Predicting Size Distributions of Pulverized Coal

INTRODUCTION Coal is geologically a sedimentary rock with distinct bedding planes containing a mixture of petrographic constituents. Yet. because of its chemical nature, it also has some of the characteristics of a polymeric material. In addition, it is extensively precracked to give a macropore structure and also has a substantial internal volume of microporosity. Add to this the mineral constituents dispersed in the coal in a variety of forms and sizes. and it can be readily appreciated that coal is a complex and heterogeneous material. It has to date not been possible to predict the particle size distributions produced by breakage of coals from a priori application of the principles of fracture mechanics. However, there is a substantial body of data resulting from empirical observation of size distributions produced under various conditions, primarily from grinding mills. It is the function of this review to outline how this empirical information can be used to predict product size distributions for those systems which have been studied systematically, and to suggest future avenues of research using similar methodology. FRACTURE THEORY APPLIED TO COAL It is, of course, possible to devise experiments for slow crack propagation in a coal. However, the evidence is that coal breaks by brittle fracture in the mills and mining machines of industrial importance and therefore the theory of brittle fracture is sufficient to illustrate the important features of the fracture of coal. In order to produce size reduction a solid must be stressed by the application of force. The force can be a tensile (stretching), compressive, or shear force, and the three dimensional stress pattern in the solid represents the tensile, compressive, and shear forces per unit area acting in any direction through any point in the solid. As an illustration consider the case of a simple one-dimensional tensile stress: then stress is defined as a=F/A where F is the force. A is the cross-sectional area of the solid normal to F and strain. E, is defined as the fractional change in the length of the solid. so that E= x/L where x is the extension of an original length of L. Coal behaves as an elastic material over short times (although viscoelastic creep can occur if the stress is maintained over long times) and if it is not stretched too far the coal returns to its original shape when the stress is removed; otherwise catastrophic failure occurs and the coal fractures at a stress termed the tensile strength. The failure under stress of an elastic material is termed brittle fracture. Elastic material fails at small stain and the stress-stain relation to where brittle fracture occurs is the empirical Hooke's law. a= YE, where Y is Young's modulus. The work done on the solid to take the solid from zero external stress to a stressed state by slowly increasing F up to a final stress u is the integral of the stress times the strain. This reversible strain energy is stored in the solid and. using Hooke's law. is u /2Y per unit volume of solid. If the solid is immediately loaded to u the work done is [EAuL] which Is a2 /Y per unit volume, that is, twice the reversible work.