Heat transfer in borehole heat exchangers and the contribution of groundwater flow

The exploitation of geothermal heat by ground source heat pumps is presently growing throughout Europe and the world. In Italy, at the end of 2010, borehole heat exchangers covered most of the 30% of the total energy used for space conditioning, showing an increase of 50%compared to 2005. The forecasts for 2015 suggest a further increase in the direct uses of the geothermal heat exceeding 50% compared to 2010 and a corresponding increase in the geothermal energy consumption. The possibility to design plants with higher ef?ciency and lower costs of installation and operation is required, to support the growth of the ground source heat pump systems and the consequent diffusion of the exploitation of the geothermal resources. Research and better knowledge of the processes involved in the heat transfer between the borehole heat exchanger and the surrounding ground is crucial to predict the behavior of the plant-geothermal source interaction in any possible operational condition. The knowledge of the hydrogeological characteristics of the speci?c site where the plant has to be installed is also essential to prevent over- or under-sizing of the heat exchanger(s) due to a rough design. Over the years, several analytical solutions have been proposed to calculate the temperature distribution around a borehole heat exchanger during operation. The in?nite line source analytical model considers an in?nite linear heat source which exchanges heat with the surrounding ground by conduction only. Other models, based on the in?nite linear heat source, have been later developed, considering also the contribution to the conductive heat transfer due to groundwater ?ow. The presence of ?owing water around a borehole heat exchanger implies forced convection, resulting in an increased ef?ciency of the heat transfer between the ground and the borehole heat exchanger. Studying this process may suggest new ways to improve the ef?ciency and to reduce the cost of ground source heat pump systems. In this thesis, the contribution of groundwater ?ow in the heat transfer process between borehole heat exchangers and surrounding ground has been investigated, in order to increase the theoretical knowledge as well as to improve the existing design tools. Two-dimensional models have been considered, taking into account the actual cylindrical geometry of the borehole. The groundwater ?ow has been modeled as steady, horizontal and with variable ?ow rates, in order to encompass most of the real ground source heat pump applications. Gravitational effects, i.e. the effects of a possible natural convection, have been neglected. The results suggest that in the considered range of Darcy number, the calculation of the heat transfer ef?ciency is not affected if Darcynian model is used to describe the velocity ?eld, although the viscous effects, and consequently the formation of the hydraulic boundary layer, are neglected. Calculations made using numerical simulations are compared with an analytical solution which takes into account forced convection due to groundwater ?ow and based on the linear heat source model. The regions of space and time where this analytical solution is affected by the effects of the line source assumption, in both cases of single- and multiple-borehole(s) systems, have been de?ned. The potential of the thermal response test analysis as a tool to predict the spacing between boreholes when groundwater ?ow occurs has been investigated, de?ning and studying the In?uence Length as function of groundwater ?ow rate. The results suggest that even relatively low ?ow rates allow to reduce signi?cantly the spacing between boreholes in the perpendicular direction with respect to groundwater ?ow. The distance from the borehole where the temperature disturbance becomes not-signi?cant (In?uence Length) is roughly predictable by thermal response test analysis. The study of the In?uence Length may be a useful tool in the design of dissipative multiple-boreholes systems, as well as in areas with a high density of single-borehole plants, to reduce the spacing avoiding thermal interferences. Moreover, an expeditious, graphical method to estimate the hydraulic conductivity of the ground by thermal response test analysis has been proposed. An example of application of the methodology is presented, taking into account experimental data as well as plausible hydrological and petrological assumptions when the data are unavailable. The obtained result is in agreement with the hydraulic conductivity range reported in literature for the type of substrate considered in the example. In order to verify this method, further inv1estigations and developments are required. In fact, the graphs used in the procedure presented in this work are referred to speci?c borehole conditions (borehole ?lled by groundwater) and are based on two-dimensional models (i.e. end-effects and natural convection are neglected). Besides, the assumptions required to compensate the unavailable data imply that the method cannot be considered veri?ed. Finally, further studies are suggested in order to improve and develop the proposed methods.