Formula
Losses per kg fuel gas, divided by the gross calorific value:
\(L_{dg} = m_{g,dry}\left[h_{g}(T_g) - h_{g}(T_{ref})\right] \qquad L_{H} = m_{H_2O,H}\left[h_v(T_g) - h_f(T_{ref})\right] \qquad L_{M} = m_{H_2O,f}\left[h_v(T_g) - h_f(T_{ref})\right]\)
\(L_{\omega} = \omega\,m_a\left[h_v(T_g) - h_v(T_{ref})\right] \qquad L_{CO} = y_{CO}\,\frac{m_{g,dry}}{M_{g,dry}}\,M_{CO}\,\Delta h_{CO}\)
\(B_{a} = m_a\left[h_{air}(T_a) - h_{air}(T_{ref})\right] \qquad B_{\omega} = \omega\,m_a\left[h_v(T_a) - h_v(T_{ref})\right] \qquad \eta_{GCV} = 1 - \frac{\sum L}{GCV} + \frac{\sum B}{GCV} \qquad \eta_{NCV} = \eta_{GCV}\,\frac{GCV}{NCV}\)
Variables
| Symbol | Meaning | SI unit |
|---|---|---|
| \(y_{CH_4}\), \(y_{C_2H_6}\), \(y_{C_3H_8}\), \(y_{C_4H_{10}}\), \(y_{C_5H_{12}}\), \(y_{C_2H_4}\), \(y_{C_3H_6}\), \(y_{C_6H_6}\), \(y_{H_2}\), \(y_{CO}\), \(y_{H_2S}\), \(y_{H_2O}\), \(y_{CO_2}\), \(y_{N_2}\), \(y_{O_2}\), \(y_{SO_2}\) | fuel gas analysis by volume; \(y_{CO}\) also names the CO reading in dry flue gas under operating data | – |
| \(EA\) | excess air fraction | – |
| \(\omega\) | air humidity, kg water per kg dry air | kg/kg |
| \(T_a\), \(T_g\) | entering air and leaving flue gas temperatures | K |
| \(T_{ref}\) | reference temperature, 298.15 K | K |
| \(m_a\), \(m_{g,dry}\) | actual dry air and dry flue gas per kg fuel | kg/kg |
| \(m_{H_2O,H}\), \(m_{H_2O,f}\) | water formed from hydrogen and water vapour carried in the fuel gas, per kg fuel | kg/kg |
| \(M_{g,dry}\), \(M_{CO}\) | molar mass of dry flue gas and of CO | kg/kmol |
| \(h_g\), \(h_{air}\), \(h_v\), \(h_f\) | enthalpies of dry flue gas, air, water vapour (IF97, 1 psia) and liquid water at 25 °C | J/kg |
| \(\Delta h_{CO}\) | heat of burning CO to CO₂, 23.63 MJ/kg | J/kg |
| \(GCV_v\) | gross calorific value per normal cubic metre | J/Nm³ |
| \(GCV\), \(NCV\) | gross and net calorific value per kg | J/kg |
| \(L_{dg}\), \(L_{H}\), \(L_{M}\), \(L_{\omega}\), \(L_{CO}\), \(L_{rc}\), \(L_{un}\) | losses: dry gas, water from hydrogen, fuel moisture, air moisture, CO, radiation and convection, unaccounted | – |
| \(\sum L\), \(\sum B\), \(B_{a}\), \(B_{\omega}\) | total losses, total credits, dry air credit, air moisture credit | – |
| \(\eta_{GCV}\), \(\eta_{NCV}\) | efficiency on the gross and the net basis | – |
Method and standards
ASME PTC 4-2013 energy balance method (owner decision 2026-11-09) applied to the mass-basis combustion balance of the gaseous combustion calculator. The heating value is built from the standard molar heats of combustion of the species (NIST) so that fuel, air and losses are consistent; gas enthalpies are integrated from Shomate heat capacities of the actual flue gas; water vapour from IF97 at 1 psia.
Assumptions and limits
- No residue, no unburned carbon; incomplete combustion appears only as CO.
- Flue gas temperature above about 39 °C and above the entering air temperature.
- Fuel sensible heat is not credited.
References
- ASME PTC 4-2013 Fired Steam Generators §5.14 and §5.15
- NIST Chemistry WebBook (heats of combustion)
Questions and answers
Why is a gas boiler's gross efficiency so much lower than its net efficiency?
Methane makes 2.25 kg of water per kg of fuel. Its latent heat is about 10 % of the gross calorific value and leaves with the flue gas unless the boiler condenses, so the HHV efficiency is roughly 10 points below the LHV efficiency.
Can I enter the GCV from the gas supplier instead?
This calculator derives it from the analysis, so the heating value and the stoichiometry are consistent. If the supplier's GCV differs by more than 2 %, the analysis is probably out of date; use the current one.
Why is there no unburned carbon loss?
Gaseous fuels leave no residue. Incomplete combustion shows up as CO, which is the loss entered here.