Title: Flow simulations in large-scale fractured porous media
Abstract
In underground environments, fractures are numerous and present at all scales (from cm to km), with very heterogeneous properties. The most commonly used model for fractured rocks is the Discrete Fracture Matrix (DFM) model, in which fractures are represented as structures of codimension 1 (Discrete Fracture Network – DFN). In this work, stochastic DFNs are generated with the software DFN.lab (https://github.com/FractoryLabcom/software). It enables the generation of cubic-meter fractured rocks. The objective is to simulate efficiently single-phase flow in large-scale fractured porous media.
My presentation will be divided into two parts. In the first part, I will present results on flow in fractured rocks such as granite rocks where flow only occurs in the fractures (the surrounding rock is impervious). These rocks are made up of millions of fractures and the meshing of this geometry is a challenge that we have taken up in recent years with the development of the MODFRAC software (https://team.inria.fr/serena/fr/research/software/modfrac/). I will then present the method we used to discretise the flow problem, the Hybrid High Order method, capable of supporting general elements. The problem is solved using a direct solver. The code we developed is called NEF++ (https://team.inria.fr/serena/fr/research/software/nefpp/).
In the second part of my talk, I will present the recent results we have obtained on flow in fractured porous rocks. Due to the porosity of the rock, a 3D flow also occurs in the rock and this flow is coupled to the 2D flow in the fractures. To discretise this problem, a mixed hybrid finite element is used. As the linear system may contain millions of unknowns, direct solvers are no longer an option due to the excessive RAM consumption and only iterative methods can be used. I will present several examples demonstrating the excellent performances obtained with GMRES preconditioned by HPDDM (https://petsc.org/main/manualpages/PC/PCHPDDM/).
