A first order kinetic formulation of brittle particle attrition is suggested. Experimental data show that it applies to coal particle attrition in Couette flow. These data reveal that particles are reduced by loss of surface protuberances, which are much smaller than their mean diameter. It is also shown how changes of the size spectrum, due to shearing, can be predicted.
A. J. KARABELAS
Westhollow Research Center Shell Development CompanyHouston, Texas 77077
SCOPEConcentrated slurries made of -1 to -103 p particles are currently studied in connection with long distance pipeline transportation of commodities such as coal and iron ore, usually with water or oil as the liquid carrier. Particle attrition can affect the slurry rheological properties and can present difficulties in the solid/liquid separation at the pipeline terminal. Attrition is caused by particle-particle collisions and particle impingement on solid boundaries. A statistical description of this process, involving a distribution of particle sizes and associated kinematic properties, although very desirable, is almost impossible at present. A more direct and fruitful approach is to study attrition in a well-defined flow field and to relate observed changes of an initial particle size distribution to some characteristic bulk flow properties, for example, the shear rate. This approach requires an appropriate mathematical formulation of the attrition process.The problem of particle attrition in slurry flow has not been adequately studied. Only a few exploratory studies on this subject have been published so far (for example, Worster and Denny, 1955; Bjorklund and Dygert, 1968). In the case of coal, for instance, there is essentially no published information about the rate at which small particles degrade in slurry flow, or about the size distribution of the resulting fragments. This lack of information is partly due to difficulties encountered in doing meaningful laboratory experiments, especially with settling suspensions.The main objective of this study is to suggest a kinetic type of formulation of particle diminution in suspension flow which can serve as the framework for interpreting experimental data and for modeling particle attrition in slurry transportation and processing systems. Another objective is to develop techniques for accurate measurement of attrition and to demonstrate how changes of a wide particle size distribution (PSD) can be predicted (as a function of initial PSD, flow conditions, and time) on the basis of a few experimentally determined parameters.
CONCLUSIONS AND SIGNIFICANCESize diminution of brittle,-irregular in shape, particles due to slurry flow is described as a rate process, similar to a first-order chemical reaction. This formulation involves two sets of parameters, that is, the coefficients ki representing the rate of material loss of a particular size fraction, of mean diameter d,, and the parameters bi,j describing the manner in which the attrition products from fraction i are distributed into various smaller size ...