A kinetic free mathematical model for the prediction of the KSt reduction with the particle size increase

Even in recent years, several major industrial accidents have involved dust explosions, clearly showing the necessity of mitigating the hazard related to the presence of flammable dusts. In this respect, the KSt is an experimental parameter used to design the deflagration vents aimed to protect industrial devices and silos by internal dust explosions. Even if it is measured using a standard 20 L sphere test, its determination is quite expensive and time consuming. This problem is even more severe when a target dust is processed into a plant, giving rise to different average diameters; in this case, an experimental investigation of all the different particle sizes would be advisable but very expensive. In this context, the main aim of the present paper has been to develop a kinetic-free model able to predict the KSt decrease with the mean particle diameter increase for organic dusts explosions. Particularly, an order of magnitude analysis of the characteristic times of the involved phenomena has showed that, in the KSt measurements, the rate determining step is usually associated to heat transfer phenomena. This evidence leads to the possibility of exploring a predictive approach for the KSt determination which does not require any chemical kinetic information, the most difficult to be obtained. Therefore, once the value of KSt has been measured through a standard 20 L test for a given mean particle diameter (the smallest possible), the approach proposed in this work allows for predicting the KSt values for the same dust at higher average particle sizes. Such an approach has been validated by comparison with several literature data as well as with a new set of experimental results.