Porous Media Flow
The research group investigates computational methods as a tool to model flow and transport of fluids in permeable media; application areas include petroleum production and CO2 deposition in subsurface formations. Our main research focus is fast flow and transport solvers, complex grids, accurate discretizations, and open-source simulators.
Project examples
Fast solvers for flow and transport
We use three principles to develop fast solvers
- Simplified physics - "full physics" is not always required and in many cases reduced models may suffice and/or geology may be more important than flow physics.
- Operator splitting - divide and conquer is a classical technique for attacking complex problems
- models generally consist of several subequations (e.g., flow and transport equations) that often have different time and length scales
- fully coupled solution is generally slow and is only required if there is a tight coupling between physical processes governing the fluid behaviour
- splitting opens up for highly efficient methods that are tailor-made for a particular type of equation
Examples of operator splitting include splitting of flow and transport (used in IMPES, sequentially implicit formulations, etc), splitting of gravity and capillary forces (used in streamline simulations, etc).
- Sparsity and multiscale structure - should be exploited to reduce computations
- physical effects may be resolved on different scales (example: fluid pressure is generally much smoother than flow velocities)
- in dynamic simulations there are typically small changes from one step to the next
- various workflows for optimization and data integration involve multiple forward simulation where the changes are small from one simulation to the next.
Examples of technologies we work with: multiscale flow solvers, streamline simulation, flow-based gridding, optimal ordering methods, adjoint formulations, streamline-based sensitivities, etc.
Complex grids and flexible discretizations
Grid models representing geological formations are often highly complex and have unstructured connections. The most widespread gridding approaches are based on extrusion of 2D shapes (corner-point and 2.5D PEBI grids), but recent approaches include fully unstructured grids with general polyhedral cells. In recent years, we have worked on methods for processing and representing various unstructured grids.
The standard two-point discretization method exhibits strong grid-orientation effects for grids that are not K-orthogonal. Modern discretization methods like the multipoint flux approximation (MPFA) method and the mimetic method eliminate this problem. We have worked with making the mimetic method suitable for industry standard problems.
