Extension of the empirical Alyavdin equation for representing batch grinding data

Abstract

The Alyavdin equation for batch grinding data is: 1 − P(χ, t) = [1 − P(χ, 0)] exp− c(x)t p ] where P( χ, t) is the weight fraction less than size χ after grinding time t, c ( χ) is constant with t and p is a constant close to one. It is shown that this equation is illogical (except for a single size of feed) unless c ( χ) varies with P( χ,0), which makes the equation of little utility. A new empirical equation is developed for finite size intervals: 1 − P(χ i+1, t) = exp − tK i 1 γ + ln 1 1 − P(χ i+1,0) 1 γ i γ i which reduces to the Alyavdin equation for a single size of feed, and which gives consistent computations for any feed size distribution. Techniques are given for determining K i , γ values from sets of batch grinding data. The values are then used to predict size distributions for other times and other feed size distributions. The equation was quite successful in predicting size distributions in batch milling: (a) providing the feed size distribution was not un-natural, that is, not truncated or (b) if a truncated feed was used, the values of K i and γ are determined from size distributions of grinding of the same type of feed. Thus, K i , γ are not, unfortunately, completely independent of the starting feed size distribution.