Modeling and analyses of thermal response tests in real and reduced-scale experiments for geothermal applications involving deep boreholes

This Ph.D. dissertation is aimed at developing models and defining innovative experimental strategies for performing and analyzing Thermal Response Tests (TRTs) for Ground Coupled Heat Pump (GCHP) applications. Three finite difference numerical models related to coaxial, single and double U Borehole Heat Exchangers (BHEs) have been developed starting from literature contributions and coupled with the Fast Fourier Transform (FFT) spectral method. The models have been implemented in three in-house Fortran90 codes that have been optimized to cope with variable longitudinal and radial mesh distribution for simulating the BHE configurations at given geothermal gradients, resembling both standard conditions and geothermal anomalies. The models have been extensively validated through the comparison of the numerical results with experimental measurements. Different ground properties and geothermal gradients along the ground depth can be handled by the models and set as initial and boundary conditions of the problem. The FFT method has been implemented in a dedicated Fortran90 code to exploit the advantage of handling different boundary conditions in terms of the heat transfer rate injected or extracted in a TRT without the need to perform the numerical simulation from scratch. The spectral analysis related to the FFT method has been also useful to highlight the importance of the numerical (that is also real) effect related to the geothermal gradient on simulated and real TRTs. The present Ph.D. study is aimed at the analysis of the BHE behavior in the early period, say for Fourier numbers typical of TRT measurements. The numerical results are addressed to the comprehension of the applicability of standard TRT analysis methods (essentially based on the Infinite Line Source model, ILS) when applied to shallow and deep BHEs (DBHEs) that may involve thermal conditions of "crossing temperatures" between ground and heat carrier fluid. The study has been carried out for single and multiple ground layers of equal thickness with different thermal conductivities along the depth. The heat transfer rate per unit length perfectly uniform with depth is the main hypothesis on which the ILS model is essentially based. On the other hand, the unavoidable variation of the distribution of the heat transfer rate per unit length along the borehole depth violates the assumption of uniform temperature at the borehole wall at each time. The developed models described in the present Ph.D. thesis take into account this aspect providing simulations closer to reality. Therefore these models and related simulation results can serve as useful numerical references for other models and approaches. The present Ph.D. study demonstrates also that the thermal conditions of "crossing temperatures" between ground and heat carrier fluid in BHE (especially for DBHE) are related to the “natural” heat rate made available by the geothermal gradient that in some cases can override the external heat input rate injected (or extracted) by the TRT machine. This affects the ground thermal conductivity estimations based on standard TRT methods. This effect is incorporated into the qratio parameter introduced by the present Ph.D. study and a specific dimensionless g-transfer function called g0. Both qratio and the g0 function incorporate the geothermal gradient. The qratio is expected to be relevant to future TRT guidelines at national and international levels. Error analyses on the BHE and ground properties estimations from the ILS model are reported in the present thesis. Besides the numerical work, the present Ph.D. thesis is aimed to present the experimental setup related to a suitable reduced-scale prototype of the real BHE and the surrounding ground for innovative TRT experiments. The scaled ground volume is realized with a slate block. The scaled heat exchanger, inserted into the slate block, is equipped with a central electrical heater along its entire depth and with temperature sensors at different radial distances and depths for the Electric Depth Distributed Thermal Response Test, EDDTRT. The measurements collected during the Ph.D. work highlight the possibility of performing reliable TRT experiments and estimating the grout/ground thermal conductivity by exploiting a central electric heater and cheap digital one-wire sensors distributed along the depth instead of the expensive optical fibers. It has to be specified that for the reduced scale experiment the digital one-wire sensors have been necessarily replaced by thermocouples. Measurement error analyses are reported in the thesis. The all-in-one BHE equipped with the central electrical heater and with temperature sensors for the EDDTRT assures continuous BHE performance monitoring, test for correct grouting, and test for aquifer presence. A Geothermal Heat Pump Portal and Online Designer for Ground Heat Exchanger Fields has been realized during the Ph.D. study (see https://en.geosensingdesign.org/). The present website offers the first worldwide ever (and completely Free) web calculation tool for the design of BHE fields based on a modified version of the Ashrae Method, also employed in the corresponding UNI Italian standard.