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Geothermics 53 (2015) 379384

Contents lists available at ScienceDirect

Geothermics

jo ur nal home p ag e: www .e lsev ier .com/ locate /geothermics

ew correlations for the prediction of the undisturbed groundemperature

ohamed Ouzzane , Parham Eslami-Nejad, Messaoud Badache, Zine AidounanmetENERGY Natural Resources Canada, 1615 Lionel Boulet Boulevard, P.O. Box 4800, Varennes, Qubec J3X 1S6, Canada

r t i c l e i n f o

rticle history:eceived 14 April 2014ccepted 4 August 2014

eywords:round source heat pumphermal response testndisturbed ground temperature

a b s t r a c t

The undisturbed ground temperature is an important parameter in the design of the ground heatexchanger connected to the ground source heat pump systems. Based on the heating mode for coldclimates, the underestimation of this parameter leads to oversizing the ground heat exchanger lengthand therefore resulting in the additional cost of the system. Using measured data obtained from thermalresponse test (TRT) reports for seventeen sites covering a wide range of climates, two different correla-tions of the undisturbed ground temperature, global and simplified have been developed. The first one,obtained using the least square method, is a function of ambient air temperature, wind velocity, globalorehole design solar radiation on a horizontal surface and sky temperature. It has been shown by using this correlationthat the air ambient temperature is the dominant parameter on the undisturbed ground temperature.Following this conclusion, the simplified correlation which is only a function of the air ambient tempera-ture was developed. Then using this latter correlation, isotherms of the undisturbed ground temperaturefor Canada were generated.

Crown Copyright 2014 Published by Elsevier Ltd. All rights reserved.. Introduction

The assessment or prediction of the ground temperature isommonly required in various environmental and several energypplications such as ground source heat pumps (GSHPs), agricul-ural greenhouses and ground energy storage systems. The groundemperature profile is characterized by three different zones: 1 urface zone (down to 1 m below the ground surface), 2 shallowone (from 1 m to 8 m), and 3 deep zone in which the temper-ture remains almost constant throughout the year (below about

m). This latter temperature is called undisturbed ground tem-erature.In ground source heat pump systems, heat is extracted/rejected

rom/to the ground via a ground heat exchanger (GHE). The totalength of the GHE which involves relatively expensive drilling workepresents a very important part of the total cost of the system.herefore, borehole sizing needs to be done as accurately as pos-

ible. The undisturbed ground temperature is a critical parameteror sizing GHE, especially for vertical boreholes.

Corresponding author. Tel.: +1 450 652 4636; fax: +1 450 652 5177.E-mail addresses: Mohamed.ouzzane@nrcan.gc.ca (M. Ouzzane),

arham.eslaminejad@nrcan.gc.ca (P. Eslami-Nejad), Messaoud.Badache@nrcan.gc.caM. Badache), Zine.aidoun@nrcan.gc.ca (Z. Aidoun).

ttp://dx.doi.org/10.1016/j.geothermics.2014.08.001375-6505/Crown Copyright 2014 Published by Elsevier Ltd. All rights reserved.It is obvious that direct measurement gives accurate values.Often, for large buildings with relatively high cooling and heatingloads, one well is drilled to perform thermal response tests (TRTs).In addition to the thermal properties of the soil (conductivity anddiffusivity) and the borehole thermal resistance, the TRT gives theundisturbed ground temperature. However, this test results in anadditional cost for the GSHP system. Another way to obtain thevalue of the undisturbed ground temperature is by using theoret-ical predictions based on the meteorological data and the thermalproperties of the ground.

Two of the earliest analytical models were developed by VanWijk (1963) and Kasuda and Achenbach (1965). Both models arebased on Fourier analysis of multi-year measured data. The cor-relation proposed by Kasuda and Achenbach (1965) is commonlyused in several commercial softwares such as TRNSYS (2005),DOE-2 (1982) and RETScreen (2005). It gives the ground tem-perature as a function of the time of the year and the depthbelow the ground surface. Among the input data for this corre-lation is the annual average surface ground temperature whichis not often accessible. For this reason, this parameter is oftensubstituted by the annual average air temperature. Such a simplifi-cation appears to be rather inaccurate in the design and prediction

of GSHP energy performance systems, as shown later in thispaper.

By introducing a correction for the daily amplitude of the groundtemperature by a sinusoidal function of time rather than a constant

dx.doi.org/10.1016/j.geothermics.2014.08.001http://www.sciencedirect.com/science/journal/03756505http://www.elsevier.com/locate/geothermicshttp://crossmark.crossref.org/dialog/?doi=10.1016/j.geothermics.2014.08.001&domain=pdfmailto:Mohamed.ouzzane@nrcan.gc.camailto:Parham.eslaminejad@nrcan.gc.camailto:Messaoud.Badache@nrcan.gc.camailto:Zine.aidoun@nrcan.gc.cadx.doi.org/10.1016/j.geothermics.2014.08.001

380 M. Ouzzane et al. / Geothermics 53 (2015) 379384

Nomenclature

h convective heat transfer coefficient (W/(m2 K))R2 coefficient of determinationt time (s)T temperature (K)V velocity (m/s)z depth coordinate (m)

Greek symbols absorption coefficient thermal conductivity (W/(m K)) emissivity

density of heat flux (W/m2)

Subscriptsamb ambientc convectivedp dew pointg groundgs ground surfaceLat latitudeLong longituder radiativesky sky

vt

tmuH1mm

b1KtgrAglt

ibittp

2

pete

until it reaches a certain depth where the temperature remainsconstant (15 m in Fig. 2). This constant temperature is often calledundisturbed ground temperature.sol solarw wind

alue, Elias et al. (2004) and Smerdon et al. (2006) have improvedhe model proposed by Van Wijk (1963).

Based on both mean annual surface air temperature (SAT) andhe mean ground surface temperature (GST) values measured ateteorological stations, Signorelli and Kohl (2004) generated aseful regional ground surface temperature map for Switzerland.owever, GSTs and SATs values were recorded from depths of 5 to00 cm and 2 m above the ground respectively. SAT is not a com-on value given by the weather stations and it associates withany uncertainties.Another category of work has been done, based on the energy

alance at the ground surface (Cellier et al., 1996; Khatry et al.,978; Mihalakakou et al., 1997; Mihalakakou, 2002; Okada andusaka, 2013; Thiers, 2008). This category of studies, in whichhe energy balance is applied as a boundary condition at theround surface, is applicable anywhere due to the availability of theequired data. However, it introduces more modeling complexities.s pointed out by different studies, the boundary condition at theround surface involves three terms including solar radiation, heatosses to the cold sky by long wave radiation and convective heatransfer between the ambient air and the ground surface.

All the above models involve several assumptions. Many of theirnputs are spatially and temporally difficult to collect as well aseing costly and time consuming. The main objective of this works to analyze the effect of the meteorological data on the undis-urbed ground temperature taken from the measurements, in ordero develop a simple correlation as a function of the ambient tem-erature.

. Undisturbed ground temperature

The assessment and/or prediction of the ground temperature

rofile is commonly required in various environmental and severalnergy applications such as ground source heat pumps, agricul-ural greenhouses, heating and cooling of buildings and groundnergy storage systems. Temperature changes in the soil areFig. 1. Energetic exchange phenomena on the ground surface.

essentially driven by transient conduction resulting from the netheat flux ( net) on the ground surface (Eqs. (1) and (2)). The differ-ent phenomena occurring at the ground surface are presented inFig. 1. The surface of the ground is heated by solar radiation ( sol)when the weather is fine. The surface also loses heat to the coldsky by long wave radiation ( r). Convective heat exchange occursbetween the ground surface and ambient air ( c).

net = sol + c + r (1)

net = g. Tz

z=0

= hc(Tamb Tgs) + sol hr(Tgs Tsky) (2)

The typical daily ground temperature profile is presentedin Fig. 2. Due to the temperature fluctuations on the groundsurface, the annual variation of the daily ground temperatureprofile varies from the summer time to the winter time. Becauseof the high thermal inertia of the soil, the amplitude of its tem-perature variation diminishes as the depth of the ground increasesFig. 2. Typical ground temperature distribution profile.

M. Ouzzane et al. / Geothermics 53 (2015) 379384 381

Table 1Comparison of borehole length using two different undisturbed ground temperatures.

Operating mode Undisturbed ground temperature (C) Borehole length, L (m) ((L6 L10)/L10) 100

Heating10 131.3

37.46 180.4

ts

ht6w(i(t

hctortiphmibttgs

3

mb

TA

Cooling10 6

The undisturbed ground temperature is an important parame-er for the design and the sizing of boreholes connected to groundource heat pump systems for the heating and cooling of buildings.

To show the influence of this parameter on the size of the groundeat exchanger, a real project of an office building located in down-own Montral has been selected. The building has a total area of000 m2 and it is designed to be an energy efficient archetype inhich a system of heat pumps is connected to 28 vertical boreholes

U-tube) in a rectangular grid arranged 7 4 with a 6.1 m spac-ng between boreholes. Other information regarding this projectground loads, ground thermal properties, fluid properties, charac-eristics of the boreholes, etc.) is given by Langlois (2010).

The design method for multiple boreholes of Mikael et al. (2010)as been used for sizing the ground heat exchanger in heating andooling modes. This method is based on the borehole sizing equa-ion given in the ASHRAE Handbook (2007). The analysis is carriedut for two ground temperatures, 10 C and 6 C, which correspondespectively to the measured undisturbed ground temperature ando the annual average ambient air temperature for Montreal (usedn the absence of the undisturbed ground temperature). The resultsresented in Table 1 are obtained for the two operating modes ofeating and cooling. It is shown that depending on the operatingode, the boreholes are oversized (heating) or undersized (cool-

ng). It is worth noting that for cold climates, where the design isased mostly on the heating mode because it is dominant, usinghe annual average ambient temperature instead of the real undis-urbed ground temperature leads to an important oversize of theround heat exchanger, which imposes an additional cost for theystem.

. Results and analysisThe results and analysis presented below concern the develop-ent of two correlations for the undisturbed ground temperature,ased on meteorological data as inputs. The first correlation, which

able 2nnual average meteorological data, undisturbed ground temperature and geographical

Site Coordinates Tamb (C)

Lat Long

Alert (Nunavut, Canada) 82.5 62.3 18.7 Iqaluit (Nunavut, Canada) 63.6 68.5 11.1 Red Creek (Yukon Territory, Canada) 65.15 138.3 7.59 Alpine Burwash (Yukon Territory, Canada) 61.5 139.4 6.75 Table Mountain (Northwest Territories, Canada) 63.5 123.5 5.15 Sept Iles (Qubec) 50.21 66.0 0.14 Montral (Qubec) 45.51 73.55 5.77 Luzern (Switzerland) 47.05 8.32 6.6 Zaghreb (Croatia) 45.82 15.98 10.5 Amsterdam (Netherlands) 52.37 4.90 10.7 Elazig (Turkey) 36.68 39.23 11.1 Oklahoma (USA) 35.47 97.52 14.8 Shanghai (China) 31.23 121.47 15.6 Hamah (Syria) 35.14 36.75 18.1 Kiln (Mississippi, USA) 30.41 89.44 19.6 Brownsville (Texas, USA) 25.90 97.5 22.7 Dhahran (Saudi Arabia) 26.28 50.11 27.4 146.2 13.3126.8

is called the global correlation, is a function of ambient air temper-ature, wind velocity, global solar radiation on a horizontal surfaceand sky temperature. The second one which is called simplifiedis correlated solely based on the air ambient temperature as it isthe dominant parameter in the global correlation. In the end, asimplified correlation was used to generate isotherms for Canada.

3.1. Correlation development

Both correlations mentioned earlier have been developed usingmeasured data obtained from in situ thermal response tests (TRTs).Seventeen sites have been chosen to cover a wide range of cli-mates from Alert (North Pole in Canada), representing cold climateat a latitude of 82.5 North to Dhahran (Saudi Arabia), repre-senting warm climate with a latitude of 26.3 North. Table 2shows the characteristic data related to the different sites, respec-tively: the geographical coordinates (latitude and longitude), theannual average meteorological data (ambient air temperature, dewpoint temperature, wind velocity and global solar energy den-sity on a horizontal surface) as well as the measured undisturbedground temperature. The meteorological data are taken from theNASA website and the measured undisturbed ground tempera-ture are taken from several TRT reports and papers (Richard andGaren, 2012; Commission scolaire du fer, 2011; CanmetENERGY-Varennes, 2012; Esen and Inalli, 2009; Ewbank geo testing, 2014;Gramlich et al., 2009; Kurevija et al., 1997; Kharseh, 2009; Leee,2000; Man et al., 2012; Sharqawy et al., 2009; Throop, 2010; Witteet al., 2002).

3.1.1. Global correlationThe net heat flux at the ground surface (Eq. (2)) which is themajor parameter influencing the ground temperature profile, aswell as the deep ground temperature depend on the followingmeteorological parameters: ambient air temperature, wind veloc-ity for the calculation of the heat convection coefficient (hc), global

coordinates for different sites.

Tdp (C) Vw (m/s) Annual averagesolar energy(W/m2)

Tg measured (C)

21.36 4.59 107.3 13.714.10 4.29 129.7 5.7511.18 3.11 131.8 2.09.65 3.90 143.2 2.09.95 3.02 142.7 1.04.50 3.52 170.3 5.91.75 3.38 183.3 10.01.44 3.72 175.5 12.53.71 1.97 183.3 15.22.15 5.58 157.3 13.81.78 3.03 250.0 15.77.94 5.35 235.9 17.211.66 4.41 198.4 18.26.71 4.42 253.6 21.214.24 3.43 230.8 21.717.61 3.93 248.0 26.714.99 4.00 291.7 32.6

382 M. Ouzzane et al. / Geothermics 53 (2015) 379384

Table 3The percentage contribution of the different terms of Eq. (4).

Site Tg (%) Percentage of contribution (%)

Tamb a Tsky b Vw c Qsol d

Alert (Nunavut, Canada) 100 118.29 17.67 0.83 0.21Iqaluit (Nunavut, Canada) 100 118.34 17.83 0.75 0.24Red Creek (Yukon Territory, Canada) 100 118.17 17.87 0.54 0.24Alpine Burwash (Yukon Territory, Canada) 100 118.35 17.94 0.67 0.26Table Mountain (Northwest territories, Canada) 100 118.16 17.91 0.52 0.26Sept iles(Qubec) 100 118.39 18.10 0.59 0.30Montral (Qubec) 100 118.58 18.35 0.56 0.32Luzern (Switzerland) 100 118.65 18.35 0.61 0.31Zaghreb (Croatia) 100 118.39 18.39 0.32 0.31Amsterdam (Netherlands) 100 119.07 18.44 0.91 0.27Elazig (Turkey) 100 118.38 18.32 0.49 0.43Oklahoma (USA) 100 119.13 18.67 0.86 0.40Shanghai (China) 100 119.21 18.84 0.71 0.34Hamah (Syria) 100 118.85 18.58 0.70 0.43Kiln (Mississippi, USA) 100 119.09 18.94 0.54 0.39Brownsville (Texas, USA) 100 119.33 19.13 0.61 0.41Dhahran (Saudi Arabia) 100 119.11 18.97 0.61 0.48a ((1.205 Tamb)/Tg) 100.b ((0.201 T )/T ) 100.

sfctmie

B

T

w(

ra

T

T

TC

sky gc ((0.466 Vw)/Tg) 100.d ((0.0049 Qsol)/Tg) 100.

olar radiation on a horizontal surface and dew point temperatureor the calculation of the sky temperature using Eq. (3). The firstorrelation between the undisturbed ground temperature Tg andhe meteorological parameters is obtained, using the least squareethod. This correlation is called the global correlation because

t takes into account almost all meteorological parameters influ-ncing the ground temperature (Tamb, Tsky, Vw, and Qsolar).The sky temperature is calculated from Eq. (3) (Duffie and

eckman, 2006):

sky=Tamb[0.711+0.0056Tdp + 0.000073T2dp + 0.013 cos(15t)]0.25

(3)

here Tsky and Tamb are in Kelvin and the dew point temperatureTdp) is in degrees Celsius. t is the hour from midnight.

The experimental data used to obtain Eq. (3) covered a dew pointange from 20 C to 30 C. The range of the difference between skynd air temperatures is from 5 C to 30 C.

The correlation obtained for Tg is presented in Eq. (4), where Tg,

amb and Tsky are in Kelvin.

g = 1.205Tamb 0.201Tsky 0.466Vw + 0.0049Qsol (4)

able 4omparison between measured and predicted of the ground temperature.

Site MeasurementsTg (C)

PrediEq. (5

Alert (Nunavut, Canada) 13.70 13.1Iqaluit (Nunavut, Canada) 5.75 5.95Red Creek (Yukon Territory, Canada) 2.00 2.61Alpine Burwash (Yukon Territory, Canada) 2.00 1.81Table Mountain (Northwest Territories, Canada) 1.00 0.29Sept Iles (Qubec) 5.90 4.47 Montral (Qubec) 10.00 10.10Luzern (Switzerland) 12.50 10.89Zaghreb (Croatia) 15.20 14.60Amsterdam (Netherlands) 13.80 14.79Elazig (Turkey) 15.70 15.17Oklahoma USA 17.20 18.69Shanghai (China) 18.20 19.45Hamah (Syria) 21.20 21.83Kiln (Mississippi, USA) 21.70 23.25Brownsville (Texas, USA) 26.70 26.20Dhahran (Saudi Arabia) 32.60 30.67Eq. (4) is linear and the coefficient of determination (R2) isaround 0.998, which is very satisfactory.

The contribution or the weight of each parameter on the undis-turbed ground temperature is determined from Eq. (4) and theresults are presented in Table 3. Calculations are based on the per-centage of the undisturbed ground temperature (Tg).

Tg is equal to the sum of the percentages of the 4 terms in Eq.(4). Because of the negative terms (for Tsky and Vw), the percentagerelated to the ambient temperature is higher than 100%. The resultsshow that the ambient temperature is the dominant parameter inEq. (4). This can be explained by the existence of a relationshipbetween ambient temperature and the other parameters (Tamb isnot an independent variable). In other words, the ambient tempera-ture is strongly affected by the solar radiation, the sky temperatureand the wind velocity. The weights of the wind velocity and thesolar radiation in Table 3 are not significant. The sky tempera-ture shows almost a constant percentage around 18.3% for all sites.Based on the fact that the contribution of the ambient temperature

is the most important among the parameters and is almost con-stant from one climate to the other, Tg can be correlated only as afunction of the ambient temperature. This relationship is presentedin the next section.

cted) (C)

PredictedEq. (4) (C)

ErrorEq. (5) (C)

ErrorEq. (4) (C)

8 13.94 0.52 0.24 6.29 0.20 0.54 2.34 0.61 0.34 1.90 0.19 0.10

0.16 0.71 1.164.74 1.43 1.16

10.29 0.10 0.29 10.97 1.61 1.53 15.56 0.60 0.36

14.12 0.99 0.32 16.21 0.53 0.51 18.13 1.49 0.93 18.74 1.25 0.54 22.15 0.63 0.95 23.08 1.55 1.38

25.62 0.50 1.08 30.92 1.93 1.68

M. Ouzzane et al. / Geotherm

Fp

3

detdco

T

w

3u

s(rtt

ig. 3. Linear correlation for undisturbed ground temperature versus ambient tem-erature.

.1.2. Simplified correlationThe relationship between measured Tg data and the ambient

ry bulb temperature can be described using a linear profile. A lin-ar regression was used to determine the relationship between thewo variables, as described in Eq. (5) and Fig. 3. The coefficient ofetermination (R2) is equal to 0.98, which is very satisfactory. Theonstant value in Eq. (5), 17.898, represents the remaining effectsf all other parameters including sky temperature:

g = 17.898 + 0.951Tamb (5)here Tg and Tamb are in Kelvin.

.2. Comparison between the predicted and measuredndisturbed ground temperature

The absolute difference between the predicted and the mea-ured undisturbed ground temperature using both correlations

global and linear) are presented for comparison in the two faright columns in Table 4. Except for Dhahran, Sept-Iles and Luzern,he absolute error does not exceed 1.5 C, which means that thewo correlations (Eqs. (4) and (5)) predict the undisturbed ground

Fig. 4. Isotherms of the undisturbed gics 53 (2015) 379384 383

temperature well. The difference between the predictions of bothEqs. (4) and (5) is not important. It is clear therefore that the sim-ple formulation of Eq. (5), which needs only one input (ambienttemperature), is recommended.

3.3. Application of the linear equation for generating data forCanada

Based on only the annual average dry ambient temperature, Eq.(5) is used to generate isotherms of the undisturbed ground tem-perature for Canada. Results are presented on the map of Canada(Fig. 4). The map boundaries were generated from Canada geo-graphic map areas (the geographic reference data for the 2011Census of Canada). The area covered by the map is from latitude42 North to 68 North, since most ground thermal applicationsare concentrated in this part of the country. For the zones not cov-ered, users can use Eq. (5). It can be seen from this map that thecontours of the ground temperatures indicate a regional differenceranging from 12 C (south) to 7 C in the north. For the same lati-tudes, temperatures are generally higher in the west compared tothe east.

4. Conclusions

Two different correlations for the undisturbed ground tem-perature, global and simplified have been developed with adetermination coefficient higher than 0.98. They are obtained frommeasurement data given in thermal response test reports (TRT) forseventeen sites, covering a wide range of climates from cold cli-mate in Alert (North Pole in Canada) with latitude of 82.5 Northto warm climate in Dhahran (Saudi Arabia) with latitude of 26.3

North. The global correlation is a function of the ambient temper-ature, the sky temperature, the wind velocity and the global solarradiation on a horizontal surface. The contribution of each parame-ter in the undisturbed ground temperature has been analyzed andit has been found that the ambient temperature is dominant. Based

on this conclusion, a simplified correlation which depends only onthe ambient temperature has been developed. This correlation isvery useful and can be implemented in commercial software forthe design of boreholes.

round temperature for Canada.

3 therm

A

R

R

2

C

C

C

D

D

E

E

G

K

K

K

K

L

84 M. Ouzzane et al. / Geo

cknowledgements

Financial support for this work was provided by Naturalesources Canadas (Grant No: EEBI 022).

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New correlations for the prediction of the undisturbed ground temperature1 Introduction2 Undisturbed ground temperature3 Results and analysis3.1 Correlation development3.1.1 Global correlation3.1.2 Simplified correlation

3.2 Comparison between the predicted and measured undisturbed ground temperature3.3 Application of the linear equation for generating data for Canada

4 ConclusionsAcknowledgementsReferences