Mathematical Modeling Applied To Analysis And Control Of Grinding Circuits Part 1. Development Of Comminution Models ? Introduction

In Part I of this paper we describe two techniques that were employed in the development of mathematical descriptions of the size reduction process which takes place in a ball mill. In Part II we show how the comminution model was imbedded in a process model to effect steady-state and dynamic simulation of a closed-circuit grinding operation. Increasing emphasis is being placed on development of approaches whereby the essential characteristics of a process can be succinctly represented in terms of a mathematical description of the relationships that exist among important process variables. This activity, commonly known as mathematical modeling, predates modern electronic computers: however, these computers with their tremendous computational capability have given new impetus to the whole field. Although the computer is quite helpful in the development of mathematical models, the real value to the engineer lies in the fact that computers represent such a powerful tool for simulating systems described by mathematical models. As a consequence, engineers may simulate and thereby study the behavior of complex. interacting, systems over a broad range of process variables and configurations once appropriate process models have been developed for the sequence of steps comprising the process.