A REEXAMINATION OF USGS VOLUMETRIC HEAT IN PLACE METHOD

Transcription

1 POCEEDINGS, ity-sixt Wksp n Getemal esevi Engineeing Stanfd Univesity, Stanfd, Califnia, Januay 31 - Febuay 2, 2011 SGP--191 A EEXAMINAION OF USGS VOLUMEIC HEA IN PLACE MEHOD Sabd K. Gag Science Applicatins Intenatinal Cpatin Campus Pint Dive San Dieg, CA, 92121, USA gags@saic.cm Jim Cmbs Ge Hills Assciates LLC 1950 Campin Hills Dive en, NV, , USA jimjeany@ix.netcm.cm ABSAC e USGS vlumetic estimatin metd tgete wit Mnte Cal simulatins is ften used t pvide estimates f te pbable electical geneatin capacity f a getemal system. e metdlgy cnsists f cmbining pbability density functins f uncetain estimates f te tempeatue, aea, tickness, and temal ecvey fact f a getemal esevi t btain te pbability distibutin functin f te sted enegy ( eat in place ) and te ecveable eat. e electical capacity f te ptential getemal esevi is ten cmputed using a cnvesin ( utilizatin) efficiency. In a pevius pape, we discussed te imptance f csing te pbability distibutins f te esevi paametes based n actual field data. Heein, we examine te specificatin f te efeence tempeatue and te cnvesin efficiency. We sw tat te cnvesin efficiency depends n bt te efeence tempeatue and te pwe cycle (flas, binay). A ppe undestanding f te latte elatinsip is essential f btaining estimates f esevi capacity f electical geneatin. INODUCION Duing ealy stage explatin f getemal esuces assciated wit an identified ydtemal cnvectin system, it is necessay t btain an estimate f te ptential electical enegy tat migt be pduced fm te delineated getemal system. In te 1970s, eseaces at te United States Gelgical Suvey (USGS) develped a metdlgy t quantify te uncetainty f estimates f te getemal esuces assciated wit an identified ydtemal cnvectin system (e.g., Natensn, 1975a; 1975b; Natensn and Muffle, 1975; Muffle and Cataldi, 1978; Bk, et al., 1979). e USGS vlumetic estimatin metdlgy cnsists f cmbining estimates wit uncetainties f te tempeatue, aea, tickness, and temal ecvey fact f a getemal esevi int estimates f te sted eat ( eat in place ) and te ecveable enegy wit uncetainty. An estimate f te ecveable enegy tgete wit a cnvesin efficiency ( utilizatin fact) is ten used t cmpute te electical capacity. e paametes equied f te cmputatin f electic capacity f te eat in place ae indicated in able 1. able 1. Paametes equied f te calculatin f te electic geneatin capacity using te USGS vlumetic eat in place metd. Gup 1 Paametes: esevi Aea (km 2 ) esevi Dept (m) esevi ickness (m) esevi empeatue ( C) emal ecvey Fact (%) Gup 2 Paametes: Vlumetic Heat Capacity (kj/m 3 -K) ejectin empeatue ( C) Cnvesin Efficiency (%) Plant Pject Life (yeas) Plant Lad Fact (%) e paametes in able 1 can be divided int tw gups. Specificatin f statistical distibutins f te paametes in te fist gup (esevi aea, esevi dept, esevi tickness, esevi tempeatue, temal ecvey fact) is at best a difficult task and is igly dependent n te stage f explatin f a getemal system. In a pevius pape (Gag and Cmbs, 2010), we emaked tat as fa as pssible, actual field data suld be used wen pescibing esevi paametes. Witut data-diven esevi paametes, use f Mnte Cal simulatins is liable t geneate uneliable estimates f esevi megawatt capacity. e secnd f tese gups (Gup 2 Paametes) cntains paametes wse value des nt eite vay substantially fm case t case (vlumetic eat capacity, pwe plant pject life, pwe plant lad fact) can be specified sufficiently accuately using available engineeing data (ejectin tempeatue, cnvesin efficiency). In tis pape, we cnside te specificatin f ejectin tempeatue (smetimes called efeence tempeatue

2 dead-state tempeatue), and cnvesin efficiency (utilizatin fact). Estimates f te ecveable eat depend diectly n te cice f te ejectin tempeatue. Futeme, te cnvesin efficiency is seen t be a functin f bt te ejectin tempeatue and te pwe cycle (e.g., flas binay) used t geneate electical pwe. Stated smewat diffeently, cnvesin efficiency cannt be pescibed independently f te ejectin tempeatue and te pwe cycle. SOED HEA AND AVAILABLE ENEGY Cnside a getemal esevi cntaining singlepase liquid. Heat sted in te getemal esevi, q, is given by: wee q = Vρc( ) (1) cw( c ) = Heat capacity f wate (ck gains) A = esevi aea H = esevi tickness = efeence ( ejectin) tempeatue = Aveage esevi tempeatue V = esevi vlume (=AH) φ = Psity ρ c = Vlumetic eat capacity f fluidsatuated ck [ = φρwcw + (1 φ) ρ c] ρ ( ρ ) = Density f wate (ck gains) w e cice f te efeence ( ejectin) tempeatue is vey imptant since it as a lage effect n te cmputed value f te available enegy and te cnvesin efficiency ( utilizatin fact). As nted by Bk et al. (1979), tw likely cices f ae te ambient (say ~15 C) and te cndense (~40 C) tempeatues. A getemal ecvey fact g is defined as te ati f te eat ecveed at te wellead, q w, t te eat sted in te esevi, q. = q / q (2) g w Assuming isentalpic flw in te wellbe and neglecting te wk equied t aise wate t te wellead, te entalpy f pduced fluid at te wellead, w, is equal t tat f liquid wate at te esevi tempeatue. us = ( ) (3) w e amunt f fluid pduced at te wellead, m w, is given by: m = q /( ) (4) w w w wee is te entalpy f liquid wate at te efeence tempeatue,. Substituting fm Eqs. (1)- (3) in t Eq. (4), tee fllws: wee m = α ( )/( ) (5) w w = g α V ρ c (6) Since te entalpy f liquid wate alng te satuatin line vaies almst linealy wit tempeatue, m w is nly a weak functin f te efeence tempeatue. e cncept f availability plays a cental le in te USGS vlumetic eat in place metd. Availability may be defined as te maximum wk ( pwe) utput tat can teetically be btained fm a substance (wate) at specified temdynamic cnditins (wellead) elative t its suundings. DiPipp (2008) bseves: acieve tis ideal utcme, tee ae tw temdynamic cnditins tat must be met: 1. All pcesses taking place witin te system must be pefectly evesible. 2. e state f all fluids being discaged fm te system must be in temdynamic equilibium wit te suundings. e fist f tese cnditins amunts t neglecting lsses due t fictin, tubulence, and te suces f ievesibility. e secnd cnditin equies tat any fluids discaged fm te system - ae in tempeatue equilibium wit te suundings (i.e., efeence tempeatue). Nne f te eal pwe cycles can meet tese cnditins, and te electical enegy tat is geneated is always less tan te available wk. e cnvesin efficiency (utilizatin fact) is te ati f te actual electical enegy t te available wk. Neglecting kinetic ptential enegy effects, te maximum enegy utput pe unit mass f te substance e is given by (DiPipp, 2008): e = ( s s ) (7) k wee and s dente te entalpy and entpy f te substance (e.g., steam ydcabn vap) at

3 tubine inlet cnditins wit tempeatue, k is te abslute efeence tempeatue (Kelvin), and s is te entpy f liquid pase (wate ydcabn liquid) at te efeence tempeatue. F mass m f te substance, te available wk is teefe given by: W = me = m[ ( s s )] (8) A K e available wk, as used in te USGS metd (Bk et al., 1979), is cmputed by eplacing mass m in Eq. (8) by m w fm Eq. (5). estimate te cnvesin efficiency (utilizatin fact), it is necessay t cnside te pwe cycle tat will be used t geneate electical enegy. Nte tat in geneal, mass m t tat entes te tubine is nt te same as m w cmputed fm Eq. (5). In single ( dual) flas systems, liquid bine (and te enegy cntained in it) is ejected at te sepaat tempeatue; nly te sepaated steam is used t geneate pwe. e binay tecnlgy invlves te use f a secnday fluid (e.g., isbutane), eated by te bine, t geneate pwe; te bine is in any event ejected at a ige tempeatue tan te efeence numbe. F a eal pwe cycle, m, and s in Eq. (8) suld be evaluated at te tubine inlet cnditins, and te mst apppiate efeence tempeatue (Eq. 8) is te cndense tempeatue. ILLUSAIVE EXAMPLES We cnside tw typical getemal esuces wit tempeatues f 150 C and 250 C. e lwe tempeatue esuce is suitable f binay applicatins wile te ige tempeatue esuce will mst likely be explited using flas tecnlgy. Befe embaking n an analysis f pwe cycles, it is useful t evaluate available wk using te USGS metdlgy (see e.g., Bk et al, 1979). In u ntatin, Equatin (10) f Bk et al. (1979) can be ewitten as fllws: WAUSGS ( ) = mw[ w k( sw s)] (9) wee mw is given by Eqs. (5) and (6), and w (= ) and s w (=s ) ae evaluated at te esevi tempeatue,. Available wk cmputed fm Eq. (10) f te tw esuce tempeatues (150 C and 250 C) and tw efeence tempeatues (15 C and 40 C) is pesented in able 2. All te wate ppeties wee evaluated alng te satuatin line. It is appaent fm able 2 tat te cmputed values f te available wk ae a stng functin f te efeence tempeatue. As expected, te available wk inceases wit a decease in te efeence tempeatue. F te ige tempeatue esuce, te diffeence between cmputed values (able 2) is abut 22 %. e pecentage diffeence (~35 %) is muc geate f te lwe tempeatue esuce. able 2: Cmputatin f Available Wk. F sake f simplicity WA / α instead f WA is given. esuce efeence Available Wk empeatue empeatue WA / α ( C ) ( C ) Pwe Eq. (9) Cycle As discussed ealie, specific pwe cycles must be cnsideed in de t estimate cnvesin efficiency (utilizatin fact). In te fllwing, we cnside tw elatively simple pwe geneatin scemes, i.e., single flas and basic binay cycles. Single Flas It is assumed tat te pduced fluid, wit entalpy equal t tat f te wate at 250 C (i.e., esevi tempeatue), is sepaated at 5 bas (satuatin tempeatue: C). e sepaated bine is injected int te esevi, and te steam is used t geneate pwe. e tubine inlet pessue is set equal t te sepaat pessue, and te cndense tempeatue is assumed t be 40 C. e mass f te fluid pduced at te wellead is given by Eq. (5) wit = C. e steam factin f te pduced fluid at a sepaatin pessue f 5 bas is: x = ( )/ = (10) l gl wee l and gl dente te entalpy f liquid wate and eat f vapizatin at 5 bas, espectively. Cmbining Eqs. (5) and (10), te mass f sepaated steam, m t, enteing te tubine is: m = α ( ) / ( ) (11) t sep l Substituting fm Eq. (11) int Eq. (8), evaluating and s f satuated steam at 5 bas, and putting equal t 40 C, we finally btain: W = 29.05α (12) Atubine Fm te data pesented in able 2, it is appaent tat te available wk given by Eq. (12) is nly ~45 % (~57%) f tat cmputed using te USGS metdlgy and a efeence tempeatue f 15 C (40 C). Because f mecanical and te lsses in te tub-geneat, nly abut 70% f te available wk given by Eq. (12) is cnveted t electical enegy (see als Natensn, 1975a). us, if te

4 available wk is cmputed using equatin (9) and a efeence tempeatue f 15 C (40 C), te veall cnvesin efficiency (utilizatin fact) is nly ~32% (~40%) f te single flas cycle cnsideed ee. Binay Cycle e pduced bine at a wellead tempeatue f 150 C is used t eat te wking fluid (e.g., isbutane), and te spent bine is injected back int te esevi. e tubine inlet pessue is assumed t be 20 bas; te satuatin tempeatue f isbutane at te latte pessue is C (NIS, 2010). Isbutane is assumed t be satuated at te tubine inlet. Wit a tempeatue diffeential f 5 C at te pinc pint (i.e., te pint in te eat excange wit te least tempeatue diffeence between te pimay and secnday fluids. e pinc pint cespnds t te bubble pint f te secnday fluid.), te tempeatue f te bine at te pinc pint is C. e amunt f isbutane vapized by eat excange wit 1 kg f bine is given by: Wit m = ( )/ (13) is wb isgl (entalpy f liquid wate at 150 C) = kj/kg wb isgl (entalpy f liquid wate at C) = kj/kg (eat f vapizatin f isbutane at C) = kj/kg tee fllws: m is = kg (14) emal enegy equied t eat kg f isbutane fm 40 C t C at a cnstant pessue f 20 bas is: emal enegy = [ is(20 bas, C) is(20 bas,40 C ) ] = ( ) = kj e abve temal enegy is supplied by 1 kg f bine as its tempeatue declines fm C t te ejectin tempeatue ej. Assuming a specific eat f kj/kg C f wate, we ave: = ( ej ) Slving f ej, we btain: ej = C (15) Wit = = C, Eq. (5) yields ej m = x10 4 α wej eefe, te amunt f isbutane tat flws tug te tubine is: m = m = x10 4 α (16) tis wej e wk equied t pessuize 1 kg f isbutane fm 5.31 bas (satuatin pessue at 40 C) t 20 bas at a cnstant tempeatue f 40 C is: 5 Wk = Vis(40 C,20 bas)( ) x10 J = kj e available wk f te binay cycle is ten given by: W m C C 0 Atubine = tis{ gis( ) lis (40 ) 0 3 sgis C slis C x [ ( ) (40 )] } = α (17) e available wk given by Eq. (17) is nly abut 43 % (~66 %) f tat cmputed using te USGS metdlgy and a efeence tempeatue f 15 C (40 C). Assuming a tub-geneat efficiency f 70% and a efeence tempeatue f 15 C (40 C), te veall cnvesin efficiency (utilizatin fact) is tus nly ~30 % (~46 %) f te binay cycle cnsideed ee. DiPipp (2004) as analyzed te cnvesin efficiency f seveal peating OC pwe plants. Altug secnd law efficiencies f ve 40% (efeed t ambient tempeatue ) ave been epted f a cuple f pwe plants utilizing advanced pwe cycles, mst peating OC pwe plants ave elatively lw (less tan 25 %) secnd law efficiencies. GetemEx (2004) used a utilizatin fact f 0.45 (efeed t 15 C) in a esuce assessment f seveal lw tempeatues getemal fields in Nevada and Califnia. Altug te latte utilizatin fact appeas t be teetically pssible, esuce caacteistics (e.g., cange in esuce tempeatue ve time) and ecnmic cnsideatins will usually dictate a muc lwe utilizatin fact. CONCLUSIONS e USGS vlumetic eat in place metd tgete wit Mnte Cal simulatins is a widely used tl f assessing te electical capacity f a getemal esevi. e metd is deceptively simple and is ften misused. In a pevius pape, we cnclude tat te pbability distibutins f te

5 esevi paametes must be based n actual field data. Heein, we ave examined te specificatin f a efeence tempeatue, and its elatin t available wk and te utilizatin fact ( cnvesin efficiency). e available wk is a stng functin f te efeence tempeatue. e utilizatin fact (i.e., ati f electic enegy geneated t available wk) depends n bt te pwe cycle and te efeence tempeatue. us, a ppe undestanding f te inteelatinsip between te efeence tempeatue, pwe cycle, and te utilizatin fact is citical if valid esults ae t be btained using te USGS eat in place metd. S. Gelgical Suvey Open-File ept , 38p. Natensn, M., and Muffle, L.J.P. (1975), Getemal esuces in Hydtemal Cnvectin Systems and Cnductin-Dminated Aeas: in Assessment f Getemal esuces f te United States D.E. Wite and D.L. Williams, edits, U.S. Gelgical Suvey Cicula, 726, 160p. NIS (2010), empysical Ppeties f Fluid Systems. Available at ttp://webbk.nist.gv/cemisty/fluid/ EFEENCES Bk, C.A., Maine,.H., Mabey, D.., Swansn, J.., Guffanti, M. and Muffle, L.J.P. (1979), Hydtemal Cnvectin Systems wit esevi empeatues > 90 C: in Assessment f Getemal esuces f te United States- 1978, L.J.P. Muffle, edit, U.S. Gelgical Suvey Cicula, 790, 170p. DiPipp,. (2004), Secnd Law assessment f binay plants geneating pwe fm lwtempeatue getemal fluids, Getemics, 33, DiPipp,. (2008), Getemal Pwe Plants: Pinciples, Applicatins, Case Studies and Envinmental Impact, 2 nd Ed., Elsevie, 493 pp. Gag, S.K. and Cmbs, J. (2010), Apppiate use f U.S.G.S. vlumetic eat in place metd and Mnte Cal calculatins, Pceedings 34 t Wksp n Getemal esevi Engineeing, Stanfd univesity, Stanfd, Califnia, U.S.A., 7 pp. GetemEx, Inc. (2004), New Getemal Site Identificatin and Qualificatin, Cnsultant ept f te Califnia Enegy Cmmissin PIE ept N. P , Apil 2004, lcated at (ttp:// PIE_epts.tm). Muffle, P., and Cataldi,. (1977), Metds f eginal Assessment f Getemal esuces, U. S. Gelgical Suvey Open-File ept , 78p. Natensn, M. (1975a), Sme esevi Engineeing Calculatins f te Vapdminated System at Ladeell, Italy, U. S. Gelgical Suvey Open-File ept , 47p. Natensn, M. (1975b), Pysical Facts Detemining te Factin f Sted Enegy ecveable fm Hydtemal Cnvectin Systems and Cnductin-Dminated Aeas, U.