Inverse heat conduction to model and optimise a geothermal field

Geothermal heat exchanger fields are complex systems that exploit the soil as a heat reservoir for space heating and cooling. They consist of several heat exchangers conveniently arranged in a given soil portion. The design of heat exchanger fields is a key phase to ensure the long-term sustainability of such renewable energy systems. This task requires modelling the relevant processes in the system, i.e., the heat transfer within and outside the exchangers. We propose a mathematical model for the study of the heat conduction into the soil that considers the presence of the exchangers. This problem is formulated and solved with an analytical approach. Some numerical experiments are used to show the effectiveness of the proposed method through a comparison with a reference approximation procedure, based on a finite difference method. Moreover, the obtained analytical solution is used in an optimisation procedure to compute the best position of the exchangers by minimising the adverse effect of neighbouring devices. The obtained results are promising and show that the proposed procedure can be exploited as an effective tool in the design of geothermal systems.