Combustion Efficiency Calculation after Pre-heating

Problem definition:

1) Calculation of Adiabatic Flame Temperature for various pre-heating temperature ranging from 298k to 600k

2) Calculation of Percentage of fuel savings to the change in pre-heating temperature

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A recuperator is a heat exchanger in which energy from a steady flow of hot combustion products, i,e., flue gas, is transferred to the air supplied to the combustion process. In this, a program had done to study the effect of Adiabatic flame temperature as a result of varying the pre-heating temperature of the air. On the meanwhile, a study was done on the percentage of fuel savings concerned to change in the pre-heating temperature.

Calculation of Combustion Efficiency:

`eta = Q/(dotm_f *LHV) ->1`

`-Q = dotm(h_"prod"-h_"react")`

`h_"react" = h_f + h_A`

`-Q = (dotm_A+dotm_f)h_p-dotm_f*h_f-dotm_A*h_A. ->2`

Applying 2 in 1:

`eta = (- (dotm_A+dotm_f)h_p+dotm_f*h_f+dotm_A*h_A)/(dotm_f*LHV) ->3`

`(A/F) = (dotm_A/dotm_f)`

We can rewrite the equation 3 as:

`eta = (-((A/F)+1)h_p +h_f + (A/F)h_A)/(LHV)`

Calculation of `(A/F)`

`phi = ((A/f)_"stoic"/(A/F))`

`(A/F)=((A/F)_"stoic")/phi`

Assuming `phi = 1`, therefore

`(A/F)=(A/F)_"stoic"`

`(A/F) = (4.76*a*MW_"air")/(MW_"fuel")`

where,

a = stoichiometric co-efficient (which is 2 in this case)

MW = Molecular weight

`MW_"air" = 28.97 g/(mol)`

Calculating the molecular weight of Fuel

Carbon = 1*12 = 12

Hydrogen = 4*1 = 4

`MW_"fuel"= 16``(A/F)=17.99`

The formula for Fuel savings:

`= 1 - eta_298/eta_"pre-heating temperature"`

Calculation of Combustion products:

The products of the combustion are `CO_2, H_2O, N_2.`

By balancing the moles of `CO_2 = 1`, `H_2O=2`

Total moles in the reaction = 10.52 (`N_2 = 7.52, O_2=2, CH_4 =1`)

Molar fraction of Nitrogen = `7.52/10.52 = 0.7148`

Molar fraction of `CO_2 = 1/10.52 = 0.09508`

Molar fraction of `H_2O = 2/10.52 = 0.1901`

Plotting:

In the above graph, Adiabatic Flame Temperature, Combustion efficiency, and fuel savings are compared with pre-heating temperature. It is noted that increasing the air temperature will affect directly on the Adiabatic Flame Temperature, the trend is growing as the pre-heating temperature increases, which also concludes that the efficiency of the system gets increased.

Python Code:

"""
    Calculation of recuperator efficieny by varying the preheat temperature
    
"""

import cantera as ct
import numpy as np
import matplotlib.pyplot as plt

T_p = np.linspace(298,600,15)
gas = ct.Solution('gri30.cti')

T = []
fuel_s = []
combustion_efficiency = []

#calculation of combustion efficiency at 298k
A = ct.Quantity(gas)
A.TPX = 298,ct.one_atm,'O2:0.21, N2:0.79'
A.moles = (2*3.76)/0.79


C = ct.Quantity(gas)
C.TPX = 1700,ct.one_atm,'CO2:0.095, H2O:0.1901, N2:0.7148'
C.moles = 10.52

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

h_prod = (C.enthalpy_mass * 0.001)
h_air = (A.enthalpy_mass * 0.001)
h_fuel = (B.enthalpy_mass * 0.001)

# Assuming LHV would be 50000 KJ
LHV = 50000
effciency_298 = (-((17.99+1)*h_prod - (17.99)*h_air - h_fuel)) / LHV
#calculation of AFT wrt pre heating with various temperature
for t in T_p:
    A = ct.Quantity(gas)
    A.TPX = t,ct.one_atm,'O2:0.21, N2:0.79'
    A.moles = (2*3.76)/0.79

    B = ct.Quantity(gas)
    B.TPX = 298.15,ct.one_atm,'CH4:1'
    B.moles = 1
    M =A+B
    M.equilibrate('HP')
    T.append(M.T)

    C = ct.Quantity(gas)
    C.TPX = 1700,ct.one_atm,'CO2:0.095, H2O:0.1901, N2:0.7148'
    C.moles = 10.52

    #calculation of combustion efficiency
    """
    nu = -((A/f)+1)h_prod - (A/F)h_air - h_fuel) / LHV
    """
    # calculation of enthalpy of reactants and products

    h_prod = (C.enthalpy_mass * 0.001)
    h_air = (A.enthalpy_mass * 0.001)
    h_fuel = (B.enthalpy_mass * 0.001)
    
    #Calculation of Combustion efficiency
    efficiency = (-((17.99+1)*h_prod - (17.99)*h_air - h_fuel)) / LHV
    combustion_efficiency.append(efficiency)
    #calculation of fuel saving
    savings = (1 - (effciency_298/efficiency)) * 100
    fuel_s.append(savings)

# plotting
X = "Pre-heating Temperature"
Y1 = "Adiabatic Flame Temperature"
Y2 = "percentage of Fuel savings"
Y3 = "combustion_efficiency"
plt.figure(1)
plt.plot(T_p,T,'o',color='red')
plt.xlabel(X)
plt.ylabel(Y1)
plt.title("{} vs {}".format(X,Y1))
plt.show()
plt.figure(2)
plt.plot(T_p,fuel_s,'*',color='blue')
plt.ylim(0,25)
plt.xlabel(X)
plt.ylabel(Y2)
plt.title("{} vs {}".format(X,Y2))
plt.show()
plt.figure(3)
plt.plot(T_p,combustion_efficiency,'o',color='green')
plt.xlabel(X)
plt.ylabel(Y3)
plt.title("{} vs {}".format(X,Y3))
plt.show()