Abstract
A novel cell-centred control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulation is presented for discrete fracture-matrix simulations in three-dimensions. The grid is aligned with the fractures and barriers which are then modelled as lower-dimensional interfaces located between the matrix cells in the physical domain. The three-dimensional(3D) pressure equation is solved in the matrix domain coupled with a two-dimensional(2D) pressure equation solved over fracture networks via a surface CVD-MPFA formulation. The CVD-MPFA formulation naturally handles fractures with anisotropic permeabilities on unstructured grids. Matrix-fracture fluxes are expressed in terms of matrix and fracture pressures and must be added to the lower-dimensional flow equation (called the transfer function). An additional transmission condition is used between matrix cells adjacent to low permeable fractures to link the velocity and pressure jump across the fractures. Numerical tests serve to assess the convergence and accuracy of the lower-dimensional fracture model for highly anisotropic fractures having different apertures and permeability tensors. A transport equation for tracer flow is coupled via the Darcy flux for single and intersecting fractures. The lower-dimensional approach for intersecting fractures avoids the more restrictive CFL condition corresponding to the equi-dimensional approximation with explicit time discretisation. Lower-dimensional fracture model results are compared with equi-dimensional model results. Fractures and barriers are efficiently modelled by lower-dimensional interfaces which yield comparable results to those of the equi-dimensional model. Highly conductive fractures are modelled as lower-dimensional entities with continuous pressure across these leading to reduced local degrees of freedom for the cluster of cells. Moreover, we present 3D simulations involving geologically representative complex fracture networks.
