大象传媒

Advisors: Inga Berre, Eirik Keilegavlen and Jan Martin Nordbotten

Short description of project:

Numerical simulations have become essential in the planning and聽execution of operations in the subsurface, whether this is geothermal聽energy production or storage, carbon sequestration, petroleum聽production, or wastewater disposal. As the computational power聽increases, more complex models become feasible, not only in the form of聽more complicated physics, but also in the details of geometric聽constraints such as fractures, faults and wells. These features are聽often of interest as they can have a profound effect on different聽physical processes in the porous medium. This thesis focuses on modeling聽and simulations of fluid flow, transport and deformation of fractured聽porous media. The physical processes are formulated in a聽mixed-dimensional discrete fracture matrix model, where the rock matrix,聽fractures, and fracture intersections form a hierarchy of subdomains of聽different dimensions that are coupled through interface laws. A new聽discretization scheme for solving the deformation of a poroelastic rock聽coupled to a Coulomb friction law governing fracture deformation is聽presented. The novelty of this scheme comes from combining an existing聽finite-volume discretization for poroelasticity with a hybrid聽formulation that adds Lagrange multipliers on the fracture surface.聽This聽allows us to formulate the inequalities as complementary functions and聽solve the corresponding non-linear system using a semi-smooth Newton聽method. The mixed-dimensional framework is used to investigate聽non-linear coupled flow and transport. Here, we study how highly聽permeable fractures affect the viscous fingering in a porous medium and聽show that there is a complex interplay between the unstable viscous聽fingers and the fractures. The computer code of the above contributions聽of the thesis work has been implemented in the open-source framework聽PorePy. The introduction of fractures is a challenge to the聽discretization and the implementation of the governing equations, and聽the aim of this framework is to enable researchers to overcome many of聽the technical difficulties inherent to fractures, allowing them to聽easily develop models for fractured porous media. One of the large聽challenges for the mixed-dimensional discrete fracture matrix models is聽to create meshes that conform to the fractures, and we present a novel聽algorithm for constructing conforming Voronoi meshes. The proposed聽algorithm creates a mesh hierarchy, where the faces of the rock matrix聽mesh conform to the cells of the fractures, and the faces of the聽fracture mesh conform to the cells of the fracture intersections. The聽flexibility of the mixed-dimensional framework is exemplified by the聽wide range of applications and models studied within this thesis. While聽these physical processes might be fairly well known in a porous medium聽without fractures, the results of this thesis improves our understanding聽as well as the models and solution strategies for fractured porous聽media.

Link to thesis at BORA-UiB:聽