24 06 21sol

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WRITTEN TEST ENERGY SYSTEMS 24 JUNE 2021 Data Values from tables/Mollier charts Data from person code Person code: 12345678 1 2 3 4 5 6 7 8 X 36 Y 260 Problem 1 Data V biogas: 2600 Nm3/h xCH4 0.6 xCO2 0.4 Air excess 36 % Electric efficiency of the engine: eta,el = 38 % Exhaust gas temperature: Tg = 450 °C DTpp in the heat recovery steam generator: 18 °C cp,gas = 1.1 kJ/kgK LHV CH4 = 50 MJ/kg Results 1) 0.6 CH4 + 0.4 CO2 + 2*0.6*1.15*(O2 + 3.76 N2) -> CO2 + 2*0.6 H2O + 2*0.6*0.15 O2 + 2*0.6*1.15*3.76 N2 Combustion products: CO2 1 kmolCO2/kmolbiogas H2O 1.2 kmolH2O/kmolbiogas O2 0.432 kmolO2/kmolbiogas N2 6.14 kmolN2/kmolbiogas Total 8.77 kmolgas/kmolbiogas Molar fractions of combustion products xCO2 0.114 xH2O 0.137 xO2 0.049 xN2 0.700 2) CH4 input: VCH4 = Vbiogas*xCH4 = 1560 Nm3/h CH4 input: mCH4 = VCH4/3600/22.414*MMCH4 = 0.3093 kg/s Fuel energy input: Qfuel = mCH4*LHV = 15.47 MW Pel = Qfuel*eta,el = 5.88 MW 3) MM biogas = 0.6*16 + 0.4*44 = 27.2 kg/kmol Biogas input: Mbiogas = Vbiogas/3600/22.414 = 0.0322 kmol/s Biogas input: mbiogas = Mbiogas*MMbiogas = 0.876 kg/s Air input: Mair = 2*0.6*1.15*4.76 *Mbiogas = 0.2503 kmolair/s MM air = 0.21*32 + 0.79*28 = 28.84 kg/kmol Air input: mair = Mair*MMair = 7.219 kg/s Exhaust gas flow rate: mgas = mbiogas+mair = 8.095 kg/s Tsat steam at 6 bar = 158.8 °C Tgas, stack = Tsteam + DTpp = 176.8 °C DTgas in heat recovery steam generator = 273.2 °C Q recovered = mgas*cp,gas*DTgas = 2433 kW 4) Thermal efficiency: eta,th = Qrecovered / Qfuel = 15.73 % PES = 1/(eta,el/40 + eta,th/90) = 0.111 Problem 2 Pel = 36 MWe eta,el = 0.98 eta,isc = 0.85 eta,ist = 0.90 Tout,c = 300 °C TOT = 526 °C Tamb = 35 °C pamb = 1.01 bar Dp,filter = 1 % Dp,he = 3 % Dp,ex = 1 % cp,a = 1.05 kJ/kgK MMa = 28.85 kg/kmole gamma = 1.38 1) pin,c = pamb * (1-Dp,filter)…