Formula
Oxygen demand per kg fuel from the elemental reactions C + O₂ → CO₂, H₂ + ½O₂ → H₂O, S + O₂ → SO₂, less the oxygen in the fuel:
\(m_{O_2} = \frac{M_{O_2}}{M_C}\,C + \frac{M_{O_2}}{2\,M_{H_2}}\,H + \frac{M_{O_2}}{M_S}\,S - O\)
\(m_{a,th} = \frac{m_{O_2}}{w_{O_2}} \qquad m_a = m_{a,th}\,(1 + EA) \qquad m_{a,wet} = m_a\,(1 + \omega)\)
Flue gas per kg fuel:
\(m_{CO_2} = \frac{M_{CO_2}}{M_C}\,C \qquad m_{H_2O} = \frac{M_{H_2O}}{M_{H_2}}\,H + M + \omega\,m_a \qquad m_{SO_2} = \frac{M_{SO_2}}{M_S}\,S \qquad m_{N_2} = N + (1 - w_{O_2})\,m_a \qquad m_{O_2,x} = w_{O_2}\,m_a - m_{O_2}\)
\(m_{g,wet} = m_{CO_2} + m_{H_2O} + m_{SO_2} + m_{N_2} + m_{O_2,x} \qquad m_{g,dry} = m_{g,wet} - m_{H_2O} \qquad y_i = \frac{m_i / M_i}{\sum_j m_j / M_j} \qquad V_g = V_m \sum_j \frac{m_j}{M_j}\)
Heating values:
\(GCV_{CP} = \left(0.3491\,C' + 1.1783\,H' + 0.1005\,S' - 0.1034\,O' - 0.0151\,N' - 0.0211\,A'\right)\,\mathrm{MJ/kg} \times (1 - M) \qquad NCV = GCV - h_{fg,25}\left(\frac{M_{H_2O}}{M_{H_2}}\,H + M\right)\)
Variables
| Symbol | Meaning | SI unit |
|---|---|---|
| \(C\), \(H\), \(O\), \(N\), \(S\), \(A\), \(M\) | carbon, hydrogen, oxygen, nitrogen, sulphur, ash, moisture, mass fractions as fired | – |
| \(C'\) … \(A'\) | the same on a dry basis, in mass % (Channiwala–Parikh) | % |
| \(GCV_{in}\) | gross calorific value entered (0 to estimate) | J/kg |
| \(EA\) | excess air fraction | – |
| \(\omega\) | humidity of the combustion air, kg water per kg dry air | kg/kg |
| \(GCV\) | gross calorific value used | J/kg |
| \(GCV_{CP}\) | Channiwala–Parikh estimate | J/kg |
| \(GCV_{D}\) | Dulong estimate | J/kg |
| \(NCV\) | net calorific value | J/kg |
| \(h_{fg,25}\) | latent heat of water at 25 °C, 2 441.7 kJ/kg (IF97) | J/kg |
| \(M_i\) | molar masses (IUPAC 2013) | kg/kmol |
| \(w_{O_2}\) | oxygen mass fraction of dry air, 0.2314 (20.95 % by volume) | – |
| \(m_{O_2}\) | stoichiometric oxygen per kg fuel | kg/kg |
| \(m_{a,th}\), \(m_{a}\), \(m_{a,wet}\) | theoretical dry air, actual dry air, actual wet air per kg fuel | kg/kg |
| \(m_{g,wet}\), \(m_{g,dry}\) | wet and dry flue gas per kg fuel | kg/kg |
| \(m_{H_2O}\) | water vapour in the flue gas per kg fuel | kg/kg |
| \(V_g\) | wet flue gas volume per kg fuel at 0 °C and 101.325 kPa | Nm³/kg |
| \(V_m\) | molar volume at normal conditions, 22.414 | Nm³/kmol |
| \(y_{CO_2}\), \(y_{H_2O}\), \(y_{N_2}\), \(y_{Ar}\), \(y_{O_2}\), \(y_{SO_2}\) | wet flue gas composition by volume | – |
| \(y_{O_2,dry}\) | oxygen in dry flue gas, as an analyser reads it | – |
Method and standards
Exact molar ratios from IUPAC 2013 atomic masses (32/12.011 for carbon, not 2.667). Air is 20.95 % O₂, 78.08 % N₂, 0.93 % Ar and 0.04 % CO₂ by volume (U.S. Standard Atmosphere, as ASME PTC 4); argon and the air's CO₂ are carried through to the flue gas, so the "nitrogen" of older methods appears here as N₂ plus Ar. The GCV estimate is the Channiwala–Parikh (2002) unified correlation (owner decision 2026-11-09); Dulong is shown for comparison. NCV uses the IF97 latent heat at 25 °C and the exact 8.936 kg of water per kg of hydrogen.
Assumptions and limits
- Complete combustion: no CO, no unburned carbon, all sulphur to SO₂. For losses with incomplete combustion use the boiler efficiency calculator.
- The analysis must sum to 100 % ± 0.5 %.
- Channiwala–Parikh range: C 0–92 %, H 0.43–25 %, O 0–50 %, N 0–5.6 %, ash 0–71 % (dry basis); outside it the estimate is flagged.
References
- ASME PTC 4-2013 (air composition
- stoichiometry)
- Channiwala & Parikh (2002) Fuel 81 1051–1063
- Dulong's formula
Questions and answers
Should the analysis be as fired, dry, or dry ash-free?
As fired, including moisture and ash, so that air and gas come out per kilogram of fuel actually burned. Convert a dry analysis by multiplying each constituent by (1 − moisture).
Why is the O₂ in dry flue gas lower than the excess air suggests?
Because nitrogen dilutes it. 20 % excess air gives only about 3.6 % O₂ in dry gas for coal. Use the flue gas analyser calculator to go the other way.
Which GCV estimate should I trust?
Channiwala–Parikh (2002) was fitted to 225 fuels from biomass to anthracite with an average error of 1.45 %. Dulong is older and overestimates high-oxygen fuels such as wood and bagasse; it is shown for comparison. A laboratory value always beats both.