Simulação computacional do escoamento de fluidos miscíveis e compressíveis em meios porosos através de técnicas livres de Jacobiana

Abstract

This work deals with numerical modeling and simulation of single-phase flow in heterogeneous porous media of a fractal nature, where fluid is considered miscible and compressible. Porous media are modeled by the Generalized Kozeny Carmam Equation with three parameters (KCG), which relates porosity to permeability. This equation is able to generalize different models existing in the literature and, therefore, is of very general use. The free Jacobian software developed here for solving problems formulated by nonlinear partial differential equations is of growing interest for similar practical engineering processes. The so-called “Free derivative spectral algorithm” was used for nonlinear equations in the transfer simulation in porous media. The model considered herein is that employed to describe the displacement of miscible compressible fluid in porous media with sources and sinks, where a density of the fluid mixture varies exponentially with pressure. The spectral algorithm used is a modern method for the solution of large nonlinear systems, it does not use any explicit information associated with the Jacobian matrix. The two-dimensional flow models are presented, together with the numerical results comparing the spectral algorithm with the Jacobian free inexact Newton method. The results of this work show that this modern spectral algorithm is a reliable and efficient method for the simulation of compressible porous media flow. The results shown in the KCG model are able to generate heterogeneous means, including features that can be captured from physical phenomena that are generally generally challenges for to access for classical finite difference simulators, as example the viscous fingering phenomena that occurs when there is an adverse mobility relation.