Crustal-scale thermal models: revisiting the influence of deep boundary conditions

Abstract

The societal importance of geothermal energy is significantly increasing because of its low carbon-dioxide footprint. However, geothermal exploration is also subject to high risks. For a better assessment of these risks, extensive parameter studies are required that improve the understanding of the subsurface. This yields computationally demanding analyses. Often, this is compensated by constructing models with a small vertical extent. This paper demonstrates that this leads to entirely boundary-dominated and hence uninformative models. It demonstrates the indispensable requirement to construct models with a large vertical extent to obtain informative models with respect to the model parameters. For this quantitative investigation, global sensitivity studies are essential since they also consider parameter correlations. To compensate for the computationally demanding nature of the analyses, a physics-based machine learning approach is employed, namely the reduced basis method, instead of reducing the physical dimensionality of the model. The reduced basis method yields a significant cost reduction while preserving the physics and a high accuracy, thus providing a more efficient alternative to considering, for instance, a small vertical extent. The reduction of the mathematical instead of physical space leads to less restrictive models and, hence, maintains the model prediction capabilities. The combination of methods is used for a detailed investigation of the influence of model boundary settings in typical regional-scale geothermal simulations and highlights potential problems.

Uncertainty quantification for basin-scale geothermal conduction models

“…A previously performed Sobol sensitivity analysis with the Saltelli sampler and 300,000 forward solves showed that the model is insensitive to eight of the 14 parameters (Fig. S1) 34 . We thus reduce the parameter dimension from 14 parameters to six.…”

“…The highest uncertainties are between 30 and 35 km depth, where no interactions of the boundary conditions are observable. For a detailed investigation of the influence of boundary conditions on a geothermal conduction model, we refer to Degen et al 34 .…”

Addressing challenges in uncertainty quantification: the case of geohazard assessments

“…Options to address the parametrisation challenge also include surrogate models, parameter reduction, and model learning (e.g. Lu and Lermusiaux, 2021;Sun et al, 2021b;Albert et al, 2022;Degen et al, 2022;Liu et al, 2022). Surrogate models are learnt to replace a complicated model with an inexpensive and fast approximation.…”

Addressing challenges in uncertainty quantification. The case of geohazard assessments

“…Options to address the parametrisation challenge also include surrogate models, parameters reduction, and model learning (e.g., Lu and Lermusiaux, 2021;Sun et al, 2021b;Albert, Callies, and von Toussaint, 2022;Degen et al 2022;Liu et al, 2022). Surrogate models are learnt in order to replace a complicated model with an inexpensive and fast approximation.…”

“…Surrogate models are learnt in order to replace a complicated model with an inexpensive and fast approximation. Parameters reduction is achieved based on either principal component analysis or global sensitivity analysis to determine which parameters significantly impact model outputs and are essential to the 160 analysis (Degen et al, 2022;Wagener, Reinecke, and Pianosi, 2022). Remarkably, versions of the model learning option do not need any prior information about model equations Eɱ but require local verification of conservation laws in the data ɗ (Lu and Lermusiaux, 2021).…”