In steady state, the Gas engine is fed a stream of natural gas at 100 moles/s ST

Question

In steady state, the Gas engine is fed a stream of natural gas at 100 moles/s STP (25°C, 1 atm).

You are the design engineer for a natural gas co-generation power facility shown in the diagrarm below. You have been asked if the facility's exhaust gas can be fed to a greenhouse in order to grow plants without having to add a make up stream of air to cool it. This can be done if the temperature of the facility's exhaust gas is less than 130°F (54.4°C). In steady state, the Gas engine is fed a stream of natural gas at 100 moles/s STP (25°C, 1 atm). The gas composition is methane and ethane in a mole ration of 19:1. It is combusted with 20%. excess dry air, which is also at STP; all the exhaust gases (CO,, HO, O., N) exit the gas engine at 900°C, 1 atm. 55.42 kW of electric power are generated, heat is lost to the surroundings at a rate of of the heat from the gas engine is removed through the cooling water loop at Heat Exchanger#1 . The exit temperature of the water from Heat exchanger#1 that becomes the feed stream for Heat exchanger#2 is 3 Steam Generator feed is city water at 20.0°C. It removes heat from the Exhaust gas of the Gas engine to produce steam at 200.0°C at 5 atm. The Exhaust gas exiting the steam generator is 200.0 °C, 1 atm. The Steam eventually returns to the Heat exchanger#1 after going throug several processes (outside of the system diagram); it returns at 20.0°C. The Facility exhaust gas exits the Heat exchanger#2 at 1 atm Air Electricity Fuel gas 1.00 kW, and the rest #1 Heat exchanger Feed water Steam generator Steam 0.0°C. The #2 Heating water Heat exchanger Heating water flow Facility Exhaust gas and the same temperature as the Heating water flow.

Explanation / Answer

Gas stream feed moles = 100 moles/s

Feed composition = 19/20 mole fraction methane, 1/20 mole fraction ethane

=> Moles of Methane in feed = 19/20*100 = 95 mole/s

=> Moles of Ethane in feed = 1/20*100 = 5 mole/s

Methane combustion reaction, CH4+2O2=>CO2+2H2O

Ethane combustion reaction, C2H6+3.5O2=>2CO2+3H2O

=> Total H2O moles produced in combusttion = 95*2+5*3=205 mol/s

=>Total CO2 moles produced in combusttion =95*1+5*2 = 105 mol/s

=> Total O2 moles required to combust feed = 95*2+5*3.5=207.5 mol/s

% excess air = 20%

=> O2 in Outlet of Gas engine = 20/100*207.5=41.5 mol/s

O2 mole fraction air = 21%

N2 mole fraction in air = 100%-21%=79%

=> N2 in outlet of Gas engine = 41.5/.21*.79=156.1 mol/s

Outlet

Total flowrate = 105+205+41.5+156.1=507.6 mol/s

Mixture Cp = Mole fraction of component i* Cp of component i = (.2*3.61+.4*3.35+.08*2.91+.32*2.9)*10^-2=.032 KJ/mol/K

Gas Engine Outlet Parameters = (900 C, 1 atm)

Steam Generator Gas outlet Parameters = (200C, 1 atm)

Total Heat released by exhaust gas from Gas engine to STeam Generator outlet = flowrate*Cp*DeltaT=507.6*.032*(900-200) = 11370 KJ/s = 11370 KW

Total Heat released by exhaust gas from Gas engine to STeam Generator outlet = Electricity generated + Heat lost to surrounding + Heat lost to Steam generator

Electricity generated= 55.42 KW

Heat lost to surrounding=1 KW

Heat lost to Steam generator = 11370-55.42-1=11313.5 KW

Heat lost to Steam generator = Heat required to generate steam @ 200 C, 5 atm from feed water @ 20 C, 1atm = flowrate of water*(hvapor(200,5)-hwater(20,1))

=>11313.5=flowrate of water*(2856-81)

=>flowrate of water = 4 Kg/s

Same water from steam generator outlet feed into Heat exchanger 1 and then feed to Heat exchanger 2 at (30C, 1 atm)

=> Heat lost to water in Heat exchanger 2 = Heat lost by exhaust gas in Heat exchanger 2

Cp of water = 7.54*10^-2 KJ/mol =4.18 KJ/Kg/C

=> 4*4.18*(T-30)=507*.032*(200-T)

(T outlet of water = T outlet of exhaust gas in Heat exchanger 2)

=> T=113.46 C

Because T of outlet exhaust gas is more than required = 54.6 C. Hence it can't be used alone for Greenhouse.

Component flowrate, mol/s Mole fraction CO2 105 0.2 H2O 205 .4 O2 41.5 .08 N2 156.1 .32

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