Analysis of the sample preparation methods based on piecewise variation coefficients of component mass fractions

Abstract

Sample preparation methods are usually developed following respective recommendations of the applicable sampling standards. Modern sampling theories allow designing and optimizing these methods. Random errors in sample preparation are calculated based on a theoretical description of the piecewise heterogeneity of the sample obtained using the formulas for the fundamental sampling error. The concept of a piecewise coefficient of variation is introduced and used to develop a formula for the relative error of the sample preparation method. Using a method compiled in accordance with GOST 14180-80 for copper ore as an example, the relative error is established for the preparation of an ore sample with the copper mass fraction of 1.3 %. It is shown that a change in the final preparation size from 0.1 to 0.08 mm affects the error only insignificantly, and sample size changes by stages allow designing a preparation method with the smallest error. It is advisable to analyze the method compiled and change its parameters on the basis of a structural assessment of the influence of individual preparation stages on the error. Sample preparation examples for copper and gold-bearing ore are used to demonstrate the analysis procedure and the parameter changes. Traditionally, the minimum sample masses are established for all stages based on the volumetric heterogeneity of the sample being tested and the size of the sample material. The minimum masses should be found depending on the grain size of the valuable mineral in the ore, the permissible relative error for the size reduction, and the material size for the sample reduced by a factor of 1.5 for nonferrous metal ores.