Statistical Modeling and Differential Evolution Optimization of Reactive Extraction of Glycolic Acid

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1 International Conference on Biology, Environment and Chemistry IPCBEE vol.4 () ()IACSIT Press, Singapoore Statistical Modeling and Differential Evolution Optimization of Reactive Extraction of Glycolic Acid Dipaloy Datta and Sushil Kumar + Department of Chemical Engineering, Birla Institute of Technology and Science (BITS), PILANI Pilani - (Rajasthan) India Abstract. The equilibrium reactive extraction of glycolic acid (GA) from aqueous solution is studied using tri-n-octylamine () as extractant dissolved in organic solvents (cyclohexane and decane--ol). Experimental studies are designed considering central composite orthogonal design method to investigate the main and interaction effects of initial GA concentration in the aqueous phase (C in, mol/l), initial amine composition in the organic phase ( C, %v/v) and modifier composition (M, %v/v) on the degree of extraction,. The process optimization is performed based on to find out the global optimum parameters using bio-inspired optimization algorithm, called differential evolution (DE). The degree of extraction of GA can be satisfactorily described by a quadratic response surface model with R of.98. The optimum conditions using DE are obtained as C in =.4 mol/l; C = 6. (%v/v); and M = 8.38 (%v/v) DE optimization shows that at this condition, a of 73.8 % can be obtained from the model. Experimental verification gives a of 69. % with a model error of 5.7 %. This indicates high reliability of the model. Keywords: reactive extraction, modeling, optimization, differential evolution. Introduction Glycolic acid (GA) has a broad spectrum of consumer and industrial applications. It is used in leather, oil, gas, laundry and textile industries and as a component in personal care products like skin care creams. Commercially, the acid is produced from petroleum feed-stocks. Therefore, it is essential to replace the petroleum based feed-stocks by renewable resources for the sustainable development of industrial sector. Recently, fermentation technology, comparatively a clean and a green technology, is found to be an attractive alternative to produce GA from renewable sources due to the limitations of chemical synthesis route. Glycolic acid can be produced by the enzymatic conversion of glycolonitrile by nitrilase as an aqueous solution of ammonium glycolate []. The hydrophilic nature of glycolic acid (log P = -.97, []) makes it poorly extractable by common organic solvents and hence reactive extraction has been considered for the separation of this acid from the aqueous solution. Generally, amine based extractants have been found to be efficient extractant for the recovery of carboxylic acids [3-6]. These amines are used with active polar diluents (modifiers) to improve their physical properties such as density, viscosity, surface tension etc. Various studies on the reactive extraction of carboxylic acid are carried out to determine the effect of various parameters such as initial acid and extractant concentration, types of extractant, and diluents on the recovery of acids [3-6]. The effective choice and optimum combinations of these parameters are essential to maximize the recovery of acid from aqueous solution. Therefore, in the present study reactive extraction of glycolic acid is chosen as a case study. In this study, initial glycolic acid concentration, initial tri-n-octylamine composition and modifier (decane-ol) composition are considered as critical and effective independent + Corresponding author: Tel Ext. 5; fax: ; address: sushilk6@gmail.com 5

2 variables of reactive extraction and degree of extraction is chosen as the dependent design variable. With the experimental design and data, an empirical model is constructed and differential evolution optimization is employed to find the global optimal conditions of reactive extraction.. Experimental Section.. Materials and method Glycolic acid of purity 99.5 %w/w is purchased from Spectrochem, India. Tri-n-octylamine (density =.89 g/cm 3 ; purity = 98 %w/w; molar mass g/mol) procured from Spectrochem, India, is used as an extractant in this study. Diluents such as cyclohexane (density =.779 g/cm 3 ; purity = 99 %w/w; S. D. Fine- Chem, India) as an inert diluent and decane--ol (density =.83 g/cm 3 ; purity = 98 %w/w; Spectrochem Pvt. Ltd., India) as a modifier are used to prepare the organic phase. Sodium hydroxide (Merck, Germany) is used for titration and phenolphthalein solution (CDH, India; ph range of 8. to.) is used as an indicator in the titration. The equilibrium extraction experiments are carried out in a temperature controlled reciprocating shaker bath (REMI labs, HS, India) using conical flasks of ml with equal volumes of aqueous and organic phase ( ml). The phase mixture is then shaken at rpm for 6 hours at 98 K. after reaching equilibrium, aqueous and organic phases is kept for hrs for separation in separating funnel ( ml) at constant temperature (98 K). The concentration of the glycolic acid in the aqueous phase is determined by titration with NaOH solution of.5 N and phenolphthalein as an indicator. The acid concentration in the organic phase at equilibrium is calculated by mass balance. The repeatability for few data points is checked and found within error limit of ±5 %. The efficiency of the equilibrium reactive extraction process is analyzed by calculating the degree of extraction (%Y) and is defined as: C Y = () C in The over bar represents the organic phase; C is the concentration of glycolic acid; subscript in refers to the initial condition. 3. Results and Discussion 3.. Response surface methodology approach and experimental design The development of an industrial process requires study of the various process parameters and which can be achieved by exhaustive experimentation. The approximation of the response function in terms of input variables is called Response Surface Methodology (RSM). RSM is applied for the construction of empirical models based on experimental data and experimental design [7-8]. In the present study, the actual values (C o, C, and M) of design variables are coded as x i (dimensionless) and are presented in Table. The experiments in the present study are designed using central composite orthogonal design and a total of 6 batch experiments are carried out. Each run in the batch experiment represents a unique combination of factor s levels and for each experiment run the degree of extraction (%Y) is determined using Eq. (Table ). The experimental data are regressed using least square method and the significance of each regression coefficient is determined by Student s t-test (a null hypothesis test) and Fischer distribution (F-test). Approximate RSM model equation of second order polynomial describing %Y of reactive extraction as a function of coded variables is represented as follows: Y = x x x3.894x3 ().84x x 5.44x x x x Subjected to: 3 α x + α and Y (3) i Statistical significance of the regression equation (Eq. ) is analyzed using analysis of variance (ANOVA) and results are summarized in Table 3. ANOVA analysis shows that P-value near about zero, and R =

3 (Figure ) are obtained for Eq. indicating better fit of the RSM regression model. The effects of design parameters (C o, C, and M) on %Y are determined by plotting response surface plots on -D planes and are shown in Figures -4. Effect of C on %Y at various C and at fixed modifier composition (M = 5 %v/v) is shown in Figure. This figure also indicates the effect of interaction between both variables (C andc ). As indicated by the Figure, an increase in the acid concentration decreases %Y for a fixed amount of composition. At higher acid concentration the competency between acid molecules to attach with the extractant molecules becomes more and hence less amount of acid molecule can be extracted by the amine molecule decreasing %Y. At higher amine composition there are sufficient amount of amine molecules available for a particular acid concentration and hence a greater the value of %Y. Figure 3 elaborates the variation of degree of extraction as a function of C o at different M values and at C = %v/v. Since has a relatively high viscosity and density, it is used along with diluents, which could facilitate good phase separation in the continuous extraction process. Diluents chosen in the study are cyclohexane from the inactive chemical class, and decane--ol as modifier from active chemical class to examine the effect of diluent-complex interactions. These interactions generally have been found to affect the stoichiometry of reaction and magnitude of the corresponding equilibrium constants. From the Figure 3 it can then be observed that the solubility of extracted species increases in the organic phase. So, %Y of GA increases with an increase in the concentration of decane--ol (modifier) in the mixture of and cyclohexane. The significant effect of M on %Y (response) with C is shown in Figure 4 at C o =.6 mol/l. In this study decane--ol has been used as a modifier which is an active polar solvent (dipole moment, μ =.6 D). Use of non-polar solvents (e.g. cyclohexane, μ = D) at higher initial concentration of glycolic acid in aqueous solutions, could lead to the formation of a stable emulsion and dimer in the organic phase. Therefore, a modifier is generally added to the organic phase to avoid such kind of problems and assures a higher solubility of the formed acid-amine complex in the organic phase. Active diluent, decane--ol is having an active group ( OH, proton donor), which enhance the extractability of low polar. On the other hand, non-polar diluents do not affect the extraction process significantly. Figure 4 dictates that with increase in both values of M andc, the %Y increases. Table : Independent variables (their coded and actual values) Actual design variables/factors Coded variables Coded levels - α - + α* Initial GA concentration (C, mol/l) x Initial composition ( C, %v/v) x Modifier composition (M, %v/v). x * α =.5 (star point for central composite orthogonal design, k = 3 design variables) Table : Experimental design points and degree of extraction Run number Run type Design variables Response C x C x M x 3 O O O O O O O O S S

4 S S S S a C b C O = orthogonal design points, C = center points, S = star points, = low value, = center value, + = high value, +/ α = star point value Table 3: Analysis of variance (ANOVA) for RSM model Source DF SS MS F-value P-value Multiple R R R adj Regression Residual Total E DF = degrees of freedom, SS = sum of squares, MS = mean square, R = coefficient of determination, R adj = adjusted statistic 3.. Optimization using differential evolution In science and engineering, optimization is defined as the method of minimizing or maximizing an objective function comprised of different independent variables and finding the values of those variables for which the objective function takes on minimum or maximum value with in the defined domains of variables. Figure 5 describes the effect of one of the parameters as coded variable on %Y. It can be seen that with the increase in the values of x, there is a decrease in the %Y, but with the increase in the values of x and x 3, the %Y increases. It means there is a trade-off or balance between the values of x i s which will optimize (maximize in this case) the response function. During the last two decades there has been a growing interest in optimization algorithms, which are based on the principle of evolution (survival of the fittest).the bestknown algorithms in this class include Genetic Algorithm, Differential Evolution, Evolutionary Programming, Evolution Strategies and Genetic Programming. A brief review of the evolutionary computation techniques is presented by Babu, 4 [9]. However, certain guidelines and heuristics are available for the choice of these parameters. Based on these heuristics, the values of DE key parameters for the present problem are set as population size (NP) = 3, cross-over frequency (CR) =.7; multiplication factor (F) =.8. The fitness function, which is to be minimized, is considered as: MSE = j = N j= MSE: mean-squared error; N is the number of experiments exp pred ( Y j Y j ) (8) For the optimization of RSM fitness function a computer code has been developed in MATLAB (v 6.). DE has converged to the optimal value only after 3 generations. Therefore, it can be said that DE is comparatively faster than other optimization techniques [8]. The optimal solution obtained by means of RSM-DE involves the following conditions: C =.4 mol/l, C = 6. %v/v, and M = 8.38 %v/v with predicted %Y is about 7.8 % by RSM model and about 69. % from experiment. This value is greater than the value of % that is obtained for the run number from initial experimental design (Table ). Therefore, the scope of optimization has been achieved by RSM-DE for this process. 5 R = Initial composition (% v/v) Initial modifier composition (% v/v) Y pred (%) Y exp (%) Initial acid concentration, mol/l Initial acid concentration, mol/l 8

5 Fig. : RSM model predicted versus experimental degree of extraction Fig. : Effect of C Fig. o andc on at M = 5 %v/v Fig. 3: Effect of C o and M on Y (%) at C = %v/v Initial modifier composition (% v/v) x x Initial composition, %v/v Fig. 4: Effect of C and M on at C o =.6 mol/l Coded variables, x i 's Fig. 5: Effect of various factors on the degree of extraction x 3 4. Conclusions In this work, RSM and DE methods are applied for modeling and optimization of equilibrium reactive extraction process of glycolic acid considering three design variables (C, C and M). The reactive extraction of glycolic acid from aqueous solutions with (amine) dissolved in organic solvents (cyclohexane and decane-ol) has been considered as the case study. The regression equation in coded variables has been constructed by RSM to describe the empirical functional relationships between input variables (factors) and response (degree of extraction) with R for empirical model equal to.98. The optimum conditions are found to be: C =.4 mol/l, C = 6. %v/v, and M = 8.38 %v/v with %Y of 7.8 % and 69. % by the RSM model and by experiment, respectively. 5. References [] L. N. Xu, W. Fox, N. Zaher, and C. F. Dicosimo, Method for the production of glycolic acid from ammonium glycolate by direct deammoniation. U. S. Patent WO/6/699, June, 3, 6. [] A. D. John, Lange s Handbook of Chemistry (XXth Ed). McGraw-Hill Book Co. Inc., New York, USA, 97. [3] S. Kumar, D. Datta, and B. V. Babu, Experimental data and theoretical (chemodel using the differential evolution approach and linear solvation energy relationship model) predictions on reactive extraction of monocarboxylic acids using tri-n-octylamine, J. Chem. Eng. Data,, 55: [4] S. Kumar, D. Datta, and B. V. Babu, Estimation of equilibrium parameters using differential evolution in reactive extraction of propionic acid by tri-n-butyl phosphate dissolved in n-decane & -Decanol. Chem. Eng. Proc., 5 (7): [5] D. Datta, and S. Kumar, Reactive extraction of glycolic acid using tri-n-butyl phosphate and tri-n-octylamine in six different diluents: Experimental data and theoretical predictions, Ind. Eng. Chem. Res., 5 (5): [6] D. Datta, and S. Kumar, Reactive extraction of -methylidenebutanedioic acid with N, N-dioctyloctan--amine dissolved in six different diluents: Experimental and theoretical equilibrium studies at (98 ± ) K. J. Chem. Eng. Data,, 56 (5): [7] M. A. Bezerra, R. E. Santelli, E. P. Oliveira, L. S. Villar, and L. A. Escaleira, Response surface methodology (RSM) as a tool for optimization in analytical chemistry, Talanta, 8, 76 (5): [8] N. Marchitana, C. Cojocarub, A. Mereuta, Gh. Duca, I. Cretescu, and M. Gonta, Modeling and optimization of tartaric acid reactive extraction from aqueous, solutions: A comparison between response surface methodology and artificial neural network, Sep. Purif. Technol., : [9] B. V. Babu, Process Plant Simulation, Oxford University Press, New Delhi, India, 4. 9