Formula
Per mole of each combustible C_cH_hS_sO_o burned to CO₂, H₂O and SO₂:
\(V_{O_2} = \sum_i y_i\left(c_i + \frac{h_i}{4} + s_i - \frac{o_i}{2}\right) - y_{O_2,f} \qquad V_{a,th} = \frac{V_{O_2}}{0.2095} \qquad V_{a} = V_{a,th}(1 + EA) \qquad V_{a,wet} = V_a + \omega\,V_a\frac{M_{air}}{M_{H_2O}}\)
\(V_{CO_2} = \sum_i y_i c_i + y_{CO_2,f} \qquad V_{H_2O} = \sum_i y_i \frac{h_i}{2} + y_{H_2O,f} + \omega V_a \frac{M_{air}}{M_{H_2O}} \qquad V_{SO_2} = \sum_i y_i s_i + y_{SO_2,f} \qquad V_{N_2+Ar} = y_{N_2,f} + 0.7905\,V_a \qquad V_{O_2,x} = 0.2095\,V_a - V_{O_2}\)
\(V_{g,wet} = V_{CO_2} + V_{H_2O} + V_{SO_2} + V_{N_2+Ar} + V_{O_2,x} \qquad V_{g,dry} = V_{g,wet} - V_{H_2O} \qquad m_j = \frac{V_j\,M_j}{M_f}\)
Heating values from the standard molar heats of combustion \(\Delta H_{c,i}\) at 25 °C:
\(M_f = \sum_i y_i M_i \qquad \rho_f = \frac{M_f}{V_m} \qquad GCV_v = \frac{\sum_i y_i\,\Delta H_{c,i}}{V_m} \qquad NCV_v = GCV_v - \frac{\sum_i y_i\,\tfrac{h_i}{2}\,h_{fg,25}\,M_{H_2O}}{V_m} \qquad GCV = \frac{GCV_v}{\rho_f}\)
Variables
| Symbol | Meaning | SI unit |
|---|---|---|
| \(y_{CH_4}\), \(y_{C_2H_6}\), \(y_{C_3H_8}\), \(y_{C_4H_{10}}\), \(y_{C_5H_{12}}\), \(y_{C_2H_4}\), \(y_{C_3H_6}\), \(y_{C_6H_6}\), \(y_{H_2}\), \(y_{CO}\), \(y_{H_2S}\) | combustible species, volume fractions of the fuel gas | – |
| \(y_{H_2O}\), \(y_{CO_2}\), \(y_{N_2}\), \(y_{O_2}\), \(y_{SO_2}\) | inert and oxygen species of the fuel gas (as inputs) | – |
| \(c_i\), \(h_i\), \(s_i\), \(o_i\) | atoms of C, H, S, O in species i | – |
| \(EA\) | excess air fraction | – |
| \(\omega\) | humidity of combustion air, kg water per kg dry air | kg/kg |
| \(M_f\) | molar mass of the fuel gas | kg/kmol |
| \(\rho_f\) | fuel gas density at 0 °C and 101.325 kPa | kg/Nm³ |
| \(GCV_v\), \(NCV_v\) | gross and net calorific value per normal cubic metre | J/Nm³ |
| \(GCV\), \(NCV\) | gross and net calorific value per kilogram | J/kg |
| \(V_{O_2}\) | stoichiometric oxygen per Nm³ fuel | Nm³/Nm³ |
| \(V_{a,th}\), \(V_{a,wet}\) | theoretical dry air and actual wet air per Nm³ fuel | Nm³/Nm³ |
| \(V_{g,wet}\), \(V_{g,dry}\) | wet and dry flue gas per Nm³ fuel | Nm³/Nm³ |
| \(m_{a,wet}\), \(m_{g,wet}\), \(m_{g,dry}\) | the same per kg of fuel | kg/kg |
| \(y_{CO_2}\), \(y_{H_2O}\), \(y_{N_2}\), \(y_{Ar}\), \(y_{O_2}\), \(y_{SO_2}\) | wet flue gas composition by volume (as outputs) | – |
| \(y_{O_2,dry}\) | oxygen in dry flue gas, as an analyser reads it | – |
| \(V_m\) | molar volume at normal conditions, 22.414 | Nm³/kmol |
| \(h_{fg,25}\) | latent heat of water at 25 °C (IF97) | J/kg |
Method and standards
Volumetric stoichiometry at normal conditions with PTC 4 air (20.95 % O₂, 79.05 % atmospheric nitrogen, carried as N₂ + Ar + CO₂). Heating values are built from the standard molar enthalpies of combustion of each species at 25 °C (NIST Chemistry WebBook) divided by the ideal-gas molar volume, so the GCV of methane is 890.6 kJ/mol ÷ 22.414 L/mol = 39.73 MJ/Nm³. The net value subtracts the IF97 latent heat of the water formed. Mass-basis results divide by the fuel gas molar mass.
Assumptions and limits
- Ideal gas: volume fraction equals mole fraction; real-gas corrections (about 1–2 % for propane and butane at normal conditions) are not applied.
- Complete combustion; H₂S goes entirely to SO₂.
- Benzene is taken as vapour; hydrocarbons heavier than pentane are not listed and should be lumped into pentane by carbon content.
References
- ASME PTC 4-2013 (air composition)
- NIST Chemistry WebBook (standard enthalpies of combustion at 25 °C)
- ideal gas at 0 °C and 101.325 kPa
Questions and answers
What is a normal cubic metre?
Gas volume referred to 0 °C and 101.325 kPa, treated as an ideal gas (22.414 m³ per kmol). Suppliers sometimes quote standard cubic metres at 15 °C, which are 5.5 % larger; convert before entering.
Why is the GCV per Nm³ of ethane almost twice that of methane?
Heating value per mole scales with the carbon and hydrogen atoms burned: ethane releases 1 561 kJ/mol against 891 kJ/mol for methane, and a normal cubic metre holds the same number of moles of either.
How does this handle inerts in the fuel gas?
CO₂, N₂ and water vapour in the fuel pass straight into the flue gas, lower the heating value per Nm³ and increase the flue gas per unit of heat. Oxygen in the fuel reduces the air needed.