Chapter 2: Literature Review Chapter Two: Literature Review Introduction The heating of wood involves physical changes such as enthalpy and moisture content One of the major links between temperature and moisture changes is water evaporation Water evaporation acts as a heat source term in the energy balance, and contributes to physical processes of heat and mass transfer in the heating of wood This chapter reviews first the chemical changes i.e pyrolysis and physical processes of heat and mass transfer within the framework of wood combustion so that any addition, alteration and omission of physical variables in the mathematical formulation could be better understood in terms of its impact Because water evaporation is an important link in wood heating, the different formulations on modeling of evaporation in wood heating are also reviewed The objective is to elucidate the most optimum way to represent this physical process in the modelling of wood heating and combustion, when the evaporation front has recessed into wood There have been different modeling approaches towards evaporation in wood heating Using one approach instead of the other represents a different understanding to the physical process of evaporation in wood drying Water evaporation in hygroscopic wood is primarily concerned with the changes in equilibrium pressure of water vapour with temperature and moisture content; this chapter hence first reviews the equilibrium and the 26 Chapter 2: Literature Review non-equilibrium approaches The different principles and formulations are discussed, and the problems for applications in wood heating are evaluated with respect to both lowtemperature and high-temperature drying Alternative approaches such as the desorption kinetics approach and the evaporation temperature approach are also discussed 2.1 Reviews of physical and chemical studies in wood combustion Combustion is a complex problem involving solid-phase and gas-phase phenomena For bench-scale methods such as Cone Calorimeter, analysis is mainly on solid-phase phenomena; gas-phase diffusion and chemical kinetics are relatively unimportant for this scale of evaluation, involving less complex geometry (Janssens 1991a) Chemical reaction and the heat and mass transfer processes constitute a complete solid-phase phenomenon Chemical and physical processes however not play equal parts in thermal model This review considers a comprehensive combustion model that includes pyrolysis as well as heat and mass transfer in the formulation of a mathematical model 2.1.1 Heat and mass transfer in solid phase In pure thermal models, heat transfer is solely accounted by conduction The flow of pyrolysate gases (henceforth known as “volatiles”) is not considered in the energy equation In the respective one-dimensional and three-dimensional model of Bamford et al (1946) and Bonnefoy et al (1993), their energy equation contains a heat diffusion 27 Chapter 2: Literature Review term with thermal decomposition described by a first-order Arrhenius equation, acting as a heat source term The convective heat transfer due to the flow of volatiles was not included Such pure thermal models are often employed to limit the problems as a conduction case, so that useful insights could be obtained to form analytical solutions Janssens (1993) has used a thermal model to successfully correlate ignition with thermal properties of wood slabs Besides, pure conduction problems are also widely used to study ignition in materials that are irradiated on one side and lose heat by Newtonian cooling (Simms 1960) There came the findings from Kanury and Blackshear (1970a and 1970b) They studied the convection of volatiles in a pyrolysing solid and demonstrated the importance of internal convection to the overall heat balance They examined the relative magnitude of convection term to conduction term, and showed that the Peclet number is greater than 0.1 Peclet number is a dimensionless number used in calculations involving convective heat transfer; it is the ratio of thermal energy convected to the fluid to the thermal energy conducted within the fluid Peclet number is in fact a product of Reynolds number and Prandtl number, which can be expressed as ρ ∗ C p ∗ V∞ ∗ (T1 − T0 ) / l k ∗ (T1 − T0 ) / l The finding that Peclet number was greater than 0.1 in this case strongly endorsed the significance of internal convective heat transfer In addition, their research further pointed out that the effect of convection would increase in tandem with the corresponding increase in specimen’s size Internal convection of volatiles was subsequently included in the energy equation of many pyrolysis models (Kanury and Blackshear 1970b, Kung 1972, Kung and Kalelkar 1973, Kansa, Perlee and Chaiken 1977, Boonmee 2004) The 28 Chapter 2: Literature Review energy transport equations in these works however did not include a convective heat transfer term for the flow of water vapour; moisture was either not considered, or not treated explicitly Kung (1972) discussed the significance of both the outward convection of volatiles and char conductivity on the pyrolysis wave propagation, but did not consider the evaporation of moisture in wood Kansa et al (1977) incorporated the momentum equation for the movement of volatiles in solid but not one for volatiles Boonmee (2004) considered the effect of water vaporisation to be insignificant in the case of oven-dry wood and ignored convection of vapour on heat transfer Vapour was added to the energy equation in some models on the ground that the vaporisation could be significant on the overall heat balance Chan et al (1985), Fredlund (1988), Alves and Figueiredo (1989) and Yuen (1998) have included moisture evaporation as an additional heat source term, treating the latent heat of evaporation as heat of reaction Convective heat transfer due to vapour was also added alongside convection of volatiles in the energy transport equation The inclusion of moisture evaporation as a heat source term creates a heat sink in the energy balance as it draws heat from inside the solid to vaporise the moisture Zhang and Datta (2004) showed that the conventional treatment of moisture evaporation as a heat source term could create problems for low rate drying or low heating of wood The heat sink effect by moisture evaporation causes the temperature to fall below the actual temperature where the initial temperature remains fairly constant for initial drying 29 Chapter 2: Literature Review For models that accounted for the production of volatiles, alone or in combination with water vapours, many of these models (Kung 1972, Kung and Kalelkar 1973, Kansa et al 1977, Chan et al 1985, Boonmee 2004) have assumed that these volatiles and vapours escape instantaneously to the surface once they are formed In doing so, these models have assumed, as well as limited, the flow of volatiles and vapour strictly in the longitudinal direction, since wood has a large permeability along grain, of which the ratio of axial to transverse permeability for softwoods is approximately 20,000 (Siau 1984); the large axial permeability permits relative ease of escape The velocity of the volatiles and vapour are given by the flow field which of course has to satisfy the continuity equation There is no accumulation of volatiles and vapour, thereby eliminating accumulation term in the continuity equation Since it is not a pressure-driven flow, pressure is assumed constant Such simplification in mass transfer is often made so that analytical models ascribed to certain complex combustion phenomenon can be made tractable (Boonmee 2004) Driving forces sometimes arise naturally in cases where there is a steep pressure build-up resulting in a pressure gradient, or concentration difference that promotes diffusion In both Fredlund’s model (1993) and Yuen’s model (1998), a pressure equation is provided as a driving force In their models, mass transfer of volatiles and vapour is based on gas flows driven by pressure gradients, the flow of which conforms to Darcy’s law Both models allow the pressure to change with porosity of the wood slab, thereby creating the pressure in the system The total pressure is then obtained according to Dalton’s law as the sum of the partial pressures of water vapour and volatiles Mass source terms are 30 Chapter 2: Literature Review created in the continuity equation to allow accumulation of volatiles and evaporation of vapour The only difference between the two mass transfer models is that in Fredlund’s work, additional pressure changes arising from elevating temperature that cause gases to expand in a constant volume according to the universal gas law have been provided for Nonetheless, this additional pressure term is small as compared to pressure change arising from vaporisation of water in rapid heating rates In the latter, rapid vaporisation results in steep pressure gradient In both Fredlund’s and Yuen’s models, moisture flow takes place mainly in vapour phase Moisture flow can occur in liquid phase, but Fredlund and Yuen have both adopted the high-temperature drying model proposed by Alves and Figueiredo (1989) which ignored free water movement The same assumption of eliminating free water movement has also been adopted in all the foregoing models that not use pressure-driven flow For vapour and volatiles transport, all models have implicitly (those with pressure driven flow) and explicitly (those not employ pressure-driven flow) excluded vapour diffusion The assumption that water vapour/ carrier gas diffusion is much slower than vapour convection reduces the model validity to high-temperature drying i.e above water boiling point 2.2 Evaporation zone in drying model Modelling of internal evaporation rate will be needed when internal evaporation is significant, such as when there is an evaporation zone inside the material It occurs at a 31 Chapter 2: Literature Review later stage of drying when diffusivity of liquid becomes small due to diminishing moisture content The escaping water flux through the surface decreases, resulting in a drier surface and a decreasing surface evaporation rate Eventually, the evaporation front moves inwards Figure 2.1 shows a conceptual model of high-temperature drying in wood where evaporation zone has retreated inwards, creating an evaporation zone within the pyrolysing wood (Stanish, Schajer and Kayihan 1986, Farid 2002) Evaporation takes place in this evaporation zone since it is the location where there is the largest moisture gradient (Ilic and Turner 1986) The water vapour partly migrates towards and escapes through the exposed surface A fraction also migrates in the opposite direction, and recondenses at a colder inner region This high-temperature drying model also models the formation of cracks and fissures at the char surface, since high-temperature drying occurs just incipient of or in tandem with flaming combustion The formation of cracks and fissures greatly affects the heat and mass transfer between flame and the solid, and hence the equilibrium of vapour pressure profile at the surface 32 Chapter 2: Literature Review Figure 2.1: Conceptual model of high-temperature drying in wood Mass and enthalpy transfer Heat transfer Wet wood Evaporation zone Dry wood Pyrolysis zone Char layer Initial location of exposed surface Flame Pyrolysate movement Fire Vapour movement 3 (Drying model adapted from Janssens 2004, ©Fire and Materials) The rate at which the evaporation zone moves into the solid can be calculated by heat conduction (Williams, 1953) The method divides the solid into two regions separated by an isothermal plane – the 100°C plateau, the plane of vaporisation The rate at which this plane moves at any depth r is assumed to depend only upon the net rate of heat transfer by conduction to that depth The equation for calculating r at time t is given by (λt )1/2 r ierfcβ = constant k 2(λt )1/2 (2.1) where λ is the thermal diffusivity, k the thermal conductivity and ierfcβ is given as 33 Chapter 2: Literature Review = ierfcβ π ∞β ∫ ∫ exp(− z β (2.2) )dz z Figure 2.2 shows the depth (r ) of the plane of vaporisation (interface B) calculated by the heat conduction method It has been pointed out that in hygroscopic materials, there is no abrupt interface between the dry zone (Zone A) and the wet zone (Zone C) (Schrader and Litchfield 1992) The capillary effect still causes water diffusion and vapour generation depends on moisture content (X) and temperature (T) So, evaporation takes place in a zone instead of on a sharp interface as shown as “interface B” in Figure 2.2 Figure 2.2 Evaporation front calculated by heat conduction in high-temperature drying T=T∞ Zone A Interface B X= r T=Tev Zone C X = constant > (Simplified model of high-temperature drying reproduced from Alves and Figueiredo 1989, ©Chemical Engineering Science) Incorporating the evaporation zone, instead of an evaporation front into a drying model yields a high-temperature drying model that has been widely used in pyrolysis studies of wood It has thus been commonly referred to as the “conventional high-temperature 34 Chapter 2: Literature Review drying model” (See Figure 2.3) Vapours are generated in Zone B (evaporation zone) when temperature reaches the moisture boiling point, or evaporation temperature Janssens (2004) pointed out that since water is adsorbed to cell walls, evaporation requires more energy than needed to boil free water and may occur at temperatures exceeding 100°C Alves and Figueiredo (1989) proposed that the evaporation temperature is governed by the moisture content (X) on dry basis For 1% < X < 14%, the evaporation temperature is given as { } Tev ( X )= 1/ 2.13 ×10−3 + 2.778 ×10−4 ln( X ) + 9.997 ×10−6 [ ln( X ) ] − 1.461× 10−5 [ ln( X ) ] (2.3) Yuen (1998) suggested that when the moisture content in wood is less than 1%, the evaporation temperature may be assumed to be 473K For wood with moisture content > 14%, the evaporation temperature can be assumed to occur at 373K, with negligible discontinuity and error (Alves and Figueiredo, 1989; Yuen, 1998) 35 Chapter 2: Literature Review pressure-driven flows, the rate of evaporation Rev , expressed in the continuity equation, requires the solution of total pressure inside the system where ∂ρv ∂ m x ρ ∂p ∂ m y ρ ∂p ∂ m z ρ ∂p − Rev = s v s − s v s − s v s ∂t ∂x ρt ∂x ∂y ρt ∂y ∂z ρt ∂z (2.10) where ρt is the total sum of the mass of volatile gases, vapour and dry air per unit volume and msj = Dsj / ηt is the respective mass transfer coefficients of the solid as j = x, y, z directions; ηt being the kinematic viscosity of gaseous mixture in the solid In Yuen’s model, the total pressure ps is readily obtained according to Dalton’s law as the sum of partial pressures of vapour, volatiles and dry air, i.e ps = pg + pv + pi Alves and Figueiredo (1989) also formulated the rate of evaporation assuming local moisturevapour equilibrium from their heating model which does not consider mass transfer The rate of evaporation Rev is formulated from their one-dimensional energy balance comprising of a thermal decomposition scheme of six constituent components where j = 1, as follow: ∂ ( ρ s Cs + ρ mCm )Ts ∂ ∂Ts + ks ∆H ev ∂t ∂x ∂x = Rev − ∂ (mg C g + mv Cv + mi Ci )Ts ∂x − ∑ ∆H pj R pj j (2.11) 39 Chapter 2: Literature Review Despite the assumption that the equilibrium between water and vapour pressure is reached instantaneously, the actual rate of evaporation itself may not be fast enough in the context of a fast heating scenario It has been shown that when a piece of material is put into a closed chamber to measure its water activity (aw) , it takes two to thirty hours for the sample to reach equilibrium (Ramanathan and Cenkowski 1995) This is particularly true when considering dry wood because the strong attraction of water to the solid matrix (Janssens, 1993) may cause it to take a longer time before the balance can be established It probably will be faster for a wet wood to reach equilibrium than a dry one due to the presence of more free water and the presence of smaller gas bubbles in wet porous structures (Zhang and Datta, 2004) Transport will also affect the establishment of equilibrium especially in the dry zone near the surface (Zhang 2003) In the location near the surface, the vapour convects without much resistance, owing to the formation of cracks and fissures (see Figure 2.1 and “Zone A” in Figure 2.3) If vapour is lost quickly, the vapour pressure will be lower than the equilibrium pressure, unless evaporation is very fast It therefore may not be mathematically appropriate to compute the rate of evaporation directly through the continuity equations assuming the equilibrium approach, because of the discrepancy between the actual rate of evaporation and the assumption of instantaneous equilibrium Besides, the rate of evaporation Rev formulated through the continuity equations contains the second derivative of the state variables such as temperature (T ) , pressure ( ps ) and mass fluxes of respective species The computational solution of Rev through the systems of equations will be two orders lower in precision 40 Chapter 2: Literature Review (Zhang and Datta, 2004) To overcome the problem, it has been proposed that the evaporation term is removed from the continuity equations (i.e Rev is not to be resolved from the formulation using continuity equation), and to compute the evaporation rate directly from the systems of modified conservation equations (Zhang, 2003) For instance, given an one-dimensional system considering water and vapour diffusion, the continuity equations may be expressed as ∂V ∂ ∂V = ( Dv ) + Rev ∂t ∂x ∂x (2.12) ∂W ∂ ∂W = ( Dw ) − Rev ∂t ∂x ∂x (2.13) The continuity equations of (2.11) and (2.12) may be combined so that Rev is removed The conservation model then consists of two equations: ∂W ∂V + = ∇ ⋅ ( Dw∇W ) + ∇ ⋅ ( Dv ∇V ) ∂t ∂t ρc ∂T ∂W = ∇ ⋅ (k ∇T ) − ∆H ev − + ∇ ⋅ ( Dw∇W ) ∂t ∂t (2.14) (2.15) ∂W where Rev = − + ∇ ⋅ ( Dw∇W ) in Equation (2.15) which can be obtained from ∂t Equation (2.11) The conservation model is solved directly by replacing variables 41 Chapter 2: Literature Review ∂V / ∂t and ∇V with state variables T and W through differentiating the ideal gas law in Equation (2.4), so that ∂V M v = ∂t RT Mv = RT ∂pv pv M v − ∂t RT ∂pv ∂T ∂pv ∂W pv M v ∂T ∂T ∂t + ∂W ∂t − RT ∂t (2.16) Mv RT Mv = RT pv M v ∇T RT ∂pv ∂pv pv M v ∂t ∇T + ∂W ∇W − RT ∇T (2.17) ∇V = ∇pv − The substitution of ∂V / ∂t and ∇V using Equations (2.16) and (2.17) eliminates the second derivatives of T and W from the conservation equations It thus prevents the computational errors associated with the second order of differentiation for computing evaporation rate 2.5 Non-equilibrium approach In non-equilibrium approach, it does not assume water vapour is in equilibrium with liquid water Indeed, how fast water-vapour can reach equilibrium, or how fast the evaporation is, needs to be quantified The rate limit of evaporation and the attainment of equilibrium are determined by the evaporation rate, either empirically derived or experimentally quantified 42 Chapter 2: Literature Review How fast evaporation is can be related to the difference between equilibrium vapour pressure and the actual local vapour pressure In addition, evaporation rate also depends on the water content in the material Bixler (1985) proposed the following evaporation rate for the non-equilibrium condition: Rev = W0 )( pv ,eqb* − pv ) c(W − (2.18) where W is the moisture content, W0 is the residual moisture content after which the moisture content does not decrease anymore c is a coefficient that varies with temperature and moisture content; it should be chosen such that the rate of mass loss obtained from simulation matches the mass loss in the experiment (Bixler, 1985) The formulation of evaporation rate such as that in Equation (2.18) is advocated for more realistic representation of heating in hygroscopic materials (Zhang, 2003) Indeed, equilibrium approach is considered a special case within the domain of the nonequilibrium approach However, there are several difficulties associated with the use of non-equilibrium approach The measurement of evaporation is difficult in porous media, only empirical parameters with unverified accuracy have been used so far (Bixler, 1985) Besides, in the numerical modeling of porous media, the sharp change of vapour pressure near the surface causes some numerical difficulty Zhang (2003) pointed out that the finite element mesh near the surface needs to be very fine to reach convergence However, there is a limit as how fine the mesh size can be reduced to match the pore size since a valid continuum assumption requires that the size of the Representative Elementary 43 Chapter 2: Literature Review Volume (REV) required for building the governing equations is at least a few times larger than the pore size Zhang and Datta (2004) indeed argued that since evaporation rate is not perfect and the knowledge of equilibrium rate remains largely qualitative, there is no need to pursue exact match between simulation and experiment Nonetheless, despite the arbitrary nature of parameters and the formulation of the rate of evaporation, the nonequilibrium approach is still more realistic than simply ignoring the transition from nonequilibrium to equilibrium in certain applications (Vafai and Hadim 2000) 2.6 Desorption kinetics approach Other than the non-equilibrium approach, the desorption kinetics approach is another alternative approach intended to address the limitations faced in assuming phase equilibrium between water and vapour throughout the material Because of the lack of equilibrium at the surface due to convective removal of vapour, using the equilibrium vapour pressure is likely to overestimate the drying rate To overcome the problems, a lower vapour pressure has to be used in the modelling or having the mass transfer coefficients at the surface reduced; these adjustments however may render the whole treatment even more empirical Desorption kinetics approach which examines the watervapour phase change at the interface between pure water and vapour offers an alternative method to approach evaporation In wood heating, the desorption kinetics approach has been used to model evaporation of adsorbed moisture as the breaking of hydrogen bonds holding the water molecules to the cell walls The rate of evaporation is governed by the instantaneous concentration of 44 Chapter 2: Literature Review adsorbed moisture and the probability of water molecules possessing sufficient activation energy required to overcome the hydrogen bonding to escape as vapour (Fang and Ward 1999) Atreya (1983) proposed an Arrhenius form of equation for describing the evaporation rate of water in wood following desorption kinetics approach: ∂ρ Rev = m = m exp(− Eev / RTs ) Aev ρ − ∂t (2.19) where Aev is the pre-exponential factor and Eev is the activation energy required for the breakage of hydrogen bond To evaluate the kinetic parameters, Atreya (1983) used a low incident heat flux of 4.9kWm-2 so that the material was not heated to decomposition He found that Aev 4.5 ×103 s −1 and Eev = 10.5kcal mol−1 by the graphical method of best fit = Desorption kinetics approach still faces some problems in application to wood Firstly, the water-vapour phase change at the interface of pure water and vapour is still not well understood even at room temperature (Bedeaux and Kjelstrup 1999, Fang and Ward 1999 ) Secondly, it will be more complicated for modelling phase change in hygroscopic materials since it involves material compositions and their chemical affinity with water 2.7 Chemical degradation in wood 2.7.1 Kinetics models of pyrolysis Pyrolysis or thermal degradation of wood is computationally a heat sink term in an energy balance 45 Chapter 2: Literature Review Kinetic studies involve the determination of kinetic mechanisms and kinetic constants, so that mathematical description of pyrolysis can be formulated and then successfully calculated One very popular approach used in the kinetic studies of wood pyrolysis is the one-step global model which uses a one-step reaction to describe degradation of the solid fuel by means of experimentally measured rates of weight loss The kinetic scheme is generally represented as k SOLID → VOLATILES + CHAR (2.20) Many studies have been carried out for wood degradation adopting one-step global models, most of them using TGA (Ramiah 1970, Fairbridge, Ross and Sood 1978, Tabatabaie-Raissi, Mok and Antal 1989, Antal, Friedman and Rogers 1980), others have employed fluidized bed reactors (Barooah and Long 1976), a tube furnace (Min 1977) and in-situ measurement techniques (Kanury 1972) Through the use of a simple kinetic scheme, the one-step global model has rendered an otherwise hopelessly complex wood and cellulosic materials degradation possible, where it is still able to account for the chemistry of solid degradations for kinetically-controlled as well as heat transfer controlled regime where secondary reactions may play a significant role (Di Blasi 1993) An extensive work to examine the competitive nature of the primary reactions and the acquisition of reliable kinetic data using the one-step global model has been carried out by Lim (2002) where good kinetic results have been obtained 46 Chapter 2: Literature Review The modeling of thermal degradation of complex solid fuels such as wood either consider the fuel as a single homogeneous species, or model the individual constituents, the sum of which make up the total mass according to the one-step global, multi-stage model or twostage semi-global models One of the most used primary degradation mechanisms was proposed by Alves and Figueiredo (1989) They model pyrolysis of small particles of wood by six independent, first order reactions Each reaction corresponds to the main wood component, which are hemicellulose (one reaction), cellulose (one reaction) and four species describing parts of the lignin macromolecule (or stages in its degradation) The scheme representing the thermal decomposition reaction of each of the six constituents is written as ∆H j Svj → G ↑ E j , Aj j= 1, 2, (2.21) where Svj is the volatile part of component of j of wood; G ↑ denotes volatile gas produced; ∆H , E , A represent heat of pyrolysis, activation energy and pre-exponential factor for the respective component Yuen (1998) modeled his wood pyrolysis in two phases: active portion and charcoal phase; the active portion is modeled as having six constituents following the scheme proposed by Alves and Figueirdo (1989) Boonmee (2004) modeled the wood decomposition as the weighted sum of three primary constituents: cellulose, hemicellulose and lignin (i.e j = ) Each reaction is an independent first order reaction represented by an Arrhenius equation with different kinetic parameters 47 Chapter 2: Literature Review An alternative description of the thermal degradation of wood considers the solid as a single homogenous species One of the widely used primary wood degradation mechanisms of such description is based on Shafizadeh and Chin (1977) work which expresses the decomposition as k1 WOOD → TAR (2.22) k2 WOOD → GAS (2.23) k3 WOOD → CHAR (2.24) Thurner and Mann (1981) have attempted the experimental measurements of tar, gas and residue mass fractions for temperatures in the limited, lower range at 300°C - 400°C Coupled with carefully selected range of evolution time, the kinetic parameters can be evaluated without the interception of secondary reactions While some studies are limited to primary (Nunn et al 1985, Font et al 1990) or secondary reactions (Boroson et al 1989), the description of thermal degradation of wood as a single homogenous species has also seen works carried out on both primary and secondary reactions (Koufopanos et al 1991) Whether studying wood as a single homogenous species or a sum of constituents, those foregoing works largely describe wood pyrolysis as one-stage, multi-step global models These proposed models have assumed the virgin solid fuel (wood or its components) 48 Chapter 2: Literature Review decomposes directly to each product j by a single independent reaction which can be described by the scheme as kj VIRGIN FUEL → PRODUCT j (2.25) The kinetics for the one-stage, multi-step global models are done via a unimolecular firstorder reaction rate as dV j dt = − E j / RT )(V j* − V j ) Aj exp( (2.26) where V j is the yield of the product j , and Aj and E j are the pre-exponential factor and apparent activation energy The quantity V j* is the ultimate attainable yield of species j Though semi-global models have been used extensively to describe the pyrolysis of individual components such as cellulose and lignin, the application of semi-global model to wood as a biomass is still rare The lack of full understanding of pyrolysis scheme and its derivatives for wood and the complexity of variations that arises from different wood species perhaps explain only the occasional attempts of such models Panton and Pittmann (1971) were the few who successfully described the pyrolysis of wood using semi-global model The virgin solid is taken as a single species By one reaction, it can decompose into a second solid species plus a gas which flows out to the surface through the pores In addition, the original solid also decomposes by a second reaction into 49 Chapter 2: Literature Review another gas The solid product of the first reaction undergoes secondary reaction to form a final inert-solid species and another vapour The model is schematically shown below k1 S1 → S + G1 (2.27) k2 S1 → G2 (2.28) k3 S → S3 + G3 (2.29) All reactions are assumed first-order with Arrhenius rate equations In all, there are three reactions, two competing and one consecutive The modeling of wood pyrolysis can be made complex by the formulation of kinetic scheme of the chemical processes and the acquisition of reliable kinetic parameters To complicate matters, there remains a large ambiguity as to the representation of energetics of the pyrolysis reactions (Di Blasi 1993), where wood pyrolysis can vary between endothermic and exothermic at different temperatures Large differences were also noted in the measured values of the pyrolysis process even at the same temperature (Kanury and Blackshear 1970a) While there are continuing efforts to improve the description of kinetic scheme in wood pyrolysis modeling, Chow (1996) has pointed out that in most cases, only the Simple Chemical Reaction Scheme (SCRS) involving direct oxidation of fuel to product i.e a simple one-step global scheme, can be successfully applied in combustion simulation in a field model The rationale for Chow’s argument can be easily understood in the context of field modeling concept Field model, which is also known as 50 Chapter 2: Literature Review Computational Fluid Dynamics (CFD) model, requires the solving of Navier-Stokes equations for a large number of control volumes for given spatial domain These partial differential equations are solved iteratively for advancing time steps The modeling of wood pyrolysis in a field model requires the addition of pyrolysis as a source term in modelling the heat transfer for the fluid flow Large input parameters are needed; greater computational resources are involved to compute and update the velocity and pressure fields; convergence of solutions and accuracy of results may not be guaranteed as scheme becomes complex as such Energetics of pyrolysis In general, it has been found that pyrolysis of hemicellulose and lignin is an exothermic process, while cellulose pyrolysis is an endothermic process at low temperatures and becomes an exothermic process at high temperatures (Ramiah 1970) The earlier findings by Roberts (1970) therefore suggested that the bulk pyrolysis process of wood should be exothermic as at high temperature, the exothermic decomposition of final cellulose and lignin controls the overall heat of pyrolysis of wood The subsequent works however acknowledged the interplay of exothermic and endothermic processes, and the final energetics varied from case to case For instance, Koufopanos et al (1991) measured the temperature-time history inside wood and showed that the process is initially endothermic and then weakly exothermic They found that the primary reactions are endothermic and estimated the heat of pyrolysis to be -255kJ/kg while the secondary reactions are exothermic and is of a value of 20kJ/kg Suuberg et al (1994) also found that wood contains a number of exothermic and endothermic processes, but the overall 51 Chapter 2: Literature Review pyrolysis of wood is endothermic, with a values ranging from -70kJ/kg to 400kJ/kg depending on char yield The more recent findings by Rath et al (2003) confirmed that the primary reactions are endothermic, and the heat of pyrolysis switches to an exothermic secondary reactions at higher temperature; the overall heat of pyrolysis is the net sum of the primary and secondary reactions They suggested that heat of pyrolysis is species-dependent; for instance beech has an overall endothermic heat of pyrolysis (122kJ/kg) and spruce has an exothermic value of 289kJ/kg Many workers have represented wood pyrolysis as an endothermic process However, the uncertainty of wood energetics has also rendered many others ambivalent In dealing with the ambiguity of wood energetics, Atreya (1998) has suggested that since the energy due to the pyrolysis term was small as compared to other terms in the energy transport equation, it should be simply neglected Some workers have assumed this approach by leaving out heat of pyrolysis in their heat source term for pyrolysis (Fredlund 1988, Boonmee 2004) 2.8 Concluding remarks The modelling of internal evaporation rate will be needed when internal evaporation rate is significant, i.e when evaporation front has retreated inwards, creating an evaporation zone Unlike the modelling of surface evaporation where the main concern is to avert creating a heat sink, the modelling of internal evaporation is concerned with modelling more accurate equilibrium vapour pressure and the parameters needed to describe the evaporation rate 52 Chapter 2: Literature Review The assumptions of using equilibrium and non-equilibrium approach should be considered on case to case basis for application in wood When wood has high moisture content and the actual vapour pressure may be approximated by equilibrium relationship, equilibrium may be a good assumption However, in high-drying model, the surface zone often fails to achieve equilibrium as the rate of evaporation may not be fast enough to replace vapour that is lost through convection at the surface The non-equilibrium approach may offer an alternative to reflect the influence of transport processes on local vapour-moisture equilibrium in such a situation Nonetheless, most studies have still adopted equilibrium formulation for high temperature drying so long as the wood interior remains largely in phase equilibrium Though the measured vapour pressure fails to reach equilibrium in modelling fast transport processes or high heating rates, equilibrium is largely achieved in cases that involve low heating rates and long exposure time, where the water activity and evaporation has sufficient time to reach equilibrium It is also faster to reach equilibrium in wet porous material because of the presence of more free water Therefore, equilibrium approach is suitable for application to study low-temperature, long-term heating in hygroscopic wood 53 ... primary wood degradation mechanisms of such description is based on Shafizadeh and Chin (1977) work which expresses the decomposition as k1 WOOD → TAR (2. 22) k2 WOOD → GAS (2. 23) k3 WOOD → CHAR (2. 24)... exp(− K / Ts ) pv , sat where K1 and (2. 8) K are constants which depend on the temperature range, and K1 4.143 ×1010 Pa and K = 4 822 K in the temperature range of 20 °C to 1000°C = The assumption that... 1, 2, (2. 21) where Svj is the volatile part of component of j of wood; G ↑ denotes volatile gas produced; ∆H , E , A represent heat of pyrolysis, activation energy and pre-exponential factor