Ind. Eng. Chem. Res. 2000, 39, 3255-3263
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Pellet Breakup Due to Pressure Generated during Wood Pyrolysis Mehmet A. Hastaoglu,*,† Ramazan Kahraman,‡ and Muhammad Q. Syed§ Department of Chemical and Petroleum Engineering, UAE University, Al Ain, United Arab Emirates, Department of Chemical Engineering, KFUPM, Dhahran 31261, Saudi Arabia, and Department of Physics, Mount Royal College, 4825 Richard Road S.W., Calgary, Alberta, T3E 6K6 Canada
A transient unimodel for reacting pellets is considered with various modes of heat and mass transfer and structural changes for wood pyrolysis. Pellet breakup was found to be possible from strength calculations. This leads to an increase in the number of pellets and a decrease in the resistance to heat and mass transfer. The pressure and temperature buildup within 2.7 mm thick pellets was measured for wood pyrolysis/combustion experimentally. The bimodal wood pyrolysis was analyzed, and the rate constant and activation energy were found. Pellet breakup may also be used as a transient catalytic process where the catalysts become smaller as they break up in time. Introduction Gas-solid reactions play an important role in industry and daily life. They are the building blocks in most reactions: gasification, pyrolysis, combustion, metal oxide reduction, flue gas treatment, and explosive reactions. An accurate modeling of the processes taking place in pellets becomes very important, as this model can be used to study, predict, and control the reactors. Laine1 reports “...we cannot ignore the results of laboratory-scale, atomistic chemical studies in well-ordered systems. If we do, the industrial-scale results are doomed to be disappointing, inconsistent, and subject to the black magic of running to process specifications in hopes of attaining product specifications, whether that product is alumina powder or unit of energy.” We would like to add that numerical modeling is also an integral part of understanding the intricate relations between various phenomena and an extremely powerful tool in simulation using physical processes taking place in small-scale to large-scale industrial operations. After all, the basic physical phenomena that take place are valid be it laboratory scale or be it giant size industrial equipment. The solution obtained for a pellet can be integrated over reactors (fluidized, fixed), and their behavior can be predicted.2,3 As a result, exploratory research could be carried out on pellets via “numerical procedures” for cases where physical experimentation is not possible due to time, funds, or explosive or other undesirable reaction behavior. In the majority of reacting systems involving gases and solids as reactants, products, or catalysts, the solid is in the shape of pellets. In some cases, although the shape is not a regular one, it can be approximated as a convenient geometric configuration: flat plate, cylinder, or sphere. The reactions take place either in the porous regions inside the pellet (homogeneous reactions) or at the internal surfaces (heterogeneous reactions). The reactant gases have to travel into the pellets due to convective/molecular motion through a gas film * To whom correspondence should be addressed. Fax: 9713-7624-262. E-mail:
[email protected]. † UAE University. ‡ KFUPM. § Mount Royal College.
surrounding the pellet and the inner porous path. The product gases travel out similarly. When gases are produced at higher rates than they are consumed or transferred out, there may be a pressure buildup within the pellet inducing bulk motion of gases outward. Apparently the size of the pellet plays a crucial role for high-rate nonequimolar reaction systems. When the stress at any point within the pellet reaches its ultimate strength, it will burst or break up. This will cause smaller or fractured pellets to form. Then the path of transfer will decrease and the necessary burst pressure for the smaller pellets may increase. Ahmed and Back4 looked at the effect of water vapor and inert gases on the carbon-oxygen reaction. They have indicated that explosive reactions may occur in a mixture of reactants and products: O2, CO, CO2, and H2O vapor. The presence of inert gases prevented explosions and allowed normal oxidation of carbon. Pyrolysis of cellulose was studied, and it was concluded that the process is mainly endothermic.5 Rao and Sharma6 have studied pyrolysis of cellulose, hemicellulose, and lignin, finding specific kinetic parameters. They have suggested decomposition rate laws from order 0 to 2 in the range 200 to 500 °C. DiBlasi7 has indicated the importance of non-steady-state behavior during pyrolysis and primary degradation and secondary decomposition of virgin biomass with parallel and consecutive reaction mechanisms. Orfao et al.8 have reported a bimodal rate behavior during the decomposition of lignocellulosic material under N2/O2 atmosphere with temperature. Milosavljevic and Suuberg9 have suggested a global rate with order ranging between zero and one. The formation of product gases will be enhanced in especially catalytic and decomposition reactions with pellet breakup. Therefore, it becomes essential to describe the internal reactions and pressures accurately. In the present work, a gas-solid reaction model is applied to a pellet and all the necessary variables are determined transiently. The pressure is used to determine pellet breakup. The changing internal structure and exterior and interior mass and heat transfer modes including radiation, convection, and molecular motion are included. The effects of important parameters are
10.1021/ie000037s CCC: $19.00 © 2000 American Chemical Society Published on Web 09/05/2000
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studied. The theoretical analysis is given in the following section. Theory It is possible to build pressure inside the reacting pellets during either heat up or the reaction period.6 Even for equimolar reactions, it is possible to have higher prevailing pressures inside pellets. When a porous pellet with high thermal conductivity is subjected to a high-temperature environment, the thermal expansion of gases could be much faster than their escape rates. Thus, there would be an internal pressure higher than the surrounding pressure. For a pellet starting at 300 K and reaching 1200 K, the pressure may be approximately four times the initial pressure in the absence of reaction and any mass flux. In the modeling exercise below, the solid pellet is assumed to consist of grains with the regular geometry of a sphere, a long cylinder, or a flat plate of micron size.3 In general, the pellet is centimeter or millimeter size. A pellet of any porous structure can be mapped on a grain structure using two approaches: (1) equal volume grains where solids are reacting and the extent of reaction in the pellet has to be found; (2) equal surface area grains. This is used to find the amount of fluid species reacting on active surfaces. For flux calculations, pore size can be used if available. A general multireaction scheme can be written as
aA + ∆h ) 0
(1a)
which can be reduced to the particular reaction
A(g) + bB(s) f cC(g) + dD(s)
∫0tfA dt
(3)
The conservation of gas A can be written as
∂(CA)/∂t ) -3NA + ApfA + fAH
(4)
Similarly, the conservation of heat can be written as
Cep ∂T/∂t ) 3ke3T -
∑i NiCpi - ApfA∆h - fAH∆hH
R ) 0; NA ) 0; 3T ) 0
(6b)
R ) Rp; NA ) kc(CAs - CAb); -ke3T ) (hc + hr)(TS - Tb) (6c) The changes in pellet size due to shrinkage or swelling are also followed with time. The mass fluxes and transport parameters are estimated from10
Nj
)
e DKj
∑ s*j
ysNj - yjNs P
3yj -
Rg T
Dejs
yj RgT
(
1+
BoP e µDKj
)
3P (7)
with e ) DKj
( )
2dp 8RgT 3τ πMj
0.5
Bo )
; Dejs ) Djs; τ
(
1 3 π 3 r - rg 2 o 6
)
2/3
; and
(
)
π dp ) 2 ro3 - rg3 6
1/3
(8)
The grain size and porosity are continuously updated from11,12
b(rFg - rFc )FDMB(1 - D) ) d(rFo - rFc )FBMD(1 - B) and (1 - )rFc V ) rFg Vo(1 - o) (9)
(2)
which is obtained by assuming that the amount of A reacting at the active site within a grain is supplied via flux through the ash layer with diffusivity DgA and a reaction front concentration of CA*. The reaction front can be followed by transforming the stoichiometric relation to the volume change of the solid as
rc ) ro - b(MB/FB)
t ) 0; 0 e R e Rp; rc ) ro ) rg; CA ) CAo; T ) Ti (6a)
(1b)
The reaction mechanism can be deduced from experimental and kinetic modeling studies. The reactant gas (except for the decomposition reactions) transfers through an outside film and the pores of a tortuous solid matrix. The mode of mass transfer could be due to molecular or Knudsen diffusion or pressure-induced convection. The product gases formed follow the reverse path. At the reaction site the following can be written
-rgDgA(CA - CA*)/(rg - rc) ) rcbfA
and the outflowing gas may be considered via thermal jumping. One should note that the pores for flow are submicron size. However, for ultrafast processes the structural changes overcome the thermal changes within the pellet. One may consider only the production of gases and a sudden increase in pressure causing important structural changes. Although the problem becomes complicated for such cases, it is intended here to show the significance of such phenomena. The initial and boundary conditions for mass and heat transfer are
(5)
where thermal equilibrium between the gas and the solid is assumed, which is not the case for ultrafast processes where the exchange of heat between the solid
The specific heat capacity and thermal conductivity are determined from13
Cep ) (1 - )FsCps + Cpgke ) (1 - )2ks + 2kg
(10)
In evaluating kg and Cpg, the mixing rule is applied.14 Solid conversion is from
X)
[
( ) ] r Fp
∫0R RF -1 1 - rcF p
p
g
p
∫0R RF -1 dR]-1
dR [
p
p
(11)
Although semianalytical solutions are available for simplified system parameters with Langmuir-Hinshelwood kinetics,15 it is not possible to solve the equations above via analytical methods. Therefore, they are solved for the transient variables using numerical schemes. This involves the Newton-Raphson method and sparse matrix solution techniques with successive iterations leading to Ci, T, P, and all other transport and thermophysical quantities. Numerical results were also checked experimentally using TGA for various cases.2,11,12,16
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Although the pressure buildup and subsequent probable pellet breakup are the primary purpose of this study, situations with a negative net rate of gas production are also considered. This could be found in desublimation, reactions leading to solid formation or reactions with the number of moles of products smaller than the number of moles of reactants. In this case, the internal pressure decreases. Eventually it is possible for low-strength pellets to collapse. The pellet breakup phenomenon in daily life takes place in combustion processes. During wood burning, the fibers which are of hollow cylindrical form produce gases via pyrolysis. If the rate of heating of the wood is slow, the gases may have time to escape from the pores, eliminating any substantial pressure buildup. On the other hand, for a fast heating rate, the pressure buildup becomes significant and pellets may break up. The bursting sound during wood combustion is due to this pressure buildup. The explosive processes also follow similar routes. The gas-solid reaction model above allows determination of the most important variable for the purpose of this study: the internal pressure. Then one should look into the bursting of the pellet due to this pressure. The pellet shape and internal structure can be ascertained via surface area, SEM/TEM measurements, and X-ray diffraction. In general, the porous space inside the pellet may be approximated to be a cube, sphere, or long cylinder. Once the shape and the necessary dimensions of the internal void space of the pellet are determined, one can use approximate expressions for burst pressure. Chirone and Massimilla17 have proposed a mechanical model of primary fragmentation with anisotropy due to embedding planes for spherical particles. Their fragmentation model has been based on a monoaxial stress field consisting of internal pressure due to volatiles generated and resisting forces of the material. They have also considered secondary fragmentation in fluidized beds. However, here simpler expressions were adapted.18 For a spherical shell
2∆RσyE for Ro - Ri e 0.356Ri or P* ) Ri + 0.2∆R P* e 0.665σyE (12) Ro3 - Ri3
P* ) 2σyE 3 for Ro - Ri g 0.356Ri or Ro + 2Ri3 P* g 0.665σyE (13) and for a cylindrical shell
P* )
2∆RσyE for Ro - Ri e 0.5Ri or Ri + 0.6∆R P* e 0.385σyE (14) Ro2 - Ri2
for Ro - Ri g 0.5Ri or P* ) 2σyE 2 Ro + Ri2 P* g 0.385σyE (15) The justification for using the expressions above is as follows. If the reactions are decomposition type, then the rate of reaction would determine the pressure buildup and the outward transfer of gases would be very
important for sustaining the rate. The pellet in this case would act like a pressure vessel where joint efficiencies will account for the pellet internal matrix as compared to a normal pressure vessel. If the pressure is high enough, vessel rupture (pellet breakup) will take place. Equations 12-15 are valid for homogeneous and isotropic material. However, as is shown in Figures 1012, it may, to some extent, be applied to a nonisotropic material such as wood if thin samples are prepared by cutting wood crosswise. A wood fiber which is of a hollow cyindrical shell form would act like a vessel. In the burst pressure calculations σy can be found from material strength handbooks. On the other hand, the joint efficiency, E, shows the extent to which the porous matrix resembles the pellet material itself. In other words, it is the strength of the joining grains and/ or nonuniformities in thickness compared to that of the solid material itself. If it is made of mostly smaller particles which are pressed together, as in most kinetic studies, E can be substantially lower than 1. As an example, take an Fe2O3 pellet made by pressing its powder at 70 900 kPa. The pellet is very fragile. Likewise, a wooden pellet which is made up of fibrous grains does not have the same strength as the compressed wood. In some cases, E may be very low where pellets may break even by touching. However, once the pellets are in a high-temperature environment, strong bonds may form between the grains due to sintering. The inner and outer radii and the wall thickness of the pore-solid scheme (pressure vessel) are derived as follows. The pore diameter is found by assuming that the pore is a cube with a base of one initial grain diameter (eq 8). Then this pore is assumed to occupy the interior of a presumed shell configuration. A spherical shell is taken as an example. Thus, the inner radius is calculated from a measured quantity: pore fraction. The grain, that is the solid fraction, (1 - ), is assumed to form the shell from which the outer radius is calculated.
Ri )
(π6r
3 o
- rg3
)
1/3
, Ro ) -1/3Ri, and ∆R ) (-1/3 - 1)Ri (16)
In the absence of structural changes ro ) rg and one gets
(π6 - 1)
dp ) 2rg
1/3
, Ri ) dp/2
(17)
Results and Discussion The differential and complimentary equations above are solved for a variety of cases. For this purpose a pellet made by compressing powders is considered. The pellet, initially at room temperature, is introduced to a hightemperature environment. The reactions are assumed to follow the Langmuir-Hinshelwood mechanism, which is reduced to simpler mechanisms as the intrinsic kinetic parameters are varied. The stoichiometric relationships are varied along the study to see the system behavior. The pellet T in a hot environment starts increasing. If the gases already present inside the pellet cannot escape on time, the pellet internal pressure starts rising. Upon reaching high enough T, the species will start
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Figure 1. Effect of pellet size on pressure at the pellet center as a function of time. Table 1. Distribution of Some Properties and Variables in a Reacting Pellet for a Typical Run at t ) 1000 S and X ) 0.304
Figure 2. Effect of grain size on pressure at the pellet center as a function of time.
grid point I ) property
1
2
3
4
5
CA, mol/m3 CC, mol/m3 P, kPa T, K rc, ×108 m DACe, ×105 m2/s DKAe, ×105 m2/s DKCe, ×105 m2/s e Cep, ×10-3 J/(m3‚K) dp, ×108 m ke, W/(m‚K) µ, ×104 kg/(m‚s)
7.683 2.134 112.27 1375.5 4.561 8.598 1.030 1.292 0.671 866 8.447 20.533 4.811
7.786 1.957 111.43 1375.5 4.534 8.814 1.052 1.319 0.677 851 8.480 19.815 4.835
7.988 1.609 107.33 1375.5 4.471 9.301 1.103 1.383 0.690 816 8.553 18.231 4.888
8.279 1.106 109.76 1375.5 4.348 10.212 1.203 1.508 0.715 750 8.688 15.427 4.972
8.630 0.493 104.32 1375.5 4.094 11.936 1.406 1.762 0.762 625 8.932 10.773 5.090
reacting, thus having a pronounced effect on internal pressure buildup. The following base data are used for carbon gasification:12 -8
) 0.566, Rp ) 0.015 m, rg ) 1.5 × 10 m, Pb ) 101 kPa, k1 ) 1094 exp(-52.317/RgT), k2 ) 3.3 × 10-9 exp(60.44/RgT), k3 ) 0.176 exp(6.7/RgT), and f ) k1PA/(1 + k2PC + k3PA) Other thermophysical parameters are taken from established data. These parameters have been varied to study their effects: Rp, rg, , ∆H, c, Tb, Pb, and k1. A map of selected system variables during the reaction is presented in Table 1 at grid points which are equally spaced nodes from the center to the surface of the pellet. The variation in these quantities along the radius is clear. The effect of pellet size is shown in Figure 1. Although all the variables at various grid points are calculated continuously, only the pressure at the pellet center is shown for an initial period of 50 s. A value of c ) 5 is used in eq 1. For very thin pellets the internal pressure rise is negligible. As the pellet size goes up (0.0005 and 0.001 m), there is a substantial pressure rise. As the thickness increases further (0.01 m), the pressure rise is at a slower rate due to slow heating compared to the previous cases. For a 0.05 m thick pellet it takes about
Figure 3. Effect of heat of reaction on pressure at the pellet center. The parameter is heat of reaction, ∆h (J/mol).
80 s for the pressure rise to start. In this set of runs the thermal conductivity is 1.89 W/m‚K. On the other hand, simulation results with a substantially higher thermal conductivity of 1890 W/m‚K indicate that the central pressure increases for a 0.05 m pellet much more than for thinner pellets. The effect of grain size from 0.001 to 0.5 µm is shown in Figure 2. With smaller grains, Ap is higher, leading to faster gas generation rates. Thus, the internal pressure increases to more than 4Pb. The drop after reaching a peak is due to the fact that the mass transfer is not fast enough to sustain such high reaction rates. The initial rise is partly due to heat transfer but mainly due to reaction of the reactants present initially. Obviously, with larger grains, the pores are larger, Ap is smaller, and the rate of outward transfer is similar to the rates of inward transfer and generation compensating any pressure buildup. As can be seen from the figure, the pellet center pressure is the same as that of the bulk for pellets with 0.5 µm and larger grains. The effect of ∆h is shown in Figure 3, and that of Pb is shown in Figure 4. From a stoichiometric behavior involving 1 mol of reactant leading to 5 mol of product gas, the reaction is suppressed and the internal pressure rise is relatively small for high Pb. The effect of the stoichiometric coefficient c is shown in Figure 5. With c ) 0.1, the internal pressure
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Figure 4. Effect of bulk pressure on pressure at the pellet center.
gases cannot have enough time to escape. Once high pressures are reached, the transfer of reactant gases is hampered, significantly reducing the reaction rate. There is a certain pressure at which the transfer and reaction mechanisms can be sustained, leading to stabilized pressures later. The effect of bulk temperature was found to have trends similar to that of changing the intrinsic kinetic coefficient. The effect of the initial pellet porosity was also studied. The pressure rise is quite faster for lowporosity pellets than high-porosity ones. As porosity increases, the effective transport properties increase, thus leading to lower internal pressures. In reality, under the conditions described above, the pellets may not withstand such high pressures and breakup. A set of calculations was performed to see the necessary rupture pressures. With the base grain diameter of 1.5 × 10-8 m and 0 ) 0.566, the following were found
dp ) 2.343 × 10-8 m, Ri ) 1.4535 × 10-8 m, Ro ) 1.7572 × 10-8 m
Figure 5. Effect of stoichiometric coefficient, c, on pressure buildup.
Figure 6. Effect of kinetic coefficient on internal pressure. The parameter is the factor in front of the original expression for k1
decreases substantially below Pb. Although the reaction is continuing, the controlling step could be transfer of reactant gases. The case with c ) 0.01 indicates that the pressure decreases to a fraction of Pb (not shown) where influx of reactants is aided due to a vacuum. The case of c ) 1 ends up with an internal pressure the same as Pb, as expected, and c > 1 leads to a substantial increase in P. The effect of the intrinsic kinetic parameter k1 is shown in Figure 6. The temperature dependence of this variable is kept the same, but the frequency factor is changed by a factor ranging from 0.001 to 100. With a value of 100 times the base, the pressure increases dramatically, reaching very high values in a few seconds. At the beginning the pellet is heated and the reaction temperatures are reached. Thus, with the gases that were present and transferred in, a substantial positive rate of reaction is achieved. But the product
Pellets made from powder were considered for porous carbon with a strength of 2.07 MPa. For an unusually high joint efficiency of E ) 0.5, the rupture gague pressure is found to be 405 kPa (4 atm), which was attained in Figure 2. However, if E is taken to be 0.01, a gauge pressure of 8.3 kPa would be sufficient for rupture. Similar calculations were performed for aluminum (σy ) 35.5 MPa), and E ) 0.03 would cause rupture at 405 kPa (4 atm gauge). For E ) 0.01, P* was found to be 138 kPa. For iron (σy ) 206.8 MPa), for rupture to occur at P* ) 405 kPa, E ) 0.005 is required, neglecting the effects of sintering, swelling, or other thermally induced physical phenomena. Naturally, the yield strengths used are at room temperature. A metal such as aluminum would melt long before temperatures under consideration are reached, and rupture would take place much earlier. The yield strength decreases considerably at higher temperatures, and the rupture pressure is strongly affected by E. In some cases E would be very high. However, if Pb is correspondingly high, it is possible to attain higher internal pressures than Pb. From a practical point of view, the following reaction schemes may also be considered.
Hematite reduction 3CO(g) + F2O3(s) f 3CO2 + 2Fe(s)
(18)
Carbon gasification CO2(g) + C(s) f 2CO(g) with f ) k1PA/(1 + k2PC + k3PA) (19) Reforming reaction in the presence of nickel on alumina catalyst CcH2c+2 + cH2O f (2c + 1)H2 + cCO
(20)
For small c, this would be a gas-phase reaction, taking place on a catalyst surface. Wood pyrolysis16,19 with the decomposition, consecutive, and competing reactions is
B(s) f A(g) f 5C(g) and B(s) f 5D(s) + 2.5C(g) (21)
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Figure 8. Arrhenius plot for the initial portion of drying/pyrolysis.
Figure 7. Bimodal conversion as a function of time. The parameter is the TGA bulk temperature.
where B is wood, D is char, A is tar (gas at high T), and C is a mixture of various light gases. The reactions above have a net production of gases with c values ranging up to 5 where rupture may not occur. There are reactions with similar c values, which lead to violent results due to the high value of their kinetic coefficients and heats of reaction, such as lead azide and ammonium nitrate decomposition
PbN6 f Pb + 3N2
(22)
NH4NO3 f 2H2O + N2 + 0.5O2
(23)
Values of c up to 50 were considered in our studies because they are realistic and do exist, as in the following:
Decomposition of ammonium picrate (effective c ) 11) C6H2(NO2)3ONH4 f H2O + 6CO + 2H2 + 2N2 (24) Nitrocellulose decomposition (effective c ) 44) C24H29O9(NO3)11 f 14.5H2O + 20.5CO + 3.5CO2 + 5.5N2 (25) These reactions have very high rate constants, ∆h, and c, leading to pellet breakup. These are explosive reactions with very small reaction times, and there would be no time for the transfer of other reactive gases such as oxygen from the outside. A set of wood pyrolysis experiments were performed using TGA. Wood samples had weight losses of 7.5 and 7.9% when kept at 100 and 105 °C for 1 h, respectively. Poplar samples (10-15 mg) were pyrolyzed between 150 and 500 °C under N2 atmosphere. The bimodal conversion behavior in time is shown in Figure 7. The initial zone with X between 0.075 and 0.09 has been analyzed through
-
dX dW ) Wo ) k1oe-∆E/RgTWRo (1 - X)R dt dt
(26)
The Arrhenius plot in Figure 8 gives R ) 0.53 ≈ 0.5, k1o ) 5.59 × 10-3 kg0.5/s, and ∆E ) 15 216 J/mol (165 000 J/mol has been reported for the main reaction).5 The transformations of the pellets at various temperatures
are shown in Figure 9. The crack formation, the decomposition of wood surfaces, and the fibrous structure are apparent in the SEM pictographs. Temperature and pressure changes within reacting wood pellets were also measured experimentally. Dry wood pellets, 4.7 cm × 4.6 cm, with an average thickness of 2.7 mm were reacted in a furnace heated under helium atmosphere with a limited amount of oxygen. Two well-type holes were drilled in the pellets lengthwise. A K-type thermocouple was inserted into one of the wells, and a stainless steel tube (o.d. ) 1.5 mm, i.d. ) 1.04 mm) was inserted into the other. The thermocouple was connected to an Omega Thermocouple Thermometer. The tube was connected to a Wallace & Tiernan digital pressure indicator. A Thermolyne Type 1500 furnace was heated to the desired temperature. The sample with all the connections was placed into the furnace after it was flushed with helium. The system was allowed to have a certain amount of air to an extent that flame combustion would not be present. This would allow pyrolysis and to some extent flameless oxidation to take place while internal pressure and temperature are recorded. There were many cracks in the samples, and they were broken into several pieces at 461 °C. Some samples which were unbroken at lower Tb are practically shattered at higher values. On the other hand, the pipe in the pressure well was very difficult to remove due to pellet shrinkage and tar formation. Tar at colder temperatures liquefied, and the lighter components in the gas phase escaped easily. Upon further cooling, the heavier components in the tar partially solidified, thus gluing the pipe to the well wall. The transient behavior of the internal pellet gauge pressure and temperature is shown in Figure 10 at a furnace temperature of 270 °C. There is a small pressure peak at 10 s with P ) 109 kPa. Then it decreases slightly. Since the temperature is small at this time, the rise in pressure is attributed to the normal gas behavior in a partially enclosed environment up to a point where some small cracks are developed. The second peak is due to reactions where product gases cannot escape at sufficient rates to keep pressure constant. The top pressure is 120 kPa for this peak. Then some major cracks are formed with a continuous pressure drop. As the temperature rises, the reaction rate increases, causing the last huge peak where new cracks are expected. Finally, the pressure decreases to Pb, indicating the end of reactions and the gas escape process. Finally, it should be noted that wood loses about 80% of its weight during pyrolysis to form gases and tar, and oxidation may push it to about 100%.
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Figure 9. SEM pictographs of wood samples. At the top, left to right, are fresh wood sample and samples pyrolyzed at 200 °C and 300 °C; and at the bottom, left to right, are samples pyrolyzed at 400 and 500 °C, respectively (magnification 9000×). The last pyrolyzed sample at the bottom right shows the fibrous structure with a magnification of 2500.
Figure 10. Transient behavior of the internal temperature and the pressure of the wood pellet during partial combustion/pyrolysis at a bulk temperature of 270 °C and an air/N2 ratio ) 0.25.
The temperature curve in the same figure is also interesting. It may be concluded that, even in a thin pellet, temperature is transient and that Tb is not assumed instantaneously. The heats of reaction lead to temperatures higher than Tb. Since there is no T-peak, the small P-peak is caused by the gases being heated. The pellet inner temperature and gauge pressure at Tb ) 461 °C are shown in Figure 11. The temperature rises up to 575 °C, and then it drops down to Tb. The pressure, on the other hand, rises to 110 kPa in about 20 s. It remains flat, up to 35 s. Upon start of gas production, it increases sharply to 118 kPa when pellet breakup leads to a sudden drop in P (108 kPa). Since
Figure 11. Transient behavior of the internal temperature and the pressure of the wood pellet at a bulk temperature of 461 °C.
the pellet is also shrinking, the reactions sustain some more growth to the second small P-peak (111 kPa) at 58 s. Later on, the pressure drops because of development of new cracks and completion of the reactions. Similar behavior is observed for a run at 400 °C under a partially oxidizing nitrogen-oxygen atmosphere (Figure 12). Although it is not possible to measure the yield strength and joint efficiency of the wood fibers (micron size), from the experimental breakup pressure of approximately 120 kPa, the group σyE was found to be 323 kPa through eq 14 and 320 through eq 15. If the joint
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Figure 12. Transient behavior of the internal temperature and the pressure of the wood pellet at a bulk temperature of 400 °C under a partially oxidizing N2/O2 atmosphere.
efficiency of the wood fiber is assumed to be 0.02 (closure at the fiber end), one obtains the yield strength σy ) 16.15 MPa in comparison to a tensile strength reported as 44.8-112 MPa for soft wood at room temperature.20 Note that the strength would drop drastically at high temperatures, especially in a reacting solid material such as wood, and varies widely with the kind of wood. Conclusions A comprehensive gas-solid reaction model is used to predict pellet behavior in terms of internal pressure variations. When the consumption of gases in reactions and the rate of outward flux are slower than the production rate, substantial pressure buildup within pellets is possible. It was found that the heating rate, the stoichiometric relationships, the rate and heat of reactions, and the thermophysical and transport properties play important roles in the pressure buildup. It is also possible to have a pressure sink within the pellet for cooling or gas-consuming reactions. If this process is too fast, then destruction may occur. Especially at early stages of the reactions, it is possible to have a maximum pressure which is substantially higher than the bulk value, leading to pellet rupture or breakup in reactors. The pellets may decrease in size and increase in number if P-caused stresses are higher than the yield strength. Experiments on wood pyrolysis/combustion indicate that the internal pressure does increase to values which may cause pellet breakup and that the temperature is transient. The initial decomposition/drying portion was governed by a power law rate with R ) 0.5, k1o ) 5.59 × 10-3 kg0.5/s, and ∆E ) 15 216 J/mol. Acknowledgment The authors acknowledge the UAE University and KFUPM. We also thank Mrs. Taghreed T. Al-Khalid for her contributions in the SEM and TGA experiments. Nomenclature A, a ) species taking part in the reactions and the coefficient matrix respectively Ap ) specific interfacial surface area, m2/m3 B, D ) reactant and product solids, respectively B0 ) parameter defined in eq 8, m2 b, c, d ) stoichiometric coefficients Cj ) concentration, kmol/m3 Cp, Cep ) specific heat capacity (J/kmol‚K) and its effective value (J/m3‚K)
DgA ) diffusivity of A in ash layer of grain, m2/s DK, Djs ) Knudsen and binary molecular diffusivities of j and s, m2/s (subscript e ) effective) dp ) pore diameter in eq 8, m E ) joint efficiency fH, f ) rates of homogeneous (mol/m3‚s) and heterogeneous reactions, (mol/m2‚s) Fp ) shape factor: sphere, 3; cylinder, 2; flat plate, 1 ∆hH, ∆h ) heats of homogeneous and heterogeneous reactions, J/mol hc, hr ) convective and radiation [σθ(TS2 + Tb2)(TS + Tb)] heat transfer coefficients, W/m2‚K kg, ks, ke ) thermal conductivity for gas, solid, and effective pellet, W/m‚K kc ) mass transfer coefficient, m/s k1, k2, k3 ) rate constants M ) molecular weight, kg/kmol Nj ) mass flux of species j, mol/m2‚s P, Pb, P* ) pressure and bulk and gague pressures, Pa R, Rp ) radial position and pellet radius, m r0, rg, rc ) initial and present grain radii and reaction interface, m Rg ) universal gas constant ) 8.314 N m/mol‚K Ro, Ri, ∆R ) outer and inner radii of fiber or vessel and shell thickness, m t ) time, s T ) temperature, K X ) pellet overall conversion V, V0 ) pellet volume and its initial value, m3 Greek Symbols , 0 ) porosity and its initial value µ ) viscosity, kg/m‚s θ ) emissivity F ) density, kg/m3 σ ) Stefan-Boltzmann constant ) 5.676 × 10-8 W/m2‚K4 σy ) yield strength, Pa τ ) tortuosity
Literature Cited (1) Laine, N. R. A Mass Spectroscopic Study of the CarbonOxygen Reactions27 Years Later. Carbon 1991, 29 (6), 729. (2) Hastaoglu, M. A.; Berruti, F.; Hassam, M. S. A Generalized Gas-Solid Reaction Model for Circulating Fluidized BedssAn Application to Wood Pyrolysis. Fluidized Bed Technology II, Proceedings of the 2nd International Conference on Circulating Beds; Compiegne, France; Basu, P., Lange, J. F., Eds.; 1988; Pergamon Press: Toronto, 1990, p 281. (3) Hastaoglu, M. A. Transient Modeling of a Packed-Tower: Mass and Heat Transfer with Reaction. Fuel 1995, 74 (11), 1624. (4) Ahmed, S.; Back, M. H. The Effect of Water-Vapor and Inert Gases on the Carbon-Oxygen Reaction. Carbon 1987, 24 (6), 783. (5) Milosavljevic, I.; Suuburg, E. M. Cellulose Thermal Decomposition Kinetics: Global Mass Loss Kinetics. Ind. Eng. Chem. Res. 1995, 34, 1081. (6) Rao, T. R.; Sharma, A. Pyrolysis Rates of Biomass Materials. Energy 1998, 23 (11), 973. (7) DiBlasi, C. Heat, Momentum and Mass Transport Through A Shrinking Biomass Particle Exposed to Thermal Radiation. Chem. Eng. Sci. 1996, 51 (7), 1121. (8) Orfao, J. J. M.; Antunes, F. J. A.; Figueiredo, J. L. Pyrolysis Kinetics of Lignocellulosic MaterialsThree Independent Reactions Model. Fuel 1999, 78, 349. (9) Milosavljevic, I.; Oja, V.; Suuburg, E. M. Thermal Effects in Cellulose Pyrolysis: Relationship to Char Formation Processes. Ind. Eng. Chem. Res. 1996, 35, 653. (10) Mason, E. A.; Malinauskas, A. P. Gas Transport in Porous Media: the Dusty Gas Model, Chem Eng. Monograph 17; Elsevier: Amsterdam, 1979. (11) Hastaoglu, M. A.; Hassam, M. S. A Gas-Solid Reaction ModelsVariable Temperature, Pressure and Structural Parameters. Can. J. Chem. Eng. 1988, 66, 419.
Ind. Eng. Chem. Res., Vol. 39, No. 9, 2000 3263 (12) Hastaoglu, M. A.; Karmann, M. G. Modeling of Catalytic Carbon Gasification. Chem. Eng. Sci. 1987, 42 (5), 1121. (13) Sotirchos, S. V.; Amundson, N. R. Dynamic Behavior of a Porous Char Particle Burning in an Oxygen Containing Environment. AIChE J. 1984, 30 (4), 537 (14) Reid, R. C.; Sherwood, T. K. The Properties of Gases and Liquids; McGraw-Hill: New York, 1977. (15) Cao, G.; Varma, A.; Strieder, W. Approximate Solutions for Nonlinear Gas-Solid Noncatalytic Reactions. AIChE J. 1993, 39 (5), 913. (16) Hastaoglu, M. A.; Berruti, F. A Gas-solid Reaction Model for Flash Wood Pyrolysis. Fuel 1989, 68, 1408. (17) Chirone, R.; Massimilla, L. The Application of Weilbull Theory to Primary Fragmentation of Coal During Developatilization. Powder Technol. 1989, 57 (3), 197.
(18) Peters, S. M.; Timmerhaus, K. D. Plant Design and Economics for Chemical Engineers, 4th ed.; McGraw-Hill: New York, 1991; p537. (19) Scott, D. S.; Piskorz, J. The Flash Pyrolysis of Aspen Poplar Wood. Can. J. Chem. Eng. 1982, 60, 666. (20) Callister, W. D., Jr. Materials Science and Engineerings An Introduction, 4th ed.; J. Wiley and Sons, Inc.: New York, 1997; p 786.
Received for review January 10, 2000 Revised manuscript received June 16, 2000 Accepted June 18, 2000 IE000037S
