Application of Statistic Theory to the Size Preparation of Coal Charge

Abstract

For the purpose of obtaining the maximum coke strength by optimum size preparation of coal charge, a mathematical theory is developed, which clarifies the relation between coke strength, inhomogeneity of charge and grain size structure of charge.
Inhomogeneity of charge is represented by variance (V) of caking property parameter (X) and of coal rank parameter (Y), and related to observed coke strength (S) by the following equation,
S=S+1/2 ∂²S/∂X² V_xx+∂²S/∂X∂Y V_xy+1/2 ∂²S/∂Y² V_yy
where S is coke strength of homogeneous charge. Furthermore the mathematical solution is derived for each variance, which is expressed by volume and coking properties of each coal particle.
The preliminary analysis of coke strength shows that the second derivatives are always negative. The mathematical solution shows that the variance is effectively lowered by the selective fine crushing of coal.
The validity of theory is examined by experiments. For practical purposes, the theoretical equation is approximated based on the experimental results.