Optimization of Aromatics Extraction of Naphtha Reformate by PropyleneCarbonate/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 wereobtained 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 amixed solvent system. On the other hand, a mathematical model was developed and compared with experimentaldata. Simulation results showed excellent agreement with the experimental results. Furthermore, an optimizationmodel was developed to obtain the optimal extraction conditions, which minimize the operating cost andsolvent losses. The optimization variables considered are solvent-to-feed ratio, solvent-to-solvent ratio, andoperating temperature. The optimization model is highly nonlinear because of the fact that solvents and naphthaproperties were estimated using the UNIFAC model. Optimization results were compared favorably with theexperimental results.

Introduction

There are a number of solvents used for extracting aromaticsfrom naphtha reformate. Propylene carbonate (PC) is a goodsolvent for the extraction of aromatics.1-4 Other good solventsfor this extraction process are diethylene glycol (DEG),5

triethylene glycol,6 and tetraethylene glycol.7,8 Sulfolane hasbeen proven to be of commercial use for the extraction ofaromatics from naphtha reformate.5

Using mixed solvents for the extraction of aromatics iscommonly practiced to balance between selectivity and capacityof different solvents. Radwan et al.9 studied the extraction ofaromatics from petroleum naphtha by 1-cyclohexyl-2-pyrroli-done/ethyl carbonate mixed solvents. In their study, the extrac-tion runs were performed at different temperatures, solvent-to-feed ratios, and solvent-to-solvent ratios. Saha and co-workers7

proposed that mixtures of tetraethylene glycol/N-formylmor-pholine and tetraethylene glycol/N-methylpyrolidone are goodsolvents for extraction of aromatics from naphtha reformate.Even though the extraction of aromatics (benzene, toluene, andxylene) from naphtha reformate has been commercially availablefor the last few decades, we believe that determining the optimaloperating conditions is particularly important in studying theperformance of the extraction process, especially when mixedsolvents are used.

Ali et al.1 studied the phase equilibria for the extraction ofaromatics from synthetic naphtha reformate with PC as a solvent.The operating conditions leading to maximum recovery ofaromatics were optimized. They considered PC as one groupfor better predictions using UNIFAC.1 The current studyinvestigates the improvement of the extraction process by mixingPC with DEG. The main objective is to determine the optimumoperating conditions for the extraction of aromatics fromsynthetic naphtha reformate using a mixed PC and DEG solvent.The proposed optimization model utilizes UNIFAC in estimatingthe interaction parameters for the solvents and synthetic naphthareformate. In addition to the UNIFAC interaction parametersreported in the open literature1,10 and for better predictions, the

current study considered also the phase equilibria for two moreternary systems (octane/toluene/DEG and octane/PC/DEG).

Experimental Section

The main purpose of the experimental work is to determinethe interaction parameters that would supplement those reportedin open literature for the mixed PC/DEG solvent system. Thehigh purity chemicals used in this study aren-hexane, benzene,n-heptane, methyl cyclohexane, isooctane (2,2,4-trimethyl pen-tane), 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 chroma-tography and found to be higher than 99.0%.

Five water-jacketed glass cells were used for extraction. The85 cm3 cells were connected to a water bath fitted with a HaakeDC1 thermostat, which enabled us to control the cells temper-atures within(0.2 K. Different mixtures were placed in theextraction vessels, followed by stirring for 1 h and then waitingfor settling over a period of 24 h. After equilibrium is reached,samples were withdrawn by syringes from both the raffinateand extract phases.

Gas chromatography was used to measure the equilibriumconcentrations of all the components in the ternary and themulticomponent systems in both the extract and the raffinatephases. A Chrompack CP9001 gas chromatograph equipped witha flame ionization detector (FID) was used. A WCOT fusedsilica (100 m length× 0.25 mm inside diameter) capillarycolumn coated with CP SIL PONA CB having a DF) 0.5 µmwas used. The FID and the injection port temperatures weremaintained at 573 K. The oven temperature program used wasas follows: initial temperature of 308 K, holding for 15 min at308 K, then increasing the temperature by a ramping rate of 1K/min until reaching a temperature of 333 K, and holding for20 min at 333 K, followed by increasing the oven temperatureby a ramping rate of 2 K/min for 90 min. The flow rate of thecarrier gas was adjusted so that toluene eluted at 30 min. TheGC was calibrated by the external standard calibration methodusing calibration mixtures composed of different weighed ratiosof pure components. The reproducibility for all the componentswas found to be higher than 99.7%. Detailed hydrocarbon

* To whom correspondence should be addressed. Tel.:+965 4895778. Fax: +965 483 9498. E-mail: lababidi@kuc01.kuniv.edu.kw.

5086 Ind. Eng. Chem. Res.2006,45, 5086-5097

10.1021/ie050537r CCC: $33.50 © 2006 American Chemical SocietyPublished on Web 06/08/2006

analyzer software, which was supplied by Chrompack, was usedto handle the data generated by the GC.

Two ternary systems were studied: octane/toluene/DEG andoctane/PC/DEG. These systems were used to generate theinteraction 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 equilibriumconcentrations of the three components in the ternary systemsaccording to the previously mentioned procedure. Equilibriummeasurements for both ternary systems at different temperaturesare listed in Table 1 and illustrated in Figures 1 and 2.

Synthetic naphtha reformate was prepared by mixingn-hexane, benzene,n-heptane, methyl cyclohexane, isooctane

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 octane/toluene/DEG system

raffinate phase (%) extract phase (%) raffinate phase (%) extract phase (%)

temp (K) octane DEG PC octane DEG PC octane toluene DEG octane toluene DEG

283 95.46 3.33 1.21 1.82 16.10 82.09 7.90 88.10 3.00 0.01 0.79 99.2097.42 1.51 1.07 2.07 45.13 52.80 17.00 80.13 2.88 0.01 0.81 99.1997.54 1.36 1.11 0.07 61.76 38.17 26.00 71.22 2.78 0.02 0.70 99.2897.23 1.89 0.88 0.54 32.19 67.27 34.00 63.38 2.62 0.02 0.68 99.3096.85 1.94 1.21 0.06 81.69 18.25 45.00 52.47 2.53 0.03 0.43 99.55

55.00 43.03 1.97 0.03 0.38 99.5974.00 23.67 2.33 0.05 0.35 99.6077.51 20.85 1.63 0.04 0.17 99.79

293 96.67 2.00 1.33 2.00 26.26 71.75 14.60 82.30 3.11 0.02 1.38 98.6097.60 1.34 1.07 1.07 28.12 70.81 22.90 74.20 2.90 0.02 1.28 98.7097.79 1.11 1.10 0.43 40.95 58.63 30.50 66.88 2.62 0.03 1.14 98.8397.79 1.17 1.04 0.09 55.30 44.61 45.00 52.59 2.42 0.03 0.92 99.0597.32 1.69 0.99 0.07 82.50 17.43 49.00 48.68 2.32 0.03 0.81 99.16

66.00 32.31 1.69 0.05 0.47 99.4882.00 16.02 1.98 0.04 0.35 99.61

303 97.10 1.33 1.57 1.67 34.61 63.72 14.60 80.20 5.20 0.03 1.62 98.3697.69 1.16 1.16 2.49 17.67 79.84 23.20 71.70 5.10 0.03 1.97 98.0097.96 1.02 1.02 0.17 53.87 45.97 30.70 64.40 4.90 0.04 1.82 98.1497.43 1.69 0.88 0.07 81.68 18.25 44.90 50.60 4.50 0.03 1.50 98.48

50.00 47.10 2.90 0.05 1.39 98.5671.00 26.50 2.50 0.05 0.75 99.2083.00 14.70 2.30 0.06 0.58 99.36

313 94.15 4.96 0.89 0.00 77.69 22.31 14.90 79.10 6.00 0.10 3.20 96.7095.64 3.12 1.25 1.60 61.55 36.85 25.00 69.10 5.90 0.10 2.90 97.0096.09 2.55 1.36 3.06 49.33 47.61 33.00 62.00 5.00 0.10 2.50 97.4096.39 2.08 1.53 4.56 32.84 62.61 45.00 50.10 4.90 0.12 2.20 97.6895.86 2.20 1.94 5.06 6.67 88.27 62.70 32.50 4.80 0.13 1.00 98.87

75.00 20.30 4.70 0.15 0.50 99.35

Ind. Eng. Chem. Res., Vol. 45, No. 14, 20065087

(2,2,4-trimethylpentane), toluene,n-octane, ethylbenzene andp-xylene. This synthetic mixture had a boiling range of 343-411 K and a specific gravity of 0.8. Table 2 shows thecomposition of the synthetic naphtha reformate as analyzed bythe GC, in addition to the number of functional groups presentin each of its constituents. The nine solutes constituting thesynthetic naphtha reformate correspond to the subgroups: C,CH, CH2, CH3, ACH, ACCH2, and ACCH3. However, PC andDEG, which form the mixed solvent, were each considered asa single UNIFAC group because of the polar nature of thesemolecules.

LLE measurements for the multicomponent systems (naphthareformate, PC, and DEG) were performed over a temperaturerange of 288-313 K and solvent- (PC+ DEG) to-feed molarratios,Rstf, of 1.0, 2.0, and 3.0. The molar PC content in thesolvent mixture,Rsts, was varied between 57.2 and 87.5%. Theequilibrium mixtures of these systems were also analyzed bythe GC under the same conditions as those mentioned above.Experimental LLE results for the multicomponent systemsconsidered in this study are included in Table 3a.

The critical miscibility temperature,Tcm, was experimentallydetermined at different conditions.Tcm is defined as the

temperature at which all the components become completelymiscible in one another. This temperature was measured todetermine the upper limit temperature at which phase equilibriaof a system can be effectively studied.Tcm was measured byadding known volumes of solvents to a known volume of thesynthetic naphtha reformate in an 85 cm3 thermostated water-jacketed cell, and the two phases were completely mixed. Amagnetic stirrer and a circulating water bath were used to raisethe mixture’s temperature gradually and uniformly. The mis-cibility temperature was marked as the point where the turbidityof the mixture disappears and the two phases become completelymiscible in one another. Heating is then cut off, and anotherreading is then taken when the solution cools and becomesturbid, indicating the beginning of phase separation. The tworeadings were within(0.2 K difference. TheTcm values obtainedat different solvent-to-feed molar ratios and different solventcompositions are listed in Table 4. From Table 4 it can benoticed that the extraction temperatures studied for the differentsolvent mixtures and solvent-to-feed ratios were much lowerthan the critical miscibility temperatures. The extraction tem-peratures were at least 60 K lower than the experimentallydeterminedTcm.

Using the experimental values listed in Table 4, the criticalmiscibility temperature,Tcm, has been linearly correlated as afunction of both the solvent-to-feed ratio,Rstf, and solventcomposition,Rsts. The following equation has been obtained withcoefficient of correlationR2 ) 0.966:

Figure 2. Experimental and correlated phase behavior for the ternary system PC/octane/DEG.

Table 2. Reformate Composition and the Number of FunctionalUNIFAC Groups in Each of Its Constituents

number of UNIFAC groupsin each component

component mole % CH3 CH2 CH C ACH ACCH3 ACCH2

1 n-hexane 4.21 2 4 0 0 0 0 02 benzene 3.59 0 0 0 0 6 0 03 n-heptane 21.81 2 5 0 0 0 0 04 methyl cyclohexane 4.76 1 5 1 0 0 0 05 2,2,4-trimethylpentane 2.42 5 1 1 1 0 0 06 toluene 37.19 0 0 0 0 5 1 07 n-octane 0.92 2 6 0 0 0 0 08 ethylbenzene 4.41 1 0 0 0 5 0 19 p-xylene 20.69 0 0 0 0 4 2 0

Figure 3. Schematic diagram of an extraction unit.

Tcm ) 402.169- 6.497(Rstf) - 24.784(Rsts) (1)

5088 Ind. Eng. Chem. Res., Vol. 45, No. 14, 2006

Mathematical Model

A schematic diagram of the extraction process is shown inFigure 3. A material balance on the system gives the followingequations:

F is the total feed flow rate to the extraction unit which consistsof naphthaFN and the solventFS. The product streams are an

extractPE which is rich in aromatics, and a raffinate streamPR, while θ is the extract-to-feed ratio,θ ) PE/F. xi

F, xiE, andxi

R

are the mole fractions of componenti in the feed, extract, andraffinate streams, respectively. The solvent-to-feed ratio is

Table 3. Experimental and Predicted LLE Results

(a) Experimental LLE of the Naphtha Reformate+ PC-DEG Mixed Solvent

S:F) 1 at 288 K S:F) 1 at 303 K 57.2% PC at 303 KS:F)

1 at 313 K

87.5% PC 79.3% PC 57.2% PC 87.5% PC 79.3% PC 57.2% PC S:F) 2 S:F) 3 87.5% PCcom-ponent Xexp

R XexpE Xexp

R XexpE Xexp

R XexpE Xexp

R XexpE Xexp

R XexpE Xexp

R XexpE Xexp

R XexpE Xexp

R XexpE Xexp

R XexpE

n-hexane 0.049 0.004 0.054 0.005 0.041 0.003 0.052 0.006 0.050 0.007 0.043 0.004 0.049 0.004 0.055 0.002 0.048 0.009benzene 0.023 0.017 0.024 0.017 0.025 0.015 0.022 0.017 0.025 0.016 0.022 0.017 0.015 0.014 0.011 0.008 0.020 0.014n-heptane 0.282 0.022 0.255 0.023 0.231 0.006 0.285 0.033 0.276 0.029 0.235 0.013 0.269 0.012 0.305 0.011 0.279 0.041methyl

cyclo-hexane

0.050 0.006 0.052 0.006 0.049 0.003 0.055 0.007 0.052 0.010 0.050 0.003 0.053 0.004 0.061 0.003 0.053 0.009

2,2,5-trimethyl-pentane

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

toluene 0.265 0.149 0.286 0.143 0.297 0.093 0.255 0.146 0.263 0.149 0.298 0.130 0.251 0.092 0.200 0.074 0.252 0.162n-octane 0.010 0.001 0.010 0.001 0.010 0.001 0.010 0.001 0.010 0.001 0.010 0.001 0.010 0.001 0.016 0.001 0.011 0.001ethyl-

benzene0.034 0.015 0.036 0.014 0.037 0.009 0.032 0.016 0.035 0.015 0.037 0.012 0.033 0.010 0.029 0.009 0.033 0.016

p-xylene 0.164 0.068 0.176 0.064 0.188 0.029 0.167 0.071 0.177 0.065 0.186 0.025 0.197 0.034 0.189 0.033 0.170 0.075DEG 0.034 0.084 0.036 0.143 0.022 0.360 0.021 0.090 0.018 0.143 0.026 0.347 0.024 0.288 0.030 0.353 0.025 0.080PC 0.060 0.631 0.046 0.581 0.076 0.480 0.070 0.609 0.064 0.562 0.068 0.447 0.070 0.539 0.069 0.504 0.078 0.589

θ 0.660 0.650 0.540 0.680 0.670 0.570 0.760 0.850 0.700Sp 0.285 0.276 0.160 0.301 0.295 0.206 0.173 0.143 0.331Cap 0.512 0.456 0.267 0.525 0.490 0.339 0.302 0.289 0.562TA 0.340 0.322 0.399 0.274 0.274 0.370 0.330 0.330 0.237Sel 5.977 4.751 6.768 4.459 4.096 5.591 5.391 7.182 3.706Yld 0.504 0.474 0.242 0.521 0.503 0.322 0.524 0.647 0.573

(b) Predicted LLE of the Naphtha Reformate+ PC-DEG Mixed Solvent

S:F) 1 at 288 K S:F) 1 at 303 K 57.2% PC at 303 KS:F) 1at 313 K

87.5% PC 79.3% PC 57.2% PC 87.5% PC 79.3% PC 57.2% PC S:F) 2 S:F) 3 87.5% PCcom-ponent Xcal

R XcalE Xcal

R XcalE Xcal

R XcalE Xcal

R XcalE Xcal

R XcalE Xcal

R XcalE Xcal

R XcalE Xcal

R XcalE Xcal

R XcalE

n-hexane 0.046 0.005 0.045 0.005 0.039 0.002 0.046 0.007 0.046 0.007 0.039 0.003 0.045 0.003 0.050 0.003 0.045 0.009benzene 0.016 0.014 0.015 0.014 0.016 0.013 0.015 0.014 0.015 0.015 0.016 0.014 0.011 0.010 0.008 0.007 0.015 0.014n-heptane 0.287 0.023 0.280 0.025 0.236 0.009 0.294 0.033 0.289 0.035 0.241 0.013 0.286 0.013 0.323 0.013 0.289 0.047methyl

cyclo-hexane

0.058 0.006 0.057 0.007 0.050 0.003 0.059 0.009 0.058 0.009 0.050 0.004 0.058 0.004 0.064 0.004 0.058 0.012

2,2,5-trimethyl-pentane

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

toluene 0.244 0.142 0.246 0.143 0.278 0.094 0.241 0.151 0.240 0.152 0.272 0.106 0.229 0.088 0.196 0.073 0.238 0.156n-octane 0.014 0.001 0.014 0.001 0.012 0.000 0.015 0.001 0.015 0.001 0.012 0.000 0.014 0.000 0.017 0.000 0.015 0.002ethyl-

benzene0.039 0.016 0.038 0.017 0.041 0.010 0.038 0.018 0.037 0.019 0.040 0.012 0.037 0.010 0.033 0.009 0.037 0.020

p-xylene 0.192 0.073 0.198 0.071 0.214 0.030 0.191 0.080 0.195 0.079 0.212 0.037 0.213 0.036 0.207 0.033 0.188 0.086DEG 0.027 0.071 0.029 0.126 0.025 0.342 0.015 0.073 0.019 0.125 0.024 0.332 0.020 0.336 0.018 0.343 0.017 0.070PC 0.039 0.647 0.040 0.588 0.059 0.495 0.047 0.610 0.047 0.555 0.062 0.478 0.049 0.499 0.41 0.514 0.060 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 0.650 0.650 0.534 0.688 0.688 0.553 0.764 0.853 0.721Sp 0.282 0.286 0.163 0.317 0.320 0.190 0.165 0.143 0.351Cap 0.494 0.493 0.269 0.544 0.542 0.311 0.292 0.276 0.580TA 0.332 0.316 0.391 0.278 0.264 0.362 0.336 0.313 0.210Sel 5.840 5.267 6.479 4.679 4.288 5.472 6.063 6.637 3.489Yld 0.489 0.489 0.242 0.557 0.557 0.286 0.504 0.641 0.612

F ) FN + FS ) PE + PR (2)

xiF ) θxi

E + (1 - θ)xiR (3)

∑i

xiF ) ∑

i

xiE ) ∑

i

xiR ) 1 (4)

Table 4. Critical Miscibility Temperatures for the NaphthaReformate-Solvent Systems

PC in solvent(% molar basis)

solvent-to-feedmolar ratio (S:F)

critical miscibilitytemperature,Tcm (K)

87.5 1 37479.3 1 37657.2 1 38157.2 2 37657.2 3 368

Ind. Eng. Chem. Res., Vol. 45, No. 14, 20065089

defined asRstf ) FS/FN. Hence, the total feed defined by eq 2becomes

Phase equilibrium between the extract and the raffinate phasesis defined by the distribution coefficient as

whereγiE andγi

R are the activity coefficients of componenti inthe extract and raffinate phases, respectively. Rearranging eqs3 and 6, we get

or

A number of performance parameters will be defined.Extraction yield, Yld, is defined as the ratio of the aromaticcomponents in the extract phase to that in the feed. On the otherhand, solvent capacity, Cap, is defined as the ratio of thearomatic components in the extract phase to that in the raffinate.

Solvents should be selective in extracting aromatics overparaffins. Selectivity of the solvent, Sel, is defined by thefollowing ratio:

Solvent power, Sp, indicates the mole fraction of hydrocar-bons in the extract phase (i.e., extract stream without thesolvents). The higher the solvent power, the lower the cost ofrecovering and recycling the solvents. The solvent power isdefined as

As the primary aim of naphtha reformate extraction withdifferent solvents is to maximize the total aromatics in theextract, an important desirable property to be studied is therelative increase in the concentration of the total aromaticcomponents, TA. It indicates the increase in the aromaticscontent of the extract phase with respect to the original feed(naphtha reformate without solvents). TA is defined as

Interaction Parameters

The UNIFAC model has been used to predict the phaseequilibrium between the extract and the raffinate phases. TheR andQ values (group volume and surface parameters) for thesubgroups in the systems studied were obtained from theliterature.10 For PC, the values ofR and Q were set equal to3.2815 and 2.736, respectively, as used by Ali et al.,1 whereastheR andQ 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 etal.10 (see Table 5). The interaction parameters for PC withrespect to the subgroups CH2, ACH, and ACCH2 were obtainedfrom our previous work, Ali et al.,1 as reported in Table 5.UNIFAC interaction parameters, as function of temperature, aredescribed by eq 14.

The UNIFAC interaction parameters for PC with respect toDEG and the subgroups CH2, ACH, and ACCH2 were obtainedas part of the current study by performing a series of LLEmeasurements for two ternary systems (octane/toluene/DEG andoctane/PC//DEG), as described before, over the temperaturerange of 283-313 K. The interaction parameters at differenttemperatures for the group pairs containing DEG were deter-mined using an iterative program described by Sørensen et al.12

and were used by a number of researchers.13,14 The programuses two objective functions,Fa andFx (eqs 15 and 16).Fa isan activity residual function that is evaluated first, and afterconvergence, the resulted parameters are used in the secondfunction, Fx, which is a concentration residual function to fitthe experimental concentrations. The objective functions aredefined as12

Table 5. UNIFAC Interaction Parameters According to Equation 14

componenti componentj aij0 (K) aij

1 aji0 (K) aji

1 ref

ACH CH2a -6.73 -0.566 64.450 0.375 10

ACH ACCH2b -155.40 -1.489 366.600 13.220 10

ACCH2 CH2 252.50 2.650 -93.370 -1.103 10CH2 PC 487.54 1.004 41.701 -0.778 1ACH PC 194.76 -3.195 -49.096 2.037 1ACCH2 PC 726.34 8.464 -6.005 0.325 1CH2 DEG 62.86 1.133 1333.5 -66.667 this workACH DEG 12.67 -1.333 186.670 2.667 this workACCH2 DEG 2000.0 4.024 600.0 -11.900 this workPC DEG 379.49 6.667 -43.333 -7.333 this work

a C, CH, CH2, and CH3 belong to the same subgroup.b ACCH2 and ACCH3 belong to the same subgroup.

TA )

xAE

xAE + xP

E- xA

FN

xAFN

(13)

aij ) aij0 + aij

1(T - 298.15) (14)

Fa ) ∑k)1

M

∑i)1

N [aikI - aik

II

aikI + aik

II]2

+ Q∑n)1

Na

Pn2 (15)

F ) FN(1 + Rstf) (5)

Ki )xi

E

xiR

)γi

R

γiE

(6)

xiE )

KixiF

1 + θ(Ki - 1)(7)

∑i

{ KixiF

1 + θ(Ki - 1)} ) 1 (8)

Yld )xA

EPE

xAFF

)xA

E

xAFθ (9)

Cap)xA

E

xAR

)γA

R

γAE

(10)

Sel)xA

E/xAR

xPE/xP

R)

γAR/γA

E

γPR/γP

E(11)

Sp) xAE + xP

E (12)

5090 Ind. Eng. Chem. Res., Vol. 45, No. 14, 2006

wherexijk,Exp is the experimental mole fraction of componentiin phasej (j ) I, II) for the kth tie line, while xijk,Pred is themole fraction of the predicted tie line.aik

I and aikII are the

activities of componenti for thekth tie line for phases I and II,respectively.M, N, andNa are numbers of tie lines, components,and interaction parameters, respectively. Both objective func-tions include penalization terms to reduce the risks of multiplesolutions associated with parameters of high values. In theseterms,Q andPn are the penalties. The third term ofFx (eq 16)accounts for working with low solute mole fractions, in whichγS∞

I and γS∞II represent the activity coefficients calculated at

infinite dilution in both phases andKs∞ is the ratio between

solute concentrations in the two phases at infinite dilution. Thequality of correlation is measured by the residual functionRx

which is defined as14

As stated previously, the interaction parameters between eachpair of the UNIFAC groups were fitted linearly with temperatureaccording to eq 14. The resulted interaction parameters for thegroup pairs containing the DEG group are reported in the lastfour rows of Table 5.

Experimental and predicted concentrations of the octane/toluene/DEG and octane/PC/DEG glycol ternary systems arecompared in Figures 1 and 2 for different temperatures. Theseplots show that the UNIFAC model adequately represents thestudied systems with minor deviations. This deviation is due tothe fact that the combinatorial expression of the UNIFAC modeldoes not satisfactorily account for the combinatorial effects atdilute regions.15 Prediction accuracy is indicated also by thelow Rx values (reported in Figures 1 and 2). Moreover, theoverall Rx and confidence interval values for the two ternarysystems are 1.53( 0.7 and 1.56( 0.8, respectively.

Simulation Results

The mathematical model expressed by eqs 2-8 will bevalidated against the experimental results presented in Table 3.This model will then be considered as part of the optimizationformulation presented below.

The first task is to predict the compositions of the extractand raffinate phases,xi

E’s and xiR’s, and to compare them

against the experimental compositions. The computation pro-cedure is similar to the common bubble-point/flash calculationprocedure. Given the extraction temperature, naphtha composi-tion, solvent-to-feed ratio, and composition of the solventmixture and starting from initial guesses of the equilibriumconstants, eq 8 is solved forθ, followed by calculating thecompositions of the extract and raffinate phases using eqs 6and 7. UNIFAC is then used, with the interaction parameterslisted in Table 5, to calculate new activity coefficients, whichwill result in corrected values of equilibrium constants (eq 6).This procedure is iteratively repeated until the error is less thana specified tolerance (ε ) 1 × 10-10). The termination error isspecified as

Experimental and predicted compositions of the extract andraffinate phases for different temperatures and solvent-to-feedand solvent-to-solvent ratios are listed in Table 3. Accuracy inpredicting the experimental mole fractions of both phases hasbeen quantified by calculating the percent-root-mean-squared-deviation (%RMSD) and the coefficient of determination (R2),which were evaluated as follows:

whereN is the number of components (N ) 11; 9 componentsin naphtha and 2 solvents),Sr is the sum of the squares of theerrors, andSt is the sum of the squares of the residuals betweenthe data point and the mean.Sr andSt are defined as

Results listed in Table 3 demonstrate clearly that the mathemati-cal model simulates the equilibrium data quite accurately. Theaverage %RMSD error is 1.098%, whereas the maximum erroris 1.589%, which is considerably low knowing that 11 concen-trations are predicted for each phase. Moreover, experimentaland predicted compositions are compared by the parity plotshown in Figure 4. The overallR2 value is 0.9929, whichindicates excellent fit of experimental data.

Simulated and experimental values of the yield, capacity,selectivity, total aromatics, and solvent power are listed also inTable 3. These values are compared in Figure 5 for differentvalues of solvent-to-feed ratios. Accuracies in predicting theseparameters were quantified byR2 values, which were calculatedas 0.956, 0.970, 0.892, 0.968, and 0.984, respectively. Figures6-10 illustrate the experimental and predicted values of yield,capacity, selectivity, total aromatics, and solvent power, re-spectively, as a function of the composition of the solventmixture. These plots illustrate that the mathematical modelpredicted the experimental data excellently. They also indicate

Fx ) ∑k)1

M

min ∑i)1

N

∑j)I,II

(xijk,Exp - xijk,Pred)2 +

Q∑n)1

Na

Pn2 + [ln(γS∞

I

γS∞II

Ks∞)]2

(16)

Rx ) 100[∑k)1

M

∑i)1

N

∑j)I,II

(xijk,Exp - xijk,Pred)2

6M ]0.5

(17)

∑i

(xiE γi

E - xiR γi

R)2 e ε (18)

%RMSD) 100[ Sr

2N]0.5

(19)

R2 )St - Sr

St(20)

Sr ) ∑i)1

N

(xi,expE - xi,pred

E )2 + ∑i)1

N

(xi,expR - xi,pred

R )2 (21)

St ) ∑i)1

N

(xi,expE - xjE)2 + ∑

i)1

N

(xi,expR - xjR)2 (22)

Figure 4. Comparison of experimental and predicted compositions ofextract and raffinate phases.

Ind. Eng. Chem. Res., Vol. 45, No. 14, 20065091

the accuracy of the determined UNIFAC interaction parameters.Hence, the model can be confidently used in evaluating theperformance of the extraction unit.

Figure 5 shows that increasing the solvent-to-feed ratio willresult in increasing both the yield (Yld) and the selectivity (Sel),decreasing the solvent capacity (Cap) and power (Sp) as wellas the total aromatics (TA).

The significance of using mixed solvents is illustrated inFigures 6-10. These figures show clearly that maximum yield,capacity, and solvent power values are realized at specific valuesof solvent-to-solvent composition, while selectivity and totalaromatics 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 anoptimization study to determine the optimum solvent composi-tion.

Extraction temperature is also an important factor whichshould be studied. Variations of the extraction yield, capacity,solvent power, selectivity, and total aromatics with operatingtemperature are illustrated in Figure 11. The plots show thatthe first three parameters increase with temperature, while thetotal aromatics and selectivity decrease with increasing tem-perature. It is necessary that the extraction temperature is keptwell below the critical miscibility temperature (Tcm). In fact,the simulation model, which is based on UNIFAC LLEcalculations, becomes inapplicable asTcm is approached.

To include the critical miscibility temperature in the analysis,a dimensionless temperature parameter will be introduced asT/Tcm. This parameter was used by Singh16 in studying theextraction of raw lubricating distillate.Tcm is estimated usingthe correlation presented by eq 1. Simulation runs indicate that

Figure 5. Experimental and predicted yield, capacity, solvent power, totalaromatics, and selectivity for different solvent-to-feed ratios atRsts) 57.2%and 303 K.

Figure 6. Experimental and predicted yields for different solvent composi-tions atRstf ) 1.

Figure 7. Experimental and predicted capacities for different solventcompositions atRstf ) 1.

Figure 8. Experimental and predicted selectivity for different solventcompositions atRstf ) 1.

Figure 9. Experimental and predicted total aromatics for different solventcompositions atRstf ) 1.

Figure 10. Experimental and predicted solvent power for different solventcompositions atRstf ) 1.

5092 Ind. Eng. Chem. Res., Vol. 45, No. 14, 2006

the experimental data may be accurately predicted forTcm/Tvalues less than 0.85.

Optimization Model

Simulation results presented above revealed that the param-eters affecting the separation performance are the solvent-to-feed ratio, Rstf, solvent composition,Rsts, and extractiontemperature,T. One more objective of the current study is toinvestigate the impact of these parameters on the optimumperformance of the extraction process using mixed solvent (PC+ DEG) systems. An optimization model will be first formu-lated. This involves formulating an objective function that wouldsatisfy certain separation criteria and subject it to a set ofconstraints. Moreover, the simulation model presented and testedabove will be utilized for LLE calculations and for determiningthe values of the performance parameters.

The following factors should be considered in formulatingthe objective function:

1. The amount of aromatics in the extract phase should bemaximized. This is equivalent to maximizing the yield (Yld).

2. The quantities of the solvent should be minimized. Thisminimizes the cost of solvent recovery and makeup. Such anobjective may be achieved by maximizing the total aromaticscontent of the extract phase, which is the equivalent ofmaximizing TA.

3. As a result of the fact that PC is characterized as a highcapacity solvent and DEG is characterized as a high selectivitysolvent, it is important to determine the optimal amounts ofeach solvent. Salem17 reported that PC has a higher capacitythan triethylene glycol for the extraction of aromatics from amixed aromatics and paraffins feed, whereas triethylene glycolhas higher selectivity for aromatics than PC.

The parameterRstsrepresents the solvent composition (molarcomposition of PC in the mixed solvent). From eqs 10 and 11,it is clear that the capacity and selectivity are functions ofaromatics compositions. Hence, they have been also consideredby items 1 and 2 above. However,Rsts should be included inthe objective function to account for the cost difference of thetwo solvents as well as the differences in physical propertiessuch as viscosity and acidity.

4. Solvent recovery is also an important issue. Solvents, whichconcentrate in the extract phase, should be recovered and reused.The more solvents used, the higher the cost; the more solventin 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 thesolvent power (Sp).

5. Extraction temperature should be optimized as well.Temperature should be as low as possible to reduce the energycost. Another consideration is that for efficient separation,temperature should be far below the critical miscibility tem-perature (Tcm). As discussed above,T/Tcm should be less than0.85.

The best approach to fulfill the above stated factors is todevelop an objective function that accounts for the main costitems of the extraction process. The assumptions used indeveloping 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 theraffinate 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 temperatureof p-xylene (the heaviest aromatic component in naphtha) is411 K. Hence, flash separation is adequate, and the mixedsolvent stream is recovered from the bottom of the flash unit.

4. The cost of heating the extract stream fed to the flash unitis assumed constant at $4/m3, while the cost of cooling waterused to cool the aromatics-rich product is $2.5/m3.

5. Cost of the PC solvent is 1.75 times the cost of the DEGsolvent. This factor was derived from market prices of bothsolvents. Prices of both industrial scale and high purity solventswere considered.

The volumetric flow rate of the raw naphtha feedFN has beenconsidered as a basis in developing the cost function. Theproposed objective function consists of three cost items inaddition to one benefit item. The cost items are solvent makeupcost, solvent recovery cost, and aromatic losses cost, while thebenefit cost accounts for added value of the aromatics-richproduct. The constituents of the objective function are definedin the following sections:

1. Cost of Makeup Amounts of PC and DEG Solvents,CS. A unit flow of naphtha feed demandsRstf of the mixedsolvent. This amount consists of theRsts fraction of PC solventand 1- Rsts of DEG solvent. Amounts of solvent makeup aredetermined as the total demanded amounts less the amountsrecovered from the extracted product stream. Hence, PC andDEG makeup amounts,FPCandFDEG, are expressed respectivelyas

and

Cost of PC solvent relative to the cost of DEG solvent has beenused, rather than actual costs of both solvents. The main benefitof this representation is in performing sensitivity cost analysislater. On the basis of the reviewed cost data18 the cost of PCsolvent is assumed to beâS times the cost of DEG solvent. Asa result, the solvent makeup cost can be expressed as

whereλS is a cost parameter ($/m3) accounting for unit cost of

Figure 11. Experimental and predicted yield, capacity, solvent power, totalaromatics, and selectivity for different operating temperatures atRstf ) 1,Rsts ) 0.875, andTcm ) 374 K.

FPC ) FNRsts[Rstf - (1 + Rstf)θxsE] (23)

FDEG ) FN(1 - Rsts)[Rstf - (1 + Rstf)θxsE] (24)

CS ) λS(âSFPC + FDEG)/FS (25)

Ind. Eng. Chem. Res., Vol. 45, No. 14, 20065093

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 performedby a simple flash operation. It is assumed that the feed (whichis the extract stream from the extraction unit) is introduced tothe flash unit as saturated liquid.CR consists of two terms: thecost of heating the feed to saturation and the cost of coolingthe aromatics-rich product. Hence, the solvent recovery cost canbe expressed as

whereâR1 andâR2 are the heating and cooling costs assumedabove as $4/m3 of feed to the flash unit and $2.5/m3 ofaromatics-rich product, respectively, andλR is cost scaling factorfor the solvent recovery cost item.

3. Loss of Aromatics Cost,CA. This cost item considers theamounts of aromatics lost in the raffinate product. It can besimply expressed as

In this cost item,λA is the unit cost of aromatics and the scalingcost factor.

4. Product Value Added Benefit,CV. The naphtha extractionprocess yields a product which is rich in aromatics. Naturally,the value of the product is higher than the value of the rawnaphtha feed. Moreover, as the concentration of aromaticsincreases, the value or selling price of the product will be higher.This type of benefit is known as “value added” which presentsthe additional profit due to increased purity of the product. Valueadded of the aromatics-rich product is assumed to be exponentialwith respect to the difference between the aromatics content ofthe product and that of the feed stream. The value added benefitcan be expressed as

whereλV is a scaling factor for this cost item, whileâV1 andâV2 describe the exponential behavior of the value added benefit.The exponential term of eq 28 is shown graphically in Figure12 with respect to the total aromatics (TA). The plots indicatethe increase in the value of the naphtha feed for different valuesof the parametersâV1 and âV2. For instance, if the aromaticscontent of the naphtha feed is 65%, TA) 0.3 (30%) meansthat the extraction unit has enriched the aromatics content ofthe extract stream to 85% (i.e.,xA

E - xAF ) 0.2). In this case, the

value of the product stream would be 1.8 times that of the feedfor âV1 ) 6 andâV2 ) 2 and twice the value of the feed when

increasing the value ofâV1 to 8. Decreasing the value ofâV2

increases the value of the product stream. As shown in Figure12, for TA ) 0.3 andâV1 ) 6, the product value increases bythreefold and fourfold forâV2 ) 1.5 and âV2 ) 1.25,respectively.

On the basis of the cost items defined above, the objectivefunction of the optimization model may be defined as minimiz-ing the sum of four cost items:

The optimization model consists of an objective function (eq29), subject to equality constraints representing the materialbalance and equilibrium model described by eqs 2-8. Theoptimization (decision) variables are the solvent-to-feed ratio,Rstf, and the solvent composition,Rsts. The extraction temper-ature is not considered as a decision variable; however, its effectwill be investigated by solving the optimization model atdifferent temperatures. For every iteration in solving theoptimization model, eq 8 is solved forθ, followed by evaluatingthe UNIFAC model to determineKi’s from the activitycoefficients,γi

E andγiR. This involves two inner loops one for

θ and the other for theK values. The proposed optimizationmodel is a nonlinear programming problem (NLP), which wassolved using the Optimization Toolbox of MATLAB.19 Theoptimization method used is Levenberg-Marquardt with a linesearch algorithm.

Results and Discussion

The optimization model proposed in the previous section issolved for the values of the parameters listed in Table 6. Valuesof the cost scaling factors,λ’s, have been set to balance thefour elements of the objective function (eq 29) and avoid thedominance of one element. A unit molar flow of feed naphthahas been considered as a basis. Figure 13 illustrates the shapeof the cost function (eq 29) when evaluated for a range ofsolvent-to-feed ratios (0.5e Rstf e 2.5) and solvent composi-tions (0e Rsts e 1) at 303 K. The surface shown in Figure 13clearly indicates a minimum value of the objective function close

Figure 12. Value added benefit for aromatics purity in the extract stream(eq 28). TA) total aromatics,Y ) eB1TAB2, B1 ) âv1, B2 ) âv2.

CR ) λR(FN/FN)θ(1 + Rstf)[âR1 + âR2(1 - xsE)] (26)

CA ) λA(FN/FN)(1 + Rstf)(1 - θ) (27)

CV ) λV(FN/FN)(1 + Rstf)(1 - xsE)[exp(âV1TAâV2)] (28)

Figure 13. Cost function forT ) 303 K.

Table 6. Values of the Parameters Used in the Optimization Model

parameter value parameter value

âR1 4.0 $/m3 λA/FN 0.750 $/kmolâR2 2.5 $/m3 λR/FN 0.025 $/kmolâS 1.75 λS/FS 0.650 $/kmoleâv1 6.0 λV/FN 0.350 $/kmoleâv2 1.5

min z ) CS + CR + CA - CV (29)

5094 Ind. Eng. Chem. Res., Vol. 45, No. 14, 2006

to Rstf ) 1.5 andRsts) 0.85. Similarly, a corresponding surfaceshowing the yield of the extraction process is plotted in Figure14. The plot exhibits a maximum close to the PC compositionof 0.85 in the solvent mixture, which is consistent with theminimum value of the cost function. Furthermore, Figure 14shows also that the yield increases as the solvent-to-feed ratioincreases. However, increase in yield is compromised with theexcessive increase in solvent makeup and recovery cost. Forthis reason, the objective function has been formulated as afunction of the extraction cost rather than the performancemeasures such as the yield, selectivity, and total aromatics.

The optimization model was solved for the two decisionvariables,Rstf andRsts, using the cost parameters listed in Table6, and for a range of extraction temperatures. Figure 15 showsthe optimal solvent-to-feed ratio and solvent composition valuesas a function of extraction temperature, together with the valueof the cost function. The plots in Figure 15 demonstrate clearlythat the extraction temperature has a minimal effect on theoptimization results. The optimal solvent-to-feed ratio decreasedslightly from 1.4 at 288 K to 1.3 at 310 K. Similarly, the PCcomposition 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 extractiontemperature. Both the optimal yield and the solvent powerincrease with increasing temperature, while total aromaticsdecreases with increasing temperature. Nevertheless, suchvariations are again not significant. Hence, it can be concludedthat extraction temperature is not a critical factor for the systemconsidered in this study.

The next step is to study the sensitivity of the optimizationresults to the values of the cost parameters used in the objectivefunction. The parameters considered here are those related tothe cost of the solvents,âs, and the product value added benefit,âv1 andâv2. The base values for these parameters are listed inTable 6. The cost of PC has been assumed in the base case as1.75 times that of the DEG solvent. Values ofâs that areconsidered in the sensitivity analysis areâs ) 1 andâs ) 2;that is, both solvents have the same cost, and the cost of PC istwice the cost of DEG, respectively. On the other hand, valuesof âv1 andâv2 that are considered in the sensitivity analysis arethose plotted in Figure 12.

Sensitivity analysis results are listed in Table 7 as averagevalues over the temperature interval 288-310 K. The fist rowrepresents the base case results discussed above and plotted inFigures 15 and 16. In general, all results show slight deviationsfrom the base case. However, it is clear that the impact of thesolvent costs on the optimal values of the decision parameters(Rstf andRsts) is more significant than that of the product valueadded cost. In fact, maximum deviation is shown for the casewhere PC and DEG solvents are assumed to have the same cost(âs ) 1). Slight variations in optimization results are alsoapparent in values of the performance parameters. The yield,total aromatics, solvent power, and selectivity varied less than10% compared with the base case.

On the basis of the sensitivity analysis results, we canconfidently postulate that for the mixed-solvent extractionsystem considered in this study, the optimum solvent-to-feedratio is around 1.5, while the PC composition in the mixedsolvent is around 85%. These results are consistent with theexperimental results discussed above and plotted in Figures6-10.

Conclusions

Extraction of aromatics from naphtha reformate using themixed PC + DEG solvent system has been investigatedexperimentally and mathematically in this study. Experimentalruns were performed for deriving the phase equilibria interaction

Figure 14. Yield of extraction atT ) 303 K.

Figure 15. Value of the objective function and the optimum solvent-to-feed ratio and solvent composition versus extraction temperature.

Figure 16. Optimal yield, solvent power, and total aromatics versusextraction temperature.

Table 7. Effect of Cost Parameters on the Optimization Results

cost parameters optimization results

âv1 âv2 âs Rstf Rsts z Yld Sp TA Sel

6.0 1.5 1.75 1.339 0.862 0.339 0.634 0.273 0.276 5.446.0 1.5 1.0 1.460 0.875 0.297 0.660 0.270 0.267 5.686.0 1.5 2.0 1.314 0.858 0.352 0.628 0.273 0.278 5.396.0 1.25 1.75 1.383 0.876 0.296 0.642 0.274 0.272 5.606.0 2.0 1.75 1.304 0.853 0.374 0.626 0.272 0.279 5.348.0 2.0 1.75 1.306 0.856 0.366 0.626 0.273 0.279 5.36

Ind. Eng. Chem. Res., Vol. 45, No. 14, 20065095

parameters as well as for determining the extraction performanceof the mixed solvent. A mathematical model was developed tovalidate and simulate the experimental results. Decision variablesused for both the experimental runs and the simulation modelare the solvent-to-feed ratio, solvent-to-solvent ratio, andextraction temperature. Defined performance parameters includethe yield, capacity, selectivity, total aromatics, and solventpower. Furthermore, an optimization mathematical model hasbeen proposed to determine the optimum values of the decisionvariables for the proposed mixed solvent system.

The proposed mathematical model simulated the equilibriumexperimental data quite accurately. Experimental and simulatedvalues of the performance parameters showed excellent agree-ment. Moreover, both experimental and simulation resultsdemonstrated clear optimum trends with respect to the composi-tion of the mixed solvent. For further justification of the results,an optimization model has been developed which is based oneconomic measures rather than just optimizing the performanceparameters.

The factors considered by the optimization model includedthe solvent makeup and recovery costs, loss of aromatics cost,and product value added benefits. The optimization model wassolved to determine the optimum solvent-to-solvent and solvent-to-feed ratios for a range of extraction temperatures (288-310K). Optimization results showed also excellent agreement withthe experimental results. Furthermore, optimization runs indi-cated that extraction temperature is not a critical factor indetermining the composition of the mixed solvents and thesolvent-to-feed ratio.

Sensitivity analysis has been conducted to study the impactof the cost parameters on the optimization results. Despite thefact that the costs of solvents have more impact than other costparameters, variations in optimization results were found notto be significant. Such results provide good evidence that theproposed objective function succeeded in accounting for boththe performance and economic factors.

On the basis of the experimental, simulation, and optimizationresults, we can conclude that using 15% DEG solvent increasesthe aromatics extraction performance of the PC solvent andreduces the solvent-to-feed ratio to as low as 1.5.

Acknowledgment

The authors are grateful to Dr. Sabiha Q. Merchant for herhelp during the course of this work.

Nomenclature

aij ) interaction parameter between moleculesi and jCA ) cost of aromatics losses, $/hCap) solvent capacityCR ) solvent recovery cost, $/hCS ) cost of makeup solvents, $/hCV ) product value added benefit, $/hDEG ) diethylene glycolF ) total molar flow rate of the feed stream to the extraction

unit, kmol/hFDEG ) amount of DEG makeup solvent, kmol/hFN ) molar flow rate of naphtha to the extraction unit, kmol/hFPC ) amount of PC makeup solvent, kmol/hFS ) molar flow rate of mixed solvent to the extraction unit,

kmol/hKi ) distribution coefficient of componentiLLE ) liquid-liquid equilibriumPC ) propylene carbonate

PE ) molar flow rate of extract product from the extractionunit, kmol/h

PR ) molar flow rate of raffinate product from the extractionunit, kmol/h

Pr ) solvent powerR2 ) coefficient of determination%RMSD ) root-mean-squared deviation errorM ) number of tie linesN ) number of componentsNa ) number of interaction parametersSel ) selectivity of the solventSp ) solvent powerSr ) sum of squares of errorsSt ) sum of squares of residuals between the data point and

the meanT ) extraction temperature, KTA ) total aromatics in the extract streamTcm ) critical miscibility temperature, Kxi

E ) mole fraction of componenti in the extract streamxi

F ) mole fraction of componenti in the feed streamxi

R ) mole fraction of componenti in the raffinate streamYld ) extraction yieldZ ) value of the objective function

Greek Letters

Rstf ) solvent-to-feed ratioRsts ) solvent composition mole fraction of PC in the solvent

mixtureâR1 ) heating cost for the feed to flash unit, $/m3

âR2 ) cooling cost for enriched naphtha, $/m3

âS ) cost of PC solvent relative to DEGâv1, âv2 ) parameters for the product value added cost itemE ) toleranceγi

E ) activity coefficients of componenti in the extract phaseγi

R ) activity coefficients of componenti in the raffinate phaseλA ) 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 costsitem, $/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 ) aromaticsE ) extractF ) feedN ) naphthaP ) paraffinR ) raffinateS ) solvent

Superscripts

E ) extractF ) feedNF ) naphtha feedR ) raffinate

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ReceiVed for reView May 8, 2005ReVised manuscript receiVed April 24, 2006

AcceptedMay 9, 2006

IE050537R

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