Bayesian uncertainty quantification in temperature simulation of borehole heat exchanger fields for geothermal energy supply

Accurate temperature prediction is crucial for optimizing the performance of borehole heat exchanger (BHE) fields. This study introduces an efficient Bayesian approach for improving the forecast of temperature changes in the ground caused by the operation of BHEs. The framework addresses the complexities of multi-layer subsurface structures and groundwater flow. By utilizing an affine invariant ensemble sampler, the framework estimates the distribution of key parameters, including heat extraction rate, thermal conductivity, and Darcy velocity. Validation of the proposed methodology is conducted through a synthetic case involving four active and one inactive BHE over five years, using monthly temperature changes around BHEs from a detailed numerical model as a reference. The moving finite line source model with anisotropy is employed as the forward model for efficient temperature approximations. Applying the proposed methodology at a monthly resolution for less than three years reduces uncertainty in long-term predictions by over 90%. Additionally, it enhances the applicability of the employed analytical forward model in real field conditions. Thus, this advancement offers a robust tool for stochastic prediction of thermal behavior and decision-making in BHE systems, particularly in scenarios with complex subsurface conditions and limited prior knowledge.