Numerical Modelling of Reactive Flows through Porous Media

Abstract

We consider a lattice Boltzmann (LB) model to solve the coupled Navier–Stokes and advection–diffusion equation with reactive boundary conditions at the interface between fluid and solid domains. The reactive boundary condition results in the position of the boundary changing continuously, and so boundary nodes may be partially filled with fluid at any instant. We develop the LB boundary conditions for both the velocity and concentration fields in the presence of partially filled boundary nodes and then validate this algorithm on some test cases—the Stefan problem for diffusion-dominated dissolution and kinetic-dominated dissolution. It is shown that the developed model agrees well with analytic results, so that they can be used for more general boundaries of arbitrary shape. Numerical simulations in three dimensions are then carried out on demonstration problems at various Peclet numbers to elucidate the transport mechanisms and their influence on solid grain dissolution.