Week 4.2 - Combustion Efficiency Calculation after Preheating

Objective:

A furnace is used to burn Methane and Air Mixture. A recuperator is connected to this furnace to recover some energy. What is the effect of preheating on the adiabatic flame temperature by changing pre-heating from 298 to 600K.

Does preheating help with fuel saving? How does combustion efficiency go up as a function of pre-heating temperature? 

Introduction

A recuperator is a special purpose counter-flow energy recovery heat exchanger positioned within the supply and exhaust air streams of an air handling system, or in the exhaust gases of an industrial process, in order to recover the waste heat. Generally, they are used to extract heat from the exhaust and use it to preheat air entering the combustion system. In this way they use waste energy to heat the air, offsetting some of the fuel, and thereby improves the energy efficiency of the system as a whole.

The stoichiometric reaction of methane and air is given by :

For balanced stoichiometric reaction,

Number of moles of CH4 = 1

Number of moles of air (O2+N2) = 9.52

Number of moles of products (CO2 + H2O + N2) = 10.52

For this reaction, CH4 is considered as fuel, N2 and O2 as air and products are CO2. H2O and N2.

Python Code

"""
Sample code for effect of pre-heating on AFT of methane
Stoichometric Reaction
CH4 + 2(O2+3.76N2) = CO2 + 2H2O + 7.52N2
"""
import cantera as ct 
import matplotlib.pyplot as plt
import math 
import numpy as np

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

# air
A = ct.Quantity(gas)
Temp = np.linspace(298, 600, 50)
T_gas = []


# fuel
B = ct.Quantity(gas)
B.TPX = 298, ct.one_atm, 'CH4:1' 
B.moles = 1

for T in Temp:
	A.TPX = T, ct.one_atm, 'O2:1, N2:3.76' 
	A.moles = 9.52

	M = A + B

	M.equilibrate('HP')
	Temperature = M.T
	T_gas.append(Temperature)

print(T_gas)
plt.plot(Temp, T_gas, '-o')
plt.xlabel('Preheating Temperature (K)')
plt.ylabel('Adiabatic Flame Temperature (K)')
plt.grid('on')
plt.title('Effect of preheating on AFT')
plt.show()

Thus, AFT increases with increase in preheating temperature.

With larger heating temperature, a large amount of useful heat is already available which causes the fuel to burn faster.

As a result, the amount of fuel consumption is reduced.

Due to using of recuperator to preheat the inlet air by utilizing waste heat from the exhaust gases, AFT increases due to available energy in the furnace. This increases combustion efficiency and results in saving of fuel.

Combustion efficiency is calculated as follows:

where, Q is the net heat 

m_f is the mass of fuel

LHV is the lower heating value which is 50MJ for methane. 

Percentage of fuel saving is calculated as follows:

where,

η is the combustion efficiency calculated at different values of preheating temperature.

η_STP is the combustion efficiency at STP conditions.

Python code

"""
Sample code for effect of pre-heating on AFT of methane
Stoichometric Reaction
CH4 + 2(O2+3.76N2) = CO2 + 2H2O + 7.52N2
"""
import cantera as ct 
import matplotlib.pyplot as plt
import math 
import numpy as np

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

# air
A = ct.Quantity(gas)
Temp = np.linspace(298, 600, 50)
A.TPX = 298, ct.one_atm, 'O2:1, N2:3.76' 
A.moles = 9.52
mass_air = A.mass
H_air = A.h
LHV = 50e6

# fuel
B = ct.Quantity(gas)
B.TPX = 298, ct.one_atm, 'CH4:1' 
B.moles = 1
mass_fuel = B.mass
H_fuel = B.h

#products
C = ct.Quantity(gas)
C.TPX = 1700,  ct.one_atm, 'CO2: 1, H2O :2, N2 :7.52'
C.moles = 10.52
mass_products = C.mass
H_products = C.h

Q_at_stp = (mass_fuel*H_fuel + mass_air*H_air - mass_products*H_products)
efficiency_at_STP = (Q_at_stp/(mass_fuel*LHV))*100

for T in Temp:
	A.TPX = T, ct.one_atm, 'O2:1, N2:3.76' 
	A.moles = 9.52
	mass_air = A.mass
	H_air = A.h

	Q = (mass_fuel*H_fuel + mass_air*H_air - mass_products*H_products)

	efficiency = (Q/(mass_fuel*LHV))*100

	saving = (efficiency/efficiency_at_STP - 1)*100

	plt.plot(T, efficiency, '-o', color = 'red')

	plt.plot(T, saving, '-o', color = 'green')

	
plt.xlabel('Preheating Temperature (K)')
plt.ylabel('Combustion Efficiency (η)')
plt.grid('on')
plt.legend(['Combustion Efficiency', 'Percentage of fuel saving'])
plt.title('Effect of preheating on Combustion Efficiency')
plt.show()

From the above graph, it can be said that upon preheating the air, combustion efficiency increases and saving of fuel also increaes.

The exit temperature of furnace depends on a number of factors such as quality of fuel, combustion rate, number of species etc. If the temperature of the products (flue gases in case of furnace) are not maintained to a limiting temperature, the output temperature can rise to a very high value which can cause damage to the components of furnace. Hence, it is important to control the exit temperatue of the furnace.