The modeling of thermal convection in porous media is a challenging task due to the inherent structural and thermophysical heterogeneities that permeate over several scales. In the present thesis, we address several issues relevant to buoyancy driven thermal convection in porous media. Our approach is based on establishing a multi-scale framework build on knowledge accrued by theoretical, numerical and experimental methods.

In Chapter 2, we develop a pore-scale computational tool based on a lattice Boltz mann (LB) model. This computational tool enables us to tackle thermal convection from a pore-scale perspective and to provide benchmarks for the development of an appropriate continuum-scale models. In Chapter 3, we use our LB model and conduct high-resolution direct numerical simulation at the pore scale. The objective is to evaluate the underlying assumptions of upscaled thermal models and to assess the role of thermophysical heterogeneties on heat transfer. We benefit from the insights gained from our pore-scale results and propose a new upscaled energy model for thermal convection in Chapter 4. The proposed model is based on a fractional-order advective term, which models the influence of thermal heterogeneities in a flexible and consistent way. In Chapter 5, we used a combination of theoretical and experimental approaches to calculate a new metric, basin stability, for quantifying the respective relative stability of coexisting convection modes in porous media. We show that transition between convective modes predicted by the basin stability analysis agrees well with the experiments from our IR thermography visualization setup.