Unstable Density-Driven Flow in Fractured Porous Media: The Fractured Elder Problem

Paiman Shafabakhsh,Behzad Ataie-Ashtiani,Craig T Simmons,Marwan Fahs

doi:10.3390/fluids4030168

Abstract

The Elder problem is one of the well-known examples of an unstable density-driven flow (DDF) and solute transport in porous media. The goal of this research is to investigate the influence of fracture networks on this benchmark problem due to the great importance of the fractured heterogeneity effect on unstable DDF. For this aim, the fractured Elder problem is solved using COMSOL Multiphysics, which is a finite element method simulator. Uniform and orthogonal fracture networks are embedded to analyze free convective flow and development of unstable salt plumes. The results indicate that the mesh sensitivity of the fractured Elder problem is greater than the homogeneous case. Furthermore, it has been shown that in the fractured cases, the onset of instability and free convection occur with lower critical Rayleigh number, which means that fracture networks have a destabilizing effect. Also, we examined the structural properties of fracture networks that control convective flow patterns, and the simulation results show that the strength of convection and instability at the beginning of the intrusion is proportional to the aperture size of the fractures. Moreover, the increase of the fracture’s density leads different modes of transient convective modes, until a specific fracture density after which the transient convective modes become similar to the homogenous case.

Highlights

Density-driven flow (DDF) in porous media has been studied extensively over the last few decades because of its practical applications in petroleum engineering, geologic carbon sequestration, geothermal energy systems, groundwater management, oxide fuel cells, solar collectors, thermal insulation systems, nuclear reactors, amongst many others [1,2,3]
The term convection is often used in connection with DDF processes, where groundwater flow is driven by density differences in the fluid, created by differences in temperature and/or concentration, as the primary driving factor that causes a density gradient to occur, and as a result flow and transport in the porous domain can occur due to the buoyancy effect
We considered a new configuration of the Elder problem by structural properties of fracture networks control convective embedding fracture networks aand performedofnumerical simulations using COMSOL

Summary

Introduction

Density-driven flow (DDF) in porous media has been studied extensively over the last few decades because of its practical applications in petroleum engineering, geologic carbon sequestration, geothermal energy systems, groundwater management, oxide fuel cells, solar collectors, thermal insulation systems, nuclear reactors, amongst many others [1,2,3]. The term convection is often used in connection with DDF processes, where groundwater flow is driven by density differences in the fluid, created by differences in temperature and/or concentration, as the primary driving factor that causes a density gradient to occur, and as a result flow and transport in the porous domain can occur due to the buoyancy effect. The term convection has been used in different ways in the literature.

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