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Thesis for the Degree of Master of Science

 

Year 1996
Maija Federley

Mathematical models of unit operations in mineral processes


In this study mathematical models of unit operations in mineral processing are presented and their utilization for simulator software are studied. The aim is develop a model library to be used for simulation of grinding circuits.

In the literature review the best known steady-state simulators for mineral processes are shortly described. The characteristics and the normal operational parameters of t rod mill, a ball mill and a hydrocyclone in a grinding circuit are presented, and the most common model equations for these units are given.

The steady-state models of the tumbling mills use mathematical model equations for the prediction of the particle size distribution in the mill discharge; other data from the process are obtained from mass balancing calculations. For a description of a grinding event three different approaches are applied traditionally. All these approaches are utilized in this work: The Rosin-Rammler law is based on a fully empirical mahtematical representation of the size reduction process. In the models based on the Rosin-Rammler, Bond and Allis-Chalmers equations the power draw of a mill is experimentally related to the size reduction that this consumption of energy brought about. The rod mill model developed by Lynch and the perfect mixing model developed by Whiten are based on the basic characteristics of the grinding process.

The composition of the overflow and the underflow from a hydrocyclone are experimentally found to be related to the dimensions of the cyclone. In the Plitt cyclone model the constant values are determined for model parameters by linear regression while the dimensions of a cyclone are used as variables. In the hydrocyclone model developed by Lynch process data used for fitting the models parameters.

In the experimental part of this paper the implementation of five models for the model library using C++-programming language was presented. Utilizing the inheritance feature of object-oriented programming, the models were determined to be subclasses of the model library and simulation algorithms. The mathematical modification of the models for the software was described, and the user interfaces implemented as Windows applications were presented.

The performance of the models and the appropriate implementation were tested by a simulation, and the results were compared with measured process data presented in literature. The comparison showed that the models gave accurate results when a normal operation was applied. Inaccuracy detected in the fractions o the fines was due to the linearizations and simplifications used in the model equations. During the tests the software also proved robust and user-friendly; those were the features emphasized in the software development.


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