Energy & Fuels 2008, 22, 675–678
675
Application of Weibull 2-Mixture Model To Describe Biomass Pyrolysis Kinetics Junmeng Cai* and Ronghou Liu* Biomass Energy Engineering Research Center, School of Agriculture and Biology, Shanghai Jiao Tong UniVersity, 800 Dongchuan Road, Shanghai 200240, People’s Republic of China ReceiVed August 28, 2007. ReVised Manuscript ReceiVed October 8, 2007
In the present paper, a new method proposed allows for fitting an overall thermogravimetric analysis (TGA) curve of biomass pyrolysis by means of the modified survival function of a two-mixed Weibull distribution. Four types of biomass (wheat straw, corn stalk, cotton stalk, and sorghum stalk) have been analyzed. It has been found that the Weibull 2-mixture model can reproduce accurately the TGA curve. Accordingly, the TGA curve can be understood as a sum of two parallel reactions, where each single reaction is represented by one Weibull mixture model component. The separation into single functions provides an approach to separate two parallel reactions of two pseudo-fractions involved in the process of biomass pyrolysis. Additionally, making use of the analytical curves of the fitting, the Arrhenius 2-mixture model has been applied to the same raw TGA curves.
1. Introduction The depletion of the natural reserves of gas and oil, forecast in the first quarter of the 21st century, has attracted great interest to the use of plant raw material, the most important of which is biomass.1 Biomass pyrolysis is important in the context of thermochemical conversion processes aimed at the production of chemicals, fuel liquids, and gases. It is also relevant in the production of charcoal, used as domestic fuel or as a reducing agent in metallurgy, and in the production of activated carbon.2–6 Biomass pyrolysis can be used as an independent process for the production of useful fuels and/or chemicals. It also occurs as the first step in a gasification or combustion process of biomass. The pyrolysis process has a great future in the world.7 The study of the kinetic behavior of the pyrolysis process is fundamental to the understanding of the pyrolysis mechanism and the optimization of engineering practice.8 There are many reactions involved in the process of biomass pyrolysis,9 which can not be described in detail. Usually, the two-independent-reaction model has been used for the kinetic description of biomass pyrolysis kinetics,10 which is based on the assumption that biomass is composed by two different * To whom correspondence should be addressed. E-mail:
[email protected] (J.C.);
[email protected] (R.L.). (1) Cai, J.; Liu, R.; Deng, C. Renewable Sustainable Energy ReV. 2007, doi: 10.1016/j.rser.2007.04.003. (2) Carrott, S. P. J. M.; Carrott, M. M. L. R. Bioresour. Technol. 2007, 98, 2301–2312. (3) Suzuki, R. M.; Andrade, A. D.; Sousa, J. C.; Rollemberg, M. C. Bioresour. Technol. 2007, 98, 1985–1991. (4) Skodras, G.; Diamantopoulou, I.; Zabaniotou, A. Fuel Process. Technol. 2007, doi: 10.1016/j.fuproc.2007.03.008. (5) Zanzi, R.; Sjöström, K.; Björnbom, E. Biomass Bioenergy 2002, 23, 357–366. (6) Hillring, B. Biomass Bioenergy 2006, 30, 815–825. (7) McKendry, P. Bioresour. Technol. 2002, 83, 47–54. (8) Conesa, J. A.; Caballero, J. A.; Marcilla, A.; Font, R. Thermochim. Acta 1995, 254, 175–192. (9) Luo, Z.; Wang, S.; Liao, Y.; Zhou, J.; Gu, Y.; Cen, K. Biomass Bioenergy 2004, 26, 455–462. (10) He, F.; Yi, W.; Sun, R.; Jia, J.; Bai, X.; Li, Y. Trans. CSAE 2002, 18 (4), 10–13 (in Chinese with an English Abstract).
pseudo-fractions. However, the separation problem of the parallel reactions of two pseudo-fractions remains unsolved. Concerned about overcoming the separation problem, this paper aims to apply a Weibull 2-mixture model for fitting the nonisothermal thermogravimetric analysis (TGA) curves of biomass pyrolysis. 2. Experimental Section Four types of biomass are analyzed in this paper: wheat straw, corn stalk, cotton stalk, sorghum stalk. As-received biomass samples are dried at 398 K for 24 h to remove free moisture absorbed during land dumping and then kept in a desiccator for further testing. The predried samples are crushed and sieved to 0.1–0.2 mm. TGA is the most common technique used for kinetic studies of slow pyrolysis of biomass. The slow pyrolysis of the samples has been carried out using a thermogravimetric analyzer (NETZSCH STA 449). These experiments are conducted with small samples at a low heating rate to minimize heat-transfer effects. A brief summary of the experimental setup is as follows: a 5 mg sample is weighted and spread evenly in a sample cup; the cup is then placed on the balance sample holder; the startup protocol is initiated; and finally, the sample is heated at a constant heating rate (10 K min-1) to 1100 K using purified nitrogen as the carrier gas at a constant flow rate of 25 mL min-1. The sample weight is measured continuously by a microbalance as a function of time or temperature. The description of the experimental setup was provided in detail by Cai.11
3. Mixture Models 3.1. Weibull 2-Mixture Model. To fit a dynamic TGA curve, many methods have been presented. Naya et al.12 proposed the logistic polynomial regression model for estimation of a TGA curve in some simple degradation processes of polymers, such (11) Cai, J. Research on Various Issues of Kinetics and Thermodynamics of Biomass Pyrolysis and Combustion (in Chinese with an English Abstract). Ph.D. Dissertation, University of Shanghai for Science and Technology, Shanghai, China, 2006. (12) Naya, S.; Cao, R.; Artiaga, R. Thermochim. Acta 2003, 406, 177– 183.
10.1021/ef700514t CCC: $40.75 2008 American Chemical Society Published on Web 11/16/2007
676 Energy & Fuels, Vol. 22, No. 1, 2008
Cai and Liu
Figure 1. Overlay of experimental data, Weibull 2-mixture model prediction, and its single components in the case of wheat straw.
Figure 3. Overlay of experimental data, Weibull 2-mixture model prediction, and its single components in the case of cotton stalk.
Figure 2. Overlay of experimental data, Weibull 2-mixture model prediction, and its single components in the case of corn stalk.
Figure 4. Overlay of experimental data, Weibull 2-mixture model prediction, and its single components in the case of sorghum stalk.
as a single step in a thermal degradation of polyvinyl chloride (PVC). Cao et al.,13 Barbadillo et al.,14 and Naya et al.15 proposed a method to evaluate the fitting of TGA curves by the logistic mixture model. Adma{evic´ et al.16 presented the possibility of applying the normalized Weibull distribution function for modeling the kinetics of nonisothermal dehydration of equilibrium swollen poly-hydrogel. Cai and Liu17 developed a new method to optimize the fitting of the kinetic conversion data by one or the linear combination of a few Weibull distribution functions. In this study, it is assumed that a TGA curve of biomass pyrolysis may be fitted by the survival function of a two-mixed Weibull distribution. The Weibull distribution originally derived by Weibull18 is a probability density function, which was first applied to study fatigue of materials. The two-mixed Weibull distribution is a probability mixture of two Weibull distributions, which differ in scale and/or shape.19 To reproduce the asymptotic value at the end of TGA curves of biomass pyrolysis, a constant was added
Table 1. Weibull 2-Mixture Model Parameters Obtained for Slow Pyrolysis of Four Biomass Samples with Corresponding Values of R2
[ ( )]
y(T) ) w1exp -
T - T0 η1
β1
[ ( )]
+ w2exp -
T - T0 η1
β2
+ w3 (1)
with 0 < w1 < 1, 0 < w2 < 1, 0 < w3 < 1, η1 > 0, η2 > 0, β1 > 0, β2 > 0, and T g T0. In the above equation, y(T) is the mass fraction at a certain temperature (T) simulated by the Weibull 2-mixture model, T0 is the initial temperature of biomass pyrolysis, w1 and w2 stand for the weight of the first and second (13) Cao, R.; Naya, S.; Artiaga, R.; García, A.; Varela, A. Polym. Degrad. Stab. 2004, 85, 667–674. (14) Barbadillo, F.; Fuentes, A.; Naya, S.; Cao, R.; Mier, J. L.; Artiaga, R. J. Therm. Anal. Calorim. 2007, 87, 223–227. (15) Naya, S.; Cao, R.; Ullibarri, I. L.; Artiaga, R.; Barbadillo, F.; García, A. J. Chemom. 2006, 20, 158–163. (16) Adma{evic´, B.; Jankovic´, B.; Kolar-Anic´, L.; Minic´, D. Chem. Eng. J. 2007, 130, 11–17.
sample
η1 (K)
β1
w1
η2 (K)
β2
w2
R2
wheat straw corn stalk cotton stalk sorghum stalk
306.057 282.601 304.267 305.365
2.291 1.881 2.345 1.950
0.183 0.255 0.184 0.182
196.978 210.873 201.676 201.785
7.586 6.754 6.522 5.957
0.490 0.424 0.528 0.533
0.999 863 0.999 813 0.999 742 0.999 700
component of the Weibull 2-mixture model, w3 is the mass fraction of solid residues, β1 and β2 are the shape parameters of the Weibull distributions, and η1 and η2 are the scale parameters of the Weibull distributions. According to dimensional analyses, β1 and β2 are dimensionless and η1 and η2 are expressed in K. When T ) T0, the y(T) function has to tend to 1. Therefore, the following expression can be obtained: w1 + w2 + w3 ) 1
(2)
For fitting the TGA data to a two-mixed Weibull model, some estimation of the parameters in eq 1 is needed. For this purpose, either general purposed mathematical software or a computer program developed in any programming language is used. In this study, the DataFit software, a statistical software that is developed by Oakdale Engineering, has been used for performing the evaluation of the parameters. For more details of the DataFit software, readers are referred to visit http://www. oakdaleengr.com/index.html. 3.2. Arrhenius Mixture Model. Although many kinetic models exist, one of the most commonly used is the nth-order (17) Cai, J.; Liu, R. J. Phys. Chem. 2007, 111, 10681–10686. (18) Weibull, W. J. Appl. Mech. 1951, 18, 293–296. (19) Blischke, W. R.; Murthy, D. N. P. Case Studies in Reliability and Maintenance; John Wiley and Sons, Inc.: New York, 2003.
Application of Weibull 2-Mixture Model
Energy & Fuels, Vol. 22, No. 1, 2008 677
Figure 5. Overlay of experimental data and Arrhenius mixture model prediction for (a) wheat straw, (b) corn stalk, (c) cotton stalk, and (d) sorghum stalk (9, experimental data; —, Arrhenius mixture model prediction).
reaction model. A mixture of two nth-order reaction functions is modeled, assuming that two parallel reactions takes place A1 d(wA/w1) ) - e-E1⁄ RT(wA/w1)n1 dT b
(3)
A2 d(wB/w2) ) - e-E2 ⁄ RT(wB/w2)n2 dT b
(4)
where A1 and A2 are the frequency factors, E1 and E2 are the activation energies, n1 and n2 are the reaction orders, b is the heating rate, and R is the ideal gas constant. The initial condition should be taken as follows: wA ) w1
(T ) T0)
(5)
wB ) w2
(T ) T0)
(6)
The estimation of the parameters in eqs 3 and 4 has been performed by means of a nonlinear regression method.20 4. Results and Discussion The Weibull mixture model proposed in this paper has been successfully applied to all samples analyzed in this paper. The overlays of experimental data, Weibull 2-mixture model prediction, and its single components for wheat straw, corn stalk, cotton stalk, and sorghum stalk are shown in Figures 1-4, respectively. Values of the Weibull 2-mixture model parameters obtained for slow pyrolysis of four biomass samples with corresponding values of R2 are listed in Table 1. It is evident from Figures 1-4 and Table 1 that the fittings are perfect (for all four cases, values of R2 are higher than 0.9997). The separation into two single component functions by the Weibull 2-mixture model provides an approach to separate two parallel reactions involved in the process of biomass pyrolysis. One of the parallel reactions corresponds to the decomposition (20) Opfermann, J. J. Therm. Anal. Calorim. 2000, 60, 641–658.
Table 2. Arrhenius Mixture Model Parameters Obtained for Slow Pyrolysis of Four Biomass Samples with Corresponding Values of R2 sample wheat straw corn stalk cotton stalk sorghum stalk
E1 A1 (min–1) (kJ mol–1) 1.016 2.949 14.581 4.227
27.043 19.441 28.831 22.512
n1
A2 (min–1)
E2 (kJ mol–1)
n2
1.281 1.273 1.317 1.331
6.077 × 109 7.635 × 107 1.639 × 108 2.745 × 107
116.596 95.633 100.525 91.706
1.143 1.145 1.166 1.182
of the first pseudo-fraction of biomass; the other corresponds to the decomposition of the other pseudo-fraction of biomass. Figure 5 shows the fittings of the TG curves by the Arrhenius mixture model for four samples. Table 2 lists the parameter values obtained with the Arrhenius mixture model. From Figure 5, it can be observed that the Arrhenius mixture models fit the experimental data very well, which indicates those Weibull mixture model components can be characterized by nth-order reaction models. Because the raw data contain some noise that affect further analysis, traditional kinetic models are easier to apply on the estimated data obtained by the newly proposed method than on the raw TGA data of biomass pyrolysis. 5. Conclusions The method proposed allows for fitting an overall TGA curve of biomass pyrolysis by means of a Weibull 2-mixture model. The TGA curves of four types of biomass have been analyzed in this paper. It can be found that the obtained TGA curves calculated by the model are in agreement with the experimental TGA curves. Therefore, the TGA curve of biomass pyrolysis can be understood as a combination of two parallel reactions, where each single reaction is represented by one model component. One of two parallel reactions corresponds to the decomposition of the first pseudo-fraction of biomass, and the other corresponds to the decomposition of the other pseudo-
678 Energy & Fuels, Vol. 22, No. 1, 2008
fraction of biomass. Additionally, a mixture of two nth-order reaction equations (Arrhenius 2-mixture model) has been applied to the same TGA curves, and the corresponding kinetic parameters have been determined. The results have shown that those Arrhenius mixture models predict all TGA curves analyzed in this paper very well.
Cai and Liu Acknowledgment. The authors thank the referees for their constructive suggestions. This research was supported by the National Natural Science Foundation of China through the Grant 50776059. EF700514T
