## Heat Recuperator - Combustion Efficiency

In this challenge, the efficiency of using a heat recuperator to pre-heat the air is analyzed. For that, we simulate a furnace burning methane and air mixture, and we analyze first how the pre-heating affects at the AFL, and then the total heat/work that could be extracted from the cycle. All this work is performed using Cantera.

1) Effect of preheating in the AFL.

To compute this, a simple program was written in Cantera, using the Quantity objects to create the mixtures. The program can be found attached at the end of the project.

As expected, pre-heating the air before entering the furnace makes that the adiabatic temperature of the products increases. It does it in an almost linear function. This way, the combustion can takes place sooner and not so much energy needs to be employed in heating the air, and therefore it can be used into further heating the products. This is, the products of the combustion are going to increase their temperature when the air is preheated.

2) Combustion Eficciency with Heat Recuperator

First, mention that the combustion efficiency refered here is calculated as the ratio from the Specific Q extracted from the reaction to the LHV. Assuming an adiabatic furnace,  Qout =(Enthalpy of Reactants - Enthalpy of Products), and the LHV is the max extractable energy from a chemical reaction taking place at STP.

What this means is that, hypothetically, if we keep increasing the Qout by simply increasing the preheat temperature without any constraint, efficiency can be greater than 1. However, the air preheating temperature is dependent on the exhaust temperature after the combustion, and we know that this will be less than the AFT, as there will be some work done and there will be some losses as well. Therefore a realistic estimate after certain approximations is that the exhaust temperature is set to a constant value of 1700 K.

The above results show what was expected. Indeed preheating the air would lead to a higher efficiency in the combustion process. The outcome of any combustion is the Total Q that can be extracted from it (normally to produce Work). This shows that preheating the air would lead to higher values of this heat, or what is the same, that we don't need to work in the stechiometric relation to achieve the desired heat. Therefore, we can save in fuel by preheating the air employing a heat recuperator, and then produce combustion with less fuel than the stoichiometric.

"""
Sample code to vary the temperature of air and oxidizier individually
And find the impact of Pre-heating the air in the AFL
"""
import cantera as ct
import matplotlib.pyplot as plt

gas = ct.Solution('gri30.cti')

B = ct.Quantity(gas)
B.TPX = 298.15, ct.one_atm, 'CH4:1'
print(B.moles) #By default, it is the number of moles in 1g of air
print(B.mass_fraction_dict())
B.moles = 1

n = 50
Tpre_min = 298
Tpre_max = 600

for i in range (0,n):

Tpre = Tpre_min + (Tpre_max-Tpre_min)*i/n
A = ct.Quantity(gas)
A.TPX = Tpre, ct.one_atm, {'O2':0.21, 'N2':0.79}
phi=1
A.moles = 2*4.76/phi #9.523

#The following step is used to apply the molar balance
M = A+B
M.equilibrate('HP')
print(M.T)
plt.plot(Tpre,M.T,'*',color='red')

plt.xlabel('Pre-Heating Temperature [K]')
plt.title('Effect of the Pre-Heating in AFL')
plt.show()
"""
This programs analyzes the effect of air pre-heating into the combustion efficiency
"""
import cantera as ct
import matplotlib.pyplot as plt

gas = ct.Solution('gri30.cti')

#By default, it is the number of moles in 1g of air.
R = ct.Quantity(gas)
R.TPX = 298.15,ct.one_atm,{'CH4':0.095,'O2':0.1901,'N2':0.7148}
R.moles = 2/0.21+ 1 #The total number of moles is 10.52. There is 1 mole of fuel per 9.52 of air.

P = ct.Quantity(gas)
P.TPX = 298.15,ct.one_atm,{'CO2':0.095,'H2O':0.1901,'N2':0.7148}
P.moles = 2/0.21 + 1

LHV = R.H - P.H
print(LHV)

n = 50
Tpre_min = 298
Tpre_max = 600

for i in range (0,n):

phi=1 #Stechiometric combustion

Tpre = Tpre_min + (Tpre_max-Tpre_min)*i/n
A = ct.Quantity(gas)
A.TPX = Tpre, ct.one_atm, {'O2':0.21, 'N2':0.79}
A.moles = 2/0.21*phi #9.523
M_air = A.mass

F = ct.Quantity(gas)
F.TPX = 298.15,ct.one_atm,{'CH4':1}
F.moles = 1
M_fuel = F.mass

P2 = ct.Quantity(gas)
P2.TPX = 1700,ct.one_atm,{'CO2':0.095,'H2O':0.1901,'N2':0.7148}
P2.moles = 2/0.21*phi + 1

H_react_A = A.H
H_react_F = F.H
H_prod = P2.H

Air_to_fuel = M_air/M_fuel

Q = Air_to_fuel*H_react_A + H_react_F - (Air_to_fuel + 1)*(H_prod)
Qsp = Q/M_fuel
eff = Qsp/LHV
plt.plot(Tpre,eff,'*',color='red')

plt.xlabel('Pre-Heating Temperature [K]')
plt.ylabel('Combustion Efficiency')
plt.title('Effect of the Pre-Heating in Combustion Efficiency')
plt.show()


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