Mathematical optimization of borehole heat exchanger fields under variable conditions

Abstract

Borehole heat exchangers (BHE) are often applied in multiple BHE fields. In current planning practice, interaction between adjacent BHEs is rarely considered and all BHEs are operated in the same mode. This means, potential adverse effects from superimposed cold or heat plumes, which simultaneously evolve around individual neighbouring BHEs, are neglected. Long-term heat extraction over decades, however, may lead to significant local cooling, especially in the interior of the field. As a consequence, the performance of the complete ground source heat pump (GSHP) system is attenuated, and ground temperatures below regulation thresholds may develop. In our work, we employ mathematical optimization techniques to strategically operate and arrange BHEs in such fields. Linear programming and an evolutionary algorithm are applied in combination with analytical equations to solve realistic problems. The presented methodology is flexible, robust and it can be applied to various conditions. The two scenarios studied in this paper represent conditions with negligible and significant groundwater flow. We inspect a field with 36 BHEs, which has a seasonally variable heating energy demand. It is demonstrated, by taking the maximum temperature decline in the ground as objective, that the BHE field performance can be improved both by case-specific ideal arrangement and time-dependently regulated individual BHE operation. It is found that instead of standard lattice arrangements, optimized geometries are favourable, with BHEs concentrated along the fringe of a field. Apparently, this enhances lateral conductive heat provision into the field. Groundwater flow means additional energy provision by advection towards the field.