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.
