The back-calculation of specific rates of breakage from continuous mill data

Abstract Computer programs for back-calculation of specific rates of breakage Si from continuous mill data, or batch grinding data, are described. A series of statistical tests to determine the statistically acceptable ranges of values are presented. The most reliable test uses independent estimates of error variance calculated from replicated data. It is shown that the interval-by-interval method of calculating Si values is especially subject to errors in the top sizes. Back-calculation methods which use only the circuit product in the calculation give different ranges of statistically acceptable values than those which use all the size distributions round the circuit. The statistically acceptable ranges of values from using only the circuit product often do not include the values determined by direct laboratory investigation, and tend to be wider than the ranges given by using all the size distributions; thus, using only circuit product is a non-preferred method. The use of a fully-mixed residence time distribution (RTD) instead of a true RTD leads to radically incorrect values, which cannot be detected by statistical analysis except in the presence of unrealistically low experimental error. It must be realized that a set of breakage parameters which reproduce the data used in their back-calculation with good accuracy are not necessarily real, and statistical analysis is essential to define the statistically acceptable ranges of the parameters.