CFD modeling of a high enthalpy geothermal context

Transcription

1 PROCEEDINGS, 43d Woshop on Geohemal Reseoi Engineeing Sanfod Uniesiy, Sanfod, Califonia, Febuay -4, 08 SGP-TR-3 CFD modeling of a high enhalpy geohemal cone Theo Renaud, Michal Sebel, Paic Vedin, Gioia Falcone Geo-Enegy Engineeing Cene, Canfield Uniesiy, MK43 0AL, UK heo.enaud@canfield.ac.u Keywods: CFD, IDDP, geohemal, eseoi. ABSTRACT The pomising deelopmen of highly enegeic geohemal esouces could consideably enhance geohemal powe poducion woldwide. The fis aemp a apping supeciical/heaed fluids was made by he Iceland Deep Dilling poec IDDP, bu unfounaely a magma laye a a deph of,00m was encouneed, and he dilling was abandoned. Ye, his dilling opeaion failue geneaed new oppouniies fo assessing he poenial powe geneaion close o shallow magmaic inusions. Deailed numeical mehods ae equied o assess he hea ansfe and fluid hemodynamics a wellboe and eseoi scale a nea supeciical condiions o poide poducion scenaios and foecass as accuae as possible. A pimay seady-sae sudy of eseoi and wellboe hea eacion fom a geohemal well nea a magmaic chambe has been pefomed wih Compuaional Fluid Dynamics CFD echniques. Using simplified geological assumpions based on he IDDP- well descipion, a D aisymmeic single phase flow model was deeloped and is esuls wee compaed o hose obained wih a full 3D CFD model. The simulaed oupu powe simulaions eached 5 MW a 350 C and a wellhead pessue of 40 bas. Mehodology and esuls fom his sudy show ha CFD echniques can be successfully used o assess geohemal enegy oupus fo unconenional geohemal wells and can poide deails of a apo supeheaed flow sucue a wellboe-eseoi scale.. INTRODUCTION The need fo susainable enegy supplies aises hilling challenges o deelop low-cabon emiing echnologies and decease dependency on fossil fuels Fuss e al., 008. Geohemal enegy aleady conibues o geneae powe and hea woldwide, eaching a oal elecic capaciy of 0.9 GW in 4 counies; his is epecing o incease in he fuue Beani, 0. In 009, he dilling ino ey high enhalpy geohemal esouces in Iceland aised new oppouniies fo inceasing he poenial powe geneaion pe well Eldes e al., 04. Moe ecenly, on he 5 Januay 07, he second well of he Iceland Deep Dilling Poec IDDP- successfully eached 47 C and a fluid pessue of 34 MPa a a deph of moe han 4,500 m. A such hemodynamics condiions aboe he ciical poin of pue wae MPa, 374 C, he enhalpy inceases shaply, he densiy deceases and he enegy aailable pe uni of olume is 0 imes highe han wih conenional eaced geohemal fluids Suaez Aiaga and Samaniego 03. Duing he iniial es in 00, supeheaed seam was ecoeed fom ciculaing wae heaed by a pemeable oc aboe he magma inusion Aelsson e al., 04. The modeling of he fluid popeies nea he boom of he well showed an enhalpy of,900 J/g a 60 bas and 390 C. In he iniial phase of he poec, he well IDDP- poduced 0- g/s of dy supeheaed seam Fiðleifsson e al., 04. The measued empeaue eached 440 C a he suface wih a well pessue aound 50 ba Ingason e al., 04. This was sopped a a deph of,07 m as a magma laye was encouneed somewhee beween,09 m and,04 m Pálsson e al., 04. Numeical codes can be used o assess supeciical fluid flow and hea ansfe in poous media. Eamples include HYDROTHERM Hayba and Ingebisen 994, HOTHO eension of STAR Piche, 995 and he TOUGH code Kissling, 995; Biowsi, 00 eended wih AUTOUGH Couche and O Sullian 008 and an inese modelling module itough Magnusdoi and Finsele 05. In addiion, a modified eension of he SHEMAT-Suie code was applied o simulae supeciical condiions in a wo-phase wae/seam eseoi in Tuscany Büsing e al., 06 and he Comple Sysem Modelling Plafom CSMP++ Weis e al., 04 was able o model supeciical condiions nea magmaic inusions wih comple geomeies Sco e al., 05a. Alhough hese simulaos ae well-esablished ools fo modeling supeciical fluid flow and hea ansfe in poous and facued media, hey do no deal wih he pocesses occuing nea he boom hole and along he wellboe. Een if he TWell code Pan e al., 05 calculaes a wellboe numeical soluion fo a Wae - NonCondensibleGas - NaCL equilibium Vasini, 06, i is limied in empeaue and pessue fo supeciical issues 350 C and 000 bas, especially fo he condiions obseed in he IDDP poec. Numeical sudies on closed well sysems ae documened in he lieaue Lenhad and Malcho 03; Huang e al. 05. Only a limied numbe of CFD based sudies hae howee been pefomed and ae epoed fo geohemal eseoi managemen wih open wells. One such sudy descibes a homogeneous 3D Enhanced Geohemal Sysem EGS un wih he seady-sae Chen and Jiang, 05 and he ansien soles o conside hemal non-equilibium condiions beween solid and fluid Jiang e al., 03. Now wih he Silesian Uniesiy of Technology, Poland

2 Renaud e al. The modeling of supeciical fluid hea ansfe using CFD echniques is mainly limied o nuclea engineeing applicaions inoling wae Cheng e al., 007. Fo supeciical CO, a double facued EGS was inesigaed using he NIST eal gas model fomulaion in he commecial code ANSYS Fluen Fluen 06, which poides supeciical hemodynamics popeies Luo e al., 04; Jiang e al., 07. Cheng e al. 007 esablished ha he choice of ubulence model -ω in his case can poduce inaccuae esuls a supeciical pessue. Howee, hei model showed easonable pedicions of Hea Tansfe Coefficien and wall empeaue. Recenly, he wellboe hea ansfe was inesigaed consideing consan wae popeies using a -ε ubulence model Huang e al. 05a, Huang e al. 05b. Fom he lae sudy, he hea in he poducion well was ansfeed o he suoundings and a seady hea ansfe pocess could be consideed afe 30 days. In he wo descibed hee, he seady sae hea ansfe and fluid flow pocesses in a geohemal well and a poous medium ae inesigaed numeically wih he CFD code ANSYS Fluen Geomey and daa fom he IDDP- well ae used o ceae he model and apply bounday condiions. CFD-based pediced esuls ae analysed o obain suface and boom hole daa, fo diffeen magma empeaues and poducion mass flow aes. Two diffeen ubulence models ae esed in he wellboe and lamina flow condiions ae applied in he poous medium. Resuls obained wih a D aisymmeic model ae compaed o hose obained wih a full 3D model.. METHODOLOGY. Model descipion The geomey and he mesh wee ceaed wih he pe-pocesso ICEM CFD Fo he model deelopmen phase and o obain esuls quicly, a D aisymmeic model was consideed fis, see Figue. The domain inesigaed conains a 80 m adius sauaed poous zone delimied by he gound suface =0 m up o =-,00 m Zone. A simplified geohemal well is pesen, fom =0 m up o =-070 m. The wall of his well is epesened by he plain blac line on Figue. To eep a mass equilibium and o allow a mass flow inle bounday condiion o be applied fa away fom he well, he domain is eended fom 80 m o 00 m in he adial diecion, beween =-,000 m and =-,00 m Zone and is eminaed by a wall. I is assumed ha no echange is pesen on his wall, alhough his is clealy no he case in ealiy. Howee, his assumpion is alid as he wall is locaed fa away fom he well, so will no hae any effec on he flow in ha egion. As a fis assumpion, he well is descibed as an open well wih same popeies and diamee as he sloed line 9-5/8'' -40 mm pesen in he IDDP- poec Ingason e al., 04. Thus, he poducing zone is only limied a a deph of,070 m, and no fom poenial uppe zones as aised by Pálsson e al. 04. A Pessue oule bounday condiion is applied a he well ei =0 m. A 0 m hic unsauaed conducie laye sepaaes he poous zone Zone fom he magma egion locaed a a deph of,00 m Zone 3. A sucued mesh was geneaed, compising,400,760 cells, wih local efinemens pesen inside and aound he wellboe. Zone Zone Zone 3 Figue : Schemaic epesenaion of he aisymmeic model The poous media popeies ae aen fom Aelsson e al. 04 and he well popeies fom Duan e al. 06. The poous media poosiy is se o 0% Aelsson e al., 04 wih a homogeneous pemeabiliy of 0-4 m² Sco e al., 05b. If no specified, he magma laye empeaue is se by defaul o 850 C Eldes e al., 0. The densiy, specific hea and hemal conduciiy of he poous media ae se o,700 g/m³, 800 J/g.K and.5 W/m.K, especiely. Fo he well, he following maeial popeies ae consideed: 7,848 g/m³, 460 J/g.K. To accoun fo he cemen which suounds he casing up o =-950 m Pálsson e al., 04, he wellboe maeial is se o 0.3 W/m.K fo Poland Cemen Thóhallsson e al., 04 ahe han consideing he casing popeies W/m.K. The wellboe consideed is 5 mm hic. The ineced fluid is wae apo; is densiy ρ is calculaed wih he ideal gas law: p. R. T whee p and T ae he saic pessue Pa and empeaue K especiely. R is he gas consan equal o 8.34 J.K - mol -. The wellhead pessue oule is se o 40 bas. The apo popeies specific hea, hemal conduciiy, iscosiy ae implemened ia a empeaue linea appoimaion based on a 60 ba consan pessue, see he Appendi secion fo deails. Use defined funcions UDFs hae been ceaed o apply a local geohemal gadien on he side of he model, based on he empeaue measuemens along he IDDP- well Aelsson e al., 04; Moensen e al., 04.

3 Renaud e al. 3 A full 3D model was also ceaed wih a sucued mesh composed of,98,0 cells. The sysem inesigaed is idenical o he D aisymmeic one, bu a conenional ecangula domain consideed in CFD geohemal modeling Huang e al., 07 was used o un he numeical simulaions.. Mahemaical model The goening equaions ae soled wih he CFD code ANSYS Fluen 7..0, which is based on he finie olume appoimaion. The flow in he poous medium is consideed as lamina while a ubulen model is applied in he well. Fo an aisymmeic model, he coninuiy equaion is wien as: 0.. Lamina model The momenum equaions in he poous medium ae defined fo a lamina flow wih he following equaions: g ] [ ]. 3 [ 3. 3 ]. 3 [ ] [ 4 whee., wih ν he fluid elociy and μ is molecula iscosiy. 5 The enegy equaions in he fluid and solid zone ae: eff eff J h T p E E... 0 T h 6 and 7 eff is he effecie hemal conduciiy +, wih he ubulence hemal conduciiy equals o 0 in he lamina zone. The sess enso eff is defined and can be eieed in he Fluen Use Guide Fluen 06. The enegy E and he sensible enhalpy h ae calculaed ia Equaions 8 and 9: p h E p cdt h T ef T, whee c is he hea capaciy 8 and 9.. Tubulence model As a high fluid elociy and he Reynolds numbe in he well ae epeced o be high, ubulence is consideed. Two models ae inesigaed: he sandad - ε and he -ω SST Mene, 993. The sandad ubulence -ε model is based on anspo equaions fo he ubulence ineic enegy and is dissipaion ae ε Fluen 06. This model is fas and has poed o be efficien a high speed and suiable fo numeous indusial applicaions. The -ω Shea Sess Tanspo SST ubulence model calculaes he ubulen ineic enegy and he specific dissipaion by modificaion of he ubulen iscosiy fomulaion o accoun fo he anspo effecs of he pincipal ubulen shea sess. Coninuum equaions can be wien as: B A i i S A C C i i, 0 and

4 Renaud e al. The effecie diffusiiy Fluen 06. A,, wih,, he ubulen Pandl numbe and he eddy iscosiy ae descibed in,, The SST fomulaion combines: i he use of a ω fomulaion in he inne pas of he bounday laye which maes his model diecly usable in he iscous sub-laye and can heefoe be used as a Low-Re ubulence model, and ii a swich o a ε model in he bul flow and heefoe aoids sensiiiy poblems encouneed by a ω fomulaion due o inle ubulence popeies Fluen 06. The diffeen ems pesen in he coninuum equaion fo boh models ae epoed in Table. Table : Tems in coninuum equaion Tubulence model A, B C S -ε A G G Y b M C G C G 3 b C -ω A G Y M G Y D G, G b epesen especiely he geneaion of ubulen ineic enegy due o mean elociy and buoyancy. They ae defined wih dilaaion in compessible ubulence,.. Numeical model D M coss-diffusion em and he consans C,,3, in Fluen 06. Fo all CFD simulaions descibed hee, he SIMPLE Semi-Implici Mehod fo Pessue Lined Equaion algoihm was used o addess he pessue-elociy coupling. A fis ode upwind diffeencing scheme was applied fo he disceizaion of he spaial-deiaie ems. Enegy, densiy, ubulence, momenum and he specific dissipaion ae componen wee all based on a fis ode upwind scheme. The sandad mehod was chosen fo he pessue soluion. The seady sole was applied and gaiy effecs wee consideed. A conegence cieion of e-03 was se-up fo eey equaion apa fom he enegy, whee a alue of e-6 was applied. 3 RESULTS AND DISCUSSION 3. Ideal gas modeling Figue a shows a D conou plo of he empeaue disibuion in he whole domain and a close iew nea he boom hole of he well, when he -ε ubulence model is used wih a wae apo inecion of 30g/s. As can be seen, he empeaue is ey high in he magma egion and deceases aially as he disance fom his egion inceases. In he boom hole zone, a empeaue of 430 C is eached and popagaes ino he well. Figue b descibes he numeical esuls of empeaue along he ceneline of he well when consideing wae apo inecions of g/s, 0g/s and 30g/s, he -ε and he - ω ubulence models, and diffeen magma empeaues: 850 C he defaul empeaue, 950 C and 050 C. A he boom hole, he apo empeaue ises locally in he well due o he pessue dop beween he poous medium and he well zone. When a mass flow ae of 0-30g/s is applied a he inle, he wellhead empeaue eaches 358 C ± 0 C wih maimum deph aiaions ealuaed aound 5 %. The g/s case dies moe hea, bu he apo shows significan hemal losses wih he suounding ocs owad he suface. A 3 % aiaion in esuls is noed beween he -ε and -ω ubulence models in he wellboe egion. A slighly highe wellhead empeaue is obseed when inceasing he magma empeaue, while he empeaue disibuion in he poous medium is highly affeced Figue b. Noe ha in his egion, a 850 C heshold appeas due o calculaion limiaions in he ideal gas fomulaion. Y M 4

5 Renaud e al. a b Figue : a Tempeaue disibuion of he nea boom hole aea lef and below,000 m igh fo he -ε_30g simulaion. b Tempeaue disibuion along he ceneline =0 m. 3. 3D s aisymmeic modeling Figue 3a shows he empeaue disibuion in he diecion nomal o he well ais a =-000 m, whee he flow is fully deeloped, fom he cene of he well =0m o he adius = m. Figue 3b summaizes he fluid elociy, densiy, enhalpy and oupu powe when he magma empeaue is 850 C wih he -ε and ω ubulence models fo diffeen inecion mass flow aes. D aisymmeic and full 3D based esuls ae compaed on Figue 3a. Only he -ε ubulence model was inesigaed in he 3D model, as i has been seen peiously fo he D aisymmeic sudy ha he diffeence of esuls beween he wo ubulence models esed is small, aound 5 C. The 3D simulaion poides esuls slighly hoe han hose obained wih he aisymmeic case, bu easonably consisen when looing a he ange of oupu empeaue alues. An aisymmeic model can heefoe be used insead of a full 3D model fo such sudies, which educes compuaional coss significanly. a b Figue 3: a Radius empeaue disibuion a,000m beween he ais cene of he well and m in he suoundings ocs. The 3D esuls ae shown fo wo ohogonal hoizonal diecions, y. b Simulaion-based oupu esuls Simulaed esuls in he poous media zone obained wih he D aisymmeic and he 3D models ae significanly diffeen, see Figue b. In he fis mees below he boom hole, he aisymmeic simulaion pesens a shap empeaue dop while he 3D model shows a slowe deceasing disibuion. The compaaie use of he -ε and -ω model gies ey wide empeaue upseam flow aiaions, which do no seem o follow any geneal ule. In he wellboe, he boom hole pessues eaches MPa aound 50 bas. The mass flow ae applied leads o unealisic alues in he poous medium bas. Thus, he popeies calculaed in he pemeable zone ae open o discussion. The model calculaes a high Reynolds numbe alue Re>0,000 beween -070 m and -069 m and apidly eaches a consan alue indicaing a 5

6 Renaud e al. lamina flow behaio. Supisingly, applying a hoe magma empeaue does no affec he wellhead empeaue. I seems ha he oupu condiions consain he model o conege a 358 C±0 C fo 40 bas. The applied ideal-gas fomulaion calculaes coecly he apo sae aboe he sauaed poin of pue wae 40 ba-336 C esimaed fom IAPWS-97 Wagne e al., 000 bu undeesimaes he gas densiy aound 50 g/m³ while a alue of 7 g/m³ is esimaed fom IAPWS-97, see Figue 3b. Assuming a sauaed apo migh no be coec fo bine geohemal fluids as he boiling poin cue of pue wae and seawae diege significanly aboe 300 C Anosson e al., 007. Consideing a pessimisic ne geneaion efficiency alue of 30% DiPippo, 05, he poenial oupu powe simulaed wih an infinie souce of hea poides almos 5 MW fo 30 g/s of seam flowing owads a dy seam plan Figue 3b. The simulaions pefomed poide a seady sae assessmen wih a consan magma empeaue and geohemal fluids ciculaion. These assumpions imply ha he geohemal sysem is coninuously supplied, which may no be ue a lage ime scale and duing ecessie poducion. The suface esuls ae undeesimaed compaed o he lieaue, bu he boom hole empeaue alues ae in a simila ange as hose obained hough modeling by Aelsson e al. 04. The diffeences of oupu esuls could be eplained by he seady sae fomulaion consideed. Indeed, he poducion of supeheaed apo duing flow esing may be seen as a ansien sae egading an iniial eseoi sae ecenly dilled. In addiion, numeous assumpions wee consideed bounday condiions, pue apo, ec.. These migh need eisiing and updaing wih poenial in-siu popeies. 5 CONCLUSION A CFD modeling sudy of a ey high enhalpy geohemal sysem including a simplified wellboe domain was pefomed. The hea ansfe and fluid flow of an ideal-gas fomulaion fo apo wee analyzed. The esuls show ha boh he D aisymmeic and he full 3D models geneae close esuls in he wellboe. Because of is highe compuaional efficiency, he aisymmeic model can be consideed suiable fo he well and he suoundings ocs, bu migh no be accuae enough in he eseoi aea. A decease of he mass flow ae poducion dies moe hea fom he eseoi, bu cools down fase when flowing up o he suface. The use of seady sae condiions wih a consan boom laye empeaue can assess a long-em powe poducion. CFD simulaions can be useful fo assessing new hea ecoey mehods in dedicaed enionmen wih an infinie souce of hea egading he suface faciliies lifeime. Howee, i has been shown in his sudy ha he wae ciculaion simulaed wih a consan mass flow wihin he poous media needs o be inesigaed fuhe. The numbe of assumpions should also be educed o geneae a moe obus model, poenially wih he inclusion of in-siu popeies. ACKNOWLEDGEMENT The financial suppo fom he UK Engineeing and Physical Sciences Reseach Council EPSRC is gaeful acnowledged. The auhos also acnowledge Tomasz Cieszewsi fo his inolemen in discussions elaed o his poec. APPENDIX Tempeaue K Specific Hea J/g.K Themal Conduciiy W/m.K Viscosiy g/m.s 43 K E K E K E K e K e K e K e K e K e K e K e K e K e K e-05 Appendi : Pue apo hemal popeies a 60 bas used in he piecewise linea funcion Wagne and Kezschma, 00 REFERENCES ANSYS Ansys Fluen Theoy Guide

7 7 Renaud e al. Anosson, S., Sefansson, A. and Banason, J. O. Fluid-Fluid Ineacions in Geohemal Sysems, Reiews in Minealogy and Geochemisy, 65, pp Aelsson, G., Egilson, T. and Sif Gyldadói, S. Modelling of empeaue condiions nea he boom of well IDDP- in Kafla, Noheas Iceland, Geohemics, 49, pp Beani, R. Geohemal powe geneaion in he wold updae epo, Geohemics, 4, pp Biowsi, T. H. Modeling Supeciical Sysems wih TOUGH: Peliminay Resuls Using he EOSSC Equaion of Sae, Tweny- Sih Woshop on Geohemal Reseoi Engineeing, pp Büsing, H., Niedeau, J. and Clause, C. Pessue-enhalpy fomulaion fo numeical simulaions of supeciical wae/seam sysems applied o a eseoi in Tuscany, Ialy, Euopean Geohemal Congess 06 Sasboug, Fance, pp Chen, J. and Jiang, F. Designing muli-well layou fo enhanced geohemal sysem o bee eploi ho dy oc geohemal enegy, Renewable Enegy, 74, pp Cheng, X., Kuang, B. and Yang, Y. H. Numeical analysis of hea ansfe in supeciical wae cooled flow channels, Nuclea Engineeing and Design, 37, pp Couche, A. E. and O Sullian, M. J. Applicaion of he compue code TOUGH o he simulaion of supeciical condiions in geohemal sysems, Geohemics, 37, pp DiPippo, R. Geohemal powe plans: Eoluion and pefomance assessmens, Geohemics, 53, pp Duan, C., Zheng, X., Xia, B. and Wang, Z. Tempeaue Disibuion Modeling in Geohemal Wellboe and Fomaion Duing he Well Tes in Yangyi Geohemal Field, Tibe, 4s Woshop on Geohemal Reseoi Engineeing, pp Eldes, W. A., Fiðleifsson, G. O. and Pálsson, B. Iceland Deep Dilling Poec : The fis well, IDDP-, dilled ino magma, Geohemics, 49, p Eldes, W. A., Fidleifsson, G. Ó., Zieenbeg, R. A., Pope, E. C., Moensen, A. K., Gudmundsson, Á., Lowensen, J. B., Mas, N. E., Owens, L., Bid, D. K., Reed, M., Olsen, N. J. and Schiffman, P. Oigin of a hyolie ha inuded a geohemal well while dilling a he Kafla olcano, Iceland, Geology, 393, pp Fiðleifsson, G. Ó., Eldes, W. A. and Albesson, A. The concep of he Iceland deep dilling poec, Geohemics, 49, pp Fuss, S., Szolgayoa, J., Obeseine, M. and Gusi, M. Inesmen unde mae and climae policy unceainy, Applied Enegy, 85, pp Hayba, D. O. and Ingebisen, S. E. The compue model HYDROTHERM a hee-dimensional finie-diffeence model o simulae Gound-Wae flow hea anspo in he empeaue ange of 0 o 00 C, Wae-Resouces Inesigaions Repo , p Huang, W., Cao, W. and Jiang, F. Hea eacion pefomance of EGS wih heeogeneous eseoi : A numeical ealuaion, Inenaional Jounal of Hea and Mass Tansfe, 08, pp Huang, X., Zhu, J. and Li, J. Analysis of Wellboe Hea Tansfe in Enhanced Geohemal Sysem using CFD Modeling, Wold Geohemal Congess 05, Apil, p a. Huang, X., Zhu, J. and Li, J. On Wellboe Hea Tansfe and Fluid Flow in he Double of Enhanced Geohemal Sysem, Enegy Pocedia, 75, pp b. Ingason, K., Kisánsson, V. and Einasson, K. Design and deelopmen of he dischage sysem of IDDP-, Geohemics, 49, pp Jiang, F., Luo, L. and Chen, J. A noel hee-dimensional ansien model fo subsuface hea echange in enhanced geohemal sysems, Inenaional Communicaions in Hea and Mass Tansfe, 4, pp Jiang, P., Zhang, L. and Xu, R. Epeimenal sudy of conecie hea ansfe of cabon dioide a supeciical pessues in a hoizonal oc facue and is applicaion o enhanced geohemal sysems, Applied Themal Engineeing, 7, pp Kissling, W. Eending MULKOM o supe-ciical empeaues and pessues, Poceedings of he Wold Geohemal Congess, 3, pp Lenhad, R. and Malcho, M. Numeical simulaion deice fo he anspo of geohemal hea wih foced ciculaion of media, Mahemaical and Compue Modelling, 57, pp Luo, F., Xu, R. N. and Jiang, P. X. Numeical inesigaion of fluid flow and hea ansfe in a double enhanced geohemal sysem wih CO as he woing fluid CO-EGS, Enegy, 64, pp Magnusdoi, L. and Finsele, S. An itough equaion-of-sae module fo modeling supeciical condiions in geohemal eseois, Geohemics, 57, pp Mene, F. R. Zonal wo equaion -ω ubulence models fo aeodynamic flows, AIAA 4h Fluid Dynamics Confeence,

8 Renaud e al. Moensen, A. K., Egilson, Þ., Gauason, B., Ánadói, S. and Guðmundsson, Á. Saigaphy, aleaion minealogy, pemeabiliy and empeaue condiions of well IDDP-, Kafla, NE-Iceland, Geohemics, 49, pp Pálsson, B., Hólmgeisson, S., Guðmundsson, Á., Bóasson, H. Á., Ingason, K., Seisson, H. and Thóhallsson, S. Dilling of he well IDDP-, Geohemics, 49, pp Pan, L., Feifeld, B., Doughy, C., Zaem, S., Sheu, M., Cuigh, B. and Teall, T. Fully coupled wellboe-eseoi modeling of geohemal hea eacion using CO as he woing fluid, Geohemics, 53, pp Piche, J. W. STAR : A geohemal eseoi simulaion sysem, Poceedings Wold Geohemal Congess Ialy, pp Sco, S., Diesne, T. and Weis, P. Geologic conols on supeciical geohemal esouces aboe magmaic inusions, Naue Communicaions. Naue Publishing Goup, 6, p a. Sco, S., Diesne, T. and Weis, P. Hydology of a Supeciical Flow Zone Nea a Magmaic Inusion in he IDDP- Well Insighs fom Numeical Modeling, Wold Geohemal Congess 05,, p b. Suaez Aiaga, M.-C. and Samaniego, F. Deep Geohemal Reseois wih Fluid a Supeciical Condiions, Tweny-seenh woshop on geohemal eseoi engineeing, Sanfod Uniesiy. 03. Thóhallsson, S., Pálsson, B., Hólmgeisson, S., Ingason, K. and Mahíasson, M. Well design fo he Iceland Deep Dilling Poec IDDP, Geohemics, 49, pp Vasini, E. M. Numeical modelling and simulaion opimizaion of geohemal eseois using he TOUGH family of codes, Thesis. 06. Wagne, W., Coope, J. R., Dimann, a., Kiima, J., Kezschma, H.-J., Kuse, a., Maeš, R., Oguchi, K., Sao, H., Söce, I., Šifne, O., Taaishi, Y., Tanishia, I., Tübenbach, J. and Willommen, T. The IAPWS Indusial Fomulaion 997 fo he Themodynamic Popeies of Wae and Seam, Jounal of Engineeing fo Gas Tubines and Powe,, p Wagne, W. and Kezschma, H.-J. D. Popeies of Wae and Seam. 00. Weis, P., Diesne, T., Coumou, D. and Geige, S. Hydohemal, muliphase conecion of HO-NaCl fluids fom ambien o magmaic empeaues: A new numeical scheme and benchmas fo code compaison, Geofluids, 43, pp