Florides-Kalogirou-2007-Ground heat exchangers—A review of systems models and applications

ARTICLE IN PRESS

Renewable Energy 32 (2007) 2461–2478

0960-1481/$ -

doi:10.1016/j

�CorrespoE-mail ad

www.elsevier.com/locate/renene

Review

Ground heat exchangers—A review of systems,models and applications

Georgios Florides, Soteris Kalogirou�

Higher Technical Institute, P.O. Box 20423, Nicosia 2152, Cyprus

Received 17 October 2006; accepted 23 December 2006

Available online 26 March 2007

Abstract

The temperature at a certain depth in the ground remains nearly constant throughout the year and

the ground capacitance is regarded as a passive means of heating and cooling of buildings. To exploit

effectively the heat capacity of the ground, a heat-exchanger system has to be constructed. This is

usually an array of buried pipes running along the length of a building, a nearby field or buried

vertically into the ground. A circulating medium (water or air) is used in summer to extract heat from

the hot environment of the building and dump it to the ground and vice versa in winter. A heat pump

may also be coupled to the ground heat exchanger to increase its efficiency. In the literature,

several calculation models are found for ground heat exchangers. The main input data are the

geometrical characteristics of the system, the thermal characteristics of the ground, the thermal

characteristics of the pipe and the undisturbed ground temperature during the operation of the

system. During the first stages of the geothermal systems study, one-dimensional models were devised

which were replaced by two-dimensional models during the 1990s and three-dimensional systems

during recent years. The present models are further refined and can accommodate for any type of

grid geometry that may give greater detail of the temperature variation around the pipes and in

the ground. Monitoring systems have been set up to test various prototype constructions with

satisfactory results.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Ground heat exchangers; Ground temperature; Heat exchanger models; Ground source heat pump

see front matter r 2007 Elsevier Ltd. All rights reserved.

.renene.2006.12.014

nding author. Tel.: +357 22 406466; fax: +357 22 406480.

dress: [email protected] (S. Kalogirou).

www.elsevier.com/locate/renene

dx.doi.org/10.1016/j.renene.2006.12.014

mailto:[email protected]

ARTICLE IN PRESSG. Florides, S. Kalogirou / Renewable Energy 32 (2007) 2461–24782462

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2462

2. Types of ground heat exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2463

2.1. Open systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2463

2.2. Closed systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2464

2.3. Miscellaneous systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2467

3. Ground thermal behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2467

4. Calculation models and evaluated performance of ground heat exchangers . . . . . . . . . 2470

5. Vertical U-tube ground heat exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2473

6. Deep geothermal systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2476

7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2476

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2477

1. Introduction

Measurements show that the ground temperature below a certain depth remainsrelatively constant throughout the year. This is due to the fact that the temperaturefluctuations at the surface of the ground are diminished as the depth of the groundincreases because of the high thermal inertia of the soil. Also, there is a time lag betweenthe temperature fluctuations at the surface and in the ground. Therefore, at a sufficientdepth, the ground temperature is always higher than that of the outside air in winter and islower in summer. The temperature variation of the ground at various depths in summer(August) and winter (January) is shown in Fig. 1. The graph shows actual groundtemperatures as measured in a borehole drilled for this purpose in Nicosia, Cyprus. As canbe seen, the temperature is nearly constant below a depth of 5m for the year round.The difference in temperature between the outside air and the ground can be utilised as a

preheating means in winter and pre-cooling in summer by operating a ground heatexchanger. Also, because of the higher efficiency of a heat pump than conventional naturalgas or oil heating systems, a heat pump may be used in winter to extract heat from therelatively warm ground and pump it into the conditioned space. In summer, the process

6

10

14

18

22

26

30

0 5 10 15 20 25 30 35 40 45 50

Depth in ground (m)

Te

mp

era

ture

(°C

)

25-Jan-05

20-Aug-05

Fig. 1. Temperature variation with depth.

ARTICLE IN PRESSG. Florides, S. Kalogirou / Renewable Energy 32 (2007) 2461–2478 2463

may be reversed and the heat pump may extract heat from the conditioned space and sendit out to a ground heat exchanger that warms the relatively cool ground.

Ground source heat pumps are receiving increasing interest in North America andEurope and the technology is now well established with over 550,000 units installedworldwide and with more than 66,000 units installed annually. About 80% of the unitsinstalled worldwide are domestic [1].

2. Types of ground heat exchangers

There are two general types of ground heat exchangers: open and closed [2]. In an opensystem, the ground may be used directly to heat or cool a medium that may itself be usedfor space heating or cooling. Also, the ground may be used indirectly with the aid of a heatcarrier medium that is circulated in a closed system. The loop of the heat exchanger ismade of a material that is extraordinarily durable but allows heat to pass throughefficiently. Loop manufacturers typically use high-density polyethylene which is a toughplastic, with heat fuse joints. This material is usually warranted for as much as 50 years.The fluid in the loop is water or an environmentally safe antifreeze solution. Other types ofheat exchangers used directly for heating and cooling utilise a copper piping placedunderground. As refrigerant is pumped through the loop, heat is transferred directlythrough the copper to the earth. The length of the loop depends upon a number of factorssuch as the type of loop configuration used, the house heating and air conditioning load,soil conditions, local climate and many more. These types of systems are examinedseparately below.

2.1. Open systems

In open systems, ambient air passes through tubes buried in the ground for preheatingor pre-cooling and then the air is heated or cooled by a conventional air conditioning unitbefore entering the building (Fig. 2).

Fig. 2. Basic principle of ground preheating or pre-cooling of air in an open system.

ARTICLE IN PRESS

Fig. 3. Ground water heat pump.

G. Florides, S. Kalogirou / Renewable Energy 32 (2007) 2461–24782464

In a similar way, the ground water of a water-bearing layer may be used as a coolingcarrier medium, brought in direct contact with the heat pump coils. In most cases two wellsare required, one for extracting the ground water and one for injecting it back into thewater-bearing layer as indicated in Fig. 3.

2.2. Closed systems

In this case heat exchangers are located underground, either in horizontal, vertical oroblique position, and a heat carrier medium is circulated within the heat exchanger,transferring the heat from the ground to a heat pump or vice versa. Fig. 4 indicates thehorizontal type which has a number of pipes connected together either in series or in parallel.This configuration is usually the most cost-effective when adequate yard space is

available and trenches are easy to dig. The trenchers have a depth of 1–2m in the groundand usually a series of parallel plastic pipes is used. Fluid runs through the pipes in aclosed system. A typical horizontal loop is 35–60m long per kW of heating or coolingcapacity [3]. Horizontal ground loops are the easiest to install while a building is underconstruction. However, new types of digging equipment allow horizontal boring and thusit is possible to retrofit such systems into existing houses with minimal disturbance of thetopsoil and even allow loops to be installed under existing buildings or driveways.In USA, some special ground heat exchangers have been developed for heat pump

systems, in which the pipe is curled into a slinky shape (Fig. 5). In this way, it is possible toplace more pipes into shorter trenches in order to reduce the amount of land space needed[3]. These collectors are best suited for heating and cooling in places where naturaltemperature recharge of the ground is not vital.For all horizontal systems in heating-only mode, the main thermal recharge is provided

by the solar radiation falling on the earth surface. Therefore, it is important not to coverthe surface above the ground heat collector.Vertical ground heat exchangers or borehole heat exchangers, shown in Fig. 6, are

widely used when there is a need to install sufficient heat exchange capacity under

ARTICLE IN PRESS

Fig. 5. ‘‘Slinky’’-type ground heat exchanger.

Fig. 4. Horizontal-type ground heat exchangers (redrawn from Ref. [2]).

G. Florides, S. Kalogirou / Renewable Energy 32 (2007) 2461–2478 2465

a confined surface area such as when the earth is rocky close to the surface, or whereminimum disruption of the landscape is desired. This is possible because the temperaturebelow a certain depth remains constant over the year (see Fig. 1). In a standardborehole, which in typical applications is 50–150m deep, plastic pipes (polyethylene orpolypropylene) are installed, and the space between the pipe and the hole is filled with anappropriate material to ensure good contact between the pipe and the undisturbed groundand reduce the thermal resistance [3].

ARTICLE IN PRESS

Fig. 6. Vertical ground heat exchangers.

Fig. 7. Common vertical ground heat exchanger designs.


Vertical loops are generally more expensive to install, but require less piping thanhorizontal loops because the earth deeper down is cooler in summer and warmer in winter,compared to the ambient air temperature.Several types of borehole heat exchangers were tested and are widely used. These are

classified in two basic categories as shown in Fig. 7:

(a).
U-pipes, consisting of a pair of straight pipes, connected with a U-turn at the bottom.Because of the low cost of the pipe material, two or even three of such U-pipes areusually installed in one hole.

ARTICLE IN PRESS

Fig. 8. Standing column well.

G. Florides, S. Kalogirou / Renewable Energy 32 (2007) 2461–2478 2467

(b).
Concentric or coaxial pipes, joint either in a very simple way with one straight pipeinside a bigger diameter pipe or joint in complex configurations.
2.3. Miscellaneous systems

A number of ground systems cannot be categorised either as open or as closed. Such asystem is the standing column well shown in Fig. 8, where water is pumped from thebottom of the well to the heat pump. The exiting water is percolated through gravel in theannulus of the well in order to absorb heat. Standing wells are typically 15 cm in diameterand may be as deep as 500m; therefore they are very expensive [3]. Other sources of heatare the use of water in mines and tunnels. This water has a steady temperature the wholeyear round and is easily accessible.

3. Ground thermal behaviour

The use of direct or indirect earth-coupling techniques for buildings and agriculturalgreenhouses requires knowledge of the ground temperature profile at the surface and atvarious depths. The ambient climatic conditions affect the temperature profile below theground surface (Fig. 9) and need to be considered when designing a heat exchanger.Actually the ground temperature distribution is affected by the structure and physicalproperties of the ground, the ground surface cover (e.g., bare ground, lawn, snow, etc.) andthe climate interaction (i.e., boundary conditions) determined by air temperature, wind,solar radiation, air humidity and rainfall. The temperature distribution at any depthbelow the earth surface remains unchanged throughout the year with the temperatureincreasing with depth with an average gradient of about 30 1C/km. The geothermal

ARTICLE IN PRESS

Fig. 9. Energy flows in ground.


gradient deviations from the average value are, in part, related to the type of rocks presentin each section.Heat flow, which is a gauge of the amount of thermal energy coming out of the earth, is

calculated by multiplying the geothermal gradient by the thermal conductivity of theground. Each rock type has a different thermal conductivity, which is a measure of theability of a material to conduct heat. Rocks that are rich in quartz, like sandstone, have ahigh thermal conductivity, indicating that heat readily passes through them. Rocks that arerich in clay or organic material, like shale and coal, have low thermal conductivity,meaning that heat passes slower through these layers. If the heat flow is constantthroughout a drill hole (i.e., water is not flowing up or down the hole), then it is obviousthat low-conductivity shale layers will have a higher geothermal gradient compared tohigh-conductivity sandstone layers [4].Mihalakakou et al. [5] present a complete model for the prediction of the daily and

annual variation of ground surface temperature. The model uses a transient heatconduction differential equation and an energy balance equation at the ground surfaceto predict the ground surface temperature. The energy balance equation involvesthe convective energy exchange between air and soil, the solar radiation absorbed by theground surface, the latent heat flux due to evaporation at the ground surface as well as the


long-wave radiation. Therefore, the ground surface temperature can be estimated from [6]:

T surðtÞ ¼ Tm þ As ReðeiwtÞ, (1)

where Tm is the mean annual ground surface temperature, As is the amplitude of thetemperature wave at the ground surface and w is the frequency of the temperature wave.

In order to solve Eq. (1), the following energy balance equation at ground surface wasused as a boundary condition equation at the ground surface [7]:

�KqT sur

qy

��y¼0

¼ CE� LRþ SR� LE; (2)

where K is the thermal conductivity of the soil, CE is the convective energy exchangedbetween air and ground surface, LR is the long-wave radiation emitted from the groundsurface, SR is the solar radiation absorbed from the ground surface and LE is the latentheat flux due to evaporation.

The model is validated against 10 years of hourly measured temperatures for bare andshort-grass covered soil in Athens and Dublin. The results are compared with thecorresponding results of models using Fourier analysis. Furthermore, a sensitivityinvestigation is performed to investigate the influence of various factors involved in theenergy balance equation at the ground surface on the soil temperature profile.

Popiel et al. [8] present the temperature distributions measured in the ground for theperiod between summer 1999 and spring 2001. The investigation was carried out inPoznan, Poland, for two differently covered ground surfaces, a bare surface and a surfacecovered with short grass. Temperatures were measured with thermocouples distributed inthe ground at a depth from 0 to 7m (bare surface) and from 0 to 17m (short grass). It wasfound that the short-period temperature variations reached a depth of approximately 1m.From July to the end of September, from the surface region at ground depth (below about1.5m), a heat flux of 3.6W/m2 was transferred. Usually, the recommended depth forhorizontal ground heat exchangers is from 1.5 to 2m. The measurements also show thatduring the summer period the ground temperature under the bare surface below 1m wasabout 4 1C higher in comparison to the temperature of the ground covered with shortgrass. Therefore, for the ground ‘‘cold’’ source, e.g., for the air conditioning applicationthe surface covered with short grass is recommended. However, in winter, the temperaturedistributions were almost the same. A comparison of the Buggs’s formula for the groundtemperature distribution adapted to the European region of Poznan shows a goodagreement with the experimental data.

From the point of view of the temperature distribution, Popiel et al. [8] distinguish threeground zones:

1.
Surface zone reaching a depth of about 1m, in which the ground temperature is verysensitive to short time changes of weather conditions.
2.
Shallow zone extending from the depth of about 1–8m (for dry light soils) or 20m (formoist heavy sandy soils), where the ground temperature is almost constant and close tothe average annual air temperature; in this zone the ground temperature distributionsdepend mainly on the seasonal cycle weather conditions.
3.
Deep zone (below about 8–20m), where the ground temperature is practically constant(and very slowly rising with depth according to the geothermal gradient).


4. Calculation models and evaluated performance of ground heat exchangers

Several calculation models for ground-coupled heat exchangers are found in theliterature. Early models generally used a one-dimensional description of the pipe to derivea relation between its inlet and outlet temperature. Tzaferis et al. [9] studied eight modelsto predict the performance of ground-to-air heat exchangers. The algorithms of the studiedmodels either calculate the conductive heat transfer from the pipe to the ground mass orcalculate the convective heat transfer from the circulating air to the pipe. Input datainclude the geometrical characteristics of the system, the thermal characteristics of theground and the thermal characteristics of the pipe together with the undisturbed groundtemperature during the operation of the system or only the temperature of the pipe surface.The algorithms of the eight models were introduced into computer programs to simulatethe behaviour of the ground-to-air heat exchangers. Experimental results were alsoobtained for a PVC horizontal pipe, buried at a depth of 1.1m and compared to thecalculated values. Six of the eight models gave very close results to the actual values withan rms error in each case of about 3.5%. In the examined models, the thermal capacity ofthe ground is not considered and therefore the influence of different pipes on each otherand the temperature profiles in the ground cannot be studied.Bi et al. [10] used a two-dimensional cylindrical coordinate system to model a vertical

double spiral coil ground heat exchanger (GHx). This ground heat exchanger was designedby the authors for a ground source heat pump (GSHP) system. The undergroundtemperature distribution of the coil was solved numerically and the results were comparedto measured temperature data. They concluded that the temperature distribution isimportant to the performance improvement of the GSHP, and especially for the GHx andthat the analytical and experimental results prove that the GHx design is reasonable.Mihalakakou et al. [11] present a model in which the ground surrounding the pipe and

the pipe itself are described in polar co-ordinates. In this model the temperature andmoisture profiles of the ground are included in the equations. The influence of the groundsurface temperature is modelled by the superposition of the algebraic solution of theundisturbed temperature field caused by the surface air temperature and the temperaturefield caused by the pipe. The authors show the importance of including the moisturecontent in the soil. The model is solved in the TRNSYS (a modular energy systemsimulation program) environment and validated with good results.Mihalakakou et al. [12] investigated the heating potential of a single ground-to-air heat

exchanger as well as the potential of a multiple parallel earth tube system. An accuratenumerical model was used to investigate the dynamic thermal performance of the systemduring the winter period in Dublin. The model had been successfully validated against anextensive set of experimental data. The results showed that the heating potential of thesystem during winter is significantly important. The obtained results showed that theeffectiveness of the ground-to-air heat exchanger increases with an increase in the pipelength (checked range: 30–70m). Also, there is an increase in effectiveness when the pipe isburied in greater depths (3m instead of 1.2m). By increasing the pipe diameter from 100 to150mm, it was shown that the heating capacity of the system was reduced. This is due to areduction in the convective heat transfer coefficient and an increase in the pipe surface,therefore, providing a lower air temperature at the pipe outlet. Finally, a higher air velocityin the pipe (checked range: 5–15m/s) leads to a reduction of the systems heating capacity,mainly because of the increased mass flow rate inside the pipe.


Bojic et al. [13] developed a model in which the soil is divided into horizontal layers withuniform temperature. All the pipes are placed in one layer at the same depth and parallel toeach other. The heat transported to the soil by convection from the air and the solarirradiation is calculated. Also an equation describing the heat flow between the airflow inthe pipe and the neighbouring soil layer is used. All equations used for the soil layers ineach time step are steady-state energy equations. This model is a two-dimensional modeltherefore the influence that pipes have on each other may not be evaluated.

Gauthier et al. [14] describe a fully three-dimensional model. A simple Cartesian co-ordinate system is used and the round pipes are replaced with square pipes of equivalentareas. The thermophysical properties of the ground are considered constant andtemperature independent, but actually the ground may not be homogenous. In this way,the influence of different layers in the ground, concrete foundations and insulation can beevaluated. The heat transfer caused by moisture gradients in the ground is assumed to benegligible with respect to that caused by temperature gradients. Heat transfer in the pipes isdominated by convection in the axial direction but coupled with the temperature field inthe ground via the boundary condition on the pipe surface. The model is thoroughlyvalidated with experimental data taken from a ground heat exchanger storage systeminstalled in a commercial-type greenhouse. Finally, the various parameters that affect thebehaviour of the ground heat exchanger storage system are examined.

De Paepe and Willems [15] further refined the above Gauthier et al. [14] approach andthe model was used to study the performance of a ground-coupled air heat exchanger inthe Belgian climate. A three-dimensional unstructured finite volume model was derivedand the FLUENT solver was used to obtain the numerical solutions. The model considerstransient and fully three-dimensional conduction heat transfer in the soil and othermaterials. The heat transfer by moisture gradients in the soil is neglected and the heattransfer in the pipe is dominated by convection.

The governing equation for the conduction in the soil may be stated as:

rcp

qT

qt¼ lrT , (3)

where r is the density (kg/m3), cp the heat capacity (J/kgK), l the thermal conductivity(W/mK), T the temperature (K) and t the time (s).

The boundary conditions for the underground lateral external surfaces of thecomputational domain are assumed to be adiabatic, thus:

qT

qn¼ 0, (4)

where n is the unit vector normal to the surface.A constant and uniform temperature for the horizontal plane deep underground is

imposed. At the ground surface the heat flux from the ambient air to the surface iscalculated from:

lqT

qz¼ hsurrðT soil � T surrÞ, (5)

where Tsurr is the temperature of the surrounding air and this can be a constant value or atime-dependent function, and hsurr is the convection coefficient.

The results show that the influence of the pipe on the temperature of the surroundingsoil is limited to a distance of twice its diameter. To make optimal use of the thermal


capacity of the soil and to eliminate the influence of the outside air, the tubes have to beburied below a depth of 2.5m and the length of the tube can be optimised with thecalculation model to obtain an efficient heat exchanger.Hollmuller and Lachal [16] examined the winter preheating and summer cooling

potential of buried pipe systems under the central European climate. The simulation modelof the air-to-ground heat exchanger used, accounts for sensible and latent heat transfer.The model additionally accounts for frictional losses and water infiltration and flow alongthe tubes. It further allows for control of airflow direction as well as for flexible geometry(inhomogenous soils, diverse border conditions, use of symmetries or pattern repetitionsfor run-time economy) and is adapted to TRNSYS. The basic equations of the modeldescribe the mass and energy exchanges between air and tube. The study concludes that inCentral Europe there is a fundamental asymmetry between heating and cooling potentialswith the ground used as a seasonal energy buffer. In winter, preheating of fresh air acts as asaving function on energy demand to which it is inherently linked by limitation of flowrate. In summer, inertial cooling (smoothening of ambient temperature below comfortthreshold) increases along with flow rate and hence becomes an energy-producing serviceon its own. Air preheating with buried pipes is more expensive than that with fuel (abouttwice the cost per kWh), which it cannot substitute completely. On the contrary, buriedpipe inertial cooling, together with an (avoided) air conditioning system, is competitive andallows simultaneous savings on electricity, capital costs and CFC gases. Buried pipesystems may be subject to water infiltration, which can lower winter performance andenhance summer performance, but also raises sanitary problems related to stagnant water.These problems can be avoided by replacing buried pipes with a closed water undergroundcircuit coupled to the fresh air system via a water/air heat exchanger. One of theeconomically important parameters to deal with is the pipe depth, which relates to surfacetemperature. Preliminary results in this climate show that for cooling purposes excavationshould be kept to a minimum.Pfafferott [17] presents a paper dealing with the dynamic temperature behaviour and

energy performance of three ground-to-air heat exchangers (GAHx) for mid Europeanoffice buildings located in Germany.The first GAHx is located at Hamm designed with pipe diameters of 200 and 300mm, a

total duct surface area of 1650m2, depth of ducts 2–4m around the foundation slab in dryrock, a mean airflow of 10,300m3/h and an air speed of 2.2m/s. As it is mentioned, themain characteristic describing energy performance is the overall heat transfer coefficient h,which in this case is 5.5W/m2K.The second GAHx is located at Freiburg designed with a pipe diameter of 250mm, a

total duct surface area of 522m2, depth of ducts 2m partly below the foundation slab indry gravel, a mean airflow of 7000m3/h and an air speed of 5.6m/s. In this case, the overallheat transfer coefficient is 5.0W/m2K.The third GAHx is located at Weilheim designed with a pipe diameter of 350mm, a total

duct surface area of 198m2, depth of ducts 2.3m around the foundation slab in moist clay,a mean airflow of 1100m3/h and an air speed of 1.6m/s. The overall heat transfercoefficient is 3.2W/m2K.The thermal performance of the GAHx is calculated using four different approaches, a

dimensionless ratio of temperature variation RT, the mean heat transfer coefficient hmean,the temperature ratio Y and the coefficient of performance COP. It is concluded that theevaluation of a GAHx depends on project-specific criteria. Each of the evaluated GAHx is


shown to be the best from a certain point of view. The first GAHx narrows the outlet airtemperature close to the undisturbed earth temperature. The second GAHx supplies thehighest specific energy gain based on the total surface area. And the third GAHx has thehighest COP. Pipe lengths up to 100m and pipe diameters around 250mm are profitable. Ifthe GAHx aims at a high specific energy performance, a small specific surface area shouldbe reached using fewer pipes. If the GAHx aims at a high temperature ratio, a high specificsurface area should be reached using more pipes. Finally, it is mentioned that all threeGAHx supply more heating and cooling energy than the primary energy they use for thefan input.

De Paepe and Janssens [18] used a one-dimensional analytical method to examine theinfluence of the design parameters of the heat exchanger on the thermo-hydraulicperformance and devise an easy graphical design method which determines thecharacteristic dimensions of the ground-air heat exchanger in such a way that optimalthermal effectiveness is reached with acceptable pressure loss. Therefore, the choice of thecharacteristic dimensions is independent of the soil and climatological conditions. Thisallows designers to choose the ground-air heat exchanger configuration with the bestperformance.

Their analysis considers the air mass flow rate, the inlet air temperature, the desiredoutlet air temperature, the ground temperature and the geometric sizing parameters whichare the diameter of the tube, the length of the tube and the number of tubes in parallel inthe heat exchanger. As they emphasise generally, lowering the diameter of the tube raisesthe effectiveness but on the contrary higher flow rates reduce the effectiveness. So it isbetter to have several tubes of small diameter over which the flow rate is divided. Longtubes with a small diameter are profitable for the heat transfer but at the same time thepressure drop in the tubes is raised, resulting in high fan energy. On the other hand, havinga small flow rate per tube and a large diameter gives the least pressure loss. This wouldmean that it is better to use many tubes, with a large diameter, which is in conflict with thethermal demand of a small diameter. In both cases a large number of tubes is beneficial.The tube length and diameter combination have to be optimised and this is achieved by agraphical method by reducing the influencing parameters and introducing the specificpressure drop. The specific pressure drop is a measure for the pressure drop needed toachieve a given thermal performance. In this way, a maximal specific pressure drop can becalculated when a value for the effectiveness of the ground-air heat exchanger is chosen.The effectiveness is dictated by the design requirements and climatic conditions, but oftenan effectiveness of 80% is considered to be an optimum value for a ground-air heatexchanger [19]. A higher effectiveness is only achievable at the cost of a large increase inthe tube length or in the number of tubes.

5. Vertical U-tube ground heat exchangers

In a vertical U-tube ground heat exchanger, a water pump circulates fluid through pipesinserted into a borehole in the ground. The borehole, after the insertion of the U-tube, isusually backfilled with grout in order to ensure good thermal contact with the ground.The grout is often a bentonite clay mixture, with the possibility of having thermallyenhanced additives in order to present a thermal conductivity significantly lower than thesurrounding ground. The circulating fluid is usually water or a water–antifreeze mixture.


A borehole heat exchanger is usually drilled to a depth between 20 and 300m with adiameter of 10–15 cm. A borehole system can be composed of a large number of individualboreholes.Several models for calculating the thermal properties of a ground heat exchanger are

available. These models, which are based on Fourier’s law of heat conduction, include theanalytical line source model [20] and the cylindrical source model [21] and severalnumerical models [22–25]. The most widely used method at this time is the line sourcemodel. The model is a simplification of the actual experiment, and data analysis is based onthe theory describing the response of an infinite line source.Mands and Sanner [26] carried out the thermal response test on a number of boreholes.

For a thermal response test, basically a specified heat load is applied into the hole and theresulting temperature changes of the circulating fluid are measured. In this way, thethermal conductivity of the borehole is measured on site allowing sizing of the boreholesbased upon reliable underground data.The test data consist of one or more curves showing the fluid temperature development

against elapsed time. The easiest way to evaluate the test data makes use of the line sourcetheory and the following formula is utilised to calculate the thermal conductivity:

leff ¼Q

4pHk, (6)

where leff is the effective thermal conductivity, including influence of groundwater flow,borehole grouting, etc. (W/mK), Q is the heat injection/extraction (J), H is the length ofborehole heat exchanger (m) and k is the inclination of the curve of temperature versuslogarithmic time (K/s).A second value that can be determined by a response test is the borehole thermal

resistance, Rb. This value gives the temperature drop between the natural ground and thefluid in the pipes. It is also possible to calculate Rb from the dimensions and materials used.The authors present a table indicating the effective thermal conductivity and the thermal

borehole resistance for various grounds in Germany (Table 1).Pahud and Matthey [27] in their paper explain how the thermal performance of a

borehole heat exchanger can be assessed with a response test. The tested boreholes differfrom one another by the filling material which may be a standard mixture of bentonite andcement, a standard mixture of bentonite and cement with the addition of quartz sand or

Table 1

Geology and results for some thermal response tests carried out in Germany since 1999

Geology Thermal conductivity, leff (W/mK) Resistance, Rb (K/(W/m))

Silt and clay (Quarternary/Tertiary) 1.6 –

Mesozoic sediments 2.7–2.8 0.10–0.18

Marl (‘‘Emschermergel’’, Cretaceous) 1.5–2.0 0.11–0.12

Sand/silt, marl (Cretaceous) 2.3 0.08a

Sand and clay (Quarternary/Tertiary) 2.8 0.11

Sand and clay (Quarternary/Tertiary) 2.2–2.3 0.07–0.08a

Marl, clayey 2.5 0.12

Marl, sandstone, limestone (Mesozoic) 4.0 0.08a

Silt, sandy (Quarternary/Tertiary) 3.4 0.06a

aFilled with thermally enhanced grout (‘‘Stuwatherm’’).


only quartz sand, and the use or omission of spacers to keep the plastic pipes apart fromeach other and close to the borehole wall. Using an average estimated ground thermalconductivity of 2.5W/mK, the tests show that the thermal resistance can be decreased by30% when quartz sand is used instead of bentonite and when spacers are used to keep theplastic pipes in contact with the borehole wall. With a common heat extraction rate of50W per metre of borehole length, the temperature gain in a heat pump evaporator is+2K. Also, it is mentioned that for a typical residential house in Switzerland, a boreholeheat exchanger of 100–200m is used with a diameter of 10–15 cm, depending on the energydemand and the ground conditions. For typical ground conditions and a single boreholeheat exchanger, the borehole length is sized for a heat extraction rate of 50W per metre ofborehole length.

Roth et al. [28] describe their in situ experiment for the determination of the thermalproperties of the soil (thermal conductivity, borehole thermal resistance and undisturbedsoil temperature), which were needed for designing a ground heat exchanger forunderground thermal energy storage (UTES). As they mention, about 10 countries inthe world are dealing nowadays with this type of investigation including Germany,Sweden, Canada, USA, Norway, Netherlands, England and Turkey.

Their test was carried out for over 9 days (24 June to 3 July 2003) while inlet andoutlet fluid temperatures of the borehole heat exchanger, the ambient temperature andvarious other necessary parameters were measured. A comparison of results between theconventional slope determination method, the geothermal properties measurement (GPM)data evaluation software method and the two-variable parameter fitting method wasperformed in order to calculate the thermal conductivity and borehole thermal resistance.The determined value of thermal conductivity was 1.8W/mK and the borehole thermalresistance was 0.3mK/W. They also concluded the following:

(a).
The application of the classical slope determination and/or two-variable parameterfitting can be used as a fast and reliable tool for data evaluation.
(b).
The accuracy of the evaluation depends on the care taken when performing the test.Important aspects are reliable temperature measurements, constant power supply, aproper determination of undisturbed underground temperature and weatherproofingthe system as much as possible.
(c).
The value of the thermal conductivity was quite insensitive to the operating hoursbefore recording but exhibited an oscillatory behaviour regarding the duration of testcondition. Large relative error for short tests, converging for test duration over 120 hwas the trend of the thermal conductivity when compared to the 1.8W/mK expectedvalue.
(d).
The fluctuations exhibited by the experimental curve are mainly governed bycorresponding fluctuations of ambient temperature and by fluctuations of electricpower supply especially during night hours.
(e).
An overall heat loss coefficient of 5.3W/K was determined applying a model based onan energy balance between the hot parts of the system and the surroundingenvironment.
Zeng et al. [29] in their paper present a new quasi-three-dimensional model for verticalground heat exchangers (GHx) that accounts for the fluid axial convective heat transferand thermal ‘‘short-circuiting’’ among U-tube legs. Analytical expressions of the borehole


resistance have been derived for different configurations of single and double U-tubeboreholes and analytical solutions of the fluid temperature profiles along the boreholedepth have been obtained. As they mention, borehole depths usually range from 40 to200m with diameters of 75–150mm. Analyses have shown that the single U-tube boreholesyield considerably higher borehole resistance than double U-tube boreholes. The doubleU-tubes in parallel configuration provide better thermal performance than those in series.Calculations show that the double U-tube boreholes are superior to those of the singleU-tube with reduction in borehole resistance of 30–90%. Calculations on typical GHxboreholes indicate that the U-tube shank spacing and the thermal conductivity of the groutare the prevailing factors in all the configurations considered in determining the boreholethermal resistance. Finally, discussions in this paper are limited to the thermal resistanceinside the boreholes with U-tubes even though the thermal conduction outside theboreholes often plays an even more important role in the GHx heat transfer process. Inaddition, many factors such as the capital cost of borehole fields and circulating pumpenergy consumption must also be taken into consideration when merits and weaknesses ofdifferent borehole configurations are to be assessed.

6. Deep geothermal systems

Kujawa et al. [30] studied the case of deep geothermal heat plants. These plants operatewith one or two-hole systems. A computational model is presented which estimates thetemperature of the geothermal water extracted to the earth’s surface as well as thetemperature of the water injected into a deposit level. The predicted characteristics do nottake into account specific working conditions of the systems.It is mentioned that the high expenditure incurred in drilling holes deters one from using

this method in gaining thermal energy. The one-hole injection system or the use of existingsingle holes, made during crude-oil and or natural-gas exploration, reduces the capitalcost. In one-hole systems, the hole is adapted to locate in it a vertical exchanger with adouble-pipe heat exchanger in which the geothermal water is extracted via the inside pipe.Published characteristics allow one to estimate the gained geothermal heat-energy flux as afunction of the difference of temperatures of extracted as well as injected water at differentvolume fluxes of the geothermal water. In general, the two-layer systems and two-holesystems are more advantageous than the one-hole system.

7. Conclusions

In this paper, various types of ground heat exchangers are described. Ground heatexchangers are used to exploit effectively the heat capacity of the soil and commonly theyare coupled to heat pumps for increasing their efficiency. One, two and three-dimensionalmodels can be found in the literature that simulate the heat transfer process. Simulationmodels may be used successfully for sizing and predicting the thermal performance ofground heat exchangers. These exchangers usually supply more heating and cooling energythan the primary energy they use for power input for the fan or pump.As it can be concluded from the studies presented in this paper at a sufficient depth, the

ground temperature is always higher than that of the outside air in winter and is lower insummer. This difference in temperature can be utilised as a preheating means in winter andpre-cooling in summer by operating a ground heat exchanger. Usually the recommended


depth for horizontal ground heat exchangers is from 1.5 to 2m. In order to minimiseinterference between multiple pipes, a separation distance of 30 cm between pipes isrecommended and trenches should be at least 2m apart. A typical horizontal loop is35–60m long per kW of heating or cooling capacity.

A vertical borehole heat exchanger is usually drilled to a depth of 20–300m with adiameter of 10–15 cm. A borehole system can be composed of a large number of individualboreholes. For a typical residential house in Switzerland, a borehole heat exchanger of100–200m is required with a diameter of 10–15 cm, depending on the energy demand andthe ground conditions. For typical ground conditions and a single borehole heatexchanger, the borehole length is sized for a heat extraction rate of 50W/m of boreholelength. Performance degradation can occur if adjacent boreholes are too close, and aseparation distance of 5m is usually considered adequate.

Calculations on typical GHx boreholes indicate that the U-tube shank spacing and thethermal conductivity of the grout are the prevailing factors in all the configurationsconsidered in determining the borehole thermal resistance.

Generally, the effectiveness of ground-to-air heat exchangers increases with an increasein the pipe length. Also, there is an increase in effectiveness when the pipe is buried ingreater depths. The heating capacity of the system was reduced by increasing the pipediameter. Finally, a higher air velocity in the pipe leads to a reduction of the systemsheating capacity, mainly because of the increased mass flow rate inside the pipe.

The line source model is an easy method of evaluating the characteristics of the boreholeand does not need expensive equipment. By evaluating the borehole characteristics, nooversized or undersized equipment are installed; therefore, there is lower investment costand the equipment function with the required output and performance.

References

[1] Lund J. Ground heat worldwide utilization of geothermal energy. Renew Energy World 2005;8(4):254–60.

[2] Mands E, Sanner B. Shallow geothermal energy, /http://www.ubeg.de/Downloads/ShallowGeothEngl.pdfS;2005.

[3] Geothermal Heat Pump Consortium. /http://www.geoexchange.orgS; 2005.

[4] Kelley S. Temperatures in the Kiowa drill hole. Denver basin project—The Denver Museum of Nature

Science (DMNS). /http://www.dmnh.org/denverbasin/r_temp.htmlS; 2005.

[5] Mihalakakou G, Santamouris M, Lewis O, Asimakopoulos D. On the application of the energy balance

equation to predict ground temperature profiles. Sol Energy 1997;60(3/4):181–90.

[6] Carlslaw HS, Jaeger JC. Conduction of heat in solids, 2nd ed. Oxford: Oxford Science Publishers; 1980.

[7] Krarti M, Lopez-Alonso C, Claridge DE, Kreider JF. Analytical model to predict annual soil surface

temperature variation. Int J Energy Eng 1995;117:91–9.

[8] Popiel C, Wojtkowiak J, Biernacka B. Measurements of temperature distribution in ground. Exp Therm

Fluid Sci 2001;25:301–9.

[9] Tzaferis A, Liparakis D, Santamouris M, Argiriou A. Analysis of the accuracy and sensitivity of eight models

to predict the performance of earth-to-air heat exchangers. Energy Buildings 1992;18:35–43.

[10] Bi Y, Chen L, Wu C. Ground heat exchanger temperature distribution analysis and experimental verification.

Appl Therm Eng 2002;22:183–9.

[11] Mihalakakou G, Santamouris M, Asimakopoulos D. Modelling the thermal performance of earth-to-air heat

exchangers. Sol Energy 1994;53(3):301–5.

[12] Mihalakakou G, Lewis J, Santamouris M. On the heating potential of buried pipes techniques-application in

Ireland. Energy Buildings 1996;24:19–25.

[13] Bojic M, Trifunovic N, Papadakis G, Kyritsis S. Numerical simulation, technical and economic evaluation of

air-to-earth heat exchanger coupled to a building. Energy 1997;22(12):1151–8.

http://www.ubeg.de/Downloads/ShallowGeothEngl.pdf

http://www.geoexchange.org

http://www.dmnh.org/denverbasin/r_temp.html


[14] Gauthier C, Lacroix M, Bernier H. Numerical simulation of soil heat exchanger-storage systems for

greenhouses. Sol Energy 1997;60(6):333–46.

[15] De Paepe M, Willems N. 3D unstructured modelling technique for ground-coupled air heat exchanger. In:

Clima 2000/Napoli World Congress, Napoli, Italy; 2001. p. 15–8.

[16] Hollmuller P, Lachal B. Cooling and preheating with buried pipe systems: monitoring, simulation and

economic aspects. Energy Buildings 2001;33:509–18.

[17] Pfafferott J. Evaluation of earth-to-air heat exchangers with a standardized method to calculate energy

efficiency. Energy Buildings 2003;35:971–83.

[18] De Paepe M, Janssens A. Thermo-hydraulic design of earth-air heat exchangers. Energy Buildings

2003;35:389–97.

[19] DBA Annex 28. Early design guidance for low energy cooling technologies. Energy conservation in buildings

and community systems programme, Annex 28: Low energy cooling, International Energy Agency, Subtask

2, Report 2; 1999.

[20] Ingersoll LR, Zobel OJ, Ingersoll AC. Heat conduction with engineering, geological and other applications.

New York: McGraw-Hill; 1954.

[21] Carslaw HS, Jaeger JC. Conduction of heat in solids, 2nd ed. Oxford: Clarendon Press; 1993.

[22] Eskilson P. Thermal analysis of heat extraction boreholes. Ph.D. thesis. Lund, Sweden: Lund University,

Department of Mathematical Physics; 1987.

[23] Muraya NK. Numerical modeling of the transient thermal interference of vertical U-tube heat exchangers.

Ph.D. thesis. College Station, TX: Texas A&M University; 1995.

[24] Shonder JA, Beck JV. Determining effective soil formation thermal properties from field data using a

parameter estimation technique. ASHRAE Trans 1999;105(1):458–66.

[25] Kavanaugh SP, Rafferty K. Ground source heat pumps: design of geothermal systems for commercial and

institutional buildings. Atlanta: American Society of Heating, Refrigeration and Air-Conditioning

Engineers; 1997.

[26] Mands E, Sanner B. In-situ-determination of underground thermal parameters. /http://www.geothermie.de/

egec-geothernet/igd2k1/In-situ-determination%20of%20underground%20thermal%20parameters.pdfS;

2005.

[27] Pahud D, Matthey B. Comparison of the thermal performance of double U-pipe borehole heat exchangers

measured in situ. Energy Buildings 2001;33:503–7.

[28] Roth P, Georgiev A, Busso A, Barraza E. First in situ determination of ground and borehole thermal

properties in Latin America. Renew Energy 2004;29:1947–63.

[29] Zeng H, Diao N, Fang Z. Heat transfer analysis of boreholes in vertical ground heat exchangers. Int J Heat

Mass Transf 2003;46:4467–81.

[30] Kujawa T, Nowak W, Stachel A. Heat-flow characteristics of one-hole and two-hole systems for winning

geothermal heat. Appl Energy 2003;74:21–31.

http://www.geothermie.de/egec-geothernet/igd2k1/In-situ-determination%20of%20underground%20thermal%20parameters.pdf

http://www.geothermie.de/egec-geothernet/igd2k1/In-situ-determination%20of%20underground%20thermal%20parameters.pdf

Documents

Florides-Kalogirou-2007-Ground heat exchangers—A review of systems models and applications