A dispersion model for initial consequence analysis based on diffusion equations

Most factories use toxic or flammable chemicals in their industrial processes; this poses a risk of leakage due to accidents, which can sometimes result in mass casualties and considerable property damage. Therefore, quantitative risk prediction and assessment are necessary to protect the public and minimize losses in the event of a chemical release. Several methods can be used to evaluate chemical dispersion in the atmosphere, but most are based on the assumption of neutral buoyancy and far-field wind conditions. With this assumption, a model is valid only after a significant amount of time has elapsed from the moment chemicals are released or dispersed from a source. However, the most dangerous locations are typically close to a leak source. Therefore, a dispersion model for the initial phase of a leak is required to quantify the risk and predict the extent of damage. This study developed a dispersion model for initial consequence analysis using a three-dimensional unsteady convective diffusion equation. A continuous point source was assumed, and ethane was used as the leak material to minimize the effects of buoyancy. The unsteady concentration field developed rapidly as the diffusion coefficient and wind velocity increased, but the steady-state concentration field was not affected by wind velocity. This dispersion model also allows for the simple consideration of ground adsorption, making it scalable to real-world situations. The time to reach a steady state required for an effective emergency response was predicted, and the results were interpreted in terms of mathematical methods and physical characteristics. •A mathematic model based on the advective diffusion equation was developed and validated fora continuous point source leakage.•The concentration field develops rapidly with increasing diffusion coefficients and wind velocities.•The time to reach a steady state was affected by mass flow rate, wind velocity, diffusivity and target concentration.•The time to reach a steady state was confirmed by the steady-state solution as well as the conservation of mass flow rates.