Motivated by subsurface flow and deformation, this part of the course series consider flow in fractures and deformation and propagation of fractures in porous media. The deformation and propagation of fractures introduce a dynamic change of the fracture network, which interacts with flow, transport and deformation in the fractured porous medium. In the course, we consider conceptual models for processes in fractured and deformable porous media as well as mathematical and numerical modeling of coupled dynamics. We also investigate how models can complement field data in understanding induced dynamics from fluid injection in the subsurface.
The course is suitable for master and PhD students and other with interest in the topic with background in mathematical modeling with partial differential equations and basic knowledge of continuum mechanics.
The lectures are given by Inga Berre and Jan M. Nordbotten, both from the University of Bergen.
Tentative plan for the lectures
• introduction to fractured porous media
• mixed-dimensional discrete fracture-matrix models for flow and transport in porous media
• mathematical modeling of fault reactivation and deformation in poroelastic media
• modeling examples and case studies
The calculus of mixed-dimensional models:
• An introduction to calculus on manifolds
• Glueing manifolds together: Mixed-dimensional models
• Flow in fractured porous media and the mixed-dimensional Poisson problem
• Corollaries: Existence, uniqueness, and a functional posteriori error bounds
The lectures will be given by Professors Inga Berre (Lecture 1 and 2) and Jan M. Nordbotten (Lecture 3) from the University of Bergen.
Lecture notes from part 1
Lecture notes from part 2
Lecture notes from part 3