Modelo de duas escalas para estudo numérico da acidificação em meios porosos considerando ácidos com comportamento reológico complexo

Abstract

This work aims to develop a two-scale model to study the ow of a reactive non-Newtonian uid in a porous medium. The model is able to provide qualitative predictions on a Darcy scale, dissolution patterns and variables of interest, such as pore volume to breakthrough. The model closure uses information from the smallest scale, the pore scale. The proposed system of equations is based on the Continuum Mixture Theory and other continuous models present in the literature. The interaction term is modeled in the classic analytical way but also numerically, allowing di erent idealized pore geometries to have an impact on the result of the Darcy scale, in addition to allowing the relaxation of other restrictive hypotheses necessary for the methodology to obtain the analytical term of interaction. A model is also proposed to account for the e ect of local variation in viscosity due to the change in pH, which is a phenomenon present in viscoelastic acids applied in the matrix acidi cation technique and that allow the uid to treat less prone regions, with less permeability. The proposed model was implemented using a solver in the open source software OpenFOAM. Simulations were performed considering the analytical interaction term for a power-law uid and preliminary results were generated to analyze the in uence of the power-law index and the pH model, for di erent Damköhler numbers. From these results, it was possible to observe the expressive impact of the rheological model on the results. Also, pore scale results were generated and indicate a strong impact of pore geometry in the analysis of the problem and these results are applied in Darcy scale simulations and their e ects are analyzed