Modelling Flow and Dispersion in Heterogeneous Porous Rocks

Porous rocks are typically complex, heterogeneous media, with fluctuations in permeability over a range of scales. From a geophysical perspective, it is of interest to understand how such heterogeneities influence flow within such rocks over a range of scales, varying from (a) the reservoir scale, over which the flow may be exposed to many layers associated with different geological flow units; to (b) intermediate scales, over which there are often lenses of different permeability, within individual geological flow units; to (c) much more localised fluctuations associated with grain size variations within individual layers. In this presentation, we combine new laboratory experiments and numerical calculations to explore the influence of heterogeneities on the dispersal of fluid-fluid fronts within a porous rock, illustrating the relationship between (i) the distribution of heterogeneities of a given scale; (ii) the permeability contrast associated with these heterogeneities, and (iii) the rate of dispersal of fluid-fluid fronts, both on short and long times. Using this model, we then assess some idealised bounds on the fraction of the pore space which may be accessible to an injected fluid as relevant, for example, for models of the storage capacity of CO₂ in subsurface aquifers.