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SEPARATIONS Prediction of Liquid-Liquid Equilibrium in the System Furfural + Heavy Neutral Distillate Lubricating Oil Rafael van Grieken,*,† Baudilio Coto,† Eva Romero,‡ and Juan J. Espada† Department of Chemical and Environmental Technology, School of Experimental Sciences and Technology (ESCET), Rey Juan Carlos University, c/ Tulipa´ n s/n, 28933 Mo´ stoles (Madrid), Spain, and Alfonso Cortina Technology Centre, REPSOL-YPF, S.A., 28933 Mo´ stoles (Madrid), Spain
In the lubricating oil manufacturing process, the aromatic content of these products is reduced by solvent extraction. In this work, a thermodynamic model is developed to simulate the properties of these mixtures when liquid-liquid equilibrium (LLE) is established with a suitable solvent. The mixtures involved in the extraction process (feed, raffinates, and extracts) are considered to be a mixture of three types of components: saturates (S), aromatics (A), and polars (P). Pseudo-components were characterized by two properties: the average boiling point obtained from the distillation curve and the specific gravity. LLE was described by means of the nonrandom two-liquid (NRTL) model with temperature-dependent interaction parameters. The use of only three pseudo-components leads to a reduced number of interaction parameters to be determined by correlation of the available experimental equilibrium data. Calculated and experimental compositions and yields of the raffinates and extracts were compared, and good agreement was obtained. 1. Introduction One of the unit operations in the process of manufacturing lubricating oils is the extraction of the aromatic components to achieve low dependence of the oil viscosity with temperature. The residue from the crude oil atmospheric distillation (long residue) is transferred to a vacuum distillation column and separated into five different lube oil cuts, depending on their boiling points: spindle distillate (SPD), light neutral distillate (LND), medium neutral distillate (MND), heavy neutral distillate (HND), and bright stock distillate (BSD).1 The search for new and selective solvents to extract aromatic compounds is ongoing.2,3 When choosing a solvent, various points must be considered: low vapor pressure, high specific gravity, adaptability to a wide range of feeds, availability at reasonable cost, as well as stability. Moreover, it should not be toxic or corrosive. Among the usual solvents, furfural is one of the most used, because its selectivity toward aromatic compounds is high and decreases slowly with increasing temperature. In addition, it shows an acceptable selectivity for both light and heavy vacuum distillates.4 To optimize the design and operation of extraction columns, a good knowledge of the process is necessary. However, experimental determination is both timeconsuming and costly, and, therefore, modeling of the process is a good tool to simulate changes in the operation conditions or feed quality. Until now, such * To whom correspondence should be addressed. Tel.: 34 91 4887007. Fax: 34 91 4887068. E-mail address:
[email protected]. † Rey Juan Carlos University. ‡ Alfonso Cortina Technology Centre, REPSOL-YPF, S.A.
models have been based on empirical methods5 and have been neither accurate nor flexible enough to simulate industrial extraction units. New models are needed to improve the predictions. The key for such a simulation model is to properly describe the liquid-liquid equilibrium (LLE) involved. A consistent thermodynamic model must be based on accurate experimental information.6 Very often, this information is not available and makes these predictions difficult. The accuracy of a model to describe equilibrium properties (and, therefore, the separation operation) is dependent not only on the thermodynamic basis but also on the number of pseudo-components that are taken into account to describe the extremely high number of compounds in petroleum mixtures. Conventional pseudocomponent definition procedures based on distillation curves are not effective in LLE processes, because the chemical structure has a much bigger effect than the boiling temperatures. Several thermodynamic models, such as nonrandom two liquid (NRTL) and group contribution methods,7-9 have been used to describe LLE in this type of system.5,10 Previous works have reported the use of empirical equations to correlate LLE data in the furfural + lubricating oils system. It was demonstrated that the furfural + heavy vacuum distillates system can be described by considering the system formed by furfural + aromatics + nonaromatics.11 Moreover, these systems present Type I isotherms and, for that reason, the NRTL model is the most appropriate model to describe LLE. However, calculated yields and compositions of extraction mixtures (raffinates and extracts) by means of the NRTL model were not presented. Recent studies of the LLE for the furfural + hydrocarbon mixtures system
10.1021/ie050069l CCC: $30.25 © 2005 American Chemical Society Published on Web 09/09/2005
Ind. Eng. Chem. Res., Vol. 44, No. 21, 2005 8107 Table 1. Experimental Results for the First Set of Extractions of Heavy Neutral Distillates (HND) fraction
furfural/feed ratio (wt/wt)
temp (K)
Feed 1 R-1 E-1 R-2 E-2 R-3 E-3 R-4 E-4 R-5 E-5 R-6 E-6 R-7 E-7 R-8 E-8 R-9 E-9 R-10 E-10 R-11 E-11 R-12 E-12 R-13 E-13 R-14 E-14 R-15 E-15 R-16 E-16 R-17 E-17 R-18 E-18 R-19 E-19 R-20 E-20 R-21 E-21
1.28 1.28 2.56 2.56 7.40 7.40 1.28 1.28 7.40 7.40 0.50 0.50 1.27 1.27 2.00 2.00 2.56 2.56 3.50 3.50 7.40 7.40 0.75 0.75 1.28 1.28 2.56 2.56 3.50 3.50 7.40 7.40 1.29 1.29 1.29 1.29 2.56 2.56 3.50 3.50 7.42 7.42
333 333 333 333 333 333 353 353 353 353 363 363 363 363 363 363 363 363 363 363 363 363 373 373 373 373 373 373 373 373 373 373 383 383 383 383 383 383 383 383 383 383
a
Component Composition (wt %)a XS XA XP 44.4 52.1 3.3 55.4 6.6 60.7 12.6 52.5 8.7 65.3 21.0 47.2 14.5 52.8 15.3 55.6 18.1 58.0 18.5 60.2 20.4 65.2 26.0 49.1 18.1 52.4 20.7 58.6 23.7 61.6 24.9 66.7 31.6 54.6 23.5 53.3 26.2 60.8 27.1 65.9 28.1 67.8 35.4
49.3 43.4 80.9 40.9 77.4 36.5 73.9 43.1 76.2 32.3 67.9 47.3 72.1 42.9 71.7 40.7 69.5 38.5 69.6 36.6 68.4 32.4 64.1 45.9 69.4 43.2 67.4 38.1 65.5 35.6 64.3 31.3 59.3 41.0 66.6 42.2 63.9 35.9 63.6 31.1 63.1 30.0 56.9
6.3 4.5 15.8 3.7 16.0 2.8 13.5 4.4 15.1 2.4 11.1 5.5 13.4 4.3 13.0 3.7 12.4 3.5 11.9 3.2 11.2 2.4 9.9 5.0 12.5 4.4 11.9 3.3 10.8 2.8 10.8 2.0 9.1 4.4 9.9 4.5 9.9 3.3 9.3 3.0 8.8 2.2 7.7
specific gravity, SG
density at 343 K, D (g/mL)
refractive index at 343 K, RI
0.9352 0.9164 1.0552 0.9083 1.0434 0.8941 1.0202 0.9160 1.0341 0.8894 0.9977 0.9291 1.0204 0.9148 1.0156 0.9079 1.0091 0.9039 1.0048 0.8992 0.9977 0.8875 0.9844 0.9236 1.0085 0.9164 1.0003 0.9028 0.9914 0.8973 0.9871 0.8849 0.9700 0.9155 0.9807 0.9164 0.9803 0.9016 0.9762 0.8961 0.9696 0.8825 0.9572
0.8977 0.8787 1.0191 0.8705 1.0071 0.8561 0.9838 0.8783 0.9977 0.8513 0.9610 0.8915 0.9839 0.8770 0.9790 0.8700 0.9725 0.8660 0.9681 0.8612 0.9609 0.8494 0.9473 0.8860 0.9719 0.8787 0.9636 0.8649 0.9546 0.8593 0.9502 0.8467 0.9329 0.8778 0.9438 0.8787 0.9434 0.8637 0.9392 0.8581 0.9325 0.8443 0.9200
1.5018 1.4875 1.5864 1.4810 1.5767 1.4722 1.5587 1.4862 1.5702 1.4689 1.5415 1.4960 1.5605 1.4859 1.5562 1.4810 1.5517 1.4785 1.5474 1.4754 1.5427 1.4689 1.5322 1.4917 1.5520 1.4877 1.5462 1.4772 1.5377 1.4742 1.5345 1.4662 1.5232 1.4865 1.5320 1.4872 1.5322 1.4767 1.5274 1.4734 1.5234 1.4652 1.5134
Subscripts denote the component: S ) saturates, A ) aromatics, and P ) polars.
are focused on correlating LLE data by means of different thermodynamic models, such NRTL and UNIQUAC, but the authors did not report application of such models.12 In this work, a model to describe LLE in the furfural + lubricating oil system is presented. Because of the complexity of lubricating oil compositions, it is necessary to reduce the number of compounds considered to describe the LLE. For that reason, in the present study, the liquid phases (feed, raffinates, and extracts) were considered to be formed by three groups of pseudocomponents: saturates (S), aromatics (A), and polars (P). To calculate a thermodynamic model suitable to describe the extraction operation, equilibrium compositions and properties of each pseudo-component are needed. A method to calculate the pseudo-component properties (such as specific gravity, density, and refractive index) is reported in this work. Thereafter, the LLE can be described by means of a thermodynamic model with a reduced number of parameters. Compositions of the different extraction experiments provided by REPSOL-YPF, S.A. for the studied system taken at different temperatures and furfural/feed ratios were correlated by means of the NRTL model. To check the accuracy of both the pseudo-component method and the thermody-
namic model, another four extraction experiments were performed by modifying the extraction temperature and the furfural/feed ratio. The compositions of the different hydrocarbon mixtures (feed, raffinates, and extracts) in saturates (lineal and branched paraffins mainly), aromatics, and polars (compounds with heteroatoms such as sulfur mainly) were experimentally determined following the ASTM D2007 standard test method.13 In addition, the liquid density and refractive index at 343 K of these mixtures (feed, raffinates, and extracts) were experimentally determined by means of the ASTM D129814 and ASTM D174715 standard test methods, respectively, and compared to calculated values, showing a good correlation. These extraction experiments were simulated by a one-stage extraction column, using Aspen Plus and the pseudo-component properties and the parameters estimated for the thermodynamic model. Predicted and experimental results were then compared, and a good agreement was obtained. 2. Experimental Section Heavy neutral distillate (HND) was provided by REPSOL-YPF, S.A. from their refinery in Puertollano (Spain). Furfural was supplied by REPSOL-YPF, S.A.
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Table 2. Experimental Results for the Second Set of Extractions of HND fraction
furfural/feed ratio (wt/wt)
temp (K)
yield (wt %)
Feed 2 R-22 E-22 R-23 E-23 R-24 E-24 R-25 E-25
1 1 9 9 1 1 9 9
323 323 323 323 348 348 348 348
87.8 12.2 58.1 41.9 84.1 15.9 56.3 43.7
a
Component Composition (wt %)a XS XA XP 42.8 43.8 5.3 56.2 16.6 46.1 10.8 55.0 17.9
49.4 50.7 72.6 40.8 68.1 48.3 71.0 41.2 69.0
7.8 5.5 22.1 3.0 15.3 5.6 18.2 3.8 13.1
density at 343 K, D (g/mL)
refractive index at 343 K, RI
0.9068 0.8857 1.0340 0.8570 0.9849 0.8843 1.0015 0.8506 0.9583
1.5093 1.4957 1.5970 1.4776 1.5620 1.4948 1.5736 1.4736 1.5436
Subscripts denote the component: S ) saturates, A ) aromatics, and P ) polars.
were obtained, although saturates are slightly underestimated, just opposite to the aromatic composition.
Table 3. Material Balance of HND Extraction Experiments
true feed composition calculated feed composition Exp. 22 Exp. 23 Exp. 24 Exp. 25
saturates (wt %)
aromatics (wt %)
polars (wt %)
42.8
49.4
7.8
39.1 39.6 40.4 38.8
53.4 52.3 51.8 53.3
7.5 8.1 7.8 7.9
and distilled before use, to remove the oxidation products formed due to contact with air. An initial set of extraction experiments was performed by REPSOL-YPF, S.A. in a 2-L cylindrical stirred glass reactor. Temperature was set by recirculating silicone oil from a thermostatic bath and controlled within (0.1 °C. A gentle stream of nitrogen was passed to prevent furfural decomposition. Agitation at 430 rpm was maintained for 1 h, followed by settling for another hour to achieve a good separation of the two phases. Furfural was removed from extracts and raffinates via vacuum distillation. Table 1 shows the composition in saturates, aromatics, and polars, as well as specific gravity (SG), liquid density at 343 K (D), and refractive index at 343 K (RI) of feed, raffinates (R), and extracts (E), as determined by means of the ASTM D2007, ASTM D1298, and ASTM D1747 test methods, respectively. Each mixture is denoted by a letter (R for raffinate, E for extract), followed by the corresponding number of the experiment. In addition, another set of four extraction experiments for a different heavy distillate cut (HND) was performed as mentioned previously, but in a 0.5-L cylindrical stirred glass reactor. Table 2 shows the experimental conditions (temperature and furfural/feed ratio), compositions in saturates (XS), aromatics (XA), and polars (XP), liquid density at 343 K (D) and refractive index at 343 K (RI). To check the limits of the model developed in this work, severe conditions, different from those of the first set of experiments, were selected. Thus, furfural/feed ratios of 1 and 9, and temperatures of 323 and 348 K, were studied. The composition, D value, and RI value of the different hydrocarbon mixtures (feed, raffinates, and extracts) were determined by means of the ASTM D2007, ASTM D1298, and ASTM D1747 standard test methods, respectively. To check the quality of experimental data obtained in the second set of extraction experiments, the mass balance was checked. True and calculated feed compositions are shown in Table 3. Calculated feed composition was obtained from the composition and yield of raffinates and extracts in each experiment, and compared with true feed composition. No important deviations
3. Results and Discussion As shown in Table 1, the raffinates are mainly formed by saturates, whereas furfural dissolves preferently aromatic compounds, which is the main compound in the extract, confirming the suitability of furfural to perform the extraction of such compounds from heavy distillates. Polars mostly appear in extracts, which is a benefit in addition to aromatics reduction, because polars are usually sulfur-containing compounds, which are undesirable in lubricating oils. Extraction experiments conducted at higher furfural/ feed ratios present raffinates with lower content of aromatics, showing that the extraction of aromatic species increases when the furfural/feed ratio becomes higher. As is shown in Table 1, raffinates of experiments performed at the same furfural/feed ratio and different temperatures do not exhibit important differences, in regard to aromatics content. However, when analyzing the compositions of the extracts, the content of saturates increases with the temperature, and therefore, furfural selectivity toward aromatic compounds decreases with temperature. To study the LLE, a good knowledge of the composition of the extraction mixtures is necessary. Because these mixtures present a very complex composition, pseudo-components definition is needed. A wide range of different methods, usually based on the distillation curve, can be used to characterize pseudo-components.16 In this work, pseudo-components were defined using two average properties: the average boiling point (T50%) and the specific gravity, which is another property that was related to molecular weight of the fraction. T50% was defined as the temperature at which 50 vol % of HND is distilled (T50% ) 801 K), according to the ASTM D1160 vacuum distillation method,17 and it was assumed to be the same for saturates, aromatics, and polars. 3.1. Pseudo-component Properties. The method described below was used to estimate the physical properties of the extraction mixtures (feed, raffinates, and extracts) as a contribution of the pseudo-component average properties through the compositions presented in Table 1 and using the following mixing rule:
Pcalc )
[
]
XA XP XS P hS + P hA + P h 100 100 100 P
(1)
where P is the physical property under consideration and Pcalc is the calculated value of the property for each mixture. P h S, P h A, and P h P are the average values of the properties of the saturates, aromatics, and polars,
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respectively, whereas XS, XA, and XP denote the compositions (in weight percent) in the saturates, aromatics, and polars, respectively. Expression 1 is applied for all the experiments, using the compositions presented in Table 1 and considering the values of P h S, P h A, and P h P as unique and adjustable parameters. Optimum values of P h S, P h A, and P h P are those which minimize the following expression for all the experiments performed:
F)
∑ |Pcalc - Pexp|
(2)
and where Pexp denotes the experimental value of the property considered from Table 1. In this work, the selected properties were specific gravity (SG), the liquid density at 343 K (D), and the refractive index at 343 K (RI). Because SG, D, and RI are not additive properties, the variables considered in expression 1 were 1/SG, 1/D, and RI/D, respectively. Obtained average values of SG, D (in units of g/mL), and RI for each pseudo-component were as follows:
For saturates: SGS ) 0.8361; D h S ) 0.7930; RIS ) 1.4311 For aromatics: SGA ) 0.9764; D h A ) 0.9900; RIA ) 1.5816 For polars: SGP ) 1.9228; D h P ) 1.2232; RIP ) 1.5830 To check the reliability of the presented method, the error was calculated by means of the absolute average deviation (j), as follows:
j )
∑i N
(3)
where N represents the number of mixtures considered and i represents the absolute deviation in each fraction i, which is calculated according to the following expression:
i ) |Pexp - Pcalc|
(4)
Absolute average deviations of 0.004 for SG, 0.006 for D, and 0.007 for RI were obtained. 3.2. Extraction Experiments. As shown in Table 2, experiments at the same temperature and different furfural/feed ratios present higher yields of extract when this ratio is increased: species undergo larger dissolution in furfural, so that the efficiency of the extraction is higher. Consequently, the yield of raffinate is lower. When experiments with the same furfural/feed ratio and different temperature are compared, higher temperatures mean better aromatic extraction, but, at the same time, the selectivity of the process decreases. The experimental compositions show that furfural dissolves preferently aromatic compounds, which is the main compound in the extract: 72.6% (T ) 323 K, furfural/feed ) 1), 68.1% (T ) 323 K, furfural/feed ratio ) 9), 71.0% (T ) 348 K, furfural/feed ) 1), and 69.0% (T ) 348 K, furfural/feed ratio ) 9), as it was stated previously. The RI value was determined for these experiments to check the accuracy of the method based on the
Figure 1. Comparison between the experimental and calculated refractive index at 343 K (RI) for heavy neutral distillates (HND). Table 4. Calculated Refractive Index (RI) Values of HND Mixtures at 343 K fraction
RI/D
RI
i × 102
Feed 2 R-22 E-22 R-23 E-23 R-24 E-24 R-25 E-25
1.6625 1.6703 1.5410 1.7049 1.5853 1.6773 1.5647 1.6999 1.5949
1.5080 1.5067 1.5717 1.4885 1.5510 1.5032 1.5614 1.4901 1.5488
0.13 1.10 2.53 1.09 1.10 0.84 1.22 1.65 0.52
pseudo-components definition and the suitability of the pseudo-component average properties presented previously. Thus, the terms 1/D and RI/D of involved mixtures from the four additional experiments were calculated, using the compositions shown in Table 2, along with the corresponding RI and D values of the pseudocomponents previously presented. The calculated RI values of the involved mixtures are listed in Table 4 and are compared to the experimental values from Table 2. Figure 1 shows the mentioned comparison, and good agreement was observed, with an average deviation of 0.011. Therefore, the method proposed can be used to calculate the physical properties of the involved mixtures using pseudo-component average properties (RI and D). 3.3. Thermodynamic Model. As previously stated, each mixture was considered to be composed of the solvent and three pseudo-components (furfural + S + A + P). The LLE can be represented through the distribution coefficient for each component i (Ki) between phases R (raffinate) and E (extract), and Ki is defined as follows:
Ki )
xRi xEi
)
γEi γRi
(5)
Activity coefficients (γi) are correlated by means of a thermodynamic model. In this work, the NRTL model was used, as suggested by other authors.11 The NRTL equation is based on the local composition concept and considers only binary interactions. The
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Table 5. Nonrandom Two-Liquid (NRTL) Binary Interaction Parameters component i
j
aij
aji
bij
bji
Rij
saturate 0.77 -4.80 1361.55 1707.14 0.29 aromatic 0.17 11.15 -592.67 4646.93 0.30 aromatic 10.49 -7.69 -6070.79 1937.20 0.20 polar -125.49 -4.01 46708.69 -627.89 0.20 polar -33.84 -0.10 13210.45 -3012.05 0.20 furfural -10.19 -2.93 2266.90 -1446.52 0.20
furfural furfural saturate saturate aromatic polar
NRTL expression for the activity coefficient is given by7-9
ln γi ) c
xjτjiGji ∑ j)1 c
∑ xkGki
k)1
[ ( )] c
c
+
∑ j)1
xjGij
c
τij -
∑ xkGkj
∑ xmτmjGmj m)1 c
(6)
∑ xkGkj
k)1
k)1
where xi is the molar fraction of component i and
Gij ) exp(-Rijτij)
Figure 2. Comparison between the experimental and predicted extraction yields for HND. For raffinates: (9) furfural/HND ) 1, T ) 323 K; ([) furfural/HND ) 9, T ) 323 K; (1) furfural/HND ) 1, T ) 348 K; and (2) furfural/HND ) 9, T ) 348 K. For extracts: (0) furfural/HND ) 1, T ) 323 K; (]) furfural/HND ) 9, T ) 323 K; (3) furfural/HND ) 1, T ) 348 K; and (4) furfural/HND ) 9, T ) 348 K.
(7)
where τij are binary interaction parameters, related to interaction energy between pairs of molecules, and Rij varies with the tendency of species i and j to be randomly distributed. The former is assumed to be temperature-dependent, according to18
τij ) aij +
bij T
(8)
By definition,
τii ) 0 aij * aji bij * bji Rij ) Rji
(9)
and, therefore, five binary parameterssaij, aji, bij, bji and Rijscan be considered as adjustable parameters, characterizing each binary interaction. LLE data from the first set of extraction experiments in Table 1 and the pseudo-component average specific gravity previously calculated were used to determine the NRTL adjustable parameters by means of a suitable algorithm provided in Aspen Plus, based on the generalized least-squares method.19 NRTL parameters obtained for HND are shown in Table 5. 3.4. Simulation Results. To examine the quality of the model, the experimental conditions for the HND extraction experiments in Table 2 were simulated by a one-stage extraction column. Such simulation was performed using Aspen Plus, the previously determined NRTL parameters, and the average specific gravity of each pseudo-component. The experimental and predicted HND extraction yields are compared in Figure 2. The predicted yields fit the experimental values reported in this work well, confirming the expected distribution of phases. Thus, at lowest temperatures and solvent/feed ratios, a raffi-
Figure 3. Comparison between the experimental and predicted compositions for HND. For raffinates: (9) saturates, (1) aromatics, and (2) polars. For extracts: (0) saturates, (3) aromatics, and (4) polars.
nate yield of 90.9% was predicted, which compares favorably with the 87.8% experimentally obtained. At higher temperature, species undergo larger dissolution, which decreases yield of raffinate. Thus, a yield of 84.2% was predicted, which again shows a good concordance with the 84.1% yield that was experimentally obtained. To determine the accuracy of the predictions of the extraction yields, an average deviation was calculated, according to expression 3, resulting a value of 5.1%. Simulated and experimental compositions are compared in Figure 3 for HND. The predicted values are in good agreement with experimental values, and no systematic deviations were observed. Thus, at the lowest temperature and furfural/feed ratio, the model predicts 46.7% in saturates for the raffinate, which is in good agreement with the 43.8% of saturates experimentally determined. To determine the accuracy of the predic-
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Figure 4. Scheme of calculations.
tions of the compositions, the average absolute deviation (in wt %) was calculated for the saturates, aromatics, and polars, obtaining values of 3.7%, 3.6%, and 1.1%, respectively. In all cases, those obtained values are within the limits of reproducibility stated in the ASTM D2007 standard test method. There is a limit in the temperature of extraction, as well as in the amount of furfural used. As it can be seen in Figure 2, the experiments conducted at a furfural/ feed ratio of 9 present greater deviation than those conducted at a lower furfural/feed ratio. Under these conditions, the system is near the miscibility region. For that reason, inaccurate predictions are obtained under these conditions. This restriction is not a big model lack, because, in practice, these severe conditions are not very usual. Figure 4 shows the scheme of calculations used to summarize all the parameters needed for the description of the LLE in the extraction operation. 4. Conclusions The experimental conditions used in this work confirm that aromatics extraction could be enhanced by increasing the furfural/feed ratio, although it is limited in practice. Similarly, the temperature must be a compromise between the solubility of the species and the solvent selectivity. A method that is based on pseudo-component physical properties can be successfully used to predict properties of different mixtures (feed, raffinates, and extracts) from heavy vacuum distillates (HND). In this work, good predictions of the refractive index at 343 K were obtained. The extraction operation can be described using Aspen Plus, with the pseudo-component properties and nonrandom two-liquid (NRTL) parameters calculated from experimental data. Good predictions were obtained for yields (average absolute deviation of 5.1%) and compositions (average absolute deviations 3.7%, 3.6%, and 1.1% for saturates, aromatics, and polars, respectively). Therefore, it is possible to apply the obtained model to the extraction operation under the usual conditions of temperature and furfural/feed ratio. The model exhibits lower accuracy at high temperature and/ or furfural/feed ratio, but it is not an important limita-
tion, because these conditions are not frequently encountered in practice. Therefore, the model presented in this study is able to describe the extraction operation for heavy distillates. Similarly, it could be considered to be a useful tool to study furfural extraction processes that are operating under the usual conditions. Furthermore, the method presented here can be used in the design and optimization of extraction units. Acknowledgment The authors thank REPSOL-YPF S.A. for providing the lubricant oil samples that have been used in this work. Nomenclature Symbols D ) liquid density at 343 K (g/mL) E ) extract F ) objective function G ) NRTL interation parameter, as given by eq 7 Ki ) distribution coefficient of component i, as defined by eq 5 P ) studied property such as density, specific gravity, or refractive index P h ) average property of pseudo-component i R ) raffinate RI ) refractive index at 343 K SG ) specific gravity at 288 K T ) temperature of extraction (K) T50% ) average temperature of the feed lubricating oil (K) X ) composition of each mixture (wt %) x ) molar fraction of component i, j, k, or m γi ) activity coefficient of component i R, a, b ) NRTL interaction parameters τ ) NRTL interaction parameter given by eq 8 Subscripts A ) aromatics i, j, k, m ) component i, j, k, or m P ) polars S ) saturates
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Received for review January 18, 2005 Revised manuscript received July 22, 2005 Accepted August 1, 2005 IE050069L
