Spline method for solving continuous batch grinding and similarity equations

Abstract

This paper investigates a numerical technique using cubic splines for solving the continuous batch grinding equation. The same approach is also used to solve the similarity equation in the case where the breakage function has a more complicated form than that for which analytical solutions are available. In the case of the similarity equation the spline coefficients are obtained from the solution of an algebraic generalized eigenvalue problem. Numerical solutions of the continuous equation for simplified selection and breakage functions are compared with those of analytical solutions in order to assess the validity of the numerical procedures. Experimental results from a limestone ore are used to test the validity of the simplified model. The spline method is also used to solve the continuous equation for a more complicated breakage function evaluated for a gold bearing ore body.