Multi-field continuum modeling of two-fluid-filled porous media fracture augmented by microscale-based machine-learning material laws

• Applicants: Dr.-Ing. Yousef Heider; Professor Dr.-Ing. Bernd Markert
• Subject Area: Applied Mechanics, Statics and Dynamics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 458375627

The fracturing of microscopically-heterogeneous, two-fluid-filled porous materials presents a multiscale problem with evolving internal discontinuities. It is characterized from a mechanical and computational point of view by a high degree of complexity and uncertainty, as It involves simultaneous fluid-fluid displacements (e.g. water-air or oil-water) alongside deformation and degradation of the hosting porous matrix. Despite the importance of the topic, it was only subjected to a few research works. In soil science, drying-induced fractures in partially-saturated clayey soils can significantly change their thermo-hydro-mechanical properties and lead to substantial loss of moisture content. In geotechnical engineering, desiccation cracks in foundation ground can endanger the stability of constructions. In geothermal energy production and petroleum engineering, it is crucial to be able to predict the paths of hydraulic fractures in order to be able to avoid possible drawbacks such as triggering of earthquakes or contamination of groundwater.In these three-phase materials, the way the fracture is initiated, i.e. drying- or wetting, and the saturation state, i.e. a complete saturation, a funicular, a pendular, or a residual state, plays a decisive role in the mathematical formulation of material degradation and the stability of the numerical model. In addition, the formulation of the history-dependent retention curve substantially affects the accuracy of the modeling, whereas the presence of cracks in the solid matrix introduces anisotropy in the effective medium. Thus, the mathematical models of fluid flow in the crack should consider the occurring anisotropic permeability and the type of flow on the crack scale, i.e. Darcy or non-Darcy flow. The major contributions of the underlying proposal are threefold. First, developing a reliable macroscopic fracture model in porous materials with different degrees of saturation, based on embedding the phase-field modeling (PFM) approach in continuum multiphase porous media mechanics. Second, introducing and implementing robust and flexible numerical simulation algorithms to solve the emerging coupled differential equations. Third, utilizing the capabilities of Machine Learning (ML), via using deep neural networks (DNN) and deep reinforcement learning (DRL) to generate ML-based material models related to the path-dependent retention behavior and fluid flow, which can also take important microstructural information into consideration. Therefore, the proposed research project with its aims and spectrum of applications will carry significant societal benefits in safety, energy, and environment.

• DFG Programme: Research Grants