Comparison of four models for thermal response tes

ComparisonoffourmodelsforthermalresponsetestevaluationSignhildEAGehlin,GoranHellstrom.ASHRAETransactions.Atlanta:2003.Vol.109Part1.pg.131»Jumptoindexing(documentdetails)FullText(5896words)CopyrightAmericanSocietyofHeating,RefrigerationandAirConditioningEngineers,Inc.2003[Headnote]ABSTRACTFourtwo-variableparameterestimationmodelsforevaluationofthermalresponsetestdataarecomparedwhenappliedonthesametemperatureresponsedata.Twomodelsarebasedonline-sourcetheory,thethirdmodelisacylinder-source-basedsolution,andthefourthisanumericalone-dimensionalfinitedifferencemodel.Thedatasetscontainmeasuredtemperatureresponse,heatload,andundisturbedgroundtemperaturefromthreethermalresponsetests,togetherwithphysicaldataofthetestedboreholeheatexchangers(BHE).ThemodelsestimategroundthermalconductivityandthermalresistanceoftheBHEandarecomparedregardingtestlengthanddataintervalused.Forthethreedefineddatasets,thelinesourceapproximationmodelshowstheclosestagreementwiththemeasuredtemperatureresponse.Thecylindersourceandnumericalmodelsshowsensitivitytotheinclusionofearlydata.Arecommendedminimumresponsetestdurationof50hoursisconcludedfromthemodelcomparison.INTRODUCTIONDuringathermalresponsetest,adefinedthermalloadisappliedtoaboreholeheatexchangerandthetemperaturedevelopmentoftheinletandoutlettemperaturesaremeasuredovertime.Thistemperatureresponseallowsextrapolationofthethermalbehaviorinfuturetime.Onepossibleconceptualmodelfortheinterpretationistoassumethegroundtobeaconductivemediumandtodeterminetheapparentthermalconductivityandotherthermalparametersofthismedium.Thetestmaybeconductedusingatransportabledevicethatisbroughtonsitetotheborehole.Sinceitsintroductionin1995-1996,thisin-situmethodhasspreadtomostcountrieswhereboreholesinthegroundareusedasaheatsource/sinkonalargerscale.Themethodservesprimarilytoassessthegroundthermalconductivityandperformanceofdifferentboreholeheatexchangerdesigns,whichareimportantforoptimaldesignandqualitycontrol.Themethodisdescribedinseveralpapers,e.g.,Gehlin(1998),Austin(1998),Austinetal.(2000),ShonderandBeck(2000),andKavanaughetal.(2000).TheprincipleofathermalresponsetestsetupisoutlinedinFigure1.Theboreholetemperatureresponseisthetemperaturedevelopmentovertimeoftheheatcarrierfluidcirculatingthroughtheboreholeheatexchangerwhenaknownheatingorcoolingloadisimposed.Byevaluatingtheincreasingfluidtemperatureversustime,informationaboutthethermalpropertiesinandaroundtheboreholeisobtained.Alowthermalconductivityis,e.g.,indicatedbyamorerapidtemperatureresponse.Theresponsealsogivesinformationaboutthetemperaturedifferencebetweentheheatcarrierfluidandthesurroundinggroundcausedbytheheattransfer,i.e.,thethermalresistanceoftheboreholeheatexchanger.Enlarge200%Enlarge400%Figure1Thermalresponsetestsetup.Severalanalyticalandnumericalmethodsareusedfortheevaluationofresponsetesttemperaturedata.Thedifferentmodelsrequiresomewhatdifferentsetsofinputdata.Variousanalyticalmethodsforevaluationofboreholeresponsetestdataarediscussedbelow.EvaluationMethodsAnumberofmethodshavebeenappliedovertheyearsforthesimulationofboreholeheatexchangerperformance.Bothanalyticalandnumericalmodelshavebeenusedandreportedinseveralpapers,reports,andbooks.Here,thefocusisonmodelsfortheevaluationofthermalresponsetestdatafordetermininggroundthermalconductivityandevaluationoftheefficiencyoftheboreholeheatexchanger.Thethermalresponsetestmethodisbasedontheso-calledsingleprobemethodfordeterminingthethermalconductivityofsolidmaterialsinalaboratoryenvironment(StalhaneandPyk1931).Initialanalyseswerebasedontheline-sourceapproximation,whichdoesnotconsiderthethermalpropertiesoftheprobematerial.In1954,Blackwellpresentedananalyticalsolutionincludingboththeprobematerialandapossiblecontactresistanceattheprobesurface.Inprinciple,thismethodmakesitpossibletoshortenthemeasurementperiods,especiallyforlargeprobediameters.Attemptstodetermineboththermalconductivityanddiffusivitysimultaneouslybytakingthecontactresistanceintoaccountwerenotsuccessful(Blackwell1954;Becketal.1956).Thedeterminationofthethermaldiffusivitywasfoundtobeverysensitivetothecontactresistance.Sundberg(1988)developedadetailedFEMmodeloftheprobeinordertoshortenthemeasurementperiod.Hefoundthatboththermalconductivityanddiffusivitywereheavilyinfluencedduringtheinitialtimeperiodbysmallchangesintheprobeproperties.Analyticalmodels,suchastheline-sourceandcylinder-sourcetheories,requireseveralsimplifyingassumptionsregardingthegeometryoftheboreholeandheatexchangerpipes.Forthepurposeofthethermalresponsetestevaluation,theheatflowtoorfromtheboreholemayberepresentedasaninfinitelylongheatsourceorsinkinthegroundwithnegligibleinfluenceofheatflowsinadirectionalongtheboreholeaxis.Inthegroundoutsidetheboreholeitiscommonpracticetoassumethatthethermalprocessdependsonlyontheradialdistancefromtheboreholeaxis.Theone-ortwo-dimensionalheatflowprocessfromthecirculatingfluidtotheboreholewallisassumedtoberepresentedbyathermalresistancethatcharacterizesthetemperaturelossbetweenheatcarrierfluidandboreholewall.Somemodelsalsoincludethethermalmassofthemater