Ind. Eng. Chem. Res. 1996, 35, 3347-3355
3347
Transient Behavior of a Coconut Shell Pyrolyzer: A Mathematical Analysis Swati Bandyopadhyay,† Ranjana Chowdhury,*,‡ and Gopal Krishna Biswas‡ Printing Engineering and Chemical Engineering Departments, Jadavpur University, Calcutta 700 032, India
A mathematical model based on the mechanistic approach to the reaction kinetics of pyrolysis reactions and the realistic analysis of the interaction between simultaneous heat and mass transfer along with the chemical reaction has been developed for the design of smoothly running pyrolyzers. The model of a fixed-bed pyrolysis reactor has been proposed on the basis of the dimensionless parameters with respect to time and radial position. The variation of physical parameters like bed voidage, heat capacity, diffusivity, density, thermal conductivity, etc., on temperature and conversion has been taken into account. A deactivation model has also been incorporated to explain the behavior of pyrolysis reactions at temperaures above 673 K. The simulated results of the model have been explained by comparing them with the experimental results. Introduction The whole world is going to face an acute shortage of commercial energy in the coming century. The fossil fuel sources will be exhausted within the next hundred years. Hence, renewable energy sources have to be harnessed. This necessitates the use of modern technology based biomass conversion systems. The thermochemical and biological conversion of biomass and wastes are the viable techniques to produce energy. Thermal conversion involves mainly three processes which are combustion, pyrolysis, and gasification. Pyrolysis is the thermal conversion process where biomass decomposes to various products like solid char, liquid tar, and gases under an inert atmosphere. It is the starting process of other thermal conversions like gasification, combustion, etc. Hence, the study of the kinetics of pyrolysis of biomass is extremely important not only for the production of high calorific value products but also for the proper understanding of the thermochemical processing for the reliable design of a biomass pyrolysis reactor. The output depends on the temperature, reaction time, heating rate, type, and size of input materials and the method of operation. In the present investigation, a coconut shell was chosen as the raw material for analyzing the transient behavior of a pyrolyzer for its high calorific value and low ash content. In the pyrolysis reactors, heat transfer and mass transfer occur simultaneously with the complex array of homogeneous and heterogeneous reactions. A mathematical model based on the mechanistic approach to the reaction kinetics of pyrolysis reactions and the realistic analysis of the interaction between simultaneous heat and mass transfer along with the chemical reaction will be of great use to the process engineers for the design of smoothly running pyrolyzers. From the literature survey, it is apparent that, although many interesting works (Kansa et al., 1977; Shafizadeh and Chin, 1977; Thurner and Mann, 1981; Antal, 1983; Nunn et al., 1985a,b; Alves and Figueiredo, 1988, 1989; Agarwal, 1988; Balci et al., 1993) have been reported * To whom all correspondence should be addressed. † Printing Engineering Department. ‡ Chemical Engineering Department.
S0888-5885(95)00695-6 CCC: $12.00
on biomass pyrolysis, only a few works have been reported in this respect. Maa and Bailie (1973) have developed a model on the basis of the assumptions of steady-state mass transfer and heat transfer. Another model, developed by Fan et al. (1977a) for a transient pyrolyzing system, utilizes the volume reaction model and takes into account the simultaneous heat and mass transfer and the variation of physical parameters with respect to temperature and solid conversion. This analysis is based on a single spherical particle and the condition with the assumption of zero bulk concentration. The latter condition is, however, very difficult to maintain in a pyrolysis reactor, if not impossible. Moreover the simulated results have not been compared with experimental results. In 1984, Pyle and Zaror have studied the heat transfer and kinetics of the pyrolysis of wood. Kothari and Antal (1985) showed that the time required for rapid pyrolysis of cellulose is composed of heat up time and devolatilization time. The heat-up time may be considered as the time required for radiative and convective heat transfer to raise the particle’s temperature to a pyrolysis temperature (sensible heat requirement). The devolatilization time is expressed as the time requirement to provide the endothermic heat of reaction (latent heat requirement). While studying the heat-transfer effect on the biomass pyrolysis, Antal (1985), Kothari and Antal (1985), Cooley and Antal (1988), Le´de´ et al. (1986, 1987, 1992), and Diebold and Scahill (1987) have shown in different manners that the true solid temperature may be quite different from that of the heat source, indicating that a thermal resistance step is also to be considered in conjunction with a mass-transfer resistance step in modeling biomass pyrolysis kinetics. In this model, the effects of chemical reaction, external heat transfer, internal heat transfer, and internal mass transfer have been considered. Chan et al. (1985) developed a mathematical model where both chemical and physical processes are described using fundamental principles. Villermaux et al. (1986) and Bilbao et al. (1993) considered heat-transfer effects on the observed rate of pyrolysis of biomass. In the previous work (Bandyopadhyay, 1995) on pyrolysis kinetics of a coconut shell in the temperature range of 523-973 K, it was observed that the rate of the pyrolysis reaction of a coconut shell decreased at © 1996 American Chemical Society
3348 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996
temperatures above 673 K. A deactivation model was incorporated to explain the kinetic behavior of a coconut shell at temperatures higher than 673 K. In the present investigation, a mathematical model of a fixed-bed pyrolysis reactor was proposed based on the dimensionless parameters with respect to time, radial position, etc. The simultaneous unsteady-state heat and mass transfer coupled with the chemical reactions were analyzed on the mechanistic approach. The variation of physical parameters on temperature and conversion was taken into account. The deactivation model (Bandyopadhyay et al., 1995) was also incorporated in the mathematical analysis to explain the behavior of the pyrolysis reaction at temperatures above 673 K. The simulated results of the model were explained by comparing these with the experimental results. Experiments The samples were first cut into short pieces and air dried. Then the samples were ground in a hammer mill to 200 mesh. After air drying a long time, the sample was dried in an oven at 373 K. Predried coconut shell had 69.11% volatile matter, 28.45% fixed carbon, and 2.44% ash content. Its calorific value was found to be 18.18 MJ/kg. Experimental Setup. A vertical fixed-bed reactor was designed and developed. The reactor had a 50.8 mm internal diameter and a 762 mm height. The system facilitated measurement of residue and gas as a function of time. Heating was provided by a vertical electric furnace, coupled with a PID temperature controller. The furnace wall temperature, Tf, was varied at the rate of 0.217 K/s (dTf/dt ) 0.217 K/s). Composite temperatures were measured by different thermocouples at different radial positions and reactor wall. A 200-mesh sieve with a porous stainless steel plate was provided at 305 mm height from the bottom. The top cap of the reactor was provided with holes of 5 mm diameter at the center, 10 mm from the center, 17.80 mm from the center, and adjacent to the reactor wall for insertion of thermocouples and a volatile outlet. Stainless steel tubes of 0.5 mm diameter were introduced through the holes of the cap for providing the passage of the volatile products at different radial positions. The tubes were provided with a 200-mesh stainless steel seive of 150 mm height (reactor bed height is 150 mm) to allow diffusion through the bed. Gas sampling bulbs were attached to the gas outlet at regular intervals of time for gas analysis. The reactor was provided with a bottom outlet for nitrogen gas purging. Since the entire process was to be operated in an inert environment, special precautions were made to provide a complete air-tight arrangement. In the present experimental setup, the radial temperature profile and the volatile concentration (weight basis) profile were not determined simultaneously. In one arrangement, the volatile concentration profile was determined (as shown in Figure 1a) by allowing the volatile to come out through the top lid at different radial positions. In this arrangement, a single thermocouple was introduced from the bottom lid at a suitable radial position. On the other hand, while measuring the temperature profile, thermocouples were introduced from the top lid at positions identical to those of the volatile exit points in the previous case. This arrangement is shown in Figure 1b. In the arrangement, the volatiles were
Figure 1. (a) Experimental setup of a fixed-bed pyrolyzer to obtain the radial volatile concentration profile. (b) Experimental setup of a fixed-bed pyrolyzer to obtain the radial temperature profile.
allowed to come out from a side port in the upper part of the reactor (not shown in the figure). This port remained closed in the other arrangement. The radial profile of the temperature obtained from this arrangement and that obtained by inserting the thermocouples from the bottom lid at different radial positions one at a time was almost identical (within (2 °C). In order to verify whether an axial profile of temperature existed,
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3349
thermocouples were placed at positions varying from top to bottom. It was observed that an axial temperature profile was absent. In order to measure the weight concentrations Ww and Wc at different radial positions at a given time, the following protocol has been maintained: After a predetermined time interval, the experiment was stopped. The solid sample from each radial position was taken and weighed. To have the values of Ww, Wc, etc., at different predetermined time intervals, experiments had to be restarted and had to be continued for the prescheduled time. For each run, a solid sample from each radial position was weighed. However, the solid samples thus obtained were mixtures of unreacted coconut shell and solid product, char. Ww and Wc were distinguished with the help of the following equations:
dWw ) (kc + kv)Ww ) kWw (since k ) kc + kv) dt dWc ) kcWw, dt
dWv ) kvWw dt
Wc - Wc0 kcWwo exp(-kt) ) Wv - Wv0 kvWwo exp(-kt) In the present case, Wc0 ) Wv0 ) 0. So,
kc Wc kc ) or Wc ) Wv W v kv kv
(A)
Thus, Wc was determined from the value of Wv. Ww was determined by the expression Ww ) WR - Wc. Wv was determined in two methods. Method I.
fraction of volatiles produced + fraction of char produced ) fraction of coconut shell reacted or
V + C ) W0 - W ) 1 - W (since W0 ) 1)
or
V ) 1 - (W + C) ) 1 - S
or
Wv ) (1 - S)Ww0
(B)
Therefore, from the weight of the solid residue, Wv was evaluated. Method II. During each time interval volatiles coming out from each radial position was collected and their volumes were measured. From the known (experimentally) composition of the volatiles, the mass of the volatiles and hence Wv were calculated. The results obtained from methods I and II were identical. Replicate experimental observations were taken. The estimation of experimental error was done by evaluating the error mean squares Se2 (Kafarov, 1976). The Se2 values for different parameters are given in Table 5.
kinetics that it is better to start in understanding the kinetics of a complex process from simpler equations. A simple model was developed where all the volatiles are lumped and assumed to form a single volatile product. Similarly solid products are lumped and assumed to be pure char. A scheme with the concept of an active complex (Bradbury et al., 1979; Alves and Figueiredo, 1988) was proposed for the reaction pathway of the pyrolysis of a coconut shell. This is as follows: kv
predried coconut shell
kc
char
(1)
The following assumptions have been made for kinetic modeling: 1. It has been observed from isothermal experiments (Bandyopadhyay, 1995) that there is a sharp rise and fall in concentration profiles of Wv, Wc, and Ww, respectively, against time right from the beginning period of the run. Thus, an absence of an initial flat period in the concentration profiles indicates that the first step is instantaneous. Hence, the first step of the scheme, i.e., the “active complex” formation, is instantaneous. 2. All the reactions occurring in the scheme are of first order with respect to the solid reactant (Shafizadeh and Chin, 1977; Thurner and Mann, 1981). 3. The solid residue obtained at infinite time, at any temperature, is entirely comprised of char (Thurner and Mann, 1981). 4. Solid residue obtained at any time other than t ) ∞ is made up of unreacted solid reactant and solid product char. 5. As the operation is a semibatch, the probability of occurrence of all the secondary reactions is assumed to be zero (Chowdhury et al., 1994). 6. An absolutely inert atmosphere prevails during pyrolysis. 7. Deactivation of a pyrolyzing coconut shell was observed (Bandyopadhyay et al., 1995) to occur at temperatures above 673 K. At 973 K, the reaction becomes almost stagnant. At 1023 K, the rate constant during the pyrolysis period decreases to zero. Similar observations have been reported by Julien et al. (1991) even at lower temperatures when working on vacuum pyrolysis of cellulose. Balci et al. (1993) observed this phenomenon during the study of almond shell and hazelnut shell pyrolysis at 723 K. According to Balci et al. (1993), the rate of deactivation is a function of temperature and activity. In the previous work of Bandyopadhyay et al. (1995), a deactivation model was proposed, which is as follows: The rates of change of activities a, av, and ac with the normalized temperature parameter, φ, have been proposed to vary linearly with the corresponding activities and nonlinearly with the normalized temperatures. The relationships are
Theoretical Analysis Pyrolysis of lignocellulosic materials proceeds through complex reactions in series, parallel, or a combination of both. Hundreds of products and intermediates are formed. In the present investigation, an attempt was made to put forward a realistic model based on simple reactions, remembering the well-known concept of
active complex
volatiles
da/dφ ) -Aφ Ba dav/dφ ) -Avφ Bvav dac/dφ ) -Acφ Bcac where
(C)
3350 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996
φ)
T - Tmax(a)1) Tmin(a)0) - Tmax(a)1)
(D)
Tmax(a)1) ) maximum temperature up to which activities remain unity and Tmin(a)0) ) minimum temperatures at which activities become zero. Here, Tmax(a)1) ) 673 K and Tmin(a)0) ) 1023 K.
a)
kactual
kArrhenius ) (actual rate constant of coconut shell decomposition)/(rate constant of coconut shell decomposition if there were no deactivation, i.e., k determined using the Arrhenius parameters k0 and E) (E)
av )
kv,actual
kv,Arrhenius ) (actual rate constant of volatile formation)/ (rate constant of volatile formation if there were no deactivation, i.e., kv determined using (F) the Arrhenius parameters kv0 and Ev)
ac )
kc,actual
kc,Arrhenius ) (actual rate constant of char formation)/ (rate constant of char formation if there were no deactivation, i.e., kc determined using the (G) Arrhenius parameters kc0 and Ec)
It has been assumed that this deactivation model is valid during the present investigation. 8. The heat of reaction of the overall pyrolysis process has been assumed to be zero (Pyle and Zaror, 1984). As evidenced by Maa and Bailie (1973), the heat of reactions of the endothermic and exothermic reactions occurring in sequence during pyrolysis are of the same order, and hence this antagonistic effect makes the net heat effect of the reactions when lumped together zero. 9. Fluid-film resistance to mass transfer of the volatile product is negligible at the solid-fluid boundary, i.e., within the film in between the outer surface of the cylindrical reacting mass and the furnace wall, and hence the bulk/film concentration of the volatiles may be taken to be the same as that at the peripheral solid surface; i.e., no concentration gradient exists at the solid-fluid boundary (δWv/δr ) 0 at r ) Ri). 10. The mass transfer is occurring by both molecular and eddy diffusion mechanisms. 11. The reaction bed volume remains constant throughout the operation. 12. Heat-transfer resistance in the gas film in between the furnace wall and the reacting mass has been neglected at the fluid-furnace wall interface, and hence the bulk/film temperature is taken to be the same as that of the furnace wall temperature. 13. There is no temperature gradient between the solid and the fluid phase in the reactant bed. In the bed, the whole system is considered to be a composite. 14. The porosity of the bed, , varies with reaction temperature and solid conversion (Wen, 1968). 15. Since the reactor geometry is cylindrical, the cylindrical coordinate has been used in the analysis of the system. 16. Since the reactor is heated along the external wall by an electrical heater, the axial variation of all the
dependent variables has been neglected. Although the volatiles produced at the bottom have more residence time in the reactor than those produced at the top, the rates of secondary reactions are so slow that, in this range of residence time, no further cracking is expected to occur. Moreover, if this happens at all, the cracking of vapor will not change the total mass of the vapor and hence the weight concentration of the vapor phase along the axial direction remains constant. 17. The solid particles under investigation are very small (-200 mesh) and thus have a very high specific surface area (6000 m-1). Thus, no intraparticle heatand mass-transfer limitation has been considered in the present modeling and simulation. General material and heat balances over a differential element in the cylindrical reacting element give rise to the following equations: The mass balance equations for coconut shell, char, and residue are as follows:
δWw ) -(kv + kw)Ww ) -kWw δt
(2)
where k ) kc + kv.
δWw E ) -k0 exp W (T < 673 K) δt RT w
(
)
) -kaWw (T > 673 K)
[ ( (
) -k0 exp -
(3)
)]
)
(3a)
E AR 1+ Tφ B+1 Ww RT (B + 1)E (T > 673 K) (4)
Similarly,
( )
δWc Ec ) kc0 exp W (T < 673 K) δt RT w ) kacWw (T > 673 K)
[ ( (
) kc0 exp -
)
(5)
)]
(5a)
AcR Ec 1+ Tφ Bc+1 Ww RT (Bc + 1)Ec (T > 673 K) (6) δWR δWc δWw ) + δt δt δt
(7)
respectively. The mass balance equation of volatiles is
(
)
( )
δWv -Ev δ 1 δ (Wv) ) rDv + kv0 exp Ww δt r δr δr RT
) avkvWw + δ (Wv) ) δt
(
[ ( (
kv0 exp -
)
δWv 1 δ rDv r δr δr
(T < 673 K) (8) (T > 673 K) (8a)
) )] )
AvR Ev 1+ Tφ Bv+1 Ww + RT (Bv + 1)Ev
(
δWv 1 δ rDv r δr δr
(T > 673 K) (9)
The heat balance equation is given by:
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3351
Fcp
δWv δT δT 1 δ δT ) c Kr + Dv δt r δr e δr δr pv δr
(
)
(10)
Fhcjp
δT h δT h NLe δ δV δT h ) cj W K h β +D hv h δθ β δβ e δβ δβ pv w0 δβ
)
(21)
δT h f /δθ ) M
(21a)
(
The rate of change of the furnace wall temperature, Tf, is given by:
dTf/dt ) m ) heating rate
(11)
The dimensionless forms of the initial boundary conditions are as follows:
The initial conditions for eqs 1-5 are as follows:
V ) 0, T h ) 1, W ) 1, C ) 0, S ) 1 for 0 e β e 1, θ ) 0 (22)
Wv ) 0, T ) T0, Ww ) Ww0, Wc ) 0, WR ) Ww0 for 0 e r e Ri, t ) 0 (12)
The boundary conditions are
In the present case, the heating rate is m ) 0.217 K/s. The boundary conditions are
δWv/δr ) 0
for r ) 0, t > 0
δT/δr ) 0
for r ) 0, t > 0
-Ke
for r ) Ri
δT ) hc(T - Tf) + hr(T4 - Tf4) δr
for r ) Ri (13)
The dimensionless forms of the above eqs 3-10 are given respectively by:
( )
-E h δW ) -Φ2 exp W (T < 673 K) δθ T h
[ ( (
(14)
[ ( (
) )]
δV )0 δβ
for β ) 1, θ > 0
The dimensionless groups and parameters are given in Table 1. The functional dependences of different physical parameters like , D h v, Fj, cjpv, cjp, and K h e on different independent variables, e.g., conversion S and temperature T h , have been determined for the present case using some basic equations from the literature (Perry and Chilton, 1973; Fan et al., 1977b; Wen, 1968) and are given in Table 2. The kinetics of pyrolysis of a coconut shell has been investigated in the temperature range of 523-1023 K (Bandyopadhyay, 1995) in an inert
W)
Ww Ww0
C)
Wc Ww0
S)
Ws Ww0
V)
Wv Ww0
T h)
T T0
M)
mRi2 Dv0T0
k0D2 4Dv0
E h )
E RT0
Φc2 )
kc0D2 4Dv0
E hc )
Ec RT0
Φv2 )
kv0D2 4Dv0
E hv )
Ev RT0 Dv Dv0
(16)
) )]
-E hc Ac δC ) Φc2 exp 1+ T h φ Bc+1 W δθ T h (Bc + 1)E hc
Φ2 )
(T > 673 K) (17) δS δC δW ) + δθ δθ δθ
for β ) 0, θ > 0
δT h ) Nuc(T h -T h f) + Nur(T h4 - T h f4) δβ for β ) 1, θ > 0 (23)
(T > 673 K) (15)
( )
δT h /δβ ) 0
Table 1. Dimensionless Groups Used in the Study
δW E h AR ) -Φ2 exp - 1 + T h φ B+1 W δθ T h (B + 1)E h
-E hc δC ) Φc2 exp W (T < 673 K) δθ T h
for β ) 0, θ > 0
D hv -K he
δWv )0 Dv δr
δV/δβ ) 0
(18)
The mass balance equation of volatiles is
(
)
( )
β)
r Ri
D hv )
Fj )
F F0
NLe )
1 δ δ δV (V) ) βD hv + Φv2W exp δθ β δβ δβ T h
-E hv
(T < 673 K) (19)
( ) [ ( ( ) )]
δ 1 δ δV (V) ) βD hv + δθ β δβ δβ Φv2W exp
-E hv T h
1+
Av T h Bv+1 φ W Bv + 1 E hv
cjpv )
cpv cpv0
cjp )
cp cp0
θ)
4Dv0 t D2
(T > 673 K) (20) The temperature variation of the composite is given by:
Nuc )
hcD 2Ke0
Ke0 F0cp0Dv0
T hf )
Tf T0
K he )
Ke Ke0
Nur )
hrT03D 2Ke0
3352 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 Table 2. Functional Dependence of Physical Parameters parameter
functional dependency
numerical values of constants used in this study
0 + b1(1 - S) T h 1.5 exp(1 - S) b2(1 - ) + b3 T b4 + b5(T h - 1) b6(1 - ) + b7(T h - 1) p00.67 + 1 - 0.67 Ke0 solid (p0 - 1)(0.67 - ) + 1
D hv Fj cjpv jcp Ke
0 ) 0.5, b1 ) 0.2
ref
b2 ) 1.99, b3 ) 0.005
Wen, 1968 Fan et al., 1977 Perry and Chilton, 1973
b4 ) 1.0, b5 ) 0.0662 b6 ) 1.26, b7 ) 0.74
Perry and Chilton, 1973 Perry and Chilton, 1973
p0 ) 0.21, Ke0 ) 0.1261 W/mK
Perry and Chilton, 1973
Table 3. Kinetic Parameters Used in This Study kinetic param k0 (s-1) kv0 (s-1) kc0 (s-1) E (kJ/mol) Ev (kJ/mol) Ec (kJ/mol) A Av Ac B Bv Bc
value
correlation coefficient
5.166 × 104 1.366 × 106 22.166 94.92 114.82 58.94 7.18 × 10-4 6.93 × 10-4 8.047 × 10-4 -0.1603 -0.1791 -0.0853
0.98 0.96 0.95 0.98 0.96 0.95 0.99 0.99 0.99 0.99 0.99 0.99
Table 4. Values of Physical and Thermal Parameters Used parameter
value
parameter
value
W0 cp0 (J/kg‚K) cpv0 (J/kg‚K) F0 (kg/m3) Fv0 (kg/m3) Φ2 E Φc2 Ec Φv2
1 1720 1010.86 510 1.35475 3.33 × 107 37.91 14344 23.54 8.62 × 108
Ev NLe Nuc Nur M 0 Dv (m2/s) T0 (K) Ww0 (kg/m3)
45.85 0.3684 1.13 0.2958 0.4658 0.5 10-6 301 510
Table 5. Values of Experimental Errors (Se2) parameter
dimension
Se2
θ t W Ww S WR C Wc V Wv
dimensionless s dimensionless kg/m3 dimensionless kg/m3 dimensionless kg/m3 dimensionless kg/m3
1.089 × 10-3 25 8 × 10-5 20.88 5.68 × 10-5 14.77 1.63 × 10-5 4.216 1.63 × 10-5 4.2395
atmosphere by a captive sampling technique. Since it has been observed that, at higher temperatures, deactivation occurs, the frequency factors, activation energies, etc., were evaluated in the temperature range of 523-673 K, by regression analysis of experimental data obtained under isothermal conditions. The values of frequency factors, activation energies, and deactivation model parameters are given in Table 3. The correlation coefficients of these regression analyses are also reported in Table 3. Above 673 K, a deactivation model (Bandyopadhyay et al., 1995) was used. The model parameters are also given in Table 3 along with the relevant correlation coefficients. The values of different physical and thermal parameters used for this study are given in Table 4. Method of Solution. The numerical solution of partial differential equations was made by the technique of “Method of Lines” (Constantinides, 1987). In this method the partial differential equations are solved by
Figure 2. Comparison of simulated temperature profile (s) with the experimental data at β ) 0 (4), 0.4 (b), 0.7 (0), and 0.9 (O).
converting the equations into a set of ordinary differential equations by discretizing only the spatial derivatives using finite differences and leaving the time derivatives unchanged. The Second-Order Central Finite Difference method is used for the spatial discretization. The mesh spacing for the spatial discretization is specified as 1/10 for this study. Thus, the number of discrete points in the β direction comes to 11. The time step size (dimensionless θ) is set at 10-4. The derived set of ordinary differential equations was solved by the Runge-Kutta Fourth-Order Method. A computer program in BASIC (Gottfried, 1986) was developed for solving this set of ordinary differential equations. The implementation technique of the Runge-Kutta method in ODE.BAS (Constantinides, 1987) was followed in this program. The initial values of different physical parameters and the numerical values of several dimensionless groups used under the present investigation are given in Table 4. Due to the particular boundary conditions at r ) 0, the partial differential equations become solvable at r ) 0. Similar to the present model, many systems of this type have been analyzed by previous workers (Fan et al., 1977a,b; Kothari and Antal, 1985; Mickley et al., 1984; Davis, 1984) by taking the origin at r ) 0. The simulation was done for the cases when the furnace wall temperature Tf was a linear function of time. The details are given in thePh.D. thesis of Bandyopadhyay (1995). Results and Discussion Radial Temperature Profile of a Coconut Shell. In Figure 2, the temperature profiles in the pyrolysis reactor are plotted against dimensionless time θ, with the dimensionless radial position β as a parameter for
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3353
Figure 3. Comparison of simulated weight loss profile of coconut shell (s) with the experimental data at β ) 0 (4), 0.4 (b), 0.7 (0), and 0.9 (O).
increasing the furnace wall temperature. The experimental data are superimposed on the same figures. From the close observation of the figures, it is evident that the simulated profiles explain the reality successfully. The temperature at each radial position increases with time almost in the same pattern as that of the furnace wall. The agreement between the simulated and the experimental profile validates the assumption that the heat of the overall pyrolysis reaction, when lumped together, is nil. Weight Loss Profile of the Reactant. In Figure 3, the simulated values of the dimensionless mass fractions of the solid reactant, i.e., a coconut shell at different dimensionless radial position β, are plotted against the dimensionless time θ, when the furnace wall temperature is a linear function of time. The same data derived on the basis of experimental results and the assumption number 3 are superimposed on the same figure. From closer observation of the figure, it is evident that the simulated profiles successfully describe the data derived from the experiments. From the figure, it is observed that, at each position, the dimensionless solid reactant concentration W on mass basis decreases with dimensionless time θ. As the time increases (θ > 2.65), the rate of decrease of the concentration decreases at higher values of dimensionless radial position β, e.g., β ) 1, and a little deviation of the simulated profile from the experimental one is observed. This may be due to the fact that in the early period of pyrolysis, at the periphery, the extent of reaction is high due to the availability of the reactant and favorable reaction temperature. As the time increases, the reactants get depleted and hence the extent of reaction diminishes, although the temperature is increased. However, in the case of the radial position near the center, the prevailing temperature is not so favorable for pyrolysis at an earlier period, and as time propagates, the temperature increases at the central position due to unsteady-state heat conduction from the peripheral position and an increase of the furnace wall temperature. Therefore, the extent of reaction increases at the central position until there is an abundance of reactant at those sites. Concentration Profile of Char. In Figure 4, the simulated dimensionless weight parameters of char are plotted against dimensionless time θ with dimensionless radial position β as a parameter when the furnace wall
Figure 4. Comparison of simulated weight profile of char formation (s) with the experimental data at β ) 0 (4), 0.4 (b), 0.7 (0), and 0.9 (O).
Figure 5. Comparison of simulated weight loss profile of residue (s) with the experimental data at β ) 0 (4), 0.4 (b), 0.7 (0), and 0.9 (O).
temperature is a function of time. The similar data derived from the experimental results and the assumption no. 3 are superimposed on the same figure. From closer observation of the data, it is evident that the simulated results tally well with the experimental ones. From closer observation of Figure 4, it is evident that simulated profiles successfully represent reality. From the figure, it appears that, at each radial position, the formation of char increases with time, as expected. The rate of increase is greater at the peripheral zones at the initial period. At higher values of dimensionless time θ, the rate of char formation decreases at higher dimensionless radial positions. This may be due to the deactivation of the reactant at higher temperatures prevailing at those zones, at the later period of pyrolysis. Variation of the Weight Loss Profile of Residue. In Figure 5, the simulated profile of residue is plotted. A similar experimental profile of the weight loss of solid residue is superimposed on the same figure. From closer observation of the figure, it appears that the simulated results describe the reality satisfactorily. The figure shows that the weight fraction of residue on mass
3354 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996
along with chemical reaction following a proposed parallel pathway and deactivation which predicts an increase in the model activation energy with temperature above 673 K is expected to be well representative of the transient behavior of the biomass pyrolyzer. Acknowledgment The authors acknowledge Prof. (Dr.) P. Bhattacharya, Professor, Chemical Engineering Department, Jadavpur University, Calcutta, India, for his valuable advice. The authors also acknowledge Mr. Sivaji Bandyopadhyay, Reader, Computer Science and Engineering Department, Jadavpur University, Calcutta, India, for the computer programming part for solution of partial differential equations. The authors are also indebted to the reviewers for their careful reading and critique of the original manuscript. Nomenclature Figure 6. Comparison of simulated weight profile of volatile formation (s) with the experimental data at β ) 0 (4), 0.4 (b), 0.7 (0), and 0.9 (O).
basis decreases with θ sharply for increasing β. However, as time increases (when θ > 2.65 at β ) 1), the rate of weight loss gradually decreases for higher β. This may be due to the deactivation of the reaction rate at higher temperature, as explained in the earlier section. Variation of the Weight Fraction Profile of Volatile Formation. In Figure 6, the simulated dimensionless weight profiles of volatiles are plotted against dimensionles time θ with dimensionless radial position β as a parameter for increasing the furnace wall temperature. Experimental results are superimposed on the same figures. From closer observation of the figure, it is evident that the simulated profile can explain reality satisfactorily. It is also observed that at the initial period of the process, the volatile concentration is slightly higher near the periphery. This may be due to the fact that, during this period, the favorable reaction temperature prevails at those sites and the reactant present is also abundant. According to the figure, as time increases, volatile formation curves at different radial positions are almost overlapped. This behavior is somewhat different from the profile of char formation and weight loss of the reactant. This may be due to the fact that, in contrast to the solid reactant coconut shell and solid product char, the volatiles diffuse at a high rate toward the lower concentration zone at the center as soon as it is formed at the periphery. As time progresses, the solid reactant gets exhausted at the peripheral zone, whereas the reaction proceeds at the central position, due to the availability of the reactant and the favorable reaction temperature prevailing at those sites. Moreover, the rate of mass transfer of volatiles also increases with an increase in time as the temperature is enhanced. Thus, at a later period of operation, the profiles of volatile concentration against time at different radial positions overlap. Thus, the present model incorporating the unsteady-state heat and mass transfer along with the pyrolysis reaction following a proposed parallel pathway, as well as the variation of a physical parameter, explains the pyrolysis system satisfactorily. Conclusion From the analysis, it may be concluded that the proposed model incorporating heat and mass transfer
A, B ) deactivation model constants a ) activity of solid C ) weight fraction of char to the basis of the initial weight concentration of the reactant Ww0, Wc/Ww0 cp ) heat capacity of fluid-solid composite, Cp0, at initial conditions (J/kg‚K) cpv ) heat capacity of fluid product (J/kg‚K) D ) diameter of the reactor bed (m) Dv ) effective diffusivity of fluid product (m2/s) E ) activation energy (kJ/mol) hc ) convective heat-transfer coefficient (W/m2‚K) hr ) radiative heat-transfer coefficient (W/m2‚K4) ∆H ) heat of reaction (J/mol) k ) rate constant, k0 ) frequency factor (s-1) Ke ) effective thermal conductivity of composite (W/m‚K) Ke0 ) thermal conductivity of solid at T0 (W/m‚K) M ) dimensionless heating rate m ) heating rate (K/s) NLe ) Lewis number, Ke0/F0cp0Dv0 Nuc ) Nusselt number for convective heat transfer, hcRi/ Ke0 Nur ) Nusselt number for radiative heat transfer, hrT03Ri/ Ke0 r ) distance from the center of the reactor bed (m) R ) ideal gas constant (J/mol‚K) Ri ) inside radius of the reactor (m) S ) weight fraction of residue to the basis of the initial weight concentration of the reactant Ww0, WR/Ww0 Se2 ) error mean square T ) temperature of fluid-solid composite (K) Tf ) temperature of the wall surrounding the reactor bed, i.e., the furnace wall temperature (K) t ) time (s) V ) weight fraction of volatiles to the basis of the initial weight concentration of the reactant Ww0, Wv/Ww0 W ) weight fraction of reactant to the basis of the initial weight concentration of the reactant Ww0, Ww/Ww0 WR ) weight concentration of residue (kg/m3) Wv ) weight concentration of volatile product, (kg/m3) Ww ) weight concentration of solid reactant, i.e., coconut shell (kg/m3) Wc ) weight concentration of solid product, i.e., char (kg/ m3) Greek Symbols ) void fraction of particle F ) density of fluid-solid composite (kg/m3) θ ) dimensionless time, Dv0t/R2 β ) 2r/D φ ) dimensionless temperature parameter
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3355 Subscripts c ) char o ) initial condition R ) residue v ) volatiles w ) coconut shell
Literature Cited Agarwal, R. K. Kinetics of Reactions involved in Pyrolysis of Cellulose II. The Modified Kilzer-Broido Model. Can. J. Chem. Eng. 1988, 66, 413-418. Alves, S. S.; Figueiredo, J. L. Pyrolysis Kinetics of Lignocellulosic Materials by Multistage Isothermal Thermogravimetry. J. Anal. Appl. Pyrolysis 1988, 13, 123-134. Alves, S. S.; Figueiredo, J. L. A Model for Pyrolysis of Wet Wood. Chem. Eng. Sci. 1989, 44, 2861-2869. Antal, M. J., Jr. Effects of Reactor Severity on the Gas Phase Pyrolysis of Cellulose and Kraft Lignin Derived Volatile Matter. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 366-375. Antal, M. J., Jr. Mathematical Modelling of Biomass Pyrolysis Phenomena. Fuel 1985, 64, 1483-1486. Balci, S.; Dogu, T.; Yucel, H. Pyrolysis Kinetics of Lignocellulosic Materials. Ind. Eng. Chem. Res. 1993, 32, 2573-2579. Bandyopadhyay, S. Studies on Pyrolysis of Coconut Shell. Ph.D. Dissertation, Jadavpur University, 1995. Bandyopadhyay, S.; Chowdhury, R.; Biswas, G. K. Studies on Thermal Deactivation of Pyrolysis of Coconut Shell. Int. J. Energy Res. 1995, submitted for publication. Bilbao, R.; Millera, A.; Murillo, M. Temperature Profiles and Weight Loss in the Thermal Decomposition of Large Spherical Wood Particles. Ind. Eng. Chem. Res. 1993, 32, 1811-1817. Bradbury, A. G. W.; Sakai, Y.; Shafizadeh, F. A Kinetic Model for Pyrolysis of Cellulose. J. Appl. Polym. Sci. 1979, 23, 3271-3280. Chan, W. R.; Kelbon, M.; Kruges, B. B. Modelling and Experimental Verification of Physical and Chemical Processes during Pyrolysis of Large Biomass Particle. Fuel 1985, 64, 505-1513. Chowdhury, R.; Bhattacharya, P.; Chakraborty, M. Modelling and Simulation of a Downdraft Rice Husk Gasifier. Int. J. Energy Res. 1994, 18, 581-594. Constantinides, A. Applied Numerical Methods with Personal Computers; Mc Graw-Hill: Singapore, 1987. Cooley, S.; Antal, M. J., Jr. Kinetics of Cellulose Pyrolysis in the Presence of Nitric Oxide. J. Anal. Appl. Pyrolysis 1988, 14 (23), 149-161. Davis, M. E. Numerical Methods and Modelling for Chemical Engineers; John Wiley & Sons: New York, 1984. Diebold, J.; Scahill, J. Biomass to Gasoline upgrading pyrolytic vapours to aromatic Gasoline with Zeolite catalyst at atmospheric pressure. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1987, 32 (2), 297-307. Fan, L.; Miyanami, K.; Fan, L. T. Transient Analysis of Isothermal Fluid-Solid Reaction Systems: Modelling the Sigmoidal Conversion-Time Behaviour of a Gas-Solid Reaction. Chem. Eng. J. 1977a, 13, 13-20. Fan, L. T.; Fan, L.; Miyanami, K.; Chen, T. Y.; Wallawender, W. P. A Mathematical Model for Pyrolysis of a Solid Particle. Can. J. Chem. Eng. 1977b, 55, 47-53. Gottfried, B. S. Theory and Problems of Programming with BASIC, 3rd ed.; Schaum’s Outline Series; McGraw-Hill: Singapore, 1986.
Julien, S.; Chornet, E.; Tiwari, P. K.; Overend, R. P. Vacuum Pyrolysis of Cellulose Fourier Transform Infrared Characterization of Solid Residue, Product Distribution and Correlations. J. Anal. Appl. Pyrolysis 1991, 19, 81-104. Kafarov, V. Cybernetic Methods in Chemistry and Chemical Engineering; Translated from Russian by Kuznetsov, B.; MIR Publishers: Moscow, 1976. Kansa, E. J.; Perlee, H. E.; Chaiken, R. F. Mathematical Model of Wood Pyrolysis including Internal Forced Convection. Combust. Flame 1977, 29, 311-324. Kothari, V.; Antal, M. J., Jr. Numerical Studies of the Flash Pyrolysis of Cellulose. Fuel 1985, 64, 1487-1494. Le´de´, J.; Verzaro, F.; Antoine, B.; Villermaux, J. Flash Pyrolysis of Wood in a Cyclone Reactor. J. Chem. Eng. 1986, 20 (6), 309317. Le´de´, J.; Li, H. Z.; Villermaux, J. Fusion like Behaviour of Biomass Pyrolysis. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1987, 32 (2), 59-67. Le´de´, J.; Li, H. Z.; Loulignac, F.; Villermaux, J. Cyclone Reactors IVsMeasurement of efficiency of heat transfer between the walls and gas and solid phase. Chem. Eng. J. (Lausanne) 1992, 48 (20), 83-99. Maa, P. S.; Bailie, R. C. Influence of Particle Size and Environmental Conditions on High Temperature Pyrolysis of Cellulosic Materials. Combust. Sci. Technol. 1973, 7, 257-269. Mickley, H. S.; Sherwood, T. S.; Reed, C. E. Applied Mathematics in Chemical Engineering, 5th Reprint; Tata McGraw-Hill Publishing Co. Ltd.: New Delhi, India, 1984. Nunn, T. R.; Howard, J. B.; Longwell, J. P.; Peters, W. A. Product Compositions and Kinetics in Rapid Pyrolysis of Sweetgum Hardwood. Ind. Eng. Chem. Process Des. Dev. 1985a, 24, 836844. Nunn, T. R.; Howard, J. B.; Longwell, J. P.; Peters, W. A. Product Compositions and Kinetics in Rapid Pyrolysis of Milled Wood Lignin. Ind. Eng. Chem. Process Des. Dev. 1985b, 24, 844-852. Perry, R. H.; Chilton, C. H. Chemical Engineers’ Handbook, 5th ed.; McGraw-Hill: New York, 1973. Pyle, D. L.; Zaror, C. A. Heat Transfer and Kinetics in the Low Temperature Pyrolysis of Solids. Chem. Eng. Sci. 1984, 39, 147158. Shafizadeh, F.; Chin, P. S. Thermal Deterioration of Wood. Wood Technology, Chemical Aspects; Goldstein, I. S., Ed.; ACS Symposium Series 43; American Chemical Society: Washington, DC, 1977. Thurner, F.; Mann, U. Kinetic Investigation of Wood Pyrolysis. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 482-488. Villermaux, J.; Antoine, B.; Lede, J.; Soulignac, F. A new Model for Thermal Devolatilisation of Solid Particles undergoing Fast Pyrolysis. Chem. Eng. Sci. 1986, 41, 151-157. Wen, C. W. Noncatalytic Heterogeneous Solid Fluid Reaction Models. Ind. Eng. Chem. 1968, 60 (9/19), 34-54.
Received for review November 17, 1995 Revised manuscript received May 3, 1996 Accepted May 4, 1996X IE950695Q
X Abstract published in Advance ACS Abstracts, July 15, 1996.
