# Mathematical models

The accident simulations performed by Riskan are based on semi-empirical equations, or physical-chemical equations with adjustment factors arising from practical experimentation. Typically a simulation of an accident comprises three main steps. After these three core simulation models, other specific models of fire, explosion, etc., may be necessary, depending on the type of substance.

The discharge models are those that calculates the total mass and rate of release material which is liberated from a container with a certain pressure and temperature, in the initial event. As we have seen, accidents typically involve the release of a hazardous material that is originally contained in a tank or vessel. The amount and rate of release of the material are determined by the discharge models.

If the discharge involves liquid or liquefied gases, a pool will be formed and will evaporate. This pool will spread in the region of interest and release vapor forming an cloud of the material. The evaporation models in fact include two models: the pool spreading model and the evaporation model itself. The end result is the expected size of the pool and the vapor release rate.

Finally with the release of vapor to the atmosphere a cloud is formed that will dissipate according to the weather conditions. The dispersion models calculate exactly how far this will cloud go and what the expected concentration at each point of the trajectory.

In addition, other models of consequence could be used:

- Explosion models - when a mass of a flammable gas encounter an ignition source, resulting in an explosion
- Fire models - when flammable liquids or liquefied gases combust
- Equation Probit - to calculate, from physical variables, the probability of harm to persons and materials

Most Riskan models are derived from models created by TNO in the Yellow Book and Green Book. Some particular models have other sources, such as the pool spreading model based on the work of Lannoy, the Bleve model based on the World Bank and the model of heavy gases dispersion, which is based on the SLAB model from the American Coast Guard.

## Quick reference

If you want some information about data entry, mathematical modeling or output results, see one of the lists below

- List of descriptions of mathematical models - A list of detailed descriptions of all mathematical models
- List of data entry screens of mathematical models - A list of the data entry screens for all models
- List of result screens of mathematical models - A list of all the screens of output results
- List of representations in text mode of mathematical models - A list of all representations in text mode of models