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.
| Method | Typical application | Main advantage | Main limitation |
|---|---|---|---|
| Simple point source approach | Preliminary flare stack height selection, early safety distance screening, quick comparison of relief cases. | Very fast calculation. Requires only basic process data and an assumed fraction of heat radiated. | Does not represent flame length, flame tilt, wind distortion or detailed flame geometry. |
| Semi-empirical flame center models | Refineries, gas processing units, petrochemical facilities and conventional elevated flares. | Includes practical correlations for flame center location, flame length and influence of wind or jet momentum. | Requires empirical charts, correlations or calibration assumptions. Accuracy depends on similarity to the original experimental basis. |
| Line source model | Large elevated flares, cases where flame length and observer position are important. | Represents the flame as an elongated radiating source instead of a single point. | More input data and assumptions are required than for the point source approach. |
| Surface source model | Large luminous flames, complex radiation distribution studies, detailed plant layout review. | Can represent flame surface and directional radiation more realistically. | More complex and less convenient for quick engineering screening. |
| CFD with radiation modeling | Complex installations, unusual fuels, hydrogen-rich mixtures, enclosed ground flares or validation studies. | Can include turbulence, combustion, flame shape, wind field and radiative transfer. | Time-consuming, specialist, sensitive to boundary conditions and usually not necessary for routine calculations. |
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.
| Radiation level | Typical engineering interpretation | Example use in flare studies |
|---|---|---|
| 1.58 kW/m² | Often associated with continuous personnel exposure for workers wearing suitable work clothing. | Evaluation of normally accessible plant areas, roads, operating zones or plot boundaries. |
| 4.73 kW/m² | Short-duration emergency action level, typically with appropriate clothing and limited exposure time. | Emergency access assessment, evacuation planning and review of operator intervention zones. |
| 6.31 kW/m² | Higher emergency exposure level, generally requiring strict limitation of exposure duration. | Assessment of severe emergency cases and short operational actions near flare radiation zones. |
| 9.46 kW/m² | Severe radiation level, usually acceptable only for very short urgent actions by properly protected personnel. | Definition of high-radiation zones and evaluation of critical emergency access restrictions. |
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.
| Input parameter | Symbol | Typical unit | Purpose in calculation |
|---|---|---|---|
| Mass flow rate | ṁ | kg/h | Defines the amount of gas sent to the flare during the selected scenario. |
| Molecular weight of flare gas | MW | kg/kmol | Used to estimate volumetric flow, density-related effects and jet parameters. |
| Gas temperature | T | K | Influences gas volume, velocity and speed of sound. |
| Lower heating value | LHV | kJ/kg or MJ/kg | Defines the chemical heat release rate of the flared gas. |
| Flare tip diameter | D | m | Used to calculate flare tip exit velocity. |
| Wind velocity | U | m/s | Influences flame tilt, flame center location and ground-level radiation. |
| Lower explosive limit | LEL | % vol. | Used in selected semi-empirical flame correlations. |
| Fraction of heat radiated | F | – | Defines what part of the heat release is emitted as thermal radiation. |
| Atmospheric transmissivity | τ | – | Accounts for atmospheric attenuation between the flame and the receiver. |
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: Uj – 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: aiso – 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: CL,av – dimensionless dilution-related parameter; LEL – lower explosive limit, % vol.; U – wind velocity, m/s; MWair – molecular weight of air.
5.2 Jet momentum to wind influence parameter
where: djR – dimensionless parameter describing the relation between jet momentum and wind influence; Tair – 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; xc, yc – 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.
| Scenario | Wind speed | Heat release Q | Radiation threshold | Calculated distance | Engineering interpretation |
|---|---|---|---|---|---|
| Emergency depressuring | Low wind | Project-specific | 1.58 kW/m² | Calculated by model | Review normally accessible areas and plot boundary. |
| Emergency depressuring | Low wind | Project-specific | 4.73 kW/m² | Calculated by model | Check short-duration emergency access. |
| Emergency depressuring | Design wind | Project-specific | 6.31 kW/m² | Calculated by model | Assess restricted emergency action zone. |
| Emergency depressuring | Design wind | Project-specific | 9.46 kW/m² | Calculated by model | Identify severe radiation zone and access limitations. |
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.