Near-instant prediction of short-term transfer functions for closed-loop boreholes in heterogeneous aquifers influenced by groundwater flow using wavelet decomposition and neural networks

Accurate simulation of the heat pump inlet fluid temperature is critical to the design of an optimal, high performance ground source heat pump system. The closed-loop ground heat exchanger must be able to meet the heating and cooling demands while maintaining the inlet temperature within specified design limits over multiple years. This simulation usually relies on the use of a transfer function. Traditional approaches, often based on Eskilson's g-function, typically neglect the short-term effects from borehole thermal capacities, as well as the aquifer's heterogeneity and advection from groundwater flow. Overlooking these physical processes can lead to sub-optimal borefield designs.

This study addresses this situation by presenting a combined model for the near-instant construction of short-term transfer functions at the borehole outlet for a single closed-loop borehole installed in a multi-layered aquifer under groundwater flow. The approach leverages a wavelet decomposition scheme as a pre-processing step to improve the prediction accuracy of the target functions, which are approximated using three different artificial neural networks. Once independently trained, these sub-networks are then combined to streamline the implementation of the model in a source code or a spreadsheet and to reduce computational costs. The database used to train and test the artificial neural networks is derived from a 3D finite element model that provides realistic and accurate simulations of the ground heat exchanger over a 7-day period. For each simulation, the borehole and pipe geometry, the circulation flow rate, the thermal properties of the borehole's components (e.g. pipe, grout, heat carrier fluid), as well as both the thermal and hydraulic properties of the five geological layers are sampled from uniform distributions using Halton set. The database covers a wide range of hydrogeological environments, borehole configurations, and operating conditions.

The combined model shows good agreement with the numerical model-based transfer functions, achieving an average relative root mean square error of 7.03×10^-3 over 4371 independent simulations. Furthermore, prediction times are as low as 0.05 milliseconds, enabling efficient design. This advancement provides a robust and efficient tool for improving the simulation and design of ground source heat pump systems. The combined model can also be used to interpret thermal response tests within a Bayesian framework for any given hydrogeological setting.