Experimental studies have shown that fracture specific stiffness and fluid flow through a fracture are implicitly related through the geometry of the fracture. We investigated numerically the fundamental geometric lengths scales that affect fracture deformation and fluid flow with the goal of developing a scaling relationship between this two fracture properties. We examined the displacement-stress and flow-stress relationships as a function of scale. Though deformation-stress and fluid flowstress relationships differed for each simulated fracture or subset of a fracture, we were able to collapse the statistical fluctuations in these relationships by using zeroth order approach.
Understanding the mechanical and hydraulic properties of single fractures is important in many scientific and engineering fields, i.e, nuclear waste isolation, oil & gas production, and carbon sequestration among others. Single fractures are composed of two rough surfaces in contact that results in a complicated distribution of void spaces, through which fluids flow, and areas of contact that provide mechanical stability. Cook [9] noted that the geometry of a single fracture primarily determines its mechanical deformation and hydraulic properties. This geometry has many length scales associated with it; for example the size and spatial distribution of the apertures (distance between the two rough surfaces or size of the voids) and contact areas. From a computational study, Pyrak-Nolte & Morris [20] surmised that the spatial correlation length of the aperture distribution in a single fracture is the defining length scale that affects the interrelationship between the hydraulic and mechanical response of a fracture. However, they did not fully explore which correlation length associated with the void geometry or contact is the most relevant length scale. For example, there are spatial correlation lengths associated with the percolation cluster (largest cluster of connected void space) and also with the separation between clusters. Both of these correlation lengths will be affected by changes in stress on a fracture because the void geometry and contact area are affected by stress. In this paper, we perform a computational study of the effect of fracture void geometry on both fluid flow and displacement of single fractures to determine the relevant length scales for future work on scaling the fluid flow-fracture specific stiffness relationship.
There are many methods for generating fracture void geometry. Most numerical approaches for simulating synthetic fracture void geometry are based on generating two rough surfaces that are then brought into contact to form the void geometry [3, 4, 15, 25, 32]. For example, Brown [4] developed a method for simulating fracture roughness by specifying the fractal dimension of the roughness, the root mean square roughness and a length describing the mismatch between the two fracture surfaces. In our approach, we use the stratified continuum percolation method to directly generate the void geometry of a fracture (i.e. the contact area and variable apertures voids) without generating two independent rough surfaces.
The stratified continuum percolation method [22-24] constructs a two-dimensional hierarchical aperture distribution with a tunable spatial correlation.
