Development of a Numerical Model to Predict Heat Extraction and Injection Rates of a Ground Heat Exchanger and Its Application to a Building in Tokyo

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1 Development of a Numercal Model to Predct Heat Extracton and Injecton Rates of a Ground Heat Exchanger and Its Applcaton to a Buldng n Tokyo Yujn Nam 1, a, Ryozo Ooka 1, b, Suckho Hang 1, c, Kentaro Sekne, d 1 C403 Insttute of Industry Scence, the Unversty of Tokyo, Tokyo, Japan, Technology Center, Tase Corporaton, 344-1, Nase-cho, Totsuka-ku, Yokohama, Japan, a namyujn@s.u-tokyo.ac.jp, b ooka@ s.u-tokyo.ac.jp, c shhang@ s.u-tokyo.ac.jp, d kentaro sekne@sakura.tase.co.jp ABSTRACT Ground-source (Geothermal) heat pump (GSHP) systems can acheve a hgher coeffcent of performance than conventonal ar-source heat pump (ASHP) systems. For the desgn of a GSHP system, t s necessary to accurately predct the heat extracton and njecton rates of the heat exchanger. Many models that combne ground heat conducton and heat exchangers have been proposed to predct heat extracton/njecton rates from/nto the ground n the research feld of heatng, ventlaton and ar-condtonng (HVAC) systems. Hoever, most analyss models have an naccuracy n ther predcton for long perods because they are based on a heat conducton model usng cylndrcal coordnates and the effectve heat conductvty. Furthermore, as they utlze the heat exchange model hch s based on the concept of an equvalent dameter, the effect of the exact shape of the heat exchanger s not consdered. In ths paper, a numercal model that combnes a heat transport model th ground ater flo and a heat exchanger model th an exact shape s developed. Furthermore, a method for estmatng sol propertes based on ground nvestgatons s proposed. Comparson beteen expermental results and numercal analyss based on the model developed above as conducted under the condtons of an experment from 004. The analytcal results agreed ell th the expermental results. Fnally, the proposed model as used to predct the heat extracton and njecton rate for an actual offce buldng n Japan. KEYWORDS: Ground-source heat pump, Ground heat exchanger, Numercal smulaton 1. INTRODUCTION Ground-source (Geothermal) heat pump (GSHP) systems can acheve a hgher coeffcent of performance than conventonal ar-source heat pump (ASHP) systems. For the desgn of a groundsource heat pump (GSHP) system, t s necessary to accurately predct the heat extracton and njecton rates of the heat exchanger. Many models that combne ground heat conducton and heat exchangers have been proposed to predct heat extracton/njecton rates from/nto the ground n the research feld of heatng, ventlaton and ar-condtonng (HVAC) systems.(ochfuj,1988, Kavanaugh,1991) Hoever, most of these models are based on a heat conducton model th cylndrcal coordnates. In most cases the effect of the ground ater flo s ncorporated nto the effectve heat conductvtes. There s a possblty that these models have an naccuracy n ther predctons for long perods. Furthermore, most of the proposed models utlze a cylndrcal-shaped heat exchanger th the concept of an equvalent dameter and do not consder the effect of the exact shape of the heat exchanger. Ths model mght cause numercal errors n the predcton. On the other hand, n the felds of hydrology, geology, and geotechncal engneerng, smulaton models of groundater flo, mass 7

2 and heat transfer n the sol have been developed. Hoever, the purpose of these models has been to analyze macroscopc groundater flo, mass and heat transfer n the sol; modelng of a ground heat exchanger s not supported. In ths paper, a numercal model that combnes a heat transport model th groundater flo and a heat exchanger model th an exact shape s developed. Furthermore, to obtan accurate smulaton results, t s necessary to ascertan the sol physcal-property values such as thermal conductvty, heat capacty and hydraulc conductvty. Thus, the authors also propose a method for estmatng sol propertes based on ground nvestgatons. Moreover, the valdty of these methods s confrmed by comparng beteen smulaton and expermental results. Fnally, the proposed model as used to predct the heat extracton and njecton rate for an actual offce buldng n Japan.. NUMERICAL MODEL FOR HEAT EXTRACTION AND INJECTION RATES.1 Smulaton Code for Heat and Water Transport n the Ground In ths research, FEFLOW of WASY Co., hch s a commercal code for the smulaton of.heat and materal transport n the ground, s adopted. Ths code s dely used for the analyss of underground ater flo or ground polluton. FEFLOW s based on the follong three preservaton equatons (mass preservaton equaton, momentum preservaton equaton, energy preservaton equaton) for the combnaton of sol partcles, lqud ater, and gas.. Incorporatng a heat exchanger model th a ground ace heat balance model To calculate boundary condtons on the aces of the heat exchanger and the ground for FEFLOW analyss, the heat exchanger and the ground ace heat balance models are ncorporated nto a user subroutne of FEFLOW. (1) Ground heat exchanger model Here, a par of U-tubes (outer dameter: 38mm, nner dameter: 8.8mm) are assumed as the ground heat exchanger, as shon n Fgure 1. The ground heat exchanger model conssts of the crculaton ater model th a 1-dmensonal advecton-dffuson equaton n the ground heat exchanger, and convectve heat transfer beteen the nner ace of the heat exchanger ppe and the crculaton ater. The temperature of the crculaton ater s gven by the follong equaton. T λ T T hp ( T T) (5) = U + 1 t ρ C z z ρ C A T,-1 The heat transfer beteen the nner ace of the heat exchanger ppe and the crculaton ater s λ 0.8 n Q= ( Ts T, ) ( 1/ ha) h= Nu Nu= 0.03Re Pr (6, 7, 8) r here Pr: Prandtle number, Re: Reynolds number, and n s 0.3 and 0.4 n coolng and heatng, respectvely. () Ground ace heat balance model Heat flux Q from the ground ace to ground s gven by the follong heat balance equaton. Q= R + R R H L (9) sol sky 1) Total solar radaton (R sol ) R sol = ( 1 α s) ( J dn sn( h) + J sh) (10) Here, J dn s the drect solar radaton on the grand ace, sn(h) s solar alttude, J sh s sky radaton, and α s s albedo (reflectvty of solar radaton on the ground). ) Donard atmospherc radaton (R sky ) R 4 σ ( Ta) ( f )( 1 0. c) (11) sky = 06 Δ z T, T,+1 T s R conv Fg. 1 Heat flux on the ace of heat exchanger R sol Solar radaton ( short ave ) R sky Sky radaton ( long ave ) R Ground ace radaton ( long ave ) Heat flux to sol Q H Convecton sensble heat L Evaporaton latent heat Fg. Thermal balance on ground ace Q 8

3 Here, σ s the Stephen-Boltzmann constant ( [W/m K 4 ]), f s the ater vapor pressure near the ground ace [mmhg], c s the degree of cloudness, T a s ar temperature. 3) Upard long ave radaton from the ground ace (R ) 4 R = σ ( TS) ( c) (1) Here, T s s the ground ace temperature. 4) Sensble heat flux (H ) H =α c( T s T a) (13) Here, the convectve heat transfer rato on the ground ace (α c ) s gven by the expermental equaton of Jürges th respect to nd velocty near the ground ace (v) α c = v ( v 5m / s), α c = 7.1v ( v> 5m / s) (14) 5) Latent Heat Flux (L ) L = β 7 α c( f sat( Ts) Ta) (15) 1000 Here, β s mosture avalablty of the ground ace, and f sat (T s ) s the saturate ater vapor flux of T s. 3. ESTIMATION METHOD FOR SOIL PROPERTIES BASED ON A GROUND INVESTIGATION In Japan, the tems for examnaton n a ground nvestgaton before constructon of a buldng are set by the Japanese Industral Standards and Japanese Geotechncal Socety Standards etc., for example, the ground ater level, vod rato and saturaton rato of sol, mechancal analyss of sol and so on. If these nvestgatons are conducted n three places, the underground ater nclnaton can be presumed. The method of presumng the sol physcal propertes s proposed by usng the measurement results of these nvestgatons n ths secton. 3.1 Fundamental sol parameters The sol s composed of three aspects; sol partcles, ater, and ar. The fundamental physcal propertes of sol can be estmated from the relatonshps among each of volume, mass, specfc heat, thermal conductvty, and thermal capacty. Fundamentally, the contents of them n sol are determned by the result of ground nvestgaton, the densty, vod rato, and ater content rato of sol. 3. Thermal sol parameters Heat conductvty and heat capacty of sol are requred to calculate heat conducton n sol. Heat conductvty of the sold part of sol s estmated from the follong geometrc average of each sold component. m n m n m+ n λ s = λ + A λb (16) Here, λ A and λ B are heat conductvtes(w/mk) of sold components A and B, respectvely; m and n are volume ratos of A and B, respectvely. Comprehensve heat conductvty λ epar and heat capacty C are gven by the follong parallel models of sold sol, gas, and lqud ater. n λ = λ (17) epar V = 1 C = n = 1 ρ c V (18) Here, λ, ρ, c, and V are the heat conductvty(w/mk), densty(kg/m 3 ), specfc heat(j/kgk) and the volume rato of each component, respectvely. 3.3 Hydraulc Conductvty Hydraulc Conductvty (permeablty) s a very mportant parameter, and nfluences heat transport n the sol. There are several expermental formulatons that estmate hydraulc conductvty (k) n saturated sol. 9

4 Hazen s formula k = Ch ( t ) D (19) Terzagh s formula C n (0) t 10 k= D10 µ 3 1- n 3 Zunker s formula C z n k= (1) Kozeny s formula C k n () D µ 1- k = D n ( 1 ) µ n Here, t s sol temperature, n s the porosty of sol, μs vscosty, and D 10 s a 10% effectve dameter n a partcle sze summaton curve, and D s the average partcle dameter. 4. COMPARISON BETWEEN EXPERIMENTAL AND NUMERICAL ANALYSES 4.1 Outlne of the experment In ths secton, the predcton accuracy of the numercal smulaton technques descrbed above are examned by comparng them th expermental results. The experment as conducted n the ground source ar-condtonng system laboratory that had been constructed at the Chba Expermental Staton of Insttute of Industral Scence the Unversty of Tokyo n 003 and 004. To cast-n-place concrete ples, th a dameter of 1.5 m and length 0m ere nstalled. 8 pars of U-tubes (45mm n outer dameter and 35mm n nner) ere set around the ace of each ple. In ths experment, usual offce buldngs ere assumed, and heatng and coolng ere operated from 9:00 to 18:00 of Monday to Frday. The heatng perod as Dec. to Feb., and the coolng perod as Jun. to Aug. for 3 months, respectvely. Heat extracton and njecton rates n the coolng and heatng perods ere calculated by the temperature and ater flo of crculaton ater n ground heat exchangers. In ths experment, sol temperatures at 10m and 19m depth at measurement ponts I and II, as shon n Fg. 3, ere measured. Furthermore, underground ater nclnatons ere observed from fve underground ater levels at fve observaton ells around the expermental ste. Ground ater flo Foundaton ple B Foundaton ple A U-tube Measurement pont Ⅰ 1.5m Measurement.75m Ⅱ pont Fg. 3 Smulaton model 4. Analyss condtons Table 3 shos the values of the physcal parameters of the sol for numercal smulaton based on Chapter 3. The underground ater level s 1m depth. The analyss doman s 6m 0m 0m and s shon n Fgure 1. To cast-n-place concrete ples (1.5m n dameter and 0m n depth) are nstalled n the analyss doman and 8 pars of meshes hch mtate U tubes are set around the ace of each ple n the same ay as n the experment. The heat flux, hch corresponds to the heat extracton and njecton rates n the experment results, s set at the ace of each mesh modeled as U tube. The underground ater nclnaton s assumed to be (m/m), from observaton. Ths corresponds to an underground ater flo speed of 13.6m/year. The drecton of the underground ater flo s also shon n Fg. 3. The calculaton perod s from January 1, 004 to December 31, Table 1 Calculaton condtons Depth (m) Porosty Hydraulc conductvty (m/s) Thermal conductvty(w/mk) Sold phase 1.5 Flud phase 0.57 Sold phase 3.0 Flud phase 0.57 Heat capacty (10 6 J/m 3 K) Sold phase.7, Flud phase 4. Hydraulc gradent(m/m)

5 004. Intal and boundary values of the underground temperatures are set to 18.1ºC at depths of 10m and 17.3ºC at a depth of 19m as n the experment. The boundary value of the underground ater temperature s also assumed constant at 16.5ºC from the expermental results. 4.3 Results Comparsons of the sol temperatures at the depth of 10m at measurement ponts I and II (Fg. 3 references) beteen the analyss and the expermental results are shon n Fg. 4. The measurement ponts I and II are 1.5m and.75m apart, respectvely, from the center of ple A. Though the analyss results are a lttle hgher than the expermental ones by about 1ºC at maxmum, they correspond ell th the expermental ones. 5 Measurement pont Ⅰ, depth 10 m 5 Measurement pont Ⅱ, depth 10 m 0 Smulaton 0 Smulaton 15 Experment 15 Experment /5 /3 4/3 6/ 8/1 10/0 1/19 1/5 /3 4/3 6/ 8/1 10/0 1/19 Fg. 4 Comparson of sol temperature varatons beteen the numercal analyss and the experment 5. APPLICATION TO A REAL BUILDING IN TOKYO 5.1. Analyss Summary In ths chapter, the proposed model as used to predct the heat extracton and njecton rate for an actual offce buldng n Tokyo, Japan. The buldng s an 8-story offce buldng (total floor space 9,304m ) th tenty concrete cast-n-ples (ø1500mm 37m) th ground heat exchanges. In ths analyss, one span (6m 6m) area s consdered as the analyss model, hch contans four of tenty ples (Fg. 5). Table shos ground propertes estmated by ground nvestgaton data on the ste, hch are used as analyss condtons. Intal temperature of ground and crculaton ater s set at 17, ntal ground ater level s G.L-0.7m, and the temperature of crculaton ater nlet s assgned by dfference of temperature (ΔT) from the temperature at ts outlet. The heat extracton and njecton rate s calculated by ΔT and ater rate flo. Hoever, ground temperature around ground heat exchanger becomes hgher by njectng the heat to ground n coolng operaton, and decreases gradually by extractng the heat n heatng operaton. In these condtons, the COP (coeffcent of performance) of heat pump decreases. Therefore, n ths calculaton, the temperature of crculaton ater s controlled belo 45 n coolng and above 5 at least n heatng to avod the decrease of COP. When the 31 Groundater Flo Heat Exchanger 熱交換器出口 Outlet (Heat ( ヒートホ ンフ 入口 pump Inlet) ) T[n+3] Groundater Flo 地下水流れ Unsaturated 不飽和層 Layer T[n+] Saturated 飽和層 Layer T[n+1] Saturated 飽和層 Layer T[n] T[1] T[] Unt : mm 制御条件 Control condton 熱交換器入口 Heat Exchanger Inlet ( ヒートホ ンフ 出口 (Heat pump Outlet) ) T[0] Slce 1 Layer 1 Layer Layer n-1 T[n-1] Slce Slce 3 Slce n Fg. 5 Analyss Model (Ground plan, Cross secton) Table Calculaton condtons Depth (m) The qualty of the sol Mxed clay Slt Porosty Hydraulc conductvty (m/s) Thermal conductvty(w/mk) Sold phase 1.5 Flud phase 0.57 Sold phase 3.0 Flud phase 0.57 Heat capacty (10 6 J/m 3 K) Sold phase.7, Flud phase 4. Hydraulc gradent(m/m)

6 temperature exceeds the lmt, ΔT s changed smaller. Intal ΔT and crculaton ater flo per a U tube are nput 4 and 3.0L/mn. Analyss perod s set out 465days and heatng and coolng schedule follos chapter 4. In ths paper, 3 calculaton cases are estmated. Base case (Case ) s set at 8 pars of U tubes around a ple, Case s 4 pars and Case 3 s 16 pars, respectvely. 5.. Analyss Results Table 3 presents the analyss results for all calculaton condtons. Case 1 acqured 91.6W/m for heat extracton/njecton rate per a ple,.9 W/m for one par of U tube. Moreover, Case, n hch each U tube as located to shorter dstance beteen the adjacent to U tubes, acheved the same heat exchange rate per U tube. On the other hand, the dstance beteen adjacent ppes n Case 3 as shorter than that of the other cases, 0.9m, and t as reduced to 1.5 W/m by heat nterference. The nlet ater temperature of heat pump (outlet temperature of ground heat exchanger) s mportant as COP of heat pump depends on the temperature sgnfcantly. The average temperature of nlet ater n Case 1 and s loer durng coolng and hgher durng heatng than that n Case 3. Consequently, among these three cases, Case could be selected as the best desgn soluton of all three cases by consderng the operaton effcency. Table 3 Analyss results Case Number Dstance from Average outlet temp. Average outlet Heat exchange Heat exchange of U tube adjacent ppe durng coolng temp. durng heatng rate per ple rate per U tube 1 4 pars 1.18 m W/m.9 W/m 8 pars 0.59 m W/m.9 W/m 3 16 pars 0.9 m W/m 1.5 W/m 6. CONCLUSIONS For the optmum desgn of GSHP system, t s necessary to estmate ts performance and economc feasblty before the ntroducton of the system. In ths paper, a numercal model as developed to predct heat extracton and njecton rates of a ground heat exchanger. It s based on smulaton code for the analyss of underground heat and ater movement, n hch crculaton ater model n the heat exchanger and the ground ace heat flux model are ncorporated. Moreover, an estmaton method for the sol thermal propertes based on a ground nvestgaton as proposed. Smulaton results usng the developed predcton model and the sol heat physcal propertes values estmated here ere compared th the expermental results, and the valdty of the predcton model developed here as confrmed. Furthermore, ths smulaton tool as appled to an offce buldng n Tokyo, Japan, and the optmum desgn of system as examned by case study. In the future, more varous consderatons for optmum desgn and operaton system ll be conducted. REFERENCES Ochfuj.K and Km.NC, 1988, Theoretcal Analyss of Heat Conducton of Long Term Heat Storage and Extracton by Bured Vertcal Ppe System, Transactons of the Socety of Heatng, Ar- Condtonng and Santary Engneers of Japan, No. 36, pp.1-9 Deerman J.D. and Kavanaugh S.P., 1991, Smulaton of Vertcal U-tube Ground coupled Heat Pump Systems usng the Cylndrcal Heat Source Soluton, ASHRAE Transactons 97(1), pp87-95 Kasubuch T., 1984, Heat conducton model of saturated sol and estmaton of thermal conductvty of sol sold phase, Journal of Sol Scence, pp Nagano, K. and Ochfuj, K.; 1994, A Study on the Ground Heat Pump System Part1 A Smulaton Model and Experments of Heat Extracton durng Sol Freezng n Unsaturated Sol, Transactons of the Socety of Heatng, Ar-Condtonng and Santary Engneers of Japan, No. 54, pp.55-66, 3