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The design of a borehole field should be based on a long-term simulation of its thermal response for the intended energy loads. A well-known method to evaluate the response is based on a pre-calculated dimensionless function, the g -function. When calculating g -functions, there are two commonly used approaches for treating the boundary condition at the borehole wall: a constant heat flux at every instant of time, or a uniform temperature at a constant total heat flow to the borehole field. This paper is focused on a new approach to model the thermal process of borehole fields; in particular with a precise representation of a uniform temperature boundary condition at the borehole wall. The main purpose of this model is to be used as a research tool to either generate g -functions for particular cases or handle situations that cannot be addressed by others methods. First, the almost constant temperature along the borehole heat exchanger in operation requires a boundary condition of essentially isothermal boreholes along the depth. In a common case, the borehole heat exchangers are connected in parallel, thus all boreholes should have the same temperature. Also, the total heat flow to the borehole field should be constant over time. For this purpose, a numerical model in which the boreholes are filled with a hypothetical highly conductive material has been built, reproducing the isothermal condition. By thermally interconnecting the boreholes, the equal temperature condition is satisfied. Finally, the specified total heat flow is fed into one spot at the highly conductive material. The model is validated by generating g -functions of some simple borehole field configurations. The g -functions present, in general, a good agreement with the existing solutions for a similar boundary condition. Moreover, the model is also tested against real experimental data from a 2 × 3 borehole field at an office building. The simulated daily fluid temperatures are compared with measured daily fluid temperatures for the sixth year of operation. The simulated values present, in general, a good agreement with the measured data. The results show that there are no significant differences with regard to the boundary conditions at the borehole wall, which for this specific case is due to the fact that the system is thermally balanced. [ABSTRACT FROM AUTHOR]

In a distributed thermal response test, distributed temperature measurements are taken along a borehole heat exchanger during thermal response tests, allowing the determination of local ground thermal conductivities and borehole thermal resistances. In this article, the first results from six heat injection distributed thermal response tests carried out on a new, thermally insulated leg type, multi-pipe coaxial borehole heat exchanger are presented. The borehole heat exchanger consists of 1 insulated central and 12 peripheral pipes. Temperature measurements are carried out using fiber-optic cables placed inside the borehole heat exchanger pipes. Unique temperature and thermal power profiles along the borehole depth as a function of the flow rate and the total thermal power injected into the borehole are presented. A line source model is used for simulating the borehole heat exchanger thermal response and determining local variations of the ground thermal conductivity and borehole thermal resistance. The flow regime in the peripheral pipes is laminar during all distributed thermal response tests and average thermal resistances remain relatively constant, independently of the volumetric flow rate, being lower than those corresponding to U-pipe borehole heat exchangers. The thermal insulation of the central pipe significantly reduces the thermal shunt to the peripheral pipes even at low volumetric flow rates.[Supplemental Materials are available for this article. Go to the publisher's online edition of HVAC&R Research to view the supplemental file.] [ABSTRACT FROM AUTHOR]

Highlights: [•] Proposed model calculates transient vertical temperature profiles in coaxial borehole heat exchanger. [•] Distributed temperature sensing (DTS) system verifies model in a test borehole during a thermal response test. [•] Model matches both short-time and long-time data in test borehole. [•] Proposed model estimates the borehole thermal resistance taking into account temperature profiles. [•] Proposed model estimates borehole resistance better than conventional methods. [Copyright &y& Elsevier]

Abstract: Ground source heat pump systems are often coupled to the ground by circulating a fluid through vertical Borehole Heat Exchangers (BHEs). The design of a system requires estimates of the ground thermal conductivity and the borehole thermal resistance, which are usually determined by an in situ thermal response test on a completed borehole. The usual test interpretation methods average the inlet and outlet fluid temperatures and use this mean temperature as the average temperature along the borehole length. This assumption is convenient but does not strictly apply. For a coaxial heat exchanger this paper develops an analytical model for the vertical temperature profiles, which can be used instead of the mean temperature approximation to estimate borehole resistance. The model is verified with measured temperatures on a BHE, where an optical technique allows continuous measurements along a coaxial borehole during a distributed thermal response test. A sensitivity study shows that the proposed method corrects errors in the mean temperature approximation, which overestimates the borehole resistance in a coaxial borehole. [Copyright &y& Elsevier]

Abstract: The design of ground source heat pump systems requires values for the ground thermal conductivity and the borehole thermal resistance. In situ thermal response tests (TRT) are often performed on vertical boreholes to determine these parameters. Most TRT analysis methods apply the mean of the inlet and outlet temperatures of the circulating fluid along the entire borehole length. This assumption is convenient but not rigorous. To provide a more general approach, this paper develops an analytical model of the vertical temperature profile in the borehole during the late-time period of the in situ test. The model also includes the vertical temperature profile of the undisturbed ground. The model is verified with distributed temperature measurements along a vertical borehole using fiber optic cables inside a U-tube for the circulating fluid. The borehole thermal resistance is calculated without the need for the mean temperature approximation. In the studied borehole, the mean temperature approximation overestimates the borehole resistance by more than 20%. [Copyright &y& Elsevier]

With bore fields for energy extraction and injection, it is often necessary to predict the temperature response to heat loads for many years ahead. Mathematical methods, both analytical and numerical, with different degrees of sophistication, are employed. Often the g-function concept is used, in which the borehole wall is assumed to have a uniform temperature and the heat injected is constant over time. Due to the unavoidable thermal resistance between the borehole wall and the circulating fluid and with varying heat flux along the boreholes, the concept of uniform borehole wall temperature is violated, which distorts heat flow distribution between boreholes. This aspect has often been disregarded. This paper describes improvements applied to a previous numerical model approach. Improvements aim at taking into account the effect of thermal resistance between the fluid and the borehole wall. The model employs a highly conductive material (HCM) embedded in the boreholes and connected to an HCM bar above the ground surface. The small temperature difference occurring within the HCM allows the ground to naturally control the conditions at the wall of all boreholes and the heat flow distribution to the boreholes. The thermal resistance between the fluid and the borehole wall is taken into account in the model by inserting a thermally resistive layer at the borehole wall. Also, the borehole ends are given a hemispherical shape to reduce the fluctuations in the temperature gradients there. The improvements to the HCM model are reflected in a changed distribution of the heat flow to the different boreholes. Changes increase with the number of boreholes. The improvements to the HCM model are further illustrated by predicting fluid temperatures for measured variable daily loads of two monitored GCHP installations. Predictions deviate from measured values with a mean absolute error within 1.1 and 1.6 K. [ABSTRACT FROM AUTHOR]