Week 4 - Combustion Efficiency Calculation after Preheating

1. Effect of pre-heating air on adiabatic flame temperature:

Increasing temperature of air from 298.15K to 600K while keeping fuel at 298.15K increases adiabatic flame temperature because pre-heating air increases the sensible heat of air and that gets added to the heat generated by the reaction in the furnace.

Moles of ch4 =1

mole of oxidiser=2*(a+b)*1/a

a=1,b=3.76

M=A+B

M.equilibrate denotes that combustion reaction takes place and products formed at equilibrium.

code:

import cantera as ct 
import matplotlib.pyplot as plt 
gas=ct.Solution('gri30.cti')
a=1
b=3.76

for T in range(298,600,50):
	A=ct.Quantity(gas)
	
	A.TPX=T,ct.one_atm,{'o2':a,'n2':b}
	A.moles=(2*(a+b)*1/a)

	B=ct.Quantity(gas) 
	B.TPX=298.15,ct.one_atm,'ch4:1'
	B.moles=1 

	M=A+B
	M.equilibrate('HP')
	plt.plot(T,M.T,'*',color='blue')
	print(M.T)
plt.xlabel('pre-heated temperture of air')
plt.ylabel('Adiabatic flame temperature')
plt.grid('on')
plt.show()

Graph:

Conclusion:

The AFT of reaction when air T=298.15K is 2224.553002663298K

the AFT of reaction when air T=600K is 2346.0108784970967K

2. Using recuperator, which is basically a heat exchanger, the heat of exhaust gases coming from the furnace is used to pre heat the incoming air, when this heated air is mixed with fuel then the amount of useful heat generated from the furnace is greater then that produced by air at standard temperature, so we get more amount of useful heat with same amount of fuel , i.e pre-heating of air saves the fuel, also the exhaust gases are used to heat the air and so the temperature of exhause gas gets reduced finally, so carbon emissions going in the environment are also reduced. Here, we have taken the exit temperature from furnace as fixed as 1700K everytime and noticed the change of combustion efficiency with temperature of pre-heated air.

Combustion efficiency= Useful heat/ LHV

LHV for combustion of methane is 50MJ/kg

Useful heat can be found by energy balance,

mass of air*enthalpy of air+mass of fuel*enthalpy of fuel - Q(useful) -mass of products*enthalpy of products =0

mass balancing also needs to be done,

mass of air= 9.52moles*mass ofair=9.52*29 or (2*32+2*3.76*28)

mass of ch4=no. of molesof ch4*16

mass of products=10.52moles*mass of products or (2*18+7.52*28+44)

After finding heat from the energy balance equation,divide this by mass of fuel to find energy per kg of fue (i.e, Qsp),

Qsp when T=600 is = 22232728.14422331 J/kg

efficiency = Qsp/LHV=0.4468 ie 44.46%

efficiency of the system without pre-heating the air was 33.87%

Code:

In code the range of code is set to 298.15K to 600K for pre-heat temperature, the furnace exit temperature is 1700K everytime here.

import cantera as ct 
import matplotlib.pyplot as plt 
import numpy as arange
from numpy import arange
gas=ct.Solution('gri30.cti')

for T in arange(298.15,600,10):
	a=1
	b=3.76
	A=ct.Quantity(gas)
	#what matters is the ratio of o2 and n2 should be correct and the moles of oxidiser should be exactly those as per required for combustion with fuel
	A.TPX=T,ct.one_atm,{'o2':a,'n2':b}
	A.moles=2*(a+b)*1/a

	B=ct.Quantity(gas) 
	B.TPX=298.15,ct.one_atm,'ch4:1'
	B.moles=1 #can also say B.mass=16, if you dont give B.moles then it automatically takes moles in 1g of B, ie 1/16 ie 0.06moles of ch4 here


	C=ct.Quantity(gas)
	C.TPX=1700,ct.one_atm,{'Co2':1,'h2o':2,'n2':7.52}
	C.moles=10.52
	Q=(A.mass*A.enthalpy_mass+B.mass*B.enthalpy_mass-C.mass*C.enthalpy_mass)
	Qsp=Q/B.mass
	print(Qsp)
	eff=Qsp/50000000
	plt.plot(T,eff,'*',color='blue')
	print(T)
	print(eff)
plt.xlabel('Temperature')
plt.ylabel('combustion efficiency')
plt.grid('on')
plt.show()

Graph:

Conclusion: The combustion efficiency keeps on increasing as the temperature of air to be pre-heated is increased, meanwhile keeping the exit temperature from furnace to be a constant,as the air pre-heating temperature is increased, heat content of air increases, the heat content of products (at 1700k) and fuel (at 298.15K) remian same, so the useful heat content also increases as per the energy balance equation because heat taken by exhaust gases is still the same(had we increased the exit gs temperature, the amount of useful heat would have lessened) , as this useful heat is increased, the combusion efficiency is also increased, so pre-heating of air inreaeses the combustion efficiency linearly.

Using a fixed furnace temperature

If we increase the furnace temperature , then useful heat content will reduce, (keeping all the parameters same), beacuse more heat will be taken by exhaust gases then . Keeping the exit furnace temperature constant helps us analyse better the variation of efficiency with temperature of air , but it is not practial always or reasonable to have a defined value fixed , because we can choose to lessen the temperature of exhaust gas(to an extent that can get temperature of air upto a set pre-heating temperature) in order to get more useful heat on the other side.