Application of matched asymptotic expansion techniques to the analysis of geothermal heat exchangers

Most theoretical models for the thermal response of geothermal heat exchangers assume the mean azimuthal borehole wall temperature to be uniform along the boreholes. This simplifying assumption, closely related to the g-functions introduced by Eskilson in 1987, has dominated the research field for the past 30 years, allowing the analysis of large geothermal heat exchangers in reasonable amounts of time. The assumption, however, is not physically correct, which hinders the attainable accuracy. By using matched asymptotic expansion techniques, analytical models for the thermal response of geothermal heat exchangers are derived, which do not require the aforementioned simplification. The resulting expressions, applicable to geothermal heat exchangers with irregularly placed heterogeneous boreholes, show accuracy and flexibility levels comparable to SBM, but with a computational cost in line with the use of g-functions

Comparison of two different models for pile thermal response test interpretation

Thermal response tests (TRTs) are regularly used to characterise the thermal resistance of borehole heat exchangers and to assess the thermal conductivity of the surrounding ground. It is becoming common to apply the same in situ testing technique to pile heat exchangers, despite international guidance suggesting that TRTs should be limited to hole diameters of 152 mm (6 in.). This size restriction arises from the increased thermal inertia of larger diameter heat exchangers, which invalidates the assumption of a steady state within the concrete needed to interpret the test data by traditional line source analysis techniques. However, new methods of analysis for pile heat exchangers have recently been developed that take account of the transient behaviour of the pile concrete. This paper applies these new methods to data from a multi-stage TRT conducted on a small diameter test pile. The thermal conductivity and thermal resistance determined using this method are then compared with those from traditional analytical approaches based on a line source analysis. Differences between the approaches are discussed, along with the observation that the thermal resistance may not be constant over the different test stages

Characterisation of ground thermal and thermo-mechanical behaviour for shallow geothermal energy applications

Increasing use of the ground as a thermal reservoir is expected in the near future. Shallow geothermal energy (SGE) systems have proved to be sustainable alternative solutions for buildings and infrastructure conditioning in many areas across the globe in the past decades. Recently novel solutions, including energy geostructures, where SGE systems are coupled with foundation heat exchangers, have also been developed. The performance of these systems is dependent on a series of factors, among which the thermal properties of the soil play one of major roles. The purpose of this paper is to present, in an integrated manner, the main methods and procedures to assess ground thermal properties for SGE systems and to carry out a critical review of the methods. In particular, laboratory testing through either steady-state or transient methods are discussed and a new synthesis comparing results for different techniques is presented. In-situ testing including all variations of the thermal response test is presented in detail, including a first comparison between new and traditional approaches. The issue of different scales between laboratory and in-situ measurements is then analysed in detail. Finally, thermo-hydro-mechanical behaviour of soil is introduced and discussed. These coupled processes are important for confirming the structural integrity of energy geostructures, but routine methods for parameter determination are still lacking

Geothermal Systems Performance and Environmental Impacts

The use of fossil fuels for heating and cooling purposes is plagued by problems including environmental impacts, unsustainable production, and increased greenhouse gas production. This had led to a worldwide interest in developing sustainable sources of energy. One such energy is ground source heat which is the ubiquitous low-enthalpy heat found in the shallow subsurface. Vertical ground source heat pumps (GSHPs) can be used to extract or inject subsurface heat by installing borehole that circulate an antifreeze-based carrier fluid which is cooled or heated through the subsurface. Although GSHPs have many advantages, they might develop thermal subsurface plumes, which can affect the efficiency of the system and other subsurface infrastructures. In the present research, the effect of a multi-borehole vertical GSHP system located in various locations in Canada was examined. To do so, a three-dimensional model was developed in FEFLOW that simulated a hypothetical GSHP system in different Canadian climates. Consequently, the resulting thermal plumes were studied and a sensitivity analysis was conducted to determine the effect of different groundwater and soil parameters on the development and movement of thermal plumes

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

The Effect of Geothermal Heat Pumps on Subsurface Flow and Contaminant Transport

Geothermal or ground source heat pumps (GSHPs) are among the growing renewable energy technologies used for heating and cooling of buildings. However, little work has been done to investigate their geo-environmental effects within the subsurface. This research uses FEFLOW software, to simulate heat and mass transport for a vertical closed-loop GSHP system. Steady and transient flow and heat transport results for a multiple borehole system are presented which indicate long-term effects on ground temperature. Moreover, the impact of heat exchanged with the subsurface on contaminant transport and biodegradation processes is studied to evaluate the possibility of utilizing this heat as a remediation strategy. The results reveal that temperature changes caused by GSHP operation can significantly enhance biodegradation of hydrocarbon contaminants. For instance, elevated subsurface temperature resulted in 96% reduction in benzene concentration, from 0.306 to 0.011 mg.L-1, after one year of GSHP operation for an office building in Toronto

Investigation on the effects of different time resolutions in the design and simulation of BHE fields

The correct design of a field of Borehole Heat Exch angers (BHE) requires the knowledge of ground thermal properties, heat pump performance and building heating and cooling demand. The sequence o f heat pulses from (to) the ground by the heat pump can be described according to different time steps , from hours to months and even years. The monthly time step approach is often the preferred design choice which involves recursive calculations (temporal superposition techniques) and the availability of precalculated temperature response factors (or g-functions) for given BHE field geometries. Such a complex computing task is usually performed thanks to commercial codes in order to fulfil a carrier fluid temperature at the end of a given time horizon, typically 10 or 25 years. In this paper the monthly design approach (EED code and TecGeo proprietary code) is compared with the three thermal pulse approach (modified ASHRAE Method Tp8) and it is demonstrated that for a representative series of case studies the three pulse calculation, easy to be performed at engineering level, is able to provide the correct BHE field overall length with 8% accuracy with respect to the reference monthly calculations

Energy and Geotechnical Behaviour of Energy Piles

Energy piles are heat capacity systems increasingly exploited for providing both energy supply and structural support to building and infrastructures. The energy and geotechnical performance of such foundations, which is governed by their thermo-mechanical behaviour, is currently not fully understood especially considering different technological solutions for the heat exchange operation. This thesis summarises a series of numerical analyses performed with respect to a real-scale energy foundation located under the Swiss Tech Convention Centre of the Swiss Federal Institute of Technology in Lausanne (EPFL), aimed to investigate the thermo-mechanical transient response of energy piles for example for different pipes layouts, aspect ratio of the foundation, magnitude of the fluid flow rate circulating in the pipes and fluid mixture composition. The study outlines the impact that the different technological solutions have on the energy and geotechnical performance of energy piles

Numerical modelling of geothermal borehole heat exchanger systems

The large proportion of energy used in the built environment has made improving energy efficiency in buildings, in particular their heating, ventilation, and air conditioning (HVAC) systems, a policy objective for reducing energy consumption and CO2 emissions nationally and internationally. Ground source heat pump (GSHP) systems, due to their high coefficient of performance (COP) and low CO2 emissions are consequently, receiving increasing attention. This work is concerned with the modelling of borehole heat exchangers (BHEs), the commonest form of ground heat exchangers found in GSHP systems. Their careful design is critical to both the short timescale and long timescale performance of geothermal heat pump systems. Unlike conventional components of HVAC systems, BHEs cannot be designed on the basis of peak load data but require 3 application of dynamic thermal models that are able to take account of the heat transfer inside the borehole as well as the surrounding ground. The finite volume method has been applied to develop a dynamic three-dimensional (3D) model for a single BHE and BHE arrays. The multi-block boundary fitted structured mesh used in this model allows the complex geometries around the pipes in BHEs and the surrounding ground around the borehole to be represented exactly. The transport of the fluid circulating along the pipe loop has been simulated explicitly in this model. The ground underneath the borehole has also been represented in this model. Validation of the 3D model has been carried out by reference to analytical models of borehole thermal resistance and fluid transport in pipes, as well as experimental data. In this work, the 3D numerical model has been applied to investigate the three-dimensional characteristics of heat transfer in and around a BHE at both short and long timescales. By implementing a two-dimensional (2D) model using the same numerical method and comparing the simulation results from the 3D and 2D models, the most significant three-dimensional effects have been identified and quantified. The findings have highlighted some of the limitations of 2D models, and based on the findings, methods to improve the accuracy of a 2D model have been suggested and validated. Furthermore, the 3D and 2D finite volume models have been applied to simulate an integrated GSHP system and their effects on overall system performance predictions have been investigated. The 3D numerical model has also been applied to examine thermal interactions within BHE arrays and to evaluate the assumptions of the line source model and their implications in the analysis of thermal response test data