Mean field lattice Boltzmann model for reactive mixtures in porous media

Abstract

A new lattice Boltzmann model (LBM) is presented to describe chemically reacting multicomponent fluid flow in homogenised porous media. In this work, towards further generalizing the multicomponent reactive lattice Boltzmann model, we propose a formulation which is capable of performing reactive multicomponent flow computation in porous media at the representative elementary volume (REV) scale. To that end, the submodel responsible for interspecies diffusion has been upgraded to include Knudsen diffusion, whereas the kinetic equations for the species, the momentum and the energy have been rewritten to accommodate the effects of volume fraction of a porous media though careful choice of the equilibrium distribution functions. Verification of the mesoscale kinetic system of equations by a Chapman--Enskog analysis reveals that at the macroscopic scale, the homogenized Navier--Stokes equations for compressible multicomponent reactive flows are recovered. The Dusty Gas Model (DGM) capability hence formulated is validated over a wide pressure range by comparison of experimental flow rates of component species counter diffusing through capillary tubes. Next, for developing a capability to compute heterogeneous reactions, source terms for maintaining energy and mass balance across the fluid phase species and the surface adsorbed phase species are proposed. The complete model is then used to perform detailed chemistry simulations in porous electrodes of a Solid Oxide Fuel Cell (SOFC), thereby predicting polarization curves which are of practical interest.