Modelling of fluid flow in fractures and faults in porous media.

The PhD project is part of an ambitious computational mechanics research programme funded through the ERC Advanced Grant “A high-fidelity isogeometric simulation methodology for fracture in porous media” (PoroFrac).

This project aims at developing a robust simulation methodology for fracture in heterogeneous, (partially) fluid-saturated porous media, both for existing faults and for propagating cracks. The project consists of three, strongly related pillars, complemented by a horizontal project that connects the developments in the three pillars, and applications to hydraulic fracturing (fracking) and fault dynamics. In pillar 1 a mesoscopic, multi-phase model will be developed for fluid transport in cracks which are embedded in a fluid-saturated porous medium. The development of an adaptive spline technology in pillar 2 will enable to capture crack propagation and branching in arbitrary directions on arbitrary discretizations. The reliability method of pillar 3 will enable a quantitative assessment of the probability that, in a layered, heterogeneous medium, a crack propagates in a certain direction.

This PhD project is situated within pillar 1, and the main aim is to develop a consistent, enhanced sub-grid scale model, which can handle multi-phase fluid flow within a cohesive crack, is capable of modelling fluid pressure driven crack growth (fracking), and is localised at the crack and naturally embedded in the surrounding porous medium. The model should be implemented in a variety of discrete representations of a crack, including interface elements, extended finite element methods and isogeometric analysis (developed in pillar 2), but also in smeared representations like phase-field methods (developed in pillar 3). Also the extension to non-Newtonian fluids should be made, since in fracking these fluids are commonplace. Finally, fluid lag should be considered, that is the difference between the position of the crack tip and the location of the fluid front in the crack.

The research has a strong modelling component, and will also require implementation of the models in modern software, using advanced discretization concepts. Knowledge of modern languages like C++ and experience in programming are therefore required.