- Email: [email protected]
Application of the distributed activation energy model to the kinetic study of pyrolysis of the fresh water algae Chlorococcum humicola
Bioresource Technology 107 (2012) 476–481
Contents lists available at SciVerse ScienceDirect
Bioresource Technology journal homepage: www.elsevier.com/locate/biortech
Application of the distributed activation energy model to the kinetic study of pyrolysis of the fresh water algae Chlorococcum humicola Kawnish Kirtania, Sankar Bhattacharya ⇑ Department of Chemical Engineering, Monash University, Clayton, VIC 3800, Australia
a r t i c l e
i n f o
Article history: Received 9 September 2011 Received in revised form 12 December 2011 Accepted 16 December 2011 Available online 24 December 2011 Keywords: Fresh water algae Chlorococcum humicola Pyrolysis Kinetics DAEM
a b s t r a c t Apart from capturing carbon dioxide, fresh water algae can be used to produce biofuel. To assess the energy potential of Chlorococcum humicola, the alga’s pyrolytic behavior was studied at heating rates of 5–20 K/min in a thermobalance. To model the weight loss characteristics, an algorithm was developed based on the distributed activation energy model and applied to experimental data to extract the kinetics of the decomposition process. When the kinetic parameters estimated by this method were applied to another set of experimental data which were not used to estimate the parameters, the model was capable of predicting the pyrolysis behavior, in the new set of data with a R2 value of 0.999479. The slow weight loss, that took place at the end of the pyrolysis process, was also accounted for by the proposed algorithm which is capable of predicting the pyrolysis kinetics of C. humicola at different heating rates. Crown Copyright Ó 2011 Published by Elsevier Ltd. All rights reserved.
1. Introduction Since some algae have a high oil content, they can be used to produce biodiesel (Demirbas, 2011); however, the separation of lipids from the algae is difficult and energy intensive (Pimentel, 2008). Instead of oil extraction, algae can be gasified to produce oil and gas (Tang et al., 2011; Bruhn et al., 2011). Pyrolysis is the first step in the combustion or gasification process. The pyrolytic behavior and kinetics of three kinds of red algae were investigated by Li et al. (2011), and it became evident that their pyrolysis behavior was more complicated than that of fossil fuels. The authors estimated the activation energy for those three algae by the Flynn–Wall–Ozawa (FWO) (Flynn and Wall, 1966; Ozawa, 1965), KAS (Kissinger, 1957) and Popescu (Popescu, 1996) methods. Brown algae pyrolysis at different conditions was investigated by Ross et al. (2009) and Anastasakis et al. (2011). For extracting kinetic parameters, Anastasakis et al. (2011) used the methods of Weber (2008) and Saddawi et al. (2010). Pyrolysis characteristics of blue–green algae with coal were studied by Yuan et al. (2011) without any kinetic parameter estimation. Due to the availability of high performance computing, the distributed activated energy model (DAEM) is widely used for different kinds of solid and liquid fuels. Miura and Maki (1998) and Scott et al. (2006) modified the DAEM so that no assumptions for the form of the activation energy distribution are required. Navarro et al. (2008), Sonobe and Worasuwannarak (2008) and ⇑ Corresponding author. Tel.: +61 3 9905 9623; fax: +61 3 99055686. E-mail address: [email protected] (S. Bhattacharya).
Wjtowicz et al. (2003) applied the DAEM to biomass pyrolysis successfully. Logistic distribution of activation energy was assumed and validated for cellulose pyrolysis by Cai et al. (2011) with nth order DAEM; however, the complex pyrolysis behavior of fresh water algae has not yet been modeled with the distributed activation energy model. For the present study, the blue–green algae, Chlorococcum humicola, was selected for pyrolytic and kinetic examination because it produces a high amount of biomass and lipids (Chaichalerm et al., 2011). Thermogravimetric experiments were performed at different heating rates to understand the pyrolytic behavior of the algae. Thereafter, a new algorithm for determining the kinetic parameters of DAEM was developed and the new algorithm for DAEM was validated with experimental data. 2. Methods 2.1. Pyrolysis experiments C. humicola biomass was grown in the Bio Engineering Laboratory, Department of Chemical Engineering, Monash University as described by Harun and Danquah (2011). The strain was cultured in 100-L bag photobioreactors outdoors and kept under semi-continuous conditions by 20% (v/v) dilution with fresh medium after harvesting an equal volume of culture on a daily basis. The medium consists of potassium nitrate, KNO3 (150 g/L, MW 101.11, 99.5%), sodium phosphate monobasic, NaH2PO4 (11.3 g/L, MW 119.98, 99.5%), manganese chloride, MnCl2 (360.0 mg/L, MW 125.84, 98.0%), zinc sulfate, ZnSO4 (44.0 mg/L, MW 161.47, 99.5%), cobalt nitrate, Co(NO3)2 (22.0 mg/L, MW 182.94, 97.5%), copper
0960-8524/$ - see front matter Crown Copyright Ó 2011 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.biortech.2011.12.094
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K. Kirtania, S. Bhattacharya / Bioresource Technology 107 (2012) 476–481
sulfate, CuSO4 (19.6 mg/L, MW 159.61, 98.5%), sodium molybdite, Na2MoO42H2O (12.6 mg/L, MW 241.95, 98.0%), sodium metasilicate, Na2SiO3 (22.7 g/L, MW 122.06, 99.7%), iron(III) citrate, C6H5O7Fe3H2O (9.0 g/L, MW 298.99, 98%), and citric acid monohydrate, COOHCH2C(OH)COOHCH2COOHH2O (9.0 g/L, MW 210.14, 99.5%). The ultimate analysis was performed with a CHNS/O analyzer (Model 2400, Perkin-Elmer, USA). To determine carbon, hydrogen, nitrogen and sulfur, the samples were combusted at 975 °C to obtain CO2, H2O, N2 and SO2 and analyzed through a chromatographic column. The system detects the gases by thermal conductivity and directly gives the concentration of C, H, N, S in percent by comparing with the standard values. Ash content was determined by combusting the alga sample at 800 °C. As the concentration of other materials are in ppm range, the oxygen concentration was calculated by difference. The pyrolysis behavior was studied in a thermobalance (Model STA 449 F3 JupiterÒ, NETZSCH-Gerätebau GmbH, Germany). The alga was dried in an oven for at least 12 h at 105 °C, ground to a size of 106–150 lm using a hand mortar. The pyrolysis was done in nonisothermal condition and the temperature was ramped to 1100 °C at heating of 5, 10, and 20 K/min with one repeat for estimating the kinetic parameters and model validation. 2.2. Kinetic modeling A Gaussian distribution based distributed activation energy model (DAEM) was developed to analyze the pyrolysis kinetics and the ‘end loss’ of the algae. Usually the distributed activation energy model has a general form for several parallel first order reactions:
Z
w ¼ w
Z t Z E exp k0 eRT dt f ðEÞdE where
1 0
0
1
f ðEÞdE ¼ 1
ð1Þ
0
where w is the weight of volatile content remaining and w⁄ is the total volatile content. k0 is the pre-exponential factor and f(E)dE is the distribution that characterizes the activation energy. To model the slow weight loss that happens after the rapid loss in case of the microalgae, the nth order model is selected over the exponential model stated above. The nth order model with distributed activation energy can be expressed as follows:
w ¼ w
1
Z
1 þ ð1 nÞ
Z
0
t
0
1 ð1n Þ E dt k0 exp f ðEÞdE where n – 1 RT
ð2Þ As the distribution is assumed to be Gaussian for this model, it can be expressed as: w ¼ w
1
Z
1 þ ð1 nÞ
Z
0
t
0
( !) 1 ð1n Þ E 1 ðE mEÞ2 pffiffiffiffiffiffiffiffiffiffiffiffi exp dE dt k0 exp 2 RT 2r 2pr2
ð3Þ where mE is the mean activation energy and r is the standard deviation of distribution. In this case it is assumed that the distribution remains the same for the whole pyrolysis process. To develop the algorithm, the equation has been represented by multiplication of two functions:
w ¼ w
Z
1
ZðE; tÞf ðEÞdE
ð4Þ
0
where Z(E,t) contains the pre-exponential factor, k0 and the order n. The Z(E,t) varies with the time and activation energy. If the heating rate is a K/min, the Z(E,T) can be equated to: ZðE; TÞ ¼
1 þ ð1 nÞ
Z
T 0
1 ð1n Þ k0 E dT exp RT a
where T ¼ T 0 þ at
ð5Þ
This limit for the integration is valid as the value of T0 can be selected low enough where no reaction occurs (Miura, 1995). To simplify the calculation, the exponential integral in Z(E,T) is evaluated by asymptotic approximation when E/R ? 1 (Burnham and Braun, 1999):
( ZðE; TÞ ¼
"
1 Þ #)ð1n k0 RT 2 E 1 þ ð1 nÞ exp RT aE
ð6Þ
This asymptotic approximation provides similar results to the actual one. Now, assuming k0 is independent of temperature, Z(E,T) can be written as:
1 RT 2 E ZðE; TÞ ¼ f1 þ ð1 nÞk0 nðE; TÞgð1nÞ where nðE;TÞ ¼ exp RT aE ð7Þ As n(E,T) is defined now, it is important to understand that the temperature integral is evaluated at each value of decomposition. So for each value of activation energy, the n(Ei,T) can be evaluated to form a matrix. This matrix is formulated as:
2
nðE1 ; T 1 Þ nðE2 ; T 1 Þ nðEL ; T F Þ
3
7 6 6 nðE1 ; T 2 Þ nðE2 ; T 2 Þ nðEL ; T F Þ 7 7 6 6 n ¼ 6 nðE1 ; T 3 Þ nðE2 ; T 3 Þ nðEL ; T F Þ 7 7 7 6 5 4 nðE1 ; T F Þ
ð8Þ
nðE2 ; T F Þ nðEL ; T F Þ
This matrix implies that Eq. (2) can be expressed in an equivalent matrix which is possible to evaluate using any mathematical package. So the integrated matrix form of the mass loss equation becomes: 1 Þ2 3 3 8 39ð1n 2 wðT 1 Þ > nðE1 ;T 1 Þ nðE2 ;T 1 Þ nðEL ;T F Þ > f ðE1 Þ > > > > > 7 7 > 7 6 6 6 > > 6f ðE2 Þ7 6wðT 2 Þ7 > 6nðE1 ;T 2 Þ nðE2 ;T 2 Þ nðEL ;T F Þ7> 7 7 < 7= 6 6 16 6f ðE3 Þ7 6wðT 3 Þ7 ¼ 1þð1nÞk0 6nðE1 ;T 3 Þ nðE2 ;T 3 Þ nðEL ;T F Þ7 7 7 > 7> 6 6 w 6 7 7 > 7> 6 6 6 > > 5> 5 > 4 5 4 4 > > > > : ; wðT F Þ nðE1 ;T F Þ nðE2 ;T F Þ nðEL ;T F Þ f ðEL Þ
2
1 w ¼ f1 þ ð1 nÞk0 ngð1nÞ f w
ð9Þ
ð10Þ
Here, T1 and TF represent the values of minimum temperature and maximum temperature, respectively in an experiment. Though only k0 and n can be seen from Eq. (10), mE and r are the other two parameters implicit in activation energy distribution vector, f. Now from Eq. (10), it is possible to form an objective function which can be optimized to estimate those four parameters. The objective function is defined by the difference between the experimental and the model predicted data:
O:F: ¼
j¼F X wj ðexpÞ j¼1
w
2 wj ðestÞ w
ð11Þ
The wj(exp) and wj(est) denotes the experimental and estimated weight, respectively and i denotes the corresponding temperature. To minimize the objective function, the algorithm checks every possible values of mass fraction within the given activation energy and temperature range. As there are four unknown parameters to be evaluated, a new minimization algorithm has been used. The algorithm is known as Multistart. Unlike other algorithms such as direct search, pattern search or genetic algorithm, it tries multiple starting points for global optimization. The Global Optimization Toolbox of Matlab with parallel computing facility was used to accelerate computing speed. The curve fitting method for the Multistart object was selected to be lsqcurvefit based on the least square method. The code was generated in Matlab and a customized number of starting points for parameter estimation was used. Since activation energies for algae were reported in the literature as 60 kJ/mol and 322 kJ/mol (Li et al., 2011; Tang et al., 2011). The expected range of activation energy was selected from 10 kJ/mol to 500 kJ/mol) to form the matrix n and the energy distribution vector f. The temperature range was selected as required for
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Table 1 Ultimate analysis of the fresh water alga, C. humicola (%db). C
H
N
S
O
Ash
33.16%
5.58%
4.8%
2.42%
27.24%
26.8%
completion of pyrolysis. By defining the ranges of activation energy and temperature, the two most important vectors were defined for the model. To avoid multiplicity of estimated parameters (Lakshmanan et al., 1991) decomposition data at two different heating rates,
5 and 10 K/min were analyzed and used to generate parameters for the model. The model parameters estimated from the algorithm were used to generate a weight loss curve which is compared with the experimental one by the fitness parameter. The fit between the experimental and estimated data can be found out by the fitness parameter stated below:
Pj¼F wjðexpÞ R2 ¼ 1
j¼1
w
wjðestÞ 2 w
Pj¼F wjðexpÞ 2 j¼1
w
Fig. 1. Pyrolysis behavior of C. humicola at different heating rates.
Fig. 2. Rate of weight loss of C. humicola at different heating rates.
ð12Þ
K. Kirtania, S. Bhattacharya / Bioresource Technology 107 (2012) 476–481
479
(a)
(b)
Fig. 3. Comparison of experimental and estimated data from the proposed algorithm at different heating rates.
3. Results and discussion
Table 2 Estimated model parameters at different heating rates. Rate (K/min)
mE (kJ/mol)
r
k0 (s1)
n
R2
5 10
189.15 190.02
14.73 14.73
1.1291 1016 2.6021 1016
7.88 6.63
0.999354 0.999569
The closer the value of R2 to 1, the better is the fit. The next step of the validation continued with testing the estimated model parameters over a new pyrolysis experiment performed at 20 K/ min. This data was not used for any model parameter generation. The raw data from the experiment was compared with the pyrolysis curve generated from the generalized model parameters from previous data.
3.1. Ultimate analysis The ultimate analysis was performed on the algae to observe the amount of its elemental constituents. The results are shown in Table 1. In the ultimate analysis, the alga was found to have a carbon content of 33% by weight on dry basis. Also the ash content was very high for the algae. 3.2. Pyrolysis The pyrolysis characteristics of the alga at different rates are shown in Fig. 1. It was found from the experiments that the pyrolysis of fresh water alga was complete by 550 °C. As it is a kind
480
K. Kirtania, S. Bhattacharya / Bioresource Technology 107 (2012) 476–481
Fig. 4. Distribution of activation energy at various heating rates during pyrolysis of C. humicola.
Fig. 5. Comparison of experimental and predicted weight loss data by the proposed algorithm.
of biomass, early devolatilization occurs. There was a rapid loss of its weight which slowed down after 500 °C. The rate curves (Derivative of Thermogravimetric curve) of algae pyrolysis in Fig. 2 showed the two steps in the rate curve during pyrolysis of algae. It can be seen that pyrolysis started around 200 °C and the rapid part of pyrolysis ended at about 365 °C and then the step completed at around 525 °C. The same behavior was observed for all the heating rates. The rate curves were consistent in the sense that the rates increased between 200 °C and 525 °C with increasing the heating rate. This rate increase was proportional to the increase in heating rate. Also two steps were found in each rate curve. Similar
rate curves were also observed during the pyrolysis of three kinds of red algae by Li et al. (2011). This indicates that the dominating reactions changed after the rate change. Anastasakis et al. (2011) studied the pyrolysis behavior of four main components of algae and found that they decomposed at different temperatures. After 525 °C, the weight loss continued at a reduced rate up to 850 °C. This tail at the end of the pyrolysis accounted for about 5.2% of the total weight loss which was a significant percentage of total volatile content of the alga. This can be denoted as ‘end loss’ for algae pyrolysis. Including the ‘end loss’, the total weight loss for C. humicola was found to be 55.6%.
K. Kirtania, S. Bhattacharya / Bioresource Technology 107 (2012) 476–481
3.3. Modeling Fig. 3 shows the weight loss curve of the algae along with the modeled weight loss at two different heating rates. The mean activation energy, standard deviation, pre-exponential factor and the order at different heating rates are listed in Table 2. The values of the fitness factor, R2 for the curves were determined to be greater than 0.999 (Table 2) for all the heating rates. So it is a quite good fit with only one set of reactions of n order with single activation energy distribution. Ideally, the values of estimated parameters at different heating rates should be similar, but practically that does not happen. As the pre-exponential factor is not truly independent of the temperature and counting all the experimental errors, the values of the parameters were quite close. To generalize the parameters for the species of fresh water algae, average values of the parameters were calculated to be mE = 189.59 kJ/mol, r = 14.73, k0 = 1.8656 1016 s1 and n = 7.2577. The distributions of activation energy at two heating rates along with average one is shown in Fig. 4. The model successfully considered the last 10% as loss of volatiles. With ±3r distribution of activation energy, the activation energy varied from 145.4 kJ/mol to 233.78 kJ/mol for decomposition of algae. A comparison of model predicted and experimental data at 20 K/min is shown in Fig. 5. The estimated curve fit the experimental data with a R2 value of 0.999479. The experiment at 20 K/min was repeated and results are shown in Fig. 5 as dotted line to check the reproducibility of the experiment. From this validation, it is evident that the developed algorithm closely predicted the pyrolysis behavior of C. humicola. 4. Conclusions Pyrolysis behavior of a fresh water alga has been investigated at different heating rates by TGA. To describe the slow weight loss kinetics at the end of the pyrolysis, a new nth order algorithm based on Gaussian distribution has been developed and used for kinetic parameter estimation. The algorithm was further tested by predicting weight loss at another heating rate which showed very good agreement with the experimental data. The new algorithm is useful for estimating kinetic parameters from only two pyrolysis experiments; these parameters can then be used for predicting pyrolysis kinetics at various heating rates for C. humicola. References Anastasakis, K., Ross, A.B., Jones, J.M., 2011. Pyrolysis behaviour of the main carbohydrates of brown macro-algae. Fuel 90, 598–607. Bruhn, A., Dahl, J., Nielsen, H.B., Nikolaisen, L., Rasmussen, M.B., Markager, S., Olesen, B., Arias, C., Jensen, P.D., 2011. Bioenergy potential of ulva lactuca:
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biomass yield, methane production and combustion. Bioresource Technology 102, 2595–2604. Burnham, A.K., Braun, R.L., 1999. Global kinetic analysis of complex materials. Energy and Fuels 13 (1), 1–22. Cai, J., Yang, S., Li, T., 2011. Logistic distributed activation energy model – Part 2: Application to cellulose pyrolysis. Bioresource Technology 102 (3), 3642–3644. Chaichalerm, S., Pokethitiyook, P., Yuan, W., Meetam, M., Sritong, K., Pugkaew, W., Kungvansaichol, K., Kruatrachue, M., Damrongphol, P., 2011. Culture of microalgal strains isolated from natural habitats in Thailand in various enriched media. Applied Energy. doi:10.1016/j.apenergy.2011.07.028. Demirbas, M.F., 2011. Biofuels from algae for sustainable development. Applied Energy 88 (10), 3473–3480 (special issue of energy from algae: current status and future trends). Flynn, J.H., Wall, A.L., 1966. A quick direct method for determination of activation energy from thermogravimetric data. Journal of Polymer Science Part B: Polymer Letters 4 (5), 323–328. Harun, R., Danquah, M.K., 2011. Enzymatic hydrolysis of microalgal biomass for bioethanol production. Chemical Engineering Journal 168, 1079–1084. Kissinger, H.E., 1957. Reaction kinetics in differential thermal analysis. Analytical Chemistry 29 (11), 1702–1706. Lakshmanan, C.C., Benett, M.L., White, N., 1991. Implications of multiplicity in kinetic parameters to petroleum exploration: distributed activation energy models. Energy and Fuels 5, 110–117. Li, D., Chen, L., Zhang, X., Ye, N., Xing, F., 2011. Pyrolytic characteristic and kinetic studies of three kinds of red algae. Biomass and Bioenergy 35, 1765–1772. Miura, K., 1995. A new and simple method to estimate f(E) and k0(E) in the distributed activation energy model from three sets of experimental data. Energy and Fuels 9, 302–307. Miura, K., Maki, T., 1998. A simple method for estimating f(E) and k0(E) in the distributed activation energy model. Energy and Fuels 12, 864–869. Navarro, M.V., Aranda, A., Garcia, T., Murillo, R., Mastral, A.M., 2008. Application of the distributed activation energy model to blends devolatilisation. Chemical Engineering Journal 142 (1), 87–94. Ozawa, T., 1965. A new method of analysing thermogravimetric data. Bulletin of the Chemical Society of Japan 38, 1881–1886. Pimentel, D. (Ed.), 2008. Biofuels, Solar and Wind as Renewable Energy Systems: Benefits and Risks. Springer, New York. Popescu, C., 1996. Integral method to analyze the kinetics of heterogeneous reactionsunder non-isothermal conditions a variant on the Ozawa–Flynn–Wall method. Thermochimica Acta 285 (2), 309–323. Ross, A.B., Anastasakis, K., Kubacki, M., Jones, J.M., 2009. Investigation of the pyrolysis behaviour of brown algae before and after pre-treatment using py-gc/ ms and tga. Journal of Analytical and Applied Pyrolysis 85 (1–2), 3–10. Saddawi, A., Jones, J.M., Williams, A., Wjtowicz, M.A., 2010. Kinetics of the thermal decomposition of biomass. Energy and Fuels 24 (2), 1274–1282. Scott, S.A., Dennis, J.S., Davidson, J.F., Hayhurst, A.N., 2006. An algorithm for determining the kinetics of devolatilisation of complex solid fuels from thermogravimetric experiments. Chemical Engineering Science 61 (8), 2339– 2348. Sonobe, T., Worasuwannarak, N., 2008. Kinetic analyses of biomass pyrolysis using the distributed activation energy model. Fuel 87 (3), 414–421. Tang, Y.T., Ma, X.Q., Lai, Z.Y., 2011. Thermogravimetric analysis of the combustion of microalgae and microalgae blended with waste in N2/O2 and CO2/O2 atmospheres. Bioresource Technology 102, 1879–1885. Weber, R., 2008. Extracting mathematically exact kinetic parameters from experimental data on combustion and pyrolysis of solid fuels. Journal of the Energy Institute 81 (4), 226–233, 8. Wjtowicz, M.A., Bassilakis, R., Smith, W.W., Chen, Y., Carangelo, R.M., 2003. Modeling the evolution of volatile species during tobacco pyrolysis. Journal of Analytical and Applied Pyrolysis 66 (1–2), 235–261. Yuan, S., Chen, X., Li, W., Liu, H., Wang, F., 2011. Nitrogen conversion under rapid pyrolysis of two types of aquatic biomass and corresponding blends with coal. Bioresource Technology. doi:10.1016/j.biortech.2011.08.047.
Contents lists available at SciVerse ScienceDirect
Bioresource Technology journal homepage: www.elsevier.com/locate/biortech
Application of the distributed activation energy model to the kinetic study of pyrolysis of the fresh water algae Chlorococcum humicola Kawnish Kirtania, Sankar Bhattacharya ⇑ Department of Chemical Engineering, Monash University, Clayton, VIC 3800, Australia
a r t i c l e
i n f o
Article history: Received 9 September 2011 Received in revised form 12 December 2011 Accepted 16 December 2011 Available online 24 December 2011 Keywords: Fresh water algae Chlorococcum humicola Pyrolysis Kinetics DAEM
a b s t r a c t Apart from capturing carbon dioxide, fresh water algae can be used to produce biofuel. To assess the energy potential of Chlorococcum humicola, the alga’s pyrolytic behavior was studied at heating rates of 5–20 K/min in a thermobalance. To model the weight loss characteristics, an algorithm was developed based on the distributed activation energy model and applied to experimental data to extract the kinetics of the decomposition process. When the kinetic parameters estimated by this method were applied to another set of experimental data which were not used to estimate the parameters, the model was capable of predicting the pyrolysis behavior, in the new set of data with a R2 value of 0.999479. The slow weight loss, that took place at the end of the pyrolysis process, was also accounted for by the proposed algorithm which is capable of predicting the pyrolysis kinetics of C. humicola at different heating rates. Crown Copyright Ó 2011 Published by Elsevier Ltd. All rights reserved.
1. Introduction Since some algae have a high oil content, they can be used to produce biodiesel (Demirbas, 2011); however, the separation of lipids from the algae is difficult and energy intensive (Pimentel, 2008). Instead of oil extraction, algae can be gasified to produce oil and gas (Tang et al., 2011; Bruhn et al., 2011). Pyrolysis is the first step in the combustion or gasification process. The pyrolytic behavior and kinetics of three kinds of red algae were investigated by Li et al. (2011), and it became evident that their pyrolysis behavior was more complicated than that of fossil fuels. The authors estimated the activation energy for those three algae by the Flynn–Wall–Ozawa (FWO) (Flynn and Wall, 1966; Ozawa, 1965), KAS (Kissinger, 1957) and Popescu (Popescu, 1996) methods. Brown algae pyrolysis at different conditions was investigated by Ross et al. (2009) and Anastasakis et al. (2011). For extracting kinetic parameters, Anastasakis et al. (2011) used the methods of Weber (2008) and Saddawi et al. (2010). Pyrolysis characteristics of blue–green algae with coal were studied by Yuan et al. (2011) without any kinetic parameter estimation. Due to the availability of high performance computing, the distributed activated energy model (DAEM) is widely used for different kinds of solid and liquid fuels. Miura and Maki (1998) and Scott et al. (2006) modified the DAEM so that no assumptions for the form of the activation energy distribution are required. Navarro et al. (2008), Sonobe and Worasuwannarak (2008) and ⇑ Corresponding author. Tel.: +61 3 9905 9623; fax: +61 3 99055686. E-mail address: [email protected] (S. Bhattacharya).
Wjtowicz et al. (2003) applied the DAEM to biomass pyrolysis successfully. Logistic distribution of activation energy was assumed and validated for cellulose pyrolysis by Cai et al. (2011) with nth order DAEM; however, the complex pyrolysis behavior of fresh water algae has not yet been modeled with the distributed activation energy model. For the present study, the blue–green algae, Chlorococcum humicola, was selected for pyrolytic and kinetic examination because it produces a high amount of biomass and lipids (Chaichalerm et al., 2011). Thermogravimetric experiments were performed at different heating rates to understand the pyrolytic behavior of the algae. Thereafter, a new algorithm for determining the kinetic parameters of DAEM was developed and the new algorithm for DAEM was validated with experimental data. 2. Methods 2.1. Pyrolysis experiments C. humicola biomass was grown in the Bio Engineering Laboratory, Department of Chemical Engineering, Monash University as described by Harun and Danquah (2011). The strain was cultured in 100-L bag photobioreactors outdoors and kept under semi-continuous conditions by 20% (v/v) dilution with fresh medium after harvesting an equal volume of culture on a daily basis. The medium consists of potassium nitrate, KNO3 (150 g/L, MW 101.11, 99.5%), sodium phosphate monobasic, NaH2PO4 (11.3 g/L, MW 119.98, 99.5%), manganese chloride, MnCl2 (360.0 mg/L, MW 125.84, 98.0%), zinc sulfate, ZnSO4 (44.0 mg/L, MW 161.47, 99.5%), cobalt nitrate, Co(NO3)2 (22.0 mg/L, MW 182.94, 97.5%), copper
0960-8524/$ - see front matter Crown Copyright Ó 2011 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.biortech.2011.12.094
477
K. Kirtania, S. Bhattacharya / Bioresource Technology 107 (2012) 476–481
sulfate, CuSO4 (19.6 mg/L, MW 159.61, 98.5%), sodium molybdite, Na2MoO42H2O (12.6 mg/L, MW 241.95, 98.0%), sodium metasilicate, Na2SiO3 (22.7 g/L, MW 122.06, 99.7%), iron(III) citrate, C6H5O7Fe3H2O (9.0 g/L, MW 298.99, 98%), and citric acid monohydrate, COOHCH2C(OH)COOHCH2COOHH2O (9.0 g/L, MW 210.14, 99.5%). The ultimate analysis was performed with a CHNS/O analyzer (Model 2400, Perkin-Elmer, USA). To determine carbon, hydrogen, nitrogen and sulfur, the samples were combusted at 975 °C to obtain CO2, H2O, N2 and SO2 and analyzed through a chromatographic column. The system detects the gases by thermal conductivity and directly gives the concentration of C, H, N, S in percent by comparing with the standard values. Ash content was determined by combusting the alga sample at 800 °C. As the concentration of other materials are in ppm range, the oxygen concentration was calculated by difference. The pyrolysis behavior was studied in a thermobalance (Model STA 449 F3 JupiterÒ, NETZSCH-Gerätebau GmbH, Germany). The alga was dried in an oven for at least 12 h at 105 °C, ground to a size of 106–150 lm using a hand mortar. The pyrolysis was done in nonisothermal condition and the temperature was ramped to 1100 °C at heating of 5, 10, and 20 K/min with one repeat for estimating the kinetic parameters and model validation. 2.2. Kinetic modeling A Gaussian distribution based distributed activation energy model (DAEM) was developed to analyze the pyrolysis kinetics and the ‘end loss’ of the algae. Usually the distributed activation energy model has a general form for several parallel first order reactions:
Z
w ¼ w
Z t Z E exp k0 eRT dt f ðEÞdE where
1 0
0
1
f ðEÞdE ¼ 1
ð1Þ
0
where w is the weight of volatile content remaining and w⁄ is the total volatile content. k0 is the pre-exponential factor and f(E)dE is the distribution that characterizes the activation energy. To model the slow weight loss that happens after the rapid loss in case of the microalgae, the nth order model is selected over the exponential model stated above. The nth order model with distributed activation energy can be expressed as follows:
w ¼ w
1
Z
1 þ ð1 nÞ
Z
0
t
0
1 ð1n Þ E dt k0 exp f ðEÞdE where n – 1 RT
ð2Þ As the distribution is assumed to be Gaussian for this model, it can be expressed as: w ¼ w
1
Z
1 þ ð1 nÞ
Z
0
t
0
( !) 1 ð1n Þ E 1 ðE mEÞ2 pffiffiffiffiffiffiffiffiffiffiffiffi exp dE dt k0 exp 2 RT 2r 2pr2
ð3Þ where mE is the mean activation energy and r is the standard deviation of distribution. In this case it is assumed that the distribution remains the same for the whole pyrolysis process. To develop the algorithm, the equation has been represented by multiplication of two functions:
w ¼ w
Z
1
ZðE; tÞf ðEÞdE
ð4Þ
0
where Z(E,t) contains the pre-exponential factor, k0 and the order n. The Z(E,t) varies with the time and activation energy. If the heating rate is a K/min, the Z(E,T) can be equated to: ZðE; TÞ ¼
1 þ ð1 nÞ
Z
T 0
1 ð1n Þ k0 E dT exp RT a
where T ¼ T 0 þ at
ð5Þ
This limit for the integration is valid as the value of T0 can be selected low enough where no reaction occurs (Miura, 1995). To simplify the calculation, the exponential integral in Z(E,T) is evaluated by asymptotic approximation when E/R ? 1 (Burnham and Braun, 1999):
( ZðE; TÞ ¼
"
1 Þ #)ð1n k0 RT 2 E 1 þ ð1 nÞ exp RT aE
ð6Þ
This asymptotic approximation provides similar results to the actual one. Now, assuming k0 is independent of temperature, Z(E,T) can be written as:
1 RT 2 E ZðE; TÞ ¼ f1 þ ð1 nÞk0 nðE; TÞgð1nÞ where nðE;TÞ ¼ exp RT aE ð7Þ As n(E,T) is defined now, it is important to understand that the temperature integral is evaluated at each value of decomposition. So for each value of activation energy, the n(Ei,T) can be evaluated to form a matrix. This matrix is formulated as:
2
nðE1 ; T 1 Þ nðE2 ; T 1 Þ nðEL ; T F Þ
3
7 6 6 nðE1 ; T 2 Þ nðE2 ; T 2 Þ nðEL ; T F Þ 7 7 6 6 n ¼ 6 nðE1 ; T 3 Þ nðE2 ; T 3 Þ nðEL ; T F Þ 7 7 7 6 5 4 nðE1 ; T F Þ
ð8Þ
nðE2 ; T F Þ nðEL ; T F Þ
This matrix implies that Eq. (2) can be expressed in an equivalent matrix which is possible to evaluate using any mathematical package. So the integrated matrix form of the mass loss equation becomes: 1 Þ2 3 3 8 39ð1n 2 wðT 1 Þ > nðE1 ;T 1 Þ nðE2 ;T 1 Þ nðEL ;T F Þ > f ðE1 Þ > > > > > 7 7 > 7 6 6 6 > > 6f ðE2 Þ7 6wðT 2 Þ7 > 6nðE1 ;T 2 Þ nðE2 ;T 2 Þ nðEL ;T F Þ7> 7 7 < 7= 6 6 16 6f ðE3 Þ7 6wðT 3 Þ7 ¼ 1þð1nÞk0 6nðE1 ;T 3 Þ nðE2 ;T 3 Þ nðEL ;T F Þ7 7 7 > 7> 6 6 w 6 7 7 > 7> 6 6 6 > > 5> 5 > 4 5 4 4 > > > > : ; wðT F Þ nðE1 ;T F Þ nðE2 ;T F Þ nðEL ;T F Þ f ðEL Þ
2
1 w ¼ f1 þ ð1 nÞk0 ngð1nÞ f w
ð9Þ
ð10Þ
Here, T1 and TF represent the values of minimum temperature and maximum temperature, respectively in an experiment. Though only k0 and n can be seen from Eq. (10), mE and r are the other two parameters implicit in activation energy distribution vector, f. Now from Eq. (10), it is possible to form an objective function which can be optimized to estimate those four parameters. The objective function is defined by the difference between the experimental and the model predicted data:
O:F: ¼
j¼F X wj ðexpÞ j¼1
w
2 wj ðestÞ w
ð11Þ
The wj(exp) and wj(est) denotes the experimental and estimated weight, respectively and i denotes the corresponding temperature. To minimize the objective function, the algorithm checks every possible values of mass fraction within the given activation energy and temperature range. As there are four unknown parameters to be evaluated, a new minimization algorithm has been used. The algorithm is known as Multistart. Unlike other algorithms such as direct search, pattern search or genetic algorithm, it tries multiple starting points for global optimization. The Global Optimization Toolbox of Matlab with parallel computing facility was used to accelerate computing speed. The curve fitting method for the Multistart object was selected to be lsqcurvefit based on the least square method. The code was generated in Matlab and a customized number of starting points for parameter estimation was used. Since activation energies for algae were reported in the literature as 60 kJ/mol and 322 kJ/mol (Li et al., 2011; Tang et al., 2011). The expected range of activation energy was selected from 10 kJ/mol to 500 kJ/mol) to form the matrix n and the energy distribution vector f. The temperature range was selected as required for
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Table 1 Ultimate analysis of the fresh water alga, C. humicola (%db). C
H
N
S
O
Ash
33.16%
5.58%
4.8%
2.42%
27.24%
26.8%
completion of pyrolysis. By defining the ranges of activation energy and temperature, the two most important vectors were defined for the model. To avoid multiplicity of estimated parameters (Lakshmanan et al., 1991) decomposition data at two different heating rates,
5 and 10 K/min were analyzed and used to generate parameters for the model. The model parameters estimated from the algorithm were used to generate a weight loss curve which is compared with the experimental one by the fitness parameter. The fit between the experimental and estimated data can be found out by the fitness parameter stated below:
Pj¼F wjðexpÞ R2 ¼ 1
j¼1
w
wjðestÞ 2 w
Pj¼F wjðexpÞ 2 j¼1
w
Fig. 1. Pyrolysis behavior of C. humicola at different heating rates.
Fig. 2. Rate of weight loss of C. humicola at different heating rates.
ð12Þ
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479
(a)
(b)
Fig. 3. Comparison of experimental and estimated data from the proposed algorithm at different heating rates.
3. Results and discussion
Table 2 Estimated model parameters at different heating rates. Rate (K/min)
mE (kJ/mol)
r
k0 (s1)
n
R2
5 10
189.15 190.02
14.73 14.73
1.1291 1016 2.6021 1016
7.88 6.63
0.999354 0.999569
The closer the value of R2 to 1, the better is the fit. The next step of the validation continued with testing the estimated model parameters over a new pyrolysis experiment performed at 20 K/ min. This data was not used for any model parameter generation. The raw data from the experiment was compared with the pyrolysis curve generated from the generalized model parameters from previous data.
3.1. Ultimate analysis The ultimate analysis was performed on the algae to observe the amount of its elemental constituents. The results are shown in Table 1. In the ultimate analysis, the alga was found to have a carbon content of 33% by weight on dry basis. Also the ash content was very high for the algae. 3.2. Pyrolysis The pyrolysis characteristics of the alga at different rates are shown in Fig. 1. It was found from the experiments that the pyrolysis of fresh water alga was complete by 550 °C. As it is a kind
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Fig. 4. Distribution of activation energy at various heating rates during pyrolysis of C. humicola.
Fig. 5. Comparison of experimental and predicted weight loss data by the proposed algorithm.
of biomass, early devolatilization occurs. There was a rapid loss of its weight which slowed down after 500 °C. The rate curves (Derivative of Thermogravimetric curve) of algae pyrolysis in Fig. 2 showed the two steps in the rate curve during pyrolysis of algae. It can be seen that pyrolysis started around 200 °C and the rapid part of pyrolysis ended at about 365 °C and then the step completed at around 525 °C. The same behavior was observed for all the heating rates. The rate curves were consistent in the sense that the rates increased between 200 °C and 525 °C with increasing the heating rate. This rate increase was proportional to the increase in heating rate. Also two steps were found in each rate curve. Similar
rate curves were also observed during the pyrolysis of three kinds of red algae by Li et al. (2011). This indicates that the dominating reactions changed after the rate change. Anastasakis et al. (2011) studied the pyrolysis behavior of four main components of algae and found that they decomposed at different temperatures. After 525 °C, the weight loss continued at a reduced rate up to 850 °C. This tail at the end of the pyrolysis accounted for about 5.2% of the total weight loss which was a significant percentage of total volatile content of the alga. This can be denoted as ‘end loss’ for algae pyrolysis. Including the ‘end loss’, the total weight loss for C. humicola was found to be 55.6%.
K. Kirtania, S. Bhattacharya / Bioresource Technology 107 (2012) 476–481
3.3. Modeling Fig. 3 shows the weight loss curve of the algae along with the modeled weight loss at two different heating rates. The mean activation energy, standard deviation, pre-exponential factor and the order at different heating rates are listed in Table 2. The values of the fitness factor, R2 for the curves were determined to be greater than 0.999 (Table 2) for all the heating rates. So it is a quite good fit with only one set of reactions of n order with single activation energy distribution. Ideally, the values of estimated parameters at different heating rates should be similar, but practically that does not happen. As the pre-exponential factor is not truly independent of the temperature and counting all the experimental errors, the values of the parameters were quite close. To generalize the parameters for the species of fresh water algae, average values of the parameters were calculated to be mE = 189.59 kJ/mol, r = 14.73, k0 = 1.8656 1016 s1 and n = 7.2577. The distributions of activation energy at two heating rates along with average one is shown in Fig. 4. The model successfully considered the last 10% as loss of volatiles. With ±3r distribution of activation energy, the activation energy varied from 145.4 kJ/mol to 233.78 kJ/mol for decomposition of algae. A comparison of model predicted and experimental data at 20 K/min is shown in Fig. 5. The estimated curve fit the experimental data with a R2 value of 0.999479. The experiment at 20 K/min was repeated and results are shown in Fig. 5 as dotted line to check the reproducibility of the experiment. From this validation, it is evident that the developed algorithm closely predicted the pyrolysis behavior of C. humicola. 4. Conclusions Pyrolysis behavior of a fresh water alga has been investigated at different heating rates by TGA. To describe the slow weight loss kinetics at the end of the pyrolysis, a new nth order algorithm based on Gaussian distribution has been developed and used for kinetic parameter estimation. The algorithm was further tested by predicting weight loss at another heating rate which showed very good agreement with the experimental data. The new algorithm is useful for estimating kinetic parameters from only two pyrolysis experiments; these parameters can then be used for predicting pyrolysis kinetics at various heating rates for C. humicola. References Anastasakis, K., Ross, A.B., Jones, J.M., 2011. Pyrolysis behaviour of the main carbohydrates of brown macro-algae. Fuel 90, 598–607. Bruhn, A., Dahl, J., Nielsen, H.B., Nikolaisen, L., Rasmussen, M.B., Markager, S., Olesen, B., Arias, C., Jensen, P.D., 2011. Bioenergy potential of ulva lactuca:
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