Análise de um modelo simplificado para descrever a instabilidade de Saffman-Taylor em meios porosos

Abstract

In this work, an analytical and numerical investigation of the viscous fingering phenomenon was conducted. This phenomenon occurs during the displacement of a more viscous fluid by a less viscous fluid in a porous medium, resulting from the Saffman-Taylor instability. To achieve this, a simplified mathematical model was proposed, considering only the differences in viscosity between the resident and injected fluids. These differences are characterized by two fingers with their respective states on the right and left, representing mass exchange and neglecting capillary effects. Additionally, it was assumed that the fluids are immiscible, meaning that no mixing occurs between them during the process. The analysis yielded an analytical estimate for the speed of the fronts, establishing conditions under which one finger is ahead of the other. The formulation derived from this model was validated through 2D numerical simulation, showing a maximum percentage error of 5% in the velocity estimates, thereby demonstrating the efficacy of the approach in capturing the behavior of the phenomenon.