Surrogate-Model-Based Calibration of Effective Transport Parameters from Push-Pull Tests in the Horonobe Aquifer (Japan)

Abstract

Aquifer characterization is essential for optimizing Aquifer Thermal Energy Storage (ATES) systems. Single well tests, also known as push-pull tests, are a common method to identify effective solute and heat transport parameters of the aquifer, which are crucial for the design and assurance of long-term performance of ATES systems. Tracer breakthrough curves from push-pull tests are commonly used to calibrate analytical or numerical models of heat and solute transport in order to infer effective transport parameters like dispersivity of heat and solutes, retardation factors, and porosity. The main bottleneck of such multiparametric calibration is the non-uniqueness of the inverse problem solution which requires ensemble-based optimization to address the parametric uncertainty. In addition, the field measurements can only be performed up to a certain confidence as well, which introduces additional uncertainty to the calibration results. To account for both sources of uncertainty while targeting computationally affordable simulation, we have developed a surrogate model-based optimization framework for stochastic parameter optimisation. The surrogate model uses Gaussian process regression (GPR) to train and predict the objective function based on up to six aquifer and tracer properties. For training and fast model evaluation, we implemented a stable 1D radial finite difference representation of the advection-dispersion equation for sorbing compounds including measured input time-series as transient boundary condition and wellbore storage to accurately model push-pull tests. The surrogate model is used to calibrate this model and to propose plausible parameter combinations. The optimisation framework was applied to push-pull experiments using uranine, iodide, lithium, and heat as tracers in a sandy aquifer in Horonobe (Hokkaido, Japan). The samples drawn from the posterior distribution resulting from the GPR-based optimisation show an overall good fit to the field observations. Based on the posterior parameter distribution, it was possible to shrink the uncertainty intervals of the solute and heat dispersivity and porosity. The outcome suggests low sensitivity to the solute retardation factors. However, the study also reveals that slight sorption may be acting in the Horonobe aquifer for some of the solute tracers commonly assumed to be conservative. Moreover, the study shows that exact porosity measurements may reveal the presence of sorption and thus improve the understanding of the tracers’ behaviour. We demonstrate the benefits of using multiple tracers and high-resolution measurements to improve calibration accuracy under measurement uncertainty. The demonstrated approach offers a computationally efficient framework for addressing parametric uncertainty in push-pull test analysis, improving the design and optimization of ATES systems.

Keywords: ATES, Push-Pull test, Simulation-based inference, Modelling, Solute and heat transport