Fracture network optimization for simulating 2D variable-density flow and transport

Numerical simulations in porous media with complex geometries such as fracture networks require irregular meshes with a large number of nodes. Discrete fracture models solve the flow and transport equations with the common node approach. These equations are usually solved simultaneously using common nodes, which increases the computational time as the number of nodes increases. Moreover, the mesh element size at fracture-matrix interfaces need to be further refined, increasing the total number of nodes and computational cost. The main objective of this paper is to efficiently model fracture networks. Therefore we: (i) modify a mesh generator algorithm to generate high-quality meshes for fracture networks where mesh refinement close to the fractures is allowed and (ii) investigate the possibility of reducing the required simulation time by reducing the number of total nodes by removing some fractures from a fracture network. Using a two-dimensional simulation domain of a fractured porous medium under saturated conditions with variable-density flow, we consider 3 statistically equivalent fracture networks embedded in a porous medium containing 50 fractures each with constant aperture. A simplified fracture network is obtained by finding the shortest path in each cluster between the 1st type boundary condition for transport and minimum points in each cluster, where a cluster is defined as all interconnected fractures with at least one fracture intersecting the contaminant source boundary condition. We compare results in terms of penetration depth of the 0.50 isochlore and the contaminant mass. This simplification strategy reduces computational times by up to 36%, while keeping the generated error below 20% both for the penetration depth of the 0.50 isochlore and for the contaminant mass. A sensitivity analysis is performed whereby the free diffusion coefficient, the matrix freshwater permeability, the porosity and the maximum density are modified. Based on these results, the proposed simplification strategy can estimate the penetration depth and the solute mass inside the domain for a wide range of parameter values, saving up to 58% of the CPU time.