A Web Application for Geothermal Borefield Design

Transcription

1 Poceedings Wold Geothemal Congess 205 Melboune, Austalia, 9-25 Apil 205 A Web Application fo Geothemal Boefield Design Davide Rolando,2, José Acuna and Maco Fossa 2 KT Royal Institute of Technology, Binellvägen 68, Stockholm, Sweden 2 Univesity of Genova, Via all Opea Pia 5a, 6 45 Genova, Italy [email protected], [email protected] Keywods: gound coupled heat pumps, boehole heat exchanges, g-functions, themal esponse test, web application ABSTRACT The coect design of a boehole heat exchange (BE) system implies the accuate knowledge of boehole and gound themal popeties, the coect evaluation of building heating o cooling demands and the coect pocedue to assess the final oveall BE length elated to BE configuation shape. A caeful design is equied to make pofitable payback plans and povide expected long time pefomance. In this pape the pinciple and desciption of a web-based suite of tools fo BE design is pesented. The web application intends to implement some of the main pocedues univesally adopted in BE system design. A section of the pesent pape descibes the implementation of an impoved ASRAE method which allows the BE system to be designed by consideing thee epesentative building heat loads, thei espective themal esistances based on ICS model and a tempeatue penalty vaiable which takes into account the long tem BE inteaction effect. A new hybid implementation of the Ashae method based on g-function calculation is also descibed fo abitay boehole field configuation design. This abitay shaped boefield design allows the designe to fit the peculia needs of each application poject. Cuent fee o commecial pogams allow the use to design BE systems accoding to a pioi detemined set of available configuations in tems of boefield shape and boehole to boehole distances while eal applications often equie the boehole field geomety not to espect a egula matix configuation. A futhe section descibes a toolkit fo Themal Response Test (TRT) analysis which allows the estimation of BE and gound themal popeties. This toolkit povides also a method fo the evaluation of the eo elated to TRT analysis esults. Futhemoe, a section fo analytical estimation of boehole themal esistance based on liteatue eview is also pesented.. INTRODUCTION Gound souce heat pumps (GSP) ae widely consideed as being among the most enegy efficient solution fo building space heating and cooling due to thei efficiency and educed maintenance cost compaed to conventional VAC systems. The boefield design goal is the definition of the best BE geomety and the optimum oveall length and location of vetical and/o inclined boeholes. The constaints of the poblem and its input infomation ae the themal enegy demand of the building ove time, the gound and BE themal popeties and a taget heat pump pefomance. To descibe and pedict the heat tansfe due to the inteaction between a BE field and the suounding gound, the assumptions of pue heat conduction and homogeneous gound popeties ae widely adopted. Unde those hypotheses some base solutions ae available and mainly diffe depending on whethe the BE is consideed as an Infinite Line Souce (ILS), an Infinite Cylindical Souce (ICS) o a Finite Line Souce (FLS). The most popula solutions, called tempeatue esponse factos, ae ILS (Ingesoll et al., 954) and ICS (Caslaw and Jaege, 947). The ILS model was fist poposed by Lod Kelvin and is based on the appoximation of the BE heat souce as in infinitely long line buied in an infinite volume of gound. The ICS model consides a constant heat tansfe ate applied to a cylindical suface of finite adius and infinite length. Both solutions allow the tempeatue distibution in the gound to be evaluated in tems of a dimensionless time and adius fom the souce axis. The tempeatue esponse facto appoach was extended by Eskilson (987) to the desciption of complex BE configuations, constituted by finite heat souces positioned in egula aangements. This appoach is based on the pope supeposition in space of the numeical solution of the single and FLS poblem. The elated non-dimensional tempeatue esponse factos ae known as g- function(s). Analytical studies of the FLS poblem have also been developed moe ecently by Zeng et al. (2004), Lamache and Beauchamp (2007) and Javed and Claesson (20). A numbe of pocedues fo designing of BE field have been suggested and ae cuently implemented in compute pogams. Kavanaugh and Raffety (997) poposed a method that has been ecommended by the Ameican Society of eating Refigeating and Ai-Conditioning Enginees (ASRAE) and is used in thei own gound loop design softwae. Eskilson (986, 987) poposed a method which late has been patially implemented in the Eath Enegy Designe (EED) softwae by the Depatment of Mathematical Physics (Lund Univesity, Sweden) and the Institute of Applied Geosciences (Justus-Liebig-Univesity, Gemany), as descibed by ellstöm and Sanne (997). Likewise, the compute pogam GLEPRO is a well-known tool fo boefield design, poposed by Mashall and Spitle (994), and developed at Oklahoma State Univesity. The Ashae method allows the BE system to be designed by consideing thee epesentative building heat loads, thei espective themal esistances based on ICS model and a tempeatue penalty vaiable which takes into account the long tem BE inteaction effect. The stength of this method is its simplicity. The design of the BE field, in tems of BE oveall length, can be easily pefomed without a dedicated compute as those based on monthly o houly desciption of the building heat load pofiles (ellstöm and Sanne, 200 and Spitle et al., 2009).

2 In the method poposed by Eskilson (987) the tempeatue esponse factos (called g-functions) ae evaluated numeically by spatial supeposition of the FLS solution. The g-function values ae then employed in a tempoal supeposition algoithm depending on the monthly building heat load pofile pe BE unit length, the gound themal popeties and the boehole geometical and themal chaacteistics. As a esult, the oveall BE length equied can be evaluated. The implementation of this method in the commecial softwae EED and GLEPRO is based on using a finite numbe of pe-calculated g-function values stoed in a dedicated database and elated to espective BE configuations. One of the limitations of this appoach is elated to the finite ange of BE configuations available. The g-function elated to an abitay BE configuation can be evaluated accoding to appoaches poposed by Zeng et al. (2004), Lamache and Beauchamp (2007) and Javed and Claesson (20) but the calculation is cuently too computationally demanding. An appoximation of the FLS solution has been ecently poposed by Fossa and Rolando (204b), which allows fast calculations of tempeatue esponse facto of complex BE fields. With this appoach the geneation of themal esponse facto fo abitay BE aangements is possible with low computational demand. In all design methods fo sizing the boeholes fo gound-souce heat pump systems, the gound and BE themal popeties ae vey impotant paametes that can lead to an eoneous estimate of the equied oveall boehole length. The evaluation of boehole effective themal esistance and effective gound themal conductivity can be assessed by means of a Themal Response Test (TRT). The TRT is a woldwide adopted in-situ methodology based on heat ate injection (extaction) to (fom) the gound though a fluid ciculating in a pilot BE. The measued fluid tempeatue evolution ecoded duing the test is analyzed with numeical o analytical appoaches based on the above mentioned models in ode to evaluate the paametes of inteest. This measuement pocedue was fist used by Mogensen (983) and it is based on the ILS model. ILS is able to descibe the themal esponse of an infinite gound medium. TRTs ae based on constantly heating (o cooling) a fluid ciculated though a BE while measuements of inlet and outlet fluid tempeatue vesus time allow the estimation of the aveage themal conductivity of the gound (k) togethe with the effective boehole esistance (R ). The fist measuement device designed and built by Mogensen (983) was based on a chille to pefom a TRT in cooling mode. Late, othe mobile measuement devices wee intoduced mainly in Sweden, USA and Nethelands fo both heating (Eklöf and Gehlin, 996, Austin, 998) and cooling (Van Gelde et al., 999) TRT puposes. Moe ecently, an extended TRT measuement technique named Distibuted Themal Response Test (DTRT) has been intoduced by Fujii at al. (2006) and Acuña et al. (2009), to allow a moe detailed desciption of the gound and BE themal popeties. Even though the theoetical backgound and laboatoy application of the line souce solution fo themal conductivity evaluation has been well known since long ago, Niven (905) and Stålhane et al. (93), the uncetainty elated to gound test measuements has not been studied with sufficient attention and is often missing in cuent TRT evaluation pocedues. An extensive study of this poblem has been pesented by Witte (203) in ode to descibe some solutions and methods to take into account the souces of uncetainty involved in TRT expeiments and evaluate thei effects on the quality of a TRT esult. The boehole themal esistance can also be detemined by means of analytical and numeical models. All those models popose to decompose R into thee contibutions: gout conductive esistance (when gouting is applied), pipe conductive esistance and fluid convective esistance. One of the fist models is the Gu and O Neal (998) equivalent diamete method, a vey simple appoach based only on the diamete of the U-pipe and the cente to cente distance between the two pipe legs. Anothe method, by Paul (996), was ceated using both expeimental data and numeical esults. Othe expessions fo the boehole esistance have been given by Bennet et al. (987), ellstöm (99), Diao et al. (2004) and Shaqawy (2009). A ecent wok of Lamache et al. (200) extensively compaes these models by means of finite element numeical simulations. In this pape a web application fo studying and designing of BEs fields is pesented. The application uses many of the methods mentioned above and it is oganized in diffeent toolkits elated to fundamental steps involved in BE field design. A flowchat is shown in the appendix section. Each toolkit is based on one o moe calculation pocedues descibed in this pape togethe with the use input settings as well as the output esults. Fist, the boefield design pocedue is consideed. The implementation of the impoved Ashae method is descibed and the pocedue fo the tempeatue penalty evaluation as suggested by Fossa and Rolando (204a) is pesented togethe with a new hybid Ashae method which allows the designing of abitay shaped BE field. A toolkit fo TRT analysis is also descibed and finally a section elated to the implemented expessions suitable fo R evaluation is discussed. 2. BOREFIELD DESIGN The pesent web application implements the impoved Ashae method and a new hybid Ashae method biefly descibed below. A step by step inteface dives the use though the settings of the equied input paametes and the choice of the design mode. Fo the sake of bevity the details of the gaphic use inteface is intentionally neglected hee and the following desciption focuses on the implemented logic and algoithm. 2. Impoved Ashae Method The Ashae method (Kavanaugh and Raffety, 997) is one of the few engineeing models that allows a system Boehole eat Exchange (BE) to be designed quickly, stating fom the knowledge of the building themal enegy equiements. The method is based on infinite souce solutions fom gound dynamic esponse to a seies of thee heat pulses, epesenting the building themal histoy fom the shot to the long peiod. The key paamete is the evaluation of the Tempeatue Penalty coection T p, which takes into account the long tem themal inteactions of neighbo boeholes. The final fomula fo BE field design can be witten accoding to the following expession: L Q y R Q R Q y m m h Tg, Tf, ave( N ) R R h T p whee L is the oveall length of BEs, R y, R m, R h ae gound themal esistances calculated accoding to the ICS model. The Q tems ae the aveage heat tansfe ates at the gound on a multiyea time scale (0 yea aveage), a monthly time scale ( month, 2 ()

3 the most demanding of the yea) and a houly time scale (6 hous, the peak load). T f,ave is the expected (fo expected COP) caie fluid tempeatue at the end of the opeating peiod N (0 yeas, plus month, plus 6 hous). R is finally themal esistance of the BE that can be estimated by a themal esponse test o suitable fomulas (see sections 3 and 4). The thee efeence times involved in the calculation can be defined as: τ = 0 yeas τ 2 = τ + month τ N = τ hous (2) The T p tem is the tempeatue penalty is intoduced in the Ashae standad as the penalty fo intefeence of adjacent boes. It has been demonstated that the oiginal Ashae T p evaluation method leads to an undeestimation of the BE oveall length. The eo inceases the lage the boefield is. A new method has been poposed by Fossa and Rolando (204a) to assue moe accuate esults in tems of oveall BE length. The impoved tempeatue penalty evaluation, implemented in the web application, is descibed biefly hee. 2.. Tempeatue penalty evaluation Accoding to the impoved method, the T p can be expessed as: T p an 4 bn3 cn 2 dn (3) 8 N tot whee N 4, N 3, N 2 and N ae the numbe of boeholes suounded by only 4 neighbo boeholes, only 3, and so on, espectively. As an example fo claifying the citeion, a ectangula boefield constituted by 3 4 BEs has N 4 =2, N 3 =6, N 2 =4, N =0, N tot =2, while an in-line configuation 4 has N 4 =0, N 3 =0, N 2 =2, N =2. The tem θ 8 can be expessed as:. E( N, B) E( N, B 2) 8 Q' (4) y kl whee B is the cente to cente distance between boeholes, k is the gound themal conductivity and E is the exponential integal (the coe of the ILS solution), that can be fo example appoximated as an expansion seies in tems of the 4Fo vaiable, being Fo the Fouie numbe based on BE adius b Use input and design mode The inputs equested ae the building monthly themal loads, the heat pump chaacteistics, the BE geometic and themal popeties, the gound themal popeties and the desied BE configuation. The heat pump chaacteistics equied by the Ashae method ae: seasonal aveage coefficient of pefomance (COP) fo heating and cooling mode, COP fo peak heating and cooling modes, inlet and outlet woking fluid tempeatue limits fo heating and cooling mode. The gound themal popeties equested ae: undistubed gound tempeatue, gound themal conductivity and gound themal diffusivity. The boehole chaacteistics equied involve both geometical and themal popeties. Fom the geometical point of view the BE is identified by its adius. Optional values ae used accoding to diffeent design mode and include minimum and maximum BE length. The BE effective themal esistance is equied fo the calculation and, if not available, can be evaluated by means of a dedicated tool, as descibed in Section 4 (it is impotant to keep in mind that this esistance is not the same fo all boeholes in the same system, but this is a typical assumption in this type of design appoach). The desied BE configuation can be set by specifying the oveall numbe of boeholes in tems of boehole numbe and spacing, configuation type (ectangula, inline, L-shape, U-shape, O-shape) and BE cente to cente distance. Figue shows a detail of the gaphic use inteface fo the settings of input paametes elated to the heat pump chaacteistics. Fo each input a dedicated paamete contol assues that the settings ae within espective ange limits and consistent with the calculation pocedue. Requied field ae maked and default settings ae povided. In the appendix section, Figue 2a shows the flowchat elated to the Ashae method implementation. Table : Use input fo impoved Ashae method implementation. INPUT MODE OUTPUT Initial boefield configuation type (ectangula, inline, L-shape, U-shape o open ectangle) P chaacteistics BE type BE themal popeties Gound themal popeties Mode A: the use sets a fixed etuning tempeatue and a maximum value of boehole depth. Mode B: the use sets a fixed boehole depth and a minimum etuning fluid tempeatue. Final boefield configuation Oveall BE length 3

4 Figue : Detail of the input use inteface elated to Ashae method implementation. The use can choose two diffeent design modes accoding to diffeent sets of design constaints. In one case (Mode A) the use is equested to select a pefeed boehole configuation type (among ectangula, inline, L-shape, U-shape and O-shape) and initial boehole numbe and spacing, the etuning fluid tempeatue to the heat pump and a maximum value fo the boehole depth. The algoithm implemented etuns the oveall BE length L and the boefield geomety which fulfil the selected inputs. The second design mode (Mode B) consists again in the use choice of an initial value of boehole configuation. The second input constaint is a fixed value of the boehole depth and a minimum value of the etuning fluid. By means of an automatic iteative pocedue, the elated optimal boehole configuation size is evaluated. 2. ybid Ashae Method One of the main estictions of the Ashae method (eithe the oiginal o the impoved one) is the impossibility fo it to be employed fo abitay BE configuation design. The tempeatue penalty appoach can only be applied fo egula matixes and this is often a big limitation fo eal case applications. Also, most commecial softwae design pocedues ae based on pecalculated values of g-functions stoed in a database, limiting the set of available BE configuations in tems of boefield shape and boehole to boehole distances. The g-function elated to an abitay BE configuation can be evaluated accoding to diffeent appoaches but the calculation is cuently too computationally demanding. Fossa and Rolando (204b) poposed an Appoximated Finite line Souce Solution (AFSS) which employs the FLS solution and is suitable fo fast spatial and tempoal supeposition. With this appoach the geneation of themal esponse facto fo abitay BE aangements is possible with low computational demand. The AFSS appoach is based on the following expessions: T ave ( ) T g, Q ' 2 k g a lna2 2 Fo a3 a 4 a 5 Fo 2 4 Fo (5) T ave ( ) T g, Q ' 2 k g a 6 a7 a 8 ln a 9 a 0 2 a Fo a2 (6) whee γ is the Eule constant and Fo is the Fouie numbe based on BE length. The constants a a 2 have been deived by means of an optimum seach pocedue. The eade is efeed to the wok of Fossa and Rolando (204b) fo a detailed desciption of Eq. (7-8) and the constant efinement pocedue. The tempeatue penalty vaiable intoduced in the Ashae method has been demonstated to be elated to the eo intoduced by calculating the gound themal esistance (Eq.4) by means of the ICS solution with espect to the pope g-function fo the boefield unde consideation (Fossa, 20). Fo the design of abitay shaped BE field the web application pesented in this pape implements a modified hybid Ashae pocedue which does not equie by definition the tempeatue penalty evaluation and consides a new expession fo the gound themal esistance elated to the long tem peiod. Eq.() becomes: whee R y,afss is defined as: L Q y R y,afss T Q g, m R T m Q f, ave h ( ) N R R h (7) 4

5 Rolando et al. R y,afss = g(τ N ) AFSS g(τ ) AFSS k (8) whee g(τ) AFSS is the FLS esponse facto evaluated at a given Fouie numbe and obtained by spatial supeposition of the AFSS fomulation shown in Eq.(7-8). With this appoach, the same pocedue descibed in the pevious paagaph can be employed to design abitay BE fields. The implementation of this algoithm allows the pesented Web Application to be employed fo fast design of BE systems that ae not ascibed to egula matixes patten. Fo eal case applications this epesents a fundamental advantage ove most typical design pocedues and popula compute softwae. 3. TERMAL RESPONSE TEST In all design methods fo gound souce heat pump boefields, the gound themal popeties and the themal popeties of the boehole ae essential input paametes. These paametes can be estimated by means of theoetical and empiical expessions. The vaiable that ules the heat conduction pocess into the gound is the themal diffusivity, which involves the gound themal conductivity and the gound heat capacity. A eview of tables of gound themal popeties eveals significant vaiability in values depending on diffeent autho esults, even when the same geological type is consideed (Banks, 2008). Gound themal conductivity can nomally vay in the ange to 5 [W/m/K] with ecuing values between 2 and 3. On the othe hand the gound heat capacity aveage value is typically aound 2[MJ/m 3 /K] vaying in most cases fom.6 to 2.4[MJ/m 3 /K]. Table 2 epots the esults of the design of a single boehole system accoding to gound themal conductivity and gound heat capacity values. Inspection of the table makes appaent the pimay ole played by the gound conductivity on the equied oveall boehole length and hence the necessity of eliable estimations of this quantity. Table 2: Results of sensitivity analysis on equied length fo a single boehole configuation. Boehole length is epoted accoding to vaiability ange limits of gound themal conductivity and heat capacity k [W/m/K] C [MJ/m 3 /K] L [m] ΔL % % The TRT is often caied out following the ASRAE ecommendations. Fist, the undistubed gound tempeatue is measued. Then a constant heat load is supplied (o extacted) to the heat caie fluid though electical esistances (o by a chille unit). The fluid inlet, outlet and ambient tempeatues (T in, T out, T amb ), the mass flow ate m and electical powe Q el ae measued and ecoded at given time intevals. The heat ate pe boehole length can be detemined by: Q = m c(t in T out ) (9) whee c is the fluid specific heat and is the boehole length (BE depth). The esult of this calculation can be compaed to the electic powe if an electic heate is used to supply heat. 3. Themal Response Test Analysis The analysis of the TRT data is usually based on the ILS model, whee an infinite long linea souce is deliveing to the gound a constant themal powe pe unit length. Accoding to this model the tempeatue field in the adial diection afte a time τ elapsed fom heat injection (o extaction) stat is given as: T(, τ) T g, = Q e u 4πk 2 du = Q E u 4πk ( 2 ) (0) 4ατ whee T g, is the undistubed gound tempeatue and α is the gound themal diffusivity. 4ατ Of pactical inteest is the evaluation of the gound tempeatue at the BE wall, say fo =. ence, consideing the exponential integal (E ) appoximation as poposed by Abamovitz and Stegun (964), the tempeatue at boehole wall can be calculated as: T(, τ) = T b = Q 4πk (ln (4ατ 2 ) γ) + T g, () The themal chaacteistics of a BE ae detemined by its effective themal esistance R which is defined in tems of the tempeatue diffeence of the fluid (T f ) and the boehole wall (T b ) as: R = T f T b Q (2) The effective boehole themal esistance in paticula is efeed at the suface fluid tempeatue diffeence (say evaluated at BE top) and it indiectly takes into account the geometical, themal and fluid-dynamic paametes aspects of the BE accounting fo the themal shunt between down and up going fluid. The lowe is the boehole esistance the highe is the quality of the BE itself. 5

6 Rolando et al. Thus, the fluid tempeatue as a function of time can be witten as: T f (τ) = Q (ln (4ατ 4πk 2 ) γ) + Q R + T g, (3) In this model T f coesponds to the aveage between the inlet and outlet fluid tempeatues. If Q is constant, the Eq. (3) becomes a simple linea expession with espect to the logaithm of time: T f (τ) = S ln(τ) + I (4) whee the slope S and intecept I ae quantities elated to gound themal conductivity k and to R espectively. As suggested by Eq.(4) an estimation of the slope S and intecept I is possible though a (log)linea egession. The gound themal conductivity and effective boehole themal esistance can hence be evaluated accoding to the expessions (5) and (6): k = Q 4πS (5) 3.. Distibuted TRT R = Q (I T g, Q 4πk 4α (ln ( 2 ) γ)) (6) Odinay TRT pocedue is based on BE inlet and outlet tempeatue measuements ight outside the gound and the aithmetic aveage tempeatue consideed in TRT analysis is assumed constant along the BE. In a Distibuted themal esponse test (DTRT) the gound themal conductivity and boehole themal esistance ae detemined at many instances along the depth. Distibuted tempeatue measuement can be caied out using vaious equipment, but a convenient technique is the use of a fibe optic cable. It is nomally ecommended to pefom the measuements duing the following thee phases: undistubed gound conditions, constant heat injection (o heat extaction) and boehole themal ecovey. A fist application of DTRT has been done by Fujii at al. (2006) with an optical fibe cable installed on the extenal wall of the pipe, hence without the oppotunity to evaluate the boehole themal esistance. Moe ecently Acuna et al. (2009) pefomed a numbe of DTRT expeiments with fibe optic cable located inside a U-BE pipe, giving the possibility to evaluate both gound themal conductivity and boehole themal esistance of a numbe of gound layes. The fist phase of a DTRT (undistubed conditions) gives a pecise pictue of the tempeatue pofile along the depth. This pofile has been poven to be athe local and dependent on a numbe of factos. Many TRT povides have stated to include tempeatue loggings befoe thei tests by slowly submesing a point senso and subsequently taking it up. The latte can take up to a couple of hous and does not allow a check of the epeatability of the measued values. A logging with fibe optics integates instantaneously along the whole depth and enables a detemination of the andom tempeatue eo with seveal epetitions that do not equie any man-hous. Because the undistubed tempeatue pofile is measued accuately at the fist phase, the pe-ciculation phase loses its impotance. This phase is, howeve, ecommended in ode to ensue a stable fluid ciculation as ai bubbles may take some time to be eleased fom the system. The heat injection o heat extaction phase is used to distub the boehole duing a convenient peiod, long enough to calculate the boehole esistance (if necessay). The compaison of the ate at which diffeent boehole sections ae heated o cooled gives an indication of high o low conductive layes. The themal ecovey peiod is used to calculate the gound themal conductivity along the depth. The latte peiod is chaacteized by the absence of a adial tempeatue gadients in the boehole, theeby eliminating any systematic tempeatue uncetainties due to the position of the fibe cable inside the boehole (as is the case fo the heating o cooling peiod), i.e. esulting in moe accuate themal conductivity values. The themal conductivities found hee ae used as inputs in case the boehole esistance is to be calculated using the data fom the heating/cooling phase. The pocedue to mathematically analyze the measued data at each section along the depth is the same as fo conventional TRTs, e.g. Eq. (0) TRT and DTRT analysis: use input and output The web application descibed in this pape povides a toolkit fo TRT and DTRT measuement analysis. DTRT section is being built but the basic algoithm stuctue has aleady being implemented. TRT and DTRT equipment typically include a data logge device which saves the measuements of inteest in a log file. This file is usually a text document whee data ae oganized in a aw gid fomat with as many columns as the numbe of paametes measued. Each ow is appended to the log file at peset time intevals and contains the measuement of evey paamete at a given time. Each data logge typically has a log file fomat that may diffe slightly fom othe devices depending on many details, such as 6

7 the column ode and the column sepaato chaacte. A tool fo impoting a numbe of TRT log file fomats is povided in the web application, but fo the sake of bevity this is not descibed futhe hee. Fo both TRT and DTRT the use can select an abitay data ange to be consideed fo the calculation. In paticula, fo DTRT analysis, a pope use fom is shown to give the possibility to select the sections to be consideed in the analysis. 3.2 Uncetainty Analysis Many vaiables ae epeatedly measued duing a TRT (by means of tempeatue sensos, flow sensos and powe metes). The undistubed gound tempeatue is measued befoe the test. Some input ae estimated independently (e.g.: gound density, gound volumetic heat capacity). Each measuement intoduces an eo which affects the final estimation of the themal conductivity and the boehole themal esistance. Cuent TRT epots often lack an estimation of the quality of the calculated esults, binging an unknown uncetainty to the esult of a BE field design. Witte (203) pesented an extensive study of the uncetainty souces to be consideed fo evaluating the quality of a TRT esults and poposed a method to calculate the oveall eo elated to gound conductivity and boehole esistance estimation. The method takes into account the uncetainty souces summaized in Table 3. Table 3: TRT uncetainty souces (Witte, 203) m eat caie mass flow ΔT Tempeatue diffeence C f eat caie heat capacity b Boehole adius T in Injection fluid tempeatue Boehole depth T out Retun fluid tempeatue C Gound heat capacity T g Undistubed gound tempeatue S Regession slope coefficient Fo each uncetainty souce the elated individual uncetainty value can be evaluated. As an example, the eo in the calculated tempeatue diffeence (i.e.: δδt) depends on the combination of the eos elated to individual sensos (i.e.: δt in, δt out ). This can be evaluated as: δ T = (δt in ) 2 + (δt out ) 2 (7) The eo of the final esult depends on how all individual eos affect the final eo. Eo popagation in the web application is calculated using the geneal pocedues as outlined by Taylo (997) and Ellison et al. (2000). The final expessions fo TRT esults uncetainty evaluation ae implemented as: δk = k ( δm ) 2 + ( δc m c )2 + ( δs S )2 + ( δ T T )2 + ( δ )2 (8) δr = ( R δ)2 + ( R Q + ( R k δq ) 2 + ( R δi) 2 + ( R 2 δt I T g ) g (9) δk)2 + ( R C δc)2 + ( R δ b ) 2 b The web application pesented in this pape implements this appoach to evaluate the oveall uncetainty elated to TRT data. A use fom is povided to set the individual uncetainty values fo the measuement sensos and the input popeties. Table 4 povides a summay of input and output paametes elated to themal esponse test toolkit. Figue 2b in the appendix section shows the flowchat elated to the themal esponse test analysis implementation. Table 4: Use input fo TRT and DTRT analysis INPUT OUTPUT Logfile columns: (Mandatoy measued data) time, ciculating fluid flow ate and themal popeties, BE inlet and outlet tempeatues. (Optional) electic powe, ambient tempeatue. Additional input infomation: Undistubed gound tempeatue, gound volumetic heat capacity, BE adius, BE length, data ange, individual input uncetainties. Fo DTRT k R δk δr Amount and length of sections to be analyzed should be given and, fo each of these, the same inputs named above ae necessay. Obseve that the undistubed gound tempeatue value vaies with depth accoding to the measued pofiled in phase of the test. 7

8 4. BOREOLE TERMAL RESISTANCE The boehole themal esistance in gouted boeholes can also be detemined by means of numeical and analytical appoaches if the geomety is known. All the poposed analytical models decompose R into thee contibutions: gout conductive esistance (R gout ), pipe conductive esistance (R cond ) and fluid convective esistance (R conv ): R = R cond + R conv + R gout (20) The fist two esistances can be expessed as: R cond = ln ( po pi ) 4πk p R conv = 4π pi h (2) (22) whee po and pi ae espectively the oute and inne pipe adius, k p is the pipe themal conductivity and h is the convective heat tansfe coefficient. Seveal coelations fo calculating h as a function of the Nusselt numbe ae available in the toolkit. The same applies fo diffeent pipe mateials and dimensions. The gout esistance gives the main contibution to the total boehole esistance and is the most difficult to evaluate. Although many appoaches of vaying complexity have been poposed, the web application pesented hee implements the following. A model suitable fo evaluating boehole esistance of single U-pipe BE is the Paul method (996) which was ceated using both expeimental data and a two-dimensional finite element pogam fo modeling a boehole coss section. Gout themal esistance is expessed as: R gout = β 0 ( po ) β k gout (23) whee the coefficients β 0 and β ae tabulated fo diffeent cente to cente distance between the two legs of the U-tube (also known as shank spacing), is the BE adius and k gout is the gout themal conductivity. Futhe development will also include the multipole appoach fo single U-tube BE as poposed by Bennet et al. (997). An expession fo the calculation of the boehole esistance in symmetically disposed double U-tubes has been poposed by ellstöm (99): R = [ln ( ) 3 + ( χ c ) 2 ln ( ( χ c ) 8 ) ln 2πk gout po (χ c 2 ) ln po 4 (χ c 2 )] + R cond po 4 (24) whee χ c is the shank spacing Finally, the expessions implemented to evaluate the conductive and gout esistance of a simple coaxial pipe ae: whee: R cond = R gout = d i,out is the inne diamete of extenal pipe d o,out is the oute diamete of extenal pipe ln ( d o,out ) (25) πd i,out h i,out 2πk p,out d i,out 2πk gout ln ( d d e,out ) (26) h i,out is the convective coefficient outside the intenal pipe. k p,out is the themal conductivity of the extenal pipe d is the BE diamete Figue 2c in the appendix section shows the flowchat elated to the implementation of the toolkit in the web application. CONCLUSIONS In this pape the fist vesion of a web application based on a set of fundamental tools fo shallow geothemal boefield design is pesented. In spite of the fact that wok is needed in efining and debugging, futhe liteatue compaison on available models, and additional numeical compaisons based on diffeent algoithms, the tool is eady to accomplish the main design goals accoding to which it was conceived. In this pape in paticula the implementation of an impoved vesion of the Ashae method fo boefield design has been descibed, togethe with a new hybid Ashae method which allows the design of abitay boefield configuation. The impotance of such featue in eal case applications has been emaked. A toolkit fo themal esponse test analysis has been pesented. Because the uncetainty evaluation elated to such test measuement is often missing in epots, paticula attention has 8

9 been given in the toolkit to evaluating the esult eo. The application also contains a module fo doing theoetical calculation of the boehole esistance based on a set of ecent liteatue models. Futhe development of the web application will include a design analysis and gound esponse pediction based on a lage set of building heating and cooling loads (e.g. on a monthly basis) and economic and financial indicatos to be applied fo compaison with taditional heating and cooling plant solution. Evey module pesented in this pape will be also futhe developed and updated on the stength of ongoing study esults. APPENDIX Figue 2: Web Application flow chat REFERENCES Abamovitz M. and Stegun I.A., 964. andbook of Mathematical Functions With Fomulas, Gaphs, and Mathematical Tables, NBS Applied Mathematics Seies 55, National Bueau of Standads, Washington, DC. Acuña, J., Mogensen P., Palm, B.: Distibuted themal esponse test on a U-pipe boehole heat exchange, Poceedings, Effstock- The th Intenational Confeence on Enegy Stoage, Stockholm, (2009). ASRAE andbook VAC Systems and Equipment, (2007). ASRAE andbook-vac Applications, Chapte 32, Geothemal Enegy, (2003). Austin, W.: Development of an in-situ system fo measuing gound themal popeties. MSc-thesis, OSU, (998), 64pp. Banks, D.: An intoduction to themogeology: gound souce heating and cooling, book, John Wiley & Sons, (202). Bennet, J., Claesson J., ellstöm G.: Multipole Method to Compute the Conductive eat Flows to and Between Pipes in a Composite Cylinde, Univesity of Lund, Depatment of Building Technology and Mathematical Physics. Lund, Sweden, (987). Caslaw,.S. and Jaege, J.C.: Conduction of eat in Solids, Claemoe Pess, book, Oxfod, U.K., (947). Claesson, J., and Javed, S.: An Analytical Method to Calculate Boehole Fluid Tempeatues fo Time-scales fom Minutes to Decades. ASRAE Tansactions, 7.2 (20). Diao N., Zeng., Fang Z.: Impovement in modeling of heat tansfe in vetical gound heat exchanges, VAC&R Reseach, 0, (2004), Eklöf, C. and Gehlin, S.: TED - A mobile equipment fo themal esponse test. MSc-thesis, LuT, (996), 62pp. Ellison SLR, Williams A.: Quantifying Uncetainty in Analytical Measuement, Euachem/CITAC guide, Thid edition, (202). Eskilson P.: Supeposition Boehole Model. Manual fo Compute Code, Dept. of Mathematical Physics, Lund Institute of Technology, Lund, Sweden, (986). Eskilson, P.: Themal Analysis of eat Extaction Boeholes, Ph.D. Thesis, Lund Univesity of Technology, Sweden, (987). 9

10 Fossa M.: The Tempeatue Penalty Appoach to the Design of Boehole eat Exchanges fo eat Pump Applications, Enegy and Buildings, 43, (20), Fossa, M., Rolando D.: Impoving the Ashae method fo vetical geothemal boefield design, Poceedings, IEA eat Pump Confeence, 2-6 May, Monteal (Québec) Canada, (204a). Fossa, M., Rolando D.: Fully Analytical Finite Line Souce Solution fo Fast Calculation of Tempeatue Response Factos in Geothemal eat Pump Boefield Design, Poceedings, IEA eat Pump Confeence, 2-6 May, Monteal (Québec) Canada, (204b). Fuijii., Okubo., Itoi R.: Themal Response Tests Using Optical Fibe Themometes, Kyushu Univesity, Fukuoka, GRC Tansactions, 30, (2006). Gu, Y., and O'Neal, D. L.: Development of an Equivalent Diamete Expession fo Vetical U-Tubes Used in Gound-Coupled eat Pumps, ASRAE Tansactions, 04.2, (998), ellstöm, G. and Sanne, B.: EED Eath Enegy Designe, Vesion.0, Use s Manual. Pof. D. Knoblich & Patne Gmb, Wetzla, Gemany, (997), 43pp. ellstöm, G. and Sanne, B.: PC-Pogams and Modeling fo Boehole eat Exchange Design, Poceedings, IGD 200 Bad Uach, Supplement, ISS Skopje, (200). ellstöm, G.: Themal pefomance of boehole heat exchanges. Depatment of Mathematical Physics, Lund Institute of Technology, (99). Ingesoll, L.R., Zobel, O.J., and Ingesoll, A.C.: eat Conduction with Engineeing, Geological, and othe Applications, book, McGaw-ill, New Yok, (954). Kavanaugh, S.P. and Raffety, K.: Gound Souce eat Pumps Design of Geothemal System fo Commecial and Institutional Buildings, ASRAE Confeence, Atlanta, (997). Lamache, L. and Beauchamp, B.: A New Contibution to the Finite Line-Souce Model fo Geothemal Boeholes, Enegy and Buildings, 39, (2007), Lamache L., Kajl S., Beauchamp B.: A eview of methods to evaluate boehole themal esistances in geothemal heat-pump systems, Geothemics, 39, (200), Mashall, C.L., Spitle, J.D.: GLEPRO The Pofessional Gound Loop heat Exchange Design Softwae, Use s Guide, (994). Mogensen, P.: Fluid to duct wall heat tansfe in duct system heat stoages, Swedish Council fo Building Reseach, 6, (983), Niven, C.: On a method of finding the conductivity fo heat, Poceedings of the Royal Society of London, Seies A, Containing Papes of a Mathematical and Physical Chaacte, 76, (905), Pahud, D., Matthey, B.: Compaison of the themal pefomance of double U-pipe boehole heat exchanges measued in situ. Enegy and Buildings, 33, (200), Paul N.D.: The Effect of Gout Themal Conductivity on Vetical Geothemal eat Exchange Design and Pefomance, Msc- Thesis, South Dakota State Univesity, (996). Shaqawy M.., Mokheime, E.M., Bad,.M.: Effective pipe-to-boehole themal esistance fo vetical gound heat exchanges Geothemics, 38, (2009), Spitle, J.D., Cullin, J., Benie, M.A, Kummet, M., Cui, P., Liu, X., Lee, E., Fishe, D.: Peliminay intemodel compaison of gound heat exchange simulation models. Poc. th Int.Conf. Effstock Stockholm, (2009). Spitle, J.D.: GLEPRO - A design tool fo commecial building gound loop heat exchange. In: Poceedings of the 4 th Intenational Confeence on eat Pumps in Cold Climates, 7-8 August, Aylme, QC, Canada, (2000), -6. Stålhane, B., Pyk, S.: Ny metod fö bestämning av vämeledningskoefficiente, Teknisk Tidskift, Svenska Teknologföeningen, 28, (93). Taylo JR.: An intoduction to eo analysis: the study of uncetainties in physical measuements, Univesity Science Books, (997). Van Gelde, G., Witte,.J.L., Kalma, S., Snijdes, A. and Wennekes, R.G.A: In-situ-Messung de themischen Eigenschaften des Untegunds duch Wämeentzug, Poceedings, OPET-Semina Edgekoppelte Wämepumpen, (999), Witte, enk JL.: Eo analysis of themal esponse tests, Applied Enegy, 09, (203), Zeng,., Diao, N., Fang, Z.: eat Tansfe Analysis of Boeholes in Vetical Gound eat Exchanges. Int, J. eat and Mass Tansfe,46 (2003),