Process Optimization by Response Surface Methodology and Kinetic

Article pubs.acs.org/IECR

Process Optimization by Response Surface Methodology and Kinetic Modeling for Synthesis of Methyl Oleate Biodiesel over H3PW12O40 Anchored Montmorillonite K10 Kakasaheb Y. Nandiwale and Vijay V. Bokade* Catalysis and Inorganic Chemistry Division, CSIRNational Chemical Laboratory, Pune-411008, India S Supporting Information *

ABSTRACT: Heterogeneous acid catalysts comprised of 10−30% (w/w) H3PW12O40 anchored to montmorillonite (K10) were used for synthesis of methyl oleate biodiesel by esterification of free fatty acid (oleic acid) with methanol in closed batch system. Response surface methodology (RSM) was employed to optimize esterification of oleic acid with methanol over 20% (w/w) H3PW12O40/K10. The effects of various process parameters such as catalyst loading, molar ratio, and reaction temperature on oleic acid conversion were addressed by Box−Behnken experimental design (BBD). Coefficient of determination (R2) of this model was 0.996. 20% (w/w) H3PW12O40/K10 was proved to be potential catalyst with 100% oleic acid conversion at optimized process parameters and with reusability of four cycles. Moreover, a second-order pseudohomogeneous (PH) kinetic model has been proposed and validated (R2 > 0.97) with experimental data. Kinetics confirmed that esterification reaction is performed in the kinetic regime due to high activation energy of 43.7 kJ mol−1.

1. INTRODUCTION In the wake of today’s limited fossil fuel resources and environmental concerns of augmented greenhouse gas emissions associated with overconsumption of petroleumbased products, particularly transportation fuels have spurred tremendous demand for alternative renewable fuels in recent years.1,2 Hence the biodiesel, which refers to fatty acid alkyl esters, has gained much attention recently as a less polluting, renewable, carbon neutral, low emission profile, superior lubricating, and biodegradable liquid fuel that can be mixed with petroleum diesel.3−5 Biodiesel can be produced by transesterification of triglycerides or esterification of free fatty acids (FFAs) with short chain alcohols over an acid catalyst. Close attention has been paid to the esterification of long chain carboxylic acids such as oleic acid for biodiesel synthesis, since as it is present in most of oil crops including jatropha curcas, soybean, sunflower, pongamia, rapeseed, sea mango, and palm. Commonly short chain alcohols, such as methanol, ethanol, propanol, and butanol, are usually used as acceptor acyl due to their cheap cost and wide availability.4 In particular, methanol is chosen for commercial application as it is of low price and it bears physicochemical benefits like short chains and polarity.6,7 Conventionally, esterification reactions were performed with homogeneous catalysts like, nitric acid, sulfuric acid, and hydrochloric acid. However, the homogeneous catalysts employed encounter several limitations, such as the demand of costly separation and purification steps, high corrosion, nonreusability, and environmental problems. Thus, the technological challenge for a sustainable biodiesel production process by esterification of fatty acids is the development of heterogeneous acid catalysts. These catalysts should offer high activity and stability, easy separation of the products, and environmental friendliness and should not pose corrosion problems to the equipment. These properties would character© XXXX American Chemical Society

ize them as environmentally friendly and industrially benign green catalysts.8,9 In this context, several solid acid catalysts have been extensively examined for esterification of oleic acid with methanol like magnetic ionic liquid,4 acid-activated pillar bentonite,8 sulfated lanthanum oxide,9 H3PW12O40,10 Bronsted acidic ionic liquids,11 chlorosulfonic acid modified zirconia,12 H3PW12O40-based core@shell nanomaterial,13 biomass carbonbased solid acid catalyst,14 amazon flint kaolin,15 1-butyl-3methylimidazolium hydrogen sulfate ionic liquid,16 H3PW12O40 supported on SBA-15,17 Hβ,18 and MCM-41.19 However, the reports on the use of anchored heteropoly acids for biodiesel production by esterification of oleic acid are scanty. To the best of our knowledge, only four reports on esterification of oleic acid by anchored heteropoly acid such as H3PW12O40 are available.17−20 At the same time, it was also found that there are no reports available for the esterification of oleic acid over H3PW12O40 anchored to K10. However H3PW12O40 anchored to K10 is used for other reactions.21,22 Clays possess advantageous properties, such as their mechanical and thermal stabilities, high specific surface area, inherent acidity and ionexchange capacity;23 hence it was of interest to investigate capability of H3PW12O40 anchored to K10 catalyst for biodiesel (methyl oleate) production by esterification of oleic acid with methanol. Response surface methodology (RSM) is an efficiant statistical technique utilized for building models, optimization of multifactor experiments, and evaluation of effects of numerous factors for required responses. The use of RSM is Special Issue: Ganapati D. Yadav Festschrift Received: February 19, 2014 Revised: March 18, 2014 Accepted: March 20, 2014

A

dx.doi.org/10.1021/ie500672v | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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advantageous since it produces huge information by performing a small number of experiments and it also provides the possibility of observing the effects of single variables and their combinations of interactions on the response.16,24,25 Until now, several researchers used RSM for optimization of biodiesel production process.16,26−29 The pseudohomogeneous (PH) model (one of the important models for heterogeneous catalysts) was applied to various esterification reactions for kinetic investigation.30−34 Very recently, a second-order PH kinetic model has been applied for esterification of oleic acid with ethanol.6,16,33 However, the combination of RSM and kinetic model for esterification of oleic acid to methyl oleate over superacids such as H3PW12O40 anchored to cheap and stable acid support such as K10, has not reported so far. This study will explore new avenues on development of highly active, cheap, and stable solid acid catalyst, optimization of process parameters by RSM and its kinetic modeling for the synthesis of methyl oleate biodiesel. Present study involves use of H3PW12O40 anchored to K10 as heterogeneous catalyst for esterification of oleic acid with methanol in closed batch system. This study also focuses on use of design expert software to optimize the process parameters for esterification reaction in view to maximize oleic acid conversion by using RSM. The interaction between three crucial variables such as catalyst loading, methanol to oleic acid molar ratio, and reaction temperature were investigated with the Box−Behnken model and subsequently an empirical mathematical model correlating the response to the variables was developed and presented as well. The data obtained from experiments was also interpreted using the PH kinetic model incorporating the effects of reaction temperature.

Figure 1. Characterization of K10 and different wt % H3PW12O40 anchored to K10 catalysts.

Table 1. Total Acidity and BET Surface Area of Catalysts BET surface area (m2 g−1)

total acidity (mmol g−1)

H3PW12O40/

223 195

0.139 0.242

H3PW12O40/

156

0.328

H3PW12O40/

135

0.423

H3PW12O40/

104

0.426

catalyst K10 10% (w/w) K10 15% (w/w) K10 20% (w/w) K10 30% (w/w) K10

Before the measurements, catalyst sample was subjected to dehydration at 773 K in the presence of He (30 cm3 min−1) for 1 h. The temperature was then decreased to 323 K and then NH3 was permitted to adsorb a gas stream consisting of 10% NH3 in He for 1 h. It was then flushed with He for another 1 h. The NH3 desorption was carried out in He flow (30 cm3 min−1) by increasing the temperature up to 723 K with a heating rate of 10 K min−1. 2.3. Catalytic Evaluation and Analysis of Product. The experiments of esterification of oleic acid with methanol to produce methyl oleate biodiesel were carried out in a 100 mL cylindrical stainless steel batch reactor, under autogenous pressure (110−120 psi) with agitation speed of 400 rpm. Oleic acid, methanol, and a given amount of catalyst (with average particle size of 82.5 μm obtained by sieve analysis) totaling to 30 mL reaction volume was mixed in the reactor. The reactor was heated by an electric heater with a proportional−integral− derivative (PID) controller. The temperature was maintained within an accuracy of ±0.5 K by PID controller. The experiments were conducted at a temperature range of 393− 453 K, catalyst loading of 1−5 (wt % of oleic acid), methanol to oleic acid molar ratio of 4−8, and reaction time of 5 h. After carrying the reaction for a desired time, the reactor was quickly immersed in cool water bath to stop the reaction. Thereafter, reaction mass including the catalyst was drained out and centrifuged to separate the catalyst. The centrifuged product after removal of catalyst was then put in the Buchi Rotavac for the removal of methanol. After removal of methanol, two layers were observed which were then transferred to the separating vessel and allowed to separate overnight. The upper layer contained biodiesel and the bottom layer contained unconverted acid and the water. The reaction mass analyzed by HPLC (Model: Perkin-Elmer, Series 200), using a UV/Visible detector, coupled with RPC-18, 250 cm × 0.46 cm × 5 mm

2. EXPERIMENTAL SECTION 2.1. Materials. H3PW12O40, montmorillonite (K10; unhydrous basis: 68.49% SiO2, 29.06% Al2O3, 1.60% CaO, and 1.77% Na2O), oleic acid (99%), and methanol (99%) were obtained from M/s SD. Fine Chemicals, Mumbai (India). All reagents used were of analytical grade and used with no further purification. 2.2. Catalyst Synthesis and Characterization. A series of catalysts containing 10−30% of H3PW12O40 anchored to K10 were synthesized by incipient wetness technique. Initially H3PW12O40 was dissolved in methanol and then added to K10. The wet paste was dried on a water bath at 363 K for 5 h to remove methanol completely. Prior to use, the catalyst was activated at 373 K in presence of air for 4 h to remove moisture. The percentage (w/w) H3PW12O40 anchored to K10 was calculated on the basis of weight gain of catalyst after impregnation. The powder X-ray diffraction (XRD) patterns of synthesized catalysts were recorded on X-ray diffractometer (P Analytical PXRD system, Model X-Pert PRO-1712) using Cu Kα radiation with 0.0671/s scanning rate at 2θ ranging from 10 to 80° (Figure 1). Low temperature (77 K) nitrogen adsorption and desorption isotherms were obtained using SA 3100 analyzer (Beckman Coulter, CA, USA). The calcined catalyst sample was subjected for degassing at 573 K for 10 h before the measurements. The specific surface area is calculated using Brunaer−Emmett−Teller (BET) method (Table 1). The total acidity (Table 1) was measured by temperature programmed ammonia desorption (TPAD) using a Micromeritics AutoChem (2910, USA) equipped with thermal conductivity detector. B



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column at oven temperature of 323 K with mobile phase of hexane:isopropanol (40:60). The collected product was also confirmed by using an evaporative light scattering detector in HPLC. Various products were quantified with standard mixtures’ response factors and mass balance of the liquid was 98 ± 2%. The reaction products were also confirmed by GCMS (Shimadzu-QP5000). All the experiments were done in triplicate and the average values obtained with an error of ±3% were presented. 2.4. Experimental Design and Mathematical Model. An experimental design for the series of parameters used for methyl oleate biodiesel production by esterification of oleic acid with methanol over 20% (w/w) H3PW12O40/K10 was built by RSM with the Design-Expert Version 8.0.7.1 (Stat-Ease, Inc., Minneapolis, USA).35 The optimum process parameters for production of methyl oleate over 20% (w/w) H3PW12O40/K10 were determined by means of response surface methodology. The independent variables chosen were catalyst loading (X1), methanol to oleic acid molar ratio (X2), and reaction temperature (X3). The percentage oleic acid conversion (Y) was chosen to be the target or response parameter as a dependent variable. Seventeen sets of experiments (12 factorial points and 5 center points) were performed according to a 33 Box−Behnken experimental design (BBD).26−29 The three variables were tested at the three levels by associated minus signs (−1) for low levels, zero (0) representing center value and plus signs (+1) for high levels. The values coded for these factors were calculated by eq 1:

Xi =

xi − xo Δxi

Table 2. Selected Variables and Coded Levels Used in the Box−Behnken Design coded levels

(1)

k

k

k

∑ βi Xi + ∑ βiiXi 2 + ∑ βijXiXij + e i=1

i=1

i=1

symbol

−1

0

+1

X1 X2 X3

1 4 393

3 6 423

5 8 453

3. RESULTS AND DISCUSSION 3.1. Characterizations of Catalyst. The crystallinity and phase purity of synthesized samples were determined by XRD. In the case of K10 (Figure 1), there is a sharp peak at 2θ = 26.2, which belongs to the quartz and there is no effect on the 2θ value of quartz, even after anchoring H3PW12O40 to K10. It was observed from Figure 1 that with anchoring H3PW12O40 to K10 some crystallinity was lost and new additional peaks of H 3 PW 12 O 40 appeared. As percentage anchoring of H3PW12O40 to K10 increased from 10% to 30%, the crystallinity of K10 decreased by increasing new additional peaks of H3PW12O40 (Figure 1). This XRD confirmed that H3PW12O40 was properly anchored to K10. The surface area calculated by the BET method is presented as Table 1. The surface area of K10 (223 m2/g) was observed to be decreased with anchoring of H3PW12O40 to K10. The surface area found to be reduced may be due to blocking of pores by H3PW12O40 molecules. The total acidity of K10 and H3PW12O40 anchored to K10 samples are depicted as Table 1. H3PW12O40 anchored to K10 samples were observed to be more acidic as compared to plain K10. FTIR (Figure S1, Supporting Information) spectra of 20% (w/w) H3PW12O40 to K10 confirmed the preservation of Keggin structure after anchoring of H3PW12O40 to K10. TGA (Figure S2, Supporting Information) of 20% (w/ w) H3PW12O40 to K10 suggested existence of chemical interaction with intermolecular bonding between H3PW12O40 and support (K10) and hence an increase in the thermal stability. 3.1. Performance of Catalysts. K10 and H3PW12O40 anchored to K10 catalysts were evaluated for esterification of oleic acid. The reaction parameters used: catalyst loading of 2%, molar ratio of methanol to oleic acid of 4, reaction temperature of 393 K, and reaction time of 8 h. In general esterification is an autocatalytic reaction; hence, esterification of oleic acid with methanol occurs even in the absence of catalyst. For this reason, thermal reaction (blank) was performed at 393 K. The time courses for the oleic acid conversion over blank, K10, and 10−30% (w/w) H3PW12O40 anchored to K10 catalysts are represented as Figure 2. H3PW12O40 anchored to K10 samples have shown better activity compared to parent K10, which is attributed to the presence of more active acid sites. Heteropolyacids like H3PW12O40 exhibit a unique phenomenon called the pseudoliquid phase. Polar and basic molecules rapidly get absorbed into the solid lattice to react there, the solid catalyst acts similarly to concentrated solution. This behavior leads to high catalytic performance of catalyst.34 As the H3PW12O40 anchoring increased from 10 to 20% (w/ w), the rapid increase in oleic acid conversion (28−56%) was observed. This may be due to good distribution of the H3PW12O40 on K10, which increases Brönsted acid sites as shown in Table 1. In 15−20% (w/w) H3PW12O40 loading, the exponential increase in oleic acid conversion (43−56%) was observed. This increase may be due to substantial increase in

where Xi is the coded value of independent variable, xi is the real value of independent variable, xo is the real value of independent variable at the center point, and Δxi is (variable at high level − variable at low level)/2. The second-order model equation recommended by RSM was used to predict the optimum value and analyze the interaction between response of experimental design (the conversion of oleic acid) and the variables (process parameters). The quadratic equation model was described according to eq 2:32 Y = β0 +

variables catalyst loading (wt % of oleic acid) molar ratio (methanol to oleic acid) reaction temperature (K)

(2)

where Y is the response variable (oleic acid conversion, %); Xi is the coded levels of the independent variables. The terms of β0, βi, βii, and βij are the regression coefficient, the linear terms, the squared terms for the variable i, and the interaction terms between variables i and j, respectively. Xij, Xii, and Xi represent interactive, quadratic, and the linear terms of the coded independent variables, respectively. The k is the total number of variables used to optimize the oleic acid conversion. The “e” is a random error. The polynomial equation visualized the relationship between the response and experimental levels of each factor and deduced the optimum conditions by response surface and contour plots. The coefficient of determination (R2) could be used to evaluate the accuracy and general ability of the second-order multiple regression models. Its regression coefficient significance was tested by F-test value. Each factor in the experiment was established and coded into levels −1, 0, and +1 as shown in Table 2. C



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Figure 2. Catalytic performance of K10 and different weight percent H3PW12O40 anchored to K10 catalysts for esterification of oleic acid with methanol.

Figure 3. Predicted versus experimental values of oleic acid conversion (%) over 20% (w/w) H3PW12O40/K10 catalyst.

total acidity. Further increase in H3PW12O40 anchoring from 20 to 30%, the marginal increase in oleic acid conversion (56− 56.5%) was obtained. This marginal increase in oleic acid conversion at (30%) H3PW12O40 may be due to multilayer formation of excess H3PW12O40 on K10 support, leads to marginal increase in Brönsted acidity and drop in surface area (Table 1). The selectivity toward methyl oleate in all the experiments was 100%. It has been observed that oleic acid conversion reached a maximum at a reaction time of 5 h; thereafter, it was stable (Figure 2). Hence, the optimum reaction time of 5 h was used for all further experiments. In present case, 20% (w/w) H3PW12O40/K10 was found to be a potential catalyst for production of methyl oleate biodiesel. Hence, the influence of various parameters for methyl oleate biodiesel production over 20% (w/w) H3PW12O40/K10 was further investigated with RSM design. The optimization of process parameters in view to maximize the oleic acid conversion over 20% (w/w) H3PW12O40/K10 catalyst is presented later. The reusability of 20% (w/w) H3PW12O40/K10 catalyst was also tested at optimized process parameters and presented later. 3.2. RSM Analysis. 3.2.1. RSM Experiments and Fitting the Model. A Box−Behnken design (BBD) center-united design was employed to design the experiments and the results obtained after running the 17 experiments for the statistical design are shown in Table S1 (Supporting Information). The best-fitting models were determined by multiregression and backward elimination. The each value of oleic acid conversion reported in Table S1 was obtained as an average of triplicate determinations with fixed reaction time of 5 h. As shown in Table S1, the oleic acid conversion increased from 58% to 97%, depending on the reaction conditions. On the basis of the RSM analysis, the second-order quadratic model relationship between the oleic acid conversion (Y) and the process variables in coded units is presented as eq 3:

and predicted oleic acid conversion (calculated by eq 3). A positive sign of the coefficients in linear terms reveals that with an increase in the variables the oleic acid conversion increases linearly (synergistic effect), while a negative sign indicates an antagonistic effect.26−29 From the eq 3, oleic acid conversion has linear and quadratic effects by the three process variables. Catalyst loading (X1) has the strongest effect on the response since the coefficient of X1 (9.63) is the largest compared to the other investigated factors. The next most significant effect on the response is reaction temperature (X3), followed by molar ratio (X2) and interaction effects between parameters (X1X2), and slightly weaker interaction effects between parameters X2X3 and X1X3 were observed. This may be due to cumulative effects of reaction parameters; similar observations were reported in literature.26,27,33 Statistical analysis includes the interaction effects and the main effects of the variables on the oleic acid conversion. The ANOVA tests give the statistical significance of each effect by comparing with the mean square and the estimated error within the range of experimental conditions (Table S2, Supporting Information). F-values (F) are estimated by sum of squares, which are ratios of the effect of respective mean square and mean square error.26−29,36,37 The model F-value of 193.32 implies that the model is significant. There is only a 0.01% chance that a “model F-value” this large (193.32) could occur due to noise. Statistical model fit summary lack of fit tests with a sequential model sum of squares advocated a quadratic model as the best fitting model. The values P < 0.05 indicate model terms are significant, in this case X1, X2, X3, X1X2, X2X3, X12, X22, and X32 are significant model terms. The coefficient of determination (R2) of 0.996 indicated that the model could explain 99.6% of the variability. The R2predicted of 0.9359 is in reasonable agreement with the R2adjusted of 0.9908. A similar range of R2 values were reported by other researchers.23,26,36,37 The value of the adjusted determination coefficient (R2-adjusted = 0.9908) is found to be very high to advocate for a high significance of the model.23,26,36,37 Adequate precision measures the signal-tonoise ratio. A ratio greater than 4 is desirable. In present study,

Y = +93 + 9.63X1 + 5X 2 + 7.88X3 + 4.85X1X 2 + 4X1X3 + 4.75X 2X3 − 11.75X12 − 4.5X 2 2 − 10.25X32

(3)

where Y represents the oleic acid conversion and X1, X2, and X3 are the coded variables in esterification reaction. Figure 3 demonstrated the good linear correlations between the actual D



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transfer rate between limiting reactant (oleic acid) and active sites of catalyst which in turn increases the oleic acid conversion. The interaction effect of two variables was significant with the shape of contour curve ellipse mound (Figure 4) and the low p-value (443 K), the marginal decrease in oleic acid conversion was observed, which may be due to slight deactivation of catalyst. The contour line with circular shape demonstrated that the combined effect of the catalyst loading and reaction temperature was significant. The result is also supported lower p-value (0.0005) of the interaction X1X3 term (Supporting Information Table S2). Figure 6 shows the effects of different molar ratio of methanol to oleic acid and reaction temperature on the oleic acid conversion in three-dimensional surface response and twodimensional interaction plots at constant catalyst loading of 3% and reaction time of 5 h. From the figures, it is obvious that at any designated quantity of molar ratio from 4 to 8, the oleic acid conversion increased proportionally with reaction temperature. At higher temperature (>443 K), there may be cracking of excess methanol to dimethyl ether, which deactivate the catalyst marginally; this was reflected in slight drop in oleic acid conversion. The interaction effect of the two variables studied was significant with shape of contour curve ellipse mound (Figure 6) and with low p-value (0.0002) of the interaction term. From the above results, we found the interaction effect between catalyst loading and molar ratio of methanol to oleic acid was the most significant parameter affecting the oleic acid conversion (Supporting Information Table S2).

Figure 4. Response surface plot for esterification of oleic acid with methanol over 20% (w/w) H3PW12O40/K10 catalyst as a function of catalyst loading and molar ratio of methanol to oleic acid at constant reaction time of 5 h and reaction temperature of 423 K.

The interaction between the corresponding variables would be negligible when the contour of the response surface is circular. On the other hand, the interactions between the relevant variables would be significant when the contour of the response surfaces is elliptical.26,29 The effect of interaction between catalyst loading and molar ratio of methanol to oleic acid at constant reaction time of 5 h and reaction temperature of 423 K is presented in Figure 4. The oleic acid conversion was higher than 58% when the catalyst loading was between 1 and 5% and the molar ratio of methanol to oleic acid was from 4 to 8. More catalyst reveals more active sites which participate in the reaction and catalyze the production of biodiesel. It seemed that the increase in methanol to oleic acid molar ratio had significant effect on the oleic acid conversion at different catalyst amounts. In general, increase in catalyst loading with more dilution of reactants enhances mass E



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Figure 6. Response surface plot for esterification of oleic acid with methanol over 20% (w/w) H3PW12O40/K10 catalyst as a function of molar ratio of methanol to oleic acid and reaction temperature at constant catalyst loading of 3% and reaction time of 5 h.

Figure 7. Reusability of 20% (w/w) H3PW12O40/K10 catalyst for esterification of oleic acid with methanol at optimized process parameters: catalyst loading of 5%, molar ratio of 8, reaction temperature of 438 K, and reaction time of 5 h.

3.2.3. Optimization of Process Parameters for Esterification. In order to generate optimal conditions for esterification of oleic acid to produce biodiesel, numerical feature of the Design-Expert Version 8.0.7.1 software was applied. The independent parameters used in numerical optimization including catalyst loading, molar ratio of methanol to oleic acid, and reaction temperature were set within the range between low (−1) and high (+1) while the oleic acid conversion was set to maximum value (Table 2), with minimum and maximum conversion preset of 58−97%.36,37 Subsequently, 43 solutions for the optimum conditions were generated by the software and the solution with the highest desirability and oleic acid conversion was selected to be verified by experiments. The optimum conditions including the predicted and experimental oleic acid conversion are shown in Table 3. The experimental value of oleic acid conversion

(fresh and three reuses). After four cycles, marginal decrease in the oleic acid conversion 100−96% was observed. The H3PW12O40 leaching test was carried out with 10% ascorbic acid solution.38 The test confirmed no leaching of H3PW12O40 during subsequent reaction cycles. The XRD (Figure S3, Supporting Information) of catalyst reused five times revealed the maintenance of crystalline structure after reusability. 3.4. Pseudohomogeneous Kinetic Model. The esterification reaction of oleic acid (A) with methanol (B) for producing methyl oleate (C) and water (D) in the presence of solid acid catalyst can be given as follows:24,30−32 oleic acid(A) + methanol(B) ↔ methyl oleate(C) + water(D)

Table 3. Optimum Process Parameters for Esterification of Oleic Acid with Methanol over 20% (w/w) H3PW12O40/K10 for Reaction Time 5 h and Validation Model Adequacy parameters

catalyst loading, X1 (wt %)

molar ratio (methanol to oleic acid), X2

reaction temperature, X3 (K)

oleic acid conversion, Y (%)

predicted experimental

4.60 5

7.71 8

437.62 438

97 100

a A + b B ↔ cC + d D

The kinetic model is built on the following assumptions:3,26,30−34 The rate of the noncatalyzed reactions is negligible compared with the catalyzed reactions. The activity of all the catalytic sites on the surface of heterogeneous catalyst is assumed to be same. The complete reaction mixture is considered to be an ideal solution. The internal and external mass transfer limitations of the heterogeneous catalyst are excluded by studying the effect of agitation speed (rpm) and catalyst particle size. It has been shown that there is no external or internal mass transfer resistance at agitation speed above 200 rpm and at an average catalyst particle size of below 82.5 μm.3,30,34 Hence, all experimentations were performed at agitation speed of 400 rpm and with average catalyst particle size of 82.5 μm. The reaction rate expression for the PH second-order reversible reaction can be described as

represented in table is the average of three independent experiments. The obtained average optimum oleic acid conversion of 100% is well in agreement with the predicted value (97%), with an error of 3%. As the experimental error is less than ±5%, it can be concluded that the proposed statistical model was adequate for predicting the oleic acid conversion. Thus, response surface methodology with Box−Behnken design with a quadratic model was found to be adequate and statistically accurate to optimize the free fatty acid oleic acid conversion to 100% over 20% (w/w) H3PW12O40/K10 catalyst. 3.3. Catalyst Reusability. The reusability of 20% (w/w) H3PW12O40/K10 catalyst was tested at optimized process parameters obtained by RSM design: catalyst loading of 5%, molar ratio (methanol to oleic acid) of 8, reaction temperature of 438 K, and reaction time of 5 h (Table 3). After completion of each reaction, the catalyst sample was filtered and used with no post-treatment. It is clear from Figure 7 that the 20% (w/w) H3PW12O40/K10 catalyst was stable for four reaction cycles

⎛ dC ⎞ −⎜ A ⎟ = kCA aC Bb − k′CCcC Dd ⎝ dt ⎠

(4)

where CA, CB, CC, and CD denote the concentration of oleic acid, methanol, methyl oleate, and water, respectively; a, b, c, and d refer to their reaction orders; k and k′ are kinetic constants for the forward and reverse reaction, respectively. The kCBb can be considered negligible due to higher methanol F



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concentration than oleic acid. Also, k > k′,30,31 so eq 4 can be simplified as follows:

⎛ dC ⎞ −⎜ A ⎟ = kCA n ⎝ dt ⎠

(5)

CA = CAo(1 − X )

(6)

X and CAo refer to the fractional conversion of oleic acid and the initial concentration of oleic acid. Thus, eq 6 can be converted to eq 7 ⎛ dX ⎞ k −⎜ ⎟ = [C (1 − X )]n = k1[CAo(1 − X )]n ⎝ dt ⎠ CAo Ao

(7)

where (k/CAo) = k1 when n ≠ 1 eq 7 is integrated to (1 − X )1 − n = 1 + (n − 1)k1tCAon

(8)

The values of kinetic parameter were calculated by minimizing the sum of square errors among all experimental data. The reaction order fitted with eq 8 at different temperatures and the reaction order was calculated to be second-order. Thus, eq 8 can be changed to eq 9. X = kCAot (9) 1−X For kinetic purpose the independent experiments were performed at different reaction temperature (403−433 K) and presented as Figure 8. The maximum variation in oleic acid

Figure 9. Pseudohomogeneous (PH) model plot of X/(1 − X) vs CAot for esterification of oleic acid with methanol over 20% (w/w) H3PW12O40/K10 at optimized reaction conditions to obtain reaction rate constants (k) at different reaction temperatures.

⎛ E ⎞ k = A exp⎜ − a ⎟ ⎝ RT ⎠

(10)

The plots of ln k can be used as a function of the reciprocal temperature: ⎛ E ⎞ ln k = ⎜ − a ⎟ + ln A ⎝ RT ⎠

(11)

The dependence of the reaction constants on reaction temperature is described by the Arrhenius equation (eqs 10 and 11). The plot of ln k vs 1/T is represented by a straight line (Figure 10). Both the frequency factor A, and the activation

Figure 8. Esterification of oleic acid with methanol over 20% (w/w) H3PW12O40/K10 at different reaction temperatures keeping other reaction conditions at catalyst loading of 5% and molar ratio of 8. Figure 10. Arrhenius plot of esterification of oleic acid with methanol over 20% (w/w) H3PW12O40/K10 at optimized reaction conditions to obtain activation energy (Ea) and pre-exponential factor (A).

conversion was obtained in the reaction temperature range of 403−433 K and the same was used for kinetic study. Figure 9 shows a linear relationship between X/(1 − X) and CAot. The reaction rate constants (k) at different reaction temperatures were obtained by linear regression, using the software OriginPro70 (Table S3, Supporting Information). The value of reaction rate constants (k) was observed to be increased with rise in reaction temperature and fitted well with the straight line (Figure 9). This clearly indicates that the PH kinetic model is valid for esterification reaction.3,30,31,34 Temperature dependence Arrhenius equation is described as

energy Ea, were obtained by linear regression, using the software OriginPro70. The pre-exponential factor (A) and activation energy (Ea) for esterification of oleic acid with methanol were calculated to be 20400.2 L min−1 mol−1 and 43.7 kJ mol−1, respectively. It has been reported that the activation energy for diffusion limited reactions is low (10−15 kJ mol−1) and for kinetically controlled reactions show activation energy excess.17−19 Hence in present case, the G



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20% (w/w) H3PW12O40/K10 is active catalyst for the esterification of free fatty acid oleic acid. The optimum values for maximum oleic acid conversion was obtained by using a Box−Behnken center-united design requiring a small number of experiments. The present method of using 20% (w/w) H3PW12O40/K10 catalyst for production of biodiesel follows green principles with potential advantages of 100% oleic acid conversion (100%), at milder operating conditions and better catalyst reusability (four cycles). The second-order pseudohomogenous (PH) kinetic model indicated that the esterification of oleic acid with methanol is kinetically controlled owing to high activation energy of 43.7 kJ mol−1.

esterification reaction is kinetically controlled owing to the high activation energy (43.7 kJ mol−1). Comparison of activation energies, obtained for esterification of oleic acid with methanol for the reported catalysts with the present catalyst, is shown in Table 4. The obtained activation energy value (43.7 kJ mol−1) Table 4. Comparison of Activation Energy with the Reported Catalyst substrate oleic acid oleic acid oleic acid oleic acid

solvent

catalyst

activation energy, Ea (kJ mol−1)

methanol

TPA3/SBA-15

44.6

methanol

TPA3/Hβ

45.2

methanol methanol

TPA3/MCM41 20% (w/w) H3PW12O40/ K10

52.4 43.7

ref

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Brahmkhatri and Patel17 Patel and Narkhede18 Patel and Brahmkhatri19 this paper

ASSOCIATED CONTENT

* Supporting Information S

Additional characterization of catalysts by FTIR (Figure S1), TGA (Figure S2), and also XRD (Figure S3) of five times used catalyst. Tables on experimental design by Box−Behnken design matrix, ANOVA, kinetic parameters, and comparison of oleic acid conversion with reported catalyst are included as Tables S1−S4. This information is available free of charge via the Internet at http://pubs.acs.org/.

for esterification of oleic acid with methanol over 20% (w/w) H3PW12O40/K10 is near to the reported activation energy (44.6 kJ mol−1) over TPA3/SBA-15 catalyst.17 The reported TPA3/ SBA-15 catalyst17 used higher (30%) loading of H3PW12O40 than in the present study (20%). Hence the 20% (w/w) H3PW12O40/K10 catalyst is better than reported catalyst (Table 4). 3.5. Merits of Present Method. Literature survey clearly reveals that operating parameters used for the esterification of oleic acid with methanol in the present study are milder than the parameters used by other researchers (Table S4, Supporting Information). The reported catalysts synthesized by anchoring of TPA to SBA-15, Hβ, and MCM-41 are costly supports than K10 (support used in present study).17−19 In this context, H3PW12O40/K10 catalyst is cheaper catalyst than reported. Use of lower oleic acid conversion process6,7,10,11,17,18 may not be economical as a separation of unreacted oleic acid from product is challenging and it will lead to the additional separation cost (equipment as well as process). The 20% (w/w) H3PW12O40/ K10 catalyst gave complete oleic acid conversion (100%), so there is no issue of unreacted oleic acid separation. The reported processes13,15,17−19 used higher molar ratio (methanol to oleic acid) than present study and involve additional separation by distillation step for the removal of excess methanol. The molar ratio (methanol to oleic acid) of 8 used in the present study is much lower than reported.9,12,13 Although, some of the reported catalysts offered better activity, the catalysts lacks in its reusability.9,12,13 Liu et al.14 reported use of biomass based sulfonated carbonized corn straw catalyst to obtain 98% yield of methyl oleate, but there is no data about catalyst deactivation behavior and regeneration of catalyst. In this context, the present method of using 20% (w/w) H3PW12O40/K10 catalyst for the production of methyl oleate biodiesel offers more principles of green engineering and chemistry with potential advantages with respect to complete oleic acid conversion, at milder operating conditions and better catalyst reusability for minimum of four cycles without considerable loss in activity (Figure 7).

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AUTHOR INFORMATION

Corresponding Author

*Phone: +91-20-25902458. Fax: +91-20-25902634. E-mail: vv. [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This paper is dedicated to Prof. G. D. Yadav on the occasion of his 60th birthday. Prof. G. D. Yadav has been a mentor, motivating force, and fantastic mind who has done Indian Chemical Engineering a great service.

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REFERENCES

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Article

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Process Optimization by Response Surface Methodology and Kinetic

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