structures of furfural (cis and trans). (c) Comparison of the σ profiles of furfural calculated with different molecular conformations.

new geometries is in better agreement with the experimental results than that based on the VT-2005 database for all investigated systems. Let us consider furfural (number 6 on the x axis in Figure 2a) as a typical example: the predicted log P using the new geometry of furfural is very close to the experimental value, while the predicted value obtained with the VT-2005 database is of opposite sign. The new molecular geometry of furfural and the geometry from the VT-2005 database are compared in Figure 2b. The molecular geometry of furfural in the VT-2005 database corresponds to the cis conformation, which is the most stable conformation in water because it gives rise to a large dipole moment.55,56 The new geometry is a trans conformation, which is the most stable structure in the gas phase. 57 The different molecular conformations for furfural give rise to different σ profiles, as shown in Figure 2c. The σ profile of the trans conformation is lower in the charge density range from −0.08 to 0.02 e Å−2 but 3760


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369.25−434.85 323.15−407.15 368.15−383.15 341.15−362.35 373.85−434.85 298.15−434.85 368.15−388.15 342.55−398.15 298.15−363.15 393.55−421−75 342.65−434.65 374.25−393.45 326.10−560.80 311.00−521.80 493.00−573.00 363.51−453.99 493.00−573.00 381.96−481.69 368.41−468.93 402.53−485.36 314.30−374.00 336.25−473.75 349.95−473.75 368.85−473.75 389.35−473.75 288.15 390.55−454.45 351.45−427.05 333.25−343.18 341.92−371.31 313.60−372.00 433.15−463.15

T (K) 94.6−101.3 38.7−107.3 11.0−76.9 3.33 101.3 0.21−101.3 10.9−51.0 101.3 0.40−61.2 101.3 26.7−101.3 101.3 14.2−101.3 32.0−101.3 3.03−11.01e 101.3 2.27−8.78e 101.3 101.3 101.3 0.05−105.0 95.5 95.5 95.5 95.5 1.17−4.85 101.3 101.3 3.34−105.5 26.7 0.1−97.3 26.3−87.6

p (kPa) 3.82 7.58 2.98 1.69 0.67 2.81 2.59 0.88 0.20 11.1 4.91 23.0 14.1 27.6 25.9 17.2 9.40 22.5 20.7 3.40 3.89 0.64 9.43

ΔT (K) 3.32 2.32 0.39 1.36 2.40 0.88e 0.63e 3.03 0.31 0.58 7.94 11.2 3.29

d

Δp (kPa)

COSMO-RS 0.0193 0.0577 0.0242 0.1025 0.0135 0.0062 0.0157 0.0211 0.0240 0.0055 0.0025 0.0083 0.0771 0.0290

Δy1 3.20 7.36 2.69 7.95 1.27 2.49 2.53 0.59 2.12 9.06 4.13 23.0 12.0 23.7 19.8 4.90 5.20 9.34 8.95 1.64 4.83 0.68 7.16

ΔT (K) 4.50 2.36 0.39 1.58 2.86 0.82e 0.39e 5.99 2.04 0.36 7.51 11.9 3.95

Δp (kPa)

COSMO-SAC 0.0391 0.0680 0.0250 0.1014 0.0687 0.0082 0.0333 0.0181 0.0321 0.0145 0.0096 0.0049 0.0809 0.0388

Δy1 3.44 7.66 2.62 7.55 1.12 2.69 2.34 0.45 1.55 9.16 4.19 23.2 12.2 22.8 20.5 5.75 4.29 9.51 9.19 2.31 4.81 0.67 7.18

ΔT (K) 4.65 2.59 0.35 1.42 3.41 0.82e 0.38e 6.41 1.96 0.28 7.88 11.4 4.04

Δp (kPa)

mCOSMO-SAC 0.0381 0.0712 0.0260 0.1025 0.0642 0.0076 0.0312 0.0196 0.0256 0.0123 0.0067 0.0046 0.0178 0.0329

Δy1 1.53 3.42 2.95 10.1 1.96 2.72 3.26 1.58 0.55 1.53 11.4 29.8 13.8 27.8 20.0 14.6 28.7 24.0 20.6 1.22 4.95 1.14 10.7

ΔT (K) 2.36 1.15 0.33 1.17 4.15 2.53 1.02 8.51 20.2 4.60

Δp (kPa)

UNIFAC 0.0208 0.0229 0.0243 0.1046 0.0596 0.0066 0.0040 0.0203 0.0380 0.0149 0.0030 0.0208 0.1085 0.0341

Δy1 45 36 32 5 15 30 36 12 26 13 185 9 87 45 22 20 22 23 20 23 36 14 14 14 14 7 10 11 41 11 59 36

NPc

and 58 and 58

and 71

and 65

reference 60 66 67 68 69 70 72 73 74 73 75 76 11 11 59 11 59 11 11 11 77 61 61 61 61 78 79 80 81 82 83 84

a cal exp The AADs for the equilibrium temperature and pressure and vapor composition were calculated using Δθ = (1/NP)∑i NP = 1|θ − θ |. The symbol “θ” is the temperature, pressure, or vapor mole fraction at equilibrium. Note that the overall deviations calculated here did not include deviations of glycerol + methanol and glycerol + ethanol mixtures at high pressures. bThe number for system names corresponds to the series number listed in Table 5. cNP = number of experimental data point. dThe symbol “-” means that no experimental data were found in the literature. eThe unit of pressure is MPa.

1+6 1+8 1 + 11 1 + 12 1 + 13 1 + 14 1 + 15 1 + 16 1 + 17 1 + 18 1 + 19 1 + 20 2+6 2+7 2+7 2+8 2+8 2+9 2 + 10 2 + 11 3+6 3+7 3+8 3+9 3 + 11 3 + 14 3 + 19 4+8 4 + 16 4 + 19 5+6 5 + 12 overall deviation

systems

b

Table 3. VLE of Some Biofuel-Related Mixtures Predicted with COSMO-RS, COSMO-SAC, and mCOSMO-SACa

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0.243 0.260 0.253 368.15 388.15 394.61 0.157 0.183 0.241 368.15 388.15 394.60 0.136 0.171 0.245 a

1 + 18

The number for system names corresponds to the series number listed in Table 5.

368.15 388.15 394.20 0.172 0.179 0.226 368.15 388.15 395.56 1 + 12 1 + 15

x1 p (kPa)

94.60 101.3 no 26.31 52.62 101.3 368.99 371.81

T (K) x1

0.048 0.050

94.60 101.3 no 24.72 49.2 101.3

p (kPa) T (K)

370.90 372.73 0.054 0.062

x1 p (kPa)

experiments as well, as shown in Table 4. Next, the attention is only paid to the comparisons and discussion among COSMObased models to show the predictive capabilities of this type of model. A comparison of the AADs for the equilibrium temperatures or pressures for mixtures containing glycerol is given in Figure 3. In general, the average deviations for temperatures and pressures obtained with COSMO-SAC are similar to those obtained with mCOSMO-SAC, while the COSMO-RS model gives rise to slightly higher deviations for both isothermal and isobaric mixtures containing glycerol. The isobaric VLE for glycerol + water mixtures at 14.19 and 95.3 kPa is depicted in Figure 4. In this figure, the predictions of the COSMO-SAC and COSMO-RS models have been compared to experimental data.58 Here, the predictions of mCOSMO-SAC are not provided because they are very similar to those of COSMOSAC. One can see that both COSMO-SAC and COSMO-RS give similar predictions over the full composition range. It can also be seen that both models are more accurate in the waterrich region. Another comparison for the VLE of glycerol + ethanol mixtures at elevated pressures is given in Figure 5, in which the x axis represents the series number of experimental data points59 at different temperatures and compositions and the liquid composition of glycerol in the mixture is in the range from 0.111 to 0.684 in mole fractions. The predictions of the equilibrium pressures are in good agreement with the experimental data at low temperatures, while the deviations between experimental data and theoretical predictions increase as the temperature and pressure are increased. This result may be due to the fact that COSMO-like models do not take pressure effects into account, while the non-ideal behavior of both liquid and vapor phases really becomes strong with the increasing pressure. Another reason is that the activity approach for VLE calculation becomes less accurate at high temperatures because the correlation for the saturated vapor pressures of ethanol is only valid for temperatures up to 514 K (ethanol critical point). Hence, the predictions in the ethanol-rich region deteriorate for the temperature above the critical point of ethanol. However, for most investigated systems, the three COSMO-like models can provide good predictions of VLE even at elevated pressures, as long as the temperature is below the critical points of the pure compounds. For temperatures above critical points, it would be necessary to use an equation of state combined with the activity coefficient models (γ−φ method) or directly use an equation of state for both vapor and liquid phases (φ−φ method) with mixing rules, such as Wong− Sandler or MHV2. The predictions of the temperature−composition phase diagram of the furfural + water mixture at 101.3 kPa are depicted in Figure 6 and are compared to experimental data.60 The predicted VLE curves using COSMO-SAC + VT-2005 database and mCOSMO-SAC + VT-2005 database are depicted in Figure 6a, and those obtained from COSMO-RS combined with the BP-TZVP and BP-SVP databases are shown in Figure 6b. The experimental60 and predicted LLE curves are also provided in Figure 6b. In general, the three COSMO approaches give satisfactory VLE predictions over the full composition range, but the COSMO-RS model, especially COSMO-RS + the BP-SVP database, gives much better predictions in the water-rich region (see the enlarged diagrams in panels a and b of Figure 6). This result is consistent with the predictions of log P for furfural, which were not accurate for

94.60 101.3 no 24.58 48.94 101.3 370.60 372.49

T (K) x1

0.082 0.088

94.60 101.3 no 26.98 53.67 101.3

p (kPa) T (K)

368.96 370.82

0.083 0.092 0.828 0.249 0.248 0.225

x1 p (kPa) T (K)

94.60 101.3 3.330 25.46 50.70 101.3

UNIFAC mCOSMO-SAC COSMO-SAC COSMO-RS experimental

Article

369.25 371.05 341.15 368.15 388.15 393.45 1+6

systems

a

Table 4. Temperature, Pressure, and Composition at the Azeotropic Point for Some Systems Predicted from Different Models

0.086 0.091

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Table 5. Antoine Constants for the Equation: ln(P (kPa)) = A − B/(T (K) + C) number

compound

A

B

C

reference

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

furfural glycerol m-cresol anisole guaiacol water methanol ethanol 1-propanol 2-propanol 1-butanol 1-octanol formic acid ethyl acetate 1,1′-oxybisbutane n-hexane n-heptane n-octane toluene methylcyclohexane methyl isobutyl ketone

14.0309 15.2218 15.2496 14.2237 17.4092 16.2884 16.5723 15.9461 15.5287 16.6755 15.1985 13.5917 9.2131 14.3407 13.6547 13.8216 13.8807 13.9276 13.9987 13.6955 13.7072

3293.00 4487.04 4274.32 3430.29 5720.99 3816.44 3626.55 3298.51 3166.38 3640.20 3137.01 2934.09 1185.83 2868.33 2999.73 2697.55 2921.14 3120.29 3096.52 2926.04 2887.66

−84.45 −140.2 −74.09 −69.61 −31.04 −46.13 −34.29 −61.82 −80.15 −53.54 −94.43 −141.3 −139.4 −55.19 −81.48 −48.78 −56.20 −63.63 −53.67 −51.73 −71.54

85 86 86 87 88 86 86 89 86 86 86 88 88 88 90 91 91 91 92 92 93

Figure 3. Comparison of the AADs for equilibrium temperatures and pressures (VLE data) obtained with the different COSMO-like models for glycerol-related mixtures.

Figure 5. VLE (saturated pressures) of the glycerol + ethanol mixture at different temperatures. Comparisons between theoretical predictions and experimental data.59 The liquid composition of glycerol in the mixture is over the range from 0.111 to 0.684 in mole fractions.

approach can provide reasonable results, while no liquid−liquid demixing is predicted with COSMO-SAC + VT-2005 database and mCOSMO-SAC + VT-2005 database. This was earlier observed by Athès et al.43 In Figure 6b, one can see that the different databases that used BP-TZVP and BP-SVP with the COSMO-RS package can give rather different predictions. For example, the COSMO-RS model combined with the BP-SVP database gives predictions that are very close to experimental data, while COSMO-RS + BP-TZVP database provides unsatisfactory results, which indicates that careful selections of molecular structures and COSMO quantum calculation methods should be made when using COSMO-type models to predict macrothermodynamic properties. Note that the BP-SVP and BP-TZVP databases are based on the same ab initio DFT method (i.e., the same level of accuracy). The difference between both databases is based on the method used to define the molecular surface: the definition of the molecular surface is based on the electronic density for the BP-SVP database (i.e.,

Figure 4. VLE of the glycerol (1) + water (2) mixture predicted with () COSMO-SAC + VT-2005 database and (- - -) COSMO-RS compared to (□ and △) experimental data.58 (□, 14.19; △, 95.3 kPa).

COSMO-SAC + VT-2005 database: in particular, the prediction of the infinite dilution activity coefficient of furfural in pure water is inaccurate. For LLE, only the COSMO-RS 3763


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Figure 7. VLE and LLE of the furfural (1) + water (2) mixture at pressure P = 101.3 kPa predicted with (- - -) COSMO-SAC + VT-2005 database and () COSMO-SAC + new geometry of furfural compared to (□ and ○) experimental data.60 (□, VLE data; ○, LLE data).

Figure 6. VLE and LLE of the furfural (1) + water (2) mixture at pressure P = 101.3 kPa predicted with ( and - · -) COSMO-based models compared to (□ and ○) experimental data:60 (a) curves predicted with () COSMO-SAC and (- · -) mCOSMO-SAC predictions and (b) curves predicted with COSMO-RS + () BPTZVP and (- · -) BP-SVP databases. (□, VLE data; ○, LLE data).

mentioned earlier, no liquid−liquid demixing were predicted with the ab initio data of furfural from the VT-2005 database. This result can be explained by the fact that the trans conformation of furfural is less polar; therefore, this conformation is less compatible with water, and the occurrence of LLE is more likely. The different predictions obtained with both geometries can also be explained by the differences in the corresponding σ profiles: the water−furfural polar interactions are less strong for the trans conformation, because the σ profile of the trans conformation is less broad than the σ profile of the cis conformation (see panels b and c of Figure 2). Hydrogen bonding between the surface segments of water and furfural is weaker for the trans conformation of furfural, which explains the prediction of liquid−liquid demixing. The predictions of the VLE for the mixtures m-cresol + methanol and m-cresol +1-butanol are depicted in Figure 8. The predicted curves using COSMO-SAC + VT-2005 database are in good agreement with the experimental data61 for the mcresol + methanol mixture, especially in the methanol-rich region, while unsatisfactory predictions for the m-cresol + 1butanol mixture are observed. In addition, both COSMO-SAC and COSMO-RS provide similar predictions of vapor-phase compositions. In general, for mixtures containing m-cresol, the COSMO-SAC model give more accurate VLE predictions among the three COSMO-based models. We recall that the log P partition coefficients were computed using the experimental 1-octanol and water mole fractions in the organic and water liquid phases. However, one should also check the capacity of the models to predict the LLE of the 1-

the molecular surface is defined when the electronic density reaches a given value), while it is based on atomic-centered spheres for the BP-TZVP database. The BP-TZVP database generally gives more accurate predictions than the BP-SVP database for the investigated mixtures, probably because the universal parameters of COSMO-RS were determined using atomic-centered spheres for the definition of the molecular surface. However, for some specific molecules, such as furfural, the BP-SVP database is more accurate. It should be noted that the COSMO-RS package allows for the simultaneous use of ab initio data from various databases. Hence, for the predictions of phase equilibria of multicomponent systems, we recommend the use of the ab initio data to provide the best predictions for the binary systems. To check further the effect of the molecular geometry of furfural, the VLE and LLE of the furfural (1) + water (2) mixture have also been predicted with the COSMO-SAC model combined with the new ab initio data for furfural. Note that the ab initio data from the VT-2005 database were kept for water. The predictions and the experimental data are compared in Figure 7. Figure 7b is an enlargement of Figure 7a around the water-rich region. One can see that the COSMO-SAC model combined with the new ab initio data of furfural leads to better predictions of the VLE and the azeotropic point. Moreover, the COSMO-SAC model used with the new furfural geometry also predicts a liquid−liquid demixing, while as 3764


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Figure 10. σ profiles of (a) 1-octanol and (b) water determined with the () COSMO-SAC + VT-2005 database, (- · -) mCOSMO-SAC + VT-2005 database, and (- - -) COSMO-RS + BP-TZVP approaches.

Figure 8. VLE of binary mixtures of m-cresol at pressure P = 95.5 kPa predicted with () COSMO-SAC and (- - -) COSMO-RS compared to (□ and ○) experimental data.61 The experimental compositions of the vapor phase are pseudo-experimental data generated with Wilson’s activity coefficient model [□, m-cresol (1) + methanol (2); ○, mcresol (1) + 1-butanol (2)].

between COSMO-RS and COSMO-SAC, especially for water. The prediction of LLE is very sensitive to the type of ab initio data used, and large deviations are observed when different COSMO-files and/or σ profiles from different sources are used. However, it is difficult to draw general conclusions for all of the investigated systems, because sometimes a given database gives much better predictions for a given system, while it is less accurate for the other mixtures. Therefore, we recommend to use different databases and select the ab initio data and/or σ profiles that give rise to the best predictions for the binary systems.

octanol + water system, because in practice, we are interested in predicting LLE for multicomponent systems involving bio-oils. A comparison between the predicted LLE curves and experimental LLE data62−64 at low and elevated pressures is depicted in Figure 9. Because the expressions of the COSMO-

5. CONCLUSION The prediction capabilities of the COSMO-RS, COSMO-SAC, and mCOSMO-SAC models for log P, VLE, and LLE and UNIFAC for log P and VLE of biofuel-related solutes and mixtures have been checked. The theoretical predictions of log P, VLE, and LLE are in reasonable quantitative agreement with the experiments, and the three COSMO-based models give slightly better predictions than those from UNIFAC. For VLE predictions, COSMO-SAC + VT-2005 database generally gives more accurate predictions of boiling temperatures (VLE), while COSMO-RS + BP-TZVP is more accurate for saturated pressures, vapor-phase compositions, and for the LLE of some mixtures, such as 1-octanol + water and systems containing furfural. The VLE of glycerol mixtures at elevated pressures have also been examined with the COSMO predictive approaches, and a good agreement between experimental data and theoretical prediction is obtained. In addition, the predictive accuracy of log P and phase behavior with COSMO-SAC can be improved for some investigated mixtures using new ab initio calculations. Generally, the three COSMObased models can be used for the prediction of basic thermodynamic properties of biofuel-related mixtures, especially when no experimental data are available in the literature, as long as proper ab initio calculations were performed to generate the σ profiles.

Figure 9. LLE of the 1-octanol (1) + water (2) binary mixture predicted with () COSMO-SAC, (- · -) mCOSMO-SAC, and (- - -) COSMO-RS compared to (□ and △) experimental data.62−64 (□, 0.1 MPa; △, 6.8 MPa).

like models are pressure-independent, they cannot predict the effect of pressure on LLE. However, this effect is expected to be small, and the experimental data at elevated and low pressures can be put together. It can be seen from Figure 9 that the COSMO-RS predictions of LLE for the 1-octanol (1) + water (2) mixture over full composition range are in good agreement with the experiment data at low and elevated pressures and are better than those obtained from COSMO-SAC and mCOSMO-SAC. In addition, the predictions of the COSMO-SAC and mCOSMO-SAC models are rather different, although no large changes in the expressions were made between these two models. In Figure 10, we compare the σ profiles of (a) 1octanol and (b) water used in the different COSMO approaches. It can be seen that there are slight differences of surface charge density profiles existing between COSMO-SAC and mCOSMO-SAC, but large differences are observed

■

ASSOCIATED CONTENT

S Supporting Information *

New geometries and detailed σ profiles for the biofuel-related compounds and comparisons of geometry between the VT2005 database and our calculations for these substances. This 3765


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Article

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material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors appreciate the financial support of the French Research National Agency (ANR-09-CP2D-10-03), and Jinlong Li also thanks the Major State Basic Research Development Program of China (2012CB720500) and the National Natural Science Foundation of China (Key Program U1162202) for financial support.

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