Modelling diffusion and reaction accompanied by capillary condensation using three-dimensional pore networks. Part 1. Fickian diffusion and pseudo-first-order reaction kinetics

Abstract

A model has been developed which simulates capillary condensation in porous media. For the first time an algorithm for calculating the critical radius below which capillary condensation occurs has been combined with a pore network model of vapour diffusion and reaction. The critical radius for capillary condensation is calculated using a multicomponent version of the Kelvin equation. Diffusion is simulated using Fick's law whilst reaction is assumed to be first order. The model is applied to the prediction of catalyst effectiveness factors for a first-order reaction occurring over typical hydroprocessing catalysts with mean pore sizes in the medium meso-pore range (128– 184 A ̊ ). It was shown that a mixture of 5 mole % diethyl sulphide in hydrogen is prone to capillary condensation within the pores of the catalyst over the range of pressures 27.5– 27.8 bar at 375 K . At low Thiele moduli, in the strong reaction-controlled limit, the presence of liquid-filled pores leads to a reduction in catalyst effectiveness of 4–7% over the range of pressures simulated. However, at high Thiele moduli, in the strong diffusion-controlled limit, effectiveness factor was not significantly influenced by the presence of capillary condensate. The model is used to demonstrate the influence of network topology (regular vs. random) and pore structure parameters (mean pore size, standard deviation pore size and network connectivity) upon the catalyst effectiveness factor in the presence of a fraction of catalyst pores that are filled with capillary condensate. Attention is here limited to pseudo-first-order reactions and Fickian diffusion; extension to general kinetic expressions and the dusty gas model of multicomponent diffusion is considered in Part 2.