Mathematical models for the use of low and medium temperature geothermal energy

This thesis looks at the geothermal energy, that is, energy emitted continuously in the form of heat from our planet, that from the deepest areas propagates towards the surface. The research activities have been carried out for evaluating different aspects related to geothermal energy and more specifically the way in which this energy can be extracted. The present work has tried to deal with all the different levels of temperature in which the geothermal energy is classified, i.e. low temperature, medium temperature and high temperature, as hereafter described more in detail. Geothermal Energy low temperature: this energy is transferred by means of ground heat exchangers coupled with a heat pump. In this case usually the heat transfer fluid can be water or a mixture containing water and an antifreeze fluid. In the frame of this technology first the characteristics of a GRT (ground response test) has been tested, in order to check the accuracy of the method to evaluate the average temperature of the ground, as well as to determine the thermal conductivity of the soil and the overall coefficient of linear heat exchange between the transfer fluid and the soil. The accuracy of the GRT has been evaluated for different sizes of the grout (an usual ground heat exchanger and a pile) as well as for different velocities of the aquifer. The simulations have been carried out by means of a Finite Element Method (FEM) software. Then the FEM has been used for evaluating the energy and structural analysis on piles foundations when they are used as ground heat exchangers. The work has shown the combined effect of structural loads in heating and cooling periods. The results are in agreement to the theory as well as to results carried out by measurements which have been found in literature. Finally a study for comparing different heat pumps and different fluids in the ground heat exchangers has been carried out in mild climates. The work shows the benefits of using pure water as heat transfer fluid in almost all conditions, since in mild climates the temperature of the ground is around 14°C and usually heat pumps are used for both heating and cooling, thus allowing the ground to be regenerated over one year. The use of flooded evaporators in the heat pumps will allow the ground heat pumps to be more attractive in the next future. Geothermal Energy medium temperature: in this case the ATES (Aquifer Thermal Energy Storage) has been investigated. ATES is a particular type of thermal storage which uses water from the subsoil where the groundwater can vary between 15 °C and 130 °C. The extraction and reinjection wells should be sufficiently distant in order to avoid short-circuits. This technology could be used also for low temperature aquifers; in this case the water of the aquifer is used for cooling the condenser during summertime, while it is cooled down in winter time to transfer heat to the evaporator. The wells are used alternatively in order to accumulate a cold storage during winter time and a warm storage during summer time. The work of the present thesis has focused on the thermal influence of the reinjection well on the undisturbed temperature conditions along the aquifer, depending on the thickness of the aquifer. Results of a FEM model have been compared to the analytical solution of various authors (Carslaw and Jaeger, Lauwerier, Ghassemi). The goal is to evaluate the distance between the two wells in order to prevent thermal interference, as a function of the thickness of the aquifer. Geothermal Energy high temperature: it allows to extract dry and superheated steam without liquid phase (in this case they are called "dominant steam systems") or liquid water mixed with steam (in this case they are called "water-dominated systems"). The usual depth of these systems is between 3 km and 15 km in correspondence of magmatic intrusions. For these systems the thesis has the aim to study the heat exchange between the rock and hot water, considering the variation of the outlet temperature of the water as a function of time. These studies were developed at first considering a single fracture in the rock, then we moving to a more realistic model consisting in a multi rock-fracture. The model proposed in literature based on analytical methods have been compared with a FEM mathematical model. The models have been then applied to a site in the Philippines where experimental data were availabl