International Journal of ISSN: 2475-5559 IPCSE

Petrochemical Science & Engineering
Research Article
Volume 1 Issue 4 - 2016
LLE of Methanol-Methylcyclohexane-Isooctane-Benzene Quaternary System
Monica Beatriz Gramajo*, Jonatan H Veliz and Alicia M Cases
Faculty of Exact Sciences and Technology, National University of Tucuman, Argentina
Received: November 16, 2016 | Published: December 28, 2016
*Corresponding author: Monica Beatriz Gramajo, Department of Physics, Faculty of Exact Sciences and Technology, National University of Tucuman, Argentina, Email:
Citation: Gramajo MB, Veliz JH, Cases AM (2016) LLE of Methanol-Methylcyclohexane-Isooctane-Benzene Quaternary System. Int J Petrochem Sci Eng 1(4): 00021. DOI: 10.15406/ipcse.2016.01.00021

Abstract

A quaternary system {methanol + methylcyclohexane + isooctane + benzene} was studied at T = 303.15 K. Only after all ternary equilibria data were determined experimentally, the quaternary binodal surface could be characterized fully. For this purpose, tie line data of {methanol + methylcyclohexane + benzene} ternary systems were obtained at the same temperature, while data for {methanol + isooctane+ benzene}, and {methanol + + isooctane + methylcyclohexane} were taken from literature. Experimental results show that the binodal surface with four quaternary sectional planes P1, P2, P3, P4 with several methylcyclohexane/isooctane in the solid diagram is small and that the highest benzene mass fraction values beyond which only one phase is present for the methanol-rich phase and hydrocarbon-rich one, respectively, are: 0.046 and 0.053 for P1, 0.053 and 0.057 for P2, 0.055 and 0.049 for P3, 0.034 and 0.041 for P4. So, if this quaternary system contains the correct methanol and hydrocarbons concentrations, this blend can be used as a reformulated gasoline because no phase separation should be observed. The distribution of benzene between both phases was also analysed. Ternary experimental results were correlated with the UNIQUAC and NRTL equation.. The UNIQUAC equation is more accurate than the NRTL equation for the ternary systems studied here. The equilibria data of the three ternary systems were used to determine interactions parameters for the UNIQUAC equation. The UNIQUAC equation fitted to the experimental data is more accurate than the UNIFAC method for this quaternary system. The main reason for this is that F is fit in the size of the quaternary binodal surface.

Keywords: Data; Liquid-liquid equilibria; Ternary system; Quaternary system

Introduction

In recent years, there has been an increasing demand to use oxygenated compounds in the reformulation of gasoline in order to substantially reduce toxic emissions into the environment and simultaneously enhance the octane number of gasoline. This is the reason why we studied the phase equilibria of systems containing representative hydrocarbons of gasoline (benzene, isooctane, or cyclohexane) and oxygenated compounds (methanol, ethanol, or methyl tert-butyl ether) [1-8].

The US Environmental Protection Agency recommends the use of alcohols as gasoline additives to provide antiknock properties and to help reduce harmful combustion emissions. However, methanol presents partial miscibility with aliphatic hydrocarbons, but not with aromatic ones. Therefore, it is of great importance to study systems composed of methanol and representative hydrocarbons of gasoline [7, 8].

Keeping this in mind, a quaternary system containing methanol, methylcyclohexane, benzene and isooctane {w1 CH4O + w2 C7H14 + w3 C8H18+ w4 C6H6} was also studied at 303.15K. Tie line data for the methanol-methylcyclohexane-benzene {w1 CH4O + w2 C7H14 + w3 C6H6} ternary system, where w is the mass fraction, were also investigated at temperature the same temperature, while data for methanol- isooctane-benzene, and methanol-isooctane- methylcyclohexane were taken from literature [8]. The fourth ternary subsystem methylcyclohexane-isooctane-benzene is completely miscible. This particular temperature was selected because it is representative of tropical and subtropical climates. Table 1 shows the respective Treybal [9] classification types for these systems.

Type

System

1

2

1

2

w1 CH4O + w2 C7H14 + (1- w1-w2) C6H6

w1 CH4O + w2 C7H14 + w3 C8H18 + (1- w1-w2-w3) C6H6

Table 1: Ternary and quaternary systems, including their Treybal’s classification type; wi denotes mass fraction of component i.

The experimental data for the ternary systems studied here were correlated with the UNIQUAC (Universal Quasi-Chemical equation) [10] and NRTL (Non-Random, Two-Liquid) [11] models.

All the pairs of the UNIQUAC interaction parameters obtained from the three partially miscible ternary subsystems included in the quaternary system were averaged and they were then used to predict the quaternary LLE of this model. The original UNIFAC (UNIQUAC Functional-group Activity Coefficients) method was also used for this purpose [12]. To the best of our knowledge, there is no reference in the literature on the LLE of the quaternary system studied in this work.

Experimental

Materials

Methanol was supplied by Merck, while methylcyclohexane and benzene by Sigma-Aldrich and isooctane by Sintorgan (Argentina). The purity of the chemicals was verified chromatographically, which showed that their mass fractions were higher than 0.998. Therefore, they were used without further purification. Methanol was maintained over 0.3 nm activated molecular sieves to prevent water absorption.

Methods

The experimental procedure used in the present study is the same as that reported in a previous work [2]. Quantification of all components in the conjugate phases was made by gas chromatography using the internal standard method. Acetone (C3H6O) (Merck, chromatographic quality) with a mass fraction purity >0.999 (GC) was the standard compound used for this purpose. A Hewlett Packard 6890 gas chromatograph with an automatic injector (Agilent G2613A) directly connected to a Chem Station (HP G2070AA) was used. Adequate separation of the five components was obtained on a 30 m long ´ 0.25 mm id ´ 0.5 mm film thickness capillary column (INN Wax, cross-linked polyethylene glycol, HP 19091N-233). The temperature program used was: initial temperature 343 K for two minutes, ramp 50 K·min-1, and final temperature 473 K for another two minutes. The nitrogen carrier gas flow rate was electronically kept constantly working with a split ratio of 20:1 and with the injector maintained at 453 K. Detection was carried out by a thermal conductivity detector at 523 K. Three or four analyses were performed for each sample in order to obtain a mean mass fraction value with repeatability better than one percent.

In order to obtain a calibration curve for each component of the internal standard method, a Mettler AG245 dual range balance with an accuracy of ± 0.1/0.01 mg was used to weigh the chemicals with the highest accuracy. Furthermore, to obtain overall mixtures for LLE studies, we weighed the components with the lowest balance accuracy. For the four components, linear correlations always provided the best fit for chromatography calibration curves.

To validate the reported mass fraction values, three samples of different known overall compositions (determined by mass) were analyzed. These mixtures were analysed with the chromatographic method and their chromatographic concentrations were compared with those obtained by mass. This comparison shows that the reported mass fraction values have an uncertainty of ± 0.001.

In order to determine the quaternary binodal surface, measurements were carried out at four different methylcyclohexane/isooctane ratios, which characterize four quaternary planes (named P1, P2, P3, and P4 in (Figure 1). Figure 1 shows a schematic representation of {w1 CH4O + w2 C7H14 + w3 C8H18 + w4 C6H6} quaternary system. The equilibria data for this system were obtained with the same procedure used in the ternary systems. In this work, the initial mixtures (corresponding to the P1, P2, P3, and P4 planes) were selected to determine tie lines within the whole heterogeneous region

Figure 1: Schematic representation of {w1 CH4O + w2 C7 H14 + w3 C8H18+ w4 C6H6} quaternary system at temperature 303.15 K. P1, P2, P3, and P4 are sectional planes or the determination of the binodal surface.

Results and Discussion

Table 2 lists the (liquid + liquid) equilibria data for the ternary systems {w1 CH4O + w2 C7H14 + w3 C6H6} at temperature (303.15 ± 0.05) K. Figure 2 shows the corresponding LLE diagrams. Data correlated by the UNIQUAC and NRTL models are also shown.

Global Compositions

 wwi

w1

w2

w3

w1

w2

w3

w1

w2

w3

CH4O

C7H14

C6H6

CH4O

C7H14

C6H6

CH4O

C7H14

C6H6

0.3537

0.6462

0

0.677

0.323

0

0.067

0.933

0

0.3479

0.6485

0.0236

0.651

0.328

0.021

0.072

0.902

0.026

0.3379

0.6199

0.0422

0.607

0.354

0.039

0.079

0.875

0.046

0.3245

0.6111

0.0643

0.560

0.38

0.06

0.133

0.799

0.069

0.3076

0.6098

0.0826

0.510

0.415

0.075

0.191

0.722

0.087

PPa

0.340

0.567

0.092

0.340

0.567

0.092

PPb

0.338

0.571

0.091

0.338

0.571

0.091

Table 1: (Liquid + liquid) equilibrium data of {w1 CH4O + w2 C7H14 + w3 C6H6} ternary system at temperature (303.15 ± 0.05) K; wi denotes mass fraction of component i.

a: Estimated plait point by the UNIQUAC model.

b: Estimated plait point by the NRTL model.

 

Figure 2: (Liquid + liquid) equilibrium of {w1 CH4O + w2 C7H14 + w3C6H6} ternary system at temperature 303.15 K. <¾<, Experimental; r, NRTL; ●, UNIQUAC; and +, global compositions.

Table 3 lists (liquid + liquid) equilibria data, expressed in mass fraction, of {w1 CH4O + w2 C7H14 + w3 C8H18+ w4 C6H6} quaternary system for each quaternary plane: P1 = (0.8067 C7H14 + 0.1933 C8H18), P2 = (0.6026 C7H14 + 0.3974 C8H18), P3 = (0.3996 C7H14 + 0.6004 C8H18), and P4 = (0.1926 C7H14 + 0.8074 C8H18). Experimental results reported in Table 2 & 3 satisfy the mass balance with a maximum deviation of 5 mass percent.

Since the concentrations of the four components were individually determined, the sums of the mass fractions for each phase shown in Table 3 may slightly differ from unity. The same consideration is applied to Table 2 for the ternary system (range ± 0.001, in mass fraction).

As can be seen in Table 3, we conclude that the benzene mass fractions values beyond which only one phase is present for the methanol-rich phase and hydrocarbon-rich are 0.046 and 0.053 for P1, 0.053 and 0.057 for P2, 0.055 and 0.049 for P3, 0.034 and 0.041 for P4. Since the binodal surface in the solid diagram is small, an adequate blend of these four components could be used as a reformulated gasoline, because no phase separation would occur.

The LLE data for the ternary systems studied here were correlated by the UNIQUAC and NRTL activity coefficient models, using an iterative computer program developed by Sørensen [13] that minimizes the values of the following objective functions:

F a = k i { ( a ik I a ik II )/( a ik I a ik II ) } 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaOaamOram aaBaaabaqcLbmacaWGHbaajuaGbeaacqGH9aqpdaWfGaqaaiabggHi LdqabeaajugWaiaadUgaaaqcfa4aaCbiaeaacqGHris5aeqabaqcLb macaWGPbaaaKqbaoaacmaabaWaaeWaaeaacaWGHbWaa0baaeaajugW aiaadMgacaWGRbaajuaGbaqcLbmacaWGjbaaaKqbakabgkHiTiaadg gadaqhaaqaaKqzadGaamyAaiaadUgaaKqbagaajugWaiaadMeacaWG jbaaaaqcfaOaayjkaiaawMcaaiaac+cadaqadaqaaiaadggadaqhaa qaaKqzadGaamyAaiaadUgaaKqbagaajugWaiaadMeaaaqcfaOaeyOe I0IaamyyamaaDaaabaqcLbmacaWGPbGaam4AaaqcfayaaKqzadGaam ysaiaadMeaaaaajuaGcaGLOaGaayzkaaaacaGL7bGaayzFaaWaaWba aeqabaqcLbmacaaIYaaaaaaa@6C5A@ (1)

  F a = k min i j ( X ijk X ijk ) 2 +Q n P n 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaOaamOram aaBaaabaqcLbmacaWGHbaajuaGbeaacqGH9aqpdaWfGaqaaiabggHi LdqabeaajugWaiaadUgaaaqcfaOaciyBaiaacMgacaGGUbWaaCbiae aacqGHris5aeqabaqcLbmacaWGPbaaaKqbaoaaxacabaGaeyyeIuoa beqaaKqzadGaamOAaaaajuaGdaqadaqaaiaadIfadaWgaaqaaiaadM gacaWGQbGaam4AaaqabaGaeyOeI0IaamiwamaaBaaabaGaamyAaiaa dQgacaWGRbaabeaaaiaawIcacaGLPaaadaahaaqabeaajugWaiaaik daaaqcfaOaey4kaSIaamyuamaaxacabaGaeyyeIuoabeqaaKqzadGa amOBaaaajuaGcaWGqbWaa0baaeaajugWaiaad6gaaKqbagaajugWai aaikdaaaaaaa@6410@            (2)

Here, a ik I,II MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbakaabggalm aaDaaajuaGbaqcLbmacaWGPbGaam4AaaqcfayaaKqzadGaamysaiaa cYcacaWGjbGaamysaaaaaaa@3FFA@  are the activities obtained from the experimental concentrations, I and II are the phases, x ijk MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbakaabIhada WgaaqaaKqzadGaamyAaiaadQgacaWGRbaajuaGbeaaaaa@3C1E@  and x ^ ijk MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbakqabIhaga qcaSWaaSbaaKqbagaajugWaiaadMgacaWGQbGaam4Aaaqcfayabaaa aa@3CC7@ are the experimental mole fraction values of the liquid phase and the calculated tie line lying close to the considered experimental line, respectively, where i represents the components, j the phases, and k the tie lines. Pn and Q are the parameter and the constant values in the penalty term, respectively.

This penalty term was established to reduce the risk of multiple solutions associated with high parameter values. Table 4 shows the structural parameters of the pure components taken from the literature [14] and the optimised binary interaction parameters of the UNIQUAC and NRTL models, for the ternary systems. The non-randomness parameter for the NRTL equation is also given.

Goodness of fit, as measured by the r.m.s. deviation in mole fraction F, is given by

F=100 { k i j ( x ijk x ^ ijk ) 2 /2nM } 1/2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbakaadAeacq GH9aqpcaaIXaGaaGimaiaaicdadaGadaqaamaaqafabaWaaabuaeaa daaeqbqaaiaacIcacaqG4bWcdaWgaaqcfayaaKqzadGaamyAaiaadQ gacaWGRbaajuaGbeaacqGHsislceqG4bGbaKaalmaaBaaajuaGbaqc LbmacaWGPbGaamOAaiaadUgaaKqbagqaaiaacMcadaahaaqabeaaju gWaiaaikdaaaqcfaOaai4laiaaikdacaWGUbGaamytaaqaaKqzadGa amOAaaqcfayabiabggHiLdaabaqcLbmacaWGPbaajuaGbeGaeyyeIu oaaeaajugWaiaadUgaaKqbagqacqGHris5aaGaay5Eaiaaw2haaSWa aWbaaKqbagqabaqcLbmacaaIXaGaai4laiaaikdaaaaaaa@637F@ , (3)

Where n is the number of components in the system. The r.m.s. relative error in the solute distribution ratio Δm is given by

 

Δm=100 k [ { ( m k m ^ k / m k ) 2 }/M ] 1/2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbakabfs5aej aab2gacqGH9aqpcaaIXaGaaGimaiaaicdadaaeqbqaamaadmaabaWa aiWaaeaadaqadaqaaiaab2galmaaBaaajuaGbaqcLbmacaWGRbaaju aGbeaacqGHsislceqGTbGbaKaadaWgaaqaaiaadUgaaeqaaiaac+ca caqGTbWaaSbaaeaajugWaiaadUgaaKqbagqaaaGaayjkaiaawMcaaS WaaWbaaKqbagqabaqcLbmacaaIYaaaaaqcfaOaay5Eaiaaw2haaiaa c+cacaWGnbaacaGLBbGaayzxaaWaaWbaaeqabaqcLbmacaaIXaGaai 4laiaaikdaaaaajuaGbaqcLbmacaWGRbaajuaGbeGaeyyeIuoaaaa@5AEB@ , (4)

 

Table 4 shows the UNIQUAC structural parameters for the pure components taken from the literature [14]. The calculated values of the residuals F and Δm, the optimized non-randomness parameter for the NRTL equation aij, and the optimized binary interaction parameters for UNIQUAC and NRTL models are also listed in Table 4. Here x ijk MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbakaabIhalm aaBaaajuaGbaqcLbmacaWGPbGaamOAaiaadUgaaKqbagqaaaaa@3CB7@ , is the experimental mole fraction of the ith component in the jth phase on the kth tie line, x ^ ijk MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiqabIhagaqcam aaBaaaleaacaWGPbGaamOAaiaadUgaaeqaaaaa@39EF@ is the corresponding calculated value, and m k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbakaab2gada WgaaqaaKqzadGaam4Aaaqcfayabaaaaa@3A36@  and m ^ k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbakqab2gaga qcaSWaaSbaaKqbagaajugWaiaadUgaaKqbagqaaaaa@3ADF@  are the experimental and calculated solute distribution ratios, respectively, given by w 2 " / w 2 ' MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbakaabEhalm aaDaaajuaGbaqcLbmacaaIYaaajuaGbaqcLbmacaGGIaaaaKqbakaa c+cacaqG3bWaa0baaeaajugWaiaaikdaaKqbagaacaGGNaaaaaaa@41FA@ .


Figure 2 shows the NRTL and UNIQUAC equations. The UNIQUAC equation fitted to the experimental results is considerably more accurate than NRTL equation taking into account overall errors, F and and Δm, listed in Table 4.

F%

%mD

i,j

aij b

aji b

jia

UNIQUAC

0.4

17.9

1.2

-1.5929

706.08

1.3

345.14

-98.318

2.3

606.45

-274.16

NRTL

0.3

50.7

1.2

499.24

564.43

0.3

1.3

995.17

-515

2.3

1021.7

-562.3

Table 4: Residuals F and Dm for UNIQUAC and NRTL optimised parameters of the UNIQUAC and NRTL equations, and non-randomness parameter (aij), for the system {w1 CH4O + w2 C7H14 + (1- w1-w2) C6H6} at temperature 303.15 Ka.

a: The following UNIQUAC structural parameters were used : for CH4O, r = 1.4311 and q = 1.4320; for C7H14, r = 4.7200 and q = 3.7760; and for C6H6, r = 3.1878 and q = 2.4000.

b: aij = (uijuji)/(R/K) for the UNIQUAC equation, where uij is the UNIQUAC binary interaction parameter (J×mol-1) and R = 8.31451 J×K-1×mol-1. aij = (gijgji)/(R/K) for the NRTL equation, where gij is the energy of interaction between an i-j pair of molecules (J×mol-1).

 

Table 5 lists the residuals for the UNIFAC and UNIQUAC models of {w1 CH4O + w2 C7H14 + w3 C8H18+ w4 C6H6} quaternary system. The fit was poor in terms of Dm for both models, due to the large relative error associated with the very low concentrations of benzene in both phases, while the goodness of fit in terms of Fwas satisfactory, particularly for the UNIQUAC model. Therefore, the UNIQUAC equation fitted to the experimental data is more accurate than the UNIFAC method of this quaternary system.

Planes

F%

Dm%

UNIFAC

P1

17.2

39.5

P2

16.4

34.6

P3

14.6

40.6

P4

11.7

33.6

UNIQUAC

P1

3.4

46.7

P2

4.6

74

P3

3.0

81.1

P4

1.5

66.5

Table 5: Residuals F and Dm of {w1 CH4O + w2 C7H14 + w3 C8H18+ w4 C6H6} quaternary system at temperature 303.15 Ka.

a: The values of Dm were calculated only for C6H6. The distribution coefficient for this compound is defined as m = mass fraction of C6H6 in the II phase ( w 4 " MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4DamaaDa aaleaacaaI0aaabaGaaiOiaaaaaaa@3881@ )/mass fraction of C8H10 in the I phase ( w 4 ' MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4DamaaDa aaleaacaaI0aaabaGaai4jaaaaaaa@3886@ ).

 

The average of all the binary interaction parameters, calculated from their respective ternary subsystems, was chosen in order to obtain a unique set of binary parameters suitable for prediction of the quaternary equilibria data using the UNIQUAC model, as previously done [3]. They are reported in Table 6.

i-j

aij

aji

1-2

-4.6795

664.945

1-3

-19.3145

647.465

1-4

183.0015

22.481

2-3

-17.974

27.111

2-4

606.45

-274.16

3-4

-5.2652

-5.5424

Table 6: Average UNIQUAC interaction parameters for the prediction of the quaternary system.

Conclusion

 (Liquid + liquid) equilibria of {w1 CH4O + w2 C7H14 + w3 C6H6} ternary systems and of {w1 CH4O + w2 C8H18 + w3 C7H14 + w4 C8H10} quaternary system were investigated at temperature 303.15 K, and the highest concentrations of hydrocarbons and methanol beyond which only one phase is present were established.

The UNIQUAC equations fitted to the experimental data is considerably more accurate than the NRTL equations taking into account both overall errors F and Δm These residuals also show that the UNIQUAC model is better than the NRTL one Table 4 for the ternary systems.

The quaternary equilibria was predicted by the UNIQUAC and UNIFAC models, showing that the fit was poor in terms of Δm for both models, due to the large relative error associated with the very low concentrations of benzene in both phases, while the goodness of fit in terms of F was satisfactory, particularly for the UNIQUAC model. Therefore, The UNIQUAC equation fitted to the experimental data is more accurate than the UNIFAC method of this quaternary system. The main reason for this is that F is fit in the size of the quaternary binodal surface.

List of symbols

a              :               Activity obtained directly from the model by insertion of the experimental
concentrations;    eq. (1)

aij, aji       :               Parameters of the UNIQUAC and NRTL models

F              :               r.m.s. deviation in mole fraction given by eq. (3)

Fa, Fx       :               Objective function given by equations (1) and (2).

LLE         :               Liquid-liquid equilibria

mk           :               Experimental solute distribution ratio; eq. (4)

m ^ k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiqab2gagaqcam aaBaaaleaacaWGRbaabeaaaaa@3807@          :               Calculated solute distribution ratio; eq. (4)

Dm          :               r.m.s. relative error in the solute distribution ratio given by eq. (4)

M            :               Number of tie lines; equations (3) and (4)

n              :               Number of the components in the system (3) or (4)

Pi             :               Quaternary planes for the construction of the binodal surface

Pn            :               Parameter in the penalty term; equations (1) and (2)

PP           :               Plait point

Q             :               Constant value in the penalty term; equations (1) and (2)

r.m.s.      :               Root mean square deviation

w i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4DamaaBa aaleaacaWGPbaabeaaaaa@380A@           :               Mass fraction of component i

x ijk MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiEamaaBa aaleaacaWGPbGaamOAaiaadUgaaeqaaaaa@39EA@         :               Experimental mole fraction of the ith component in the jth phase on the kth tie line
(Equations (2) and (3))

x ^ ijk MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabeiEayaaja WaaSbaaSqaaiaadMgacaWGQbGaam4Aaaqabaaaaa@39FA@        :               Calculated mole fraction of the ith component in the jth phase on the kth tie-line
(Equations (2) and (3))

w i ' MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4DamaaDa aaleaacaWGPbaabaGaai4jaaaaaaa@38B6@           :               Mass fraction of the ithcomponent in the methanol (’) phase

w i " MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4DamaaDa aaleaacaWGPbaabaGaaiOiaaaaaaa@38B1@          :               Mass fraction of the ith component in the hydrocarbon (’’) phase

Subscripts

i               :               lower index-denoting components (1-4)

j               :               lower index-denoting phases (’ or ’’)

k              :               lower index denoting tie lines (1 to M)

’               :               methanol phase

’’              :               hydrocarbon phase

Greek letters

α ij MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS baaSqaaiaadMgacaWGQbaabeaaaaa@399E@ : Non-randomness parameter for the NRTL equation

Acknowledgement

Financial support from the Consejo de Investigaciones de la Universidad Nacional de Tucumán, Argentina (CIUNT, Grant 26/E518) and Secretaria de Políticas Universitarias de la Nación Argentina “Proyecto Jorge Sabato” Res. Nº 1150 SPU, 20/02/2016 are gratefully acknowledged.

References

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