Colloid Adhesive Parameters for Chemically Heterogeneous Porous Media

Abstract

A simple modeling approach was developed to calculate colloid adhesive parameters for chemically heterogeneous porous media. The area of the zone of electrostatic influence between a colloid and solid-water interface (A(z)) was discretized into a number of equally sized grid cells to capture chemical heterogeneity within this region. These cells were divided into fractions having specific zeta potentials (e.g., negative or positive values). Mean colloid adhesive parameters such as the zeta potential, the minimum and maximum in the interaction energy, the colloid sticking efficiency (α), and the fraction of the solid surface area that contributes to colloid immobilization (S(f)) were calculated for possible charge realizations within A(z). The probability of a given charge realization in A(z) was calculated using a binomial mass distribution. Probability density functions (PDFs) for the colloid adhesive parameters on the heterogeneous surface were subsequently calculated at the representative elementary area (REA) scale for a porous medium. This approach was applied separately to the solid-water interface (SWI) and the colloid, or jointly to both the SWI and colloid. To validate the developed model, the mean and standard deviation of the interaction energy distribution on a chemically heterogeneous SWI were calculated and demonstrated to be consistent with published Monte Carlo simulation output using the computationally intensive grid surface integration technique. Our model results show that the PDFs of colloid adhesive parameters at the REA scale were sensitive to the size of the colloid and the heterogeneity, the charge and number of grid cells, and the ionic strength.