Soret Diffusion and Non‐Ideal Dufour Conduction in Macroporous Catalysts with Exothermic Chemical Reaction at Large Intrapellet Damköhler Numbers

Abstract

AbstractThe adiabatic temperature rise in catalytic pellets is predicted from a modified version of the Prater equation. Onsager reciprocal relations for coupled heat and mass transfer are violated in an analysis of thermal diffusion in macroporous catalysts with exothermic chemical reaction when Dufour conduction (i.e., the diffusion‐thermo effect) is neglected. In this contribution, Dufour conduction is analyzed for both ideal and non‐ideal pseudo‐binary gas mixtures that simulate the production of methanol from carbon monoxide and hydrogen. In the diffusion‐controlled regime at large intrapellet Damköhler numbers where intermolecular collisions provide the dominant resistance to mass transfer within the catalytic pores, temperatures in the catalytic core could be much greater than predictions based on the original Prater equation when the Prater number exceeds 0.30. The molecular flux of thermal energy includes Fourier's law, the interdiffusional flux, and Dufour conduction. Diffusional mass flux includes Fick's law and the Soret effect. All physicochemical properties of the reactive gas mixture exhibit temperature dependence. There is essentially no difference between maximum intrapellet temperature predictions that include or neglect ideal Dufour conduction when external catalytic surface temperatures range from 300‐400 K and thermal diffusion enhances the flux of “smaller” reactants toward the centre of the catalyst. For “large‐molecule reactants” that participate in exothermic reactions, thermal diffusion opposes Fick's law and Dufour conduction opposes Fourier's law. Under these conditions, it is demonstrated that core temperatures are overestimated by neglecting both off‐diagonal coupling mechanisms (i.e., Soret diffusion and Dufour conduction). Prater numbers greater than unity and unrealistically high gas pressures are required to distinguish between maximum intrapellet temperatures for ideal and real gas simulations, where the latter consider two‐body interactions for Lennard‐Jones molecules in the virial equation of state.