Multi objective optimization of the MED-TVC system with exergetic and heat transfer analysis

Transcription

1 Energy Equp. Sy./ Vol. 5/No.4/December 207/ Energy Equpment and Sytem Mult objectve optmzaton of the MED-TVC ytem wth exergetc and heat tranfer analy Author Somayyeh Sadr a Ramn Haghgh Khohkhoo a * Mohammad Amer a a Faculty of Mechancal and Energy Engneerng, Shahd Beheht Unverty,.O. Box , Tehran, Iran Artcle htory: Receved : 8 June 207 Accepted : 24 September 207 ABSTRACT The mathematcal model to predct the performance and the exergetc effcency n a mult-effect dealnaton ytem wth thermal vapor compreon (MED-TVC ytem) ha been preented. The energy and the concentraton conervaton law were developed for each effect, conderng the bolng pont elevaton and the varou thermodynamc loe by developng the mathematcal model. Thee analye led to the determnaton of the thermodynamc properte at dfferent pont and to the gan output rato (GOR) value. Then, a heat tranfer equaton wa developed n each effect and the requred heat tranfer area were determned. Fnally, rreverblty analy wa performed, from whch the exergy detructon (conderng chemcal and phycal exergy) and the exergetc effcency were calculated. To obtan the optmum pont of a ytem, mult-objectve optmzaton wa ued. Determnaton of the bet trade-off between GOR and heat tranfer area wa the fnal goal of th optmzaton. The optmum degn led to a elected ytem wth the lowet heat tranfer area (and related cot) and the hghet GOR. Keyword: Dealnaton, Exergy Analy, Heat Tranfer Analy, Mult-Effect Dtllaton, Optmzaton.. Introducton In recent year, the lack of freh water a challenge faced by 40% of the world populaton. Dealnaton of brackh or alne water one way to enure the upply of th vtal ubtance. Amer et al. [] provded a thermodynamc model for an MED to produce 2,000 cubc meter per day and analyzed the mpact of the number of effect on the dealnaton performance value. Sayyaad et al. [2] alo developed and optmzed a model of an MED-TVC ytem ung thermo-economc * Correpondng author: Ramn Haghgh Khohkhoo Addre: Faculty of Mechancal and Energy Engneerng, Shahd Beheht Unverty,.O. Box , Tehran, Iran E-mal addre: r_haghgh@bu.ac.r analy. Th developed model wa related to the Kh Iland' dealnaton plant. Shakour et al. [3] developed a model for an MED-TVC ytem unt o a to connect to Lavan land ga, and then optmzed the developed model wth thermo-economc analy. Luo et al. [4] analyzed the ga turbne cycle wth a teammethane reformer to reduce emon. Zhao et al. [5] ued MED for a alne watewater refnery n Chna. The thermodynamc model baed on ma and energy balance wa developed at varou tage of dealnaton. Kamal et al. [6] developed a model to mulate and optmze the thermodynamc MED-TVC ytem. Th model, along wth expermental data from the Kh land dealnaton plant, ha

2 420 Somayyeh Sadr et al. / Energy Equp. Sy. / Vol. 5/No. 4/Dec. 207 been compared and valdated. The model wa developed baed on the hell-tube exchanger prncple, but t d not nclude the economc apect. Shakb et al. [7] evaluated an MED-RO hybrd dealnaton ytem and ga turbne cycle for the producton of power, heat, and freh water. Maraver et al. [8] tuded a cogeneraton ytem (organc Rankne cycle, MED, and the coolng ytem) to produce electrcty, heat, freh water, and coolng. Al- Mutaz and Wazeer [9] revewed the current tatu of MED-TVC. The prmary goal of th paper to preent a prevew of ome apect related to the technologcal theory and parametrc tudy of MED-TVC ytem and t development. Kah [0] nvetgated the effect of ome nput parameter on energy effcency and the produced water n an MED plant. In th tudy, the mathematcal modellng of an MED-TVC ytem wa carred out. Alo, the concentraton and energy conervaton law were developed for each dealnaton effect. Baed on concentraton and energy analye, the thermodynamc property at each pont of a conderable cycle wa determned. For the energy and concentraton analy, varable thermodynamc properte were condered. In the next tep, the heat tranfer analye of each effect and condener were performed followed by determnaton of the requred tranfer area n each effect and the total requred heat tranfer area. In the fnal tep, the rreverblty analy of a mentoned ytem wa performed baed on an exergy analy for each control volume. In the exergetc analy, the term of chemcal exergy wa condered and evaluated n an exergy equaton. Baed on th analy, the exergy detructon and exergetc effcency were determned. Fnally, to obtan the optmum pont of the dealnaton ytem, a genetc algorthm, mult-objectve, optmzaton tool wa ued. Maxmzaton of GOR and mnmzaton of the total heat tranfer area were the fnal goal of optmzaton. The operatonal parameter of the dealnaton ytem were the decon varable. The reult how good mprovement n GOR ncrement and heat tranfer area reducton. Nomenclature A heat tranfer area (m 2 ) B brne water flow rate(kg/) Cp pecfc heat (kj/kg K) D dtllate water flow rate (kg/) e exergy (kw) F feed eawater flow rate(kg/) h Enthalpy (kj/kg) M Q S T U X flow rate (kg/) preure (ka) pecfc heat conumpton (kj/kg) entropy (kj/k kg) temperature (K) overall heat tranfer coeffcent (kw/m 2 K) alnty (ppm) Greek letter Λ latent heat vcoty 0 chemcal potental denty Abbrevaton BE bolng pont elevaton (K) CR compreon rato Ev entraned vapor ER expanon raton GOR gan output rato LMTD logarthmc mean temperature dfference (K) NEA non-equlbrum allowance (K) ppm part per mllon Subcrpt 0 raw water c condenng vapor cw coolng eawater f feed water p permeate water m motve team n number of effect team t total v vapor 2. Sytem decrpton A chematc vew of a parallel-cro (C) MED-TVC ytem hown n Fg.. In th paper, the C confguraton of MED-TVC wa elected becaue of t capablty n water dealnaton. The man component of a conderable ytem were evaporaton effect, condener, flah boxe, and thermal vapour compreor. In th ytem, the output brne of each effect entered the next effect, and flahed and mxed wth the nput feed water (F). In C, the brne flahng tarted from Effect 2 and carred on untl the fnal effect. The eawater entered the down condener and aborbed the fnal effect output team latent heat. In th procedure, the temperature of eawater reache the nput feed water temperature. A porton of

3 Somayyeh Sadr et al. / Energy Equp. Sy. / Vol. 5/No. 4/Dec the warm eawater returned to ea and the ret wa ued a feed water for the effect. The motve team entered a dealnaton ytem from the external boler. Th team wa condened n the frt effect and returned to the boler. The nput feed water n the frt effect wa heated by motve team to top brne temperature (TBT). The feed water evaporated and entered nto the next effect a a heat ource. The output brne water n Effect entered Effect 2. Fnally, the producton n the lat effect wa dvded nto two part. One part entered the thermo-compreor and the other entered the down condener. 3. Energy and exergy balance (mathematcal modellng) The followng aumpton have been ued to derve the mathematcal model: The temperature dfference between the effect equal, the product alt-free, teady-tate operaton beng dcued, the feed-flow rate n the effect the ame, the pecfc heat capacty, bolng pont elevaton (BE), and other parameter have been calculated and thermodynamc loe have been tuded. The mathematcal model wa baed on concentraton, energy, and exergy balance n each effect, thermal vapour compreor, flah box, and condener. 3.. Thermal analy For the evaluaton of ma and energy conervaton, and heat tranfer calculaton, ome unknown parameter, uch a heat tranfer coeffcent and phycal properte of water, hould be determned. Thee unknown varable have been defned n the followng ecton. The temperature dfference between the effect, compreed team temperature, and lat-effect team temperature can be calculated a follow: T T T n n () T T T (2) Tv Tn BE (3) where, T and n are temperature n K and the number of effect, repectvely. The bolng pont elevaton (BE) related to the dolved alt value n the water. Th factor can be evaluated a gven below: BE X B CX 0 b 3 n n 3 Tn Tn Tn B T T 0 C [ b (4) Fg.. Schematc vew of a parallel-cro MED-TVC ytem

4 Energy Equp. Sy./ Vol. 5/No.4/December 207/ The pecfc heat capacty (cp) of water can be calculated a follow: c p a b T c T d T S S S S a S S b S S c d X F S 000 (5) where, X the alnty n ppm. Ettouney and El- Deouky preented a new correlaton to evaluate compreed team preure and entraned team preure ev, a gven below []: exp 9.5 T ev exp 9.5 Tvn (6) (7) The expanon rato (ER) and compreon rato (CR) can be calculated a: ER m ev CR ev (8) (9) The entranment rato (Ra) can be calculated a follow []: R a ev ER 0.05 (0) The amount of entraned vapour wa calculated ung the followng formula. D ev D R m a () Brne and vapour temperature n each effect can be computed a: T,,2, T T, n (2) T T BE (3) v The feed eawater flow rate n each effect wa calculated by: X 0 and X 70000, F. X B X D* X d b F b d F F,,2,, n n F X b, F B D, (4) D X X b F (5) where, D and B are dtlled water and brne water n kg/, repectvely. The condenaton temperature of vapor wa affected by preure loe n the demter, and frcton n the connectng lne and condenaton proce. Th temperature can be calculated a: Tc T BE T p Tt T c (6) Steam latent heat can be etmated a follow: λ T T T λ T λ m T T T T T m m m (7) (8) (9) The ma balance n each effect can be calculated by: B F D (20) B F B D, 2,, n (2) The alnty of brne at the outlet of each effect can be obtaned a gven below: X F X f B F B X X X, 2,3,, n f B B (22) (23) The energy balance n each effect can be calculated wth: D M λ F c T T p f λ [ p f λ D D D λ F c T T B c T T p (24) (25) The unknown parameter n the above equaton can be evaluated a follow:

5 Somayyeh Sadr et al. / Energy Equp. Sy. / Vol. 5/No. 4/Dec D D v, c p T T v, λ T T BE T T v, NEA 33 NEA T T 0.55 T v, (26) (27) (28) (29) where, NEA the non-equlbrum allowance n k. The vapor generated n the lat effect wa dvded n two part: condenng vapour DC and entraned vapour Dev. Thee can be calculated by: D D D (30) c n ev The overall heat tranfer coeffcent U wa etmated ung: T T T U (3) The heat tranfer area n each effect (A) can be calculated by: A D D λ ev U T T Dλ A, 2,3,, n U T T c, (32) (33) The total heat tranfer area wa calculated by the followng relaton: n A A A A A (34) e 2 n The logarthmc mean temperature dfference (LMTD) and overall heat tranfer coeffcent of the condener can be calculated by []: LMTD c Tf Tcw Tv, n T ln Tc, n T U T.5970 T 2 5 c v, n v, n T v, n 3 cw f 2 (35) (36) The condener heat tranfer area and coolng eawater flow rate wa calculated a follow: A D λ LMTD c n c U c c (37) M A cw Dcλn c T T p f cw The pecfc heat tranfer area equal to: A A D e c d t (38) (39) Fnally, the total dtlled water and GOR were calculated wth the followng equaton: M D (40) d n M GOR M d m (4) The pecfc heat conumpton, a an mportant charactertc of the thermal dealnaton unt, can be calculated wth the followng equaton: Q D λ D m m t 3.2. Exergy analy (42) Exergy the maxmum amount of obtanable work when a ytem brought nto equlbrum from t ntal tate to the envronmental (dead) tate. In the abence of nuclear, magnetc, electrcal, and urface tenon, the exergy of a ytem can be dvded nto four part: k ph kpo ch E E E E E (43) where, are knetc exergy, phycal exergy, potental exergy, and chemcal exergy, repectvely. Wth repect to the elected reference of th tudy, the knetc and potental exergy can be neglected from the exergy balance. The exergy balance equaton for the control volume can be expanded a follow: de T 0 dv cv. Q j W c. v 0 dt T dt m e m e E e e D (44) In the abence of output work ( ) and wate heat and conderng the teady-tate condton, the followng equaton for exergy balance can be rewrtten a: m e m e E (45) e e e e D where, E D denote the exergy detructon n th tudy. Calculatng the thermodynamc property of eawater requred for the exergetc analy

6 424 Somayyeh Sadr et al. / Energy Equp. Sy. / Vol. 5/No. 4/Dec. 207 of a conderable ytem n th tudy. Th thermodynamc property of eawater can be found n the Appendx ecton [2]. 4. Reult and dcuon The bac degn parameter to analyze the dealnaton ytem are hown n Table. The dtllate water n the ytem wa 0,000 cubc meter per day, n two unt. Mathematcal calculaton were performed baed on the degn parameter gven earler. The fnal reult of th modellng can be een n Table. The valdty of the model wa teted ung avalable data from the Trpol Wet lant [3], the reult of whch are hown n Table 2. To confrm thee obervaton, modellng for another dealnaton unt wa carred out. In addton, the model wa valdated ung data for the Gehm ower and Water Cogeneraton lant (Table 2). The mpact caued by the number of effect on GOR of the Trpol lant wa evaluated. The reult howed that GOR value ncreaed lnearly wth an ncreang number of dealnaton effect. Th occur becaue an ncreae n the number of dealnaton effect lead to an ncreae n alne water evaporaton and a decreae n the rejecton of alne watewater to the envronment. The dtrbuton of GOR value at dfferent TBT and the number of effect hown n Fg. 2. The reult how that the GOR value ncreaed lowly wth an ncreae n TBT. Moreover, for a pecfed value for TBT, an ncreae n the number of effect lead to an ncreae n the GOR value. Wth an ncreae n the number of effect, the poblty of heat exchange between dfferent flow ncreaed, whch led to the ncreae n the amount of freh water. Table. Input parameter and reult of the MED-TVC modelng Motve team flow rate, Dm, (kg/) 8.8 Motve team preure, m, (ka) 2300 Feed eawater temperature, TF, (ºC) 4.5 Coolng water temperature, Tcw, (ºC) 3.5 Feed water alnty, XF, (ppm) Top brne temperature, T (ºC) 60. Bottom brne temperature, Tn (ºC) 45.4 Temperature dfference, ΔT, c 4.9 Entranment rato, Ra.265 Expanon rato, ER Compreon rato, CR Dtllate producton, Dt, (kg/) GOR Coolng water flow rate, Mcw (kg/) Specfc heat conumpton, Q, kj/kg Specfc heat tranfer area, Ad, m 2 /kg/ Exergetc effcency, % 4.4 Table 2. Mathematcal model comparon wth two et of avalable data the Trpol plant, and the Qehm water and power cogeneraton plant arameter Temperature dfference, ΔT, c Entranment rato, Ra Expanon rato, ER Compreon rato, CR Dtllate producton, Dt, (kg/) GOR Current tudy Ref. [4] Ref. [3] Current model Qehm data[5] T 4, 2 T 3.7, 23 T 3.8, 34,

7 Somayyeh Sadr et al. / Energy Equp. Sy. / Vol. 5/No. 4/Dec Fg. 2. Change n GOR n term of dfferent top brne temperature The effect of heatng team temperature on the dealnaton ytem GOR value wa nvetgated. The reult how that the GOR value decreaed lnearly wth an ncreae n the heatng team temperature. Th occur a an ncreae n the heatng team temperature lead to an ncreae n the heatng team preure reultng n an ncreae n the entranment rato value. Thu, for a contant motve flow rate, the entraned vapor flow rate decreaed. Due to th the producton of freh water n the frt effect reduced. Th reducton n the producton of freh water lead to a decreae n the GOR value. The effect of feed water temperature on GOR value can be evaluated. The reult how that the ncreae n feed water temperature caued an ncreae n the GOR value. Next, the effect of motve team flow rate on GOR value wa analyzed. In contant motve team, entraned vapour, heatng team preure, and the expanon rato reman contant. In th condton, an ncreae n the motve team flow rate lead to an ncreae n the entraned vapour flow rate and dtlled water n the frt effect. Thu, the total amount of water produced and the GOR ncreaed. The effect of motve preure n the thermo-compreor on GOR ha been evaluated n Fg. 3. The reult how that an ncreae n the motve team preure led to a decreae n the GOR value. Th becaue the ncreae n motve team preure caued an ncreae n the expanon rato n the contant heatng team preure a well a the entraned vapour preure. The ncreae n expanon rato led to an ncreae n the entranment rato, and hence a decreae n the entraned vapour flow rate. A decreae n the entraned vapour flow rate led to a decreae n the amount of freh water produced n the frt effect, whch led to a decreae n the total amount of freh water and GOR. It evdent that an ncreae n TBT lead to a decreae n freh water producton. That becaue an ncreae n TBT lead to an ncreae n enble heat. Th ncreae n enble heat caue an ncreae n the bolng temperature of the feed water. Thu, the latent heat of team and total dtlled water decreae. The effect of TBT on pecfc heat conumpton can be evaluated. Fg. 3. Change n GOR n term of motve team preure

8 426 Somayyeh Sadr et al. / Energy Equp. Sy. / Vol. 5/No. 4/Dec. 207 The reult how that an ncreae n TBT lead to an ncreae n pecfc heat conumpton. Th occurr becaue an ncreae n TBT caue an ncreae n vapour preure and alo n the requred motve team. Th ncreae reult n an ncreae n the pecfc heat conumpton. The effect of TBT and the number of effect on pecfc exergy detructon hown n Fg. 4. It an alo be oberved that an ncreae n the top brne temperature lead to an ncreae n exergy detructon. At a pecfed TBT, pecfc exergy detructon decreaed wth an ncreae n the number of effect. The varaton of the pecfc heat tranfer area at the varou number of effect can be evaluated. The reult how that an ncreae n the number of effect lead to an ncreae n the rate of the pecfc heat tranfer area. The reult of the exergy analy are hown n Table 3. They how that the exergy detructon n the frt effect hgher than n the other. The exergy detructon n dfferent part of the MED TVC ytem hown n Fg. 5. A evdent, effect and leavng tream have the hghet and lowet rate of exergy detructon, repectvely. Fg. 4. The pecfc exergy change n term of top brne temperature Fg. 5. Exergy detructon on dfferent part of the MED TVC ytem Fg. 6. Exergy detructon on effect

9 pecfc exergy conumpton pecfc exergy detructon TVC Effect All effect Condener Leavng tream Total Somayyeh Sadr et al. / Energy Equp. Sy. / Vol. 5/No. 4/Dec The frt effect ha the maxmum exergy detructon out of all the effect (Fg. 6). Specfc exergy detructon and pecfc exergy conumpton, a two key parameter of exergy analy, can be calculated a how n Table 3. The varaton of exergy detructon per unt of dtllate n the condener, evaporator, and team ejector, a a functon of TBT, are hown n Fg. 7. The reult howed that an ncreae n the TBT n turn ncreae the exergy detructon per unt of dtllate. To obtan the optmum parameter for conderable ytem (Trpol lant), two objectve functon (GOR and total heat tranfer area) were elected. Mult-objectve optmzaton problem uually exhbt an uncountable et of oluton for aeng the tatu of vector, whch how the bet poble trade-off n the objectve functon pace. In order to determne a oluton that actually one of the bet poble tradeoff, the areto optmalty a key concept for expreng the relatonhp between multobjectve optmzaton reult. GOR a key goal n the optmzaton of thermal ytem, uch a a dealnaton ytem. However, ncreang the GOR of thee thermal ytem lead to an ncreae n heat tranfer urface and the related captal cot. In th regard, thee two functon are ued a a goal functon n multobjectve optmzaton. The genetc algorthm optmzaton toolbox ued due of t capablty n mult-objectve optmzaton. The reult how that an ncreae n GOR lead to an ncreae n the heat tranfer area and the related captal cot. The optmum pont hould be elected from the areto front optmzaton pont baed on elected decon-makng. Hence, the cloet pont on the areto front, wth repect to the deal unreachable pont, wa elected a an optmum pont. To enure the bet electon of the optmum pont, the orgnal areto front optmum data hould be normalzed and a normalzed areto front hould be created. Fgure 8 how the normalzed areto front, whch baed on mathematcal calculaton. Table 3. Exergy detructon [kw] and pecfc exergy parameter n the Trpol plant [kj/kg] Bn Dc ev Fg. 7. Varaton n exergy detructon per unt dtllate n condener, evaporator, and team ejector

10 Somayyeh Sadr et al. / Energy Equp. Sy. / Vol. 5/No. 4/Dec Fg. 8. The normalzed areto front n conderable mult-objectve optmzaton The optmum goal functon and decon varable are lted n Table 4. Thee reult how that wth mult-objectve optmzaton, GOR ncreaed by about.32 % (actual percent) wth repect to the bae degn. In addton, the total heat tranfer area decreaed by about 7.29 % (relatve percent) wth repect to the bae degn. Exergetc effcency wa reached at 4.7%. Table 4. Optmum pont data arameter Optmum value GOR Heat tranfer area (m 2 ) BBT( c ) TBT( c ) Feed water temperature ( c ) Steam motve preure (ka) 97.6 Steam motve flow rate (kg/) Concluon In th paper, the MED-TVC ytem wa analyzed for t energy, heat tranfer, and exergy approach. Baed on the derved mathematcal model, the effect of degn parameter on GOR, dtlled water producton, energy conumpton, and exergy detructon were evaluated. The reult howed that exergy detructon n the frt effect wa hgher than n other effect. Among the effect of exergy detructon, 73% are related to the frt effect. Baed on mult-objectve optmzaton, the optmum pont of the hghet GOR and lowet heat tranfer area (and related cot) wa determned. The optmal reult how an.32% ncrement n GOR. Analy of the MED-TVC ytem n the Trpol lant howed that evaporator are the man ource of exergy detructon. Therefore, effort hould be drected toward mnmzng thee loe by mprovng the degn of thee component. Fundng: Th reearch dd not receve any pecfc grant from fundng agence n publc, commercal, or not-for-proft ector. Acknowledgement The author would lke to thank the Monenco Iran Conultng Engneer Company (MANA Group), Tehran, Iran for ther help and upport. Reference [] Amer M., Sef Mohammad S., Hoen M., Sef M., Effect of Degn arameter on Mult Effect Dealnaton Sytem Specfcaton, Dealnaton (2009) 245: [2] Sayyaad H., Saffar A., Mahmoodan A. Varou Approache n Optmzaton of Mult Effect Dtllaton Sytem Ung a Hybrd Meta-Heurtc Optmzaton Tool, Dealnaton (200) 254: [3] Shakour M., Ghadaman H., Sheholelam R., Optmal Model for Mult Effect Dealnaton Sytem Integrated wth Ga Turbne, Dealnaton (200) 260: [4] Luo C., Zhang N., Lor N., Ln H., ropoal and Analy of a Dual urpoe Sytem Integratng a Chemcally Recuperated Ga

11 Somayyeh Sadr et al. / Energy Equp. Sy. / Vol. 5/No. 4/Dec Turbne Cycle wth Thermal Seawater Dealnaton, Energy (20) 36: [5] Zhao D., Xue J., L S., Sun H., Zhang Q., Theoretcal Analy of Thermal and Economcal Apect of Mult Effect Dtllaton Dealnaton dealng wth Hgh Salnty Watewater, Dealnaton (20) 273: [6] Kouhkamal R., Sanae M., Mehdzadeh M., roce Invetgaton of Dfferent Locaton of Thermo Compreor ucton n MED-TVC lant, Dealnaton (20) 280: [7] Shakb S. E., Amdpour M., Aghanajaf C., Smulaton and Optmzaton of Mult Effect Dealnaton Coupled to a Ga turbne lant wth HRSG Conderaton, Dealnaton (202) 285: [8] Maraver D., Uche J., Royo J., Aement of Hgh Temperature Organc Rankne Cycle Engne for polygeneraton wth MED Dealnaton, A prelmnary approach, Energy Converon and Management (202) 53: [9] Al-Mutaz I. S., Wazeer I., Current Statu and Future Drecton of MED-TVC Dealnaton Technology, Dealn, Water Treatment (204) 55: -9. [0] Kah A., Invetgaton of Energy Effcency and roduced Water n Dealnaton Dtllaton Sytem, Internatonal Water Technology Journal (205) 5: -9. [] Ettouney H.M., El-Deouky H. Fundamental of Salt Water Dealnaton, Kuwat Unverty (2002). [2] Sharqawy M.H., Lenhard V J.H., Zubar S.M., On Exergy Calculaton of Seawater wth Applcaton n Dealnaton Sytem, Internatonal Journal of Thermal Scence (20) 50: [3] Ahour M.M., Steady State Analy of the Trpol Wet LT-HT-MED lant, Dealnaton (2002) 52: [4] Al-Mutaz I.S., Wazeer I., Development of a Steady-State Mathematcal Model for MEE-TVC Dealnaton lant, Dealnaton (204) 35: 9-8. [5] MANA Group, Qehm Water and ower Cogeneraton lant Data, Iran (20).

12 430 Somayyeh Sadr et al. / Energy Equp. Sy. / Vol. 5/No. 4/Dec. 207 Appendx A The thermodynamc property of eawater can be found n the followng ecton. Specfc volume v w ρ w (A.) ρw ρw w a a2t at 3 a4t a5w T (A.2) ρ T T w T T a , a 2.00, a.677 0, a , a (A.3) where v w,, w w, and T are eawater-pecfc volume, eawater and pure water denty, alt alnty, and temperature, repectvely. Specfc enthalpy The pecfc enthalpy can be calculated a follow: h h w ( b b w b w b w b T 2 3 w w b T b T b w T b w T b w T ) h T T 2 w T 3 b , b , b , b.446 0, b , b , b , b.990, b , b ,,,, h T w h T w v w w 0 0 (A.4) (A.5) (A.6) Specfc entropy The followng equaton can be ued for the calculaton of eawater-pecfc entropy: w ( c c w c w c w c T 2 3 w w c T c T c w T c w T c w T ) (A.7) Chemcal potental The alt and water chemcal potental n eawater can be calculated by dfferentatng the Gbb energy wth repect to t compoton a follow: Gw μ g w m w w w g w Gw μ g w m w w g w w (A.9) (A.0) gw hw T w (A.), where, are the chemcal potental and the Gbb energy, repectvely. g h T w w w w w w hw 2 3 b 2b 2w 3b 3w 4b 4w b5t w b T b T 2b w T 3b w T 2b w T w 2 3 c 2c 2w 3c 3w 4c 4w c5t w c T c T 2c w T 3c w T 2c w T (A.2) (A.3) (A.4) Therefore, the flow exergy can be expreed a follow: * * * 0 0 n f e h h T μ μ (A.5) On the rght-hand de of Equaton 60, part one and two are related to phycal exergy, whle the thrd part related to the chemcal exergy. In the above equaton, the envronmental temperature and preure, and the ntal tate concentraton (named retrcted dead tate) have been pecfed wth the * gn. In envronmental temperature, preure, and concentraton (named the dead tate), the 0 gn ha been ued. T T 2 2 w T.3700 T c 4.230, c.4630, c , c , c , c.4430, 5 6 c , c 6.0, c 8.040, c (A.8)