A hybrid pore-scale and continuum-scale model for solute diffusion, reaction, and biofilm development in porous media

It is a challenge to upscale solute transport in porous media for multispecies bio-kinetic reactions because of incomplete mixing within the elementary volume and because biofilm growth can change porosity and affect pore-scale flow and diffusion. To address this challenge, we present a hybrid model that couples pore-scale subdomains to continuum-scale subdomains. While the pore-scale subdomains involving significant biofilm growth and reaction are simulated using pore-scale equations, the other subdomains are simulated using continuum-scale equations to save computational time. The pore-scale and continuum-scale subdomains are coupled using a mortar method to ensure continuity of solute concentration and flux at the interfaces. We present results for a simplified two-dimensional system, neglect advection, and use dual Monod kinetics for solute utilization and biofilm growth. The results based on the hybrid model are consistent with the results based on a pore-scale model for three test cases that cover a wide range of Damköhler (Da = reaction rate/diffusion rate) numbers for both homogeneous (spatially periodic) and heterogeneous pore structures. We compare results from the hybrid method with an upscaled continuum model and show that the latter is valid only for cases of small Damköhler numbers, consistent with other results reported in the literature.