Geofluids

Volume 2017 (2017), Article ID 1285428, 11 pages

https://doi.org/10.1155/2017/1285428

## Thermal Performance Analyses of Multiborehole Ground Heat Exchangers

^{1}School of Energy Resources, China University of Geosciences (Beijing), Beijing 100083, China^{2}Exploration Research Institute, Anhui Provincial Bureau of Coal Geology, Hefei, Anhui 230088, China^{3}University of Louisiana at Lafayette, Lafayette, LA 70504, USA^{4}Beijing Key Laboratory of Unconventional Natural Gas Geological Evaluation and Development Engineering, Beijing 100083, China

Correspondence should be addressed to Wanjing Luo

Received 30 June 2017; Revised 24 September 2017; Accepted 14 November 2017; Published 11 December 2017

Academic Editor: Paolo Fulignati

Copyright © 2017 Wanjing Luo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Geothermal energy known as a clean, renewable energy resource is widely available and reliable. Ground heat exchangers (GHEs) can assist the development of geothermal energy by reducing the capital cost and greenhouse gas emission. In this paper, a novel semianalytical method was developed to study the thermal performance of multiborehole ground heat exchangers (GHEs) with arbitrary configurations. By assuming a uniform inlet fluid temperature (UIFT), instead of uniform heat flux (UHF), the effects of thermal interference and the thermal performance difference between different boreholes can be examined. Simulation results indicate that the monthly average outlet fluid temperatures of GHEs will increase gradually while the annual cooling load of the GHEs is greater than the annual heating load. Besides, two mechanisms, the thermal dissipation and the heat storage effect, will determine the heat transfer underground, which can be further divided into four stages. Moreover, some boreholes will be malfunctioned; that is, boreholes can absorb heat from ground when the GHEs are under the cooling mode. However, as indicated by further investigations, this malfunction can be avoided by increasing borehole spacing.

#### 1. Introduction

Geothermal energy is attractive due to its enormous potential, renewability, availability, and low gas emission. With improvements in drilling, completion, and energy conversion systems, geothermal energy is becoming an economically viable alternative. Nonetheless, many challenges remain. The development of geothermal resource may be impeded by high capital requirements. Produced groundwater needs to be reinjected rather than disposing to surface waters to avoid environmental impacts, which raises the operational difficulties and maintaining cost. The ground heat exchangers (GHEs) such as geothermal heat pumps can reduce the cost effectively, and the close-loop system will eliminate the necessary of any reinjections (no groundwater produced). The ground can offer a steady and large heat storage medium as a heat source/sink and for thermal energy utilization, such as geothermal heat pumps. As one of the main geothermal heat pump technologies, the ground source heat pump (GSHP) has been widely used as a viable and economical alternative to traditional air conditioning systems owing to its high-efficient performance in the world [1–7]. It is well known that the efficiency of GSHP is related to the outlet fluid temperature of ground heat exchangers (GHEs), which is required to be in a certain range. Hence, it is very important to develop a reliable and efficient method to model the thermal performance of GHEs in order to predict/optimize the outlet fluid temperature [2–7].

Many methods, such as analytical/semianalytical, numerical method, and fractal methods [8–27], have been reported in literatures for heat transfer analysis. To study the underground heat transfer for GHEs, the semianalytical and numerical method are always preferred [8–22]. Generally, the model for underground heat transfer consists of two submodels [6–8], which account for the heat transfer inside the boreholes and outside the boreholes, respectively [2–7].

For the heat transfer inside the borehole, a steady-state process is usually approximated using 1D, 2D, or quasi-3D models [7]. Regarding the heat transfer outside the borehole, several models are available [9–12], such as line source model, cylinder source model, and finite length source model. Nevertheless, these models mentioned above are normally only valid for single borehole with a constant heat flux. In a real field, a single borehole is usually not sufficient to satisfy load demands, as the GHEs always consist of multiple boreholes. For a multiple-borehole system, the heat transfer capacity for each borehole may be reduced due to the thermal interference among different boreholes. Thus, simulating heat transfer for a multiborehole GHEs is a very important task. For this purpose, semianalytical methods [8–14] and numerical methods [14–19] are the main approaches. Hellström [15] presented a numerical method for simulating ground heat storage systems consisting of densely packed ground loop heat exchangers used for seasonal thermal energy storage. In Hellström’s model, a duct ground heat storage system (DST) is defined to divide the ground storage volume with multiple boreholes into two regions: one “global” region, where the ground temperature is solved with a two-dimensional finite difference scheme and one “local” region, the temperature of which is calculated by one-dimensional numerical method. Zhang [19] used a finite element method to investigate the thermal performance of each borehole in a multiple-borehole system with a thermal effectiveness factor. It demonstrated that the thermal effectiveness factor for each borehole is less than 1 due to the thermal interference.

Although the numerical simulations are flexible, they require significantly more computational time, which is not efficient for practical applications. In contrast, the semianalytical methods are more convenient and have been widely used in practice [13, 14, 23]. With the help of nondimensional temperature response “-functions” that can be calculated from numerical methods, Eskilson [14] used the superposition principle to study the thermal response of GHEs. However, Eskilson’s “-function” method is not practically convenient as the “-functions” is not universal and needs to be precomputed with respect to the GHEs’ configurations with numerical approaches. Many semianalytical methods have also been presented with the superposition principle with respect to different forms of “-function” [12, 13].

However, an unreasonable assumption with uniform heat flux (UHF) was adopted for these semianalytical methods mentioned above [12–14]. As a result, only the overall performance of GHEs, such as the average outlet fluid temperature and total heat flux of the GHEs, can be studied, while the heat capacity difference between different boreholes cannot be well examined. Furthermore, it has been reported that the UHF assumptions may give rise to errors when predicting the thermal performance of multiborehole GHEs. Claesson and Javed [23] noticed errors between their analytical -functions and Eskilson’s -functions for different configurations, and the errors become greater with more boreholes and increase with time. Similar results were also pointed out by Malayappan and Spitler [24] using a numerical approach. They found that the GHEs system could be oversized by around 5-6% with uniform heat flux assumptions used in a semianalytical approach. The reason why the UHF assumptions are inaccurate is that the nonuniform heat fluxes are common for the heat transfer of multiple boreholes. For example, for a bundle of boreholes, the outer boreholes have higher heat fluxes than the inner boreholes. However, the heat flux difference between boreholes due to the interference cannot be considered using the UHF assumptions. Furthermore, by noticing that the fluids entering different boreholes actually come from the same container (Figure 1), and the effluent fluid from each borehole will be accumulated by a collector before entering the heat pump, the assumption of uniform inlet fluid temperatures (UIFT) for all boreholes in GHEs is more reasonable.