An improved method for estimating the feed-size breakage distribution functions

Abstract

The discrete-size equation of batch grinding in cumulative fraction retained has an approximate, but adequately accurate, solution in the form of a second-order polynomial in time. For a single-size feed, the leading coefficient G of the polynomial is the product of the feed-size breakage-rate constant and the breakage distribution function. This coefficient as well as the second coefficient H are readily computed from the grinding data by solution of two linear algebraic equations, or by least squares, or by simple graphical techniques. In the last case, a new method of graphical display of grinding data as straightline plots is presented the intercepts of which are breakage distribution functions. Using both computer-generated as well as experimental grinding data, it is shown that the proposed G-H method of estimating breakage distribution functions is highly accurate, is not restricted to short grinding time data and is not subjected to any restrictive interrelationship between breakage-rate constants and breakage distribution functions. As such, this method is an improvement over the existing schemes, i.e. the method based on zero-order production of fines and the BII method, which are in fact shown to be time-restricted and grinding parameters-restricted specialized cases of the more general G-H method.