Estimation of the anisotropy of hydraulic conductivity through 3D fracture networks using the directional geological entropy

With an extension of the geological entropy concept in porous media, the approach called directional entrogram is applied to link hydraulic behavior to the anisotropy of the 3D fracture networks. A metric called directional entropic scale is used to measure the anisotropy of spatial order in different directions. Compared with the traditional connectivity indexes based on the statistics of fracture geometry, the directional entropic scale is capable to quantify the anisotropy of connectivity and hydraulic conductivity in heterogeneous 3D fracture networks. According to the numerical analysis of directional entrogram and fluid flow in a number of the 3D fracture networks, the hydraulic conductivities and entropic scales in different directions both increase with spatial order (i.e., trace length decreasing and spacing increasing) and are independent of the dip angle. As a result, the nonlinear correlation between the hydraulic conductivities and entropic scales from different directions can be unified as quadratic polynomial function, which can shed light on the anisotropic effect of spatial order and global entropy on the heterogeneous hydraulic behaviors.