Multiscale pressure solvers. Multiscale simulation is a promising approach to facilitate direct simulation of large and complex grid-models for highly heterogeneous petroleum reservoirs. We have for many years worked on developing a particular multiscale methods, the multiscale mixed finite-element (MsMFE) method. We use this method in various forms in several of our ongoing projects, and the method has been implemented for general unstructured grids in MRST. Connected to our ongoing research, there are several interesting and challenging topics for student projects and master theses:

Parallelization - The method has an inherent parallelism in the computation of basis functions (and correction functions) that has not yet been utlized in our implementations. A prototype parallel implementation can be devloped using e.g., MRST and the Matlab Parallelization toolbox. Goal-oriented error control - The accuracy of the MsMFE method is affected by how often basis functions (and correction functions) are updated. In many cases, the calculation of fluid production from a reservoir does not require accuracy over the full domain. By utilizing sensitivities, e.g., from an adjoint problem or computed approximately using streamlines, one can estimate how local inaccuracies in the solution affect the calucation of fluid production. Then, this information can be used to determine how much effort should be put into computing and accurate solution locally by e.g., updating basis/correction funtions and/or iterating on these. A simple version of this idea was successfully in a recent PhD thesis on history matching. Coarsening of unstructured grids - For corner-point grids, we have a very efficient method for generating coarse grids for the MsMFE method. The key point in our methodology is that coarse grids follow geological structures like layers etc. Information of geological structures is available implicitly in index space for corner-point grids. For more general grids like PEBI grids (2D Voronoi grids extruded to 3D) and other fully unstructured grid, it is more difficult to identify the geological structures that the coarse grid should adapt to. However, in this project we challenge you to give it a try! Black-oil formulations - There are several ways to formulate a computational strategy for the black-oil model, which is the industry-standard model for reservoir simulation. In this project, you will look at various formulations, implement them with a MsMFE discretization and try to determine which one is most robust and efficient. To this end, you will use an inhouse version of MRST.

We offer supervision at NTNU and at the universities of Bergen and Oslo. For all the projects listed above, you must work in close collaboration with the GeoScale team and we expect you to do quite a bit of programming. 

Contact: Knut-Andreas Lie