Fractures can be of significant importance in porous media flows. However, many of the current simulations for hydraulically stimulated fractures work in a homogeneous setting, often resultion in too regular fracture patterns. We explore potential randomisations of fracture generating models to overcome this.
The underlying belief of this project can be summarised as follows: In many appli- cations full knowledge at small scales cannot be obtained. Thus, it makes sense to lump these uncertainties together at the REV scale. Randomisation at the REV scale is then the best bet to model the resulting quasi-randomness.
The plan to achieve this includes several steps: Relevant fracture models need to be identified and sufficiently understood to find points of attack for the randomisation. Random fields to describe the material homogeneity, as well as energy based sampling during the fracture generation are among the approaches.
We aim to implement a Bayesian inference loop to ensure the usefulness and quantify the uncertainty of the randomised models; first on synthetic and eventually on real world data. Sensible statistical properties for the use of the randomised fracture models have to be defined as target characteristics for this. They need to be sufficiently descriptive, attainable and at the same time functional for the further use of the fracture models in flow simulations. A comparative study between the different randomised models is done. The tradeoff between expressiveness and simplicity can be quantified in a Bayes model selection setting.
On a longer time scale, use of the randomised fracture models in flow simulations constitutes the next part of the project. The flow models and fracture models are combined to account for hydraulically stimulated fracture creation. After a similar Bayesian calibration step, the aim is to use the combined models for process understanding, exploring questions such as: What parameters of the model are most influential? Is the flow or the material domain more important for the overall behaviour? Which implicitly modeled heterogeneities cause the biggest deviation from their homogeneous complements? This research project takes place within the CRC 1313, enabling the collaboration with experts from at least four major relevant areas: fracture models, flow models, stochastic processes and Bayesian inference.
