Designing coaxial ground heat exchangers with a thermally enhanced outer pipe
 Jasmin Raymond^{1}Email author,
 Serge Mercier^{2} and
 Luc Nguyen^{2}
DOI: 10.1186/s4051701500273
© Raymond et al.; licensee Springer. 2015
Received: 7 November 2014
Accepted: 17 March 2015
Published: 8 April 2015
Abstract
Background
Ground heat exchangers installed in boreholes are an expensive component of a groundcoupled heat pump system, where minimizing the borehole length with appropriate materials and configuration can reduce the overall cost of the system.
Methods
Design calculations performed analytically indicate that the coaxial pipe configuration can be more advantageous than the single Upipe configuration to reduce the total borehole length of a system.
Results
A decrease of the borehole thermal resistance and an increase of the thermal mass of water contained in the coaxial exchanger helped to reduce borehole length by up to 23% for a synthetic building load profile dominated by cooling. The decrease of the borehole thermal resistance was achieved with an outer pipe made of thermally enhanced highdensity polyethylene, where the thermal conductivity is 0.7 W m^{1} K^{1}.
Conclusions
The coaxial configuration requires further investigations of the technical barriers related to the installation of ground heat exchangers in the field.
Keywords
Geothermal Heat pump Ground heat exchanger Borehole Coaxial Concentric Pipe Thermally enhancedBackground
Groundcoupled heat pump systems used for heating and cooling buildings are a highly efficient technology that takes advantage of the Earth’s subsurface acting as a heat source or heat sink. The operation of heat pumps reduces the need for conventional energy. However, the systems are expensive because of the drilling or trenching required for installation of the ground heat exchangers (GHEs). Technological innovations can help reduce the length of GHEs for building energy needs to be fulfilled at lower installation cost. Reducing installation costs is particularly important for vertical systems with boreholes that tend to be more expensive than horizontal systems (Canadian GeoExchange Coalition 2010). Significant advances in addressing this market barrier can reduce the payback period of geothermal systems and increase the shares of the geothermal sector on the global heating and cooling market.
To determine the required length of vertical GHEs, one of the various parameters considered in the equation is the borehole thermal resistance (Bernier 2000), which is the ability of the GHE to resist heat transfer. Selecting appropriate materials and configurations to optimize the borehole thermal resistance can help decrease borehole length. To reduce the borehole thermal resistance of GHEs made with one or more Upipe, advances were made to develop space clips holding pipes separately, thermally enhanced grout (Kavanaugh and Allan 1999; Allan and Kavanaugh 1999; Carlson 2000; BorinagaTreviño et al. 2013a, 2013b) and thermally enhanced pipe (Raymond et al. 2011a, 2011c). Further work has recently been conducted on coaxial GHEs, where the exchanger consists of two pipes imbricated into each other. The impact of the flow rate and the pipe diameter and thermal conductivity on the heat transfer rate was investigated with numerical simulations (Zanchini et al. 2010). Detailed experimental work was performed in the field to evaluate the borehole thermal resistance of different coaxial GHE configurations, where the external flow channel was made of several small pipes (Acuña et al. 2011) or a flexible liner molding the borehole wall and avoiding the use of backfill material (Acuña and Palm 2013). An analytical solution was also developed to estimate the vertical temperature distribution in the ascending and descending pipe of a coaxial GHE to improve the analysis of thermal response tests (Beier et al. 2013).
While previous research showed potential advantages of using coaxial GHEs, none of the above authors have investigated the possible bore length reduction associated with coaxial configurations. When compared to GHEs with a single or a double Upipe that are commonly used, coaxial GHEs can contain a larger amount of water allowing greater heat storage to buffer the building peak loads. Thermally enhanced pipes made of carbon nanoparticles and highdensity polyethylene (HDPE) can further reduce the borehole thermal resistance of coaxial GHEs. Design calculations were performed in this study using analytical models with the objective of evaluating the possible bore length reduction that can be achieved when using coaxial GHEs for groundcoupled heat pumps. The focus was given to pipe parameters to verify how this part of the heat exchanger can be improved. Calculations of borehole thermal resistance and heat storage capacity are initially presented to facilitate the design of coaxial GHEs. A synthetic building load profile was then used to size a groundcoupled heat pump system with either Upipe or coaxial GHEs.
Methods
GHE materials and configurations
The alternative coaxial design considered in this study involves the use of two pipes installed in each other to make the GHE (Figures 1c, d). Grout fills the space between the borehole wall and the outer pipe. The boreholes selected had a diameter equal to 152.4 and 203.2 mm (6 and 8 in.), respectively, with outer and inner pipes having a nominal diameter equal to 101.6 and 50.8 mm (4 and 2 in.) and 152.4 and 101.6 mm (6 and 4 in.). The heat carrier fluid enters the annulus and exits the inner pipe. Only pure water was selected for the heat carrier fluid to maintain a low pumping power at the higher flow rate required for turbulence to occur in the GHE annulus.
Range of each parameter used for borehole thermal resistance calculation
Parameter  Minimum  Maximum  Average 

Water flow rate (L s^{−1})  0.5  6  3.25 
Borehole length (m)  50  250  150 
Backfilling thermal conductivity (W m^{−1} K^{−1})  0.6  2.8  1.7 
Pipe thermal conductivity (W m^{−1} K^{−1})  0.1  0.7  0.4 
Pipe outside diameter (mm)/thickness (mm)  SDR11  SDR17  SDR13.5 
31.75mm (1.25 in.) nominal diameter  42.0/3.8  Not used for Upipe  Not used for Upipe 
50.8mm (2 in.) nominal diameter  59.7/5.5  60.3/3.6  59.8/4.5 
101.6mm (4 in.) nominal diameter  113.1/10.4  114.3/6.7  113.3/8.5 
152.4mm (6 in.) nominal diameter  166.4/15.3  168.3/9.9  166.8/12.5 
Design calculations
where H (m) is the GHE length, ṁ _{w} (kg s^{−1}) is the mass flow rate of water circulating inside the GHE, and c _{w} (J kg^{−1} K^{−1}) is the water specific heat capacity. Equation 1 assumes a constant heat injection rate along the borehole depth, which is convenient but departs from field observations (Beier et al. 2013). Using Hellström’s method (1991) implemented in EED, it is possible to take into account the internal resistance, which can be significant for long boreholes typically drilled for coaxial GHEs. Calculating borehole thermal resistances with the program GLHEPro involves a twodimensional approach that would not be suitable for determining the impact of increasing the borehole length or insulating the inner pipe.
Effective threedimensional borehole thermal resistances of GHEs with a single and a double Upipe were also calculated with Equation 1 and compared with the resistances of coaxial GHEs. In that case, the twodimensional borehole thermal resistance was determined using the multipole method, with recent improvements about boundary conditions (Claesson and Hellström 2011).
where T _{s} (°C) is the undisturbed temperature of the subsurface, q (W m^{−1}) is the heat transfer rate per unit length of GHE, k _{s} is the subsurface thermal conductivity (W m^{−1} K^{−1}), t _{sc} (s; t _{sc} = H ^{2}/9α _{s}) is the time scale, and r _{b} (m) is the borehole radius. When normalizing the time with the time scale, α _{s} (m^{2} s^{−1}) is the subsurface thermal diffusivity. The superposition principle takes into account temporal variations of the heat transfer rate calculated from monthly and peak building loads as well as the heat pump coefficient of performance affected by the water temperature leaving the GHEs. The longterm response of the GHE field is defined according to (Eskilson 1987) g (−) function, whose shortterm response has been modified to consider the effect of the thermal mass of water contained in the system (Xu and Spitler 2006). When sizing and simulating GHEs, temperatures computed with GLHEPRO are affected by heat stored inside the water contained in the GHEs and all surface piping, an approach that is neglected with EED. Temperature changes due to shortterm peak loads can be damped by the thermal mass of water, especially for coaxial GHEs that contain a greater amount of water than single and double Upipe GHEs. An adequate approach for coaxial GHE design was to manually calculate the borehole thermal resistance affected by internal heat transfer with EED, and then specifying that value in GLHEPRO in an iterative manner for sizing and simulation, accounting for the thermal mass of water.
After sizing and simulating a groundcoupled heat pump system with various GHE configurations, the pumping power was calculated for Upipe and coaxial GHEs and compared to one another. The DarcyWeisbach equation was used to calculate head loss through piping under a worstcase scenario, i.e., when the viscosity of water is higher at lower temperatures. Those conditions are expected during each heating season when the GHEs are use to extract energy from the subsurface and the water temperature in the GHEs decreases. The pumping power was then calculated by multiplying the water flow rate and density, the gravitational acceleration and the head loss through all the GHEs.
Results and discussion
Sensitivity of design parameters to the borehole thermal resistance
Thermal mass of water in the GHEs
Sizing and simulation of a groundcoupled heat pump system
GHE configuration and sizing calculation results for the synthetic load profile
ᅟ  ᅟ  ᅟ  ᅟ  ᅟ  ᅟ  ᅟ 

GHE configuration  
Borehole diameter  mm (in.)  152.4 (6)  152.4 (6)  152.4 (6)  152.4 (6)  152.4 (6)  203.2 (8) 
GHE configuration  1 Upipe  1 Upipe  2 Upipe  2 Upipe  Coaxial  Coaxial 
Pipe nominal diameter  mm (in.)  31.8 (1.25)  31.8 (1.25)  31.8 (1.25)  31.8 (1.25)  101.6 (4) outer  152.4 (6) outer 
50.8 (2) inner  101.6 (4) inner  
Pipe SDR  11  11  11  11  17 outer  17 outer 
11 inner  11 inner  
Pipe thermal conductivity  W m^{−1} K^{−1}  0.4  0.7  0.4  0.7  0.7 outer  0.7 outer 
0.4 inner  0.4 inner  
Grout thermal conductivity  W m^{−1} K^{−1}  1.7  1.7  1.7  1.7  1.7  1.7 
Sizing calculation results when applying the full building loads  
Total flow rate  L s^{−1}  7  7  7  7  9.6  8 
Borehole thermal resistance  m K W^{−1}  0.0955  0.0777  0.0563  0.0443  0.0734  0.0630 
GHE grid  4 × 4  4 × 4  3 × 4  2 × 5  3 × 4  2 × 4 
Individual GHE length  m  159  151  181  203  194  246 
Total GHE length  m  2,544  2,416  2,172  2,030  2,328  1,968 
Total water volume in GHE  m^{3}  4.62  4.39  7.89  7.37  16.43  27.48 
Pumping power for peak conditions  W  246  234  138  213  130  31 
Borehole length reduction  %    5  15  20  9  23 
Sizing calculation results for a hybrid system with a 55kW cooling tower  
Total flow rate  L s^{−1}  4.6  4.6  4.6  4.6  6  6 
Borehole thermal resistance  m K W^{−1}  0.0948  0.0768  0.0547  0.0442  0.0701  0.0587 
GHE grid  2 × 5  2 × 5  2 × 4  2 × 3  2 × 3  2 × 3 
Individual GHE length  m  146  137  158  199  222  198 
Total GHE length  m  1,460  1,370  1,264  1,194  1,332  1,188 
Total water volume in GHE  m^{3}  2.65  2.49  4.59  4.37  9.40  16.59 
Pumping power for peak conditions  W  160  152  77  160  137  19 
Borehole length reduction  %    6  13  18  9  19 
Conclusions
Design calculations performed for a fictive groundcoupled heat pump system using a synthetic load profile demonstrated that coaxial GHEs can reduce the total borehole length required for the system to fulfill a building’s energy needs. Boreholes of coaxial GHEs studied in this manuscript had a diameter of 152.4 and 203.2 mm (6 and 8 in.) and have been compared with single and double Upipe GHEs with a borehole diameter of 152.4 mm (6 in.). The parameters that needed to be improved for the coaxial GHEs to result in less total borehole length were the water flow rate as well as the outer pipe thermal conductivity and dimensions. It was helpful to select a thermally enhanced pipe made of HDPE with a thermal conductivity of 0.7 W m^{−1} K^{−1} and with a standard dimension ratio equal to 17 to form the outer flow channel of coaxial GHEs. Calculations suggested that at a high flow rate, the borehole thermal resistance of the proposed coaxial GHEs can be below 0.05 m K W^{−1}, which is significantly below single Upipe GHEs but remains above double Upipe GHEs. Another possible configuration to reduce the borehole thermal resistance is a coaxial GHE made with a flexible liner (Acuña and Palm 2013), which was shown to have a measured resistance that is 40% smaller than the lowest resistance of coaxial GHE considered in this study. Insulating the inner pipe with materials of thermal conductivity lower than that of HDPE had a negligible effect on the borehole thermal resistance reported in this study. Thermal shortcircuiting between the inner and outer flow channel was not a major concern for the studied GHEs with a large diameter, which can be different for GHEs of small diameter (Zanchini et al. 2010). The volume of water in the proposed coaxial GHEs was up to 28 times greater than the volume for Upipe GHEs, which is a second factor explaining the borehole length reduction. The large coaxial GHEs with a high heat storage capacity provided more bore length reduction than the double Upipe GHEs even though the borehole thermal resistance was higher.
Sizing calculations considered the internal borehole thermal resistance (Hellström 1991) and the thermal mass of water (Xu and Spitler 2006) of the coaxial GHEs and enthusiastically revealed borehole length reductions of up to 23%. However, technical barriers still have to be addressed for those reductions to provide savings on installation costs. The coaxial GHEs with a borehole diameter of 203.2 mm (8 in.) showed most advantages associated with borehole thermal resistance and heat storage capacity. Commercial drilling capacity available in North America may need to accommodate larger boreholes for coaxial GHEs to be installed at competitive cost. Assembling HDPE pipes with a large diameter can complicate the installation process because large pipes are commonly shipped in sections to be joined with fusion tools in the field. The double Upipe GHEs were shown to provide slightly smaller but similar advantages for the total borehole length reduction (up to 20%), especially when considering thermally enhanced pipe and deeper boreholes. While efficient technology to install coaxial GHEs may not be available at the moment, installation of double Upipe GHE can be achieved with current tools and expertise. The drilling depth is an important factor for balancing flow rate of both double Upipe and coaxial GHEs. Determining the depth at which this practice remains economical would require further research. In any cases, the thermally enhanced pipe was shown to be an asset for the alternative GHE configurations studied.
Abbreviations
 A :

Constant (W)
 B :

Constant (W)
 c :

Specific heat capacity (J kg^{1} K^{1})
 g :

Thermal response function (−)
 GHE:

Ground heat exchanger
 H :

GHE length (m)
 h :

Hour rank in a given period (−)
 HDPE:

High density polyethylene
 k :

Thermal conductivity (W m^{−1} K^{−1}).
 ṁ :

Mass flow rate (kg s^{−1})
 Q :

Heat load (W)
 q :

Heat transfer rate per unit length of GHE (W m^{−1})
 R :

Thermal resistance (m K W^{−1})
 r :

Radius (m)
 SDR:

Surface dimension ratio
 \( \overline{T} \) :

Average temperature (°C)
 α :

Thermal diffusivity (m^{2} s^{−1})
 a:

Internal
 b:

Borehole
 bl:

Building
 d:

Day
 s:

Subsurface
 sc:

Scale
 w:

Water
 y:

Year
 *:

Effective
Declarations
Acknowledgements
Professor Jeffrey Spitler at Oklahoma State University is kindly acknowledged for providing the program GLHEPRO to conduct the work presented in this manuscript. The comments of two anonymous reviewers were appreciated to improve this manuscript.
Authors’ Affiliations
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