Process optimization, kinetic and thermodynamic studies on biodiesel production by supercritical methanol transesterification with CH3ONa catalyst

Process optimization, kinetic and thermodynamic studies on biodiesel production by supercritical methanol transesterification with CH3ONa catalyst

Fuel 203 (2017) 739–748 Contents lists available at ScienceDirect Fuel journal homepage: Full Length Article Process ...

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Fuel 203 (2017) 739–748

Contents lists available at ScienceDirect

Fuel journal homepage:

Full Length Article

Process optimization, kinetic and thermodynamic studies on biodiesel production by supercritical methanol transesterification with CH3ONa catalyst Dan Zeng a, Liu Yang b, Tao Fang c,⇑ a b c

Department of Chemical Engineering and Applied Chemistry, University of Toronto, 200 College Street, Toronto, Ontario M5S 3E5, Canada School of Energy and Power Engineering, Xi’an Jiaotong University, Shaanxi 710049, China School of Chemical Engineering and Technology, Xi’an Jiaotong University, Shaanxi 710049, China

a r t i c l e

i n f o

Article history: Received 9 February 2017 Received in revised form 12 April 2017 Accepted 5 May 2017

Keywords: Biodiesel Transesterification Supercritical methanol Kinetics Thermodynamics

a b s t r a c t This study provided a novel supercritical methanol transesterification process with little amount of CH3ONa catalyst to synthesize biodiesel from soybean oil by response surface technology. The maximum biodiesel yield was 97.42% under the optimal conditions of 250 °C, methanol to oil molar ratio of 23:1, 1.0 wt% CH3ONa and 20 min. Temperature was proved to have the most significant effect on transesterification, followed by methanol to oil molar ratio and catalyst amount. The kinetic model suggested a 1.5th order reaction with the activation energy of 27.06 kJmol1 and the pre-exponential factor of 102.71. The values of thermodynamic parameters including enthalpy, entropy and Gibbs free energy for this process were calculated as 23.15 kJmol1, 0.22 kJmol1K1 and 137.43 kJmol1 at 250 °C, respectively. Reduced reaction temperature, catalyst amount, and reaction time are among the advantages of the integrated process for biodiesel production over single supercritical process and conventional catalytic methods. Ó 2017 Published by Elsevier Ltd.

1. Introduction As the majority of global energy, the fossil sources are limited and assumed to be exhausted by the explosive increment of energy demand. Biodiesel has gained interest around the world over the last few decades because of its environmental benefits. As an alternatively renewable fuel, biodiesel is generally produced by transesterification of vegetable oils or animal fats. It is renewable, biodegradable, non-toxic, sulfur-free, and can be used to reduce most regulated exhaust emissions [1,2]. Four main approaches to synthesize biodiesel are direct use and blending of vegetable oils, micro-emulsions, thermal cracking (pyrolysis) and transesterification [3]. Among them, transesterification reaction of renewable sources is the most common method for biodiesel production catalyzed by acids, alkalis, and lipases [4– 10]. Methanol is the most frequently used alcohol in transesterification because of its low cost and its physical and chemical advantages as the shortest chain alcohol. The relatively slow reaction rate of acid-catalyzed transesterification and the high cost of lipases limit these two kinds of methods in the commercial pro⇑ Corresponding author. E-mail address: [email protected] (T. Fang). 0016-2361/Ó 2017 Published by Elsevier Ltd.

duction of biodiesel [11,12]. Conversely, alkali-catalyzed transesterification has been widely applied in industry as they can catalyze the reaction at low temperature and atmospheric pressure, which leads to high conversion within a specified time [13]. Rashid et al. [14] synthesized biodiesel by base-catalyzed transesterification of rice bran oil and the highest biodiesel yield of 83.3% was achieved at the optimized conditions of 7.5:1 methanol to oil molar ratio, 0.88% catalyst concentration, 55 °C and 60 min. AminiNiaki et al. [15] obtained the sunflower biodiesel similar yield of 83.4% at the conditions of molar ratio of oil to methanol at 1:5.5, 1.0% percentage of KOH catalyst at 51.7 °C in 65.5 min. Vicente et al. compared four primary alkali catalysts (CH3ONa, CH3OK, NaOH, KOH) for methanolysis of vegetable oil. It demonstrated that near 100% biodiesel yields were only obtained with methoxide catalysts because the methoxide anion is strongly basic and has high catalytic activity in transesterification [16,17]. Among them, CH3ONa is the most commonly used catalyst for chemical transesterification [18]. Borugadda et al. [19] summarized biodiesel production from various feedstock under different conditions using homogeneous alkali catalysts. They found that the catalyst amount is usually over 1.0%, even 6.0% and the reaction time takes several hours for conventional catalytic transesterification methods. Moreover, when the raw material has a high percentage of free fatty


D. Zeng et al. / Fuel 203 (2017) 739–748

acids (FFA) or water, the alkali catalyst will be consumed by undesired saponification reactions, and the process needs complicated downstream separation and purification processes [13]. To overcome the limitations of conventional catalytic processes, Saka and Kusdiana proposed a new supercritical methanol (SCMeOH) process for biodiesel production, which requires shorter reaction time and simpler purification procedure. He et al. [20] studied biodiesel synthesis via supercritical methanol transesterification from soybean oil and found that the biodiesel yield was more than 96% at 310 °C, methanol to oil weight ratio of 40:1 for 25 min with the gradual heating reaction process. RománFigueroa et al. [21] investigated a non-catalytic transesterification of crude castor oil into fatty acid methyl esters (FAME) and obtained 96.5% of biodiesel yield at the optimized conditions of methanol to oil molar ratio of 43:1within 90 min at 300 °C. García-Martínez et al. [22] presented the biodiesel produced from tobacco seed oil by supercritical methanolysis and achieved the maximum yield of 91.1% at 303.4 °C and 90 min with a molar ratio of methanol to oil 43:1. In summary, the biodiesel yield enhanced prominently with the usage of supercritical technology; however, optimum reaction conditions were found to be at higher temperature (>300 °C) and longer reaction time (25–90 min). These drawbacks lead to expensive equipment cost and high energy consumption hindering the application of supercritical technology in the biodiesel industry. This research presents a novel integrated process for supercritical methanol and little amount of CH3ONa catalyst to produce biodiesel from soybean oil. The proposed method combines the advantages of supercritical technology and base-catalyzed transesterification method. It has minimal undesired reactions with a relatively low reaction temperature in contrast to supercritical technology; and requires less catalyst amount, much shorter reaction time, and without the saponification reactions compared with the conventional base-catalyzed transesterification process. Process parameters including reaction temperature, molar ratio of methanol to soybean oil, and catalyst amount (mass percent of CH3ONa to soybean oil) were discussed. Besides, the kinetic and thermodynamic study of the integrated process were also conducted.

2. Experimental section 2.1. Materials and methods Soybean oil was purchased from Xi’an Jiali Oil Industry Co., Ltd. (Xi’an, Shaanxi Province, China). Methanol (analytical grade purity) was obtained from Tianjin Fuyu Fine Chemical Co., Ltd., CH3ONa (analytical grade purity) from Tianjin Fuchen Chemical Reagents Factory, and methyl oleate (CAS number: 112-62-9) from Yake Chemical Reagent Co., Ltd. (Suzhou) with purities of 99.0%. The self-designed experiment reactor (Huaxing Petroleum Instrument Co., Ltd., Nantong, Jiangsu Province, China) for biodiesel production is presented in Fig. 1. Briefly, it consists of a batch reaction vessel (with an inner volume of  10 ml, and the maximum pressure and temperature of 50 MPa and 500 °C, respectively) and a heating furnace. Firstly, soybean oil and CH3ONa-dissolved methanol solution in the specified proportions (the total amount was 6 mL) were charged into three batch reaction vessels and then the vessels were placed in the high-temperature furnace that has been preheated to the set temperature. After the transesterification with oscillating the reactor at the rate of 50–60 rpm, the vessels were taken out of the furnace and quenched by cold water for 5 min. Finally, the product of each reactor was collected, and the oil phase was completely separated by washing with hot water (80 °C) to prepare for

1- high temperature furnace; 2-oscillator; 3-temperature controller; 4-batch reaction vessel Fig. 1. Schematic diagram of the experimental reactor.

the following analysis. The yield data were obtained by calculating the average yield of three reactors with the deviation lower than 5%. 2.2. Property of the raw material The saponification value (SV) and the acid value (AV) of soybean oil were measured according to the methods specified by American Oil Chemists’ Society (AOCS) in our previous study [23]. They were 193.5 mg KOHg1 oil and 6.4 mg KOHg1 oil, respectively. Thus, the average molecular weight (Mr) was 841.8, calculated by Eq. (1).

Mr ¼

56:1  1000  3 ðSV  AVÞ


2.3. FAME analysis The contents of FAME in the samples diluted by n-hexane were analyzed by the gas chromatography-mass spectrometry (GC–MS) 5973-6890 (Agilent Technologies Inc., Palo Alto, California, USA) equipped with an HP-5 capillary column (30 m  £ 0.25 mm  0.25 lm). The analysis conditions were as follows: the detector temperature of 300 °C, the injector temperature of 250 °C, a carrier gas of helium with a flow rate of 1.0 mL/min, a split ratio of 30 and the sampling volume of 1 lL. The oven temperature was initially held at 200 °C for 10 min and then elevated to 230 °C at a ramp rate of 5 °C/min, finally held at 230 °C for 2 min. The external standard was methyl oleate. The biodiesel yield (Y) was determined by Eq. (2).



where CS is the concentration of external standard (g/g), AFAME is the total peak area of FAME, AS is the peak area of external standard and CB is the concentration of the biodiesel product (g/g). 2.4. Experimental design Response surface methodology (RSM), which is originated by Box and Wilson in 1951 [24], has received noticeable attention in recent decades as an important branch of experimental design. It is an efficient way to find the relationship between the reaction variables and the response variables within the region of interest [25]. Many studies [14,26–28] have proved that the RSM is a suitable technique for optimizing transesterification of biodiesel production.


D. Zeng et al. / Fuel 203 (2017) 739–748

Three variables of transesterification including reaction temperature (150–250 °C), methanol to oil molar ratio (23:1–69:1) and CH3ONa amount (0.5–1.5 wt%) were employed to design the experiments by RSM coupled with Box-Behnken design (BBD). As this model uses points outside the design space (1.00, 1.00 levels) which provides a reliable estimation over the entire design space, it is more efficient and economical than the corresponding full three-level factorial design [29]. The central point was performed three times to consider reproducibility. The results of the experimental design matrix and the biodiesel yield (response value) are shown in Table 1, which were performed in a random order and in triplicate to achieve repeatable results. The reaction time was fixed at 20 min in the optimization experiments. 2.5. Statistical analysis

3 3 2 X 3 X X X b i xi þ bii x2i þ bij xi xj i¼1


3.1.2. Development of mathematical model Table 3 shows the ANOVA results to explore the model fitness. The F-value of 174.84 indicates the model is significant, and the Pvalue is less than 0.0001, implying that only a 0.01% chance that a model with such large F-value could occur due to noise. For individual terms, only those with Prob. > F less than 0.05 are deemed as significant. Besides, the ‘‘Lack-of-fit F-value” of 3.23 implying the Lack of Fit is not significant relative to pure error. Therefore, the proposed model is valid and statistically significant. Subsequently, the final equation regarding coded factors after eliminating the insignificant parameters is given in Eq. (4).

X ¼ 0:95 þ 0:13A  0:047AB  0:062BC  0:11A2  0:029B2

A quadratic polynomial model was developed to predict the biodiesel yield as a function of the independent variables. The general form of this second-order polynomial can be expressed as:

X ¼ b0 þ

(46.636%) gave a high cetane number and decreased the viscosity of biodiesel [30].


i¼1 j¼iþ1

where X is the predicted response; xi and xj are the experimental factor levels; b0 is the offset term; bi, bii and bij are the linear, quadratic and interactive coefficients, respectively. A complete analysis of variance (ANOVA) was performed by Design Expert Software Version 8.0.6 (Stat-Ease, Inc. 2021 East Hennepin Ave., Suite 480 Minneapolis, MN 55413) at a significance level of 95%. Subsequently, the quality of the proposed model was evaluated by the correlation coefficient (R2) while indicating the consideration of a complete quadratic model and eliminating terms that were not significant as the analysis continued.

 0:069C 2

ð4Þ 2

A correlation coefficient R = 0.9968 which was found to be very close to unity shows the excellent correlation between the experimental data and the predicted data. It reveals that the regression model can successfully predict the biodiesel yield by transesterification. The predicted R2 of 0.9568 was in reasonable agreement with the adjusted R2 of 0.9911 in the refined model. The signal to noise ratio is measured with sufficient precision, and a ratio greater than four is desirable. In this case, the ratio of 36.935 indicated an adequate signal. Thus, the model can be used to navigate the design space. 3.2. Effect of experimental factors The surface plots of the biodiesel yield versus interactions of two variables are presented in Figs. 3–5. In each graph, the remaining variables are set constant at the center point.

3. Results and discussion 3.1. Process optimization 3.1.1. Analysis of FAME with GC–MS A detailed quantification of the biodiesel composition was performed by GC–MS, and the GC chromatogram is shown in Fig. 2. FAME profile of the experimental run conducted at the optimum conditions (250 °C, methanol to oil molar ratio of 23:1, 1.0 wt% CH3ONa and 20 min) is summarized in Table 2. 9-Octadecenoic acid, methyl ester, (9E)-(C18:1) and 9,12-Octadecadienoic acid, methyl ester (C18:2) are the two major constituents present in FAME. The presence of these monounsaturated compounds

3.2.1. Effect of temperature Fig. 3 depicts the 3D response curve of the biodiesel yield against reaction temperature and methanol to oil molar ratio. The higher F-value of the model term represents a greater impact of temperature on biodiesel yield. Thus, it is apparently found that temperature significantly affects the conversion of soybean oil to FAME compared with the other two parameters (i.e. methanol to oil molar ratio and catalyst amount). As temperature increases from 150 to 250 °C, the yield increased from 63.47% to 97.42%. The variation tendency suggests that a higher temperature could lead to a higher conversion yield. It is consistent with Demirbas’ conclusion that increasing reaction temperature, especially super-

Table 1 Experimental design matrix and the corresponding biodiesel yield in transesterification. Std. order

Run order

Temperature (°C)

Methanol to oil molar ratio

Catalyst amount (wt.%)

Observed yield (%)

Predicted yield (%)

1 4 13 12 7 8 3 15 10 9 14 6 5 2 11

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

150 250 200 200 150 250 150 200 200 200 200 250 150 250 200

23 69 46 69 46 46 69 46 69 23 46 46 46 23 23

1.0 1.0 1.0 1.5 1.5 1.5 1.0 1.0 0.5 0.5 1.0 0.5 0.5 1.0 1.5

63.47 90.01 94.09 78.91 64.78 90.16 74.79 94.98 92.89 78.84 95.62 92.32 62.57 97.42 89.76

62.81 90.67 94.90 79.39 65.14 89.03 73.96 94.90 92.59 78.36 94.90 91.96 63.70 98.25 90.06


D. Zeng et al. / Fuel 203 (2017) 739–748

Fig. 2. A typical GC chromatogram of biodiesel.

critical temperatures has a favorable influence on the biodiesel yield [31]. The thermodynamic reason has been explained in our Table 2 Fatty acid profile of biodiesel (as % of methyl esters). Residence time

Type of FAME

% Area

5.323 5.611 9.442 9.649 9.724 9.954

9-Hexadecenoic acid, methyl ester (C16:1) Hexadecanoic acid, methyl ester (C16:0) 9,12-Octadecadienoic acid, methyl ester (C18:2) 9-Octadecenoic acid, methyl ester, (9E)-(C18:1) 11-Octadecenoic acid, methyl ester (C18:1) 9,12,15-Octadecatrienoic acid, methyl ester, (Z,Z,Z)(C18:3) Octadecanoic acid, methyl ester (C18:0) Docosanoic acid, methyl ester (C22:0) cis-11-Eicosenoic acid, methyl ester (C20:1) Eicosanoic acid, methyl ester (C20:0)

0.198 8.691 38.452 42.686 2.915 0.861

10.250 12.502 14.948 15.558

Saturated fatty acid Monounsaturated fatty acid Polyunsaturated fatty acid

3.898 0.836 0.837 0.625 14.050 46.636 39.313

previous article [32]. Since the enthalpy for the transesterification has become positive in the SC-MeOH temperature domain, the reaction equilibrium is displaced in the direction of higher FAME concentration. Considering that in Fig. 3 biodiesel yield does not considerably increase by elevating reaction temperature beyond 250 °C and higher reaction conditions cause higher energy consumption, the reaction temperature was chosen at 250 °C. 3.2.2. Effect of methanol to oil molar ratio The experiment results indicated that the methanol to oil molar ratio has a gradually increasing impact on the conversion into FAME, as illustrated in Fig. 4. A high molar ratio of methanol pushes the chemical equilibrium forward. Furthermore, an excess amount of methanol increases the contact between methanol and soybean oil, improving transesterification reaction [33]. However, with the increase of methanol ratio, the solubility of byproduct glycerol in biodiesel increases that shifts reaction equilibrium backsides. Considering the interaction between factors, temperature gives the most prominent effect on the biodiesel yield. As shown in Table 1, the highest value of 97.42% was


D. Zeng et al. / Fuel 203 (2017) 739–748 Table 3 Result of ANOVA for response surface quadratic model. Source

Sum of square

Degree of freedom

Mean square




Model A-A B-B C-C AB AC BC A2 B2 C2

0.22 0.14 6.301E004 1.133E004 8.780E003 4.774E004 0.016 0.041 3.142E003 0.017

9 1 1 1 1 1 1 1 1 1

0.024 0.14 6.301E004 1.133E004 8.780E003 4.774E004 0.016 0.041 3.142E003 0.017

174.84 984.29 4.56 0.82 63.56 3.46 112.22 298.07 22.75 126.52

<0.0001 <0.0001 0.0858 0.4067 0.0005 0.1221 0.0001 <0.0001 0.0050 <0.0001

Yes Yes No No Yes No Yes Yes Yes Yes

Residual Lack of fit Pure error Cor. Total

6.906E004 5.725E004 1.181E004 0.22

5 3 2 14

1.381E004 1.908E004 5.904E005




R2 = 0.9968, R-Sq(adj) = 0.9911, R-Sq(pred) = 0.9568.

Fig. 3. Effects of temperature and methanol to oil molar ratio on biodiesel yield (catalyst amount = 1.0 wt%, reaction time = 20 min).

Fig. 4. Effects of methanol to oil molar ratio and catalyst amount on biodiesel yield (reaction temperature = 250 °C, reaction time = 20 min).

obtained at the reaction conditions of the methanol to oil molar ratio at 23:1, so single factor analysis is not so accurate and prac-

tical for a multi-factor influence experiment. Therefore, the optimum molar ratio of methanol to oil was 23:1.


D. Zeng et al. / Fuel 203 (2017) 739–748

Fig. 5. Effects of temperature and catalyst amount on biodiesel yield (methanol to oil molar ratio = 23:1, reaction time = 20 min).

3.2.3. Effect of catalyst amount In our previous study, the biodiesel yield was only 94.80% by the transesterification from soybean oil in supercritical methanol without catalysts. The optimum reaction conditions were methanol to soybean oil molar ratio of 46:1 at 300 °C for 45 min [23]. In this work, little amount of CH3ONa (0.5–1.5 wt%) can lead to relatively mild reaction conditions. Fig. 5 shows the interaction effect between temperature and catalyst amount on the biodiesel yield. In the beginning, the biodiesel yield raised with the increase of CH3ONa amount. CH3ONa dissociation in methanol produces the necessary methoxide anion to begin the reaction. Methoxide anion (CH3O-) is strongly basic and has high catalytic activity in transesterification reactions [17]. The reaction mechanism for methoxidecatalyzed oil transesterification is formulated as three steps. As expressed by Fig. 6, transesterification is a nucleophilic substitution reaction in the presence of methanol, and methoxide functions as a nucleophile [18]. The methoxide anion first attaches to the carbonyl carbon atom of the triglycerides (TG) to form a tetrahedral intermediate. Then, the tetrahedral intermediate reacts with methanol to generate methoxide anion. At last, diglycerides (DG) and alkyl ester are formed by the rearrangement of the tetrahedral intermediate. DG and monoglycerides (MG) are converted by the same mechanism to produce alkyl ester and the by-product glycerol, where R1, R2, and R3 represent long chain alkyl groups, respectively. The maximum yield of 97.42% shown in Table 1 was obtained at the CH3ONa amount of 1.0 wt%.

3.2.4. Effect of interaction process variables The results of ANOVA in Table 3 revealed that A, AB, BC and all the quadratic terms are significant model terms having large effect on the biodiesel yield because of their low P-values. The higher F value for a parameter demonstrate its higher significance on the biodiesel yield. Thus, the order of influences of these parameters was as follows: reaction temperature (A) > methanol to oil molar ratio (B) > catalyst amount (C). Namely, the reaction temperature is the most important variable for the catalytic-supercritical transesterification reaction. Figs. 3–5 show the 3D response curves related to the effect of two variables on the biodiesel yield. The curved nature of 3D response in Fig. 3 and 5 indicated relatively significant interactions of reaction temperature with methanol to oil molar ratio and methanol to oil molar ratio with catalyst

amount. However, a weaker interaction between reaction temperature and catalyst amount was illustrated in Fig. 4. 3.2.5. Evaluation of the integrated process An additional experiment was performed under the optimum reaction conditions to evaluate the accuracy of the model. The experimental value of the biodiesel yield was 97.83%, which only has a percentage error of 4.27% with the predicted yield of 98.25%. Since the verification value well agreed with the estimated value of the fitted model equation, it offers a reasonable accuracy of the regression model to predict the optimum conditions for achieving a maximum biodiesel yield. 3.3. Kinetic study of the transesterification process 3.3.1. Experiment The kinetics of the transesterification process was investigated, and the variation curves of the biodiesel yield from 150 °C to 250 °C with respect to time are shown in Fig. 7. The other conditions are settled at the methanol to oil molar ratio of 23:1 and 1.0 wt% CH3ONa with the reactor oscillating velocity of 50– 60 rpm. From Fig. 7, it is evident that with an increase in time, the biodiesel yield increases gradually and tails at 20 min. 3.3.2. Kinetic parameters of the process The overall transesterification reaction of TG to form FAME and glycerol (GL) in the presence of methanol (MeOH) is shown in Eq. (5).

TG þ 3MeOH ! 3FAME þ GL


The rate of formation of product has been found to be well correlated by the following rate equation

r A ¼ k0 cnA cm B


As the amount of methanol is excess, we may assume that the concentration of methanol is constant. Besides, set k ¼ k0 cm B :Thus,

r A ¼ 

dcA n ¼ kcA dt


Because the concentration of TG at any moment of the reaction can be expressed as cA ¼ c0 ð1  xÞ, so


D. Zeng et al. / Fuel 203 (2017) 739–748

Fig. 6. Mechanism of methoxide-catalyzed transesterification of soybean oil.

By taking the natural logarithm Eq. (9) can be written as Eq. (10)


dx ¼ n ln½c0 ð1  xÞ þ ln k0 dt



In Eq. (6), k ¼ k=c0 As shown in Eq. (10), the order of the reaction and the rate convs. ln[c0(1  x)]. Here, we stant are determined from the plot of ln dx dt use the differential method to identify the order of the reaction by Exponential function in Origin software. The exponential function expressed as

y ¼ y0 þ AeR0 x


Taken the obtained plot at 150 °C as an example, the fitting function can be expressed as

xðtÞ ¼ 0:7586  0:7636 eð0:0396tÞ


The differential equation governing the transesterification reaction of TG is expressed by Fig. 7. Effect of temperature on biodiesel yield (experimental assessed).

r A ¼ 

dcA d½c0 ð1  xÞ dx ¼ c0 ¼ k½c0 ð1  xÞn ¼ dt dt dt

dx ¼ 0:0303eð0:0396tÞ dt ð8Þ

According to the experiment results, a well-fitted differential vs. ln [c0(1  x)] can be obtained in Fig. 8. A straight line plot of ln dx dt is observed as



From Eq. (8), the rate equation can be expressed as Eq. (9)

dx k ¼ ½c0 ð1  xÞn dt c0


dx ¼ 1:3965 ln½c0 ð1  xÞ  2:5979 dt



D. Zeng et al. / Fuel 203 (2017) 739–748

Fig. 8. Plot of ln[c0(1  x)] vs.ln dx at 150 °C. dt

Fig. 9. Plot of 1/T vs. ln k.

with the R2 value of 0.9884. From Eqs. (10) and (14), the reaction order is obtained as 1.4, and the reaction rate constant is 0.0387. Similarly, the linear fitting plots at 175 °C, 200 °C, 225 °C and 250 °C can be obtained, and the results are listed in Table 4.

ature in Table 4 [34]. After taken the obtained parameters into Eqs. (15) and (7), the kinetic model of this integrated process can be expressed as Eq. (17).

3.3.3. Activation energy determination The Arrhenius equation can be written as Eq. (15). By taking the natural logarithm, Eq. (15) can be written as Eq. (16). Ea

k ¼ AeRT ln k ¼ 


Ea þ ln A RT


dcA 27:06103 ¼ 102:71e RT c1:5 A dt


Table 5 shows the comparison of kinetic parameters between this integrated process and other researchers’ work, the activation energy for tannery waste [35], linseed oil [36], castor oil [36] and rapeseed oil [33] is higher than the value obtained in this study. It is because the different fatty acid composition of oil used and the small amount of the involved catalyst, which lowered the activation energy.

where A is the pre-exponential factor, and Ea is the activation energy (kJmol1). R is the molar universal gas constant (8.314 Jmol1K1), and T represents the absolute temperature (K). A linear correlation between ln k and T1 can be found in Eq. (16). By using the rate constants listed in Table 4 and the corresponding temperature from 150 °C to 250 °C, The straight line with the R2 value of 0.9016 was obtained in Fig. 9. The activation energy and pre-exponential factor can be calculated from the intercept and the slope as 27.06 kJmol1 and 102.71, respectively. Besides, the reaction order of SC-MeOH and CH3ONa-catalyzed transesterification is 1.5 which is averaged by the order value at each temper-

Table 4 Reaction order, reaction rate constant and relative value at different temperatures. T/°C

Rate constant k /min1

Order n


150 175 200 225 250

0.0387 0.0858 0.1207 0.1578 0.1730

1.4 1.9 1.8 1.4 1.0

0.9884 0.9946 0.9964 0.9905 0.9722

Fig. 10. Plot of 1/T vs. ln k/T.

Table 5 Comparison of the kinetic parameters calculated by different methods. Method


Reaction order n

Pre-exponential factor A

Activation energy Ea /kJmol1


Integrated process

Soybean oil




This study

SC-MeOH Transesterification

Tannery waste Linseed oil Castor oil Rapeseed oil


1176.67 4.68 32.40 3.21  105

36.01 46.50 35.00 67.76

[35] [36] [36] [33]


D. Zeng et al. / Fuel 203 (2017) 739–748 Table 6 Thermodynamic parameters in the integrated transesterification process. Feedstock

DH (kJmol1)

DS (kJmol1K1)

DG (kJmol1)


Soybean oil Tannery waste Rapeseed oil Soybean oil

23.15 31.37 19.59 28.33

0.22 0.23 0.19 0.18

137.43 153.64 75.26–79.06 83.30–87.69

This study [35] [37] [38]

3.4. Thermodynamic analysis


Thermodynamic parameters mainly including the enthalpy (DH), entropy (DS), and the Gibbs free energy (DG) are important features to evaluate the behavior of transesterification reactions. As the value of Gibbs free energy can be calculated from the Eyring-Polanyi equation, which can be written as Eq. (18).

The authors would like to acknowledge financial support for this research from the National Natural Science Foundation of China (No. 21376186).


  kB T DG exp  h RT


where j is the transmission coefficient and usually taken as unity, kB is the Boltzmann constant (1.38  1023 JK1), and h is the Planck’s constant (6.63  1034 Js). Taking the natural logarithm of Eq. (18) and substituting DG ¼ DH  T DS gives


        k  DH 1 kB DS ¼ þ ln j þ ln þ T R T R h


Eq. (19) describes the relationship between enthalpy and entropy with the connection of rate constant. The values of these two thermodynamic parameters can be obtained from the slope and the intercept of the linear plot of 1/T vs. ln (k/T). From Fig. 10, values of enthalpy and entropy were found to be 23.15 kJmol1 and 0.22 kJmol1K1, respectively. Thus, the value of Gibbs free energy can be calculated as 137.43 kJmol1 at 523 K. The positive value of enthalpy indicates that the external heat input is required to raise the energy level for the reactants to transform to their transition state. The negative value of entropy means the reactants joined to form transition state, which is more structured to the ground state. The positive Gibbs free energy shows that the SC-MeOH and CH3ONa-catalyzed transesterification is unspontaneous and endergonic. Similar trends for the thermodynamic parameters of the transesterification reaction have been reported in many previous works. Some examples are presented in Table 6. Various feedstock and different transesterification methods lead to some differences in values of thermodynamic parameters for biodiesel production. 4. Conclusions The process combining supercritical technology and alkalicatalyzed transesterification possesses the advantages of significantly decreased temperature, relatively small catalyst consumption, and enhanced reaction rate compared with either single method. It was successfully used to synthesize biodiesel under the optimum conditions of 250 °C, methanol to oil molar ratio of 23:1, 1.0 wt% CH3ONa and 20 min, the biodiesel yield exceeded 97%. The temperature was found to be the most significant parameter based on RSM analysis. The second-order polynomial regression model was validated to be appropriate in designing the similar reaction system. The kinetic model of this integrated pro27:06103

cess was found to be  dcdtA ¼ 102:71e RT c1:5 A . Further, the thermodynamic parameters of the transesterification process were evaluated. The values of DH, DS and DG were found to be 23.15 kJmol1 and 0.22 kJmol1K1 and 137.43 kJmol1 at 523 K, respectively, which show that the reaction process was endothermic, endergonic and unspontaneous.

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