Dual virtual element methods for discrete fracture matrix models

The accurate description of fluid flow and transport in fractured porous media is of greatest importance to capture the macroscopic behavior of an oil reservoir, a geothermal system, or a CO2 sequestration Site. However, the construction of accurate simulation models for flow in fractures is challenging due to the high ratio between a fracture's length and width. To address this, a mixed-dimensional Darcy problem which can represent the pressure and Darcy velocity in all the dimensions, e.g., in the rock matrix, in the fractures, and in their intersections, is described. Also, a mixed-dimensional transport problem is presented, which, given the Darcy velocity, describes advection of a passive scalar into the fractured porous media. The approach can handle both conducting and blocking fractures. The computational grids are created by coarsening of simplex tessellations that conform to the fracture's surfaces. The performance of this method is illustrated by comparing to benchmark studies for two-dimensional fractured porous media, as well as a complex three-dimensional fracture geometry.