Population Modeling for Transport and Retention in Porous Media
Population model, Size exclusion, Multispecies adsorption kinetics, Multispecies isotherm, Particle and pore size distribution, Excluded and inaccessible pore volume, Vroman and {\it overshoot} effects, KT high order finite volume method.
In this work, we developed a population model to analyze the retention process of multiple species in porous media. In the context of retention, we consider size exclusion and adsorption mechanisms as the main capture processes. A significant contribution of this work is the formulation of new adsorption kinetics, which takes into account particle and pore distributions. This kinetics can predict the adsorption of multiple species and capture the notable overshoot and Vroman effects, characteristic of the adsorption of multiple species. Furthermore, our approach results in the formulation of a generalized isotherm for the adsorbed species. It is important to highlight that we incorporated into our model the influence of the effects excluded pore volume (EPV) and inaccessible pore volume (IPV), through the introduction of accessibility factors and flow reduction. From a numerical point of view, we propose the application of the high-order method known as the Kurganov and Tadmor (KT) finite volume method to discretize the species transport equation. To numerically solve the adsorption kinetics, we used Runge-Kutta finite difference methods. We conducted extensive computer simulations to validate our numerical results through comparisons with analytical solutions. Furthermore, we explored various configurations of particle and pore size distributions to comprehensively analyze the transport and retention of species in porous media. To address the resolution of the inverse problem from experimental effluent concentration data, we present a methodology that is based on the least squares method, implemented through the Levenberg-Marquardt algorithm. Finally, we apply the proposed methodology to adjust experimental data available in the literature, considering adsorption as the predominant capture mechanism.