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  Chemrcol Engineering Science, Vol. 44, No. 12, pp. 2861b2869, 1989. 000%2509/89 %3.00+0.00 Printed in Great Britain. 0 1989 Pergamon Press plc A MODEL FOR PYROLYSIS OF WET WOOD S. S. ALVES and J. L. FIGUEIREDO’ Centro de. Engenharia Quimica, Faculdade de Engenharia, 4099 Porte, Portugal (First received 22 December 1988; accepted in revised,form 28 April 1989) Abstract-A mathematical model of the pyrolysis of wet particles of wood is presented. The model integrates: (i) a conventional description of the physical and chemical phenomena involved in the pyrolysis pf dry particles of wood, and (ii) a simplified drying model. The dry-pyrolysis model assumes a complex reaction scheme independently determined. The most important parameters were experimentally measured, including the thermal conductivities and all the kinetic parameters; other parameters were taken as average values from the literature. The drying model neglects bound-water diffusion, air/vapour diffusion and pressure gradients inside the solid. Free-water movement is not described. Drying is therefore controlled by heat supply. These assumptions restrict the model validity range to: (a) temperatures higher than 15O”C, (b) initial moisture content below the free-water continuity point (-45%), and (c) sample dimension in the wood longitudinal direction not much greater than the dimensions in the transversa1 directions. The combined wet pyrolysis model has been experimentally validated in the simulation of: (i) drying of pine wood cylinders of variable diameter above 15O”C, and (ii) pyrolysis of dry and wet cylinders of pine wood of variable diameter between 300 and 800°C. No parameter optimization was required. INTRODUCTION Pyrolysis of a big particle of wood is a complex phenomenon,’ even if the particle is dry. It involves heat transfer to and through the particle, chemical reactions within the particle, and escape of volatiles through and from the particle. If the particle is wet, as it is initially in most cases of interest to industry, the whole process is delayed. Additional heat must be supplied for water evapor- ation, before pyrolysis temperatures are reached. Drying and pyrolysis may occur simultaneously in different regions of the same particle and cannot therefore be separately modelled. The rate of drying depends on water movement (free water, bound water and water vapour) by several mechanisms. Several pyrolysis models have been proposed for dry wood particles, either related to fire research (Bamford et al., 1945; Panton and Rittman, 1971; Kung, 1972, 1973; Maa and Bailie, 1973; Fan et al., 1977; Kansa et al., 1977) or, more recently, to pyro- lysis/gasification/fuel combustion studies (Pyle and Zaror, 1984; Chan et al., 1985; Miller and Ramohalli, 1986; Villermaux et al., 1986; Hemati and Laguerie, 1987). Most of these models are developments of the classical work of Bamford et al. (1945). Some models assume a reaction scheme with more than one reac- tion, but few include independent measurement of kinetic parameters, which are either taken from the literature or optimized. Most models are for dry particle pyrolysis alone. Only the model by Chan et al. (1985) includes some treatment of drying, which is described as an additional chemical reaction; no simu- lation results of wet pyrolysis are presented. A wet particle pyrolysis model would be of the utmost interest for the modelling of equipment for + Author to whom correspondence should be addressed. wood pyrolysis/gasification and for wood burning, since most such processes start out with wet raw material. In this work such a model is attempted. The most important parameters are independently meas- ured, including thermal conductivities and all of the reaction kinetic parameters. The model is able to predict temperature profiles and weight loss in wet wood particles of variable geometry subjected to high temperatures in an inert atmosphere. MODEL DESCRIPTION When a big particle of wet wood is subjected to external high temperatures, a very complex chain of events is started, most of which may occur simulta- neously: (i) heat is conducted inwards; (ii) the particle begins to dry, more intensely at the outer boundary, where the temperature is higher: (iii) bound and free water move outwards by diffusion and capilarity; (iv) water vapour moves by convection and diffusion (most of it moves outwards, but there may be some migration towards the inner, colder parts of the solid, where recondensation will occur); (v) pyrolysis starts to be important as the temperature approaches 250°C (it starts therefore at the outer particle surface, and moves inwards as the inner zones of the solid heat up); (vi) volatiles resulting from pyrolysis move outwards, mostly by convection; and (vii) additional phenomena occur, such as shrinking and fissuring. A mathematical description of these phenomena inevitably involves assumptions and simplifications, which are next described. Model assumptions The model is unidimensional. It is applicable to spheres, infinite cylinders and infinite slabs, depending on the geometric parameter I (= 0, 1 and 2, respect- ively). fi can take intermediate values and hence some treatment of irregular shapes may be possible. The 2861  2862 S. S. LVE~ and J. L. FIGUEIREDO initial solid is homogeneous. The solid volume is assumed constant throughout drying and pyrolysis. Heat is transferred to the solid external boundary by convection and radiation. Within the solid, heat accumulation is due to conduction through the solid, convection of volatile gases and water vapour, chemi- cal reaction and water evaporation. Escaping volatiles and water vapour are assumed to be in thermal equilibrium with the solid matrix. The drying rate is controlled by heat supply and vapour-liquid equilibrium alone. This is a conse- quence of several assumptions_ Bound-water move- ment is shown in the Appendix to be negligible. Free- water movement, on the other hand, is shown to be sometimes significant; by not describing it, the model validity range is reduced to moisture contents below free-water continutiy. Water vapour/carrier gas dif- fusion is assumed to be much slower than vapour convection, which reduces model validity to high- temperature drying (above the water boiling temper- ature), as is the case in the pyrolysis of wet particles. Solid permeability is assumed sufficiently high for the pressure gradients inside the particle to be negli- gible. Hence, the pressure is assumed to be constant throughout, and equal to the external pressure. As discussed in the Appendix, this is only valid if the particle longitudinal direction is not much bigger than the transversal directions. There is a local moisture-vapour equilibrium. The vapour pressure depression is treated as a rise in the “moisture boiling point”. The moisture boiling point in wood, Tb, may be defined as the temperature at which moisture is in equilibrium with water vapour at atmospheric pressure. The equilibrium moisture con- tents of wood, X,, are given in Kent et al (1981) as a function of temperature T (above 100°C), at atmos- pheric pressure, in an atmosphere of superheated steam. These results may be understood as X, =f(T) or as T, = g(X); they were correlated by a third-degree polynomial: Tb = 1/(2.130x lo-‘+2.778 x lo-“ ln(%X) +9.997 x lop6 [ln (%X)lz-- 1.461 x 10e5[ln (“/OX)]‘) (1) with Tb in K, and where %X is the percentage moisture content (dry basis). Equation (1) is only valid interface--a for %X < 14.4%. For %X > 14.4%, it can be as- sumed that Tb (X) = lOO”C, with negligible discon- tinuity and error. The drying/moisture movement assumptions above define three zones in the drying-pyrolysing solid. These can be visualized in Fig. 1. In zone C, near the centre of the particle, the temperature has not reached T,,(X) yet. Since air/vapour diffusion is negligible, and there is no free- or bound-water movement, moisture content is constant here: there is no drying in region C. The solid temperature is determined by heat balance. In zone B, the temperature reached T,(X). There is water-vapour equilibrium and the solid temperature is determined by it [eq. (l)]. In this region the heat balance determines not the temperature, but the amount evaporated. In zone A, near the heated bound- ary, the solid is completely dry and the temperature is above Tb (for any value of X). There is no water-vapour equilibrium in this region, hence the solid temperature is again determined by the heat balance. In this region, the temperature may be high enough for pyrolysis to significantly occur. At any point in a particle, pyrolysis reactions and reaction kinetics are assumed not to depend on the previous drying history. The reaction scheme assumed and corresponding kinetics were experimentally deter- mined (Alves and Figueiredo, 1988) for very small samples of dry pine wood sawdust, with negligible internal temperature gradients. Six independent reac- tions were identified: S ,:Gt s ,,:Gt S ,AGt S “4 fGt S ,:Gt S .f GT where SVi is the volatile part of component i of wood. interface-- I I LOrIB? ’ ” <-___---___ x = 0 --_-----_->,<___, = Tb _-_>I<_-_____-___ , < Tb __________-____>] ;____________________________~_____________________________~i I I I TbtXl I <--- vapour convcciion I I without resistance I I , I I Evaporation I I is function 1 1 of available I heat f ____________________----__---- -----__----__-- X= constant ._________. I I I I *w Heated bcwndar; heat trP”sfr, ----- -____-- -_- __-________ -___- _______ -_a SymmAry axis or ptanr Fig. 1. Consequences of assumptions on high-temperature drying model.  A model for pyrolysis of wet wood 2863 Table 1. Value of chemical reaction parameters used in the model Enthalpy of Activation energy Pre-exponential reaction Component Mass fraction Ei factor, koi i mi (kJ/mol) (s-l) (k$g) 1 0.19 83 0.70 x 105 -233 2 0.50 146 0.20 X 1 ’ 322 3 0.02 77 0.43 X 104 -233 4 0.03 60 0.29 x 10’ -233 5 0.02 139 0.51 x 10’ -233 6 0.02 130 0.32 x 106 -233 Components are numbered in order of increasing thermal stability. Component 1 is thought to corres- pond mostly to hemicelluloses, component 2 is mostly cellulose, while the higher components correspond mainly to parts of the lignin macromolecule (or stages in its degradation). The mass fractions of these com- ponents were experimentally determined by Alves and Figueiredo (1988) for the pine wood sawdust and reactions l&6 were found to be approximately first- order. Experimental activation energies and pre-expo- nential factors obtained with pine wood sawdust are given in Table 1, and were used in the simulations. An error may be involved in using data obtained with sawdust to model the pyrolysis of bigger par- ticles: the extent of secondary reactions is certainly different. This is reflected in the volatile fraction of the various components and the corresponding char yield. The initial mass fraction, mi, of these components has accordingly been slightly adjusted from the data in Alves and Figueiredo (1988) by making m,(big particle) = m,(sawdust) water (kJ/kg K), C,, is the specific heat of water vapour (kJ/kg K), H,i is the enthalpy of pyrolysis of component i at 0°C (kJ/kg), H, is the wood moisture vaporization enthalpy (kJ/kg), k is the solid thermal conductivity (kW/m K), M, is the mass flux of the volatile pyrolysis products (kg/m2 s), M, is the mass flux of water vapour due to drying (kg/m2 s), r is the linear dimension in the direction of heat and mass transfer (m), rci is the rate of reaction of component i (kg/m3 s), rev is the evaporation rate (kg/m3 s), t is time (s), Tis the solid temperature (K), Vis the solid volume (m3), X is the solid moisture content (dry basis), pS is the dry solid density (kg/m3), and pr is the water density (kg/m3). Moisture-vapour equilibrium: T = T*(X) rev = 0 (zone B’) (zones A’ and C’) (4) (5) with Tb(X) given by eq. (1) above. Chemical reactions: 1 -(char yield of big particle at 8OOC) x d i 1 -(char yield of sawdust at 8OOC) _ = rci = pikoi exp( -E,/R,T) at (6) 0.78 = m,(sawdust) x __ 0.82. (2) for i = 1, . . . , 6 where Ei is the activation energy (kJ/kmol), k,i is the pre-exponential factor (s-r), rci is The mass fraction of a seventh component, which the rate of reaction of wood component i (kg/m3 s), R, reacts between 600 and 800°C and for which no is the gas constant (kJ/kmol K), and pi is the density of reliable kinetic data were obtained (Alves and component i (kg/m3). Figueiredo, 1988), is added to the value of m6. Material balances: Model equations Enthalpy balance: dY=; k 4 dr ( > - CM, C,, + M,C,,)A Tl dr Solid/pyrolysis gas with Ps=Pc+CPi - C H,ir,i+revH, dV > (3) where pc is the final char density (kg/m3). i where A is the transfer area (perpendirular to r) (m2), c pB is the specific heat of the volatile pyrolysis products (kJ/kg K), C,, is the specific heat of liquid Moisture/vapour a(xPw)dV=a(M,dr=r,,dV. ___ at & (7) (8) (9)  2844 S. S. ALVES and J. L. FIGUEIREDO Boundary conditions: For t = 0, Vr Pi = %Pw Pc=Pw-_cPi 1 T= T0 M,=O M,=O x=x, where p, is the dry-wood density (kg/m3). (10) (11) (12) (13) (14) (15) l?T For r= 0, Vt -=0 ar M,=O 1 M,=O (16) (17) (18) Forr=R,t>O kg=h(T-T,)tos(T4-_T3) (19) where h is the convection heat transfer coefficient (kW/m’ K), R is the solid half-thickness (m), Tf is the reactor temperature (K), E is the solid emissivity, and 0 is the Stephan-Boltzmann constant (kW/m* K4). Equations (l), (7) and (9) may be simplified using dA j?dV dr r dr (20) with p = 0 for infinite slabs, p = 1 for inifinite cylin- ders, and /I = 2 for spheres. The system of equations which constitutes the mathematical model is not analytically soluble. It was solved using the Crank-Nicholson method (Jenson and Jeffreys, 1963; Rice, 1983; Kung, 1972; Kansa et al., 1977; Pyle and Zaror, 1984). Details are given by Alves (1988). Model parameters The pine wood thermal conductivity was exper- imentally determined for moisture contents up to 0.66 and temperatures between 35 and 118°C. It was found not be sensitive to temperature in this range. Results in Table 2. Value or expression or physical parameters used in the pyrolysis model Parameter Value or expression sourcet _ pw (kg@) 590-640 1 C,, J/kg K) 1.95 2 C, J/kg K) 1.35 2 C,, @J/kg K) 1.20 2 k, (w/m K) 0.166 0.396X 1 k, (w/m K) 0.091 8.2 x lo-‘Z- 1 h (W/m K) 5.69 0.0098 T, 1 tl = experimental, 2 = literature (average between maxi- mum and minimum values quoted in the references). the radial and tangential directions were correlated and averaged to obtain the expression given in Table 2. This expression is also used for temperatures out- side the experimental range. The char thermal conductivity was determined in the range 3&22O”C. The correlation of these results is shown in Table 2. The expression is used for temper- atures outside the experimental range. The exper- imental char thermal conductivities have to be correc- ted before use in the model, as the model is based on initial wood dimensions and some shrinkage occurs during pyrolysis. Thus k, (wood dimension basis) = k, wood dimension char dimension ’ (21) In the transversal directions, the ratio of wood to char dimension is - 0.7; in the longitudinal direction it is - 0.85. The expression shown in Table 2 refers to transversal directions after correction. The pine wood and char specific heats used are shown in Table 2. These were taken from the litera- ture. The properties of the pyrolysing solid are interpolated between those of wood and char, as- suming proportionality to solid density: k=ak,+(l -a)k, (22) C, = UC,, + (1 ~ c, (23) with a- P.--c. Pw-PC (24) Volatile and gaseous products of pyrolysis are treated as a lumped species with specific heat C,, = 1.2 kJ/kg K (average value between maximum and minimum values in the references). The enthalpy of vaporization, H,(X), of bound moisture depends on solid moisture content according to data in Siau (1984). These were correlated by a third-degree polynomial: H,(X) = 3348 - 13,085X + 60,262X2 -95,778X3 for X < 0.3 (25) with H, in kJ/kg. For X > 0.3, H, = 2260 kJ/kg. Enthalpies of reaction are taken from Beall (1971). Working under an inert atmosphere, he obtained values of 64 kJ/kg wood for the enthalpy of pyrolysis of cellulose in wood and - 510 kJ/kg wood for the pyrolysis of ligninf hemicelluloses in wood. To be used in the model, Beall’s values have to be converted from a reaction reference temperature to a reference temperature of 0°C. Table 1 shows the adjusted values, which were obtained assuming average pyrolysis tem- peratures in Beall’s work of 360°C for cellulose and 400°C for the other components. The convective heat transfer coefficient between the sweeping gas and a cylinder in the furnace, exper- imentally determined (see Experimental), is given in Table 2.  A model for pyrolysis of wet wood 865 EXPERIMENTAL Thermogravimetric experiments were carried out inside a vertical cylindrical refractory steel reactor 50 mm in diameter surrounded by a furnace. The temperature-controlled reactor was continuously swept with 3 l/min of nitrogen (99.995% pure). The furnace was heated up to the desired temperature and the sample was then quickly lowered to the constant- temperature zone of the reactor, suspended from a Mettler AElOO balance whose signal was continu- ously recorded. The samples used were cylinders of pine wood (“Pinus pinaster”) of variable diameter, and length at least 3 times greater than the diameter. Above this length-to-diameter ratio, the pyrolysis time increases very little for the same diameter and furnace temper- ature. The results were therefore considered represen- tative of the pyrolysis of infinite cylinders. The cylin- ders were such that the direction of the axis was well defined in relation to the fiber direction (unless other- wise stated, results presented concern experiments where these were parallel). Dry samples were obtained by drying at 103°C for 24 h. Wet samples were ob- tained by immersion in water followed by a homo- genization period of not less than 3 weeks. The convective heat transfer coefficient between the sweeping gas and a cylinder in the furnace was deter- mined from the results of two types of experiments: (i) measurement of the wet bulb temperature as a func- tion of furnace temperature, and (ii) measurement of the rate of evaporation of a cylinder of water-soaked cloth (constant-rate drying period) as a function of furnace temperature. The convective heat transfer coefficient can then be calculated from a heat balance over the wet thermocouple [details in Alves (1988)]. The resulting function is given in Table 2. RESULTS AND DISCUSSION Pyrolysis of dry wood Figure 2 compares simulated and experimental thermograms of the pyrolysis of dry-wood cylinders at furnace temperatures between 300 and 786”C, for cylinders of about 18.5 mm in diameter. The simulation agrees fairly well with the exper- iment for such a wide range of conditions. This is attributed to the independent measurement of the most important parameters, and to the adequacy of the experimentally determined reaction scheme. We had previously found that it is impossible to simulate pyrolysis over a range of temperatures that included both high temperatures (- XOOYZ) and temperatures lower than, say, 35O”C, with a single reaction, even with multiple-parameter optimization. With the inde- pendently determined reaction scheme, on the other hand, a reasonable agreement between simulation and experiment is possible without a single-parameter optimization. The main discrepancies are: (i) The onset of pyrolysis is delayed in the simu- lations, particularly at temperatures around 400°C. This is believed to be mainly due to the inadequacy of using a constant temperature of 35°C as the initial particle temperature profile in the simulations. In the experiments, the particle had to be lowered through the furnace down to the constant-temperature zone, and then there were a few seconds of stabilization, before the time was started and the weight recorded. During this time, the particle was heated to an extent which varied from experiment to experiment, partly randomly, partly depending on the furnace temper- ature. (ii) The delay in the onset of pyrolysis is somewhat compensated by the slope of the thermograms, par- ticularly around 400°C. This is probably due to the inaccuracy of the enthalpies of reaction used in the simulations. Beall’s (1971) values were obtained with small particles and at a much slow r rate of heating than those occurring inside the particles in the present work. The secondary reactions involved are certainly different and this should affect the global enthalpies of reaction. From the comparison between the simu- lation and the experiment, it appears that the simu- lated reactions are more exothermic than the real Fig. 2. Simulated (- - - -) and experimental (- ) pyrolysis thermograms of dry-wood cylinders at various temperatures. Samples: 73 (T, = 3OO”C, 6 = 18.2 mm); 74 (T, = 345 “C, 4 = 18.2 mm); 75 (TJ = 406”C, 4 = 18.3 mm); 11 (TJ = 6OO”C, I J 18.5 mm); 6 (T/ = 786”C, 4 = 19.4 mm).
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