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Convection, Reaction & Diffusion in Porous Catalysts

Catalyst slab showing the asymmetric profiles of concentration of reactant (blue) and of temperature (red) for an exothermic reaction.
Catalyst slab showing the asymmetric profiles of concentration of reactant (blue) and of temperature (red) for an exothermic reaction.
Many chemical and biochemical reactions take place within porous catalyst particles. Most of these processes have an appreciable heat of reaction. As a result, the interaction between heat conduction, diffusion of reactants and products, and chemical reaction has an important role in the performance of the catalyst. In large-pore catalysts (with pore diameters above 50 nm), the transport of heat and chemicals by convection, in addition to diffusion, inside the catalyst needs to be considered. Such large-pore solids are used, for example, in oxidation reactions, in membrane reactors and in some biological applications.

In this project, we considered the problem of simultaneous convection, diffusion and reaction inside a porous catalyst slab. A combination of perturbation and integral mathematical techniques are used to derive approximate analytical solutions for the concentration and temperature profiles, as well as the maximum temperature and the effectiveness factor, for a first order, non-isothermal reaction.

(click images to enlarge)

Reactant concentration profile inside a catalyst slab for a first-order chemical reaction.  Shown are the numerical results of Quinta Ferreira (1988, grey lines), the regular perturbation predictions for low Thiele modulus (solid black lines), the singular perturbation predictions for high Thiele modulus (dashed black lines) and the singular perturbation predictions for intermediate values of the Thiele modulus (dotted black line).
Reactant concentration profile inside a catalyst slab for a first-order chemical reaction. Shown are the numerical results of Quinta Ferreira (1988, grey lines), the regular perturbation predictions for low Thiele modulus (solid black lines), the singular perturbation predictions for high Thiele modulus (dashed black lines) and the singular perturbation predictions for intermediate values of the Thiele modulus (dotted black line).