Analysis of short-to-long term heat flow in GSHP systems based on heat pump power

This paper presents a semi-analytical model based on the spectral element method for three-dimensional, short-to-long term heat flow in multiple borehole, multilayer ground source heat pump systems. The model is distinguished by its computational technique for expressing the input signal at the boundary of the borehole heat exchanger, giving rise to two important engineering features. First, the calculation can be conducted from seconds to years in a single run. This is achieved by discretizing the input signal at the inlet boundary of the borehole heat exchanger using a tailored fast Fourier transform with multiple time-stepping algorithm. Second, the calculation can be conducted using a Neumann boundary condition, instead of the commonly utilized Dirichlet boundary condition. This is achieved by mathematically relating the heat pump power to the heat flux at the inlet of the borehole heat exchanger, allowing direct use of the heat pump power signal as input instead of the inlet temperature. These features make the model computationally efficient that can readily be utilized for system design and included in inverse calculations. The two features are discussed in detail, verified against experimental measurements, and their functionality is highlighted by numerical examples.