Simplified Dynamic Boundary Conditions for Numerical Models of Borehole Heat Exchangers

Abstract

This work describes the development and validation of a computational model for vertical borehole heat exchangers in residential ground-source heat pump energy systems. Due to the size and shape of vertical borehole heat exchangers, their operation thermally impacts a large volume of surrounding soil and thus discretized models have largely been confined to short-term transient simulations, such as the case of a thermal response test. The proposed model employs a computationally efficient physics-based models at variable spatial dimensions which can be used for long-time simulation of the ground heat transfer. The model can generally be considered as a composition of three separate domains: the borehole domain, which combines one-dimensional, three-dimensional and equations-based physics, the near-field soil domain, which resolves three-dimensional transient heat conduction and the far-field soil domain which is modelled as one-dimensional axisymmetric transient heat conduction. The main purpose of this work is to present each component of the model and validate their behaviours and assumptions through a combination of comparison to experimental data, highly cited published works, and well-known analytical models. The complete composite model ignores the three-dimensional effects of fluid heat transfer, and the axial heat transfer in the far-field in order to reduce the computational effort, and the level of uncertainty introduced by each simplification is explored. Finally, to support the composite model, a new method determining the thermal impact of the borehole operation mentioned previously was devised and presented alongside the model development and validations. This method, based on the previously defined thermal impacting radius, improves the consistency and theoretical foundation of the value’s definition based on a system energy balance, rather than local temperature conditions.