With excess air, determine the following:
Theoretical amount of air needed to burn the fuel oil.
Actual amount of air needed to burn the fuel oil.
Higher and Lower Heating Value of the Fuel.
The Correct Answer and Explanation is:
To determine the theoretical and actual amount of air needed to burn fuel oil, along with its Higher Heating Value (HHV) and Lower Heating Value (LHV), we must first know the fuel oil’s composition. However, for typical fuel oil (say No. 2 fuel oil, a common distillate fuel), we can approximate its empirical formula as C₁₂H₂₆ for calculation purposes.
1. Theoretical Air Requirement
Combustion reaction of C₁₂H₂₆: C12H26+O2→CO2+H2O\text{C}_{12}\text{H}_{26} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}
Balanced Reaction: C12H26+18.5 O2→12 CO2+13 H2O\text{C}_{12}\text{H}_{26} + 18.5\ \text{O}_2 \rightarrow 12\ \text{CO}_2 + 13\ \text{H}_2\text{O}
Each mole of O₂ needs 4.76 moles of air (21% O₂ by volume): Theoretical air=18.5×4.76=88.06 moles of air per mole of fuel\text{Theoretical air} = 18.5 \times 4.76 = 88.06\ \text{moles of air per mole of fuel}
Molecular weight of C₁₂H₂₆ = (12×12 + 26×1) = 170 g/mol
So, air-to-fuel ratio (AFR) by mass:
- O₂ mass = 18.5 × 32 = 592 g
- Air mass = 592 × 100 / 23.2 ≈ 2552 g (using O₂ is 23.2% by mass in air)
Theoretical AFR = 2552 / 170 ≈ 15.01
2. Actual Air Requirement (with Excess Air)
If excess air is 20%, then: Actual AFR=15.01×(1+0.20)=18.01\text{Actual AFR} = 15.01 \times (1 + 0.20) = \mathbf{18.01}
3. Higher and Lower Heating Value
Typical heating values for fuel oil:
- HHV ≈ 45.5 MJ/kg
- LHV ≈ 42.5 MJ/kg
LHV is lower because it assumes the water formed during combustion remains as vapor (latent heat is not recovered).
Explanation
To fully combust a hydrocarbon fuel like fuel oil, it must react with oxygen in air. The theoretical air is the minimum amount of air that provides just enough oxygen to complete the combustion of all carbon and hydrogen in the fuel without excess. In this case, assuming the fuel oil has an empirical formula of C₁₂H₂₆, stoichiometry shows it needs 18.5 moles of oxygen per mole of fuel to yield CO₂ and H₂O. Since only 21% of air is oxygen by volume (or about 23.2% by mass), this translates to a theoretical air-to-fuel mass ratio (AFR) of approximately 15:1.
In real combustion systems, a certain amount of excess air is supplied to ensure complete combustion and avoid the formation of pollutants like CO or soot. If 20% excess air is used, the actual AFR becomes about 18:1.
The Higher Heating Value (HHV) represents the total energy released when the fuel is burned and the water produced is condensed, recovering latent heat. In contrast, the Lower Heating Value (LHV) excludes this condensation energy, assuming the water remains as vapor. Fuel oils typically have an HHV around 45.5 MJ/kg and LHV near 42.5 MJ/kg. The difference is important in engineering calculations for boiler and engine efficiency, especially where the exhaust temperature is too high to recover the latent heat from water vapor.
Accurate estimation of air requirements and heating values is essential for efficient combustion, minimizing fuel consumption and emissions in industrial and residential heating applications.
