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 (), mean, or one, two, or maximum three percentiles (e.g., ). 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 (). 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 as a coarse distribution contains a long tail of fine particles.

中文翻译：

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使用二参数威布尔分布描述颗粒尺寸对粉尘最低爆炸浓度的影响

可燃粉尘爆炸特性，如最低爆炸浓度 (MEC) 和最低点火能量（或温度），对颗粒表面积与质量比有很强的依赖性，该比随颗粒尺寸分布而变化。不幸的是，由于缺乏对颗粒尺寸分布的描述，文献中报道的给定粉尘材料的粉尘爆炸特性的比较通常很困难，颗粒尺寸分布通常仅限于有关中值（）、平均值或一个的分散信息。 、两个或最多三个百分位数（例如， ）。这种方法经常给出相互矛盾的结论或观察结果，即与测量的独立参数没有趋势。看来需要采用不同的方法来全面描述粉尘爆炸特性对粒径分布的依赖性。这种改进可以使用连续概率分布来实现，其中一个例子是二参数正态分布。然而，正态概率密度函数只能表示对称的钟形分布，不适用于粉尘粒径分析，经常会导致偏斜的钟形直方图。本研究探讨了使用双参数（形状和尺度）威布尔概率密度函数来描述粒度分布。使用测量颗粒分布的硫和聚乙烯粉尘样品的最低爆炸浓度 (MEC) 的一系列实验数据来估计威布尔尺度和形状参数。生成二维和三维图来证明这些参数与 MEC 的相关性。结果表明，随着尺度和形状参数的增加，MEC 增加，并且对尺度参数的依赖性更高 ()。这与 MEC 随着颗粒尺寸的增加而增加的初步结论一致。本文讨论了使用这种方法来描述颗粒尺寸分布对粉尘爆炸特性的影响的优点，但也表明仅使用颗粒尺寸分布的中值或平均值来描述 MEC 可能会产生误导，特别是如果样本表示为因为粗分布包含细颗粒的长尾。