Abstract

Many analytical results have been obtained for gravity-driven flow in uniform porous media, which provide checks on numerical methods and furnish insight into the underlying physical processes. However, subsurface porous rocks are typically highly heterogeneous, which strongly influences the flow. In this talk, I examine the effect of some simple heterogeneities on the classical solutions for flow in porous media and relate the results to applications in CO2 sequestration. First, the interaction of free-surface flow with a cylindrical inclusion of different permeability is explored. The flow thickness and streamlines are obtained through simple flux-balance arguments in various regimes for the relative inclusion width and permeability. Second, I will discuss displacement flow in a confined layer with a vertical gradient of permeability and analyse how gravity and permeability variations compete to drive the flow and control the interface evolution.