Agradecimentos: The authors would like to thank the National Petroleum Agency (ANP) grant 2017/00577-7. Thanks are also due to Petrobras S.A.

A mathematical model predicting the fluid flow dynamics of accidental clouds is introduced. It has been found that the dimensionless flammable cloud is related to the accidental leak rate, wind speed, and fluid by means of the balance between the release momentum and the convective wind flow. The...

A mathematical model predicting the fluid flow dynamics of accidental clouds is introduced. It has been found that the dimensionless flammable cloud is related to the accidental leak rate, wind speed, and fluid by means of the balance between the release momentum and the convective wind flow. The non-dimensional cloud volume ranges from 0.16 to 62 for the cases investigated. Numerical findings suggest a sinusoidal waveform (sine-cosine function) as in the trigonometric circle. This observation goes in line with the wind rose from meteorological data. The proposed mathematical model agrees very well with numerical data calculated using computational fluid dynamics

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