5th May – ‪Daniel Zegarra Vasquez: Simulation of single-phase flows in fractured porous media using the mixed hybrid finite element method

In underground environments, fractures are very numerous and present at all scales, with very heterogeneous sizes. In particular for flows, they are preferential channels: flows are much faster there than in the neighboring rock. Indeed, the permeability of rock is generally about two orders of magnitude lower than that of fractures. This makes fractures play a vital role in a large number of industrial and environmental applications. These particularities of the fractured porous domain make the modeling and simulation of the flows passing through it a major challenge today for which it is necessary to develop dedicated, robust and efficient models and numerical methods.

The most commonly used model for representing fractures is the discrete fracture network (DFN) in which fractures are represented as structures of codimension 1. The model of single-phase flows in fractured porous media is described in [5]. The particularity of the fractured porous problem, compared to the porous-only or fractured-only problem [3], is the coupling between
the flow in the fractures and the flow in the rock. Due to the difficulties encountered in taking into account the geometric complexity of large fractured networks in simulations, the test cases recently proposed in the literature are mainly 2D, or 3D with a limited number (about ten) of fractures [1].

In this talk, we will present the nef-flow-fpm solver, which solves the stationary 3D fractured porous problem using the mixed hybrid finite element method. The method developed in the solver is inspired by [4]. To mesh the domain, a first simplical and conforming 2D mesh is generated for the DFN and for the boundaries of the domain, then a second simplical and conforming 3D mesh is generated from the first mesh. The solvers integrated in nef-flow-fpm are direct solvers, like LU and Cholesky, and iterative solvers, like PCG and AMGCL [2]. We validated nef-flow-fpm on the test cases presented in [1]. We will propose new test cases with a larger number of fractures (a few thousand).

References :
[1] I. Berre et al. Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources, 147, 2021.
[2] D. Demidov. AMGCL : An efficient, flexible, and extensible algebraic multigrid implementation. Lobachevskii Journal of Mathematics, 40, 2019.
[3] A. Ern, F. Hédin, G. Pichot, N. Pignet. Hybrid high-order methods for flow simulations in extremely large discrete fracture networks. Pre-print https ://hal.inria.fr/hal-03480570/, 2021.
[4] H. Hoteit, A. Firoozabadi. An efficient numerical model for incompressible two-phase flow in fractured media. Advances in Water Resources, 31(6), 2008.
[5] V. Martin, J. Jaffré, J. E. Roberts. Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing, 26(5), 2005.