Geometric characterization, hydraulic behavior and upscaling of 3D fissured geologic media

In this article, we present numerical modeling and upscaling procedures for highly fissured and discontinuous geologic media, such as ‘karsts’. In particular, we propose a geomorphological generation model, and we address the ‘upscaling’ problem for flow in a highly fissured porous medium (‘what is the macroscale hydraulic behavior of the fissured porous medium?’). The morphological model is partly Boolean, based on statistical distributions of discrete objects (voids), combined with a (random) continuum representation for the underlying porous matrix. Various methods for constraining these two types of media are discussed (self-consistent thresholding; genetic dissolution). Hydraulic simulations are then conducted with the 3D finite volume code BIGFLOW, for the case of 3D composite media with constant matrix and high ‘fissure/matrix’ permeability contrast. The hydrodynamic equations are based on either Darcy’s linear head loss law, or on a linear/quadratic combination of Darcy and Ward–Forchheimer quadratic law (inertial effects). The numerical experiments are conducted for saturated steady flow under permeametric boundary conditions. They are used to analyze the equivalent macroscale behavior of fissured media, as well as quasi-percolation effects, in comparison with analytical results and bounds (Darcian case, low Reynolds). In addition, at moderate to large Reynolds numbers, the macroscale effects of non-Darcian (inertial) head losses are also analyzed.