Energy Conversion and Management 60 (2012) 134–142

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Energy Conversion and Management

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Effect of borehole array geometry and thermal interferences on geothermalheat pump system

Tomislav Kurevija ⇑, Domagoj Vulin, Vedrana KrapecFaculty of Mining, Geology and Petroleum Engineering, University of Zagreb, Croatia

a r t i c l e i n f o a b s t r a c t

Article history:Available online 29 March 2012

Keywords:Geothermal heat pumpsModeling of borehole array geometryThermal interferencesThermogeology

0196-8904/$ - see front matter � 2012 Elsevier Ltd. Adoi:10.1016/j.enconman.2012.02.012

⇑ Corresponding author. Tel.: +385 919558701.E-mail address: tkurevi@rgn.hr (T. Kurevija).

Properly sized borehole heat exchanger in geothermal heat pump system (widely known also as groundsource heat pump system) needs to minimize long-term ground and working fluid temperature changes.These changes occur due to imbalances of heat extracted from the ground during winter and heatrejected into the ground during summer months, as well as thermal interferences of adjacent boreholesin borehole array. Simple calculations and spreadsheet-based analogical solutions of required boreholelength for heat transfer run into difficulties when dealing with such large, complex ground source heatpump heating and cooling systems which use compact borehole array. A number of analytical computerprograms are available to simulate how ground loop fluid temperature varies in such complex systems,using so-called ‘g-function’ – a mathematical function dependent on the geometry and shape of the bore-hole array. The type of calculation involves a type of ‘step-function’, where 24 h ‘step’ of peak loading issuperimposed on a top of a long-term base load. In analytical simulation models, the base load is typicallyspecified as the heating and cooling load per month of a typical year, and is simulated as the combinationof sequential monthly steps. This paper will show, by simulating long-term operation of complex geo-thermal heat pump system with multiple boreholes in various geometric arrays, how spacing of adjacentboreholes and thermal interferences influence required borehole length for heat transfer.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The need for alternative low-cost and environment-friendly en-ergy sources has given rise to the development of geothermal heatpump systems (GHP) for residential and commercial heating andcooling applications. Basic principle is to extract heat from/or re-ject it into the ground by means of buried vertical pipes throughwhich a heat transfer fluid circulates (antifreeze solution).Although these systems are also widely known as ground sourceheat pumps (GSHPs), these vertical ground heat exchangers (GHEs)utilize, in fact, heat of geothermal origin. Long term utilizationundoubtedly leads to undercooling of the ground. Since all thermo-dynamic systems tend to reach thermal equilibrium, undercoolingof the ground induces two heat flows; one from the surface and an-other from the Earth’s interior. Consequently, even after 25 years ofheat extraction, 2/3 of total heat still comes from geothermalsource and other 1/3 as generated heat flow from surface [1].Therefore, system of vertical closed ground loop heat exchangerand heat pump should be correctly categorized as geothermal heatpump (GHP).

ll rights reserved.

Over the years various analytical and numerical models of dif-ferent complexities have been developed and used as design andresearch tools. They can also be used to predict a heat transfermechanism inside a borehole, the conductive heat transfer fromthe ground and the thermal interferences of adjacent boreholes.Multiyear modeling and simulation needs to consider a series ofthermogeological, climate, economical and technical parameterswhich affect the efficiency and economics of the entire GHP sys-tem. If a vertical borehole is surrounded by other boreholes, theheat extraction range is limited to one-half of the distance betweenthem. Hence, the entire cylinder of the earth surrounding the ver-tical borehole will be subcooled in some extent, if the heat ex-tracted is greater then the heat rejected. In undersized systemsthis phenomena increases which eventually leads to system failuredue to working fluid freezing. Therefore, considering all technoeco-nomical factors, properly sized GHE should minimize multiyearground and working fluid temperature changes which occur dueto the imbalances in extracted/rejected heat, as well as thermalinterferences of adjacent boreholes in the borehole array.

This paper will present one standard commercial project whereGHP system is plan to be used to heat and cool a building. To ana-lyze a thermal interferences impact on sizing of GHE, modeling of asystem will be carried out by using two different numerical solu-tions; ASHRAE/Kavanaugh cylinder source solution (A/K) [2] and

Nomenclature

Fsc short circuit heat loss factorFo Fourier numberH single bore depth (m)J Basel function of first kindL total required GHE length (m)P power input at design load (W)R thermal resistance (m�C W�1)r radius (m)r0 nondimensional radiusq heat flow per unit length of GHE (W m�1)Q net annual average heat transfer to the ground (W)T temperature (K)Y Basel function of second kind

Greek symbolsa thermal diffusivity (m2/s)b integral parameterk thermal conductivity (Wm�1 K�1)r part-load factor during design months time (h)

Subscripts and superscriptsa annualb boreholec coolingd dayg groundh heatingif interferencem months steady-state

AbbreviationsA/K ASHRAE/KavanaughCOP coefficient of performanceGHE ground heat exchangerGHP geothermal heat pumpGSHP ground source heat pumpELT entering load temperatureL/E Lund/EskilsonLLT leaving load temperatureEST entering source temperatureLST leaving source temperature

T. Kurevija et al. / Energy Conversion and Management 60 (2012) 134–142 135

improved Lund/Eskilson line source solution (L/E) [1,3]. Two bore-hole arrays will be discussed; one compact rectangular 7 � 6 array,which is presumed to be significantly influenced by thermal inter-ferences and one stretched rectangular 21 � 2 array, which is pre-sumed to have minor thermal interferences.

2. Fundamentals of vertical ground heat exchanger design

Today most of the commercially available simulation programpackages, used for sizing GHP systems, apply one of two (or both)theoretical heat transfer models. The first model is based on thecylindrical source solution and allows for a quick but accuratelength or temperature calculations based on the limited data input[4]. The second model is based on a simple line source theory but itis more detailed in its ability to generate monthly temperatureprofiles over time, given monthly loads and peak data. Althoughthe solutions of the two models do not always agree and stronglydiffer on valuation of thermal interferences effect, they do give anengineer more information on which to base a final GHE systemdesign.

2.1. ASHRAE/Kavanaugh numerical model

The vertical borehole length equations used in the first model,also known as ASHRAE/Kavanaugh model, are based upon the solu-tion for heat transfer from a cylinder buried in the earth. The solu-tion that gives a temperature difference between the outercylindrical surface and the undisturbed ground temperature wasproposed by Carslaw and Jaeger [4]. Ingersoll [5,6] developed solu-tion for sizing borehole heat exchangers where heat extraction orrejection occurs in periods that are less than 6 h, where the simpleline source model fails. Kavanaugh and Deerman [7], adjusted themethod of Ingersoll to account for U-tube arrangement and hourlyheat variations. Borehole resistance calculation techniques aresuggested by Remund [8] to account for pipe placement, groutconductivity, and borehole size. Conditions are calculated forlong-term, steady state operation of borehole fields, based on thedesired heat pump inlet temperatures. In order to provide an opti-mum design and prevent system failure, the combination of

parameters must allow for proper extraction or dissipation of en-ergy from or to the ground. The solution has the following generalform [2]:

Tg � T ¼ q0

kgGðF0; r0Þ; Fo ¼

agsr2

b

ð1Þ

GðF0; r0Þ ¼1p2

Z 1

0

e�ðb2F0Þ � 1

J21ðbÞ þ Y2

1ðbÞ½J0ðr0bÞY1ðbÞ � J1ðbÞY0ðr0bÞ�

db

b2 ð2Þ

Eq. (1) is an exact solution to the radial heat transfer in a plane per-pendicular to the line source. As the temperature response at thewall of the borehole is sought, the dimensionless time, i.e. Fouriernumber (Fo), is based on the borehole radius (rb). The integral inEq. (2) is often referred to as the G-factor in literature. As withthe exact integral, the G-factor has also been approximated usingvarious tabular and algebraic expressions [2].

The most complete description of this method was introducedby Kavanaugh and Rafferty [2]. In extensive tests, Hughes andShonder [9] showed that this model consistently proved to bethe most accurate when compared to calibrated data from actualinstallations. The Eq. (3) of simple steady-state heat transfer wassolved for L, which is required vertical borehole length:

q ¼ LðTg � TÞR

ð3Þ

The steady-state equation can be then transformed to represent thevariable heat rate of a GHE by using a series of constant heat pulses.The thermal resistance of the ground per unit length is calculated asa function of time, which corresponds to the time in which partic-ular heat pulse occurs. A term is also included to account for thethermal resistance of the pipe wall and interfaces between pipeand the ground. The resulting equation takes the following formfor heating or cooling [2]:

Lh;c ¼Q aRga þ ðqh;c � PhÞðRb þ rRgm þ RgdFscÞ

Tg � TESTþTLST2 � Tif

ð4Þ

In Eq. (4) heat rates, building loads and temperature penalties arepositive for heating, and negative for cooling. Eq. (4) considers threedifferent pulses of heat to account for long term imbalances,

Table 1Required heating and cooling energy for a building at the Zagreb location.

Month Heating(kWhth)

Cooling(kWhth)

January 92,213 64February 58,732 616March 31,184 1702April 9163 4518May 928 13,203June 28 21,771July 0 28,183August 0 21,334September 1047 8215October 15,363 1933November 52,479 147December 86,593 0Total (kWhth) 347,730 101,686Heating/cooling ratio 3.42Peak load 8 h (kWth) 195.0 192.0Annual full load hours of the system (h) 1781 530

Table 2Borehole heat exchanger and thermogeological ground parameters at the Zagreblocation.

Loop solutionproperties

– Water 76.5% ; Propylene-glycol 23.5%, (% mass)– Freezing point: -9.4 �C;– Specific heat capacity: 3.992 kJ/kg �C;– Density 1024.5 kg/m3

Polyethylene single U-tube parameters

– Pipe size 1’’ (27.40 mm ID/33.40 mm OD);– Pipe type SDR11;– Thermal resistance: 0.060 m �C/W;– Average radial pipe placement inside borehole

Borehole parameters – Diameter 130 mm;– Grout thermal conductivity: 2.13 W/m �C;– Borehole eq. thermal resistance: 0.121 m �C/W;– Separation distance between boreholes: 6.0 m

Ground properties – Lithology: mostly brown wet clay and uncon-solidated coarse sand with thin layers of graveland marl;

– Mean volume-specific heat capacity: 2.77 MJ/m3 �C;

– Undisturbed ground temperature at depth of10.0 m is 13.1 �C; Geothermal gradient 5.5 �C/100 m

– Mean thermal conductivity: 1.70 W/m �C;– Mean thermal diffusivity: 0.053 m2/day

Table 3Example of heat pump system designed input parameters used in ground loopsimulation for borehole array 7 � 6 and borehole separation distance of 6.0 m.

Borehole array 7 � 6 Heating Cooling

Source side fluid temperatures (�C) 0/�2.3 (EST/LST)

24.0/27.8 (EST/LST)

Load side fluid temperatures (�C) 37.8/40.8 (ELT/LLT)

12.0/8.5 (ELT/LLT)

Source side flow rate (L/min) 903.6 888.6System peak load (kWth) 195.3 192.0Compressor peak demand (kWe) 56.34 44.68Heat pump COP (kWth/kWe) 3.5 5.0Heat extracted/rejected from/to ground

(kWth)139.5 236.7

Heat pump partial load factor 1.00 0.85

136 T. Kurevija et al. / Energy Conversion and Management 60 (2012) 134–142

average monthly heat rates during the design month, and maxi-mum heat rates for a short term period during a design day. Thisperiod could be as short as 1 h, but this design procedure recom-mends a 4 h block. The required borehole length is then larger oftwo calculated lengths resulting from Eq. (4).

2.2. Lund/Eskilson model

The second model, also known as Lund/Eskilson model, is basedon the solution of the problem relating to the heat conductionexclusively in a homogenous medium. This problem was solvedby approximating the borehole as a finite line sink using superpo-sition principle [1]. The steady state solution relates to the casewhere heat is extracted continuously from the borehole withoutever exhausting the heat source, making it a fully renewable sourceof energy. The difference between first and second model is that byapplying the second model it is possible to calculate the evolutionof the borehole wall temperature over time when a constant heatrate is extracted from the borehole. It is more detailed in its abilityto generate monthly temperature profiles over time, givenmonthly loads and peak data and it makes use of a dimensionlessg-function method to model the temperature variations, takinginto account the ratio of the borehole radius and length and thephysical layout of the borehole field. The temperature responseto a unit step heat pulse is calculated using the finite difference ap-proach. The model accounts for the influence between boreholesby an intricate superposition of numerical solutions with transientradial-axial heat conduction, one for each borehole. The responseto any heat input can be calculated by devolving the heat rejectedinto the ground by a series of step functions. The temperature re-sponse of the boreholes is then obtained from a sum of step re-sponses and calculated using equation [1]:

Tb � Tg ¼Xn

i¼1

Dqi

2pkgg

sn � si

ss;rb

H

� �; ss ¼

H2

9agð5Þ

The change in extracted or rejected heat at time si is Dqi. Thelimitation of the numerically calculated g-functions are that theyare only correct for times greater than (5r2

b=ag), as estimated byEskilson [1]. This implies times of 3–6 h for typical boreholes whichwas noted and further investigated by Yavuzturk [3]. Simulationsoftware used in this paper incorporates this improvement of thebasic Eskilson model.

3. Geothermal heat pump and borehole heat exchanger systemanalysis

A new building in Zagreb, Croatia, with total area of 5000 m2

completely heated and cooled with shallow geothermal resourcewill be discussed as an example. Numerical computation and siz-ing of borehole heat exchanger will be done with commerciallyavailable software [10] which uses both heat transfer solutions.Analysis will be based on a fixed number of boreholes in heat ex-changer field. As mentioned in the introduction, two borehole ar-ray geometries will be discussed to determine the effect ofthermal interferences over an extended period of utilization. Oneof them will be rectangular and compactly arranged in form7 � 6 and one rectangular in form of 21 � 2. Both arrays will besimulated using two different models. Table 1 shows the input datafrom the building’s annual energy consumption. This was calcu-lated by incorporating Croatian directives regarding the rationaluse of energy in buildings and prescribes the allowable thermalconductivity factors of building insulation.

From Table 1 it can be seen that the ratio between the energyused during the heating season (extracted heat from the ground)and the energy used during the cooling season (energy rejectedto the ground) is 3.42. This indicates that more heat would be ex-tracted from the ground than it would be rejected to it (in coolingmode, however, the total rejected heat to the ground is the sum ofthe heat rejected from the building and the heat of compressionfrom the heat pump) which doubtlessly would cause undercoolingof the ground in a long-term period. Borehole input parameters

T. Kurevija et al. / Energy Conversion and Management 60 (2012) 134–142 137

and thermogeological characteristics of the ground at the locationcan be seen from Table 2.

Table 3 and Fig. 1 show examples of designed input parametersand simplified schematic for the heat pump system (two Waterfur-nace EKW130 units were used for the purpose of this analysis). Thebuilding is presumed to have floor heating system with leavingload temperature (LLT) of 40.8 �C and entering load temperature

Fig. 1. Simplified schematic of analyzed GHP with 7 � 6 b

3500,0

3700,0

3900,0

4100,0

4300,0

4500,0

4700,0

4900,0

5100,0

5300,0

5500,0

5700,0

5900,0

6100,0

6300,0

6500,0

1

Req

uire

d lo

op le

ngth

, m

Modelling according to year

7x6 borehole grid: ASHRAE/Kavanaugh cylindrical sour

21x2 borehole grid: ASHRAE/Kavanaugh cylindrical sou

7x6 borehole grid: Lund/Eskilson line source solution

21x2 borehole grid: Lund/Eskilson line source solution

Fig. 2. Modeling GHP according to ye

(ELT) to the heat pump of 37.8 �C. Loop side is set with enteringsource temperature (EST) of 0 �C and leaving source temperature(LST) of �2.3 �C.

The investigations carried out in relevant literature [1,2,11,12]suggest that geothermal borehole heat exchanger should be sizedfor at least 30 years period of operation to minimize the thermalinterferences effects and account for the undercooling of the

orehole array and geological strata at Zagreb location.

10010s of planned system operation

ce solution

rce solution

ars of planned system operation.

138 T. Kurevija et al. / Energy Conversion and Management 60 (2012) 134–142

ground. The principle of multi-year sizing is to prevent minimumtemperature of the working fluid during the peak-load conditionsto approach its freezing point. The mean temperature of the work-ing fluid under average ‘base-load’ conditions should not drop sig-nificantly below 0 �C over the design life of the system. Operationalcarrier fluid temperatures in the range �4 to 0 �C are typical. Thisleads to oversized system in the first years of utilization (more effi-cient system with higher coefficient of performance, COP) andslightly undersized in last years (lower COP). COP was calculatedas average value over the entire period of operation. Value of3.50 was chosen as minimum required, so the system can be

3600

3800

4000

4200

4400

4600

4800

5000

5200

5400

5600

5800

6000

4,0 4,5 5,0 5,5 6,0

Req

uire

d lo

op le

ngth

, m

Bores separa

7x6

21x

7x6

21x

Fig. 3. Modeling of GHE according to variable borehole

-10,0

-5,0

0,0

5,0

10,0

15,0

20,0

25,0

0 24 48 72 96 120

144

168

192

216

240

264

288

312

336

360

Tem

pera

ture

, °C

Months

Maximum ESTMinimum ESTMean EST

21x2 borehole array: ASHRAE/Kavanaugh cylindrical source solution

Fig. 4. The evolution of working fluid tempera

classified as renewable and to benefit from government supportof the renewable energy [13].

For example, if the geothermal system is designed just for1 year of operation, the loop length is smaller because the spread-ing cold front around the borehole during the heat extraction doesnot reach the outer boundary of the hollow cylinder. This outerboundary is equivalent to half separation distance of adjacentboreholes. As seen from Fig. 2, both examined borehole arraysshow similar loop length for heat transfer. This suggests the ab-sence of thermal interferences in the numerical analysis for thefirst several years and then gradually increases with time. Both

6,5 7,0 7,5 8,0 8,5 9,0tion distance, m

borehole grid: ASHRAE/Kavanaugh cylindrical source solution

2 borehole grid: ASHRAE/Kavanaugh cylindrical source solution

borehole grid: Lund/Eskilson line source solution

2 borehole grid: Lund/Eskilson line source solution

separation distances for fixed number of boreholes.

-10,0

-5,0

0,0

5,0

10,0

15,0

20,0

25,0

0 24 48 72 96 120

144

168

192

216

240

264

288

312

336

360

Tem

pera

ture

, °C

Months

Maximum ESTMinimum ESTMean EST

7x6 borehole array: ASHRAE/Kavanaugh cylindrical source solution

tures over 30 year period for A/K solution.

T. Kurevija et al. / Energy Conversion and Management 60 (2012) 134–142 139

models consider increase of required area for heat transfer becauseof thermal interferences, or in other words, as an increase in looplength. Also, Lund/Eskilson numerical solution is more detailed inits ability to generate monthly temperature profiles over time gi-ven monthly loads and peak data for periods above 30 years, as op-pose to A/K model.

The separation distance of 6.0 m was chosen for further analysisas optimum in economical and efficiency aspects [2]. The Fig. 3shows that for maximum analysed borehole separation distance of9.0 m, thermal interferences could be neglected. This is due to hugeground volume available for the heat transfer between adjacentboreholes in array. In case of smaller separation distances, looplength increases exponentially for both models to compensate forthe thermal interferences and process of ground undercooling. Sincethe borehole heat exchanger length during heating is larger than

-10,0

-5,0

0,0

5,0

10,0

15,0

20,0

25,0

0 24 48 72 96 120

144

168

192

216

240

264

288

312

336

360

Tem

pera

ture

, °C

Months

Maximum ESTMinimum ESTMean EST

21x2 borehole array: Lund/Eskilson line source solution

Fig. 5. The evolution of working fluid tempera

Fig. 6. The evolution of mean borewall tempera

cooling, whole system is sized for heating. This means that in coolingseason borehole heat exchanger will be somewhat oversized. Mod-eling the system by bringing down cooling entering source temper-ature (EST), system COP in cooling mode will increase. Eventually byincreasing COP in analysis, at some point two lengths from Eq. (4)will equalize as more length of ground heat exchanger will beneeded to satisfy set cooling conditions (when this value is reachedthis is initial value for cooling). In other words, in cooling mode sys-tem benefits from oversized system. As shown by Fig. 8, due to yearlyimbalances of rejected and extracted heat in/from ground heat ex-changer, EST in cooling mode becomes lower in function of time(as ground gets subcooled). This results in higher COP in coolingmode over time and more efficient system in summer periods.

Complete numerical calculation according to the two differentmodels is shown in Table 4 and in Fig. 3.

-10,0

-5,0

0,0

5,0

10,0

15,0

20,0

25,0

0 24 48 72 96 120

144

168

192

216

240

264

288

312

336

360

Tem

pera

ture

, °C

Months

Maximum ESTMinimum ESTMean EST

7x6 borehole array: Lund/Eskilson line source solution

tures over 30 year period for L/E solution.

tures over 30 year period for A/K solution.

140 T. Kurevija et al. / Energy Conversion and Management 60 (2012) 134–142

4. Prediction of the working fluid temperature evolution

The prediction of the working fluid temperature change wascarried out with available commercial software [10]. Three sinusoi-dal curves are shown: the upper, thinner red curve represents themaximum monthly temperature of working fluid under coolingpeak load conditions and the lower thinner black curve representsthe minimum monthly temperature of working fluid under heatingpeak load conditions. The middle thicker blue curve shows thechange of fluid temperature under the monthly base load. As visi-ble from Fig. 4, at the end of the 30 year period, the typical baseheating load working fluid temperatures vary between �4.9 and

Fig. 8. Average borehole fluid temperatures o

Fig. 7. The evolution of mean borewall temper

�2.1 �C for the ASHRAE/Kavanaugh cylindrical source solution;for 7 � 6 array and 21 � 2 respectively. Under heating peak loadconditions, the average working fluid temperatures may drop aslow as �7.1 and �4.4 �C for 7 � 6 array and 21 � 2 arrayrespectively.

As opposed to ASHRAE/Kavanaugh model, the Lund/Eskilsonline source solution assumes the smaller temperature drops during30 years of operation because of the greater presumed loop lengthfor heat transfer to compensate thermal interferences effect, asshown in Fig. 5. It can be seen that at the end of operation period,the typical base heating load working fluid temperatures vary be-tween �2.3 and �0.3 �C for 7 � 6 array and 21 � 2 array respec-

ver 30 year period for A/K and L/E model.

atures over 30 year period for L/E solution.

Table 4Results of sizing borehole ground loop using two different numerical models.

Boreholespacing(m)

ASHRAE/Kavanaugh LUND/Eskilson Change in loop sizebetween A/K and L/E(%)

Depth perborehole(m)

Effective groundtemperature(�C)

Entering sourcetemperature in coolingmode (EST) (�C)

Depth perborehole (m)

Effective groundtemperature(�C)

Entering sourcetemperature in coolingmode (EST) (�C)

21 � 2 Borehole array geometry4.0 106.6 13.96 22.0 118.0 14.23 19.5 10.75.0 99.5 13.80 23.9 111.1 14.07 20.9 11.76.0 95.5 13.70 25.1 106.1 13.95 22.0 11.17.0 93.1 13.65 25.8 102.8 13.88 22.9 10.58.0 91.6 13.61 26.3 100.2 13.81 23.6 9.49.0 90.5 13.59 26.7 98.5 13.77 24.1 8.8

7 � 6 Borehole array geometry4.0 116.2 14.20 19.9 138.6 14.71 16.1 19.35.0 105.1 13.93 22.4 123.9 14.40 18.3 17.96.0 99.1 13.79 24.0 115.7 14.17 20.0 16.87.0 95.5 13.71 25.1 109.4 14.03 21.3 14.68.0 93.2 13.65 25.8 104.6 13.91 22.4 12.29.0 91.7 13.62 26.3 101.4 13.84 23.3 10.7

Fig. 9. Average borehole wall temperatures over 30 year period for A/K and L/E model.

T. Kurevija et al. / Energy Conversion and Management 60 (2012) 134–142 141

tively. Under heating peak load conditions, the average workingfluid temperatures may drop as low as �4.3 and �2.3 �C for7 � 6 array and 21 � 2 array respectively.

On the basis of the selected data from Figs. 4 and 5 for the A/Kand L/E model, Fig. 8 shows the envelopes data of minimum baseload and maximum base load.1 This data brackets the sinusoidalbase load curve (blue curves), as well as peak heating (blackcurves) and cooling curves (red curves). Likewise, same dataextraction was carried out on Fig. 9, on basis of results from sinu-soidal curves of average borehole wall temperature (green curves)from Figs. 6 and 7.

1 For interpretation of color in Figs. 1–9, the reader is referred to the web version othis article.

f

Even these extracted envelope curves are only temperaturetrends; the real working fluid temperature will exhibit complexpattern of daily temperature fluctuations. The heating and coolingbase load curves show the general trend of working fluid temper-atures. The peak load curves represent the minimum and maxi-mum fluid temperatures under the worst case heating andcooling conditions. On the basis of the analysis shown in Figs. 8and 9 it can be deduced that the system’s performance is accept-able: the peak load temperature is above the freezing point ofthe antifreeze (23.5% propylene glycol mixture with freezing pointof �9.4 �C) and the base load temperature does not drop signifi-cantly below the designed value of EST which equals 0 �C .

From Fig. 9 it can be seen that borehole wall temperature dropsbelow freezing point of water. It is only evident for compact 7 � 6

Table 5Loop sizes ratio for 7 � 6 and 21 � 2 borehole array in two different numericalmodels.

Borehole spacing (m) A/K L/E

Difference between 7� 6 and 21� 2 borehole array (m)Change in loop size (%)

m % m %

4 400.4 8.2 865.4 14.95 234.8 5.3 538.1 10.36 151.7 3.6 403.7 8.37 101.0 2.5 276.8 6.08 67.5 1.7 183.4 4.29 49.0 1.3 124.2 2.9

142 T. Kurevija et al. / Energy Conversion and Management 60 (2012) 134–142

array with significant impact of thermal interferences. After30 years of operation, minimum temperature in A/K model that oc-curs in winter months at borehole wall is �3 �C, and �1 �C for L/Emodel respectively. It can be concluded that in very small areaaround borehole water in ground pores freezes at minimum pre-dicted temperatures in A/K model.

Freezing of soil moisture at small radius near the borehole hasrelatively small positive effect on overall thermal conductivityand thermal resistivity of ground, and consequently on boreholeheat exchanger (due to a high value of released latent heat of freez-ing of soil moisture). For example, water content of impermeablewet clays at location (which constitute 1/3 of strata interval) isaround 30%. Since water ice has larger thermal conductivity thanwater (2 W/m �C opposed to 0.6 W/m �C) there is slight benefit inthermal conductivity for clay layers [14]. However, overall effecton thermal conductivity and system analysis could be neglectedbecause of relatively small diameter around borehole where thisphenomena occurs, as opposed to large thermal mass of groundaround boreholes and groundwater flow in permeable sand andgravel layers [15,16].

5. Discussion and conclusion

According to two different borehole array geometry, this papershowed thermal interferences progress with borehole array com-paction; considering two arrays, 7 � 6 and 21 � 2. Also, differencesof two modeling approaches are clearly evident through discrepan-cies of required borehole loop length. Table 4 shows increment ofrequired loop length for 21 � 2 borehole array from 8.8% to10.7% and increase of 10.7–19.3% in 7 � 6 array, depending on dif-ferences between simple-line source (L/E) and cylindrical-sourcemodel (A/K) and as a function of variable borehole spacing.

Final inclusive Table 5 shows increment in loop length for eachmodel separately as a function of variable borehole spacing andconsidered two arrays. It can be seen that required loop lengthfor 7 � 6 borehole array according to A/K model is 1.3–8.2% greater

than required one for 21 � 2 array, while for L/E model differencefor two considered arrays in function of borehole spacing are great-er 2.9–14.9% respectively.

Distinguishable discrepancy in results between two models iscaused by fact that A/K model uses a somewhat simplistic boreholeinteraction model for predicting heat build up in the ground overtime. The L/E model however uses a more advanced borehole inter-action model to predict thermal interference/heat build up whichresults in higher values of required loop length. Two heat transfertheories give closer loop length results as the borehole spacing inborehole array increases. When both models give similar results,it is a very strong indication of a good engineering design. The A/K model is good for quick calculations with minimal loads data(peak and annual data) and the L/E model requires more detailedmonthly or hourly data.

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