Week 4 - Combustion Efficiency Calculation after Preheating

Problem Statement

A furnace is used to burn Methane and Air Mixture. A recuperator is connected to this furnace to recover some energy.

1. What is the effect of preheating on the adiabatic flame temperature?

   1. Change pre-heating from 298 to 600K

   2. Explain your results

Answer :

Recuperator

A high percentage of energy losses is seen to a intergal part of furnace . Recovering waste heat by pre heating incoming air or fuel can lead to substantial savings in the fuel. The preheating of air can be possible with recuperator.

Figure 1: Recuperator (*http://www.a2zenergies.com)

The methane is mixed with air in a furnace with recuperator (preheating). If we assume to have complete combustion then products will be CO2, H2O, and N2. The reaction may be written as

CH₄ + 2(O₂ + 3.76N₂) = CO₂ + 2H₂O + 7.52N₂

Methane (CH₄) is considered as Fuel, Air is an mixture of Oxygen(O₂) and Nitrogen(N₂) and products are (CO₂, H₂O, and N₂). Effect of preheating on AFT is shown in graph (Figure 2) , AFT temperature increases with increases in inlet air with the help of per-heating. Due to preheating we have Higher flame temperatures result in improved heating system efficiency and Less amount of heat is carried away with exhaust gases through chimney.

Figure 2: The effect of preheating on the adiabatic flame temperature

2. Does preheating help with fuel saving? If yes, how does combustion efficiency go up as a function of pre-heating temperature? Assume that the furnace exit temperature is 1700K (For this case assume that the combustion products are CO2, H20, and N2).

1. Write the formula for combustion efficiency

2. Plot the effect of pre-heat temeprature on combustion efficiency

3. Is it right or wrong to assume a fixed furnace exit temperature? Explain your answer.

NOTE: You will use cantera for these calculations. Assume the LHV of combustion of Methane as 50 MJ/KG.

Effect of preheating on AFT is shown in graph (Figure 2) , AFT temperature increases with increases in inlet air with the help of per-heating. It means we required less amount of fuel to reach at same temperature or by same amount of fuel we can reach to higher temperature by preheating of air by recuperator. The combustion efficiency can be find by following equations. It is noted that increasing the air temperature is result in increase in the Adiabatic Flame Temperature which also result, increse in efficiency of the system(Figure 3).

Q_generated = Q = ( mass_air * h_air + mass_fuel * h_fule – (mass_product * h_product )

Q_supplied = mass_fuel * LHV

combustion efficiency : Ƞ = Q / Q _supplied

Figure 3: Effect of pre-heat temeprature on combustion efficiency

For simplicity we may assume to have constant fixed furnace exit temperature . Practically it will not be constant. For efficient heat transfer in furnace and to enhance the life of furnace we required to maintained in specific range. This also necessary to reduced the emissions which reduce the after treatment cost.

What is the effect of preheating on the adiabatic flame temperature?

"""
EFFECT OF PRE_HEATING ON AFT
"""
import cantera as ct
import matplotlib.pyplot as plt
gas = ct.Solution('gri30.cti')

A = ct.Quantity(gas)
#A.TPX = 298.15,ct.one_atm,'CH4:1'
A.TPX = 298.15,101325,'CH4:1'
A.moles = 1
#pre heating temperatur
T_min = 298
T_max = 600
B = ct.Quantity(gas)
for T in range (T_min,T_max,10):
	B.TPX = T,101325,{'O2':0.21 , 'N2':0.79}
	B.moles = 2/.21
	M = A + B
	M.equilibrate('HP','auto')
	plt.plot(T,M.T,'.',color = 'red')

plt.title('EFFECT OF PRE-HEATING ON AFT')
plt.xlabel('PRE_HEATING TEMPERATURE')
plt.ylabel('AFT')
plt.show()

Programe for for combustion efficiency with Assume that the furnace exit temperature is 1700K (For this case assume that the combustion products are CO2, H20, and N2).

"""
Program to calculate combustion efficiency using cantera 
system with pre-heating , Assume that the furnace exit temperature is 1700K 
(For this case assume that the combustion products are CO2, H20, and N2)
"""
import cantera as ct
import numpy as np
import matplotlib.pyplot as plt

gas = ct.Solution('gri30.cti')
T_min = 298
T_max = 600
LHV = 50*pow(10,6)
fuel = ct.Quantity(gas)
fuel.TPX = 298.15, 101325, {'CH4':1}
fuel.moles = 1
#mass_fuel = fuel.mass
products = ct.Quantity(gas)
products.TPX = 1700, 101325, {'CO2':0.094, 'H2O':0.189, 'N2':0.715}
products.moles = 10.56
#mass_products = products.mass
for T in range (T_min,T_max,10):
	air = ct.Quantity(gas)
	air.TPX = T, 101325, {'O2':0.21, 'N2':0.79}
	air.moles = 2/.21
	Q = ((air.mass*air.h) + ((fuel.mass)*fuel.h - (products.mass)*products.h ))
	Q_s = fuel.mass * LHV  # heat supplied = mass of fuel * LHV
	efficiency = (Q/Q_s)
	print(fuel.mass , air.mass , Q , Q_s)
	plt.plot(T, efficiency, '*',color= 'red')
	


plt.grid()
plt.xlabel('Pre Heating Temperature')
plt.ylabel('efficiency')
plt.title('Effect of preheating on efficiency')
plt.show()