Probits and Fatality Assessments

A toxic or thermal release does not have a single threshold above which everyone is killed and below which no one is harmed. The relationship between the dose received and the probability of fatality is statistical, and varies with both the substance and the exposure profile. The standard mathematical tool for expressing this relationship is the probit function, which converts an integrated dose into a fatality probability through a substance-specific equation. As of version 4.0, in:Flux includes probit functions for toxic substances and thermal radiation directly in the fluids database, computes dose during simulation, and produces fatality variables and maximum fatality footprints as standard post-processing outputs.

 

The Probit Function

A probit (probability unit) function takes the form:

Pr = a + b · ln(Cn · t)

where C is concentration, t is exposure duration, and a, b, and n are substance-specific coefficients published in standards such as the TNO Green Book and the UK HSE SLOT/SLOD methodology. The probit value is converted to a fatality probability via the cumulative normal distribution: a probit of 5.0 corresponds to 50% lethality (LD50), while lower probits correspond to lower fatality fractions.

 

Where Probits Are Defined

Probit coefficients are stored in the in:Flux Fluids Database alongside the other physical properties for each substance. Open the Project Menu and select Fluids Database, then locate the substance of interest - the probit row appears in the property panel for substances with published probit data (for example, ammonia, hydrogen sulfide, and chlorine).

 

For substances not in the database, define a new pure gas in the database and enter the probit coefficients manually based on the standard or assessment your project follows.

 

Dose Recording

How dose is recorded depends on the simulation type:

  • Transient simulations - dose is integrated automatically over the simulation duration. The dose variable can then be plotted at any time during the run.

  • Steady-state simulations - the simulation has no time component, so an exposure time must be specified at post-processing time. in:Flux multiplies the steady-state concentration field by the chosen exposure time when computing dose.

 

Dose and Fatality Variables in Post-Processing

Once a simulation completes, dose and fatality variables become available wherever you can select a variable - monitor points, monitor lines, monitor regions, contours, and isosurfaces. Each toxic component is tracked separately so that single-component or multi-component fatality can be assessed independently.

 

For thermal fatality, the same approach applies to fire simulations: thermal dose accumulates from incident radiation, and the relevant probit is applied to convert dose to fatality probability.

 

Maximum Fatality Footprint on Risk Data Sets

For risk data sets that include a dose variable, in:Flux can output a Maximum Fatality Footprint on risk contours and risk isosurfaces. The footprint represents the envelope across all simulated scenarios where the fatality probability exceeds a chosen threshold.

 

This output requires a risk data set whose variable is a toxic or thermal dose (see the Dose Recording section above, and Tutorial 11 for setting up risk data sets).

 

To configure:

  1. Add a risk contour or risk isosurface to the project.

  2. For the Type, select Maximum Fatality Footprint.

  3. Set the Exposure time. This is used to compute dose for any steady-state simulations in the risk data set.

  4. If the risk data set contains transient simulations, open the risk data set's Advanced tab and set the Time Option. Final uses the last timestep of each transient simulation; Specified Time samples the closest saved time to a user-entered value of t. Steady-state simulations in the same set are unaffected by this setting and continue to use their final results.

 

The result is a single contour or isosurface showing the spatial footprint of the worst-case fatality outcome across the full risk-weighted scenario set. This is useful for emergency planning, exclusion-zone definition, and toxic dispersion sections of QRA deliverables.

 

Important Things to Consider

  • Probit coefficients vary between sources (TNO, HSE, AIChE) and even between revisions of the same source. Confirm with your project's basis-of-design which probit set is to be used. The values shipped with in:Flux are starting points and can be edited per substance for project-specific assessments.

  • Probit fatality estimates apply to the population at the location of interest. They do not account for shelter-in-place, evacuation, PPE, or medical intervention - those mitigations are part of the broader risk assessment, not the dose calculation.

  • For long-range toxic dispersion, near-field CFD must be coupled with a Gaussian model since CFD only accurately represents neutral atmospheric stability. See in:Flux and Stability Classes for details.

 

See also: Toxic Dose Variable, Tutorial 8 - Transient Simulations.

 

References:

  1. TNO, Methods for the Determination of Possible Damage to People and Objects Resulting from Releases of Hazardous Materials (the "Green Book", CPR 16E).

  2. UK HSE, Assessment of the Dangerous Toxic Load (DTL) for Specified Level of Toxicity (SLOT) and Significant Likelihood of Death (SLOD) - SLOT and SLOD definitions and n-Factor table.