Effective properties of pore network elements derived from reactive transport in individual pores

Adsorption of solutes in porous media is typically represented as an equilibrium process. The adsorption process is determined by the concentration of the solute in the fluid next to the solid grain in individual pores. The concentration near the solid surface is different from the average concentration within the pore due to the development of concentration gradients within the pore space. Simulations with pore network models are usually based on the average concentration in individual pore throats. To advance the realism of such models, we develop a relationship between pore-scale adsorption coefficients and corresponding coarse-grained adsorption parameters. A numerical scheme is proposed: firstly the solute transport within a single pore is simulated undergoing equilibrium adsorption at the pore wall, and secondly flux-averaged concentration breakthrough curves are obtained. By fitting the breakthrough curves, the coarse-grained adsorption parameters are determined from the pore-scale hydraulic and adsorption parameters.