Inverse heat conduction to model and optimise a geothermal field

TL;DR

This paper develops an analytical model for heat conduction in geothermal fields and introduces an optimization method to position heat exchangers effectively, enhancing sustainability and efficiency of geothermal energy systems.

Contribution

It presents a novel analytical approach to model soil heat conduction and an optimization procedure for exchanger placement, improving upon existing numerical methods.

Findings

Analytical model accurately predicts heat transfer in geothermal fields.

Optimization reduces adverse effects among neighboring exchangers.

Numerical experiments validate the effectiveness of the proposed method.

Abstract

The design of heat exchanger fields is a key phase to ensure the long-term sustainability of such renewable energy systems. This task has to be accomplished by modelling the relevant processes in the complex system made up of different exchangers, where the heat transfer must be considered within exchangers and outside exchangers. We propose a mathematical model for the study of the heat conduction into the soil as consequence of the presence of exchangers. Such a problem is formulated and solved with an analytical approach. On the basis of such analytical solution, we propose an optimisation procedure to compute the best position of the exchangers by minimising the adverse effects of neighbouring devices. Some numerical experiments are used to show the effectiveness of the proposed method also by taking into account a reference approximation procedure of the problem based on a finite difference method.