A New Method to Determine the Thermal Properties of Soil Formations from In Situ Field Tests

Transcription

1 ORNL/M-2000/97 A New Mehod o Deemine he hemal Popeies of Soil Fomaions fom In Siu Field ess J. A. Shonde J. V. Beck

2 DOCUMEN AVAILABILIY Repos poduced afe Januay 1, 1996, ae geneally available fee via he U.S. Depamen of Enegy (DOE) Infomaion Bidge: Web sie hp:// Repos poduced befoe Januay 1, 1996, may be puchased by membes of he public fom he following souce: Naional echnical Infomaion Sevice 5285 Po Royal Road Spingfield, VA elephone ( ) DD Fax Web sie hp:// Repos ae available o DOE employees, DOE conacos, Enegy echnology Daa Exchange (EDE) epesenaives, and Inenaional Nuclea Infomaion Sysem (INIS) epesenaives fom he following souce: Office of Scienific and echnical Infomaion P.O. Box 62 Oak Ridge, N elephone Fax epos@adonis.osi.gov Web sie hp:// his epo was pepaed as an accoun of wok sponsoed by an agency of he Unied Saes Govenmen. Neihe he Unied Saes Govenmen no any agency heeof, no any of hei employees, makes any waany, expess o implied, o assumes any legal liabiliy o esponsibiliy fo he accuacy, compleeness, o usefulness of any infomaion, appaaus, poduc, o pocess disclosed, o epesens ha is use would no infinge pivaely owned ighs. Refeence heein o any specific commecial poduc, pocess, o sevice by ade name, ademak, manufacue, o ohewise, does no necessaily consiue o imply is endosemen, ecommendaion, o favoing by he Unied Saes Govenmen o any agency heeof. he views and opinions of auhos expessed heein do no necessaily sae o eflec hose of he Unied Saes Govenmen o any agency heeof.

3 ORNL/M-2000/97 A New Mehod o Deemine he hemal Popeies of Soil Fomaions fom In Siu Field ess J. A. Shonde Enegy Division, Oak Ridge Naional Laboaoy J. V. Beck Pofesso Emeius, Michigan Sae Univesiy Apil 2000 Pepaed by OAK RIDGE NAIONAL LABORAORY Oak Ridge, ennessee managed by U-BAELLE, LLC fo he U.S. DEPARMEN OF ENERGY unde conac DE-AC05-00OR22725

4 CONENS Lis of Figues and ables... Acknowledgmens... Abbeviaions and Symbols... v vii ix 1. INRODUCION A NEW MEHOD FOR DEERMINING SOIL HERMAL PROPERIES Inoducion he Physical Poblem Enegy Fluid Model Enegy Model fo Soil, Gou, and Film he GPM Sofwae Conclusions FIELD ESS OF HE GPM SOFWARE Field Rig ess In Siu ess a wo Elemenay Schools Descipion of ess es Resuls Compaison wih Ohe Analysis echniques Conclusions GPM SOFWARE UORIAL Inoducion Main Menu Oupu Window CONCLUSIONS REFERENCES iii

5 FIGURES AND ABLES Figues 2.1 Geomey of boehole hea exchange Conol volume fo hemal analysis of boehole hea exchange Measued and pediced aveage wae empeaue fo expeimen using he Oklahoma Sae Univesiy es ig Residuals fo he expeimen on he Oklahoma Sae Univesiy es ig Sequenial esimaes of sand and gou hemal conduciviy Powe inpu and aveage wae empeaue, Campbell Elemenay School es # Powe inpu and aveage wae empeaue, Campbell Elemenay School es # Powe inpu and aveage wae empeaue, Maxey Elemenay School es # Model eo fo Campbell Elemenay School es # Model eo fo Campbell Elemenay School es # Model eo fo Maxey Elemenay School es # Sequenial hemal conduciviy esimaes, Campbell Elemenay School es # Sequenial hemal conduciviy esimaes, Campbell Elemenay School es # Sequenial hemal conduciviy esimaes, Maxey Elemenay School es # empeaue and powe inpu vs ime fo a case in which he geneao developed mechanical poblems Sequenial hemal conduciviy esimaes fom he daa of Fig he main daa inpu sceen in GPM A sample of he file dialog box Coss-secional view of boehole showing dimensions he GPM oupu window ables 3.1 Paamees of hee in siu hemal popeies ess pefomed a Lincoln, Nebaska, elemenay schools Resuls of soil hemal conduciviy and boehole esisance esimaes fom hee in siu ess hemal conduciviy esimaes deived by hee es mehods fom 50-h ess v

6 ACKNOWLEDGMENS he auhos would like o expess hei appeciaion o he following individuals and insiuions fo hei suppo and collaboaion in his wok: Lew Pasch of he U.S. Depamen of Enegy; Lay Hennings, im Pa, Paick Decke, Julie Kleage, and Ben Adams of he Lincoln Public School Disic; D. Mavin Smih and D. Jeffey Spile of Oklahoma Sae Univesiy; and D. Cenk Yavuzuk of he Univesiy of Wyoming. vii

7 ABBREVIAIONS AND SYMBOLS Abbeviaions BHEx Bu cfm CV diam EMS GHP GPM h HVAC ORNL ms MY VAV boehole hea exchange Biish hemal uni cubic fee pe minue consan volume diamee enegy managemen sysem geohemal hea pump Geohemal Popeies Measuemen (sofwae) hou heaing, venilaing, and ai-condiioning Oak Ridge Naional Laboaoy oo mean squae ypical meeoological yea vaiable ai volume Vaiables and Consans a b c p adius of U-ube pipe adius of effecive pipe specific hea k hemal conduciviy L boehole lengh &m flow ae q ae of hea flow pe uni lengh q ae of hea flow pe uni aea $q 0 ae a which hea is added o he fluid adial vaiable 0 boehole adius ime empeaue aveage empeaue $ measued empeaue x axial vaiable α hemal diffusiviy δ film hickness ρ densiy ρc p volumeic hea capaciy Subscips c cold o oule side h ho o inle side i ime incemen i s soil g gou φ hin film infiniy ix

8 1. INRODUCION he geohemal o gound-souce hea pump (GHP) has been shown o be a vey efficien mehod of poviding heaing and cooling fo buildings. GHPs exchange (ejec o exac) hea wih he eah by way of ciculaing wae, ahe han by use of ciculaing oudoo ai, as wih an ai-souce hea pump. he empeaue of wae eneing a GHP is geneally coole han ha of oudoo ai when space cooling is equied, and wame han ha of oudoo ai when space heaing is equied. Consequenly, he empeaue lif acoss a GHP is less han he lif acoss an ai-souce hea pump. he lowe empeaue lif leads o geae efficiency, highe capaciy a exeme oudoo ai empeaues, and bee indoo humidiy conol. hese benefis ae achieved, howeve, a he cos of insalling a gound hea exchange. In geneal, his cos is popoional o lengh of he hea exchange, and fo his eason hee is an incenive o insall he minimum possible lengh such ha design cieia ae me. he design of a gound hea exchange fo a GHP sysem equies, a a minimum, he opeaing chaaceisics of he hea pumps, esimaes of annual and peak block loads fo he building, and infomaion abou he popeies of he hea exchange: he size of he U-ubes, he gouing maeial, ec. he design also equies some knowledge of he hemal popeies of he soil, namely hemal conduciviy, hemal diffusiviy, and undisubed soil empeaue. In he case of a veical boehole hea exchange (BHEx) hese popeies geneally vay wih deph; heefoe, in he design, effecive o aveage hemal popeies ove he lengh of he boehole ae usually sough. When he cos of doing so can be jusified, hese popeies ae measued in an in siu expeimen: a es well is dilled o a deph on he same ode as he expeced deph of he hea pump hea exchanges; a U-ube hea exchange is inseed and he boehole is goued accoding o applicable sae and local egulaions; wae is heaed and pumped hough he U-ube (using a field geneao o powe he equipmen, o line volage whee available); and he inle and oule wae empeaues ae measued as a funcion of ime. Daa on inle and oule empeaue, powe inpu o he heae and pump, and wae flow ae ae colleced a egula inevals ypically 1 o 15 min fo he duaion of he expeimen, which may be as long as 60 h. wo common mehods fo deemining soil hemal popeies fom such measuemens ae he line souce mehod (Mogensen 1983) and he cylinde souce mehod (Kavanaugh and Raffey 1997). Boh ae based on long-em appoximae soluions o he classical hea conducion poblem of an infiniely long hea souce in an infinie homogeneous medium. Alhough hee ae some diffeences in he way he wo mehods ae implemened, he only diffeence beween he wo models is whehe he hea souce is consideed o be a line o a cylinde. In boh mehods, powe inpu o he wae loop is assumed o be consan. he simpliciy of hese mehods makes hem aacive, bu hey also have some disadvanages. Fis of all, because he line souce and cylinde souce appoximaions ae inaccuae fo ealy ime behavio, some of he iniial daa fom he field es mus be discaded. he amoun of daa discaded can affec he popey measuemen. Also, boh mehods assume ha he hea ansfe o he gound loop is consan. In pacice, hea inpu o he loop may vay significanly ove he couse of a field es due o ough opeaion of he geneao o sho-em sags and swells in powe line volage. Pesumably, his vaiaion affecs he accuacy of he hemal popey measuemen, bu eo analysis is aely pefomed. his epo pesens a new mehod fo deemining hemal popeies fom sho-em in siu ess using a paamee esimaion echnique. Because i is based on numeical soluions o he hea conducion equaion, he new mehod is no affeced by sho-em vaiaions in hea inpu. Also, 1-1

9 since he model is accuae even fo sho imes, hee is no need o discad iniial daa. he paamee esimaion echnique used o deemine he popeies is based on saisical pinciples ha povide quaniaive esimaes of measuemen accuacy. he paamee esimaion mehod has now been esed wih a laboaoy es ig a Oklahoma Sae Univesiy and in field ess a wo elemenay schools in Lincoln, Nebaska. Using ou esimaion algoihms, and building on he validaion achieved duing esing, we have developed a compue pogam, he Geohemal Popeies Measuemen (GPM) model, ha allows uses o deemine hemal popeies fom sho-em in siu field ess. his pogam is cuenly available fee of chage. In Chape 2 of his epo, we descibe he paamee esimaion mehod and discuss he heoy behind his mehod. Chape 3 descibes he es ig expeimen and he field ess o validae he mehod. Chape 4 povides a uoial fo he GPM sofwae. 1-2

10 2. A NEW MEHOD FOR DEERMINING SOIL HERMAL PROPERIES 2.1 INRODUCION As noed in Chape 1, wo common mehods fo deemining soil hemal popeies fom in siu field ess ae he line souce mehod and he cylinde souce mehod. Boh ae based on analyical soluions o he classical hea conducion poblem of an infiniely long hea souce in an infinie homogeneous medium. he line souce mehod is based on classical heoy, accoding o which, a sufficienly lage imes, he gound hea exchange can be modeled as a line hea souce in an infinie medium (Caslaw and Jaege 1947; Ingesoll, Zobal, and Ingesoll 1954). Given he ae of hea inpu o he loop and he inle and oule empeaues as a funcion of ime, he effecive hemal conduciviy of he soil fomaion can be deemined. A poblem wih his mehod, howeve, is ha i assumes he ae of hea inpu o he wae loop o be consan. his is aely he case, since in he field he heae is usually poweed by a poable geneao. Even whee line elecical sevice is available, sho-em sags and swells in volage may cause vaiaions in hea inpu o he wae loop. he andom vaiaion in powe inpu as well as andom eos in he empeaue measuemens pesumably cause vaiaions in he value of hemal conduciviy obained fom a paicula expeimen, bu he classical heoy povides no infomaion on he vaiance. Anohe aea of unceainy is when o begin measuing inle and oule empeaues and fo how long he daa should be colleced i.e., he peiod duing which he line souce model is valid. In he cylinde souce mehod, gound hea exchanges ae modeled as a cylindical, consan hea souce in an infinie medium (Ingesoll, Zobal, and Ingesoll 1954). Deeman and Kavanaugh (1991) exended his model o accoun fo vaiable hea flux, bu in a manne no geneally suiable fo he analysis of sho-em field daa. Ohe auhos (Eskilson 1987; Hellsom 1991; Romaye, Beckmann, and Michell 1997; Ausin 1998) have poposed moe deailed wo- and hee-dimensional numeical models. he mehod we descibe in his epo is based on a simple one-dimensional hemal model ha descibes he empeaue field aound he boehole. he inle and oule pipe flows ae modeled as one, and a hin film may be added o accoun fo he hea capaciy of he pipes and he fluid. Wih his mehod, gound conduciviy can be elaively accuaely esimaed even hough he condiions a he boehole ae unceain. Based on numeical soluions o he hea conducion equaion in cylindical coodinaes, he paamee esimaion mehod includes he effec of gou inside he boehole, allowing boehole esisance o be esimaed in addiion o soil hemal conduciviy. his is significan because afe soil hemal conduciviy, boehole esisance is he mos impoan paamee in he design of a veical BHEx. In he absence of a mehod o measue boehole esisance, his paamee is usually calculaed on he basis of he assumed hemal popeies of he gou and U-ube piping, and he assumed spacing beween he U-ube pipes (which some auhos efe o as he shank spacing). Since he shank spacing is neve accuaely known once he U-ube goes ino he gound, and he hemal popeies of he gou ae aely measued on-sie, a boehole esisance calculaed in his manne may be vey diffeen fom he acual value. Measuing boehole esisance a he sie will educe his unceainy. 2-1

11 Anohe benefi o he mehod we have developed is ha because he hea conducion poblem is solved numeically ahe han analyically, i is no necessay o assume consan hea inpu o he wae loop. he hea ansfe model uses he field-measued powe inpu daa ahe han an aveage value. his feaue is paiculaly useful in siuaions whee unsable volage (eihe fom he powe line o fom he oupu of a poable geneao) causes he powe inpu o he wae loop o vay ove ime. Because he line souce and cylinde souce mehods boh assume consan powe inpu, hei esimaes of soil hemal popeies end o be inaccuae when he powe inpu vaies significanly. A fuhe benefi o ou mehod is ha i povides saisical esimaes of he confidence inevals fo he paamees esimaed. Ohe mehods of deemining effecive hemal popeies have adiionally epoed only he paamee value iself, wih no esimae of accuacy. Obviously, he accuacy of a paicula paamee value deemined fom a field expeimen depends upon he accuacy of he daa collecion equipmen, he lengh of he expeimen, and ohe facos. he model we popose uses a saisical echnique o povide a quaniaive esimae of he confidence ineval fo he paamees measued. he emainde of his secion descibes he heoy behind ou mehod. 2.2 HE PHYSICAL PROBLEM Because he gound is no homogeneous in composiion o densiy, and is affeced by he pesence of moisue, gound hemal popeies can vay significanly wih deph. A coss-secion of a boehole of adius 0 is shown in Fig he inle and oule pipes have an inside adius of a and ae suounded by gou o a adius 0. he empeaues of he fluid in he inle and oule pipes ae consideed o be only a funcion of axial posiion, x. he empeaue of he fluid in he pipes does change wih ime, bu he ime consan of he fluid is assumed o be much smalle han ha fo he hea conducion in he gound. Hence, he fluid hea ansfe in he pipes is modeled in a seady-sae manne; howeve, he hea capaciy of he fluid is lumped ino a film because he ubulen flow causes negligible adial empeaue vaiaion in he fluid. he empeaue vaiaions of he fluid in he axial diecion ae aveaged so ha he inle and oule empeaues appea. he enegy ansfeed fom he boehole (o o he boehole) is absobed by he suounding gound, wih mos of he enegy absobed some disance away fom he boehole. As he cooling (o heaing) ime inceases, he hemally affeced egion becomes lage ha is, he empeaue peneaion inceases wih ime. Moeove, as he disance fom he boehole inceases, he empeaue disibuion becomes one-dimensional. Since he hemally acive egion inceases wih ime and becomes one-dimensional away fom he ceneline of he boehole, he empeaue disibuion a a lage disance fom he U-ube is simila o ha which would be caused by a single pipe wih an effecive adius. δ (Film) a b 0 a Soil Gou he wo pipes in he boehole ae encased in a gou whose hemal popeies ae geneally diffeen fom Fig Geomey of he boehole hea exchange. 2-2

12 he hemal popeies of he suounding gound. he spacing (also called he shank disance) of he wo pipes is difficul o mainain in he x diecion, and he disances of he pipes fom he edge of he boehole vay. he pesence of he gou and he geomeical aangemen of he pipes is modeled by a single pipe of adius b. A hin film of hickness δ a he adius b is included o incopoae he hea capaciy of he fluid in he pipes and any diffeenial hea capaciy in he gou compaed o ha in he suounding gound. he film s hea capaciy is an addiional paamees ha can be esimaed along wih he gound hemal conduciviy. Wihou loss of genealiy bu fo simpliciy in hinking, he inle pipe is assumed o have ho fluid eneing i a a mass flow ae of m = ρva, kg/s, whee ρ is densiy, V is fluid velociy and A is he coss-secional aea of a pipe, πa 2. See Figs. 2.1 and 2.2. he hea flux q h (x,), W/m 2, is leaving he ho fluid and eneing he suoundings. he ohe pipe is assumed o have he same fluid flow ae leaving and o be heaed wih a hea flux q c (x,). In he following secions we will fis conside he fluid model based on an oveall hemal conol volume, and hen he hea conducion in he gound. q (x,) c Conol Volume. mc pf c () 2a q (x,) h. mc pf h () Fig Conol volume fo hemal analysis of boehole hea exchange. L 2.3 ENERGY FLUID MODEL An enegy balance on he fluid fo he oal lengh and fo boh pipes (see Fig. 2.2) gives L [ ( 0, ) ( 0, ) ] = [ q ( x, ) q ( x, ) ] Pdx = 0 mc pf h c h c. (2.1) x= 0 he inflow ho fluid empeaue, h (x,), and he ouflow cold fluid empeaue, c (x,), ae funcions of ime, bu he ae of enegy soed in he fluid is no included in Eq. (2.1). Enegy absobed by he fluid is lumped ino an effecive hea capaciy of a hin film a he effecive adius, b. he symbol P denoes he effecive pipe peimee; q h (x,) and q c (x,) ae he ho and cold side hea flux, especively, and c pf is he specific hea of he fluid. Because Eq. (2.1) does no accoun fo he hea soed by he fluid and he pipes, i is accuae only fo seady-sae condiions; howeve, since he ime consan fo he fluid is assumed o be much 2-3

13 shoe han ha of he suounding soil, modeling he fluid hea ansfe as a seady-sae pocess should no inoduce lage eos. As shown below, he hea soed by he fluid and piping will be included in anohe manne. In he gou and he soil, hea ansfe akes place hough conducion. he enegy ansfeed fom he U-ube is absobed by he gou and evenually by he suounding soil. As he heaing (o cooling) ime inceases, he hemally affeced egion becomes lage ha is, he hemal peneaion inceases wih ime. Moeove, as he disance fom he boehole inceases, he empeaue disibuion becomes one-dimensional in he -diecion. his suggess ha he empeaue disibuion in he soil a a lage disance fom he U-ube is simila o ha which would be caused by a single pipe wih some effecive adius. hus, in he model developed below, he wo pipes of he U-ube ae eplaced by a single pipe wih an effecive adius, as shown in Fig ENERGY MODEL FOR SOIL, GROU, AND FILM he one-dimensional model fo hea ansfe in he soil is he ansien hea conducion equaion. One equaion is equied fo he hemal esisive film, anohe fo he gou, and anohe fo he suounding soil. he model fo he soil is k s s = s ( ρc) < < s, (2.2) 0 whee he subscip s denoes soil. he gou is consideed o exend fom b+ δ o 0. he enegy equaion fo he gou is simila o Eq. (2.2) wih s eplaced by g fo gou, k g g = g ( ρc) g, b + δ < < 0. (2.3) Finally, a simila equaion is wien fo he film, which exends fom b o b+ δ: k = ( ρc), b < < b + δ, (2.4) whee he subscip denoes he hin film. he adius b is he effecive adius, which is used o lump boh pipes ino one in he analysis. In Eqs. (2.2), (2.3), and (2.4) he empeaue is a funcion of, x, and bu he hea conducion in he x diecion is assumed o be negligible compaed o ha in he 2 2 diecion. Hence, he ne hea conducion em in he x diecion, k x, is no included in hese equaions. he bounday condiion a he effecive pipe adius (whee he film of hickness, δ, is locaed) is ( b, x, ) k = qh( x, ) qc ( x, ), (2.5) 2-4

14 2-5 which applies a each x; howeve, i is moe convenien o aveage ove x in Eq. (2.5) and also in Eqs. (2.2), (2.3), and (2.4). Inegaing Eq. (2.5) fom x = 0 o L gives ( ) ( ) ( ) ( )dx x q x q L b k L x c h = =0,, 1,, (2.6) whee ( ) ( )dx x b L b L x = =0,, 1,. (2.7) he diffeenial equaions fo he conducion in he soil, gou, and film ae now aveaged ove x fom 0 o L. Equaions (2.2), (2.3), and (2.4) become ( ) < < ρ = c k s s s s 0, (2.8) ( ) 0, b c k g g g g < + δ < ρ = (2.9) ( ) δ + < < ρ = b b c k, (2.10) whee he aveage empeaues ae defined by ( ) ( )dx x L L x s s = =0,, 1,, (2.11) ( ) ( )dx x L L x g g = =0,, 1,, (2.12) ( ) ( )dx x L L x = =0,, 1,. (2.13) A complee mahemaical saemen is hen Eqs. (2.8), (2.9), and (2.10) wih he bounday condiion a = b given by Eq. (2.6) and he ineface condiions given by ( ) ( ) b k b k g g + δ = + δ,,, (2.14) ( ) ( ) b b g,, δ + = δ +, (2.15) ( ) ( ) k k s s g g =, 0, 0, (2.16)

15 ( ) ( ) g, s 0, 0 =. (2.17) he bounday condiion given by Eq. (2.6) can also be elaed o he inpu and oupu fluid empeaues o ge he alenae bounday condiion, he bounday condiion a = is and he iniial condiions ae ( b, ) he aio mc pf /PL in Eq. (2.13) is also equal o mc pf k = [ h( 0, ) c ( 0, ) ]. (2.18) PL ( ) = s,, (2.19) ( 0) =, (,0) =, g ( ) =,. (2.20) s, mc pf PL 2 2 Gπa c pf Ga c pf = =, (2.21) 2πbL 2bL whee G is he mass flux in kg/m 2 -s. he bounday condiion given by Eq. (2.18) can also be wien as ( b, ) k = q0( ), (2.22) whee he hea flux q 0 () is he field-measued hea flux divided by he boehole deph L. In summay, he diec poblem is descibed by Eqs. (2.8), (2.9), and (2.10) wih ineface condiions, Eqs. (2.14) hough (2.17); he condiion a infiniy, Eq. (2.19); and iniial condiions, Eq. (2.20). he bounday condiion a = b is Eq. (2.22). he equaions above ae a complee mahemaical saemen of he diec poblem. Howeve, he poblem canno be solved wih classical echniques because no all of he elevan paamees (such as he gound and film hemal conduciviies) ae known. Some exa infomaion is available ha allow hese and ohe paamees o be esimaed. he aveage fluid empeaue, defined by he aveage of he inle and oule empeaues, is known: Y ( ( ) ( ) )/ 2 =. (2.23) f h + his aveage empeaue may no be pecisely equal o he inegaed aveages of he inle and oule fluid empeaues bu is expeced o be as accuae as he lumping of he wo pipes ino one. Fuhemoe, he inle and oule empeaues ae he only empeaues ha ae measued. his empeaue is equal o he aveage of he suface film empeaue given by Eq. (2.6). Hence, wo condiions ae given a he film suface: hea flux and empeaue hisoies. Fo diec poblems only c 2-6

16 one condiion can be used; hus, hee is excess infomaion. his infomaion is used o esimae one o moe paamees in a leas squaes sense. he Y symbol is used in Eq. (2.19) o denoe a measued quaniy. he calculaed aveage suface empeaue hisoy given by Eq. (2.6) is made o agee in a leas squaes sense wih he measued aveage fluid empeaue given by Eq. (2.19) by minimizing a sum of squaes funcion wih espec o paamees, such as he gound hemal conduciviy. he sum of squae funcion, S, is n i= 1 ( ) 2 S = Y i, i, (2.24) whee i denoes a measuemen ime, Y i he aveage fluid empeaue, and,i he aveage empeaue of he film a = b. Noe ha if he film hickness is aken o be zeo, if he film is assumed o have no volumeic hea capaciy and no esisance o hea ansfe, and if he gou has he same hemal popeies as he soil, hen he poblem educes o ha of a cylindical hea souce in an infinie medium. Fo consan hea flux, his poblem has an analyical soluion involving a ahe complicaed inegal of Bessel and ohe funcions (Ingesoll, Zobal, and Ingesoll, 1954). he mehod can be exended o he case of non-consan hea flux using a convoluion pocess, bu his is difficul o implemen numeically. Fo his eason, and so ha he effec of he hin film and he gou can be included, we solve he diec poblem numeically using a finie diffeence gid and a Cank-Nicolson inegaion scheme. Alogehe, he model pesened above conains nine paamees: he hemal conduciviies of he soil, gou, and hemal film; he volumeic hea capaciies of he soil, gou, and hemal film,; he hickness of he hemal film; he effecive pipe adius, and he fa-field empeaue. In geneal, howeve, i will no be possible o esimae all of hese paamees wih a single expeimen, as some may be dependen on ohes. Fo example, since he hin film is used o accoun fo he hemal capaciance of he fluid and pipes, we would expec he hickness, δ, o be elaed o he film s volumeic hea capaciy. he paamee esimaion algoihm poceeds by fis assuming ial values fo he paamees in quesion. Given hese values, he (measued) hea flux is used o dive he numeical model. he numeical model gives a pediced value of as a funcion of ime fo he duaion of he expeimen. he sum of squaed eos beween he pediced and measued empeaues ae calculaed as in Eq. (2.20). he Gauss mehod of minimizaion is hen used o deemine he paamee values ha minimize he sum of he squaed eos. While he deivaion is beyond he scope of his epo, use of he Gauss minimizaion echnique enables calculaion of appoximae confidence egions fo he paamees (Beck and Anold 1977). he validiy of hese confidence inevals depends on a numbe of saisical assumpions ha may o may no be saisfied in a given expeimen. A numbe of ohe souces of eo ae unaccouned fo by hese confidence inevals: he assumpion ha he soil popeies ae homogeneous, when in fac hey vay wih deph; he assumpion ha he fa-field empeaue,, is accuaely measued; and of couse, he assumpion ha a ahe complicaed hee-dimensional hea ansfe pocess can be epesened by a one-dimensional model. Fo his eason we expec he confidence inevals deived fom he daa o be somewha smalle han he ue confidence inevals; he ue confidence inevals on he paamee esimaes may be as much as wice he value indicaed. Neveheless, hese 2-7

17 appoximae confidence inevals ae useful fo qualiaive assessmen of he accuacy of popey values and fo compaing one expeimen o anohe. 2.5 HE GPM SOFWARE he mehod descibed above has been incopoaed ino a sand-alone sofwae pogam called GPM (geohemal popeies measuemen). he pogam equies as inpu a ex file conaining aveage fluid empeaue (i.e., he aveage beween U-ube inle and oule empeaues) and hea inpu a consan ime inevals. his daa is usually measued in a sho-em in siu field es. he pogam uses paamee esimaion echniques o deemine he soil fomaion hemal popeies ha bes mach he daa. As indicaed in Secion 2.4, he model descibed above includes no fewe han nine paamees ha could poenially be deemined by way of paamee esimaion: he hemal conduciviies of he soil, gou, and hemal film; he volumeic hea capaciies of he soil, gou, and hemal film; he hickness of he hemal film; he effecive pipe adius; and he fa-field empeaue. In geneal, howeve, i is no possible o esimae all of hese paamees wih a single expeimen. he GPM pogam povides he opion o deemine (a) soil hemal conduciviy and fa-field empeaue o (b) soil hemal conduciviy, boehole esisance, and fa-field empeaue. Chape 3 pesens he esuls of a validaion sudy of he GPM sofwae, and Chape 4 povides a bief use s manual. 2.6 CONCLUSIONS he one-dimensional paamee esimaion model descibes he hemal behavio of a boehole hea exchange fo a GHP. he model lumps he inle and oule pipes ino one pipe of an effecive adius b and adds a film a he oue suface of he pipe o accoun fo he hea ansfe esisance of he suounding gou and he convecive hea ansfe coefficien. he film also has an effecive hea capaciy o model he hea capaciy of he fluid and he diffeen hea capaciy of he gou compaed o he gound. Paamee esimaion echniques ae used o deive values of soil and gou hemal conduciviy fom he model and expeimenal daa. An impoan feaue of his echnique is ha i povides appoximae confidence inevals on he paamee esimaes; hese inevals can be used o assess he accuacy of expeimens and he hemal conduciviies deived fom such expeimens. 2-8

18 3. FIELD ESS OF HE GPM SOFWARE 3.1 FIELD RIG ESS A majo poblem in validaing a model such as he one pesened in Chape 2 is ha he ue soil fomaion hemal popeies a a given sie ae geneally unknown. Whee esimaes of hese popeies ae available, hey ae usually based on pevious expeimens and ohe simplified hea ansfe models such as he line hea souce. Recenly, howeve, a es ig was consuced a Oklahoma Sae Univesiy o simulae he condiions in which a veical hea exchange opeaes. he ig consiss of a box made of ¾-in. plywood, wih appoximae dimensions of f. A U-ube hea exchange consising of nominal 1-in.-diam polyehylene piping is placed hoizonally along he ceneline of he box, paallel o he long axis. he U-ube is goued o a diamee of 5 in. fom he ceneline, and he box is filled wih a homogeneous maeial wih known hemal conduciviy. As in a field expeimen, wae is heaed and pumped hough he U-ube a a known flow ae while he ae of hea inpu and inle and oule wae empeaues ae measued a egula inevals. Alhough we ecognize ha his ig does no exacly duplicae he hea ansfe pocesses ha ake place in a veical hea exchange in a field insallaion, i does povide an oppouniy o build confidence in hea ansfe models such as he one we have developed, since he maeial which epesens he soil is homogeneous, and is hemal conduciviy can be measued independenly. A daa se fom a 63-h expeimen was obained fom D. Mavin Smih (pesonal communicaion fom M. Smih, Oklahoma Sae Univesiy, o J. Shonde, Mach 1998). Fo he expeimen he ig was filled wih we sand, and he U-ube was goued wih a commecially available gou. he hemal conduciviy of he sand was measued wice using a hemal pobe, giving values of 1.40 and 1.45 Bu/h-f- F. A he beginning of he expeimen he sand was a a unifom empeaue of 72.0 F. Duing he expeimen, he aveage flow ae of wae was appoximaely 4 gal/min, and he aveage ae of hea inpu was 363 W. Boh of hese values vaied by only abou ±0.5% of hei aveage values ove he 63-h peiod. Wae inle and oule empeaue, flow ae, and powe o he heae wee measued a 1-min inevals. o analyze he expeimenal daa, some modificaions wee made o he model o accoun fo he physical chaaceisics of he es ig. Since he model is adially symmeical, he ig was modeled as a cylinde consising of fou egions wih diffeen maeials. he U-ube was modeled as a single pipe wih an effecive diamee of 0.75 in. (A value of 0.5 in. was also used; as discussed below, he effecive pipe diamee appeas o have only a small effec on he hemal popey esimaes.) A hin film is assumed o exis a he suface of he pipe o simulae he hea capaciy of he wae and he pipes; he film is assumed o be in. hick. he diamee of he gou is given as 5 in.; hus, he maeial fom he oue edge of he hin film o a adius of 2.5 in. is assumed o be gou. he bulk of he egion is he sand, fom he oue adius of he gou o an effecive adius of f. Plywood wih a hickness of 0.75 in. is a he oue adius. o summaize, in he adial diecion hee is he film, gou, sand, and plywood. he finie diffeence model includes 72 nodes: 2 in he film, 6 in he gou, 60 in he sand, and 4 in he plywood. he inenal ime sep was 15 s. In he analysis, he oue bounday of he plywood is assumed o be isohemal a he iniial empeaue of 72.0 F. A volumeic hea capaciy of 35 Bu/f 3 -h was assumed fo boh he sand and he gou. he hemal conduciviy of he film was assumed o be a lage value; hus, all of he esisance o hea ansfe is conained in he soil and he gou. hee paamees ae esimaed: he hemal conduciviy of he soil, he hemal conduciviy of he gou, and he volumeic hea capaciy of he hin film. 3-1

19 Fig. 3.1 plos he measued aveage wae empeaue and he model s pediced aveage empeaue fo he fis 30 h of he expeimen, a he conveged values of he paamees. hee is excellen ageemen beween he wo. In ode o disinguish beween model and daa, he pediced wae empeaue is ploed only a inevals of 1 h. Figue 3.2 pesens he esiduals i.e., he diffeence beween he measued and pediced aveage wae empeaue as a funcion of ime fo he fis 30 h. he lage esiduals a ealy imes ae pobably due o he assumpion of one-dimensional hea ansfe. Howeve, since he lages esidual is only 0.2 F, he eo is no lage. Alhough he esiduals ae small oveall, wih a oo mean squae (ms) value of F, if he model wee uly an accuae epesenaion of he hea ansfe pocess aking place in he es ig, we would expec he esiduals o be andom and uncoelaed, which hey clealy ae no. hei slow ise and fall ove he 30 h indicaes ha hee may be some seconday effecs which he model does no capue. 88 Aveage empeaue ( F) Measued Pediced ime (hous) Fig Measued and pediced aveage wae empeaue fo expeimen using he Oklahoma Sae Univesiy es ig Residual ( F) ime (hous) Fig Residuals fo he expeimen on he Oklahoma Sae Univesiy es ig. 3-2

20 he esimae of hemal conduciviy fom he model is in excellen ageemen wih he measued values. Afe 30 h he conveged value of hemal conduciviy fo he we sand is Bu/h-f- F, compaed wih he measued values of 1.40 and he 95% confidence egion fo he hemal conduciviy value is ±0.172 Bu/h-f- F, o abou 12% of he esimaed value. he conveged value fo he hemal conduciviy of he gou is Bu/h-f- F wih a 95% confidence egion of Bu/h-f- F, which is abou 6% of he esimaed value. he acual hemal conduciviy of he gou was no available, bu he value of Bu/h-f- F is in he ange of values epoed in he lieaue. In any case, we expec ha he esimaed gou hemal conduciviy accouns fo ohe effecs, such as he conac esisance beween he pipes and he gou. he ime equied o convege o a soluion depends, of couse, on he iniial guesses fo he paamee values. Neveheless, even fo guesses 50% lage han he ue values, he model equies only abou 60 s o convege on a 200-MHz PC. We pefomed a second un assuming an effecive pipe diamee of 0.5 in. In his case he conveged value of he sand hemal conduciviy was ± Bu/h-f- F, which indicaes ha he effecive pipe diamee has only a small effec on he hemal conduciviy measuemen. Bose, Pake, and McQuison (1985) have ecommended using an effecive diamee of 2 imes he diamee of he U-ube piping, which in his case would coespond o a adius of Since hee was lile diffeence beween he hemal conduciviy esimaes using effecive adii of 0.5 and 0.75 in., we would agee wih he ecommendaion of hese auhos. he hemal popey esimaes changed somewha when daa up o 60 h wee used. Wih an effecive pipe adius of 0.75 in., he ms value of he esiduals inceased slighly, o F. he conveged value fo he hemal conduciviy fo he sand inceased o ± Bu/h-f- F. his is highe han he value obained afe 30 h, bu he measued value of hemal conduciviy sill lies wihin he 95% confidence egion. he conveged value of he gou hemal conduciviy was slighly lowe in his case, 0.593± Bu/h-f- F. Sequenial esimaes of he sand and gou hemal conduciviy ae pesened in Fig his figue shows, fo each ime, he values of he hemal conduciviies esimaed using all daa up o and including ha ime. If he model wee an accuae epesenaion of he hea ansfe pocesses aking place in he es ig, we would expec boh cuves o flaen ou a lae imes. In he case of he gou hemal conduciviy his does seem o occu; he esimae of he sand hemal conduciviy appeas o be ising slighly even a 60 h. his may be due o he assumpions made in he analysis, pimaily he assumpion ha he ecangula es ig could be modeled as a cylinde. We would expec eos associaed wih his assumpion o become moe impoan a lae imes. Of couse, his would no be a concen in a field es IN SIU ESS A WO ELEMENARY SCHOOLS he ess a Oklahoma Sae Univesiy showed ha ou mehod could pedic he hemal conduciviy of a known maeial (mois sand) accuaely, given daa colleced in an expeimen on a laboaoy es ig. Howeve, fuhe wok was needed o validae he model and gain expeience in is use. We also waned o esimae ohe paamees, especially boehole esisance (he oal esisance of hea ansfe fom he fluid o he boehole wall), a paamee ha is equied by many design algoihms. heefoe, we se up a seies of field expeimens in which he model s hemal conduciviy esimaes would be compaed wih esimaes fom ohe commonly used models and 3-3

21 hemal conduciviy (BU/h-f- F) Sand Gou ime (hous) Fig Sequenial esimaes of sand and gou hemal conduciviy. wih he ue o effecive hemal conduciviy of he soil, deemined fom daa on acive boefields a he sies. We conduced hee in siu ess a wo elemenay schools, Maxey and Campbell, in Lincoln, Nebaska, in 1998 and Daa fom in siu field ess povide a moe igoous es of a popeies measuemen echnique han daa fom laboaoy expeimens, bu a field es has he dawback ha he ue hemal conduciviy of he soil fomaion and boehole esisance a he sie ae geneally unknown. Fo he Maxey School sie, howeve, analysis of one yea of daa fom he opeaing boefield povided an esimae fo he effecive soil hemal conduciviy ha could be compaed wih he measued values. A Campbell Elemenay School, wo boeholes wee dilled wih he same diamee and he same appoximae deph, abou 60 f apa. A hid boehole was dilled a Maxey. hee diffeen gous wee used: hemal gou 85, fine sand, and soil cuings. he ess wee blind in ha he dille did no infom us of which gou was used in which boehole. One objecive of he in siu field ess was o deemine whehe he soil conduciviy esimaes fo he wo boeholes a Campbell ageed wih each ohe and whehe he conduciviy esimae a Maxey ageed wih he hemal conduciviy esimae obained fom analysis of he opeaing daa. Anohe objecive was o deemine whehe he numeical mehod could idenify he diffeen boehole esisances esuling fom he diffeen gous. able 3.1 shows he paamees of he ess. Fo puposes of compaison, he hee daa ses wee also analyzed using he line souce and cylinde souce mehods Descipion of ess Fo each es, a 4.25-in. diamee boehole was dilled o an appoximae deph of 245 f. Nominal 1-in. SDR-11 U-ube pipe was inseed, and he boeholes wee goued wih eihe hemal gou o 3-4

22 able 3.1. Paamees of hee in siu hemal popeies ess pefomed a Lincoln, Nebaska, elemenay schools es designaion Dae pefomed Boehole deph (f) Aveage soil empeaue ( F) Aveage powe inpu (W) Maxey 09/19/ Campbell #1 09/15/ Campbell #2 10/08/ fine sand, o no goued a all. In geneal, he boeholes wee dilled abou 75 f fom he acive boefield. he wo boeholes a Campbell school wee appoximaely 60 f apa. he equipmen used o pefom he in siu ess has been descibed by Ausin (1998). Housed in a aile ha is owed o he sie, he appaaus includes wo ciculaing pumps, a flowmee, and hee in-line wae heaes, all poweed by a poable elecic geneao. A wa ansduce measues he powe consumpion of he heaes and ciculaing pumps, and he inle and oule empeaues ae measued using wo high-accuacy hemisos immesed in he flow. he wae flow ae, oal powe inpu, and inle and oule empeaue wee logged a 15-min inevals. Befoe he U-ube was conneced o he es appaaus, a hemiso was inseed ino one end of he U-ube and he wae empeaue was measued a 10-f inevals. he aveage undisubed soil empeaue a each sie was assumed o be he aveage of hese measuemens. he acual lengh of he insalled hea exchange was also deemined fom hese measuemens. Figues 3.4 and 3.5 pesen he powe inpu and aveage wae empeaue as a funcion of ime fo he wo expeimens a Campbell School, and Fig. 3.6 pesens he daa fo he expeimen a Maxey School. he hee ess ae unemakable excep fo he es on he second well a Campbell. Jus noiceable in Fig. 3.5 ae wo jumps in aveage empeaue a 27.5 h and a 33.5 h. Beginning a Aveage Wae empeaue 4500 empeaue ( F) Powe Inpu Powe Inpu (Wa) ime (h) Fig Powe inpu and aveage wae empeaue, Campbell Elemenay School es #

23 empeaue ( F) Aveage Wae empeaue Powe Inpu Powe Inpu (BU/h/f 2 ) ime (h) Fig Powe inpu and aveage wae empeaue, Campbell Elemenay School es # Aveage Wae empeaue 4000 empeaue ( F) Powe Inpu Powe Inpu (BU/f-h) ime (h) Fig Powe inpu and aveage wae empeaue, Maxey Elemenay School es #

24 27.5 h, he wae flow ae hough he hea exchange dopped by abou 15%, possibly due o he pesence of ai in he hea exchange. his does no appea o have affeced he accuacy of he paamee esimaes es Resuls One indicaion of a model s eliabiliy is is abiliy o pedic he empeaue ise of he wae as a funcion of ime. Alhough he one-dimensional numeical model includes a numbe of simplificaions, i is able o pedic he aveage wae empeaue in he hea exchange wih good accuacy. Figues 3.7 hough 3.9 pesen plos of he esiduals beween he measued and pediced aveage empeaue as a funcion of ime. Fo imes afe abou 30 min, he esiduals ae quie small, on he ode of 0.17 F. he model did no accuaely follow he sysem behavio duing he shap decease in flow ae ha occued duing he second Campbell expeimen, bu again, his did no seem o affec he popey esimaes in ha case. hemal Conduciviy able 3.2 pesens he esimaes fo soil hemal conduciviy and boehole esisance. hee is good ageemen beween he wo hemal conduciviy measuemens a each sie. he value of 1.36 obained fo he Maxey es agees well wih he value of 1.3 obained fom analysis of a yea s opeaing daa fom he boefield (honon 1999). he aveage of he wo Campbell measuemens is 1.20 BU/h-f- F, and he wo ess wee consisen wih one anohe (he hemal conduciviy esimaes diffe by only 2%), so i appeas hee is a definie diffeence beween soil hemal conduciviy a he wo schools Model Eo ( F) ime (hous) Fig Model eo ( measued calculaed ) fo Campbell Elemenay School es #1. 3-7

25 Model Eo ( F) ime (hous) Fig Model eo ( measued calculaed ) fo Campbell Elemenay School es # Model Eo ( F) ime (hous) Fig Model eo ( measued calculaed ) fo Maxey Elemenay School es #1. 3-8

26 able 3.2. Resuls of soil hemal conduciviy and boehole esisance esimaes fom hee in siu ess es designaion Soil hemal conduciviy (BU/h-f- F) Boehole esisance (h-f- F/BU) Gou maeial Maxey 1.36± ±.003 hemal gou 85 Campbell #1 1.20± ±.015 Soil cuings Campbell #2 1.19± ±.008 Fine sand Boehole Resisance Alhough able 3.2 indicaes a definie diffeence beween he boehole esisances measued a each sie, i is difficul o say whehe he measued boehole esisances coespond o he expeced values. Fo a given U-ube size, boehole esisance is a funcion of gou hemal conduciviy and shank spacing. Spile (1996) has developed a speadshee pogam ha is useful fo calculaing boehole esisance given shank spacing and gou conduciviy. As an example, fo a 1-in. SDR-11 U-ube goued wih hemal gou 85 (nominal hemal conduciviy of 0.85 Bu/h-f- F), he speadshee calculaes boehole esisances beween and 0.313, depending on he shank spacing assumed. he measued boehole esisance fo hea exchange #1 a Maxey School does lie wihin his ange, and he fac ha i is close o he lowe limi may indicae ha he U-ube legs ae close o he boehole wall. Deemining he boehole esisance of he hea exchanges goued wih fine sand is moe poblemaic, since he hemal conduciviy of sand depends on moisue conen. Wih a nominal value of 1.5 Bu/h-f- F fo he sand hemal conduciviy, he calculaed boehole esisance is beween and.237. he measued esisances fo Maxey es #2 and Campbell es #2 ae boh wihin hese limis, and boh ae close o he lowe limi han he highe one, indicaing again ha he U-ube legs may be close o he boehole wall. Hea exchange #1 a Campbell school was goued wih soil cuings. If he gou is assumed o have he same hemal conduciviy as he soil, he calculaed boehole esisance would lie beween and he measued boehole esisance does in fac lie beween hese limis, bu ceainly, fuhe expeimens would have o be conduced o deemine whehe boehole esisance can be measued eliably wih his mehod Compaison wih Ohe Analysis echniques able 3.3 compaes he hemal conduciviy esimaes fom he hee ess using ou numeical mehod wih he values obained using he line souce and cylinde souce mehods. hese ae 50-h esimaes. Fo he line souce mehod, daa pio o 4 h was ignoed. In geneal he paamee esimaes agee well wih he esimaes using he line souce and cylindical souce mehods, wih diffeences on he ode of only 2 o 3%. able 3.3. hemal conduciviy esimaes deived by hee es mehods fom 50-h ess es Numeical Line souce Cylinde souce designaion mehod mehod mehod Maxey Campbell # Campbell #

27 In addiion o compaing he 50-h hemal conduciviy esimaes, i is also infomaive o examine plos of sequenial esimaes fom he hee mehods. hese plos show, fo evey ime, he esimae of hemal conduciviy obained by using all he daa up o ha ime. A plo of sequenial paamee esimaes can indicae whehe he mehod is conveging o a paicula value, o whehe he esimae changes significanly ove ime. Sequenial plos ae also useful fo esimaing how long he daa mus be colleced in ode o obain an accuae paamee esimae. Figues 3.10 hough 3.12 pesen sequenial hemal conduciviy esimaes fo he hee expeimens fom 10 o 50 h, using he one-dimensional numeical mehod, he line souce mehod, and he cylinde souce mehod. Daa pio o he fouh hou was ignoed fo he line souce analysis, and a volumeic hea capaciy of 30 Bu/f 3 - F was assumed fo boh he one-dimensional numeical mehod and he cylinde souce mehod. Fo he wo Campbell ess, all hee mehods conveged o wihin abou 5% of hei 50-h values wihin 24 h (Figs ). his was no he case wih he Maxey es, howeve (Fig. 3.12). Alhough he esimaes fom he hee mehods agee among each ohe, he plos in Fig sugges ha had he measuemens coninued beyond 50 h, he hemal conduciviy esimae a he Maxey sie would have coninued o ise. One possibiliy is ha hee is modes goundwae flow a he sie. Condiions such as hese, which vay fom sie o sie, make i difficul o make geneal ecommendaions as o how long hemal conduciviy ess should poceed. he compaisons indicae ha hee is lile diffeence beween he hemal conduciviy esimaes deived fom ou mehod and he line souce mehod. Howeve, he sable powe supply and ohewise good qualiy of he hee daa ses end o mask he usefulness of he mehod we have developed. Figue 3.13 pesens daa fom a hemal conduciviy es caied ou a anohe sie. Duing his es, he field geneao developed mechanical poblems (pesonal communicaion fom C. Remund, Souh Dakoa Sae Univesiy, o J. Shonde, ORNL, Apil 1999). Ou convesaions wih field pesonnel indicae ha sho-em volage spikes ae no uncommon, even when line powe is used in place of a geneao. hese spikes can cause significan poblems if he line souce o cylinde souce mehods ae used o esimae hemal conduciviy because boh mehods assume ha he powe inpu is consan. he one-dimensional numeical mehod we have developed does no assume consan powe. Because he model is diven wih he field-measued powe inpu, volage spikes cause vey lile change in he hemal conduciviy esimaes. Figue 3.14 is a plo of sequenial hemal conduciviy esimaes fom he daa of Fig deived using he line souce mehod, he cylinde souce mehod, and ou one-dimensional numeical mehod. Because he cylinde souce mehod calculaes hemal conduciviy based only on he measued empeaue ise fo a paicula ime, i is much moe sensiive o sho-em vaiaions in powe. Fo example, beween 30 and 33 h he cylinde souce esimae of hemal conduciviy dops by almos 10%, owing pimaily o flucuaions in he powe inpu. he line souce mehod is somewha less affeced by sho-em flucuaions because i uses all of he empeaue daa up o a given ime. Neveheless, he line souce mehod sill assumes consan powe inpu, and his can cause abup changes in he hemal conduciviy esimae. Ou one-dimensional numeical mehod is he mos sable of all because i uses all of he powe daa and all of he empeaue daa. As shown in Fig. 3.14, he esimae of hemal conduciviy fom ou mehod changes by only 1 o 2% ove he enie expeimen. 3-10

28 hemal conduciviy esimae (BU/h-f- F) Numeical mehod Line souce mehod Cylinde souce mehod es ime (hous) Fig Sequenial hemal conduciviy esimaes, Campbell Elemenay School es # hemal conduciviy esimae (BU/h-f- F) Numeical mehod Line souce mehod Cylinde souce Mehod es ime (hous) Fig Sequenial hemal conduciviy esimaes, Campbell Elemenay School es #

29 hemal conduciviy esimae (BU/h-f- F) Numeical mehod Line souce mehod Cylinde souce mehod es ime (hous) Fig Sequenial hemal conduciviy esimaes, Maxey Elemenay School es #1. Aveage empeaue ( F) ime (hous) Powe inpu (Was) Fig empeaue and powe inpu vs ime fo a case in which he geneao developed mechanical poblems. 3-12

30 hemal conduciviy esimae (BU/h-f- F) Numeical mehod Line souce mehod Cylinde souce mehod ime (hous) Fig Sequenial hemal conduciviy esimaes fom he daa of Fig CONCLUSIONS he new mehod of deemining soil hemal popeies fom in siu ess, which is based on a onedimensional numeical hea ansfe model, uses paamee esimaion echniques o deemine soil hemal conduciviy and boehole esisance fom field-colleced daa. ess wee needed o validae he mehod. Fo his pupose we used es daa fom an expeimenal es ig conaining sand wih a known hemal conduciviy. We also conduced ess a schools in Lincoln, Nebaska, ha aleady had one yea of daa fom opeaing boefields. Fo he es ig expeimen a Oklahoma Sae Univesiy, in which a U-ube hea exchange was placed in a medium wih independenly measued hemal popeies, he model s pediced hemal conduciviy showed excellen ageemen wih he measued value afe 30 h. Afe 60 h he model pediced a slighly highe value of soil hemal conduciviy (due pehaps o edge effecs associaed wih he finie volume of he es ig), bu he confidence ineval sill included he measued value. Fo he ess in Lincoln, a oal of hee boehole hea exchanges wee insalled, wo a Campbell Elemenay School and one a Maxey Elemenay School. he hemal conduciviy es a Maxey ageed o wihin 4% wih a sepaae hemal conduciviy value fo he sie deived fom one yea of opeaing daa fom he boefield. he wo ess a Campbell ageed wih each ohe o wihin abou 2%, bu wee lowe han he values obained fo he Maxey sie. he boehole esisance values of he hee hea exchanges wee also esimaed fom he field daa. he values measued wee wihin he ange of boehole esisances calculaed fo he gou maeials, bu because of unceainy in shank spacing and he acual conduciviy of he gou, we ecommend ha fuhe expeimens be pefomed o deemine he eliabiliy, accuacy, and epeaabiliy of he boehole esisance measuemens. 3-13

31 he hemal conduciviy measuemens fom ou mehod agee wih he values obained fom he line souce and cylinde souce mehods. his is o be expeced because he powe inpu was elaively sable duing he couse of he hee expeimens. Analysis of a sepaae daa se showed ha hemal conduciviy esimaes fom he line souce and cylinde souce mehods ae significanly affeced by vaiaions in powe inpu, while he hemal conduciviy esimae fom he mehod we have developed vaied by only abou 1% ove he couse of he expeimen. 3-14

32 4. GPM SOFWARE UORIAL 4.1 INRODUCION his chape povides an inoducion o he feaues of he GPM pogam, including he opions available in he main inpu menu and he infomaion ha is povided in he oupu window. Numeous illusaions show wha he use will see on he compue sceen. 4.2 MAIN MENU he main menu, used fo inpu, comes up auomaically following an iniial 3-s idenificaion sceen. A sample of he main page is shown in Fig In he example shown in Fig. 4.1, he uni selecion is he defaul value, which is he English uni sysem. he expeimenal daa file and he oupu file ae shown in he file name windows. he expeimenal daa file name and/o he oupu file name can be manually yped ino he appopiae file window. Fig he main daa inpu sceen in GPM. 4-1

33 Alenaively, he use can selec he desied expeimenal daa file o oupu file, as applicable, by using he Bowse buon. A file dialog box appeas when Bowse is seleced. A sample of he file dialog box is shown Fig o make a selecion, he use simply double-clicks he appopiae diecoy, if he desied diecoy is no aleady displayed. Following his, he use double-clicks he appopiae file name. If a disk dive ohe han he one conaining gpm.exe is desied, his can be seleced in he uppe igh hand cone of he file dialog box. Fig A sample of he file dialog box. Similaly, if an exension ohe han he defaul.ou is desied, he appopiae selecion can be made in he lowe lefhand cone. he following secions explain he inpu feaues on he main menu. Expeimenal daa file name he expeimenal daa file, conaining he measuemens fom he boehole es, is povided by he use. he daa configuaion mus be hee columns: ime, aveage (of he inle and oule) wae empeaue, and hea flux. Assuming English unis ae seleced, he ime should be in hous, he empeaue in degees Fahenhei, and he hea inpu in was. (he hea inpu uni is paiculaly impoan o noe because i is no consisen wih he English unis.) he hee columns may be sepaaed by spaces o ab delimies. he ime seps, as given in he fis column of he expeimenal daa file, mus be unifom. he expeimenal daa file name will be loaded auomaically if a peviously saved oupu file is used and eloaded. In his case, he use should veify he pah lised o ensue ha i is sill valid. his is especially impoan when using a file fom anohe use s machine, since he file may have been saved in a diffeen diecoy sucue on he ohe machine which does no exis on he use s machine. Oupu file name he beginning of he oupu file conains all of he infomaion eneed by he use on he main menu (dae, ime, file names and all ohe use selecions). I also includes all of he oupu fom he paamee esimaion pogam, including eveyhing displayed in he oupu window. he oupu daa file name is chosen by he use. I is ypically given a.ou file name exension bu can be saved unde any name. he oupu file name can eihe be seleced fom he exising diecoy sucue, if an oupu file aleady exiss, o eneed manually. If i is desiable o save he file in a diecoy ohe han he GPM pogam diecoy, ha diecoy should be eneed in he Oupu file name window on he main menu. 4-2

34 If a new oupu file is being developed, he applicable expeimenal daa file can be locaed using he Bowse buon nex o he expeimenal daa file line. Selecing his buon auomaically opens he file dialog box and allows he use o selec he appopiae file by double-clicking on he desied diecoy and file name. Uni selecion Alhough English unis ae by fa he mos common selecion, and he sysem defaul, an opion is povided fo meic unis. he use is auomaically pomped o inpu daa in he daa boxes (descibed below) accoding o he uni sysem seleced. he use mus execise cae egadless of he sysem seleced because he unis designaed fo daa inpu ae no consisen; fo example, daa inpu in he English sysem uses boh inches and fee. (See Fig. 4.1.) Paamee esimaion opions he main menu povides wo opions fo analyzing boehole empeaue daa. hese ae found in he Paamee esimaion opions box. he available opions ae Deemine soil hemal conduciviy and boehole esisance (gou-soil model) and Deemine soil hemal conduciviy (homogeneous soil model). Deemine soil hemal conduciviy and boehole esisance. his opion povides wo hemal paamee esimaes. One paamee is soil hemal conduciviy, and he ohe is boehole esisance. In addiion, he deep eah empeaue is esimaed. Fo his model, he boehole gou is assumed o be a hollow cylinde of oue adius equal o he boehole adius and inne adius equal o he effecive U-ube adius, i (Fig. 4.3). (Fo moe discussion of i see he discussion of he U- ube diamee below.) Boehole esisance is simply he ecipocal of he hea ansfe coefficien fo a uni hickness of maeial, accoding o he equaion Fig Coss-secional view of boehole showing dimensions. Boehole Resisance = 1 2πk g 0 ln i, (4.1) whee o is he oue adius of he gou (i.e., he boehole adius), i is he effecive inne adius (i.e., he acual ouside U-ube adius muliplied by 2 ) and k g is he hemal conduciviy of he gou. he soil in his case is consideed as a sepaae egion, which is fom o o a hemally lage adius. Deemine soil hemal conduciviy only. his is he simples opion and euns he soil hemal conduciviy and he deep eah empeaue, boh wih confidence egions. he model fo his opion assumes ha he hemal popeies of he gou ae he same as ha of he soil and lumps boh maeials ino one egion. U-ube diamee he U-ube diamee is he diamee of he inne ube of he boehole in he unis shown on he capion fo he daa box. (English unis ae inches, and meic unis ae cenimees.) Sandad sizes may be pulled down fom a menu inside he daa eny box. When sandad U-ube diamees of ¾, 1, 1¼, 1½, o 2 in. ae seleced, hese values ae eplaced auomaically by he acual oue-diamee dimensions of 1.050, 1.315, 1.660, 1.900, o in., especively. One-half of hese diamees is he 4-3

35 adius denoed u, which GPM hen muliplies by gives he effecive adius of i = (2) 1/2 u. 2 o simulae he inle and oule pipes. his Boehole diamee he boehole diamee is he diamee of he oue boehole in he unis (inches fo English unis) shown on he capion fo he daa box. Boehole deph he boehole deph is he deph of he boehole in he unis (fee fo English unis) shown on he capion fo he daa box. Deep eah empeaue he deep eah empeaue nomally eneed is he saing empeaue of he wae exiing he boehole. I is an esimaed quaniy in GPM, bu a ealisic value should be eneed hee. Because i is used as pio infomaion by he pogam, is value will have a small effec upon he final esimae of he deep eah empeaue and a much smalle effec on he esimaes of he hemal paamees. Expeimen heading/commens his opional eny iem allows he use o keep noes on paicula iems of inees having o do wih an expeimen o an analysis of an expeimen. Since moe han one analysis can be pefomed on one expeimen, his can be used o disinguish beween analyses. Soil volumeic hea capaciy he defaul eny fo soil volumeic hea capaciy 30 Bu/f 3 -EF in he English sysem is ypical fo mos soils. he ange of volumeic hea capaciy does no vay much aound his. Even moe impoan, he hemal conduciviy esimaes ae elaively insensiive o he value of he volumeic hea capaciy. If a value is known fo a paicula soil, howeve, i can be eneed hee. When a gou laye is included, a sepaae value fo he gou can be eneed. View A pull-down menu allows he use o choose whehe o no he DOS shell pogam is o be viewed. he paamee esimaion calculaions ae acually pefomed by a sepaae pogam called sub.exe ha is called up by GPM. he use can view his pogam while i is unning if desied. he defaul condiion is o allow he pogam o un in a minimized sae ha is no visible o he use. A un-ime indicaion is displayed in ode o show he use ha he calculaions ae being pefomed. Calculae paamees Once he Calculae Paamees buon is seleced, he paamee esimaion calculaions will begin. A his ime, he oupu infomaion is saved in he oupu file. If an oupu file of he name seleced has aleady been saved by he use, a waning window will appea o ensue ha he use ealizes ha he pevious file will be ovewien. Following his, he calculaions will begin, and he un-ime indicaion will begin o display he numbe of seconds of un ime. he oupu sceen will auomaically appea when he calculaions ae compleed. Exi If he exi buon is depessed, he pogam will sop. A use who wishes o coninue using GPM will have o esa he pogam. 4-4

36 4.3 OUPU WINDOW he oupu window conains all of he infomaion conained in he oupu file. he window has fou ab selecion opions, labeled abula Oupu, Residuals, Sensiiviy Coef., and Sequenial Es. (see Fig. 4.4). he oupu pesened in each of hese windows is summaized below. abula oupu he abula oupu window is he iniial window ha appeas upon compleion of he paamee esimaion calculaions. I povides he equesed calculaed paamee values in bold pin a he op of a scollable ex sceen. he emainde of he sceen conains he conens of he enie oupu file, including inpu daa, confidence egions, esiduals, sequenial paamee esimaes, and sensiiviy coefficiens. Residual plo he esidual plo is a gaphical plo of he esiduals vs ime. he esiduals ae defined as he measued empeaue values minus he calculaed empeaues fom he mahemaical model. A plo of he esiduals is valuable because his gaph can be examined fo a chaaceisic signaue. Ideally, he esidual gaph should be puely andom, eflecing andom empeaue measuemen eos. Fig he GPM oupu window. his sceen, showing abula oupu, is he oupu window ha appeas fis. 4-5