Determination of ternary solutions concentration in liquid--liquid extraction by the use of attenuated total reflectance-Fourier transform infrared spectroscopy and multivariate data analysis.

Gallardo-Velazquez, T. ; Osorio-Revilla, G. ; Cardenas-Bailon, F. 等

INTRODUCTION

Liquid-liquid extraction (LLE) is a mass transfer operation where solutions of at least three components are present. The feed, formed by solute and diluent, is contacted with an immiscible or nearly immiscible liquid (solvent) that exhibits preferential affinity or selectivity towards one or more components in the feed. Two ternary streams result from this contact: the extract, which is the solvent rich solution containing the desired extracted solute with some diluent, and the raffinate, formed by a rich diluent solution containing little solute with some solvent.

Since quantification of composition of ternary mixtures is not an easy task, modern analytical techniques like high performance liquid chromatography (HPLC) (Resk et al., 2006; Zgola-Grzeskowiak et al., 2006), mass spectrometry (MS) (Donglin and Nilufer, 1998; Lekkas and Nikolaou, 2006), and gas chromatography (GC) (Wen et al., 1998; Brodkorb et al., 1999; Darwish et al., 2003) have been used to quantify the concentration of solute, diluent, and solvent in both raffinate and extract layers. Even though the above analytical methods are accurate, they are expensive, time consuming, they require sample preparation prior analysis, and skilful operators. Based on this, it is desirable to develop a simple, rapid, and reliable method to estimate the composition of ternary streams resulted from LLE processes to take immediate adjusting process decisions if necessary. The use of chemometrics is one of these possible alternatives. Chemometrics is a powerful statistical tool that uses multivariate regressions to generate mathematical models that correlate the spectrophotometrical response of a sample with different variables that could be used to predict its composition.

Recently, Fourier transform infrared spectroscopy (FTIR) combined with multivariate data analysis has been used in the quantitative analysis of multicomponent samples in food and pharmaceutical matrixes (Ribone et al., 2001; Bunaciu et al., 2002; Cozzolino et al., 2004; Jie et al., 2004; Cocchi et al., 2006).

FTIR can be thought of a molecular "fingerprinting" method. An infrared spectrum contains features arising from vibrations of molecular bonds, and the mid-infrared region (MIR; 4000-400 [cm.sup.-1]), is highly sensitive to the precise composition of the sample being analyzed (Van de Voort and Ismail, 1991). Recent MIR-FTIR instrumentation and multivariate statistical analysis techniques (chemometrics) allow for the detection of constituents present in very low concentrations (as low as 0.0003%) as well as subtle compositional differences between and among multiconstituent specimens (Sivakesava and Irudayaraj, 2001). In addition to this, the development of a wide range of sampling accessories, such as the attenuated total reflectance (ATR) cells, has led to major improvements by simplifying sample handling (Armenta et al., 2005; Ferrao and Davanzo, 2005; Llario et al., 2006).

In the ATR cell, the infrared radiation is not guided through the sample itself, but rather through a crystal with high refractive index that is in contact with the sample (Figure 1) (Etzion et al., 2004). The beam is reflected several times inside the crystal before being directed to the detector. When the beam hits the reflecting surface, it penetrates into the sample up to a depth of approximately 0.1 [lambda] where [lambda] is the wavelength of the radiation. For MIR-FTIR, the penetration depth is less than 10 _m, which is similar to thin transmittance cells. However, by comparison to transmission cells, repeatability is enhanced because sample dimensions do not affect the optic path (Mizaikoff, 2002).

[FIGURE 1 OMITTED]

Multivariate analysis is often used to extract subtle information from complex spectra such as FTIR that might contain overlapping peaks, interference bands, and instrumental artifacts due to measurement conditions (Beebe et al., 1998). From the several multivariate methods available (principal component analysis, partial least squares (PLS) regression, and artificial neural networks), the PLS method has the largest number of applications of chemometric methods for multicomponent analysis.

Based on the aforementioned, in this work, the feasibility of using MIR-Fourier transform infrared-attenuated total reflectance (FTIR-ATR) spectroscopy, combined with PLS multivariate data analysis to evaluate the composition of the ternary streams from LLE process was investigated.

EXPERIMENTAL

Preparation of Calibration and Validation Solutions Sets

The type I LLE systems used in this work, were selected to represent the three most common solute-solvent affinity situations encountered: (a) solute exhibits preferential affinity towards the solvent than for the diluent; (b) solute exhibits more affinity towards the diluent than for the solvent; and (c) there is not a markedly solute preferential affinity for the solvent or diluent. Figure 2 shows the LLE systems used in this work (Sorensen, 1980).

In order to prepare the calibration solutions sets, the raffinate branch of each LLE systems used, was represented in rectangular coordinates as %w solute versus %w solvent. Forty calibration solutions (40 g each) were prepared at concentrations resulted from the interpolation on this curve at 0.2-0.4 solvent concentration intervals. Ten validation solutions for each extraction system were also prepared in the same way. The concentration of the validation sets was not included in the calibration sets.

It was preferred to use raffinate solutions for analysis instead of extract solutions for each one of the five selected extraction systems, to reduce the effect of the evaporation of the solvent during the FTIR analysis. The solvent rich extract proved to change composition during the FTIR analysis due to evaporation of solvent. Once the concentration of raffinate was known, extract concentration was calculated by mass balance.

Spectral Acquisition

All FTIR spectra were obtained in a Perkin-Elmer 1600 MIR-Fourier transform infrared (MIR-FTIR) spectrometer system, fitted with a sealed and desiccated interferometer and deuterated triglycine sulphate (DTGS) detector. The sampling compartment was equipped with an overhead ATR accessory, comprising of transfer optics within the chamber through which infrared radiation is directed to a detachable ATR zinc selenide crystal mounted in a shallow trough for sample containment. The crystal geometry was a 45. parallelogram with mirrored angled faces, with 12 nominal internal reflections. Single beam MIR-FTIR spectra of the samples were collected over the range of 600-4000 [cm.sup.-1] and 30 co-added scans were taken at a resolution of 4 [cm.sup.-1]. Air background spectrum was obtained (with the empty ATR-ZnSe crystal) before analyzing each sample and subtracted from the sample spectrum prior statistical analysis. The ATR crystal was carefully cleaned between samples and dried using nitrogen gas.

Multivariate Data Analysis

[Quant.sup.+] v.4.5 software, Perkin-Elmer, Waltham, MA, U.S.A., was used in this work for the multivariate analysis of data. Calibration models were developed with PLS algorithm, employing the 1st derivative-transformed spectra. PLS was chosen to analyze data because its calibrations have shown better predictability of components concentration in a mixture than other quantitative chemometric methods (Brereton, 2004). PLS quantitative analysis condenses relevant concentration and spectral information in the selected spectral region of the calibration standards into a number of factors. Each factor represents a source of variation in the data (Beebe and Kowalski, 1987; Van de Voort, 1992).

[FIGURE 2 OMITTED]

Optimum number of factors selected for calibration was automatically optimized by the software based on the predicted residual sum of squares (PRESS) which should be minimized by proper selection of the spectral range considered in the model building. The performance of the obtained predicting models was evaluated by: (a) the standard error of calibration (SEC) for calibration data sets, which refers to the uncertainty of calibration for a selected ternary system; a small SEC value shows that the calibration has less error and (b) the standard error of prediction (SEP) for validation data sets, that indicates how well the developed model will perform on new samples; small SEP value shows that the concentration prediction of the new sample has less error.

Liquid-Liquid Extraction

Three stages crosscurrent LLE operation was carried out for each one of the extraction systems used in this work. The extraction operation was performed at laboratory level using separating funnels as extraction stages. The validated mathematical model for each system was used to evaluate the concentration of solute and solvent in the raffinate layer of each stage. With this information the stage and overall efficiency for each system were graphically estimated as described in engineering books (Wankat, 1988; Geankoplis, 1993). Feed concentration was in the range of 25-35%w solute depending on the extraction system as shown in Table 1.

In the first stage (separating funnel), 50 mL of solvent were added to 100 mL of feed, the resulted mixture was vigorously shaken by hand for 10 min in order to disperse the feed into the solvent. The separating funnel was left to settle until the two layers (raffinate and extract) were clearly separated. The raffinate layer was collected in a flask previously dried and weighed, and the mass of the raffinate layer in this first step was calculated by difference. Aliquot (1 mL) of the raffinate layer was used to obtain the MIR-FTIR-ATR spectrum under the above-mentioned conditions. The remaining raffinate was fed into the second separating funnel (second stage) and additional 50 mL of solvent were added; the extraction process was repeated as in the first stage. The raffinate from the second stage was treated in the same way as before to complete the third extraction stage. Once the concentration of the raffinate from each stage was known using the multivariate algorithm obtained (PLS) for each extraction system, the concentration and mass of the extract layer was calculated by material balance. The stage and overall efficiency for each system were then graphically estimated.

[FIGURE 3 OMITTED]

RESULTS AND DISCUSSION

Selection of Spectral Region for Calibration Figure 3a shows an example of the infrared spectra obtained for the calibration solutions set for the system acetone-diethyl ether-water in the concentration range: 1% acetone, 6.2% diethyl ether, 92.8% water to 30% acetone, 10.9% diethyl ether, 59.1% water.

The MIR-FTIR-ATR spectra in Figure 3a consist of fundamental and characteristic bands whose wavenumbers determine the relevant functional groups of the ternary system. The spectra show a strong broad band due to OH functional group of water at 3600-3200 [cm.sup.-1], which showed no correlation with the concentration of the ternary system. The bands at 1710 and 1225 [cm.sup.-1] are characteristic of the carbonyl functional group (C=O) and the -C-CO-C- group of the acetone, respectively. The methylene (-CH2-) and methyl (-CH3) groups of ether and acetone are associated with the bands at 1470 and 1380 [cm.sup.-1], respectively. The most important band due to the carbon oxygen link (C-O-C) of the ether appears near 1100 [cm.sup.-1]. All the aforementioned bands clearly responded to the concentration variation of the ternary system.

An important parameter used in computing a multivariate calibration method is the spectral range selected for the model building. If there are regions in the spectrum with very strong absorption peaks (thus non-linear with respect to Beer's law), it is usually best to choose the regions on either side, thus excluding that band. Therefore, is necessary to make a spectral analysis and select regions that show high correlation between absorbance (or %transmittance) and concentration (Sivakesava and Irudayaraj, 2001).

Different spectral regions were tried for each extraction system and its effect on the correlation and prediction accuracy was assessed until the best correlation was obtained. The selected spectral regions used in this work to build the calibration models for the ternary systems are shown in Table 2. The selected region for the system acetone-diethyl ether-water used above as an example is presented in Figure 3b. The spectral regions selected, not only encompassed regions of expected structural differences, but also contained the spectral regions identified by the software as containing the greatest differences between samples.

Analysis of Spectral Data of the Ternary Systems Using PLS

The multivariate calibration model developed using PLS, established a correlation between the spectral data and the three component concentrations of the ternary system. The PLS predicting model performance parameters mentioned above, together with the spectral region used in the model building are shown in Table 2. Correlation coefficients R2 (for calibration and validation models), the optimum number of factors used in the calibration method, the SEC values (SEC model), and the SEP values (SEP) are also included in this table.

As can be seen in Table 2, [R.sup.2] values for the calibration set for the five ternary systems are in the range of 0.987-0.997 and the SEC is in the range of 0.279-1.17 which gives confidence for the model building.

The PLS model obtained with the first derivative data treatment, were then applied to the corresponding validation data sets, obtaining a predicted composition of the ternary systems with a SEP in the range of 0.289-1.303 and [R.sup.2] values within the range of 0.917-0.991 (Table 2). The values of both parameters give confidence in the prediction of raffinate concentrations, which were very close to the real values of the validation sets, showing that the spectroscopic technique applied to the raffinate of the different extraction systems could predict with confidence, its concentration for the five ternary systems.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

Figure 4 shows the results of the calibration for the five ternary systems, in terms of predicted (estimated) composition by the PLS model developed, versus the actual (specified) composition in the validation sets for the different extraction systems used.

The best calibration method among the five extraction systems studied, was that for the system acetone-diethyl ether-water, based on its high correlation coefficients and lower SEC (0.279) and SEP (0.289), followed by ethanol-diethyl ether-water system (SEC=0.407; SEP=0.547), acetic acid-methylisobutyl ketone-water system (SEC=0.528; SEP=0.675), acetic acid-isopropyl ether-water system (SEC=0.795; SEP=0.877), and finally the acetone-methylisobutyl ketone-water system (SEC=1.17; SEP=1.303). But in general, these results indicate that a confident prediction can be obtained for the five different ternary systems used.

The validated models were used to evaluate the concentration of solute and solvent in the raffinate layer in the threestage crosscurrent extraction process used for each one of the five selected systems. Figure 5, shows an example of the extraction diagram obtained with the real extract and raffinate concentrations for each stage and Figure 6 shows the ideal stages required to obtain a change in concentration from that in the feed to that in the final raffinate obtained in the three-stage process. With these diagrams the stage and overall efficiencies were determined for the five systems used in this work. Table 3 shows the actual feed concentration to each stage, the ideal raffinate concentrations obtained with the amount of feed and solvent used in each stage, the stage efficiency, the number of ideal stages required to change the feed concentration to that obtained in the raffinate of the actual third stage, and the overall efficiency for the three-stage crosscurrent extraction of each one of the ternary systems used.

CONCLUSIONS

The results of this study indicate that MIR-FTIR-ATR spectroscopy can be used with confidence to determine the concentration of three or more components in the raffinate layer in LLE processes. The prediction of the composition of ternary systems using the PLS method with first derivative data transformation has shown to be suitable for this purpose. The FTIR-ATR chemometric method obtained, is an effective analytical tool requiring no sample preparation, carriers of consumables unlike the more conventional methods, and can be successfully used to evaluate in a fast and reliable way the composition of ternary streams in LLE processes, which can be used in conjunction with mass balance, for the calculation of stage and overall efficiencies of a multistage process.

ACKNOWLEDGEMENT

The authors are grateful to the Instituto Politecnico Nacional de Mexico for financial support for this project.

Manuscript received January 14, 2007; revised manuscript received June 21, 2007; accepted for publication June 30, 2007.

REFERENCES

Armenta, S., S. Garrigues, M. De la Guardia and P. Rondeau, "Attenuated Total Reflection-Fourier Transform Infrared Analysis of the Fermentation Process of Pineapple," Anal. Chim. Acta 545, 99-106 (2005).

Beebe, K. R. and B. R. Kowalski, "An Introduction to Multivariate Calibration and Analysis," Anal. Chem. 59, 1007A-1017A (1987).

Beebe, K. R., R. J. Pell and M. B. Seasholtz, "Chemometrics--A Practical Guide," John Wiley and Sons Inc., New York (1998).

Brereton, R. G., "Chemometrics. Data Analysis for the Laboratory and Chemical Plant," John Wiley & Sons, Ltd., Sussex, England (2004).

Brodkorb, M. J., V. Gomis and M. J. Slater, "Determination of Phase Equilibria and Densities of the Quaternary System Toluene + Acetone + Phenol + Water," J. Chem. Eng. Data 44, 591-596 (1999).

Bunaciu, A. A., S. Fleschin and H. Y. Aboul-Enein, "Analysis Improvement of Drugs Using Modern Methods," Roum. Biotechnol. Lett. 7, 647-654 (2002).

Cocchi, M., C. Duarte, C. Foca, A. Marchetti, L. Tassi and A. Ulrici, "Durum Wheat Adulteration Detection by Near Spectroscopy Multivariate Calibration," Talanta 68, 1505-1511 (2006).

Cozzolino, D., M. J. Kwiatkowski, M. Parker, W. U. Cynkar, R. G. Dambergs, M. Gishen and M. J. Herderich, "Prediction of Phenolics Compounds in Red Wine Fermentation by Visible and Near Infrared Spectroscopy," Anal. Chim. Acta 513, 73-80 (2004).

Darwish, N. A., M. A. Abdelkarim, N. Hilal and I. Ashour, "Analysis and Evaluation of the Liquid-Liquid Equilibrium Data of the Extraction of Aromatics from Hydrocarbons by Tetraethylene Glycol," J. Chem. Eng. Data 48, 1614-1619 (2003).

Donglin, P. and H. D. Nilufer, "Multicomponent Adsorption of Chloroform, Carbon Tetrachloride, and 1,1,1-Trichloroethane on Soils," J. Chem. Eng. Data 43, 283-288 (1998).

Etzion, Y., R. Linker, U. Cogan and I. Shmulevich, "Determination of Protein Concentrations in Raw Milk by Mid-Infrared Fourier Transform Infrared/Attenuated Total Reflectance Spectroscopy," J. Dairy Sci. 87, 2779-2788 (2004).

Ferrao, M. F. and C. U. Davanzo, "Horizontal Attenuated Total Reflection Applied to Simultaneous Determination of Ash and Protein Contents in Commercial Wheat Flour," Anal. Chim. Acta 538, 181-193 (2005).

Geankoplis, C. J., "Transport Processes and Unit Operations," 3rd ed., Prentice Hall Inc., New Jersey, U.S.A. (1993).

Jie, Y. C., Y. Miao, H. Zhang and R. Matsunaga, "Non-Destructive Determination of Carbohydrate Content in Potatoes Using Near Infrared Spectroscopy," J. Near Infrared Spectrosc. 12, 311-3142 (2004).

Lekkas, T. D. and A. D. Nikolaou, "Determination of Bromo Propylate in Grapes by Gas Chromatography: Evaluation of Two Analytical Methods," Int. J. Environ. Anal. Chem. 86, 25-32 (2006).

Llario, R., F. A. Inon, S. Garrigues and M. De la Guardia, "Determination of Quality Parameters of Beers by the Use of Attenuated Total Reflectance-Fourier Transform Infrared Spectroscopy," Talanta 69, 469-480 (2006).

Mizaikoff, B., "Sensory Systems Based on Mid-Infared Transparent Fibers," in "Handbook of Vibrational Spectroscopy," J. M. Chalmers and P. R. Griffts, Eds., John Wiley & Sons, Chichester, UK (2002), Vol. 2, pp. 1560-1573.

Resk, N. L., K. C. Brown and A. D. M. Kashuba, "A Simple and Sensitive Bioanalytical Assay for Simultaneous Determination of Omeprazole and its Three Mayor Metabolites in Human Blood Plasma Using RP-HPLC after a Simple Liquid-Liquid Extraction Procedure," J. Chromatogr. B Analyt. Technol. Biomed. Life Sci. 884, 314-321 (2006).

Ribone, M. E., A. P. Pagani and A. C. Olivieri, "Simultaneous Multivariate Spectrophotometric Analysis of Ear Drops Containing a Ternary Mixture of Antipyrine, Sulfathiazole, and Rivanol," Anal. Lett. 34, 2077-2088 (2001).

Sivakesava, S. and J. Irudayaraj, "A Rapid Chemometric Technique for Determining Honey Adulteration with Corn Syrup," J. Food Sci. 66, 787-792 (2001).

Sorensen, J. M., "Liquid-Liquid Equilibrium Data Collections: Ternary Systems," DECHEMA Chemistry Data, C Vol. 5, Part 2, DECHEMA, Frankfurt, Germany (1980), pp. 261, 283, 341, 470, 485.

Van de Voort, F. R., "Fourier Transform Infrared Spectroscopy Applied to Food Analysis," Food Res. Int. 25, 397-403 (1992).

Van de Voort, F. R. and A. A. Ismail, "Proximate Analysis of Foods by Mid-FTIR Spectroscopy," Trends Food Sci. Tech. 2, 13-17 (1991).

Wankat, C. P., "Equilibrium Staged Separations," Prentice Hall Inc., New Jersey, U.S.A. (1988).

Wen, W., G. Zeming and Z. Shenlin, "Liquid-Liquid Equilibria for Aromatics Extraction Systems with Tetraethylene Glycol," J. Chem. Eng. Data 43, 81-83 (1998).

Zgola-Grzeskowiak, A., T. Grzeskowiak, J. Zembrzuska and Z. Lukaszewski, "Comparison of Biodegradation of Poly(Ethylene Glycol)s and Poly(Propylene Glycol)s," Chemosphere. 64, 803-809 (2006).

T. Gallardo-Velazquez (1), G. Osorio-Revilla (2) *, F. Cardenas-Bailon (2) and M. C. Beltran-Orozco (2)

(1.) Escuela Nacional de Ciencias Biologicas del I.P.N., Departamento de Biofisica, Prolongacion de Carpio y Plan de Ayala, 11340 Mexico D.F., Mexico

(2.) Escuela Nacional de Ciencias Biologicas del I.P.N., Departamento de Ingenieria Bioquimica, Prolongacion de Carpio y Plan de Ayala, 11340 Mexico D.F., Mexico

* Author to whom correspondence may be addressed. E-mail address: gosorio@encb.ipn.mx

DOI 10.1002/cjce.20002

Table 1. Feed concentration for the crosscurrent liquid-liquid
extraction (LLE) process for each system

Extraction system Feed concentration [%.sub.w]

 Solute Diluent (water)

Acetone-MIK (a)-water 35 65

Acetone-diethyl ether-water 35 65

Acetic acid-isoproppyl ether-water 25 75

Acetic acid-MIKa-water 25 75

Ethanol-diethyl ether-water 30 70

(a) MIK, methylisobutyl ketone

Table 2. PLS predicting model performance parameters for the
calibration and validation sets for the selected spectral regions

LLE system Factors (a) Spectral region,
 [cm.sup.-1]

Acetic acid-isopropyl ether-water 2 1696-736

Acetone-MIK (e)-water 2 1564-874

Acetone-diethyl ether-water 2 1714-662

Acetic acid-MIK (e)-water 3 4000-742

Ethanol-diethyl ether-water 4 3990-748

LLE system Calibration set

 [R.sup.2] (b) SEC (c)

Acetic acid-isopropyl ether-water 0.987 0.795

Acetone-MIK (e)-water 0.997 1.17

Acetone-diethyl ether-water 0.995 0.279

Acetic acid-MIK (e)-water 0.996 0.528

Ethanol-diethyl ether-water 0.997 0.407

LLE system Validation set

 [R.sup.2] (b) SEP (d)

Acetic acid-isopropyl ether-water 0.993 0.877

Acetone-MIK (e)-water 0.917 1.303

Acetone-diethyl ether-water 0.950 0.289

Acetic acid-MIK (e)-water 0.934 0.675

Ethanol-diethyl ether-water 0.991 0.547

(a) Optimum number of factors

(b) Correlation coefficient

(c) Standard error of calibration

(d) Standard error of prediction

(e) MIK, methylisobutyl ketone

Table 3. Actual feed concentration, real and ideal raffinate
concentration for each stage, and calculated stage and overall
efficiency for the three-stage crosscurrent extraction process
for the five systems used in this work

Stage no. [X.sub.F] [X.sub.R] actual

Acetone-MIK (a)-water
 1 0.35 0.199
 2 0.199 0.098
 3 0.098 0.042

Acetone-diethyl ether-water
 1 0.30 0.192
 2 0.192 0.115
 3 0.115 0.064

Acetic acid-isopropyl ether-water
 1 0.35 0.306
 2 0.306 0.26
 3 0.26 0.21

Acetic acid-MIKa-water
 1 0.25 0.179
 2 0.179 0.131
 3 0.131 0.094

Ethanol-diethyl ether-water
 1 0.25 0.188
 2 0.188 0.154
 3 0.154 0.135

Stage no. [X.sub.R] ideal Stage efficiency

Acetone-MIK (a)-water
 1 0.17 83.8%
 2 0.06 72.6%
 3 0.02 71.7%

Acetone-diethyl ether-water
 1 0.161 77.6%
 2 0.08 68.7%
 3 0.04 68%

Acetic acid-isopropyl ether-water
 1 0.29 73.3%
 2 0.24 69.9%
 3 0.18 62.5%

Acetic acid-MIKa-water
 1 0.175 94.6%
 2 0.123 85.7%
 3 0.083 77.1%

Ethanol-diethyl ether-water
 1 0.184 93.9%
 2 0.145 78.1%
 3 0.118 53.2%

Stage no. No. ideal stages

Acetone-MIK (a)-water
 1
 2 2.3
 3

Acetone-diethyl ether-water
 1
 2 2.2
 3

Acetic acid-isopropyl ether-water
 1
 2 2.1
 3

Acetic acid-MIKa-water
 1
 2 2.6
 3

Ethanol-diethyl ether-water
 1
 2 2.1
 3

Stage no. Overall efficiency

Acetone-MIK (a)-water
 1
 2 76.6%
 3

Acetone-diethyl ether-water
 1
 2 73.2%
 3

Acetic acid-isopropyl ether-water
 1
 2 70.3%
 3

Acetic acid-MIKa-water
 1
 2 87.2%
 3

Ethanol-diethyl ether-water
 1
 2 70.2%
 3

[X.sub.F], feed concentration; [X.sub.R], raffinate concentration

(a) MIK, methylisobutyl ketone