Energy & Fuels 2000, 14, 791-800
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Mathematical Model for Wood PyrolysissComparison of Experimental Measurements with Model Predictions Morten G. Grønli* SINTEF Energy Research, Thermal Energy, N-7465 Trondheim, Norway
Morten C. Melaaen Telemark Institute of Technology (HiT-TF), N-3914 Porsgrunn, Norway Received August 11, 1999
Experimental and modeling work on pyrolysis of wood under regimes controlled by heat and mass transfer are presented. In a single-particle, bell-shaped Pyrex reactor, one face of a uniform and well-characterized cylinder (D ) 20 mm, L ) 30 mm) prepared from Norwegian spruce has been one-dimensionally heated by using a Xenon-arc lamp as a radiant heat source. The effect of applied heat flux on the product yield distributions (char, tar, and gas yield) and converted fraction have been investigated. The experiments show that heat flux alters the pyrolysis products as well as the intraparticle temperatures to a great extent. A comprehensive mathematical model that can simulate pyrolysis of wood is presented. The thermal degradation of wood involves the interaction in a porous media of heat, mass, and momentum transfer with chemical reactions. Heat is transported by conduction, convection, and radiation, and mass transfer is driven by pressure and concentration gradients. The modeling of these processes involves the simultaneous solution of the conservation equations for mass and energy together with Darcy’s law for velocity and kinetic expressions describing the rate of reaction. By using three parallel competitive reactions to account for primary production of gas, tar, and char, and a consecutive reaction for the secondary cracking of tar, the predicted intraparticle temperature profiles, ultimate product yield distributions, and converted fraction agreed well with the experimental results.
Introduction The environmental awareness related to CO2 and other greenhouse gas emissions as well as concern over the ultimate availability of fossil fuels have increased the interest in using biomass as a renewable resource for chemical feedstock and energy production. As produced, however, biomass has many disadvantages compared with fossil fuels. The physical form is rarely homogeneous. Biomass has usually only a modest energy content and when harvested, the moisture content is very high. In its solid form, biomass is therefore difficult to use in many applications without substantial modification. To adapt the fuel to a particular end use, technologies for converting and upgrading the biomass into more convenient energy forms such as gaseous and liquid fuels may be introduced. One of the most promising ways to do so is pyrolysis. Pyrolysis is the thermal degradation (devolatilization) of a feedstock in the absence of an oxidizing agent, leading to the formation of a mixture of liquid (tarry composition), gases, and a highly reactive carbonaceous char, of which the relative proportions depend on the method used. Temperature, pressure, heating rate, and reaction time can be used to influence and determine the proportions and characteristics of the main products of the process. Pyrolysis can be used as an independent process for the * Corresponding author. Phone: +47 73 59 37 25; fax: +47 73 59 28 89; e-mail:
[email protected].
production of useful energy holders or chemicals. The char can be upgraded to activated carbon, used as a reducing agent in the metallurgical industry, as a domestic cooking fuel, or for barbecuing. Pyrolysis gas can be used for power generation or heating, or synthesized to produce methanol or ammonia, whereas the tarry liquid (pyrolysis oil or bio-oil) can be upgraded to high-grade hydrocarbon liquid fuels for combustion engines or used directly for power generation or heat. Pyrolysis will always be the first step in the gasification and combustion process. The development of thermochemical processes for biomass conversion and proper equipment design require knowledge and good understanding of the several chemical and physical mechanisms that are interacting in the thermal degradation process. Mathematical modeling of single-particle pyrolysis represents a very useful tool for the understanding of some of these processes. Then one can focus on the solid-phase internal processes such as heat and mass transfer that control the release of products, results that can be used in the design and control of large-scale converters. Formulation of the Problem. Wood is a heterogeneous, porous substance consisting mainly of three major components: cellulose, the skeletal polysaccharide; hemicelluloses, which form the matrix; and lignin, the encrusting substance that binds the cells together. Additionally, wood contains many low-molecular-weight
10.1021/ef990176q CCC: $19.00 © 2000 American Chemical Society Published on Web 05/31/2000
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Figure 1. Schematic drawing of the thermal degradation process.
organic compounds known as extractives, small amounts of mineral matter and moisture. When a tree is harvested or felled it contains water in three phases: bound (hygroscopic or adsorbed) water, which is believed to be hydrogen-bonded to the hydroxyl groups of cellulose and hemicelluloses; free (liquid or capillary) water; and water vapor, which fills the cell cavities or voids of the wood. The moisture content for which the cell walls are saturated with no free water in the cell cavities is called the fiber saturation point (Mfsp). This point for most wood is 30% of the oven-dry weight, emphasizing the large amount of water that can be adsorbed.1 A schematic drawing of the successive events that will take place during drying and pyrolysis of wood is shown in Figure 1, and a qualitative description will be given in the following. When moist wood is heated, it first undergoes an initial drying period. Intraparticle temperature profiles found in laboratory experiments of moist pellets or slabs show inflection points or plateaus located near 100 °C.2,3 During this initial drying period, most of the energy received by the pellet is consumed by heating and evaporating water. If the initial moisture content is above the fiber saturation point (M > Mfsp ≈ 30%), the pores contain liquid water and the internal moisture transfer is mainly attributable to capillary flow of free water through the voids. As drying proceeds, the surface moisture content reaches its maximum sorptive value (M ) Mfsp), and the evaporation front begins to travel into the solid, leaving behind a sorption zone (M < Mfsp). Ahead of the evaporation front, the material will still contain liquid water in the pores. Behind the evaporation front, no liquid water exists and the main transfer mechanisms are bound water diffusion and convective and diffusive transport of water vapor. Evaporation takes place at the front as well as in the sorption zone. As time proceeds, the solid reaches the temperature at which the thermal decomposition takes place at the surface, forming a pyrolyzing zone. After a certain period the pyrolyzing solid loses all of its volatiles and (1) Siau, J. F. Transport Processes in Wood. Springer-Verlag Ser. Wood Sci. 1984. (2) White, R. H.; E. L. Schaffer. Transient Moisture Gradient in FireExposed Wood Slab. Wood Fiber 1981, 13, 17-38. (3) Fredlund, B. A Model for the Heat and Mass Transfer in Timber Structures During Fire. Ph.D. Thesis, Lund University, Sweden, 1988.
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the pyrolyzing zone propagates slowly into the interior of the solid, leaving behind a thermally insulating layer of char. As volatiles (tar, water vapor, and gases) from the pyrolysis and water vapor formed during drying in the interior flow out through this high-temperature char layer, secondary reactions may occur, both homogeneously and heterogeneously: homogeneously in the gas phase, where the heavy tar components crack into lighter hydrocarbons, and heterogeneously, with exothermic char gasification and combustion reactions of the oxygen-rich part of the volatiles. Dry wood loses up to 80% of its mass during pyrolysis and it is quite obvious that this leads to changes in the physical structure, such as internal shrinkage, surface recession, and formation of surface fissures. If oxygen is available at the surface, oxidation reactions of the volatiles lead to flaming combustion, whereas char-oxidation leads to smoldering or glowing combustion. Previous Work. Much effort has been expended through the years, both experimentally and theoretically, in an attempt to better understand the complex mechanisms interacting in the thermal degradation of “thermally thick” particles of wood and related substances. An extensive critical review of modeling studies and the experimental data has been given in refs 4 and 5. The driving forces for doing such research have, however, been somewhat different. Some have developed models for use in the field of fire prevention for studying ignition,6 flame spread,7 or fires in load-bearing building structures.3 These have used very simple, onestep global expressions for the chemical reactions. Other have developed models to study the effect of different process parameters on the product composition (tar, gas, and char yields) in an attempt to establish guidelines for optimizing conversion processes.5,8-11 In this case, more complex reaction schemes including parallel, consecutive, or competitive reactions have been used for the chemical kinetics. The effects of moisture and drying on the thermal degradation have either been neglected or treated in a very simple way by (a) describing the drying process as an additional chemical reaction;9 (b) inserting a boiling temperature at which the evaporation of moisture take place;12,13 or (c) describing the (4) Grønli, M. Experimental and Modelling Work on the Pyrolysis and Combustion of BiomasssA Review of the Literature; SINTEF Report STF12 A95013, 1995. (5) Grønli, M. A Theoretical and Experimental Study of the Thermal Degradation of Biomass. Ph.D. Thesis, Norwegian University of Science and Technology, Norway, 1996. (6) Bamford, C. H.; Crank, J.; Malan, D. H. The Combustion of WoodsPart 1. Proc. Cambridge Philos. Soc. 1946, 42, 166-182. (7) Atreya, A. Pyrolysis, Ignition and Fire Spread on Horizontal Surfaces of Wood. Ph.D. Thesis, Harvard University, Cambridge, MA, 1983. (8) Chan, W. C. R. Analysis of Chemical and Physical Processes During the Pyrolysis of Large Biomass Pellets. Ph.D. Thesis, University of Washington, Seattle, WA, 1983. (9) Chan, W. C. R.; Kelbon, M.; Krieger-Brockett, B. Modelling and Experimental Verification of Physical and Chemical Processes during Pyrolysis of a Large Biomass Particle. Fuel 1985, 64, 1505-1513. (10) Di Blasi, C. Analysis of Convection and Secondary Reaction Effects Within Porous Solid Fuels Undergoing Pyrolysis. Combust. Sci. Technol. 1993, 90, 315-340. (11) Di Blasi, C.; Russo, G. Modelling of Transport Phenomena and Kinetics of Biomass Pyrolysis. In Advances in Thermochemical Biomass Conversion; Bridgwater, A. V., Ed.; 1994, pp 906-921. (12) Saastamoinen, J.; Aho, M. The Simultaneous Drying and Pyrolysis of Single Wood Particles and Pellets Made of Peat. Presented at the American Flame Research Committee, 1984, International Symposium on Alternative Fuels and Hazardous Wastes. (13) Alves, S. S.; Figueiredo, J. L. A Model for Pyrolysis of Wet Wood. Chem. Eng. Sci. 1989, 44, 2861-2869.
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Figure 2. Schematic drawing of experimental apparatus.
evaporation by a simplified local moisture-vapor equilibrium relation.3 A quantitative comparison between model predictions and experimental data has proved to be rather difficult because of (a) the widely varying property values (solid density, specific heat, thermal conductivity, porosity, permeability) among the different wood species used in the experiments; (b) the large uncertainty on the properties of the charred and partially charred solid including structural failure and shrinkage; (c) the different chemical composition of wood, that is, the different percentage of cellulose, hemicellulose, and lignin; (d) the different amount and composition of inorganic matter, which leads to different yields of primary pyrolysis products; and (e) the high uncertainty in the kinetic model and rate constants used for global reaction mechanisms. Present Work. In the work of Grønli,5 a comprehensive mathematical model for wood drying and pyrolysis is presented. The general differential and algebraic equations for mass, momentum, and energy are described. Different pyrolysis reaction models are discussed together with necessary property relations and thermophysical data. Results from pyrolysis experiments on dry wood particles are presented and discussed along with the details of the test facility, diagnostic system, and the experimental program. Model predictions are compared with the experiments to assess the validity of the mathematical model. This paper will highlight some of the findings presented in ref 5; first the experiments will be briefly discussed.
Experimental Section Experimental Apparatus and Data Acquisition. Experiments used to verify the model presented in this paper are briefly described below and in detail in ref 5. A schematic drawing of the experimental setup, adopted from KriegerBrockett and co-workers,8,9,20 is shown in Figure 2. In a singleparticle, bell-shaped Pyrex reactor, one face of a uniform and well-characterized cylinder (D ) 20 mm, L ) 30 mm) of Norwegian birch, pine, and spruce were one-dimensionally heated by using a xenon arc lamp as a radiant heat source. The samples were carefully lathed from knot-free uniformgrain slabs, and tightly fitted into a glass tube that was inserted into the reactor from the back. A variable-power xenon arc lamp capable of combustion-level heat fluxes was used as the source of energy to sustain pyrolysis. The xenon arc lamp
Figure 3. Temperature histories of three replicated runs on spruce, 80 kW/m2 heat flux. provides a spatially uniform, relatively constant and high radiant heat flux that can be directly focused onto the pellet surface. The front face of the reactor consisted of a fused silica window that allowed maximum transmission of radiant energy (approximately 10% loss). The reactor had three inlet ports for purge gas (N2) located close to the window. This kept the hood free from smoke, and prevented condensation of volatiles on the window, which could reduce the transmittance of incoming radiation. To prevent smoke from flowing backward between the glass tube enclosing the pellet and the reactor, a small amount of purge gas was introduced through three inlet ports at the back of the reactor. Pyrolysis products flowed from the reaction zone toward the heated surface under a slightly positive pressure applied at the unheated surface. With such a configuration, laminar flow was observed in the reactor hood, and the pyrolysis products were swept out of the reactor through an outlet port located above and close to the pellet surface with negligible back-mixing. Outflowing gases were transported to a cold trap where water and tars were collected as a time-integrated sample. Uncondensed gases were continuously measured by conventional gas analyzers. Two different heat fluxes, that is, 80 kW/m2 (low heat flux) and 130 kW/m2 (high heat flux), were used, and the effect of grain orientation relative to the heat flux (longitudinal and radial direction) were investigated. The following parameters were measured: surface and seven internal temperatures; gas composition (CO, CO2, and total hydrocarbons); char yield, tar/ water yield (condensable gases), and gas yield (by mass balance); converted fraction; and longitudinal shrinkage. The total time of exposure (heating time) was 5 and 10 min, respectively. Because the mathematical model does not take shrinkage into account, model parameters and predictions in this article were chosen for comparison with experimental results for spruce (Picea abies) heated parallel with the grain, because of the lowest axial shrinkage both at low and high heat fluxes. Experimental Results. Temperature Histories. Temperature profiles for dry spruce exposed to a low (80 kW/m2) and a high (130 kW/m2) heat flux are shown in Figures 3 and 4, respectively. Obviously, the surface and in-depth temperatures are significantly higher when exposed to a heat flux of 130 kW/m2 compared to 80 kW/m2. The shaded areas give an indication of the reproducibility of the experiments, because the temperature histories of three identical (replicated) runs have been compared. The temperatures for replicates are within 50 °C of each other for most depths. At both heat fluxes, the temperature profiles coincide fairly well in two of three
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Table 1. Mean Values and Standard Deviation (() of Converted Fraction, Axial Shrinkage, and Ultimate Product Yield Distributions Obtained from Pyrolysis of Spruce low heat flux (80 kW/m2) converted fraction (wt %) axial shrinkage (%) char yield (wt %) tar yield (condensable gases)a (wt %) gas yield (noncondensable gases) (wt %) a
high heat flux (130 kW/m2)
5 min heating
10 min heating
10 min heating
25.7 ( 1.63 2.9 ( 0.75 26.2 ( 0.53 38.0 ( 1.22 35.9 ( 1.44
45.5 ( 3.61 2.7 ( 2.34 28.7 ( 1.06 31.3 ( 5.06 40.0 ( 5.45
72.1 ( 3.05 1.5 ( 0.92 27.0 ( 0.06 27.9 ( 0.61 45.2 ( 0.62
Condensable gases include condensed water vapor and tar.
Figure 5. Photos showing axial shrinkage and virgin reminder after char layers have been cut off.
Figure 4. Temperature histories of three replicated runs on spruce, 130 kW/m2 heat flux. runs, which must be regarded as satisfactory. The temperature differences between the replicates, at for instance 8 mm from the surface, may be attributed to the positioning of the thermocouples, which could slightly vary approximately a half millimeter or so from pellet to pellet. Differences between replicates are also a reflection of the sample-to-sample variation of wood. Because of its inhomogeneous grain structure, it is impossible to prepare two or more identical samples from the same wood log. A noticeable temperature plateau around 380 °C can be seen for both the low and high heating of spruce. This is found especially at locations 4, 8, and 12 mm from the surface where the temperature gradients are not so steep as at the front surface. A first explanation would be that this plateau is caused by the endothermic heat of pyrolysis. By using the mathematical model, insight into this phenomenon was gained. The predictions proved that an endothermic heat of reaction delays the overall decomposition but does not give any sudden change in the temperature gradient, as seen in these experiments. The most likely reason for the flattening or slope change of the temperature curves around 380 °C is a reduction in the local thermal conductivity. When the substrate changes from wood to a more porous char, the local thermal conductivity decreases in a short period of time until the temperature reaches the level where the radiant contribution to the effective thermal conductivity becomes significant. This will be discussed more thoroughly in a later section where the experiments will be compared with model predictions. Converted Fraction, Axial Shrinkage, and Ultimate Product Yield Distributions. Photos of the axial shrinkage and virgin reminder after the char layer has been cut off are shown in Figure 5. The measured mean values and standard deviations of the converted fraction, axial shrinkage, and ultimate product yield distributions (char, tar, and gas yield)
are presented in Table 1. From the experimental findings summarized in Table 1, the following observations may be made: (1) Effect of heating time. By doubling the total time of exposure (at 80 kW/m2 heat flux) from 5 to 10 min, the converted fraction increases by almost 77%; the ultimate yields of char and noncondensable gases increase while the yield of condensable gases (tar/water) decreases. Explanation: The char layer thickness will increase as a consequence of longer pyrolysis time. Hence, the distance that the tar molecules must travel before they escape from the surface will also increase. Cracking of the tar components to form gas products may then explain the increase in ultimate yield of noncondensable gases and the decrease in condensable gas yield. If the local char density is assumed to be dependent on the local temperature history, one may expect that the char density close to the surface going through a very rapid heating (steep temperature gradients) is lower than the char density in the interior of the pellet where the heating rate is much slower. Hence, the local char density will slightly increase with pellet depth and so does the average (integrated) char yield as the pyrolyzing front propagates into the wood pellet. Another reason that may explain the increase in ultimate char yield is that more char is formed through a repolymerization reaction of the tar. (2) Effect of heat flux. By increasing the heat flux (at 10 min of exposure) from 80 to 130 kW/m2, the converted fraction increases by almost 59%; the ultimate yields of char and condensable gases (tar/water) decrease while the yield of noncondensable gases increases. Explanation: Higher heat fluxes mean that there are higher temperatures in the char layer and more of the solid is converted. Hence, the distance the volatiles must travel, that is, the residence time in the hot char layer, increases as the pyrolyzing front propagates into the wood, promoting secondary reactions of the heavy tar molecules. Higher heat fluxes mean steeper temperature gradients inside the pellet. By assuming the local char density to be dependent on the local temperature history, a lower char density and, hence, a lower integrated char yield is expected when a higher heat flux is applied.
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Modeling Section
mixture is given by Darcy’s law
The mathematical model that has been derived5,14,28 is based on earlier work on drying of nonhygroscopic and hygroscopic media by Whitaker,15 Ouelhazi et al.,16 Perre et al.,17 and earlier work on pyrolysis of wood by Krieger-Brockett and co-workers8,9,18-20 and Di Blasi and co-workers.10,11 The most important assumptions of the mathematical model are (a) all the phases are at the same temperature and the partial pressure of vapor is equal to its equilibrium pressure (local thermodynamic equilibrium); (b) the transport of bound water is modeled as a diffusion process given by a diffusion coefficient that is a function of the local moisture content; (c) binary diffusion in the gas mixture phase; (d) Darcy’s law for the bulk flow of gas mixture and liquid water; (e) a linear variation between the virgin wood and char for the properties related to the solid structure; (f) wood shrinkage and crack formation are not considered. Compared to previous work, the present mathematical model has fewer restrictions and the coupling between drying and pyrolysis is emphasized. Because the experiments presented herein have been done on dry wood, the differential and algebraic equations related to the drying mechanisms have been omitted. For further details regarding the mathematical model we refer the reader to refs 5, 14, and 28. Mass Conservation Equations. Mass Conservation of Solid Substance.
∂ 〈F 〉 ) 〈w˘ s〉 ∂t s
(1)
where 〈w˘ s〉 is the rate of consumption or production of solid matter. The solid wood is consumed while char is produced during thermal degradation. Mass Conservation of Component i in Gas Mixture Phase.
∂ ∂ ( 〈F 〉g) + (〈Fi〉g〈vg〉) ) 〈w˘ i〉 ∂t g i ∂x
(2)
where 〈w˘ i〉 is the rate of production or consumption of component i (tar and gases) formed during the thermal degradation process. The superficial velocity of the gas (14) Melaaen, M. C.; Grønli, M. Modelling and Simulation of Moist Wood Drying and Pyrolysis. In Developments in Thermochemical Biomass Conversion; Bridgwater, A. V., Boocock, Eds.; 1997, pp 132146. (15) Whitaker, S. Simultaneous Heat, Mass and Momentum Transfer in Porous Media: A Theory of Drying. Adv. Heat Transfer 1977, 13, 119-203. (16) Ouelhazi, N.; Arnaud, G.; Fohr, J. P. A Two-Dimensional Study of Wood Plank Drying. The Effect of Gaseous Pressure Below Boiling Point. Transp. Porous Media 1992, 7, 39-61. (17) Perre, P.; Moser, M.; Martin, M. Advances in Transport Phenomena During Convective Drying with Superheated Steam and Moist Air. Int. J. Heat Mass Transfer 1993, 36, 2725-2746. (18) Glaister, D. S. The Prediction of Chemical Kinetic, Heat and Mass Transfer Processes During the One- and Two-Dimensional Pyrolysis of a Large Wood Pellet. M.Sc. Thesis, University of Washington, Seattle, WA, 1987. (19) Krieger-Brockett, B.; Glaister, D. S. Wood Devolatilizations Sensitivity to Feed Properties and Process Variables. In Research in Thermochemical Biomass Conversion; Bridgwater, A. V., Ed.; 1988, 127-142. (20) Lai, W.-C. Reaction Engineering of Heterogeneous Feeds: Municipal Solid Waste as a Model. Ph.D. Thesis, University of Washington, Seattle, WA, 1991.
Kg ∂ 〈vg〉 ) 〈P 〉g µg ∂x s
(3)
where Kg and µg are the intrinsic permeability and dynamic viscosity of the gas mixture, respectively. Diffusion in the gas mixture phase has been neglected, because the diffusive transport of volatiles is assumed to be comparatively smaller than the convective transport. Energy Conservation Equation. By assuming thermal equilibrium between the solid and gas mixture phases, the energy conservation equation is given by
∂〈T〉
(〈Fs〉CP,s + g〈Fg〉gCP,g)
∂t
∂〈T〉
+ (〈Fg〉g〈vg〉CP,g) ∂ ∂x
(
keff
)
∂〈T〉 ∂x
-
)
∂x
∑i 〈w˘ i〉∆hi
(4)
The first term accounts for the accumulation of energy; the second term is the convective heat transfer, caused by volatile movement; the third term accounts for the conductive heat transfer, which is represented by an effective thermal conductivity; and the last term accounts for the net heat of reaction due to pyrolysis reactions. Algebraic Equations. In addition to the differential equations for mass, energy, and Darcy’s law for momentum, the mathematical model requires data for the thermophysical and transport properties. Because some of these depend on the fiber direction (e.g., the thermal conductivity of wood along the grain is 1.75-2.25 times the thermal conductivity radial to the grain), properties along the fibers (longitudinal direction) will consistently be used in the following. The gas mixture is assumed to be an ideal mixture of perfect gases; hence, the following relations exist
〈Fg〉 ) g
〈Fg〉gR0〈T〉 〈Fi〉 , 〈Pg〉 ) , Mg ) Mg
∑i
g
g
(
∑i
〈Fi〉g
〈Fg〉g Mi
)
-1
(5)
Interpolation Factor. For the properties related to the solid structure, a linear variation between the virgin wood and char is assumed
φ ) ηφSD + (1 - η)φC, where η ) 〈Fs〉/〈FSD〉
(6)
Effective Thermal Conductivity. The thermal conductivity of wood varies with the direction of heat flow with respect to the grain, with temperature, density, and moisture content. The heat transfer takes place through a complex interaction between the transfer mechanisms: conduction, convection, and radiation. Hence, an effective thermal conductivity is introduced
keff ) kcond + krad
(7)
which is assumed to be made of the usual conductivity term given by Fourier’s law
kcond ) gkg + ηkSD + (1 - η)kC
(8)
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and a radiant conductivity term21
krad )
Table 2. Thermophysical Data Used in the Model (Ref 5) symbol
4g
3
σωdporT , dpor ) ηdpor,SD + (1 - η)dpor,C
(1 - g)
(9)
where g ) 1 - 〈FSD〉/〈Fs〉s is the porosity and dpor is the pore diameter, which is assumed to be the characteristic length over which the radiation can pass. Radiation in the pores is believed to play an important role at higher temperatures. Brown22 measured the char thermal conductivity in the temperature range 550-650 °C to be three times greater than that measured at room temperature; in fact, it was nearly twice as high as that of the virgin wood. Specific Heat Capacities. The specific heat capacity of the gas mixture and the dry solid substance is given by
CP,g )
∑i CP,i
〈Fi〉g
〈Fg〉g
, CP,s ) ηCP,SD + (1 - η)CP,C
(10)
Permeability. The intrinsic permeability of the gas mixture is given by
Kg ) ηKg,SD + (1 - η) Kg,C
(11)
Dynamic Viscosity. The dynamic viscosity of the gas mixture is given by
µg )
∑i µi
〈Fi〉g
〈Fg〉g
(12)
Boundary Conditions. The irradiated surface of the pellet is subjected to a heat flux, Fflux, that balances the convective and radiant heat losses to the surroundings and the inward conduction of heat (see Figure 1). Hence the boundary condition for the energy equation gets the following form
Fflux - hT(〈Ts〉 - 〈T∞〉) - ωsσ(〈Ts4〉 - 〈T∞4〉) ) ∂〈T〉 - keff (13) ∂x where hT, ωs, and σ are the convective heat transfer coefficient, surface emissivity, and Stefan-Boltzmann constant, respectively. Subscript ∞ denotes ambient and s denotes surface. The pressure at the irradiated surface is assumed to be equal to the atmospheric pressure
〈Pg〉 gs ) 〈Ts〉 g∞ ) Patm
(14)
A piece of high-temperature-resistance insulation material (glass wool) was glued onto the nonheated surface at the rear of the sample. This makes the boundary adiabatic and impermeable for gas flow. Hence, symmetry can be assumed, that is, the velocities are zero and the gradients of the dependent variables are zero. (21) Panton, R. L.; Rittmann, J. G. Pyrolysis of a Slab of Porous Material. Thirteenth International Symposium on Combustion, 1971, pp 881-891. (22) Brown, L. E. An Experimental and Analytical Study of Wood Pyrolysis. Ph.D. Thesis. The University of Oklahoma, 1972.
CP,SD CP,C CP,A CP,T CP,G kSD kC kg dpor,SD dpor,C ω Kg,SD Kg,C µA µT µG MA MT MG Fflux,low Fflux,high hT Patm T∞ σ ωs
expression ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
1.5 + (1.0 × 10-3) T [kJ/(kg K)] 0.42 + (2.09 × 10-3) T + 6.85 × 10-3 T2 [kJ/(kg K)] 0.95 + (1.88 × 10-4) T [kJ/(kg K)] -0.10 + (4.40 × 10-3) T - (1.57 × 10-6) T2 [kJ/(kg K)] 0.77 + (6.29 × 10-4) T - (1.91 × 10-7) T2 [kJ/(kg K)] 3.5 × 10-1 [W/(m K)] 1.0 × 10-1 [W/(m K)] 25.8 × 10-3 [W/(m K)] 5.0 × 10-5 (m) 1.0 × 10-4 (m) 0.9 1.0 × 10-14 (m2) 1000 × Kg,SD ) 1.0 × 10-11 (m2) (9.12 × 10-6) + (3.27 × 10-8) T (kg m/s) (-3.73 × 10-7) + (2.62 × 10-8) T (kg m/s) (7.85 × 10-6) + (3.18 × 10-8) T (kg m/s) 2.9 × 10-2 (kg/mol) 1.1 × 10-1 (kg/mol) 3.8 × 10-2 (kg/mol) 80 (kW/m2) 130 (kW/m2) 5.0 [W/(m2K)] 1.01325 × 105 (N/m2) 423 (K) 5.6703 × 10-8 [W/(m2 K4)] 0.85
Initial Conditions. Pyrolysis of spruce with a pellet length of 30 mm is modeled. Spruce has a dry solid density of 〈FSD〉 ) 450 kg/m3 and a specific density (ovendry cell-wall substance) of about 〈Fs〉s ) 1400 kg/m3, which gives an initial porosity of g ) 1-450/1400 ) 0.68. The initial temperature and pressure are 298 K (25 °C) and 1 atm, respectively, and the voids or lumens are initially assumed to be filled with air. The thermophysical data used in the model are listed in Table 2. Numerical Solution. The differential and algebraic equations with initial and boundary conditions and an appropriate reaction model for thermal degradation (discussed below) are solved numerically. The convective terms are discretized by first-order upwinding, whereas central differencing is used for the diffusive terms. The time integrator must manage a system of differential and algebraic equations, and the numerical code DASSL has been chosen. A detailed description of the numerical solution procedure is given in refs 5, 14, and 28. Kinetic Model. The most difficult task is, however, to choose a reaction model with proper rate constants for the thermal decomposition process that satisfactorily predicts the experimental data (converted fraction, char, tar, and gas yield) listed in Table 1. Decomposition of wood and its main constituents, cellulose, hemicellulose, and lignin, takes place through a reaction network consisting of parallel and competitive reactions. Hence, kinetic modeling is very complicated and after nearly 30 years of research, starting with the pioneering work of Arseneau23 and Broido,24 there is still no consensus concerning the kinetics of wood and cellulose pyrolysis.5,25,26 (23) Arseneau, D. F. Competitive Reactions in the Thermal Decomposition of Cellulose. Can. J. Chem. 1971, 49, 633-638. (24) Broido, A. Kinetics of Solid-Phase Cellulose Pyrolysis. In Thermal Uses and Properties of Carbohydrates and Lignins; Shafizadeh, F., Sarkanen, K. V., Tillman, D. A., Eds.; 172nd National Meeting of the American Chemical Society; Academic Press: San Diego, 1976; pp 19-36. (25) Antal, M. J.; Varhegyi, G. Cellulose Pyrolysis Kinetics: The Current State of Knowledge. Ind. Eng. Chem. Res. 1995, 34, 703717.
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Figure 6. Kinetic scheme used in the model. Table 3. Kinetic Data and Heat of Reactions Used in the Model reaction i
Ai (1/s)
Ei (kJ/mol)
∆hi (kJ/kg)
1 2 3 4
1.30 × 108 2.00 × 108 1.10 × 107 2.30 × 104
140.3 133.1 121.3 80.0
150.0 150.0 150.0 -50.0
Because our experiments have shown that there exists a competition between char, tar, and gas formation that is dependent on the wood pellet’s temperature history, we have used a kinetic scheme that includes three parallel reactions to account for primary production of gas, tar, and char, and a consecutive reaction for the secondary cracking of tar (see Figure 6). The reactions are assumed to follow an Arrhenius type expression of the form
ki ) Ai exp(-Ei/R0T) Rate coefficients (activation energy and preexponential factor) for the primary reactions have been taken from ref 9. Secondary reactions are complex, being influenced by several factors such as wood species, heating rates, temperature, and mass transfer conditions. The latter includes changes in the physical structure (increasing porosity, shrinkage, and fissuration) of the reacting medium that will influence the volatile residence time inside the partially pyrolyzed wood pellet. Because rate coefficients for the secondary tar cracking reaction are not available in the literature, these have been adjusted through a parametric study. Endothermic reactions have been assumed for the primary reactions, whereas tar cracking has been modeled as a slightly exothermic process. The rate coefficients and heats of reaction used in this study are presented in Table 3. We urgently tell the reader that this kinetic model is a gross simplification of reality. Critics would argue that this model suggests that certain experimental conditions permit the entire conversion of wood to an individual product species at the expense of the other two species (ref 27: “...char cannot be formed without the simultaneous evolution of tar and/or gas.”) However, this is highly unlikely because the rate constants (k1, k2, and k3) and the activation energies (E1, E2, and E3) for the formation of the various product species are of comparable size. For our modeling purpose, this kinetic model has proved to be useful. (26) Grønli, M.; Antal, M. J.; Varhegyi, G. A Round-Robin Study of Cellulose Pyrolysis Kinetics by Thermogravimetry. Ind. Eng. Chem. Res. 1999, 38, 2238-2244. (27) Antal, M. J. Biomass Pyrolysis: A Review of the Literature Part IIsLignocellulose Pyrolysis. In Advances in Solar Energy; Boer, K. W., Duffie, J. A., Eds.; American Solar Energy Society, 1985, 175-255. (28) Melaaen, M. C. Numerical Analysis of Heat and Mass Transfer in Drying and Pyrolysis of Porous Media. Numer. Heat Transfer 1996, 29 Part A, 331-355.
Figure 7. Upper: Predicted (solid line) and experimental (shaded area) temperature histories. Middle: Converted fraction and product yield distributions versus time (predicted). Bottom: Local density versus temperature (predicted).
Results and Discussion Comparison of Model Predictions with Experimental Data. Time and space evolution of the pyrolysis process is shown through variable distributions in Figures 7-9 for the heated surface and in positions 1, 4, 8, 12, 16, 20, and 24 mm from the heated surface as a function of time, and for every 60 s as a function of the distance from the heated surface. As revealed in Figure 7 (upper), the temperature profile predicted by the mathematical model coincides quite well with the experimental temperatures at both high and low heat fluxes. The thick solid lines represent model predictions and the shaded areas represent temperature histories of three identical (replicated) runs. The temperatures follow an exponential growth history with a rapid increase initially. At a depth of 4 mm and deeper, both experimental and predicted temperature curves flatten before they further increase and approach their final temperatures. As previously discussed in the Experimental Section, this sudden change in temperature gradient is due to a reduction in local thermal conductivity. This is revealed in Figure 8 where the predicted temperature, effective thermal conductivity, and density spatial profiles at several times are presented. The temperature profiles indicate that there is consistently a slope change, or two main temperature gradients along the pellet, where the first slope reflects the thermal properties of the char layer and the second
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Figure 8. Upper: Temperature profiles (predicted). Middle: Effective thermal conductivity profiles (predicted). Bottom: Density profiles (predicted).
Figure 9. Upper: Total gas mixture (tar + gas) production profiles (predicted). Middle: Tar production profiles (predicted). Bottom: Gas production profiles (predicted).
slope the thermal properties of the unreacted substrate. The effective thermal conductivity decreases from the surface value and has its minimum value at the reaction front beyond, which it again increases to the initial value of the solid substrate. This is confirmed by superimposing the density profiles at the same reaction time. As shown earlier (eqs 8 and 9), the effective thermal conductivity is a function of density (∼ porosity) and temperature raised to power 3. The initial decline in effective thermal conductivity happens in the char layer where the density variation is small and the temperature difference is significant, implying that the effective thermal conductivity is mainly temperature dependent. The location at which the thermal conductivity begins to increase is in the reaction zone, and corresponds to partially converted substrate. In that region, the temperature gradient is small but the density gradient is steep, and the effective thermal conductivity appears to be mainly density dependent. A graph of the local density versus local temperature, as shown in Figure 7 (bottom), indicates the relative speed of the chemical kinetic and heat transfer processes. At a depth of 24 mm, heat transfer from the pellet surface is slow, that is, the temperature rise is much slower than at the surface. Once pyrolysis temperatures are reached, reaction occurs over a smaller temperature range (about 300-450 °C) than at the surface (about 300-550 °C). Thus, in the pellet interior, heat transport is the rate-controlling mechanism,
whereas the chemical reaction is the rate-controlling mechanism at the pellet surface. The effect of secondary tar cracking may be seen in Figure 9, where the spatial gas mixture, tar, and gas production rate profiles at several times are presented. The tar production, Figure 9 (middle), becomes negative after it has reached its maximum value, which means that the tar molecules are consumed as they flow toward the heated surface. The effect of this tar consumption is revealed in the gas production rate profiles in Figure 9 (bottom), which have two peaks. The innermost peak is due to primary reactions of the solid wood, and the second peak, which is closer to the surface, is gas produced from secondary reactions of the tar. The temporal evolution of the converted fraction and product yield distributions predicted by the model are shown in Figure 7 (middle). A comparison of the ultimate values obtained from the experiments and those predicted are presented in Table 4. The converted fraction is very well predicted at low heat flux but is underpredicted by almost 16% at high heat flux. The model predicts well the experimental char yields at both heat fluxes and the tar and gas yields at high heat flux. The adjusted rate constants for secondary tar cracking give, however, a too-low tar-to-gas conversion at low heat flux. By considering the uncertainties inherent in the experiments, for example, in the mass balance, and the simplifying assumptions used in the mathematical model, the predicted results must, however, be regarded as satisfactory.
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Table 4. Comparison of Experimental Data and Those Predicted by the Mathematical Model low heat flux (80 kW/m2) converted fraction (wt %) char yield (wt %) tar yield (wt %) gas yield (wt %)
a
experiments predicted differencea experiments predicted differencea experiments predicted differencea experiments predicted differencea
high heat flux (130 kW/m2)
5 min heating
10 min heating
10 min heating
25.7 ((1.63) 26.8 1.1 26.2 ((0.53) 26.1 -0.1 38.0 ((1.22) 49.2 11.2 35.9 ((1.44) 24.7 -11.2
45.5 ((3.61) 43.5 -2.0 28.7 ((1.06) 27.1 -1.6 31.3 ((5.06) 38.9 7.6 40.0 ((5.45) 34.0 -6.0
72.1 ((3.05) 56.7 -15.4 27.0 ((0.06) 26.4 -0.6 27.9 ((0.61) 25.8 -2.1 45.2 ((0.62) 47.8 2.6
Difference ) predicted value - experimental value.
Model Sensitivity. The mathematical model requires many input parameters and property-relations of which numerical values are uncertain. Sensitivity analysis is a subject of its own and an extensive study is presented in ref 5. The input parameters studied have been classified into the categories of heat transfer properties (thermal conductivity, specific heat), mass transfer properties (permeability, dynamic viscosity), and decomposition properties (kinetic rate coefficients, heats of reaction). The sensitivity analysis has been performed by using the classical one-variable-at-a-time approach, that is, one variable at a time is varied with the rest kept constant. In the following, we will highlight parameters to which the model prediction is most sensitive. Thermal Conductivity. The most important heat transfer property is the thermal conductivity. The sensitivity of the thermal conductivity model has been evaluated simply by changing the values of the thermophysical properties (kg, kSD, kC, dpor,SD, dpor,C, ω) in eqs 8 and 9 from the reference values presented in Table 2. Two examples: (1) Instead of using the radiant term, eq 9, to account for the temperature-dependent increase in the effective thermal conductivity, we assumed the conductivity of char to be two times greater than that of the virgin wood [kC ) 2kSD ) 0.7 W/(mK)]. The temperature inside the particle increased more rapidly and approximately 30 wt % more of the wood was converted within a fixed pyrolyzing time of 10 min. ( 2) To evaluate the effects of an increase in the radiant part, eq 9, of the effective thermal conductivity, we increased the pore diameter of virgin wood (dpor,SD) and char (dpor,C) to 75 and 125 µm, respectively. The predicted intraparticle temperatures increased by almost 50 °C and approximately 5 wt % more of the wood was converted. The parametric study revealed the importance of an accurate heat transfer model and also that the functional form of the thermal conductivity model is of great importance to model the S-shaped temperature profiles. Permeability. To study the importance of mass transfer of volatiles inside the partially pyrolyzed wood, the effects of changing the char permeability were examined. The reference simulation (Kg,SD ) 1.0 × 10-14 m2, Kg,C ) 1.0 × 10-11 m2) intends to describe a mediumpermeable wood with the resulting charred region, as a consequence of strong structural changes, 1000 times more permeable, giving a maximum overpressure of 0.0008 bar inside the wood pellet. As the char perme-
ability was decreased and finally reached the value of the virgin wood (Kg,SD ) Kg,C), larger pressure peaks and lower velocities in the char region were calculated. Higher residence time of volatiles in the hot char region promote secondary cracking of the tar components, leading to an increase in the ultimate yield of gases (+7 wt %) at the expense of tar. Although the volatiles transfer some convective heat as they flow toward the heated surface, the gas pressure and velocity field in the wood pellet have negligible influence on the temperature distribution. Hence, the permeabilities will have no influence on the converted fraction and ultimate char yield. Kinetic Rate Coefficients. The effect of pyrolysis kinetics was examined by varying the activation energy and frequency factor of the four reactions by (5%, one at a time. [Remark: Because the activation energy (E) and frequency factor (A) are strongly coupled through the compensation effect, the activation energy should not be varied without simultaneously changing the frequency factor.] Variation of the kinetic rate coefficients over a reasonable range caused a few percentages change in the converted fraction and relative product yield distributions. For example, a 5% decrease in the kinetic rate coefficients for the char-forming reaction (E3 ) 115.3 kJ/mol, A3 ) 3.2 × 106 s-1) from the reference values (see Table 3) reduced the local char density by 25-30 kg/m3. Lower char density means higher porosity. Recall that the porosity is included in both the numerator and denominator of the radiant conductivity term, eq 9. Higher porosity increases the radiant contribution to the effective thermal conductivity and heat is transferred through the char region at a faster rate, and approximately 4 wt % more of the wood was converted. In conclusion, the strong interaction between the chemical (kinetics) and physical (heat and mass transfer) processes involved in the thermal degradation of wood makes the modeling difficult. Concluding Remarks The experiments have evidenced that there exists a competition between char, tar, and gas formation during wood pyrolysis that is dependent on the heating conditions. Hence, a competitive reaction model that includes a secondary tar cracking step is needed to be able to predict the effects caused by a variation in heat flux on the product yields distribution. Heat flux arriving at the
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particle surface has a large effect on the reaction rates and product yield distributions as well as the intraparticle temperature distribution. The model predictions revealed the importance of an accurate heat-transfer model. The thermal conductivity of dry wood is a function of density, temperature, and grain orientation. Variable thermal conductivity, which includes a radiant heat transfer term, is needed to predict the intraparticle temperature history throughout the pyrolysis process. The sensitivity analysis revealed that mass transfer is not important in modeling of the char yield, but is important in the modeling of secondary reactions. The strong interaction between the chemical reactions and heat and mass transfer processes involved in the thermal degradation of wood makes the mathematical modeling difficult. However, the model that has been presented in this paper agrees well with the experimental results. Acknowledgment. This research was supported with a scholarship from the Nordic Energy Research Program-Solid Fuel Committee and a grant from the Norwegian Ferroalloy Producers Association (founded by Elkem ASA, FESIL ASA, and Tinfos Jernverk A/S), the Norwegian Research Council through the KLIMATEK programme, and Statoil. We also thank the reviewers for their constructive remarks. Nomenclature Ai ) preexponential factor in the pyrolysis model, 1/s CP ) specific heat capacity at constant pressure, J/(kg K) dpor ) pore diameter, m Ei ) activation energy in the pyrolysis model, J/mol F ) incident heat flux to surface, W/m2
Grønli and Melaaen hT ) heat transfer number, W/(m2K) k ) thermal conductivity, W/(m K) ki ) reaction rate constant, 1/s K ) intrinsic permeability, m2 M ) molecular weight, kg/mol Ng ) number of components in the gas mixture phase P ) pressure, N/m2 〈Pg〉g ) pressure in the gas mixture phase, N/m2 R0 ) universal gas constant [) 8.3144 J/(mol K)] t ) time, s T,〈T〉 ) temperature, K 〈vi〉 ) superficial velocity of component i, m/s 〈i〉 ) rate of production of component i, kg/(m3s) X ) Cartesian coordinates, m ∆hi ) heat of pyrolysis, J/kg Greek Letters ) volume fraction µ ) dynamic viscosity, kg/(m s) η ) interpolation factor 〈Fγ〉 ) (phase averaged) density of phase γ, kg/m3 〈Fi〉γ ) intrinsic (phase averaged) density of component or phase i in phase γ, kg/m3 σ ) Stefan-Boltzmann constant [) 5.67 × 10-8 W/(m2 K4)] ω ) emissivity Subscripts and Superscripts A ) air in the gas mixture phase C ) char g ) gas mixture phase G ) gas in the gas mixture phase i ) component or phase i s ) solid phase, boundary surface S ) virgin or unreacted solid during pyrolysis SD ) dry solid wood T ) tar in gas mixture phase ambient ∞ ) ambient EF990176Q
