Onset of convection in a layered porous medium heated from below

Abstract

The formalism required to determine the criterion for the onset of convection in a multi-layered porous medium heated from below is developed using a straightforward linear stability analysis. Detailed results for two- and three-layer configurations are presented. These results show that large permeability differences between the layers are required to force the system into an onset mode different from a homogeneous system.

Numerical techniques for simulating groundwater flow in the presence of temperature gradients

“…For a three-layer system the values of the critical Rayleigh number are increasing with decreasing permeability of the middle layer [10]. In [10] the middle layer occupied 20% of the total aquifer thickness and had a permeability k 1 different to that of the top and bottom layers. (The top and bottom layers had equal permeability k 2 .)…”

“…Nondimensional criteria for the onset of thermal convection in layered systems have been developed in [10,11,13]. In these works the Rayleigh number is calculated using permeability and thermal properties of the bottom layer and the temperature difference and thickness of the whole system.…”

“…The critical Rayleigh number was first calculated in [7] for a homogeneous porous medium saturated by a single-phase fluid. This work was further advanced in [10,11,12,13] through incorporating more realistic features such as inhomogeneity and anisotropy of a porous medium. Linear stability problems of two-phase liquid-vapour thermal convection in porous media were consid-C1117 ered by numerous authors, mainly in works related to geothermal reservoir modelling, cf.…”

Numerical Simulation of Conjugate Free Convection in a Vertical Cylinder Having Porous Layer

“…Lai and Kulacki [12] have studied steady-state free convection in a differentially heated square cavity filled with a two-layer porous system using the Darcy-Boussinesq approximation. It should be noted that the authors have used special boundary conditions at porous-porous interface [13], [14]. The authors have found that the heat transfer begins as a conduction heat transfer in the less permeable sublayer and as a thermal convection in the layer with higher permeability.…”

Numerical Simulation of Natural Convection in Heterogeneous Porous media for CO2 Geological Storage

“…Nield and Bejan (1999), McKibbin and O'Sullivan (1980), and Malkovsky and Pek (1999) developed analytical solutions for the onset conditions of density-driven natural convection in heterogeneous media for simple geometry and boundary conditions using linear stability analysis. However, this theory does not describe the convective mixing after onset of natural convection.…”