Sustainable Power Generation Applied Heat and Power Technology. Equations, diagrams and tables

Sustainable Power Generation Applied Heat and Power Technology Equations, diagrams and tables 1

STEAM CYCLE Enthalpy of liquid water h = c p,liquid (T T ref ) T ref = 273 K (normal conditions). The specific heat capacity for liquid water is: c p = 4.18 kj/(kg K) & Heat supply (kg/s kj/kg = kw): = m& ( ) Q Boiler h 3 h 2 Turbine power (kg/s kj/kg = kw): = m& ( ) P T h 3 h 4 Isentropic efficiency turbine: η T = h h 3 3 h h 4 4s Steam cycle efficiency: η = PT ( Pp ) Q& Fuel Boiler efficiency: η B = Q& Q& Boiler Fuel Heat balance for one open heater: m& extr h2 + ( m& m& ) h5 m& extr h6 = 0 m, h6 mextr, h2 m-mextr, h5 Heat balance for one closed heater & m extr ( h2 h7 ) = m& ( h6 h5 ) 2

GAS TURBINE CYCLE Fuel 2. 3. G Air 1. 4. Compressor power [kg/s kj/kg = kw ] or [kg/s kj/(kg K) K = kw ]: P C = m& ( ) or P m& c ( T ) air h 2 h 1 C = air P, 1 2 2 T1 Turbine power [kg/s kj/kg = kw ] or [kg/s kj/(kg K) K = kw ]: P T = m& ( ) or P m& c ( T ) gas h 3 h 4 T = gas P, 3 4 3 T4 Electric net power output: P GTel = ( P η P ) η T m C G Gas turbine efficiency: η Enthalpies: h 1 = h 1,AIR h 2 = h 2,AIR h 3 = h 3,AIR + x DH t3 h 4 = h 4,AIR + x DH t4 GT P = Q& GT Fuel = m& Fuel P GT LHV Temperature increase compressor where the temperature T 1 is in [K] and η SC is the isentropic efficiency of the compressor: T 2 T 1 T1 = η SC p p 2 1 κ C 1 κ C 1 3

Temperature decrease turbine where the temperature T 3 is in [K] and η ST is the isentropic efficiency of the turbine: T 3 T 4 = T 3 η ST κ T 1 κ T 3 1 1 p p4 The heat supplied in the combustion chamber: Q& FUEL = m& fuel LHV Specific fuel consumption, β, is defined as: m& fuel β = [kg m& fuel / kg air ] air Gas flow after combustion chamber: m & gas = m& + m& = ( 1+ β ) m& air fuel air Heat balance on the combustion chamber: m& h & ( β m& h air 2 + m fuel LHV = 1+ ) Gas content x = ( 1+ f ) β 1+ β air where f is the the stoichiometric air to fuel ratio (kg air/kg fuel). For light oil, f = 14.52. 3 Solving the heat balance for the specific fuel consumption: β = LHV h h h 3, AIR 2 3, AIR ( 1+ f ) DH t3 4

COMBINED CYCLE Stack tg4 tfw hfw Temperature tg3 Economizer Δtpp ts Evaporator hs1 (saturation) tg2 hs2 Superheater Heat transferred Gas tg1 turbine exhaust tsh hsh Economizer tg4 tg3 To the stack hfw Feed water pump hs1 Drum Evaporator hs2 hs1 tg2 Circulation pump Superheater Superheater hsh hs2 Gas turbine Exhaust tg1 Superheated Steam Pinch point temperature difference: Δt PP = t g3 - t s Approach temperature: Δt appr = t s t eco,out Heat balance HRSG: Qrecovered mgt cpg (tg1- tg4) Gas side mst (hsh- hfw) Steam side Heat balances for each component in the HRSG are as follows (without the economizer approach temperature): Economizer: m gt c pg (t g3 t g4 ) = m st (h S1 h fw ) Evaporator: m gt c pg (t g2 t g3 ) = m st (h S2 h S1 ) Superheater: m gt c pg (t g1 t g2 ) = m st (h sh h S2 ) Heat balances for each component in the HRSG with the economizer approach temperature: Economizer: m gt c pg (t g3 t g4 ) = m st (h appr h fw ) Evaporator: m gt c pg (t g2 t g3 ) = m st (h S2 h appr ) 5

COMBUSTION Calculation of the amount of flue gas per kg fuel Consider a fuel with the following composition on total substance (%-mass): a% C, b% O 2, c% H 2, d% S, e% N 2, f% humidity, g% ash, a + b + c + d + e + f + g = 100% The first step is to convert the content of the different elements to moles: Element Molar mass (g/mol) Analysis (g/kg fuel) Analysis (mol/kg fuel) C 12 a*10 a*10/12 O 2 32 b*10 b*10/32 H 2 2.02 c*10 c*10/2.02 S 32 d*10 d*10/32 N 2 28 e*10 e*10/28 H 2 O 18.02 f*10 f*10/18.02 Ash 1 - g*10-1 Ash is not contributing to the combustion or the flue gas and will not be further considered. Elemental combustion reactions C + O 2 CO 2 S + O 2 SO 2 H 2 + 0.5 O 2 H 2 O Needed air supply according to the elemental reactions: Element Analysis (mol/kg fuel) Oxygen needed (mol/kg fuel) C a*10/12 a*10/12 O 2 b*10/32 - b*10/32 H 2 c*10/2.02 0.5* c*10/2.02 S d*10/32 d*10/32 N 2 e*10/28 - H 2 O f*10/18.02-6

Oxygen needed [O 2 ] = a*10/12 b*10/32 + 0.5*c*10/2.02 + d*10/32 [mol/kg fuel] Since air is most often used for combustion, N 2 has to be included in the analysis: Nitrogen in air: [N 2 ] = 3.76*[O 2 ] [mol/kg fuel] The molar amount of air needed for stoichiometric combustion of 1 kg of the fuel is: l 0 = [O 2 ] + [N 2 ] [mol/kg fuel] From the set of elemental reactions, the gases produced (which constitute the flue gas) are also obtained: Element Analysis H 2 O CO 2 SO 2 N 2 O 2 (mol/kg fuel) C a*10/12 a*10/12 O 2 b*10/32 H 2 c*10/2.02 c*10/2.02 S d*10/32 d*10/32 N 2 e*10/28 e*10/28 H 2 O f*10/18.02 f*10/18.02 N 2 in air [N 2 ] The stoichiometric amount of flue gas is the sum of the compounds: g 0 = a*10/12+ c*10/2.02 + d*10/32 + e*10/28 + f*10/18.02 + [N 2 ] [mol/kg fuel] Excess air is required for the combustion process. For an air/fuel ratio m, the real amount of air becomes: l = m*l 0 [mol/kg fuel] Since air comes in excess, in the flue gas there will be oxygen and more nitrogen. The real amount of flue gas becomes: g = g 0 + l 0 *(m-1) [mol/kg fuel] To convert the flue gas amount from mol to m n 3 the equation of state pv=nrt is used, assuming the flue gas is ideal at normal conditions (1atm, 273K) so that: 1 mol of gas in normal conditions corresponds to 0.0224 m n 3 (V/n = RT/p) If the calorific (higher) heating value HHV is known, the lower heating value LHV can be estimated from LHV = HHV 2.44 * (8.94 * h 2 + F) [MJ/kg] h 2 is the hydrogen mass fraction in the fuel; F is the fuel humidity. 2.44 is a mean value for heat of vaporization in [MJ/kg H 2 O] at 25ºC 7

BOILER EFFICIENCY Indirect method: η p = (100- P fg -P CO -P ash -P rad ) % P fg = Flue gas losses. Can be estimated from Siegerts formula: P fg t gas t = k * [ CO ] 2 REF DRY t ref = 25ºC, t = flue gas temperature in ºC, [CO 2 ] dry is the carbon dioxide fraction in % on dry flue gas (from combustion table), k is taken from a diagram and is dependent on fuel type. P CO are losses because of CO in the flue gas. If the CO-fraction is measured in x ppm on dry flue gas, the loss is: P CO g *[ CO] LHV * LHV t DRY CO = [%] fuel If the measurement is performed in wet (total) flue gas, g t is replaced by g. LHV CO is the heat of combustion for CO in [MJ/m n 3 CO]. LHV CO = 12.634 MJ/ m n 3. P ash = Losses because of unburned in the residual ash. If [A] is the mass fraction of ash in the fuel and [bb] is the mass fraction of unburned in the ash taken out from the furnace (residual ash) then the amount of residual ash is: [ A] Re sidualashamount = 1 [ bb] The loss of combustible substance in the residual ash is: [ bb] [ A]* * LHV 1 [ bb] Pash = LHV fuel C where LHV c is the lower heating value of the combustible part of the residual ash 30 MJ/kg Emissions: Assume that the measurement of a certain emission is given as x ppm in dry flue gas. The desired unit is [mg/mj fuel]. The transition of unit is: [emission] = 10 6 * (x * 10-6 * g t * ρ emission )/LHV fuel [mg/mj fuel] where 8

ρ emission is the density of the emission [kg/m n 3 ] which can be found in a property table. g t is the dry flue gas amount in [m n 3 /kg fuel] If the measurement is performed in wet (total) flue gas, g t is replaced by g 9

NUCLEAR POWER 1 [amu] = 1.66 10-24 [grams] The nucleons mass in [amu] are as follows: Neutron: 1.00898 [amu] Proton: 1.00759 [amu] 1 [amu] = 931 [MeV] The activity, which means the amount of decays to occur per time unit, is proportional to the amount of isotopes: A = λ N A 0 = λ N 0 Were A 0 represents the activity at the initial time t 0. N is the amount of isotopes and λ is the decay constant The activity in matter decreases with time due to A = λ N 0 e -λ t = A 0 e -λ t The activity can be given in the units Becquerel [Bq] or Curie [Ci], 1 [Bq] = 1 [decay/second] 1 [Ci] = 3.7 10 10 [decays/second] The half-life-time T 1/2 is defined as the time taken to reach half the value of the initial activity. If this time is inserted in the activity equation above, we get: A 0 /2 = A 0 e -λ T½, were T½ represents the half-life-time The half-life-time can therefore be written as: T½ = ln 2/λ Microscopic target 1. The absorption target, σ a. 2. The fission target, σ f. 3. Radioactive capturing target, σ c. 4. The spreading target, σ s. 10

σ s = σ e + σ i, were σ e is the elastic and σ i the inelastic target. σ a = σ c + σ f The total microscopic target becomes: σ t = σ a + σ s The size of a target is given in the unit barns: 1 [barn] = 10-24 [cm 2 ] A neutron flux with Φ 0 [neutrons / cm 2, s] irradiating perpendicular to a plate or a wall: N = the number of nuclei per cm 3 in the wall x = wall thickness A = wall frontal area in cm 2 σ = microscopic target in cm 2 The neutron flux behind the wall is Φ = Φ 0 e -σ N x The definition the macroscopic target, Σ, is written: Σ = N σ where σ represents the microscopic target and N the number of nuclei per cm 3. Therefore, Σ is the total target for a certain exchange in 1 cm 3 of the substance, and the dimension is [1/cm]. The inverse of this target is the mean free path in [cm], which is a mean distance a neutron travels before a certain type of exchange occurs. The number of nuclei per cm 3 in a material can be calculated according to: N = [ρ 6.023 10 23 ] / A ρ = the density in [g/cm 3 ] A = the atomic weight in [g/mole] 6.023 10 23 corresponds to Avogadro s constant, [atoms/mole] If different kinds of atoms exist inside a volume, the macroscopic target is calculated according to: Σ = N 1 σ 1 + N 2 σ 2 + N 3 σ 3 + If the calculation refers to molecules the atomic weight A is replaced of the molecular weight MW. When calculating Σ, for a molecule, the following equation is used: Σ = ([ρ 6,023 10 23 ] / MW) (μ 1 σ 1 + μ 2 σ 2 + + μ i σ i ) where μ i represents the number of atoms, of the same kind, per molecule. R = Σ Φ [exchanges/cm 3, s] The following relation is special for fission: R f = Φ Σ f [fissions/cm 3, s] Where Φ is the neutron flux [cm -2, s -1 ] And Σ f is the macroscopic target for fission 11

The power per cm 3 in a nuclear core, P/V, is: P / V = R f / (3,1 10 10 ) [W/cm 3 ] The effective multiplication factor is defined as k = ε p f η P Where ε is the fast fission factor p is the resonance escape probability f = Σ au / [Σ au + Σ ak ] = thermal utilization factor Σ ak represents the absorption in moderator, cladding etc The thermal fission factor, termed η, states the number of produced neutrons per absorbed thermal neutron. η = ν [ Σ f (235) / {Σ c (238) + Σ c (235) + Σ f (235)}] The number ν represents the average number of emitted neutrons per fission. In the case for U-235 the value of ν is approx. equal to 2.47. Shorter, η can be written η = ν [ Σ f / Σ au ] P is the probability for NO leakage of neutrons from the core Enrichment e = N U235 /(N U235 +N U238 ) The reactivity ρ is defined as: ρ k eff 1 The power increase with time t in a nuclear core is given as: P = P 0 e ρ t/a Where a is the average lifetime per neutron generation The reactor period is defined as T = a/ρ 12

Enthalpies and heat of vaporization of saturated water and steam as function of Pressure Pressure (bar) Temperature ( C) Enthalpy Saturated Liquid Water (kj/kg) 13 Enthalpy Saturated Steam (kj/kg) Heat of vaporization (kj/kg) 0.01 6.14 29.7 2520.5 2490.8 0.02 16.86 70.8 2532.3 2461.5 0.03 23.90 100.2 2544.1 2443.9 0.04 28.79 120.7 2552.1 2431.4 0.05 32.82 137.5 2559.9 2422.4 0.06 36.12 151.3 2565.8 2414.5 0.07 38.81 162.6 2571.0 2408.4 0.08 41.19 172.5 2575.5 2403.0 0.09 43.41 181.8 2579.5 2397.7 0.10 45.49 190.5 2583.1 2392.6 0.12 49.34 206.6 2589.4 2382.8 0.14 52.47 219.7 2594.9 2375.2 0.16 55.22 231.2 2599.8 2368.6 0.18 57.76 241.8 2604.1 2362.3 0.20 60.03 251.3 2608.0 2356.7 0.22 62.09 259.9 2611.6 2351.7 0.24 64.04 268.1 2614.9 2346.8 0.26 65.83 275.6 2618.0 2342.4 0.28 67.50 282.6 2620.8 2338.2 0.30 69.09 289.2 2623.5 2334.3 0.32 70.59 295.5 2626.1 2330.6 0.34 71.99 301.4 2628.5 2327.1 0.36 73.34 307.1 2630.8 2323.7 0.38 74.63 312.5 2632.9 2320.4 0.40 75.86 317.6 2635.0 2317.4 0.42 77.03 322.5 2637.0 2314.5 0.44 78.17 327.3 2638.9 2311.6 0.46 79.26 331.9 2640.7 2308.8 0.48 80.31 336.3 2642.5 2306.2 0.50 81.33 340.6 2644.1 2303.5 0.55 83.72 350.6 2648.1 2297.5 0.60 85.93 359.9 2651.8 2291.9 0.65 88.00 368.6 2655.2 2286.6 0.70 89.94 376.8 2658.3 2281.5 0.75 91.77 384.5 2661.3 2276.8 0.80 93.50 391.7 2664.1 2272.4 0.85 95.14 398.6 2666.7 2268.1 0.90 96.70 405.2 2669.2 2264.0 0.95 98.19 411.5 2671.6 2260.1 1.00 99.62 417.5 2673.8 2256.3 1.10 102.27 428.7 2678.1 2249.4 1.20 104.74 439.2 2682.0 2242.8 1.30 107.07 449.0 2685.6 2236.6 1.40 109.28 458.3 2688.9 2230.6 1.50 111.37 467.2 2692.0 2224.8 1.60 113.30 475.4 2695.0 2219.6 1.70 115.14 483.2 2697.8 2214.6

1.80 116.91 490.7 2700.4 2209.7 1.90 118.60 497.9 2702.9 2205.0 2.00 120.23 504.8 2705.2 2200.4 2.10 121.77 511.3 2707.5 2196.2 2.20 123.26 517.6 2709.6 2192.0 2.30 124.69 523.8 2711.7 2187.9 2.40 126.08 529.7 2713.6 2183.9 2.50 127.43 535.4 2715.5 2180.1 2.60 128.72 540.9 2717.4 2176.5 2.70 129.98 546.3 2719.1 2172.8 2.80 131.20 551.5 2720.8 2169.3 2.90 132.39 556.6 2722.4 2165.8 3.00 133.54 561.5 2724.0 2162.5 3.20 135.75 571.0 2727.0 2156.0 3.40 137.86 580.0 2729.8 2149.8 3.60 139.87 588.6 2732.4 2143.8 3.80 141.79 596.9 2734.9 2138.0 4.00 143.63 604.8 2737.3 2132.5 4.20 145.40 612.4 2739.5 2127.1 4.40 147.10 619.7 2741.7 2122.0 4.60 148.74 626.8 2743.7 2116.9 4.80 150.32 633.6 2745.6 2112.0 5.00 151.86 640.2 2747.5 2107.3 5.50 155.48 655.9 2751.8 2095.9 6.00 158.85 670.5 2755.7 2085.2 6.50 162.01 684.2 2759.2 2075.0 7.00 164.97 697.2 2762.4 2065.2 7.50 167.78 709.4 2765.3 2055.9 8.00 170.43 721.0 2768.0 2047.0 8.50 172.96 732.1 2770.5 2038.4 9.00 175.38 742.7 2772.9 2030.2 9.50 177.69 752.9 2775.0 2022.1 10.00 179.91 762.7 2777.0 2014.3 10.50 182.04 772.1 2778.9 2006.8 11.00 184.09 781.2 2780.6 1999.4 11.50 186.07 790.0 2782.3 1992.3 12.00 187.99 798.5 2783.8 1985.3 12.50 189.84 806.7 2785.2 1978.5 13.00 191.63 814.7 2786.6 1971.9 13.50 193.38 822.5 2787.8 1965.3 14.00 195.07 830.1 2789.0 1958.9 14.50 196.71 837.5 2790.1 1952.6 15.00 198.32 844.7 2791.2 1946.5 15.50 199.88 851.7 2792.2 1940.5 16.00 201.40 858.6 2793.1 1934.5 16.50 202.88 865.3 2794.0 1928.7 17.00 204.34 871.8 2794.8 1923.0 17.50 205.75 878.3 2795.6 1917.3 18.00 207.14 884.6 2796.3 1911.7 18.50 208.50 890.7 2797.0 1906.3 19.00 209.83 896.8 2797.6 1900.8 19.50 211.13 902.7 2798.2 1895.5 20.00 212.41 908.6 2798.7 1890.1 14

21.00 214.89 919.9 2799.7 1879.8 22.00 217.28 930.9 2800.6 1869.7 23.00 219.59 941.6 2801.3 1859.7 24.00 221.82 951.9 2802.0 1850.1 25.00 223.98 961.9 2802.5 1840.6 26.00 226.08 971.7 2802.9 1831.2 27.00 228.11 981.2 2803.2 1822.0 28.00 230.09 990.4 2803.5 1813.1 29.00 232.01 999.5 2803.7 1804.2 30.00 233.88 1008.3 2803.8 1795.5 31.00 235.71 1016.9 2803.8 1786.9 32.00 237.49 1025.4 2803.7 1778.3 33.00 239.23 1033.6 2803.6 1770.0 34.00 240.93 1041.7 2803.5 1761.8 35.00 242.59 1049.7 2803.2 1753.5 36.00 244.21 1057.5 2803.0 1745.5 37.00 245.80 1065.1 2802.6 1737.5 38.00 247.36 1072.6 2802.3 1729.7 39.00 248.89 1080.0 2801.9 1721.9 40.00 250.38 1087.3 2801.4 1714.1 41.00 251.85 1094.5 2800.9 1706.4 42.00 253.29 1101.5 2800.4 1698.9 43.00 254.71 1108.4 2799.8 1691.4 44.00 256.10 1115.2 2799.2 1684.0 45.00 257.47 1122.0 2798.5 1676.5 46.00 258.81 1128.6 2797.8 1669.2 47.00 260.13 1135.2 2797.1 1661.9 48.00 261.43 1141.6 2796.3 1654.7 49.00 262.71 1148.0 2795.5 1647.5 50.00 263.97 1154.3 2794.7 1640.4 52.00 266.43 1166.7 2793.0 1626.3 54.00 268.82 1178.8 2791.1 1612.3 56.00 271.15 1190.6 2789.2 1598.6 58.00 273.41 1202.1 2787.1 1585.0 60.00 275.61 1213.5 2785.0 1571.5 62.00 277.76 1224.6 2782.7 1558.1 64.00 279.86 1235.5 2780.4 1544.9 66.00 281.90 1246.2 2777.9 1531.7 68.00 283.90 1256.8 2775.4 1518.6 70.00 285.86 1267.1 2772.8 1505.7 72.00 287.77 1277.3 2770.2 1492.9 74.00 289.64 1287.4 2767.4 1480.0 76.00 291.48 1297.3 2764.6 1467.3 78.00 293.28 1307.1 2761.7 1454.6 80.00 295.04 1316.7 2758.7 1442.0 82.00 296.77 1326.3 2755.7 1429.4 84.00 298.46 1335.7 2752.5 1416.8 86.00 300.13 1345.0 2749.3 1404.3 88.00 301.77 1354.2 2746.1 1391.9 90.00 303.37 1363.3 2742.8 1379.5 92.00 304.96 1372.3 2739.4 1367.1 94.00 306.51 1381.2 2735.9 1354.7 96.00 308.04 1390.0 2732.4 1342.4 15

98.00 309.55 1398.8 2728.8 1330.0 100.00 311.03 1407.5 2725.1 1317.6 105.00 314.63 1428.9 2715.6 1286.7 110.00 318.11 1449.9 2705.7 1255.8 115.00 321.46 1470.5 2695.3 1224.8 120.00 324.70 1490.9 2684.6 1193.7 125.00 327.84 1511.1 2673.3 1162.2 130.00 330.88 1531.1 2661.5 1130.4 135.00 333.83 1550.9 2649.3 1098.4 140.00 336.69 1570.7 2636.5 1065.8 145.00 339.48 1590.4 2623.1 1032.7 150.00 342.18 1610.0 2609.1 999.1 155.00 344.82 1629.8 2594.4 964.6 160.00 347.38 1649.6 2579.0 929.4 165.00 349.88 1669.7 2562.8 893.1 170.00 352.32 1689.9 2545.7 855.8 175.00 354.70 1710.6 2527.5 816.9 180.00 357.02 1731.7 2508.1 776.4 185.00 359.29 1753.5 2487.4 733.9 190.00 361.51 1776.1 2464.9 688.8 195.00 363.67 1799.9 2440.2 640.3 200.00 365.78 1825.4 2412.5 587.1 205.00 367.85 1853.5 2380.8 527.3 210.00 369.86 1886.0 2342.4 456.4 215.00 371.83 1927.7 2291.0 363.3 220.00 373.74 2010.0 2190.2 180.2 16

Enthalpies and heat of vaporization of saturated water and steam as function of Temperature Temperature ( C) Pressure (bar) Enthalpy Saturated Liquid Water (kj/kg) 17 Enthalpy Saturated Steam (kj/kg) Heat of vaporization (kj/kg) 1 0.0036 6.7 2510.1 2503.4 2 0.0053 11.8 2514.1 2502.3 3 0.0067 16.5 2516.4 2499.9 4 0.0079 20.9 2518.1 2497.2 5 0.0089 25.1 2519.3 2494.2 6 0.0099 29.1 2520.4 2491.3 7 0.0108 33.1 2521.3 2488.2 8 0.0116 36.9 2522.0 2485.1 9 0.0124 40.7 2522.7 2482.0 10 0.0131 44.4 2523.3 2478.9 11 0.0139 48.0 2523.9 2475.9 12 0.0145 51.6 2524.4 2472.8 13 0.0152 55.1 2524.8 2469.7 14 0.0161 58.8 2526.0 2467.2 15 0.0175 63.0 2528.3 2465.3 16 0.0188 67.2 2530.5 2463.3 17 0.0202 71.4 2532.6 2461.2 18 0.0216 75.6 2534.5 2458.9 19 0.0230 79.7 2536.3 2456.6 20 0.0244 83.9 2538.0 2454.1 21 0.0258 88.1 2539.7 2451.6 22 0.0272 92.3 2541.3 2449.0 23 0.0287 96.5 2542.8 2446.3 24 0.0301 100.7 2544.2 2443.5 25 0.0318 104.8 2545.8 2441.0 26 0.0339 109.0 2547.8 2438.8 27 0.0360 113.2 2549.7 2436.5 28 0.0382 117.4 2551.5 2434.1 29 0.0405 121.6 2553.3 2431.7 30 0.0428 125.7 2555.0 2429.3 31 0.0451 129.9 2556.7 2426.8 32 0.0476 134.1 2558.4 2424.3 33 0.0505 138.3 2560.3 2422.0 34 0.0535 142.5 2562.1 2419.6 35 0.0565 146.6 2563.9 2417.3 36 0.0596 150.8 2565.6 2414.8 37 0.0629 155.0 2567.3 2412.3 38 0.0667 159.2 2569.4 2410.2 39 0.0708 163.4 2571.3 2407.9 40 0.0749 167.5 2573.3 2405.8 41 0.0792 171.7 2575.2 2403.5 42 0.0836 175.9 2577.0 2401.1 43 0.0881 180.1 2578.8 2398.7 44 0.0928 184.3 2580.6 2396.3 45 0.0976 188.4 2582.3 2393.9 46 0.1025 192.6 2584.0 2391.4

47 0.1076 196.8 2585.7 2388.9 48 0.1128 201.0 2587.3 2386.3 49 0.1182 205.2 2588.9 2383.7 50 0.1236 209.3 2590.4 2381.1 51 0.1300 213.5 2592.2 2378.7 52 0.1368 217.7 2594.0 2376.3 53 0.1437 221.9 2595.9 2374.0 54 0.1509 226.1 2597.6 2371.5 55 0.1583 230.3 2599.4 2369.1 56 0.1660 234.4 2601.1 2366.7 57 0.1738 238.6 2602.8 2364.2 58 0.1819 242.8 2604.4 2361.6 59 0.1905 247.0 2606.1 2359.1 60 0.1997 251.2 2607.9 2356.7 61 0.2092 255.4 2609.7 2354.3 62 0.2191 259.5 2611.4 2351.9 63 0.2292 263.7 2613.1 2349.4 64 0.2396 267.9 2614.8 2346.9 65 0.2504 272.1 2616.5 2344.4 66 0.2620 276.3 2618.2 2341.9 67 0.2739 280.5 2620.0 2339.5 68 0.2862 284.7 2621.7 2337.0 69 0.2989 288.9 2623.4 2334.5 70 0.3119 293.0 2625.1 2332.1 71 0.3258 297.2 2626.8 2329.6 72 0.3401 301.4 2628.5 2327.1 73 0.3549 305.6 2630.2 2324.6 74 0.3700 309.8 2631.9 2322.1 75 0.3859 314.0 2633.5 2319.5 76 0.4024 318.2 2635.2 2317.0 77 0.4194 322.4 2636.9 2314.5 78 0.4369 326.6 2638.6 2312.0 79 0.4552 330.8 2640.3 2309.5 80 0.4741 335.0 2641.9 2306.9 81 0.4935 339.2 2643.6 2304.4 82 0.5137 343.4 2645.3 2301.9 83 0.5346 347.6 2646.9 2299.3 84 0.5561 351.8 2648.6 2296.8 85 0.5785 356.0 2650.2 2294.2 86 0.6016 360.2 2651.9 2291.7 87 0.6253 364.4 2653.5 2289.1 88 0.6499 368.6 2655.2 2286.6 89 0.6753 372.8 2656.8 2284.0 90 0.7015 377.0 2658.4 2281.4 91 0.7286 381.2 2660.0 2278.8 92 0.7565 385.4 2661.7 2276.3 93 0.7853 389.6 2663.3 2273.7 94 0.8150 393.8 2664.9 2271.1 95 0.8457 398.1 2666.5 2268.4 96 0.8772 402.3 2668.1 2265.8 97 0.9099 406.5 2669.7 2263.2 98 0.9434 410.7 2671.3 2260.6 99 0.9780 414.9 2672.9 2258.0 18

100 1.0139 419.1 2674.5 2255.4 101 1.0513 423.4 2676.1 2252.7 102 1.0896 427.6 2677.7 2250.1 103 1.1290 431.8 2679.3 2247.5 104 1.1694 436.0 2680.9 2244.9 105 1.2108 440.3 2682.4 2242.1 106 1.2533 444.5 2684.0 2239.5 107 1.2968 448.7 2685.5 2236.8 108 1.3415 452.9 2687.0 2234.1 109 1.3872 457.2 2688.5 2231.3 110 1.4341 461.4 2690.0 2228.6 111 1.4821 465.6 2691.5 2225.9 112 1.5323 469.9 2693.0 2223.1 113 1.5843 474.1 2694.5 2220.4 114 1.6376 478.3 2696.1 2217.8 115 1.6922 482.6 2697.6 2215.0 116 1.7482 486.8 2699.0 2212.2 117 1.8055 491.1 2700.5 2209.4 118 1.8641 495.3 2702.0 2206.7 119 1.9242 499.6 2703.4 2203.8 120 1.9857 503.8 2704.9 2201.1 121 2.0496 508.0 2706.3 2198.3 122 2.1153 512.3 2707.8 2195.5 123 2.1826 516.6 2709.3 2192.7 124 2.2514 520.8 2710.7 2189.9 125 2.3218 525.1 2712.1 2187.0 126 2.3939 529.3 2713.5 2184.2 127 2.4676 533.6 2714.9 2181.3 128 2.5436 537.8 2716.3 2178.5 129 2.6218 542.1 2717.7 2175.6 130 2.7018 546.4 2719.1 2172.7 131 2.7836 550.7 2720.5 2169.8 132 2.8672 554.9 2721.9 2167.0 133 2.9526 559.2 2723.3 2164.1 134 3.0404 563.5 2724.6 2161.1 135 3.1307 567.8 2726.0 2158.2 136 3.2229 572.0 2727.3 2155.3 137 3.3172 576.3 2728.7 2152.4 138 3.4135 580.6 2730.0 2149.4 139 3.5120 584.9 2731.3 2146.4 140 3.6133 589.2 2732.6 2143.4 141 3.7168 593.5 2733.9 2140.4 142 3.8226 597.8 2735.2 2137.4 143 3.9305 602.1 2736.5 2134.4 144 4.0411 606.4 2737.8 2131.4 145 4.1544 610.7 2739.0 2128.3 146 4.2701 615.0 2740.3 2125.3 147 4.3882 619.3 2741.6 2122.3 148 4.5088 623.6 2742.8 2119.2 149 4.6325 627.9 2744.0 2116.1 150 4.7588 632.2 2745.2 2113.0 151 4.8876 636.5 2746.5 2110.0 152 5.0191 640.8 2747.7 2106.9 19

153 5.1539 645.2 2748.9 2103.7 154 5.2913 649.5 2750.0 2100.5 155 5.4315 653.8 2751.2 2097.4 156 5.5747 658.1 2752.4 2094.3 157 5.7211 662.5 2753.5 2091.0 158 5.8704 666.8 2754.7 2087.9 159 6.0227 671.2 2755.8 2084.6 160 6.1784 675.5 2756.9 2081.4 161 6.3371 679.9 2758.1 2078.2 162 6.4989 684.2 2759.2 2075.0 163 6.6643 688.6 2760.2 2071.6 164 6.8329 692.9 2761.3 2068.4 165 7.0047 697.3 2762.4 2065.1 166 7.1802 701.6 2763.5 2061.9 167 7.3590 706.0 2764.5 2058.5 168 7.5412 710.4 2765.6 2055.2 169 7.7272 714.7 2766.6 2051.9 170 7.9167 719.1 2767.6 2048.5 171 8.1099 723.5 2768.6 2045.1 172 8.3068 727.9 2769.6 2041.7 173 8.5074 732.3 2770.6 2038.3 174 8.7119 736.7 2771.5 2034.8 175 8.9202 741.1 2772.5 2031.4 176 9.1325 745.5 2773.4 2027.9 177 9.3487 749.9 2774.4 2024.5 178 9.5689 754.3 2775.3 2021.0 179 9.7933 758.7 2776.2 2017.5 180 10.022 763.1 2777.1 2014.0 181 10.254 767.5 2778.0 2010.5 182 10.491 771.9 2778.8 2006.9 183 10.732 776.4 2779.7 2003.3 184 10.978 780.8 2780.6 1999.8 185 11.228 785.2 2781.4 1996.2 186 11.482 789.7 2782.2 1992.5 187 11.741 794.1 2783.0 1988.9 188 12.004 798.5 2783.8 1985.3 189 12.272 803.0 2784.6 1981.6 190 12.545 807.5 2785.4 1977.9 191 12.822 811.9 2786.1 1974.2 192 13.104 816.4 2786.9 1970.5 193 13.391 820.8 2787.6 1966.8 194 13.683 825.3 2788.3 1963.0 195 13.980 829.8 2789.0 1959.2 196 14.281 834.4 2789.7 1955.3 197 14.588 838.8 2790.3 1951.5 198 14.900 843.3 2791.0 1947.7 199 15.217 847.8 2791.6 1943.8 200 15.540 852.3 2792.3 1940.0 201 15.868 856.8 2792.9 1936.1 202 16.201 861.3 2793.5 1932.2 203 16.539 865.8 2794.0 1928.2 204 16.883 870.3 2794.6 1924.3 205 17.233 874.9 2795.2 1920.3 20

206 17.588 879.4 2795.7 1916.3 207 17.949 883.9 2796.2 1912.3 208 18.315 888.5 2796.7 1908.2 209 18.687 893.0 2797.2 1904.2 210 19.066 897.6 2797.7 1900.1 211 19.450 902.1 2798.1 1896.0 212 19.840 906.7 2798.6 1891.9 213 20.236 911.3 2799.0 1887.7 214 20.638 915.9 2799.4 1883.5 215 21.046 920.5 2799.8 1879.3 216 21.461 925.0 2800.1 1875.1 217 21.882 929.6 2800.5 1870.9 218 22.309 934.3 2800.8 1866.5 219 22.743 938.9 2801.2 1862.3 220 23.183 943.5 2801.5 1858.0 221 23.630 948.1 2801.7 1853.6 222 24.083 952.7 2802.0 1849.3 223 24.543 957.4 2802.3 1844.9 224 25.010 962.0 2802.5 1840.5 225 25.483 966.7 2802.7 1836.0 226 25.964 971.3 2802.9 1831.6 227 26.451 976.0 2803.1 1827.1 228 26.946 980.7 2803.2 1822.5 229 27.447 985.3 2803.4 1818.1 230 27.956 990.0 2803.5 1813.5 231 28.472 994.7 2803.6 1808.9 232 28.995 999.4 2803.7 1804.3 233 29.526 1004.1 2803.7 1799.6 234 30.064 1008.8 2803.8 1795.0 235 30.609 1013.6 2803.8 1790.2 236 31.162 1018.3 2803.8 1785.5 237 31.732 1023.0 2803.7 1780.7 238 32.292 1027.8 2803.7 1775.9 239 32.868 1032.5 2803.6 1771.1 240 33.452 1037.3 2803.6 1766.3 241 34.044 1042.1 2803.5 1761.4 242 34.644 1046.9 2803.3 1756.4 243 35.252 1051.7 2803.2 1751.5 244 35.869 1056.4 2803.0 1746.6 245 36.493 1061.3 2802.8 1741.5 246 37.126 1066.1 2802.6 1736.5 247 37.767 1070.9 2802.4 1731.5 248 38.417 1075.7 2802.1 1726.4 249 39.075 1080.6 2801.8 1721.2 250 39.742 1085.4 2801.5 1716.1 251 40.417 1090.3 2801.2 1710.9 252 41.102 1095.2 2800.8 1705.6 253 41.795 1100.1 2800.5 1700.4 254 42.497 1104.9 2800.1 1695.2 255 43.208 1109.9 2799.6 1689.7 256 43.928 1114.8 2799.2 1684.4 257 44.657 1119.7 2798.7 1679.0 258 45.395 1124.6 2798.2 1673.6 21

259 46.143 1129.6 2797.7 1668.1 260 46.900 1134.5 2797.1 1662.6 261 47.667 1139.5 2796.6 1657.1 262 48.443 1144.5 2796.0 1651.5 263 49.228 1149.5 2795.3 1645.8 264 50.024 1154.5 2794.7 1640.2 265 50.829 1159.5 2794.0 1634.5 266 51.644 1164.5 2793.3 1628.8 267 52.469 1169.5 2792.5 1623.0 268 53.304 1174.6 2791.8 1617.2 269 54.149 1179.7 2791.0 1611.3 270 55.004 1184.7 2790.1 1605.4 271 55.870 1189.8 2789.3 1599.5 272 56.746 1194.9 2788.4 1593.5 273 57.632 1200.0 2787.5 1587.5 274 58.529 1205.2 2786.5 1581.3 275 59.437 1210.3 2785.6 1575.3 276 60.355 1215.5 2784.6 1569.1 277 61.284 1220.7 2783.5 1562.8 278 62.224 1225.8 2782.4 1556.6 279 63.175 1231.0 2781.3 1550.3 280 64.137 1236.3 2780.2 1543.9 281 65.110 1241.5 2779.0 1537.5 282 66.095 1246.7 2777.8 1531.1 283 67.090 1252.0 2776.6 1524.6 284 68.097 1257.3 2775.3 1518.0 285 69.116 1262.6 2774.0 1511.4 286 70.146 1267.9 2772.6 1504.7 287 71.188 1273.2 2771.2 1498.0 288 72.242 1278.6 2769.8 1491.2 289 73.308 1283.9 2768.4 1484.5 290 74.386 1289.3 2766.9 1477.6 291 75.475 1294.7 2765.3 1470.6 292 76.577 1300.1 2763.7 1463.6 293 77.691 1305.6 2762.1 1456.5 294 78.818 1311.0 2760.5 1449.5 295 79.957 1316.5 2758.8 1442.3 296 81.109 1322.0 2757.0 1435.0 297 82.273 1327.5 2755.2 1427.7 298 83.450 1333.1 2753.4 1420.3 299 84.640 1338.7 2751.5 1412.8 300 85.843 1344.2 2749.6 1405.4 301 87.059 1349.9 2747.6 1397.7 302 88.288 1355.5 2745.6 1390.1 303 89.531 1361.1 2743.5 1382.4 304 90.787 1366.8 2741.4 1374.6 305 92.057 1372.5 2739.3 1366.8 306 93.340 1378.3 2737.0 1358.7 307 94.637 1384.0 2734.8 1350.8 308 95.947 1389.8 2732.5 1342.7 309 97.272 1395.6 2730.1 1334.5 310 98.611 1401.4 2727.6 1326.2 311 99.964 1407.3 2725.2 1317.9 22

312 101.33 1413.2 2722.6 1309.4 313 102.71 1419.1 2720.0 1300.9 314 104.11 1425.1 2717.3 1292.2 315 105.52 1431.1 2714.6 1283.5 316 106.95 1437.1 2711.8 1274.7 317 108.39 1443.1 2708.9 1265.8 318 109.84 1449.2 2706.0 1256.8 319 111.31 1455.3 2703.0 1247.7 320 112.80 1461.5 2699.9 1238.4 321 114.30 1467.7 2696.8 1229.1 322 115.82 1473.9 2693.6 1219.7 323 117.35 1480.2 2690.3 1210.1 324 118.90 1486.5 2687.0 1200.5 325 120.46 1492.8 2683.5 1190.7 326 122.05 1499.2 2680.0 1180.8 327 123.64 1505.7 2676.4 1170.7 328 125.26 1512.1 2672.7 1160.6 329 126.89 1518.7 2668.9 1150.2 330 128.53 1525.2 2665.0 1139.8 331 130.20 1531.9 2661.1 1129.2 332 131.88 1538.5 2657.0 1118.5 333 133.58 1545.3 2652.8 1107.5 334 135.29 1552.1 2648.5 1096.4 335 137.02 1558.9 2644.1 1085.2 336 138.77 1565.8 2639.6 1073.8 337 140.54 1572.8 2635.0 1062.2 338 142.33 1579.8 2630.3 1050.5 339 144.13 1586.9 2625.4 1038.5 340 145.95 1594.1 2620.5 1026.4 341 147.80 1601.4 2615.3 1013.9 342 149.66 1608.7 2610.1 1001.4 343 151.53 1616.1 2604.6 988.5 344 153.43 1623.6 2599.1 975.5 345 155.35 1631.2 2593.3 962.1 346 157.29 1638.8 2587.4 948.6 347 159.24 1646.6 2581.4 934.8 348 161.22 1654.5 2575.1 920.6 349 163.22 1662.5 2568.6 906.1 350 165.23 1670.6 2562.0 891.4 351 167.27 1678.8 2555.1 876.3 352 169.33 1687.2 2548.0 860.8 353 171.41 1695.7 2540.6 844.9 354 173.51 1704.4 2533.0 828.6 355 175.64 1713.2 2525.1 811.9 356 177.78 1722.3 2516.9 794.6 357 179.95 1731.5 2508.4 776.9 358 182.14 1740.9 2499.4 758.5 359 184.35 1750.6 2490.1 739.5 360 186.59 1760.6 2480.4 719.8 361 188.85 1770.8 2470.2 699.4 362 191.13 1781.4 2459.5 678.1 363 193.44 1792.4 2448.1 655.7 364 195.78 1803.8 2436.1 632.3 23

365 198.14 1815.7 2423.2 607.5 366 200.52 1828.2 2409.4 581.2 367 202.94 1841.5 2394.5 553.0 368 205.38 1855.8 2378.1 522.3 369 207.85 1871.3 2359.9 488.6 370 210.35 1888.6 2339.2 450.6 371 212.88 1908.3 2315.1 406.8 372 215.45 1932.5 2285.0 352.5 373 218.05 1965.7 2243.4 277.7 24

Enthalpy-entropy diagram (h-s) for steam 25

Ratio of specific heats (isentropic exponent) 26

Enthalpy for air and gases from light oil firing as function of temperature β x = ( 1 + f ) h GAS = h AIR + x Dh where x is the gas content defined as: 1 + β. f is the stoichiometric air-to-fuel ratio, f = 14.52 for light oil. The specific fuel consumption, β, is defined as β= m fuel /m air For pure air: x = 0. For pure combustion gases (= no air content): x = 1. Dh is the enthalpy difference (kj/kg) between 100% gases (x=1) and 100% air (x=0). Temperature ( C) Enthalpy for air, h AIR, (kj/kg) x=0 Dh (kj/kg) 10 10 0,5 20 20,1 1 30 30,1 1,6 40 40,2 2,1 50 50,2 2,7 60 60,3 3,3 70 70,3 3,9 80 80,4 4,6 90 90,5 5,2 100 100,6 5,9 110 110,7 6,6 120 120,8 7,3 130 130,9 8 140 141,1 8,7 150 151,2 9,4 160 161,4 10,2 170 171,6 10,9 180 181,8 11,7 190 192 12,5 200 202,2 13,3 210 212,5 14,1 220 222,7 14,9 230 233 15,7 240 243,3 16,6 250 253,6 17,4 260 264 18,3 270 274,3 19,1 280 284,7 20 290 295,1 20,9 300 305,6 21,8 310 316 22,7 320 326,5 23,6 330 337 24,5 340 347,5 25,4 350 358 26,4 360 368,6 27,3 370 379,2 28,3 380 389,8 29,2 390 400,4 30,2 400 411,1 31,2 410 421,8 32,2 27 Temperature ( C) Enthalpy for air, h AIR (kj/kg) x=0 Dh (kj/kg) 420 432,5 33,1 430 443,2 34,1 440 454 35,1 450 464,8 36,2 460 475,6 37,2 470 486,4 38,2 480 497,2 39,2 490 508,1 40,3 500 519 41,3 510 529,9 42,4 520 540,9 43,4 530 551,8 44,5 540 562,8 45,6 550 573,9 46,7 560 584,9 47,8 570 596 48,9 580 607 50 590 618,1 51,1 600 629,3 52,2 610 640,4 53,3 620 651,6 54,5 630 662,8 55,6 640 674 56,7 650 685,2 57,9 660 696,5 59,1 670 707,7 60,2 680 719 61,4 690 730,3 62,6 700 741,7 63,8 710 753 65 720 764,4 66,2 730 775,8 67,4 740 787,2 68,6 750 798,6 69,8 760 810 71 770 821,5 72,3 780 833 73,5 790 844,5 74,8 800 856 76 810 867,5 77,3

Temperature ( C) Enthalpy for air, h AIR (kj/kg) x=0 Dh (kj/kg) 820 879,1 78,6 830 890,6 79,8 840 902,2 81,1 850 913,8 82,4 860 925,4 83,7 870 937 85 880 948,7 86,3 890 960,3 87,6 900 972 89 910 983,7 90,3 920 995,4 91,6 930 1007,1 93 940 1018,9 94,3 950 1030,6 95,6 960 1042,4 97 970 1054,1 98,4 980 1065,9 99,7 990 1077,7 101,1 1000 1089,5 102,5 1010 1101,4 103,9 1020 1113,2 105,3 1030 1125,1 106,7 1040 1136,9 108,1 1050 1148,8 109,5 1060 1160,7 110,9 1070 1172,6 112,3 1080 1184,5 113,7 1090 1196,4 115,2 1100 1208,3 116,6 1110 1220,3 118 1120 1232,2 119,5 1130 1244,2 120,9 1140 1256,2 122,4 1150 1268,2 123,8 1160 1280,2 125,3 1170 1292,2 126,8 1180 1304,2 128,2 1190 1316,2 129,7 1200 1328,3 131,2 1210 1340,3 132,7 1220 1352,4 134,2 1230 1364,4 135,7 1240 1376,5 137,2 1250 1388,6 138,7 1260 1400,7 140,2 1270 1412,8 141,7 1280 1424,9 143,2 1290 1437 144,8 28

Specific heat, cp, for gases from light oil firing as function of temperature β x = ( 1+ f ) x is the gas content defined as: 1+ β. f is the stoichiometric air-to-fuel ratio, f = 14.52 for light oil. The specific fuel consumption, β, is defined as β= m fuel /m air. For pure air: x = 0. For pure combustion gases (= no air content): x = 1. 1390 Specific heat, J/kgK 1340 1290 1240 1190 x = 1.0 x = 0.9 x = 0.8 x = 0.7 x = 0.6 x = 0.5 x = 0.4 x = 0.3 x = 0.2 x = 0.1 x = 0 1140 1090 1040 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 Temperature, grad C 29

Gas and air amounts (m n 3 /kg of fuel) as function of LVH for different fuels 30

' CO 2 and O 2 contents in flue gas as function of air excess factor (equivalence ratio)

Siegerts formula: P fg t gas t = k * [ CO ] 2 REF DRY t ref = 25ºC, t = flue gas temperature in ºC, [CO 2 ] dry is the carbon dioxide fraction in % on dry flue gas (from combustion table), k is taken from a diagram and is dependent on fuel type. 32