Combustion Efficiency Calculation after Preheating

In this challenge, a furnace is used to combust methane and air. A recuperator is connected to utilize the waste heat and preheat the incoming air to the furnace. This study includes the effect of preheating on Adiabatic Flame Temperature (AFT), combustion efficiency and fuel saving.

Recuperator is a counter-flow energy recovery heat exchanger positioned within the supply of airstreams and exhaust gases of the furnace in order to recover the waste heat. In general, they are used to preheat air entering the combustion system.

Stoichiometric equation of methane is as follows:

`CH_4+2(O_2+3.76N_2)=CO_2+2H_2O+7.52N_2`

Effect of Pre-heating on AFT:

Here two instances of \'Air\' and \'Fuel\' of the quantity class are created to handle the air-fuel mixture. TPX is used to define the state of fuel and air. Fuel is at STP and a mole fraction of methane in fuel is 1. Moreover, moles of fuel needs to be defined or else Cantera by default assumes moles/grams of fuel which is 1 in this case. As far as, the air is concerned temperature of air varies from 298-600 K, 1 atm pressure and, appropriate mole fraction and the total number of moles of O2 and N2 from the above equation are specified. After this \'Air\' and \'Fuel\' are added by another variable called \'Mixture\' to determine the properties and the effects of pre-heat temperature for combustion of \'Mixture\'.

\"\"\"
Creating mixtures
CH4+2(O2+3.76N2)=CO2+2H2O+7.52N2
\"\"\"
import cantera as ct
import matplotlib.pyplot as plt
gas = ct.Solution(\'gri30.cti\')

Air = ct.Quantity(gas)
Fuel = ct.Quantity(gas)
Fuel.TPX = 298.15,ct.one_atm,\'CH4:1\'
Fuel.moles = 1

AFT=[] #adaibatic flame temperature
preheat_T = [] # preheating

for T in range (298,601):
	Air.TPX = T,ct.one_atm,{\'O2\':0.21,\'N2\':0.79}
	Air.moles = 9.52
	preheat_T.append(T)
	Mixture=Air+Fuel
	Mixture.equilibrate(\'HP\')
	AFT.append(Mixture.T)
plt.plot(preheat_T,AFT)
plt.xlabel(\'Preheating Temperature\')
plt.ylabel(\'Adiabatic Flame Temperature\')
plt.title(\'Effect of Preheating Temperature on AFT\')
plt.show()

From the above result, it is evident that upon preheating the incoming Air, AFT rises. At 298K the AFT is 2224K which is the same as AFT of methane at constant pressure as we are using a constant pressure furnace and \'HP\' (set enthalpy/pressure) to solve the equilibrate. Preheated air is at a higher temperature than the standard atmospheric temperature (298K) which increases the energy content (enthalpy) of air. Hence, it increases the AFT as well.

Effect on Combustion Efficiency and Fuel Saving:

Upon using the recuperator to preheat the inlet air by utilizing the waste heat from exhaust gases, AFT rises due to increase in energy available in the furnace. Here the same amount of fuel is used but with an increase in combustion efficiency. Hence, it saves fuel as well.

`% of Fuel Savi ng =((m ̇_f (with out Recu perat o r)-m ̇_f (withRecu pera t o r)))/(m ̇_f (with out Recu perat o r) )*100`

Since we are using the same amount of fuel, then the % of fuel-saving can be calculated as:

`% of Fuel Savi ng =(η-η_(STP))/η_(STP )`

Here η is the combustion efficiency which can be calculated as:

`Combustion efficie ncy = (Q_(air)+Q_(fuel)-Q_(p roducts))/Q_(LHV)*100`

`Q_(air)=m ̇_(air) h_(air,T)`

`Q_(fuel)=m ̇_(fuel) h_(fuel,298)`

`Q_(p roducts)=m ̇_(p roducts)h_(p roducts,1700)`

and η_(STP ) is the combustion efficiency when air and fuel are at STP.

\"\"\"
Creating mixtures
CH4+2(O2+3.76N2)=CO2+2H2O+7.52N2
\"\"\"
import cantera as ct
import matplotlib.pyplot as plt
gas = ct.Solution(\'gri30.cti\')


#---------------------------------------------------------------------------------
#                          Calculating LHV from Cantera
#---------------------------------------------------------------------------------

Air = ct.Quantity(gas)
Air.TPX = 298.15,ct.one_atm,{\'O2\':2/9.52,\'N2\':7.52/9.52}
Air.moles = 9.52

Fuel = ct.Quantity(gas)
Fuel.TPX = 298.15,ct.one_atm,\'CH4:1\'
Fuel.moles = 1

Mixture=Air+Fuel


Y_CH4 = gas[\'CH4\'].Y[0] #mass fraction of fuel in mixture


Products = ct.Quantity(gas)
Products.TPX = 298.15,ct.one_atm,{\'CO2\':1/10.52,\'H2O\':2/10.52,\'N2\':7.52/10.52}
Products.moles = 10.52

LHV = (((-Products.enthalpy_mass+Mixture.enthalpy_mass)/Y_CH4))# remember cantera gives J/kg of mixture converting the del_h in terms of per mass of fuel
print(LHV)

Q_LHV = Fuel.mass*LHV
#---------------------------------------------------------------------------------------------------------------------------------
#                                   Combustion Efficiency & Fuel Saving Calculation
#---------------------------------------------------------------------------------------------------------------------------------
Air = ct.Quantity(gas)
Air.TPX = 298.15,ct.one_atm,{\'O2\':0.21,\'N2\':0.79}
Air.moles = 9.52
mass_air = Air.mass
h_air = Air.enthalpy_mass
Q_air = mass_air*h_air

Fuel = ct.Quantity(gas)
Fuel.TPX = 298.15,ct.one_atm,\'CH4:1\'
Fuel.moles = 1
mass_fuel = Fuel.mass
h_fuel = Fuel.enthalpy_mass
Q_fuel = mass_fuel*h_fuel

Products = ct.Quantity(gas)
Products.TPX = 1700,ct.one_atm,{\'CO2\':1/10.52,\'H2O\':2/10.52,\'N2\':7.52/10.52}
Products.moles = 10.52
mass_products = Products.mass
h_products = Products.enthalpy_mass
Q_products = mass_products*h_products

eff_STP = (Q_air+Q_fuel-Q_products)/Q_LHV*100
print(eff_STP)

preheat_T = [] # preheating
Efficiency = [] #efficiency 
Efficiency1 = [] # fuel saving efficiency 

for T in range (298,601):
	Air.TPX = T,ct.one_atm,{\'O2\':0.21,\'N2\':0.79}
	Air.moles = 9.52
	preheat_T.append(T)
	mass_air = Air.mass
	h_air = Air.enthalpy_mass
	Q_air = mass_air*h_air
	eff = (Q_air+Q_fuel-Q_products)/Q_LHV*100						   # to calculate combustion efficiency
	eff1 = abs(eff-eff_STP)/eff_STP*100                                # to calculate improvement in efficiency or % of fuel saving
	Efficiency.append(eff)
	Efficiency1.append(eff1)

plt.plot(preheat_T,Efficiency)
plt.plot(preheat_T,Efficiency1,color =\'red\')
plt.xlabel(\'Preheating Temperature\')
plt.ylabel(\'Efficiency\')
plt.title(\'Effect of Preheating Temperature on Efficiency\')
plt.legend([\'Combustion Efficiency\',\'Fuel Saving\'])
plt.show()

It is evident from the above graph that upon preheating the air, combustion efficiency increases as well as, the fuel is also saved.

Preheating temperature depends on the temperature of the products after the combustion, if the temperature of the products is not maintained to a limiting temperature (furnace exit temperature), the output temperature (i.e., exhaust temperature) will continue to rise as the cycle proceeds. Therefore, not maintaining the temperature may lead to damage to components.