(427b) Convection, Diffusion And Reaction In A Non-Isothermal, Porous Catalyst Slab

The coupling of chemical reaction and diffusive transport in porous catalytic particles has been the subject of intense investigation in chemical engineering for many years. In his treatise, The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts, Rutherford Aris (1) presented a comprehensive review of the literature up to 1975. Since then, a number of scientific publications have considered the effect of transport by convection, in addition to diffusion, inside porous catalyst particles undergoing chemical reaction. The contribution of intraparticle convection to the total mass transfer increases with the magnitude of the intraparticle mass Peclet number. In practice, significant mass Peclet numbers are achieved more easily in liquid systems than in gas phase reactions, due to the much higher chemical diffusivities in the latter. However, gaseous systems operating at high pressure (2) or involving diffusion in very large pore solids can exhibit significant intraparticle convection. Indeed, several studies have shown that intraparticle convection in large-pore catalysts (with pore diameters above 500 Å) can contribute significantly to the total transport rate inside the particle and thereby increase its effectiveness factor (2-8). More recently, numerous publications have arisen considering the effects of intraparticle convection in chromatographic separations (9-12), biological applications13 and in the design of membrane reactors (14,15). Despite the large number of publications in the field (2-17), until now there has been no generalized theoretical analysis of the non-isothermal catalyst particle with simultaneous convection, diffusion and reaction. The contribution of the analytical approach presented here is two-fold. First, the analytical solutions validate numerical results for extreme singular cases, such as those encountered when convective transport is much more important than diffusion in the particle. Secondly, analytical work provides a framework to identify different regimes of operation of a catalyst particle and transitions between such regimes. The latter contribution is particularly important as a gateway to understanding the operation of actual catalytic pellets with non-simple geometry and/or a complex intraparticle velocity field. In this work, we consider the interaction between the transport of heat by conduction and convection, transport of reactants and products by diffusion and convection, and chemical reaction within a porous catalyst particle of slab geometry. A combination of perturbation and integral mathematical techniques is used to derive approximate analytical solutions for the concentration and temperature profiles, as well as for the maximum temperature and the effectiveness factor, for a first order, non-isothermal reaction. Three regimes of operation are characterized: regime I, in which convection and diffusion are dominant (small Thiele modulus); regime II, in which diffusion and reaction are dominant (large Thiele modulus); and regime III, in which convection and reaction dominate (intermediate Thiele modulus). Our analytical solutions are validated by comparison with previous numerical results. It is shown that the maximum temperature inside the catalyst slab, as well as the maximum effectiveness factor, is achieved in regime III. Interestingly, the maximum temperature is equal to the temperature that would occur after complete, adiabatic reaction in a catalyst slab with initially uniform reactant concentration equal to the surface concentration of the slab operating in convective regime. We also show that, to leading order, the maximum effectiveness factor is approximately proportional to the mass Peclet number and is independent of the heat Peclet number.

References

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