Minerals Beneficiation - Kinetics of Batch Grinding-Part B: An Approximate Solution to the Grinding Equation

An approximate but simple and practical solution to the discretized batch grinding equation has been obtained. The solution is based on a new grind function, a combination of selection and breakage parameters and particle-size distribution of the feed. The grind function, which is readily computed from limited experimental data, has significant implications for analysis of the particle-size reduction processes. Using the practical solution, three ball-mill comminution systems—dry dolomite, wet quartz, and limestone—have been simulated with acceptable precision. The application of the discretized batch-grinding equation1 to routine comminution analysis is frustrated by two principal difficulties. First, the selection and breakage parameters of the grinding equation must be computed separately. This is usually a difficult and uncertain task although, recently, a number of experimentally and computationally efficient strategies have been proposed for determination of these parameters?" Second, for actual computation, the solution to the batch-grinding equation becomes progressively tedious and unwieldly for finer particle-size range.1,2 The purpose of this part of the report is to present an approximate solution to the batch-grinding equation, which is practical in that it seems to overcome the aforementioned obstacles. The solution involves the concepts of a new grind function, a lumped parameter of the selection-breakage functions, and particle-size distribution of the feed, which is readily computed from a limited amount of experimental data.