Upscaling of Normal Stress-Permeability Relationships for Fracture Networks Obeying Fractional Levy Motion

Abstract Understanding and modeling coupled thermal, hydrological, mechanical, and chemical (T-H-M-C) processes in fractured rocks are of interest to many areas of active research, including geological disposal of nuclear waste. A key parameter for modeling these processes is the relationship between in situ stress and permeability. Since this relationship is generally measured at small scales, upscaling is needed for large-scale models. Few studies on the upscaling of this relationship have appeared in the literature. The major objective of our present effort is to develop closed-form upscaled normal stress-permeability relationships for fracture networks. Focusing on data from Sellafield site, UK, we demonstrate that measured permeability data form a distribution very well described by fractional Levy motion (fLm). This is consistent with findings reported in the literature indicating that fractures are spatially clustered and that the clustering patterns could be described by fractals. Assuming several different correlations between local permeability and fracture apertures, we develop two upscaling relationships between normal stress and permeability for fracture networks. These relationships capture the relevant large-scale effects of normal stress change on rock permeabilities, at least for the case of permeability distributions characterized by fLm.