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Kinetics for the Synthesis of Biodiesel Based on the Calculation of Hot Spot Temperatures in the Catalyst Hong Yuan,†,‡ Xingxing Li,† and Bolun Yang*,† †

Department of Chemical Engineering, State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an Shaanxi 710049, China ‡ School of Chemistry and Chemical Engineering, Beifang University of Nationalities, Yinchuan 750021, China ABSTRACT: Microwave-absorbing catalyst H3PW12O40·xH2O/C (HPW/C) was prepared for biodiesel synthesis using cottonseed oil and methanol as feed materials. The hot spot temperatures in the catalyst were calculated by considering the absorbed microwave power, temperature rise, and heat transfer between catalyst and liquid phase. The intrinsic kinetics model for heterogeneous transesterification was established on the basis of the Langmuir−Hinshelwood−Hougen−Watson (LHHW) mechanism, and the model parameters were decided by using the kinetics experimental data and the calculated results under the hot spot temperatures. Results showed that the hot spot temperatures of the catalyst were far higher than the temperature of bulk liquid, and the simulated kinetics results agreed well with the experimental data.

1. INTRODUCTION As diesel fuel demands increase continuously and the crude oil reserves deplete in the future, the research in alternative renewable fuels is becoming more and more important. Biodiesel, because of its renewable nature and the low carbon dioxide emission, can be considered as a substitute for diesel fuel. Biodiesel can be obtained by a transesterification reaction using vegetable oils or animal fats with short-chain alcohols, especially methanol, in the presence of acidic or basic catalysts. Compared to basic homogeneous catalysts, solid acid catalysts are more suitable for making biodiesel from cheap waste vegetable oils, which can make a simple separation from the product and reduce the catalysts’ waste. However, the reaction using solid acid catalysts always proceeded at a relatively slow rate. In our previous work,1 a microwave-absorbing solid acid catalyst, H2SO4/C, was used under microwave radiation to enhance the biodiesel production process. Results showed that the activity of H2SO4/C under microwave was far higher than that under conventional heating methods, even though the same catalyst was used. The reason was thought that “microwave hot spots” could be formed in the catalyst H2SO4/C, and the hot spot temperatures were far higher than the temperature of the bulk liquid. However, how the values of hot spot temperatures were obtained and where the reaction rates could be enhanced under the hot spot temperatures were not explained by the authors at that time. In some reported kinetics research for biodiesel synthesis under microwave catalysis condition, reaction temperatures were considered as bulk liquid temperatures.2−7 However, the temperatures of microwave hot spots formed in the solid catalysts are greatly different from the temperatures of the bulk liquid under microwave radiation;8 therefore, the kinetic analysis results based on the temperatures of the bulk liquid would not reflect the actual kinetics accurately. In this work, H3PW12O40·xH2O/C (HPW/C) was prepared to catalyze the reactions between cottonseed oil and methanol © XXXX American Chemical Society

under the microwave radiation condition, the hot spot temperatures in catalyst were calculated by considering absorbed microwave power, and the temperature rise and heat transfer between catalyst and liquid phase under different microwave working conditions were calculated. Furthermore, the intrinsic kinetics model for heterogeneous transesterification was established on the basis of the Langmuir−Hinshelwood−Hougen− Watson (LHHW) mechanism, and the model parameters were determined using the Runge−Kutta method through the kinetics experimental data under the hot spot temperatures.

2. EXPERIMENTAL METHODS 2.1. Preparation of the Catalyst. After it was boiled in deionized water for 3 h, activated carbon was washed by deionized water several times and then was dried at 393 K until the mass did not change. Pretreated activated carbon (11 g) was impregnated in 90 g of HPW aqueous solution (10 wt %) at 303 K for 12 h. Then the mixture was evaporated in a rotary evaporator at 393 K and 0.01 MPa until dry. The obtained catalyst was designated as 45 wt % HPW/C. 2.2. Kinetics Experiments for Heterogeneous Transesterification. 2.2.1. Transesterification Procedures. The cottonseed oil was industrial grade, and its average molecular weight (905 g mol−1) was calculated from the saponification value (S.V. = 185.6 mg KOH g−1). The reactions were carried out in a microwave synthesis reactor (Shanghai Sineo Microwave Chemistry Technology Co., Ltd., Shanghai, China) working at 2.45 GHz. Cottonseed oil (40 g) and a certain amount of methanol (17, 25, and 42 g) and catalyst (1.4, 2.2, and 3.8 g) were put into the 250 mL three-necked round-bottomed quartz flask, which was put into the microwave synthesis equipment to carry out the transesterification at the set temperature. During the Received: April 29, 2013 Revised: October 6, 2013 Accepted: October 7, 2013

A

dx.doi.org/10.1021/ie401370n | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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the material surface, which was the rated power of microwave reactor; x represents the depth from surface along axial or radial direction, m; α represents the attenuation constant, m−1, which is expressed by eq 29,11

experimental process, a 0.05 mL sample was taken from the reactor for concentration analysis in regular intervals (15, 30, 45, 60, 75, 90, 120, 180, and 240 min); thus, the experimental data of the reactants concentration (triglyceride, diglyceride, monoglyceride and methyl ester) vs reaction time was obtained. 2.2.2. Kinetics Experiment Conditions. Cottonseed oil is mainly composed of linoleic acid, oleic acid, and palmitic acid triglyceride, among which the linoleic acid triglyceride is largest in quantity. Therefore, all the triglycerides were lumped as linoleic acid triglyceride in this work, and the reaction rate of the transesterification was expressed as the variation of this component.9 Similarly, the intermediate products (diglyceride and monoglyceride) and the final product (methyl ester) were also lumped as linoleic acid diglyceride, linoleic acid monoglyceride, and linoleic acid methyl ester to investigate the kinetic behavior. In order to study the influence of internal and external diffusion on the kinetic behavior, experiments were carried out using catalysts with different particle sizes (0.18−0.25 mm, 0.15−0.18 mm, 0.12−0.15 mm, and 0.113−0.12 mm) and under different agitation speeds (200, 400, 600, and 800 rpm). A series of experiments in different experimental conditions, such as reaction temperature of the bulk liquid (328, 333, 338, and 343 K), the molar ratio of methanol to oil (12:1, 18:1, and 30:1), and the mass ratio of catalyst to oil (3.5%, 5.5%, and 9.5%), were also conducted. 2.3. Product Analysis. The concentrations of triglyceride, diglyceride, monoglyceride, and methyl ester in the product were analyzed by high-performance liquid chromatography (HPLC) with a Shim-pack VP-ODS polymer-based column (column temperature: 303 K) and a UV−vis detector. The mobile phase was a mixture of methanol and hexane in the volumetric ratio of 90:10 with a flow rate of 1 mL/min and a loop of 10 μL.

α=

Figure 1. Schematic diagram of the spherical cap describing the reactant in flask.

infinitesimal volume within the spherical cap can be expressed by eq 3 Qr =

φ2

θ2

1

1

1

r2

πR2 + (2θ − π )r 2 2p0 [πR2α + (2θ − π )r 2α − (2θ − π )r ]e−2α(R − r) [πR2 + (2θ − π )r 2]2 (3)

where θ is the angle values of two mutually perpendicular planes, θ = 2arccos(r/R); r is the distance between the center of sphere and the cross section of the spherical cap; R is the radius of the sphere. The total absorbed microwave power in a spherical cap is expressed by the volume integral in eq 4

where Pmic represents microwave power at any depth from the material surface; P0 represents the incident microwave flux from

∫φ ∫θ ∫r

2rp0 e−2α(R − r)

+

(1)

Pmic =

(2)

where ε′ is the dielectric constant; tan δ is the dielectric loss tangent; λ0 is the microwave wavelength in vacuum, 0.122 m. The reaction vessel was a three-necked round-bottomed quartz flask, and the reactant in the flask can be viewed as a spherical cap, as shown in Figure 1. The power absorbed by an

3. RESULTS 3.1. Calculation of Microwave Hot Spot Temperatures in Catalyst. 3.1.1. Model Building. 3.1.1.1. Calculation of Microwave Power. The power generated by the microwave can be evaluated by the following expression:9,10 Pmic = P0exp( − 2αx)

2π 0.5ε′((1 + tan 2 δ)0.5 − 1) λ0

2P0[πR2(r + α) + (2θ − π )(r 3 + r 2α − r )]e−2α(R − r) [πR2 + (2θ − π )r 2]2

where φ is the angle values of two mutually perpendicular planes, φ = θ; R = 0.040 m; θ1 = 2arccos(r2/R); θ2 = 2arccos(r1/R); r1 is the distance between the center of sphere and the cross section of the spherical cap, 0.005 m; r2 is the distance between the center of sphere and the cross section of the spherical cap formed by agitator, 0.038 m. The fact that vegetable oil is nonpolar has been reported by Kusdiana and Saka.12 On the basis of the microwave-absorbing principle that nonpolar substances do not absorb the radiation,13 vegetable oil shows very weak microwave-absorbing capacity, whereas methanol is a polar material and shows good microwave absorbing capacity. Activated carbon with a high dielectric loss factor is also a good microwave-absorbing material, which was

dr dθ dφ

(4)

reported in the literature.14 Furthermore, the heat capacity of activated carbon is 1 kJ kg−1 K−1, whereas those of cottonseed oil and methanol are 2.19 × 103 kJ kg−1 K−1 (340.1 K) and 3.24 × 103 kJ kg−1 K−1 (340.1 K), respectively. Known from the above analysis, activated carbon shows good microwave absorbing capacity and low heat capacity; therefore, when activated carbon is added in the mixture of cottonseed oil with methanol and heated by microwave energy, the increasing rate of temperature for this system will be fast. Because oil is a nonabsorbing microwave material and methanol and activated carbon are absorbing microwave material, the total dielectric constant εeff ′ and dielectric loss B



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Table 1. Work Conditions of Microwave Reactor and Calculated Results of Hot Spot Temperatures set temperature of bulk liquid (K)

initial temperature of bulk liquid (K)

343 338 333 328

293 293 293 293

heating time (s) and power (W) in temperature rise stage 20 25 20 20

500 400 400 400

heating interval time (s) 1 1 2 3

3 3 3 3

tangent tan δeff are considered only for methanol and activated carbon, which are expressed as eqs 5 and 6 ′ = εac′ wac + εMt ′ wMt εeff

(5)

tan δeff = wac tan δac + wMt tan δMt

(6)

h(V /A) λ

dT = hA(T − Tb) dt

433−469 409−437 362−390 344−372

451 423 376 358

300 200 200 200

(10)

3.1.2. Model Solving. The total absorbed microwave power of the reaction system Pmic can be obtained by solving eqs 2 and 4 and the fluctuation range of hot spot temperatures in the catalyst can be obtained by solving eqs 7 and 10. The work conditions of the microwave reactor are shown in Table 1. The calculated results of hot spot temperature variation are shown in Figure 2. Because this model was solved with microwave power in the range of 200−500 W, it is able to predict other experimental data at several incident microwave fluxes if the microwave power values were in the range of 200−500 W. As shown in Figure 2a, the hot spot temperatures in the catalyst rise to more than 700 K in the starting stage of the heating process and then decrease gradually and eventually stabilize around 433−469 K. Figure 2b−d also showed similar change regularities for hot spot temperatures in other working conditions. The average temperatures listed in Table 1 can be used to calculate the activation energies of the reactions in the following kinetics studies. 3.2. Study on Heterogeneous Kinetics of Transesterification. 3.2.1. Influence of Internal and External Diffusion. The catalyst particles were screened in four groups (Tyler standard screen), and the diameters were 0.18−0.25, 0.15−0.18, 0.12−0.15, and 0.113−0.12 mm. The influence of internal diffusion can be excluded when the diameter of the catalyst particle was less than 0.15 mm from the evaluation of reaction results. This conclusion also can be confirmed by the application of the Weisz−Prater criterion. Because the methanol was present in far greater quantities than cottonseed oil (the molar ratio of methanol to oil was 24:1), the reaction was considered as a pseudo-first-order reaction; the Weisz−Prater criterion as eq 11 thus can be applied21 r ΦS = L2 obs c*De (11)

(7)

(8)

where λ is the thermal conductivity of actived carbon, 2.0 W m−1 K−1;20 h is the convective heat transfer coefficient between liquid and activated carbon, 4.9 W m−2 K−1;20 V is the volume of activated carbon particle, V = (4/3)πrac3 ; A is the surface area of activated carbon particle, A = 4πrac2 ; rac is the average radius of activated carbon particle, 0.75 × 10−4 m. When the above values are put into eq 8, the Biot number is calculated (Bi = 6.1 × 10−5 < 0.1). Therefore, the lumped capacity method is suitable. The heat balance equation is −ρVCp

average value of hot spot temperatures (K)

⎛ −hAt ⎞ T − Tb ⎟⎟ = exp⎜⎜ T0 − Tb ⎝ ρVCp ⎠

where Cp is specific heat capacity of activated carbon at constant pressure, 1 kJ kg−1 K−1;17 T1 and T2 are the initial temperature and final temperature of activated carbon, respectively, K; t is the heating time, s; η is correction factor for the absorbed microwave energy distribution, η = (tan δac/tan δMt)(ε′ac/ε′Mt)(mac/mMt) . 3.1.1.3. Heat Transfer between Activated Carbon and the Liquid Phase. The lumped capacity method (LCM)18,19 was adopted to simplify the heat transfer process between the activated carbon and the liquid. The principle of the LCM is to assume a uniform temperature distribution within the solid material at any time, which is decided by checking that whether the Biot number (Bi) for heat transfer is less than 0.1. The Biot number is expressed by eq 8 Bi =

fluctuation range of hot spot temperatures (K)

With the initial conditions (t = 0, T = T0 = 293 K), the integral equation of eq 9 is expressed as follows:

where εac ′ is the dielectric constant of activated carbon, 17.9;15 εMt ′ is the dielectric constant of methanol, 32.7;16 tan δac is the dielectric loss tangent of activated carbon, 2.95;16 tan δMt is the dielectric loss tangent of methanol, 0.941,16 wac is the mass fraction of activated carbon, mac/m; wMt is the mass fraction of methanol, mMt/m; m is the mass of the total reactants, which contains oil (40 g), methanol (33.95 g), and activated carbon (1.65 g); mac is the mass of activated carbon; mMt is the mass of methanol. 3.1.1.2. Temperature Rise by Microwave Radiation Heating. The temperature rise of activated carbon by microwave heating is expressed by eq 7 macCp(T2 − T1) = ηPmict

heating time (s) and power (W) in temperature control stage

where L corresponds to one-sixth of the particle diameter for catalyst, 0.00015/6 m; c* is the equilibrium concentration, kmol m−3; robs is the observed reaction rate, kmol gcat−1 s−1; De is the effective diffusion coefficient of methyl ester in catalyst which was estimated as one-tenth of the diffusion coefficient for methyl ester in water.21 The diffusion coefficient of methyl ester in water was calculated using Wilke−Chang equation:

(9)

D = 7.4 × 10‐8

where ρ is the density of activated carbon, 570 kg m−3; Tb is the ambient temperature, K. C

(ϕM )0.5 T μL V b0.6

(12)



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Figure 2. Fluctuation ranges of the microwave hot spot temperatures as function of time.

where water is the solvent and methyl ester is the solute; φ is the associating factor of solvent (2.6 for water); M is the molecular weight of solvent, kg kmol−1; μL is the viscosity of solvent, mPa s; Vb is the volume of solute at its normal boiling temperature. The value was 0.411 × 10−3 m3 mol−1. When the diameter of catalyst particle was less than 0.15 mm, the calculated values of the Weisz−Prater modulus (ΦS) for methyl ester at 343, 338, 333, and 328 K were 7.3 × 10−4, 8.1 × 10−4, 8.3 × 10−4, and 8.4 × 10−4, respectively. The effectiveness factor is obtained by eq 1322 ζ=

1 ⎡ 1 1 ⎤ − ⎢ ⎥ ΦS ⎣ tanh(3ΦS) 3ΦS ⎦

⎛ N d 5N3d 4ρ 3 ⎞1/4 ⎛ μ ⎞1/3 p I p L ⎟ ⎜⎜ L ⎟⎟ = 2 + 0.4⎜⎜ ⎟ 3 D μL VL ⎝ ⎠ ⎝ ρL D ⎠

ksld p

(15)

where μL is liquid viscosity; N is stirring velocity, 13.33 s−1; power number (Np = 5) has been obtained as function of the agitator turbine impeller with six flat blades; dI is diameter of stirring blade, 0.05 m; ρL is liquid density, kg m−3. The diffusion coefficient D was calculated using the Wilke−Chang equation (eq 12), where methyl ester is the solute and the mixture (methanol and triglyceride) is the solvent. When the agitation speed reached 800 rpm, the calculated values of the Carberry number (Ca) were 0.18 (343 K), 0.18 (338 K), 0.18 (333 K), and 0.17 (328 K). These values were close to 0.1, indicating that the influence of external diffusion can be neglected in this case.24 On the basis of these analysis results, all the kinetics experiments were carried out with the diameter of catalyst particles less than 0.15 mm and an agitation speed of 800 rpm. 3.2.2. Influence of Temperature on Transesterification. Figure 3a−d presents the experimental results of concentration changes for every component with the reaction time at different temperatures of bulk liquid. When the temperature was 343 K, the concentration of the final product ME reached about 1.2 kmol m−3 at 120 min and then did not increase obviously. For reactant triglyceride (TG), its concentration decreased sharply in the initial stage of the reaction and reached 0.1 kmol m−3 at 120 min. The concentration of diglyceride (DG) and monoglyceride (MG) maintained lower values (less than 0.2 kmol m−3) all along. When the temperature was 338 K, a similar trend also was observed. When the temperature was low, such as 333 and 328 K, the concentration of the methyl ester only reached about 1.1 kmol m−3 at 120 min and reached 1.2 kmol m−3 at about 180 min. For the

(13)

The calculated effectiveness factors were all larger than 0.99. These results indicated that the influence of internal diffusion can be neglected21 when the diameter of the catalyst particle was less than 0.15 mm. Four different agitation speeds, 200, 400, 600, and 800 rpm, were used to study the influence of agitation speed on the concentration of ME. The concentration of ME increased with the increase of agitation speed from 200 to 600 rpm and then did not increase obviously when the agitation speed reached 800 rpm. This shows that the influence of the external diffusion resistance can be neglected when the agitation speed is over 800 rpm. Also, this conclusion can be evaluated from Carberry number. The Carberry number is defined as eq 14 robs Ca = * klsc (6W /dPρ) (14) where dP is the particle diameter of catalyst, 0.00015 m; kls is the liquid−solid mass transfer coefficient estimated by the correlation equation from Creeze et al.23 D



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Figure 3. Influence of temperature on biodiesel synthesis from cottonseed oil and methanol. Reaction time: 240 min. Molar ratio of methanol to oil: 24/1. Catalyst load: 7.5 wt %. H3PW12O40·xH2O/C: 40 wt %.

3.2.4. Mechanisms and Kinetics Model. Transesterification is where a triglyceride is mixed with short-chain alcohols, especially methanol, in the presence of a catalyst to form fatty acids methyl esters. Transesterification consists of three consecutive reversible reactions. Triglyceride (TG) reacts with methanol stepwise to produce diglyceride, monoglyceride, and methyl ester. The kinetic mechanism can be represented by the following reactions:

reactant triglyceride, its concentration decreased more slowly than it did in the high temperature. The concentration of diglyceride and monoglyceride also maintained in lower values (less than 0.1 kmol m−3) all along. Therefore, the temperature showed a significant effect on concentration variation of methyl ester and triglyceride, and the higher temperature led to a higher reaction rate and a higher concentration of the final product methyl ester, correspondingly. 3.2.3. Catalyst Deactivation. In order to study catalyst deactivation, the experiments on the repeated use of the catalyst were carried out, and the results are shown in Figure 4. It can be seen that the concentration of methyl ester still was about 1.2 kmol m−3 after use four times, which was close to the reaction result in first time; therefore, the catalyst deactivation can be neglected.

Three surface reaction steps (r1, r2, and r3) were assumed as the rate-limiting steps, and the kinetic model was built on the basis of the Langmuir−Hinshelwood−Hougen−Watson mechanism (LHHW) as follows:25 KTG

TG + δ XoooY TG·δ

(19)

KMt

CH3OH + δ XoooY CH3OH·δ Figure 4. Effect of catalyst reuse on concentration of methyl ester. Reaction temperature: 343 K. Reaction time: 180 min. Molar ratio of methanol to oil: 24/1. Catalyst load: 7.5 wt %. H3PW12O40·xH2O/C: 40 wt %.

(20)

k1

r1 : TG·δ + CH3OH·δ XooY DG·δ + ME·δ k −1

E

(21)



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Figure 5. Relationship between adsorption equilibrium constants and microwave hot spot temperatures. Reaction time: 240 min. Molar ratio of methanol to oil: 24/1. Catalyst load: 7.5 wt %. H3PW12O40·xH2O/C: 40 wt %. KDG

DG·δ XoooY DG + δ

KME

ME·δ XoooY ME + δ

(22)

(26)

k2

r2 : DG·δ + CH3OH·δ XooY MG·δ + ME·δ k −2

KMG

MG·δ XooooY MG + δ

(23)

k Gly

Gly·δ XoooY Gly + δ

k3

r3 : MG·δ + CH3OH·δ XooY Gly·δ + ME·δ k −3

r1 =

(27)

(24)

With the above mechanism and assumptions, the reaction rates presented in the following equations were derived:

(25)

KTGKMtk1c TGc Mt − KDGKMEk −1c DGc ME [1 + KTGc TG + KMtc Mt + KDGc DG + KMEc ME + (K Gly(c ME − c DG − 2c MG))/3 + KMGc MG]2

F

(28)



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Table 2. Regressed Kinetics Parameters k1

k−1

k2

k−2

k3

k−3

0.0087 ± 0.0005 31.3 ± 1.7

0.6971 ± 0.035 35.2 ± 1.6

7.2111 ± 0.6038 46.1 ± 3.6

0.0022 ± 0.0003 10.5 ± 0.7

2.1134 ± 0.1987 44.1 ± 2.3

0.0022 ± 0.006 14.7 ± 4.3

parameters pre-exponential factor (m3 gcat−1 s−1) activation energy or adsorption heat (kJ mol−1)

Figure 6. Comparison of experimental and simulation results of transesterification in different temperatures. Reaction time: 240 min. Molar ratio of methanol to oil: 24/1. Catalyst load: 7.5 wt %. H3PW12O40·xH2O/C: 40 wt %.

r2 =

r3 =

KDGKMtk 2c DGc Mt − KMGKMEk −2c MGc ME [1 + KTGc TG + KMtc Mt + KDGc DG + KMEc ME + (K Gly(c ME − c DG − 2c MG))/3 + KMGc MG]2

(29)

KMGKMtk 3c MGc Mt − K GlyKMEk −3cGlyc ME [1 + KTGc TG + KMtc Mt + KDGc DG + KMEc ME + (K Gly(c ME − c DG − 2c MG))/3 + KMGc MG]2

where r1, r2 and r3 are the reaction rates of the three ratelimiting steps, kmol gcat−1 min−1; k1, k−1, k2, k−2, k3, and k−3 are reaction rate constants, m3 gcat−1 s−1; KTG, KMt, KDG, KMG, KGly, and KME are the adsorption equilibrium constants for TG, methanol, DG, MG, and ME, respectively; cTG, cMt, cDG, cMG, cGly, and cME are the concentration of TG, methanol, DG, MG, and ME, respectively. Then, the differential equations describing variations of the reactants concentration can be written as follows: dn TG V dc TG = = −r1 W dt W dt dnMt V dc Mt = = −(r1 + r2 + r3) W dt W dt

(31)

(30)

dnDG V dc DG = = r1 − r2 W dt W dt

(33)

dnMG V dc MG = = r2 − r3 W dt W dt

(34)

dnME V dc ME = = r1 + r2 + r3 W dt W dt

(35)

where n is the amount of substance, kmol; t is the reaction time, min; W is the catalyst mass, g; V is the volume of the liquid phase, m3.

(32) G



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Table 3. Correlation Coefficient (r2) of Predicted and Experimental Data r2 Figure 6 ME TG DG MG

Figure 7

Figure 8

a

b

c

d

a

b

c

a

b

c

0.998 0.999 0.968 0.972

0.999 0.999 0.986 0.981

0.999 0.997 0.990 0.968

0.998 0.998 0.991 0.989

0.990 0.988 0.977 0.948

0.994 0.990 0.960 0.926

0.990 0.984 0.952 0.930

0.987 0.968 0945 0.940

0.992 0.981 0.930 0.954

0.974 0.976 0.932 0.928

Figure 7. Comparison of experimental and simulation results of transesterification at different molar ratios of methanol to oil. Reaction time: 240 min. Reaction temperature: 338 K. Catalyst load: 7.5 wt %. H3PW12O40·xH2O/C: 40 wt %.

calculated and summarized in Table 2. From Table 2, it can be seen that the activation energy values were all between 10.5 and 46.1 kJ mol−1, and standard errors of activation energies were all less than 4.3 kJ mol−1. López et al. reported their results for the reaction of triacetin with methanol using Nafion acid resins and H2SO4 as catalysts under conventional heating. The activation energies were found to be 48.5 ± 1.6 kJ mol−1 (Nafion SAC-13) and 46.1 ± 2.1 kJ mol−1 (H2SO4) when the reaction temperature was around 303−333 K.26 The reason that the activation energy values in this work were smaller than the literature values may be considered as the specific microwave effect.27 3.2.6. Validation of Kinetics Model. The kinetics model was verified by the consistency of the calculated results with experimental results under the changes in the temperature, the molar ratio of methanol to oil, and the mass ratio of catalyst to oil. 3.2.6.1. Effect of Temperature on Transesterification. The results of transesterification under different temperatures are shown in Figure 6a−d. The solid lines and the dots in these figures are the predicted and experimental data, respectively; the correlation coefficients (r2) in different temperatures (343, 338, 333, and 328 K) are shown in Table 3. It can be seen that the predicted data agreed well with the experimental data.

We combined eqs 23−30 with the following initial conditions: 0 0 t = 0, C TG = C TG , CMt = CMt , C DG = 0, CMG = 0,

CME = 0

(36)

The kinetic model for synthesis of ME over the HPW/C catalyst was then obtained. 3.2.5. Calculation of the Kinetics Model. The fourth-order Runge−Kutta method by Matlab 7.0 software was used to solve the above kinetic model under the range of microwave hot spot temperatures shown in Table 1. The relationship between the adsorption equilibrium constants and different microwave hot spot temperatures is presented in Figure 5. It can be seen that the adsorption equilibrium constants for reactants such as methanol (Mt), triglyceride (TG), diglyceride (DG), and monoglyceride (MG) all decreased with the increase of temperature. So, the higher temperature went against the absorption on catalyst. The adsorption equilibrium constant for the product methyl ester (ME) increased with the increase of temperature, and the higher the temperature, the more difficult the desorption is. Activation energies and pre-exponential factors were H



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Figure 8. Comparison of experimental and simulation results of transesterification with different catalyst loads. Reaction time: 240 min. Reaction temperature: 338 K. Molar ratio of methanol to oil: 24/1. H3PW12O40·xH2O/C: 40 wt %.

3.2.6.2. Effect of Molar Ratio of Methanol to Oil on Transesterification. The results of different molar ratios of methanol to oil (12:1, 18:1, and 30:1 mol/mol) are shown in Figure 7a−c. The solid lines and the dots in these figures are the predicted and experiments results, respectively, and the correlation coefficients (r2) are shown in Table 3; it can be seen that the simulation result agreed well with the experimental data. From Figure 7, it can be seen that the reaction reached equilibrium after 120 min when the molar ratio of methanol to oil was 30:1; yet when the molar ratio of methanol to oil was 12:1 and 18:1, the reaction could not reach equilibrium even after 240 min. From the stoichiometric coefficient of the reaction, 1 mol triglyceride with 3 mol methanol converts to 3 mol methyl ester by transesterification. When the reversible characteristic of transesterification is considered, a higher molar ratio is favorable for the conversion to methyl ester. 3.2.6.3. Effect of Mass Ratio of Catalyst to Oil on Transesterification. The simulation and experimental results with the change of catalyst load (3.5, 5.5, and 9.5 wt %) are presented in Figure 8, and the coefficient coefficients (r2) are shown in Table 3. It can be seen that the model fits these experimental data well. With the increase of the catalyst load, the time for ME concentration reaching the equilibrium is reduced. Generally speaking, when the catalyst concentration increases, the initial reaction rate will increase proportionally for the case of heterogeneous reaction at a set temperature. However, the transesterification in this work is enhanced with microwave technology, and the larger the catalyst concentration, the higher the microwave hot spot temperature in solid catalyst is; therefore, not only catalyst concentration but also the hot spot temperature in the solid catalyst increased when

the catalyst load was increased. For this reason, the initial reaction rate did not increase proportionally to the increase of the catalyst concentration.

4. CONCLUSIONS The hot spot temperatures for the microwave-absorbing catalyst were calculated, and the results showed that these values were far higher than the bulk liquid temperatures (30−110 K). After eliminating the influence of internal and external diffusion of the catalyst, the intrinsic kinetics model for heterogeneous transesterification using the Langmuir−Hinshelwood−Hougen− Watson (LHHW) mechanism was established on the basis of the six surface reaction steps under the hot spot temperatures of the catalyst. The calculated activation energies were 31.4 ± 1.7, 35.3 ± 1.6, 46.2 ± 3.6, 10.6 ± 0.7, 44.2 ± 2.3, and 14.7 ± 4.3 kJ mol−1, respectively. The reliability of the model was verified by using experimental results and simulation results under different molar ratios of methanol to oil and different mass ratios of catalyst to oil. Simulation results agreed well with the experimental data.

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AUTHOR INFORMATION

Corresponding Author

*B. Yang. Telephone: +86-29-82663189. Fax: +86-29-82668789. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial supports for this work from the National Basic Research Program of China (973 Program, 2009CB219906), Specialized Research Fund for the Doctoral Program of Higher I



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Education of China (20110201130002), National Natural Science Foundation of China (21276203, 21266001), and Ningxia Science and Technology Support Program (2012zyg008) are gratefully acknowledged.

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Article

REFERENCES

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NOMENCLATURE

A = surface area, m2 Bi = Biot number c = concentration, kmol m−3 c* = equilibrium concentration, kmol m−3 Ca = Carberry number Cp = specific heat capacity, kJ kg−1 K−1 dI = diameter of stirring blade, m dP = particle diameter, m D = diffusion coefficient, m2 s−1 De = effective diffusion coefficient, m2 s−1 h = convective heat transfer coefficient, W m−2 K−1 k = reaction rate constants, m3 gcat−1 s−1 kls = liquid−solid mass transfer coefficients, m s−1 K = adsorption equilibrium constant m = mass of substance, g M = molecular weight of solvent, kg kmol−1 n = amount of substance, kmol N = stirring velocity, s−1 Np = power number Pmic = power generated by microwave at any depth from the surface of the material P0 = power of microwave reactor rac = average radius of activated carbon, m ri = reaction rate of rate-limiting step (i = 1, 2, or 3), kmol gcat−1 min−1 robs = observed reaction rate, kmol gcat−1 min−1 R = radius of the sphere, m t = time, s T = temperature, K Tb = ambient temperature, K V = volume, m3 Vb = volume of solute at its normal boiling temperature, m3 mol−1 w = mass fraction W = catalyst mass, g x = depth from surface along axial or radial direction, m

Greek Symbols

α = attenuation constant, m−1 ε′ = dielectric constant tan δ = dielectric loss tangent λ0 = microwave wavelength in vacuum, m φ, θ = angle values of two mutually perpendicular planes η = correction factor λ = thermal conductivity, W m−1 K−1 ρ = density of activated carbon, kg m−3 ρL = liquid density, kg m−3 φ = associating factor of solvent ΦS = Weisz−Prater modulus μL = liquid viscosity, mPa s ζ = effectiveness factor

Subscripts

Mt = methanol TG = triglyceride DG = diglyceride MG = monoglyceride ME = methyl ester J



Article

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K


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