Uncertainty Quantification and Visualization Techniques for Numerical Integrity Analyses

This study explores the quantification of uncertainties in integrity assessments of geological barriers in repository systems, which is a crucial aspect required by German law (§5 Endlagersicherheitsanforderungsverordnung (EndlSiAnfV)). The analysis includes numerical approximations of thermally-hydraulically-mechanically coupled processes. The legal framework necessitates documentation of the impact of uncertainties on safety-oriented evaluations, thereby requiring a systematic investigation of uncertainties in simulated results from integrity analyses.

The German Federal Institute for Geosciences and Natural Resources (BGR) has been engaged in various projects such as ANSICHT-II, MeQUR, and ThermoBase to address the forward propagation of input parameter uncertainties through numerical approximations and have collectively contributed to developing methods for quantifying uncertainties related to repository systems.

The study focuses on quantifying uncertainty within two primary steps: sensitivity analyses and stochastic modeling. Sensitivity analyses are employed first to identify the significance of each individual input parameter in a numerical simulation, as it is likely that uncertainty in many parameters may have negligible effects on the integrity of the containment providing rock zone (CRZ). The result is a set of essential input parameters that are then used in the second step to make quantitative statements about the stochastic state space, which is sampled using methods like Monte-Carlo sampling or stochastic collocation.

In the project ANSICHT, criteria were developed based on the EndlSiAnfV to indicate integrity within the CRZ in clay rock. These criteria can be represented as functions. For stochastic models, these functional dependences are expanded to include all parameters in the state space, known as stochastic dimensions. Methods for stochastic post-processing have been developed that allow for analysis without any prior data reduction.

The study also highlights the development of specialized software tailored to handle the computational demands associated with uncertainty quantification in numerical integrity analyses for repository systems. This includes the OpenGeoSys Uncertainty Quantification framework (OpenGeoSysUncertaintyQuantification.jl) developed by BGR, which has been published in the Julia programming language (Bittens, 2024).

Additionally, an interactive dashboard is presented that provides intuitive visual access to the results and can thus contribute to knowledge transfer about safety-relevant processes in the repository and the underlying uncertainties.

Bittens, M. (2024). OpenGeoSysUncertaintyQuantification.jl: a Julia library implementing an uncertainty quantification toolbox for OpenGeoSys. Journal of Open Source Software, 9(98), 6725.