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Flame temperature

Interactive calculator of the theoretical (adiabatic) and practical flame temperature of industrial gas blends, with an animated reheating furnace.

TFT, PFT and the K1, K2, K3 coefficients

When a gaseous fuel burns, the energy released heats the combustion products. The temperature those products would reach in perfect combustion, with no losses, is the theoretical (adiabatic) flame temperature. In practice, radiation losses, imperfect mixing and the geometry of the space bring it down to the practical flame temperature.

TFT — Theoretical temperature

Also called the adiabatic flame temperature. It is the temperature the flue gases would reach if all the fuel energy (LHV) plus the sensible heat of fuel and air went into heating the products, with no losses.

Found by energy balance: energy released = energy needed to heat CO₂, H₂O, N₂ and excess O₂ up to the TFT.

PFT — Practical temperature

The temperature actually observed in the flame. It is always lower than the TFT, because part of the heat is lost by radiation to walls and load, and through turbulence and imperfect mixing with air.

Calculated as PFT = TFT × K1 × K2 × K3, where each coefficient represents one kind of pyrometric efficiency loss.

K1, K2, K3

K1 depends on the gas LHV: the leaner the gas, the higher K1 (0.78 for LHV < 1,000; 0.75 for LHV > 2,250 kcal/Nm³, linear in between).

K2 depends on the space where the flame develops (open, semi-enclosed, enclosed). K3 depends on burner turbulence.

Reference compositions and LHV of each gas Editable table: change any gas composition and the flame temperature is recalculated in the calculator below

Volumetric composition (%) of each reference gas. Every composition cell is editable: change a value to simulate a new gas analysis. LHV, density, specific heat, the blend column and TFT/PFT update with every digit you type.

Use a dot or comma as the decimal separator (e.g. 63.62 or 63,62). Totals may not add up to exactly 100% because of trace components not listed (e.g. heavier hydrocarbons in natural gas). Each gas LHV is computed from the standard LHV of each pure component plus a small fixed correction, calibrated to reproduce the reference LHV of the original gas.

How it is calculated

The engine runs a component-by-component combustion energy balance rather than a simplified average.

The model, step by step
  • 1. Blend composition: each of the 10 components (CH₄, CO, H₂, CO₂, N₂, C₂H₆, C₂H₄, C₂H₂, O₂, C₃H₈) is the weighted average of the 6 input gases by their share in the blend.
  • 2. LHV of each gas: computed from the standard LHV of each pure component (CH₄ ≈ 8,555; CO ≈ 3,018; H₂ = 2,575; C₂H₆ ≈ 15,280 kcal/Nm³ etc.) plus a small fixed correction per gas. Blend density and specific heat are weighted averages of the input gases.
  • 3. Stoichiometric air: computed component by component (CH₄ + 2 O₂ → CO₂ + 2 H₂O; CO + ½ O₂ → CO₂; H₂ + ½ O₂ → H₂O etc.), using the O₂ content of the oxidant (21% for air, higher with oxygen enrichment) and the excess air.
  • 4. Combustion products: CO₂, H₂O, N₂ and excess O₂, from the stoichiometry of each component.
  • 5. Energy balance: input energy (LHV + sensible heat of preheated fuel and air, referenced to 25 °C) equals the energy needed to heat the products up to the TFT, using mean specific heats that vary with temperature. The TFT is solved by numerical iteration.
  • 6. PFT = TFT × K1 × K2 × K3, with the chosen coefficients.
Model validated against the reference case of the original spreadsheet (82% BFG / 5% LDG / 5% COG / 8% NG, air at 450 °C, 10% excess air, K1 = 0.78): computed TFT ≈ 1,821 °C (reference 1,808 °C) and PFT ≈ 1,421 °C (reference 1,410 °C), less than 1% difference.

Flame temperature calculator Adjust the gas blend and combustion conditions; the furnace flame responds in real time

Share of each gas in the blend 100%

Combustion conditions

Pyrometric efficiency

K2 — flame space
Theoretical flame temp. (TFT)
adiabatic
Practical flame temp. (PFT)
TFT × K1 × K2 × K3
Blend LHV
kcal/Nm³
Blend density
kg/Nm³ · 0 °C / 1 atm
Relative density
relative to air
Specific heat
kcal/Nm³·°C
Lower Wobbe index
kcal/Nm³

Reheating furnace with animated flame

Flame colour and length follow the calculated practical temperature (PFT) and the excess air.
Pyrometric efficiency
  • PFT = TFT × K1 × K2 × K3
  • K1 depends on gas LHV: LHV < 1,000 kcal/Nm³ → K1 = 0.78; LHV > 2,250 kcal/Nm³ → K1 = 0.75; linear in between (suggested automatically, but editable).
  • K2 depends on the flame space: open (reheating furnace) K2 = 1; semi-enclosed (combustion chamber) K2 = 1.04; enclosed (radiant tube) K2 = 1.09.
  • K3 depends on the burner: stable flame without excessive turbulence, K3 = 1; very turbulent flame with strong gas recirculation, K3 between 0.95 and 1.

Summary

  • The theoretical flame temperature (TFT) comes from an energy balance: gas LHV + sensible heat of preheated fuel and air = heat needed to warm the combustion products.
  • The practical flame temperature (PFT) is always lower than the TFT because it accounts for real losses: PFT = TFT × K1 × K2 × K3.
  • Preheating combustion air (recuperators and regenerators) raises both TFT and PFT. More excess air lowers flame temperature because it dilutes the products.
  • Enriching the oxidant with oxygen (above 21%) reduces the inert N₂ to be heated and raises the flame temperature for the same fuel.
  • Lean gases (low LHV, such as BFG) reach lower flame temperatures than rich gases (NG, H₂) unless the air is strongly preheated. That is why preheating is essential in furnaces firing blast furnace gas.
  • The composition of each gas can be edited in the table in section 2 to simulate new lab analyses, and every result updates.