Learning from data - validation and improvement of modeling thermo-osmosis effects in THM simulations based on the Mont Terri DeepBorehole experiment

This contribution presents an improved explanation for the field data from the the Deep Borehole experiment in Mont Terri underground research laboratory (MTDB) presented by Gonçalvès et al. [1]. The formulation of the THM process with thermo-osmosis (TO) is introduced and discussed. Field data and analytical solution are used to validate the implementation of the thermo-hydro-mechanical (THM) model with TO in multiphysical simulator OpenGeoSys Bilke et al. [2]. Furthermore, the improved explanation of the observed data from the MTDB experiment is presented and discussed. The closer match between field data and numerical and analytical solutions was achieved by inclusion of the spatial variability of the geothermal gradient and intrinsic permeability, and applying SciPy’s Dual Annealing optimizer [3]. With those extensions of the model, the observed data (pressure and temperature) is reproduced more closely and uncertainties has been reduced. The results from the original and this studies are compared in Fig. 1.

Figure 1: Comparison of the results from the original study by Gonçalvès et al. [1] and presented by the authors [4] (paper submitted for publication to a journal).

Acknowledgments
This work has been funded by the German Federal Office for the Safety of Nuclear Waste Management (BASE), ThORN project: “Experimental investigations on thermo-osmotic flow in argillaceous materials relevant to deep geological repositories for radioactive waste” (Grant number: 4723F00104).

References
[1] Julio Gonçalvès, Jean-Michel Matray, and Catherine Ji Yu. Assessing relevant transport processes in Opalinus Clay at the Mont Terri rock laboratory using excess-pressure, concentration and temperature profiles. Applied Clay Science, 242:107016, September 2023. ISSN 0169-1317. doi: 10.1016/j.clay.2023.107016.
[2] Lars Bilke, Dmitri Naumov, Wenqing Wang, Thomas Fischer, Feliks K. Kiszkurno, Christoph Lehmann, Jäschke Max, Florian Zill, Jörg Buchwald, Norbert Grunwald, Kristof Kessler, Ludovic Aubry, Maximilian Dörnbrack, Thomas Nagel, Lion Ahrendt, Sonja Kaiser, and Tobias Meisel. OpenGeoSys. Zenodo, January 2025.
[3] Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson, Eric Jones, Robert Kern, Eric Larson, C J Carey, İlhan Polat, Yu Feng, Eric W. Moore, Jake VanderPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Henriksen, E. A. Quintero, Charles R. Harris, Anne M. Archibald, Antônio H. Ribeiro, Fabian Pedregosa, Paul van Mulbregt, and SciPy 1.0 Contributors. SciPy 1.0: Fundamental algorithms for scientific computing in python. Nature Methods, 17:261–272, 2020. doi: 10.1038/s41592-019-0686-2.
[4] Feliks Kuba Kiszkurno, Fabien Magri, and Thomas Nagel. Learning from data - validation and improvement of modeling thermo-osmosis effects in THM simulations based on the Mont Terri Deep Borehole experiment, January 2026.