The application of continuum equations to diffusion and reaction in pore networks

Abstract

Two problems that arise in the use the continuum diffusion—reaction model to describe diffusion and reaction in pore networks are investigated: (i) the question of whether the appropriate value of the effective diffusivity is different from the one measured or calculated in the absence of reaction, and (ii) the magnitude of the error involved in applying the continuum model to a network close to its percolation threshold (i.e. one in which the blocking of a few pores would cause the network to become disconnected), where it is expected on theoretical grounds to break down. We have carried out numerical simulations of diffusion and reaction in model pore networks and compared the results with solutions to the continuum model. We find that the continuum model with an effective diffusivity calculated in the absence of reaction is in good agreement with the pore network simulations, except where the reaction occurs mostly within a few pore lengths of the particle surface (or the surface of the microparticles for a catalyst with a bidisperse structure) or where the network is very close to the percolation threshold. In these circumstances, diffusion and reaction should be simulated directly using a pore network model.