Multiple source ground heat storage

Abstract

Sharing geothermal borefields is usually done with each borehole having the same inlet conditions (flow rate, temperature and fluid). The objective of this research is to improve the energy efficiency of shared and hybrid geothermal borefields by segregating heat transfer sources. Two models are briefly presented: The first model allows the segregation of the inlet conditions for each borefields; the second model allows circuits to be defined independently for each leg of double U-tubes in a borehole. An application couples residential heat pumps and arrays of solar collectors. Independent circuits configuration gave the best energy savings in a symmetric configuration, the largest shank spacing and with solar collectors functioning all year long. The boreholes have been shortened from 300 m to 150 m in this configuration.

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Multiple source ground heat storage
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2016 J. Phys.: Conf. Ser. 745 032067
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Multiple source ground heat storage
P. Belzile, L. Lamarche, D.R. Rousse
École de technologie supérieure
1100 Rue Notre-Dame O, Montréal, QC Canada H3C 1K3
E-mail: patrick.belzile.1@ens.etsmtl.ca
Abstract. Sharing geothermal borefields is usually done with each borehole having the same
inlet conditions (flow rate, temperature and fluid). The objective of this research is to improve
the energy efficiency of shared and hybrid geothermal borefields by segregating heat transfer
sources. Two models are briefly presented: The first model allows the segregation of the inlet
conditions for each borefields; the second model allows circuits to be defined independently
for each leg of double U-tubes in a borehole. An application couples residential heat pumps
and arrays of solar collectors. Independent circuits configuration gave the best energy savings
in a symmetric configuration, the largest shank spacing and with solar collectors functioning
all year long. The boreholes have been shortened from 300 m to 150 m in this configuration.
Keywords: Ground source heat pumps, hybrid geothermal, geothermal model
1. Introduction
Ground source heat pumps, low temperature geothermal systems, are used in heating and cooling
applications; mainly buildings. The Intergovernmental Panel on Climate Changes (IPCC) projects that
the heat energy produced by ground source heat pumps will pass from 0.4 EJ/year in 2010 to 7.2
EJ/year in 2050 [1]. In cold climates, more heat is extracted from the ground during heating period
than injected during cooling period. Hybrid systems are a solution for such issue.
Sharing a ground source heat pump borefields is becoming more common. Many buildings and
processes with different heating and cooling loads profiles can share the same geothermal loop. It is
possible, even preferable to couple complementary load profiles. An example of hybrid geothermal
system would be to couple solar thermal collectors with heat pumps to a geothermal loop.
Nearly all available geothermal models consider only one inlet condition for all of the U-tubes and
boreholes of a borefield, limiting the amount of possible configurations and control strategies to be
evaluated. The objective of this research is to improve the efficiency of shared and hybrid geothermal
systems by segregating heat transfer sources. This will be achieved by developing a semi-analytical
model that considers independent inlet conditions for each borehole of a borefield in one part, and
developing a model that considers independent circuits of double U-tubes in each borehole in second
part.
In both models, the ground is modeled as a 2D diffusion control volume finite difference method.
In the independent boreholes model, an analytical model based on thermal resistances is used to
describe the heat transferred between the fluid and the borehole wall [2]. A second model is developed
to describe the behavior of a double U-tube borehole where the two legs of the U-tubes are coupled to
different sources [3]. It is a complement of an existing model [4, 5] that could simulate the same, in
addition of having different capacitances in each leg.
7th European Thermal-Sciences Conference (Eurotherm2016) IOP Publishing
Journal of Physics: Conference Series 745 (2016) 032067 doi:10.1088/1742-6596/745/3/032067
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Geothermal boreholes can be modelled in two main concepts: the borehole itself and the
surrounding ground. Classical analytical ground models are: Infinite line source model [6], Infinite
cylindrical source and Finite line source [7-9]. Many models are available to evaluate the borehole
thermal resistance (R’g) : Paul [10]; Sharqawy [11]; Line-source [12]; Multipole [13, 14].
This paper will present both independent boreholes and independent circuits models and compare
the performances of some configurations to a base case without solar collectors.
2. Independent boreholes
The proposed model is a semi-analytical model that evaluates temperature exchange between a fluid
and the ground through geothermal boreholes.
The numerical part uses a 2-D control volume finite difference method (CVFDM) to solve the
conduction problem in the ground. As a result, the problem is assumed to be independent of depth, Lp.
A point-by-point Gauss-Seidel iterative method is used to evaluate the temperature field caused by
diffusion in the surrounding ground. The analytical part of the model is composed of a Multipole
borehole thermal resistance [14]. The link between the analytical and numerical parts is done with a
shape factor, under a quasi-steady-state assumption.
For a ground assumed to involve constant thermophysical properties, the two-dimensional
Cartesian heat conduction governing equation in a horizontal plane is based on Fourier’s law:
s
sT
TTT
ck S
txxyy










 

(1)
The heat rate between the borehole heat exchanger and the surrounding ground is calculated from the
heat transfer of the fluid passing through the U-tubes of the boreholes.


,,
f
ffin fout
qmcT T
 (2)
The heat flux equation per unit depth between the borehole and the control-volume is then given by:



''
ba
s
ba
bc
TT
Sf k
qTT
LR



(3)
The thermal resistance analogy circuit is presented in Figure 1.
Figure 1.Combined borehole and shape factor thermal resistance
analogy
The outlet fluid temperature Tf,out is a function of the average ground temperature Ta. This temperature
is evaluated from a weighted average of the eight ground control volume temperatures adjacent and
contiguous for which the central control volume embeds a borehole, as depicted in Figure 2.
R
c
ControlVolume
Borehole
R’
12
Tij
Tf2
Tf1
7th European Thermal-Sciences Conference (Eurotherm2016) IOP Publishing
Journal of Physics: Conference Series 745 (2016) 032067 doi:10.1088/1742-6596/745/3/032067
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Figure 2.Ground temperature surrounding a source term
Hence, Ta is defined such that:
,
16 16 2
ij
n e s w ne se sw nw
a
T
TTTT T T T T
T
   
 
 

 
 

(4)
The heat rate per unit length transferred from the fluid to the control volume surface (or conversely)
can be expressed as a function of the inlet fluid temperature such that:
,
,
(1) 2
(1 )
f
in a
f out
zT T
Tz






(5)
Where dimensionless constant z is defined so that:
2
f
ftot
b
mcR
zL

 (6)
The model has been compared with the DST model [15, 16] in constant inlet conditions and variable
inlet conditions with good agreement. The absolute difference between both models outlet temperature
peaked at 0.15°C, with an average of 0.07°C on a global basis.
3. Independent circuits
Eslami-Nejad and Bernier [4, 5] were the first to model the thermal behavior of a borehole with two
independent circuits. Their approach is a generalization of the Zeng et al. [17] method that was used to
simulate a double U-tube configuration in parallel or in series. The proposed model is a contribution to
Eslami-Nejad works, adding the possibility to change the angle between the circuits and simulation
different capacitance and mass flowrates of fluid in each circuit. The physical problem is represented
in Figure 3.
+
++
++
+
+
+
T
ij
T
a
7th European Thermal-Sciences Conference (Eurotherm2016) IOP Publishing
Journal of Physics: Conference Series 745 (2016) 032067 doi:10.1088/1742-6596/745/3/032067
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Figure 3.Independent circuit in symmetric (left) and non-
symmetric (right) configurations
Eslami-Nejad and Bernier [5] showed that the above described configuration 1-3, 2-4 is the best for
two reasons: heat transfer between the hot and cold fluid is better and the thermal short-circuit is
reduced. One cannot argue with the second reason, since the distance between each leg of a circuit
must be as far as possible. However, better heat transfer could be achieved if the pipes of the two
independent circuits are closer, ≠0. The new model is presented in details in a paper [3]. In a very
brief way, the energy balance would be
1123 4
21234
31234
4123 4
dab c d e
dZ
dba d c e
dZ
dcd ab e
dZ
ddc b a e
dZ

 
 

  


  
 
(7)
where
,1, ,2, 1, 2,
1, 2,
()( )
, 1,2,3,4
fi f in fi f in
ifinfin
fin f in
TT TT TTi
TT




1121314 12 13 14 1
11 1 1 1 1 1
,,, ,
222 2 2 2
b
abcde
SS S S S S S S

       
(8)
The model showed perfect match with the previous one and showed good agreement with a Runge-
Kutta numerical method.
4. Application
A TRNSYS model couples residential heat pumps with solar collectors to the same borefield. The
objective is to present the effect on energy consumption of heat pumps for different hybrid geothermal
borefield configurations.
Three main configurations are compared to a base case without solar collectors: a classic mitigated
loop, independent boreholes and independent circuits. A detailed hourly simulation is executed over
three years to compare the solutions. The geothermal borefield is composed of 12 boreholes for 12
residential building heat pumps. Solar collectors with a surface of 24 m2 are installed for each
residential building. The Figure 4 shows a single residential building thermal load.
3
HPout
HPout 3
2HPin
HPin
ß=0
2
4
SCin
ß=ßmax
4
SCin
1
SCout SCout
1
7th European Thermal-Sciences Conference (Eurotherm2016) IOP Publishing
Journal of Physics: Conference Series 745 (2016) 032067 doi:10.1088/1742-6596/745/3/032067
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Figure 4. Residential thermal loads
The thermal loads are largely unbalanced. This would result in a reduction of the performances of the
ground source heat pump system through time. The Figure 5 shows a diagram of the mitigated loop
configuration.
Figure 5. Mitigated loop configuration
This configuration and the base case can be modelled with known models, such as DST, but the next
ones cannot. An independent borehole in central configuration is shown in Figure 6.
SolarCollectors
(24m²)
Heatpump
HX
GeothermalBorefield
3x4Boreholes
7th European Thermal-Sciences Conference (Eurotherm2016) IOP Publishing
Journal of Physics: Conference Series 745 (2016) 032067 doi:10.1088/1742-6596/745/3/032067
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Figure 6.Independent boreholes, central configuration
In this configuration, the heat from the solar collectors is injected in the centre of the borefield and the
heat pumps are coupled to the outer boreholes. The Figure 7 shows a different configuration of the
independent boreholes: the staggered configuration.
Figure 7.Independent boreholes, staggered configuration
In this configuration, the heat pump and residential circuits are closer to one another than with the
centre configuration. The Figure 8 presents independent circuit the non-symmetric configuration.
Figure 8.Independent circuits, non-symmetric configuration
The symmetric configuration is the same, except for the angle between legs of the U-tubes, which are
equally spaced, as presented in Figure 3.
The simulations used two control strategies: one where the solar collectors loop does not function
during summer (no sum) and the other where they function all year long (all year). There are also two
leg spacing configurations compared: Type A and Type C, shown in Figure 9.
Heatpump
SolarCollectors
(24m²)
4x6Independentboreholes
GeothermalBorefield
GeothermalBorefield
SolarCollectors
(24m²)
2x12Independentboreholes
Heatpump
SolarCollectors
(24m²)
4
2
Heatpump
4x4Borefieldand
4x6Borefield
(Typicalborehole)
3
1
7th European Thermal-Sciences Conference (Eurotherm2016) IOP Publishing
Journal of Physics: Conference Series 745 (2016) 032067 doi:10.1088/1742-6596/745/3/032067
6

Figure 9.Spacing of Type A (left) and Type C (right)
The energy consumption of each heat pump for a three years of simulation are presented in Table 1.
Table 1. Single heat pump energy consumption [kWh].
BHE Configurations Type Ctrl Energy HP Savings
3x4 Base C - 10884 -
3x4 Mitigated C All year 10771 113
3x4 Symmetric 150m C All year 10675 209
3x4 Mitigated C No sum 10621 263
3x4 Non-symmetric A All year 10501 383
3x4 Symmetric A No sum 10334 550
3x4 Symmetric C No sum 10222 662
3x4 Non-symmetric C All year 10201 683
3x4 Non-symmetric C No sum 10190 694
3x4 Symmetric C All year 10184 700
4x6 Central 6m C All year 10670 214
2x12 Ind staggered 6m C All year 10651 233
2x12 Ind staggered 3m C All year 10622 262
2x12 Ind staggered 4.5m C All year 10619 265
4x6 Central 4.5m C All year 10614 270
4x6 Non-symmetric A All year 10066 818
4x6 Non-symmetric C All year 9877 1007
The electrical energy consumption of the heat pumps over a three years simulation of the base case is
10884 kWh. The best savings of the 12 BHE simulations has been achieved with the independent
circuits with Type C shank spacing. The symmetric and non-symmetric parameters did not show much
advantage; neither did the all year and no sum control strategies. With the all year control strategy, the
ground temperature tends to rise over the years, which would be beneficial on the heating mode of the
heat pump, but would be disadvantageous in cooling mode. For the 24 BHE configurations, the
independent circuits also have shown the best savings. The independent boreholes configurations
required twice as much boreholes as the independent circuits with less energy savings. The
independent circuits symmetric Type C All Year configuration has allowed to cut in half the length of
the boreholes and keep fluid temperatures above 0°C.
1
SCout
SCin
4 2 HPin
TypeC
SCout
1
3
HPoutHPin
TypeA
2 4
SCin
HPout
3
7th European Thermal-Sciences Conference (Eurotherm2016) IOP Publishing
Journal of Physics: Conference Series 745 (2016) 032067 doi:10.1088/1742-6596/745/3/032067
7

5. Conclusion
Hybrid ground source heat pump systems are useful when the thermal loads on the borefield are
unbalanced. Two models have been developed to segregate circuits of hybrid systems. The first one
allows simulating geothermal borefields with independent inlet conditions for each borehole. The
second allows separating the circuits in two different legs of double U-tubes. In a residential heat
pump/solar collector application, the independent circuits, Type C, all year control strategy
configuration has given the most energy efficient results. It has allowed the boreholes to be shortened
from 300 m to 150 m.
References
[1] B. Goldstein, G. Hiriart, R. Bertani, C. Bromley, L. Gutiérrez-Negrín, E. Huenges, H.
Muraoka, A. Ragnarsson, J. Tester, V. Zui, Geothermal Energy, in: O. Edenhofer, R. Pichs-
Madruga, Y. Sokona, K. Seyboth, P. Matschoss, S. Kadner, T. Zwickel, P. Eickemeier, G.
Hansen, S. Schlömer, C. von Stechow (Eds.) IPCC Special Report on Renewable Energy
Sources and Climate Change Mitigation, Cambridge University Press, Cambridge, United
Kingdom and New York, NY, USA, 2011.
[2] P. Belzile, L. Lamarche, D.R. Rousse, Semi-analytical model for geothermal borefields with
independent inlet conditions, Geothermics, 60 (2016) 144-155.
[3] P. Belzile, L. Lamarche, D.R. Rousse, Geothermal heat exchange in boreholes with
independent sources, Appl Therm Eng, (2016).
[4] P. Eslami-Nejad, M. Bernier, Coupling of geothermal heat pumps with thermal solar
collectors using double U-tube boreholes with two independent circuits, Appl Therm Eng, 31
(2011) 3066-3077.
[5] P. Eslami-Nejad, M. Bernier, Heat Transfer in Double U-Tube Boreholes With Two
Independent Circuits, Journal of Heat Transfer, 133 (2011) 082801.
[6] L. Ingersoll, H. Plass, Theory of the ground pipe heat source for the heat pump, ASHVE
transactions, 47 (1948) 339-348.
[7] H. Zeng, N. Diao, Z. Fang, A finite line-source model for boreholes in geothermal heat
exchangers, Heat Transfer—Asian Research, 31 (2002) 558-567.
[8] J. Claesson, S. Javed, An Analytical Method to Calculate Borehole Fluid Temperatures for
Time-scales from Minutes to Decades, ASHRAE Transactions., 117 (2011) 279-288.
[9] L. Lamarche, B. Beauchamp, A new contribution to the finite line-source model for
geothermal boreholes, Energ Buildings, 39 (2007) 188-198.
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[12] G. Hellström, Ground heat storage: thermal analyses of duct storage systems, University of
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[14] J. Claesson, G. Hellström, Multipole method to calculate borehole thermal resistances in a
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[15] TRNSYS, TRNSYS, in, 2011.
[16] D. Pahud, A. Fromentin, J. Hadorn, The duct ground heat storage model (DST) for TRNSYS
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7th European Thermal-Sciences Conference (Eurotherm2016) IOP Publishing
Journal of Physics: Conference Series 745 (2016) 032067 doi:10.1088/1742-6596/745/3/032067
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6. Nomenclature
c Fluid specific heat (J kg-1 K-1)
d diameter (m)
h heat transfer coefficient, (W m−2K −1)
k thermal conductivity (W m−1K −1)
L Length (m)
 mass flow rate (kg s −1)
q Heat extraction/injection rate (W)
r radius (m)
ρ Density or specific weight (kg m-3)
R Thermal resistance (W m-1 K-1)
Rc Shape factor equivalent thermal resistance
S modified thermal resistances
Sf Shape factor between borehole and control volume boundaries
ST Source term
T temperature (C)
W Control volume width used in shape factor definition
Z dimensionless depth
α mass flow ratio
ß angle of rotation (deg)
θ non-dimensional temperature
 delta circuit
Subscripts
1 Inlet leg of 1-3 Circuit
2 Inlet leg of 2-4 Circuit
3 Outlet leg of 1-3 Circuit
4 Outlet leg of 2-4 Circuit
a Average
b Borehole
c related to the thermal resistance between the borehole and its control-volume
f Fluid
g Grout
s Ground
tot Total
in inlet
out outlet
n,s,e,w North, South, East, West neighbors of node i,j
ne, se, nw, sw North-east, South-east, North-west, South-west
f mean fluid
fo fluid outlet
7th European Thermal-Sciences Conference (Eurotherm2016) IOP Publishing
Journal of Physics: Conference Series 745 (2016) 032067 doi:10.1088/1742-6596/745/3/032067
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