Pall Valdimaron Capter 8 PRODUCION OF ELECRICIY FROM A GEOHERMAL SOURCE Pall Valdimaron 9.. Energy and Power, Heat and Work e prodution of eletriity from a geotermal oure i about produing work from eat. Eletriity prodution from eat will never be ueful unle appropriate repet i paid to te eond law of termodynami. Energy i utilized in two form, a eat and a work. Work move bodie, ange teir form, but eat ange temperature (ange te moleular random kineti energy). Work i tu te ordered energy, werea eat i te random unorganized energy. Heat and work are totally different produt for a power tation, but tee two energy form an not be produed independent of ea oter. Independent prodution of eat and work i in a way imilar to ave attle produing tree ind leg per animal wen required. It i a well appropriate to diu te relation between power and energy rigt ere in te introdution to ti apter. A power tation i built to be able to upply ertain maximum power. e oure eat upply and te deign of te power plant internal are baed on ti maximum power. On te oter and te inome of te power tation will be depending on te energy old, on te integral of produed power wit repet to time. Geotermal intallation ave normally zero energy ot. e inflow into te well i not arged for. e only ot i te invetment ot in equipment and intallation to get te fluid to te urfae, and to proe it appropriately in te power plant in order to obtain te produt, be it eat for a diret ue appliation or an eletriity produing power plant. A a onequene of ti, a geotermal power plant i a typial bae load plant, te bulk portion of te ot i tere regardle of ow mu power te plant i produing. Duration urve and utilization time will be diued later in ti apter. 9.. Converion of Heat to Work Work an alway be anged into eat. Even during te Stone Age, work wa ued to ligt fire by frition, by rubbing wood tik to a ard urfae. e ame applie today, te eletri eater i onverting work into eat wit % effiieny. Converion of eat into work i diffiult and i limited by te law of termodynami. A part of te eat ued a alway to be rejeted to te urrounding, o tere i alway an up-per limit of te poible work prodution from a given eat tream. extbook ue te Reverible Heat Engine (RHE, Carnot engine) a a referene. RHE i te bet engine for produing work from eat, auming tat te engine i operating between two infinitely large eat reervoir. e referene to te Carnot engine a to be taken wit aution, a te real eat reervoir are uually not infinitely large, and te eat upply or rejetion will appen at a variable temperature. 5
Prodution of Eletriity from a Geotermal Soure Figure. Semati of a geotermal power plant 9.. Exergy e eond law of termodynami demand tat a part of te eat input to any eat engine i rejeted to te environment. e portion of te input eat, wi an be onverted into work i alled Exergy (availability, onvertible energy). e unonvertible portion i alled Anergy. u te exergy of any ytem or flow tream i equal to te maximum work (or eletriity) wi an be produed from te oure. e termodynami definition of exergy for a flow tream i: x ( ) e zero index refer to te environmental ondition for te ubjet onverion. e loal environment for te power plant define te available old eat reervoir, and all te anergy rejeted tot te environment will finally be at te environmental ondition. e exergy of a flow tream i tu te maximum teoretial work wi an be produed if te tream i ubjeted to a proe bringing it down to te environmental ondition. If te tream i a liquid wit ontant eat apaity, te above equation an be written a: x liquid ( ) Eonomi of power prodution aredonveniently analyzed by uing exergy. A power plant a te main purpoe of onverting eat into work, and terefore te relevant pyial variable for ot and eonomi performane alulation i te exergy rater tan te total energy or te eat flow. Figure. e Carnot engine 5
Pall Valdimaron Produed power Heat to powerplant Heat from well Heat re-injeted Heat from generation Fig.. Energy tream in a binary power plant 9.. Effiieny definition Effiieny i te ratio of input to output, a performane meaure for te proe. ere are many poibilitie of defining input and output, but te mot tandard definition of effiieny i te power plant termal effiieny. e following emati ow te energy tream for a binary power plant. e termal effiieny i een a te ra-tio of produed power to te eat tranferred to te power plant. e effetivene i te ratio of te eat tranferred to te power plant to te eat available from te well. It i obviou tat te total power plant effiieny will be te multiple of power plant effiieny and effetivene. 9... Power plant termal effiieny e power plant termal effiieny i te ratio between power produed and te eat flow to te power plant. e power plant termal effiieny i traditionally defined a: t «W «in e eat input i ten te eat input to te power plant, and take no notie of ow mu eat i available from te well. i an be very mileading. e well make up a great portion of te power plant ot, and te eonomi of te power plant will be deided by te utlization of te well invetment. e Carnot effiieny i a well mileading, it i baed on te aumption tat te termal reervoir are infinitely large, no ooling will our in te ot reervoir by eat removal, and no eating will be in te old reervoir by eat addition. erefore te only relevant performane meaure will ave to be baed on te exergeti effiieny, and due to te importane of te well invetment, te effetivene a well. Calulating effiieny baed on te firt law for a ogeneration power plant i in no way eay, beaue te plant a two produt, eat and work. e firt law doe not provide any equivalene between eat and work, or te value of tee produt. A ogeneration plant will only be analyzed properly by exergeti analyi. If te power plant effetivene i ig, te geotermal fluid return temperature i low, and te average temperature of te eat input to te power plant i low. i will lead to lower effiieny, but larger power plant. If te well flow i given, ten ig effetivene will lead to a plant wit iger power, but lower firt law effiieny. 5
Prodution of Eletriity from a Geotermal Soure, [ C] W rev 57 [kw] m 5 [kg/] t,rev,7 [%] in 57 [kw], 8 [ C] out 959 [kw], [ C], [ C] Fig.. A low effetivene ideal power plant 9... Example Aume tat an ideal power wit % ientropi effiieny plant a a oure of C and 5 kg/ flow. e ooling water i aumed to enter te power plant at C and leave te plant at C. Let aume tat te firt ideal power plant i able to ool te geotermal fluid down to 8 C. e obtained power i 5.7 MW, effiieny i.7%. Wat will appen if te effetivene i doubled, and te geotermal return water temperature i brougt down to C? e effiieny fall down to 8.%, but te output power i inreaed to 9. MW. It i very obviou tat te power plant wit lower effiieny, but iger effetivene i more powerful and will be more eonomi, at leat if te tenial deign limitation do not urt too badly. e general relation between output power and effiieny for ti example are given in te following diagram., [ C] m 5 [kg/] t,rev 8,9 [%] W rev 95 [kw] in 5 [kw], [ C] out 5 [kw], [ C], [ C] Fig.5. A ig effetivene ideal power plant 5
Pall Valdimaron 9 8 5 5 55 6 65 7 75 8 85 Fig.6. Relation between output power and effiieny 9... Effetivene e power plant effetivene i te ratio between te available energy to te energy input to te power plant. e available energy i found by auming tat te geotermal fluid an be ooled down to te environmental ondition. Effetivene will be te deiding fator for te poible power plant ize, rater tan te quality of te power plant. 9... Seond law effiieny and effetivene Exergy i te portion of te energy wi an teoretially be onverted into work. It i logial to bae perfomane riteria for prodution of eletriity on exergy rater tan eat or energy, beaue ten te performane alulation will take into aount wat an be done, and not inorporate any perpetuum mobile in te alulation. e eond law approa make a well eay to treat ogeneration. en te exergy tream in te old eat i treated in te ame way a te produed eletrial power, aving te ame exergy unitary ot. 9... Analyi Effiieny i te ratio of benefit to ot. In order to be able to define an effiieny, te input (ot) and output ave to be defined. In a low temperature eat onverion proe, two ae regarding te tream m are poible, depending on if te eat ontained in tat tream an be old to a eat onuming proe. e onverion effiieny i a meaure of ow mu of te available eat i onverted into work. It a to be kept in mind tat only a part of te eat an be onverted into work due to te limitation impoed by te eond law of termodynami. Exergy, te potential of any ytem to produe work, i te orret property to onider, wen te onverion effiieny i analyzed. Exergy i dependent of te propertie of te oure a well a te propertie of te environment, were te environmental temperature and preure are te main propertie. e temperature of te entering ooling fluid i taken to be te environmental temperature, te lowet temperature wi an be obtained, a well a defining te termal ink temperature for te Carnot engine effiieny. e environmental preure i logially te ambient atmoperi preure. i proe an be een a a nononerving eat exange proe between te oure tream and te ooling fluid tream. Figure. i a blok diagram for a non-onerving eat exanger repreenting a power plant. Figure 7 i a blok diagram of a power plant onverting eat into eletriity. e variable related to te onverion are a follow: 5
Prodution of Eletriity from a Geotermal Soure e variable related to te onver-ion are a follow: Soure fluid eat apaity m Flow rate of oure fluid Soure fluid inlet temperature Soure fluid outlet temperature Cooling fluid eat apaity m Cooling fluid flow rate Cooling fluid outlet temperature Cooling fluid inlet temperature (Environmental temperature) In te following ti ytem will be analyzed in order to gain a better undertanding of te onverion of low temperature eat into eletriity. It i aumed tat te geotermal oure fluid i liquid water wit ontant eat apaity. e tream in and out of te y-tem ave four flow propertie: ma, eat apaity, entalpy and exergy. e ma onervation i obviou, no mixing of te oure Figure 7. Eletrial power plant emati m ( ) and ooling tream i aumed. e eat apaity i important for te arateriti of te eat onverion, and will be treated ere a a eat apaity flow, te produt of fluid eat apaity and flow rate. e produt of te entalpy relative to te environmental temperature and te flow rate define te eat flow in and out of te ytem. e exergy will give information on te work produing potential of te ytem, and i alulated in te ame way a te entalpy. Referene textbook u a Cengel () give bai information on exergy and it definition, but ere te analyi i a well baed on Kota (985) and Szargut (988). órólfon (), Valdimaron () and Dorj (5) apply tee metod on peifi geotermal appliation. e eat ( ) and exergy (X ) flow are given by: (.) m ( ) (.) m ( ) (.) 55
Prodution of Eletriity from a Geotermal Soure 56 ( ) m m X (.) ( ) m m X (.5) ( ) m m X (.6) e energy (. law) and exergy (. law) balane are: W (.7) rev W X X X or rev W m m + (.8) e energy balane i valid for all proee, ideal and real. e exergy balane give only information on te reverible work, or te larget amount of work tat an be obtained from te power plant. If te power plant i ideal, ten: + m m or W W rev (.9) en te eat apaity flow ratio for a reverible power plant i: m m C rev rev (.) Aume tat eletriity i te only output of te power plant. e eat ontained in te tream m i rejeted to te urrounding. and W Rejeted: : Input : Produt
Prodution of Eletriity from a Geotermal Soure 57 Firt law effiieny: ( ) ( ), C W E I (.) Firt law maximum effiieny: rev E I m m X X X W + +,max, ( ) ( ) ( ) ( ) C ( ) ( ) ( ) (.) Seond law effiieny: +, m m X X X W W rev E II ( ) ( ) ( ) ( ) C C (.) 9.5. ermoeonomi ermoeonomi analyze te power generation eonomi from te exergeti viewpoint. A toroug treatment of termoeonomi i found in Bejan et al (996) and El-Sayed (). Exergy lo due to irreveribilitie will our in all omponent. i i te oalled exergy detrution, and te tream i termed exergy detrution tream for te ubjet omponent. In ome omponent tere will be a rejeted exergy tream, wi i of no furter ue in te proe. i i te exergy lo, and exergy lo tream for te ubjet omponent. Anergy i aumed to ave no value, a well a all exergy lo tream and detrution tream. e unitary exergy ot i alulated for ea point in te energy on-
Prodution of Eletriity from a Geotermal Soure verion proe, and ot tream are ued to gain an overview over te eonomi of Fig.8. Cot flow for a power plant omponent te power generation proe. Ea omponent will ave tree type of ot flow aoiated, te input exergy ot flow, te omponent invetment ot flow, and te produt exergy ot flow. A ot balane, equating te produt ot flow (all aving te ame unitary exergy ot) to te um of te input exergy ot flow and te omponent invetment ot flow. A emati ow ti relationip better. ermoeonomi optimization will not be treated furter ere, but ti diipline a very powerful tool, enabling te deigner to keep onitent eonomi quality in all omponent in te power prodution ain. 9.6. e Power Cain from Well to Eletriity Geotermal power prodution i imply a ain of omponent or proee from te inflow into te well all te way over to te power plant tranformer tation. e objetive i to onvert a mu of te exergy found in te well inflow to ellable power, eletriity or eat. And a typial wit any ain, it will never be tronger tan te weaket link. e power plant old end and te aoiated ooling fluid upply i a part of ti ain. In order to define a power plant for a ertain ituation, around 5- deign parameter ave to be eleted. e optimization proe a terefore a uge number of degree of freedom, and tere are not many general univerally uable olution available, wi an give atifatory performane. ere i no way around a areful deign and eletion of all tee deign parameter. 9.7. Geotermal Field and Well e well i one of te mot expenive part of te power prodution ytem. e well will ave prodution dependent on te wellead preure. e maximum flow will our wit wellead preure zero, and zero flow will yield te well loure preure, wi i again te maximum wellead preure. e well arateriti urve will be a deiding fator in te eletion of te eparator preure in te fla plant for 58
Prodution of Eletriity from a Geotermal Soure iger entalpy field. Lower eparator preure, iger well flow, iger team ratio from te eparator, but lower quality team. e lower te wellead preure, te lower in te well te boiling of te fluid will tart, and finally boiling will our in te formation, uually wit orrible reult. Saling may our in te formation, detroying te well. e field entalpy i a mayor riterion for te power plant deign, and will more or le determine wi power plant type an be ued. e fluid emitry i anoter deiive fator. Saling beaviour of te fluid uually demand a ertain minimum geotermal fluid temperature to be eld trougout te entire power plant. Corroion may require ertain material or te ue of additive. Non-ondenible ga in te fluid may require ga extration ytem wit te aoiated paraiti lo. erefore te power plant deigner i bound by te fluid entalpy and emitry for i eletion of te deign parameter. o diregard te omment of te geoemit i a ure way to failure. From te viewpoint of termoeonomi, te inflow to te well i free of arge, but wen te fluid a reaed te urfae te exergy tream from te well a to arry te field development, drilling and well ontrution invetment ot., 9.7.. Example of ot alulation Aume tat te field development and well ot amount to 5 for ea well. wo prodution well are drilled and one re-injetion well. e well prodution i 5 kg/, and te well i low entalpy, produing only liquid water. e environment i taken at C, bar preure. Yearly apital ot and operation and maintenane are taken a % of invetment. Utilization time i aumed 8 our per year. Under tee aumption te well exergy flow an be alulated a well a te unitary exergy ot. ee reult ow, tat a ubtantial part of te final ot of eletriity i already defined by te well. If we ould buy an ideal lole power plant at zero prie, ti would be te final ot of eletriity. 9.8. Power Plant ype e geotermal power plant an be divided into two main group, team yle and binary yle. ypially te team yle are ued at iger well entalpie, and binary yle for lower entalpie. e team yle allow te fluid to boil, and ten te team i eparated from te brine and expanded in a turbine. Uually te brine i rejeted to te environment (re-injeted), or it i flaed again at a lower preure. Here te Single Fla (SF) and Double Fla (DF) yle will be preented.,,8,6,,,,8,6 5 6 7 8 9 Fig.9 Unitary well exergy ot 59
Pall Valdimaron A binary yle ue a eondary working fluid in a loed power gene-ration yle. A eat exanger i ued to tranfer eat from te geotermal flu-id to te working fluid, and te ooled brine i ten rejeted to te environment or re-injeted. e Organi Rankine Cyle (ORC) and Kalina yle will be preented. 9.8.. Single fla Following i a flow eet for te SF yle. e geotermal fluid enter te well at te oure inlet temperature, tation. Due to te well preure lo te fluid a tarted to boil at tation, wen it enter te eparator. e brine from te eparator i at tation, and i re-injeted at tation, te geotermal fluid return ondition. e team from te eparator i at tation 5, were te team enter te turbine. e team i ten expanded troug te turbine down to tation 6, were te ondener preure prevail. e ondener own ere i air ooled, wit te ooling air entering te ondener at tation and leaving at tation. e ondener ot well i at tation 7. e fluid i re-injeted at tation. ypially, u a proe i diplayed on a termodynami - diagram, were te te temperature in te yle i plotted againt te entropy. e ondition at tation i uually ompreed liquid. In vapour dominated field, u a Lardarello in Italy, te inflow i in te wet region loe to te vapour aturation line. 9.8.. Double fla Following i a flow eet for te DF yle. e geotermal fluid enter te well at te oure inlet temperature, tation. Due to te well preure lo te fluid a tarted to boil at tation, wen it enter te eparator. e brine from te eparator i at tation, and i trottled down to a lower preure level at tation 8. e partly boiled brine i ten led to a low preure eparator, were te team i led to te turbine at 5 urbine Separator Prodution well 6 Condener 7 Re-injetion pump Condener pump Fig.. Single fla yle emati 6
Pall Valdimaron 5 5 75 5 5 75 bar 5 5 5 bar 5 bar 75 7 5, bar 5,,,6,8 6,,,,, 5, 6, 7, 8, 9,, Fig.. - diagram of a ingle fla yle 5 5 75 5 5 5 6 75 bar 5 5 bar 5 5 bar 7 75 7 5 k J/ k g- K, bar 5,,,6,8 6 5 5 75 5 5 75 5 5 75 Fig.. - diagram of a ingle fla yle were te team i led to te turbine at tation 9. e turbine i deigned in u a way, tat te preure differene over te firt tage i te ame a te pre-ure differene between te ig and low preure eparator. e ma flow in te lower preure tage of te turbine i ten 6
Prodution of Eletriity from a Geotermal Soure iger tan in te ig preure tage, jut te oppoite of wat appen in a traditional fuel fired power plant wit a bleed for te feed-water eater from te turbine. e brine from te low preure eparator i at tation, and i ten reinjeted at tation, te geotermal fluid return ondition. e team from te ig preure eparator i at tation 5, were te team enter te turbine. e low preure team enter te turbine a few tage later, at tation 9. e team i ten expanded troug te turbine down to tation 6, were te ondener preure prevail. e ondener own ere i air ooled, wit te ooling air entering te ondener at tation and leaving at tation. e ondener ot well i at tation 7. e fluid i re-injeted at tation. 9.8.. Organi Rankine Cyle Following i a flow eet for te ORC yle. e geotermal fluid enter te well at te oure inlet temperature, tation. e fluid i frequently liquid water. If te preure i kept uffiiently ig, no non-ondenible gae will be eparated from te liquid, and a ga extration ytem i not neeary. e fluid i ten ooled down in te vaporizer, and ent to reinjetion at tation. Pre-eated (in te regenerator) ORC fluid enter te vaporizer at tation. e fluid i eated to aturation in te vaporizer, or even wit upereat in ome ae. e vapour leave te vaporizer at tation, and enter te turbine. e exit vapour from te turbine en-ter te regenerator at tation, were te upereat in te team an be ued to preeat te ondened fluid prior to vaporizer entry. e now ooled vapour enter te ondener at tation 5, were it i ondened down to aturated liquid at tation 6. Hig preure eparator 5 urbine Condener Prodution well 9 6 rottling valve 8 Low preure eparator 7 Re-injetion pump Condener pump Fig.. Double fla yle emati 6
Prodution of Eletriity from a Geotermal Soure e next Figure preent te double fla yle on a - diagram. 5 5 75 5 5 75 5 5 75 5 8 bar, bar bar 5 bar 5 7,,,6,8 6,,,,, 5, 6, 7, 8, 9,, 5 9 Fig.. - diagram of a double fla yle 5 Water 5 75 5 5 75 5 5 75 5 5 5 5 bar 6 5 bar 8 bar k J/ k g- K 7, bar 9 7,,,6,8 6 5 5 75 5 5 75 5 5 75 Fig.5. - diagram of a double fla yle 6
Pall Valdimaron urbine Vaporizer Regenerator 5 Cirulation pump 6 Air-ooled ondener Fig.6. Flow diagram for an ORC yle wit regeneration 75 5 5 5 bar 5 bar 75 5 bar 5 5 6 bar 5,,,6,8 -,8 -,5 -, -,9 -,6 -,, Fig.7. - diagram of an ORC yle wit regeneration 6
Prodution of Eletriity from a Geotermal Soure 75 5 5 5 bar 5 bar 75 5 bar 5 5 6 bar 5,,,6,8 - - - - Fig.8. - diagram of an ORC yle wit regeneration A irulation pump raie te preure from te ondener preure up to te ig preure level in tation. ere te fluid enter te regenerator for pre-eat before vaporizer entry. e ondener own ere i air ooled, wit te ooling air entering te ondener at tation and leaving at tation. 9.8.. Regeneration Regeneration will inreae te power plant effiieny. en a part of te rejeted eat i reovered for input to te power plant. If te plant were run on fuel, ti would lead to diret fuel aving. i i not te ae in geotermal power prodution. ere te well ave ertain maximum flow rate, and te well ot i uually entirely fixed, a very little if any relation to te flow from te well. e more te fluid from te well an be ooled, te more eat an be input to te power plant. Regeneration inreae te temperature of te working fluid at te vaporizer entry, and lead tu to iger geotermal fluid exit temperature from te vaporizer. e eat removal from te geotermal fluid i tu partly replaed by te reovered eat. ere i frequently a lower temperature limit on te geotermal fluid temperature. i limit may be impoed by emitry (danger of aling) or te requirement of a eondary proe, u a ditrit eating. If ti i te ae, regeneration an elp. e following diagram i a alu-lation of an iopentane ORC yle, wit geotermal fluid temperature of C. It i aumed tat te well flow i kg/, ondenation temperature i C. ree urve are alulated, no regeneration at all, if 5% of te eat available i ued for regeneration and finally if all te available eat i ued. e available eat i te eat wi an be removed from te turbine exit vapour until te vapour reae dew point. After tat te vapour temperature i te ame a te ondenation temperature and no regeneration an our. Note tat te following alulation reult are baed on an ideal ORC yle. It an be een from te diagram, tat te point of iget power i moved upward by a C by te effet of te regeneration. Regeneration an tu keep 65
Pall Valdimaron 5 95 9 85 8 % regeneration 75 5% regeneration No regeneration 7 5 6 7 8 9 Fig.9. Power obtained from kg/ of C geotermal fluid (ideal yle) te maximum power for geotermal fluid temperature from a 65 C to a 85 C. It a to be kept in mind tat a regenerator will be large and expenive, a well a auing preure drop and aoiated loe. A yle witout regeneration will be more eonomial, if te geotermal fluid doe not ave any temperature limitation. Regeneration will not, repeat not, inreae te produed power, even if it inreae te effiieny. e inreae of effiieny reult only from le input of eat from te geotermal fluid. And ti eat i normally free of arge. e termal effiieny inreae wen te geotermal return temperature inreae. i i in aordane wit te eond law of termodynami, a te average input temperature of te eat inreae, and tereby te effiieny.,6,,,,8,6, % regeneration 5% regeneration No regeneration, 5 6 7 8 9 Fig,. ermal power plant effiieny (ideal yle) 66
Pall Valdimaron,95,9,85,8,75,7,65,6,55 5 6 7 8 9 Geoterm al fluid return tem perature [ C] Fig.. Power plant effetivene (ideal yle),65,6,55,5,5,,5,,5 % regeneration 5% regeneration No regeneration, 5 6 7 8 9 Fig.. ermal power plant total effiieny (ideal yle) e power plant effetivene i independent of te regeneration ratio, if te effetivene i drawn a a funtion of te geotermal return temperature. And obviouly ti i a linear relation of te return temperature. e total effiieny i found by multiplying te termal effiieny by te effettivene, and logially ti i te ame et of urve a te urve for te power obtained from te geotermal flow at te very beginning. e onluion i imply tat regeneration erve only to move te iget power prodution toward iger geotermal return temperature. 67
Pall Valdimaron 5 5 75 Lat droplet Dew urve 5 5 Bubble urve Firt bubble 75 5,,,6,8 Fig.. Ammonia-water pae diagram at bar preure 9 8 7 6 5,,,6,8 Fig.. Ammonia-water boiling range at bar preure 68
Prodution of Eletriity from a Geotermal Soure e entalpy of vaporization i a well dependent on te ammonia onentration. 8 6,,,6,8 Fig.5. Ammonia-water entalpy of vaporization at bar preure A final note i tat a real yle will ow lower effiieny for iger regeneration, o regeneration will alway redue te maximum power available from a given geotermal flow tream. Regeneration will a well inreae te plant ot, and a tu to be een a a meaure to preerve power, if a eondary proe or geotermal fluid emitry limit te return fluid temperature. 9.8.5. Kalina e Kalina yle i patented by te inventor, Mr Alexander Kalina. ere are quite a few variation of te yle. e Kalina power generation yle i a modified Clauiu-Rankine yle. e yle i uing a mixture of ammonia and water a a working fluid. e benefit of ti mixture i mainly tat bot vaporization and ondenation of te mixture appen at a variable temperature. ere i no imple boiling or ondenation temperature, rater a boiling temperature range a well a ondenation range. i i due to te fat, tat te pae ange proe i a ombined proe, bot te pae ange of te ubtane and aborption/eparation of ammonia from water. 9.8.5.. e fluid A pae diagram for ammonia water mixture at bar preure i own on te following diagram. e lower urve i te o-alled bubble urve, wen te firt vapour bubble i reated. i bubble a iger ammonia ontent tan te boiling liquid. A te bubble ammonia ontent i iger tan tat of te liquid, te ammonia ontent in te liquid pae will be redued. e upper urve i te o-alled dew urve, wen te lat liquid drop evaporate. i drop a oniderably lower ammonia ontent tan te vapour. e boiling proe for 5% mixture i indiated on te diagram e temperature range for te boiling of te mixture at bar i own on te next figure. e temperature range from bubble to dew i larget at approximately 67% ammonia onentration, and i ten loe to 95 C. 69
Pall Valdimaron Fig.7. Fig.8. 7
Prodution of Eletriity from a Geotermal Soure Fig.9. e mixture a tu a finite eat apaity, wi i benefiial if te eat oure i a liquid wit ontant or loe to ontant eat apaity. Ammonia-water mixture i tenially well known and widely ued a a working fluid. Ammonia-water mixture ave been ued in aborption refrigeration ytem for deade. And ammonia i no newomer to te tenial field, it a been ued in emial and refrigeration proee for very long time. Ammonia i toxi, but te afeguard are well etablied. Following are temperature entalpy diagram for te mixture, at 5%, 75% and 95% ammonia onentration. e ange in te urve form for boiling at ontant preure i to be noted. For low ammonia onentration, te larget temperature inreae i at te beginning of te boiling, for ig onentration at te end of te boiling. Intermediate onentration a S-for-med boiling urve, and i terefore bet uitable for power generation. 9.8.5.. e yle Following i a flow eet for te Kalina aturated yle. e yle i aturated beaue tere i no upereat in te yle. e fluid i not boiled entirely in te vaporizer, and te vapour-liquid mixture i ten eparated afterward. i i done in order to maximie te vapour temperature at te vaporizer outlet. e geotermal fluid enter te well at te oure inlet temperature, tation. e fluid i frequently liquid water. If te preure i kept uffiiently ig, no nonondenible gae will be eparated from te liquid, and a ga extration ytem i not neeary. e fluid i ten ooled down in te vaporizer, and ent to re-injetion at tation. Pre-eated (in te regenerator) li-quid ammonia-water mixture enter te vaporizer at tation. e fluid i boiled partly in te vaporizer. e liquid-vapour mixture leave te vaporizer at tation, and enter te eparator. 7
Pall Valdimaron Separator 5 urbine 7 Hig temperature regenerator 6 8 Vaporizer 9 Low temperature regenerator Condener Cirulation pump Fig.. Flow diagram of a aturated Kalina yle e eparated liquid leave te eparator and enter te ig temperature regenerator at tation 7. After te ig temperature regenerator te liquid i trottled down to te ondener preure in tation 8, and mixed wit te turbine exit vapour from tation 6. e ammonia-ri vapour enter te turbine at tation 5, and i expanded to te ondener preure at tation 6. e exit vapour mixed wit te trottled liquid (now at te average ammonia onentration) from te ig temperature regenerator enter te low temperature regenerator at tation 9. e ooled fluid from te low temperature regenerator enter te ondener at tation. e fluid ga now tarted to ondene, and te ammonia onentration i not te ame in liquid or vapour pae. An aborption proe i going on, were te ammonia ri vapour i aborbed into te leaner liquid, in addition to ondenation due to lowering of te mixture temperature. e kineti of te aborption proe determine te rate of aborption, werea eat tranfer and eat apaity ontrol te ondenation proe. Finally all te mixture i in aturated liquid pae in te ot well of te ondener at tation. e irulation pump raie te fluid preure up to te iger ytem pre-ure level, and te liquid i ten pre-eated in te regenerator in tation troug. e ondener own ere i water ooled, wit te ooling water entering te ondener at tation and leaving at tation. 9.8.5.. External eat exange A mixture of ammonia and water will not boil leanly, but a well ange te emial ompoition. e vapour will be more ammonia ri, werea te liquid will be leaner for te partially boiled mixture. 7
Prodution of Eletriity from a Geotermal Soure Geotermal oure fluid 8% A W mixture 8 6 Iopentane 6 8 Fig.. Heat exanger diagram for a vaporizer in a binary power plant x i at geotermal fluid entry, and x at te outlet. i an be een from te pae diagram of ammonia water mixture preented earlier. Similar variation of te emial ompoition will be enountered in te ondener for te partially ondened mixture. i reult in a variable temperature during te eat exange proe bot in te vaporizer and te ondener. Following i a eat ex-anger diagram for a vaporizer, were typial urve ave been drawn bot for iopentane and 8% ammonia water mixture. e temperature differene between te primary and te eondary fluid in te Kalina vaporizer i mall ompared for te iopentane vaporizer, even for imilar or ame pin temperature differene. Entropy i genera-ted wenever eat i tranferred over a finite temperature differene, tu i te entropy generation in te Kalina vaporizer le, and tereby te detrution of exergy le. On te oter and te Kalina vaporizer will need larger eat exange area due to te maller temperature differene. And te diagram ow well tat te logaritmi temperature differene approa for te izing annot be ued, a te fluid eat apaity i far from being ontant. A imilar ituation i in te ondener. ere ammonia ri vapour i aborbed and ondened, wit te aoiated ange in emial ompoition of bot liquid and vapour. Following i a eat exanger diagram of bot iopentane and ammonia water mixture in a water ooled ondener. Bot fluid will ave te pin point internally in te ondener, and te am-monia water mixture will even ave te pin at an unknown point. e iopentane will obviouly ave te pin at te fluid dew point, but it annot be known beforeand at wi vapor ratio te pin for te ammonia water mixture will be. 9.8.6. Kalex / New Kalina A novel yle a been invented by Mr Kalina, uing ammonia water mixture a well. Information on ti yle i pare, and no ommerial appliation i preently known. It eem tat Mr Kalina i employing more preure tage in te new yle, reulting in tat te mixture onentration in te yle an be better optimized. at 7
Pall Valdimaron 8 7 Iopentane 6 5 8% A W mixture Condener ooling water 6 8 Fig.. Heat exanger diagram for a ondener in a binary power plant x i at ooling water entry, and x at te outlet. w w w 5 w w5 w6 6 7 8 Fig.. A ingle fla bak preure yle ombined wit an ORC yle mean a well tat tere are more onentration variation in te yle. ime will ow if te inreaed omplexity of ti yle prove to be wort te laimed inreae in effiieny. 9.8.7. Combined yle e yle treated previouly are fre- quently ombined. A binary yle i ten ued a a bottoming yle to a fla yle, inreaing te total plant effiieny at te ot of omplexity. e fla yle a te benefit of low invetment, and te binary bottoming yle erve ten to inreae te effiieny for ubtantially inreaed invetment ot. 7
Pall Valdimaron Sample of two u ombination are own below. w w 5 w w 6 w6 w5 7 8 Fig.5. A ingle fla ondening yle ombined wit an ORC yle 9.8.8. Cyle omparion e fla team yle require ig entalpy of te geotermal fluid to be feaible. e fluid i eparated, wi an lead to emial problem wit te brine, wen te mineral onentration inreae due to te flaing. All non-ondenible ga releaed from te fluid in te flaing proe will ave to be removed from te ondener (if preent) and dipoed of in an environmentally ound way. i a limited te ue of fla yle to te ig temperature geotermal field in parely populated area. e binary yle ave te benefit of aving eat exange only wit te geotermal fluid. e geotermal fluid an ten be kept under uffiiently ig preure during te eat exange proe to avoid boiling and releae of non-ondenible gae. e fluid an ten be re-injeted bak into te reervoir, ontaining all mineral and diolved gae. By appropriate eletion of working fluid, te geotermal fluid an be eonomially ooled furter down ten wat i poible wit te fla yle. i will inreae te power plant effetivene at te ot of effiieny, a previouly aid. But at te end an optimum value for te plant return temperature of te geotermal fluid emerge, and ti temperature will give te iget power plant output for a given flow tream from te well. e binary yle ave te diadvantage of aving a eondary working fluid, often expenive, toxi and flammable. i lead to expenive afety meaure required for te power plant. Wen te geotermal fluid temperature i medium to low, te ORC yle beome more eonomial tan te fla yle. If te fluid temperature i below ay 8 C it i likely tat an ORC yle will be more eonomial tan a fla yle. i i a well valid for iger temperature if te ga ontent in te fluid i ig. 75
Pall Valdimaron e ORC yle give normally ig power plant effetivene. e yle an be modified by adjuting te level of regeneration to uit te eondary proe requi- rement (u a bottoming ditrit eating ytem) or emial limitation regarding te plant geotermal fluid return temperature. Wen regeneration i ued, te plant effiieny inreae and te plant effettivene i redued, a diued before. Anoter advantage of te ORC yle i tat it an be eaily adapted to fluid wit partial team. e ontant vaporizer boiling temperature a ten to fit wit te ondenation temperature of te partial team in te geotermal fluid. Wen te geotermal fluid temperature get lower tan ay 5-6 te Kalina yle eem normally to be uperior to te ORC yle. Kalina i better fit for ituation were te geotermal fluid i only liquid water, due to te variable temperature of te vaporizer boiling and eparation proe in te ammonia water mixture. Oter tenial differene between tee two binary yle are tat te preure level of te Kalina yle are iger tan for a orreponding ORC yle. e turbine ot in te ORC yle i tu iger, due to ig volume flow in te turbine at lower preure. On te oter and, ten all equipment in te Kalina yle will ave a iger preure la tan in te ORC yle. e piping dimenion will be larger in te ORC yle due to iger volume flow. ere doe not eem to be any major differene in requirement of te piping/ equipment material for tee two yle, wit te exeption of te turbine. urbine orroion a been enountered in te Kalina yle, leading to te ue of titanium a material for te turbine rotor. Fluid afety meaure are imilar, a te ORC yle ue ommonly flammable working fluid. e preaution needed due to te flammability eem to be at te ame order of magnitude a te requirement due to te toxiity of ammonia. e tenial omplexity of te two yle i at te ame order of magnitude. e omplexity i igly dependent on te level of regeneration ued in te yle, and terefore a omparion of te yle omplexity a to be made wit aution. Obviouly a non-regenerated ORC yle i a lot le omplex tan a igly regenerated Kalina yle wit two temperature level of regeneration. But ti i not a fair omparion. At te time of writing ti text, te only geotermal Kalina plant i at Huavik, Ieland. A eond plant i being built at Unteraing in Bavaria, Germany. Preently te limited ue of te Kalina yle may be it bigget diadvantage, but ti will mot probably ange during te oming year. ORC yle are widepread and ave been in ue for deade. 9.9. Power Plant Component i apter treat te main equation and ort diuion of te main power plant omponent. e mot relevant item related to geotermal engineering are a well diued ortly. 9.9.. Well and eparator A implified model of te well and eparator i preented below. Station i te unditurbed geotermal reervoir. 76
Prodution of Eletriity from a Geotermal Soure e main termal parameter for te reervoir wit regard to te power plant deign i te field entalpy, or energy ontent of te fluid. Station i te entry of te team water eparator, tation i te team outlet from te eparator and tation i te brine outlet of te eparator. e well ave ertain produtivity, i.e. tere i a relation between te wellead preure and te flow from te well. e produtivity i individual from well to well, and ti relation i furter ompliated by te fat tet te well may not be arteian, tat i a well pump i required to arvet fluid from te well. Generally ti relation an be preented a: m f ( ) p were te funtion take te preene of a well pump into aount, a well te field arateriti. e flow up te well and in te geotermal primary ytem an uually be treated a ientalpi, te i tat te eat lo in te well and te piping i negleted. No fluid lo i aumed, leading to: m m e trottling in te well and primary ytem reult mot frequently in tat te fluid tart to boil, wi reult in tat te temperature i a diret funtion of te eparator preure (Station ). If te well i non-arteian and a well pump i ued, te preure may be kep uffiiently ig to avoid boiling, in wi ae a eparator i Fig.6. not needed at all and te oure fluid i liquid in te ub-ooled region at all time. If boiling our and a eparator i employed, te relation between temperature and preure i: ( ) at p defined by te termodynami proper-tie of team and water. e team fration i ten defined by te energy balane over te epa-rator. e eat flow in te inoming mix-ture of team and water (from te well) equal te um of te energy flow in te team and te brine from te eparator. e ma flow of team from te eparator will tu be: m m e eparator i working in te (termodynami) wet area, ontaining a mixture of eam and water in equi-librium. All temperature in te epara-tor will tu be equal, auming tat tere are no ignifiant preure loe or preure differene witin te eparator. ( ) at p e entalpy of te team outgoing tream from te eparator i tu te entalpy of aturated team at te eparator preure. ( ) g p Ma balane old over te eparator, te um of team ma flow and brine ma flow equal te ma flow of te mixture from te well toward te eparator. m mm 77
Pall Valdimaron e eletion of eparator preure i very ritial for te power plant. If te wellead preure i low, boiling may our in te formation around te well, wi may lead to aling witin te rak and narrow flow paage in te formation. i will lead to ort well life. Higer eparator preure mean tat better team i available for te turbine (iger entalpy), but te amount will be le, ditated by te eparator energy balane a well a le well produtivity due to iger wellead preure. i may a well influene te eparation of nonondenible gae from te geotermal fluid. e eletion of te eparator preure i tu an optimization proe, eonomial, termodynami and geotermal. 9.9.. Vaporizer e vaporizer i te firt omponent of an ORC or a Kalina power plant. Station i te entry of te geotermal fluid to te vaporizer, and tation i te outlet. Station i te entry of te power plant working fluid (liquid) to te vaporizer, and tation i te outlet of te working fluid vapour or mixture toward te turbine. e fluid ondition at tation i determined by te yle and te turbine requirement, for an ORC yle ti would be aturated or ligtly uper-eated, for mot Kalina yle it would be in te wet region, wit vapor fration at 5-%. e vaporizer i noting but a eat exanger between te ot oure fluid and te old working fluid of te yle. It a to be oberved tat te temperature of te ot fluid i iger tan te one of te old fluid trougout te vaporizer. A well it mut be kept in mind tat te relation between te entalpy and te temperature i igly nonlinear, requiring tat te vaporizer i divided into appropriate etion for te alulation. e oure fluid outlet temperature i ritial a regard aling. i temperature mut be kept uffiiently ig to avoid aling on te oure fluid ide of te exanger. Cleaning of te oure fluid ide may be neeary, o te vaporizer deign mut take ti into aount. Any geotermal fluid may be orroive, o an appropriate material a to be ued for te vaporizer. 9.9.. urbine e turbine onvert a part of te vapour entalpy to aft work, and ten eletriity in te generator. Station i te vapour inlet to te turbine, and tation i te turbine exit. Fig.7. Obviouly te eat removed from te oure fluid a to equal te eat added to te working fluid. m ( ) m ( ) workingfluid Fig.8. e ideal turbine i ientropi, aving no eond law loe. In ti ae te entropy of te inoming vapor equal te entropy in te exaut team. e orreponding entalpy ange (redution) of te vapor i te larget entalpy ange po- 78
Prodution of Eletriity from a Geotermal Soure ible. e ientropi exit entalpy i ten te entalpy at te ame entropy a in te inlet and at te exit preure, wi i rougly te ame a prevail in te ondener. ( ),,p e turbine ientropi effiieny i given by te turbine manufaturer. i effiieny i te ratio between te real entalpy ange troug te turbine to te larget poible (ientropi) entalpy ange. e real turbine exit entalpy an ten be alulated: ( ) i, e work output of te turbine i ten te real entalpy ange multiplied by te working fluid ma flow troug te turbine. ( ) W m e expanion troug te turbine may reult in tat te exit vapor i in te wet region, or tat a fration of te ma flow i liquid. i an be very armful for te turbine, reulting in eroion and blade damage. e Kalina yle ue a mixture of ammonia and water, o tat te droplet re- ated in te turbine are eletrially ondutive. It i te meaning of te writer tat ti ondutivity i te reaon for te orroion enountered in te turbine in Huavik, Ieland. i orroion a been avoided by te uage of non-magneti titanium for te turbine rotor. Many of te working fluid for te ORC yle are retrograde, wi mean in ti ontext tat te exit vapor i upereated. e eat removal in te ondener will ten partly be de-uper-eat, eat tranfer out of te vapor at temperature iger tan te final ondening temperature. Ammonia-water mixture i not retrograde, but a te ondenation will our at a variable temperature, te eat removal proe i very imilar to tat of te retrograde fluid. 9.9.. Regenerator e regenerator i a eat ex-anger between te ot exit vapour from te turbine and te ondener. It i a de-upereater in te ORC yle, tranferring eat from te turbine exit vapour to te ondenate from te ondener. Station i te turbine exit vapour, tation i te regenerator outlet toward te ondener, tation i te inlet of te ondenate from te ondener, and tation i te pre-eated feed to te vaporizer. Fig.9. e eat removed from te turbine exaut vapor i equal te eat added to ondenate: m ( ) m ( ) e ma flow i te ame on bot ide of te regenerator. e ot fluid from te turbine i on te ot ide, will be ondened in te ondener and ten pumped rigt away troug te old ide of te regenerator toward te vaporizer. It a to be oberved tat te temperature of te ot fluid i iger tan te one of te old fluid trougout te regenerator. e fluid beavior i uually loe to linear, o it i normally not neeary to divide te regenerator into etion. e effet of regeneration on te yle a been treated earlier in ti text. 79
Pall Valdimaron 9.9.5. Condener e ondener may be eiter water or air ooled. e alulation for te ondener are rougly te ame in bot ae, a te ooling fluid (air or water) i very loe to linear. Station i te working fluid oming from te regenerator (or turbine in te ae of a non-regenerated yle). Station i te ondened fluid, normally aturated liquid wit little or no ub-ooling. Station i te entry of te ooling fluid, tation te outlet. Fig.. e ondener i noting but a eat exanger between te ot vapor from te regenerator/turbine and te ooling working fluid of te yle. It a to be oberved tat te temperature of te ot fluid i iger tan te one of te old fluid trougout te ondener. A well it mut be kept in mind tat te relation between te entalpy and te temperature i non-linear, requiring tat te vaporizer i divided into appropriate etion for te alulation. i i epeially valid for Kalina yle, in te ORC yle tere i only a property ange at te dew point, were de-upereat end and ondenation begin.. Referene Cengel; Bole: ermodynami: An Engineering Approa, MGraw-Hill, ISBN: 76898 () Kota,. J.: e exergy metod of termal plant analyi, Butter-wort, Aademi Pre, London (985) Szargut, J., Morri, D. R., Steward, F. R. Exergy Analyi of ermal, Cemial,and Metallurgial Proee, Springer-Verlag, Berlin (988) órólfon, G.: Betun á ntingu lágita jarvarma til raforkuframleilu. (Optimization of low temperature eat utilization for prodution of el-etriity), MS tei, Univerity of Ieland, Dept. of Meanial Engineering () Valdimaron, P.: Cogeneration of ditrit eating water and eletriity from a low temperature geotermal oure, Pro. of te 8t International Sympoium on Ditrit Heat-ing and Cooling, NEFP and te International Energy Ageny, rondeim, Augut - 6,, ISBN 8-59-- () El-Sayed, Y. M., ermoeonomi of Energy Converion, Pergamon Pre A. Bejan, G. ataroni, and M. Moran, ermal Deign and Optimization, J. Wiley, New York, 996. 8