- Email: [email protected]

S0960-8524(13)00032-1 http://dx.doi.org/10.1016/j.biortech.2013.01.009 BITE 11173

To appear in:

Bioresource Technology

Received Date: Revised Date: Accepted Date:

8 June 2012 1 January 2013 4 January 2013

Please cite this article as: Wu, L., Zhu, H., Huang, K., Thermal Analysis on the Process of Microwave-assisted Biodiesel Production, Bioresource Technology (2013), doi: http://dx.doi.org/10.1016/j.biortech.2013.01.009

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Thermal Analysis on the Process of Microwave-assisted Biodiesel Production Li Wu

Huacheng Zhu

Kama Huang *

College of Electronics and Information Engineering, Sichuan University, Chengdu 610064, Sichuan, China

Abstract: The aim of this work was firstly to do a precise thermal analysis of microwave assisted production of biodiesel. In this paper, the effective permittivity of biodiesel synthesis was updated with two methods: a traditional method and a bivariate function of temperature and concentration of one component, then the thermal analysis of the reaction process were accomplished with multi-physics calculation. The results show that there exists large distinction in temperature between these two simulation results calculated by the two methods. The two hot spots locate in the opposite side and their temperature’s difference is up to 9

when the reaction is just carried

out for 18 seconds. But the temperature risings and distributions calculated by the new method are closer to the measured results. The thermal analysis based on the new method will be helpful for the industrial design of biodiesel production.

Key words: thermal analysis, multi-physics calculation, biodiesel 1. Introduction

With petroleum reserves dwindling, the search is on to replace gasoline with a cleaner, greener alternative. The biofuel looks more likely to replace petroleum on a large scale. And some

1 Corresponding Author: Kama Huang. E-mail: [email protected] Tel and Fax: +862885408779 Postal Address: College of Electronics and Information Engineering, Sichuan University Chengdu 610064, Sichuan, China

researches on microwave heating the production of biofuels such as biodiesel and bioethanol had been reported (Nicholas E. Et al., 2006; Aharon Geganken, 2010; Miri Koberg et al., 2011; Xuebin et al., 2011), which have shown many advantages of microwave heating over the traditional heating methods, such as needing shorter time, saving more energy, easier to control, having a greater developing prospect in the transformation of biomass energy (Miura et al.,2004; Omar et al., 2011; Ruan et al., 2011, 2007; Honglei Zhang et al.,2012) and so on, therefore using microwave to heat reactions presents an impressive application prospect. Unfortunately, some difficulties limited the application of high-power microwaves in biodiesel production. Two of the main problems are as follows: (1) Thermal runaway still exists because the reflection and absorption of microwave by the reactants change nonlinearly with time during the reaction. It may destroy the microwave generator and burn the reactants, even lead to an explosion when high-power microwaves are applied (T. Santos et al, 2011); (2) Hot spot in the reaction solution cannot be eliminated due to the microwave’s inhomogeneous heating. (Satoshi Horikoshi et al., 2011). Therefore, to overcome these difficulties, the thermal analysis of microwave-assisted biodiesel production process based on the multi-physics calculation needs to be further studied. It’s well known that the effective permittivity can be used to describe the reflection and absorption of microwave in the mixture solution during the reaction procedure. For a liquid chemical reaction, the effective permittivity can be determined by the reaction solution’s component and temperature. Therefore, obtaining the effective permittivity determined by the reaction solution’s temperature and concentration of one component is preliminary and necessary for multi-physics calculation. However, most previous researches of microwave heating on the reaction simply treated the reaction solution as a mixture and the effective permittivity as a

2

constant or simple function of components’ volume fractions. Consequently, the calculated temperature distributions of esterification reaction solution were quite different from the measured results. Especially the hot spots, they may locate at different positions. 'The aim of this work was firstly to describe the effective permittivity of the reaction solution as a function of temperature and the concentration of one component, and then applied it to update the effective permittivity in multi-physics calculation to deal with the thermal analysis of microwave-assisted biodiesel production process. To validate the thermal analysis based on the new method, biodiesel synthesis is carried out under microwave heating with oleic acid and methanol. The results calculated by the new method show a better agreement with the experimental results.

2. Methods 2.1 Biodiesel synthesis

Generally, biodiesel is produced by esterification of fatty acids and methanol. Oleic acid, as a typical fatty acid, is applied to produce biodiesel with methanol in this paper. Concentrated sulfuric acid acts as catalyst in this reaction. The molar ratio of methanol to oleic acid is 6:1, and mass fraction of concentrated sulfuric acid is 1% of the whole reaction solution (Peng Baoxiang, 2009). The oleic acid is provided by Chengdu Kelong Chemical Reagent Factory. Methanol and concentrated sulfuric acid are produced by Chengdu Changlian Chemical Reagent Co., Ltd. All the chemicals are analytical reagent grade.

2.2 Calculation model

The schematic diagram of calculation model is shown in Fig.1. The origin of coordinates

3

locates at the center of microwave oven which provides 700W power at a frequency of 2450MHz. A beaker’s capacity is 500ml. The reaction solution is 225ml, which is less than 1/2 of total beaker’s capacity. Under the beaker, a hollow glass plate, which is 4mm in thickness, is placed on the center of microwave oven’s bottom to support the beaker. The BJ-26 waveguide connects to the right side of microwave oven and its center coordinate is (0.17m, 0.005m, 0.005m). The microwave power is fed in through the right port of the waveguide.

2.3 Bivariate function of effective permittivity

For a liquid chemical reaction, the effective permittivity of the reaction solution should be a bivariate function with the concentration of one reactant and temperature. Unfortunately, there is still lack of formulas that can be used to describe the effective permittivity. In the past, one of the simple ways to describe the effective permittivity is adopting the volume fractions of components (Takashi Nakamura, 2005). The formula can be expressed as follows: n

ε eff = ∑ ρi ⋅ε i

(2)

i =1

Where ρ i (i=1,2,…n) are the volume fractions of components,

ε i (i=1,2,…n) are the

corresponding permittivities of components. A method was proposed to calculate the effective permittivity with a bivariate function [Zhu Huacheng, 2012], which can be directly used for multi-physics calculation of microwave-assisted chemical reactions. The formula is given by:

(T / T0 )−α (C ) '

ε r (C , T ) = '

e

β ' ( C )⋅(T −T0 )

(T / T0 ) −α ( C )

ε r'T (C ) 0

(3b)

''

ε r (C , T ) = ''

eβ 4

''

( C )⋅(T −T0 )

(3a)

ε (C ) ''T0 r

Where

ε 'r (C ,T ), ε ''r (C , T )

are respectively the real and imaginary part of the relative effective

permittivity of biodiesel synthesis under any temperature, while ε r'T ''

α ( C ) ,α ( C ) '

constant temperature T0 (T0 is 44℃in this paper)..

and

0

''T ( C ) , ε r 0 (C )

'

''

β (C ) , β (C )

are under a are functions

of concentration of a reactant, which are determined by experiments. T is the temperature of the reaction solution. ''

To obtain the coefficients of α ' ( C ) , α ( C ) , β

'

(C )

and

''

β (C )

in Eq. (3), three curves of

effective permittivity at three constant temperatures need to be measured [Zhu Huacheng, 2011]. Therefore, the biodiesel synthesis were carried out under three constant temperatures at 35℃，44 ℃ and 55℃. Consequently, the distributions of relative effective permittivity of biodiesel synthesis solution with the concentration and temperature are obtained, which are shown in Fig. 2(a) and Fig.2 (b). To validate Eq. (3), the calculated and measured relative effective permittivity at 50℃ is compared in Fig.2 (c) and Fig.2 (d). The maximum errors shown in Fig.2 (c) and Fig.2 (d) were respectively 7.9% and 4.3%.

2.4 Thermodynamic parameters

The specific heat C p of the reaction solution is approximately regarded as a function of mass ratios and specific heats of reactants and products in the solution, while the thermal conductivity Kt

is related to the volume ratios and thermal conductivities. n

C p = ∑ χ i ⋅ C pi

(4)

i =1

n

Kt = ∑ γ i ⋅Kti

(5)

i =1

Where χ i (i=1,2,…n) are mass ratios, γ i (i=1,2,…n) are volume fractions, C pi (i=1,2,…n) are

5

specific heats and Kti (i=1,2,…n) are thermal conductivities. The values of specific heats and thermal conductivities of reactants and resultants in the calculations are shown in Table 1.

2.5 Multi-physics calculation

Calculation of the microwave-assisted production of biodiesel involves Maxwell’s equations, heat conduction equation and chemical reaction kinetics equation. Maxwell’s equations need to be solved to determine the electric field inside the oven cavity and reaction solution. Power absorbed at any location can be determined by the electric field distribution inside the reaction solution. The heat conduction equation is then solved using the source of microwave heating to determine the temperatures inside the reaction solution. The chemical reaction kinetics equation is solved to determine the concentrations of a reactant with temperature. At last, the effective permittivity and thermodynamic parameters are updated. Until now, one calculation is accomplished and this process will be repeated. Maxwell’s equations are given by:

JK JJK ∂ D JK ∇× H = +J ∂t JK JK ∂B ∇× E = − ∂t JK K D = ε eff ⋅ E JK

(6)

JK

JJK

Where E is the electric field intensity, H is the magnetic field intensity, D is the electric flux JK JK intensity, B is the magnetic flux intensity, J is the conduction current.

The heat conduction equation is:

6

K K K ∂T (r , t ) ρ mC p = K t ∇ 2T (r , t ) + Pd (r , t ) ∂t

(7)

Where ρ m is the medium density, C p is the specific heat of the medium, Kt is the thermal K

conductivity of the medium, Pd (r , t ) is the electromagnetic power dissipated per unit volume, which can be described as:

JK JK K 1 JK ∂ D JK ∂ E JK JK − D⋅ )+ J ⋅E Pd (r , t ) = ( E ⋅ ∂t ∂t 2

(8)

Referring to (Peng Baoxiang, etc., 2009), using the concentration of water to present those of oleic acid, methanol and biodiesel, the chemical reaction kinetics equation of biodiesel synthesis can be described as:

− Where C

0 RCOOH

0 d (CRCOOH − CH 2O )

dt 0 CH 3OH

and C

0 0 = k1 (CRCOOH − CH 2O )(CCH − CH 2O ) − k−1CH2 2O 3OH

(9)

are the initial concentrations of oleic acid and methanol respectively,

CH 2O stands for the concentration of water,

k1 indicates the forward reaction rate constant,

k−1 is

the reverse reaction rate constant, both satisfy Arrhenius equation.

E a' ) RT E '' k 1 = A1 e x p ( − a ) RT k − 1 = A− 1 exp( −

(9a) (9b)

Where the pre-exponential factor A−1 , A1 and activation energy Ea' , Ea'' are given in Table 2. R is universal gas constant. In these calculations, Maxwell’s equations, heat conduction equation and chemical reaction kinetics equation are inter-coupling. Fig.3 is the calculation flow chart by updating the effective permittivity with Eq. (3).

3. Results and discussion

The two methods to update the effective permittivity are applied into multi-physics

7

calculation of biodiesel synthesis. The temperature distributions and risings calculated by the new method will be compared with those by the conventional method and the experiment results below.

3.1 Comparison of calculation by two methods

The two ways to update the effective permittivity mentioned in Section 2.2 can obtain different values of effective permittivity during the calculation process, which will lead to different temperature distributions of the reaction solution. Fig.4 (a) is the top view of temperature distribution of biodiesel synthesis solution after 18 seconds heating, whose effective permittivity is updated by the traditional method. It is obviously different from that shown in Fig.4 (b), whose effective permittivity is updated by the new method. In Fig.4 (a), the hot spot (60.939℃) locates in the south while the hot spot (51.98℃) in Fig.4 (b) is on the opposite side. The temperature difference between these two hot spots is up to 9℃ when the reaction is just carried out for 18 seconds. Fig.4 (c) and Fig.4 (d) are the global temperature distributions obtained by the conventional and new method respectively. We can also see that there still exists large distinction in temperature between these two pictures. Though the input powers in the two calculations are the same, since the effective permittivities are different, the dissipation powers absorbed by the reaction solutions vary from each other, the temperature distributions absolutely differ. From the comparison above, we can see that the value of effective permittivity plays a vital role in the interaction between microwave and chemical reactions. Therefore, it is significantly important to find an effective way to describe the effective permittivity of biodiesel reaction solution.

3.2 Comparison of calculation and experiment results

8

The experiment is carried out in a customization microwave oven which has three cut-off waveguides on its top surface. An InfraTech VarioCAM infrared camera is used to catch the temperature distributions of the top surface of the reaction solution real-timely through a cut-off waveguide. Optical fiber temperature probes are inserted into the reaction solution through another cut-off waveguides to measure the temperature risings of two certain points. Temperature risings of two points are measured and compared during the 18 seconds heating process below. Fig. 5 shows the temperature risings of different points during the heating process of the two calculations and experiment. Both the figures reveal obviously that the temperature risings obtained by new method are closer to the measurement results. The biggest temperature difference between fraction and measured reaches 9℃(shown in Fig.5 (b)). The more rapidly the temperature climb, the more distinction exists between the results of measured and fraction. Fig.6 (a) is the top view of temperature distribution of experiment when the reaction has been heated for 3 seconds. Fig.6 (b) is the calculation results by the new method. The calculated temperature distribution shows a good agreement with the measured one, though there is tiny difference between them. It is obviously that the hot spots in Fig.6 (a) and Fig.6 (b) locate at the similar position. Besides, the maximum temperature in these two pictures vary from each other marginally, with 24.39℃ in Fig.6 (b) and 23.12℃ in Fig.6 (a), though Fig.6 (a) has higher temperature in the right side and the bottom of the picture. The possible reasons caused these differences are as follows: (1) the calculation didn’t consider the natural convection which will affect the temperature distribution, (2) the parameters, especially the thermodynamic parameters in the calculation were idealized and simplified，while the experiment environment was affected by external conditions.

9

Fig.6 (c) and Fig.6 (d) are the corresponding top view of temperature distributions after 18 seconds heating. The locations of the hot spots in Fig.6 (c) and Fig.6 (d) still stand at the same positions, and the temperature distributions are quite similar. In summary, different ways can get significantly different results of temperature distribution. The thermal analysis based on the new method is more accurate to describe the temperature distributions of biodiesel synthesis solution.

4. Conclusion

Microwave-assisted production of biodiesel by esterification has been reported as a high efficient and energy saving method. Thermal analysis based on multi-physics calculation is preliminary and necessary to industrialize microwave-assisted biodiesel production. The comparisons indicates that the results obtained by the new method show good agreement with the experimental results. Therefore, the new method is effective to deal with the thermal analysis during the microwave-assisted production of biodiesel. The thermal analysis based on the new method will be helpful to prevent hot spot and thermal runaway and instruct the industrial design of biodiesel production.

Acknowledgement This project was supported by the National Science Foundation of China (No. 61001019) and the CAS Key Laboratory of High Power Microwave Sources and Technologies, Institute of Electronics, Chinese Academy of Sciences

References

Aharon Geganken, 2010. Bio-diesel production directly from the microalgae biomass of Nannochloropsis by microwave and ultrasound radiation. Bioresource Technology J. 102. 4265-4269.

10

Karuppan Muthukumar, 2007, An overview of enzymatic production of biodiesel. Bioresource Technology J. 99. 3975-3981.

Miri Koberg, Moshe Cohen , Ami Ben-Amotz, Aharon Gedanken, 2011,Bio-diesel production directly from the microalgae biomass of Nannochloropsis by microwave and ultrasound radiation, bioresource technology, Vol 102,4265-4269

Miura, M., Kaga, H., Sakurai, A., Kakuchi, T., Takahashi, K., 2004. Rapid pyrolysis of wood block by microwave heating. J. Anal. Appl. Pyrolysis 71, 187–199.

Nicholas E. Leadbeater, Lauren M. Stencel, 2006, Fast, Easy Preparation of Biodiesel Using Microwave Heating, Energy & fuels, Vol 20, 2281-2283

Omar, R., Idris, A., Yunus, R., Khalid, K., Isma, M.I.A., 2011. Characterization of empty fruit bunch for microwave-assisted pyrolysis. Fuel 90, 1536–1544.

Peng Baoxiang, Shu Qing, Wang Guangrun, Wang Jinfu, 2009. Kinetics of Esterification for Acid2Catalyzed Preparation of Biodiesel, Chemical Reaction Engineering and Technology, Vol 25, No 3, 250-255.

Ruan, R., Du, Z.Y., Li, Y.C., Wang, X.Q., Wan, Y.Q., Chen, Q., Wang, C.G., Lin, X.Y., Liu, Y.H., Chen, P., 2011. Microwave-assisted pyrolysis of microalgae for biofuel production. Bioresour. Technol. 102, 4890–4896.

Ruan, R., Yu, F., Deng, S.B., Chen, P., Liu, Y.H., Wan, Y.Q., Olson, A., Kittelson, D., 2007. Physical and chemical properties of bio-oils from microwave pyrolysis of corn stover. Appl. Biochem. Biotechnol. 137, 957–970.

Satoshi Horikoshi, Atsushi Osawa, Masahiko Abe, Nick Serpone, 2011, On the Generation of Hot-Spots by Microwave Electric and MagneticFields and Their Impact on a Microwave-Assisted Heterogeneous Reaction in the Presence of Metallic Pd Nanoparticles on an Activated Carbon Support. JOURNAL OF PHYSICAL CHEMISTRY C. Vol46. 23030-23035.

T. Santos a, M.A. Valente, J. Monteiro , J. Sousa , L.C. Costa a,2011. Electromagnetic and thermal history during microwave heating, Applied Thermal Engineering,Vol.31,Issue.16,3255–3261.

11

Takashi Nakamura, 2005. Effective Permittivity of Amorphous Mixed Materials, Electronics and Communications in Japan, Part 1, Vol. 88, No. 10.

Xuebin Lu, Bo Xi, Yimin Zhang, Irini Angelidaki, 2011, Microwave pretreatment of rape straw for bioethanol production: Focus on energy efficiency, biosource technology, Vol 102, No. 17, 7937-7940.

Zhu Huacheng, 2012，The effective permittivity of the reacting mixture solution for multiphysics calculation, journal of solution chemistry. Vol41. 1729-1737.

12

Figure Captions Table1 Values of C p and Kt of reactants and resultants in the reaction Table 2 Constants in Eq. (8) and (9) Fig.1 The calculation model Fig.2 Relative effective permittivity of biodiesel reaction solution: (a) Imaginary part, (b) Real part, (c) Comparison of the imaginary part, (d) Comparison of the real part. Fig.3 The calculation flow chart Fig.4 The comparison of temperature distributions calculated by two methods: (a) Traditional method (top view), (b) New method (top view), (c) Traditional method, (d) New method Fig.5 Comparison of temperature risings by two methods and experiment at different points: (a) At point (0.014, 0,-0.07), (b) At point (0,0.036,-0.037). Fig.6 Comparison of top views of temperature distributions measured by experiment and calculated by the new method

13

Tables and Figures Table1. Values of C p and Kt of reactants and resultants in the reaction

Substances

Value

Oleic acid

Methanol

Biodiesel

Water

Cp

Kt

Cp

Kt

Cp

Kt

Cp

Kt

2.05

0.11

2.51

21.35

6.75

0.12

4.18

0.63

The unit of C p is kJ/(kg.K), Kt is W/m.K.

14

Table 2. Constants in Eq. (8) and (9)

Forward reaction Constant

0 CRCOOH

0 CCH 3OH

Value

12.36mol/L

1.56mol/L

Reverse reaction

A1

Ea''

A−1

Ea'

743.6

33.8kJ/mol

0.606

13.9kJ/mol

15

Fig.1 The calculation model

16

(a)

(b)

(c)

(d)

Fig.2 Relative effective permittivity of biodiesel reaction solution: (a) Imaginary part, (b) Real part, (c) Comparison between calculated and measured imaginary part results, (d) Comparison between calculated and measured real part results.

17

Initial Settings

Calculate E&H Fields

Calculate the Dissipation Power

Calculate the Temperature Distribution

Calculate the Chemical Reaction Rate Constant k and k −1

Update the Concentration

1

C H 2O

Update the Effective Permittivity ε eff (C , T ), Specific Heat Thermal Conductivity K t

Fig.3 The calculation flow chart

18

C p and

(a)

(b)

(c)

(d)

Fig.4 The comparison of temperature distributions calculated by two methods: (a) Traditional method (top view), (b) New method (top view), (c) Traditional method, (d) New method

19

(a)

(b)

Fig.5 Comparison of temperature risings by two methods and experiment at different points: (a) At point (0.014, 0,-0.07), (b) At point (0, 0.036, -0.037).

20

(a)

(c)

(b)

(d)

Fig.6 Comparison of top views of temperature distributions measured by experiment and calculated by the new method: (a) experiment after 3 seconds heating, (b) New method after 3 seconds heating, (c) Experiment after 18 seconds heating, (d) New method after 18 seconds heating.

21

Black and white figures for print

Fig.1 The calculation model

22

(a)

(b)

(c)

(d)

Fig.2 Relative effective permittivity of biodiesel reaction solution: (a) Imaginary part, (b) Real part, (c) Comparison between calculated and measured imaginary part results, (d) Comparison between calculated and measured real part results.

23

Initial Settings

Calculate E&H Fields

Calculate the Dissipation Power

Calculate the Temperature Distribution

Calculate the Chemical Reaction Rate Constant k and k −1

Update the Concentration

1

C H 2O

Update the Effective Permittivity ε eff (C , T ), Specific Heat Thermal Conductivity K t

Fig.3 The calculation flow chart

24

C p and

(a)

(b)

(c)

(d)

Fig.4 The comparison of temperature distributions calculated by two methods: (a) Traditional method (top view), (b) New method (top view), (c) Traditional method, (d) New method

25

(b)

(b)

Fig.5 Comparison of temperature risings by two methods and experiment at different points: (a) At point (0.014, 0,-0.07), (b)At point (0,0.036,-0.037).

26

(a)

(c)

(b)

(d)

Fig.6 Comparison of top views of temperature distributions measured by experiment and calculated by the new method: (a) experiment after 3 seconds heating, (b) New method after 3 seconds heating, (c) Experiment after 18 seconds heating, (d) New method after 18 seconds heating.

27

(1) Bivariate function was originally applied to describe the effective permittivity (2) Thermal analysis based on two methods were finished by multiphysics calculation (3) Great differences of temperature between the new and the traditional method (4)

Thermal analysis based on the new method is more close to the experiment results

28