Fast fluid and ground temperature computation for geothermal ground-loop heat exchanger systems

Heat pumps (HPs) coupled to ground-loop heat exchangers (GLHEs) have become increasingly popular for heating and cooling purposes in the context of growing energy costs. Precise design of GLHEs requires the computation of hourly fluid and ground temperatures, especially when the geothermal system is coupled to another system (e.g. boiler, cooling tower). However, because of the computational burden, hourly computation is often simplified in actual designs by rules of thumb or approximations that can cause over- or under-design of the GLHE system. The hourly temperature computation can be seen as a convolution in the time domain that is most efficiently evaluated by fast Fourier transform (FFT). An additional substantial reduction in computing time is obtained by subsampling the analytical function at a few selected times according to a geometric sequence and then using a good quality interpolant such as the cubic spline. This combined “FFT-S approach” enables one to obtain a 30-year hourly simulation in less than a second on a standard laptop computer, even for the computationally intensive finite line-source model. This reduction of one to two orders of magnitude in computing time compared to time-domain approaches with load aggregation should help promote the use of hourly temperature simulation for GLHE design purposes.