Example of Applications to Catalytic reactions

An important problem in catalysis is to predict diffusion and reaction rates in porous catalysts when the reaction rate can depend on concentration in a non-linear way. The heterogeneous system is modeled as a solid material with pores through which the reactants and products diffuse. We assume for diffusion that all the microscopic details of the porous medium are lumped together into the effective diffusion coefficient De for reactant. 

In the system considered it is assumed that there is no variation in the rate constant locally in the structure. For electrochemical systems this is equivalent to assuming a constant potential in the stmcture and is an approach used in plane or agglomerate models of electrocatalysts. 

Assuming that diEfusion, in the porous catalyst can be described by Pick s law, we have 

With this approximation a mass balance on a volume of the porous medimn gives 

We consider the reaction A— B, with the rate depending on the nth power of concentration of A, denoted by R(c) = kc , where k is the reaction rate constant. The goal is to predict the overall reaction rate, or the mass transfer in and ont of the catalyst pellet. 

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