North-Eastern Federal University named after M. K. Ammosov (Yakutsk, Russia):

Grigoriev Yu. M., Head of the Chair of Theoretical Physics (Institute of Physics and Technologies), Doctor of Physical and Mathematical Sciences, e-mail: grigyum@yandex.ru

Sivtsev V. I., Associate Professor of the Chair of General and Experimental Physics (Institute of Physics and Technologies), Candidate of Physical and Mathematical Sciences, e-mail: vasiliy_sivtsev@mail.ru

Yakovlev B. V., Professor of the Chair of Theoretical Physics (Institute of Physics and Technologies), Doctor of Physical and Mathematical Sciences

«Yakutniproalmaz» Institute (Mirnyy, Russia):

Savitskiy L. V., Head of the Laboratory in 2001–2011, e-mail: b-yakovlev@mail.ru

The enterprises of «ALROSA» JSC planned the introduction of stage crushing for the preparation of kimberlite ore to the enrichment process. According to such technology schemes, there exist some risks of crushed ore freezing during the emergency shutdown. For the purpose of these risks assessment, this research paper shows the development of thermodynamic calculations method. The physical and mathematical models are developed for various sizes of thawing ore. The physical model is based on the fact that the heat transfer occurs only through the surface of contact bodies. Therefore, a system, consisting of liquid and pieces of various shapes of ore, can be displayed on a flat system. There is estimated the area of contact elements of the system for a flat statement. Thus, a three-dimensional problem is converted into a one-dimensional problem. For the simplicity, the phase transition is not considered. Based on the proposed physical model and the Newton-Richman law, there is obtained the Cauchy problem for a system of linear differential equations. The computational implementation of the model is carried out. The system behavior is described qualitatively and correctly by the calculation results. The model parameters are adopted with the experimental data. This model takes into account the size of ore pieces. It can be used for theoretical estimation parameters for the freezing of humid ore pieces to each other, and the ore freezing to the equipment wall, at different environmental temperatures. At the same time, there can be estimated the ore parameters at the equipment for freezing suspension:
NP crushers, when the particle size of humid ore (–200+50 mm) lies motionless in a metal bin after the surgery disintegration;
redistribution of X-ray separators, when the particle size of humid ore (–50+16 mm and –16+5 mm) lies motionless in metal bins after surgery screening;
installation of equipment separation, when the particle size of humid ore (–5+2 mm) lies motionless in a metal bin after surgery screening.
This research work was held with the financial support of the Ministr  of Education and Science of Russian Federation, within the project No. 2010-218-01-001 “Creation of complex innovation environmentally safe technology of extraction and processing of diamondiferous ores in the Far North”, which is being held with the participation of North-Eastern Federal University named after M. K. Ammosov and “ALROSA” JSC.