Modelagem Matemática e Computacional do Processo de Filtração em Meios Porosos

Abstract

This final paper approaches a problem associated with fluid flow, transport and retention of particles in oil reservoirs. Such phenomenon is commonly refereed as deep bed filtration. The filtration phenomenon occurs in porous media during transport of suspended particles where large particles (with a characteristic dimension larger than the porous medium) are captured. A typical case of this phenomenon occurs during the injection process of polymer solutions in advanced oil recovery. The main purpose of this work is to deduce a mathematical and computational model for deep bed filtration in porous media. Initially, the mathematical model governing the particle motion and retention kinetics will be derived. The system of equations consists of a nonhomogeneous hyperbolic differential equation for the transport of the particles along with a first order ODE for retention. From the mathematical model, analytical solutions are obtained considering some particular cases for the filtration coefficient. From the computational modeling perspective, the finite volume method of Kurganov & Tadmor (KT) is considered in order to obtain numerical solutions for the hyperbolic equation for transport and the third order Runge-Kutta method is considered to obtain numerical solutions for the kinetics retention equation. Finally, numerical simulations are proposed for the filtration process enabling us to understand the deep bed filtration and to evaluate the optimal properties of the proposed finite volume method.