Bayesian inference of coupled groundwater flow and radiogenic helium-4 production and transport at the catchment scale.

Hydrogeological numerical models are essential for assessing radioactive waste disposal by understanding groundwater flow systems. These models typically rely on hydraulic head data, with other state variables often underutilized in model inversions. In Flanders' Neogene aquifer, where safety studies for Boom Clay are ongoing, existing models face uncertainties due to dependence on hydraulic heads alone. This study aims to: i) develop a conceptual model of radiogenic Helium-4 (He) production and transport to reproduce observed concentrations; ii) evaluate the usefulness of He observations as an additional state variable for inverse conditioning; and iii) assess how including He affects model calibration and uncertainty reduction. We address these objectives by incorporating radiogenic Helium-4 (He) as an unconventional state variable in model inversion to tackle parameter non-uniqueness. Utilizing a Bayesian approach, we employ two 3D models: a groundwater flow (GWF) model conditioned by hydraulic heads and a coupled GWF model with He production and transport, conditioned by both hydraulic heads and He concentrations. We hypothesize that integrating He will improve model accuracy and reduce uncertainties compared to using hydraulic head data alone. Findings indicate that major He sources include crustal fluxes (~57 %) and in situ Boom Clay production (~25 %). The coupled inference narrows the posterior distributions of parameters, especially for hydraulic conductivity (e.g., Mol, Diest, Berchem formations, and the Rauw Fault) and recharge, showing that He observations effectively reduce uncertainty beyond hydraulic head data. Including He improves model reliability and prediction accuracy, highlighting its importance for refining groundwater flow parameters and derived fluxes. To the best of our knowledge, this study marks the first-ever attempt at harnessing He quantitative insights into flow and transport parameters following a Bayesian approach at a catchment scale, setting a precedent for future research and emphasizing the innovative nature of this work. This study showcases a state-of-the-art approach in hydrogeological modelling, demonstrating the effectiveness of integrating He with hydraulic head observations to produce more reliable model predictions. By reducing uncertainties in crucial groundwater fluxes, this approach offers significant potential for improving geological disposal safety studies. This pioneering work advocates for the continued use of He in hydrogeological modelling, emphasizing its innovative contribution to future research and safety studies. PLAIN LANGUAGE SUMMARY: Understanding how groundwater flows is crucial for safely storing radioactive waste. Traditionally, models used to study groundwater rely mostly on measurements of water pressure, while other valuable data often go unused. In the Neogene aquifer in Flanders, where researchers are studying the Boom Clay formation for potential waste storage, relying only on water pressure has created uncertainties in the models. This study explores a new approach by using a different type of measurement: radiogenic Helium-4 (He). The goals of the study are threefold: first, to build a model that accurately represents how He is produced and moves through the groundwater; second, to test whether including He as an additional measurement improves the model compared to using only water pressure data; and third, to see how using He affects the accuracy and reliability of the model. The study uses two types of models: one that relies only on water pressure data and another that includes both water pressure and He measurements. The idea is that He could provide additional insights and help reduce uncertainties in the model. The findings show that He comes mainly from two sources: the surrounding crust and the Boom Clay itself. Including He in the model helps narrow down uncertainties, particularly regarding how water moves through different layers and how much water is being replenished. This research is the first to use He in this way, using a formal statistical method to improve groundwater models. The results suggest that He is a valuable addition for making more accurate predictions and improving safety assessments for radioactive waste storage.