Space-time methods for poroviscoelastic flow and mass transport

The flow of fluids within porous rocks is an important process with numerous applications in Earth sciences. Modeling the compaction-driven fluid flow requires solving coupled nonlinear partial differential equations that account for the fluid flow and the solid deformation within the porous medium. Despite the commonly encountered nonlinear relationshipt between porosity and permeability, natural data shows evidence of channelized fluid flow in layered rock formations. Layers of different rock types often have discontinuous hydraulic and mechanical properties, which influences the distribution of chemical trace elements within these rocks.
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 without losing its optimal convergence rate. Furthermore, it enables a straightforward coupling to models of mass transport for trace elements as the entire evolution history stored efficiently. Our results show the influence of different kinds of layering in the development of fluid-rich channels and, consequently, on the subsequent mass transport processes [1].

 

References

[1] Fluid flow channeling and mass transport with discontinuous porosity distribution, S. Boisserée, E. Moulas and M. Bachmayr, Geoscientific Model Development (2025), https://doi.org/10.5194/gmd-18-8143-2025.

[2] An adaptive space-time method for nonlinear poroviscoelastic flows with discontinuous porosities, M. Bachmayr and S. Boisserée, Journal of Numerical Mathematics (2025), https://doi.org/10.1515/jnma-2024-0150.

[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.