An Analytical Method to Calculate Borehole Fluid Temperatures for Time-scales from Minutes to Decades

Knowledge of borehole exit fluid temperature is required to optimize the design and performance of ground source heat pump systems. The borehole exit fluid temperature depends upon the prescribed heat injection and extraction rates. This paper presents a method to determine the fluid temperature of a single or a multiple borehole heat exchanger for any prescribed heat injection or extraction rate. The fluid temperature, from minutes to decades, is determined using step response functions. An analytical radial solution is used for shorter times. A finite line-source solution is used for longer times. The line-source response function has been reduced to one integral only. The derivative, the weighting function, is given by an explicit formula both for single boreholes and any configuration of vertical boreholes.