Biodiesel production from the esterification of fatty acid over organophosphonic acid

Biodiesel production from the esterification of fatty acid over organophosphonic acid

Accepted Manuscript Title: Biodiesel production from the esterification of fatty acid over organophosphonic acid Author: Wei Liu Ping Yin Xiguang Liu ...

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Accepted Manuscript Title: Biodiesel production from the esterification of fatty acid over organophosphonic acid Author: Wei Liu Ping Yin Xiguang Liu Shaohua Zhang Rongjun Qu PII: DOI: Reference:

S1226-086X(14)00227-5 http://dx.doi.org/doi:10.1016/j.jiec.2014.04.029 JIEC 2019

To appear in: Received date: Revised date: Accepted date:

10-2-2014 5-4-2014 27-4-2014

Please cite this article as: W. Liu, P. Yin, X. Liu, S. Zhang, R. Qu, Biodiesel production from the esterification of fatty acid over organophosphonic acid, Journal of Industrial and Engineering Chemistry (2014), http://dx.doi.org/10.1016/j.jiec.2014.04.029 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Biodiesel production from the esterification of fatty acid over

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Wei Liu, Ping Yin*, Xiguang Liu, Shaohua Zhang, Rongjun Qu*

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organophosphonic acid

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School of Chemistry and Materials Science, Ludong University, Yantai 264025, P. R.

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China

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Research highlights

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The catalyst PA/NaY (PA= organophosphoric acid) was developed Esterification of free fatty acid stearic acid with ethanol was catalyzed by PA/NaY Effects of experimental parameters in the esterification reaction were studied The biodiesel production process optimization was carried out by RSM The catalytic kinetics study was conducted and modeled

ABSTRACT

Biodiesel production from the esterification of fatty acid (stearic acid) with ethanol catalyzed by PA/NaY (PA= organophosphonic acid, NaY = NaY molecular sieve) was investigated, and the effects of PA loading, catalyst amount, molar ratio of ethanol to acid, reaction time and temperature on the esterification reaction were examined. The

* Corresponding authors. Tel: + 86-535-6696162; fax: + 86-535-6697667. E-mail address: [email protected], [email protected]

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optimum values for maximum esterification percentage can be obtained by using a Box-Behnken center-united design with a minimum of experimental work. The pseudohomogeneous (PH) model has been used to simulate the experimental data, and

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the calculated values of Arrhenius coefficient and activation energy are 6.394×103 and

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70.51 kJ/mol, respectively.

Keywords: Biodiesel; Catalysis; Kinetics; Optimization; Esterification; Stearic acid

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1. Introduction

Recently, alternative fuels for diesel engines are becoming increasingly important

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because of the diminishing petroleum reserves and the environmental consequences of exhaust gases from petroleum-fueled engines. Therefore, a clean alternative fuel is

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increasingly in demand. Biodiesel obtained from renewable feedstock, such as vegetable oils or animal fats, possesses many advantages, i.e. cleaner engine

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emissions, biodegradable, renewable and superior lubricating property [1-4], which makes it an excellent substitute or additive to conventional diesel fuels. It is usually produced by chemical reaction of triglyceride (vegetable oil/animal fat) with short-chain alcohol (methanol/ethanol). However, there are some oils including significant amounts of free fatty acids (FFAs), for example, non-edible oils, animal fats and oils, waste oil and byproducts of the refining vegetable oils. Dias et al. found that for high acidity values (> 20 mgKOH/g) the cheap lime catalyst used in biodiesel

synthesis from waste frying oil became amorphous and inactive because of soap formation [5]. Due to some animal and vegetable oils contain a certain amount of

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stearic acid, the study on the esterification reactions for the stearic acid has a significant effect on the biodiesel production. Esterification is one of the most important reactions in chemical industry where ethyl stearate is usually produced by

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using homogeneous acid catalysis method. Homogeneous acid-catalyzed reactions

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can generate environmental and corrosion problems. The heterogeneously catalyzed

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esterification reactions are attracting attentions more and more because of their easy separation of products, decreasing the amount of waste water, downsizing the process

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equipment, and, in consequence, reducing the environmental impact and the process cost. Therefore, the use of solid catalysts in the esterification reactions is extremely

wide variety of fine chemicals.

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important in developing cleaner and more economically improved processes for a

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Recently, to improve the conversion of acid and the efficiency of work, a statistical method is presented to indicate the parameters for an optimized synthesis

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process, which uses the response surface methodology (RSM). The advantage of RSM is that it allows the user to gather large amounts of information from a small number of experiments [6]. The use of RSM is also possible to observe the effects of individual variables and their combinations of interactions on the response. The kinetics for the esterification catalyzed by various catalysts has been studied

in several reports. Oliveira et al. [7] studied the kinetics of the esterification of oleic acid with ethanol using a free or immobilized lipase as catalyst, and they found that the reaction followed the Michaelis–Menten kinetics and the kinetic constants were evaluated. Umar et al. [8] investigated ethyl tert-butyl ether synthesis from ethanol

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and tert-butyl alcohol with different macroporous ion exchange resin catalysts, and the quasi-homogeneous (QH) model represented the system very well over the wide range of reaction conditions. Zhang et al. [9] studied the esterification of lactic acid

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[80% (by mass)] with ethanol in the presence of five acid ion-exchange resins. The

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LH model based on the selective adsorption of water and ethanol on the catalyst was

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found to be a more appropriate model to describe the kinetic behavior of these systems. Song et al. [10] studied the kinetics of the esterification of oleic acid

by: dcA = kcαA cBβ − k ' cCγ cDλ dt

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catalyzed by zinc acetate in sub-critical methanol, and the reaction rate was expressed

(1)

where cA, cB, cC and cD denote the concentrations of oleic acid, methanol, methyl

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oleate and water, respectively; α, β, γ and λ refer to their reaction orders. k and k’ are the kinetic constants for the forward and reverse reactions, respectively. The reaction

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order n= 2.2 and activation energy Ea=32.62 kJ/mol were obtained. In the present work, the esterification of stearic acid with ethanol catalyzed by

PA/NaY was investigated, and the effect of the loading of PA, catalyst amount, molar ratio of alcohol to acid, reaction time and temperature on the esterification reaction was examined. Response surface methodology (RSM) was employed to optimize the levels of catalyst amount, molar ratio of alcohol to acid, reaction time and temperature. Moreover, a kinetic model was proposed and the kinetic parameters were determined by fitting the model with the experimental results.

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2. Experimental 2.1 Materials and synthesis of the catalyst The chemicals used in the work were of AR grade purchased from Tianjin

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Chemical Industry, China. The preparation of PA/NaY was carried out by immersion

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method using organophosphoric acid and NaY zeolite. Organophosphoric acid (PA) for requirement and 2g of NaY molecular sieve were added in 20 ml of water, and

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allowed to stirred on a magnetic stirrer using a magnetic paddle at 50 oC for 4 h. Then

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the obtained product was filtered by centrifugal machine, and dried at 50 oC for 3 h. The solid acid catalyst (PA/NaY) was obtained.

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2.2 Esterification reaction

Esterification reactions were carried out under batch reaction conditions using a

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250 ml flask fitted with a stirrer, a thermometer and a water divider. The outlet of the water divider was full of alcohol and connected to a reflux condenser. The

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experimental setup for the esterification reaction of the biodiesel production using PA/NaY catalyst was shown in Scheme (available in the Supplementary Materials). A typical reaction mixture in the reactor contained stearic acid (21.3g), ethanol and a freshly activated catalyst. The temperature of the oil bath was fixed at a setting value (90 – 110 °C). After a certain time of reaction operation, the reaction mixture was filtered by vacuum filtration to separate the solid catalyst, and the product was transferred to a three-necked flask to remove water and ethanol by reduced pressure distillation. 2.3 Analytical procedure

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The esterification reaction between stearic acid and alcohol can be represented as: catalyst

stearic acid (A) + alcohol (B)

ethyl stearate (C) + water (D)

(2)

The amount of unreacted stearic acid in the product mixture was obtained from its

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acid value (AV), which can be determined by titration with NaOH-C2H5OH solution.

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The conversion of stearic acid can be calculated according to the following equation,

(3)

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x = (1 − AV 1 / AV 0) × 100%

where AV0 and AV1 are the acid values of feed and products, respectively, which is

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similar with that of Ref.[10]. 2.4 Experimental design and optimization by RSM

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RSM was employed to analyze the operating conditions of the esterification reaction to obtain a high conversion percent. The experimental design was carried out

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by three chosen independent process variables at three levels (Table 1). The studied factors were: catalyst amount, molar ratio of alcohol acid, reaction time and

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temperature. The software Minitab was used for designing and analyzing the experimental data. The independent variables (factors) and their levels, real values as well as coded values are presented in Table 1. The conversion percent of stearic acid was the response of the experimental design. The model equation was used to predict the optimum value and subsequently to

elucidate the interaction between the factors. The quadratic equation model for predicting the optimal point was expressed according to Eq. (4): 4

4

i =1

i =1

3

Y = λ0 + ∑ λi xi + ∑ λii xi2 + ∑

4

∑λ x x

i =1 j = i +1

ij i

j

(4)

where λ 0 , λi , λii and λij are regression coefficients ( λ 0 is constant term, λi is linear 6

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effect term, λii is squared effect term, and λij is interaction effect term), and Y is

3. Results and discussion

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3.1.1 Effect of the loading of PA on the esterification reaction

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3.1 Effect of the operating conditions on the esterification reaction

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the predicted response value [11].

As shown in Fig.1, the conversion of stearic acid increases with the loading of

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PA up to 40 ml, which is because with increase of the loading of PA, the number of active site increases. And then decreases with further increase of the loading of PA up

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to 50 ml because high concentration of organophosphonic acid might destroy the pore structure of NaY, as a result, the activity of this catalyst becomes lower. Therefore,

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the optimal loading amount of catalyst was 40 ml of PA in the further research work.

3.1.2 Effect of catalyst amount on the esterification reaction

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Esterification reactions usually have low equilibrium constants and require the

addition of a catalyst in order to obtain high yields. Generally, they were carried out with Brφnsted acid catalysts. The effect of catalyst amount on stearic acid conversion was investigated. The results are shown in Fig. 2. It can be seen from Fig. 2 that catalyst amount of 2.0g produced higher conversion compared to catalyst amount of 1.5g. Therefore, 2.0g of PA/NaY was considered optimum for this study.

3.1.3 Effect of molar ratio of alcohol to acid on the esterification reaction The effect of molar ratio of alcohol to acid added to the reaction system on stearic acid conversion has been investigated, and Fig. 3 displayed that molar ratio of alcohol

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to acid of 4:1 provided the best conversion. The reason for a drastic drop of conversion with the increase of mole ratio from 4: 1 to 8: 1 can be attributed to the saturation of the catalytic surface with the alcohol or prevention of nucleophilic attack

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by shielding protonated alcohol by its own excess. This confirms Eley–Rideal

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mechanism with chemisorption of alcohol on the Bronsted acid sites [12]. As a result,

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4:1 was considered to be the optimum molar ratio of the reactants for this reaction.

3.1.4 Effect of reaction time on the esterification reaction

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Reaction time studies are useful in identifying product formation and reactant disappearance, and Fig. 4 showed the esterification reaction progress versus the

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reaction time. The stearic acid conversion showed an increasing-decreasing pattern. The result indicate that when reaction time up to 4 h, the esterification had reached

to 7 h.

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equilibrium, and then the conversion decreases with further increase of reaction time

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3.1.5 Effect of temperature on the esterification reaction Temperature is one of the most important variables affecting the conversion of

stearic acid. In order to optimize the reaction conditions, the effect of different reaction temperature on the esterification was investigated in the range of 90 – 140 oC,

and the results were shown in Fig.5. Stearic acid conversion increased with temperature from 90 to 100oC. This was because increase in temperature caused higher molecule motion speed and mass transfer rate. A high temperature could greatly accelerate the reaction rate and improve the mass transfer limitation between reactant and catalyst. However, a decrease in temperature from 100 to 110oC reduced

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stearic acid conversion. And then, the conversion slightly changes with temperature from 110 to 140oC. This result for the trend of reaction temperature corroborated those obtained by Chongkhong et al. [13] where the esterification reaction of palm

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fatty acid distillate was carried out. Then, the result in the present work suggested that

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there was an optimum value for the temperature because there was a chance of loss of

ethanol and increasing of darkness color of the product at higher temperature (> 100

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°C). Moreover, biodiesel production reactors involve a complex set of chemical

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reactions and heat transfer characteristics. Energy consumption for industrial scale production will increase with the increase of reaction temperature [14]. Therefore, in

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order to save the energy of the process, 100 oC was selected as the optimum reaction

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3.2 RSM analysis

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temperature.

3.2.1 RSM experiments and fitting the models

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RSM is a technique for designing experiment, evaluating the effects of reaction

parameters on the response, and also optimizing the process. It has been widely used for multivariable optimizing the reaction process [15-16]. A Box-Behnken center-united design was employed to design the experiments. The results obtained after running the 27 trials for the statistical design are shown in Table 2. The best-fitting models were determined by multi-regression and backward elimination. Table 2 also presented the experimental values of stearic acid conversion and the fitting values of stearic acid conversion, and then the results indicated a good fit. Table 3 lists the significant (P< 0.05) regression coefficients of the established model

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equation. Three linear coefficients (Catalyst amount, Molar ratio of ethanol to acid and reaction temperature), all the quadratic terms except quadratic of temperature (X4*X4) and all the cross-product coefficients except two terms(X1*X4 and X2*X3)

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were highly significant (P< 0.02). One quadratic terms (temperature) and two

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cross-product coefficients (X1*X4 and X2*X3) was very insignificant (P> 0.5). The

values of the coefficients and the analysis of variance (ANOVA) are also presented in

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Table 3. According to the ANOVA, R2, which means the fraction of the variation of

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the response explained by the model, and Q2, which indicates the fraction of the variation of the response predicted by the model, were 0.9661 and 0.8069,

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respectively (Table 3). Table 3 also showed that the probabilities for the regression of the model were significant (P < 0.001), meaning that the models were statistically

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good, and the models had no lack of fit at 92% level of significance. As a result, well-fitting models for were successfully established [11]. Using the designed

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experimental data, the polynomial model for the conversion of stearic acid was regressed by considering the significant terms and was shown as follows: Y = 68.9800 + 0.9867 X 1 + 1.7625 X 2 + 2.7083 X 4 − 6.3554 X 12 − 2.2417 X 22

− 3.3392 X 32 + 3.1975 X 1 X 2 + 1.9425 X 1 X 3 − 2.4375 X 2 X 4 + 2.5625 X 3 X 4

(5)

3.2.2 Effects of the process variables on stearic acid conversion The response surfaces and contour plot for the abovementioned model for stearic acid conversion (Eq. 5) are generally used to evaluate the relationships of parameters. However, it was plotted as a function of two variables, while keeping other variables at the zero level.

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Fig. 6 demonstrated the effects of four process variables on stearic acid conversion. Fig. 6(a) shows the effects of catalyst amount, molar ratio of alcohol to acid and their reciprocal interaction on stearic acid conversion. At low introduced

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catalyst amounts, stearic conversion slightly decreases with increasing of molar ratio

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of alcohol to acid. However, at high catalyst amounts, molar ratio of alcohol to acid

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enhances stearic acid conversion. Stearic acid increases with catalyst amount up to 2.0g (level 0), and then decreases with further increase of catalyst amount up to 2.2g

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(levels 1). The effects of catalyst amount, reaction time and their reciprocal on stearic acid conversion are shown in Fig.6 (b). Stearic acid conversion slightly increases with

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the increase of reaction time. It was clear that when the reaction time was fixed at one level, the change of stearic acid conversion showed a parabolic pattern with catalyst

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amount. Fig. 6(c) depicted the effects of molar ratio of alcohol to acid and temperature on stearic acid conversion. It was evident that the stearic acid conversion

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linearly increased with the increase of molar ratio of alcohol to acid or temperature. The saddle point (minimax) nature of the plot indicates that the interaction between molar ratio of alcohol to acid and temperature is likely to affect the esterification reaction. It can be seen from Fig. 6(c) that if any movement is done from the stationary point, depending on the direction of the movement, stearic acid conversion increases or decreases. In this case, lower molar ratio of alcohol to acid and higher temperature results in higher stearic acid conversion, or higher molar ratio of alcohol to acid and lower temperature exhibit a similar tendency. It was found that reaction time and temperature affected stearic acid conversion in a similar fashion as that

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affected by molar ratio of alcohol to acid and temperature shown in Fig. 6(d) which was just like the case in [17]. 3.2.3 Optimization of reaction conditions

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The optimum values of selected variables were obtained by solving the

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regression equation (Eq. (5)) using the software Matlab6.5. For convenience, the optimal conditions for synthesis of ethyl stearate by the solid acid catalyst estimated

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by the model equation were X1= 2.0 g, X2= 4: 1, X3= 4 h and X4= 95 oC. The

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theoretical conversion yield predicted under the above conditions was Y = 69.10%. To confirm the prediction by the model, the optimal conditions were applied to three

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independent replicates for ethyl stearate synthesis. The average conversion yield reached 69.6 ± 0.7% and was well within the estimated value of the model equation.

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Therefore, in the optimization process, the software Minitab was used to conduct data analysis related to this study, mathematical model that described the relationship and

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interaction between the independent variables and the response was produced for the stearic acid conversion. The application of RSM yielded the regression equation (Equ. (5)) which was an empirical relationship between the response variable and the test variables in coded units. This model has been developed for predicting the response as a function of independent variables and their interactions. The optimal values of the selected variables were obtained by solving the regression equation using the software Matlab 6.5. This model was employed find the value of the process variables that gave maximum conversion of stearic acid. 3.3 Kinetic model

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Qu et al. [18] investigated PH, LH and ER models to simulate the experimental data for the esterification of lactic acid with butanol and isobutanol catalyzed by ion-exchange resins, and found that all these models were able to describe the kinetics

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of this esterification. Oliveira et al. [11] found that the integrated Michaelis-Menten

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equation described successfully the experimental for the enzymatic esterification of

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oleic acid with ethanol. Induri et al. [19] studied the esterification of maleic anhydride with methanol catalyzed by H-Y zeolite. They found that Langmuir-Hinshelwood and

homogeneous kinetic model was proposed.

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Eley-Rideal mechanism were not satisfactorily fitted for this esterification, and the

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In this work, the esterification reactions were carried out under the optimal conditions, and the conversion of stearic acid on the different time at different

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temperatures are shown in Table 4. It is supposed that the forward and reverse reactions for this esterification were second order reactions. So the apparent reaction

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rate for the esterification of stearic acid and ethanol can be described as:



dCA = k + C A C B − k − CC C D dt

(6)

where CA, CB, CC and CD denote the concentrations of stearic acid, alcohol, ethyl stearate, water, respectively. k+ and k- are the kinetic constants for the forward and

reverse reactions, respectively [20]. In this work, the produced water is continuously separated using the azeotropic method with ethanol during the esterification reaction. Therefore, this study thinks that the concentration of water in reaction system is very low. Thus this esterification can be approximately described by the irreversible reaction. Based on the

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above-mentioned assumptions, the solid acid catalysed esterification could be depicted by the pseudohomogeneous (PH) second order irreversible model as follows: dCA = k C AC B dt



(7)

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The conversion of stearic acid is assumed to be X at t=0, hence the concentration

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of the reactants can be expressed as: CA =CA0-X and CB =CB0-X, where CA0 and

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CB0 are the initial concentration of stearic acid and alcohol, respectively. For this reason and Y= CB0 -CA0, Eq. (7) was expressed as dCA = k C A (Y + C A ) dt

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(8)

Eq. (8) can be expressed using integral transformation as follows:

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ln(Y / C A + 1) / Y = kt + C

(9)

Fig.7 indicated that the relations of [ln(Y/CA + 1)]/Y with time were straight

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lines for the varied temperature, which implied that the kinetic equation of Eq. (9) for this esterification is correct, and the rates of grade of the straight line are the reaction

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rate constants. Reaction rate constants were obtained by linear regression (Table 4). The influence of temperature on the reaction rate was determined by fitting k to

the Arrhenius equation:

lnk = -Ea/RT + lnA

(10)

The Arrhenius plot was drawn from Eq.(10) using five different temperatures that

was used in the present work and is given in Table 5. The calculated values of Arrhenius coefficient and activation energy are 6.394×103 and 70.51kJ/mol, respectively. Therefore, the kinetic equation of this esterification reaction is as follows:

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r = −6.3948 ×103 exp(−7.051×10 4 / RT )C AC B

(11)

Mean relative errors, kinetic and adsorption parameters were calculated and tabulated in Tables 6. Experimental data were represented by PH mechanism

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successfully, and the adsorption and desorption of reactants and products were

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neglected.

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Moreover, as mentioned in the literature [21], some feedstocks such as waste frying oils for biodiesel production usually contain significant amounts of FFA. This

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literature reported another possible method for the pre-treatment of oils with a high content of FFA (20 to 50 %) by esterification with glycerol. Glycerolysis is a

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promising pretreatment to acidic oils or fats as they led to the production of intermediary material with a low content of FFA that can be used directly in the

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transesterification reaction for the biodiesel production. Then, we would try to study the PA/NaY catalyst for the glycerolysis reaction of high free fatty acid oils in our

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further research work.

4. Conclusions

Biodiesel production from the esterification of stearic acid with ethanol catalyzed

by PA/NaY was investigated. The research results suggest that PA/NaY is catalytically active for the esterification of stearic acid, and the optimum values for maximum esterification percentage can be obtained by using a Box-Behnken center-united design with a minimum of experimental work. Under the optimal conditions (catalyst amount: 2.0 g, reaction time: 4 h, molar ratio of alcohol to acid: 4:1 and temperature:

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95 oC), the predicted value of the conversion of stearic acid was 69.10 %. Validation experiments were also carried out to verify the availability and the accuracy of the model, and the result showed that the predicted value was in agreement with the

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experimental value well.

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The pseudohomogeneous (PH) model has been used to simulate the experimental

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data. It was found that this model was able to describe the kinetics of this esterification reaction, and we calculated the reaction constants at the different

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temperatures, activation energy and Arrhenius coefficient. The calculated values of Arrhenius coefficient and activation energy are 6.394×103 and 70.51 kJ/mol,

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respectively.

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Acknowledgements

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The support provided by the National Natural Science Foundation of China (51102127, 51073075, 51373074, 51302127 and 51143006), Natural Science Foundation

of

Shandong

Province

(No.

ZR2013BQ020,

2009ZRB01463,

2008BS04011, Y2007B19), the Nature Science Foundation of Ludong University (No.08-CXA001,

032912,

042920,

LY20072902),

Educational

Project

for

Postgraduate of Ludong University (No. YD05001, Ycx0612) and Program for Scientific research innovation team in Colleges and universities of Shandong Province is greatly appreciated.

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Ac ce p

of n-butyl acetate catalyzed by ionic liquid [Hnmp] HSO4. Ind Catal. 2008; 16: 45-48.

[21] Felizardo P, Machado J, Vergueiro D, Correia MJN, Gomes JP, Bordado JM. Study on the glycerolysis reaction of high free fatty acid oils for use as biodiesel feedstock. Fuel Process Technol. 2011; 92: 1225-1229.

19

Page 19 of 28

ip t cr us an M

80

50

Ac ce p

40

d

60

te

stearic acid conversion/%

70

10

20

30

40

50

the loading of PA/ml

Fig.1. Effect of the loading of PA on the esterification reaction (the reaction temperature: 125 oC, the catalyst amount: 1.5 g, the molar ratio of ethanol to acid: 4: 1, the reaction time: 4 h).

20

Page 20 of 28

80

ip t

60

50

cr

stearic acid conversion/%

70

1.2

1.4

1.6

1.8

2.0

2.2

an

catalyst amount/g

us

40

Ac ce p

80

te

d

M

Fig.2. Effect of the catalyst amount on the esterification reaction (the reaction temperature: 100 oC, the loading of PA: 40 ml, the molar ratio of ethanol to acid: 4: 1, the reaction time: 4 h).

stearic acid conversion/%

70

60

50

40

2

4

6

8

10

molar ratio of ethanol to acid

Fig.3. Effect of the molar ratio of alcohol to acid on the esterification reaction( the reaction temperature: 100 oC, the loading of PA: 40 ml, the catalyst amount: 2.0 g, the reaction time: 4 h).

21

Page 21 of 28

80

ip t

60

50

cr

stearic acid conversion/%

70

2

4

6

reaction time/h

us

40

8

stearic acid conversion/%

Ac ce p

70

te

d

M

an

Fig.4. Effect of the reaction time on the esterification reaction (the reaction temperature: 100 oC, the loading of PA: 20 ml, the catalyst amount: 2.0 g, the molar ratio of ethanol to acid: 4: 1).

60

50

90

100

110

120

130

140

o

tem perature/ C

Fig. 5. Effect of the reaction temperature on the esterification reaction (the loading of PA: 40 ml, the catalyst amount: 2.0 g, the molar ratio of ethanol to acid: 4: 1, the reaction time: 4 h).

22

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ip t cr us an M d

Ac ce p

te

Fig. 6. The interaction and response surface of the four process variables on the conversion of stearic acid

24

Page 23 of 28

0.40

o

90 C o 100 C o 110 C

ip t

0.30

cr

ln(Y/CA+1)/Y

0.35

-2000

0

2000

4000

6000

8000

t/s

us

0.25

10000

12000

14000

16000

Ac ce p

te

d

M

an

Fig. 7. The linear relation of [ln(Y/CA + 1)]/Y with the reaction time at different temperatures.

Table 1. Coded levels for independent factors used in the experimental design. 25

Page 24 of 28

X1 X2

+1 2.2 4

X3 X4

3 90

4 100

5 110

cr

Catalyst amount (g) Molar ratio of ethanol to acid Reaction time (h) Temperature (oC)

-1 1.6 2

Coded levels 0 1.9 3

ip t

Symbol

Ac ce p

te

d

M

an

us

Table 2. Experimental design and results of the response surface design. No. X1 X2 X3 X4 Conversion/% Experimental value Fitted value 1 -1 -1 0 0 59.54 60.83 2 1 -1 0 0 56.47 56.41 3 -1 1 0 0 57.22 57.96 4 1 1 0 0 66.94 66.33 5 0 0 -1 -1 66.05 66.00 6 0 0 1 -1 58.31 59.43 7 0 0 -1 1 66.73 66.30 8 0 0 1 1 69.24 69.97 9 -1 0 0 -1 59.92 58.97 10 1 0 0 -1 61.07 60.43 11 -1 0 0 1 63.85 63.87 12 1 0 0 1 66.02 66.36 13 0 -1 -1 0 63.43 62.27 14 0 1 -1 0 66.95 65.98 15 0 -1 1 0 60.65 61.00 16 0 1 1 0 63.80 64.34 17 -1 0 -1 0 60.18 60.97 18 1 0 -1 0 57.23 59.06 19 -1 0 1 0 57.52 55.63 20 1 0 1 0 62.34 61.49 21 0 -1 0 -1 59.53 59.61 22 0 1 0 -1 67.57 68.01 23 0 -1 0 1 70.41 69.90 24 0 1 0 1 68.70 68.55 25 0 0 0 0 69.39 68.98 26 0 0 0 0 68.63 68.98 27 0 0 0 0 68.92 68.98

26

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P-value 0.000 0.016 0.000 0.061 0.000 0.000 0.001 0.000 0.686 0.000 0.008 0.682 0.882 0.002 0.001

14

Linear

4

Square

4

24.45

143.302

35.8255

24.26

255.946

63.9866

43.33

6

106.315

17.7191

12.00

Residual error

12

17.720

1.4767

Lack of fit

10

17.426

1.7426

Pure error Total

2 26

0.294 523.283

0.1471

R2

0.9661

Q2

0.8069

Ac ce p

Interaction

505.563

d

36.1116

te

Regression

M

an

us

cr

ip t

Table 3. Coefficients of the model and ANOVA. Terms Coefficients Standard error t-Stat Intercept 68.9800 0.7016 98.319 X1 0.9867 0.3508 2.813 X2 1.7625 0.3508 5.024 X3 -0.7258 0.3508 -2.069 X4 2.7083 0.3508 7.721 X1* X1 -6.3554 0.5262 -12.078 X2* X2 -2.2417 0.5262 -4.260 X3* X3 -3.3392 0.5262 -6.346 X4* X4 -0.2179 0.5262 -0.414 X1* X2 3.1975 0.6076 5.263 X1* X3 1.9425 0.6076 3.197 X1* X4 0.2550 0.6076 0.420 X2* X3 -0.0925 0.6076 -0.152 X2* X4 -2.4375 0.6076 -4.012 X3* X4 2.5625 0.6076 4.217 ANOVA Source Degrees of Sum of Mean sum F freedom squares of squares

11.85

P

<0.001

0.080

27

Page 26 of 28

stearic acid with k/[L/(mol·s)-1]

ip t

4.2537×10-6

us

cr

Table 4. Reaction rate constants for the esterification reaction of ethanol using the PA/NaY catalyst. No. Temperature Reaction CA/(mol·L-1) [ln(Y/CA+1)]/Y /oC time/h 1 90 0.0 1.9777 0.2420 0.5 1.8598 0.2503 1.0 1.7963 0.2550 1.5 1.6463 0.2671 2.0 1.5698 0.2738 2.5 1.4950 0.2807 3.0 1.4062 0.2896 3.5 1.3517 0.2953 4.0 1.2882 0.3024 2 100 0.0 1.8598 0.2478 0.5 1.7074 0.2594 1.0 1.5302 0.2746 1.5 1.4334 0.2838 2.0 1.2636 0.3019 2.5 1.1158 0.3202 3.0 0.9094 0.3511 3.5 0.7735 0.3762 4.0 0.7258 0.3862 3 110 0.0 2.2386 0.2304 0.5 2.0931 0.2394 1.0 1.9443 0.2496 1.5 1.7825 0.2619 2.0 1.5177 0.2852 2.5 1.2851 0.3103 3.0 1.0554 0.3411 3.5 0.9285 0.3617 4.0 0.7835 0.3896

1.14361×10-5

Ac ce p

te

d

M

an

1.04241×10-5

28

Page 27 of 28

Table 5. Activated energy for the esterification reaction of stearic acid with ethanol using the PA/NaY catalyst. Temperature/oC 90 100 110

1/T(×10-3K-1) 2.754 2.680 2.610

lnk Ea/(kJ·mol-1) -12.3677 70.51 -11.5006 -11.1510

A/[L·(mol·s)-1] 6.394×103

us

cr

ip t

NO. 1 2 3

P-test

1

90

0.9979

0.00145

<0.0001

2

100

0.98824

0.00826

<0.0001

3

110

0.98411

M

an

Table 6. Mean relative errors for the PH mechanism. No Temperature/ oC R2 Standard deviation

<0.0001

Ac ce p

te

d

0.01087

29

Page 28 of 28