Use of a two-parameter Weibull distribution for the description of the particle size effect on dust minimum explosible concentration

Abstract

Combustible dust explosion properties, like Minimum Explosible Concentration (MEC) and Minimum Ignition Energy (or Temperature), have a strong dependency on the particle surface area to mass ratio which varies with the particle size distribution. Unfortunately, the comparison of the dust explosion properties reported in the literature for a given dust material is often difficult because of the lack of description of the particle size distribution which is usually limited only to scattered information about the median (d50), mean, or one, two, or maximum three percentiles (e.g., d10,d50,andd90). This approach often gives conflicted conclusions or observations of no trend with measured independent parameters. It seems that a different approach is necessary to comprehensively describe the dependency of dust explosion properties on the particle size distribution. Such improvement could be achieved using a continuous probability distribution of which an example is a two-parameter normal distribution. However, the normal probability density function can only represent a symmetrical bell-shaped distribution which does not apply to the dust particle size analysis that often results in a skewed bell-shaped histogram. This study explored the use of a two-parameter (shape and scale) Weibull probability density function to describe a particle size distribution. A series of experimental data on the Minimum Explosible Concentration (MEC) of sulfur and polyethylene dust samples for which the particle distribution is measured were used to estimate the Weibull's scale and shape parameters. Two- and three-dimensional plots were generated to demonstrate the correlations of these parameters with MEC. The results show that as the scale and shape parameters increase, the MEC increases with higher dependence on the scale parameter (b). This is consistent with the initial conclusion where the MEC increases with increasing particle size. The paper discusses the advantages of using such an approach to describe the effect of particle size distribution on dust explosion properties but also shows that using only a median or mean of a particle size distribution to describe MEC may be misleading, especially if a sample represented by d50 as a coarse distribution contains a long tail of fine particles.