A Group Contribution Equation of State for Biorefineries. GCA-EOS

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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A Group Contribution Equation of State for Biorefineries. GCA-EOS Extension to Bioether Fuels and Their Mixtures with n‑Alkanes Mariana Gonzaĺ ez Prieto,† Francisco A. Sań chez,† and Selva Pereda*,†,‡ †

J. Chem. Eng. Data Downloaded from pubs.acs.org by UNIV AUTONOMA DE COAHUILA on 04/10/19. For personal use only.

Planta Piloto de Ingeniería Química (PLAPIQUI) − Departamento de Ingeniería Química, Universidad Nacional del Sur (UNS)−CONICET, Camino La Carrindanga Km7, 8000B Bahía Blanca, Argentina ‡ Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa ABSTRACT: Biomass processing routes involve mixtures of organo-oxygenated compounds of almost all the organic families. Typically, these mixtures are highly nonideal, and models to describe their phase behavior should take into account specific association interactions. In this work, the group contribution with association equation of state (GCA-EOS) is applied to the thermodynamic modeling of mixtures comprising ethers and alkanes. A databank of about 2800 experimental data points of phase equilibria and excess enthalpies is used to parametrize the GCA-EOS and challenge its predictive capacity. Based on the correlation of selected equilibrium data of linear monoethers and n-alkanes, the model is able to predict accurately the phase behavior of linear and branched monoethers not included in the parametrization, as well as that of the polyethers. This work is part of a broader project for the development of a robust and predictive thermodynamic model for process and product design in the context of biomass valorization.

1. INTRODUCTION Biomass processing and the valorization of the waste that this activity entails are fields of growing interest; they are gaining special attention as consumers are concerned about the environmental impact of using nonrenewable resources, as well as that of the residues of renewable resources processing. An indication of this is the large investments that traditional chemical companies are making in the development of new sustainable synthesis routes. For example, the Swiss company AVA Biochem is producing 5-hydroxymethylfurfural (5-HMF) from sugar cane. This biobased platform chemical is a precursor of many compounds that could replace petroleumbased chemicals, fuels, and pharmaceuticals.1 Another example is Butamax, the joint venture of British Petroleum and DuPont, which produces bioisobutanol in a bioethanol facility located in Kansas (USA).2 Isobutanol can be used as a gasoline additive, showing better blending properties than ethanol,3,4 or in the chemical industry as a building-block for a wide range of products.5 Also, the Brazilian company Braskem produces “green” ethylene by dehydration of sugar cane ethanol, which is further used to produce either polyethylene or the biofuel ethyl-tert-butyl ether.6 These are only a few examples, among many other ventures under development, that illustrate the growing importance of this field in the industrial sector. The potential of biomass as an alternative source of chemicals, fuels, and materials calls for new technologies capable of efficiently processing complex and inhomogeneous raw materials. Regardless of its origin, biomass is composed mainly by four types of materials, that is, lignocellulose, © XXXX American Chemical Society

proteins, lipids, and carbohydrates (saccharose and starch). Except for proteins, which have currently high added value, the other fractions are being used or investigated, in one way or another, as raw material for the production of fuel, chemicals, and materials. In particular, lignocellulosic biomass is available in large quantities but its conversion is more costly than that of the lipids or sugars.7 Lignocelullosic biomass must be first depolymerized and partially deoxygenated by either a hydrolysis or a thermochemical route. Thereafter, bio-oils comprising hundreds of oxygenated polyfunctional compounds constitutes a chemical platform to obtain a wide variety of valuable industrial products.8,9 In general, these compounds share the same characteristic functional groups, such as hydroxyl, ketone, or carboxylic acid, while aliphatic chains and/or aromatic rings are the typical backbones, as organic chemistry dictates. This fact makes the group contribution approach an attractive alternative for modeling biobased chemicals, in order to predict the properties of pure compounds and mixtures that have not yet been studied experimentally. Furthermore, compared to molecular models, the group contribution approach requires fewer binary interaction parameters to describe highly multicomponent mixtures. Special Issue: Latin America Received: December 2, 2018 Accepted: March 13, 2019

A

DOI: 10.1021/acs.jced.8b01153 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Ethers are not only regarded as biofuels individually, but as coblending agents as well. For instance, the blend DBE + butanol + diesel has shown favorable combustion properties and improves the fuel conversion.36,37 Remarkably, Smith et al.38 studied the distillation curves of mixtures of diesel with glycol ethers such as ethylene glycol dimethyl ether (EGDME) or diethylene glycol dimethyl ether (DEGDME) and also their mixture, known as cetaner, and considered them very promising as oxygenated agents for fuels.39 Finally, it is important noting that ethers are also involved as byproducts, intermediates, and/or products in several biomass conversion routes. For instance, di-n-octyl ether is a byproduct in the synthesis of octanol from furfural and acetone.40 The latter, as well as all the possible ether-based biofuels, indicates the importance of developing a predictive thermodynamic model for process and product design and optimization.

Branched ethers have been used as gasoline additives for a long time. Nowadays, for most of them there are synthesis routes starting from renewable raw materials. Moreover, in the last years, an intensive research on new ether-based biofuels is ongoing and, hand in hand with this, several thermodynamic models are proposed in the literature to describe their phase behavior, both as a pure compound and in mixtures. For instance, Dominik et al.10 model systems comprising linear monoethers and polyethers with the polar PC-SAFT. They achieve a good description of ether vapor pressures, as well as, of their phase behavior and excess enthalpies in binary mixtures with alkanes. On the other hand, Peng et al.,11 Burger et al.,12 and Nguyen-Huynh et al.13 apply the group contribution approach using the GC-SAFT-VR, SAFT-γ Mie, and GC-PPC-SAFT, respectively. The first two only model pure ether vapor pressures and density data, while NguyenHuynh et al. also model the phase equilibria of linear monoethers + n-alkanes mixtures. The development of efficient biorefineries requires integrating the design of new processes with innovative products that facilitate their market penetration. In this context, predictive thermodynamic models are required for conceptual design and optimization of process and products. The group contribution with association equation of state (GCA-EOS) has been successfully applied to renewable products14−17 and mixtures involving first generation and advanced biofuels.18−20 In this work, we extend the GCA-EOS to mixtures comprising etherbased biofuels and alkanes, with the interest to assess the phase behavior of fuel/biofuel blends in future works.

3. THERMODYNAMIC MODEL The GCA-EOS41 is an extension of the GC-EOS42 to association mixtures. The original GC-EOS is based on the generalized van der Waals partition function, combined with the local composition principle and a group contribution approach. The GCA-EOS comprises three contributions to the Helmholtz energy (see eq 1): free-volume, attractive, and association. AR = Afv + Aatt + Aassoc

(1)

The free-volume or repulsive contribution is represented by the Carnahan−Starling equation for hard spheres,43 extended for mixtures by Mansoori and Leland.44 This term is characterized by the critical hard-sphere diameter (dc) of pure compounds. On the other hand, the attractive contribution is a van der Waals term combined with a density-dependent local-composition mixing rule, based on a group contribution version of the nonrandom two liquid (NRTL) model.45 This term is characterized by the number of surface segments of each group (qi), defined as in the UNIFAC method,46 and the surface energy (gii), which is temperature dependent. Furthermore, each binary group interaction is characterized by one interaction parameter (kij), and two asymmetric binary nonrandomness parameters (αij ≠ αji). Finally, the association term is a group contribution version of the SAFT equation developed by Chapman et al.47 Details of the model equations are given in the Appendix. 3.1. Model Parametrization. The group contribution approach is based on the Langmuir principle,48 which states that the groups should be as neutral as possible, so that their characterization performs well independently of the molecule where they are assembled. In UNIFAC and the original GCEOS, the ether group is defined as CHxO. However, from ab initio calculations, Wu and Sandler49 showed that the CHx groups attached to the oxygen atom hold a different charge than a CHx group within an alkane molecule. Therefore, in this work, we define the ether group as the oxygen atom capped by the neighbor alkyls, that is, CHxOCHy. Regardless of the degree of substitution, a single surface energy parameter (gii) is correlated to describe the generic ether group, while each subgroup holds its characteristic surface area calculated with Bondi,50 like in UNIFAC. Regarding their binary interaction parameters, we distinguished between terminal and central ether groups. It is worth noting that the same group parameters are used to describe linear and branched ethers.

2. BIOETHER FUELS Over the past few years, several ether-based compounds have been proposed as biofuels for blending with gasolines,21−23 as well as with diesel fuels.24−28 While the former usually are branched low molecular weight monoethers (such as the conventional petroleum-based additives), those for diesel also include higher molecular weight polyethers.29 In addition, recently developed synthesis routes allow the production of bioethers from lignocellulosic or residual biomass,25,26,30 which is the first condition that an advanced biofuel has to fulfill, in contrast with first generation biofuels. Moreover, advanced biofuels should reduce the carbon dioxide emissions of the transport sector and increase engine combustion efficiency. On the other hand, petroleum-based ethers have been traditionally used as a blending agent of gasolines. In particular, ethers such as methyl tert-butyl (MTBE), ethyl tert-butyl (ETBE), tert-amyl methyl (TAME), diisopropyl (DIPE), and di-n-propyl ether (DPE)31,32 are of special interest because they improve the fuel octane rating and reduce exhaust pollution. However, MTBE is banned in some countries due to the jeopardy of groundwater contamination. In contrast, ETBE constitutes a greener alternative since it is more biodegradable and less soluble in water than MTBE,33 and nowadays there are catalytic routes to produce ETBE from renewable sources (isobutene and bioethanol).34 On the other hand, di-n-butyl ether (DBE) has recently been suggested as a promising fuel for compression ignition engines, and can be synthesized by dehydration of biobutanol.35 The lowest molecular weight ether, dimethyl ether (DME), has also been proposed as an attractive additive for diesel engines due to its high cetane number;26 however, the engine injection systems require modifications in order to use DME as a blending agent. B



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Table 1. GCA-EOS Pure Group Surface Energy Parameters for the Attractive Contribution group i

qi

CH3OCH3/CH3OCH2/CH2OCH2/ COCH3/COCH2

1.936/1.628/1.320/ 1.088/0.780

gi*/atm cm6 mol−2 418350

gi′ −0.7236

gi′

correlated data

−0.1369

dimethyl ether and 1,2-dimethoxyethane vapor pressure55

Table 2. GCA-EOS Binary Interaction Parameters between Ether and Alkane Groups for the Attractive Contribution (αij = αji = 0)a i

j

kij*

kij′

CH3OCH3/CH3OCH2/COCH3

CH3/CH3(B)/CHCH3 CH2/CH2(B) CH3/CH3(B)/CHCH3 CH2/CH2(B)

0.9765 0.9883 0.9353 0.9104

0.020 0.020 0.005 −0.016

CH2OCH2/CHOCH/COCH2

data correlated VLE n-decane + 1,2-dimethoxyethane at 0.95 bar56 VP DPE55 and DBE.55 VLE n-hexane + DBE at 308 K57

a

VP, vapor pressure; VLE, vapor−liquid equilibria; DPE, di-n-propyl ether; DBE, di-n-butyl ether.

ethane + n-decane. Afterward, we test the model predictive capacity against the phase equilibrium data not included in the correlation procedure. In addition, we also apply the parameters of the terminal ether group to predict the phase behavior of DME. Last, the parametrization of the free-volume contribution requires setting the critical hard sphere diameter (dc), which is characteristic of the pure-compound molecular size and has no binary or higher-order parameters. There are three different ways to calculate dc of each component: (i) direct calculation so that the model fulfills the critical point and its stability conditions (first and second derivatives of pressure with regard to volume equal to zero);42 (ii) fix the dc to match one experimental pure-component vapor pressure data point (Tsat, Psat);42 and (iii) computation with the predictive equation proposed by Espinosa et al.54 for nonvolatile compounds, based on van der Waals volume of compounds. In this work, during the parametrization, the critical diameters of ethers are set to the value that fulfills the critical constraints (method (i)). Since the ethers do not self-associate, we calculate dc as follow:42

The correlation of GCA-EOS parameters is carried out with selected experimental data sets by minimizing the following objective function: O.F. =

2 wsat

Nsat

∑

Neq 2 esat, i

+

∑ eeq,2i

i=1

i=1

(2)

where Nsat and Neq are the number of saturation pressure and equilibrium points respectively and esat, i and eeq, i are the error between experimental and calculated data as follows: sat sat y ij Pexp, i − Pcalc, i z 2 jj zz = esat, zz i sat jjj z Pexp, i k {

2 eeq, i

2

(3)

2 l 2 o o ij Pexp, i − Pcalc, i yz jij yexp,1i − ycalc,1i zyz o o 2 j z zz o zz + wy jjj o (1 − IFL)jjj zz o zz jj o j Pexp, i yexp,1i z o o k { o k { o =m o 2 o 2 o iy o − ycalc,1i zyz ij Texp, i − Tcalc, i yz o o jj zz + w 2jjjj exp,1i zz o IFL o j z j zz y o j z jj o z Texp, i yexp,1i z o jk o { k { n

dc =

(4)

where P is the pressure, T the temperature, and y the molar fraction in the vapor phase. IFLi is an auxiliary variable, which sets the type of flash calculations: 1 for Px flash, and 0 for Tx flash. The weighting factors, wsat and wy , are chosen according to the typical precision of the experimental information. In this work, we set wsat and wy to values of 2 and 0.2, respectively, as recommended by Skjold-Jørgensen.51 In this work, we simulate all binary vapor−liquid equilibria (VLE) systems through bubble point calculation, while we perform a TP flash52,53 in the case of liquid−liquid equilibria (LLE). The objective function is minimized drawing upon the Levenberg− Marquardt algorithm of finite differences coded in Fortran77. First, we correlate the surface energy parameter (gii) of the new ether group to vapor pressure data of DME and 1,2dimethoxyethane. We select these two compounds because they comprise solely ether groups, therefore, no binary interaction parameters are needed. Second, we fit the binary interaction parameters (kij) with alkyl groups to selected data of ether vapor pressures and binary phase behavior. In this case, we correlate the central (CH2OCH2) ether group to the vapor pressure of DPE and DBE and the binary system DBE + n-hexane, while the terminal ether (CH3OCH2) correlates only to the phase behavior of the binary system 1,2-dimethoxy-

3

0.08942656

RTc Pc

(5)

Subsequently, after the attractive parameters are determined, we apply method (ii) for all ethers, except for DME because it is described by a single group. This procedure ensures that the critical diameter that provides high accuracy in pure compound vapor pressure does not differ substantially from the one that fulfills the critical point conditions. By this manner, the fitting weight is balanced between the experimental critical point and the vapor pressure data.

4. RESULTS AND DISCUSSION Binary mixtures of linear monoethers with alkanes show a near ideal behavior. Nonetheless, the increase of their molecular weight and oxygen content leads to nonideal behavior, for instance liquid split at low temperatures. This is an interesting challenge for a group contribution model. In this work, we model the ethers using a single group, regardless of the size of the molecule. Table 1 depicts the new group energy parameter and its temperature dependence, together with the data used for correlation, that is, vapor pressure of DME and 1,2dimethoxyethane. On the other hand, higher molecular weight ethers, also need binary interaction parameters with the alkyl groups, whose characteristic parameters can be found elseC



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Table 3. GCA-EOS Pure Compound Critical Temperature and Diameter for the Repulsive Contribution. Correlation of Linear Monoethers Vapor Pressure and Critical Points: Model Deviations with Respect to Experimental Data in the Reduced Temperature Range ΔTra compound dimethyl ether (DME) 1,2-dimethoxyethane di-n-propyl ether (DPE) di-n-butyl ether (DBE)

Tc (K)

dc (cm mol−1/3) b

400.10 536.15 530.60 584.10

3.8117 4.6318c 5.0999c 5.6452c

ARD Tc (%)

ARD Pc (%)

ΔTr

AARD P (%)

N

source

0.10 0.10 0.04 0.37

0.11 3.5 1.7 2.3

0.50−0.95 0.56−0.95 0.52−0.73 0.50−0.95

0.98 1.6 1.1 2.3

94 44 68 86

55,58−61 55,62 55,63−65 55,65−67

a ARD, absolute relative deviations in critical pressure and temperature with respect to experimental data;55 AARD, average absolute relative deviation in vapor pressure data; N, number of experimental data points. bCalculated using method (i). cCalculated using method (ii).

Table 4. GCA-EOS Vapor−Liquid Equilibria Correlation of Linear Monoether (1) + n-Alkane (2) Binary Mixtures binary system

T (K)

P (bar)

AARDa T or P (%)

AARD y1 (%)

Nb

source

di-n-butyl ether + n-hexane 1,2-dimethoxyethane + n-decane

308 357−445

0.04−0.91 0.95

1.7 (P) 0.24 (T)

2.8 0.33

14 7

57 56

a

AARD, average absolute relative deviations in P pressure and T temperature. bN, number of experimental data points.

Table 5. GCA-EOS Pure Compound Critical Temperature and Diameter for the Repulsive Contribution. Prediction of Linear-, Branched- and Polyethers Vapor Pressure and Critical Points: Model Deviations with Respect to Experimental Data in the Reduced Temperature Range ΔTra compound

Tc (K)

dc (cm mol−1/3)

ARD Tc (%)

diethyl ether (DEE) di-n-pentyl ether methyl n-ethyl ether (MEE) methyl n-propyl ether (MPE) ethyl n-propyl ether (EPE) methyl n-butyl ether (MBE) ethyl n-butyl ether (EBE)

466.70 622.00 437.80 476.25 500.23 512.74 531.00

isopropyl methyl ether (IPME) methyl tert-butyl ether (MTBE) diispropyl ether (DIPE) ethyl tert-butyl ether (ETBE) diisobutyl ether (DIBE) tert-amyl methyl ether (TAME)

464.48 497.10 500.05 514.00 526.00 534.00

diethylene glycol dimethyl ether (DEGDME) triethylene glycol dimethyl ether (TEGDME) tetraehylene glycol dimethyl ether (TeEGDME) 1,2-diethoxyethane diethylene glycol diethyl ether (DEGDEE)

617.00 651.00 705.00 542.00 612.00

Linear Monoethers 4.4421 1.3 6.1183 0.63 4.1372 1.2 4.5116 0.54 4.7807 0.81 4.8358 0.055 5.0837 0.56 Branched Monoether 4.4918 0.65 4.6439 2.5 5.1682 0.016 4.9771 1.3 5.6635 0.51 4.9741 0.62 Linear Polyether 5.3427 0.048* 5.9764 6.5417 5.1807 5.0* 5.8130 4.2*

diethylene glicol diebutyl ether (DEGDBE)

680.00

6.7842

ARD Pc (%)

ΔTr

AARD P(%)

N

source

10 2.9 5.9 2.1 1.9 0.089 1.1

0.54−0.95 0.55−0.74 0.62−0.94 0.49−0.70 0.52−0.72 0.51−0.72 0.56−0.95

1.3 1.1 3.0 1.2 1.6 1.6 2.8

33 8 18 50 52 52 12

55,68 55 55 55,64 55,64 55,64,66,69,70 55,71−73

2.0 11 6.5 3.6 9.6 7.0

0.54−0.70 0.53−0.86 0.50−0.94 0.54−0.90 0.59−0.70 0.55−0.79

2.3 2.8 5.3 7.9 1.3 1.5

22 114 88 253 15 112

0.53−0.93 0.58−0.75 0.59−0.78 0.54−0.70 0.53−0.74 0.58−0.73 0.55−0.61 0.59−0.69 0.58−0.64

7.0 11 2.7 3.3 4.2 7.2 1.7 4.5 21

15 3 14 22 9 13 3 10 4

55,64 55,74−77 55,76,78−81 55,82−84 85 55,75,86,87 55 55,88 55,89 55,90 91 92 55 92 55

a

dc, critical diameter, adjusted to match a saturation point; ARD, absolute relative deviation of critical properties with respect to data from ref 55 (except for values mark with an asterisk (∗), data from ref 93); AARD, average absolute relative deviations; N, number of experimental data.

where.18,42 Table 2 lists the binary interaction parameters between the new ether group and the alkyl groups, together with the data sets that are used to fit them. As mentioned before, we distinguish between terminal and central ether groups, independently of the degree of substitution that is needed to assemble the compound. It is worth noting that modeling ether + alkane phase equilibrium does not require fitting the nonrandomness parameters, that is, αij and αji are set

On the other hand, to model phase equilibria of branched ethers and/or alkanes, the interaction between the ether group and those groups bounded to a ternary (CHCH3) and quaternary carbons (CH3(B) y CH2(B)) are required. As it is discussed later, the GCA-EOS depicts good accuracy using the same binary interactions fitted for CH3 and CH2 (see Table 2). Finally, Tables 3 and 4 show GCA-EOS deviations in the correlation of pure compound vapor pressure and binary VLE data, respectively. Table 3 also lists the critical diameter of each component and GCA-EOS accuracy to correlate their critical point.

equal to zero. D



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Figure 1. Vapor pressure of ethers. (a) Linear monoethers: (□) dimethyl ether (DME), (○) diethyl ether (DEE), (▲) ethyl propyl ether (EPE), (△) di-n-propyl ether (DPE), (◆ di-n-butyl ether (DBE), and (◇) di-n-pentyl ether. Symbols: experimental data.55,58−61,63−68,93 (b) Branched monoethers: (▲) isopropyl methyl ether (IPME), (△) methyl tert-butyl ether (MTBE), (◆) tert-amyl methyl ether (TAME), and (◇) diisobutyl ether (DIBE). Symbols: experimental data.55,64,74−77,85−87 (c) Vapor pressure of polyethers: (□) 1,2-dimethoxyethane, (○) 1,2-diethoxyethane, (▲) diethylene glycol dimethyl ether (DEGDME), (△) diethylene glycol diethyl ether (DEGDEE), (◆) triethylene glycol dimethyl ether (TEGDEM) and (◇) tetraethylene glycol dimethyl ether (TeEGDME). Symbols: experimental data.55,62,88−92 Dashed and solid lines: GCA-EOS correlations and predictions, respectively.

Table 6. GCA-EOS Prediction of VLE of Binary Mixtures Containing Linear Monoethers (1) with n-Alkanes (2) binary systems

T (K)

propane n-butane n-decane n-dodecane i-butane

273−323 283−387 323 323 280−320

i-butane n-pentane n-hexane

323 307−309 307−341

n-heptane n-octane n-nonane

343 363 363

n-hexane n-heptane n-octane n-nonane

298 313 363.15 298 373−423

n-undecane

404

n-heptane

323, 343

P (bar)

AARDa T or P (%)

Dimethyl Ether (DME) 0.78 (P) 1.5 (P) 1.6 (P) 1.3 (P) 1.0 (P) Diethyl Ether (DEE) 1.7−2.2 0.35 (P) 1 0.080 (T) 1 0.070 (T) Di-n-propyl Ether (DPE) 0.4−0.53 1.6 (P) 0.4−1.0 3.7 (P) 0.2−1.0 10 (P) Di-n-butyl Ether (DBE) 0.02−0.19 4.0 (P) 0.12−0.02 5.5 (P) 0.26−0.76 5.1 0.009−0.02 2.2 (P) 0.26−1 0.17 (T) Di-n-pentyl Ether 0.14−0.19 3.5 (P) Methyl n-butyl Ether (MBE) 0.18−1.0 0.70 (P) 2.6−17 1.5−42 0.012−11 0.002−11 2.0−10

a

AARD y1(%)

Nb

source

1.5 2.2

1.5

71 112 39 36 64

96,97 60 98 98 99

3.0 1.7

17 14 16

100 101 101

7.9 3.6

11 11 11

102 94 94

11 24 9 10 36

103 95 94 103 104

10

88

25

88

3.5 8.2 2.8

1.4 0.90 b

VLE: vapor liquid equilibria, AARD:average absolute relative deviations in (P) presure and (T) temperature. N: number of experimental data points.

except for the critical pressure of dietheyl ether (DEE) and diisobutyl ether (DIBE), in which it deviates about 10%. Regarding vapor pressure data, deviation in monoethers, both linear and branched, are in average around 4.1%. In the case of polyethers, the deviations are only slightly higher (5.5% in average), which is naturally due to their lower vapor pressure and its consequent higher experimental uncertainty. For example, most of the vapor pressure data points available for DEGDME are below 0.05 bar. In addition, it is important to highlight that the experimental data available for DEGDEE and DEGDBE, from different sources, are in disagreement. Figure 1 shows the model performance to predict the vapor pressure of some linear and branched ethers, as well as polyethers.

On the bais of the correlation of limited number of data points, we simulate the rest of the experimental data available in the literature. The parameters fitted to the data of 4 ethers allow a quantitative prediction of the phase behavior of almost 20 different ethers. In general, the GCA-EOS predicts accurately the vapor pressure of linear and branched monoethers, as well as that of polyethers. Table 5 reports the critical temperature and diameter of all pure compounds not included in the model parametrization. Furthermore, it lists GCA-EOS deviations in the prediction of vapor pressures and critical points of the ethers under study, whenever the experimental data are available. The GCA-EOS is able to predict correctly the critical point of all components assessed, E



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Figure 2. Vapor liquid equilibria of light ethers + alkanes. (a) Dimethyl ether (DME) + light alkane binary systems at 313 K: (×) propane and (□) n-butane. Symbols: experimental data.60,97 (b) diethyl ether (DEE) + alkane binary systems at atmospheric pressure: (◇) n-hexane and (×) npentane. Symbols: experimental data.101 Lines: GCA-EOS predictions.

4.1. Linear Monoethers + n-Alkane Binary Systems. Table 6 summarizes the performance of GCA-EOS to predict VLE of linear monoether + n-alkane binary systems. As can be seen, in general, the GCA-EOS deviations are below 3% in bubble pressure/temperature and vapor composition, except for a few data sets, whose deviations are bounded below 5%. The only systems showing notably higher errors, that is, DPE + n-octane/n-nonane and DBE + n-heptane systems at 363 K,94 are further analyzed by the end of this section.

Figure 4. Temperature−composition projection of the critical locus of n-hexane + ethers binary mixtures: (□) diethyl ether (DEE), (◇) di-n-propyl ether (DPE) and (○) di-n-butyl ether (DBE). Empty symbols: experimental data.105,106 Filled symbols: pure ethers critical points.93 Lines: GCA-EOS predictions.

illustrates the VLE of methyl n-butyl ether + n-heptane binary mixtures at two different temperatures. In general, the model describes accurately the effect of temperature on the phase equilibria of binary systems comprising linear monoethers and alkanes. Moreover, the GCA-EOS also predicts quantitatively the critical locus of the binary systems under study. For instance, Figure 4 shows the model predictions of the critical temperature locus of the binary systems n-hexane with DEE, DPE, and DBE. Last, Figure 5 shows the GCA-EOS predictions of the binary systems DPE + n-octane/n-nonane and DBE + n-heptane, which depict the larger deviations in Table 6. For the three systems, the GCA-EOS deviations (AARD P = 6.3% and AAD y = 2.0%) are similar to the ones reported by Nguyen−Huyhn et al.13 with a group contribution version of the PC-SAFT (AARD P = 5.7% and AAD y = 1.9%). As can be seen in Figure 5, the data under analysis is very scattered. Figure 5b also depicts the ideal behavior of DBE + n-heptane from a different

Figure 3. Vapor liquid equilibria of the binary mixture methyl n-butyl ether (MBE) + n-heptane at (◇) 323 K and (□) 343 K. Symbols: experimental data.88 Lines: GCA-EOS predictions.

Figures 2 to 5 illustrate the GCA-EOS capacity to predict phase behavior of linear ethers with alkanes. Figure 2 shows the VLE prediction of DME and DEE with alkanes from C3 up to C6. As can be seen, the GCA-EOS performs well using the same set of binary group interaction parameters, as the alkyl chain of the alkane increases. Moreover, the GCA-EOS is capable of correctly simulating the DEE and n-pentane narrow volatility range, at atmospheric pressure, caused by their similar boiling point and ideal behavior (see Figure 2b). Figure 3 F



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Figure 5. Vapor liquid equilibria of linear monoethers + alkane binary systems. (a) Di-n-propyl ether (DPE) + n-alkanes at 363 K: (◇) n-octane and (△) n-nonane. (b) Di-n-butyl ether (DBE) + n-heptane at (◇) 363 K and (△) 313 K. Symbols and source of experimental data: empty symbols for binary data94,95 and filled for pure component vapor pressure.55 Lines: GCA-EOS predictions.

depicts the first two, while Figure 7b shows the data available for dibutyl ether. As can be seen in Figure 7a, the GCA-EOS predicts satisfactorily the binaries with di-n-pentyl ether and din-propyl ether. In the case of di-n-pentyl ether, there are two sources in disagreement, and the model follows the data of Wang et al.107 rather than that reported by Maronglu et al.108 On the other hand, Figure 7b shows the DBE + n-heptane experimental excess enthalpy data from three sources, the GCA-EOS prediction being closer to the data of Benson et al.109 4.2. Branched Monoether + Alkane Binary Systems. On the basis of the parametrization of linear monoether, we challenged the GCA-EOS predictive capacity to model the phase behavior of branched ethers. Even though we do not correlate any of the following compounds discussed in this section, the GCA-EOS predicts their behavior accurately. The model deviations are lower than 1% and 4%, in saturation temperature and pressure, respectively, while the deviation in the vapor phase composition is between 3 and 5% (see Table 7). Figure 8 depicts the isothermal and isobaric phase behavior of ETBE, a gasoline additive used to increase the octane number of fuels, with compounds typically found in gasoline. On the other hand, Figure 9 illustrates the GCA-EOS predictions of the phase behavior of i-octane, a major gasoline component, with various branched alkanes. Even though the GCA-EOS correctly predicts the VLE phase behavior of branched ethers, the model shows limitations to simulate part of the excess enthalpy data available for mixtures of branched ether + linear alkanes.133−138 In contrast, the GCA-EOS performs well in the case of binary mixtures comprising i-octane with MTBE and TAME (see Figure 10), while it is unable to reproduce the two data sets available for ETBE, which indeed are in disagreement between them. At this point, it is worth noting the importance of having equilibrium data under a wide temperature range to achieve a robust model for excess properties. On the other hand, in many cases, the excess enthalpy data available are inappropriate for fitting the parameters of a model, since they may show important deviations (see discussion above), and, in contrast with phase equilibrium data, it is difficult to appreciate when these excess enthalpy data are reliable, and when they are

source95 at a lower temperature, which is well predicted by the GCA-EOS. After assessing the model performance to predict phase behavior, we use the GCA-EOS to simulate excess enthalpy data of binary mixtures. The latter is an important type of property as it sets the temperature dependence of mixture nonideality. Figure 6 illustrates the effect of the n-alkane

Figure 6. Excess enthalpy of binary mixtures of di-n-propyl ether (DPE) with n-alkanes at 298 K: (○) n-hexadecane, (×) n-dodecane, (△ ) n-decane, (□ ) n-octane and (◇ ) n-hexane. Symbols: experimental data.110 Lines: GCA-EOS predictions.

molecular weight in the excess enthalpy of mixtures with di-npropyl ether (DPE). The model predicts satisfactorily the increase in the excess enthalpy with the molecular weight of the n-alkane, an interesting challenge for a group contribution model. It is worth highlighting that in many cases we find high discrepancies in excess enthalpy data of different sources. For this reason, this kind of data are excluded from the parametrization procedure; nonetheless, in some cases, it is useful to assess the model predictive capacity. Figure 7 depicts the excess enthalpies of n-heptane with linear monoethers: dipropyl, dipentyl, and dibutyl ether. Specifically, Figure 7a G



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Figure 7. Excess enthalpy of binary mixtures of n-heptane with linear monoethers at 298 K. (a) Di-n-propyl ether (DPE) (□),111 (■)108 and di-npentyl ether (△)107 (▲);108 (b) di-n-butyl ether (DBE) (◇)109 (gray),112 and (◆).108 Symbols: experimental data. Lines: GCA-EOS predictions.

Table 7. GCA-EOS Prediction of Vapor Liquid Equilibria of Binary Mixtures Comprising Branched Monoethers (1) with Alkanes (2) Binary Systems i-hexane n-hexane n-heptane i-octane

n-octane n-decane i-hexane n-heptane i-octane n-octane n-decane i-pentane i-hexane n-hexane n-heptane i-octane n-octane n-butane 2,4-dimethylpentane n-heptane i-octane

T (K) 328−333 313 325−338 298, 308 325−366 318−339 327−370 330−366 325−396 308, 318, 328 333−359 298−313 293−338 359−372 323, 423 308, 318, 328 293, 303 333−346 339−343 313 343−369 343−369 3.43−369 273, 373 343 323, 343 342−407 303, 333 340−370

P (bar)

AARDa T or P (%)

Methyl tert-Butyl Ether (MTBE) 1 0.17 (T) 0.37−0.59 1.9 (P) 0.93 0.39 (T) 0.06−0.48 2.2 (P) 0.93 0.38 (T) 0.16−1.38 2.8 (P) 0.95 0.21 (T) 1 0.46 0.93 0.40 (T) 0.005−1.0 3.4 (P) tert-Amyl Methyl Ether (TAME) 1 0.10 (T) 0.06−0.19 2.2 (P) 0.05−0.50 2.4 (P) 1 0.030 (T) 0.07−4.9 2.1 (P) 0.01−0.35 2.3 (P) Ethyl tert-Butyl Ether (ETBE) 0.13−1.1 2.2 (P) 1 0.070 (T) 0.93 0.070 (T) 0.12−0.31 3.8 (P) 0.93 0.17 (T) 0.93 0.16 (T) 0.93 0.14 (T) Diisopropyl Ether (DIPE) 0.06−15 1.9 (P) 0.72−1.1 1.1 (P) 0.19−1.1 1.8 (P) 1,2,3 0.10 (T) 0.02−0.98 3.5 (P) 0.95, 1 0.22 (T)

AARD y1(%) 3.4 2.8 3.4

Nb

source

4.9 4.0 3.0 3.5 3.4 0.27

23 23 20 48 26 81 13 22 21 56

75 113 114 115 114 116,117 118 119 114 120

1.8 1.8 1.7 1.9 0.46

20 72/26 100 23 36 71

75 115,121 122,123 124 86 120

0.60 0.89 3.0 2.8 0.84

30 22 27 26 20 25 18

125 75 126 127 126 128 128

5.6 1.4 1.3 2.1 4.0 2.4

36 14 29 26 44 30

86 88 88 129 130,131 118,132

3.3

a

AARD:average absolute relative deviations in (P) pressure and (T) temperature. bN, number of experimental data points.

not. In particular, the predictions shown here for branched

parameters, if we would have reliable experimental information covering a wider temperature range. 4.3. Polyether + Alkane Binary Systems. Since nowadays polyethers are also proposed as higher molecular weight oxygenated additives for diesel fuels, we assess here the

ethers are full predictions, based on the parameters correlated for linear ethers solely; therefore, there still is room to improve the characterization of branched alkyl groups binary interaction H



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Figure 8. Vapor−liquid equilibria of ethyl tert-butyl ether (ETBE) + alkanes binary systems. (a) At 0.93 bar: (◇) n-octane, (○) isooctane and (×) n-hexane. Symbols: experimental data.126,128 (b) At (□) 303 K and (◇) 293 K with i-pentane. Symbols: experimental data.125 Lines: GCA-EOS predictions.

GCA-EOS capacity to predict the phase behavior of polyethers, based on the parametrization of monoethers. Table 8 reports the GCA-EOS deviations in the prediction Table 8. GCA-EOS prediction of VLEa of Binary Mixtures Containing Polyethers (1) with n-Alkanes (2) binary systems n-heptane 2,4-dimethyl pentane n-heptane n-decane n-dodecane a

T (K) 343 343

1,2-Dimethoxyethane 0.4−0.64 2.6 0.6−0.81 0.57

AARD y1(%)

Nb

source

4.5 1.6

12 12

102 88

1,2-Diethoxyethane 343 0.17−0.4 5.0 4.5 13 Diethylene Glycol Dimethyl Ether (DEGDME) 393 0.2−0.3 1.1 1.8 12 Triethylene Glycol Dimethyl Ether (TEGDME) 435 0.17−0.25 4.0 3.9 10

VLE, vapor liquid equilibria,. points.

Figure 9. Vapor liquid equilibria of i-octane with a branched ether at near atmospheric pressure: (□) tert-amyl methyl ether (TAME), (×) diisopropyl ether (DIPE), and (◇) methyl tert-butyl ether (MTBE). Symbols: experimental data.119,124,132 Lines: GCA-EOS predictions.

AARD P (%)

P (bar)

b

90 102 88

N, number of experimental data

of polyethers VLE behavior with alkanes, which are in all cases lower than 5%. Moreover, Figure 11 shows the model performance with selected polyethers + alkanes binary systems. At low temperatures, mixtures of polyether with alkanes may

Figure 10. Excess enthalpy of mixtures of isooctane with branched ethers at 298 K. (a) Methyl tert-butyl ether (MTBE), (b) tert-amyl methyl ether (TAME), and (c) ethyl tert-butyl ether (ETBE). Symbols: experimental data (◇),139 (◆),140 (□),141 (■),142 (○)134 and (●).143 Lines: GCAEOS predictions. I



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Figure 11. (a) Vapor−liquid equilibria of polyethers + n-heptane binary systems at 343 K: (△) 1,2-dimethoxyethane and (□) 1,2-diethoxyethane. (b) Vapor liquid equilibria of the binary mixture of diethylene glycol dimethyl ether (DEGDME) + n-decane at 393 K. Symbols: experimental data.90,102 Lines: GCA-EOS predictions.

exhibit liquid−liquid immiscibility. For instance, Figure 12 compares the experimental and predicted LLE of TEGDME

Figure 13. Excess enthalpy of binary mixtures of polyethers with nheptane at 298 K: (□) diethylene glycol diethyl ether (DEGDEE) and (◇) 1,2-diethoyethane. Symbols: experimental data.108 Lines: prediction with the GCA-EOS.

Figure 12. Liquid−liquid equilibria of binary mixtures of polyethers + n-decane binaries systems: (□) tetraethylene glycol dimethyl ether (TeEGDME) and (◇) triethylene glycol dimethyl ether (TEGDME). Symbols: experimental data.144,145 Lines: GCA-EOS predictions.

5. CONCLUSIONS The valorization of biomass and waste is a field of growing interest and is calling for the development of new efficient technologies and innovative products. Specially in the area of biofuels, the focus is highly set on the use of residual biomass as a key condition for future generation biofuels. In addition, over the past few years, several authors have highlighted the potential of ether-based compounds as blending agents for gasolines and diesel fuels. In any case, thermodynamic models for the development of biorefineries and new biobased products are highly needed. In this work, we extend the GCA-EOS table of parameters to describe the phase behavior of mixtures comprising ethers and alkanes. The proposed parametrization allows describing accurately the vapor pressure of linear monoethers and the VLE behavior of their mixtures with alkanes. On the basis of the correlation of the data for only four monoethers, the model predicts the phase behavior of almost 20 other linear ethers, as well as branched ethers and polyethers. The same set of

and TeEGDME with n-decane close to the mixture upper critical solution temperature (UCST). In these cases, the GCA-EOS only describes qualitatively the mutual solubility and overpredicts the UCST. Finally, the GCA-EOS is also able to describe qualitatively well the excess enthalpy of mixtures of polyethers with nalkanes. Figure 13 depicts the prediction of the excess enthalpy of n-heptane with polyethers of two oxygen atoms: 1,2diethoxyethane and diethylene glycol diethyl ether. For higher molecular weight polyethers, Figure 14 illustrates the excess enthalpies of n-dodecane with 1,2-dimethoxyethane, triethylene glycol dimethyl ether and tetraethylene glycol dimethyl ether binary mixtures at constant temperature and pressure. As can be observed, the model is able to predict the increase in excess enthalpy, as the number of oxygen atoms in the ether compound increases. J



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The attraction contribution to the residual Helmholtz energy, Aatt, accounts for dispersive forces between functional groups. It is a van der Waals expression combined with a density-dependent local-composition mixing rule based on a group contribution version of the NRTL model.45 The van der Waals expression for the attractive Helmholtz energy is equal to −a·n·ρ, where a is the energy parameter, n is the number of moles, and ρ is the mole density. For a pure component, a is computed as follows: z a = q 2g (A.5) 2 where g is the characteristic attractive energy per segment and q is the number of surface segments as defined in the UNIFAC method.46 The interactions are assumed to take place through the surface and the coordination number (z) is set equal 10 as usual.46 In GCA-EoS the extension to mixtures is carried out using the NRTL model, but with the use of local surface fractions like in UNIQUAC147 rather than local mole fractions: Figure 14. Excess enthalpy of binary mixtures of polyethers with ndodecane at 323 K: (○) tetraethylene glycol dimethyl ether (TeEGDME), (△) triethylene glycol dimethyl ether (TEGDME), and (□) 1,2-dimethoxyethane. Symbols: experimental data.146 Lines: prediction with the GCA-EOS.

z

q 2̃ gmix Aatt 2 =− RT RTV

(A.6)

where q̃ is the total number of surface segments and gmix is the mixture characteristic attraction energy per total segments calculated as follows: NG

parameters also allows predicting the excess enthalpy of mixtures of mono- and polyethers with alkanes, preserving an accurate extrapolation in temperature of the model predictions. The results achieved in this work encourage the extension of the GCA-EOS to model the phase behavior of mixtures comprising ethers and other organic compounds with applications in fuel blending.

gmix =

i=1

θτ j jigji

NG

∑ θi ∑ j=1

NG

∑k = 1 θkτki

and NC NG

q̃ =

■

∑ ∑ niνijqj i=1 j=1

APPENDIX: THE GCA-EOS MODEL The GCA-EOS model has three contributions to the residual Helmholtz energy. The free volume contribution is represented by the extended Carnahan−Starling43 equation for mixtures of hard spheres developed by Mansoori and Leland:44

θj =

λλ λ A = 3 1 2 (Y − 1) + 22 (Y 2 − Y − ln Y ) + n ln Y RT λ3 λ3 (A.1)

with

πλ y i Y = jjjj1 − 3 zzzz 6V { k

−1

(A.2)

λk =

∑ i=1

1 q̃

NC

∑ niνijqj

(A.9)

̃ gji zy ji q Δ zz τji = expjjjjαji z j RTV zz k {

(A.10)

Δgji = gji − gii

(A.11)

i=1

gji is the attractive energy between groups i and j, and αji is the nonrandomness parameter. It is worth highlighting that, in the absence of nonrandomness (αij = 0), eq A.7 gives the classical quadratic mixing rule. The attractive energy, gij, is calculated from the energy between like-group segments through the following combination rule:

NC

nidik

(A.8)

where νij is the number of groups of type j in molecule i; qj stands for the number of surface segments assigned to group j, θj represents the surface fraction of group j

3

fv

(A.7)

(k = 1, 2, 3) (A.3)

where ni is the number of moles of component i, NC stands for the number of components, V represents the total volume, R stands for the universal gas constant, T is temperature, and di is the hard-sphere diameter per mole of species i. The following generalized expression gives the temperature dependence of the hard sphere diameter: ÄÅ É ij −2Tci yzÑÑÑÑ ÅÅÅ j z di = 1.065655dciÅÅ1 − 0.12 expj zÑÑ ÅÅ (A.4) k 3T {ÑÑÖ Ç where dci and Tci are, respectively, the critical hard-sphere diameter and critical temperature of component i.

gij = kij gii gjj (kij = kji)

(A.12)

with the following temperature dependence for the energy and interaction parameters: ÄÅ É ij T yz ij T yzÑÑÑÑ ÅÅÅ − 1zzz + gii″ lnjjj zzzÑÑÑ gii = gii*ÅÅÅ1 + gii′jjj j T* z j T * zÑÑ ÅÅ (A.13) ÅÇ k i { k i {ÑÖ K


Journal of Chemical & Engineering Data ÄÅ É ÅÅ ij 2T yzÑÑÑÑ ÅÅ zzÑÑ kij = kij*ÅÅÅ1 + kij′ lnjjjj zÑ j Ti* + T *j zzÑÑÑ ÅÅ ÅÇ k {ÑÖ

Article

AAD(Z)

and

Average absolute deviation in variable Z:

1 N ∑ Zexp,i − Zcalc,i N i AARD(Z)% Average relative deviation in variable Z:

(A.14)

where gii* is the attraction energy and kij* is the interaction parameter at the reference temperature Ti* and (Ti* + T *j )/2 ,

1 N

respectively. Finally, the association term,41 Aassoc, is a group contribution version of the SAFT equation of Chapman et al.:47 ÄÅ M ÉÑ NGA ÅÅ i i Xki yz Mi ÑÑÑÑ Aassoc Å j Å zz + ÑÑ = ∑ ni*ÅÅ∑ jjln Xki − ÅÅ k RT 2 { 2 ÑÑÑ ÅÇ k = 1 (A.15) i=1 Ö

di dci gi kij Mi N NC NG NGA P qj R Rk T Tci V wsat

In this equation NGA represents the number of associating functional groups, ni* is the total number of moles of associating group i, Xki is the fraction of group i nonbonded through site k, and Mi is the number of associating sites in group i. The total number of moles of associating group i is * of associating groups i present calculated from the number νmi in molecule m and the total amount of moles of specie m (nm): NC

ni* =

∑ νmi*nm

(A.16)

m=1

The fraction of groups i nonbonded through site k is determined by the expression: ij j Xki = jjj1 + jj k

NGA Mj

∑∑ j=1 l=1

n*j XljΔki , lj yzz zz zz V z {

Xki

−1

yi z

(A.17)

■

AUTHOR INFORMATION

REFERENCES

(1) Kläusli, T. AVA Biochem: Commercialising Renewable Platform Chemical 5-HMF. Green Process. Synth. 2014, 3, 235−236. (2) BP and DuPont joint venture, Butamax, announces next step in commercialization of bio-isobutanol with acquisition of ethanol facility in Kansas. https://www.bp.com/en/global/corporate/media/ press-releases/bp-and-dupont-joint-venture.html (accessed May 28, 2018). (3) Andre, A.; Nagy, T.; Toth, A. J.; Haaz, E.; Fozer, D.; Tarjani, J. A.; Mizsey, P. Distillation Contra Pervaporation: Comprehensive Investigation of Isobutanol-Water Separation. J. Cleaner Prod. 2018, 187, 804−818. (4) Yanowitz, J.; Christensen, E.; McCormick, R. Utilization of Renewable Oxygenates as Gasoline Blending Components; Report NREL/TP-5400−50791, National Renewable Energy Laboratory: Golden, CO, 2011. (5) Kolodziej, R.; Scheib, J. Bio-Isobutanol: The next-Generation Biofuel. Hydrocarbon Process. 2012, 79−85. (6) Werneck, R. Renewable Chemicals at Braskem: Current and Future Scenarios. In Word Bioenergy Symposium; Brasilia, 2015; p 20.

Corresponding Author

*E-mail: [email protected]. ORCID

Selva Pereda: 0000-0002-2320-4298 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors acknowledge the financial support granted by the ́ Consejo Nacional de Investigaciones Cientificas y Técnicas (PIP 112 2015 010 856), the Secretariá de Ciencia, Tecnologiá e Innovación Productiva (PICT 2016-0907), and Universidad Nacional del Sur (PGI 24/M153).

A

Effective hard sphere diameter of component i Effective hard sphere diameter of component i evaluated at Tc Group energy per surface segment of group i Interaction parameter between groups i and j Total number of associating sites in group i Number of experimental data points Number of components in the mixture Number of attractive groups in the mixture Number of associating groups in the mixture Pressure Number of surface segments of group j Universal gas constant van der Waals reduce volume of component k Temperature Critical temperature of component i Total volume of the mixture wy, Weighting factors for saturation pressure and vapor mole fraction Fraction of nonbonded associating sites of type k in group i Molar composition in vapor phase of component i Coordination number

αij Nonrandomness parameter between groups i and j εki,lj Energy of association between site k of group i and site l of group j κki,lj Volume of association between site k of group i and site l of group j νij Number of groups j in compound i νij* Number of associating groups j in compound i

The association strength between site k of group i and site l of group j depends on the temperature T and on the association parameters κki,jl and εki,jl, which represent the volume and energy of association, respectively.

■

N Zexp, i − Zcalc, i i Zexp, i

Greek Symbols

where the summation includes all NGA associating groups and Mj sites. Xki depends on the association strength, Δki , lj : ÄÅ ÉÑ ÅÅ i εki , lj y Ñ zz − 1ÑÑÑ Δki , lj = κki , ljÅÅÅexpjjj z ÑÑ ÅÅÇ k RT { ÑÖ (A.18)

■

∑

LIST OF SYMBOLS Helmholtz free energy L



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