DIRECT AND INDIRECT LOW TEMPERATURE GEOTHERMAL DISTRICT HEATING SYSTEMS Cuansan Dai and Jun Liang Tianjin Geoteal Reseac and Taining Cente, Tianjin Univesity, 30007, Tianjin, P.R.Cina Key Wods: low teeatue geoteal syste, distict eating systes, late eat excange, otiu design ABSTRACT Te selection of diect o indiect use of low teeatue geoteal distict eating systes is based on te quality of geoteal wate. An indiect geoteal eating distict syste is stongly ecoended if te concentation of soe coosion inducing ceicals suc as cloite in geoteal wate is ig. In te ae, a teoetical etod caable of quantitatively evaluating te teodynaic diffeences between diect and indiect geoteal distict eating systes is oosed. Te contents include: te ain factos effecting te diffeence between te two kinds of eating systes; te deteination of a best oeation ode fo an indiect geoteal distict eating syste and te etod of finding otiu design aaetes. Since late and fae eat excanges (PHEs ae coonly used in indiect geoteal distict eating systes; te advantages of using te PHEs wit vaiable late sacing ae also discussed. Fo coaing te teal efoance between diect and indiect geoteal distict eating systes, a concet of elative teal efficiency is oosed. Once te PHEs ae designed in an indiect geoteal distict eating syste; te otiu flowate atio of geoteal wate to ciculating wate can be found toug an equation deived in te ae, wic as been oved in actice.. INTRODUCTION Distict eating systes wit low teeatue geoteal esouces (< 00 C geoteal wate ae diffeent fo tose wit te fossil fuels boiles. Since te wellead teeatue is diffeent fo well to well, te design suly wate teeatue cannot be set to a standad as it is in conventional boile eating systes. Soe featues about te diect and indiect geoteal distict eating systes ave been discussed by Dai (997. In tis ae a fute analysis is esented. To concise te ae, te detailed deivation of soe equations and te assutions uon wic tese ae based on ae not given. Howeve eades ae efeed to te ae by Dai (997.. THE THERMAL PERFORMANCE COMPARISON Te teal efoance coaison between diect and indiect geoteal distict eating systes is based on te sae wellead teeatue, eating load, and outdoo and indoo teeatues.. Teal balance Equations All te equations below ae deived at te teal steady state conditions, i.e. te abient conditions ae eained uncanged. Te tansient eat tansfe o te eat stoage effect of te building wall on te distict eating syste as not been conseed. Te teal balance equation fo te diect eating syste is: Q d G C + C ln( + ( T Ta ( + C GC GC C C C V A α v in wic Q d is te eat tansfeed o eat load fo a diect eat syste. G is te ass flowate of geoteal wate. C is te secific eat caacity of wate at constant essue (kj/kg C; is te teeatue do of geoteal wate flowing toug te consue s in-building equient (T - T do. T is te suly teeatue of geoteal wate; T do is te outlet teeatue of geoteal wate used fo a diect eating syste. T a is te outdoo teeatue. C v is te secific voluetic eat load caacity of building (W/ 3 C. V is te total volue of a eated building. α and ae eiical constants of eat adiatos in te fo of k α. k is te oveall eat tansfe coefficient of adiatos. is te ean teeatue diffeence between te eat adiato suface and te ai in oos. A is te total eat tansfe aea of eat adiatos. Te above equation can be solved fo by iteation etod, beginning wit a oe initial guess value. Ten te eat load Q d can be obtained. Te indiect eating syste is diffeent fo te diect eating systes as it as PHEs fo te eat tansfeed fo geoteal wate to te ciculating wate. Te teal balance equation can be witten as: wee B B B 3 B Q + BQ B3 C G ( α A G C R C + ( + + ( T P T in wic R is te eat caacity ate atio. P is te teeatue effectiveness based on te stea of geoteal wate. It is a function of Nube Heat Tansfe Unit (Ntu and R (Kays and London, 984. R can be aoxiately given as G /G c since te flus on bot ses ae wates. a (3 3395
ex( Ntu ( R fo R R ex( Ntu ( R P ( Ntu, R Ntu fo R + Ntu. Te Relative Teal Efficiency (4 Suose two wells ave te sae wellead aaetes and used fo distict eating wit te sae eating duty. But one is a diect eating syste and te ote is an indiect eating syste. Te geoteal wate flowates sould be diffeent. Te diect geoteal distict eating syste needs less. But ow te diffeence canges, fo exale wit te outdoo teeatue, te eating load facto and te ciculating wate flowate of te indiect eating syste. Te concet of elative teal efficiency is oosed, wic can be witten as: T T o (5 T Tdo in wic T o and T do ae te outlet teeatues fo indiect and diect geoteal distict eating systes, esectively. Fo a secific designed indiect geoteal distict eating syste, an otiu unning condition exists on wic as te best flowate atc of geoteal wate and ciculating wate (Dai, 997. Teefoe fo te indiect eating syste itself sould ave a teal efficiency wic naed as teal efficiency of indiect syste to evaluate te otial unning conditions. We ave: T To (6 T ( To ot Te otiu indiect distict eating syste gives a axiu elative teal efficiency called elative otiu teal efficiency ot. Since it sulies te sae aount of eat as te diect eating syste (Q Q d, ot can be witten as: T ( To ot ( G d ot (7 T Tdo ( G subscit ot eans otiu and d and ae fo diect and indiect eating systes, esectively. Accodingly, te equation (5 can be witten as ot. 3. THE ACCESS OF BEST OPERATION FOR INDIRECT SYSTEMS Note tat te fist at of equation ( is ainly te conseation of te eated building and te PHEs, te second at te teinal eat adiatos, and te tid at te outdoo teeatues. Fute insection of equation ( eveals tat if B and B 3 ae known, te iniu of B is te oint wee te axiu of Q can be acieved. B is a function of P and R. Teefoe, te best oeation oble of tis kind of eating systes becoes tat of finding a suitable flowate of ciculating wate G c o R (G is constant in ode to get te iniu B o te axiu eat Q. Diffeentiating equation ( wit esect to G c and let it equal to zeo, we ave: dp G (8 P dgc Gc wee dp /dg c can be witten in te following fo: dp A P dk G P (9 dgc GC Ntu dgc Gc R above A is te effective eat tansfe aea of PHEs. Te oveall eat tansfe coefficient k of PHEs is: + + k α α c α o k C R + C (0 ( if ignoe te teal oeties diffeence due to te teeatue. wee C + α ( fo odinay PHEs and C ( ϕ Ã fo PHEswit unequal (3 flow coss- section aea in equation (0 α, α c ae te fil convective eat tansfe coefficients of PHEs at te ot and cold ses of PHEs, esectively. is te teal esistance due to fouling. Te owe index is an eiical constant of eat tansfe efoance of PHEs in te fo of Nu CRe P n. ϕ and γ ae te flow cannel coss-section aea atio and te equivalent diaete atio of we cannel se to tat of naow se. Te deivative of k wit esect to G c is + dk α C R (4 dgc G ( C R + C Substitution into equation (9 and using equation (0 we get finally a diffeential equation, P R P P Ntu + (5 Ntu ( R + C / C R Te above equation can be silified by using te following definitions, Ntu P ε (6 P Ntu wee ε, is te sensitivity of effectiveness to Ntu, and R P ε (7 P R is te sensitivity of effectiveness to te eat caacity ate atio R. Tese definitions ae te sae as descibed by Kovaik (989. Consequently, equation (5 can be witten as: R 0. 5P + ε (8 ( R + C / C ε Equation (8 is a nonlinea equation of R. Even toug it is difficult to exibit te solution of tis equation in exlicit fo, nueical analysis oves a eans to find a solution. Note tat te igt se of te above equation is a geneal function of te eat tansfe units Ntu, te caacity ate atio R and te aangeent of a eat excange. It can be calculated wit te sae ocedue as te teeatue effectiveness. 3396
4. THE OPTIMUM DESIGN OF PHEs AND HEAT RADIATORS Tee ae two eat tansfe aeas tat ae needed to be deteined in te equation (. One is te eat tansfe aea of te late eat excange, A, wic is included in te teeatue effectiveness P. And te ote is tat of te teinal eat excange, A. Wen te flow aangeent of te PHE is selected, P is a function of te nube of eat tansfe units Ntu and te eat caacity ate atio R, noted as P (Ntu, R (see equation (4.Te oveall eat tansfe coefficient in Ntu is also a function of A wen te ass flowate of geoteal wate and R ae constants. On eaanging te equation (, te eat tansfe aea of teinal adiato A can be obtained: + GC Q A B B Q (9 3 α Te uose is to find te iniu total initial caital cost of te late eat excange and te teinal eat adiatos. Suose te costs of te late eat excange and te adiatos ae linea functions of tei eat tansfe aeas, esectively. Tis eans lage te size of PHE, te ceae e unit eat tansfe aea will be wen a and a ae ositive. COST a + b A (0 COST a + b A ( So te otiu oble becoes tat of finding te iniu total cost of COST t. COST t COST + COST a + a + b A + b A ( wee COST and COST ae te costs of PHEs and te teinal eat adiatos, esectively. b and b ae te costs of te PHE and te teinal eat adiatos e unit eat tansfe aea, esectively. Te unning cost due to uing te two flus toug te eat excanges is not conseed in te ae. Since te estiation of eat load always coesonds to a secific outdoo teeatue, te eat load Q and T a sould be given in ais. Te ai values can be given in two ways. One is as taking te eak loading eat (te axiu eat deand and te lowest outdoo teeatue, and te ote using te tie accuulated aveage eat load wit te aveage outdoo teeatue. Howeve, Q can not exceed C (T -T a, te teoetical axiu eat tat can be dawn fo te geoteal wate wile its disosal teeatue eaces te abient teeatue. In geneal te disosal teeatue is aound 40 C, in tun, te eat extacted fo te geoteal wate is C (T -40, wic sould be a little bit oe tan te eat deand. Tis does not include te case wee geoteal wate afte te PHE is used fo ote eating o bating uoses. In tose cases te outlet teeatue of geoteal wate is about 45 C instead of 40 C. Wen te aveage eat deand is acceted in te design of a eating scee, a eak loading set suc as te back-u boile o te eat u is equied. But in any case, te otiu esults sould be val because usually te eak eat deand can be acieved by egulating te inlet teeatue of te flu flow toug te boile o te eat u. Geneally, te tie eiod of tese eaking sets being loaded is sot. 5. RESULTS AND DISCUSSION Te given calculation exale was based on a eal geoteal eating oject in Tianjin. Te wellead teeatue is 9.5 C. Te oduction ate is about 50 3 /. Ote aaetes ae sown in Table. 5. Coaison of Results fo Diect and Indiect Heating Systes Wit inceasing outdoo teeatue, te elative otiu teal efficiency inceases as sown in te Figue. Te iniu equied geoteal wate flowates fo indiect eating syste (otiu oeation state and fo diect eating syste wit te inceasing outdoo teeatue is sown in te Figue. Cuves fo tee eating load factos of,.0 (oiginal design and. ave been sown in te figue. It can be seen tat wit inceasing te outdoo teeatue and deceasing te eating load facto, te elative otiu teal efficiency inceases. Te consevative design o te lowe eating load facto of an indiect eating oject can ake it to un at ig elative teal efficiency. Howeve, te caital costs would be ig. Te consevative design eans bot te eat tansfe aeas of te PHEs and te eat adiatos sould be lage. Te benefit by inceasing te eat tansfe aea of one se alone is liited. Te elative teal efficiency at diffeent ciculating wate flowates is sown in te Figue 3. Te dased line in te Figue 3 is te best oeation state of te indiect eating syste at diffeent eating load factos. Te ove eating load facto uges te indiect eating syste unning at ig ciculating wate flowate, even wit tis te elative teal efficiency is low. 5. Te Best Oeation of Indiect Heating Systes Te designed eat tansfe aeas of PHEs, A, and of te eat adiatos, A, ae 9 and 30000, esectively. As descibed in te section, wen te geo-wate flowate is fixed, te best oeation oble is to find te best eat caacity atio R o te ciculating wate flowate wen ignoing te secific eat caacity diffeence due to te cange of teeatue. Let te left and igt ses of equation (8 to be denoted as H and F, esectively. In te Figue 4, H and F ae lotted against R. Te value of R at wic H and F ae equal, i.e. te connect oint of H and F is te best oeation ode to be deteined. Fou kinds of situations ae conseed. One is te oiginal designed situation sown as te oint A. Point B is te situation of te owe index,, inceasing, o te eat tansfe efoance of PHEs is bette. Point C indicates te fouling eat esistance facto being doubled. Point D eans tat double late sacing of te PHEs is acceted at te cold ciculating watese. It can be seen tat te ige te eat tansfe efoance of te PHE (te lage is te close (R ot to one, because te unbalance of te two ses flow esults in an aaent sacifice of deceasing te oveall eat tansfe coefficient of te PHE (oint B. Te incease of te fouling eat esistance uges te PHE unning at ig flowate of ciculating wate, i.e. te lowe (R ot (oint C. Te PHE wit te unequal coss-sectional aea of flow cannels as te lowest (R ot in 3397
ode to balance te fil eat tansfe coefficients of cold and ot ses (oint D. Te dased lines in te Figue 4 ae te values of H at constant Ntu. Te benefit fo te otial oeation of a geoteal distict eating syste is not aaent as sown in te Table. Tee is not uc diffeence fo te eat suly Q by te syste in a quite we ange of eat caacity atio R. But it does not ean tat te esult is eaningless. On te contay, since te eat load Q is always canging wit te outdoo teeatue, te flowate of geoteal wate sould be egulated accoding to te ule oosed. Otewise, te ciculation u is doing a at of useless wok, wic ay not attact te use s attention. It is teoetically oved tat te best flowate atio is about, wic is coonly oosed in actice (Haison et al 990. Te deceasing of R is elful to ovecoe te isdistibution oble of te flu flow in diffeent bances of a eating netwok, and only a sligt decease of te eat load Q as been obtained duing tis ocess. Howeve, uing owe would be a oble if R wee too low. To incease R is unfavoable fo bot te efficiency of eat utilization and te ydaulic stability of a geoteal eating syste. REFERENCES Dai C. (997. Teal Analysis of Indiect Geoteal Distict Heating Systes, Geoteics, vol. 6,.35-364. Haison, R., Motie, N. D. and Saason, O. B. (990. Geoteal Heating, Pegaon Pess. Kays, W. M. and London, A. L. (984. Coact Heat Excanges, McGaw-Hill, New Yok. Kovaik, M. (989. Otial Heat Excanges, Tans. ASME, vol.,.87-93 5.3 Te Best Design of PHEs and Heat Radiatos Fist of all, te eating load is fixed as Q equals 6.0 MW. Te conventional design etod is to design PHEs and te eat adiatos seaately at given disosing teeatue of geo-wate. Since te suly and etun teeatues cannot be given befoe te PHEs ave been designed, te conventional design etod is not suitable fo tis case. Substituting Equation (9 into Equation (, a new equation fo te total cost is obtained, wic as A as te only indeendent vaiable. Te iniu value of COST t can be deteined, teefoe, by finding te solution of te diffeential equation wit esect to A diectly. Te otiu value of A ot is obtained by a nueical etod. Te equation is given by: dp da + C + Q P C P b ( + Q b (3 Figue 5 sows te best design values of A and A against te cange of cost atio e unit eat tansfe aea of te eat adiato to PHEs. Table. Paaete set in te exale PHE aangeent : ass - ass countecuent PHE Heat efoance 0.6 0.3 o 0.4 : Nu 0.35 Re P Heat adiato efoance : k α, α.05, 0.35 Heat loss caacity of te : 000 W/ C building, C v V Flowate of geo-wate : 50 3 /ou Well ead teeatue, T : 9.5 C Outdoo teeatue, T a : -9 C Heat deand (T 8 C : 6.0 MW Cost of PHE e : 50 USD (Titaniu Cost of adiato e : 7.5 USD (Cast ion 6. CONCLUSIONS Te best design and oeation etod of te indiect geoteal distict eating systes and tei efoance coaison wit te diect eating systes wee oosed in te ae. Te effects of soe teal aaetes on te design and oeation of low teeatue geoteal distict eating systes ave been sown in foula and Figues, wic is elful fo te enginees and tecnicians to undestand te geneal beavios of a low teeatue geoteal eating syste and its design. 3398
ot.0 0.9 0.7 0.6.0. Heating load facto 0.5-0 -8-6 -4-0 T a ( C Figue. Relative otiu teal efficiency against te outdoo teeatue at diffeent eating load factos H and F.0 0.6 0.4 0. 0.0-0. -0.4-0.6 - D Paaetes fo Point A,B, C and D A (,, C B (.3,, C C (,, C D (,, 4 C C A H -.0 0.4 0.5 0.6 0.7 0.9.0...3.4.5.6 B Ntu 6 5 4 3 F R G ( 3 / 50 00 50 00 50 Indiect Syste Diect Syste Heating load facto 0-0 -8-6 -4-0 T a ( C..0 Figue. Te iniu equied geo-wate flowates fo indiect eating syste (otiu oeation state vs. te outdoo teeatue Figue 4. Te left se H and igt se F of Equation (8 against te eat caacity atio R Table. Calculation esults fo equation (8 R Ntu H F Q (MW 0.5.956 0.4060 0.379 7.040 0.6.884 0.355 0.50 7.0807 0.7.866 78 0.6 7.074.757 0.058 0.709 7.0 35 *.7375 0.739 0.74 7.77 0.9.707 0.00 0.799 7.88.0.656 0.0000 8 7.040..606-0.49 0.958 7.0765 * Te otiu oint A in Figue 4.00 0.95 0.90 5 0 0.75 0.70 0.65 0.60 0.55 Heating load facto.0. 0.50 50 00 50 00 50 300 G c ( 3 / Figue 3. Te elative teal efficiency at diffeent ciculating wate flowates A ( 40 0 00 80 60 40 0 00 80 A A 0.00 0.0 0.04 0.06 0.08 0.0 000 0000 9000 8000 7000 6000 5000 b /b Figue 5. Otiu A and A wit te canging of cost atio of adiatos to PHEs e unit eat tansfe aea b /b (at R A ( 3399