EFFECT OF PREHEATING OF AIR USING A RECUPERATOR IN THE COMBUSTION  OF METHANE

                             EFFECT OF PREHEATING OF AIR USING A RECUPERATOR IN THE COMBUSTION  OF METHANE

l. OBJECTIVE

1. Write a program to observe the effect of preheating of air on the adiabatic flame temperature in the combustion of methane.

2. write a program to observe the effect of preheating of air on the combustion efficiency in the combustion of methane. Also, determine the percentage of fuel saved at different preheating temperatures.

ll. INTRODUCTION

Let us consider that a furnace is used to burn a mixture of methane and air. The heat released can be converted to work using an energy harvesting system. The product of combustion carries a lot of unutilized heat which exits the system.

A recuperator is connected to the furnace to recover some energy, to heat the atmospheric air, which can be further fed to the mixing valve.

In the present situation, two possibilities can occur-

1. An uncontrolled increase in the temperature of the furnace:

The heated air causes the temperature of the system to increase. This can cause an increase in the furnace heat generated during the combustion process which further causes an increase in the temperature of the furnace and exhaust gases and the process continues.

However, this situation is undesirable as an uncontrolled increase in the temperature of the exhaust gases can result in damage to the components involved in this setup.

2. The temperature of the furnace is kept constant:

The constant temperature of the furnace implies that the temperature of the exhaust gases is fixed. This further implies that to balance the additional heat in the hot air generated by the recuperator, the quantity of the fuel supplied to the mixing valve should be reduced.

lll. COMBUSTION OF METHANE IN A FURNACE ATTACHED TO A RECUPERATOR

A. CASE 1 - EFFECT OF  PREHEATING OF AIR ON THE ADIABATIC FLAME TEMPERATURE.

For this case, we will analyze how the preheating temperature of air affects the AFT of the methane-air combustion. The program starts by creating instances of fuel and air by using the Quantity class. As per the reaction:

`CH_4+2(O_2+3.76N_2) rarr CO_2+2H_2O+7.52N_2`

the fuel is set at STP conditions with a temperature of 298.15 K and a pressure of 1 atm. The number of moles of `CH_4` for the reaction is 1 whereas the number of moles of air (`2O_2+7.52N_2`) is  2+7.52 = 9.52. Air contains `O_2`with a mole fraction of 0.21 and `N_2` with a mole fraction of 0.79. The temperature of the air is varied with the preheating temperature while the pressure is kept constant at 1 atm. The flue gas instance is created by mixing the fuel and air instances at their respective conditions. The flue gas is then equilibrated under constant enthalpy and pressure to calculate the AFT of the reaction.

CODE:

"""
	Program to study the effect of preheating on AFT

	Reaction: CH4 + 2(O2 + 3.76N2) <=> CO2 + 2H2O + 7.52N2
"""
import cantera as ct 
import matplotlib.pyplot as plt 
import numpy as np 

# Creating the gas instances from the gri30 mechanism file
gas = ct.Solution('gri30.cti')	 
# Creating the fuel and gas instances from the gas
fuel = ct.Quantity(gas)
fuel.TPX = 298.15, ct.one_atm, {'CH4':1}
fuel.moles = 1


air = ct.Quantity(gas)
# Defining the preheating conditions
T_pre = np.linspace(298, 600, 16)
T_aft = []


# Calculating AFT from different preheating temperatures
for T in T_pre:
	air.TPX = T, ct.one_atm, {'O2':0.21, 'N2':0.79}
	air.moles = 2 + (2*3.76)

	flue = fuel + air
	flue.equilibrate('HP','auto')
	T_aft.append(flue.T)

print('preheating Temperature =', T_pre)	
print('Adiabatic Flame Temperature =',T_aft)

plt.plot(T_pre,T_aft,'-o', color = 'red')
plt.title('Effect of Preheating of Air on the AFT', fontsize=16, fontweight='bold')
plt.xlabel('PreheatingAir Temperature [K]', fontsize=14)
plt.ylabel('Adiabatic Flame Temperature [K]', fontsize=14)
plt.grid(which = 'major')
plt.minorticks_on()
plt.grid(which = 'minor',alpha = 0.2)
plt.show()

 OUTPUT:

preheating Temperature = [298, 318.13, 338.26, 358.41, 378.53, 398.66, 418.84, 438.93, 459.06, 479.27, 499.33, 519.46, 539.68, 559.73, 579.86 600 ]        ]

Adiabatic Flame Temperature = [2224.3475229290475, 2232.952907838183, 2241.4873825750406, 2249.951710433773, 2258.346956318603, 2266.674434565984, 2274.9356625511186, 2283.1323201142295, 2291.266211315922, 2299.3392310165495, 2307.353333846174, 2315.3105059735108, 2323.2127393171636, 2331.062007992554, 2338.860246815974, 2346.609331706231]
[Finished in 42.0s]

RESULTS:

Increasing the temperature of preheated air causes a direct increase in the AFT. This will increase the temperature of the exhaust gases increasing the heat transfer at the recuperator. This will further increase the temperature of the preheated air and the process continues.

Thus, it is required to control the preheating temperature as its uncontrolled increase can result in the damage of the components within the system. The best method is to set the furnace exit temperature to a constant value by reducing the quantity of fuel input to the furnace while maintaining a constant Air-Fuel ratio. This method will not only protect the components of the system but also increase combustion efficiency and reduce fuel consumption.

B. CASE 2 - EFFECT OF PREHEATING OF AIR ON THE COMBUSTION EFFICIENCY

Another aspect of the combustion performance that can be tested is the efficiency of the combustion under preheating. Combustion efficiency is a measure of how efficiently the heat content of a fuel is transferred into usable heat. 

1. Assumptions:

1. The fuel is at STP conditions.
2. 1 mole of air is assumed to be composed of 0.21 moles of oxygen and 0.79 moles of nitrogen.
3. The combustion takes place in a constant pressure chamber.
4. The heat loss through the walls of the system is neglected.
5. The fuel involved in the combustion process is Methane.
6. The mixture is stoichiometric i.e `phi`=1.
7. Only the major species (i.e `CO_2, H_2O, N_2`) are considered as the product of combustion. All the minor species are neglected.
8. The LVH of the combustion of Methane is 50 MJ/kg.
9. The furnace exit temperature is 1700 K.

2. General Equation of Combustion of Methane:

The general equation of combustion of methane can be represented as-

• `CH_4+2(O_2+3.76N_2) rarr CO_2+2H_2O+7.52N_2`

3. Calculation:

Let us consider te control volume of the system as shown below-

3.1. Mass Balance:

• `dotm_(air)+dotm_(fuel)=dotm_(exhaust)`

3.2. Energy Balance;

• `dotm_(air)h_(air)+dotm_(fuel)h_(fuel)=Q_(output)+dotm_(text(exhaust))h_(exhaust)`
• `Q_(output)=dotm_(fuel)h_(fuel)+dotm_(air)h_(air)-(dotm_(fuel)+dotm_(air))h_(exhaust)`
• `Q_(output)=dotm_(fuel)[h_(fuel)+dotm_(air)/(dotm_(fuel))h_(air)-(1+dotm_(air)/(dotm_(fuel)))h_(exhaust)]`

Notes:

1. The heat output of the system can be represented as-

• `Q_(output)=Q_(text(useful))+Q_(loss)`

Sonce the system is assumed to be adiabatic `impliesQ_(loss)=0`

• `thereforeQ_(output) = Q_(text(useful))`

2. The Air-Fuel ratio can be represented as-

• `A/F =m_(air)/m_(fuel)=dotm_(air)/(dotm_(fuel))`

Simplifying the energy balance equation by the above two equations-

• `Q_text(useful)/dotm_(fuel)=h_(fuel)+(dotm_(air)/(dotm_(fuel)))h_(air)-(1+dotm_(air)/(dotm_(fuel)))h_(exhaust)`
• `Q_text(specific)=h_(fuel)+(dotm_(air)/(dotm_(fuel)))h_(air)-(1+dotm_(air)/(dotm_(fuel)))h_(exhaust)`
• `Q_text(specific)=(dotm_(air)/(dotm_(fuel)))(h_(air)-h_(exhaust))+h_(fuel)-h_(exhaust)`

3.3 Combustion Efficiency:

• `eta=Q_text(specific)/(LHV)xx100`

3.4 Fuel Savings:

• Fuel Saving = `(1-(eta_(0))/(eta_(1)))xx100`

where `eta_(0)`is the combustion efficiency with no preheating and `eta_1` is the combustion efficiency at a specified preheating.

4. CODE:

"""
	Program to study the effect of preheating on AFT

	Reaction: CH4 + 2(O2 + 3.76N2) <=> CO2 + 2H2O + 7.52N2
"""
import cantera as ct 
import matplotlib.pyplot as plt 
import numpy as np 

# Creating the gas instances from the gri30 mechanism file
gas = ct.Solution('gri30.cti')	 
# Creating the fuel and gas instances from the gas
fuel = ct.Quantity(gas)
fuel.TPX = 298.15, ct.one_atm, {'CH4':1}
fuel.moles = 1
h_fuel = fuel.enthalpy_mass


air = ct.Quantity(gas)
# Creating the exhaust product instance from the gas
exhaust_prod = ct.Quantity(gas)
n_tot = 1 + 2 + (2*3.76)
n_co2 = 1/n_tot
n_h2o = 2/n_tot
n_n2 = 7.52/n_tot
exhaust_prod.TPX = 1700, ct.one_atm, {'CO2':n_co2, 'H2O':n_h2o, 'N2':n_n2}
exhaust_prod.moles = n_tot
h_exhaust_prod = exhaust_prod.enthalpy_mass


#Defining the preheating conditions
T_pre = np.linspace(298, 600, 51)
LVH = 50e6
eff = []
fuel_saving = []
plot_interval = 5

# Calculating efficiency from different preheating temperatures
for T in T_pre:
	air.TPX = T, ct.one_atm, {'O2':0.21, 'N2':0.79}
	air.moles = 2 + (2*3.76)
	air_fuel_ratio = air.mass/fuel.mass
	h_air = air.enthalpy_mass

	Q_spec = air_fuel_ratio*(h_air - h_exhaust_prod) + h_fuel - h_exhaust_prod

	eff.append((Q_spec/LVH)*100)

	# Calculating the fuel saving from the efficency
	fuel_saving.append((1-(eff[0]/eff[-1]))*100)


# Print the results
print('Efficiency with no preheating = '+ str(round(eff[0],2)) + '%')
print('Efficiency at preheating of 600 K =' + str(round(eff[-1],2))+ '%')
slope = (eff[1]-eff[0])/(T_pre[1]-T_pre[0])
print('Rate of change of efficencywith preheating =' + str(round(slope,4))+'%/K')
print('Fuel saving at preheating of 600 K =' + str(round(fuel_saving[-1],2)) + '%')
T_pre_plot = [T_pre[i] for i in range(0,len(T_pre),plot_interval)]
eff_plot = [eff[i] for i in range(0,len(eff),plot_interval)]
fuel_saving_plot = [fuel_saving[i] for i in range(0,len(fuel_saving),plot_interval)]


fig, ax = plt.subplots()
plt.plot(T_pre_plot, eff_plot,'-o',color='red',linewidth=2)
plt.grid('both', linestyle ='--', linewidth=1.2)
plt.xlabel('Preheating Temperature [K]', fontsize=14)
plt.ylabel('Combustion Efficiency [%]', fontsize=14)
plt.title('Effects of Air Preheating on Combustion Efficiency', fontsize =15)
x_ticks = [250, 300, 350, 400, 500, 550, 600, 650]
y_ticks = [32, 34, 36, 38, 40, 42, 44, 46]
plt.show()

fig, ax = plt.subplots()
plt.plot(T_pre_plot,fuel_saving_plot,'-o',color='red', linewidth=2)
plt.grid('both',linestyle='--',linewidth=1.2)
plt.xlabel('Preheating Temperature [K]',fontsize=14)
plt.ylabel('Fuel Saving [%]', fontsize=14)
plt.title('Effect of Air preheating on Fuel Saving',fontsize=15,fontweight='bold')
x_ticks = [250, 300, 350, 400, 450, 500, 550, 600, 650]
y_ticks = [-5, 0, 5, 10, 15, 20, 25, 30 ]
plt.show()

5. OUTPUT:

Efficiency with no preheating = 33.87%
Efficiency at preheating of 600 K =44.53%
Rate of change of efficencywith preheating =0.0346%/K
Fuel saving at preheating of 600 K =23.93%
[Finished in 43.9s]

As seen from the graph, the efficiency of the combustion increases linearly with the preheating temperature at the rate of 0.0346%/K. 

The efficiency increases from 33.87% to no preheating to 44.53% at a preheating of 600 K. The fuel savings also increase almost linearly with the preheating temperature. At a preheating temperature of 600 K, we can save almost 23.93% more fuel than without the presence of preheating.

lV. CONCLUSIONS

The effect of preheating of air on the adiabatic flame temperature, combustion efficiency, and the fuel savings in the combustion of methane is observed and analyzed at different temperatures.