Investigation of REV scale and anisotropy for 2D permeable fracture Networks: The role of geological entropy

To investigate the intrinsic association between geometrical properties and permeability of anisotropic fractured media, a methodology of geological entropy is applied to anisotropic fracture networks for the evaluation of seepage fields. By integrating the synthetic effect of fracture geometrical parameters (e.g., trace length, spacing, dip angle, and aperture), the global connectivity of fracture networks is quantified by the entropy scale (Hs), while the directional entropy scale (Hs,α) is used to characterize the local geometrical anisotropy in arbitrary orientations. A series of hydraulic representative elementary volumes (REVs) of fracture patterns with various geometrical properties are acquired based on continuum analysis. The permeability in the continuum scale is obtained from steady-state flow simulations. Sensitivity analyses are performed to understand the geometrical dependence of permeability parameters regarding entropy indices. It is found that a systematic increase in trace length, spacing, and dip angle is correlated with an increase, decrease, and equilibrium in entropy, respectively, which corresponds to a change in hydraulic REV sizes that can be expressed as a power-law function related to the Hs. Moreover, Hs,α can well explain the permeability anisotropy resulting from the spatial order of fracture networks, and a unified mathematical relationship for the effective permeability coefficients in arbitrary orientations versus the Hs,α is proposed, independent of variations in fracture patterns and scales. The results indicate that geological entropy, related to the geometrical properties and spatial distribution of fractures, is appropriate to characterize the permeability of anisotropic systems.