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Uncontrolled heat extraction by multiple interacting borehole heat exchangers (BHEs) in high-density energy-use districts can lead to undesirable thermal conditions in the subsurface which can affect both system performance and regulatory compliance. The difficulty in controlling heat extraction arises in particular from predictive uncertainties, such as when forecasting trends in energy demand or groundwater flow. In this study, a combined simulation-calibration-optimization framework is introduced to consider BHE fields with the presence of a transient groundwater flow regime. In the first part, a semi-analytical modeling technique is proposed based on temporal superpositioning of variable flow conditions. Two synthetic case studies verify its accuracy under different groundwater fluctuation patterns. The mean absolute error of the proposed model in comparison to numerical calculation does not exceed 0.18 K over ten years of operation. In the second part, the model is augmented by a parameter estimation algorithm that is employed for continuous model updating. The benefit of resolving transient flow conditions is demonstrated by using this for monthly optimization of individual BHE heat extraction. The result of dynamic optimization compared to a synthetic case without calibration shows a 10% lower imposed temperature change in the subsurface.
Mohammadi et al. (Mon,) studied this question.