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Risk mitigation in production facilities has been an issue of great interest for decades, especially in activities which represent a serious hazard to human health, environment and industrial plants. Dust explosions are a major hazard in many industrial processes: only in the first part of 2019 (January–June) 34 dust explosions, mainly due to organic powders, occurred worldwide. An explosion may take place whenever there is the presence of combustible dusts, which are frequently generated by activities such as grinding, crushing, conveying and storage. Currently, a relatively expensive experimental test, carried out into a 20-L Siwek apparatus, is used to address the order of magnitude (class) of explosive dust: this piece of information is referred to as the deflagration index, Kst. At the current state, only a few pioneering models have been developed in order to predict the value of the Kst as a function of some relevant properties of the dust: e.g. particle size distribution (PSD), humidity, thermal conductivity, etc‥ Most of these models condense the information about the PSD of a given dust into an average value, referred to as D50. In this work, a kinetic free mathematical model aimed at predicting the deflagration index for organic dusts is presented. This model, unlike the older ones, considers the whole particle size distribution for the computation of the deflagration index. In order to be implemented, only a single experimental Kst value (which works as a reference) and a particle size analysis on the dust are required. The model was validated using the whole granulometric distribution of three different organic powders (fosfomycin, sugar and niacin). In addition, the same estimations were done by considering only the D50 data. It was noticed that, for highly polydispersed dusts, results were less accurate with respect to those obtained using the complete PSD, highlighting the importance of considering a complete granulometric distribution for process safety purposes.

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.