Modeling colloid transport and retention in saturated porous media under unfavorable attachment conditions

A mathematical model is presented for colloid transport and retention in saturated porous media under unfavorable attachment conditions. The model accounts for colloid transport in the bulk aqueous phase and adjacent to the solid surface, and rates of colloid collision, interaction, release, and immobilization on the solid phase. Model parameters were estimated using (1) filtration theory; (2) calculated interaction energies in conjunction with the Maxwellian kinetic energy model of diffusion; (3) information about the velocity magnitude and distribution adjacent to the solid phase that was obtained from pore scale water flow simulations; (4) colloid and collector sizes; (5) the balance of applied hydrodynamic and resisting adhesive torques; and (6) time dependent filling of retention locations using a Langmuirian approach. The presented theory constrains the model parameters and output to physically realistic values in many instances, and minimizes the need for parameter optimization. Example simulations demonstrate that our modeling formulation is qualitatively consistent with observed trends for retention with colloid size and concentration, grain size, and velocity for many systems. The model provides a clear conceptual explanation for the causes of hyperexponential, exponential, uniform, and nonmonotonic retention profiles without invoking hypotheses with regard to colloid heterogeneity, aggregation, or multiple deposition rates. Furthermore, the model formulation and research presented herein helps to identify areas where additional research and theory development are still needed.