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

The main objective of this research is to enhance our understanding of the relation between pore-scale adsorption and Darcy-scale parameters using a 3D 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 will be carried out in two stages: i) from pore scale to the scale of a tube, which is the main element of a pore-network model, and ii) from tube scale to the scale of a core represented by the pore-network model. The first stage of this upscaling from pore to tube scale has been reported in an earlier manuscript. There we found relationships between micro-scale parameters (such as equilibrium adsorption coefficient, kd, and Peclet number, Pe) and tube-scale parameters (such as attachment coefficient, katt, and detachment coefficient, kdet). Here, we perform upscaling by means of a 3D multi-directional network model, which is composed of a large number of interconnected pores bodies and pore throats (represented by tubes). We use the expressions which were developed in our earlier work to estimate tube-scale adsorption parameters for each and every pore in the network. Transport parameters are then upscaled over the whole network by fitting average concentration breakthrough curves at the outlet to the solution of classical advection-dispersion equation with adsorption. This procedure has resulted in relationships for upscaled adsorption parameters in terms of micro-scale coefficients.