Modelagem matemática e computacional da injeção de polímero em reservatórios de petróleo

Abstract

Polymer injection in petroleum reservoirs represents a significant technique to optimize oil recovery in mature fields. However, this methodology can be compromised by reactive phenomena such as adsorption and mechanical retention, which lead to formation damage in the porous medium and consequent loss of injectivity. In light of this challenge, it is imperative to develop realistic mathematical and computational models that accurately describe the governing processes of polymer injection in porous media. The mathematical modeling developed in this research involves the derivation of equations governing hydrodynamics and polymer transport in porous media. Hydrodynamics is governed by the total mass balance of the fluid phases, along with Darcy’s law, while polymer transport is governed by the advection-dispersion-reaction transport equation. The reactive nature of polymer transport is modeled by kinetic laws expressed by ordinary differential equations. Regarding computational modeling, due to the heterogeneity of the hydraulic conductivity term, hydrodynamics is discretized using the dual mixed finite element method. On the other hand, due to its hyperbolic nature, the polymer transport equations are discretized using the Central-Upwind finite volume method. Finally, the developed numerical methods are subjected to accuracy and precision tests, demonstrating robust performance in describing the polymer injection process in porous media.