Evaluation of Connectivity Characteristics on the Permeability of Two-Dimensional Fracture Networks Using Geological Entropy

A systematic approach has been developed to estimate the relationship between the permeability and connectivity of two-dimensional fracture networks, in which the network connectivity is evaluated with the concept of geological entropy as informative index of spatial disorder. The geological entropy is quantified by the entropic scale, a metric developed by Bianchi and Pedretti (2018), which is here applied to integrate multiple properties of two-dimensional fracture networks, including aperture, spacing, length, orientation. Through the comparisons among several existing connectivity indicators including the entropic scale in an illustrative example, only the entropic scale is positively correlated with the permeability concerning aperture and can be successfully used to quantify the network connectivity. In order to understand connectivity characteristics dependence of the permeability, a computational method combining fracture network generation and steady-state flow simulation is developed. Based on the results of detailed numerical simulations considering hydraulic behavior and connectivity characteristic in various fracture networks, the entropic scale and permeability are simultaneously inversely proportional to length and proportional to spacing with the same global entropy, but exhibit weak dependence on the orientation variation. A simple closed-form empirical expression in terms of quadratic polynomial model between the permeability and entropic scale is proposed. The results indicated that geological entropy is valid and appropriate to quantify the connectivity and predict the permeability of two-dimensional fracture networks.