Dual Virtual Element Methods for Discrete Fracture Matrix Models

TL;DR

This paper introduces dual virtual element methods for simulating fluid flow and transport in fractured porous media, effectively modeling pressure, velocity, and scalar transport across multiple dimensions with high accuracy and computational efficiency.

Contribution

It presents a novel mixed-dimensional Darcy and transport model using virtual finite element and finite volume methods for complex fractured media.

Findings

Accurate simulation of flow and transport in 2D and 3D fractured media.

Effective handling of conducting and blocking fractures.

Good balance between accuracy and computational cost.

Abstract

The accurate description of fluid flow and transport in fractured porous media is of paramount importance to capture the macroscopic behaviour of an oil reservoir, a geothermal system, or a CO2 sequestration site, to name few applications. The construction of accurate simulation model for flow in fractures is challenging due to the high ratios between a fracture's length and width, which makes modeling by lower-dimensional manifolds a natural option. In this paper we present a mixed-dimensional Darcy problem able to describe pressure and Darcy velocity in all the dimensions, i.e. in the rock matrix, in the fractures, and in their intersections. Moreover, we present a mixed-dimensional transport problem which, given the Darcy velocity, describes coupled advection and diffusion of a passive scalar into the fractured porous media. The approach can handle both conducting and blocking fractures. Our computational grids are created by coarsening of simplex tessellations that conform to the fractures surfaces. An accurate choice of the discrete approximation of the previous model, by virtual finite element and finite volume, allows us to simulate complex problem with a good balance in term of accuracy and computational cost. We illustrate the performance of our method by comparing to benchmark studies for two-dimensional fractured porous media, as well as a complex three-dimensional fracture geometry.