Método dos volumes finitos Central-Upwind em malhas não estruturadas: aplicação à simulação numérica do transporte de polímeros em meios porosos

Abstract

Polymer flooding in oil reservoirs has been one of the enhanced oil recovery (EOR) methods most applied in the last decades. The main objective of the technique is to increase the viscosity of the water, adjusting the unfavorable mobility ratio and increasing sweep and displacement efficiency. On the other hand, the polymer is subject to the effects of adsorption and mechanical retention, which may cause formation damage, and, in consequence, the injectivity loss. In this context, it is imperative to develop robust and accurate computation models in order to analyze the technical feasibility and to propose optimal scenarios for oil recovery. Therefore, in this work, a new mathematical and computational model applied to polymer flooding in porous media is proposed. The mathematical model proposes the Darcy’s Law for the water and oil phases, where the water viscosity is a function of the polymer concentration. Furthermore, conservation laws for the phases govern the two-phase flow and the flow of polymer. The polymer transport in the water phase is modeled by a transient differential equation in a convectiondiffusion-reaction regime, where the reactive effects are associated with adsorption and mechanical retention. From a computational perspective, Darcy’s velocity of the water phase is obtained analytically and the discreet solution for the motion of the water and the polymer transport is obtained making use of the finite volume Central-Upwind method, considering 2D and 3D domains with unstructured meshes. Finally, we propose several numerical simulations aiming to analyze the stability and accuracy of the semi-discrete formulation proposed to numerically the transport of polymer in porous media.