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
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
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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E-mail address: firstname.lastname@example.org (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 d