Fuel 102 (2012) 499–505

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Fuel

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Biodiesel production from esterification of oleic acid over aminophosphonicacid resin D418

Ping Yin ⇑, Lei Chen, Zhi Wang, Rongjun Qu ⇑, Xiguang Liu, Qiang Xu, Shuhua RenSchool of Chemistry and Materials Science, Ludong University, Yantai 264025, PR China

h i g h l i g h t s

" Biodiesel production fromesterification of oleic acid wasconducted over aminophosphonicacid resin D418.

" D418 had excellent catalyticproperty for this esterificationreaction.

" The biodiesel production processoptimization was conducted byresponse surface methodology.

" The pseudohomogeneous model wasused to simulate the kineticexperimental data.

0016-2361/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.fuel.2012.05.027

⇑ Corresponding authors. Tel.: +86 535 6696162; faE-mail addresses: yinping426@163.com (P. Yin), ro

g r a p h i c a l a b s t r a c t

a r t i c l e i n f o

Article history:Received 4 August 2011Received in revised form 12 May 2012Accepted 16 May 2012Available online 6 June 2012

Keywords:BiodieselEthyl oleateAminophosphonic acid resin D418Response surface methodologyKinetics

a b s t r a c t

Biodiesel (fatty acid methyl/ethyl esters) is a popular possible alternative to fossil fuels due to the potentialexhausting of traditional fuels and increasing price of petroleum together with environmental concerns. Inthe present work, biodiesel production from the esterification of the free fatty acid oleic acid with ethanolover aminophosphonic acid resin D418 has been studied, and the effects of experimental factors such asamount of D418, reaction temperature and molar ratio of ethanol to oleic acid on the conversion ratio wereevaluated. The process optimization using response surface methodology (RSM) was performed and theinteractions between the operational variables were elucidated. The optimum values for maximum ester-ification percentage can be obtained by using a Box–Behnken center-united design with a minimum ofexperimental work, and the oleic acid conversion reached 92.02 ± 0.74% with the molar ratio of alcoholto oleic acid being 14:1 and a content of 10.2 wt.% D418 catalyst at 115 �C. Moreover, the kinetics forthe esterification catalyzed by D418 catalyst has been studied, and the pseudohomogeneous (PH) modelhas been used to simulate the experimental data.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Due to the heavy consumption of fossil fuels, particular focus hasbeen given on global warming and exhaustion of non-renewableresources. Biodiesel (fatty acid methyl/ethyl esters) is a popularpossible alternative to fossil fuels because of the potential

ll rights reserved.

x: +86 535 6697667.ngjunqu@sohu.com (R. Qu).

exhausting of traditional fuels and increasing price of petroleumtogether with environmental concerns. Compared to fossil-basedfuels, biodiesel possesses many advantages, such as cleaner engineemissions, biodegradable, renewable and superior lubricating prop-erty. Then. Interest in biodiesel is continuing to increase throughoutthe world, and increasing research is now being directed towardsthe use of alternative renewable fuels that are capable of fulfillingan increasing energy demand [1–5]. Methyl and ethyl estersderived from vegetable oil or animal fat, known as biodiesel, have

500 P. Yin et al. / Fuel 102 (2012) 499–505

good potential as alternative diesel fuel. It is produced bychemically reacting a triglyceride (vegetable oil or animal fat) witha short-chain alcohol such as methanol or ethanol. Such oils andfats should not contain more than 1% free fatty acids (FFAs) sincesaponification of these FFAs reduces the yield of fatty acid alkyl es-ters. Recycled or waste oil and byproducts from the refining of veg-etable oils, some non-edible oils, animal fats and oils can containhigher levels of FFAs, and crude mahua oil and tobacco seed oil con-tain about 20% and 17% FFAs, respectively [6,7]. Therefore, the studyon the esterification reactions for the free fatty acids has a signifi-cant effect on the production of biodiesel. Esterification is one ofthe most an important reaction in chemical industry; and the rela-tive this reactions is usually conducted by using homogeneous acidcatalysts. Homogeneous acid catalyzed reactions may generatemany environmental and corrosion problems. Hence, esterificationreactions catalyzed by heterogeneous catalysts are attractingincreasing attention [8–11]. They provide advantage of easy separa-tion of products from the reaction medium without any contamina-tion. Then. The use of solid catalysts in the esterification reactions isextremely important in developing cleaner and economically im-proved processes.

To improve the conversion of acid and the efficiency of work,the response surface methodology (RSM) is usually presented tooptimize the operating parameters for the relative synthesis pro-cess. RSM is an effective statistical technique for optimizing mul-tifactor experiments, building models, evaluating the effects ofseveral factors for desirable responses. The advantage of RSM isthat it allows the user to gather large amounts of informationfrom a small number of experiments, and it also provides the pos-sibility of observing the effects of individual variables and theircombinations of interactions on the response [12]. So far, therehave been several papers reported on the subject of optimizationand RSM applied to biodiesel production [13–15]. On the otherhand, the kinetics for the esterification catalyzed by various cata-lysts has been studied in recent years. For example, Oliveira et al.[16] studied the kinetics of the esterification of oleic acid withethanol using a free or immobilized lipase as catalyst, and theyfound that the reaction followed Michaelis–Menten kinetics, andthe kinetic constants were also evaluated; Umar et al. [17] inves-tigated ethyl tert-butyl ester synthesis with different macropo-rous ion exchange resin catalysts, and found that the quasi-homogeneous model represented the system very well over awide range of reaction conditions; Zhang et al. [18] studied theesterification of lactic acid with ethanol in the presence of fiveacid ion-exchange resins, and the Langmuir–Hinshelwood (LH)model based on the selective adsorption of water and ethanol

ð1Þ

on the catalyst was found to be a more appropriate model to de-scribe the kinetic behavior of these systems; Song et al. [19] stud-ied the kinetics of the esterification of oleic acid catalyzed by zincacetate in subcritical methanol and found that the reaction orderwas n = 2.2 and activation energy was Ea = 32.62 kJ/mol. However,few studies on kinetics of the esterification with solid acid cata-lysts have been reported.

Resins have become more and more important both in scienceand technology, and they are gaining an increasing interest world-wide due to their superior properties and excellent performance inthe field of chromatography, adsorption and so on [20,21]. How-ever, there are few data about the esterification of free fatty acidswith ethanol over resin with organophosphonic acid functionalgroups as well as the effects of molar ratio of ethanol to free fattyacid, catalyst amount and reaction temperature so far. Therefore,the esterification of the free fatty acid oleic acid with ethanol overaminophosphonic acid resin D418 was investigated in this work,and the effects of experimental factors such as amount of D418,reaction temperature and molar ratio of ethanol to oleic acid onthe conversion ratio were evaluated. Response surface methodol-ogy (RSM) was employed to optimize the levels of catalyst amount,molar ratio of ethanol to acid and temperature. Moreover, a kineticmodel was proposed and the kinetic parameters were determinedby fitting the model with the experimental results.

2. Experimental

2.1. Materials

Aminophosphonic acid resin D418 was obtained from TianjingBohong Resin Sci & Tec. Limited Company, China. The other chem-icals were of analytical reagent (AR) grade and used without fur-ther purification.

2.2. Esterification reaction

A biodiesel production from oleic acid with ethanol was inves-tigated in the presence of D418. The experimental setup for theproduction of ethyl oleate over D418 catalyst was shown inFig. S1 (available online in the supplemental materials). Esterifica-tion reactions were carried out in a reflux system according to Ref.[22]. They were conducted under under batch reaction conditionsusing a 250 mL flask fitted with a stirrer, a thermometer and a re-flux condenser at 90, 100, 110 and 120 �C. A typical reaction mix-ture contained oleic acid (32 mL), ethanol and the solid catalystD418. The zeolite was added to prevent from bumping. The molarratio of ethanol to oleic acid was 4:1, 6:1, 8:1, 10:1, 12:1, 14:1 and16:1, and the quantity of catalysts was 5.6 wt.%, 7.0 wt.%, 8.4 wt.%,9.8 wt.% and 11.2 wt.% (wt of catalysts/wt of oleic acid). The exper-iments were conducted for 10 h with stirring.

The esterification reaction between oleic acid and alcohol canbe represented as follows:

The conversion of oleic acid can be calculated according to thefollowing equation:

X ¼ ð1� AV1=AV0Þ � 100% ð2Þ

where AV0 and AV1 are the acid values of feed and products, respec-tively, and the relative acid value is determined by titration method[23].

0 2 4 6 8 100

30

60

90

Con

vers

ion/

%

Time/h

4:1 6:1 8:1 10:1 12:1 14:1 16:1

Fig. 2. Effect of molar ratio of alcohol to acid on the esterification reaction. Reactionconditions: 100 �C and the catalyst amount being 9.8 wt.%.

0 2 4 6 8 100

30

60

90

Con

vers

ion/

%

Time/h

5.6% 7.0% 8.4% 9.8% 11.2%

Fig. 1. Effect of catalyst amount (Catalyst to FFA weight ratio) on the esterificationreaction. Reaction conditions: 100 �C and the molar ratio of alcohol to acid being8:1.

P. Yin et al. / Fuel 102 (2012) 499–505 501

2.3. Experimental design and optimization by RSM

Factors considered included the amount of D418 (8.4%–11.2 wt.%, wt of catalysts/wt of oleic acid), molar ratio of ethanolto acid (12:1–14:1), and reaction temperature (100–120 �C). Re-sponse surface methodology (RSM) was employed to analyze theoperating conditions of esterification to obtain a high percent con-version. The experimental design was carried out by three chosenindependent process variables at three levels, and the studied fac-tors included catalyst amount, molar ratio of ethanol to acid andtemperature. For each factor, the experimental range and the cen-tral point were shown in Table S1 (available online in the supple-mental materials).

The software Minitab was used for designing and analyzing theexperimental data. The coded levels for the independent factorsused in the experimental design were presented in Table S1. Thepercent conversion of oleic acid was the response of the experi-mental design.

The model equation was used to predict the optimum value andsubsequently to elucidate the interaction between the factors, andthe quadratic equation model for predicting the optimal point wasexpressed according to the following equation:[24]:

Y ¼ k0 þX4

i¼1

kixi þX4

i¼1

kiix2i þ

X3

i¼1

X4

j¼iþ1

kijxixj ð3Þ

where k0, ki, kii and kij are regression coefficients (k0 is constantterm, ki is linear effect term, kii is squared effect term, and kij isinteraction effect term), Xi and Xj are the independent variables (fac-tors), and Y is the predicted response value.

2.4. Statistical analysis

All data were analyzed with the assistance of the software Mini-tab, and the significant second-order coefficients were selected byregression analysis with backward elimination. Then, the fit of themodel was evaluated by coefficients of determination and a test forlack of fit, which was performed by comparing mean square lack offit to mean square experimental error, from the analysis of vari-ance (ANOVA).

3. Results and discussion

3.1. Effect of catalyst amount on the esterification reaction

D418 with aminophosphonic acid functional groups could pro-vide H+ species and protonate the carboxylic moiety of oleic acid,increasing the electrophilicity of the carbonyl carbon atom andfacilitating the following step of the nuclephilic attack of ethanol.Fig. 1 showed the relationships between the conversion ratio andreaction time at various catalyst amounts with ethanol/oleic acidmolar ratio 8:1 and 100 �C, and the effect of the catalyst amountwas examined from 5.6 wt.% to 11.2 wt.% of D418 to oleic acid. Itcould be found that the reactions had higher initial reaction rate,but reached steady state at 10 h. The conversion ratio increasedwith increasing the catalyst amount in general trend, which couldbe attributed to the reason that more D418 catalyst would providemore active reaction sites. However, more catalysts might not leadto the obvious increase of conversion ratio and could increase theproduction cost. Then, 9.8 wt.% of D418 catalyst to oleic acid can berecommended.

3.2. Effect of molar ratio of alcohol to acid on the esterification reaction

Esterification reaction is a reversible reaction, then and theamount of ethanol must be in excess to force the reaction towards

the formation of ethyl oleate. Fig. 2 represented the variations ofthe molar ratio of alcohol to acid for five different experiments,and it displayed the relationships between the conversion ratioand reaction time at various ethanol/oleic acid molar ratios with9.8 wt.% of D418 catalyst to oleic acid and 100 �C under the stirringconditions. It could be seen that the conversion ratio depended lar-gely upon ethanol/oleic acid molar ratio, and the conversion ratioincreased as the molar ratio of ethanol/acid increased from 6:1 to14:1, however, with the increase of the molar ratio of ethanol/acidfrom 14:1 to 16:1, the conversion ratio decreased. Shu et al. alsofound a similar trend in their work, the conversion of FFA increasedas the molar ratio of methanol/acid increased from 10.6 to 16.8,and it decreased with the increase of molar ratio from 16.8 to21.0 [9]. The decrease in conversion ratio could be explained bythe reason that the large excess of ethanol might cause floodingof the active sites, and the saturation of the catalytic surface withthe alcohol or prevention of nucleophilic attack by shielding pro-tonated alcohol by its own excess. This outcome was likely dueto chemisorption of alcohol onto the Bronsted acid sites [25].

3.3. Effect of temperature on the esterification reaction

The free fatty acid FFA oleic acid initially requires the activationof its carbonyl function by protonation under acid-catalyzed condi-tions to start the reaction, and temperature is one of the importantvariables for acid-catalyzed esterification because the rate of reac-

0 2 4 6 8 100

20

40

60

80

100

Con

vers

ion/

%

Time/h

90oC 100oC 110oC 120oC

Fig. 3. Effect of temperature on the esterification reaction. Reaction conditions: thecatalyst amount being 9.8 wt.% and the molar ratio of alcohol to acid being 14:1.

Table 1Experimental design and results of the response surface design.

No. X1 X2 X3 Conversion/%

Experimental Fitted value

1 �1 �1 0 81.63 81.702 1 �1 0 83.76 83.903 �1 1 0 88.54 88.404 1 1 0 90.08 90.015 �1 0 �1 85.81 85.586 1 0 �1 88.75 88.457 �1 0 1 86.89 87.198 1 0 1 87.90 88.139 0 �1 �1 83.85 84.0110 0 1 �1 89.26 89.6311 0 �1 1 84.23 83.8612 0 1 1 91.23 91.0713 0 0 0 89.36 89.4714 0 0 0 89.68 89.4715 0 0 0 89.36 89.47

Table 2Coefficients of the model and ANOVA.

Terms Coefficients Standarderror

t-Stat P-value

Intercept 89.4667 0.2197 407.251 <0.001X1(catalyst amount) 0.9525 0.1345 7.080 0.001X2(ethanol/acid ratio) 3.2050 0.1345 23.824 <0.001X3(reaction

temperature)0.3225 0.1345 2.397 0.062

X1 � X1 �1.6346 0.1980 �8.255 <0.001X2 � X2 �1.8296 0.1980 �9.239 <0.001X3 � X3 �0.4946 0.1980 �2.498 0.055X1 � X2 �0.1475 0.1903 �0.775 0.473X1 � X3 �0.4825 0.1903 �2.536 0.052X2 � X3 0.3975 0.1903 2.089 0.091

ANOVA

Source Degrees offreedom

Sum ofsquares

Mean sum ofsquares

F P

Regression 9 112.793 12.5325 86.56 <0.001Linear 3 90.266 30.0888 207.82 <0.001

502 P. Yin et al. / Fuel 102 (2012) 499–505

tion is strongly influenced by the reaction temperature. The effectof the reaction temperature was examined from 90 to 120 �C withethanol/ oleic acid molar ratio 14:1 and 9.8 wt.% of D418 catalyst tooleic acid and it was shown in Fig. 3. As expected, increasing thetemperature of the process increased the oleic acid conversion ra-tio because of the increase in the equilibrium constant. It could beseen that the conversion ratio increased with increasing tempera-ture, and it reached the maximum conversion ratio at 110 �C, char-acteristic behavior of an endothermic reaction. The increasedconversion might not only due to the effect of increase of the reac-tion rate by increasing temperatures but also some improvementof the mass transfer limitation between reactant and catalyst. Sincethis esterification reaction was a reversible reaction, further higherreaction temperature might result in the decrease of the conver-sion, and one possible explanation was that there was superheatedexcessive evaporation of the reactants in the reaction system athigher temperature, which might lead to the loss of ethanol. There-fore, the esterification reaction temperature should be set at110 �C.

Square 3 20.876 6.9588 48.06 <0.001Interaction 3 1.65 0.5501 3.80 0.092Residual

error5 0.724 0.1448

Lack of fit 3 0.656 0.2185 6.40 0.138Pure error 2 0.068 0.0341Total 14 113.517R2 0.9936Q2 0.9062

3.4. RSM analysis

3.4.1. RSM experiments and fitting the modelsResponse surface methodology (RSM) is an efficient statistical

technique for optimization of multiple experimental variables topredict the best performance conditions with minimum numbersof synthesis experiments. Then RSM was applied to model the con-version ratio of oleic acid with ethanol to produce ethyl oleate withthree reaction parameters: amount of catalyst, molar ratio of eth-anol to oleic acid and reaction temperature. A Box–Behnken cen-ter-united design was employed to design the experiments, andthe results obtained after running the 15 trials for the statisticaldesign were shown in Table 1. The best-fitting models were deter-mined by multi-regression and backward elimination. Table 1 alsopresented the experimental value of oleic acid conversion and thefitting value of oleic acid conversion. The results indicate a good fit,and Table 2 listed the significant regression coefficients of theestablished model equation. The linear coefficients of catalystamount and molar ratio of ethanol to acid, the quadratic terms ofcatalyst amount and molar ratio of ethanol to acid were highly sig-nificant (P < 0.05). The values of the coefficients and the analysis ofvariance (ANOVA) were also presented in Table 2. According to theresults of ANOVA, R2, which means the fraction of the variation ofthe response explained by the model, and Q2, which indicates thefraction of the variation of the response predicted by the model,were 0.9936 and 0.9062, respectively. In this case, the R2 value

indicated that the model could explain 99.36% of the variability.As a result, the well-fitting models for the esterification were suc-cessfully established. The polynomial model for the conversion ofoleic acid was regressed by considering the significant terms andthe equation was shown as follows:

Y ¼ 89:4667þ 0:9525X1 þ 3:2050X2 þ 0:3225X3 � 1:6346X21

� 1:8296X22 � 0:4946X2

3 � 0:1475X1X2 � 0:4825X1X3

þ 0:3975X2X3 ð4Þ

where Y was the conversion ratio of oleic acid (%), X1 the catalyst toFFA weight ratio (%); X2 the molar ratio of ethanol to acid; X3 thereaction temperature (�C). It is well known that the larger the mag-nitude of the t-value and smaller the P-value, the more significant isthe corresponding coefficient, then, this implies that the variablewith the largest effect was the squared term of molar ratio of etha-nol to oleic acid. Moreover, the quadratic effect of catalyst amountis more significant than that of reaction temperature, and the inter-

Fig. 4. The interaction and response surface of the three process variables on the conversion of oleic acid.

P. Yin et al. / Fuel 102 (2012) 499–505 503

active effect of catalyst amount and reaction temperature might besignificant to some extent. The linear effects of catalyst amount andethnol/oleic acid molar ratio are more significant than that of theother factor (reaction temperature).

3.4.2. Effects of the process variables on oleic acid conversionThe response surfaces of the above mentioned model for the

free fatty acid oleic acid conversion (Eq. (5)) were used to evaluatethe relationships of parameters, and it was plotted as a function oftwo variables, while keeping other variables at the zero level. Fig. 4

Table 3Concentrations of ethyl oleate in the product at different reaction temperat

Number Temperature (�C) Time (h) Concentraoleate (mo

1 90 1 0.27042 90 2 0.39523 90 3 0.54084 90 4 0.60325 90 5 0.66576 90 6 0.70727 90 7 0.74898 100 1 0.21489 100 2 0.351510 100 3 0.566211 100 4 0.683512 100 5 0.722613 100 6 0.761614 100 7 0.781115 110 1 0.394416 110 2 0.540917 110 3 0.624118 110 4 0.707219 110 5 0.790520 110 6 0.832121 110 7 0.8529

demonstrated the effects of the four process variables on oleic acidconversion. Fig. 41 depicted the response surface plot showing theeffects of molar ratio of ethanol to acid and catalyst amount. Asseen from the figure, increasing quantities of D418 catalystbrought about a high conversion ratio, but excess amounts of cat-alyst led to a decline in the conversion ratio. Moreover, it wasnoted that the conversion ratio of oleic acid increased with increas-ing ethanol/oleic acid molar ratios, and then decreased. The effectsof different reaction temperature and catalyst amount on the con-version ratio were shown in Fig. 42. The interaction between the

ure and time.

tion of ethyll L�1)

Concentration of ethyl oleatein balance (mol L�1)

Y

0.8397 0.02520.8397 0.04100.8397 0.06620.8397 0.08090.8397 0.10010.8397 0.11710.8397 0.14070.8529 0.01920.8529 0.03500.8529 0.07130.8529 0.10510.8529 0.12200.8529 0.14470.8529 0.16010.8736 0.03790.8736 0.06530.8736 0.08460.8736 0.11170.8736 0.15820.8736 0.20450.8736 0.2509

100 200 300 4000.00

0.05

0.10

0.15

0.20

0.2590oC

100oC

110oC

Y/L

mol

-1

Time/min

Fig. 5. Y–t plots at different temperatures.

0.00260 0.00264 0.00268 0.00272 0.00276

-8.0

-7.8

-7.6

-7.4

-7.2

lnk+ lnk-

lnk+

/lnk-

1/T K-1

Fig. 6. Effects of temperature on the reaction rate.

504 P. Yin et al. / Fuel 102 (2012) 499–505

corresponding variables was negligible when the contour of the re-sponse surface was circular. On the contrary, the interactions be-tween the relevant variables were significant when the contourof the response surfaces was elliptical. Fig. 42 indicated that theinteractions of reaction temperature and catalyst amount werenot obvious. Fig. 43 represented the effects of reaction temperatureand molar ratio of ethanol to acid, and their reciprocal interactionon oleic acid conversion. Oleic acid conversion changed a little withthe increase of reaction temperature, and it was evident that whenreaction temperature was fixed at one level, the change in oleicacid conversion showed a parabolic pattern with molar ratio ofethanol to acid.

3.4.3. Optimization of reaction conditionsThe optimum values of selected variables were obtained by

solving the regression equation (Eq. (5)) using Matlab6.5 software.For convenience, the optimal conditions for synthesis of ethyl ole-ate by the as-synthesized solid catalyst estimated by the modelequation were X1 = 10.2 wt.%, X2 = 14:1, X3 = 115 �C. The theoreticalconversion yield predicted under the above mentioned conditionswas Y = 91.19%. To confirm the prediction by the model, the opti-mal conditions were applied to three independent replicates forethyl oleate synthesis. The average conversion yield reached92.02 ± 0.74% and was close to the predicted value. Thus, responsesurface methodology with appropriate experimental design can beeffectively applied to optimize the process of factors in this ester-ification synthesis of ethyl oleate with D418 catalyst.

Furthermore, to test the reusability of the D418 catalyst, it wasrepeatedly used for ethyl oleate synthesis. The catalyst was fil-tered, leached and reused in a new reaction cycle. The reusabilityof the catalyst under the optimal experimental conditions wasinvestigated, and the results were presented in Fig. S2 (availableonline in the supplemental materials). It is clear that the oleic acidconverstion ratio could still reach 88.19% after four reaction cycles.However, the catalytic activity of other heterogeneous catalystsuch as Amberlyst 15 gradually decreased with recycling [26].Therefore, the D418 catalyst was favorable and useful for thesynthesis of ethyl oleate, and it appears as a great alternative to

Table 4Rate constants and Mean relative errors for the model at different temperatures.

Temperature(K)

k+ (L(mol min))�1

k� (L(mol min))�1

K R P-test

363 3.17 � 10�4 6.62 � 10�4 0.4790 0.9985 <0.0001373 4.12 � 10�4 7.39 � 10�4 0.5573 0.9915 <0.0001383 5.90 � 10�4 8.07 � 10�4 0.7314 0.9861 <0.0001

produce biodiesel and it could probably be used industrially in per-spective. The slight decrease in the activity of the catalyst might bedue to the explanation that the catalytic species were partially lostin the reaction system, so we would try to improve the reusabilityof the catalyst by film-coating technology in our subsequent re-search work.

3.5. Kinetic model

In this work, the pseudohomogeneous (PH) model has beenused to simulate the experimental data, the esterification reactionof biodiesel production was carried out under the optimal condi-tions, and the oleic acid conversion at different temperatures fordifferent time was shown in Table 3. It was supposed that the for-ward and reverse reactions for this esterification were second-or-der reactions, then, as for the esterification reaction of the freefatty acid oleic acid and ethanol, the apparent reaction rate couldbe described as follows:

�dCAdt¼ kþCACB � k�CCCD ð5Þ

where CA, CB, CC and CD denote the concentrations of oleic acid, alco-hol, ethyl oleate, water, respectively; k+ and k� are the kinetic con-stants for the direct reaction and the reverse reaction, respectively[27]. The initial concentrations of oleic acid and ethanol are a andb, respectively. Meanwhile, the initial concentration of ethyl oleateand water are zero, however, the concentration of two products arex at t time. So Eq. (6) can be integrated to the following equation:Z x

0

dxða� xÞðb� xÞ � 1

K x2¼Z t

0kþdt ð6Þ

where K ¼ kþk�

, t is reaction time. Meanwhile:

K ¼ c2

ða� cÞðb� cÞ ð7Þ

where c denotes the concentration of the product.

Y ¼ kþt ð8Þ

Table 5Activation energy and Arrhenius coefficient for the esterification of oleic acida.

A+ (L�(mol min))�1 A� (L�(mol min))�1 Ea+ (kJ mol�1) Ea� (kJ mol�1)

62.18 3.24 � 10�2 36.89 11.76

a Mean relative error (R) for Arrhenius equation is 0.9974 and 0.9960 for thedirect reaction and the reverse reaction, respectively.

P. Yin et al. / Fuel 102 (2012) 499–505 505

The values of K (equilibrium constant) and Y were calculated bythe Eqs. (7) and (8) using MATLAB7.0 software, and then Y is a lin-ear function of t at different temperature, as shown in Fig. 5. Itdemonstrated that positive reaction and reverse reaction of thisesterification reaction were second-order reaction. Then, the posi-tive and reverse reaction rate constants (k+, k�) at different temper-atures were listed in Table 4. The influence of temperature on thereaction rate was determined by fitting k+ and k� to the Arrheniusequation. Both the frequency factor (A) and the activation energy(Ea) were attained via nonlinear regression by employing plots oflnk as a function of T�1 (Fig. 6). The results were listed in Table5, the activation energy of the direct reaction and the reverse reac-tion are Ea+ = 36.89 kJ/mol and Ea� = 11.76 kJ/mol, respectively,and the kinetic equation of this esterification reaction was asfollows:

r ¼ 62:18 expð�36:89=RTÞ½CA�½CB� � 3:24� 10�2 expð�11:76=RTÞ� ½CC �½CD�

4. Conclusions

Biodiesel production from the esterification of the free fatty acidoleic acid catalyzed by D418 was investigated. The research resultssuggest that D418 is catalytically active for the esterification ofoleic acid, and the optimum values for maximum esterificationpercentage can be obtained by using a Box–Behnken center-uniteddesign with a minimum of experimental work. Under the optimalconditions (10.2 wt.% of D418 catalyst to oleic acid, 14:1 of the mo-lar ratio of ethanol to oleic acid and 115 �C of the reaction temper-ature), the predicted value of the conversion ratio was 91.19%.Validation experiments were also carried out to verify the avail-ability and the accuracy of the model, and the result showed thatthe predicted value was in good agreement with the experimentalvalue (92.02 ± 0.74%). Furthermore, the kinetics for the esterifica-tion catalyzed by D418 catalyst has been studied, and the pseudo-homogeneous PH model for this esterification reaction wasestablished to simulate the experimental data, and the resulting ki-netic equation of this esterification was as follows:

r ¼ 62:18 expð�36:89=RTÞ½CA�½CB� � 3:24� 10�2 expð�11:76=RTÞ� ½CC �½CD�

Acknowledgements

The support provided by the National Natural Science Founda-tion of China (Grant No. 51102127 and 51073075), the Nature Sci-ence Foundation of Shandong Province (2009ZRB01463), and theFoundation of Innovation Team Building of Ludong University(08-CXB001) were greatly appreciated.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.fuel.2012.05.027.

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