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Multiple source ground heat storage

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2016 J. Phys.: Conf. Ser. 745 032067

(http://iopscience.iop.org/1742-6596/745/3/032067)

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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

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution

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Published under licence by IOP Publishing Ltd 1

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

ControlVolume

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

HPout

HPout 3

2HPin

HPin

ß=0

2

4

SCin

ß=ßmax

4

SCin

1

SCout SCout

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.

SolarCollectors

(24m²)

Heatpump

HX

GeothermalBorefield

3x4Boreholes

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.

Heatpump

SolarCollectors

(24m²)

4x6Independentboreholes

GeothermalBorefield

GeothermalBorefield

SolarCollectors

(24m²)

2x12Independentboreholes

Heatpump

SolarCollectors

(24m²)

4

2

Heatpump

4x4Borefieldand

4x6Borefield

(Typicalborehole)

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

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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

SCout

SCin

4 2 HPin

TypeC

SCout

1

3

HPoutHPin

TypeA

2 4

SCin

HPout

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

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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.

[10] N.D. Paul, The effect of grout thermal conductivity on vertical geothermal heat exchanger

design and performance, Mechanical Engineering Dept., South Dakota State University,

1996.

[11] M.H.E. Sharqawy, Modeling of heat transfer in a vertical ground heat exchanger, King Fahd

University of Petroleum Minerals .King Fahd University of Petroleum and Minerals (Saudi

Arabia), 2008.

[12] G. Hellström, Ground heat storage: thermal analyses of duct storage systems, University of

Lund. Department of Mathematical Physics, 1991.

[13] J. Bennet, J. Claesson, G. Hellström, Multipole method to compute the conductive heat

flows to and between pipes in a composite cylinder, Department of Building Technology and

[Department of] Mathematical Physics, Lund Institute of Technology, 1987.

[14] J. Claesson, G. Hellström, Multipole method to calculate borehole thermal resistances in a

borehole heat exchanger, Hvac&R Res, 17 (2011) 895-911.

[15] TRNSYS, TRNSYS, in, 2011.

[16] D. Pahud, A. Fromentin, J. Hadorn, The duct ground heat storage model (DST) for TRNSYS

used for the simulation of heat exchanger piles, DGC-LASEN, Lausanne, (1996).

[17] H. Zeng, N. Diao, Z. Fang, Heat transfer analysis of boreholes in vertical ground heat

exchangers, Int J Heat Mass Tran, 46 (2003) 4467-4481.

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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

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