Week 4.2 - Combustion Efficiency Calculation after Preheating

Aim:
1. What is the effect of preheating on the adiabatic flame temperature?
2. Change pre-heating from 298 to 600K
3. Explain your results
4. Does preheat 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

Objectives :
• Write the formula for combustion efficiency
• Plot the effect of pre-heat temperature on combustion efficiency
• Is it right or wrong to assume a fixed furnace exit temperature? Explain your answer.

The formula used for efficiency

A fixed furnace exit temperature helps us determine the enthalpy of product species, and hence, we are able to benchmark the results. Moreover, the given temperature could also be an average after estimating all losses.

Introduction:
Certain procedures that require heat are carried out in industrial furnaces. The furnace gets its heat from

(i) fuel energy,

(li)chemical energy,

(iii) electrical energy, or

(iv) a combination of these energies.

Gases produced during the process exit the furnace at a temperature equal to the furnace's internal temperature, resulting in high sensible heat content. Because of this chemical energy, exhaust gases can sometimes carry some chemical energy, which elevates the temperature of exhaust gases owing to post-combustion. Because the thermal energy contained in exhaust gases is released into the environment, it is considered waste energy. However, by investing in waste heat recovery technologies, it is feasible to recover a portion of this energy. Among the waste heat recovery methods are:

(i) transferring heat between exhaust gases and combustion air for its preheating,

(ii) transferring heat to the load entering furnaces,

(iii) generation of steam and electrical power, or

(iv) using waste heat with a heat pump for heating or cooling facilities.

The principle of heat exchange is used by WHRDs. The heat energy of the exhaust gases is transferred to another fluid medium during heat exchange. This heat exchange lowers the temperature of the exhaust gases while raising the temperature of the fluid medium. The heated fluid medium is either recycled back to the processor or used to create utilities like steam or electricity. The advantages of WHRDs devices are numerous, including

(i) economic,

(i) resource

(iii) fuel-saving, and

(in) environmental.

The benefits of these devices include

(i) saving of fuel,

(ii) generation of electricity and mechanical work,

(iii) reducing cooling needs,

(iv) reducing capital investment costs in case of the new facility.

(v) increasing production,

(vi) reducing greenhouse gas emissions, and

(vi) transforming the heat to useful forms of energy.

The most typical application of heat exchangers is to transmit heat from combustion exhaust gases to air entering the furnace. Because warmed combustion air enters the furnace at a greater temperature, the fuel must provide less energy. Recuperators, furnace regenerators, recuperative and regenerative burners, passive air preheaters, shell and tube heat exchangers, finned tube heat exchangers or economizers, rotary regenerator or heat wheel, preheating of load, waste heat boilers, and heat pumps are examples of typical WHRDS used for air preheating.

Recuperators:-
In a recuperator, heat is transferred directly. A heat transfer surface separates the two fluids (exhaust gases and combustion air), preventing them from mixing. Through metallic or ceramic barriers, heat is exchanged between the exhaust gases and the air. Ducts or tubes convey the pre-heated air for combustion, while the waste heat stream is contained on the opposite side.

In a recuperator, heat is transferred directly. A heat transfer surface separates the two fluids (exhaust gases and combustion air), preventing them from mixing. Through metallic or ceramic barriers, heat is exchanged between the exhaust gases and the air. Ducts or tubes convey the pre-heated air for combustion, while the waste heat stream is contained on the opposite side.

(i) 'in parallel-flow heat exchangers' where both the gases flow in the same general direction,

(ii) 'in counterflow exchangers' where both the gases flow in opposite directions, or

(iii) "in cross-flow where the gases flow at right angles to each other.

Counterflow heat exchangers are the most efficient, whereas parallel-flow heat exchangers are the least efficient.
Heat transfer through radiation, convection, or a mix of the two can be used in recuperators. Metal or ceramic materials are used in the construction of recuperators. Heat recovery at higher temperatures is better suited to ceramic tube recuperators, which may function with hot side temperatures as high as 1500 deg C and cold side temperatures of roughly 950 deg C. Metallic recuperators are employed in applications with temperatures below 1050 deg C.

Combustion Efficiency of Recuperator:
We are going to write an energy balance for the control volume, assuming both the heat transferred to the load and the heat losses are the same, with and without preheating.
Assuming steady flow, heat is transferred out of the control volume.

`-dotQ = -dotQ_(load) -dotQ_(loss) = dotm.(h_(Products) - h_(Reactants))`

`-dotQ = (dotm_a + dotm_f)h_(Products) - dotm_f.h_f-dotm_a.h_a`

`frac(a)(f) = frac(dotm_a)(dotm_f)`

Above equation will be rewrite as,

`-dotQ = [(frac(a)(f)+1).h_(Products) - (frac(a)(f).h_a-h_f)]`

Fuel utlizatio energy will be given as

`eta = frac(dotQ)(dotm_f.LHV`

Therefore

`eta = frac((frac(a)(f)+1).h_(Products) - (frac(a)(f)).h_a -h_f)(LHV)`

Assuming the equivalence ratio as 1

`frac(a)(f) = frac((frac(a)(f))_(St))(phi)`

Therefore

`frac(a)(f) = 17.1`

Fuel Saving defined as

Fuel_Saving = `1-frac(eta_(298))(eta_(600)`

Python Coding :

In this program, The code is divided into three parts to find

PART-1: To know the effect of preheating inlet air temperature on adiabatic flame temperature. Assume fuel as METHANE (CH4) Here, we are going to look at how adiabatic flame temperature is being affected by varying inlet air temperatures ranging from 298 K to 600K.

PART-2: To plot the effect of preheating temperature on combustion efficiency. Here, we are utilizing the waste heat of flue gases to increase the temperature of the inlet air and how this preheating of inlet temperature affects the combustion efficiency of methane is visualized. Assumptions made here are, equivalence ratio is 1, LHV of methane is 50 MI. A/F ratio is 17.1.

Part 3: To plot the effect of preheating temperature on fuel saving.

Coding :

import matplotlib.pyplot as plt 
from numpy import *
import cantera as ct 

gas = ct.Solution('gri30.cti')
Fuel = ct.Quantity(gas)
Fuel.TPX = 298.15,ct.one_atm,{'CH4':1}
Fuel.moles = 1

air = ct.Quantity(gas)

# Preheating Conditions 
Temperature_Preheating = linspace(298,600,100)
Temperature_AFT = []
plot_interval = 5

#Calculating AFT for Different Temperatures 
for Temperature in Temperature_Preheating :
	air.TPX = Temperature,ct.one_atm,{'O2':0.21,'N2':0.79}
	air.moles = 2+(2*3.76)
	Flue = Fuel + air
	Flue.equilibrate('HP','auto')
	Temperature_AFT.append(Flue.T)

#plotting the results 
print('Effect Of Preheating on AFT')
print('AFT with no Preheating = ' + str(round(Temperature_AFT[0],2)) + 'K')
slope = (Temperature_AFT[1] - Temperature_AFT[0])/(Temperature_Preheating[1]-Temperature_Preheating[0])
print('Rate of change of AFT wih Preheating = ' + str(round(slope,2)) + 'Kelvin per Kelvin')
print('**********************************************************************')
Temperature_Preheating_plot = [Temperature_Preheating[i] for i in range(0,len(Temperature_Preheating),plot_interval)]
Temperature_AFT_plot = [Temperature_AFT[i] for i in range(0,len(Temperature_AFT),plot_interval)]

plt.plot(Temperature_Preheating_plot,Temperature_AFT_plot,'-*',color = 'green', linewidth = 1.2 )
plt.grid('both', linestyle = '--', linewidth = 1.2)
plt.xlabel('Preheating Temperature [K]')
plt.ylabel('Adiaatic Flame Temperature[K]')
plt.title('Effect of Air Preheating on AFT')
plt.show()

# Impact of Preheating On combustions Efficiency 
gas= ct.Solution('gri30.cti')
Fuel = ct.Quantity(gas)
Fuel.TPX = 298.15, ct.one_atm, {'CH4' : 1}
Fuel.moles = 1
Enthalpy_Fuel = Fuel.enthalpy_mass
air = ct.Quantity(gas)

Estimated_Products = ct.Quantity(gas)
n_total = 1+2+(2*3.76)
n_co2 = 1/n_total
n_h2o = 2/n_total
n_n2 = 7.52/n_total
Estimated_Products.TPX = 1700,ct.one_atm, {'CO2':n_co2,'H2O' : n_h2o , 'N2' : n_n2}
Estimated_Products.moles = n_total
Enthalpy_Estimated_Products = Estimated_Products.enthalpy_mass

Temperature_Preheating = linspace(298,600,51)
LHV = 50e6
efficiency = []
Fuel_Saving = []
plot_interval = 5

for Temperature in Temperature_Preheating:
	air.TPX = Temperature,ct.one_atm,{'O2' :0.21 , 'N2' : 0.79}
	air.moles = 2 + (2*3.76)
	air_fuel_ratio = air.mass/Fuel.mass
	Enthalpy_air = air.enthalpy_mass

	Specific_Heat = air_fuel_ratio*(Enthalpy_air- Enthalpy_Estimated_Products) + Enthalpy_Fuel - Enthalpy_Estimated_Products

	efficiency.append(Specific_Heat/LHV*100)

	Fuel_Saving.append((1-(efficiency[0]/efficiency[-1]))*100)


print('n_Effect of Temperature_Preheating on Combustion Efficiency')
print('Efficiency Without Temperature_Preheating = ' + str(round(efficiency[0],2))+'%')
print('Efficiency at Temperature_Preheating of 600 k = ' + str(round(efficiency[-1],2))+ '%')
slop = (efficiency[1] - efficiency[0])/(Temperature_Preheating[1] - Temperature_Preheating[0])
print('Rate of change of Efficiency with pre Temperature_Preheating = ' + str(round(slope,4)) + '%/K')
print('Fuel Saving at pre heating of 600 K = ' + str(round(Fuel_Saving[-1],2)) + '%n')
print('**********************************************************************')

Temperature_Preheating_plot = [Temperature_Preheating[i] for i in range(0,len(Temperature_Preheating),plot_interval)]
Efficiency_plot = [efficiency[i] for i in range(0,len(efficiency),plot_interval)]
Fuel_Saving_plot = [Fuel_Saving[i] for i in range(0,len(Fuel_Saving),plot_interval)]

plt.figure(1)

plt.plot(Temperature_Preheating_plot,Efficiency_plot,'-*',color = 'red' , linewidth=2)
plt.grid('both',linestyle = '--',linewidth=1.2)
plt.xlabel('Preheating Temperature [K]')
plt.ylabel('Combustion Efficiency [%]')
plt.title('Effect of air Pre heating on combustion efficiency ')

plt.figure(2)
plt.plot(Temperature_Preheating_plot,Fuel_Saving_plot,'-*',color= 'blue',linewidth=2)
plt.grid('both',linestyle='--',linewidth=1.2)
plt.xlabel('Preheating Temperature[K]')
plt.ylabel('Fuel Saving [%]')
plt.title('Effect of air Prre Heating on Fuel Saving')
plt.show()

Plots :

Result:

AFT and preheating have a linear relation (slope of 0.43) hence, more heat is liberated as heat is added to the combustion process.
• Efficiency without preheating was 33.87% and after preheating @ 600K, it became 44.53%.
• Fuel savings had a linear relation to preheating which increased to 23.93% on preheating @ 600K.
• Hence, preheating is beneficial.

Q.is it right or wrong to assume a fixed furnace exit temperature? Explain your answer.
Here we have assumed a fixed furnace exit temperature which is 1700 Kelvin. Assume that is correct for the minimum value of preheat temperature (that is 298.15 Kelvin). With that, we got 34 % combustion efficiency. But with the increase in preheat temperature till 600 kelvin we have kept exhaust gas temperature constant at 1700 kelvin. So combustion efficiency increased from 33.87 to 44.53% and varied linearly also.