# Influence of debonding in ground heat exchangers used with geothermal heat pumps

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Inuence 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 backll materials or surrounding formation,improper grouting and thermal mismatch. The eect of thermal contact resistance on the heatconduction due to debonding in ground heat exchangers was investigated using a set of one-

dimensional simplied analytical models as well as two-dimensional nite element models.From the cases studied, debonding at the backll/pipe interface was found to be of greatersignicance 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, thebackll (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 Raerty, 1997). In addition, solutions of

Geothermics 30 (2001) 527545

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0375-6505/01/$20.00 # 2001 CNR. Published by Elsevier Science Ltd. All rights reserved.PI I : S0375-6505(01 )00011 -6

* Corresponding author. Fax: +1-631-344-2359.

E-mail address: ajph@bnl.gov (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 rst deals with the development of meth-odologies and numerical techniques required to evaluate the heat eld associatedwith the heating and cooling modes of operation. Using the properties of the com-ponents of the system (e.g. thermal conductivities of the backll, 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 congurations because of the complexity of the problem. Thiscomplexity arises mainly from two sources. The rst is due to the thermal load,which is dierent 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 reected 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 ONeal, 1998a) by combining the two pipesinto one, thus eliminating the need for non-symmetric solutions of the heat transferproblem. Although this simplies 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 ow in innite bodiesthat corresponds to fundamental heat conduction solutions. An eort was madeto extend them to radially nonhomogeneous bodies by enforcing a set of interfaceconditions between the two media (Gu and ONeal, 1995, 1998b). The latter mediarepresented the backll 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 nite dierence method. The nite 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 nite, 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.

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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 aninnite constant-property body). Similar solutions for inhomogeneous spaces(cylindrical source in a nonhomogeneous medium) have been also reported (Gu andONeal, 1995). Lateral inhomogeneity is produced by the dierence 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 nite 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 nite dierence 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, backll and surrounding formation. The contact resistance willbe exacerbated by the formation of interfacial gaps as a result of additional geo-metric eects. These interfacial gaps may arise for several reasons. Shrinkage ofgrout/backll, 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 eect is not included in design methods but observed in practice.Soil shrinkage is also a possibility for vertical ground heat exchangers considered inthis paper. Dierential 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 dierences in coecients of thermal expansion, i.e.thermal mismatch.The types of grouts commonly used to backll 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). Specically, bentonite grout with a solids content of30%, neat cement grouts with various water/cement ratios and superplasticizedcementsand grouts were tested. Linear shrinkage measurements were performedand it was determined that shrinkage after 90 days of drying in ambient conditionswas 0.230.59% for neat cement grouts with water/cement ratios of 0.40.8,respectively, and 0.260.31% for dierent 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) 527545 529

grout with water/cement ratio of 0.4 and U-loop pipes revealed gaps 0.050.32 mmwide (Allan and Philippacopoulos, 1998). Gaps for superplasticized cementsandgrouts tend to be smaller (0.0250.075) and discontinuous both radially and axially(Allan and Philippacopoulos, 1998). Coecient of permeability and bond strengthstudies conrmed better bonding between superplasticized cementsand 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 eects 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 sucheects. Consequently, we tackle this problem in two dierent ways. First, simpliedmodels 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, nite elementanalysis is performed assuming a variety of spatially distributed air gaps formed inthe system. Using both simplied and nite element models, parametric variationstudies are performed considering dierent 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 eects 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. Specically, 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 ux should be zero. For the purpose of our analysis, r4 isthe far-eld radius associated with the far-eld temperature T. The thickness of the

530 A.J. Philippacopoulos, M.L. Berndt / Geothermics 30 (2001) 527545

system is taken to be equal to L along the axis of the borehole. Consequently, themodel is completely dened geometrically in terms of the ve 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 denitionof the system, the input Tin and far-eld temperatures T must be known. Based onthe above, the system is completely dened by ve 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 ux varies inversely proportional to the radial dis-tance r (1/r variation). The rst 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 ux, respectively. By enforcing continuity of heat ow at both inter-faces r=r2 and r=r3, respectively, then the temperatures in question can be obtainedfrom the solution of a 22 problem as follows

T2T3

1

1 1Tin TffTin 1Tff

1

where and are dimensionless quantities expressing thermal resistance ratiosdened as

Rt;bRt;g

2a

1

Rt;g

Rt;s2b

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

Rt;b 12Lkb

lnr2r1

3a

Rt;g 12Lkg

lnr3r2

3b

Rt;s 12Lks

lnr4r3

3c

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

A.J. Philippacopoulos, M.L. Berndt / Geothermics 30 (2001) 527545 531

Tbr ln

r

r2

lnr1r2

Tb T2; for : r14r4r2 4a

Tgr ln

r

r3

lnr2r3

Tg T3; for : r24r4r3 4b

and

Tsr ln

r

r4

lnr3r4

Ts Tff ; for : r34r4r4 4c

In Eq. (4) Ti are temperature dierentials dened by

Tb Tin T2; Tg T2 T3; Ts T3 Tff 5

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

q00i qi

2Lr; i b; g; s 6a

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

qi TiRt;i

; i b; g; s 6b

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-

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

q000 q00 rrr0; q0 2Lr0q

000 7

532 A.J. Philippacopoulos, M.L. Berndt / Geothermics 30 (2001) 527545

are the input heat ux and heat transfer rates, respectively. Enforcing continuity ofthe heat rate at all interfaces yields a 33 system. The latter can be solved for theinput Tin and interface temperatures, T2 and T3, as follows

TinT2T3

8

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