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

Abstract

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 O 2 towards the particle and also of the sole product, CO 2, away from it is considered. Next, CO is considered to be the only product of combustion (as in a fluidized bed), so the chemistry requires a nonzero net flux 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 EMCD = 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 b ) and (1 + y s ), where y b and y s 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 + α Re 1/2 ( Sh o and α are constants) can always be rewritten as Sh EMCD = Sh o {1 + ( d/2)/δ}, where δ is the mean thickness of the mass transfer film. This means that Sh EMCD = 2 + d/δ = 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 δ from infinity at Re = O to a finite value with Re > O. Finally, the magnitude of δ 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.