Free convection in fractured porous media: a numerical study

TL;DR

This study introduces a numerical model and a novel eigenvalue-based method to analyze free convection in fractured porous media, revealing the critical role of the porous matrix and offering efficient stability assessment tools.

Contribution

The paper presents a new eigenvalue analysis method for stability assessment and demonstrates its effectiveness in complex fracture configurations, advancing understanding of convection in fractured porous media.

Findings

Eigenvalue method agrees with existing literature.

Porous matrix is crucial for enabling convection.

Eigenvalue method provides detailed stability insights.

Abstract

The objective of this study is to better understand the influence of fractures on the possibility of free convection in porous media. To this aim, we introduce a mathematical model for density driven flow in the presence of fractures, and the corresponding numerical approximation. In addition to the direct numerical solution of the problem we propose and implement a novel method for the assessment of convective stability through the eigenvalue analysis of the linearized numerical problem. The new method is shown to be in agreement with existing literature cases both in simple and complex fracture configurations. With respect to direct simulation in time, the results of the eigenvalue method lack information about the strength of convection and the steady state solution, they however provide detailed (quantitative) information about the behavior of the solution near the initial equilibrium condition. Furthermore, not having to solve a time-dependent problem makes the method computationally very efficient. Finally, the question of how the porous matrix interacts with the fracture network to enable free convection is examined: the porous matrix is shown to be of key importance in enabling convection for complex fracture networks, making stability criteria based on the fracture network alone somewhat limited in applicability.