GLOBAL CLIMATE AND ENERGY PROJECT STANFORD UNIVERSITY. Energy Tutorial: Exergy 101 GCEP RESEARCH SYMPOSIUM 2012 STANFORD, CA.

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1 GLOBAL LIMATE AND ENERGY PROJET STANFORD UNIVERSITY Energy Tutrial: Exergy 101 GEP RESEARH SYMPOSIUM 2012 STANFORD, A hris Edwards Prfessr Department f Mechanical Engineering Stanfrd University GLOBAL HALLENGES GLOBAL SOLUTIONS GLOBAL OPPORTUNITIES

2 Which wuld yu chse? 1 kg Air 20 1 bar 1 kg Air 20 8 bar Hint: Bth have exactly the same amunt f energy... The ability t d wrk depends upn bth the state f the resurce and the state f the surrundings.

3 Energy, Entrpy, Exergy Energy is the extensive, cnserved quantity that is inter-cnvertible with heat and wrk: du Q W in ut Entrpy is the extensive measure f the number f micrscpic rearrangements f energy: S k B ln Exergy is the ptential f an energy resurce t d wrk in a given set f surrundings ( a.k.a. envirnment)

4 Resurce in cntact with envirnmental reservir - reservir is (fixed intensive state, nt extensive) - reservir has large but finite fast internal transprt (bundary prps fixed, irrev. in system) E : du Q W h N W b k k any species k Q S : ds s N S T k k k gen W du P dv T ds h T s N T S k 0 W rev Exergy k k k gen k 0 envirnmental species i

5 Reactin must reversibly transfrm all resurce species ( j) t species that are naturally present in the envirnment ( i). nsider a reactin that des this transfrmatin fr species j: Rxn A : a A bb " j" with extent f reactin The balance fr envirnmental species i then becmes N : dn N c dd aa bb c dd M M i i i ij j j j j ij i i while the balance fr a nn-envirnmental species j is N j : dn j j j Exergy j (extensive) (signed cefs.) N dn dn i i ij j j j Nte: Any envirnmental species present in the resurce reacts t frm itself.

6 Exergy Revisited W du P dv T ds dn dn rev i i i ij j j i i j RHS has exact differentials. The state f the envirnment enters nly thrugh fixed, intensive parameters ( T, P, ). i Since it is exact & with cnstant cef., integral is path independent. Integrate alng a tw-part path: I: At fixed cmpsitin t the therm-mechanical ( restricted) dead state. (N diffusin r reactin permitted.) II: At fixed therm-mechanical state, but with diffusin and reactin t the envirnmental ( unrestricted) dead state.

7 max max T-M Dead State Resurce State Exergy Revisited W du P dv T ds dn dn i i i ij j j i i j W du P dv T ds Fixed mp. N Reactin The first integral is smetimes referred t as the Dead State du P dv T ds dn dn T-M Dead State ij i i i j i i j j TT PP exergy,. The secnd integral is the chemical exergy,. TM The internal exergy f the resurce is then: therm-mechanical int TM Adding th e external exergy, KE PE gives the ttal exergy: KE PE TM

8 T-M Exergy T-M Dead State du P dv T ds TM Resurce State Fixed mp. N Reactin U U P V V T S S r TM TM TM TM U PV T S TM Resurce Intensive State: T, P, Resurce Extensive mpsitin: x j N j Availability Functin, A U PV T S TM TM TM Therm-mechanical Intensive State: T, P, x Resurce Extensive mpsitin: = Gibbs Functin in TM State, where j dentes any species present in the resurce. TM A G TM Original cmpsitin. Held fixed! j N j G TM

9 hemical Exergy du P dv T ds dn dn Dead State ij T-M Dead State i i i j i i j j TT PP U U P V V T S S TM TM TM i NiTM N i i ij j N jtm N j i i j U PV T S TM TM TM Gibbs Functin in TM Dead State G TM U PV T S ( ) i NiTM N i i ij j N jtm N j N Envirnmental Intensive State: T, P, x Unknwn Extensive mpsitin: i Envirn. Unknwn i j Intensive 0 Extensive State mp. i i N j 0 The unknwn cmpsitin in the system cancels ut. (Whew!)

10 hemical Ptential f Resurce (at TM Dead State) hemical Exergy We can interpret this n the basis f the chemical ptential f the initial resurce and what it will becme in the envirnment. GTM i ij j N j i If we define the last term as hemical Ptential f Env. Species Frmed frm Species Originally Present in Resurce (at Env. Dead State) G GTM G and A GTM GTM G A G TM The chemical exergy is the difference between the chemical ptential (Gibbs functin) f the resurce befre and after it has reacted and diffused t becme part f the envirnment (all at T and P ). j

11 Example: G N TM i ij j j j i Find the chemical exergy f ne kml f methan e. Envirnmental (dead) state: T 25, P 100 kpa x 370 ppm, x 3%, x 20. 3%, x 76.66% O, H O, O, N, N 1 kml, H 2O O 2H O H 4 1, 2, H O O , H, TM O, O, H O, H, TM H O, O O, aa bb c dd aa bb c dd A RT ln x, RT ln x A j j ij i i O, O O, H O, H O H O, MJ/kg H ) HO, RT ln x MJ (51.9 4

12 Example: G N TM i ij j j j i Find the chemical exergy f 1 kml f methane mixed with 2 kml prpane and 1 kml nitrgen. (Same,, i, H 2O O 2 H O, H 5O 3O 4H O N 1 kml, N 2 kml, N 1 kml x H H N H, TM 25%, x 50%, x 25% H, TM N, TM , 1, 2, 5, H H O, H O, H TP 1, 2, 3, 4 0 O, H H O, H O, H H O, H N H, TM H, TM N, TM N, O, 1O, 2H O, 25 O, 23 O, 24 2, RT ln x, RT ln x k, TM k k, TM k, k k, 5116 MJ (49.2 MJ/kg fuel) x ) H O

13 Example: Find G N TM i ij j j j i fr 1 kml f methane mixed with stichimetric air. H 2 O 3.76N O 2H O N N 1 kml, N 2 kml, N 7.52 kml H O N x 9.51%, x 19.01%, x 71.48% H, TM O, TM N, TM H 1, O 2, O 1, 2 0 H O N O H, TM O, TM N, TM O, N, O, O, H O, RT ln x, RT ln x k, TM k k, TM k, k k, MJ (51.4 MJ/kg H r 2.83 MJ/kg mix) 4

14 Example: G N TM i ij j j j i Find fr the prducts f cmplete cmbustin f 1 kml f methane with a stichimetric amunt f air. H 2 O 3.76N O 2H O N N 1 kml, N 2 kml, N 7.52 kml x O H O N %, x 19.01%, x 71.48% O, TM H O, TM 2 2 N, TM O, TM H O, TM N, TM O, H O, N, k, TM k, ln k, TM k, 21.6 MJ (1.35 MJ/kg H r 2.6% f fr H ) RT x x 2 4 4

15 Example: G N TM i ij j j j i Find 2 fr 1 kml f pure O. (Inverse sequestratin frm air.) Express the answer per unit mass f N O 1 kml All stichimetric cefficients 2 O RT ln RT ln x H that generated the O. 4 2 are zer except O O, TM, TM O, O, xo, 19.6 MJ MJ/kg O x MJ/kg H (2.4% f fr H ) 4 4 There is sufficient exergy in the prducts f stichimetric methane-air cmbustin t drive the cmplete separatin f all f the O 2 prduced by the reactin! (Lts f water!) 2.

16 x (MJ/kml) Single-mpnent Ideal Gases Methane arbn Dixide Water Oxygen Nitrgen T (K)

17 x (MJ/kml-) Methane Prducts & O Methane-Air Reactants (Stich.) Methane-Air Prducts (Stich.) arbn Dixide T (K)

18 Example: G N TM i ij j j j i Find fr the prducts f cmplete cmbustin f 1 kml f prpane with O N O H O N H N 3 kml, N 4 kml, N 18.8 kml x %, x %, O, TM H O, TM 2 2 stichimetric air. O H O N x,,,,,, i, TM i, N i, TM i, 2, TM 72.87% O TM O H O TM H O N TM N ln 56.7 MJ (18.9 MJ/kml-O. Less than pure O.) RT x x 2 2

19 x (MJ/kml-) Prpane Prducts & O Prpane-Air Reactants (Stich.) Prpane-Air Prducts (Stich.) arbn Dixide rsses at lw T! Separatin pssible! T (K)

20 hemical Exergy f mmn Fuels Fuel hemical hem. Exergy H Reactin* G Reactin* S Reactin* Exergy Species+ Frmula MJ per fuel MJ per fuel MJ per fuel kj/k per fuel t LHV kml kg kml kg kml kg kml kg Rati Methane H Methanl H3OH arbn Mnxide O Acetylene Ethylene 2H2 2H Ethane Ethanl 2H6 2H5OH Prpylene 3H Prpane 3H Butadiene 4H i-butene 4H i-butane 4H n-butane n-pentane 4H10 5H i-pentane 5H Benzene 6H n-heptane 7H i-octane 8H n-octane 8H Jet-A Hydrgen 12H23 H All species taken as ideal gases. Envirnment taken as: 25, 1 bar, 363 ppm O 2, 2% H 2 O, 20.48% O 2, balance N 2. *Reactin with stichimetric air at 25, 1 bar. All prducts present as ideal gases, including water. Fr simple fuels the exergy can be calculated directly. Fr cmplex fuels (cal) it is nt pssible t calculate the exergy (need entrpy) and sme frm f crrelatin is required.

21 Standard-State hemical Exergy may be expressed in terms f the standard state chemical ptential and chemical activity since RT ln a. Defining the standard-state chemical exergy i i i k ; when k is an envirnmental species k i ik k ; when k is a nn-envirnmental species i and the effective activity k a k i ; when k is an envirnmental species a i ik G N RT k ; when k is a nn-envirnmental species TM k k k Nk lnk k

22 Standard-State hemical Exergy Tabulated values f the standard-state chemical exergy can be fund in references such as: J. Szargut, D.R. Mrris, and F.R. Steward, Exergy Analysis f Thermal, hemical, and Metallurgical Prcesses, Hemisphere, New Yrk, Values fund in the literature can differ frm each ther accrding t the chice f species fr the envirnmental dead state (since the envirnment is nt, itself, in equilibrium). Fr ur purpses, tables f standard-state exergies are nt needed--we will calculate the chemical exergy directly.

23 Definitin: Exergy Balances KE PE TM External Internal m 2 V V mg z z U PV T S G 2 Balance: : d Transfers: cmp./exp. Other irrev. system in ut prduced destryed Accumulatin Transfers = 0 T Sgen 0 (2nd Law) (Guy-Stdla) W P P dv W rev W 1 Heat Q 1 T T W W T T Matter x P P v N where x N (mlar exergy) arnt fractin Flw exergy

24 Example: LN2 Precler nsider a precler fr hydrgen liquefactin d in ut dest : dt dt dt dt, steady dt Must cnsider 5 transfers as shwn: 1 Heat Q 1T T dest in ut 4 Matter x P P v N i i hi T si mi If the device is cnfigured such that the exergy f a stream cannt be transferred, the exergy f that stream is necessarily destryed. (Recall extending the bundary t the envirnment in S calcs.?) Hw des the entrpy generated in the rth-para catalyst shw up? gen

25 mments n Efficiencies Thermal: First-Law: t I W Q m ut in W ut fuel, in HV Applies t heat engines nly. Is all heat equal in value? Engine is mdeled as heat engine. Which heating value? a.k. a.: fuel cnversin efficiency, arbitrary verall efficiency Secnd-Law: Exergy: II x W W ut ut, Rev ut a.k.a.: ratinal efficiency Utilizatin: u W m in ut fuel, in W a.k.a.: cmbined-heat-and- pwer ( HP) efficiency ut in Qut HV Engine must still be mdeled. What are the prcess cnstraints? Mdel independent. (Need dead state) Applicable beynd engines. (Any ut ) Assigns equal value t heat and wrk. Which heating value?

26 Sme Exergy Analysis Illustratins Exergy Resurces GT/NG/STIG NG Refrming ASU SATR SOF/GT LHR Engines Envirnmental Impact Optimal Architectures