Modellazione su modello fisico dello scambio di energia geotermica a bassa entalpia: analisi di dati sperimentali

The aim of this thesis work is to present an experimental apparatus designed to study the energy exchange that occurs between a geothermal probe and the surrounding environment, under low enthalpy conditions. The physical model in question simulates the behavior of a probe inserted inside a material, which can be granular but also rocky, present in nature. The experimental apparatus has a volume of about 1m3 and is crossed by a thermal probe made of copper; the thermal probe is served by a closed hydraulic circuit. The water flow rate, which passes through the thermal probe, is set as well as the temperature of the fluid. In the granular material (Risetta del Brenta) that fills the experimental apparatus, 24 high precision temperature probes are opportunely distributed. The experimental apparatus can be saturated with water and it is possible to realize a filtration motion by using a second hydraulic circuit. In the present work, a water-free configuration is considered. The first part of the paper is aimed to a detailed description of the physical model and the physical principles governing the heat transfer within it. Subsequently, an analysis of the behavior of the physical model with respect to the ideal case is made highlighting its limitations. The focal point of the paper is the solution of the heat equation in non-stationary conditions in two different configurations: for the flat wall an analytical solution was found, for the case of the hollow cylinder, where this was not possible due to mathematical limitations, a numerical solution had to be used. The validity of the hypotheses and solutions that are proposed is further strengthened by comparing the data obtained through the numerical model with those obtained through the mathematical model. After verifying the truthfulness of the numerical solution, the model is used to estimate the thermal diffusivity of the Brenta Risetta in experimental configuration and, finally, the thermal conductivity coefficient, λ, of experimental material.