A discussion of equations for the analysis of batch grinding data

Abstract

It is shown that solutions of the integro-differential equation of batch grinding and the size discrete-time continuous Reid form for the equation of batch grinding give almost identical results for typical data. It is argued that the Reid form is as equally likely to be the 'correct' form as the integro-differential form, and it is much easier to use and program. If the specific rates of breakage fit the form S(i)=Ax(i)(α), and the primary breakage functions fit the form B(i,j)=Φ(x(i-1)/x(j))(γ)+(1-Φ)(x(i-1)/x(j))(β) for the Reid equation, then the corresponding forms for the integro-differential equation are S(x)=ax(α), B(x/y)=φ(x/y)(γ)+(1-φ)(x/y)(β) and equations are given for the relations between a and A and φ and Φ. Copyright (C) 1999 Elsevier Science S.A.