Claudius Proissl (SRP NUPUS Scholarships Holder 2017)

Title of Master's thesis: Dependent Stochastic Processes for Simulating Transport in Porous Media

Supervisors: Prof. Dr.-Ing. Wolfgang Nowak (University of Stuttgart), Sebastian Most, M. Sc. (University of Stuttgart)

Description: This master's thesis is about modeling a transport process through porous media as stochastic process. The stochastic process is simulated by re-sampling from so-called training trajectories. These are particle flow paths obtained from a particle-based transport simulation within a highly-resolved porous medium.

Transport processes in porous media are too complex to be simulated realistically with deterministic models. Either, we do not have access to the necessary detailed information or, in the very rare cases we have enough information, we are limited to very small simulation domains as computational power is limited. Hence, for simulating real world transport problems the porous medium has to be simplified. Simplification however means loss of detail and this means problems! Simplification usually means assigning an effective flow velocity to a representative volume. Essentially this is averaging over the complex pore geometry and thereby we lose important pore-scale information. The objective of this master's thesis is to develop a framework that compensates for that loss by using particle trajectories from detailed simulations as training data to simulate particle motion at larger scale.

The used method is related to a technique called training images that is used in geostatistics in order to represent complex spatial patterns. The approach of this thesis is to translate the idea of training