Mathematical Models for a Closed-Circuit Grinding

Abstract

New continuous and discrete mathematical models are elaborated for describing some types of closed-circuit grinding mill-classifier systems. Based on the discrete model computer simulation is also developed for investigation of grinding processes. The starting point in developing the model is the continuous grinding equation for the open-circuit grinding which is a partial integro-differential equation describing axial mixing and breakage of particles in the grinding mill. The convective flow in the mill is modeled as particle size-dependent process. The boundary conditions at the inlet and outlet of the mill, the initial conditions, and the equations describing the operation of the classifier and its mass balance are the additional equations of the model. The properties and capabilities of the new computer model are demonstrated and analyzed by simulation developed in Matlab environment. The effects of all parameters of the grinding process, among others of parameters of the classifier, are studied via simulation. The main statistical characteristics of the steady states, the hold-up of the grinding device and the operation of the classifier are also studied. The models presented appear to be very flexible and useful tools for analysis and design of closed-circuit grinding processes, and are suitable for the deeper understanding of the aimed processes.