Phase Behavior Modeling of Mixtures Containing N-, S-, and O

Article Cite This: Ind. Eng. Chem. Res. 2019, 58, 11038−11059

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Phase Behavior Modeling of Mixtures Containing N‑, S‑, and O‑Heterocyclic Compounds Using PC-SAFT Equation of State Ehsan Razavi,† Ali Khoshsima,*,† and Reza Shahriari‡ †

School of Petroleum and Chemical Engineering, Hakim Sabzevari University, Sabzevar 96179-76487, Iran Thermodynamics Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran

‡

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S Supporting Information *

ABSTRACT: In this study, thermodynamic modeling of mixtures including heterocyclic compounds using the perturbed chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) is studied. The oxygen-, nitrogen-, or sulfurcontaining heterocyclic molecules are modeled as nonassociating components. For some more aggregative associating compounds with −OH (furfuryl alcohol, tetrahydrofurfuryl alcohol, 2-thiophenemethanol, and 5-hydroxymethylfurfural) or −NH (azetidine, aziridine, pyrrole, pyrazole, pyrrolidine, pyrrolidone, piperidine, morpholine, imidazole, piperazine, and n-methylpiperazine) groups, two association sites are considered for each molecule. The pure component parameters of the PC-SAFT EoS are adjusted to vapor pressure and liquid density experimental data with average absolute relative deviation of 0.88 and 0.77%, respectively. Using the obtained parameters, the isobaric and isothermal phase behavior of binary systems is studied over a wide range of thermodynamic conditions. The average deviations between model calculations and experimental data for heterocycle + aromatics, heterocycle + cycloalkane, heterocycle + haloalkanes, heterocycle + alcohol, heterocycle + heterocycle, heterocycle + organic solvents, and heterocycle + hydrocarbon systems are about 1.79, 2.15, 1.03, 1.68, 2.81, 1.24, and 1.81% respectively. Furthermore, the solid−liquid equilibria of heterocycle mixtures have been predicted by estimation of melting and eutectic points over a wide range of compositions. The second-order-derivative thermodynamic properties of heterocyclic compounds including speed of sound (us) and heat capacity (Cp) have been also predicted. The obtained results are in good agreement with the experimental data.

1. INTRODUCTION The heterocyclic compounds are considered as a kind of interesting aromatic substance.1 They constitute one of the largest and most varied family of organic compounds regarding their ability extensively change both in structure and intermolecular interactions. This diversity allows them to be categorized as a cornerstone and one of the most complex branches of organic chemistry. Besides carbon and hydrogen, the heterocyclic compounds usually contain heteroatoms including nitrogen, oxygen, sulfur, and so on. The most common heterocyclic compounds are those with five-membered (e.g., thiophene, furan, pyrrole, imidazole, dioxolane) or six-membered (e.g., pyridine, morpholine) heterocyclic rings and extensively exist in plants, herbs, animals, coal, and fossil oil.1,2 Thiophene and its derivatives have acquired increasing interdisciplinary research interest according to their multiple practical properties.3,4 Pyridine is used as solvent (for both organic and inorganic compounds) or preservative. It can also be utilized in the synthesis of medicine, dyestuffs, and production of agricultural chemicals (herbicides and insecticides).5,6 2-Methylpyridine (synonyms: 2-picoline, α-picoline, and α-methylpyridine) is an intermediate reagent in the © 2019 American Chemical Society

synthesis of pharmaceutical products (e.g., 2-PAM cholinesterase reactivator) and amprolium (coccidiostat)). It can also be used as a solvent or as a chemical intermediate to produce 2-vinylpyridine.7−11 3-Methylpyridine (synonyms: 3-picoline, β-picoline) is often used as a starting substance for pharmaceuticals and agrochemicals including insecticides, feed additives, and herbicides.7 Sulfolane is used as a high polarity solvent for extraction of BTXs (benzene, toluene, and xylene isomers)12,13 and as hybrid solvent for removing H2S and CO2 in sour gas treatment processes.14−17 Morpholine is used largely in the rubber industry (as an intermediate, stabilizer, or bloom inhibitor), steam boiler systems (as corrosion inhibitor against carbonic acid), pharmaceuticals (as an intermediate), and the detergent industry (as a brightener).18−20 Trioxane is considered as the basic chemical during the production of polyacetal resin from formaldehyde in acidic aqueous solutions.21−23 As probe molecules in heterogeneous catalysis, furan and its Received: Revised: Accepted: Published: 11038

March 14, 2019 May 10, 2019 May 28, 2019 May 28, 2019 DOI: 10.1021/acs.iecr.9b01429 Ind. Eng. Chem. Res. 2019, 58, 11038−11059

Article

Industrial & Engineering Chemistry Research

Figure 1. Schematic representation of the studied heterocyclic compounds. The ordered arrangement of the molecular structure is based on molecular weight.

family are of great interest for a variety of chemical reactions.24 Some furan derivatives (2-methylfuran, 2,5-dimethylfuran, γ-valerolactone) obtained from cellulosic biomass have the immense potential to be used as biofuels for substitution or relieving the petroleum-based fuels.25−35 Benzofuran derivatives have remarkable biological potentials and can be used as antitumor, kinase inhibitor, antimicrobial, analgesic, antihyperglycemic, and antiparasitic agents.36−41 Tetrahydrofurfuryl alcohol (THFA) is extensively used as a water-miscible solvent or chemical intermediate in the production of THFA acrylates, UV curables, esters of oleic/stearic acids, and formulation of epoxy resins.42 Furfural (synonym: 2-furaldehyde) is a heteroaromatic aldehyde and is used as a selective green extractant43 to extract and remove aromatic hydrocarbons from lubricating oils with a high yield.44−48 Although nitrogen and sulfur heterocycles are very interesting compounds, they may cause industrial problems if they are not managed reasonably. Apart from the catalyst poisoning and corrosion problems during chemical processing, the presence of sulfur and nitrogen compounds in fuel oil leads to SOx and NOx emission and affects the efficiency of emission control systems.49,50 Therefore, to manage the industrial applications, a comprehensive knowledge of the thermophysical characterization, synthesis reactions, and intermolecular interactions of heterocycles is crucial from economic and environmental points of view. According to the wide industrial applications of heterocyclic mixtures, different teams have increasingly studied the phase equilibria and thermodynamic properties of heterocyclic systems.51−56 Sapei et al.57 measured vapor−liquid equilibrium (VLE) for binary systems of thiophene + n-hexane at 338.15 and 323.15 K and thiophene + 1-hexene at 333.15 and 323.15 K. Linek et al.58 measured isothermal VLE for n-methyl-2-pyrrolidone in

the presence of benzene, toluene, heptane, or methylcyclohexane. Sapei et al.59 determined isothermal phase equilibria on four binary systems containing 3-methylthiophene and cyclohexane, hexene, or trimethylpentene. Wang et al.60 measured phase equilibria of three binary systems containing 2,5-dimethylthiophene and 2-ethylthiophene in decane and mesitylene. Reyes et al.61 measured VLE and volumetric properties for binary mixtures of 1,4-dioxane with isomeric chlorobutanes. Zielkiewicz54 studied vapor−liquid equilibrium in 2-methylpyridine + benzene at temperature 303.15 K. Calvo et al.62 measured isothermal VLE of 1,3-dioxolane or 1,4-dioxane + hexane or + cyclohexane or + ethanol mixtures at 308.15 K. Francesconi et al.63,64 investigated isothermal VLE and excess volumes of 1,3-dioxolane or oxolane + isooctane or chlorobenzene. Giner et al.65 experimentally and theoretically studied isobaric VLE at 40, 70, and 101 kPa for mixtures containing tetrahydrofuran, tetrahydropyran, 1,3-dioxolane, and 1,4-dioxane with 1-chloropropane. Castellari et al.66,67 measured vapor− liquid equilibria in binary systems containing 1,3-dioxolane with 1,4-dioxane, acetone, and 1,1,2,2-tetrachloroethane. Gascón et al.68,69 worked on isobaric VLE of 1,3-dioxolane/1,4-dioxane +1-butanol/2-butanol/cyclohexane/n-hexane at 40.0 and 101.3 kPa. Wu and Sandler70 studied VLE of binary 1,3-dioxolane with cyclohexane at 313.15 and 333.15 K, with heptane at 313.15 and 343.15 K, with ethanol at 313.15 and 338.15 K, and with chloroform at 308.15 and 323.15 K. Elizalde-Solis and GaliciaLuna71 measured solubility of thiophene in carbon dioxide and carbon dioxide + 1-propanol mixtures at temperatures from 313 to 363 K. In another work,72 they studied high pressure VLE for the systems containing thiophene at 333−383 K and 1.9− 15.3 MPa. Kasprzycka-Guttman and Chojnacka73 measured isothermal VLE of pyridine/α-picoline + C6 to C10 n-alkanes at 348.15 K. Domańska et al.51 investigated phase equilibria of 11039

DOI: 10.1021/acs.iecr.9b01429 Ind. Eng. Chem. Res. 2019, 58, 11038−11059

aziridine ethylene oxide azetidine oxetane ethylene sulfide pyrrole furana imidazole 1H-pyrazole oxazole 2,5-dihydrofuran pyrrolidine tetrahydrofuran 1,3-dioxolane thietane pyridinea pyridazine pyrazine pyrimidine 2-methylfurana 1-methylimidazole thiophenea 2-pyrrolidone thiazole N-methylpyrrolidine piperidine γ-butyrolactone 2-methyltetrahydrofuran tetrahydropyran piperazine morpholine 1,4-dioxane tetrahydrothiophene 1,3,5-trioxane 2-methylpyridinea 3-methylpyridinea furfurala 2,5-dimethylfurana furfuryl alcohola 2-methylthiophenea 3-methylthiophenea N-methyl-2-pyrrolidone

substances

43.07 44.05 57.09 58.07 60.11 67.08 68.07 68.07 68.08 69.06 70.08 71.12 72.10 74.07 74.14 79.10 80.08 80.08 80.08 82.10 82.10 84.14 85.10 85.12 85.14 85.14 86.09 86.13 86.13 86.13 87.13 88.10 88.17 90.08 93.13 93.13 96.08 96.12 98.09 98.17 98.17 99.13

MW (g/mol) 248−348 218−458 273−303 248−328 243−348 308−628 200−485 333−385 350−710 195−545 253−353 268−368 170−540 258−368 273−400 235−615 273−473 345−605 298−628 288−353 278−318 243−553 393−543 298−408 258−373 268−398 376−503 263−373 263−378 323−630 273−401 274−398 293−413 293−408 298−428 308−438 240−660 283−368 270−580 283−403 288−408 279−479

Psat 255−455 200−400 293−298 200−370 170−500 260−500 283−338 368−383 400−570 250−450 270−360 220−520 164−540 293−313 255−555 298−328 325−525 285−555 298−590 283−338 298−343 283−338 298−750 298−383 200−510 270−550 273−333 288−328 293−313 420−570 270−550 325−515 225−525 340−570 298−328 298−328 283−338 283−338 283−338 283−323 283−338 253−363

ρL

temp range (K) 2.4220 2.0472 2.2020 2.1015 1.9564 2.5855 2.5537 3.1648 2.1958 2.5041 2.5816 2.3739 2.4368 2.8236 2.4537 2.7084 2.6681 2.1610 2.4492 2.8926 3.5000 2.5599 2.8967 2.7872 2.3150 2.4267 2.6297 3.2932 2.6206 2.6519 3.1522 2.7258 2.4144 3.2630 2.9738 2.9568 2.7467 3.3520 3.4288 2.2832 2.6012 3.2423

m 3.0133 3.1480 3.4560 3.4329 3.4314 3.3668 3.2969 3.0531 3.2802 3.2792 3.3527 3.6292 3.5321 3.1905 3.5167 3.4465 3.4187 3.5756 3.6695 3.4145 3.2061 3.4574 3.4444 3.2673 3.9284 3.8365 3.4795 3.4057 3.6681 3.7136 3.3537 3.4760 3.6833 3.1247 3.5660 3.5715 3.1160 3.4616 3.2319 3.8719 3.6965 3.4837

σ (Å) 188.11 269.57 257.53 295.43 317.56 317.63 245.61 409.64 425.59 283.56 272.75 289.37 279.52 267.77 304.67 304.12 387.69 352.60 327.23 249.70 321.77 288.13 379.692 305.19 293.50 302.32 388.81 240.72 281.50 274.10 286.01 290.05 326.74 276.10 293.67 306.74 349.63 247.66 201.79 327.78 306.13 336.42

ε/kB (K)

11040

3219.68

0.07419

0.07275 0.00557

1923.25 1031.26

0.02470

1105.27

0.05592

0.00075 0.00728

1702.98 1073.01

643.56

0.03299

1102.48

0.08433

0.12085

1124.47

1299.74

0.27910

κAB

1749.13

εAB/kB (K)

Table 1. PC-SAFT Parameters Adjusted for Pure Heterocyclic Compounds, Ordered by Molecular Weight Increase

1.29 0.51 0.44 2.06 0.09 0.56 0.88 0.28 0.29 1.74 0.18 0.39 1.51 0.20 0.29 0.83 1.85 1.46 0.38 0.15 2.11 0.87 0.89 0.24 0.50 0.68 0.59 0.67 0.38 0.33 0.20 0.69 0.36 0.20 0.39 0.12 2.38 0.14 0.83 0.83 0.67 1.19

0.82 1.15 0.10 0.93 0.58 0.41 0.21 3.25 2.96 1.99 0.04 0.50 2.35 0.21 0.94 0.74 0.87 1.68 0.83 0.23 2.66 0.22 2.19 0.36 0.77 0.75 0.11 0.04 0.02 1.65 0.29 0.15 0.43 0.21 0.19 0.13 0.20 1.92 0.80 0.31 0.29 0.51

Δρ

AARD (%) ΔP 100 100 131 100 100 100 96−98 134 136 136 100 100 98 100 100 136 136 136 136 99 139 100,101 100 100 100 100 100,141 100 100 100,136 131 100 100 100 100 100 98 99,145 98 100 100 146

Psat

refs 130 130 132,133 130 130 130 99 135 130 130 130 130 98 137 130 138 130 130 130 99 140 102 130 136 130 130 142 143 144 130 130 130 130 130 138 138 43 99 43 102 102 146

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11041

k

100 i jj∑N j Np j i

χi ,exp

χi ,exp − χi ,calc

278−403 280−480 273−383 274−319 276-318 303−450 298−433 313−438 337−444 303−460 333−463 283−433 303−428 283−433 276-319 333−468 310−501 380−560 313−368 336−445 310−740 305−555 380−880

250−450 293−453 275−350 273−450 293−343 283−338 293−590 273−500 298.150 283−338 265−505 283−433 283−338 283−433 273−460 288−298 385−499 298−398 298−353 283−338 310−740 325−555 380−860

ρL

temp range (K) Psat 2.9147 2.9374 3.4419 2.53670 3.0058 3.6166 2.5970 3.7882 4.3869 3.9680 3.2887 3.8052 3.2913 3.9045 4.5006 2.9663 1.9525 2.6410 4.9980 4.0086 2.8910 3.2637 3.7239

m 3.7985 3.6067 3.5538 3.8880 3.6601 3.3646 3.7949 3.4728 3.1489 3.2678 3.4896 3.2353 3.6111 3.2700 3.3376 3.7221 3.0790 3.7835 3.0711 3.3626 3.8575 3.6415 3.9790

σ (Å) 274.82 358.10 241.22 277.62 278.47 293.68 326.98 263.64 265.37 289.77 307.05 303.07 277.68 298.25 226.65 326.56 472.28 448.85 321.90 303.84 366.06 354.74 384.26

ε/kB (K)

0.09308 0.00101

0.0159

0.00478 0.00103

2346.90

1800.033

1190.02 1559.55

κAB

1597.59

εAB/kB (K) 0.41 0.70 0.58 0.28 0.12 1.65 0.23 0.42 1.96 1.42 0.45 2.54 0.65 0.94 4.61 0.35 1.58 0.68 2.55 2.35 0.30 0.16 1.40 0.88

0.97 0.74 0.33 0.71 0.25 0.36 0.89 0.82 0.16 0.14 1.19 0.21 0.30 0.28 2.97 0.16 1.11 0.06 0.39 0.17 0.98 0.39 1.35 0.77

Δρ

AARD (%) ΔP

yz zz where χ is vapor pressure Psat or liquid density ρliq. aFitted on density data at high pressure (HP) conditions. bAdjusted by Antón et al.154 z {

99.17 100.12 100.15 100.16 101.15 102.13 102.19 107.15 110.11 110.11 110.19 112.15 112.19 114.16 114.18 118.13 119.12 120.17 126.11 126.17 134.20 135.18 184.26

N-methylpiperidine γ-valerolactonea 2,5-dimethyltetrahydrofuran N-methylpiperazine N-methylmorpholine tetrahydrofurfurylalcohola thiacyclohexane 2,6-lutidine 2-acetylfuran 5-methylfurfurala thiophenol 2-thiophenecarboxaldehydeb 2,5-dimethylthiophenea 2-thiophenemethanolb N,N′-dimethylpiperazine benzofuran benzoxazole sulfolane 5-hydroxymethylfurfural 2-acetylthiophenea benzothiophene benzothiazole dibenzothiophene avg deviation (%)

AARD% =

MW (g/mol)

substances

Table 1. continued

100 98,147 100 131 131 150 100 100 151,152 150,151 100 154 101 154 131 100 155 146 157 159 136 155 136

Psat

refs 130 147 130 130 148,149 150 130 130 153 150 130 154 102 154 130 133 156 146 158 159 130 156 130

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Industrial & Engineering Chemistry Research Table 2. PC-SAFT Pure Component Parameters for Non-heterocyclic Components Used in This Work86,87,160,161 Component

r (−)

σ (Å)

ε/k (K)

n-propane n-hexane n-heptane n-octane n-nonane n-decane n-dodecane 1-hexene 1-dodecene cyclopentane cyclohexane methylcyclohexane dichloromethane 1-chloropropanea 1-chlorobutane 1-chloropentane 1-chlorohexanea 1,1,1-trichloroethane 1,1,2,2-tetrachloroethanea 1,2-dichloroethane 2-methylbutane 2-methylpentane 2,3-dimethyl-2-butene 2,2,4-trimethylpentane 3-methylpentane methanol ethanol 1-propanol 1-butanol 1-pentanol 1-hexanol 1-octanol 2-propanol 2-butanol 2-methyl-1-propanol 2-methyl-2-propanol acetone ethyl acetate acetonitrile benzene toluene cumene ethylbenzene chlorobenzene chloroform dimethyl ether N-methylacetamide methyl isobutyl ketone o-xylene

2.0020 3.0576 3.4831 3.8176 4.2079 4.6627 5.3060 2.9853 4.9880 2.3655 2.5303 2.6637 2.2632 2.6030 2.8585 2.7513 3.6299 2.4646 4.1531 2.5964 2.5620 2.9317 2.9546 3.1413 2.8852 1.5255 2.3827 2.9997 2.7515 3.6260 3.5146 4.3555 3.0929 2.7143 5.2456 3.5190 2.7740 3.6000 1.9693 2.4653 2.8149 3.3198 3.0799 2.6485 2.5038 2.3071 3.8728 3.3590 3.1362

3.6184 3.7983 3.8049 3.8373 3.8448 3.8384 3.8959 3.7753 3.9470 3.7114 3.8499 3.9993 3.3380 3.5456 3.6424 3.9027 3.7163 3.7558 3.2608 3.4463 3.8296 3.8535 3.7334 4.0862 3.8605 3.2300 3.1771 3.2522 3.6139 3.4508 3.6735 3.7145 3.2085 3.6080 2.8333 3.2392 3.2557 3.2719 3.3648 3.6478 3.7169 3.8675 3.7974 3.7533 3.4709 3.2528 3.0585 3.6810 3.7600

208.11 236.77 238.40 242.78 244.51 243.87 249.21 236.81 255.14 265.83 278.11 282.33 274.20 250.01 258.66 284.31 258.99 279.13 253.74 285.01 230.75 235.58 247.03 249.77 240.48 188.90 198.24 233.4 259.59 247.28 262.32 262.74 208.42 250.44 201.76 171.35 253.40 228.92 344.90 287.35 285.69 284.09 287.35 315.04 271.62 211.06 313.07 261.74 291.05

εAB/k (K)

κAB (−)

2899.5 2653.4 2276.8 2544.6 2252.1 2538.9 2754.8 2253.9 2558.3 1996.3 2577.9

0.035176 0.032384 0.015268 0.006692 0.010319 0.005747 0.002197 0.024675 0.003991 0.006260 0.035810

Adjusted in this work by fitting on the experimental vapor pressure and liquid density data.

a

tetrahydrofuran, tetrahydropyran) with chlorohexane. Bendiaf et al.78 studied isothermal vapor−liquid equilibria of binary systems furfuryl alcohol + toluene, furfuryl alcohol + ethanol, or furfural + toluene. Cabezas et al.79 focused on isobaric VLE for furfural with chlorinated hydrocarbons (dichloromethane, 1,2dichloroethane, trichloroethylene and tetrachloroethylene). Kurihara et al.80 investigated phase equilibria for systems methanol +1,3-dioxolane, water +1,3- dioxolane, and methanol +1,3-dioxolane + water at 101.3 kPa.

binary systems containing pyrrole + hydrocarbon/alcohol systems. Haimi et al.74 performed isothermal VLE measurements for tetrahydrothiophene with hydrocarbons between 288 and 303 K. Li et al.75 measured isobaric VLE for 2-methylthiophene with n-heptane, 2,2,4-trimethylpentane, n-nonane, and n-decane at 90 kPa with a modified Rose-Williams still. Romero et al.56 measured VLE of binary 1,4-dioxane with benzene, hexane, cyclopentane, cyclohexane. Bandrés et al.76,77 measured isobaric phase behavior of cyclic ethers (1,3-dioxolane, 1,4-dioxane, 11042


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Figure 2. Vapor pressure versus temperature diagram for (a) oxygen heterocyclic compounds, (b) nitrogen heterocyclic compounds, and (c) sulfur heterocyclic compounds. The symbols are experimental data,96,99,100,131 and solid lines are PC-SAFT models.

group contribution based statistical associating fluid theory approach (GC-SAFT-VR). Giner et al. correlated the experimental VLE data of cyclic ethers 1-chloropentane by Wilson,

In the case of thermodynamic modeling and theoretical calculation, Haley and McCabe50 modeled the thermodynamic properties and phase behavior of organic sulfur molecules with a 11043


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Figure 3. Density−pressure diagram at different temperatures for (a) thiophene, (b) furan, (c) furfural, and (d) 2-picoline and 3-picoline. The symbols are experimental data,43,99,102,138 and solid lines are PC-SAFT estimations.

NRTL, and UNIQUAC model81 and with 1-chloropropane by SAFT-VR EoS.82 Bandrés et al.77,81 correlated the experimental data of some oxygenated heterocyclic compounds with the UNIFAC group contribution method77 and SAFT EoS.76 Sapei et al.59 correlated the properties of 3-methylthiophene with the Wilson model. Lee et al.83 correlated VLE for cyclic ethers and hydrocarbons systems using UNIQUAC model. Gascón et al.69 correlated the phase behavior of heterocycles with different models (Wilson, van Laar, Margules, NRTL, and UNIQUAC) and with the group contribution methods ASOG and UNIFAC. Domańska et al.51,84 correlated VLE for the systems pyrrole, pyridine or sulfolane utilizing DISQUAC, NRTL and UNIQUAC models. Linek et al.58 correlated VLE for n-methyl-2-pyrrolidone + benzene, + toluene, + heptane, and + methylcyclohexane using the Redlich−Kister equation. Zhang et al.85 modeled VLE of n-methyl-2-pyrrolidone + benzene + thiophene using the Monte Carlo method. In this work, the capability of the PC-SAFT EoS86,87 in the correlation and prediction of thermodynamic properties of systems containing heterocyclic compounds has been investigated. The PC-SAFT pure parameters are calculated for N-, S-, and O-heterocycles by fitting on experimental vapor pressure and liquid density data. Binary interaction parameter, kij, was obtained for mixtures containing associating and nonassociating chemicals such as heterocycle + aromatics, heterocycle + haloalkanes, heterocycle + alcohol, heterocycle + cycloalkane, and heterocycle + organic solvent systems. In the case of solid− liquid equilibria (SLE), the melting and eutectic points of

systems containing heterocycle compounds have been modeled over wide range of composition. Also, the second order derivative properties of heterocyclic compounds including speed of sound (us) and heat capacity (Cp) have been predicted.

2. THEORY In the PC-SAFT model, the residual Helmholtz free energy is written as follows Ares Ahc Adisp Aassoc = + + NkBT NkBT NkBT NkBT

(1)

where the superscripts res, hc, disp, and assoc refer to residual, hard chain, dispersion, and association contributions, respectively. The hard-chain (Ahc), hard-sphere (Ahs), and dispersion (Adisp) terms are given by87 Ahc Ahs = m̅ − NAkBT NkBT

∑ xi(mi − 1)ln giihs(σii)

ÅÄ ÑÉÑ ij ξ23 yz Ñ ξ23 Ahs 1 ÅÅÅ 3ξ1ξ2 jj zz ln(1 − ξ )ÑÑÑ = ÅÅÅÅ + + − ξ jj 2 0z 3 Ñ 2 z ÑÑ NAkBT ξ0 ÅÅÅ (1 − ξ3) ξ (1 − ξ ) ξ ÑÑÖ 3 3 k 3 { Ç (3) i

(2)

Adisp 2 2 3 = −2πρI1(η , m̅ )m2 ϵσ 3 − πρmC ̅ 1I2(η , m̅ )m ϵ σ NAkBT (4) 11044


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Figure 4. Isothermal vapor liquid equilibrium for binary heterocyclic + aromatic systems: (a) 2-methylfuran (1) + benzene (2) system at 323.95 and 338.95 K; (b) n-methyl-2-pyrrolidone (1) + toluene (2) system at 343.15 and 373.15 K; (c) 2-picoline (1) + benzene (2) system at 303.15 and 313.15 K; (d) pyrrole (1) + benzene (2) system at 338.15, 348.15, and 358.15 K. The symbols are the experimental data,51,54,58,103,104 and solid lines are PC-SAFT estimations.

More details are given in ref 87. The association term given by Chapman et al.88,89 is written as follows ÅÄÅ ÄÅ ÑÉÑ É Ai Ñ ÅÅ ÅÅ ÑÑ Mi ÑÑÑ Aassoc X Å A Ñ Å i ÑÑ + = ∑ xiÅÅÅ∑ ÅÅÅln X − ÑÑ ÅÅ ÅÅÇ NAkBT 2 ÑÑÑÖ 2 ÑÑÑÑ i ÅÅÇ A i (5) ÑÖ

ΔAiBj is the association strength between two association sites A and B which belong to two different molecules i and j and is expressed as follows: ÄÅ ÉÑ Å i ε A iBj y ÑÑ j z Å Ñ A iBj hs + Å j z Δ = gij (dij )ÅÅÅexpjj zz − 1ÑÑÑσij 3k A iBj ÅÅ j kBT z ÑÑ (7) { ÅÇ k ÑÖ

where xi is the mole fraction of component i in the mixture, and XAi is the mole fraction of molecules not bonded at specific interaction site A. The summation is over all association sites on the molecule i. The nonbonded fraction XAi in the mixture is expressed as follows: 1 X Ai = 1 + ρ ∑i xi ∑B X BjΔA iBj

The Boublik−Mansoori−Carnahan−Starling equation has been utilized for the radial distribution function of hard sphere mixtures.90 The kAB and εAB are the volume parameter and association energy between two sites, respectively.

j

3. RESULTS AND DISCUSSION 3.1. Pure Parameter Estimation. The model parameters are obtained using pure components experimental VLE data

(6)

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Figure 5. PC-SAFT modeling for heterocyclic + cycloalkane systems: (a) 2-methylfuran (1) + cyclohexane (2) system at 318.85 and 338.95 K; (b) 3-methylthiophene (1) + methylcyclopentane (2) system at 343.15 K and 3-methylthiophene (1) + cyclohexane (2) system at 348.15 K. The symbols are experimental data,59,104,162 and solid lines are PC-SAFT estimations.

and picolines at different temperatures. These molecules were selected as representative substances with different chemical functional group. It is clear that acceptable results have been obtained even at high pressures up to 60 MPa. As a novel and interesting study, Guennec et al.93−95 developed a translated and consistent version of the well-known Peng− Robinson (tc-PR) and Redlich−Kwong (tc-RK) cubic equations of state. They mentioned that the used α-function passes the consistency test94 and makes it possible to safely extrapolate in the supercritical region and calculate VLE in multicomponent systems. Based on their results, the tc-PR EoS can be considered as the safest and the most accurate three-parameter cubic EoS.93 To study the performance of these models, a comparison between the experimental vapor pressure and liquid density data,96−102 with tc-PR, tc-RK and PC-SAFT results for thiophene and furan as two important heterocyclic molecules, has been presented in Figure S1 (see the Supporting Information). 3.2. Phase Behavior of Mixtures. 3.2.1. Vapor−Liquid Equilibrium. As mentioned above, the heterocyclic compounds are diversely used in different industrial applications where they are usually present in systems containing alcohol, aromatics, haloalkanes, cycloalkanes, and organic solvents under isothermal or isobaric conditions. In this regard, vapor−liquid equilibria for the binary mixtures containing associating and nonassociating chemicals such as heterocycle + aromatics, heterocycle + haloalkanes, heterocycle + alcohol, heterocycle + cycloalkane, and heterocycle + organic solvent systems were calculated by PC-SAFT EoS. The obtained results for calculation of VLE in binary heterocycle + aromatic mixtures are tabulated in Table S1 (see the Supporting Information). The results indicate that PCSAFT EoS is able to correlate the phase behavior with an average deviation of 1.79%. Figure 4 depicts isothermal VLE for binary systems including (a) 2-methylfuran + benzene at 323.95 and 338.95 K, (b) n-methyl-2-pyrrolidone + toluene at 343.15 and 373.15 K, (c) 2-picoline + benzene at 303.15 and 313.15 K, and

such as vapor pressure and liquid densities. Based on the SAFT theory, the physical parameters must be shown the ordered arrangement compare to molecular weight. Figure 1 depicts a schematic representation of the studied heterocyclic compounds, where the ordered arrangement of the molecular structures is based on molecular weight (Mw). The heterocyclic compounds were modeled as nonassociative molecules. For some more aggregative associating compounds with −OH (furfuryl alcohol, tetrahydrofurfuryl alcohol (THFA), 2-thiophenemethanol, and 5-hydroxymethylfurfural (HMF)) or −NH (azetidine, aziridine, pyrrole, pyrazole, pyrrolidine, pyrrolidone, piperidine, morpholine, imidazole, piperazine, and n-methylpiperazine) groups, and sulfolane, two association sites are considered per each molecule as type 2B in the terminology of Huang and Radosz.91 The pure parameters were fitted to vapor pressure and liquid density data using the following objective function sat y2 i ρ l − ρ l zy N j ij Pisat j i ,calc ,calc − Pi ,exp z i ,exp z j z zz j z OF = ∑ jj zz +∑ jjjj zz sat l j z j z P ρ i ,exp i k i k i ,exp { { N

2

(8)

sat l l where Psat i,calc, Pi,exp, ρi,calc, and ρi,exp are the calculated and experimental vapor pressure and liquid density of heterocycle, respectively. The adjusted PC-SAFT parameters for different heterocycle molecules have been listed in Table 1. The AARD for vapor pressure and liquid density are 0.88% and 0.77%, respectively. For nonheterocycle compounds, we have used the PC-SAFT parameters fitted by Gross and Sadowski86,87 and Lee and Kim92 (see Table 2). Parts a−c of Figure 2 depict a comparison between the calculated and the experimental vapor pressure data of different heterocyclic compounds at different temperatures for a variety of O-, N-, and S-heterocycles, respectively. As can be seen, accurate results are evident. Figure 3a−d presents density− pressure diagrams to compare the PC-SAFT results with experimental data for liquid density of thiophene, furan, furfural,

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Figure 6. Vapor−liquid equilibrium for heterocyclic + haloalkane systems: (a) 1,3-dioxolane (1) + 1-chloropentane (2) system at 308.15, 313.15, and 318.15 K; (b) 1,3-dioxolane (1) + 1-chloropentane (2) system at 40 and 101.3 kPa; (c) furfural (1) + dichloromethane (2) and furfural (1) + 1,2dichloroethane (2) systems both at 101.3 kPa; (d) tetrahydrofuran (1) + 1-chlorohexane (2) system at 40 and 101.3 kPa; (e) tetrahydrofuran (1) + 1-chloropentane (2) system at 298.15, 313.15, and 328.15 K; (f) 1,2-dichloroethane (1) + 1,4-dioxane (2) system at 273.15, 293.15, 303.15, 323.15, and 343.15 K. The symbols are experimental data,77,79,81,105,106 and solid lines are PC-SAFT model estimations.

(d) pyrrole + benzene at 338.15, 348.15, and 358.15 K. The symbols are experimental data,51,54,58,103,104 and solid lines are

PC-SAFT estimations. The PC-SAFT results give good agreement with the experimental data. 11047


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Figure 7. Phase behavior of heterocyclic + alcohol systems: (a) NMP (1) + 2- propanol (2) and NMP (1) + 2-methyl-1-propanol (2) systems both at 95.3 kPa; (b) furfuryl alcohol (1) + 2-propanol (2) system at 353.2, 373.2, and 408.2 K; (c) pyrrole (1) + propanol (2) system at 348.2, 358.2, and 368.2 K; (d) thiophene (1) + propanol (2) system at 308.15, 313.15, and 318.15 K. The symbols are experimental data,107−110 and solid lines are PC-SAFT model estimations.

(c) furfural + dichloromethane and furfural +1,2-dichloroethane both at 101.3 kPa, (d) tetrahydrofuran +1-chlorohexane at 40 and 101.3 kPa, (e) tetrahydrofuran +1-chloropentane at 298.15, 313.15, and 328.15 K, and (f) 1,2-dichloroethane +1,4dioxane at 273.15, 293.15, 303.15, 323.15, and 343.15 K. The symbols are the experimental dat,a77,79,81,105,106 and solid lines are PC-SAFT model estimations. According to the obtained results, good agreement is observed with the experimental data. Table S4 (see the Supporting Information) presents the adjusted binary interaction parameters in heterocyclic + alcohol systems with AARD % of 1.68. Meanwhile, Figure 7 illustrates the phase behavior of heterocycle + alcohol systems including (a) NMP + 2- propanol and NMP + 2-methyl-1-propanol both at 95.3 kPa; (b) furfuryl alcohol +2-propanol at 353.2, 373.2, and 408.2 K; (c) pyrrole + propanol at 348.2, 358.2, and 368.2 K; and (d) thiophene + propanol system at 308.15, 313.15, and 318.15 K. The symbols are experimental data,107−110 and

The adjusted binary interaction parameters in heterocycle + cycloalkane systems are presented in Table S2 (see the Supporting Information), where the calculated AARD is about 2.15%. For better comparison, Figure 5 illustrates phase behavior of mixtures including 2-methylfuran + cyclohexane at 318.85 and 338.95 K, 3-methylthiophene + methylcyclopentane at 343.15 K, and 3-methylthiophene + cyclohexane at 348.15 K. The results indicate that PC-SAFT model can satisfactorily correlate the VLE data. The capability of PC-SAFT in the estimation of VLE for binary heterocycle + haloalkanes systems (chloroalkanes, dichloroalkanes and trichloroalkanes) is investigated. Table S3 (see the Supporting Information) presents the adjusted binary interaction parameters in heterocycle + haloalkanes with AARD = 1.03%. Figure 6 also presents isothermal and isobaric VLE at constant pressures and temperatures, respectively, including (a) 1,3-dioxolane +1-chloropentane at 298.15, 313.15, 328.15 K, (b) 1,3-dioxolane +1-chloropentane at 40.0 and 101.3 kPa, 11048


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Figure 8. Experimental data and calculated lines for heterocycle + heterocycle systems: (a) 1,4-dioxane (1) + 1,3-dioxolane (2) system at 20, 40, 66.6, 86.6, and 98.6 kPa; (b) 2-methylfuran (1) tetrahydrofuran (2) system at 35 kPa; (c) furan (1) + furfural (2) system at 353.2, 373.2, and 408.2 K; (d) 2-methylfuran (1) + thiophene (2) system at 318.85 and 338.95 K. The symbols are experimental data,66,104,111,112 and solid lines are PC-SAFT model estimations.

phase behavior of these systems where AARD is about 2.81%. In addition, Figure 8 depicts the experimental data66,104,111,112 and PC-SAFT model estimations for isobaric and isothermal heterocycle + heterocycle systems including (a) 1,4-dioxane +1,3dioxolane at 20, 40, 66.6, 86.6, and 98.6 kPa; (b) 2-methylfuran + tetrahydrofuran at 35 kPa; (c) furan + furfural at 353.2, 373.2, and 408.2 K; and (d) 2-methylfuran + thiophene system at 318.85 and 338.95 K. In 2-methylfuran + tetrahydrofuran mixture, although the boiling points of these furan compounds are very close at P = 35 kPa (308.2 and 309.6 K, respectively), PC-SAFT can adequately estimate the azeotropic behavior. The obtained VLE results and the adjusted binary interaction parameters in binary mixtures of heterocyclic compounds with organic solvents including acetone, methyl isobutyl

solid lines are PC-SAFT model estimations. The comparison of the experimental data and calculated PC-SAFT values indicates that the calculated results give a good agreement with the experimental data. In the case of thiophene + 1-propanol system at 308.15, 313.15, and 318.15 K, the mixture shows the azeotrope points at xthiophene ≈ 0.87. It must be noted that, the robust thermodynamic models must be able to correlate or predict the azeotrope points over wide range of pressure and temperature. In this regard, the PC-SAFT model shows satisfactorily results for aforementioned systems at three different temperatures. The VLE calculated results and the adjusted binary interaction parameters in heterocycle + heterocycle mixtures are summarized in Table S5 (see the Supporting Information). The PC-SAFT model can satisfactorily correlate the VLE 11049


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Figure 9. VLE diagram for heterocyclic + organic solvent systems: (a) thiophene (1) + dimethyl ether (2) system at 308.15 and 335.63 K; (b) 2-picoline (1) + ethyl acetate (2) system at 303.15 K; (c) 1,3-dioxolane (1) + acetone (2) system at 40, 66.7, and 98.7 kPa; (d) 2,5-dimethylfuran (1) + methyl isobutyl ketone MIBK (2) system at 313.15, 333.15, 353.15, 373.15, and 393.15 K. The symbols are experimental data,54,67,113,114 and solid lines are PC-SAFT model estimations.

ketone (MIBK), ethyl acetate, acetonitrile, n-methylacetamide, and dimethyl ether (DME) are tabulated in Table S6 (see the Supporting Information). The presented results show that the average deviation between model calculations and experimental data for correlation of VLE is about 1.24%. Meanwhile, Figure 9 presents VLE diagrams for different heterocyclic + organic solvent systems including (a) thiophene + dimethyl ether at 308.15 and 335.63 K; (b) 2-picoline + ethyl acetate at 303.15 K; (c) 1,3-dioxolane + acetone at 40.0, 66.7, and 98.7 kPa; and (d) 2,5-dimethylfuran + methyl isobutyl ketone (MIBK) at 313.15−393.15 K. The experimental data54,67,113,114 shown by symbols are compared with solid lines as the PC-SAFT results. The figures show that the results of the mentioned model are clearly in good agreement with the

experimental data and the vapor−liquid equilibrium is welldescribed. The binary interaction parameters in binary systems of nonpolar hydrocarbon + heterocycles are obtained and compiled in Table S7 (see the Supporting Information). Both normal alkanes (n-propane to n-dodecane) and branched alkanes (dimethylalkanes and trimethylalkanes) are studied. The presented results show that the average deviation between the model calculations and experimental VLE data is about 1.81%. Figure 10 shows a comparison of the experimental data53,57,73,75,115 and calculated results for thiophene + hexane, tetrahydrofuran + 3-methylpentane, pyridine + heptane, and 2-methylthiophene + nonane/decane systems. Some of these heterocycle + hydrocarbon binary mixtures show azeotropic behavior. For example, 11050


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Figure 10. Comparison between the experimental VLE data53,57,73,75,115 (shown by symbols) and the correlated PC-SAFT results (solid lines) for the binary systems of (a) thiophene (1) + hexane (2), (b) tetrahydrofuran (1) + 3-methylpentane (2), (c) pyridine (1) + heptane (2), and (d) 2-methylthiophene (1) + nonane/decane (2).

4. PREDICTION OF THE SECOND-ORDER DERIVATIVE THERMODYNAMIC PROPERTIES OF HETEROCYCLIC COMPOUNDS

the binary mixture of pyridine + heptane has azeotrope points at both 313.15 and 348.15 K. The system containing tetrahydrofuran +3-methylpentane shows an azeotropic composition at 101.3 kPa (Taz = 333.3 K), while the boiling point of these compounds are very close (339.15 and 337.15, respectively). As depicted in Figure 10, the model is able to accurately estimate the azeotrope point. Auger et al.116 modeled the phase equilibria of systems containing oxygenated heterocycles (furan and furfural) and potential solvents of extraction (n-hexane, ethanol, and n-octanol) using a group contribution model based on the PC-SAFT EoS (GC-PPC SAFT). A comparison between PC-SAFT (this work) and GC-PPC-SAFT (performed by Auger et al.116) in the calculation of vapor−liquid equilibria at atmospheric pressure for binary systems containing (a) furan + furfural, (b) furan + n-octanol, and (c) furan + ethanol is presented in Figure 11. The obtained results are in good agreement with the experimental data.

It is the aim of this study to predict pure and mixed thermodynamic properties of heterocyclic compounds. In this regard, the second-order derivative thermodynamic properties such as speed of sound are the most important properties to evaluate the ability of a molecular-based EoS. Usually, the EoS parameters are fitted based on first-order derivative thermodynamic properties (such as vapor pressure and saturated density experimental data).86,87,117−120 It is quite obvious that the obtained parameters using the mentioned methodology give appropriate predictions in the case of mixture phase equilibriums, while a reliable EoS must be able to estimate all thermodynamic properties over wide range of pressure and temperature. Therefore, the capability of PC-SAFT EoS and the obtained parameters must be evaluated 11051


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Figure 12. Experimental99,101 and PC-SAFT predicted values for speed of sound as a function of temperature for (a) furan, (b) 2-methylfuran, and (c) thiophene at P = 1 bar.

us = Figure 11. Comparison between PC-SAFT (this work) and GC-PPCSAFT (performed by Auger et al.116) in calculation of VLE at atmospheric pressure for binary systems: (a) furan + furfural, (b) furan + n-octanol, and (c) furan + ethanol.

res ij ∂ 2(Ares /kBT ) yz zz − 2RT ijjj ∂(A /kBT ) yzzz Cvres(T , V , n) = − RT jjjj z j z z ∂T ∂T 2 k {v , n k {v , n (9)

( ∂∂TP )V ,n ( ∂∂VP )T ,n

Cpres(T , V , n) = Cvres(T , V , n) −

V 2 Cp ij ∂P zy jj zz MW Cv k ∂V {T

(11)

To check the capability of PC-SAFT EoS, the speed of sound (us) of furan, 2-methylfuran, and thiophene, also the specific heat capacity (Cp) of pyrrole, tetrahydropyran, pyrrolidine, and 1,4-dioxane are predicted and compared with the available experimental data. Figure 12 depicts the experimental99,101 and PC-SAFT predicted speed of sound as a function of temperature for (a) furan, (b) 2-methylfuran, and (c) thiophene at atmospheric pressure. The results show that the average absolute relative deviations (AARD) for furan, 2-methylfuran, and thiophene are 5.3, 3.5, and 7.4%, respectively. In Figure 13, the specific heat capacity (Cp) of pyrrole, tetrahydropyran, pyrrolidine, and 1,4-dioxane is predicted using PC-SAFT where the AARD (%) between the predicted and the experimental data121−126 are 9.06, 3.39, 2.99, and 2.11%, respectively.

by prediction of second order derivative thermodynamics properties. The heat capacity and speed of sound are calculated by the follow equations:

T

−

2

(10) 11052


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Figure 13. Predicted PC-SAFT results for specific heat capacity of (a) pyrrole, (b) tetrahydropyran, (c) pyrrolidine, and (d) 1,4-dioxane as a function of temperature compared with the experimental data121−126 at P = 1 bar.

As mentioned above, Guennec et al.93−95 presented a translated and consistent version of the Peng−Robinson (tc-PR) and Redlich−Kwong (tc-RK) cubic equations of state. They claimed that the tc-PR EoS is definitely the most precise three-parameter cubic EoS ever published.93 A comparison between the experimental heat capacity data121,126 and tc-PR, tc-RK, and PC-SAFT results for pyrrole and 1,4-dioxane is presented in Figure S2 (see the Supporting Information).

In this study, the fugacities are obtained by PC-SAFT EoS, and the solid−liquid equilibrium is established by equality of the solid- and liquid-phase fugacities of each component. The binary thiophene + dodecane and benzene + pyridine systems have been considered as two important case studies. Figure 14 presents a comparison between the experimental128,129 and the PC-SAFT predicted melting points for binary (a) thiophene− dodecane and (b) benzene−pyridine system where the obtained AARD values are 0.9 and 1.0%, respectively. In the case of binary benzene + pyridine, the mixture shows a minimum freezing value as the “eutectic point” at xPyridine = 0.7 and TEutectic = 216.12 K, and the PC-SAFT model can satisfactorily predict this behavior.

5. PREDICTION OF SOLID−LIQUID EQUILIBRIA OF MIXTURES CONTAINING HETEROCYCLES The capability of the PC-SAFT model has been studied in the case of SLE calculation of binary mixtures containing heterocyclic compounds. In the binary heterocycle mixtures, two components and three phases exist. On the basis of the phase rule criteria, the degree of freedom is 1. The formulation of solid−vapor−liquid equilibrium for binary mixture can be described by the isofugacity criterion as follows fi ̂

V

= fi ̂

6. CONCLUSION In this work, the capability of the perturbed chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) was investigated for thermodynamic modeling of the oxygen-, nitrogen-, or sulfur-containing heterocyclic molecules. Phase behavior in mixtures containing heterocycles and nonpolar and polar compounds were investigated. The mentioned model allowed the satisfactory correlation and prediction of both liquid and vapor phase properties for systems containing heterocyclic compound. The results of this work clearly show that this model is able to correlate thermodynamic properties of binary polar + heterocycle and nonpolar + heterocycle mixtures in a wide range of temperatures and pressures. In comparison to previous models, the PC-SAFT model shows appropriate capability considering its powerful theoretical background. Meanwhile, the PC-SAFT can be used as a predictive method allowing prediction of secondorder derivative thermodynamic properties. In this regard, the second-order derivative thermodynamic properties of heterocycles including speed of sound (us) and specific heat capacity

L

S F fi ̂ = fi ̂

(12) (13)

where fVî , fLî , fSî ,and fFî are the fugacity of vapor, liquid, solid, and fluid phases, respectively. The solid-phase fugacity can be calculated as follows120,127 É ÅÄÅ f i f yÑ ÑÑ Å ̂f S = f ̂SCL expÅÅÅÅ ΔHi jjjj1 − Ti zzzzÑÑÑÑ i i ÅÅ RT f j T z{ÑÑÑ ÅÅÇ i k (14) ÑÖ ̂ is the component fugacity of subcooled liquid phase where fSCL i at the given temperature and pressure.

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Figure 14. Comparison between the experimental128,129 and the PC-SAFT predicted melting points for the binary (a) thiophene−dodecane and (b) benzene−pyridine system.

ORCID

(Cp) have been satisfactorily predicted. On the other hand, the solid−liquid equilibria (SLE) have been acceptably modeled by predicting the melting and eutectic points of systems containing heterocycle compounds over a wide range of composition.

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Ali Khoshsima: 0000-0002-3210-7203 Notes

The authors declare no competing financial interest.

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ASSOCIATED CONTENT

S Supporting Information *

A g kB kij M m NA P R T XA

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.9b01429. VLE results and the values of adjusted binary interaction parameter, kij, for heterocycle + aromatics, heterocycle + cycloalkane, heterocycle + haloalkanes, heterocycle + alcohol, heterocycle + heterocycle, heterocycle + organic solvents, and heterocycle + hydrocarbon systems; comparison between the experimental vapor pressure and liquid density data with tc-PR, tc-RK, and PC-SAFT models for thiophene and furan; comparison between the experimental heat capacity (Cp) data with tc-PR, tc-RK, and PC-SAFT models for pyrrole and 1,4-dioxane (PDF)

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xi

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LIST OF SYMBOLS Helmholtz free energy (J) Radial distribution function Boltzmann constant, 1.38065 × 10−23 (J/K) Binary interaction parameter no. of association sites on the molecule no. of segments Avogadro’s number pressure gas constant (8.31451 Pa.m3 mol−1 K−1) temperature (K) mole fraction of molecules not bonded at specific interaction site A mole fraction of component i

ABBREVIATIONS EoS equation of state OF objective function SAFT statistical associating fluid theory

AUTHOR INFORMATION

Corresponding Author

*E-mail address: [email protected], ali.khoshsima@gmail. com. Tel: +98 51 4401 2852. Fax: +98 51 4401 2850. 11054


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Industrial & Engineering Chemistry Research PC-SAFT perturbed chain statistical associating fluid theory

(11) Wong, S.-S., 4.2 - 2-Methylpyridine. In Nitrogen and Phosphorus Solvents, 2nd ed.; Buhler, D. R., Reed, D. J., Eds.; Elsevier: Amsterdam, 1990; Vol. 2, pp 218−224. (12) Gutiérrez, A.; Atilhan, M.; Aparicio, S. A nanoscopic approach on benzene-toluene-xylenes extraction by sulfolane. J. Mol. Liq. 2018, 249, 1039−1046. (13) Wang, Q.; Chen, J. Y.; Pan, M.; He, C.; He, C. C.; Zhang, B. J.; Chen, Q. L. A new sulfolane aromatic extractive distillation process and optimization for better energy utilization. Chem. Eng. Process. 2018, 128, 80−95. (14) Luo, W.; Guo, D.; Zheng, J.; Gao, S.; Chen, J. CO2 absorption using biphasic solvent: Blends of diethylenetriamine, sulfolane, and water. Int. J. Greenhouse Gas Control 2016, 53, 141−148. (15) Shokouhi, M.; Jalili, A. H.; Zoghi, A. T.; Sadeghzadeh Ahari, J. Carbon dioxide solubility in aqueous sulfolane solution. J. Chem. Thermodyn. 2019, 132, 62−72. (16) Torabi Angaji, M.; Ghanbarabadi, H.; Karimi Zad Gohari, F. Optimizations of Sulfolane concentration in propose Sulfinol-M solvent instead of MDEA solvent in the refineries of Sarakhs. J. Nat. Gas Sci. Eng. 2013, 15, 22−26. (17) Jalili, A. H.; Shokouhi, M.; Samani, F.; Hosseini-Jenab, M. Measuring the solubility of CO2 and H2S in sulfolane and the density and viscosity of saturated liquid binary mixtures of (sulfolane+CO2) and (sulfolane+H2S). J. Chem. Thermodyn. 2015, 85, 13−25. (18) Canovese, L.; Visentin, F.; Uguagliati, P.; Crociani, B.; Di Bianca, F. Solvent and temperature effects in the mechanism of allyl amination of the α-diimine complex [Pd(η3-C3H5)-(C5H4N-2-CH NC6H4OMe-4)]+ by piperidine and morpholine. Inorg. Chim. Acta 1995, 235 (1), 45−50. (19) Riechert, O.; Zeiner, T.; Sadowski, G. Phase Equilibria in Systems of Morpholine, Acetonitrile, and n-Alkanes. J. Chem. Eng. Data 2015, 60 (7), 2098−2103. (20) Conway, C. C., 4.6 - Morpholine. In Nitrogen and Phosphorus Solvents; 2nd ed.; Buhler, D. R., Reed, D. J., Eds.; Elsevier: Amsterdam, 1990; Vol. 2, pp 218−224. (21) Albert, M.; Hasse, H.; Kuhnert, C.; Maurer, G. New Experimental Results for the Vapor−Liquid Equilibrium of the Binary System (Trioxane + Water) and the Ternary System (Formaldehyde + Trioxane + Water). J. Chem. Eng. Data 2005, 50 (4), 1218−1223. (22) Hasse, H.; Hahnenstein, I.; Maurer, G. Revised vapor-liquid equilibrium model for multicomponent formaldehyde mixtures. AIChE J. 1990, 36 (12), 1807−1814. (23) Brandani, S.; Brandani, V. Isothermal Vapor-Liquid Equilibria and Solubility in the System Methanol + 1,3,5-Trioxane. J. Chem. Eng. Data 1994, 39 (2), 203−204. (24) A. Werpy, T.; Holladay, J.; White, J., Top Value Added Chemicals From Biomass: I. Results of Screening for Potential Candidates from Sugars and Synthesis Gas; U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, 2004; Vol. 1. (25) Qian, Y.; Zhu, L.; Wang, Y.; Lu, X. Recent progress in the development of biofuel 2,5-dimethylfuran. Renewable Sustainable Energy Rev. 2015, 41, 633−646. (26) Jężak, S.; Dzida, M.; Zorębski, M. High pressure physicochemical properties of 2-methylfuran and 2,5-dimethylfuran − second generation biofuels. Fuel 2016, 184, 334−343. (27) Khoshsima, A.; Dehghani, M. R.; Touraud, D.; Marcus, J.; Diat, O.; Kunz, W. Nanostructures in clear and homogeneous mixtures of rapeseed oil and ethanol in the presence of green additives. Colloid Polym. Sci. 2015, 293 (11), 3225−3235. (28) Román-Leshkov, Y.; Barrett, C. J.; Liu, Z. Y.; Dumesic, J. A. Production of dimethylfuran for liquid fuels from biomass-derived carbohydrates. Nature 2007, 447, 982. (29) Brock, D.; Lopian, T.; Khoshsima, A.; Bauduin, P.; Diat, O.; Touraud, D.; Kunz, W. Nanostructuring in ethanol/“ethanolotrope”/ rapeseed oil automotive biofuels. Colloid and Interface Science Communications 2016, 14, 1−3. (30) Xu, H.; Wang, C., A Comprehensive Review of 2,5Dimethylfuran as a Biofuel Candidate. In Biofuels from Lignocellulosic Biomass; Wiley-VCH Verlag GmbH & Co, 2016; Vol. 1.

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SUPERSCRIPTS assoc association term calc calculated disp dispersion exp experimental hc hard chain term hs hard sphere term ref reference sat property at saturation condition

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SUBSCRIPTS i, j, k component index GREEK LETTERS ε dispersion energy parameter (J) εAB energy parameter of the association between sites A and B (J) κAB volume of interaction between sites A and B π ξ packing fraction (Ån−3), ξn = 6 ρ ∑i ximidin σ temperature-independent segment diameter (Å) ΔAB Strength of interaction between sites A and B (Å3)

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