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Show By assuming that the particle temperature vanes very slightly between discrete time integration steps, the equation (9) can be integrated analytically to yield: m (t + __) = (!- f.0 - /w0)m.0 + [-i(0 - (1 - f0 - /K0)mp0]exp(-/;AO (ID Coal Devolatilization Coal devolatilization is modeled by using the two competing rates expression proposed by Kobayashi et al. (1976): (12) /?, = AlQxp(-El/RTP) /?, = A,exp(-EJRTP) where R| and R2 are the competing rates that control the devolatilization over two different temperature ranges, and A!=3.7E-f-5 s'1, A2=1.5E+13 s'1, E[=7.04 E+7 J/Kgmol and E2=2.51E+8 J/Kgmol. The two kinetic rates are weighted to yield an expression for the devolatilization as: mv(t) •„o = j(a{R{+a2R2)txp - j(R] + R2 )dt (13) where m v (t) is volatile yield up to time t, nipo is initial mass of the particle, m a is the ash-content in the particle, and ct|, oc2 are the yield factors. The above equation is integrated in time analytically, assuming the particle temperature is constant over the discrete integration time step. During devolatilization, the particle diameter is changed based on the ratio of the mass that has been devolatilized to the total volatile mass of the particle: D/DB0=1+(C -1) >o ( 1 - A Q ) " I P Q - " ' / , (14) /vOmpO where C s w is the swelling coefficient, D p is the current particle diameter, and Dpo is the particle diameter at the start of devolatilization. The heat transfer to the particle during the devolatilization process includes the contributions from convection, radiation, and the heat consumed during devolatilization. Biomass Char Combustion After the volatile component of the particle is completely evolved, a surface reaction begins which consumes the combustible fraction of the particle. The surface combustion consumes the reactive content of the particle as governed by the stoichiometric requirement, Sb, of the surface burnout reaction: char + Sb0 Pr oducts(g) where Sb is the mass of the oxidant per unit mass of char. Because of the large size of biomass char, the surface reaction proceeds at a rate determined by the diffusion of the gaseous oxidant to the surface of the particle: drrtp . = -4xD0<pD,m moToP, dt "' Sb(Ta+TJ (15) where Di'.m is the diffusion coefficient for oxidant in the bulk, pg is the gas density, m o is the local mass fraction of oxidant in the gas, <J> is an enhancement factor that accounts for the non spherical shape of the biomass. It is |