Ind. Eng. Chem. Res. 1993,32, 1811-1817
1811
Temperature Profiles and Weight Loss in the Thermal Decomposition of Large Spherical Wood Particles Rafael Bilbao,' Angela Millera, and Maria B. Murillo Department of Chemical and Environmental Engineering, Faculty of Science, University of Zaragoza, 50009 Zaragoza, Spain
The thermal decomposition of relatively large particles of pine wood has been studied. By use of spherical particles of different sizes (2-5.6 cm in diameter), the experimental solid conversion values and the temperature a t different points of the solid are analyzed for different heating rates of the system. T h e experimental results have been compared with those calculated with a simple model, which involves the solution of the heat and mass balances and the kinetic equations, using experimental values as boundary conditions. A good agreement has been obtained for particles up to 4 cm in diameter. For larger particles the mass transfer resistance inside the solid and the existence of secondary reactions may acquire an appreciable importance.
Introduction Knowledge of the thermal decomposition of lignocellulosic materials is important because this process allows us to obtain interesting products and it is also a previous stage to other biomass thermochemical processes such as gasification and combustion. For a given material, the product yield and quality obtained depend on the operating conditions, mainly the solid temperature and heating rate. They also depend on the chemical and physical phenomena involved in the process. In previous works, several studies with different lignocellulosic materials and their main constituents were carried out. These studies were performed in thermobalance in an inert atmosphere (nitrogen) and using small particle sizes (Bilbao et al., 1987a,b, 1989, 1990). In some reactors (moving bed, rotatory furnace) used in gasification and pyrolysis processes, larger particle sizes are processed (Carre et al., 1983; Bridgwater et al., 1990). In these cases, heat and mass transfer resistances may appear. Significant temperature profiles can be produced inside the solid which influence the solid conversion and the amount and composition of the products obtained. Since the first work of Bamford et al. (1946), several models have been proposed for the thermal decomposition of these materials. Most of them (Pyle and Zaror, 1984; Capart et al., 1985; Villermaux et al., 1986; Koufopanos et al., 1991)include the inner conduction mechanism and the kinetic equations. Other models (Chan et al., 1985; Alves and Figueiredo, 1989) incorporate the convection heat transfer inside the solid. The diffusion of volatiles inside the solid in several directions is included in other works (Antal, 1985; Fan et al., 1978). Kansaet al. (1977)incorporated the momentum equation for the motion of pyrolysis gas within the solid and the influence of the physical structure on these phenomena. In order to check several of these models, some experimental temperature results using cylindrical particles are reported in the literature (Havenset al., 1972; Belleville et al., 1984; Chan et al., 1985;Koufopanos et al., 1991). The aim of this work is the study of the influence of the particle size on the thermal decomposition of wood for different heating rates of the system. This study has been carried out from both the experimental and the theoretical point of view. To whom correspondence should be addressed.
1.- Rucm
2.- Slmplc
4.- Thamocouples
5.- FumKe c4ntrdlcr 6.- DRII looea 7.- BJucc 8.- ~ ~ ~ ~ l o v l m ~ s r 10.- crmpulu
Figure 1. Experimental system.
Spherical particles were chosen to obtain the experimental results, being a different geometrical shape to the particles used in other works. This geometry allows us to study particles of relatively large diameter and it also allows us to establish and solve the equations in given geometric coordinates. The conclusions attained could be applied to other geometries taking into account the corresponding coordinates and boundary conditions. For this study, an experimental system has been used that enabled us to obtain the temperature profiles inside and outside the particle and the weight loss of the solid during its pyrolysis. The theoretical study has been realized using a simple mathematical model, which predicts the results of local conversion and temperature. From the local conversion values, the global solid conversion has been calculated.
Experimental Method The experimental system, Figure 1, consists of a cylindrical reactor of 8 cm in diameter discontinuous for the solid, an electrical furnace connected to a temperature and heating rate control system, and a data logger which allows us to join up 20 thermocouples, and which provides data for every 5 s. This experimental device allows measurement of the weight loss of the solid during its thermal decomposition by means of a precision balance connected to the sample support inside the reactor. Experiments from 30 up to 650"Cwith different heating rates of the system (B = 12,5, and 2 OC/min) have been performed. Once 650 OC is reached, the system remains at this temperature for 12 min. Nitrogen has been used as an inert gas with a flow rate of 15 cm3/s. The particle was placed in the reactor at a depth of between 12 and 18
0888-5885/93/2632-1811$04.00/00 1993 American Chemical Society
1812 Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993
I
t
Nz
(P
-0
10
20
30 t
40
(min)
50
60
70
Figure 3. Angular temperature profiles on the solid surface for D = 5.6 cm and @ = 12 OC/min.
1W
Figure 2. Points where the thermocouples are located.
cm. In a previous work (Bilbao et al., 1992a) a complete study of the temperature profiles inside the empty reactor was carried out, and it was concluded that with these values of flow rate and depth of sample position, the angular and longitudinal temperature profiles existing inside the reactor are eliminated and only radial temperature profiles remain in the reactor. Pine wood spheres of D = 2,3,4, and 5.6 cm have been used. These spheres were made by a numerical control lathe with an accuracy of kO.1 mm. Two types of experiments have been performed: (i) Experiments to obtain the temperature profiles inside the solid and on its surface. Thermocouples of 0.5 mm diameter were placed a t several points in the solid, correspondingto different values of particle reduced radius (r/R = 0,0.47,0.83, and 1.0) and of the angle 8 (0, 45, 90, 135,and 180°),Figure 2. It is important to point out that, for the particle sizes used in this work, these values of 8 correspond to different reactor radii. (ii) Experiments to obtain the solid weight loss versus the time for different particle sizes and heating rates of the system.
Results and Discussion The experimental results have shown the existence of significant angular and radial temperature profiles in the solid and these profiles depend on the particle size and on the heating rate of the system. In the range 8 = 0-90", the temperature on the solid surface increases when 6 increases. This fact can be explained because the points correspond to different reactor radii (the radius value increases as 6 does) and by the influence of the deviation in the gas flow direction. In the range 8 = 90-180°, both effects tend to compensate each other and similar temperatures are obtained at different 8 values (Bilbao et al., 1992b). As an example, Figure 3 shows the results obtained for D = 5.6 cm and @ = 12 "C/min. These angular temperature profiles on the solid surface are less pronounced as the heating rate and particle size decrease. Moreover, for the smallest particle size, the temperature increases from 8 = 0" up to 6 = 180". Angular temperature profiles also exist inside the solid. These profiles follow the same trends as those explained for the solid surface, but they are less significant toward the particle center. The heat transfer mechanisms in the solid together with the heat generated or consumed during the thermal
,
I-
"0
10
20
30
40
50
60
70
t (min)
Figure 4. Radial temperature profiles inside the solid at B = OD, D = 5.6 cm, and @ = 12 OC/min.
"0
10
20
30
40
t (min)
50
60
70
Figure 5. Radial temperature profiles inside the solid a t B = MOD, D = 5.6 cm, and @ = 12 OC/min.
decomposition of the material cause the existence of different radial temperature profiles inside the particle. Owing to the angular temperature profiles on the solid surface, the radial temperature profiles depend on the 8 value. Figures 4 and 5 show the results obtained for D = 5.6 cm, @ = 12 "C/min, and two different 8 values. It can be observed that the temperature decreases as the radius does. It is important to note that at the inner points, especially at r/R = 0.0, a plateau appears at 100 "C in the temperature profile, the temperature remaining at this value for a certain time. During this time, the solid conversion is still low; therefore the influence of the heat of the reaction is insignificant. In these circumstances, the predominant heat transfer mechanism inside the solid would be conduction, and this cannot explain the plateau and the steep radial temperature profiles existing a t this time. For this reason, this period may correspond to the elimination of the moisture, which requires a determinate amount of the heat flow directed toward the interior of the solid. At the end of the plateau, there is a sudden increase of the temperature at the inner points. This may be due not only to the conduction heat transfer caused by the high temperature differences (-250 to 300 "C) in the solid but also to hot gas flow from the exterior to the interior of the particle, since, while the inner points, rlR = 0.0 remain at 100 "C, the outer points achieve high temperatures, and their conversions are high. The particle porosity becomes greater and therefore the hot gas could flow into the solid, contributing to its increase in temperature.
Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993 1813 Figures 4 and 5 also show a sharp increase of the slope of the temperature versus time near the end of the heating. This fact is especially noticeable at rlR = 0, and is less steep a t r/R = 0.47, and is probably due to both the exothermic decomposition of the lignin which prevails at high conversions and, mainly, the breakdown of the wood structure. For 8 = 0" and long reaction times, an inversion in the radial temperature profiles is observed, Figure 4, now the temperature is higher as the value of r / R decreases. It is important to notice that this fact happens when the conversion is total in the outer zones and high at the inner points. This fact was observed by other authors (Belleville et al., 1984; Koufopanos et al., 1991). This inversion may be explained mainly by the heat transfer mechanisms, since the points with high values of 19 have higher temperatures and this contributes to the rise in temperature a t the inner points. The exothermic heat generated during the lignin thermal decomposition also contributes to this effect, since this exothermic process occurs at the inner points when the outer have already been converted. For t9 = 180°, Figure 5 shows that the inversion does not happen but an important reduction of the radial temperature profiles is produced. In general, the experimental results of radial temperature profiles show that for t9 I90" the inversion occurs and for t9 2 90" only a reduction of the radial temperature profiles is observed. The experimental results also show that as the heating rate decreases, the same trends are observed but are less pronounced. The plateau at 100 "C becomes practically inestimable for /3 = 2 OC/min. The sudden increase of the temperature at the inner points, at the end of the plateau, appears also for lower values of 0 but is now less noticeable. The temperature differences in the solid are lower. Likewise,the sharp increase of the slope of the temperature versus time near the end of the heating is now practically inappreciable for /3 = 2 "C/min. The inversion and the reduction of the radial temperature profiles, for t9 I90" and t9 1 90°, respectively, are also observed for /3 = 5 and 2 "C/min. For the three values of /3 studied, the difference in these facts is the temperature at which the inversion or reduction starts. This temperature is lower as /3 decreases. The radial temperature profiles in the solid also depend on the particle size. On the one hand, the temperature on the solid surface is different for each particle size. On the other hand, as the solid size decreases, smaller heat transfer resistance exists in the solid, which causes higher temperatures in the particle center. It is important to note that the influence of the particle size becomes less significant as the heating rate decreases. In general, the results obtained with solids of smaller particle size show the same trends as those explained above for D = 5.6 cm, although they are less pronounced. For t9 = 0" a light inversion in the radial temperature profiles is also noted, but it is less steep as the particle size decreases. Moreover, this inversion happens at shorter reaction times than in the case of D = 5.6 cm. Likewise the plateau at 100 "C is practically inestimable for the lowest particle sizes studied. So, the influence of the particle size on the radial temperature profiles is clear: these profiles become lower as the particle size decreases, being insignificant for D = 2 cm. To summarize the influence of the particle size, heating rate, and the value of the angle 8 on the radial temperature profiles, the highest temperature differences between the surface and the center of the particle can be used. The values obtained are shown in Table I. I t can be observed
""
1
6 = 12 "C/min
0.8
"'"0
10
20
30
40
t (min)
50
60
70
Figure 6. Experimental solid conversion obtained for different particle sizes. Table I. Highest Temperature Differences between r / R = 1.0 and r / R = 0.0 temperature differences, "C @,OC/min 8,deg 5.6cm 4cm 3cm 2cm 12 0 250 120 95 50 45 290 150 100 60 90 330 190 140 60 135 330 220 150 IO 180 350 240 170 80 5 0 95 60 40 30 45 110 70 40 30 90 175 85 45 30 135 185 100 60 35 180 190 110 75 40 2 0 15 50 30 10 10 45 75 45 30 90 100 50 30 10 135 100 55 30 10 180 110 60 45 10
that for a given heating rate and angle, as the particle size increases these temperature differences also increase. On the other hand, for a given 0 and particle size the temperature differences are higher as the heating rate increases. The influence of the value of the angle, 8, is such that the temperature differences between r / R = 0.0 and r/R = 1.0 increase with 8. The analysis of the experimental results has also shown that the inversion in the radial temperature profile appears at lower temperatures as the heating rate and particle size decrease. For example in the case of 0 = 5 and 2 "C/min the solid conversion at which inversion happens is about 0.1. This fact strengthens the previous supposition that the inversion is caused mainly by the angular temperature profiles on the solid surface and that the heat transmission is by a conduction mechanism. Referring to the sudden increase in the temperature profile, this fact appears at high conversion and temperatures in which the exothermic decomposition of the lignin is already significant and can contribute to this temperature increase. This effect is practically inestimable in the case of 0 = 2 "C/min. For a given heating rate, the existence of radial and angular temperature profiles causes the solid conversion, XM,obtained at a given time to be lower as the particle size increases. The case of 0 = 12 "C/min is presented in Figure 6. The same trend appears for lower heating rates but as /3 decreases the influence of the particle size does too, as can be observed for the case of /3 = 2 "C/min, Figure 7.
Mathematical Model A mathematical model of the thermal decomposition of a spherical pine wood particle has been used to calculate the temperature and solid conversion a t different points of the particle. Moreover, with the local solid conversion results, an average global conversion of the solid is
1814 Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993
(4)
u,u---
0
50
103
lS0
200
I-?_\
250
300
where Mg and M, represent the mass flux of volatiles and steam, respectively, and H is the moisture fraction of the solid, in dry basis of the solid. The boundary conditions used to solve the equations of the model are 350
t=0,
O 5 "C/min (dX$dt), = &(A, - X,)
+ O.O043(j3, - 5) (11)
T > 290 "C, j3 I5 "C/min
(dX6/dt), = k,(A, - X,) (12) X,being the local solid conversion in dry basis, without considering the sample moisture. These equations are applied at each point of the solid. At each point the heating rate, pi, can be different from that of the system, 8. The value of & is calculated for each time from the consecutive values of the local temperatures obtained. The kinetic constants are
T 5 290 "C
k,(min-') = 0.017
(13)
Ind. Eng. Chem. Res., Vol. 32, No. 9,1993 1815 290 < T 5 400 "C k,(min-') = 4.987 X
lo' exp(-24208/RT)
(14)
T>400OC k,(min-') = 0.68 (15) The A, values were shown in another paper (Bilbao et al., 1991). (2) The reaction heat has been measured experimentally by means of DSC, obtaining two stages: An endothermic stage which correspond mainly to the thermal decomposition of cellulose
AHr = 274 kJ/kg X,5 0.6 An exothermic stage corresponding mainly to the thermal decomposition of lignin
AHr = -353 kJIkg
X, > 0.6
The endothermic effect of the moisture release is taken into account considering that when a point in the solid reaches a temperature of 100 f 5 "C all the heat flow that arrives at this point is used for the evaporation of water, until this has been completely eliminated. (3) The thermal conductivities of the wood and of the char have been measured experimentally. With these two values a correlation in function of the solid conversion has been made K, = Ko(1.0 - 0.44XJ (16) where KOis the initial thermal conductivity of the wood, 6.18 X 10-6 kJ cm-' min-l K-1. Equation 16 is applied in each point of the solid using the local conversion. The heat capacity value has been obtained from those corresponding to wood and char (Pyle and Zaror, 1984). A linear variation with the solid conversion has been assumed, using the equation
C, = 1.67(1.0 - 0.53XS)
(17) The solid density in each point of the solid changes as a function of the solid conversion according to = Po(1 - X,) (18) where the initial density of the wood was also measured experimentally obtaining a value of 500 kg/m3. (4) The initial distribution of the moisture is the only parameter that has been calculated to fit, in the case of a heating rate of /3 = 12 OCImin, with the model for the four particle sizes studied in this work. These values thus determined were used to solve the equations of the model for other heatingrates /3 = 5 and 2 OC/min. The theoretical results obtained were contrasted with the experimental ones and they agree for the stage of the plateau a t 100 "C. The mathematical model consists of a series of parabolic equations in nonlineal partial derivatives. The resolution of these equations has been carried out through an explicit finite-difference method, by means of a FORTRAN language program. The resolution of the equations provides temperature and conversion at different points of the solid. With these local conversion values an averaged global solid conversion has been determined, X,M. P
Experimental Verification of the Model The results of local temperature and global solid conversion calculated with the model have been compared with those obtained experimentally. Previously, the validity of different assumptions of the model was analyzed.
2O0
t +
-0
10
20
30 t
40
50
Theo. 1 Theo.2
60
70
(min)
Figure 8. Comparison between the experimental results and those theoretically calculated without and with the convection term, theoretical 1 and 2, respectively. With respect to the particle volume, previous experiments were carried out with the different particle sizes and were stopped at different temperatures and solid conversions. An appreciable particle shrinkage was only observed a t high solid conversions. In addition, in other studies including the particle shrinkage (Pyle and Zaror, 19841, a variation of the overall numerical solution by less than 3% was obtained with this modification. So, a constant particle volume was used during the process. The applicability of the kinetic equations obtained in thermobalance to the experimental system used in the present work has been checked by comparing the experimental values of conversion obtained in this system with those calculated from the kinetics equations, in the case of the lowest particle size used, D = 2 cm, for which the temperature profiles in the solid are inestimable (Bilbao et al., 1991). A good agreement between the results was obtained. It was concluded that the equations could be applied using the true temperature of the solid. The assumption that volatiles are in thermal equilibrium with the solid and that they are eliminated in the radial direction toward the solid surface just after they have been generated is questionable. This simplification has been used in similar cases (Chan et al., 1985) with cylindrical particles laterally isolated in which the heat flow is longitudinal, coinciding this direction with the wood fiber direction. For the analysis of this assumption, the experimental temperatures have been compared with those obtained theoretically with the model both using and not using the above mentioned term of convectioninside the solid. Figure 8 shows this comparison of temperatures at rlR = 0.0 for a particle of D = 5.6 cm and a heating rate of p = 12 "Clmin. I t can be observed that the temperatures obtained without considering the convection term, theoretical 1in Figure 8, show a good agreement with the experimental results. When this term is considered, theoretical 2 in Figure 8, the temperatures predicted show lower values than those obtained experimentally, especially when a significant weight loss is produced. This delay in the temperature could be due to the assumption that the volatiles formed leave the particle instantaneously, which overestimates the heat loss. On the other hand, the consideration that volatiles only flow radially toward the solid surface and without diffusional resistance is also questionable. Due to its anisotropy, preferential paths for volatiles to escape may exist in the wood and pressure gradients, which could force the gas products toward the particle center, may appear inside the solid. Therefore it is difficult to establish the true paths that the generated volatiles follow. Taking into account these difficulties and the results obtained, it has not been considered appropriate to include the assumption of the convective heat transfer of the volatiles.
1816 Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993 B = 12ochni
9 -Theoretical 0'
10
20
30
40
t (min)
50
60
"0
70
Figure 9. Comparison between the theoretical and experimental results of temperature.
20
I
0.6 XSM
0.4
1
-Theoretical 20
t (min)
0.2 50
100
150 200 t (min)
250
300
350
30 40 t (min)
50
60
70
Figure 13. Comparison between the theoretical and experimental results of solid conversion. LO[
0
70
B 10
Figure 10. Comparison between the theoretical and experimental results of temperature.
60
50
1
I-Theoretical I
100
v
30 40 t (min)
Figure 12. Comparison between the theoretical and experimental results of temperature.
I
t
10
O,O*
1
B = 5"c/min
1
20
40
'
60 80 t (min) '
I] '
loo '
'
120 ' . 140
Figure 11. Comparison between the theoretical and experimental results of temperature.
Figure 14. Comparison between the theoretical and experimental results of solid conversion.
The influence of the angular temperature profiles on the solid surface has been also analyzed. The model equations were solved in several hypothetical cases in which the temperature on the solid surface was considered homogeneous. These results were compared with those obtained using the temperatures on the solid surface obtained experimentally. An important result of this study is that by use of a homogeneous temperature on the solid surface, inversion in the radial temperature profiles does not appear. From this result and from the comparison with other experimental results, it was concluded that for boundary conditions it is necessaryto use the temperature on the solid surface obtained experimentally, which depends on the 0 values. Using these temperatures, and once the term of the convection heat transmission of the volatiles has been eliminated, the model equations have been solved and the temperature and solid conversion calculated have been compared with the experimental ones. With respect to the temperatures corresponding to different points, in general a good agreement between the experimental and the theoretical ones was obtained. Figures 9-11 show several examples. Only in some cases, which correspond to high particle size and heating rates, are some differences observed. An example is shown in Figure 12, for D = 5.6 cm, B = 12 OC/min, rlR = 0.47, and two 0 values (0 and MOO). It can be observed that the theoretical values are slightly lower than the experimental ones. This small disagreement could be due to the fact that the mass transfer resistance is significant in big particles and, therefore, the residence time of the volatiles
in the inner part of the solid could be long enough to start secondary reactions between such volatiles and char. Most of these secondary reactions are exothermic and imply an extra energy contribution to the solid which the model does not take into account. On the other hand, the structural change of wood during pyrolysis causes an increase of the porosity which could originate several paths to the convective flow of the volatiles and even the inlet of the outer hotter inert gas through possible fissures or cracks. The results of solid conversion have also shown a good agreement between the values predicted by the model and those obtained experimentally, in the cases of D = 2, 3, and 4 cm. An example is shown in Figure 13. However the results predicted for the largest particle size, D = 5.6 cm, Figure 14,are higher than those obtained experimentally. The reason for this difference can be found in the kinetic model, since the model does not take into account the possibility of secondary reactions between volatiles and char, which are promoted in situations of high diffusional resistance. This is the case for big particle sizes, in which the volatile8 are not released from the particle just after they appear, and therefore the weight loss does not occur at the same time as the reaction. This effect is less pronounced as the particle size decreases.
Conclusions The main conclusions obtained from the results of this work can be summarized as follows:
Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993 1817
A simple model can be applied to study some aspects of the thermal decomposition of relatively large wood particles in which significant radial and angular temperature profiles appear. When a convective heat transfer in the solid due to the volatiles is used, the temperatures predicted show lower values than those obtained experimentally, especiallywhen a significant weight loss is produced. In general, the local temperatures predicted show a good agreement with the experimental ones, and only in some cases which correspond to the highest particle size and heating rate used are some differences observed. The results of global solid conversion predicted show a good agreement with the experimental ones up to a diameter of 4 cm. For larger particles, the values calculated are higher than those obtained experimentally. For particles larger than 4 cm, mass transfer resistance can appear inside the solid, in which case' it would be necessary to consider secondary reactions.
Acknowledgment The authors express their gratitude to DGICYT for providing financial support for this work (Project PB88-0388)and also to Ministerio de Educaci6n y Ciencia (Spain) for a research grant awarded to M. B. Murillo.
Nomenclature A, = pyrolyzable weight fraction at a given temperature, dry basis C, = specific heat capacity of the solid (kJ k g l K-l) ,C, = specific heat capacity of volatiles (kJ k g l K-1) ,C, = specific heat capacity of the steam (kJ k g l K-1) D = particle diameter (cm) H = solid moisture fraction, dry basis HO= initial solid moisture fraction, dry basis AHr = heat of reaction (kJ k g l ) k, = kinetic coefficientfor thermal decompositionof the solid (min-1) K,= effectivethermal conductivity of the solid (kJ cm-l min-l K-1) KO= initial thermal conductivity of the solid (kJ cm-1 min-1 K-1) M, = mass flux of volatiles (kg cm-2 min-1) M, = mass flux of steam (kg cm-2 min-1) r = radial spherical coordinate rA = reaction rate of the thermal decomposition (kg cm-3 min-1) rlR = reduced radius R = radius of the solid particle (cm) t = time (min) T = temperature ("C) T,= temperature on the solid surface ("C) X M = experimental solid conversion X , = local solid conversion, dry basis X,M = mean solid conversion, dry basis Greek Letters /3 = heating rate of the system ("C min-') /3i = local heating rate ("C min-1) r#~ = angular spherical coordinate 0 = angular spherical coordinate p = density of the solid, dry basis (kg cm-3) PO = initial density of the solid, dry basis (kg cm-3)
Literature Cited Alves, S. S.; Figueiredo, J. L. A model for pyrolysis of wet wood. Chem. Eng. Sci. 1989,44 (12),2861-2869. Antal, M. J., Jr. Mathematical modelling of biomass pyrolysis phenomena. Fuel 1985,64,1483-1486. Bamford, C. H.; Crank, J.; Malan, D. H. The combustion of wood. Part I. Proc. Cambridge Philos. SOC.1946,166-182. Belleville, P.; Capart, R.; GBlus, M. Pyrolysis of large wood samples. Appl. Energy 1984,16,223-237. Bilbao, R.; Arauzo, J.; Millera, A. Kinetics of thermal decomposition of cellulose. Part I. Influence of experimental conditions. Thermochim. Acta 19878,120,121-131. 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 1987b,120,133141. Bilbao, R.; Millera, A.; Arauzo, J. Kinetics of weight loss by thermal decomposition of xylan and lignin. Influence of experimental conditions. Thermochim. Acta 1989,143,137-148. 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.; Murillo, M. B.; Millera, A.; Mastral, J. F. Thermal decomposition of lignocellulosic materials: comparison of the results obtained in different experimental svstems. Thermochirn. Acta 1991,190,163-173. Bilbao, R.; Murillo, M. B.; Millera, A.; Arauzo, J.; Caleya, J. M. Thermal decomposition of a wood particle. Temperature profiles on the solid surjace. Thermochim. Acta 1992a; 197,431-442. Bilbao, R.; Murillo, M. B.; Millera, A. Angular and radial temperature profiles in the thermaldecomposition of wood. Thermochim.Acta 1992b,200,401-411. Bridgwater, A. V.; Maniatis, K.; Masson, H.A. Gasification Technology. Commercial and Marketing Aspects of Gasifiers; Commission of the European Communities: Luxembourg, 1990; pp 41-65. Capart, R.; Fagbemi, L.; GBlus,M. Wood pyrolysis: a model including thermal effect of the reaction. Energy from Biomass; Palz, W., Coombs, J., Hall,D. O., Eds.; Elsevier Applied Science: London, 3rd E.C. Conference, 1985;pp 842-846. Carre, J.; Hebert, J.; Lacrose,L.; Van Roosbroeck,W. Critical analysis of the methods for upgrading ligneous raw materials into useful fuels by means of dry processes; Vol. 11. Commission of the European Communities: Brussels, 1983;pp 38-69. Chan, W. C. R.; Kelbon, M.; Krieger, B. Modelling and experimental verification of physical and chemical processes during pyrolysis of a large biomass particle. Fuel 1985,64 (ll),1505-1513. Fan, L. S.; Fan, L. T.; Tojo, K.; Walawender, W. P. Volume reaction model for pyrolysis of a single solid particle accompanied by a complex reaction. Can. J. Chem. Eng. 1978,56,603-609. Havens, J. A.; Hashemi, H. T.; Brown, L. E.; Welker, J. R. A mathematical model of the thermal decomposition of wood. Combust. Sci. Technol. 1972,5,91-98. Kansa, E. J.; Perlee, H. E.; Chaiken, R. F. Mathematical model of wood pyrolysis including internal forced convection. Combust. Flame 1977,29,311-324. Koufopanos, C. A.; Papayannakos, N.; Maschio, G.; Lucchesi, A. Modellingof the pyrolysisof biomass particles. Studies on kinetics, thermal and heat transfer effects. Can. J. Chem. Eng. 1991,69, 907-915. Pyle, D. L.;Zaror, C. A. Heat transfer and kinetics in the low temperature pyrolysis of solids. Chem. Eng. Sci. 1984,39 (l), 147-158. Villermaux, J.; Antoine, B.; Lede, J.; Soulignac, F. A new model for thermal volatilization of solid particles undergoing fast pyrolysis. Chem. Eng. Sci. 1986,41,151-157. Received for review January 7, 1993 Revised manuscript received April 29, 1993 Accepted May 13,1993
