Unresolved Issues in Fractured Rock Hydrology

Many subsurface rock formations are most accurately conceptualized and modelled as being fractured-porous media. The hydrological behavior of fractured-porous rocks has been studied extensively since the 1960s and 1970s, with early major contributions by researchers such as Barenblatt, Snow, and Witherspoon, among others. This field is now sufficiently mature that several monographs have been written on the topic of fluid flow and transport in fractured rocks, including Fractured Porous Media, by Adler, Thovert, and Mourzenko (Oxford University Press, 2013) and Fluid Flow in Fractured Rocks, by Zimmerman and Paluszny (Wiley, 2024). Nevertheless, a few key issues in this field are still not fully resolved, and perhaps deserve further consideration. For example, (1) the Reynolds lubrication approximation for flow through a single fracture reduces the problem to a 2D “effective medium” problem, eventually allowing the transmissivity of a fracture to be expressed as a function of mean aperture, standard deviation of the aperture, and contact area fraction, but it is known that the geometry of many fractures are too irregular for the lubrication approximation to apply. The question then arises as to whether the full Stokes equations will permit the transmissivity to be expressed in terms of simple geometrical parameters. (2) The Darcy-like relationship between pressure gradient and flowrate breaks down as the Reynolds number increases, after which the flow can be modelled with the Forchheimer equation. However, a robust correlation between the Forchheimer coefficient and aperture geometry is not yet available. (3) Dual-porosity models require a “shape factor” parameter that controls flow between the fractures and matrix blocks. Although the relationship between shape factors and matrix block geometry is well understood for discrete, clearly-defined blocks, the appropriate shape factor for a sparsely-fractured rock mass has not received much study. (4) A key ingredient in models for solute transport through fractured rocks is the Taylor-Aris relation between “effective diffusivity” and Peclet number. Yet even for the simplest possible geometry, a rectangular channel, two different “exact” expressions can be found in the literature. Furthermore, the results for narrow elliptical channels and narrow rectangular channels are completely inconsistent with each other. These facts seem to call for a re-investigation of the Taylor-Aris conceptual model.