Heat transfer analysis of ground heat exchangers with inclined boreholes

doi:10.1016/j.applthermaleng.2005.10.034

Applied Thermal Engineering

Volume 26, Issues 11–12, August 2006, Pages 1169-1175

https://doi.org/10.1016/j.applthermaleng.2005.10.034 Get rights and content

Abstract

Consisting of closed-loop of pipes buried in boreholes, ground heat exchangers (GHEs) are devised for extraction or injection of thermal energy from/into the ground. Evolved from the vertical borehole systems, the configuration of inclined boreholes is considered in order to reduce the land plots required to install the GHEs in densely populated areas. A transient three-dimensional heat conduction model has been established and solved analytically to describe the temperature response in the ground caused by a single inclined line source. Heat transfer in the GHEs with multiple boreholes is then studied by superimposition of the temperature excesses resulted from individual boreholes. On this basis, two kinds of representative temperature responses on the borehole wall are defined and discussed. The thermal interference between inclined boreholes is compared with that between vertical ones. The analyses can provide a basic and useful tool for the design and thermal simulation of the GHEs with inclined boreholes.

Introduction

Due to reduced energy consumption and maintenance costs, ground-coupled heat pump (GCHP) systems, which use the ground as a heat source/sink, have been gaining increasing popularity for space conditioning in buildings [1], [2]. The efficiency of the GCHP systems is inherently higher than that of air source heat pumps because the ground maintains a relatively stable temperature throughout the year. The system is environment-friendly, producing less CO₂ emission than the conventional alternatives. The ground heat exchanger (GHE) is devised for extraction or injection of heat from/into the ground. These systems consist of a sealed loop of pipes, buried in the ground and connected to a heat pump through which water/antifreeze is circulated. The GCHP systems require a certain plot of ground for installing the GHEs, which often becomes a significant restriction against their applications in densely populated cities and towns. The vertical GHE is the most popular design of GCHP systems currently employed, since it requires less ground area than the horizontal trench systems. These boreholes should be separated by certain distances to ensure long term operation of the system. Evolved from the vertical borehole systems, inclined boreholes are considered as a favorable alternative to further reduce the land areas required for the GHEs. The inclined boreholes can alleviate the thermal interference among them in the ground while occupying less land area on the ground surface than the vertical GHEs.

Despite all the advantages of the GCHP systems, commercial growth of the technology has been hindered by higher capital cost of the system, of which a significant portion is attributed to the GHEs. Thus, it is crucial to work out appropriate and validated tools, by which the thermal behaviour of the GCHP systems can be assessed and then, optimised in technical and economical aspects. However, the thermal analysis on the GHE with inclined boreholes is extremely difficult for engineering applications, for it has to be treated as transient and three-dimensional. Few studies, therefore, have been carried out on the GHE with inclined boreholes due to complexity of its heat transfer analysis, except some qualitative discussions from a Swedish researcher [3] who did some numerical simulation on the heat conduction of inclined boreholes in a specific GHE. However, the numerical solution of transient three-dimensional heat transfer is too computationally intensive to be applied generally in engineering designs.

On the basis of our previous studies on heat transfer of GHEs with vertical boreholes, a model has been established and solved analytically to describe the temperature response in the ground caused by a single inclined line source. Heat transfer in the GHE with multiple boreholes can then be studied by superimposition of the temperature excesses resulted from individual boreholes. The main objective of this paper is to provide a practical algorithm for engineers to design or analyze the GCHPs with inclined boreholes.

Section snippets

Heat transfer analysis of an inclined line source of finite length

In order to develop the theoretical model of inclined GHEs, a basic and simple case is to study a single inclined borehole and introduce other complications step by step. In a similar way to the vertical borehole analysis [4], [5], [6], [7], the inclined borehole buried in the ground can be approximated as an inclined line source of finite length in a semi-infinite medium. In the model, the ground is regarded as a homogeneous semi-infinite medium; and its thermophysical properties do not change

Temperature response on the inclined borehole wall

In design and simulation of the GHEs in GCHP systems, a characteristic temperature response on the borehole wall is usually required [9]. However, the temperature responses on the inclined borehole wall perimeter of any cross-section perpendicular to its axis are unequal and vary with the borehole depth because the heat transfer of the inclined line source is three-dimensional.

Thermal interference among inclined boreholes

In engineering practices the radius of a borehole (typically from 0.05 m to 0.1 m) is much smaller than the space between adjacent boreholes, which is usually above 3 m. Thus, the temperature response on the concerned borehole wall caused by its adjacent boreholes can be approximately treated as the response on its axis since its radius can be ignored. Take two boreholes (referred to as i and j) as an example, and suppose the borehole i is the one concerned, and j is its adjacent one as shown in

Temperature response on the borehole wall in GHEs with multiple inclined boreholes

U-tubes in the multiple boreholes of GHEs are generally joined in parallel configurations. The temperature responses on each borehole caused by its adjacent boreholes are obviously different, which mainly depends on the spacing and geometric disposal of the boreholes. Hence, a base borehole needs to be found out, which has the highest temperature rise or the worst heat transfer condition among all the boreholes, as the benchmark temperature rise on the borehole wall in a GHE.

For each borehole,

Conclusions

This paper presents an extensive analysis of the heat transfer of the inclined GHEs from a basic case of a single inclined borehole to practical cases of the GHEs with multiple boreholes of mixed vertical and inclined ones. For a single inclined borehole, the model of an inclined line source with finite length in a semi-infinite medium is developed to describe the heat conduction process in GHEs, especially for long-term operation. The representative temperature of a specific point on the

Acknowledgements

The authors wish to thank the financial supports from the Natural Science Foundation of China (Project No. 50476040) and the Hong Kong Research Grants Council (RGC) (Project No. 530204).

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