My research is inspired by the natural phenomena I encountered during my undergraduate education in geology. However, the mathematical tools for my research have been acquired in my rather long graduate career, and serve as a justification for it.
I have changed subjects/disciplines several times, but my primary interest has always been in porous media flows. I first got interested in this subject, on geology field trips during my undergraduate in Munich and Edinburgh. Transport in porous media is an important process in the genesis of all rocks, and hence in planetary evolution. On the practical side it is the key to the management of our water and hydrocarbon resources, both of which are at the base of modern civilization.
My research is inspired by the natural phenomena I encountered during my undergraduate education in geology. However, the mathematical tools for my research have been acquired in my rather long graduate career, and serve as a justification for it.
Currently my approach to research is to try and understand processes using a combination of approximate theoretical models and carefully designed numerical "experiments". In this context theoretical models and numerical experiments serve to validate each other. While the theoretical models are valuable to gain understanding in the limiting cases, numerical experiments can show us the often severe limitations of the theoretical models. In the absence of experiments numerical models are the only way investigate fully non-linear processes.
I am investigating the different mechanisms trapping the injected CO2 in the subsurface, and try to obtain estimates of the time scales over which they are operating. Currently I am formulating approximate models that allow me to asses the importance of the following 3 trapping mechanisms that have been identified in the literature:
I am interested in the development of multiscale methods for heterogeneous Poisson equations. And the application of these methods to the efficient numerical simulation of the long term evolution of geological CO2 storage.
The simulation of CO2 is challenging because, the dominant physical processes change as the plume evolves. During the injection phase advection and gravity are important. After the end of injection gravitational forces dominate initially before capillary forces become dominant. Finally geochemical reactions binding the CO2 in minerals will become important. This change in the dominant forces over time severely restricts the use of highly specialized/efficient numerical methods such as streamline simulation, which are commonly used in reservoir simulation in the oil industry.
The enormous size of the simulation domain is another main challenge in the numerical simulation of geological CO2 storage. In comparison to reservoir engineering, much larger lateral domains have to be simulated. Large simulation domains are necessary because the CO2 may move as a gravity current over long distances, 10's to 100's of kilometers. The leakage of injected CO2 requites the simulation of fluid movement in the overburden of the storage site, usually neglected in reservoir engineering. To lead to a meaningful reduction of CO2 emissions large quantities of of CO2 have to be injected. These large quantities may lead to displacements of the interface between brine and fresh water on a basin scale! These displacements may have effects on shallow aquifer systems used for irrigation and drinking water.
Many first order physical processes during CO2 storage require very high resolution. Due to the adverse mobility ratio dynamical instabilities such as long thin gravity tongues and viscous fingers require meter scale resolution. Convective currents in the brine that determine the dissolution rate of CO2 may require even higher (centimeter scale) resolution!
Finally the uncertainty in description of the geological storage site requires many simulations to assess the uncertainty in model predictions. Similarly the updating of the geological model through monitoring data requires optimization runs requiring many simulations.
It has therefore been recognized that current reservoir simulation technology will not be able to allow adequate simulation of CO2 storage. This makes multiscale methods essential for the simulation of CO2 storage. Multiscale methods currently under development for transport in porous media allow reduction in computational time by providing inexpensive approximate solutions and may be the key to adaptive solution strategies in heterogeneous porous media.In the future I hope to apply the multiscale finite volume (MSFV) method to the simulation of Co2 storage in saline aquifers. Currently I am working on some fundamental problems in the formulation of the MSFV method. In particular I addressed the following issues: