Introduction to the “Exergy” Concept 2.83/2.813 T. G. Gutowski 2 Readings 1. Ch.2 Thermodynamics Revisited (p 7-13), and 2. Ch 6 Exergy, a Convenient Concept (p 59-62), Jakob de Swaan Arons, 2004 3. Ch 6 Thermodynamic Analysis of Resources Used in Mfg Processes, Gutowski & Sekulic, in TDR 2011 4. Appendix, Tables of Standard Chemical Exergy, Szargut, Morris & Steward, 1988 3 Exergy Accounting • Exergy Units: Joules J, rate in Watts, W • Exergy symbols: B, Ex, X, and b, ex, x • Also called “Availability” by Keenan, 1941 and “Available Energy”, ΩR, by Gyftopoulos and Beretta, 1991 4 Definition of Exergy “Exergy is the amount of work obtainable when some matter is brought to a state of thermodynamic equilibrium with the common components of the natural surroundings by means of reversible processes, involving interaction only with the above mentioned components of nature” [Szargut et al 1988]. 5 Exergy System State Maximum work obtainable between System and Reference States. Reference State 6 Exergy System State The minimum work needed to raise System from the reference state to the System State Reference State 7 Aggregate Exergy Accounting Exin Exout Exlost Exin ! Exout = Exlost 8 Thermodynamics Overview • • • • • Systems Heat Interactions Exergy of heat interaction Entropy and Enthapy Physical and Chemical Exergy 9 Open System Work interaction W massin Mass massout Q Heat interaction 10 Closed System X W massin Mass X massout Q 11 Isolated System X X W massin Mass X massout X Q 12 The 1st Law #U = Qin " Wout dU = !Qin " !Wout dQ " dW = 0 ! ! 13 Heat Interaction Q TH Q Wout = Q ! Qo Qo To Wout Qo != = 1" Q Q 14 Carnot’s “Reversible” Heat Engine !reversible = f (TH ,TL ) Qout TL = Qin TH TL " = 1! TH 15 Maximum Work Output max out W TL = Qin (1 ! ) TH • Qin is at TH, let TL be Tref or To • This gives the “available energy” of a heat interaction at TH in reference To. • Work and Heat are no longer equivalent! 16 Exergy “Ex” of Heat Interaction To E = Q(1 ! ) T Q X • Exergy, “Ex” is the available energy w.r.t. a reference environment, T0, and P0… • Ex(work) = W; Ex (heat) = Q(1-T0/T) 17 Availability “The First Law states that in every cyclic process either work is converted into heat or heat is converted into work. In this sense it makes no distinction between work and heat except to indicate a means of measuring each in terms of equivalent units. Once this technique of measurement is established, work and heat become entirely equivalent for all applications of the First Law.” Keenan, 1941 18 Availability • “The Second Law, on the other hand, marks the distinction between these two quantities by stating that heat from a single source whose temperature is uniform cannot be completely converted into work in any cyclic process, whereas work from a single source can always be completely converted into heat.” Keenan, 1941 19 Availability “The efforts of the engineer are very largely directed toward the control of processes so as to produce the maximum amount of work, or so as to consume the minimum amount of it. The success of these efforts can be measured by comparing the amount of work produced in a given process with the maximum possible amount of work that could be produced in the course of a change of state identical with that which occurs in the process.” 20 Keenan, 1941 Energy, E and Exergy, B = Ex E2, B2 E1, B1 B1- B2 = E1- E2 B1- B2 > E1- E2 Properties for two different states of the system shown by the boxes. This change may come about due to spontaneous changes or due to heat or work interaction, or mass transfer. reversible process irreversible process Ref: Gyftopoulos and Beretta 21 Define Entropy 1 "#( E1 ! Eo ) ! (B1 ! Bo ) $% S1 = So + CR • They show CR = TR = T0 • Entropy is a Property • Entropy is a measure of something lost Ref: Gyftopoulos and Beretta 22 Entropy Difference 1 "#( E2 ! E1 ) ! (B2 ! B1 ) $% S2 ! S1 = CR • ∆S = 0, reversible process • ∆S > 0, irreversible process Ref: Gyftopoulos and Beretta 23 Example, Heat Interaction Q, T T T0 E2 = E1 +Q B2 = B1 + Q(1-T0/T) ΔS = (1/T0)(Q – Q + Q(T0/T)) = Q/T ΔS = Q/T 24 Example, Work Interaction W E2 = E1 +W B2 = B 1 + W ΔS = (W - W) = 0 25 Homeworks 1 & 2 TH Qin Qout 1. Calculate the entropy change for a reversible heat engine,and 2. Calculate the entropy loss for a reversible heat engine. Use the results given in this Presentation. TL 26 Answers for 1 & 2 Consider the process in two stages; 1) you transfer heat in, and 2) You transfer heat and work out. Use the result from Carnot to Show that the change in entropy is zero. This leads to the result that The exergy lost is also zero. 1 QL QH !S = S2 " S1 = #$( E2 " E1 ) " (B2 " B1 ) %& = " To TL TH Blost = QH " QL + To !S " W 27 Properties or State Variables • • • • • • • • T = temperature intensive variables P = pressure V = volume U = internal energy E = energy extensive B = exergy and H = enthalpy (H = U + PV) intensive variables S = entropy 28 State Variables 2 dU = 0 ! d ! = ! " ! 2 1 # dQ = 0 !T d ( U + PV ) = 0 ! 1 29 Enthalpy H=U+PV 2 1 Here the Work done is The First Law can be written as W = P(V2 – V1) Q = (U+PV)2 – (U + PV)1 The quantity in parenthesis is Enthalpy H = U + PV The First Law can be written as Qin = ΔH Constant Pressure Equilibrium Process 30 For Flow System Energy 1 1 2 U + P! + mV + mgz = H + mV 2 + mgz 2 2 Control Volume F d Wboundary = Fd = Pν 31 Open System with H, S H, S W po, To H, S Q, To p, T Consider the Work to bring the system from the reference environment at standard conditions, To, po to the state at T, p See Ch 6 de Swaan Arons 32 From EQ 1 & 2(Ch 6), de Swaan Arons H! in ! H! out ! Q! out + W!in = 0 ! Q S!in ! S!out ! out + S! generated = 0 To ! = !H! " T !S! + T S! W o o generated Steady State Work to bring system from Po, To to P, T 33 Minimum Work = Exergy Wmin W! rev = = "H ! To "S ! m = ( H p ,T ! H po ,To ) ! To ( S p ,T ! S po ,To ) B = ( H ! To S ) ! ( H ! To S ) o Wmin W! rev = = Bout ! Bin m! 34 Lost Work & Lost Exergy Recall: ! = B! out ! B! in + To S!generated W Let: ! =W ! min + Wlost then W ! lost = B ! lost = To S!generated W 35 Exergy also is p, T W W! max b! = wmax ! m po, To Q B = ( H ! To S ) ! ( H ! To S ) o the maximum amount of work that can be obtained from a system in reference to the environment at standard conditions, To, Po Standard ref. values T0 = 298.2! K , Po = 101.3kPa 36 Open flow system 37 First Law for a Flow System ' $ ui2 ' dU $ ! i %% hi + + gzi "" % " = )m 2 & dt # cv in & # ' $ ui2 ! j %% h j + + gz j "" !)m 2 out & # + ) Q! in ! ) Q! out + ) W! sh ,in ! ) W! sh ,out ' $ ! (u 2 ! %% (H + m + g(z "" + Q in ! W!out = 0 2 & # EQ 1 38 one stream steady state Second Law for a Flow System ' dS $ ! i Si ! ( m ! jSj % " = (m & dt # cv in out *Q! k *Q!1 ! +() !() + Sgenerated T T in out Q! surr ! ! !S + m + Sgenerated = 0 T one stream steady state EQ 2 39 From EQ 1 & 2 ' $ ! (u 2 ! %% (H + m + g(z "" + Q ! W!out = 0 2 & # ! !S + m ! W rev Q! T0 + S! generated = 0 2 ( % !u ! && !H + ! To !S =m + g!z ## " m 2 ' $ 40 Physical and Chemical Exergy • B = Bph + Bch • Bph(T=To, p=po , µ= µ* ≠ µο) =0 – this is the “restricted dead state” • Bch(µ* = µο) = 0 • when B = Bph + Bch = 0 – this is the “dead state” 41 Thank you Jan Szargut 42 Chemical Reaction, at To, po n1R1 + n2 R2 → n3Π3 R1 Π3 R2 Q 43 Chemical Reactions stoichiometric mass balance va Ra + vb Rb + .... # v j " j + vk " k + ... exergy " balance" va bRa + vbbRb + .... ! v j b" j ! vk b" k = Blost where exergy b is given in kJ/mole 44 Example: Burning Carbon C BC + O2 CO2 + BO2 - 410.3 kJ + 3.97 kJ mol BCO2 = ΔB – 19.9 kJ = 394.4kJ mol mol The maximum work you can get out of one mol of carbon is 394.4 kJ = 32.9 MJ mol of carbon kg These exergy values come from Szargutʼs Appendix Tables 45 Burning Octane 2C8H18(l) + 25 O2(g) 16 CO2(g) + 18H2O(g) 2(5413.1) + 25(3.97) - 16(19.87) - 18(9.5) = ΔB ΔB = 10,436.53 kJ/2 mols of octane 10,436.53 = 45.8 MJ (2[(8 x 12) + 18]= 228g) kg Note: ΔB = -ΔGºf = ΔH - ToΔS ≈ LHV 46 Note that Δg°≈ Δh° (lower heating value) for fuels Ref Gyftopolous & Beretta 47 48 Example: Oxidation of Aluminum 3 2Al + O2 ! Al2O3 2 kJ 3 kJ kJ 2 " 888.4 + " 3.97 # 200.4 mol 2 mol mol Blost = Blost kJ = (1776.8 + 6.0 # 200.4 ) = 1582.4 mol(Al2O3 ) See Appendix of Szargut for exegy values49 Materials can do work? System State (TH) QH Wrev Insert reversible heat engine between high and low temperatures QL Reference State (TL) 50 Chemical Properties referenced to the “environment” Crust Oceans Atmosphere T0 = 298.2 K, P0 = 101.3 kPA 51 Exergy Reference System pure metal, element chemical reactions oxides, sulfides… crustal component earthʼs crust (ground state) extraction 52 Exergy Reference System Aluminum (c=1) 888.4 kJ/mol Al2O3 (c=1) 200.4 kJ/mol Al2SiO5 (c=1) Al2SiO5 (c = 2 x 10-3) 15.4kJ/mol 0 kJ/mol (ground) 53 Example; making pure iron from the crust Fe (c = 1) 376.4 kJ/mol reduction Fe2O3 (c=1) 16.5 kJ/mol Fe2O3 (c = 1.3 x 10-3) extraction 0 kJ/mol (ground) 54 55 Extraction from the crust Extracting Fe 2O 3 from c = 1.3x10 !3 (crust) to c = 1 1 B = To R ln 1.3x10 !3 J 1 kJ B = 298.2 K " 8.314 " ln = 16.5 !3 mol K 1.3 " 10 mol o Note: R = k Navo (Boltzmannʼs constant X Avogadroʼs number) 56 Reduction of Fe2O3 (Hematite) 2Fe2O3 + 3C 4Fe + 3CO2 2 x 16.5 + 3 x 410.3 – 4 x 376.4 – 3 x 19.9 = Blost = - 301.4 kJ this is an endothermic reaction i.e. minimum energy required to reduce 2 mole of hematite 57 Iron Ore Reduction Recall C + O2 CO2 produces 394.8 kJ/mol C 301.4 = 0.76 We need 394.8 mols of carbon 2Fe2O3 + 3.76C + 0.76O2 4Fe + 3.76 CO2 58 Iron Ore Reduction but the efficiency of the use of carbon is only 30.3% therefore the actual reaction is 2Fe2O3 + 12.42C + 9.42O2 4Fe + 12.42CO2 33kJ + 5095.9 + 37.7 - 1505.6 - 247.2kJ = 3,413.8 kJ for 4 mol of Fe this is 15.2 MJ/kg (Fe) 59 Iron Ore Reduction 12.42 ! 394.8 4.903MJ MJ Fuel (C) Intensity = = = 22 4 ! 55.85 g .2234kg kg 12.42 ! 44 kg CO2 CO2 Intensity = = 2.5 4 ! 55.85 kg Fe Exergy value of pure Fe is 376.4 kJ/mole = 6.7 MJ/kg 60 Summary for Iron Ore fuel used = 22 MJ/kg ≈ 15.2(Blost) + 6.7(BFe) “Credit” for producing pure iron from the crust Lost exergy from making iron from Fe2O3 See Smil Table A.12, iron from ore 20 - 25 MJ/kg 61 Exergy Balance, Open System B!W ,in B!Q,in B! in B!W ,out B! loss B!Q,out B! out B! in + B!W ,in + B!Q,in = B! out + B!W ,out + B!Q,out + B! loss Includes: materials flows, heat and work interactions 62