Transport in Porous Media

Most natural soils and rocks are porous and convey water and solutes. Groundwater is an important source of fresh water all over the world and its quality is deteriorating due to pollution. The present brief article is focused on quantitative models of transport of contaminants (solutes). At the pore-scale, mechanical dispersion is the result of a complex interaction between a few mechanisms: shear flow within pores, branching of streamlines at junctions between pores, and mixing by diffusion. The spread of a solute pulse in a small laboratory sample is quantified by the total longitudinal dispersion coefficient, and the concentration field can be described by the Gauss distribution. Natural porous formations (upper soil layer, aquifers, petroleum reservoirs) are characterized by much larger scales. Furthermore, in most applications, the interest is in average values of flow and transport variables over much larger scales than the laboratory one. As a rule, natural formations are heterogeneous, that is, their properties vary in space, at scales that are larger than the laboratory scale. Field-scale heterogeneity (primarily of hydraulic conductivity) has a large impact on the flow pattern and on contaminant spreading. In particular, solute transport is nonlocal, as the dispersion coefficient depends on the travel time from the source. Furthermore, the dispersion coefficient depends on the degree of heterogeneity of the porous formation.