I n d . Eng. Chem. Res. 1995,34, 786-793
786
Kinetics and Modeling of Gas Formation in the Thermal Decomposition of Powdery Cellulose and Pine Sawdust Rafael Bilbao,*t+Jeslis Arauzo, and Maria L. Salvador Department of Chemical and Environmental Engineering, University of Zaragoza, 50009 Zaragoza, Spain
The formation of different gases in the thermal decomposition of cellulose and pine sawdust has been studied. The kinetic constants of C02 and H2 formation in cellulose decomposition have been determined from results obtained in isothermal experiments. These kinetic constants have been taken as representative of pine sawdust decomposition at T > 292 "C, and values for lower temperatures have been obtained from isothermal experiments performed with pine sawdust. For both materials, a simple model without adjustable parameters has been applied that allows us to calculate the local temperature, solid conversion, and yield of each gas. The results obtained in dynamic experiments with heating rates ranging between 2 and 53 "C/min have been compared with the theoretical results, and a n acceptable agreement has been achieved.
Introduction The thermal decomposition of wood and other lignocellulosic materials has been widely studied, and several papers have been published showing the influence of different operating conditions on the weight loss and product formation. One of the lesser known aspects concerns the formation rate of the different products. The reaction scheme can be complex due to the heterogeneity of the materials and the significant influence of different variables (such as temperature, heating rate, and solid and volatile residence time) on the product distribution. Generally it is assumed that the different products are formed from the solid through parallel and competitive reactions. This reaction pathway is adequate when it is possible to neglect secondary reactions. Some proposed models (Shafizadeh and Chin, 1977; Thurner and Mann, 1981) suggest a reaction pathway with three lumped products (char, tar, and gas). With a similar kinetic model, other authors (Chan and Krieger, 1981; Font et al., 1990; Samolada and Vasalos, 1991) used the ultimate yield of each lumped product as an adjustable parameter. Some studies have been performed in order t o calculate the kinetics of the formation of the individual gas products obtained in the thermal decomposition of lignocellulosic materials. Generally, these studies are carried out at a high heating rate of the sample. In this way, Hajaligol et al. (1982) and Nunn et al. (1985a,b), assuming first order parallel reactions, determined the kinetic constants corresponding to the rapid pyrolysis of cellulose, lignin, and sweet gum. Baker (1975)carried out experiments with cellulose at two different heating 6 300-600 "C/min), obtaining that the rates ( ~ 6 and Arrhenius parameters for the CO and C 0 2 formation depend on the heating rate. Another interesting paper is that by Simmons and Gentry (1986), who analyzed the formation of gaseous products in cellulose pyrolysis for temperatures between 360 and 595 "C, discussing whether the different gases were produced from primary or secondary reactions. This paper presents a study of the formation of the different gases evolved at relatively low heating rates and temperatures, because in these conditions a unique pyrolysis mechanism can be considered. Cellulose (the
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address:
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main component of lignocellulosic materials) and pine sawdust have been used. The materials are powdered in order to minimize the anisotropic effect of the solid and to avoid the heat and mass transfer resistances inside the particle.
Experimental System Experiments at atmospheric pressure have been carried out in two installations, each one allowing us to work in a different heating rate range. Both experimental systems have a similar design, which has been shown in an earlier paper (Bilbao et al., 1993a). A scheme of the experimental system is shown in Figure 1. A tubular reactor is introduced vertically into an electrically heated furnace connected to a temperature and heating rate control system which allows us to program different heating rates. The materials used in this study were cellulose Sigmacell S-3755 from Sigma Chemical Co., with a particle size between 0.10 and 0.25 mm, and Pinaster pine sawdust with a particle size between 0.63 and 1.60 mm. The sample is supported by a ceramic cup 5 cm i.d. and 0.9 cm high. The initial weight of the sample, WO, was 2.5 g. Thermal decomposition of these materials is performed in an Nz inert atmosphere with a flow rate of 15 normal cm3/s. The exit gas passes through tar condenser vessels and is analyzed by gas chromatography. The presence of C02, CO, CH4, and Hz has been detected. The temperature at different points is measured by type K thermocouples of 0.5 mm introduced through the top flange of the reactor. These values are simultaneously monitored by a computerized system. The solid temperature was measured at two radii positions, r = 0 and 2.4 cm, and four bed heights h = 0, 0.2, 0.5, and 0.8 cm. Isothermal experiments at temperatures between 265 and 328 "C and dynamic experiments at different heating rates have been carried out. Significant temperature profiles appear in the bed when heating dynamic experiments are performed. In previous works (Bilbao et al., 1993a,b, 1994)these temperature profiles were analyzed for different operation conditions. Here, only some of these results are indicated. Figures 2 and 3 show respectively both the radial and longitudinal maximum temperature gaps obtained in the bed at
0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34,No. 3, 1995 787
N* --
4
I .- PRECISION BALANCE 2.,3.- MASS FLOWMETER 4.-
REACTOR
5.- CONDENSERS 6.- FURNACE 7.- SAMPLE 8.,9.,10.- THERMOCOUPLES 1 1 .- TEMPERATURE AND
HEATING RATE CONTROL
12.- DATA LOGGER SYSTEM 13.- COMPUTER
Figure 1. Experimental system. 60 I
I
80
9
0
0 0
-
10
0
m I
0
10
20
30
40
50
/
60
B (Wmin)
Figure 2. Maximum radial temperature gaps for different heating rates.
different heating rates. It is observed that the temperature differences can reach values up to 80 "C, which are very significant taking into account the bed sample size. The appearance of these temperature profiles makes it difficult to quantify the heating rate of the sample in each experiment. An average value of the eight different temperatures measured has been used, and these average values corresponding to the different experiments were 2, 5 , 12, 31, and 53 "C/min.
Experimental Results The gas composition a t different times has been determined in the experiments. From these results, the
20
lo
0 0
10
20
30
40
50
60
B ("Umjn) Figure 3. Maximum longitudinal temperature gaps for different heating rates.
evolution of the mass flow of each gas formed and the gas yield have been calculated. Table 1shows the total yield of each gas corresponding to the isothermal experiments. These values are expressed as a percentage of the initial weight of the sample. The values of W,,the mass of biomass at infinite time, are also shown. As the temperature increases, an increase in the gas yield can be observed. CO2 is the most abundant gaseous product, H2 is formed at temperatures above 300 "C, and CO is only detected at 322 "C. Comparing the results obtained with both materials, higher amounts of CO2 for sawdust at lower temperatures are observed than for cellulose. This fact has been found by other authors (Nunn et al., 1985a; Hajaligol et al., 1982),and
788 Ind. Eng. Chem. Res., Vol. 34, No. 3,~1995 Table 1. Gas Yield from Isothermal Experiments run CGIl CGI2 CG13 CG14 CG15 CGI6 CGI7 SGIl SGIB SGI3 SGI4 SGIB SGI6 a
0.010
%
%
%
%
CO
Hz
W,(g)
nd 0.09 0.17 0.10 0.15 0.08 0.15 nd nd nd nd 0.25 0.19
0.58 0.60 0.58 0.62 0.59 0.60 0.51 1.48 1.57 1.01 1.08 0.85 0.57
material
Tj("C)
gases
COz
cellulose cellulose cellulose cellulose cellulose cellulose cellulose sawdust sawdust sawdust sawdust sawdust sawdust
292 299 306 314 318 322 328 265 272 278 290 308 325
2.87 2.70 4.93 5.34 5.64 5.49 4.77 4.57 3.77 5.63 6.33 7.12 8.07
2.87 nda 2.61 nd 4.76 nd 5.24 nd 5.49 nd 4.98 0.43 4.62 nd 4.57 nd 3.77 nd 5.63 nd 6.33 nd 6.87 nd 6.41 1.47
1
I --I o
&12°CJmin
I
&53*Umin
cellulosc
0.000 L+--eab 0
'
'
'
I ? '
20
'
-
/ ^ I
40
100
80
60
Time (min)
Figure 5. Mass flow of CO vs time. Material: cellulose.
nd, not detected.
Table 2. Gas Yield from Dynamic Experiments
B run CGDl CGD2 CGD3 CGD4 CGD5 SGDl SGD2 SGD3 SGD4 SGD5
%
%
%
material ("C/min) gases COZ CO cellulose 2 4.86 4.71 nda cellulose 5 8.22 6.64 1.38 cellulose 12 16.10 10.70 5.17 cellulose 31 17.81 12.36 4.75 cellulose 53 25.40 15.08 8.52 sawdust 2 4.15 3.90 0.25 sawdust 5 7.75 5.55 2.05 sawdust 12 15.63 8.57 5.64 sawdust 22.46 14.47 6.51 31 sawdust 53 32.01 16.86 12.02
%
%
H2
CHI
0.15 0.20 0.23 0.70 0.86 nd 0.15 0.27 0.70 1.04
nd nd nd nd 0.94 nd nd 1.15 0.78 2.09
0
&12Thill
cellulosc
20
0
80
60
40
nd, not detected.
100
Time (min)
0.010 I
I
Figure 6. Mass flow of Hz vs time. Material: cellulose. 0.010 1 X X
x 0
0
&I2"C/min
O O
8
&53"C/IIh
0 x x
x
0
o
P
x
o x x
0
20
40
60
80
Pine sawdust
0
x
x
o Q
A A b A. A
0
0
OO:, 00
100
A
A
0
A b A
A A.
Time (min)
Figure 4. Mass flow of COz vs time. Material: cellulose.
it can be explained as a result of the thermal decomposition of the hemicellulose present in wood a t this range of temperatures (from 265 "C up to 292 "C). Table 2 shows the total gas yields obtained in dynamic experiments. Besides the C02 and H2 formation, significant amounts of CO are obtained and some CH4 formation is detected. Some examples of the evolution of the mass flow of CO2, CO, and H2 obtained in dynamic experiments with both materials are shown in Figures 4-9. The mass flow values are expressed as gram of gas per minute per gram of sample, and in all the cases these values achieve a maximum with the pyrolysis time. For a given gas and material, the maximum value decreases as the heating rate decreases. Simultaneously the diminution of the heating rate implies longer pyrolysis times for observing each maximum value. Due t o the pronounced temperature profiles existing in the sample, a rigorous analysis of these results implies the calculation and use of the corresponding local temperature and solid conversion.
. so
0.006 -
8
;
k
Pine sawdust
8
0.004 -
0
x
0 . 0 0 0 ~ " " " ' ' ~ ~ * c k . ' ' " - ~ 0 20 40 60 80
100
Tim (min)
Figure 8. Mass flow of CO vs time. Material: pine sawdust.
Kinetics of Gas Formation in the Thermal Decomposition of Cellulose The kinetics of COz, Ha, and CO formation have been calculated assuming that these products are formed from the solid through parallel primary reactions.
Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 789 0.0005
I
I
kcoz (min-l) = 2992e-12566'RT
h
M
3
kH2(min-l) = 2.7 x 106e-20663iRT
o &IZ°Chnin
o.oO04
0
20
40 60 Time (min)
80
100
Figure 9. Mass flow of Hz vs time. Material: pine sawdust.
dmCddt = k,,e
Table 3. Values of kco, and k ~ in , the Pyrolysis of Cellulose for Different Temperatures
292 299 306 314 318 322 328
0.05088 i 0.00347 0.04427 f 0.00252 0.04582 f 0.002 56 0.052 92 f 0.00273 0.064 55 i 0.004 99 0.07892 f 0.00494 0.09312 f 0.007 68
0.98625 0.99035 0.98768 0.98689 0.97663 0.98836 0.973 49
0.03615 i 0.00559 0.041 65 i 0.00154 0.05004 f 0.00226 0.06127 f 0.00379 0.076 87 i 0.00209 0.081 29 i 0.013 2
where the activation energy is expressed in caYmol. In the isothermal experiments, the CO formation was only detected at the highest temperatures and therefore its kinetic constant has been obtained from dynamic experiments carried out at low heating rates (p I 12 "C/min). The experimental data have been fitted by a differential method of data analysis:
where W Ois the initial mass of biomass and W, the mass of biomass at infinite time. A kinetic of gas formation has been proposed according to the equation: m*, - mi r . = k. ZWo-W, where ki is the kinetic constant of formation of each gas and m*i the mass of product i formed at infinite time. Therefore the equation which must be solved is dm, - m*,-mi W, - W, dt "W0 - W,
(3)
In order to determine the ki values, data corresponding to a known solid temperature must be applied. This implies the use of results obtained in isothermal experiments or in dynamic ones with low heating rates in which the temperature profiles are not significant and the use of an average solid temperature is suitable (Bilbao et al., 1993a). The kinetic constants for the COZand HZformation have been obtained from the results corresponding to isothermal experiments. Integrating eq 3, the following expression is obtained: ln(m*i - mi) = ln(m*i - mio) - kit
(7)
0.93300 0.99459 0.989 91 0.98489 0.99779 0.90463
where T is in K. The fitting of the experimental data to eq 7 has been made by means of a modification of the NewtonRaphson method (Miquel and Castells, 1986). The kinetic constant obtained was k,,
--
(m*co - mco)
where the values of m*co obtained from dynamic experiments have been assigned to the maximum temperature reached in the experiment. The variation with the temperature of m*i/Iiio can be expressed as
The rate of formation of each gas, ri, has been defined as the mass flow of product i formed (g/min) per mass of pyrolyzable biomass:
1
-EIRT
(4)
where mi0 is the amount of product i formed until the sample raises the isothermal temperature. The experimental data have been fitted t o eq 4. The values of kcoz and K H obtained ~ are shown in Table 3 for each temperature. The variation of these constants with the temperature can be expressed as:
(min-l) = 657.1e-893wRT
(9)
where the error of the preexponential factor is 34.2 and of the activation energy is 545. The R2value is 0.9867.
Modeling of the COz and H2 Formation in Dynamic Experiments in the Thermal Decomposition of Cellulose The kinetic equations of COn and HZ formation obtained with data from the isothermal experiments have been applied to determine the yield of these gases in dynamic experiments. As has been mentioned previously, increasing the heating rate causes significant temperature profiles to appear in the solid sample. Therefore it is necessary to know the solid temperature at different sample points. A mathematical model without adjustable parameters has been used to calculate, a t different points of the sample, the solid temperature, the solid conversion, and the amount of gas generated. Moreover, with the local values an average conversion and gas yield is calculated in order to be able to compare the theoretical and experimental results. The basic assumptions of the model are (i) The volume of the sample bed remains constant during the process and the sample is considered isotropic. (ii) The heat transmission in the solid bed is due to the conduction mechanism, with the thermal conductivity and heat capacity of the solid changing with its conversion. (iii) There is no mass resistance inside the bed. It is assumed that the gaseous products are released from the sample when they appear. The heat balance equation in the sample bed has been derived taking into consideration a cylindrical geometry:
790 Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995
a[~,c,(i - x)nat
Table 4. Values of the Properties of Cellulose and Sawdust Considered in the Model ~~
1 aT r ar
--
ax a2T a2T ++ - + (-AH& - (10) O at ar2 ah2
The kinetic equations of weight loss used in the model are those obtained in a thermobalance (Bilbao et al., 1987). These are first order equations and the constant values depend on the ranges of solid conversion and temperature:
T
I250
axiat
"C: = 9.5 x 1018e-53800/RT(~ - x) o.ooo6p (11)
+
250 "C < T I325 "C: axiat = 9.5 x 1018e-53800/RT (A - X)
property initial bed density eo (kg m-3) heat capacity, Cp (kcal kg-I K-l) CPO CPC
thermal conductivity, K, (kcal min-' cm-I K-l) Keo Kec heat of reaction AHH,(kcal kg-') 270 "C 4 T 5 400 "C 400 "C < 5" 5 490 "C
cellulose 172.7
sawdust 127.7
0.320a 0.260'
O.39gb 0.239d
1.016 x lo-& 8.556 x lo-& 7.446 x 10-6f 7.446 x 108.08
65.55 -80.22
a Perry and Green (1974). F'yle and Zaror (1984). Di Blasi (1993). Kansa et al. (1977). e Elvers et al. (1992). f Weast (1974).
+ 0.0023p (12)
T > 325 "C: axiat = 1.53 x 104e-13286/RT (A - X) 0.0023p (13)
+
The boundary conditions used are obtained from the experimental temperature profiles:
t = 0,O
Ih IL,
a n d 0 Ir
IR: T = TO and
aTlar = o
t>O,r=O:
=eo
(14) (15)
t > 0, r = R:
T = f(t,h)
(16)
t > 0, h = 0:
T = f(t,r)
(17)
t > 0, h = L i f p t > 0, h = L if /3
L
12 "C/min:
aT/ah = 0
(18)
12 "C/min:
T = f(t,r)
(19)
30
25
15 20 Time (min)
35
Figure 10. Experimental and calculated values of temperature at r = 0 and h = 0.2 cm a t /3 = 12 W m i n for cellulose. 500
where T = f(t,r)and T = f(t,h)summarize the heat transferred from the system to the solid. It is assumed that the thermal conductivity and the heat capacity of the solid change with its conversion according to the equations f-X x +C cp=cPoAA, PCAf
x
Af-X +K A, ,'Af
K, = Keo-
IO
5
0
(20)
&53 "Umin
100
0
(21)
where Af is the pyrolyzable weight fraction at the final temperature reached in each experiment, Xis the solid conversion at a given time. Cpo, C ,,, Keo and Ke, have been obtained from the bibliography while AHr has been determined experimentally by differential scanning calorimetry. Table 4 shows the values applied for this work. The mathematical resolution of eq 10 has been carried out through an explicit finite-differencemethod. Previously the equations were nondimensionalized and discretized by the "forward-difference''method. The solution of the equation provides temperature and solid conversion at different points of the solid. A comparison between experimental and calculated temperature at r = 0 cm and h = 0.2 cm ( 2 ' ~ has ) been made. This point has been chosen because it is the most distant from the boundary conditions and is where the validity of the model can best be tested. Some examples of this comparison are shown in Figures 10 and 11for /3 = 12 and 53 Wmin. An acceptable agreement is observed, although the experimental data are greater
1
2
3
4
5
6
7
8
9
10
I1
Time (min)
Figure 11. Experimental and calculated values of temperature at r = 0 and h = 0.2 cm a t /3 = 53 "C/min for cellulose.
that the theoretical ones, especially at a high temperature range. The local CO2 and H2 yields with time have been calculated with eq 3, using the Ki values given by eqs 5 and 6 and the local temperatures determined by eq 10. The variation of m*i with temperature has been obtained in a similar way as for CO and is expressed by:
m*co,lWo = -0.10803 m*H,/Wo= -0.008993
+ 0.0002642T + 1.682 x 10-5T
(22) (23)
where T is expressed in K. An average gas yield in the sample has been calculated using the local gas yield values and then compared with that obtained experimentally. Figures 12-17 show the results obtained for COz and Hz at different heating rates. A good agreement is observed between the theoretical and experimental results.
Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 791 0.010
0.008
1
0.002
I
0.00 0
20
I
I
#
40
l
I
I
I
l
I
~
,
I
I
loo
80
60
,
'
o.oO0
~
0
120
d o o
0
'
'
l
,
.
r
M
s
,
,
,
l
,
,
,
l
,
loo
80
,
,
I20
Time (min)
0.20 I
0.16
l
60
Time (min)
Figure 12. Experimental and calculated results of COz yield at 8, = 12 W m i n for cellulose.
-
,
40
20
Figure 15. Experimental and calculated results of H2 yield at /3 = 12 W m i n for cellulose.
I
0.010
cellulose &3 I Y h i n
-
0.12
0.008
cellulosc &31 "Umin
. 0.04
1 1 l
0
"
'
20
l
'
'
40
'
l
"
'
"
'
60 Time (min)
'
"
80
'
c
loo
120
Figure 16. Experimental and calculated results of H2 yield at /3 = 31 "C/min for cellulose. 0.010 r
0.20 0.16
so 0.12 M
.Ef
0.08 0.04
-
1
I
cellulosc k 5 3 "Umin
. cellulcse
k 5 3 aUmin
0.008
/---
0
0
11
0.00 0
1
20
,
-THEomcAL 1
1
1
40
,
I
I
I
/
,
60
I
1
80
,
I
,
I
loo
,
,
O.oO0
,
120
0
20
40
60
80
loo
120
Time (min) Time (min)
Figure 14. Experimental and calculated results of C02 yield at /3 = 53 "C/min for cellulose.
Thermal Decomposition of Pine Sawdust. Kinetics and Modeling of Gas Evolution The main constituents of lignocellulosic materials behave in different ways in their thermal decomposition. When a sample is continuously heated, the first loss of weight may be attributed to the hemicellulose decomposition. A posterior and more significant weight loss is due mainly to the cellulose, and finally a slow continuous decomposition of lignin is observed (Salazar and Connor, 1983). The idea that the thermal decomposition of a lignocellulosic material can be analyzed as a contribution of the pyrolytic properties of the individual constituents is widely employed in the literature (Alves and Figueiredo, 1988; Koufopanos et at., 1989; Bilbao et al., 1989). In this work a study of the gas formation in the thermal decomposition of pine sawdust has been per-
Figure 17. Experimental and calculated results of Hz yield at /3 = 53 " C h i n for cellulose.
formed. Pine sawdust has been chosen because the kinetic equations of its thermal decomposition have been previously determined (Bilbao et a1.,1990). Considering that cellulose is the most representative constituent of this material, the study takes the results obtained with cellulose as a basis. Moreover, for sawdust the gas formation starts at a lower temperature (265 "C) than for cellulose (292 "C), which could be due to hemicellulose decomposition. The results obtained for the largest gas evolved, COz, are shown. Two different temperature ranges have been considered. At T > 292 "C it is the cellulose decomposition which is mainly considered and its corresponding kinetic, eq 5, is used. At T < 292 "C, the kcon values would correspond to hemicellulose decomposition. These values could be calculated using some compound, such as xylan, representative of hemicellulose. However, hemicellulose is
792 Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 500
400
350
Pine sawdust k12"Umin
300 h
250
150 50
I/
0
' 0
E
300
+
31 "C/min the experimental yield is greater than the theoretical one at the final stage of the thermal decomposition. This fact may be explained by an increasing influence of the thermal decomposition of lignin as the temperature increases.
Conclusions The main conclusions obtained from the results of this work can be summarized as follows:
r
0.16
290 "C < T I400 "C: axiat = 4.99 x 107e-24208JRT (A - x)
T > 400
8
Figure 19. Experimental and calculated values of temperature at r = 0 and h = 0.2 cm at /3 = 53 W m i n for pine sawdust.
A negligible influence of the temperature on the kinetic equation has been obtained and therefore an average value of k = 0.03 min-' is considered for C02 a t T < 292 "C. A model similar to that shown for cellulose has been used to calculate the formation of the different gases in dynamic experiments performed with pine sawdust. Equation 10 has been solved. The kinetic equations of weight loss were also determined in a thermobalance (Bilbao et al., 1990):
T I290 o c :
7
Time (min)
Figure 18. Experimental and calculated values of temperature a t r = 0 and h = 0.2 cm at /3 = 12 "Clmin for pine sawdust.
m*co,lWo = -0.07563
6
-
0.04
r-**
**
I
I*-
/*
EXPERIMPFTAL.1
I-THEoRErlcAL
1
I
I
L
0.00
0
20
40
60
80
100
120
Time (min)
Figure 21. Experimental and calculated results of COz yield at = 31 "C/min for pine sawdust.
p
CO2 is the most abundant gas formed in isothermal experiments of thermal decomposition of the materials used. The COz presence is detected at lower temperatures for sawdust than for cellulose, which could be due to hemicellulose decomposition. Significant amounts of CO are also observed in dynamic experiments. The formation rate of each gas in the cellulose thermal decomposition follows first order kinetic equations. The COz formation in the sawdust decomposition can be analyzed using the kinetic constants obtained with cellulose, and extending them with the values corresponding to T < 292 "C. A mathematical model without adjustable parameters that involves the solution of the heat and mass balances and the kinetics of solid weight loss and gas formation allows us to calculate the local temperature and average gas yield obtained in dynamic experiments.
Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 793
Acknowledgment The authors express their gratitude to DGICYT for providing financial support for this work (Project PB910284) and also to Ministerio de Educaci6n y Ciencia (Spain) for a research grant awarded to M.L.S.
Nomenclature A = pyrolyzable weight fraction at a given temperature Af = pyrolyzable weight fraction at the final temperature reached in each experiment C, = specific heat capacity of the solid (kcal kg-l K-l) C,, = specific heat capacity of the char (kcal kg-l K-l) O C , = specific heat capacity of the initial solid (kcal kg-l K-1) E = activation energy (cal mol-') h = longitudinal cylindrical coordinate (cm) AHr = heat of reaction (kcal kg-l) k, = kinetic coefficient for the formation of gas i (min-') K, = thermal conductivity of the solid (kcal min-l cm-l K-l) K,, = thermal conductivity of the char (kcal min-' cm-l K-1) K,o = thermal conductivity of the initial solid (kcal min-l cm-l K-l) L = height of the sample bed (cm) m, = mass of product i formed at a given time (9) m*, = mass of product i formed at infinite time (g) m,o = mass of product i formed until the sample raises the isothermal temperature (g) r = radial cylindrical coordinate (cm) r, = formation rate of gas i (min-l) R = radius of the sample bed (cm) R2= coefficient of determination t = time (min) T = temperature ("C or K) Tu = temperature at r = 0 cm and h = 0.2 cm ("C) W O= initial mass of biomass (g) W, = mass of biomass at infinite time (g) X = solid conversion at a given time Greek Letters p = average heating rate of the sample ("Cmin-'1 e = bed density (kg m-3) eo = initial bed density (kg m-3) Literature Cited Alves, S. S.; Figueiredo, J. L. Pyrolysis Kinetics of Lignocellulosic Materials by Multistage Isothermal Thermogravimetry. J. Anal. Appl. Pyrolysis 1988, 13, 123-134. Baker, R. R. Thermal decomposition of cellulose. J. Thermal Anal. 1975,8, 163-173. Bilbao, R.; Arauzo, J.;Millera, A. Kinetics of Thermal Decomposition of Cellulose. Part 11. Temperature Differences Between Gas and Solid at High Heating Rates. Thermochim. Acta 1987,120, 133-141. Bilbao, R.; Millera, A.; Arauzo, J. Thermal Decomposition of Lignocellulosic Materials: Influence of the Chemical Composition. Thermochim. Acta 1989,143, 149-159. Bilbao, R.; Millera, A.; Arauzo, J. Kinetics of Weight Loss by Thermal Decomposition of Different Lignocellulosic Materials. Relation between the Results Obtained from Isothermal and Dynamic Experiments. Thermochim. Acta 1990,165,103-112. Bilbao, R.; Salvador, M. L.; Garcia, P.; Arauzo, J. Solid Weight Loss in the Thermal Decomposition of Cellulose and Pine Sawdust. J . Anal. Appl. Pyrolysis 1993a, 24, 257-271.
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* Abstract published in Advance ACS Abstracts, December 1, 1994.
