A hybrid upwind scheme for two-phase flow in fractured porous media

TL;DR

This paper introduces a hybrid upwind scheme for simulating two-phase flow in fractured porous media, improving solver convergence by better discretizing advective fluxes in complex fracture networks.

Contribution

It extends hybrid upwinding to a mixed-dimensional fracture model, enhancing convergence speed in two-phase flow simulations with heterogeneous fractures.

Findings

Improved convergence of nonlinear solvers in fractured media.

Robustness of the discretization across different flow regimes.

Reduction in Newton iterations compared to previous methods.

Abstract

Simulating the flow of two fluid phases in porous media is a challenging task, especially when fractures are included in the simulation. Fractures may have highly heterogeneous properties compared to the surrounding rock matrix, significantly affecting fluid flow, and at the same time hydraulic aperture that are much smaller than any other characteristic sizes in the domain. Generally, flow simulators face difficulties with counter-current flow, generated by gravity and pressure gradients, which hinders the convergence of non-linear solvers (Newton). In this work, we model the fracture geometry with a mixed-dimensional discrete fracture network, thus lightening the computational burden associated to an equi-dimensional representation. We address the issue of counter-current flows with appropriate spatial discretization of the advective fluid fluxes, with the aim of improving the convergence speed of the non-linear solver. In particular, the extension of the hybrid upwinding to the mixed-dimensional framework, with the use of a phase potential upstreaming at the interfaces of subdomains. We test the method across several cases with different flow regimes and fracture network geometry. Results show robustness of the chosen discretization and a consistent improvements, in terms of Newton iterations, compared to use the phase potential upstreaming everywhere.