How Uncertainty Quantification and Reduced Order Modeling Change our Model Understanding

Abstract:

Understanding subsurface processes and predicting their behavior is substantial for many scientific and economical applications. This involves, for instance, the assessment of suitable locations for geothermal wells, which requires knowledge about the temperature distribution at the target depth.

In addition to the distribution of the state variable (e.g temperature), we also require knowledge about the associated uncertainties for a better risk evaluation. However, uncertainty quantification methods, such as Markov Chain Monte Carlo, are already for conductive heat transfer applications prohibitive for basin-scale applications with current state-of-the-art finite element frameworks.

Therefore, we use in this work the reduced basis method to construct suitable surrogate models. This physics-based learning approach significantly reduces the degrees of freedom while preserving the physical structure of the problem and maintaining an accuracy above typical measurement accuracies. As shown in previous studies, this yields a speed-up of four to six orders of magnitude for real-case basin-scale applications.

In this work, we present how we can take advantage of this speed-up to perform uncertainty quantifications for the real-case basin-scale model of Brandenburg (north-east Germany). In contrast to other surrogate models, the reduced basis method returns the entire temperature distribution. We demonstrate, how this leads to a significantly improved model understanding and which implications this has for future modeling approaches. Furthermore, we illustrate how we extend the existing approach to enable coupled physical simulations, such as hydrothermal applications. Hydrothermal simulations are crucial in geothermal studies to account for fluid interactions.

The methodology is not limited to geothermal applications but can be applied to a wide range of geophysical applications. Therefore, we show how the approach can be beneficially used in other geophysical fields.