Optimal liberation of ore minerals for ore beneficiation

Ore minerals are normally complexly interlocked with adjacent gangue and/or ore minerals in most ores. Optimal liberation of ore minerals is essential for low-grade ores, so that maximal profits can be made by marketing such beneficiated ores by removing gangues after crushing these ores. Cost minimization for liberation is useful to achieve maximum profit for beneficiated ores through recovering as much ore minerals (in weight fraction) as feasible using statistical size distributions of ore minerals and gangue minerals, separately. Ore and gangue minerals are usually having log-normal size distributions, in 3D space, on weight frequency basis which have different (size) means and (size) variances as well as different weight proportions (fractions) in the ores. However, since the price of marketable ores is often several times (or several tens/hundreds of times) that of the crushing cost for liberation, optimal crushing size is calculable from the actual size distributions of ore and gangue minerals in the ore. But, the measured sizes (circle radii or semi-intercepts) in 2D on thin/polished sections are not the true size distributions of ore and gangue minerals on weight basis in 3D space, and thus probabilistic corrections as proposed by author[1–3] and transformation of corrected number frequency moments to equivalent 3D sphere size moments on weight frequency basis[1–3] are essential to compute the true optimal libration size (on weight basis) for crushing the ores for ore beneficiation purposes.