Comparison between Van Genuchten and Brooks-Corey Parameterizations in the Solution of Multiphase Problems in Rigid One-Dimensional Porous Media

Abstract

Multiphase problems in porous media involve the complex flow of multiple fluid phases within porous structures, covering areas of Engineering, Medicine, Geology, among others. Understanding these phenomena is crucial in natural processes, resource management, and Engineering system design. Due to its great importance, several researchers have contributed by developing different formulations to describe the multiphase problem. Through laboratory experiments, research lines emerged to numerically determine relative permeability and capillary pressure, parameters that were previously obtained only through experiments, giving rise to two distinct models to solve the flow problem: the van Genuchten and Brooks-Corey parameterizations. This work aims to analyze, through numerical simulations, the resolution of multiphase problems in rigid porous media using both parameterization models, in order to compare the efficiency of each method in different settings. Apparently, this study is unique in its focus, uncovering valuable insights into performance and applicability of both parameterization, providing a comprehensive view of their advantages and constraints in several settings. The results of this study have indicated an advantage in employing Brooks-Corey parameterization, particularly in reducing the error between the numerical and analytical solutions. The findings of this study can help, for example, to better understand oil recovery from naturally fractured reservoirs.

Keywords:

• Two-phase flow
• porous media
• multigrid
• modified Picard
• coupled Gauss-Seidel

Acknowledgments

The authors would acknowledge the Fundação da Universidade Federal do Paraná - Brazil (FUNPAR) and the infrastructure provided by the Department of Mechanical Engineering (DEMEC) of Federal University of Paraná (UFPR).

Disclosure statement

The authors hereby confirm that they are the sole liable persons responsible for the authorship of this work, and that all material that has been herein included as part of the present paper is either the property (and authorship) of the authors.

Additional information

Funding

This study was financed by the Fundação da Universidade Federal do Paraná - Brazil (FUNPAR).