Analysis of permeability coefficient along a rough fractures using a homogenization method

To compute a permeability coefficient along a rough fracture that takes into account the fracture geometries, this study performed detailed measurements of fracture roughness using a confocal laser scanning microscope, a quantitative analysis of roughness using a spectral analysis, and a homogenization analysis to calculate a permeability coefficient at the microand macro-scale. The homogenization analysis is a type of perturbation theory that characterizes the behavior of microscopically inhomogeneous material with a periodic boundary condition in microstructure. Therefore, it is possible to analyze accurate permeability characteristics that are represented by the local effect of the facture geometry. The C-permeability coefficients that are calculated using the homogenization analysis for each rough fracture model exhibit an irregular distribution and do not follow the relationship of the cubic law. This distribution suggests that the permeability characteristics strongly depend on the geometric conditions of fractures, such as the roughness and the aperture variation. The homogenization analysis may allow to produce more accurate results than the preexisting equations for calculating permeability.