Analytical solution of discontinuous heat extraction for sustainability and recovery aspects of borehole heat exchangers

• We develop an analytical solution for temperature distribution around borehole heat exchangers.
• Single- and multi-borehole heat exchanger system have been considered.
• Discontinuous heat extraction is addressed.
• We study the impact of 30 years of heat extraction on the recovery and sustainability aspects.
• This analytical solution provides an efficient tool for heat extraction optimization.

Existing analytical solutions for thermal analysis of ground source heat pump (GSHP) systems evaluate temperature change in the carrier-fluid and the surrounding ground in the production period of a single borehole heat exchanger (BHE) only if a continuous heat load is assigned. In the present study, we modified the Green's function, which is the solution of heat conduction/advection/dispersion equation in porous media, for discontinuous heat extraction by analytically convoluting rectangular function or pulses in time domain both for single and multi-BHEs field. The adapted analytical models for discontinuous heat extraction are verified with numerical finite element code. The comparison results agree well with numerical results both for conduction and advection dominated heat transfer systems, and analytical solutions provide significantly shorter runtime compared to numerical simulations (approx. 1500 times shorter). Furthermore, we investigated the sustainability and recovery aspects of GSHP systems by using proposed analytical models under different hydro-geological conditions. According to the engineering guideline VDI 4640, a linear relationship between thermal conductivity of the ground and the sustainable heat extraction rate is demonstrated for multi-BHEs.