A fast numerical method and optimization of 3D discrete fracture network considering fracture aperture heterogeneity

Abstract

A novel numerical method was developed to evaluate the effect of the aperture heterogeneity of individual fractures on fluid flow through three-dimensional discrete fracture networks (DFNs). First, the rock fractures are modelled as circular discs with sizes, orientations, and positions following exponential, Fisher, and uniform distributions, respectively. Isolated fractures (clusters) that make no contribution to fluid flow through the DFN were then removed by optimization programming using breadth optimization and deep optimization algorithms. Subsequently, individual fractures with heterogeneous apertures were developed using successive random addition algorithms. After that, fracture networks were triangulated, and the Reynolds equations were solved for fluid dynamics computations. The verification showed that the developed method provides advantages in computational accuracy and efficiency. Finally, the influence of the aperture heterogeneity of individual fractures on fluid flow through a DFN was evaluated with the proposed method. For comparison, DFN models with identical mechanical apertures (DFN-I) and another model with heterogeneous apertures (DFNH) were developed. The results show that a preferential flow phenomenon appeared in both the DFN-I and DFNH models. However, owing to the aperture heterogeneity of the individual fractures, the results of the DFNH model were more substantial than those of the DFN-I model. This preferential flow phenomenon would be weakened by an increase in either the mechanical aperture or the fracture density. The results also showed that the permeability difference between the DFN-I and DFNH models was obvious for DFN models with small apertures and low fracture densities, but this permeability discrepancy decreased with increasing mechanical aperture or fracture density. Therefore, a critical mechanical aperture exists for a DFN model with a specified fracture density. Beyond this threshold, the influence of aperture heterogeneity within individual fractures on fluid flow can be neglected, and the DFN-I model can be selected to replace the DFNH model for efficient modelling and computation.