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Ind. Eng. Chem. Res. 2006, 45, 5086-5097
Optimization of Aromatics Extraction of Naphtha Reformate by Propylene Carbonate/Diethylene Glycol Mixed Solvent Haitham M. S. Lababidi,* Sami H. Ali, and Mohamed A. Fahim Chemical Engineering Department, College of Engineering & Petroleum, Kuwait UniVersity, P.O. Box 5969, Safat 13060, Kuwait
Extraction of aromatics from naphtha reformate using a mixed solvent composed of propylene carbonate (PC) and diethylene glycol (DEG) has been considered in this study. Interaction parameters for DEG were obtained experimentally from the equilibrium data for two ternary systems (octane/toluene/DEG and octane/ PC/DEG). An experimental program was set up to study the extraction performance of aromatics using a mixed solvent system. On the other hand, a mathematical model was developed and compared with experimental data. Simulation results showed excellent agreement with the experimental results. Furthermore, an optimization model was developed to obtain the optimal extraction conditions, which minimize the operating cost and solvent losses. The optimization variables considered are solvent-to-feed ratio, solvent-to-solvent ratio, and operating temperature. The optimization model is highly nonlinear because of the fact that solvents and naphtha properties were estimated using the UNIFAC model. Optimization results were compared favorably with the experimental results. Introduction There are a number of solvents used for extracting aromatics from naphtha reformate. Propylene carbonate (PC) is a good solvent for the extraction of aromatics.1-4 Other good solvents for this extraction process are diethylene glycol (DEG),5 triethylene glycol,6 and tetraethylene glycol.7,8 Sulfolane has been proven to be of commercial use for the extraction of aromatics from naphtha reformate.5 Using mixed solvents for the extraction of aromatics is commonly practiced to balance between selectivity and capacity of different solvents. Radwan et al.9 studied the extraction of aromatics from petroleum naphtha by 1-cyclohexyl-2-pyrrolidone/ethyl carbonate mixed solvents. In their study, the extraction runs were performed at different temperatures, solvent-tofeed ratios, and solvent-to-solvent ratios. Saha and co-workers7 proposed that mixtures of tetraethylene glycol/N-formylmorpholine and tetraethylene glycol/N-methylpyrolidone are good solvents for extraction of aromatics from naphtha reformate. Even though the extraction of aromatics (benzene, toluene, and xylene) from naphtha reformate has been commercially available for the last few decades, we believe that determining the optimal operating conditions is particularly important in studying the performance of the extraction process, especially when mixed solvents are used. Ali et al.1 studied the phase equilibria for the extraction of aromatics from synthetic naphtha reformate with PC as a solvent. The operating conditions leading to maximum recovery of aromatics were optimized. They considered PC as one group for better predictions using UNIFAC.1 The current study investigates the improvement of the extraction process by mixing PC with DEG. The main objective is to determine the optimum operating conditions for the extraction of aromatics from synthetic naphtha reformate using a mixed PC and DEG solvent. The proposed optimization model utilizes UNIFAC in estimating the interaction parameters for the solvents and synthetic naphtha reformate. In addition to the UNIFAC interaction parameters reported in the open literature1,10 and for better predictions, the * To whom correspondence should be addressed. Tel.: +965 489 5778. Fax: +965 483 9498. E-mail:
[email protected].
current study considered also the phase equilibria for two more ternary systems (octane/toluene/DEG and octane/PC/DEG). Experimental Section The main purpose of the experimental work is to determine the interaction parameters that would supplement those reported in open literature for the mixed PC/DEG solvent system. The high purity chemicals used in this study are n-hexane, benzene, n-heptane, methyl cyclohexane, isooctane (2,2,4-trimethyl pentane), toluene, n-octane, ethylbenzene, p-xylene, DEG, and PC. These chemicals were obtained from Fluka and used as received. The purity of these chemicals was measured by gas chromatography and found to be higher than 99.0%. Five water-jacketed glass cells were used for extraction. The 85 cm3 cells were connected to a water bath fitted with a Haake DC1 thermostat, which enabled us to control the cells temperatures within (0.2 K. Different mixtures were placed in the extraction vessels, followed by stirring for 1 h and then waiting for settling over a period of 24 h. After equilibrium is reached, samples were withdrawn by syringes from both the raffinate and extract phases. Gas chromatography was used to measure the equilibrium concentrations of all the components in the ternary and the multicomponent systems in both the extract and the raffinate phases. A Chrompack CP9001 gas chromatograph equipped with a flame ionization detector (FID) was used. A WCOT fused silica (100 m length × 0.25 mm inside diameter) capillary column coated with CP SIL PONA CB having a DF ) 0.5 µm was used. The FID and the injection port temperatures were maintained at 573 K. The oven temperature program used was as follows: initial temperature of 308 K, holding for 15 min at 308 K, then increasing the temperature by a ramping rate of 1 K/min until reaching a temperature of 333 K, and holding for 20 min at 333 K, followed by increasing the oven temperature by a ramping rate of 2 K/min for 90 min. The flow rate of the carrier gas was adjusted so that toluene eluted at 30 min. The GC was calibrated by the external standard calibration method using calibration mixtures composed of different weighed ratios of pure components. The reproducibility for all the components was found to be higher than 99.7%. Detailed hydrocarbon
10.1021/ie050537r CCC: $33.50 © 2006 American Chemical Society Published on Web 06/08/2006
Ind. Eng. Chem. Res., Vol. 45, No. 14, 2006 5087
Figure 1. Experimental and correlated phase behavior for the ternary system toluene/octane/DEG. Table 1. Experimental LLE Data for Ternary Systems octane/DEG/PC system raffinate phase (%)
octane/toluene/DEG system
extract phase (%)
raffinate phase (%)
extract phase (%)
temp (K)
octane
DEG
PC
octane
DEG
PC
octane
toluene
DEG
octane
toluene
DEG
283
95.46 97.42 97.54 97.23 96.85
3.33 1.51 1.36 1.89 1.94
1.21 1.07 1.11 0.88 1.21
1.82 2.07 0.07 0.54 0.06
16.10 45.13 61.76 32.19 81.69
82.09 52.80 38.17 67.27 18.25
7.90 17.00 26.00 34.00 45.00 55.00 74.00 77.51
88.10 80.13 71.22 63.38 52.47 43.03 23.67 20.85
3.00 2.88 2.78 2.62 2.53 1.97 2.33 1.63
0.01 0.01 0.02 0.02 0.03 0.03 0.05 0.04
0.79 0.81 0.70 0.68 0.43 0.38 0.35 0.17
99.20 99.19 99.28 99.30 99.55 99.59 99.60 99.79
293
96.67 97.60 97.79 97.79 97.32
2.00 1.34 1.11 1.17 1.69
1.33 1.07 1.10 1.04 0.99
2.00 1.07 0.43 0.09 0.07
26.26 28.12 40.95 55.30 82.50
71.75 70.81 58.63 44.61 17.43
14.60 22.90 30.50 45.00 49.00 66.00 82.00
82.30 74.20 66.88 52.59 48.68 32.31 16.02
3.11 2.90 2.62 2.42 2.32 1.69 1.98
0.02 0.02 0.03 0.03 0.03 0.05 0.04
1.38 1.28 1.14 0.92 0.81 0.47 0.35
98.60 98.70 98.83 99.05 99.16 99.48 99.61
303
97.10 97.69 97.96 97.43
1.33 1.16 1.02 1.69
1.57 1.16 1.02 0.88
1.67 2.49 0.17 0.07
34.61 17.67 53.87 81.68
63.72 79.84 45.97 18.25
14.60 23.20 30.70 44.90 50.00 71.00 83.00
80.20 71.70 64.40 50.60 47.10 26.50 14.70
5.20 5.10 4.90 4.50 2.90 2.50 2.30
0.03 0.03 0.04 0.03 0.05 0.05 0.06
1.62 1.97 1.82 1.50 1.39 0.75 0.58
98.36 98.00 98.14 98.48 98.56 99.20 99.36
313
94.15 95.64 96.09 96.39 95.86
4.96 3.12 2.55 2.08 2.20
0.89 1.25 1.36 1.53 1.94
0.00 1.60 3.06 4.56 5.06
77.69 61.55 49.33 32.84 6.67
22.31 36.85 47.61 62.61 88.27
14.90 25.00 33.00 45.00 62.70 75.00
79.10 69.10 62.00 50.10 32.50 20.30
6.00 5.90 5.00 4.90 4.80 4.70
0.10 0.10 0.10 0.12 0.13 0.15
3.20 2.90 2.50 2.20 1.00 0.50
96.70 97.00 97.40 97.68 98.87 99.35
analyzer software, which was supplied by Chrompack, was used to handle the data generated by the GC. Two ternary systems were studied: octane/toluene/DEG and octane/PC/DEG. These systems were used to generate the interaction parameters for DEG with PC and with CH2, ACH, and ACCH2 groups. A series of liquid-liquid equilibrium (LLE) measurements were performed over a temperature range of
283-313 K. The GC was used to measure the equilibrium concentrations of the three components in the ternary systems according to the previously mentioned procedure. Equilibrium measurements for both ternary systems at different temperatures are listed in Table 1 and illustrated in Figures 1 and 2. Synthetic naphtha reformate was prepared by mixing nhexane, benzene, n-heptane, methyl cyclohexane, isooctane
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Ind. Eng. Chem. Res., Vol. 45, No. 14, 2006
Figure 2. Experimental and correlated phase behavior for the ternary system PC/octane/DEG. Table 2. Reformate Composition and the Number of Functional UNIFAC Groups in Each of Its Constituents number of UNIFAC groups in each component component 1 2 3 4 5 6 7 8 9
n-hexane benzene n-heptane methyl cyclohexane 2,2,4-trimethylpentane toluene n-octane ethylbenzene p-xylene
mole % CH3 CH2 CH C ACH ACCH3 ACCH2 4.21 3.59 21.81 4.76 2.42 37.19 0.92 4.41 20.69
2 0 2 1 5 0 2 1 0
4 0 5 5 1 0 6 0 0
0 0 0 1 1 0 0 0 0
0 0 0 0 1 0 0 0 0
0 6 0 0 0 5 0 5 4
0 0 0 0 0 1 0 0 2
0 0 0 0 0 0 0 1 0
(2,2,4-trimethylpentane), toluene, n-octane, ethylbenzene and p-xylene. This synthetic mixture had a boiling range of 343411 K and a specific gravity of 0.8. Table 2 shows the composition of the synthetic naphtha reformate as analyzed by the GC, in addition to the number of functional groups present in each of its constituents. The nine solutes constituting the synthetic naphtha reformate correspond to the subgroups: C, CH, CH2, CH3, ACH, ACCH2, and ACCH3. However, PC and DEG, which form the mixed solvent, were each considered as a single UNIFAC group because of the polar nature of these molecules. LLE measurements for the multicomponent systems (naphtha reformate, PC, and DEG) were performed over a temperature range of 288-313 K and solvent- (PC + DEG) to-feed molar ratios, Rstf, of 1.0, 2.0, and 3.0. The molar PC content in the solvent mixture, Rsts, was varied between 57.2 and 87.5%. The equilibrium mixtures of these systems were also analyzed by the GC under the same conditions as those mentioned above. Experimental LLE results for the multicomponent systems considered in this study are included in Table 3a. The critical miscibility temperature, Tcm, was experimentally determined at different conditions. Tcm is defined as the
Figure 3. Schematic diagram of an extraction unit.
temperature at which all the components become completely miscible in one another. This temperature was measured to determine the upper limit temperature at which phase equilibria of a system can be effectively studied. Tcm was measured by adding known volumes of solvents to a known volume of the synthetic naphtha reformate in an 85 cm3 thermostated waterjacketed cell, and the two phases were completely mixed. A magnetic stirrer and a circulating water bath were used to raise the mixture’s temperature gradually and uniformly. The miscibility temperature was marked as the point where the turbidity of the mixture disappears and the two phases become completely miscible in one another. Heating is then cut off, and another reading is then taken when the solution cools and becomes turbid, indicating the beginning of phase separation. The two readings were within (0.2 K difference. The Tcm values obtained at different solvent-to-feed molar ratios and different solvent compositions are listed in Table 4. From Table 4 it can be noticed that the extraction temperatures studied for the different solvent mixtures and solvent-to-feed ratios were much lower than the critical miscibility temperatures. The extraction temperatures were at least 60 K lower than the experimentally determined Tcm. Using the experimental values listed in Table 4, the critical miscibility temperature, Tcm, has been linearly correlated as a function of both the solvent-to-feed ratio, Rstf, and solvent composition, Rsts. The following equation has been obtained with coefficient of correlation R2 ) 0.966:
Tcm ) 402.169 - 6.497(Rstf) - 24.784(Rsts)
(1)
Ind. Eng. Chem. Res., Vol. 45, No. 14, 2006 5089 Table 3. Experimental and Predicted LLE Results (a) Experimental LLE of the Naphtha Reformate + PC-DEG Mixed Solvent S:F ) 1 at 288 K component n-hexane benzene n-heptane methyl cyclohexane 2,2,5trimethylpentane toluene n-octane ethylbenzene p-xylene DEG PC θ Sp Cap TA Sel Yld
87.5% PC
79.3% PC
S:F ) 1 at 303 K 57.2% PC
87.5% PC
79.3% PC
S:F ) 1 at 313 K
57.2% PC at 303 K S:F ) 2
57.2% PC
S:F ) 3
87.5% PC
XexpR
XexpE
XexpR
XexpE
XexpR
XexpE
XexpR
XexpE
XexpR
XexpE
XexpR
XexpE
XexpR
XexpE
XexpR
XexpE
XexpR
XexpE
0.049 0.023 0.282 0.050
0.004 0.017 0.022 0.006
0.054 0.024 0.255 0.052
0.005 0.017 0.023 0.006
0.041 0.025 0.231 0.049
0.003 0.015 0.006 0.003
0.052 0.022 0.285 0.055
0.006 0.017 0.033 0.007
0.050 0.025 0.276 0.052
0.007 0.016 0.029 0.010
0.043 0.022 0.235 0.050
0.004 0.017 0.013 0.003
0.049 0.015 0.269 0.053
0.004 0.014 0.012 0.004
0.055 0.011 0.305 0.061
0.002 0.008 0.011 0.003
0.048 0.020 0.279 0.053
0.009 0.014 0.041 0.009
0.029
0.003
0.025
0.003
0.024
0.001
0.031
0.004
0.030
0.003
0.025
0.001
0.029
0.002
0.035
0.002
0.031
0.004
0.265 0.010 0.034
0.149 0.001 0.015
0.286 0.010 0.036
0.143 0.001 0.014
0.297 0.010 0.037
0.093 0.001 0.009
0.255 0.010 0.032
0.146 0.001 0.016
0.263 0.010 0.035
0.149 0.001 0.015
0.298 0.010 0.037
0.130 0.001 0.012
0.251 0.010 0.033
0.092 0.001 0.010
0.200 0.016 0.029
0.074 0.001 0.009
0.252 0.011 0.033
0.162 0.001 0.016
0.164 0.034 0.060
0.068 0.084 0.631
0.176 0.036 0.046
0.064 0.143 0.581
0.188 0.022 0.076
0.029 0.360 0.480
0.167 0.021 0.070
0.071 0.090 0.609
0.177 0.018 0.064
0.065 0.143 0.562
0.186 0.026 0.068
0.025 0.347 0.447
0.197 0.024 0.070
0.034 0.288 0.539
0.189 0.030 0.069
0.033 0.353 0.504
0.170 0.025 0.078
0.075 0.080 0.589
0.660 0.285 0.512 0.340 5.977 0.504
0.650 0.276 0.456 0.322 4.751 0.474
0.540 0.160 0.267 0.399 6.768 0.242
0.680 0.301 0.525 0.274 4.459 0.521
0.670 0.295 0.490 0.274 4.096 0.503
0.570 0.206 0.339 0.370 5.591 0.322
0.760 0.173 0.302 0.330 5.391 0.524
0.850 0.143 0.289 0.330 7.182 0.647
0.700 0.331 0.562 0.237 3.706 0.573
(b) Predicted LLE of the Naphtha Reformate + PC-DEG Mixed Solvent S:F ) 1 at 288 K component n-hexane benzene n-heptane methyl cyclohexane 2,2,5trimethylpentane toluene n-octane ethylbenzene p-xylene DEG PC
87.5% PC
79.3% PC
S:F ) 1 at 303 K 57.2% PC
87.5% PC
79.3% PC
S:F ) 1 at 313 K
57.2% PC at 303 K 57.2% PC
S:F ) 2
S:F ) 3
87.5% PC
XcalR
XcalE
XcalR
XcalE
XcalR
XcalE
XcalR
XcalE
XcalR
XcalE
XcalR
XcalE
XcalR
XcalE
XcalR
XcalE
XcalR
XcalE
0.046 0.016 0.287 0.058
0.005 0.014 0.023 0.006
0.045 0.015 0.280 0.057
0.005 0.014 0.025 0.007
0.039 0.016 0.236 0.050
0.002 0.013 0.009 0.003
0.046 0.015 0.294 0.059
0.007 0.014 0.033 0.009
0.046 0.015 0.289 0.058
0.007 0.015 0.035 0.009
0.039 0.016 0.241 0.050
0.003 0.014 0.013 0.004
0.045 0.011 0.286 0.058
0.003 0.010 0.013 0.004
0.050 0.008 0.323 0.064
0.003 0.007 0.013 0.004
0.045 0.015 0.289 0.058
0.009 0.014 0.047 0.012
0.038
0.002
0.037
0.002
0.030
0.001
0.039
0.003
0.038
0.004
0.031
0.001
0.038
0.001
0.044
0.001
0.039
0.005
0.244 0.014 0.039
0.142 0.001 0.016
0.246 0.014 0.038
0.143 0.001 0.017
0.278 0.012 0.041
0.094 0.000 0.010
0.241 0.015 0.038
0.151 0.001 0.018
0.240 0.015 0.037
0.152 0.001 0.019
0.272 0.012 0.040
0.106 0.000 0.012
0.229 0.014 0.037
0.088 0.000 0.010
0.196 0.017 0.033
0.073 0.000 0.009
0.238 0.015 0.037
0.156 0.002 0.020
0.192 0.027 0.039
0.073 0.071 0.647
0.198 0.029 0.040
0.071 0.126 0.588
0.214 0.025 0.059
0.030 0.342 0.495
0.191 0.015 0.047
0.080 0.073 0.610
0.195 0.019 0.047
0.079 0.125 0.555
0.212 0.024 0.062
0.037 0.332 0.478
0.213 0.020 0.049
0.036 0.336 0.499
0.207 0.018 0.41
0.033 0.343 0.514
0.188 0.017 0.060
0.086 0.070 0.579
%RMSD
1.040
1.272
0.969
0.963
1.005
1.261
1.589
0.939
0.847
R2
0.994
0.991
0.995
0.995
0.994
0.990
0.986
0.995
0.996
θ Sp Cap TA Sel Yld
0.650 0.282 0.494 0.332 5.840 0.489
0.650 0.286 0.493 0.316 5.267 0.489
0.534 0.163 0.269 0.391 6.479 0.242
0.688 0.317 0.544 0.278 4.679 0.557
0.688 0.320 0.542 0.264 4.288 0.557
0.553 0.190 0.311 0.362 5.472 0.286
0.764 0.165 0.292 0.336 6.063 0.504
0.853 0.143 0.276 0.313 6.637 0.641
0.721 0.351 0.580 0.210 3.489 0.612
Table 4. Critical Miscibility Temperatures for the Naphtha Reformate-Solvent Systems
Mathematical Model A schematic diagram of the extraction process is shown in Figure 3. A material balance on the system gives the following equations:
F ) FN + F S ) P E + P R
(2)
xFi ) θxEi + (1 - θ)xRi
(3)
∑i xFi ) ∑i xEi ) ∑i xRi ) 1
(4)
F is the total feed flow rate to the extraction unit which consists of naphtha FN and the solvent FS. The product streams are an
PC in solvent (% molar basis)
solvent-to-feed molar ratio (S:F)
critical miscibility temperature, Tcm (K)
87.5 79.3 57.2 57.2 57.2
1 1 1 2 3
374 376 381 376 368
extract PE which is rich in aromatics, and a raffinate stream PR, while θ is the extract-to-feed ratio, θ ) PE/F. xFi , xEi , and xRi are the mole fractions of component i in the feed, extract, and raffinate streams, respectively. The solvent-to-feed ratio is
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Ind. Eng. Chem. Res., Vol. 45, No. 14, 2006
Table 5. UNIFAC Interaction Parameters According to Equation 14
a
component i
component j
aij0 (K)
aij1
aji0 (K)
aji1
ref
ACH ACH ACCH2 CH2 ACH ACCH2 CH2 ACH ACCH2 PC
a
-6.73 -155.40 252.50 487.54 194.76 726.34 62.86 12.67 2000.0 379.49
-0.566 -1.489 2.650 1.004 -3.195 8.464 1.133 -1.333 4.024 6.667
64.450 366.600 -93.370 41.701 -49.096 -6.005 1333.5 186.670 600.0 -43.333
0.375 13.220 -1.103 -0.778 2.037 0.325 -66.667 2.667 -11.900 -7.333
10 10 10 1 1 1 this work this work this work this work
CH2 ACCH2b CH2 PC PC PC DEG DEG DEG DEG
C, CH, CH2, and CH3 belong to the same subgroup. b ACCH2 and ACCH3 belong to the same subgroup.
defined as Rstf ) FS/FN. Hence, the total feed defined by eq 2 becomes
Phase equilibrium between the extract and the raffinate phases is defined by the distribution coefficient as
As the primary aim of naphtha reformate extraction with different solvents is to maximize the total aromatics in the extract, an important desirable property to be studied is the relative increase in the concentration of the total aromatic components, TA. It indicates the increase in the aromatics content of the extract phase with respect to the original feed (naphtha reformate without solvents). TA is defined as
xEi
γRi
xEA
xi
γEi
F ) FN(1 + Rstf)
Ki )
) R
(5)
(6)
where γEi and γRi are the activity coefficients of component i in the extract and raffinate phases, respectively. Rearranging eqs 3 and 6, we get
xEi ) or
∑i
KixFi 1 + θ(Ki - 1)
{
KixFi
1 + θ(Ki - 1)
}
)1
(7)
(8)
A number of performance parameters will be defined. Extraction yield, Yld, is defined as the ratio of the aromatic components in the extract phase to that in the feed. On the other hand, solvent capacity, Cap, is defined as the ratio of the aromatic components in the extract phase to that in the raffinate.
Yld )
xEAPE xFAF
Cap )
xEA xRA
)
)
xEA θ xFA γRA γEA
(9)
(10)
Solvents should be selective in extracting aromatics over paraffins. Selectivity of the solvent, Sel, is defined by the following ratio:
Sel )
xEA/xRA xEP /xRP
)
γRA/γEA γRP /γEP
(11)
Solvent power, Sp, indicates the mole fraction of hydrocarbons in the extract phase (i.e., extract stream without the solvents). The higher the solvent power, the lower the cost of recovering and recycling the solvents. The solvent power is defined as
Sp ) xEA + xEP
(12)
TA )
xEA + xEP
- xFN A (13)
xFN A
Interaction Parameters The UNIFAC model has been used to predict the phase equilibrium between the extract and the raffinate phases. The R and Q values (group volume and surface parameters) for the subgroups in the systems studied were obtained from the literature.10 For PC, the values of R and Q were set equal to 3.2815 and 2.736, respectively, as used by Ali et al.,1 whereas the R and Q values for DEG were obtained from Bastos et al.11 and were set equal to 4.0013 and 3.568, respectively. The interaction parameters for the subgroups CH2, ACH, and ACCH2 were adopted from the published work of Hansen et al.10 (see Table 5). The interaction parameters for PC with respect to the subgroups CH2, ACH, and ACCH2 were obtained from our previous work, Ali et al.,1 as reported in Table 5. UNIFAC interaction parameters, as function of temperature, are described by eq 14.
aij ) aij0 + aij1(T - 298.15)
(14)
The UNIFAC interaction parameters for PC with respect to DEG and the subgroups CH2, ACH, and ACCH2 were obtained as part of the current study by performing a series of LLE measurements for two ternary systems (octane/toluene/DEG and octane/PC//DEG), as described before, over the temperature range of 283-313 K. The interaction parameters at different temperatures for the group pairs containing DEG were determined using an iterative program described by Sørensen et al.12 and were used by a number of researchers.13,14 The program uses two objective functions, Fa and Fx (eqs 15 and 16). Fa is an activity residual function that is evaluated first, and after convergence, the resulted parameters are used in the second function, Fx, which is a concentration residual function to fit the experimental concentrations. The objective functions are defined as12 M N
Fa )
∑∑ k)1 i)1
[ ] aIik - aIIik
aIik + aIIik
2
Na
+Q
∑Pn2 n)1
(15)
Ind. Eng. Chem. Res., Vol. 45, No. 14, 2006 5091 M
Fx )
∑i (xEi γEi - xRi γRi )2 e
N
∑ min ∑ ∑ (xijk,Exp - xijk,Pred)2 + k)1 i)1 j)I,II Na
Q
∑
n)1
P2n
[ ( )]
I γS∞ + ln K∞s II γS∞
2
(16)
where xijk,Exp is the experimental mole fraction of component i in phase j (j ) I, II) for the kth tie line, while xijk,Pred is the mole fraction of the predicted tie line. aIik and aIIik are the activities of component i for the kth tie line for phases I and II, respectively. M, N, and Na are numbers of tie lines, components, and interaction parameters, respectively. Both objective functions include penalization terms to reduce the risks of multiple solutions associated with parameters of high values. In these terms, Q and Pn are the penalties. The third term of Fx (eq 16) accounts for working with low solute mole fractions, in which I II γS∞ and γS∞ represent the activity coefficients calculated at infinite dilution in both phases and K∞s is the ratio between solute concentrations in the two phases at infinite dilution. The quality of correlation is measured by the residual function Rx which is defined as14
[∑∑ ∑ M N
Rx ) 100
k)1 i)1 j)I,II
]
(xijk,Exp - xijk,Pred)2 6M
Experimental and predicted compositions of the extract and raffinate phases for different temperatures and solvent-to-feed and solvent-to-solvent ratios are listed in Table 3. Accuracy in predicting the experimental mole fractions of both phases has been quantified by calculating the percent-root-mean-squareddeviation (%RMSD) and the coefficient of determination (R2), which were evaluated as follows:
%RMSD ) 100 R2 )
Simulation Results The mathematical model expressed by eqs 2-8 will be validated against the experimental results presented in Table 3. This model will then be considered as part of the optimization formulation presented below. The first task is to predict the compositions of the extract and raffinate phases, xEi ’s and xRi ’s, and to compare them against the experimental compositions. The computation procedure is similar to the common bubble-point/flash calculation procedure. Given the extraction temperature, naphtha composition, solvent-to-feed ratio, and composition of the solvent mixture and starting from initial guesses of the equilibrium constants, eq 8 is solved for θ, followed by calculating the compositions of the extract and raffinate phases using eqs 6 and 7. UNIFAC is then used, with the interaction parameters listed in Table 5, to calculate new activity coefficients, which will result in corrected values of equilibrium constants (eq 6). This procedure is iteratively repeated until the error is less than a specified tolerance ( ) 1 × 10-10). The termination error is specified as
Sr 2N
0.5
St - Sr St
N
∑ i)1
(17)
As stated previously, the interaction parameters between each pair of the UNIFAC groups were fitted linearly with temperature according to eq 14. The resulted interaction parameters for the group pairs containing the DEG group are reported in the last four rows of Table 5. Experimental and predicted concentrations of the octane/ toluene/DEG and octane/PC/DEG glycol ternary systems are compared in Figures 1 and 2 for different temperatures. These plots show that the UNIFAC model adequately represents the studied systems with minor deviations. This deviation is due to the fact that the combinatorial expression of the UNIFAC model does not satisfactorily account for the combinatorial effects at dilute regions.15 Prediction accuracy is indicated also by the low Rx values (reported in Figures 1 and 2). Moreover, the overall Rx and confidence interval values for the two ternary systems are 1.53 ( 0.7 and 1.56 ( 0.8, respectively.
[ ]
(19) (20)
where N is the number of components (N ) 11; 9 components in naphtha and 2 solvents), Sr is the sum of the squares of the errors, and St is the sum of the squares of the residuals between the data point and the mean. Sr and St are defined as
Sr )
0.5
(18)
N
E E (xi,exp - xi,pred )2 +
N
St )
R R (xi,exp - xi,pred )2 ∑ i)1
(21)
N
E R (xi,exp - xjE)2 + ∑(xi,exp - xjR)2 ∑ i)1 i)1
(22)
Results listed in Table 3 demonstrate clearly that the mathematical model simulates the equilibrium data quite accurately. The average %RMSD error is 1.098%, whereas the maximum error is 1.589%, which is considerably low knowing that 11 concentrations are predicted for each phase. Moreover, experimental and predicted compositions are compared by the parity plot shown in Figure 4. The overall R2 value is 0.9929, which indicates excellent fit of experimental data. Simulated and experimental values of the yield, capacity, selectivity, total aromatics, and solvent power are listed also in Table 3. These values are compared in Figure 5 for different values of solvent-to-feed ratios. Accuracies in predicting these parameters were quantified by R2 values, which were calculated as 0.956, 0.970, 0.892, 0.968, and 0.984, respectively. Figures 6-10 illustrate the experimental and predicted values of yield, capacity, selectivity, total aromatics, and solvent power, respectively, as a function of the composition of the solvent mixture. These plots illustrate that the mathematical model predicted the experimental data excellently. They also indicate
Figure 4. Comparison of experimental and predicted compositions of extract and raffinate phases.
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Figure 8. Experimental and predicted selectivity for different solvent compositions at Rstf ) 1. Figure 5. Experimental and predicted yield, capacity, solvent power, total aromatics, and selectivity for different solvent-to-feed ratios at Rsts ) 57.2% and 303 K.
Figure 9. Experimental and predicted total aromatics for different solvent compositions at Rstf ) 1.
Figure 6. Experimental and predicted yields for different solvent compositions at Rstf ) 1.
Figure 10. Experimental and predicted solvent power for different solvent compositions at Rstf ) 1.
Figure 7. Experimental and predicted capacities for different solvent compositions at Rstf ) 1.
the accuracy of the determined UNIFAC interaction parameters. Hence, the model can be confidently used in evaluating the performance of the extraction unit. Figure 5 shows that increasing the solvent-to-feed ratio will result in increasing both the yield (Yld) and the selectivity (Sel), decreasing the solvent capacity (Cap) and power (Sp) as well as the total aromatics (TA). The significance of using mixed solvents is illustrated in Figures 6-10. These figures show clearly that maximum yield, capacity, and solvent power values are realized at specific values of solvent-to-solvent composition, while selectivity and total aromatics plots (Figures 8 and 9) exhibit a minimum. In fact, all plots indicate that the performance of the mixed solvent (PC + DEG) is superior to that of a single solvent (100% PC). Such
behavior provides an attractive incentive for conducting an optimization study to determine the optimum solvent composition. Extraction temperature is also an important factor which should be studied. Variations of the extraction yield, capacity, solvent power, selectivity, and total aromatics with operating temperature are illustrated in Figure 11. The plots show that the first three parameters increase with temperature, while the total aromatics and selectivity decrease with increasing temperature. It is necessary that the extraction temperature is kept well below the critical miscibility temperature (Tcm). In fact, the simulation model, which is based on UNIFAC LLE calculations, becomes inapplicable as Tcm is approached. To include the critical miscibility temperature in the analysis, a dimensionless temperature parameter will be introduced as T/Tcm. This parameter was used by Singh16 in studying the extraction of raw lubricating distillate. Tcm is estimated using the correlation presented by eq 1. Simulation runs indicate that
Ind. Eng. Chem. Res., Vol. 45, No. 14, 2006 5093
Figure 11. Experimental and predicted yield, capacity, solvent power, total aromatics, and selectivity for different operating temperatures at Rstf ) 1, Rsts ) 0.875, and Tcm ) 374 K.
the experimental data may be accurately predicted for Tcm/T values less than 0.85. Optimization Model Simulation results presented above revealed that the parameters affecting the separation performance are the solvent-tofeed ratio, Rstf, solvent composition, Rsts, and extraction temperature, T. One more objective of the current study is to investigate the impact of these parameters on the optimum performance of the extraction process using mixed solvent (PC + DEG) systems. An optimization model will be first formulated. This involves formulating an objective function that would satisfy certain separation criteria and subject it to a set of constraints. Moreover, the simulation model presented and tested above will be utilized for LLE calculations and for determining the values of the performance parameters. The following factors should be considered in formulating the objective function: 1. The amount of aromatics in the extract phase should be maximized. This is equivalent to maximizing the yield (Yld). 2. The quantities of the solvent should be minimized. This minimizes the cost of solvent recovery and makeup. Such an objective may be achieved by maximizing the total aromatics content of the extract phase, which is the equivalent of maximizing TA. 3. As a result of the fact that PC is characterized as a high capacity solvent and DEG is characterized as a high selectivity solvent, it is important to determine the optimal amounts of each solvent. Salem17 reported that PC has a higher capacity than triethylene glycol for the extraction of aromatics from a mixed aromatics and paraffins feed, whereas triethylene glycol has higher selectivity for aromatics than PC. The parameter Rsts represents the solvent composition (molar composition of PC in the mixed solvent). From eqs 10 and 11, it is clear that the capacity and selectivity are functions of aromatics compositions. Hence, they have been also considered by items 1 and 2 above. However, Rsts should be included in the objective function to account for the cost difference of the two solvents as well as the differences in physical properties such as viscosity and acidity. 4. Solvent recovery is also an important issue. Solvents, which concentrate in the extract phase, should be recovered and reused. The more solvents used, the higher the cost; the more solvent in the extract phase, the higher the separation and recovery cost. The cost of solvents is accounted for by item 2 above. However, recovery costs can be minimized by minimizing the composition
of the solvents in the extract phase, hence, maximizing the solvent power (Sp). 5. Extraction temperature should be optimized as well. Temperature should be as low as possible to reduce the energy cost. Another consideration is that for efficient separation, temperature should be far below the critical miscibility temperature (Tcm). As discussed above, T/Tcm should be less than 0.85. The best approach to fulfill the above stated factors is to develop an objective function that accounts for the main cost items of the extraction process. The assumptions used in developing the cost function can be summarized as follows: 1. Solvents are completely recovered from the extract phase. Extracted product consists of aromatics and paraffins only. 2. Solvents are not recovered from the raffinate stream. Amounts left in the raffinate product are considered as losses. It is assumed here that the cost of solvent recovery from the raffinate stream is not economically feasible. 3. Solvent recovery is carried out using flash separation. Normal flash temperatures of PC and DEG are 513 and 518 K, respectively. On the other hand, the normal flash temperature of p-xylene (the heaviest aromatic component in naphtha) is 411 K. Hence, flash separation is adequate, and the mixed solvent stream is recovered from the bottom of the flash unit. 4. The cost of heating the extract stream fed to the flash unit is assumed constant at $4/m3, while the cost of cooling water used to cool the aromatics-rich product is $2.5/m3. 5. Cost of the PC solvent is 1.75 times the cost of the DEG solvent. This factor was derived from market prices of both solvents. Prices of both industrial scale and high purity solvents were considered. The volumetric flow rate of the raw naphtha feed FN has been considered as a basis in developing the cost function. The proposed objective function consists of three cost items in addition to one benefit item. The cost items are solvent makeup cost, solvent recovery cost, and aromatic losses cost, while the benefit cost accounts for added value of the aromatics-rich product. The constituents of the objective function are defined in the following sections: 1. Cost of Makeup Amounts of PC and DEG Solvents, CS. A unit flow of naphtha feed demands Rstf of the mixed solvent. This amount consists of the Rsts fraction of PC solvent and 1 - Rsts of DEG solvent. Amounts of solvent makeup are determined as the total demanded amounts less the amounts recovered from the extracted product stream. Hence, PC and DEG makeup amounts, FPC and FDEG, are expressed respectively as
FPC ) FNRsts[Rstf - (1 + Rstf)θxEs ]
(23)
FDEG ) FN(1 - Rsts)[Rstf - (1 + Rstf)θxEs ]
(24)
and
Cost of PC solvent relative to the cost of DEG solvent has been used, rather than actual costs of both solvents. The main benefit of this representation is in performing sensitivity cost analysis later. On the basis of the reviewed cost data18 the cost of PC solvent is assumed to be βS times the cost of DEG solvent. As a result, the solvent makeup cost can be expressed as
CS ) λS(βSFPC + FDEG)/FS
(25)
where λS is a cost parameter ($/m3) accounting for unit cost of
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Figure 12. Value added benefit for aromatics purity in the extract stream (eq 28). TA ) total aromatics, Y ) eB1TAB2, B1 ) βv1, B2 ) βv2.
DEG solvent in addition to a factor for scaling the cost items. FS is the molar density of the solvent. 2. Solvent Recovery Cost, CR. Solvent recovery is performed by a simple flash operation. It is assumed that the feed (which is the extract stream from the extraction unit) is introduced to the flash unit as saturated liquid. CR consists of two terms: the cost of heating the feed to saturation and the cost of cooling the aromatics-rich product. Hence, the solvent recovery cost can be expressed as
CR ) λR(FN/FN)θ(1 + Rstf)[βR1 + βR2(1 - xEs )]
(26)
where βR1 and βR2 are the heating and cooling costs assumed above as $4/m3 of feed to the flash unit and $2.5/m3 of aromatics-rich product, respectively, and λR is cost scaling factor for the solvent recovery cost item. 3. Loss of Aromatics Cost, CA. This cost item considers the amounts of aromatics lost in the raffinate product. It can be simply expressed as
CA ) λA(FN/FN)(1 + Rstf)(1 - θ)
(27)
In this cost item, λA is the unit cost of aromatics and the scaling cost factor. 4. Product Value Added Benefit, CV. The naphtha extraction process yields a product which is rich in aromatics. Naturally, the value of the product is higher than the value of the raw naphtha feed. Moreover, as the concentration of aromatics increases, the value or selling price of the product will be higher. This type of benefit is known as “value added” which presents the additional profit due to increased purity of the product. Value added of the aromatics-rich product is assumed to be exponential with respect to the difference between the aromatics content of the product and that of the feed stream. The value added benefit can be expressed as
CV ) λV(FN/FN)(1 + Rstf)(1 - xEs )[exp(βV1TAβV2)]
(28)
where λV is a scaling factor for this cost item, while βV1 and βV2 describe the exponential behavior of the value added benefit. The exponential term of eq 28 is shown graphically in Figure 12 with respect to the total aromatics (TA). The plots indicate the increase in the value of the naphtha feed for different values of the parameters βV1 and βV2. For instance, if the aromatics content of the naphtha feed is 65%, TA ) 0.3 (30%) means that the extraction unit has enriched the aromatics content of the extract stream to 85% (i.e., xEA - xFA ) 0.2). In this case, the value of the product stream would be 1.8 times that of the feed for βV1 ) 6 and βV2 ) 2 and twice the value of the feed when
Figure 13. Cost function for T ) 303 K. Table 6. Values of the Parameters Used in the Optimization Model parameter
value
parameter
value
βR1 βR2 βS βv1 βv2
4.0 $/m3 2.5 $/m3 1.75 6.0 1.5
λA/FN λR/FN λS/FS λV/FN
0.750 $/kmol 0.025 $/kmol 0.650 $/kmole 0.350 $/kmole
increasing the value of βV1 to 8. Decreasing the value of βV2 increases the value of the product stream. As shown in Figure 12, for TA ) 0.3 and βV1 ) 6, the product value increases by threefold and fourfold for βV2 ) 1.5 and βV2 ) 1.25, respectively. On the basis of the cost items defined above, the objective function of the optimization model may be defined as minimizing the sum of four cost items:
min z ) CS + CR + CA - CV
(29)
The optimization model consists of an objective function (eq 29), subject to equality constraints representing the material balance and equilibrium model described by eqs 2-8. The optimization (decision) variables are the solvent-to-feed ratio, Rstf, and the solvent composition, Rsts. The extraction temperature is not considered as a decision variable; however, its effect will be investigated by solving the optimization model at different temperatures. For every iteration in solving the optimization model, eq 8 is solved for θ, followed by evaluating the UNIFAC model to determine Ki’s from the activity coefficients, γEi and γRi . This involves two inner loops one for θ and the other for the K values. The proposed optimization model is a nonlinear programming problem (NLP), which was solved using the Optimization Toolbox of MATLAB.19 The optimization method used is Levenberg-Marquardt with a line search algorithm. Results and Discussion The optimization model proposed in the previous section is solved for the values of the parameters listed in Table 6. Values of the cost scaling factors, λ’s, have been set to balance the four elements of the objective function (eq 29) and avoid the dominance of one element. A unit molar flow of feed naphtha has been considered as a basis. Figure 13 illustrates the shape of the cost function (eq 29) when evaluated for a range of solvent-to-feed ratios (0.5 e Rstf e 2.5) and solvent compositions (0 e Rsts e 1) at 303 K. The surface shown in Figure 13 clearly indicates a minimum value of the objective function close
Ind. Eng. Chem. Res., Vol. 45, No. 14, 2006 5095
Figure 16. Optimal yield, solvent power, and total aromatics versus extraction temperature. Figure 14. Yield of extraction at T ) 303 K.
Table 7. Effect of Cost Parameters on the Optimization Results cost parameters
Figure 15. Value of the objective function and the optimum solvent-tofeed ratio and solvent composition versus extraction temperature.
to Rstf ) 1.5 and Rsts ) 0.85. Similarly, a corresponding surface showing the yield of the extraction process is plotted in Figure 14. The plot exhibits a maximum close to the PC composition of 0.85 in the solvent mixture, which is consistent with the minimum value of the cost function. Furthermore, Figure 14 shows also that the yield increases as the solvent-to-feed ratio increases. However, increase in yield is compromised with the excessive increase in solvent makeup and recovery cost. For this reason, the objective function has been formulated as a function of the extraction cost rather than the performance measures such as the yield, selectivity, and total aromatics. The optimization model was solved for the two decision variables, Rstf and Rsts, using the cost parameters listed in Table 6, and for a range of extraction temperatures. Figure 15 shows the optimal solvent-to-feed ratio and solvent composition values as a function of extraction temperature, together with the value of the cost function. The plots in Figure 15 demonstrate clearly that the extraction temperature has a minimal effect on the optimization results. The optimal solvent-to-feed ratio decreased slightly from 1.4 at 288 K to 1.3 at 310 K. Similarly, the PC composition in the mixed solvent varied between 0.84 and 0.87, while the cost function changed from 0.355 to 0.315. Optimal yield (Yld), solvent power (Sp), and total aromatics (TA) are plotted in Figure 16 as a function of the extraction temperature. Both the optimal yield and the solvent power increase with increasing temperature, while total aromatics decreases with increasing temperature. Nevertheless, such variations are again not significant. Hence, it can be concluded that extraction temperature is not a critical factor for the system considered in this study.
optimization results
βv1
βv2
βs
Rstf
Rsts
z
Yld
Sp
TA
Sel
6.0 6.0 6.0 6.0 6.0 8.0
1.5 1.5 1.5 1.25 2.0 2.0
1.75 1.0 2.0 1.75 1.75 1.75
1.339 1.460 1.314 1.383 1.304 1.306
0.862 0.875 0.858 0.876 0.853 0.856
0.339 0.297 0.352 0.296 0.374 0.366
0.634 0.660 0.628 0.642 0.626 0.626
0.273 0.270 0.273 0.274 0.272 0.273
0.276 0.267 0.278 0.272 0.279 0.279
5.44 5.68 5.39 5.60 5.34 5.36
The next step is to study the sensitivity of the optimization results to the values of the cost parameters used in the objective function. The parameters considered here are those related to the cost of the solvents, βs, and the product value added benefit, βv1 and βv2. The base values for these parameters are listed in Table 6. The cost of PC has been assumed in the base case as 1.75 times that of the DEG solvent. Values of βs that are considered in the sensitivity analysis are βs ) 1 and βs ) 2; that is, both solvents have the same cost, and the cost of PC is twice the cost of DEG, respectively. On the other hand, values of βv1 and βv2 that are considered in the sensitivity analysis are those plotted in Figure 12. Sensitivity analysis results are listed in Table 7 as average values over the temperature interval 288-310 K. The fist row represents the base case results discussed above and plotted in Figures 15 and 16. In general, all results show slight deviations from the base case. However, it is clear that the impact of the solvent costs on the optimal values of the decision parameters (Rstf and Rsts) is more significant than that of the product value added cost. In fact, maximum deviation is shown for the case where PC and DEG solvents are assumed to have the same cost (βs ) 1). Slight variations in optimization results are also apparent in values of the performance parameters. The yield, total aromatics, solvent power, and selectivity varied less than 10% compared with the base case. On the basis of the sensitivity analysis results, we can confidently postulate that for the mixed-solvent extraction system considered in this study, the optimum solvent-to-feed ratio is around 1.5, while the PC composition in the mixed solvent is around 85%. These results are consistent with the experimental results discussed above and plotted in Figures 6-10. Conclusions Extraction of aromatics from naphtha reformate using the mixed PC + DEG solvent system has been investigated experimentally and mathematically in this study. Experimental runs were performed for deriving the phase equilibria interaction
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parameters as well as for determining the extraction performance of the mixed solvent. A mathematical model was developed to validate and simulate the experimental results. Decision variables used for both the experimental runs and the simulation model are the solvent-to-feed ratio, solvent-to-solvent ratio, and extraction temperature. Defined performance parameters include the yield, capacity, selectivity, total aromatics, and solvent power. Furthermore, an optimization mathematical model has been proposed to determine the optimum values of the decision variables for the proposed mixed solvent system. The proposed mathematical model simulated the equilibrium experimental data quite accurately. Experimental and simulated values of the performance parameters showed excellent agreement. Moreover, both experimental and simulation results demonstrated clear optimum trends with respect to the composition of the mixed solvent. For further justification of the results, an optimization model has been developed which is based on economic measures rather than just optimizing the performance parameters. The factors considered by the optimization model included the solvent makeup and recovery costs, loss of aromatics cost, and product value added benefits. The optimization model was solved to determine the optimum solvent-to-solvent and solventto-feed ratios for a range of extraction temperatures (288-310 K). Optimization results showed also excellent agreement with the experimental results. Furthermore, optimization runs indicated that extraction temperature is not a critical factor in determining the composition of the mixed solvents and the solvent-to-feed ratio. Sensitivity analysis has been conducted to study the impact of the cost parameters on the optimization results. Despite the fact that the costs of solvents have more impact than other cost parameters, variations in optimization results were found not to be significant. Such results provide good evidence that the proposed objective function succeeded in accounting for both the performance and economic factors. On the basis of the experimental, simulation, and optimization results, we can conclude that using 15% DEG solvent increases the aromatics extraction performance of the PC solvent and reduces the solvent-to-feed ratio to as low as 1.5. Acknowledgment The authors are grateful to Dr. Sabiha Q. Merchant for her help during the course of this work. Nomenclature aij ) interaction parameter between molecules i and j CA ) cost of aromatics losses, $/h Cap ) solvent capacity CR ) solvent recovery cost, $/h CS ) cost of makeup solvents, $/h CV ) product value added benefit, $/h DEG ) diethylene glycol F ) total molar flow rate of the feed stream to the extraction unit, kmol/h FDEG ) amount of DEG makeup solvent, kmol/h FN ) molar flow rate of naphtha to the extraction unit, kmol/h FPC ) amount of PC makeup solvent, kmol/h FS ) molar flow rate of mixed solvent to the extraction unit, kmol/h Ki ) distribution coefficient of component i LLE ) liquid-liquid equilibrium PC ) propylene carbonate
PE ) molar flow rate of extract product from the extraction unit, kmol/h PR ) molar flow rate of raffinate product from the extraction unit, kmol/h Pr ) solvent power R2 ) coefficient of determination %RMSD ) root-mean-squared deviation error M ) number of tie lines N ) number of components Na ) number of interaction parameters Sel ) selectivity of the solvent Sp ) solvent power Sr ) sum of squares of errors St ) sum of squares of residuals between the data point and the mean T ) extraction temperature, K TA ) total aromatics in the extract stream Tcm ) critical miscibility temperature, K xEi ) mole fraction of component i in the extract stream xFi ) mole fraction of component i in the feed stream xRi ) mole fraction of component i in the raffinate stream Yld ) extraction yield Z ) value of the objective function Greek Letters Rstf ) solvent-to-feed ratio Rsts ) solvent composition mole fraction of PC in the solvent mixture βR1 ) heating cost for the feed to flash unit, $/m3 βR2 ) cooling cost for enriched naphtha, $/m3 βS ) cost of PC solvent relative to DEG βv1, βv2 ) parameters for the product value added cost item E ) tolerance γEi ) activity coefficients of component i in the extract phase γRi ) activity coefficients of component i in the raffinate phase λA ) unit cost and a scaling factor for the aromatics losses cost item, $/m3 λR ) cost scaling factor for the solvent recovery cost item, $/m3 λS ) unit cost of DEG and cost scaling factor for solvent costs item, $/m3 λV ) cost scaling factor for the product value added cost item, $/m3 F ) molar density, kmol/m3 θ ) extract-to-feed ratio, θ ) PE/F Subscripts A ) aromatics E ) extract F ) feed N ) naphtha P ) paraffin R ) raffinate S ) solvent Superscripts E ) extract F ) feed NF ) naphtha feed R ) raffinate Literature Cited (1) Ali, S. H.; Lababidi, H. M. S.; Merchant, S. Q.; Fahim, M. A. Extraction of aromatics from naphtha reformate using propylene carbonate. Fluid Phase Equilib. 2003, 214, 25-38.
Ind. Eng. Chem. Res., Vol. 45, No. 14, 2006 5097 (2) Fahim, M. A.; Merchant, S. Q. Liquid-liquid equilibria of systems containing propylene carbonate and some hydrocarbons. J. Chem. Eng. Data 1998, 43 (5), 884-888. (3) Salem, A. B. S. H.; Hamad, E. Z.; Al-Naafa, M. A. Quaternary liquidliquid equilibrium of n-heptane-toluene-o-xylene-propylene carbonate. Ind. Eng. Chem. Res. 1994, 33, 689-692. (4) Annesini, M. C.; Gironi, F.; Marreill, L.; Kikic, I. Liquid-liquid equilibria for ternery systems containing hydrocarbons and propylene carbonate. J. Chem. Eng. Data 1985, 30, 195-196. (5) Yorulmaz, Y.; Karpuzcu, F. Sulpholane versus diethylene glycol in recovery of aromatics. Chem. Eng. Res. Des. 1985, 63, 184-190. (6) Naithani, J.; Khanna, M. K.; Nanoti, S. M.; Rawat, B. S. Quaternary liquid-liquid equilibrium studies on hydrocarbon-solvent systems, J. Chem. Eng. Data 1992, 37, 104-106. (7) Saha, M.; Rawat, B. S.; Khanna, M. K.; Nautiyal, B. R. Liquidliquid equilibrium studies on toluene + heptane + solvent. J. Chem. Eng. Data 1998, 43, 422-426. (8) Wang, W.; Gou, Z.; Zhu, S. Liquid-liquid equilibria for aromatics extraction with tetraethylene glycol. J. Chem. Eng. Data 1998, 43, 81-83. (9) Radwan, G. M.; Al-Muhtaseb, S. A.; Dowaidar, A. M.; Fahim, M. A. Extraction of aromatics from petroleum naphtha reformate by a 1-cyclohexyl-2-pyrrolidone/ethylene carbonate mixed solvent. Ind. Eng. Chem. Res. 1997, 36 (2), 414-418. (10) Hansen, H. K.; Coto, B.; Kuhlmann, B. UNIFAC with linearly temperature-dependent group-interaction parameters; Technical Report (SEP 9212); IVC-SEP Research Engineering Center, Institute for Kemiteknik, The Technical University of Denmark: Lyngby, 1992. (11) Bastos, J. C.; Soares, M. E.; Medina, A. G. Infinite dilution activity coefficients predicted by UNIFAC group contribution. Ind. Eng. Chem. Res. 1988, 27, 1269-1277.
(12) Sørensen, J. M.; Magnussen, T.; Rasmussen, P.; Fredenslund, A. Liquid-liquid equilibrium data: Their retrieval, correlation and prediction. Part II: Correlation. Fluid Phase Equilib. 1979, 3 (1), 47-82. (13) Fahim, M. A.; Al-Muhtaseb, A.; Al-Nashef, I. Phase Equilibria of the Ternary System Water + Acetic Acid + 1-Pentanol. J. Chem. Eng. Data 1996, 41, 562-565. (14) Arce, A.; Marchiaro, A.; Rodriguez, O.; Soto, A. Liquid-liquid equilibria of limonene + linalool + diethylene glycol system at different temperatures. Chem. Eng. J. 2002, 89, 223-227. (15) Voutsas, E. C.; Tassios, D. P. Analysis of the UNIFAC-type groupcontribution models at the highly dilute region. 1. Limitations of the combinatorial and residual expressions. Ind. Eng. Chem. Res. 1997, 36, 4965-4972. (16) Singh, K. P. Effect of miscibility-to-extraction temperature ratio on selectivity, refining power, and overall processing solvent index in solvent extraction. Chem. Eng. J. 1995, 60, 169-172. (17) Salem, A. B. S. H. Liquid-liquid equilibria for the systems triethylene glycol-toluene-heptane, propylene carbonate-toluene-heptane and propylene carbonate-o-xylene-heptane. Fluid Phase Equilib. 1993, 86, 351361. (18) Aldrich Chemical Co. Handbook for Fine Chemicals and Laboratory Equipment; Aldrich: Germany, 2003. (19) Branch, M. A.; Grace, A. MATLAB Optimization Toolbox, User’s Guide, MathWorks, Inc.: Natick, MA, 1996.
ReceiVed for reView May 8, 2005 ReVised manuscript receiVed April 24, 2006 Accepted May 9, 2006 IE050537R
