Combustion Calculations

Calculate the theoretical flame temperature of combustion of hydrogen with theoretical amount of air assuming

(a) No dissociation of combustion product (i.e. H2O)

(b) Assuming 4 % dissociation of H2O

NCV of H2 = 10.16 MJ/m3

Assume that both the hydrogen and air are dry at 0 C

Mean value of Cp (of combustion product H2O):

Temp C 2000 2100 2200

Cp kJ/m3C 1.643 1.651 1.657

Combustion Calculations

• H2 + ½ O2 = H2O• Air required for 1 m3 of H2= 2.38 m3• Total flue gas= N2+ H2O= 0.79 x 2.38 +1• = 2.88 m3 / m3 of H2• (a) Theoretical flame temp T = (10.16 x 1000)/(2.88 xCp)

• Assuming T=2100 C (Cp=1.651) • Calculated T= 2136 C which is quite close to assumed• (b) T =(10.16 x 1000 x (1-0.04))/(2.88 xCp)• Assuming T=2000 C calculated T = ?• Assuming T =2100 calculated T= ?

3

2. Adiabatic Flame Temperature

• Table shows flame temperatures for some common fuels. The higher the flame temperature, the greater should be the effectiveness of the heat exchanger section.

Table Flame temperatures for some common fuelsTable Flame temperatures for some common fuelsFuelFuel Adiabatic flame temperature Adiabatic flame temperature

(℃)(℃)Natural gasNatural gasKerosine Kerosine Light fuel oilLight fuel oilMedium fuel oil Medium fuel oil Heavy fuel oil Heavy fuel oil Bituminous CoalBituminous CoalAnthraciteAnthracite

2,0702,0702,0932,0932,1042,1042,1012,1012,1022,1022,1722,1722,1802,180

4

5. Calculated Adiabatic Flame Temperatures

• Values of the predicted adiabatic flame temperature for hydrocarbon fuels are affected by the following factors:(1) the calorific value (and chemical composition) of the fuel;(2) the air-to-fuel ratio at which combustion takes place; and(3) the initial temperature (preheat) of the air and fuel.

5

Effect of CALORIFIC VALUE

• It would be expected that the higher the calorific value of the fuel the higher the final flame temperature produced.The picture is, however, not quite as simple as this since the chemical composition of the fuel also plays a part.

• For example, natural gas has a carbon-to-hydrogen ratio of around 3.1 and a calorific value of 54 MJ/kg (gross). A typical coal, on the other hand, has a carbon-to-hydrogen ratio of around 18.0 and a calorific value of 33.3 MJ/kg.

6

Effect of CALORIFIC VALUE

• Fuels with a higher proportion of hydrogen will generate more water vapor in their combustion products; a glance at Table 4.3 shows that water vapor has a higher specific heat than the other combustion products, which will lower the adiabatic flame temperature.

• The adiabatic flame temperature for a number of common hydrocarbon fuels are given before in Table 4.1. In each case combustion is stoichiometric and the initial temperature of the air and fuel is 25 .℃

7

Effect of CALORIFIC VALUE

• It can be seen that there is quite a small variation in the calculated flame temperature, given the wide variation between the calorific values of these fuels.

• The “conformity” is due to the effect of the hydrogen in the fuel discussed above.

8

AIR-TO-FUEL RATIO

• Any excess air will increase the mass of flue gas relative to the mass of fuel, with a corresponding reduction in temperature.

• With sub-stoichiometric air supply the flame temperature will also fall, as although the mass of flue gas is reduced, the effective calorific value of the fuel is also reduced by an amount equivalent to the calorific value of the carbon monoxide which is present in the flue gas.

9

AIR-TO-FUEL RATIO

• The net calorific value of carbon monoxide is 10.11 MJ/kg.

• Next slide (Fig. 4.2)It shows the temperature calculated for a natural gas flame as a function of the excess air ratio, and demonstrates the effects described above.

air fuel ratio

11

PREHEAT

• Common sense (and equation (2)) suggest that preheating the air will increase the final temperature of the flame.

• This is a useful feature because by increasing the temperature difference between the flue gas and the heat extracting fluid, greater heat transfer will be obtained for the same fuel input rate.

12

PREHEAT

• This will result in an increase in the thermal efficiency of the plant.

• An example of the effect of preheat on the adiabatic temperature of a natural gas flame at 5% excess air is shown in Fig. 4.3 (next slide).

14

• In practice, there are a number of reasons why the actual flame temperature will be lower than the value predicted by this procedure.

• The most significant of these is that at the high temperature achieved in flames the combustion products will “dissociate” back into reactants or other higher reactive species: this process is accompanied by an absorption of energy, hence reducing the actual flame temperature.

15

• The results of above calculations are then more correctly referred to as “undissociated adiabatic flame temperatures”, which acknowledges the simplifications inherent in them.

• In order to understand the more complete picture it is necessary to gain some insight into the principles of chemical equilibrium, which are introduced in the next chapter.

Adiabatic Flame Temperature

Adiabatic flame

Fuel

oxident

diluent

Combustion products

Adiabatic Flame Temperature

• A fuel gas containing 20 % CO and 80 % N2 is burned

with 150 % excess air (both air and gas being at 25 C).

Calculate the theoretical flame temperaure of the gas.

• Following data is available

CO2 O2 N2 CO

Av. Sp. Heat kcal/mole K

12.10 7.90 7.55 -

Heat of formation at 25 C kcal/kg mole

-94052 -26412

Material BalanceBasis: 100 kg moles of fuel gas

Material enteringKg moles

Materials leavingKg moles

COO2N2CO2

202580 + 94.05-

-15174.0520

total 219.05 209.05

Energy Balance: assuming reference temp. 25 CHeat of reaction = -94052 –(-26412)= -67640 kcal / kg moleHeat produced by combustion = 20 x -67640 = -1352800

Cp kcal / kg mole K Amount kg mole

mCp dT

CO2 12.10 20 20x12.10xdT

O2 7.90 15 7.90 x 15 x dT

N2 7.55 174.05 7.55 x 174.05 x dT

Total=1674.58 dT

1674.58(Tf -298)= 1352800Tf= 832.8 C

Adiabatic Flame Temperature

NCV+∆hf +A∆Ha=V∆Hfg +qd + ql

A= air supplied m3/m3 fuel

V=flue gases produced m3/m3 of fuel

∆Hf=enthalpy of fuel above reference temperature

∆Hfg=tf. Cpfg(0-tf) –trCpfg(0-tr)

Tf=(NCV+∆hf +A∆Ha -qd– ql +V. trCpfg(0-tr))/ V. Cpfg(0-tf)

Adiabatic Flame Temperature

Calculate the theoretical flame temperature for a fuel gas under the following conditions:

(i) Both fuel and theoretical air are at 15 C(ii) 50 % excess air at 15 C and fuel gas at 15 C(iii) Theoretical air at 60 C and gas at 400 C(iv) Theoretical oxygen at 15 C and fuel gas at 15 CData:Fuel gas: CO : 22% CO2 : 18% H2 : 2% N2 : 58%NCV: 719 kcal/m3Mean sp. Heat of fuel gas at 600 C= 0.342 kcal/m3 C