Modelagem computacional multiescala do transporte de solutos iônicos em meios porosos carregados eletricamente

• Ano de defesa: 2019
• Autor(a) principal: Santos Júnior, Ronaldo Dias dos
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Rio Grande do Norte; Brasil; UFRN; PROGRAMA DE PÓS-GRADUAÇÃO EM MATEMÁTICA APLICADA E ESTATÍSTICA
• Palavras-chave em Português: Modelagem multiescala; Teoria da camada dupla; Técnica de homogenização; Método de elementos finitos; Parâmetros efetivos; Permeabilidade; Tortuosidade
• Link de acesso: https://repositorio.ufrn.br/jspui/handle/123456789/29985

In this work we present a multiscale computational modeling of the electrochemical coupling in electrically charged porous media. For this, considering the rigid and incompressible solid matrix, the hydrodynamics and the reactive transport of monovalent and bivalent ionic solutes on the nano/micro/macroscopic scales were modeled considering a multiscale formulation based on the homogenization of periodic structures. At the nanoscopic scale, mathematical modeling was obtained considering double-layer theory to obtain the Poisson-Boltzmann equation together with the protonation/deprotonation and cation exchange reactions. The proposed computational model allowed to quantify the electric potential, electric charge density and electrochemical adsorption in the electric double layer.The modeling at the microscale was given considering the Stokes equation for hydrodynamics and Nernst-Planck equations for the transport of the ionic solutes supplemented by conditions at the fluid/solid interface from nanoscopic modeling. Macroscopic equations are derived by applying the homogenization theory on the nano/micro scale equations. In possession of the macroscopic model with the respective microscopic equations, numerical simulations are obtained using the finite element method allowing to quantify the effective parameters of the model given by the permeability tensor and tortuosity vector field for four microgeometries. With the nano and microscopic parameters, we simulated the macroscopic model applied to clayey porous media in different salinity, pH and bivalent ion concentrations considering circular and hexagonal microgeometry.