**Heat Transfer Modeling of the Ground Heat Exchangers for the Ground-Coupled Heat Pump Systems**

Yi Man, Ping Cui and Zhaohong Fang

*Key Laboratory of Renewable Energy Utilization Technologies in Buildings, Ministry of Education, China; Shandong Jianzhu University, Jinan, Shandong, China* 

#### **1. Introduction**

116 Modeling and Optimization of Renewable Energy Systems

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Ground-coupled heat pump (GCHP) systems have been gaining increasing popularity for space air conditioning in buildings due to their reduced energy and maintenance costs. The efficiency of GCHP systems is inherently higher than that of the traditional options because it utilizes the ground which maintains a relatively stable temperature all the year round as a heat source/sink. Compared with traditional air-conditioning systems, the GCHP system features its ground heat exchanger (GHE), whether it is horizontally installed in trenches or as U-tubes in vertical boreholes. The advantages of vertical GHEs are that they require smaller plots of land areas, and can yield the most efficient GCHP system performance. The vertical GHEs are usually constructed by inserting one or two high-density polyethylene Utubes in vertical boreholes, which are referred to as single U-tube or double U-tube GHEs, respectively. The boreholes should be grouted to provide better thermal conductance and prevent groundwater from possible contamination. Borehole depths usually range from 40 to 200 meters with diameter of 100 to 150 millimeters. The schematic diagram of a borehole with U-tubes in vertical GHEs is illustrated in Fig. 1.

Fig. 1. Schematic diagram of boreholes in the vertical GHE exchanger

Heat Transfer Modeling of the Ground

et al., 2011).

**2.1 Overview** 

Heat Exchangers for the Ground-Coupled Heat Pump Systems 119

preferred to facilitate the computation. Following such an approach, some important analytical solutions have been derived by our research group (Diao & Fang, 2006) for heat transfer processes both inside and outside the boreholes, which can be easily incorporated into computer programs for thermal analysis and sizing of the GHEs while providing better

In practice, the boreholes of GHEs may penetrate several geologic strata. It is desirable to account for the groundwater flow in the heat transfer model to avoid over-sizing of the GHE. Taking the groundwater advection into account, the combined heat transfer of conduction and advection in the GHE has been solved by an analytical approach, and explicit expressions of the temperature response has been derived (Diao et al., 2004; Nelson

Recently, a novel configuration of GHE with a spiral coil has been proposed and applied in practical projects due to its distinct thermal and economical advantages especially combined with the foundation piles of buildings. For better simulating the heat transfer of buried spiral coils, our research group have proposed two new kinds of models and resolved their

This chapter analyzes in detail every links of the heat transfer process in borehole heat exchangers, including the influence of the groundwater movement. Adequate analytical solutions are suggested for modeling of the GHEs. The superposition procedures for multiple boreholes and variable loads are also discussed to provide an integrated solution of the thermal analysis of the GHEs. This approach can be easily incorporated into computer programs for thermal analysis and sizing of the GHEs while providing better insight into

The main objective to analyze the heat transfer inside boreholes is to determine the entering and leaving temperatures of the circulating fluid in the GHE according to the borehole wall temperature and its heat flow. Compared with the infinite ground outside it, both the dimensional scale and thermal mass of the borehole are much smaller. Moreover, the temperature variation inside the borehole is usually slow and minor. Thus, it is a common practice that the heat transfer in this region is approximated as a steady-state process.

It is obvious that the double U-tube configuration provides more heat transfer area between the circulating fluid and the ground than the single U-tube GHE does, and will reduce thermal resistance inside the borehole. On the other hand, however, it might require more pipes and consume more pumping power on operation for a certain project. Thus, analysis on performance and costs of different configurations of the GHEs has been a task for

A few models of varying complexity have been established to describe the heat transfer inside the GHE boreholes. Models for practical engineering designs are often oversimplified in dealing with the complicated geometry inside the boreholes. One-dimensional (1-D) model (Bose et al., 1985) has been recommended for engineering design, conceiving the U-

insight into influences of various factors on the GHE performance.

analytical solutions (Cui et al., 2011; Man et al., 2011).

influences of various factors on the GHE performance.

**2. Heat transfer inside boreholes** 

scholars and engineers to study.

However, the commercial growth of the GCHP systems has been hindered by its higher capital cost, of which a significant portion is attributed to the GHE. Besides the structural and geometrical configuration of the exchanger a lot of factors influence the exchanger performance, such as the ground temperature distribution, soil moisture content and its thermal properties, groundwater movement and possible freezing and thawing in soil. Thus, heat transfer between a GHE and its surrounding soil/rock is difficult to model for the purpose of sizing the GHE or simulation of the GCHP systems. In order to assess the thermal behaviour and to optimise the technical as well as economical aspects of GCHP systems, it is crucial to work out appropriate and validated heat transfer models of the GHE.

To determine the heat transfer in the GHEs with adequate accuracy is a crucial task, and has great impact on sizing and simulating GHE. The design goal is to control the temperature rise of the ground and the circulating fluid within acceptable limits over the lifetime of the system. A fundamental task for application of the GCHP technology is to grasp the heat transfer process of a single borehole in the GHE. Heat transfer in a field with multiple boreholes may be analyzed on this basis with the superposition principle.

There are roughly two categories of approaches in dealing with the thermal analysis and design of the GHEs. Empirical or semi-empirical formulations are recommended in textbooks and monographs for GHE design purposes (Bose et al., 1985; Kavanaugh, 1997). These approaches are relatively simple, and may be manipulated easily by design engineers. However, they do not reveal in detail the impacts of complicated factors on the GHE performance. The second kind of approaches involves numerical simulation of the heat transfer in the GHEs (Mei & Baxter, 1986; Yavuzturk & Spitler, 1999). While having provided important understandings on GHE heat transfer, these studies of numerical simulation have not yet been suitable to design and/or energy analysis of full scale engineering projects because it takes too substantial computing time.

Theoretical study on the GHE with an analytical approach is presented by some Swedish and American scholars (Eskilson, 1987; Spitler, 2005). Involving a time span of several years, the heat transfer process in the ground around the vertical boreholes is rather complicated, and should be treated, on the whole, as a transient one. Because of all the complications of this problem and its long time scale, the heat transfer process may usually be analyzed in two separated regions. One is the solid soil/rock outside the borehole, where the heat conduction must be treated as a transient process. With the knowledge of the temperature response in the ground, the temperature on the borehole wall can then be determined for any instant on specified operational conditions. Another sector often segregated for analysis is the region inside the borehole, including the grout, the U-tube pipes and the circulating fluid inside the pipes. The main objective of this analysis is to determine the inlet and outlet temperatures of the circulating fluid according to the borehole wall temperature, the thermal resistance inside the borehole and the heat rate of the GHE.

In this approach for GHE analysis a single borehole is investigated in detail experiencing a step heating/cooling. Then, the principle of superimposition is used to deal with the more complicated situation of GHEs with multiple boreholes as well as the variable load. It is more adequate and accurate than the empirical approaches and yet much more convenient for computations than the numerical simulations. In this regard, better understanding of every thermal resistances of the GHE is crucial, and their analytical solutions are especially preferred to facilitate the computation. Following such an approach, some important analytical solutions have been derived by our research group (Diao & Fang, 2006) for heat transfer processes both inside and outside the boreholes, which can be easily incorporated into computer programs for thermal analysis and sizing of the GHEs while providing better insight into influences of various factors on the GHE performance.

In practice, the boreholes of GHEs may penetrate several geologic strata. It is desirable to account for the groundwater flow in the heat transfer model to avoid over-sizing of the GHE. Taking the groundwater advection into account, the combined heat transfer of conduction and advection in the GHE has been solved by an analytical approach, and explicit expressions of the temperature response has been derived (Diao et al., 2004; Nelson et al., 2011).

Recently, a novel configuration of GHE with a spiral coil has been proposed and applied in practical projects due to its distinct thermal and economical advantages especially combined with the foundation piles of buildings. For better simulating the heat transfer of buried spiral coils, our research group have proposed two new kinds of models and resolved their analytical solutions (Cui et al., 2011; Man et al., 2011).

This chapter analyzes in detail every links of the heat transfer process in borehole heat exchangers, including the influence of the groundwater movement. Adequate analytical solutions are suggested for modeling of the GHEs. The superposition procedures for multiple boreholes and variable loads are also discussed to provide an integrated solution of the thermal analysis of the GHEs. This approach can be easily incorporated into computer programs for thermal analysis and sizing of the GHEs while providing better insight into influences of various factors on the GHE performance.
