Modelagem populacional para o transporte e retenção em meios porosos

Abstract

In this thesis, we developed a population model to analyze the retention process of multiple species in porous media, considering size exclusion and adsorption mechanisms. A significant contribution of this work is the formulation of new adsorption kinetics, which take into account the distributions of transported species and pores. These kinetics are able to predict multiple species adsorption and capture the notable “overshoot”/Vroman effects characteristic of multiple species adsorption. Furthermore, our approach results in the formulation of a generalized multispecies adsorption isotherm. The model consists of the species mass conservation equations, species adsorption, and capture kinetics, in addition to the pore blocking kinetics. 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 solve the kinetics numerically, we use Runge-Kutta finite difference methods. We conducted extensive computer simulations with the aim of validating our numerical results through comparisons with analytical solutions. Furthermore, we explored various configurations of transported species distributions and pores to comprehensively analyze species transport and retention in porous media. To address the resolution of the inverse problem using experimental data on effluent concentrations, we present a methodology that is based on the least squares method, implemented through the Levenberg-Marquardt algorithm. Finally, we apply the methodology to adjust the experimental data available in the literature. The results obtained in this thesis provide a deeper understanding of the retention process of multiple species in porous media.