The mass transfer coefficient for oxygen reacting with a carbon particle in a fluidized or packed bed

Simple models for the burning of either a single carbon or a porous coal char particle are reconsidered, because combustion in, for example, a fluidized bed is analyzed using such models. First, equimolar counterdiffusion of Oz towards the particle and also of the sole product, CO2 away from it is considered. Next, CO is considered to be the only product of combustion las in a fluidized bed), so the chemistry requires a nonzero net Bw: of gases near such a burning particle. This leads to the general conclusion that the Sherwood number (dk(g)/D), giving k(g), the effective mass transfer coefficient, depends on the stoichiometry of the reactions occurring at a carbon sphere of diameter d. The important parameter is in fact Sh(EMCD) the Sherwood number for there being equimolar counterdiffusion (of reactants and products) near the reacting particle. Thus Sh(EMCD) is given by the well-known statement Sh(ECMD) = 2.0 + 0.69 Re-1/2 Sc-1/3 for air flowing over a single isolated spherical particle, with which it reacts. In general, the actual Sherwood number (which gives k(g)) does not equal Sh(EMCD); the ratio (Sh/Sh(EMCD)) is shown to depend on (i) the change in the number of moles (in the fluid) caused by the chemical reaction and (ii) the concentration of reactant in the fluid. Consequently, if carbon oxidizes in C-s + 1/2 O-2 --> CO, the effect is to diminish k(g) as derived from Sh(EMCD) by a factor (1 + y)(logm) the logarithmic mean of (1 + y,) and (1 + y,), where y, and y, are the mole fractions of O-2 in the bulk fluid and at the solid's surface, respectively. In this particular case (Sh/Sh(EMCD)) = 1/(1 + y)(logm). If the CO oxidizes around the burning carbon particle, it is important to know the thickness of the mass transfer film. For a fluidized or packed bed, the general empirical correlation for equimolar mass transfer Sh(EMCD) = Sh(o) + alpha Re-1/2 (Sh(o) and alpha are constants) can always be rewritten as Sh(EMCD) = Sh(o) {1 + (d/2)/delta}, where delta is the mean thickness of the mass transfer him. This means that Sh(EMCD) = 2 + d/delta = Nu for one single isolated sphere reacting with a species in a flowing fluid. Thus the effect of forced convection is to increase Sh(EMCD) by reducing delta from infinity at Re = O to a finite value with Re > O. Finally, the magnitude of delta is calculated and compared with the thickness of a two-film model for the combustion of a carbon sphere and also of a liquid droplet. (C) 2000 by The Combustion Institute.