Thermal Radiation: Fraction of Heat Radiated
In flare radiation studies, one of the most important input assumptions is the fraction of heat radiated, commonly marked as F, F-factor, χ or Fs. This parameter describes what part of the chemical heat released by the burning gas is emitted from the flame as thermal radiation. Although it is only one dimensionless number, it has a direct influence on calculated radiation intensity, safety distances, flare stack height assessment and the interpretation of radiation contours around the flare.
The fraction of heat radiated is especially important because flare calculations usually begin with the total heat release rate of the relief case. This total heat release is not the same as the radiant heat that reaches people, equipment or surrounding structures. A flame loses energy through different mechanisms. Part of the released energy is radiated outward from the flame, part remains in the hot combustion products, part contributes to plume rise and part is transferred by convection and entrainment into the surrounding air.
1. What does fraction of heat radiated mean?
The fraction of heat radiated can be understood as the ratio between the radiant power emitted by the flame and the total chemical heat release of the flared gas. In a simplified form, it can be written as:
where: F – fraction of heat radiated, dimensionless; Qrad – radiant heat output from the flame, kW; Q – total heat release rate based on the lower heating value of the gas, kW.
If F = 0.20, it means that 20% of the heat release is assumed to be emitted as thermal radiation. If F = 0.40, the assumed radiant part of the same flare duty is twice as high. This is why the selected F-factor can significantly change calculated heat flux values, even when all process inputs remain unchanged.
In practical engineering calculations, the heat release rate is usually calculated from the flare gas mass flow rate and lower heating value:
where: Q – heat release rate, kW; ṁ – mass flow rate, kg/h; LHV – lower heating value, kJ/kg.
The radiant part of the heat release is then:
This simple relationship is the reason why the F-factor appears explicitly or implicitly in many flare radiation workflows, from point source screening calculations to semi-empirical and surface-source approaches.
2. Why the F-factor matters in radiation calculations
In a point source radiation model, the received heat flux at a selected location is commonly calculated from the radiant heat release, atmospheric transmissivity and distance from the effective flame center:
where: K – received thermal radiation, kW/m²; τ – atmospheric transmissivity; F – fraction of heat radiated; Q – heat release rate, kW; R – distance from the radiating source to the receiver point, m.
This equation represents an isotropic single-point source approximation. It is useful for screening and for many API 521 related calculation methodologies, but it does not fully represent flame surface radiation, receiver orientation, near-field effects, directional emissive power or complex flare tip geometry.
The equation shows that the received radiation is directly proportional to the F-factor. If the assumed F-factor increases, the predicted heat flux increases in the same proportion at the same receiver location. For example, changing F from 0.15 to 0.30 doubles the radiant heat term in the equation.
The impact on calculated safety distance is slightly different because distance is related to the square root of the radiant heat term. For a selected radiation limit, the required distance can be written as:
This means that the calculated distance is proportional to the square root of F. A twofold increase in F does not double the safety distance, but it increases it by approximately 41%. In plot plan review, this difference can still be very important, especially when flare radiation contours approach access roads, equipment, platforms, buildings or the site boundary.
3. Physical interpretation of F
The F-factor is not only a mathematical coefficient. It represents the combined result of flame chemistry, combustion quality, soot formation, flame temperature and radiating surface behavior. A luminous, smoky, hydrocarbon-rich flame generally emits more thermal radiation than a clean, well-mixed, low-soot flame. This is because soot particles and luminous flame zones can be effective emitters of radiation.
For light gases such as methane or hydrogen-rich mixtures, the visible flame may be less luminous and the radiated fraction can be lower than for heavier hydrocarbon flames. For heavier hydrocarbons, incomplete mixing and soot formation can increase flame luminosity and radiative output. However, this trend should not be used too mechanically. A flare tip that improves air entrainment or uses steam or air assist can reduce smoke and change the effective fraction of heat radiated, even for relatively heavy gas mixtures.
The F-factor therefore combines several effects into a single engineering parameter. It does not describe only the fuel. It also reflects how the fuel burns in a particular flare system.
4. Main variables influencing the fraction of heat radiated
A practical flare radiation assessment should treat F as a parameter influenced by several groups of variables. Some of them are related to the gas itself, while others are related to the flare tip, flame aerodynamics and operating conditions.
| Variable | Influence on F | Engineering comment |
|---|---|---|
| Gas composition | Changes flame temperature, soot tendency, luminosity and heating value. | Methane-rich, hydrogen-rich and heavy hydrocarbon streams may require different assumptions. |
| Carbon-to-hydrogen character of the fuel | Higher carbon content can increase soot formation and flame luminosity. | This trend can be reduced by good mixing, steam assist or air assist. |
| Gas exit velocity | Can affect flame length, air entrainment, soot oxidation and flame surface characteristics. | Some experimental studies show a decrease in radiated fraction with increasing jet velocity, but the trend is not universal for all flare types. |
| Wind speed | Changes flame tilt, mixing, residence time and radiation geometry. | In many practical calculations, wind is used primarily to determine flame tilt, flame center and received radiation geometry rather than to directly select F, unless the selected model specifically includes such dependence. |
| Flare tip design | Controls discharge pattern, mixing, flame stability and assist medium effectiveness. | Vendor-specific flare tips should not be treated as identical simple pipes. |
| Steam or air assist | Can reduce smoke and flame luminosity, but may also affect flame shape and stability. | Assist conditions should be consistent with the actual operating case. |
| Flame scale | Large field flares and small laboratory flames may not radiate in exactly the same way. | Scale effects are one reason why laboratory correlations must be applied carefully. |
| Combustion efficiency | Affects the actual amount of heat released and the composition of combustion products. | It should not be hidden inside the F-factor unless this is explicitly part of the selected method or data basis. |
5. Typical F-factor values and why they are not enough
Engineering literature contains many reported values for the fraction of heat radiated. Some sources provide approximate values for selected pure gases, some relate the value to gas molecular weight or composition, and some derive it from field measurements or flame surface emissive power.
Values used in screening calculations for hydrocarbon flares are often in the approximate range of 0.15 to 0.40, but published and measured values can fall outside this range depending on gas composition, flare scale, velocity, smoke formation, measurement basis and flare tip design. Therefore, this range should be treated as an engineering orientation, not as a universal design rule.
Using a typical value without checking its background can be dangerous. Many published F-factors were obtained for a specific fuel, stack diameter, exit velocity, flame size, wind condition, radiometer location or flare design. If these details are missing, the value may still be useful for understanding the order of magnitude, but it should not automatically become the final design basis.
| Type of assumption | Typical use | Main risk |
|---|---|---|
| Fixed conservative value | Early project screening, preliminary flare stack height checks, quick comparison of relief cases. | May be overly conservative for clean-burning gases or not conservative enough for luminous smoky flames. |
| Fuel-based value | Cases where fuel composition is known and similar to literature data. | Composition alone does not fully represent mixing, flare tip design, assist medium or exit velocity. |
| Correlation-based value | More detailed engineering calculations using empirical or semi-empirical methods. | Correlation may only be valid within the experimental range from which it was developed. |
| Vendor-confirmed value | Final design review for a specific flare tip and operating envelope. | Must be checked against the exact relief case, gas, assist medium and guarantee conditions. |
| Measured project-specific value | Operating plant assessment, validation studies, special cases. | Requires suitable instrumentation, measurement procedure and careful interpretation. |
6. F-factor and fuel composition
Fuel composition is one of the first aspects considered when selecting the fraction of heat radiated. Methane-rich streams usually produce cleaner and less luminous flames than heavier hydrocarbon streams. Propane, butane and heavier hydrocarbons generally have a greater tendency to form luminous soot-containing flames, which can increase the radiative fraction.
Hydrogen-rich gases are a special case. Hydrogen flames can be difficult to see and may have relatively low luminosity compared with heavier hydrocarbons. However, this does not mean that hydrogen flare studies are simple. Hydrogen has high flame speed, different flame stability behavior and different visibility and detection issues. Many hydrocarbon-based F-factor correlations should not be transferred directly to hydrogen-rich or syngas flames without checking their validation range.
For mixed gases, the situation becomes more complex. A relief stream may contain methane, ethane, propane, hydrogen, carbon dioxide, nitrogen, hydrogen sulfide, water vapor or other components. Some components contribute significantly to heat release, some dilute the flame, some affect molecular weight, and some influence combustion behavior. Because of this, the selected F-factor should be linked to the actual mixture and not only to one dominant component.
7. F-factor, gas exit velocity and flame aerodynamics
Gas exit velocity influences the way the flare jet interacts with the surrounding air. A higher velocity jet can increase air entrainment, change flame length and affect soot oxidation. In some experimental datasets, the fraction of heat radiated decreases as gas exit velocity increases. This can be interpreted as the result of improved mixing and less luminous combustion, but it should not be generalized without checking the flare type, fuel composition and test range.
For very high velocity flares, sonic or near-sonic discharge, the flame can be shorter, more aerodynamically stretched and less similar to a low velocity luminous diffusion flame. The same heat release rate can therefore produce a different radiation pattern depending on flare tip diameter and discharge velocity.
where: Uj – flare tip exit velocity, m/s; V̇ – volumetric gas flow rate at flare conditions, m³/s; D – flare tip diameter, m.
This relationship shows why flare tip diameter is connected to radiation assessment. For the same volumetric flow rate, a smaller diameter gives a higher exit velocity. The change in velocity may affect flame geometry, flame center position and, depending on the selected method or data basis, the assumed or calculated F-factor.
8. How to select F in your study
The selection of F should follow the maturity of the project and the available data. In early screening, a conservative assumed value may be acceptable. In detailed design, the selected value should be justified using project standards, API 521 methodology, literature data, flare vendor information or project-specific validation.
A practical selection workflow may include the following steps:
- define the relief scenario and confirm that the mass flow rate and gas composition are realistic,
- calculate the heat release rate from the lower heating value of the actual flare gas,
- identify whether the gas is methane-rich, hydrogen-rich, heavy hydrocarbon-rich, inert-rich or mixed,
- check whether the flare tip is a simple pipe flare, sonic flare, staged flare, steam-assisted flare or air-assisted flare,
- estimate flare tip exit velocity and Mach number,
- review project or company standards for default F-factor values,
- compare the selected value with literature ranges and vendor recommendations,
- check whether the selected correlation or value is valid for the flare type, gas composition and velocity range,
- perform sensitivity calculations for low, base and high F values,
- document the final selected value and its basis in the flare radiation report.
Sensitivity analysis is particularly useful because it shows whether the conclusion depends strongly on the assumed F-factor. If a small change in F moves a radiation contour across an access road or equipment area, the design should be reviewed more carefully.
9. Why digital tools are useful
Flare radiation calculations can be performed manually, in spreadsheets or in dedicated engineering software. However, the workflow becomes more difficult when many relief cases, flare tips, gas compositions, wind speeds and radiation thresholds must be compared.
FlareQ521 is developed to support this type of engineering workflow. The objective is to make flare radiation assessment clearer, faster and more repeatable by combining input data, calculation logic and visual radiation zones in one environment. The software can support the engineer by:
- organizing input data for multiple flare cases,
- calculating heat release rate and flare tip velocity,
- estimating flame center and flame length,
- calculating radiation levels at selected receiver points,
- comparing API 521 exposure thresholds,
- visualizing radiation contours and safety distances,
- preparing consistent results for engineering review.
10. Engineering judgement remains essential
No calculation method should be used without engineering review. Before accepting flare radiation results, the engineer should verify the selected relief scenario, mass flow rate, gas composition, lower heating value, flare tip diameter, fraction of heat radiated, wind basis, exposure criteria and the treatment of solar radiation.
For flare tips specified by vendors, final verification should also consider supplier data, smokeless capacity, assist medium, flame stability, operating envelope, noise, mechanical design and project requirements.
Conclusion
The fraction of heat radiated is one of the key assumptions in flare radiation calculations. It links the chemical heat release of the relief stream with the thermal radiation field around the flare, so the selected value can significantly influence heat flux results, safety distances and radiation contour interpretation.