Formulation for Gas-Solid Reactions in Multiparticle Systems

Let US consider an infinitesimally thin section of a fixed bed reactor through which a reactant gas is flowing, as sketched in Fig. 7.15. In an isothermal regime and for equimolar counterdiffusion, the system may be de- 

Schematic diagram of the mass balance over an infinitesimal reactor element. 

In general the rate at which the solid reacts, i.e., the time derivative appearing on the r.h.s. of Eq. (7.4.2), will depend on a number of factors, such as the solid structure, the order of the surface reaction, and pore diffusion. Thus we may write 

The initial and boundary conditions for these equations would typically specify the reactant gas concentration at the inlet, the initial gaseous reactant profile within the bed, and the initial conversion of the solid reactant. Thus we have 

It is noted that not even this relatively simple system of equations has a general analytical solution, principally because of the possible nonlinearities that may be contained in the reaction term, viz. Eq. (7.4.3). 

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