On the Continuum Representation of Fracture Networks

Discrete Fracture Network (DFN) and Stochastic Continuum (SC) are the two dominant modeling approaches used for simulating of fluid flow and solute transport in fractured media. While the SC approach has several variants, we focus on two methods introduced by Svensson [2001] and McKenna and Reeves [2002] where discrete fracture networks are directly mapped onto a finite-difference grid as grid cell conductivities. These methods combine the merits of each approach; a computationally efficient grid is utilized for the solution of fluid flow, and details of the fracture network are preserved by assigning a permeability contrast between the grid cells representing the rock matrix and fracture cells. In this paper, we focus on several outstanding issues that are associated with SC models: enhanced connectivity between fractures that would otherwise not be in connection in a DFN simulation, the formulation of grid cell conductivity for cells containing multiple fractures, and the influence of grid size. To addresses these issues, both DFN and SC models are used to solve for fluid flow through two-dimensional, randomly generated fracture networks. To minimize connectivity between fractures in the SC model, a percolation algorithm is used to define the hydraulic backbone before fractures are mapped onto a model grid. The effect of grid size is studied by using two different regularly-spaced grids with cell lengths of 1m and 10m. The resultant DFN flow solutions are used as a metric to evaluate different approaches used to assign grid cell conductivity. Results from this study are presented as guidelines for representing fracture networks as grid cell conductivities.