Strategies to Model De-Gassing in Porous Media

De-gassing in porous media is a complex, non-linear process that is governed by multi-phase mass transfer, multiphase flow and diffusion within detailed pore geometries. Yet, we wish to predict the de-gassing of larger systems without the need to know the geometry of each individual pore. For such predictions, we want to find suitable mathematical models for computer-based simulations. The largest question is: with what strategy should such a model be built? A simple model with few parameters that is easy to calibrate and runs fast? A complex, detailed model that could be highly accurate but consumes many experimental data before it can be built and calibrated, and then runs slow on a computer? While many possible model concepts could be proposed, we are interested in the question how to select between these models in some optimal way.

As machinery for objectively choosing between models, we will adopt the framework of Bayesian Model Selection (BMS). The idea behind BMS is to decide based on the degree to which models are able to predict data in validation experiments. If models have uncertain parameters (which they have when they have many parameters that could not be calibrated uniquely), then the average ability to predict is used. A highly complex model with many parameters could potentially be highly accurate, but will also make very imprecise (uncertain) predictions, unless enough data was available to calibrate the model uniquely. The resulting metric for model selection is called Bayesian Model Evidence (BME), and resembles an accuracy-precision trade-off.

In the proposed PhD project, we will collect and add several candidates that describe degassing in porous media. They will include, for example, apparent first-order mass transfer models, inversion-percolation models, fully blown multiphase multi-component flow/transport models. Then we calibrate them to data from an experimental setup, and use data from a separate experiment to validate and rank the models via BMS. We will use latest extensions of BMS that add computer time as additional criterion to the precision-accuracy trade-off. We will also use different types and subsets of data to explore the quality and quantity of data required to prefer the more complex models over the simpler ones. The featured model problem could include air or methane injection in sand, steam from boiling water in sand, or hydrogen production by chemical reaction.

The focus will be on implementing the competing models and the BMS framework, and on providing guidance for modeling.