Statistical effect of sampling particle number on mineral liberation assessment

Appropriate assessment of mineral liberation is vital for the efficient operation of the entire mineral processing process. Recently, the automated high speed analysis of ore particles that are mounted in resin, sectioned, and polished has become popular. However, these particle sectional analysis methods include two inadequately studied errors: a statistical dispersion correlated with the number of analyzed particles and a stereological bias, which unavoidably overestimates the degree of liberation in 2D. In addition, even if the stereological bias can be overcome using a correction method, the estimated degree of liberation in 3D also exhibits a statistical dispersion. A series of numerical analysis on more than one million biphase particles with various types of inter-particle structures was conducted to systematically investigate these errors, and the previously proposed stereological correction method was attempted. A method was proposed for estimating the number of particle sections that should be analyzed in order to achieve a degree of apparent liberation in 2D and a degree of liberation in 3D for a desired arbitrary reliability. Validation studies showed the reliability of the proposed method was averagely 97.6% in 2D and 3D.