Conversion of thermal energy into electricity. F.Marechal LENI-IGM-STI-EPFL Dr. François Marechal

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1 Conversion of thermal energy into electricity Dr. François Marechal 1

2 Theoretical efficiency On the basis of Carnot efficiency: Q + Q Heat source at Thot Ė Mechanical reservoir Thermal reservoir at T cold 1st principle: Heat balance Ė = Q + Q η e = Ė Q + nd principle: Carnot If reversible process Ė = Q + (1 T froide ) ma T chaude η Carnot = Ė ma Q = (1 T froide ) + T chaude

3 Maimal electricity production Eergy efficiency η e = Cycle efficiency ɛ = Ė Q + b ɛ η e = = θ Carnot Ė (1 T a T lm ) Q + b ɛ (1 T lm Ta ) Ė = Q + b (1 T a T lm ) T Electricity Ė Environment Q! + Qout avec Thermal reservoir at Ta Q a = Q + b T lm = T ad T b ln( T ad T b ) Ė 3

4 Energy balance Q fuel = ṁ fuel (LHV fuel + ĥfuel(t fuel )) ĥ fuel (T fuel ) = Tfuel Combustion T 0 cp fuel (T )dt + α fuel h vap (T fuel ) Fuel O (air) Q air = ṁ air (ĥair(t air )) T Boiler η b = Q p = Q r + Q gc Q + b = Q fuel + Q air ( Q r + Q gc ) Q b Q fuel + Q air =1! Q p Q fuel + Q air Q r Q! + Fumes (Chimney) Q gc = ṁ gc Tch T 0 cp gc (T )dt 4

5 Energy balance Q + fuel = ṁ+ fuel (LHV fuel + ĥfuel(t fuel )) ĥ fuel (T fuel ) = Tfuel T 0 cp fuel (T )dt + α fuel h vap (T fuel ) Fuel Air inlet Q + air = ṁ+ O (air) Q + air (ĥair(t air )) air = ṁ+ air (h air(t air ) h air (T 0 )) System efficiency Ė η = Q + fuel + Q + air Cycle efficiency η c = Ė Q b = η ch η c = (1 T a[k] T lm [K] ) Electricité Ė T Q! + Q p = Q r Thermal reservoir at Ta + Q gc Q + b = Q fuel + Q air ( Q r + Q gc ) Q a = Q + b Radiative losses (%) η b = Q b Q fuel + Q air =1! Ė Fumes (chimney) Q gc = ṁ gc Tch T 0 Q r Q p Q fuel + Q air cp gc (T )dt 5

6 Gaz naturel Belgique Mer du Nord Gaz de charbon η Carnot Tad mo Tstack LHV UHV W carnot h Carnot CO min K kg air/kg K kj/kg kj/kg kje/kg kg/gje 70 13, % , % , % , % 81.6 Essence , % 91.9 Vaporizing oil % 98.1 Diesel 46 14, % 97.7 Kérozène 49 14, % 94.8 Fuel léger 45 14, % 99.1 Fuel lourd 43 14, % Anthracite , % Bitume , % Lignite 111 7, %

7 Rankine cycle Fluid : Water/Steam Preheating Vaporization Superheating Steam/superheated Liquid Steam or W/S min 85% steam 7

8 T(C) T Diagramme entropique de la vapeur d eau Point critique : Tc = 374,15 C Pc = 1,0 bar 3-1 vc = 0,00317 m.kg -1 hc = 107,4 kj.kg s = 4,449 kj.kg.k Unités : T en C P en bar v en m 3-1.kg -1 h en kj.kg s en kj.kg.k T = 0,1 c Thermodynamic properties of steam 1000 = 0, = 0, v =0,0015 0,05 0,1 0, ,0 0,5 v = 1 s 50 0 h = 000 0,006 0,01 = 0,4 00 = 0,5 0,01 0, , 0,1 0,05 0, Thermodynamic state , P =1 0, ISOTHERMS : T ( C) 3300 ISOBARS : P (bar) 3100 ISOCHORS 900 : v (m3/kg) 800 0,06 0,08 0,01 0, ,05 0,1 P =100 0, 50 ISENTHALPS : h (kj/kg) ISENTROPS : s (kj/kg/k) ISOhumidity : v h P = 0,6 = 0,7 = 0,8 = 0,9 h,p 0,5 v = ,5 0, 0,1 0,05 0, h = s CBP s (kj/kg/c)

9 T(C) T Diagramme entropique de la vapeur d eau Point critique : Tc = 374,15 C Pc = 1,0 bar 3-1 vc = 0,00317 m.kg -1 hc = 107,4 kj.kg s = 4,449 kj.kg.k Unités : T en C P en bar v en m 3-1.kg -1 h en kj.kg s en kj.kg.k T = 0,1 c Thermodynamic properties of steam 1000 = 0, = 0, v =0,0015 0,05 0,1 0, ,0 0,5 v = 1 s 50 0 h = 000 0,006 0,01 = 0,4 00 = 0,5 0,01 0, , 0,1 0,05 0, ,04 v 100 = 0,6 P =1 0, ,06 0,08 0, = 0, , P 3700 = 0, ,05 = 0,9 0,1 P =100 0, 50 0,5 v =1 0 h ,5 0, 0,1 0,05 0, h = s CBP s (kj/kg/c)

10 Thermodynamic state T=00 C T=00C P=5 b s= kj/kg/c h=855 kj/kg p=5 bar p= bar h=900 kj/kg h=800 kj/kg T=100 C s=6 kj/kg/c s=7 kj/kg/c 10

11 Mechanical work e = q E + q a = T (K) 647 K 500 K Mass work : kj/kg Tds Tds 1 q E + = 1 Tds 3 4 Tc=647 K Pc=1 bar Fuel Air Cycle Rankine 1 Ė = Ṁcp(T T 3 ) 3 98 K 0 K 1 4 q a = 3 4 Tds 3 s kj/ K/kg 4 Ė = Ṁ(h (T, P ) h 3 (T 3, P 3 )) Q + b = M (h (T, ) h 1 (T 1, 1)) Q a = Ṁ(h 3(T 3, P 3 ) h 4 (T 4, P 4 )) 11

12 T-S Diagram Isentropic epansion Non-ideal epansion 1

13 Rankine cycle h (kj/kg) s (kj/kg/c) 13

14 e is = h (T, P ) h is (s, P 3 ) η is = e e is = h (T, P ) h 3 (T 3, P 3, 3 ) h (T, P ) h is (s, P 3 ) e = h (T, P ) h 3 (T 3, P 3 ) 14

15 Molier diagram Work calculation Isentropic efficiency of epansion e is = h (T, P) his(s(t, P), P3) T = 450 C P = 30 bar e = h(t, P) h3(t3, P3) T3 = 100 C P3 = 1 bar η is = e e is = h (T, P ) h 3 (T 3, P 3, 3 ) h (T, P ) h is (s (T, P ), P 3 ) e = η is e is η is = 70 95% e = η is (h (T, P ) h is (s (T, P ), P 3 )) = (h (T, P ) h 3 (T 3, P 3 )) 15

16 Increase the efficiency e = q E + q a = Tds Tds Maimal area between the curves T (K) 647 K Tc=647 K Pc=1 bar Super-critical limit and boiler materials Increase the superheating temperature 500 K q E + = 1 Tds Increase the vaporization pressure 98 K 1 4 q a = 3 4 Tds 3 Decrease the condensor pressor Limit Environment 0 K s kj/ K/kg 16

17 Heat echange Composite Others (DF_STM) Mech. power T(K) Combustion gases Steam production Rankine cycle 4 Steam condensation Q(kW)

18 Eergy losses in the heat echange Eergy losses Stack 18

19 Increase the efficiency of a cycle Increase the vaporization pressure Decrease the condensation pressure Preheating steam bleeding for liquid preheating at high pressure Resuperheating steam bleeding HP (after epansion) and back to boiler Air preheating with steam or combustion gases bleeding increases the quantity of high temperature energy and therefore the production of high pressure steam 19

20 Rankine cycle Preheating + 8% reheating + 5% Air Air preheating and draw off Fuel Draw-off + 7% Total : + 0 % 0

21 Preheating + 8% reheating + 5% Air Air preheating and draw off Steam (Rankine) Cycle air preheating Fuel Draw-off + 7% Reheating Draw-off Total : + 0 % 1

22 Ways of improving efficiency

Lecture 35: Vapor power systems, Rankine cycle

ME 00 Thermodynamics I Spring 015 Lecture 35: Vapor power systems, Rankine cycle Yong Li Shanghai Jiao Tong University Institute of Refrigeration and Cryogenics 800 Dong Chuan Road Shanghai, 0040, P. R.