Characterizing a rock fracture rough surface using spatial continuity and kriging: From semi-variograms and an upscaled

Fluid flow through low permeability rocks is mainly accomplished through fractures. Coupled Thermo-Hydraulic-Mechanical-Chemical (THMC) numerical models rely on fractures’ surfaces representations to construct a distribution model of the empty space (aperture) between the two. The generally used statistical representations of fracture surfaces often overlook directionality which may result in a poor representation of the aperture distribution and thus a poor model. Semi-variograms are used as spatial continuity methods in areas such as ore deposits and geological facies prediction but few studies have applied these techniques to fracture face characterization. The aim of this study is to investigate the possibility of characterizing a fracture surface roughness using semi-variograms and heavily upscaled fracture surface. Comparing the kriging originated fracture surface to the original offers a measurement of methodological quality. A statistical analysis was performed in a greywacke in order to acquire the semi-variograms’ parameters necessary to describe the spatial continuity of the fracture surface topography. The surface will then be interpolated using Simple (SK) and Ordinary (OK) Kriging techniques. A reasonable match between the kriged and original surfaces is expected to be achieved and the fit quantified by analyzing the residuals between the two. These results may provide a new alternative to current storing and computing solutions for fracture representation, especially in aperture distribution calculation for coupled THMC numerical models and simulations. To verify the applicability of this work in coupled processes, the comparison of results and computing time of models using apertures derived from original versus kriged surfaces must be made.