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A model for pyrolysis of wet wood
Chemrcol Engineering Science, Printed in Great Britain.
Vol. 44, No.
12, pp. 2861b2869,
1989. 0
A MODEL
FOR
PYROLYSIS
S. S. ALVES Centro de. Engenharia Quimica,
OF WET
000%2509/89 %3.00+0.00 1989 Pergamon Press plc
WOOD
and J. L. FIGUEIREDO’ 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
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 evaporation, 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 pyrolysis/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 reaction, 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 simulation results of wet pyrolysis are presented. A wet particle pyrolysis model would be of the utmost interest for the modelling of equipment for phenomenon,’
+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 measured, 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 simultaneously: (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, respectively). fi can take intermediate values and hence some treatment of irregular shapes may be possible. The
2861
S. S. ALVE~ and J. L. FIGUEIREDO
2862
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, chemical 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 consequence of several assumptions_ Bound-water movement is shown in the Appendix to be negligible. Freewater 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 diffusion is assumed to be much slower than vapour convection, which reduces model validity to hightemperature drying (above the water boiling temperature), 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 negligible. 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 contents of wood, X,, are given in Kent et al. (1981) as a function of temperature T (above 100°C), at atmospheric pressure, in an atmosphere of superheated as X, steam. These results may be understood =f(T) or as T, = g(X); they were correlated by a third-degree polynomial: Tb = 1/(2.130x
+9.997
lo-‘+2.778
x lo-“
x lop6 [ln (%X)lz--
x 10e5[ln
s ,,:Gt S .,AGt S “4 fGt S .,:Gt
1.461
(“/OX)]‘)
(1)
S .f$GT
where SVi is the volatile
interface--a
x
S .,:Gt
ln(%X)
with Tb in K, and where %X is the percentage moisture content (dry basis). Equation (1) is only valid
<-___---___
for %X < 14.4%. For %X > 14.4%, it can be assumed that Tb (X) = lOO”C, with negligible discontinuity 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 boundary, 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 determined (Alves and Figueiredo, 1988) for very small samples of dry pine wood sawdust, with negligible internal temperature gradients. Six independent reactions were identified:
=
0
--_-----_->,<___,
part of component
i of wood.
interface--
I ”I
=
Tb
LOrIB? C’
_-_>I<_-_____-___
,
<
Tb
__________-____>]
;___-_____-__________-____-_-_‘--_---__--_--~-_-.____-_-___--____--___--_____________~
I
I
I
TbtXl i
I
I
<---
vapour without
I I
convcciion resistance
I
,
I
I
I 1
I 1 I
____________________----__----*-----__----__--
X=
Evaporation is function of available heat
f Heated
bcwndar;
heat
trP”sfr,
-----
-____--
-_-
constant
II
._________.
__-________
-___-
_______
I I
*w -_a
Fig. 1. Consequences of assumptions on high-temperature drying model.
SymmAry
axis
or ptanr
A model for pyrolysis of wet wood
2863
Table 1. Value of chemical reaction parameters used in the model
Component
mi
Activation energy Ei (kJ/mol)
0.19 0.50 0.02 0.03 0.02 0.02
83 146 77 60 139 130
Mass fraction
i
1 2 3 4 5 6
Components are numbered in order of increasing thermal stability. Component 1 is thought to correspond 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 components were experimentally determined by Alves and Figueiredo (1988) for the pine wood sawdust and reactions l&6 were found to be approximately firstorder. Experimental activation energies and pre-exponential 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 particles: 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) 1 -(char x
yield of big particle
1 -(char
= m,(sawdust)
0.70 0.20 0.43 0.29 0.51 0.32
x X X x x x
Enthalpy of
reaction (k$g)
105
-233 322 -233 -233 -233 -233
10’0
104 10’ 10’ 106
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)
(zone B’)
(4)
rev = 0
(zones A’ and C’)
(5)
with Tb(X) given by eq. (1) above. Chemical reactions:
at 8OOC)
dPi _ = rci = pikoi exp( -E,/R,T) at
yield of sawdust at 8OOC) 0.78
x __ 0.82.
Pre-exponential factor, koi (s-l)
(2)
The mass fraction of a seventh component, which reacts between 600 and 800°C and for which no reliable kinetic data were obtained (Alves and Figueiredo, 1988), is added to the value of m6.
(6)
for i = 1, . . . , 6 where Ei is the activation energy (kJ/kmol), k,i is the pre-exponential factor (s-r), rci is the rate of reaction of wood component i (kg/m3 s), R, is the gas constant (kJ/kmol K), and pi is the density of component i (kg/m3). Material balances: Solid/pyrolysis
gas
Model equations Enthalpy balance: (7) dY=;
-
$ CM, C,, + M,C,,)A C H,ir,i+revH,
i
>
dV
(
k$4
>
dr
with
Tl dr
Ps=Pc+CPi
(3)
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
(8)
where pc is the final char density (kg/m3). Moisture/vapour -___ a(xPw)dV=a(M,dr=r,,dV. at &
(9)
S. S. ALVES and J. L. FIGUEIREDO
2844
Boundary For
conditions:
t = 0, Vr
Pi = %Pw
(10)
Pc=Pw-_cPi T=
(11)
1
T0
(12)
M,=O
(13)
M,=O
(14)
x=x,
(15)
where p, is the dry-wood For r= 0, Vt
density
(kg/m3).
l?T -=0 ar
(16) (17)
M,=O
(18)
1M,=O
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
the pyrolysis model
pw (kg@) C,, &J/kg
K) C, &J/kg K) C,, @J/kg K) k, (w/m K) k, (w/m K) h (W/m K)
1.95
1.35 1.20 0.166 + 0.396X 0.091+8.2 x lo-‘Z5.69 + 0.0098 T,
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 literature. The properties of the pyrolysing solid are interpolated between those of wood and char, assuming proportionality to solid density: k=ak,+(l
-a)k,
C, = UC,, + a-
Table 2. Value or expressionfor physical parametersused in
590-640
wood dimension
(22)
(1- ~)c,
(23)
(20)
Model parameters The pine wood thermal conductivity was experimentally 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
Value or expression
k, (wood dimension basis) = k,
with
with p = 0 for infinite slabs, p = 1 for inifinite cylinders, 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).
Parameter
the radial and tangential directions were correlated and averaged to obtain the expression given in Table 2. This expression is also used for temperatures outside 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 temperatures outside the experimental range. The experimental char thermal conductivities have to be corrected before use in the model, as the model is based on initial wood dimensions and some shrinkage occurs during pyrolysis. Thus
sourcet
_
1
2 2 2 1 1 1
tl = experimental, 2 = literature (average between maximum and minimum values quoted in the references).
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 temperatures 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, experimentally determined (see Experimental), is given in Table 2.
A model for pyrolysis of 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 constanttemperature zone of the reactor, suspended from a Mettler AElOO balance whose signal was continuously 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 temperature. The results were therefore considered representative of the pyrolysis of infinite cylinders. The cylinders were such that the direction of the axis was well defined in relation to the fiber direction (unless otherwise stated, results presented concern experiments where these were parallel). Dry samples were obtained by drying at 103°C for 24 h. Wet samples were obtained by immersion in water followed by a homogenization period of not less than 3 weeks. The convective heat transfer coefficient between the sweeping gas and a cylinder in the furnace was determined from the results of two types of experiments: (i) measurement of the wet bulb temperature as a function 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
wet wood
2865
furnace temperatures between 300 and 786”C, for cylinders of about 18.5 mm in diameter. The simulation agrees fairly well with the experiment 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 independently 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 simulations, 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 temperature. (ii) The delay in the onset of pyrolysis is somewhat compensated by the slope of the thermograms, particularly 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 slower 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 simulation and the experiment, it appears that the simulated 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 = 18.2mm); 74 (T, = 345 “C, 4 = 18.2mm); 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).
2866
S. S. ALVES
and J. L. FIGUEIREDO
ones. This effect is most important around 400°C. At higher temperatures, the heat generated or removed by reaction is small compared to the heat conducted. At low temperatures, on the other hand, things happen slowly enough to allow the heat generated to dissipate with minimum temperature rise. (iii) Finally, simulated and experimental char yields do not Agree at all temperatures. This is mainly the result of the mass fraction of wood volatile components employed in the simulation, which was adjusted as mentioned above [eq. (2)]. Other errors are obviously involved, both experimental errors (particularly furnace temperature precision) and errors resulting from model assumptions, both explicit and implicit. A much better agreement would be obtained by optimization of one or more of the parameters mentioned: initial particle temperature profile, enthalpies of reaction and mass fraction of wood components. This, however, would be at the cost of sacrificing simplicity. The agreeement is sufficiently good for the model to be tested without parameter optimization in the simulation of high-temperature drying and the pyrolysis of wet particles. The simulation of pyrolysis of smaller-diameter cylinders (4 - 7.5 and - 13.5 mm) likewise gave a reasonable agreement with experiment. High-temperature drying Figure 3 compares experimental and simulated thermograms and drying curves of wood cylinders (axis parallel to fibre) drying at a furnace temperature of 150°C. The effect of some of the model simplifications is apparent. There is a delay in simulating the beginning of drying, since the model has to wait for the solid to reach “boiling temperature” before drying starts. In reality, drying starts at time zero, since water
I
0
SO
can reach the particle outer surface by several mechanisms (bound-water and water vapour diffusion) not described in the model. This effect is worse at lower temperatures but is negligible above 195°C (results not shown) and hence at pyrolysis temperatures. In addition, since the only drying mechanism considered is “boiling”, the model does not simulate any water loss for moistures below which the boiling point, Tb(X), is higher than the furnace temperature (150°C in this case). In reality, combined bound-water and water vapour diffusion leads to drying below the boiling point. This effect, still significant at 150°C (Fig. 3), decreases with temperature and totally disappears at 196”C, which is the boiling point for X = 0 [eq. (l)]. The drying of wood cylinders with an axis parallel to the radial direction of wood was also simulated. The agreement with the experiment (results not shown) was also good at high temperatures, despite the fact that the sample cylindrical symmetry is broken. The only alteration to the parameters introduced in these simulations was in the wood thermal conductivity, which was taken as the average between the longitudinal and the transversal thermal conductivities, experimentally determined as a function of moisture. Pyrolysis of wet particles Figure 4 compares experimental and simulated thermograms of the pyrolysis of wet cylinders with diameter - 18.5 mm, for temperatures between 298 and 780°C. The agreement is quite good. The major disparities are attributable not to the drying assumptions used (agreement is particularly good for M’ > l), but to the pyrolysis model parameters. Results were likewise good in the simulation of the pyrolysis of smaller-diameter cylinders of wet wood (4 - 7.5 and - 13.5 mm).
100
t [min)
:
0
Fig.
3. X,
Thermograms (a) and drying curves = 0.467. Sample 84A: 4 = 7.5 mm,
(b and c) of wood cylinders at 150°C. (X, = 0.362. (- ~ ~ - -) Simulated;
Sample 78: r#~= 18.2 mm, ) experimental.
A model for pyrolysis of wet wood
2867
Fig. 4. Simulated (- - - -) and experimental (------) pyrolysis thermograms of wet-wood cylinders at various temperatures. Samples: 86 (T, = 298°C 4 = 18.5 mm, X, = 0.486); 88 (j”, = 398°C 4 = 18.6mm, X, = 0.463); 89 ( Ts = 588°C 4 = 18.3 mm, X, = 0.430); 90 (r, = 78O”C, 4 = 18.2 mm, x, = 0.450).
CONCLUSIONS
(i) The weight loss due to pyrolysis of cylinders of dry wood can be well simulated between 300 and 800°C by a model which describes the heat transfer and pyrolysis kinetics of the major components of the wood. A reasonable agreement between the experiment and the simulation can be obtained without any parameter optimization. (ii) The drying of wood at high temperatures can be well simulated by a model which neglects water vapour diffusion, bound-water diffusion and pressure gradients if the following conditions are fulfilled: (a) the drying temperature is greater than 15O”C, (b) the initial wood moisture content is below the free-water continuity point (- 0.49, and (c) the sample dimension in the wood longitudinal direction is not much greater than the dimensions in the transversal directions. Under these circumstances, therefore, neither momentum nor mass transfer parameters are required for simulation. (iii) The pyrolysis of wet cylinders of wood can be well simulated by a model which combines characteristics (i) and (ii), if the above-mentioned conditions (b) and (c) are fulfilled_ Acknowiedwments-This work received financial sunport from Junta National de Investigacgo Cientifica e TkcnoIbgica, under R. and D. contract No. 410.82.24, and from In&ituto National de InvestigacHo Cientifica, through a grant to S. S. Alves. NOTATION
A
CP
D
D,, E
transfer area (perpendicular to r), m2 specific heat, kJ/kg K bound-water diffusivity, m2/s effective bound-water diffusivity (Of), m2/s activation energy, kJ/kmol
_f h H, ff, k ko KP
M M’
mi PC PC3 r R RE3 ‘; rev t T Tll Tf V x %
x
fraction of cell wall area in area perpendicular to flux convection heat transfer coefficient, kW/m2 K enthalpy of pyrolysis at 0°C kJ/kg wood moisture vaporization enthalpy, kJ/kg solid thermal conductivity, kW/m K pre-exponential factor, s- 1 permeability, m2 mass flux, kg/m* s fraction of solid mass remaining (referred to initial mass of dry solid) mass fraction of component i in wood capillary pressure, N/m* gas phase pressure, N/m’ linear dimension in the direction of heat and mass transfer, m solid half-thickness, m gas constant, kJjkmo1 K rate of reaction, kg/m3 s evaporation rate, kg/m3 s time, s solid temperature, K boiling temperature, K reactor temperature, K solid volume, m3 solid moisture content (dry basis) percentage solid moisture content (dry basis)
Greek
letters
B
geometric parameter ( = 0 for infinite slab, = 1 for infinite cylinder, = 2 for sphere) thermomigration coefficient, K- 1 solid emissivity viscosity, kg/m s solid density, kg/m3 Stephan-Boltzmann constant, kW/m2 K4 diameter, mm
s
& P P u 9
S. S. ALVES
2868
and J. L. FIGUEIREUO
Subscripts bl bound water C
(1 9 ; s SU V
0”
char reactor free water gaseous/volatile products wood component i liquid water dry solid solid outer surface water vapour wood initial
REFERENCES Alves, S. S., 1988, Modelacgo da pir6lise de madeira e outros materiais linhocelulosicos. Ph.D. dissertation, Instituto Superior Tecnico, Lisboa. Alves, S. S. and Figueiredo, J. L., 1988, Pyrolysis kinetics of lignocellulosic materials by multistage isothermal thermogravimetry. J. analyt. appl. Pyrolysis 13, 123. Bamford, C. H., Crank, J. and Malan, D. H., 1945, The combustion of wood. Proc. Camb. Phil. Sot. 42, 166. Basilica, C. and Martin, M., 1984, Approche experimentale des mecanismes de transfert au tours du stchage convectif a haute temperature d’un bois rcsmeux. Int. J. Heat Mass Transfer 27, 657. Beall, F. C., 1971, Differential calorimetric analysis of wood and wood components. Wood Sri. Technol. 5, 159. Chan, R. W. C., Kelbon, M. and Krieger. B. B., 1985, Modelling and experimental verification of chemical processes during pyrolysis of a large biomass particle. Fuel 64, 1505. Comstock, G. L. and Cbte, W. A., 1968, Factors affecting permeability and pit aspiration in coniferous sapwood. Wood Sci. Technol. 2, 279. Fan, L. T., Fan, L. S., Miyanami, K., Chen, T. Y. and Walawender, W. P., 1977, A mathematical model for pyrolysis of a solid particle: effect of the Lewis number. Can. J. them. Engng 55, 47. Hemati, M. and Laguerie, C., 1977, Etude cinttique de la pyrolyse de bois g haute temperature en thermobalance II: etude experimentale et modtlisation de la pyrolyse de bbtonnets. Chem. Engng J. 35, 1577. Jenson, V. G. and Jeffreys, G. V., 1963, Mathematical Methods in Chemical Engineering. Academic Press, London. Kansa, E. J., Perlea, H. E. and Chaiken, R. F., 1977, Mathematical model of wood pyrolysis including internal forced convection. Combust. Flame 29, 311. Kent, A. C., Rosen, H. N. and Hari, B. M., 1981, Determination of equilibrium moisture content of yellow-poplar sapwood above 100°C with the aid of an experimental psychrometer. Wood Sci. Technol. 15,93. Kung, H. C., 1972, A mathematical model of wood pyrolysis. Cornbust. Flame 18, 185. Kung, H. C., 1973, A mathematical model of wood pyrolysis. Combust. Flame 20, 91. Lee, C. K.. Chaiken. R. F. and Singer, J. M., 1976, Charring pyrolysis of wood in fires by laser simulation, in 16th Symposium (International) on Combustion, p. 1459. Maa, P. S. and Bailie, R. C., 1973, Influence of particle sizes and environmental conditions on high temperature pyrolysis of cellulosic material. Combust. Sci. Technol. 7, 257. Miller, C. A. and Ramohalli, K. N. R., 1986, A theoretical heterogeneous model of wood pyrolysis. Combust. Sci. Technol. 46, 249. Moyne, C. and Martin, M., 1986, etude experimentale du transfert simultanc de chaleur et de masse au tours du
s&hage par contact sur vide d’un bois rhineux. inc. J. Heat Mass Transfer 29, 1443. Panton, R. L. and Rittman, J. G., 1971, Pyrolysis of a slab of porous material, in 13th Symposium (International) on Combustion, p. X81. Pyle, D. L. and Zaror, C. A., 1984, Heat transfer and kinetics in the low temperature pyrolysis of solids. Chem. Engng Sci. 39, 147. Rice, J. R., 1983, Numerical Methods, Software and Analysis. McGraw-Hill, New York. Siau, J. F., 1984, Transport Processes in Wood. Springer, Berlin. Spolek, Cl. A. and Plumb, 0. A., 1981, Capillary pressure in softwoods. Wood Sci. Technol. 15, 189. Villermaux, J., Antonie, B., Lede, J. and Souliganc, F., 1986, A new model for thermal volatilization of solid particles undergoing fast pyrolysis. Chem. Engng Sci. 41, 151. APPENDIX:
A PRIORI LIMITS TO THE VALIDITY DRYING MODEL
OF THE
Bound-water movement To evaluate the importance of bound-water movement, we may compare the bound-water flux through the particle M,,, with the vapour flux due to boiling inside the particle, M,. To estimate these, let us consider Fig. Al which depicts some modelling consequences of the assumptions. Zone A’, of thickness r, is the dry zone. Since we are interested in hightemperature drying, we assume that the outer surface temperature, T,. is greater than the boiling temperature, Tb. Zone C’ is wet, of constant moisture content X,. To simplify the discussion, one may start by assuming that Tb is independent of moisture, which reduces the intermediate zone B’, where evaporation occurs, to a mobile surface. The ratio of the fluxes, M,/M,,, indicates the relative importance of the contributions of the mechanisms of boiling +convection and of bound-water diffusion to the recession of surface B’. However
where D,, is the effective bound moisture diffusivity, based on the total area; D is the bound-water diffusivity through the cell wall materiahfis the fraction of cell wall area in the area perpendicular to the flux; and 6 is the thermomigration coefficient. In addition:
Mu=- Ts, - Tb HJ
Therefore
-M”
Mb1
UT,,-- Tb)
(A3)
.1
H,Dfp,EX,
~ a(T,u-
Tdl
.
At X = 0. I5 and T = 373 K, bound-water diffusivities have values of D - 3.2 x 10-i” m2/s in the longitudinal direction and D - 1.3 x lo-“’ mZ/s in the transversal directions; f - 0.2 in the longitudinal direction and f - 0.4 in the transversal directions; and the coefficient of thermomigration is 6 - 1.8 x lo-’ K- i (Siau, 1984). The thermal conductivity is k - 0.23 x lo-’ kW/m K (Table 2) in the transversal directions and about twice that value in the longitudinal direction. Using these in eq. (A3) we find that, so long as the temperature difference (T,,- Tb) is greater than - lO”C, the contribution of the bound-water movement is less than 3% in the transversal directions. In the longitudinal direction, this contribution is much smaller. Free-water movement If free water is continuously according to the equation
present,
it tends to move
2869
A model for pyrolysis of wet wood T = Tsu f
Interface
8’
Fig. Al.
Zones in a simplified model of high-temperature
where M,, = flux of free water, P, = capillary pressure, P, = pressure of gaseous phase, K, = permeability, and p, = liquid-water viscosity. If the gas phase pressure gradients are neglected (see discussion below), one gets
k(Ts14- Tb)
M”
drying.
Static pressure rise within rhe s&id An important modelling assumption was that moisture vaporizes inside the solid whenever the temperature reached the moisture boiling point, T*(X), which was calculated for atmospheric pressure. This is only valid if the pressure gradients created inside the particle are small. The pressure gradient can be estimated using
-N
Mf,
H,V&IP,)P,AP,
The capillary pressure is of the order of AP, - 1 x lo* N/m2 (Spolek and Plumb, 1981). Permeability, on the other hand, may vary by several orders of magnitude, depending on biological species, and direction (Siau, 1984): 1 x 10-‘5m4/Ns
< K,/fi,
< 1 x 10-13m4/Ns (transversal directions)
(longitudinal direction). Using these values, it is found that, no matter how great the temperature difference (T_ - Tb). free-water movement is always important in the longitudinal direction and is only negligible in the transversal directions for the most permeable woods. This agrees with data obtained by Moyne and Martin (1986) concerning the drying of pine wood at low pressures (hence T,, > Tb) and that obtained by Basilic0 and Martin (1984) at high temperatures. We conclude that this assumption is not valid for moisture contents above the free-water continuity point, which is around 0~45 for most woods.
(-46) where p, and p, are respectively, the water vapour density and viscosity. For most woods, the longitudinal permeability is greater than 1 x lo-l4 m’. For pine wood, in this direction, it is K -1x10-‘2 m2 before torus aspiration and - 1 x 10 - 1Pm2 after torus aspiration (Comstock and CBti, 1968). This means that the pressure differences established in wood are small in this direction [e.g., for (T’,, - l’*) = lOO”C, This is consistent and K, - 1 x lo- L3, AP, - 950 N/m’]. with the pressure gradients measured by Lee et of. (1976) inside wood pyrolysing at high temperatures. Hence, for particles with longitudinal dimension not greater than the transversal dimensions, the longitudinal direction is an “easy” escape way for the vapour, which prevents a significant pressure rise inside the solid. On the other hand, when the longitudinal direction is much bigger than the others (as in the drying of wood boards), significant pressure gradients may be created inside the solid. Basilic0 and Martin (1984) measured a maximum pressure of - 1 atm (gauge) inside a wood board drying at 184°C.
Vol. 44, No.
12, pp. 2861b2869,
1989. 0
A MODEL
FOR
PYROLYSIS
S. S. ALVES Centro de. Engenharia Quimica,
OF WET
000%2509/89 %3.00+0.00 1989 Pergamon Press plc
WOOD
and J. L. FIGUEIREDO’ 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
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 evaporation, 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 pyrolysis/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 reaction, 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 simulation results of wet pyrolysis are presented. A wet particle pyrolysis model would be of the utmost interest for the modelling of equipment for phenomenon,’
+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 measured, 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 simultaneously: (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, respectively). fi can take intermediate values and hence some treatment of irregular shapes may be possible. The
2861
S. S. ALVE~ and J. L. FIGUEIREDO
2862
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, chemical 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 consequence of several assumptions_ Bound-water movement is shown in the Appendix to be negligible. Freewater 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 diffusion is assumed to be much slower than vapour convection, which reduces model validity to hightemperature drying (above the water boiling temperature), 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 negligible. 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 contents of wood, X,, are given in Kent et al. (1981) as a function of temperature T (above 100°C), at atmospheric pressure, in an atmosphere of superheated as X, steam. These results may be understood =f(T) or as T, = g(X); they were correlated by a third-degree polynomial: Tb = 1/(2.130x
+9.997
lo-‘+2.778
x lo-“
x lop6 [ln (%X)lz--
x 10e5[ln
s ,,:Gt S .,AGt S “4 fGt S .,:Gt
1.461
(“/OX)]‘)
(1)
S .f$GT
where SVi is the volatile
interface--a
x
S .,:Gt
ln(%X)
with Tb in K, and where %X is the percentage moisture content (dry basis). Equation (1) is only valid
<-___---___
for %X < 14.4%. For %X > 14.4%, it can be assumed that Tb (X) = lOO”C, with negligible discontinuity 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 boundary, 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 determined (Alves and Figueiredo, 1988) for very small samples of dry pine wood sawdust, with negligible internal temperature gradients. Six independent reactions were identified:
=
0
--_-----_->,<___,
part of component
i of wood.
interface--
I ”I
=
Tb
LOrIB? C’
_-_>I<_-_____-___
,
<
Tb
__________-____>]
;___-_____-__________-____-_-_‘--_---__--_--~-_-.____-_-___--____--___--_____________~
I
I
I
TbtXl i
I
I
<---
vapour without
I I
convcciion resistance
I
,
I
I
I 1
I 1 I
____________________----__----*-----__----__--
X=
Evaporation is function of available heat
f Heated
bcwndar;
heat
trP”sfr,
-----
-____--
-_-
constant
II
._________.
__-________
-___-
_______
I I
*w -_a
Fig. 1. Consequences of assumptions on high-temperature drying model.
SymmAry
axis
or ptanr
A model for pyrolysis of wet wood
2863
Table 1. Value of chemical reaction parameters used in the model
Component
mi
Activation energy Ei (kJ/mol)
0.19 0.50 0.02 0.03 0.02 0.02
83 146 77 60 139 130
Mass fraction
i
1 2 3 4 5 6
Components are numbered in order of increasing thermal stability. Component 1 is thought to correspond 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 components were experimentally determined by Alves and Figueiredo (1988) for the pine wood sawdust and reactions l&6 were found to be approximately firstorder. Experimental activation energies and pre-exponential 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 particles: 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) 1 -(char x
yield of big particle
1 -(char
= m,(sawdust)
0.70 0.20 0.43 0.29 0.51 0.32
x X X x x x
Enthalpy of
reaction (k$g)
105
-233 322 -233 -233 -233 -233
10’0
104 10’ 10’ 106
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)
(zone B’)
(4)
rev = 0
(zones A’ and C’)
(5)
with Tb(X) given by eq. (1) above. Chemical reactions:
at 8OOC)
dPi _ = rci = pikoi exp( -E,/R,T) at
yield of sawdust at 8OOC) 0.78
x __ 0.82.
Pre-exponential factor, koi (s-l)
(2)
The mass fraction of a seventh component, which reacts between 600 and 800°C and for which no reliable kinetic data were obtained (Alves and Figueiredo, 1988), is added to the value of m6.
(6)
for i = 1, . . . , 6 where Ei is the activation energy (kJ/kmol), k,i is the pre-exponential factor (s-r), rci is the rate of reaction of wood component i (kg/m3 s), R, is the gas constant (kJ/kmol K), and pi is the density of component i (kg/m3). Material balances: Solid/pyrolysis
gas
Model equations Enthalpy balance: (7) dY=;
-
$ CM, C,, + M,C,,)A C H,ir,i+revH,
i
>
dV
(
k$4
>
dr
with
Tl dr
Ps=Pc+CPi
(3)
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
(8)
where pc is the final char density (kg/m3). Moisture/vapour -___ a(xPw)dV=a(M,dr=r,,dV. at &
(9)
S. S. ALVES and J. L. FIGUEIREDO
2844
Boundary For
conditions:
t = 0, Vr
Pi = %Pw
(10)
Pc=Pw-_cPi T=
(11)
1
T0
(12)
M,=O
(13)
M,=O
(14)
x=x,
(15)
where p, is the dry-wood For r= 0, Vt
density
(kg/m3).
l?T -=0 ar
(16) (17)
M,=O
(18)
1M,=O
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
the pyrolysis model
pw (kg@) C,, &J/kg
K) C, &J/kg K) C,, @J/kg K) k, (w/m K) k, (w/m K) h (W/m K)
1.95
1.35 1.20 0.166 + 0.396X 0.091+8.2 x lo-‘Z5.69 + 0.0098 T,
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 literature. The properties of the pyrolysing solid are interpolated between those of wood and char, assuming proportionality to solid density: k=ak,+(l
-a)k,
C, = UC,, + a-
Table 2. Value or expressionfor physical parametersused in
590-640
wood dimension
(22)
(1- ~)c,
(23)
(20)
Model parameters The pine wood thermal conductivity was experimentally 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
Value or expression
k, (wood dimension basis) = k,
with
with p = 0 for infinite slabs, p = 1 for inifinite cylinders, 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).
Parameter
the radial and tangential directions were correlated and averaged to obtain the expression given in Table 2. This expression is also used for temperatures outside 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 temperatures outside the experimental range. The experimental char thermal conductivities have to be corrected before use in the model, as the model is based on initial wood dimensions and some shrinkage occurs during pyrolysis. Thus
sourcet
_
1
2 2 2 1 1 1
tl = experimental, 2 = literature (average between maximum and minimum values quoted in the references).
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 temperatures 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, experimentally determined (see Experimental), is given in Table 2.
A model for pyrolysis of 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 constanttemperature zone of the reactor, suspended from a Mettler AElOO balance whose signal was continuously 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 temperature. The results were therefore considered representative of the pyrolysis of infinite cylinders. The cylinders were such that the direction of the axis was well defined in relation to the fiber direction (unless otherwise stated, results presented concern experiments where these were parallel). Dry samples were obtained by drying at 103°C for 24 h. Wet samples were obtained by immersion in water followed by a homogenization period of not less than 3 weeks. The convective heat transfer coefficient between the sweeping gas and a cylinder in the furnace was determined from the results of two types of experiments: (i) measurement of the wet bulb temperature as a function 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
wet wood
2865
furnace temperatures between 300 and 786”C, for cylinders of about 18.5 mm in diameter. The simulation agrees fairly well with the experiment 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 independently 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 simulations, 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 temperature. (ii) The delay in the onset of pyrolysis is somewhat compensated by the slope of the thermograms, particularly 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 slower 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 simulation and the experiment, it appears that the simulated 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 = 18.2mm); 74 (T, = 345 “C, 4 = 18.2mm); 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).
2866
S. S. ALVES
and J. L. FIGUEIREDO
ones. This effect is most important around 400°C. At higher temperatures, the heat generated or removed by reaction is small compared to the heat conducted. At low temperatures, on the other hand, things happen slowly enough to allow the heat generated to dissipate with minimum temperature rise. (iii) Finally, simulated and experimental char yields do not Agree at all temperatures. This is mainly the result of the mass fraction of wood volatile components employed in the simulation, which was adjusted as mentioned above [eq. (2)]. Other errors are obviously involved, both experimental errors (particularly furnace temperature precision) and errors resulting from model assumptions, both explicit and implicit. A much better agreement would be obtained by optimization of one or more of the parameters mentioned: initial particle temperature profile, enthalpies of reaction and mass fraction of wood components. This, however, would be at the cost of sacrificing simplicity. The agreeement is sufficiently good for the model to be tested without parameter optimization in the simulation of high-temperature drying and the pyrolysis of wet particles. The simulation of pyrolysis of smaller-diameter cylinders (4 - 7.5 and - 13.5 mm) likewise gave a reasonable agreement with experiment. High-temperature drying Figure 3 compares experimental and simulated thermograms and drying curves of wood cylinders (axis parallel to fibre) drying at a furnace temperature of 150°C. The effect of some of the model simplifications is apparent. There is a delay in simulating the beginning of drying, since the model has to wait for the solid to reach “boiling temperature” before drying starts. In reality, drying starts at time zero, since water
I
0
SO
can reach the particle outer surface by several mechanisms (bound-water and water vapour diffusion) not described in the model. This effect is worse at lower temperatures but is negligible above 195°C (results not shown) and hence at pyrolysis temperatures. In addition, since the only drying mechanism considered is “boiling”, the model does not simulate any water loss for moistures below which the boiling point, Tb(X), is higher than the furnace temperature (150°C in this case). In reality, combined bound-water and water vapour diffusion leads to drying below the boiling point. This effect, still significant at 150°C (Fig. 3), decreases with temperature and totally disappears at 196”C, which is the boiling point for X = 0 [eq. (l)]. The drying of wood cylinders with an axis parallel to the radial direction of wood was also simulated. The agreement with the experiment (results not shown) was also good at high temperatures, despite the fact that the sample cylindrical symmetry is broken. The only alteration to the parameters introduced in these simulations was in the wood thermal conductivity, which was taken as the average between the longitudinal and the transversal thermal conductivities, experimentally determined as a function of moisture. Pyrolysis of wet particles Figure 4 compares experimental and simulated thermograms of the pyrolysis of wet cylinders with diameter - 18.5 mm, for temperatures between 298 and 780°C. The agreement is quite good. The major disparities are attributable not to the drying assumptions used (agreement is particularly good for M’ > l), but to the pyrolysis model parameters. Results were likewise good in the simulation of the pyrolysis of smaller-diameter cylinders of wet wood (4 - 7.5 and - 13.5 mm).
100
t [min)
:
0
Fig.
3. X,
Thermograms (a) and drying curves = 0.467. Sample 84A: 4 = 7.5 mm,
(b and c) of wood cylinders at 150°C. (X, = 0.362. (- ~ ~ - -) Simulated;
Sample 78: r#~= 18.2 mm, ) experimental.
A model for pyrolysis of wet wood
2867
Fig. 4. Simulated (- - - -) and experimental (------) pyrolysis thermograms of wet-wood cylinders at various temperatures. Samples: 86 (T, = 298°C 4 = 18.5 mm, X, = 0.486); 88 (j”, = 398°C 4 = 18.6mm, X, = 0.463); 89 ( Ts = 588°C 4 = 18.3 mm, X, = 0.430); 90 (r, = 78O”C, 4 = 18.2 mm, x, = 0.450).
CONCLUSIONS
(i) The weight loss due to pyrolysis of cylinders of dry wood can be well simulated between 300 and 800°C by a model which describes the heat transfer and pyrolysis kinetics of the major components of the wood. A reasonable agreement between the experiment and the simulation can be obtained without any parameter optimization. (ii) The drying of wood at high temperatures can be well simulated by a model which neglects water vapour diffusion, bound-water diffusion and pressure gradients if the following conditions are fulfilled: (a) the drying temperature is greater than 15O”C, (b) the initial wood moisture content is below the free-water continuity point (- 0.49, and (c) the sample dimension in the wood longitudinal direction is not much greater than the dimensions in the transversal directions. Under these circumstances, therefore, neither momentum nor mass transfer parameters are required for simulation. (iii) The pyrolysis of wet cylinders of wood can be well simulated by a model which combines characteristics (i) and (ii), if the above-mentioned conditions (b) and (c) are fulfilled_ Acknowiedwments-This work received financial sunport from Junta National de Investigacgo Cientifica e TkcnoIbgica, under R. and D. contract No. 410.82.24, and from In&ituto National de InvestigacHo Cientifica, through a grant to S. S. Alves. NOTATION
A
CP
D
D,, E
transfer area (perpendicular to r), m2 specific heat, kJ/kg K bound-water diffusivity, m2/s effective bound-water diffusivity (Of), m2/s activation energy, kJ/kmol
_f h H, ff, k ko KP
M M’
mi PC PC3 r R RE3 ‘; rev t T Tll Tf V x %
x
fraction of cell wall area in area perpendicular to flux convection heat transfer coefficient, kW/m2 K enthalpy of pyrolysis at 0°C kJ/kg wood moisture vaporization enthalpy, kJ/kg solid thermal conductivity, kW/m K pre-exponential factor, s- 1 permeability, m2 mass flux, kg/m* s fraction of solid mass remaining (referred to initial mass of dry solid) mass fraction of component i in wood capillary pressure, N/m* gas phase pressure, N/m’ linear dimension in the direction of heat and mass transfer, m solid half-thickness, m gas constant, kJjkmo1 K rate of reaction, kg/m3 s evaporation rate, kg/m3 s time, s solid temperature, K boiling temperature, K reactor temperature, K solid volume, m3 solid moisture content (dry basis) percentage solid moisture content (dry basis)
Greek
letters
B
geometric parameter ( = 0 for infinite slab, = 1 for infinite cylinder, = 2 for sphere) thermomigration coefficient, K- 1 solid emissivity viscosity, kg/m s solid density, kg/m3 Stephan-Boltzmann constant, kW/m2 K4 diameter, mm
s
& P P u 9
S. S. ALVES
2868
and J. L. FIGUEIREUO
Subscripts bl bound water C
(1 9 ; s SU V
0”
char reactor free water gaseous/volatile products wood component i liquid water dry solid solid outer surface water vapour wood initial
REFERENCES Alves, S. S., 1988, Modelacgo da pir6lise de madeira e outros materiais linhocelulosicos. Ph.D. dissertation, Instituto Superior Tecnico, Lisboa. Alves, S. S. and Figueiredo, J. L., 1988, Pyrolysis kinetics of lignocellulosic materials by multistage isothermal thermogravimetry. J. analyt. appl. Pyrolysis 13, 123. Bamford, C. H., Crank, J. and Malan, D. H., 1945, The combustion of wood. Proc. Camb. Phil. Sot. 42, 166. Basilica, C. and Martin, M., 1984, Approche experimentale des mecanismes de transfert au tours du stchage convectif a haute temperature d’un bois rcsmeux. Int. J. Heat Mass Transfer 27, 657. Beall, F. C., 1971, Differential calorimetric analysis of wood and wood components. Wood Sri. Technol. 5, 159. Chan, R. W. C., Kelbon, M. and Krieger. B. B., 1985, Modelling and experimental verification of chemical processes during pyrolysis of a large biomass particle. Fuel 64, 1505. Comstock, G. L. and Cbte, W. A., 1968, Factors affecting permeability and pit aspiration in coniferous sapwood. Wood Sci. Technol. 2, 279. Fan, L. T., Fan, L. S., Miyanami, K., Chen, T. Y. and Walawender, W. P., 1977, A mathematical model for pyrolysis of a solid particle: effect of the Lewis number. Can. J. them. Engng 55, 47. Hemati, M. and Laguerie, C., 1977, Etude cinttique de la pyrolyse de bois g haute temperature en thermobalance II: etude experimentale et modtlisation de la pyrolyse de bbtonnets. Chem. Engng J. 35, 1577. Jenson, V. G. and Jeffreys, G. V., 1963, Mathematical Methods in Chemical Engineering. Academic Press, London. Kansa, E. J., Perlea, H. E. and Chaiken, R. F., 1977, Mathematical model of wood pyrolysis including internal forced convection. Combust. Flame 29, 311. Kent, A. C., Rosen, H. N. and Hari, B. M., 1981, Determination of equilibrium moisture content of yellow-poplar sapwood above 100°C with the aid of an experimental psychrometer. Wood Sci. Technol. 15,93. Kung, H. C., 1972, A mathematical model of wood pyrolysis. Cornbust. Flame 18, 185. Kung, H. C., 1973, A mathematical model of wood pyrolysis. Combust. Flame 20, 91. Lee, C. K.. Chaiken. R. F. and Singer, J. M., 1976, Charring pyrolysis of wood in fires by laser simulation, in 16th Symposium (International) on Combustion, p. 1459. Maa, P. S. and Bailie, R. C., 1973, Influence of particle sizes and environmental conditions on high temperature pyrolysis of cellulosic material. Combust. Sci. Technol. 7, 257. Miller, C. A. and Ramohalli, K. N. R., 1986, A theoretical heterogeneous model of wood pyrolysis. Combust. Sci. Technol. 46, 249. Moyne, C. and Martin, M., 1986, etude experimentale du transfert simultanc de chaleur et de masse au tours du
s&hage par contact sur vide d’un bois rhineux. inc. J. Heat Mass Transfer 29, 1443. Panton, R. L. and Rittman, J. G., 1971, Pyrolysis of a slab of porous material, in 13th Symposium (International) on Combustion, p. X81. Pyle, D. L. and Zaror, C. A., 1984, Heat transfer and kinetics in the low temperature pyrolysis of solids. Chem. Engng Sci. 39, 147. Rice, J. R., 1983, Numerical Methods, Software and Analysis. McGraw-Hill, New York. Siau, J. F., 1984, Transport Processes in Wood. Springer, Berlin. Spolek, Cl. A. and Plumb, 0. A., 1981, Capillary pressure in softwoods. Wood Sci. Technol. 15, 189. Villermaux, J., Antonie, B., Lede, J. and Souliganc, F., 1986, A new model for thermal volatilization of solid particles undergoing fast pyrolysis. Chem. Engng Sci. 41, 151. APPENDIX:
A PRIORI LIMITS TO THE VALIDITY DRYING MODEL
OF THE
Bound-water movement To evaluate the importance of bound-water movement, we may compare the bound-water flux through the particle M,,, with the vapour flux due to boiling inside the particle, M,. To estimate these, let us consider Fig. Al which depicts some modelling consequences of the assumptions. Zone A’, of thickness r, is the dry zone. Since we are interested in hightemperature drying, we assume that the outer surface temperature, T,. is greater than the boiling temperature, Tb. Zone C’ is wet, of constant moisture content X,. To simplify the discussion, one may start by assuming that Tb is independent of moisture, which reduces the intermediate zone B’, where evaporation occurs, to a mobile surface. The ratio of the fluxes, M,/M,,, indicates the relative importance of the contributions of the mechanisms of boiling +convection and of bound-water diffusion to the recession of surface B’. However
where D,, is the effective bound moisture diffusivity, based on the total area; D is the bound-water diffusivity through the cell wall materiahfis the fraction of cell wall area in the area perpendicular to the flux; and 6 is the thermomigration coefficient. In addition:
Mu=- Ts, - Tb HJ
Therefore
-M”
Mb1
UT,,-- Tb)
(A3)
.1
H,Dfp,EX,
~ a(T,u-
Tdl
.
At X = 0. I5 and T = 373 K, bound-water diffusivities have values of D - 3.2 x 10-i” m2/s in the longitudinal direction and D - 1.3 x lo-“’ mZ/s in the transversal directions; f - 0.2 in the longitudinal direction and f - 0.4 in the transversal directions; and the coefficient of thermomigration is 6 - 1.8 x lo-’ K- i (Siau, 1984). The thermal conductivity is k - 0.23 x lo-’ kW/m K (Table 2) in the transversal directions and about twice that value in the longitudinal direction. Using these in eq. (A3) we find that, so long as the temperature difference (T,,- Tb) is greater than - lO”C, the contribution of the bound-water movement is less than 3% in the transversal directions. In the longitudinal direction, this contribution is much smaller. Free-water movement If free water is continuously according to the equation
present,
it tends to move
2869
A model for pyrolysis of wet wood T = Tsu f
Interface
8’
Fig. Al.
Zones in a simplified model of high-temperature
where M,, = flux of free water, P, = capillary pressure, P, = pressure of gaseous phase, K, = permeability, and p, = liquid-water viscosity. If the gas phase pressure gradients are neglected (see discussion below), one gets
k(Ts14- Tb)
M”
drying.
Static pressure rise within rhe s&id An important modelling assumption was that moisture vaporizes inside the solid whenever the temperature reached the moisture boiling point, T*(X), which was calculated for atmospheric pressure. This is only valid if the pressure gradients created inside the particle are small. The pressure gradient can be estimated using
-N
Mf,
H,V&IP,)P,AP,
The capillary pressure is of the order of AP, - 1 x lo* N/m2 (Spolek and Plumb, 1981). Permeability, on the other hand, may vary by several orders of magnitude, depending on biological species, and direction (Siau, 1984): 1 x 10-‘5m4/Ns
< K,/fi,
< 1 x 10-13m4/Ns (transversal directions)
(longitudinal direction). Using these values, it is found that, no matter how great the temperature difference (T_ - Tb). free-water movement is always important in the longitudinal direction and is only negligible in the transversal directions for the most permeable woods. This agrees with data obtained by Moyne and Martin (1986) concerning the drying of pine wood at low pressures (hence T,, > Tb) and that obtained by Basilic0 and Martin (1984) at high temperatures. We conclude that this assumption is not valid for moisture contents above the free-water continuity point, which is around 0~45 for most woods.
(-46) where p, and p, are respectively, the water vapour density and viscosity. For most woods, the longitudinal permeability is greater than 1 x lo-l4 m’. For pine wood, in this direction, it is K -1x10-‘2 m2 before torus aspiration and - 1 x 10 - 1Pm2 after torus aspiration (Comstock and CBti, 1968). This means that the pressure differences established in wood are small in this direction [e.g., for (T’,, - l’*) = lOO”C, This is consistent and K, - 1 x lo- L3, AP, - 950 N/m’]. with the pressure gradients measured by Lee et of. (1976) inside wood pyrolysing at high temperatures. Hence, for particles with longitudinal dimension not greater than the transversal dimensions, the longitudinal direction is an “easy” escape way for the vapour, which prevents a significant pressure rise inside the solid. On the other hand, when the longitudinal direction is much bigger than the others (as in the drying of wood boards), significant pressure gradients may be created inside the solid. Basilic0 and Martin (1984) measured a maximum pressure of - 1 atm (gauge) inside a wood board drying at 184°C.