Método de decomposição de domínios de múltiplos passos de tempo de Dirichlet-Neumann aplicado à injeção de polímeros em meios porosos

Abstract

This thesis proposes an innovative mathematical and computational model for injecting polymer solutions into porous media, efficiently coupling the process in the near-well region and the reservoir. For the mathematical model, in addition to the single-phase flow and transport equations, we postulate closure relationships for the adsorption isotherms, mechanical retention kinetics, and non-Newtonian pseudoplastic behavior. For the computational model, we propose a space-time domain decomposition method based on a predictor-corrector strategy. The resulting system of equations is discretized by the finite element method and linearized by the Newton-Raphson method. Additionally, we apply a consistent flux method to obtain the flow at the boundaries and quantify the injectivity ratio. We then validate the accuracy of the proposed method by comparing the discrete solutions with analytical and high-fidelity solutions. We also discuss the loss of injectivity due to non-Newtonian behavior, mechanical retention, and formation damage in twodimensional and three-dimensional domains that replicate a five-spot injection pattern. Numerical simulations show that the proposed computational model accurately captures the solutions with low computational costs in various scenarios of polymer injection in porous media.