[Article] THE VIRTUAL ELEMENT METHOD FOR DISCRETE FRACTURE NETWORK SIMULATIONS

Porto, the institutional repository of the Politecnico di Torino, is provided by the University Library and the IT-Services. The aim is to enable open access to all the world. Please share with us how this access benefits you. Your story matters. Abstract. In this work, an optimization based approach presented in [5, 6, 7] for Discrete Fracture Network simulations is coupled with the Virtual Element Method (VEM) for the space discretization of the underlying Darcy law. The great flexibility of the VEM in handling rather general polygonal elements allows, in a natural way, for an effective description of irregular solutions starting from an arbitrary triangulation, which is built independently of the mesh on other fractures. Only partial conformity is in fact obtained with this approach. Numerical results performed on several DFN configurations confirm the viability and efficiency of the resulting method. 1. Introduction. Subsurface fluid flow has applications in a wide range of fields, including e.g. oil/gas recovery, gas storage, pollutant percolation, water resources monitoring, etc. Underground fluid flow is a complex heterogeneous multi-scale phenomenon that involves complicated geological configurations. Discrete Fracture Networks (DFNs) are complex sets of planar polygonal fractures used to model subsurface fluid flow in fractured (porous) rocks. Typically, a DFN is obtained stochastically using probabilistic data to determine a distribution of orientation, density, size, aspect ratio, aperture and hydrological properties of the fractures [1, 11, 12], and it is a viable alternative to conventional continuum models in sparse fracture networks. DFN simulations are very demanding from a computational point of view and due to the uncertainty of the statistical data, a great number of numerical simulations is required. Furthermore, the resolution of each configuration requires vast computational effort, increasing greatly with problem size. In this work, we focus on the resolution of the steady-state flow in large fracture networks. The quantity of interest is the hydraulic head in the whole network, which is the sum of pressure and elevation and is evaluated by means of the Darcy law. We consider impervious rock matrix and fluid can only flow through fractures and traces (intersections of fractures), but no longitudinal flow along the traces is allowed. Matching conditions need to be added in order to preserve continuity along traces and flux balance at fracture intersections. The classical approach to DFN simulations consists in a finite element discretization of the network and in the resolution of the resulting algebraic …