Elsevier

Energy and Buildings

Volume 116, 15 March 2016, Pages 593-601
Energy and Buildings

Simplified heat transfer analysis method for large-scale boreholes ground heat exchangers

https://doi.org/10.1016/j.enbuild.2016.02.001Get rights and content

Highlights

  • A method to simplify analysis of heat transfer of large scale boreholes heat exchangers is proposed.

  • Representative boreholes matrix can be used to replace the original large-scale boreholes for heat transfer analysis.

  • The representative boreholes matrix can be determined by thermal analysis of a single borehole.

Abstract

A simplified heat transfer method to analyze the thermal performance of large-scale boreholes ground heat exchangers (GHE) has been proposed considering the geometric symmetry of borehole layout. Taking the ground heat exchanger with matrix layout of vertical boreholes as the example, the ground temperature distribution is analyzed under the conditions of no groundwater advection by the proposed simplified method. Based on the simulation results, a representative boreholes matrix can be proposed to replace the original large-scale ground heat exchanger for heat transfer analysis. Meanwhile, the results show that the representative boreholes matrix can be determined by the thermal influence radius of a single borehole by assuming all the boreholes have the same thermal loads and also in the same geological conditions, geometry parameters and operating conditions. It is indicated that the thermal influence radius of a single borehole can be obtained according to the allowed error range of the ground temperature responses, which can correspondingly determine the number of the representative boreholes matrix.

Introduction

The ground-coupled source heat pump (GCHP) systems using the shallow underground geothermal energy to provide space heating and cooling have been widely applied in commercial and residential buildings in China, among which the most widely used applications are the GCHP systems with vertical boreholes. The heat transfer process of the ground heat exchanger (GHE) with vertical boreholes is relatively complex especially for the system with a great number of boreholes and long-term operation because of the inevitable thermal interference phenomenon among adjacent boreholes [1], [2]. The most currently utilized methods of the GHE are based on the heat transfer model of a single borehole in surrounding ground under the assumption of the constant thermal properties of the ground. Then the superposition principle is employed to analyze the ground temperature responses caused by all the boreholes constituting the GHE. The common heat transfer models for a single borehole include analytical models such as the line heat source model [3], [4], cylindrical heat source model[5] and numerical models[6], [7], [8]. It is noticed that some large-scale GHE systems usually include hundreds or even thousands of boreholes, and the thermal analyses of such systems may be computationally inefficient due to the large number of boreholes involved. Therefore, the conventional models based on the single borehole model and the superposition principle are inconvenient for the design of the large-scale GHE systems in engineering applications.

In order to reduce the tedious computation workload, some simplified calculation methods have been proposed in previous studies. Xu [9] and Li [10] made a simplified assumption by taking the heat released by boreholes as the inner heat source of the buried pipe area. This method may reduce the complexity of calculation and save substantial computation time, yet it might result in less accurate temperature responses around the boreholes because the heat released intensively from the buried pipes was assumed to be a kind of uniform inner heat source in the whole buried pipe area. Zhang [11] conducted a study on the underground temperature variations of two different borehole configurations (i.e., 3 × 3 and 4 × 4 matrix layouts) with the operation time of dozens of days. The author drew a conclusion that a representative boreholes matrix of 3 × 3 can be employed to substitute the large-scale borehole GHEs according to the simulation results. Obviously, this method can definitely reduce the calculation work. However, the thermal influence radius of each borehole will exceed the distance of three rows of boreholes after a long-term operation. In addition it is difficult to employ a uniform borehole layout of 3 × 3 to replace different large-scale borehole GHEs under different geological, thermal loads and operation conditions.

It can be found from the literature review that a few studies have been conducted on how to simplify the heat transfer analysis of the large-scale borehole GHEs. However, currently, there is a lack of a convenient and efficient method for the heat transfer analysis of large-scale borehole GHEs. In view of this, the objective of this work is to find a new simplified heat transfer method which can not only ensure accuracy enough for engineering applications but also reduce the computational effort effectively.

Section snippets

The simplified calculation method

According to the basic principle of heat transfer, the plane of symmetry in a symmetric temperature field ought to be adiabatic, which means there is no heat flux through the plane. In this case, only half of the heat transfer region rather than the whole region needed to be analyzed because of the symmetric temperature distribution segmented by the adiabatic surface. It is clear that there may be some symmetry planes in the large-scale borehole region. The whole buried area can be divided into

Results and discussion

It is well known that the thermal conductivity and the ratio of the annual heating load to cooling load of the ground are the most critical parameters which affect the thermal influence radius of the boreholes and further may affect the results of the simplifying strategy. Thus following discussion mainly focuses on the influence of the two factors. Three case studies with different ground thermal conductivity (1.2, 1.6 and 2.0 W(m K)−1) are involved in this section. For each case study, both the

The heat transfer analysis of a single borehole

The above method to obtain a representative boreholes matrix of a GHE is based on the condition that all the boreholes of the GHE have been calculated. However, this is impracticable for engineering application because simplification would be unnecessary if the calculation on the whole GHE had been finished. As well known, the temperature change caused by a borehole will decline with the distance away from the borehole. This means even in a large scale GHE, for a given borehole, only the

Conclusions

The ground temperature distribution around some boreholes of some GHEs, especially large-scale GHEs, has very similar periodic variation even after the whole life operation. Thus, the heat transfer analysis of the boreholes with almost the same temperature distribution can be substitute by that of one or several boreholes. In view of this and the geometric symmetry of the GHEs, this paper has used representative GHEs to replace the original GHEs for thermal analysis, and which can significantly

Acknowledgments

This work is supported by the Natural Science Foundation of China (NSFC) No. 51176104.

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