Relationship between the Averaged Deposition Rate Coefficients for Colloids in a Single Pore and Various Pore-scale Parameters

Abstract:

The colloid deposition behavior observed at the Darcy scale represents an average of the processes occurring at the pore scale. Hence, a better understanding of the processes occurring at the Darcy scale can be obtained by studying colloid transport at the pore-scale and then upscaling the results. In this study, we have developed a mathematical model to simulate the transport of colloids in a cylindrical pore by considering various processes such as advection, diffusion, colloid-soil surface interactions and hydrodynamic wall effects. The pore space is divided into three different regions, namely, the bulk, diffusion and potential regions, based on the dominant processes acting in each of these regions. In the bulk region, colloid transport is governed by advection and diffusion; whereas in the diffusion region, colloid mobility due to diffusion is retarded by hydrodynamic wall effects. Colloid-solid interaction forces dominate the transport in the potential region where colloid deposition occurs and are calculated using DLVO theory. The expressions for mass transfer rate coefficients between the diffusion and potential regions have been derived for different DLVO energy profiles. These are incorporated in the pore-scale equations in the form of a boundary condition at the diffusion-potential region interface. The model results are used to obtain the colloid breakthrough curve at the end of a long pore, and then it is fitted with 1D advection-dispersion-adsorption model so as to determine the averaged attachment and detachment rate coefficients at the scale of a single pore. A sensitivity analysis of the model to six pore-scale parameters (colloid and wall surface potentials, solution ionic strength, average pore-water velocity, colloid radius, and pore radius) is carried out so as to find the relation between the averaged deposition rate coefficients at pore scale vs the pore-scale parameters. We found an hyper exponential relation between the colloid attachment rate coefficient vs the parameters describing DLVO energy profile, and a power law relationship between colloid attachment rate coefficient vs the average pore-water velocity. The current model forms the building block for upscaling colloid transport from pore scale to Darcy scale using Pore Network Modeling.