Free convection in fractured porous media: A numerical study

The objective of this study is to better understand the influence of fractures on the possibility of free convection in porous media. Fractures are ubiquitous in porous media and criteria based on upscaled permeability are known to fail for fractured porous media. To this aim, we introduce a novel method for the assessment of convective stability through the eigenvalue analysis of the linearized numerical problem instead of solving the problem in time until a steady state is reached. 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. The results of this work allow us to determine the dominant convective modes in 2D and 3D and to shed light on the role of the porous matrix in convective circuits.