Upscaling transport of adsorbing solutes in porous media: pore-network modeling

The main objective of this research was to enhance our understanding of and obtain quantitative relation between Darcy-scale adsorption parameters and pore-scale flow and adsorption parameters, using a three-dimensional multidirectional pore-network model. This helps to scale up from a simplified but reasonable representation of microscopic physics to the scale of interest in practical applications. This upscaling is performed in two stages: (i) from local scale to the effective pore scale and (ii) from effective pore scale to the scale of a core. The first stage of this upscaling from local scale to effective pore scale has been reported in an earlier manuscript. There, we found relationships between local-scale parameters (such as equilibrium adsorption coefficient, k d, and Peclet number, Pe) and effective parameters (such as attachment coefficient, k att, and detachment coefficient, k det). Here, we perform upscaling by means of a three-dimensional multidirectional network model, which is composed of a large number of interconnected pore bodies (represented by spheres) and pore throats (represented by tubes). Upscaled transport parameters are obtained by fitting the solution of classical advectiondispersion equation with adsorption to the average concentration breakthrough curves at the outlet of the pore network. This procedure has resulted in relationships for upscaled adsorption parameters in terms of the microscale adsorption coefficient and flow velocity.