The Non-Linear Regression - the Levenberg- Marquardt Algorithm for Assumption the Energy Losses of Hydraulic Transport in a Case of the Mine Trepca

Abstract

The main problem of hydraulic transport is the resistance generated during the mixture transport through the pipe-line. Testing the flow characteristics of mixtures, shown in this paper, are based on the principles of determining the unit energy losses by a mathematical calculation using the non-linear regression – the Levenberg-Marquardt algorithm. Such obtained results allow determining a transport rate in the horizontal pipe-line, depending on the mixture bulk density and pipe-line diameter. The flotation tailings is mainly used as a filling material in the mine “Trepca” - Stari Trg. According to the grain size distribution, it is a fine-grained material of a size of 0.074 mm to 1.2 mm. It is a multicomponent material containing pyrite, pyrrhotine and other heavy metals, and therefore, has a high bulk mass. The average rate of the hydromixture, in which the energy losses reach the minimum value, depends on the pipe-line diameter and kinetic bulk density of the mixture. For the test interval of change in the pipe-line diameter, shown in this paper (0.168 mm, 0.176 mm, 0.193 mm, and 0.225 mm), and kinetic bulk density of the hydraulic mixture (1-1.6 kg/m3), this rate ranges from 3-5.5 m/s. The increase of the energy losses in the hydraulic mixture transport increases proportionality with the increase of its kinetic bulk density. The results, presented in this paper, show that the required bulk density of 1.6 kg/m3 should be accepted as a limit from a point of view of the hydraulic transport cost-efficiency.