A fast convolution-based method to simulate time-varying flow rates in closed-loop and standing column well ground heat exchangers

Abstract

The superposition principle is widely used to accelerate the computation of hourly fluid temperatures in ground heat exchangers. This work presents a first attempt at adapting this technique to non-stationary situations of ground-source heat pump operations that involve time-variant parameters, such as flow rates. An advanced response model is first employed to evaluate the outlet temperature signals corresponding to different sets of constant operating conditions. The transitions are then considered by combining the functions linearly and by using a scaled correction function. Eight synthetic validation studies were conducted, representing the dynamic operation of a closed-loop and a standing column well with time-variant circulation, pumping, and discharge rates, and groundwater velocities. It is shown that the developed method reproduces reference numerical results with mean absolute and relative errors that are lower than 0.04°C and 0.68%, respectively, and achieves a 30-day simulation with a 5-min time step in a few hundredths of a second. This represents a reduction of five to seven orders of magnitude in computing times and demonstrates the potential of the proposed method to accelerate the simulation of ground heat exchangers that operate with time-variant flow rates.