influence of debonding in ground heat exchangers used with geothermal heat pumps

Influence of debonding in ground heatexchangers used with geothermal heat pumps

Aristodimos J. Philippacopoulos*, Marita L. Berndt

Department of Energy Sciences and Technology, Brookhaven National Laboratory, Upton,

New York 11973, USA

Received 4 April 2000; accepted 12 February 2001

Abstract

Debonding in ground heat exchangers used with geothermal heat pumps may occur for avariety of reasons, such as shrinkage of the backfill materials or surrounding formation,improper grouting and thermal mismatch. The effect of thermal contact resistance on the heatconduction due to debonding in ground heat exchangers was investigated using a set of one-

dimensional simplified analytical models as well as two-dimensional finite element models.From the cases studied, debonding at the backfill/pipe interface was found to be of greatersignificance than debonding between grout and surrounding formation. # 2001 CNR.

Published by Elsevier Science Ltd. All rights reserved.

Keywords: Geothermal heat pumps; Grout; Debonding; Thermal resistance; Heat transfer

1. Introduction

A key component of a geothermal heat pump system (GHP) is the ground heatexchanger. In the case of a closed loop vertical system this consists of a U-loop, thebackfill (usually a grouting material) and the surrounding formation. Because of itsimportance, the ground heat exchanger has become the subject of intensive engi-neering evaluations in recent years. The majority of them have focused on the heattransfer that takes place between the U-loop and the surrounding formation.Knowledge of this heat transfer is necessary to compute the required length of theground heat exchanger. There are several approaches available today to perform thistask (e.g. Kavanaugh, 1984; Kavanaugh and Rafferty, 1997). In addition, solutions of

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E-mail address: [email protected] (A.J. Philippacopoulos).

the heat transfer problem are employed by studies motivated towards increasing thereliability of GHPs. Such studies typically can be divided into two general cate-gories, which are intimately related. The first deals with the development of meth-odologies and numerical techniques required to evaluate the heat field associatedwith the heating and cooling modes of operation. Using the properties of the com-ponents of the system (e.g. thermal conductivities of the backfill, pipe and the for-mation), one can use any of the existing approaches to compute the temperaturedistribution near and around the ground heat exchanger. The second category dealswith in-situ measurements and experimental studies designed to evaluate funda-mental properties of the system such as its thermal conductivity. Examples of recentresearch on the heat transfer in vertical ground heat exchangers include Muraya(1994), Gu (1995), Rottmayer et al. (1997), Yavuzturk et al. (1999), and Austin et al.(2000).The development of methods to analyze the heat transfer in ground heat exchan-

gers includes analytical as well as numerical approaches. The former approaches arerestricted to limited configurations because of the complexity of the problem. Thiscomplexity arises mainly from two sources. The first is due to the thermal load,which is different in both legs of the U-loop and therefore requires asymmetricsolutions. The complexity of the problem is further compounded by the geometricrequirement to have asymmetric solutions due to the presence of the two pipes.Therefore, if it were assumed that the surrounding formation is reasonably uniform,a symmetric solution of the heat transfer problem would not be generally applicabledue to geometric and loading conditions reflected by what is inside the borehole. Inorder to take advantage of line or cylindrical source solutions it was proposed to usesome equivalent diameter (e.g. Gu and O’Neal, 1998a) by combining the two pipesinto one, thus eliminating the need for non-symmetric solutions of the heat transferproblem. Although this simplifies the analysis, several studies have questioned thevalidity of the equivalent diameter (e.g. Mei and Baxter, 1986). Pure closed-formanalytical two-dimensional solutions do not exist today for the non-symmetricproblem. A set of solutions exists for cylindrical radial heat flow in infinite bodiesthat corresponds to fundamental heat conduction solutions. An effort was madeto extend them to radially nonhomogeneous bodies by enforcing a set of interfaceconditions between the two media (Gu and O’Neal, 1995, 1998b). The latter mediarepresented the backfill inside the borehole and the surrounding formation. Thus,most of the research conducted to date focuses on numerical techniques and pri-marily that of the finite difference method. The finite element method has been usedto a limited extent. It is also pointed out that other types of variations associatedwith the system, such as those along the depth of the heat exchanger, have beenneglected. Such variations represent the fact that the temperature is not constant butit depends on the depth. Furthermore, soil properties do change with depth, espe-cially when layering is pronounced at the site of interest. Finally, even if the forma-tion was modeled as a layered halfspace for heat transfer analysis, the length of theground heat exchanger is finite, thus requiring additional modeling considerations.In order to take into account all the above issues a three-dimensional analysis of theproblem should ultimately be considered.

528 A.J. Philippacopoulos, M.L. Berndt / Geothermics 30 (2001) 527–545

Summarizing the above, in the current state-of-the-art, analytical solutions existfor the one-dimensional uniform case (i.e. line or cylindrical source problems for aninfinite constant-property body). Similar solutions for inhomogeneous spaces(cylindrical source in a nonhomogeneous medium) have been also reported (Gu andO’Neal, 1995). Lateral inhomogeneity is produced by the difference in materialproperties between the material inside the borehole and that of the surroundingformation. Complete explicit two-dimensional solutions (non-asymmetric solutionsin terms of both the radial distance as well as the azimuth) of the heat transfer pro-blem do not exist. Finally, three-dimensional rigorous solutions of the problem dueto the existence of a finite depth (geometry) and due to variations in temperaturealong the loop (loading) are also not available in the current state-of-the-art. Mostpractical applications primarily resort to various finite difference techniques (seereviews by Muraya, 1994; Gu, 1995).Current solutions of the two-dimensional heat conduction equation for applica-

tion to vertical ground heat exchangers assume perfect bonding between the systemcomponents. In reality, thermal contact between any two solids is imperfect. In thecase of ground heat exchangers, contact resistance will exist and the interfacesbetween the U-loop, backfill and surrounding formation. The contact resistance willbe exacerbated by the formation of interfacial gaps as a result of additional geo-metric effects. These interfacial gaps may arise for several reasons. Shrinkage ofgrout/backfill, porosity and inhomogeneities in the surrounding formation, orentrained air in the grout due to improper borehole grouting techniques are possiblescenarios that will cause interfacial contact resistance and modify the heat transferprocess. Excessive drying during heat rejection may cause shrinkage of grout or soiland resultant gaps at the grout/U-loop and grout/soil interface. Formation of airgaps due to soil shrinkage when the heat pump operates in cooling mode in systemswith horizontal ground heat exchangers is discussed by Tarnawski and Leong (1993)who note that this effect is not included in design methods but observed in practice.Soil shrinkage is also a possibility for vertical ground heat exchangers considered inthis paper. Differential thermal contraction of the high density polyethylene U-loopand grout when the heat pump operates in heating mode will also potentially causeinterfacial gaps. This is due to differences in coefficients of thermal expansion, i.e.thermal mismatch.The types of grouts commonly used to backfill the boreholes of geothermal heat

pumps can be broadly categorized into bentonite-based and cement-based. Perfor-mance of these types of grouts has been compared (Allan, 1997, 2000; Allan andPhilippacopoulos, 1998, 1999). Specifically, bentonite grout with a solids content of30%, neat cement grouts with various water/cement ratios and superplasticizedcement–sand grouts were tested. Linear shrinkage measurements were performedand it was determined that shrinkage after 90 days of drying in ambient conditionswas 0.23–0.59% for neat cement grouts with water/cement ratios of 0.4–0.8,respectively, and 0.26–0.31% for different superplasticized cement-sand grouts. Thesame tests were attempted on the bentonite grout. However, the specimens crackedon drying. The product literature for the bentonite grout stated a linear shrinkagepotential of 40%. Studies of the interfacial microstructure between neat cement

A.J. Philippacopoulos, M.L. Berndt / Geothermics 30 (2001) 527–545 529

grout with water/cement ratio of 0.4 and U-loop pipes revealed gaps 0.05–0.32 mmwide (Allan and Philippacopoulos, 1998). Gaps for superplasticized cement–sandgrouts tend to be smaller (0.025–0.075) and discontinuous both radially and axially(Allan and Philippacopoulos, 1998). Coefficient of permeability and bond strengthstudies confirmed better bonding between superplasticized cement–sand grout andU-loop pipes than neat cement (Allan, 1997; Allan and Philippacopoulos, 1998).Thus, although interfacial bonding remains imperfect, better heat transfer can beexpected for suitably designed superplasticized cement-sand grouts. When bento-nite/U-loop specimens were allowed to dry under the same ambient conditions,severe cracking, disbondment and shrinkage occurred and all cohesion was lost. Inaddition to potential shrinkage of bentonite grout under drying conditions, it hasbeen found that this material can be lost to surrounding dry soil (Martinez andSullivan, 1994). The presence and observed discontinuity of interfacial gaps forbentonite and cementitious grouts require that heat transfer be analyzed usingmodels that can take these into account.In this paper we concentrate on relevant effects due to the presence of gaps

(debonding) at basic interfaces of the system. A variety of gaps that developed at the(a) pipe/grout and (b) grout/formation interfaces are considered. The currentlyavailable continuous solutions of the heat conduction equations discussed abovehave inherent restrictions and therefore are not appropriate for analyzing sucheffects. Consequently, we tackle this problem in two different ways. First, simplifiedmodels are obtained that incorporate the basic ingredients of the problem. Suchmodels are developed from fundamental one-dimensional heat conduction formulasthat are applied to a composite cylindrical system. In addition, finite elementanalysis is performed assuming a variety of spatially distributed air gaps formed inthe system. Using both simplified and finite element models, parametric variationstudies are performed considering different materials and gap sizes. All models arebased on steady-state heat transfer.

2. One-dimensional models

Simple models that can be used to evaluate qualitatively the effects of potentialinterfacial gaps on the heat transfer in ground heat exchangers were derived usingbasic formulas for uniform radial heat conduction. Concentric cylinder models havebeen used in previous studies of total thermal resistance (e.g. Kavanaugh, 1984;Braud, 1991). The present study considers a three-component medium to model thegrouted borehole of the ground heat exchanger together with the surrounding for-mation. The components of the medium consist of the grout around the U-loop, aninterfacial air gap between the grout and surrounding formation and the surround-ing formation itself. Specifically, in the radial direction the grout extends from r1 tor2 (zero corresponds to the axis of the borehole). A gap is then introduced betweenr2 and r3. Finally, the surrounding formation extends from r3 to r4. Theoretically,r4 ! 1 where the heat flux should be zero. For the purpose of our analysis, r4 isthe far-field radius associated with the far-field temperature Tff. The thickness of the


system is taken to be equal to L along the axis of the borehole. Consequently, themodel is completely defined geometrically in terms of the five parameters: r1, r2, r3,r4 and L. In addition to geometry, the material properties required by the one-dimensional model are the thermal conductivities of the grout, air gap and sur-rounding formation. These are kb, kg and ks, respectively. To complete the definitionof the system, the input Tin and far-field temperatures Tff must be known. Based onthe above, the system is completely defined by five geometric parameters, threematerial properties and two temperature values, that is, a total of ten parameters.Such parameters are readily available or can be estimated for typical ground heatexchangers of GHPs.Steady-state heat conduction is assumed. The heat rate associated with this model

is then constant while the heat flux varies inversely proportional to the radial dis-tance r (1/r variation). The first step is to compute the interface temperaturesT2=T(r2) and T3=T(r3). Let Rt,i; i=b, g, s denote the thermal resistances of thegrout, gap and soil respectively. Furthermore, let qr,i and q

00r;i denote the heat transfer

rate and heat flux, respectively. By enforcing continuity of heat flow at both inter-faces r=r2 and r=r3, respectively, then the temperatures in question can be obtainedfrom the solution of a 2�2 problem as follows

T2T3

� �¼

1

�þ �þ 1

ð�þ 1ÞTin þ �Tff

�Tin þ ð�þ 1ÞTff

� �ð1Þ

where � and � are dimensionless quantities expressing thermal resistance ratiosdefined as

� ¼Rt;b

Rt;gð2aÞ

1

�¼

Rt;g

Rt;sð2bÞ

The thermal resistances are (see e.g. Incropera and De Witt, 1990)

Rt;b ¼1

2�Lkbln

r2r1

� �ð3aÞ

Rt;g ¼1

2�Lkgln

r3r2

� �ð3bÞ

Rt;s ¼1

2�Lksln

r4r3

� �ð3cÞ

Having obtained the interface temperatures T2 and T3 the temperature distribu-tion in the model becomes


TbðrÞ ¼

lnr

r2

� �

lnr1r2

� ��Tb þ T2; for : r14r4r2 ð4aÞ

TgðrÞ ¼

lnr

r3

� �

lnr2r3

� ��Tg þ T3; for : r24r4r3 ð4bÞ

and

TsðrÞ ¼

lnr

r4

� �

lnr3r4

� ��Ts þ Tff ; for : r34r4r4 ð4cÞ

In Eq. (4) �Ti are temperature differentials defined by

�Tb ¼ Tin T2; �Tg ¼ T2 T3; �Ts ¼ T3 Tff ð5Þ

The corresponding heat flux in the system is inversely proportional to the distancefrom the borehole axis. Its distribution within the grout, gap and formation becomes

q00i ¼qi2�Lr

; i ¼ b; g; s ð6aÞ

respectively, where qi is the corresponding heat transfer rate in the system

qi ¼�Ti

Rt;i; i ¼ b; g; s ð6bÞ

Eqs. (1)–(6) present explicit solutions of the heat transfer in the three-componentmedium and can be easily solved in a spreadsheet.In the above derivations it has been assumed that one knows the input and far-

field temperatures Tin and Tff, respectively. In certain applications, however, insteadof the input temperature Tin, the input heat flux is known. This, for example, is thecase for field tests, which are performed to measure in-situ thermal properties (seee.g. Austin et al., 2000). Such cases require a different set of boundary conditions forthe three-medium system. Specifically:

q000 ¼ q00 rÞð��r¼r0

; q0 ¼ 2�Lr0q000 ð7Þ


are the input heat flux and heat transfer rates, respectively. Enforcing continuity ofthe heat rate at all interfaces yields a 3�3 system. The latter can be solved for theinput Tin and interface temperatures, T2 and T3, as follows

Tin

T2T3

8<:

9=; ¼ q0

1 1 10 1 10 0 1

24

35 Rt;b

Rt;g

Rt;s

8<:

9=;þ

111

8<:

9=;Tff ð8Þ

where Rt,i ; i=b, g, s are the thermal resistances of the components of the systemgiven by Eq. (3) and q0 is the prescribed heat rate at the inner surface. Havingobtained the input and interface temperatures from Eq. (8), backsubstitution intoEqs. (4), (5) and (6) results in the required temperature and heat flux distributions inthe system.

3. Numerical evaluation of debonding

The effect of debonding in ground heat exchangers of GHPs was investigatedusing (a) the simple radial one-dimensional models presented in the previous sectionand (b) finite element two-dimensional heat conduction models. Both types ofmodels were sufficiently adequate in capturing the fundamental effects in the heatconduction process due to formation of gaps in the system. One-dimensional modelsdo not account for spatial variability in the circumferential direction that wasobserved in interfacial microstructure studies. Hence, effects due to the latter wereevaluated by finite element two-dimensional heat conduction. Primarily, two casesof debonding were considered in this study: (a) debonding at the grout/formationinterface and (b) debonding at the pipe/grout interface.A typical 102 mm diameter borehole containing two high-density polyethylene

pipes with inner diameter of 25.4 mm and outer diameter of 33.0 mm was con-sidered. The center-to-center separation of the two pipes was 50 mm. Analysis wasperformed considering two types of grouts. The first was superplasticized cement–sand grout, which will be referred to as Mix 111. The mix proportions and proper-ties of this grout are presented elsewhere (Allan, 2000; Allan and Philippacopoulos,1998; 1999). The second grout used in the analysis was high solids bentonite. Thetemperature for the heating mode was taken as 3.3C. This represents an average ofthe entering (5.0C) and leaving water temperatures (1.7C) in the piping loop forthis mode of operation. Similarly, the cooling mode temperature was taken as 33C,which also represents the average of the entering and leaving water temperatures 30and 36C, respectively.In the two-dimensional finite element analysis the entering and leaving tempera-

tures can be directly applied at the two pipes that are incorporated into the models.The far-field temperature was set to 13C. After several parametric computer runs, afar-field radius of 3.05 m was selected. Our analysis showed that, for the chosenparameters and steady-state conditions, further increases in the far-field radius did


not affect the results significantly. Finally, the following values for the thermal con-ductivities were used for both the one-dimensional and two-dimensional analyses:(a) Mix 111: 2.42 W/mK; (b) bentonite: 0.75 W/mK; (c) formation: 1.72 W/mK.The grout conductivities are based on experimental results (Allan and Philippaco-poulos, 1998). The formation conductivity was chosen to represent what might beexpected for a sandy or clayey soil, sandstone or limestone. The correspondingvalue for the air-filled gaps was 0.027 W/mK (Mills, 1992). All thermal con-ductivities refer to values at 25C; thus some variations with temperature could beexpected.

3.1. One-dimensional analysis

Fig. 1 demonstrates the effects of debonding on the temperature and heat fluxdistributions near the borehole of the ground heat exchanger. The grout material isMix 111. A 1.6 mm (1/16 in) air gap has been introduced at the grout/formationinterface as an arbitrary value to indicate the impact of debonding. From Fig. 1(a) itcan be seen that when the distance becomes equal to the borehole radius (0.05 m), atemperature drop takes place for both modes of operation of the heat pump. Thisdrop is about 2.8C for the heating and 5.5C for the cooling modes, respectively. Inaddition, the presence of the gap also reduces the heat flux as can be seen in Fig. 1(b).Note that for the heating mode the flux is negative, signifying that during this modeheat is flowing from the surrounding formation into the borehole. Furthermore,from Fig. 1(a) it can be seen that as the distance from the axis of the boreholeincreases, the temperature for both modes of operation converges to the far-fieldtemperature. Similarly, from Fig. 1(b) it can be seen that as the distance from theaxis of the system increases the flux converges to zero, as expected.Comparisons between different grout materials are shown in Fig. 2. Temperature

and heat variations in the vicinity of the ground heat exchanger were obtained forsuperplasticized cement-sand (Mix 111) and bentonite. Perfect bonding at the grout/formation interface is considered for both Mix 111 and bentonite. For comparison,a case with a gap is also indicated. The results shown in Fig. 2 correspond to thecooling mode of operation. Fig. 2(a) indicates the significant influence of groutthermal conductivity and the presence of a grout/formation air gap on temperaturedistribution in the borehole and surrounding formation. Finally, as shown inFig. 2(b), the behavior of the heat flux for these cases is also similar. Specifically, theheat flux is much less for bentonite grout with or without a gap.Parametric variations were also performed considering different thermal con-

ductivity ratios for the grout and the formation. Consistent with uniform radial heatflow theory, the temperature distribution depends on the conductivity ratio betweenthe materials. These results are shown in Fig. 3 for the heating and cooling modes ofoperation. Both temperature and heat flux variations were evaluated. The thermalconductivity of the grout was taken as equal, then half and, finally, twice that ofthe formation. The plots of Fig. 3 illustrate the influence of grout/formationconductivity ratio on temperature and heat flux distributions. These plots indicatethat higher grout/formation ratio yields higher heat flux. For example, in the


cooling mode of operation the heat transfer rate increased from 3.4 to 3.9 W whenthe grout/formation conductivity ratio increased to 2. This, in turn, reflects areduction in the total resistance of the system. Specifically, the total resistance was

Fig. 1. Effect of gaps on (a) temperature and (b) heat flux distributions near the borehole.


decreased from 2.8 to 2.5 K/W. Similarly, when the grout/formation conductivityratio was reduced to 0.5, the overall heat transfer rate was reduced from 3.4 to2.7 W.

Fig. 2. Comparison between different grout materials: (a) temperature and (b) heat flux distributions.


3.2. Finite element analysis

A two-dimensional finite element analysis of the heat conduction in the groundheat exchanger was performed in order to account for asymmetric heat responseresulting from the spatial distribution of the gaps. Such analysis enables us to obtain

Fig. 3. Influence of conductivity ratio (grout-to-formation: kb/ks) on heat transfer for both modes of

GHP operation (continued on next page).


a better understanding of the spatial distribution, which cannot be studied throughone-dimensional models. The finite element modeling of the ground-coupled heatpump system was performed using the ANSYS code. The finite element modelincorporated both pipes, the grout and the surrounding formation. It consisted of608 nodal points and 588 elements. Specifically, element PLANE55 (thermal solid)was employed, which can be applied in either plane or axisymmetric two-dimensionalthermal conduction problems. PLANE55 has four nodes having a single degree-of-

Fig. 3. (continued)


freedom (temperature) at each node. A triangular option also exists. A finer meshwas used inside the ground heat exchanger. The fineness of the grid representing thesurrounding formation was reduced with the distance from the borehole axis.The boundary conditions considered were: (a) prescribed constant heat flux at the

inside surface of pipes and, (b) prescribed constant far-field temperature. Whensymmetric distributions of gaps are considered, then only half of the model isrequired. In this case, the axis that is defined by the centers of the two pipes becomesan axis of symmetry in the solution. Along the latter, a zero heat flux condition isrequired. However, for general scenarios of gap spatial distribution, no symmetry inthe heat conduction solution exists and therefore the whole finite element modelmust be considered in the analysis.Several heat conduction finite element analyses were performed. Bentonite was

considered as the grouting material. The thermal conductivities of the bentonite,formation and air gap were the same as those used in the one-dimensional analysisdescribed above. Since high solids bentonite and neat cement grouts with water/cement ratio of 0.8 have similar thermal conductivities (0.75 and 0.80 W/mK,respectively), the computed results obtained for bentonite will be similar to that forneat cement. The thermal resistance and overall heat transfer coefficient of theground heat exchanger were evaluated by applying a heat flux of 3.1 W/m2 at theinner surface of both pipes. Generally, the fluxes will vary between the two pipes.However, a uniform distribution was assumed for simplicity. The temperature fieldwas evaluated for different gap scenarios. In order to deal with the two-dimensionalnature of the results certain averages were used. For example, the temperature ofeach pipe associated with the input fluxes was computed as the average of all interiornodes associated with the pipe. The average between the two pipes was then treatedas the input temperature for the system. Similarly, the output temperature for cal-culating the heat transfer coefficient was obtained as the average of all nodes at acircle just outside the borehole. Finally, the borehole resistance was obtained bydividing the difference between the input and output temperature by the total inputheat rate. Since two-dimensional analyses were performed, all computations wereconducted considering a unit length of the borehole/formation system.As indicated previously, two types of debonding were investigated in the present

study, i.e. debonding between: (a) grout and formation and (b) grout and pipes.Figs. 4 and 5 demonstrate results obtained on the temperature distribution for theformer case. For clarity, Figs. 4 and 5 display results only in the vicinity of theborehole (i.e. up to about 30 cm distance from the borehole axis while the overallfinite element model extends radially up to 3.05 m from the borehole axis). Fig. 4ashows the temperature distribution near the borehole for the no gap case. Asexpected, in the absence of gaps the temperature distribution is smooth and sym-metric. A 1.6 mm gap was then introduced at the grout/formation interface. Thisvalue was arbitrary. Its spatial distribution corresponds to a 90 sector at the rightside of the model. Fig. 4b shows the corresponding temperature distribution. Notethat, consistent with the physics of the problem, the gap inhibits the heat dissipationtowards the right side of the model. In these figures we display the total responsefield for completeness.


The extent of the gap was subsequently increased to 180 on the right side. Fig. 5ashows the corresponding temperature contours. In response to the increasing extentof the grout/formation air gap, the temperatures decrease on the right hand side ofthe formation surrounding the borehole and increase in the vicinity of the right handpipe. In fact, from Fig. 5a it can be seen that the temperatures around the left handpipe increase (pipe-to-pipe thermal interaction). Finally, Fig. 5b displays the tem-perature field when complete debonding is assumed at the grout/formation interface.In the latter case, increased borehole temperatures, particularly near the center of thegrout between the two pipes, and decreased formation temperature are observed. Theactual magnitude of temperature change due to gaps at the grout/formation interfacefor the parameters considered is relatively small. However, these plots indicate thatchanges in the spatial distribution of the temperature are more predominant.

Fig. 4. Effect of gap at grout/formation interface. Temperature distribution near borehole: (a) no gap and

(b) 90 gap.


In order to quantify further these results, the overall thermal resistance and theheat transfer coefficient were evaluated for different debonding cases using the tem-perature response field from the finite element heat transfer analysis. The base case(no gap), associated with Fig. 4a, yields a thermal resistance of 3.8 K/W and corre-sponding heat transfer coefficient equal to 0.23 W/m2K. The presence of a 90 gap(see Fig. 4b) caused a 20% reduction in the overall heat transfer coefficient. Simi-larly, the 180 (see Fig. 5a) and complete debonding (see Fig. 5b) cases resulted in 33and 60% reductions in the overall heat transfer coefficient, respectively. Finally, sincethe temperature field depends on the fineness of the grid, a finer model was used toobtain the results for the 90-gap case. The difference between the two results wasinsignificant.

Fig. 5. Effect of gap at grout/formation interface. Temperature distribution near borehole: (a) 180 gap

and (b) 360 gap.


Results associated with potential debonding between the grout and pipes withinthe borehole are given in Figs. 6 and 7, which illustrate the temperature field within theborehole. Fig. 6a displays the corresponding temperature field when both pipes areconsidered to be completely bonded to the grout. In Fig. 6b a small gap (60 sector) hasbeen introduced at the exterior of the right pipe. This caused the temperature to riselocally near the debonded area. A similar situation occurs when a 60 gap is introducedat both pipes interior to the borehole and the resultant temperature attenuation is evi-dent from Fig. 7a. When the right pipe is assumed as completely debonded (Fig. 7b),this locally increased the temperature. The sharp attenuation of heat shown in Figure 7breflects a corresponding reduction of the heat transfer coefficient. Specifically, the heattransfer coefficient was reduced by 66%. Note that this reduction is higher than thatof a 360o debonding at the grout/formation interface (see Fig. 5b). In turn, thisindicates that, for the cases studied above, bonding between the pipes and grout is

Fig. 6. Effect of gap at grout/pipe interface. Temperature distribution inside the borehole: (a) no gap and

(b) 60 gap (right pipe-exterior).


more important in terms of heat transfer than bonding between the grout and theformation.In summary, the results described above indicate that debonding can have a sig-

nificant impact on the heat transfer associated with ground heat exchangers. Thiscan be minimized by selecting and properly placing grouting material with lowshrinkage and sound bond quality. Similarly, it is important that the uncertainty dueto potential debonding be considered in the design of ground heat exchangers andfor the interpretation of in situ measurements.

4. Conclusions

In this study the influence of debonding on the heat transfer in ground heatexchangers of GHPs was investigated. First, simple analytical one-dimensional

Fig. 7. Effect of gap at grout/pipe interface. Temperature distribution inside the borehole: (a) 60 gap

(both pipes-interior) and (b) 360 gap (right pipe).


radial flow models were used to examine continuous circumferential gaps at thegrout/formation interface. Such models should be limited to qualitative analysis.Subsequently, solutions of the two-dimensional heat conduction were obtained byfinite element analysis to evaluate the spatial distribution of potential interfacialgaps. Such solutions cannot be obtained from existing methods of heat transferanalysis in GHPs. Specific findings are summarized below.

. Gaps developed at the grout/formation interface generally cause: (a) tempera-ture drop along the interface, (b) reduction of heat flux especially near theborehole, (c) increase of the total resistance of the system, (d) decrease of theoverall heat transfer rate.

. The use of grouting materials with high shrinkage on loss of moisture that arelikely to form interfacial gaps and reduce heat transfer rate should be avoidedunder drying conditions.

. Variation-of-parameter studies conducted using different thermal conductivityratios (grout-to-formation) show that better heat transfer rates are associatedwith grout conductivities close to or higher than that of the formation.

. Two-dimensional finite element analysis of the influence of spatial variation ofgaps led to the following conclusions: (a) a 90 debonding at grout/formationinterface caused 20% reduction in the overall heat transfer coefficient; (b) a 180

debonding at the grout/formation interface produced 33% reduction in theoverall heat transfer coefficient; (c) a 360 debonding at the grout/formationinterface produced 60% reduction of the overall heat transfer coefficient; (d) a360 debonding of one of the pipes (all around gap at grout/pipe interface)produced 66% reduction of the overall heat transfer coefficient.

Acknowledgements

This work was supported by the US Department of Energy Office of GeothermalTechnologies and performed under contract number DE-AC02-98CH10886.

References

Allan, M.L., 1997. Thermal Conductivity of Cementitious Grouts for Geothermal Heat Pumps. FY 1997

Progress Report, BNL 65129, Brookhaven National Laboratory.

Allan, M.L., 2000. Materials characterization of superplasticized cement–sand grout. Cement and Con-

crete Research 30, 937–942.

Allan, M.L., Philippacopoulos, A.J., 1998. Thermally Conductive Cementitious Grouts for Geothermal

Heat Pumps. FY 1998 Progress Report, BNL 66103, Brookhaven National Laboratory.

Allan, M.L., Philippacopoulos, A.J., 1999. Properties and Performance of Cement-Based Grouts for

Geothermal Heat Pump Applications. FY 1999 Final Report, BNL 67006, Brookhaven National

Laboratory.

Austin, W.A., Yavuzturk, C., Spitler, J.D., 2000. Development of an in situ system for measuring ground

thermal properties. ASHRAE Transactions 106, 365–379.

Braud, H.J., 1991. Grout effect in vertical heat pump bores. Proceedings of International Energy Agency

Ground Coupled Heat Pump Conference, Montreal.


Gu, Y., 1995. Effect of Backfill on the Performance of a Vertical U-tube Ground-coupled Heat Pump.

PhD thesis, Texas A&M University, College Station, Texas.

Gu, Y., O’Neal, D.L., 1995. An analytic solution to transient heat conduction in a composite region with

a cylindrical heat source. Journal of Solar Energy Engineering, ASME 117, 242–248.

Gu, Y., O’Neal, D.L., 1998a. Development of an equivalent diameter expression for vertical U-tubes used

in ground-coupled heat pumps. ASHRAE Transactions 102, 1–9.

Gu, Y., O’Neal, D.L., 1998b. Modeling the effect of backfills on U-tube ground coil performance. ASH-

RAE Transactions 104, 1–10.

Incropera, F.P., DeWitt, D.P., 1990. Fundamentals of Heat and Mass Transfer, 3rd Edition. John Wiley

& Sons, New York.

Kavanaugh, S.P., 1984. Simulation and Experimental Verification of Vertical Ground-coupled Heat

Pumps Systems. PhD thesis, Oklahoma State University, Stillwater, Oklahoma.

Kavanaugh, S.P., Rafferty, K., 1997. Ground Source Heat Pumps: Design of Geothermal Systems for

Commercial and Institutional Buildings, Atlanta, ASHRAE.

Martinez, G.M., Sullivan, W.N., 1994. Geothermal Heat Pump Research and Development Studies at

Sandia National Laboratories. SAND94-1552C, Sandia National Laboratories.

Mei, V.C., Baxter, V.D., 1986. Performance of a ground coupled heat pump with multiple dissimilar U-

tube coils in series. ASHRAE Transactions 92, 30–42.

Mills, A.F., 1992. Heat Transfer. Irwin, Homewood.

Muraya, N.K., 1994. Numerical Modeling of the Transient Thermal Interference of Vertical U-tube Heat

Exchangers. PhD thesis, Texas A&M University, College Station, Texas.

Rottmayer, S.P., Beckman, W.A., Mitchell, J.W., 1997. Simulation of a single vertical U-tube ground heat

exchanger in an infinite medium. ASHRAE Transactions 103, 651–659.

Tarnawski, V.R., Leong, W.H., 1993. Computer analysis, design and simulation of horizontal ground

heat exchangers. International Journal of Energy Research 17, 467–477.

Yavuzturk, C., Spitler, J.D., Rees, S.J., 1999. A transient two-dimensional finite volume model for the

simulation of vertical U-tube ground heat exchangers. ASHRAE Transactions 105, 465–474.


influence of debonding in ground heat exchangers used with geothermal heat pumps

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