806
Znd.Eng. Chem. Res. 1996,34, 806-812
New Kinetic Model for Thermal Decomposition of Heterogeneous Materials Jose A. Caballero,* Rafael Font, Antonio Marcilla, and Juan A. Conesa Departamento de Ingenieria Quimica, Universidad de Alicante, Apartado 99, Alicante, Spain
In the kinetic studies of thermal decomposition of lignocellulosic materials using dynamic TG, relationships between the biomass fraction "w" and the time "t" of the form dwldt = -k(w w,)n are usually admitted, and the residue fraction at infinite time (w,) is considered constant. However, in heterogeneous solids such as lignocellulosic materials, the different polymers decompose a t different temperatures, and so the value of w, is not constant, Therefore, the previous equation must be considered approximate. To illustrate this feature, experiments with kraft lignin, which decomposes in an interval of temperatures between 150 and 750 "C,have been carried out. A kinetic model is proposed, bearing in mind that there is a maximum pyrolyzable fraction at each temperature. This model considers that the thermal decomposition of a heterogeneous material occurs through a great number of reactions and that a t a given temperature only some fractions can decompose. The kinetic parameters (activation energy and preexponential factor) can change during the decomposition process as functions of the reactions taking place. Under some assumptions, it is deduced that this model is equivalent to assume the kinetic law dwldt = -k(w - w,) for first-order reaction, where the residue yield w, is a function of the temperature.
Introduction To study the kinetics of thermal decomposition of a solid material, it has been admitted that the Arrhenius equation used for gas or liquid homogeneous phase reactions, is also valid to describe solid decomposition. This equation can be written as follows: daldt = kfla)
(1)
where a is the extension of the reaction, t the time, k the kinetic constant, and fla)a function of a. Equation 1 is usually presented as
where w is the biomass fraction and w, is the residue fraction at time infinity. In the solid decomposition reactions, there is a destruction of the solid phases. This differs sharply from reactions in the gas or liquid phase, in which the fluid reacting phase exists continuously throughout the reaction, with a continuous variation in the concentration of the components. Consequently, the concept of reaction order, as it is understood in the fluid phases, is not applicable to solids (Baker 1978). However, in the thermal decomposition of solid materials, a kinetic first-order reaction is usually admitted. This can be justified with the following assumptions: (a) the internal and external diffusion of mass and heat are fast; (b) the rate of solid decomposition is proportional to its specific surface; (c) the ratio specific surfacelnonreacted biomass remains constant, and (d) the yield coefficient defined as residue formedhiomass reacted remains constant. The kinetic first-order reaction has been used with success to describe the kinetics of thermal decomposition of a great number of fine solid materials (Varhegyi and Antal, 1989; Bilbao et al., 1987; Alves and Figueiredo,
* To whom correspondence should be addressed. E-mail:
[email protected].
1988,1989; etc.). Kinetic laws with order different from unity have also been proposed to fit experimental data (Chen et al., 1993; Urban and Antal, 1982). Dynamic TG has been widely used for studying solid decomposition with a constant heating rate. In many correlations of experimental data obtained at nonisothermal conditions, w, has been considered as constant, and coincides with the weight loss at infinite time in the dynamic TG curve. However, when experiments of TG in isothermal conditions are carried out at different temperatures between the range of solid decomposition, different values of w, are obtained. These values depend only on the final temperature and the type of biomass and are independent of the time. This is a consequence of the heterogeneity of the residue formed by the different fractions that can decompose in different ranges of temperature. From the results corresponding to many isothermal TG experiments, it is possible to obtain the relation w, = fltemperature) (Agrawal, 1988). Taking this fact into account, eq 2 should be written as dwldt = -k(w - w,(T))"
(3)
where the value of w, depends on the temperature at any given moment. In this way, the experimental results obtained with isothermal and dynamic TG could be fitted with only one equation. Otherwise, it is obvious that eq 2 with the maximum value "w," obtained at high temperature cannot represent the decomposition at isothermal TGs with different nominal temperatures. The variation of w, with temperature is discussed in the next sections of this paper. Experiments with krafi lignin have been used to illustrate the different kinetic aspects considered. From the discussion carried out, a new kinetic model is proposed for studying the decomposition of heterogeneous solids.
Experimental Section Thermobalance. The experiments were carried out in a Model TGA7 Perkin-Elmer thermobalance, con-
0888-5885/95/2634-0806$09.0QlQ @ 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 807 l
0.8 0.6
Maximum Pyrolyzable Fraction
Weight loss , ,
1
Ih
1
300°C 500 “C
o ! 0
I 10
20
30
40
50
60
Time (min)
Figure 1. TG experiments at different final temperatures (initial heating rate 50 Wmin). trolled by a PC AT compatible system. The atmosphere used was N2 with a flow rate of 60 mumin. The thermobalance uses a servooperated system in which an electrical signal from an optical null detector is applied directly to control the current in a torque motor. The balance has provisions for digital mass readout using four-digit thumbwheels and two-digit vernier with three full-scale ranges of 10, 100, and 1000 mg. Materials and Experimental. In all the experiments the material used was kraft lignin obtained by the method explained elsewhere (Corder0 et al., 1990). The ash content of the lignin sample used in this work is 1.56%. The elemental analysis of the lignin used is C = 63.9%; H = 6.12% ; N = 0.8%; S = 1.7% and by difference 0 = 27.4% (dry weight basis). Experiments in isothermal conditions were carried out in a range of temperatures that comprise all the range of solid decomposition, in order to calculate the relation between the residue w, and the operating temperature. A heating rate of 100 “C/min was used to reach the nominal temperature before the period of constant temperature. The mass of sample used in all the experiments was about 7-8 mg. TG experiments were duplicated in order t o calculate the experimental error. The maximum difference obtained in the final residue yield was always lower than 2% and nearly always lower than 1%.
Kinetic Model The biomass is a heterogeneous mixture formed by different fractions that can decompose at different temperatures. It can be considered that at a given temperature, there is a ‘maximum pyrolyzable fraction” (MPF) independent of the time. That means that at a temperature T,only a fraction of solid material can decompose. This fact can be tested with isothermal TG experiments at different temperatures within the range of thermal decomposition of biomass. Figure 1 shows the decomposition curves correspond to the Kraft lignin. From the values of weight loss obtained at time infinity (25 experiments), at different temperatures, the relationship between the maximum pyrolyzable fraction, MPF, and the temperature T can be obtained (see Figure 2). These experiments were carried out at a heating rate of 100 “C/min to the final constant temperature. Nevertheless, it has been tested that the same weight loss takes place with other heating rates in the previous heating period with the same final temperature.
04 273
473
673
a73
1073
Temperature (K)
Figure 2. Maximum pyrolyzable fraction for kraft lignin. The fact that the char yields is asymptotic with final temperature was pointed by Iatridis and Gavalas (1979) and commented on by Anta1 in a review (1985). In literature, different kinetic models have been considered for correlating experimental data. Avni and Couglin (1985)proposed a first-order kinetic model, with the activation energy changing with the reaction extension. Other interesting models are those which assume distribution of activation energies (Anthony and Howard, 1976). These models are based on the hypothesis that there are an infinite number of first-order parallel reactions, each one with its own activation energy and the same preexponential factor that is a function of the activation energy-admitting a compensation effect (Kenji Hashimoto et al., 1982; Chornet and Roy, 1980; Agrawal, 1985). The contribution of each one of these reactions is given by the activation energy distribution function. The following equation can summarize the Anthony and Howard model:
The new model presented in this paper is applicable to some biomass (such as lignin) that decompose in a very wide temperature range and when the residue at time infinity depends on the final temperature but does not depend on the heating rate. This model assumes that the biomass is formed by a great number of “fractions”. A given fraction can start its decomposition only if the temperature of the biomass is greater than or equal to a characteristic temperature TR of this fraction. Then, if the biomass temperature is T , only those fractions whose TRis lower than T can undergo decomposition. To determine the fraction of biomass that can begin to decompose a t a given temperature, a distribution function of TRis defined. This function is the “C curve”. So if the temperature of the system at a given moment is T , the area included under the C curve between zero and TR= T corresponds to the portion of biomass that can undergo decomposition. Consequently, (5) If T Ris~the temperature at which the biomass starts decomposing (e.g., the first fraction of biomass begins to decompose), and T Ris~the minimum temperature at which all the fractions of biomass have begun their decomposition, then
808 Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995
C (1/K)
The curve C cannot be measured directly but under some assumptions can be determined. In the most simple scheme, the biomass decomposition can be expressed by the reaction
B
+
ss
\
fraction of blomass that can decompose tn the inlerval ‘I”
biomass that cannot
+ vv
where V is the volatile fraction and S is the solid residue, s and u are the yield coefficients expressed as “weight of solid or volatile formedweight of biomass decomposed”. If R(TR)is the residue that is obtained when the pyrolysis temperature is TRa t time infinity (see Figure 2), it can be written that
T
(actua, IeTperature)
(7) In the previous equation, the first integral corresponds to the biomass residue for the fraction decomposed from T R to ~ TR at time infinity, and the second one is the biomass fraction that has not been decomposed (see Figure 3). The yield coefficient s can vary from one fraction to the other, but assuming a constant value for all the fractions, the following equation can be obtained derivating eq 7 with respect to TR:
If s is not considered constant, the determination of the C curve is much more complex. On the other hand, the variation of s with TRis not known, and different functions should be tested. The good agreement between the experimental and the calculated values justifies the aproximation used. The value of s can be calculated if eq 7 is applied for the whole interval of decomposition, between T R and ~ TR2, leading to
Consequently assuming a value s constant, that is equal to the minimum residue yield, the curve C(TR) can be determined from the variation of R(TR)vs TR, by eq 8. In addition to the experimental fact that the different fractions begin to decompose at distinct temperatures, each fraction probably follows a particular kinetic law. In order to calculate the kinetic parameters, the C curve is divided into small intervals of temperature, TR,and for each interval the Arrhenius equation is used:
where w,i is equal to sC~ATR.The value of biomass fraction wi can vary between wp which equals C~ATR and w,i. On the other hand
where k o ( T ~ and ) E(TR) are functions of TR. The variation of the preexponential factor and the activation energy with TRagrees with the fact that each fraction can have its own kinetic parameters. Only those fractions whose temperature (TR)is lower than the
Figure 3. Curve C of thermal decomposition.
operating temperature (2‘) at any given moment can begin to decompose (see Figure 3). The total extension of the reaction is the sum of the extensions corresponding to each small fraction. When the activation energy ( E ) and the preexponential factor (ko)are constants (have the same value for all the fractions)and for runsin which temperature does not decrease with time, this model is equivalent to that shown by eq 3 in where the order of reaction n is unity. This is deduced as follows: For a fraction i, the equation used is
where pi is defined as nondecomposed biomass of fraction i divided by the initial biomass of fraction i (C~ATR).In the previous equation, pi varies between 1 and p w i . It can be considered, at a given moment, that the sample is at temperature T,between T R (minimum ~ temperature of decomposition)and TR2 (temperature for maximum decomposition) in a run with temperature increasing with time. In the C curve model, the total conversion a t that moment t is the sum of the conversions of all the fractions whose temperature TRis lower than the process temperature T. For the fractions that are decomposing, where TR is less or equal than the operating temperature T,it can be written that
Due to the fact that the fractions whose TRis greater than the operating temperature T,cannot decompose, it can be deduced that
Considering eqs 13 and 14
In the same way, the right-hand side of eq 13 can be written as
Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 809 because for the fractions whose temperature TR is higher than the operating temperature T, /3 =1 and /3= 1. Then, eq 13 becomes
c curve (1nq
0.007 0.006 -
A \
0.005 -
0.004 -
0.003 -
0.002 0.001 0
On the other hand, it can be written that
273
473
673
073
Temperature (lr)
1073
(K)
Figure 4. Curve C for kraft lignin thermal decomposition.
where w, is the residue yield which decreases with temperature. From eqs 17-19 it can be deduced that
which coincides with eq 3. Note that this discussion is valid only for runs with increasing temperature with time. If temperature increases and then decreases with time, there is a fraction of the solid that has decomposed at higher temperatures than the operating temperature. It would then be possible to obtain a value of w lower than WJT) (Tis the operating temperature). That means that the value of w,(T) defined in eq 3 is valid only for runs in which temperature increases with time. In the curve C model this problem is easily avoided. For runs in which temperature decreases with time eq 19 becomes
where /3* is the nonconverted fraction of biomass at temperatures higher than the operating temperature. The use of the C curve is therefore an alternative way to simulate the kinetic behavior of biomass thermal decomposition. When s is not constant, then the calculation of the curve C is difficult and not always possible, a t least in a direct form. With this model the experimental data can be satisfactorily correlated considering a total process or a great number of processes that can be described by equations in which the kinetic constants change with an intrinsic characteristic of the material, such as temperature TR (as explained in the following sections).
Results and Discussion Figure 4 shows the curve C for lignin, obtained from the data R(TR)presented in Figure 2, by the differentiation indicated by eq 8. To evaluate the kinetic parameters of different models, the following experiments were carried out: three dynamic TGs with heating rates of 10, 25, 50 "Clmin, and an experiment with an initial heating rate of 50 "Clmin t o 400 "C, followed by 10 min at 400 "C and then a new heating rate of 50 "Clmin t o 700 "C.
The following models were tested for correlating the data: (1) Using eq 2 with n = 1 and w, constant: the parameters optimized were the activation energy, preexponential factor, and the residue yield a t time infinity (WJ.
(2) Using the Anthony and Howard model with constant preexponential factor and with a Gaussian distribution of activation energies: the parameters optimized were the preexponential factor, the mean value of activation energy, the standard deviation u and W,:
1 nE)=-exp[ a&
]
(E - E)2 2 2
(22)
(3) Using eq 2 with n different from unity and the residue yield at time infinity constant. The parameters optimized were the activation energy, the preexponential factor, the extension of reaction at time infinity, and the order of reaction. (4) Using eq 2 with an order of reaction different from unity and the residue yield at time infinity changing with temperature (see Figure 3). The parameters optimized were the activation energy, the preexponential factor and the order of reaction. (5) Model of C curve. In this model, the C curve was divided into small intervals of temperature (ATR)each of them characterized by a temperature TR. Different functions E(TR)and k o ( T ~were ) tested. A modified Simplex Program (Himmelblau, 1968)was used in all cases to carry out the optimization. The objective function (OF) used t o be minimized was N
(23) i=l
where the subscript cal refers to values calculated by the models and the subscript exp refers t o experimental values. As not all the TG experiments have been correlated using the same number of experimental values, to compare the results of the different experiments, a variation coefficient (VC) was defined as
where N is the number of points t o be correlated and P is the number of parameters.
810 Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 1.2
,
Weight loss
Temperature (K)
r
1000
Table 1. Comparation between the Different Kinetic Models no. of TG
1
- 800
0.8
- 600 0.6
- 400 0.4
Models 1,2
- 200
model 1 2 3 4 5
EIR (K-l)
ln(k0)
curves fitted w, (%) simultaneously 0.52 5.82 1 0.52 5.82 1 VC
n
5.85 1 4541 4541(0=58) 5.85 1 13889 23.13 7.23 0.21 1.93 1.28 1.40 7268 11.51 1.07 3817 24.53 7.98 24.53 1 (TR - 273) (TR - 273)
+
+
(e) In the case of the C curve the best correlation, considering different functions E(TR)and k o ( T ~was ) obtained with lineal relationships between E, and In ko, these functions with the optimum parameters are the following:
EIR = 3817 + 24.5(TR - 273) 1
Temperature K
Weight loss
1000
1 4 4
ln(Ko)= 7.98
(25)
+ 24.53(TR - 273)
t
t
0.8
t
0.6
-
800
-
600
- 400
0.4
Experiment& 200
0.2 -Model 5 -Temperature Profile
0
0 0
5
10
15
20
25
Time (Min)
Figure 6. Comparation between experimental and calculated TG values (models 4 and 5).
First, the TG curve with two ramps were selected to compare the accuracy of the different models. Figures 5 and 6 show the calculated values of yields using the best parameters optimized together the experimental points of weight sample vs time. (a) The correlation obtained considering order of reaction equal to unity and w, constant cannot reproduce correctly the two ramps of heating and the optimum value of the residue yield at time infinity is 0.53. The accuracy of adjustment depends on the time between ramps of heating. This model is therefore not valid for representing the kinetics of lignin. (b)The Anthony and Howard model exactly yields the same values of the preexponential factor and the mean activation energy as the previous model. The standard deviation u has a value of 0.482 kJ/mol, which is very small in comparison with the value of activation energy, 37.75 kJ/mol. This model is, therefore, no better than the previous model. (c) The third case (n different from unity and w, constant) shows a better correlation than that of the previous one. Nevertheless the weight loss cannot be explained, and the values of the order of reaction and the residue yield at time infinity are 7.23 and 0.21, respectively. These parameters have no physical significance. (d) With the fourth model (order of reaction different from unity and the residue yield at time infinity changing with temperature) and with the curve C model, the fitting obtained was very good.
In accordance with eq 25 the activation energy varies linearly between 72.4 kJ1mol for T R =~ 200 "C and 174 kJ/mol for T R =~ 700 "C that means that the fractions that decompose at high temperatures have activation energies higher than those that decompose at low temperatures, which appears t o be a logical conclusion. In many chemical processes, including biomass pyrolysis, a compensation effect between E and ln(ko) is assumed as commented previously. This consideration has also been included in the model presented in this paper. On the other hand, In ko also increases with TRthe preexponential factor is related to many factors such us the entropy change and the surface of material where the volatiles escape from the reaction points. The fractions that decompose a t high temperatures have probably a specific surface greater than the fractions that decompose a t low temperatures, as a consequence of increase of internal porosity when the heterogeneous material is decomponing. Table 1 shows the results for all the correlations. Koga et al. (1991) have commented on the necessity of testing the kinetic models proposed, since any TG can be fitted to different kinetic models, resulting in very different values of the kinetic parameters, depending on the model. However, despite the fact that many models can represent with enough accuracy a single experiment at a given heating rate, only those models capable of explaining the data of different runs of TG with distinct heating rate with the same kinetic parameters can be considered correct. To compare those models that can reproduce with accuracy a single TG curve, the three experiments at different heating rates were adjusted simultaneously together with the experiment with two ramps, maintaining the same kinetic parameters for each of four experiments. The results are shown in Figures 7 and 8. The C curve model fit the experimental data better than model 4. Both these models reproduce the experimental data with sufficient accuracy. The value of activation energy 60 kJ/mol, obtained by model 4, is not near the range of activation energies,125-291.6 kJ/mol, given by Suuberg et al. (1978). It is comparable with the values of 81.7 kJ/mol given by Nunn et al. (1985),97.5 kJ/mol Wend (19701, and 70.8158.3 kJ/mol by Domburg and Seergeeva (1974).
Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 811 1
0.8
0.6
o,2jF i 0.4
,
,
~
0 350
450
550
650
750
850
950
Temperature K
Figure 7. Comparation between experimental and calculated TG values using the fourth model. Adjust of all TG curves simultaneously. eight loss
1
is possible to assume correlations between the kinetic parameters, preexponential factor and activation energy, with the temperature TR for the fractions considered. When these kinetic parameters are assumed identical for all the fractions and for first-order reactions in runs with increasing temperature with time, the curve C model leads to the relation dwldt = -kO exp(-E/RT)(w - we) where W* is the residue yield a t the temperature of the sample at any moment. The model proposed has been tested with the data obtained from a compound which decomposes in a very large range of temperatures. This is the case of the kraft lignin decomposition (200-700 "C).
Acknowledgment Support for this work was provided by CICYT Spain, Research Project AMB93-1209.
Nomenclature a = conversion = biomass present at any time in the fraction ilinitial biomass of the fraction i p-i, .= biomass present at infinity time in the fraction zlinitial biomass of the fraction i B = biomass present at any time C = symbol for distribution of thermal decompositioncurve pi
0.8
.*
. '. . *.
0.6
(IC1) 0.4
0.2 Experimental
-
Modal5
0 350
450
550
650
750
850
950
Temperature K
Figure 8. Comparation between experimental and calculated TG values using the C curve model. Adjust of all TG curves simultaneously.
The values of activation energies between 72.4 and 174 kJ/mol obtained by the C curve model are comparable with the interval of activation energy given by Suuberg et al. (1978) and with the values given by Domburg and Seerggeva (1974)but are higher than the values obtained in model 4 in which activation energy cannot change.
Conclusions The models dwldt = -K(w - w,)n used for correlating experimental data in the lignocellulosic material decomposition cannot be appropriate when different runs obtained a t distinct heating rates and final temperatures or with runs obtained at different ramps. Taking into account that the different fractions decompose a t different temperatures, a new kinetic model has been proposed for satisfactorily correlating the experimental results obtained in the pyrolysis of kraft lignin. This model is based on a function of distribution of solid decomposition C, where C dTR means the fraction of biomass that can decompose between TRand TR dTR. This temperature TRis different from the temperature of the sample at any moment. Assuming a residue yield constant for all the fractions, the relation C = ATR) can be deduced from the variation of the residue yield obtained at time infinity vs the operating temperature TR. Using this model, it
+
E = activation energy (kJlmol) k = kinetic constant (min-1 if n = 1) ko = preexponential factor (min-l if n = 1) n = order of reaction N = number of values to be adjusted OF = objective function P = number of parameters R = perfect gas law constant (kcaumol K) s = yield coefficient (weight of residue present at any time/ biomass reacted) S = solid residue present at any time t = time (min) T = temperature (K) TR= temperature at which C curve is calculated (K) u = yield coefficient (weight of volatiles present at any time1 biomass reacted) V = volatiles present at any time VC = variation coefficient (%) w = biomass present at any timelinitial biomass weal, = biomass present at any timehnitial biomass calculated by the different models wexp,= biomass present at any timehnitial biomass measured experimentally w, = biomass present at time infinitylinitial biomass
Literature Cited (1) Agrawal, R. K. Compensation Effect in the Pyrolysis of Cellulosic Materials. Thermochim. Acta 1985, 90, 347-351. (2) Agrawal, R. K. Kinetics of Reaction Involved in Pyrolysis of Cellulose. I the Three Reaction Model. Can. J . Chem. Eng. 1988, 66, 403. (3) Alves, S. S.; Figueiredo, J. L. Pyrolysis Kinetics of Lignocellulosic Materials by Multistage Isothermal Thermogravimetry. J . Anal. Appl. Pyrol. 1988, 13, 123-134. (4) Alves, S. S.; Figueiredo, J. L. Kinetics of cellulose Pyrolysis Modelled by Three Consecutive First-order Reactions. J . Anal. Appl. Pyrol. 1989, 17, 37-46. (5) Anta1 , M. J. Biomass Pyrolysis. A Review of Literature. In Advances in Solar Energy, Boer, K. W., Duffle, J. A., Eds.; Plenum Press: New York, 1985. (6) Anthony, D. B.; Howard J. B. Coal devolatilization and hydrogasification. AICHE J . 1976,22, 625.
812 Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 (7) Avni, E.; Coughling, R. W. Flash Pyrolysis of Lignin. Thermochim. Acta 1985, 90, 157. (8) Baker, R. R. Kinetic Parameters from the Non-isothermal Decomposition of a Mdticomponet Solid. Thermochim.Acta 1978, 23,201'-212. (9) Bilbao, R.; Arauzo, J.; Millera, A. Kinetics of Thermal DecomDosition of Cellulose. Part I. Influence of exDerimenta1 conditibns. Thermochim. Acta 1987, 120, 121-131. (10)Boroson, M. L.; Howard, J. B.; Lonwell, J. P.; Peters, W. A. Product Yields and Kinetics from the Vapor Phase cracking of Wood Pyrolysis Tars. AIChE J. 1989, 35 (11, 121. (11) Chen, D.; Gao, X.; Dollimore, D. A Generalized Form of Kissinger Equation. Thermochi. Acta 1993,215, 109-107. (12) Chornet, E.; Roy, C. Compensation Effect in the Thermal Decomposition of Cellulosic Materials. Thermichim.Acta 1980,35, 389-393. (13) Cordero, T.; Rodriguez, J. M.; Rodriguez, J.;Rodriguez, J. J. On the Kinetics of Thermal Decomposition of Wood and Wood Components. Thermochim. Acta 1990,164, 135- 144. (14) Domburg, G. E. In Thermal Analysis, Proceedings, 4th International Conference on Thermal Analysis, Budapest, 1994; VOl. 2, p 211. 115) Gavalas. G. R. Coal wvrolvsis: Elsevier Scientific Publishing: Amsterdam, 1982; Ch&er"6, p 112. (16) Hashimoto, K.; Miura; K Watanabe, T. Kinetics of Thermal regeneration of Acticvated Carbons Used in Waste Water. AIChE J. 1982,28, 737-746. (17) Himmelblau, D. M. Process Analysis Statistical Methods; Wiley & Sons: New York, 1968.
(18) Iatridis, B.; Gavalas, G. Pyrolysis of Precipitated Kraft Lignin. Ind. Eng. Chem. Prod. Res. Dev. 1979, 18, 127-130. (19) Koga, N.; Sestak, J.; Malek; J. Distorsion of the Arrhenius Parameters by Inappropiate Kinetic Model Function. Thermochim. Acta 1991,188, 333-336. (20) Nunn, T. R.; Howard, J. B.; Longwell, J. P.; Peters, W. A. Product Composition and Kinetics in the Rapid Pyrolysis of Milled Wodd Lignin. Ind. Eng. Chem. Proc. Des. Dev. 1985,24, 844. (21) Suuberg, E. M.; Peters, J. B.; Howard,J. B. Product Composition and Kinetics of Lignin Pyrolysis. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 37. (22) Urban, D. L.; Antal, M. Study of the Kinetics of Swage Sludge Pyrolysis Using DSC and TGA. Fuel 1982, 61, 799. (23) Varhegyi, G.; Antal M. J. Kinetics of the Thermal Decomposition of Cellulose, Hemicellulose, and Sugar Cane Bagasse. Energy Fuels 1989,3, 329-335. (24) Wenzl, H. F. J. The Chemical Technology of Wood; Academic Press: New York, 1970.
Received for review February 3, 1994 Revised manuscript received October 27, 1994 Accepted November 14, 1994@
IE940073P Abstract published in Advance ACS Abstracts, February 1, 1995. @
