Fluid flow channeling and mass transport with discontinuous porosity distribution

The flow of fluids within porous rocks is an important process with numerous applications in Earth sciences. Modeling the compaction-driven fluid flow requires the solution of coupled nonlinear partial differential equations that account for the fluid flow and the solid deformation within the porous medium. Despite the nonlinear relation of porosity and permeability that is commonly encountered, natural data show evidence of channelized fluid flow in rocks that have an overall layered structure. Layers of different rock types routinely have discontinuous hydraulic and mechanical properties.
We present numerical results [1] obtained by a novel space-time method [2] based on a fixed-point scheme inspired by the mathematical analysis [3], combined with a space-time least-squares formulation. This approach can handle discontinuous initial porosity (and hence permeability) distributions. It furthermore exhibits optimal convergence independently of the discontinuities, while standard approximations, as e.g. finite differences, tend to show lower order convergence in discontinuous regimes.
The space-time method enables a straightforward coupling to models of mass transport for trace elements. Our results show the influence of different kinds of layering in the development of fluid-rich channels and mass transport [1].

References
[1] Fluid flow channeling and mass transport with discontinuous porosity distribution, S. Boisserée, E. Moulas and M. Bachmayr, arXiv Preprint (2024), https://doi.org/10.48550/arXiv.2411.14211.
[2] An adaptive space-time method for nonlinear poroviscoelastic flows with discontinuous porosities, M. Bachmayr and S. Boisserée, arXiv Preprint (2024), https://doi.org/10.48550/arXiv.2409.13420.
[3] Analysis of nonlinear poroviscoelastic flows with discontinuous porosities, M. Bachmayr, S. Boisserée and L. M. Kreusser, Nonlinearity (2023), https://doi.org/10.1088/1361-6544/ad0871.