Advanced computation of steady-state fluid flow in Discrete Fracture-Matrix models: FEM–BEM and VEM–VEM fracture-block coupling

An optimization approach for flow simulations in poro-fractured media with complex geometries

“…The hydraulic trasmissivity is set to one for matrix and fractures. The same problem is solved with a VEM based approach on a polygonal/polyhedral conforming mesh, following the approach described in [23], and with the proposed FEM based optimization method. A fine mesh is used for the VEM based reference solution and for the optimization based solution, with elements of maximum size of about 1.5 × 10 −5 , shown again in Figure 9.…”

“…Two or multi-point flux approximation based techniques are described in [21,22] and gradient schemes in [10]. Virtual Element (VEM) based discretizations have also been recently investigated to ease the mesh generation process in complex DFMs, as in [23] where the VEM is coupled to the Boundary Element method, and in [24], in [25] for poro-elasticity problems, or in [26] where an arbitrary order mixed VEM formulation is proposed.…”

A virtual element method for the miscible displacement of incompressible fluids in porous media

“…In the realm of diffusion problems, virtual elements have been developed for linear model diffusion-convection-reaction equations in primal and mixed form [5,8,9,14,17,31,58]. It was soon recognized that the flexibility of VEM in terms of meshing could lead to appealing advantages in the presence of complex geometries, such as for discrete fracture network simulation [16,18,21] and, more in general, in the presence of fractures in porous 3D media [19,43]. Nevertheless, although in other frameworks (such as solid mechanics) VEM have indeed proven themselves also on tough nonlinear problems, to the best knowledge of the authors, virtual elements have never been developed and tested for more complex diffusion models.…”

Flow and Transport in Three-Dimensional Discrete Fracture Matrix Models using Mimetic Finite Difference on a Conforming Multi-Dimensional Mesh

“…There are several computational models for simulating the flow of fluids and the associated transport of dissolved chemicals through subsurface fractured systems, which is of great importance for understanding the behavior of natural subsurface fracture systems and a variety of industrial and civil engineering endeavors, including the environmental restoration of contaminated fractured media [1,2,3], aquifer storage and management [4], hydrocarbon extraction [5,6], longterm storage of spent civilian nuclear fuel [7,8], and CO 2 sequestration [9,10]. The computational models currently used today can be loosely grouped into three categories [11]: (1) continuum models -including stochastic continuum [2,12,13] and dual-porosity / dual-permeability models [14,15,16], (2) discrete fracture networks (DFN) models [17,18,19,20,21], and (3) discrete fracture matrix (DFM) models [22,23,24,25,26,27,28,29,30,31,32,33,34]. The distinguishing feature between the categories is the relative fidelity with which the rock matrix and embedded fractures are represented.…”

“…An example of this is a sparsely fractured medium with little to no flow in the surrounding matrix. In between the two methodologies is the discrete fracture matrix (DFM) model where both the fracture network and surrounding matrix are explicitly resolved [22,23,24,27,28,29,30,31,32,34]. Similar to DFN, the fractures are represented as N − 1 dimensional objects, but the matrix is N dimensional volume surrounding the fracture network that is also considered.…”