Mathematical model to assess energy consumption using water inflow-drainage system of iron-ore mines in terms of a stochastic process

Oleg Sinchuk¹, Ryszard Strzelecki², Igor Sinchuk¹, Теtуаnа Веridzе¹, Vladyslav Fedotov¹, Vladyslav Baranovskyi¹, Kyrylo Budnikov¹

¹Kryvyi Rih National University, Kryvyi Rih, Ukraine

²Gdańsk University of Technology, Gdańsk, Poland

Min. miner. depos. 2022, 16(4):19-28

https://doi.org/10.33271/mining16.04.019

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      ABSTRACT

      Purpose is to develop a unified mathematical model to assess energy efficiency of a water inflow-drainage process as the real variant of stochastic method for water pumping from underground workings of iron-ore mines.

      Methods. The research process was based upon the methods of probability theory as well as stochastic modelling methods. The stochastic function integration has been reduced to summation of its ordinates and further transition to a proper boundary.

      Findings. A mathematical model of a water inflow-drainage system as a stochastic process has been developed in terms of input parameters of a standard operating iron-ore mine. The abovementioned has made it possible to assess realistically, substantiate, and obtain possibilities for a specific production facility as well as for generalization of the results involving determination of stochastic characteristics of drainage process.

      Originality. For the first time, a mathematical model of drainage from underground levels of iron-ore mines has been developed as a stochastic process. The process characteristics have been identified relying upon randomness of a water pumping technique. In contrast to the available settings, the new model parameters characterize their dispersion. Possibility to obtain complete characteristics of energy consumption has been obtained: for drainage; for water accumulation volume in underground water collectors; for water pumping from the specified mine depths over the specific period as random processes. A number of drainage features have been analyzed and differentiated being determined with the help of nor-mal law of water accumulation velocity in the underground water collectors in iron-ore mines.

      Practical implications. In terms of operating iron-ore mine, a generalized drainage mathematical model has been developed as a stochastic process using statistical data concerning water accumulation velocity in the underground water collectors. It has been proved that if the ordinates of water accumulation velocity in the underground water collectors obey the normal distribution law then it is expedient to characterize drainage as a stochastic process. The developed methods, studying drain-age as a stochastic process, help expand the research boundaries involving other auxiliary operations performed during underground mining of iron ore raw materials.

      Keywords: efficiency, methodology, model, mine, drainage, stochastic process

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