A mathematical model for the prediction of the KSt for metallic dusts as a function of the particle size distribution

For several years, dust explosions have been one of the major causes of industrial accidents, spanning from metalworking to pharmaceuticals sectors. In accordance with the latest Chemical Safety Board (CSB) investigations, three out of four dust explosions in the United States involved metallic dusts (iron, titanium, zirconium and aluminum). Many chemical processes involve metal powders for their exceptional mechanical, optical and catalytic properties, such as the production of plastics, rubber, paints, coatings, inks, pesticides, detergents and even drugs. The severity of a dust explosion can be defined using experimental parameters such as the maximum explosion pressure (pmax), the maximum rate of pressure rise ((dp/dt)max) and the deflagration index (Kst), which are employed to predict the consequences of a dust explosion for a given scenario. Among these parameters, the deflagration index plays a fundamental role, as it is used for the design of deflagration nozzles aimed to protect industrial equipment and silos from internal dust explosions. The purpose of this work is to develop a mathematical model able to predict the Kst value of metal powders as a function of chemical-physical data and the particle size distribution (DD50 was used as global information). The model structure is based on the writing and resolution of the material and energy balance equations on the single dust particle, also estimating the contribution of oxygen diffusion which, in the case of metal powders, greatly depends on both tortuosity and porosity. The results well agreed with experimental data, providing the basis for the development of more detailed models.