Fuels and Combustion – Calorific Value & Combustion Analysis
Overview: Fuels release energy via oxidation (combustion). Key parameters are calorific values (higher and lower), methods of measurement, and quantitative analysis of products. Understanding stoichiometry, calorimetry, and fuel characterization is critical for energy engineering and competitive exams.
1. Classification of Fuels
- Primary (Natural) Fuels: Coal (lignite, bituminous, anthracite), crude oil fractions, natural gas (CH₄), wood
- Secondary (Manufactured) Fuels: Producer gas (CO + H₂), water gas (CO + H₂ from steam–coke reaction), coal gas, synthetic petrol (Fischer–Tropsch)
- By Physical State:
- Solid: Coal, coke, charcoal
- Liquid: Petrol, diesel, kerosene, furnace oil
- Gaseous: Natural gas, LPG (C₃H₈ + C₄H₁₀), biogas
2. Calorific Value (Heat of Combustion)
2.1 Definitions
- Higher Calorific Value (HCV/Gross CV): Heat released when fuel oxidizes completely and products (CO₂, H₂O) return to 25 °C, including latent heat from condensation of H₂O.
- Lower Calorific Value (LCV/Net CV): Heat released excluding latent heat of vaporization of water (assumes H₂O remains vapor at 150 °C).
2.2 Relationship
LCV = HCV − (m × hvap)
- m = mass of H₂O produced per kg fuel = (nH/2) × 18/1000 kg of H₂O per kg fuel, where nH = mass% H / 1
- hvap = latent heat of vaporization of water at 25 °C ≈ 2442 kJ/kg
2.3 Units
- Gases: kJ/Nm³ or kcal/Nm³
- Liquids/Solids: kJ/kg or kcal/kg
3. Bomb Calorimetry – Measurement of HCV
3.1 Principle
Fuel sample burned in oxygen inside a constant-volume “bomb.” Heat released raises temperature of surrounding water; measured ΔT yields HCV.
3.2 Apparatus
- Bomb: Stainless steel vessel with O₂ inlet, sample holder, ignition coil
- Calorimeter: Insulated water jacket (mw ~2–3 kg) with stirrer and precise thermometer (±0.001 °C)
- Oxygen Supply: Pure O₂ at ~30 bar for complete combustion
- Heat Capacity: Ccal (water + calorimeter jacket) determined via calibration
3.3 Calculation Steps
- Weigh dry fuel sample (mf) accurately
- Fill bomb with O₂ to 25–30 bar; record initial water temperature Ti
- Ignite sample; record final temperature Tf
- Calculate ΔT = Tf − Ti
- Heat absorbed:
Qabs = (mw·Cw + Ccal)·ΔT
where Cw = 4.184 kJ/kg·K - Subtract ignition fuse energy Qign (<1–2 kJ):
Qfuel = Qabs − Qign - Higher calorific value:
HCV = Qfuel / mf (kJ/kg)
4. Combustion Analysis
4.1 Ultimate (Elemental) Analysis
Determines weight% of C, H, S, N, and O in fuel sample.
- Carbon: Convert CO₂ via combustion; absorb in KOH; weigh CO₂ absorbed
- Hydrogen: Absorb H₂O in fused CaCl₂; weigh increase
- Sulfur: Oxidize to SO₂; absorb in H₂O₂; titrate SO₄²⁻ with BaCl₂ or iodometrically
- Nitrogen: Kjeldahl digestion → NH₃, distil and titrate
- Oxygen: By difference: 100% − (C% + H% + S% + N% + Ash% + Moisture%)
4.2 Proximate Analysis
Quick determination of moisture, volatile matter, fixed carbon, and ash.
- Moisture: Heat at 105 °C to constant weight; loss = moisture%
- Volatile Matter: Heat in covered crucible at 950 °C for 7 min; weight loss = volatile matter%
- Ash: Burn sample at 750–800 °C; residue = ash%
- Fixed Carbon: By difference = 100% − (Moisture + Volatile Matter + Ash)
5. Stoichiometric Air and Flue Gas Calculation
5.1 Theoretical Air Requirement
For fuel formula CaHbOcSd:
Complete combustion:
CaHbOcSd + \bigl(a + b/4 − c/2 + d\bigr) O₂ → a CO₂ + (b/2) H₂O + d SO₂
Theoretical O₂ moles per mole fuel = a + b/4 − c/2 + d
Theoretical air m³ per m³ fuel = 4.76 × (O₂ moles)
5.2 Dry Flue Gas Composition (Vol %)
| Component | Volume (per mol fuel) |
|---|---|
| CO₂ | a |
| O₂ | Excess O₂ moles |
| SO₂ | d |
| N₂ | 4.76 × (O₂ moles) − N₂ in fuel |
6. Correlations for Calorific Value
6.1 Dulong’s Formula (Solid Fuels)
HCV (kJ/kg) = 338C + 1442(H − O/8) + 94S where C, H, O, S = mass% of elements
6.2 Approximation for Liquid Fuels
HCV (kcal/kg) ≈ 85,000 – 90 × (sulfur% by weight)
7. Example Calculation
7.1 Bomb Calorimeter Example
A 1.000 g coal sample burned in a bomb calorimeter containing 2000 g water. Calorimeter constant = 4.50 kJ/K; ignition energy = 1.20 kJ. Temperature rise = 2.350 K. Calculate HCV.
Q_abs = (m_w·C_w + C_cal)·ΔT
= (2000·4.184 + 4.5)·2.350
= (8368 + 4.5)·2.350
= 8372.5·2.350
= 19672.4 kJ
Q_fuel = Q_abs – Q_ign
= 19672.4 – 1.20
= 19671.2 kJ
HCV = Q_fuel / m_f
= 19671.2 / 1.000
= 19671.2 kJ/kg
7.2 Stoichiometric Air Example
Fuel: C₄H₁₀ (butane). Calculate theoretical air required per mole.
O₂ required = a + b/4 − c/2 + d
= 4 + 10/4 − 0/2 + 0
= 4 + 2.5
= 6.5 mol O₂ per mol C₄H₁₀
Air required = 6.5 × 4.76 = 30.94 mol air per mol fuel
8. Exam Focus Points
- Differentiate HCV and LCV; derive LCV from HCV formula
- Describe bomb calorimetry steps and calculations
- Perform ultimate and proximate fuel analyses
- Calculate theoretical air and flue gas composition from fuel formula
- Apply Dulong’s formula correctly; know its limitations
This expanded guide includes precise definitions, detailed procedures, correct formulas, and illustrative examples for calorific value determination and combustion analysis—designed for thorough understanding and exam success.
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