Study of steel ball recharge and consumption in a wet cement industrial mill via a population balance model

Abstract

A population balance model is applied to a steel ball mill. Experimental data were obtained for two types of balls with different chemical compositions using a marked ball test in an industrial mill of a recognized cement producer company. The balls were marked since their manufacture by an international ball supplier who guided the entire experimental process. The mill was monitored for about eight months in 12 time cycles. It is found that the law of wear of balls was of zeroth order. The wear law is introduced to the model to predict and analyze the steel consumption due to the wear of the balls, the mass density function, the distribution function of balls, and the mill ball charge at steady state. Experimental data and theoretical predictions match in excellent agreement.

Keywords:

• Population balance model
• wear law
• steel ball
• ball grinding

Additional information

Funding

Fondecyt 1210610 Centro de Modelamiento Matemático (CMM) BASAL10.13039/100008674ACE210010FB210005; Institución Universitaria Pascual Bravo IN202010 and IN202006; RB acknowledges support by ANID (Chile) through Fondecyt project 1210610; Anillo ANID/P IA/ACT210030; CRHIAM, project ANID/FONDAP/15130015; and Centro de Modelamiento Matemático (CMM) BASAL projects ACE210010 and FB210005. IER and MRF thank Institución Universitaria Pascual Bravo for the financial support within the research projects with grant numbers [IN202010 and IN202006] to attend the academic internship at the Oviedo University (Spain).