Liquid–Liquid Equilibria for the Systems: Heptane + Benzene + Solvent (Propylene carbonate, N,N -Dimethylformamide, or Mixtures) at Temperatures from (303.2 to 323.2) K

Liquid−Liquid Equilibria for the Systems: Heptane + Benzene +Solvent (Propylene carbonate, N,N-Dimethylformamide, or Mixtures)at Temperatures from (303.2 to 323.2) KJing-jing Li,*,†,‡ Qian-shu Zhao,†,‡ Xiao-dong Tang,†,‡ Kun-liang Xiao,† and Jiao-yang Yuan†

†State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation and ‡College of Chemistry and Chemical Engineering,Southwest Petroleum University, Chengdu, 610500, P. R. China

*S Supporting Information

ABSTRACT: The extraction of benzene from heptane by thesolvents such as N,N-dimethylformamide (DMF), propylenecarbonate, and complex solvent (DMF + propylene carbonate)were researched. The liquid−liquid equilibrium (LLE) datawere experimentally obtained for the ternary systems heptane+ benzene + DMF and heptane + benzene + propylenecarbonate at 313.2 K and atmospheric pressure and for thequaternary systems heptane + benzene + DMF + propylenecarbonate at (303.2, 313.2, and 323.2) K and atmosphericpressure. The nonrandom two-liquid (NRTL) and universalquasichemical activity coefficient (UNIQUAC) models wereused to correlate the LLE data satisfactorily, and the selectivity and distribution coefficients of benzene were calculated. Due to itshigh selectivity and suitable distribution coefficient, DMF + propylene carbonate can be used as a potential extracting solvent toseparate benzene from heptane.

■ INTRODUCTION

Nowadays, with the increasing strict control of environmentalpollution and the demand of clean fuel,1−5 fuel oil and solventnaphtha etc. also need deep removal of the aromatics due totheir toxicity. Although catalytic hydrogenation can obtainpetroleum fractions with low aromatic contents, extraction ismore preferred due to the mild operation conditions and theavailability of aromatic byproducts.6−8

Propylene carbonate has been reported as an efficient solventfor the recovery of aromatics, such as benzene, toluene, andxylene from refinery process streams. The liquid−liquidequilibrium data for the ternary system of aliphatic compound+ aromatic compound + propylene carbonate have beenpublished.9−11 However, the disadvantage of propylenecarbonate is the low viscosity and high density which canlead to the poor phase contact of the extraction system,particularly when the interfacial tension is high. Besides, if thereformate under consideration contains a substantial amount ofC9+ aromatics, their recovery from the solvent will besignificantly more problematic than their separation fromother solvents such as sulfolane and triethylene glycol becausethe boiling points of the C9+ aromatics are higher than that ofthe propylene carbonate.12

In order to improve the extract efficiency of propylenecarbonate, N,N-dimethylformamide (DMF) was used as acosolvent in this paper.13,14 DMF has been reported that it canwork with ethylene glycol,15,16 KSCN,17 and NH4SCN

18,19 toachieve high solvent capacity in aromatics extraction, but DMF

+ propylene carbonate in aromatics extraction has not beenwell-researched.In this work, heptane + benzene + solvent systems were

researched. Propylene carbonate, DMF, and complex solvent(DMF + propylene carbonate) were used as solvents,respectively. To understand the role of solvent combinationin separation processes, liquid−liquid equilibrium (LLE) datawere measured for benzene + heptane + solvent systems attemperature range from (303.2 to 323.2) K and atmosphericpressure. Selectivity (S) and distribution (D) coefficients forsolvents were discussed accordingly. The nonrandom two-liquid (NRTL) and universal quasichemical activity coefficient(UNIQUAC) models were applied to correlate LLE data of therelevant mixtures.

■ EXPERIMENTAL SECTION

Materials. Benzene, heptane, DMF, propylene carbonate,and chlorobenzene were supplied by Kelong Chemical Co.China with mass fractions purity higher than 0.998, 0.997,0.995, 0.998 and 0.998, respectively. The reagents were usedwithout any further purification.

Apparatus and Procedures. Complex solvents wereprepared by adding a certain amount of DMF in propylene

Received: January 21, 2014Accepted: September 26, 2014Published: October 7, 2014

Article

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© 2014 American Chemical Society 3307 dx.doi.org/10.1021/je500442m | J. Chem. Eng. Data 2014, 59, 3307−3313

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carbonate under stirring, with the DMF mole fraction rangingfrom 0.318 to 0.807.The experimental setup of extraction process is shown in

Figure 1. A 100 mL conical flask with a magnetic stirrer was

used as the equilibrium cell for the experiment. The heptane−benzene mixtures with the benzene mole fraction ranging from0.125 to 0.658 was put in the conical flask. Then the solventwas added into the solution, and the mass ratio of (heptane +benzene) to solvent was 1. The liquid temperature wasmeasured by a K-type thermocouple inside. Temperatures wereobserved to be within ± 0.1 K of the set temperature and weretaken to be uniform for the cell liquids, as the total volumeinside was not more than about (50 to 70) mL, and the liquidwas well-stirred. The whole conical flask was put into athermostatic bath (MP-5H, Shanghai Bluepard Instrument Co.,China) that was controlled by a temperature controller with anaccuracy of ± 0.1 K to maintain a stable circumstancetemperature. The feed mixture was first stirred for 1 h, andthen maintained for about 4 h until it formed two clear phasesat the temperature of (303.2, 313.2, or 323.2) K andatmospheric pressure. Samples were carefully taken from eachphase and measured by gas chromatography (GC), employingthe internal standard method of analysis.The gas chromatography used in this work was GC-4000A

by Hefei Wanyi Science and Technology Co., China. It wasequipped with a flame ionization (FID) detector and CB-WAXcolumn (30 m × 0.32 mm × 0.33 μm). The injectortemperature was 453.15 K, and the detector temperature was478.15 K. The column temperature was programmed for aninitial temperature of 333.15 K maintained for 5 min and a finaltemperature of 473.15 K maintained for 3 min. Heating wasdone at the rate of 10 K·min−1. The other analysis conditionswere as follows: the injected volume, 0.2 μL; air pressure, 0.05MPa; hydrogen pressure, 0.05 MPa; carrier gas: nitrogen(nitrogen pressure: 0.05 MPa); spilt ratio, 100 mL·min−1. Theweight correction factors of benzene, heptane, DMF, andpropylene carbonate were measured by standard sample. Eachsample was prepared by adding known masses of thecomponents, and chlorobenzene was used as the internalstandard. A KM220 analytical balance (Shanghai LiangpingInstrument Co., China) with an accuracy of ± 0.0001 g wasused for weighing. After obtaining the calibration plots, otherknown mixtures (different from those used for calibration)

were analyzed, and their mass compositions were determined.The differences in the mass values were found to be in therange (0.001 to 0.005) g, and the maximum deviation wasestimated to be 0.008 in mole fraction. Two samples were takenfrom each phase, and triplicate injections were made for eachsample into the GC. The standard uncertainty is listed inTables 1 to 4.

■ RESULTS AND DISCUSSIONOptimizing the Composition of the Complex Solvent.

DMF, propylene carbonate, and their mixtures with the DMFmole fraction of 0.318, 0.411, 0.583, 0.736, and 0.807, wereused to separate benzene from the benzene + heptane systemwith the initial mass ratio of the two phases being 1. Thenbenzene concentrations in the heptane-rich phase weredetermined by GC. Mole fractions of benzene in theheptane-rich phase after extraction at 313.2 K were showedin Table 1. The lower concentration of benzene in the heptane-rich phase, the better separation effect of the solvent was. Theresults indicated the complex solvent with the DMF molefraction of 0.583 exhibits the best extract capability.

Experimental LLE Data. To compare the complex solventcapability, the LLE data were measured for the systems ofheptane + benzene + DMF, heptane + benzene + propylenecarbonate, and heptane + benzene + DMF + propylenecarbonate (complex solvent with the DMF mole fraction of0.583) at 313.2 K and atmospheric pressure. The data areshown in Tables 2 to 4. More LLE data for the quaternarysystems heptane + benzene + DMF + propylene carbonate(complex solvent with the DMF mole fraction of 0.583) weredetermined at (303.2 and 323.2) K and listed in Table 4.The LLE data of heptane (1) + benzene (2) + DMF (3) at

303.15 K were reported by Yang et al.17 In this work, the LLEdata of heptane + benzene + DMF at 303.2 K were measuredand compared with the literature data.19 The results werepresented in Figure S1, and the details were shown in theSupporting Information. The data matched the literature19 well.Selectivity (S) and distribution coefficients (D) are important

parameters to evaluate the feasibility of the liquid−liquidextraction system. The following eqs 1 and 2 defined theselectivity and distribution coefficients of benzene, respectively.

=Sx x

x x//

2I

1I

2II

1II

(1)

Figure 1. Schematic diagram of experimental setup.

Table 1. Mole Fraction of Benzene in the Heptane-Rich afterExtraction with Standard Uncertainty

solventsbenzene in heptane-

rich

pure DMF 0.099pure propylene carbonate 0.142complex solvent with the DMF mole fraction of0.318

0.138

complex solvent with the DMF mole fraction of0.411

0.102


0.094


0.099


0.109

u(x) 0.004

Journal of Chemical & Engineering Data Article

dx.doi.org/10.1021/je500442m | J. Chem. Eng. Data 2014, 59, 3307−33133308

=Dxx

2I

2II

(2)

where x is the mole fraction and superscripts I and II refer tothe solvent-rich phase and heptane-rich phase, respectively.Subscripts 1 and 2 denote heptane and benzene, respectively.The values of S and D are shown in Tables 2 to 4 along with

Table 2. LLE Data in Mole Fraction with Standard Uncertainty for the Heptane (1) + Benzene (2) + DMF (3) System at 313.2K and 0.1 MPa and Selectivity (S) and Distribution (D) Coefficients of Benzene versus Heptanea

solvent-rich phase heptane-rich phase

T/K x1I x2

I x3I x1

II x2II x3

II S D

313.2 0.028 0.000 0.972 0.982 0.000 0.0180.085 0.051 0.864 0.874 0.069 0.057 7.60 0.740.111 0.073 0.816 0.828 0.095 0.077 5.73 0.770.143 0.097 0.760 0.757 0.126 0.117 4.08 0.770.190 0.126 0.684 0.678 0.155 0.167 2.90 0.810.243 0.144 0.613 0.602 0.173 0.225 2.06 0.83

u(x) 0.004 0.004 0.005 0.006 0.005 0.005aStandard uncertainty of temperature u(T) = 0.1 K.

Table 3. LLE Data in Mole Fraction with Standard Uncertainty for the Heptane (1) + Benzene (2) + Propylene Carbonate (3)System at 313.2 K and 0.1 MPa and Selectivity (S) and Distribution (D) Coefficients of Benzene versus Heptanea


T/K x1I x2

I x3I x1

II x2II x3

II S D

313.2 0.015 0.000 0.985 0.999 0.000 0.0010.019 0.032 0.949 0.913 0.085 0.002 18.09 0.380.022 0.065 0.913 0.816 0.175 0.009 13.78 0.370.025 0.094 0.881 0.727 0.259 0.014 10.55 0.360.028 0.117 0.855 0.655 0.320 0.025 8.55 0.370.033 0.170 0.797 0.506 0.439 0.055 5.94 0.390.038 0.204 0.758 0.401 0.511 0.088 4.21 0.40

u(x) 0.004 0.005 0.007 0.004 0.006 0.004aStandard uncertainty of temperature u(T) = 0.1 K.

Table 4. LLE Data in Mole Fraction with Standard Uncertainty for Heptane (1) + Benzene (2) + DMF (3) + PropyleneCarbonate (4) at (303.2 to 323.2) K and 0.1 MPa with the DMF Mole Fraction of 0.583 and Selectivity (S) and Distribution(D) Coefficients of Benzene versus Heptanea


T/K x1I x2

I x3I x4

I x1II x2

II x3II x4

II S D

303.2 0.031 0.000 0.534 0.435 0.998 0.000 0.001 0.0010.035 0.061 0.501 0.403 0.842 0.128 0.028 0.002 11.46 0.480.049 0.089 0.473 0.389 0.796 0.161 0.039 0.004 8.98 0.550.066 0.119 0.450 0.365 0.741 0.206 0.048 0.005 6.49 0.580.077 0.149 0.436 0.338 0.695 0.233 0.063 0.009 5.77 0.640.090 0.171 0.418 0.321 0.651 0.262 0.073 0.014 4.72 0.650.107 0.193 0.390 0.310 0.600 0.281 0.104 0.015 3.85 0.69

313.2 0.032 0.000 0.553 0.415 0.997 0.000 0.002 0.0010.044 0.077 0.504 0.375 0.845 0.106 0.047 0.002 13.95 0.730.059 0.114 0.462 0.365 0.785 0.152 0.059 0.004 9.98 0.750.070 0.148 0.428 0.354 0.720 0.193 0.073 0.014 7.89 0.770.082 0.177 0.394 0.347 0.672 0.223 0.088 0.017 6.50 0.790.098 0.207 0.384 0.311 0.629 0.238 0.107 0.026 5.58 0.870.115 0.232 0.359 0.294 0.576 0.264 0.128 0.032 4.40 0.88

323.2 0.038 0.000 0.543 0.419 0.966 0.000 0.028 0.0060.045 0.095 0.474 0.386 0.811 0.129 0.050 0.010 13.27 0.740.065 0.123 0.438 0.374 0.749 0.157 0.083 0.011 9.03 0.780.102 0.150 0.421 0.327 0.710 0.182 0.094 0.014 5.74 0.820.104 0.174 0.396 0.326 0.673 0.209 0.104 0.014 5.39 0.830.117 0.194 0.386 0.303 0.622 0.227 0.130 0.021 4.54 0.850.124 0.228 0.372 0.276 0.585 0.241 0.143 0.031 4.46 0.5

u(x) 0.004 0.004 0.006 0.007 0.006 0.004 0.005 0.005aStandard uncertainty of temperature u(T) = 0.1 K.



the experimental LLE data. It was seen that the selectivitycoefficient was decreased significantly with increasing aromaticconcentration x2

Π in the heptane-rich phase, while no obviouschanges for the distribution coefficient.To compare the separation effect of these solvents, their

selectivity and distribution coefficients at 313.2 K are shown inFigures 2 and 3, respectively. As illustrated in Figure 2, the

selectivity coefficient of complex solvent with the DMF molefraction of 0.583 is generally lower than that of propylenecarbonate in our experimental range. But it is improved a lotcomparing to DMF. Figure 3 indicated that the distributioncoefficient of complex solvent was much higher than propylenecarbonate, though slightly lower than DMF. Considering theselectivity and distribution coefficient together, complex solventwas better than pure DMF or propylene carbonate.Modeling and Data Correlation. The NRTL20 and

UNIQUAC21 models were used to correlate the LLEexperimental data, which were plotted on the triangulardiagrams as shown in Figures 4 to 8.

In the correlation using the NRTL model, the two binaryinteraction parameters (Δgij/R) and (Δgji/R) were calculated.The value of the third nonrandomness parameter, aij, in theNRTL model were fixed for each system (from aij = 0 to 0.5).The NRTL binary interaction parameters of the ternarysystems correlated were listed in Table 5.The required van der Waals parameters, ri and qi, for the

UNIQUAC model were adopted from the literatures,22−24 aspresented in Table 6. The UNIQUAC binary interactionparameters were summarized in Table 7. Root-mean-squaredeviation (RMSD), the measure of agreement between theexperimental and calculated data, was defined as

=∑ ∑ ∑ −

⎪ ⎪⎪ ⎪⎧⎨⎩

⎫⎬⎭

x x

MRMSD

( )

6i j k ijk ijk

exp cal 2 1/2

(3)

where xijkexp and xijk

cal are the experimental and calculated molefractions, respectively, i is the number of components, j is thenumber of phases, and k is the number of tie lines. The value of

Figure 2. Comparison of the selectivity coefficient (S) of differentsolvents at 313.2 K. ●, DMF; ▲, propylene carbonate; ★, complexsolvent with the DMF mole fraction of 0.583.

Figure 3. Comparison of the distribution coefficient (D) of differentsolvents at 313.2 K. ●, DMF; ▲, propylene carbonate; ★, complexsolvent with the DMF mole fraction of 0.583.

Figure 4. Comparison of the measured heptane (1) + benzene (2) +DMF (3) LLE data with the correlation results at 313.2 K. ■,experimental tie lines; ---○---, NRTL model; ---△---, UNIQUACmodel.

Figure 5. Comparison of the measured heptane (1) + benzene (2) +propylene carbonate (3) LLE data with the correlation results at 313.2K. ■, experimental tie lines; ---○---, NRTL model; ---△---,UNIQUAC model.



M designated the number of tie lines, and 6 was the number ofcompositions measured per tie line for ternary systems. Forquaternary systems this number was 8. The results of RMSDcalculations (Table 8) suggested that both NRTL andUNIQUAC models were satisfactorily applied to correlate theexperimental LLE data. The comparison of the experimentaland calculated tie lines on the phase diagram is shown inFigures 4 to 8. All of the tie lines in these figures showedexcellent correlation by the NRTL and UNIQUAC models.

■ CONCLUSIONSLiquid−liquid equilibria for heptane + benzene + DMF,heptane + benzene + propylene carbonate, and heptane +benzene + DMF + propylene carbonate (complex solvent withthe DMF mole fraction of 0.583) at 313.2 K and atmosphericpressure were determined. The experimental results showedthat complex solvent with the DMF mole fraction of 0.583 hada high selectivity and a suitable distribution coefficient. LLEdata for the quaternary systems heptane + benzene + DMF +propylene carbonate at (303.2 and 323.2) K and atmospheric

pressure were also measured. The selectivity of the complexsolvent ranged from 3.85 to 13.95. All of the LLE data were

found to correlate well with both the NRTL and UNIQUAC

models.

Figure 6. Comparison of the measured heptane (1) + benzene (2) +DMF (3) + propylene carbonate (4) LLE data with the correlationresults at 303.2 K. ■, experimental tie lines; ---○---, NRTLmodel; ---△---, UNIQUAC model.



Table 5. Parameters of NRTL Model for Heptane (1) +Benzene (2) + DMF (3) at 313.2 K, Heptane (1) + Benzene(2) + Propylene Carbonate (3) at 313.2 K, and Heptane (1)+ Benzene (2) + DMF (3) + Propylene Carbonate (4) at(303.2 to 323.2) K with the DMF Mole Fraction of 0.583

T/K i-j (Δgij/R)/K (Δgji/R)/K aij

Heptane (1) + Benzene (2) + DMF (3)313.2 1−2 850.70 −482.54 0.3

1−3 997.28 809.962−3 −192.39 440.24Heptane (1) + Benzene (2) + Propylene Carbonate (3)

313.2 1−2 93.80 209.68 0.31−3 1832.58 1088.062−3 479.48 287.07

Heptane (1) + Benzene (2) + DMF (3) + Propylene Carbonate(4)

303.2 1−2 −267.41 627.052 0.31−3 1355.64 2239.221−4 1206.04 571.242−3 −526.98 554.872−4 958.78 276.603−4 −396.29 −671.95

313.2 1−2 −127.92 794.99 0.31−3 162.12 1121.161−4 1357.44 596.552−3 −1584.29 2394.802−4 285.40 354.083−4 −255.75 −1626.66

323.2 1−2 309.92 722.57 0.31−3 903.57 768.121−4 1907.59 1000.002−3 −19.33 748.162−4 1357.41 1053.793−4 609.74 791.69



■ ASSOCIATED CONTENT*S Supporting InformationLLE data for heptane + benzene + DMF at 303.2 K measuredand compared with ref 19, presented in Figure S1. This materialis available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected]. Tel.: (+86)-28-83033009. Fax: (+86)-28-83033009.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

We thank the editors and anonymous reviewers for thesuggestions on improving our manuscript.

■ REFERENCES(1) Mohsen-Nia, M.; Modarress, H.; Doulabi, F.; Bagheri, H. Liquid+ Liquid Equilibria for Ternary Mixtures of (Solvent + AromaticHydrocarbon + Alkane). J. Chem. Thermodyn. 2005, 37, 1111−1118.(2) Mahmoudi, J.; Lotfollahi, M. N. Extraction of benzene from anarrow cut of naphtha via liquid-liquid extraction using pure-sulfolaneand 2-propanol-sulfolane-mixed solvents. Korean J. Chem. Eng. 2010,27, 214−217.(3) Letcher, T. M.; Zondi, S.; Naicker, P. K. Liquid-Liquid Equilibriafor Mixtures of (Furfural + an Aromatic Hydrocarbon + an Alkane) atT) 298.15 K. J. Chem. Eng. Data 2003, 48, 23−28.(4) Gonzalez, E. J.; Calvar, N.; Gonzalez, B.; Domínguez, A. LiquidExtraction of Benzene from Its Mixtures Using 1-Ethyl-3-methyl-imidazolium Ethylsulfate as a Solvent. J. Chem. Eng. Data 2010, 55,4931−4936.(5) Arce, A.; Earle, M. J.; Rodríguez, H.; Seddon, K. R. Separation ofaromatic hydrocarbons from alkanes using the ionic liquid 1-ethyl-3-methylimidazolium bis{(trifluoromethyl) sulfonyl}amide. Green Chem.2007, 9, 70−74.(6) Kumar, U. K. A.; Mohan, R. Liquid-Liquid Equilibria Measure-ment of Systems Involving Alkanes (Heptane and Dodecane),Aromatics (Benzene or Toluene), and Furfural. J. Chem. Eng. Data2011, 56, 485−490.(7) Villaluenga, J. P. G.; Tabe-Mohammadi, A. A Review on theSeparation of Benzene/Cyclohexane Mixtures by PervaporationProcesses. J. Membr. Sci. 2000, 169, 159−174.(8) Ruiz, C.; Coca, J.; Vega, A.; Díez, F. V. Extractive Distillation ofHydrocarbons with Dimethylformamide: Experimental and SimulationData. Ind. Eng. Chem. Res. 1997, 36, 4934−4939.(9) Anneslnl, M. C.; Glronl, F.; Marreill, L. Liquid-Liquid Equilibriafor Ternary Systems Containing Hydrocarbons and PropyleneCarbonate. J. Chem. Eng. Data 1985, 30, 195−196.(10) Fahim, M. A.; Merchant, S. Q. Liquid-Liquid Equilibria ofSystems Containing Propylene Carbonate and Some Hydrocarbons. J.Chem. Eng. Data 1998, 43, 884−888.(11) Ali, S. H.; Lababidi, H. M. S.; Merchant, S. Q.; Fahim, M. A.Extraction of aromatics from naphtha reformate using propylenecarbonate. Fluid Phase Equilib. 2003, 214, 25−38.(12) Salem, A. B. S. H.; Hamad, E. Z.; Al-Naafa, M. A. QuaternaryLiquid-Liquid Equilibrium of n-Heptane-Toluene-o-Xylene-PropyleneCarbonate. Ind. Eng. Chem. Res. 1994, 33, 689−692.(13) Hanson, C.; Patel, A. N.; Chang-Kakoti, D. K. Separation ofthiophene from benzene by solvent extraction: I. J. Appl. Chem. 1969,19, 320−323.(14) Jiang, H.; Zheng, Y.; Shi, J. Liquid-Liquid Equilibrium of DMF−Benzene−n-Heptane Ternary System. J. Chem. Eng. Chin. Univ. 1993,7, 96−100.(15) Radwan, G. M.; A1-Muhtaseb, S. A.; Fahim, M. A. Liquid-liquidequilibria for the extraction of aromatics from naphtha reformate bydimethylformamide/ethylene glycol mixed solvent. Fluid Phase Equilib.1997, 129, 175−186.(16) Aspi, K. K.; Surana, N. M.; Ethirajulu, K.; Vennila, V. Liquid-Liquid Equilibria for the Cyclohexane + Benzene + Dimethylforma-mide + Ethylene Glycol System. J. Chem. Eng. Data 1998, 43, 925−927.

Table 6. UNIQUAC Structural Parameters

component ri qi

heptanea 5.17 4.40benzenea 2.40 3.19DMFb 3.09 2.74propylene carbonatec 3.28 2.74

aFrom ref 22. bFrom ref 23. cFrom ref 24.

Table 7. Values of the UNIQUAC Binary InteractionParameters for Heptane (1) + Benzene (2) + DMF (3) at313.2 K, Heptane (1) + Benzene (2) + Propylene Carbonate(3) at 313.2 K, and Heptane (1) + Benzene (2) + DMF (3) +Propylene Carbonate (4) at (303.2 to 323.2) K with theDMF Mole Fraction of 0.583

T/K i−j (Δuij/R)/K (Δuji/R)/K

Heptane (1) + Benzene (2) + DMF (3)313.2 1−2 −86.40 327.12

1−3 −758.78 −27.242−3 94.10 −124.27

Heptane (1) + Benzene (2) + Propylene Carbonate (3)313.2 1−2 −548.29 287.93

1−3 −961.22 −14.492−3 −216.37 −7.89

Heptane (1) + Benzene (2) + DMF (3) + PropyleneCarbonate (4)

303.2 1−2 −285.24 260.051−3 995.72 −475.701−4 1224.88 195.362−3 2104.46 −4027.522−4 1843.89 −476.473−4 2535.65 2149.12

313.2 1−2 −386.47 349.431−3 −968.53 72.921−4 −894.52 67.392−3 −1032.91 635.362−4 −193.01 −1560.523−4 59.05 218.54

323.2 1−2 560.11 184.491−3 −667.97 −2724.741−4 −1049.66 145.932−3 −3684.30 1112.942−4 −857.33 862.973−4 −291.77 −388.24

Table 8. NRTL and UNIQUAC Models Root-Mean-SquareDeviation (RMSD) Values

mixture T/K NRTL UNIQUAC

heptane + benzene + DMF 313.2 0.0058 0.0042heptane + benzene + propylene carbonate 313.2 0.0055 0.0070heptane + benzene + DMF + propylenecarbonate

303.2 0.0087 0.0126

313.2 0.0240 0.0281323.2 0.0110 0.0082



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Liquid–Liquid Equilibria for the Systems: Heptane + Benzene + Solvent (Propylene carbonate, N,N -Dimethylformamide, or Mixtures) at Temperatures from (303.2 to 323.2) K