Week 4.2 - Combustion Efficiency Calculation after Preheating

Combustion Efficiency Calculation after Preheating

OBJECTIVE:

To know about the effect of preheating the inlet air from the exhaust gases of a recuperator on the adiabatic Flame Temperature and also the combustion efficiency. We can also caluculate the fuel saved due to preheating.

RECUPERATOR:

In simple words, Recuperator is used to claim the heat comes after combustion and recycle it . The term recuperator refers as well to liquid-liquid counterflow heat exchangers used for heat recovery in the chemical and refinery industries and in closed processes such as ammonia-water or LiBr-water absorption refrigeration cycle.

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.

Combustion efficiency Caluculation:

Assuming the heat transferred to the load and the heat losses are same, from energy balancing the control volume, the heat transferred out of control volume is,

-Q = -Qload - Qloss

= m(Hprod - Hreac)

= m_prod*h_prod - m_A*h_A - m_F*h_F

Q = -(m_prod*h_prod - m_A*h_A - m_F*h_F)

Specific Work, Qspec = Q/m_F

Combustion efficiency,η = Qspec/LHV

Fuel saved = 1 - η_298/ η_600

EFFECT OF PREHEATING ON ADIABATIC FLAME TEMPERATURE:

"""
	Caluculating the effect of Pre-Heating on the Adiabatic Flame Temperature.
	CxHy + a(O2 + 3.76N2) = xCO2 + (y/2)H2O + 3.76aN2
	Considering the Fuel as Methane combusying with Air.
	CH4 + 2(O2 + 3.76N2) = CO2 + 2H2O + 7.52N2
"""

import cantera as ct  
import matplotlib.pyplot as plt

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


#Fuel
#Defining the quantity of the gas by using quantity class
Fuel = ct.Quantity(gas)
Fuel.TPX = 298.15,ct.one_atm,{'CH4':1}
Fuel.moles = 1

Tpre_min = 298
Tpre_max = 600

#Air
Air = ct.Quantity(gas)
for T_pre in range(Tpre_min, Tpre_max+1):
	Air.TPX = T_pre,ct.one_atm,{'O2':0.21,'N2':0.79}
	Air.moles = 9.52

	#Adding both the fuel and air for combustion
	M = Air + Fuel
	M.equilibrate('HP','auto')
	AFT = M.T
	if T_pre%10 == 0:
		plt.plot(T_pre,AFT,'*',linewidth=1,linestyle='dashed',marker='o',markerfacecolor='blue',markersize=1.5)



plt.xlabel('Pre-Heat temperature[K]')
plt.ylabel('Adiabatic Falme Temperature [K]')
plt.title('Fuel Saving with Pre Heating')
plt.grid(True)
plt.show()

PROCEDURE:

• Importing the Cantera and matplot libraries for solving the chemical combustion and for plotting the results.
• Creating the 'gas' object by using the solution class with 'gri30.cti.
• By using the 'quantity' class, defing the Fuel with 'TPX' data. After that defining the number of moles of fuel species involving in combustion.
• Defining the initial and final preheating temperatures.
• By using a For loop, we wil define the 'Air' quantity and defining the number of moles of air.
• Caluculating the Adiabatic Flame Temperature using Equilibrate method.
• Plotting the results.

Results:

Observation:

• By looking the above plot, we can observe the adiabatic flame temperature increasing with the increase in preheating temperature linearly.
• For an increse of pre-heating temperature from 298k to 600k, the AFT increses from 2224.35k to 2346.61k.

FUEL SAVING CALUCULATION:

1.Formula for combustion efficiency: As discussed in the theory of recuperator, the formula for comsution efficinecy is,

Combustion efficiency,η = Qspec/LHV

"""
CxHy + a(O2 + 3.76N2) = xCO2 + (y/2)H2O + 3.76aN2
Considering the fuel as methane
CH4 + 2(O2 + 3.76N2) = CO2 + 2H2O + 7.52N2
Heat transferred or heat loss is
-Q = -Qload - Qloss
   = m(Hprod - Hreac)
   = mexhaust* Hprod + mreac*Hreac
   = (m_A + m_F)* hprod -m_A*h_A - m_F*h_F
 comb_eff = Q / m_F * LHV
  A_F = m_A/m_F

  comb_eff = -(A-F*hprod -A_F*h_A-h_F)/LHV

"""




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

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

LHV = 50e6  #j

#fuel
Fuel = ct.Quantity(gas)
Fuel.TPX = 298.15,ct.one_atm,{'CH4':1}
Fuel.moles = 1
h_F = Fuel.enthalpy_mass                   #Enthalpy of the fuel
m_F = Fuel.mass                            #Mass of the fuel
#print("Enthalpy of fuel:", Fuel.enthalpy)

#products
Products = ct.Quantity(gas)
Products.TPX = 1700,ct.one_atm,{'CO2': 0.0950 , 'H2O': 0.1901, 'N2': 0.71483}
Products.moles = 10.52
h_prod = Products.enthalpy_mass            #Enthalpy of the products
m_p=Products.mass                          #Mass of the products
#print("Enthalpy of Products:", Products.enthalpy)

Tpre_min = 298
Tpre_max = 600
LHV = 50e6
eff = []
fuel_saving = []
T_ph = []


for T_pre in range(Tpre_min,Tpre_max+1):

	#air
	Air = ct.Quantity(gas)
	Air.TPX = T_pre,ct.one_atm,{'O2':0.21,'N2':0.79}
	Air.moles = 9.52
	m_a = Air.mass   					#Mass of the air
	h_air = Air.enthalpy_mass 			#Enthalpy of the air
	#print("Enthalpy of air:", Air.enthalpy)
	
	#Heat transferred out from the system	
	Q = m_a*h_air+m_F*h_F-m_p*h_prod

	Qsp = Q/m_F #sp = specific work
	#Combustion Efficiency
	η = (Qsp/LHV ) 

	#Caluculating the fuel saved
	if T_pre==298:
		η_0=η
	secured_fuel = 100*(1-(η_0/η))

	#Appending the values of fuel saved
	fuel_saving.append(secured_fuel)
	T_ph.append(T_pre)
	eff.append(η)

	if (T_pre%10==0):
		plt.figure(1)
		plt.plot(T_pre,η,'.',color='teal',markersize=5)


# plotting the results for Pre Heat temperature vs Combustion efficiency.
plt.figure(1)
plt.plot(T_pre,η,color='blue')
plt.xlabel('Pre Heat Temperature(K)')
plt.ylabel('Combustion Efficiency')
plt.title('Effect of Pre Heating on Combustion Efficiency')
plt.grid(True)

#plotting the results for Preheat temperature vs Fuel Saved.
plt.figure(2)
plt.plot(T_ph,fuel_saving,linewidth=1,linestyle='dashed',marker='o',markerfacecolor='blue',markersize=1.5)
plt.xlabel('Pre-Heat temperature(K)')
plt.ylabel('Percentage Fuel Saved')
plt.title('Fuel Saving with Pre Heating')
plt.grid(True)

plt.show()

PROCEDURE:

• As similar as part 1, defining the all the quantityies of fuel, air and products by using the quantity class.
• Getting the values for mass and enthalpy for fuel, air and prodcuts by using x.enthalpy and x.mass methods.
• As per the formula caluculating the specific heat and the combustion effeciencies.
• To caluculate the Fuel saved, we need the effeciencies at 298k and 600k, these can get by appending all the values.
• Plotting the results for Pre heat vs combustion effeciecncy and pre heat vs fuel saved.

RESULTS:

Obseravtion:

• The increase in the pre heat temperature, we can observe the increase in the combustion effecincy from 33% to 45%. This is beacuse, we know efficiency will increase with the output or decreasing the input. As the increase in the adiabatic flame temperature indicates the increase in output.
• Similarly, by looking the second plot, we can observe the increase in the fuel saving as 23.94% from incresing the preheat temperature to 600k.

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

In my woeds, the furnace exit tempearture depends on the adiabatic falme temperature. As from the part-1 challenge, we can get the idea that the AF will incresae with the increase in Preheat temperature. In the initial set up, if we set the furnace temperature at a high values then the air pre-heated at high temperature and AFT will be high, and the furnace temperature at the exit will becomes high as well. If the recuperator is operated at these cycle for long time, then the high rise in the exit furnace temperature will effects the recuperator walls. So, it is right to assume a fixed furance exit temperature value to maintain the exhaust temperature in a recuperator working condition.