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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 F_s. 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; Q_rad – 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.

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.

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: U_j – 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.

Flare Radiation Modeling Methods

Flare systems are safety-critical elements of refineries, petrochemical plants, gas processing facilities and LNG installations. Their primary function is to safely dispose of gases released during pressure relief, emergency depressuring, start-up, shutdown or other abnormal operating conditions. However, safe flaring is not only a question of combustion. One of the most important design aspects is the thermal radiation generated by the flame and its impact on personnel, equipment and surrounding plant areas.

In engineering practice, flare radiation assessment is used to determine whether the heat flux received at a given point remains acceptable for continuous personnel presence, short emergency actions, access routes, platforms, nearby equipment or plot-limit areas. This is why API 521-based flare studies usually combine process data, flare geometry, gas properties, wind conditions and selected radiation exposure criteria.

1. Overview of flare radiation calculation methods

Several methods can be used to estimate thermal radiation from industrial flare systems. The appropriate approach depends on the project phase, the amount of available data and the required accuracy. Simple methods are useful for early screening, while more advanced models are typically applied when flame geometry, wind influence or low-luminosity fuels become important.

For many engineering applications, semi-empirical methods provide a practical compromise between simplicity and physical realism. They are more informative than a pure point source calculation, but still fast enough for design iterations, scenario comparison and early project decision-making.

2. Radiation exposure levels used in flare studies

Flare radiation studies commonly compare calculated heat flux values with selected exposure limits. These values are used to define safety distances, restricted access zones and emergency action areas. The exact interpretation may depend on project standards, local regulations, company requirements, exposure duration, clothing and whether solar radiation is included.

3. Required input data

Before calculating thermal radiation, the flare case must be defined using process, mechanical and environmental data. The table below summarizes the most important inputs typically required for an API 521-style flare radiation workflow.

4. Basic calculation sequence

The first stage of a flare radiation assessment is the conversion of process data into the main quantities required for radiation modeling. These include volumetric flow rate, heat release rate, exit velocity and Mach number at the flare tip.

4.1 Volumetric flow rate

For a gas stream with known mass flow rate and molecular weight, the ideal-gas-based volumetric flow can be estimated using the following form:

where: V̇ – volumetric gas flow rate, m³/s; ṁ – mass flow rate, kg/h; MW – molecular weight, kg/kmol; T – gas temperature, K. The exact form depends on whether normal, standard or actual volumetric conditions are used.

4.2 Heat release rate

The chemical heat release rate is calculated from the mass flow rate and lower heating value of the flare gas:

If LHV is expressed in kJ/kg, Q is obtained in kW. If LHV is expressed in MJ/kg, the unit conversion must be applied accordingly.

4.3 Flare tip exit velocity

The gas exit velocity at the flare tip is calculated from the volumetric flow rate and flare tip cross-sectional area:

where: U_j – flare tip exit velocity, m/s; D – flare tip diameter, m.

4.4 Reference speed of sound and Mach number

For preliminary engineering calculations, a reference speed of sound may be estimated from gas temperature and molecular weight:

The Mach number is then calculated as:

where: a_iso – reference speed of sound, m/s; M – Mach number.

5. Semi-empirical flame center approach

In a simple point source method, the flame is represented by one radiating point. In semi-empirical methods, this point is not placed arbitrarily. Instead, the effective flame center is estimated from correlations that account for jet velocity, wind speed, gas properties and flammability characteristics.

A typical semi-empirical workflow uses dimensionless groups to estimate the normalized location of the flame center. The flame center coordinates are then used to calculate the distance between the radiating source and the receiver point.

5.1 Dilution-related dimensionless group

where: C_L,av – dimensionless dilution-related parameter; LEL – lower explosive limit, % vol.; U – wind velocity, m/s; MW_air – molecular weight of air.

5.2 Jet momentum to wind influence parameter

where: d_jR – dimensionless parameter describing the relation between jet momentum and wind influence; T_air – ambient air temperature, K.

Based on these dimensionless parameters, the flame center coordinates can be obtained from empirical correlations, charts or implemented curve fits. The resulting coordinates describe the effective radiating position of the flame relative to the flare tip.

5.3 Flame length estimation

After estimating the flame center coordinates, the total flame length may be approximated as:

where: L – total flame length, m; x_c, y_c – flame center coordinates.

6. Thermal radiation at the receiver point

Once the heat release rate and effective flame position are known, the thermal radiation received at a selected point can be estimated. In a point source formulation, the received heat flux decreases with the square of the distance from the radiating source.

where: K – received thermal radiation, kW/m²; τ – atmospheric transmissivity; F – fraction of heat radiated; Q – heat release rate, kW; R – distance from the flame center to the receiver point, m.

For a selected radiation limit, the corresponding distance can be estimated by rearranging the equation:

This equation is useful for quick screening, but in realistic flare layouts the receiver point location, flame tilt, wind direction, flare elevation and ground-level projection should also be considered.

7. Example findings of flare radiation study

A clear flare radiation report should not only provide one maximum distance. It should present the calculated radiation zones for each selected threshold and operating scenario. This allows engineers to compare wind cases, relief cases and flare geometries in a transparent way.

8. Flare radiation is only one part of flare management

Best Available Techniques for refinery and gas processing installations emphasize that flaring should not be treated as a normal operating mode. A flare is primarily a safety device and should be used mainly for safety reasons, emergency situations and non-routine operating conditions such as start-up or shutdown.

A BAT-oriented flare management philosophy may include:

• minimization of routine flaring,
• flare gas recovery where technically and economically feasible,
• routing recoverable gases back to the process or fuel gas system,
• reliable ignition and flame monitoring,
• proper liquid removal in flare knockout drums,
• monitoring and review of flare events,
• identification of recurring causes of flaring,
• consideration of radiation, noise, emissions and smoke together.

Therefore, flare radiation assessment should be understood as part of a wider process safety and environmental management framework. The purpose is not only to calculate a distance, but to support safe layout decisions, emergency planning and responsible flare system operation.

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-style 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 vendor-specific flare tips, final verification should also consider supplier data, smokeless capacity, assist medium, flame stability, operating envelope, noise, mechanical design and project-specific requirements.

Conclusion

Flare radiation assessment remains a key element of process safety engineering. API 521-style methods provide a practical basis for estimating heat flux, flare stack height and safety distances. Simple point source models are useful for early screening, semi-empirical methods provide a stronger engineering basis, and advanced CFD-based methods may be justified for complex or high-risk cases. A good flare study should not only produce a single number. It should clearly show the method, assumptions, input data, radiation thresholds and resulting safety distances. This is the engineering gap that FlareQ521 is designed to support: transparent, repeatable and practical flare radiation assessment for industrial applications.