A comparison between the duplicate series method and the heterogeneity test as methods for calculating Gy?s sampling constants, K and alpha

The compilation of the sampling nomogram is an essential tool in the optimization of a sampling protocol and allows the operator to track the change in relative variance of the sampling error (the Fundamental Sampling Error) during steps of comminution and mass reduction in the process of recovery of the aliquot for analysis. The data required for the compilation of the nomogram are centered on the sampling constant K and the exponent, alpha (a), of the nominal fragment size. Five methods for establishing K have been identified, but two of them, the duplicate sampling analysis (DSA) method and the heterogeneity test (HT) method purport to provide such a constant. The step by step procedure for each of these two methods was examined using broken ores from three mines, Mponeng mine, Kloof mine and Lily mine. Two of these mines (Mponengand Kloof) are typical Witwatersrand-type gold mines, while the third is an Archaean-type, shear related gold deposit situated in the Barberton Greenstone belt. The results suggest that the factor K derived using the heterogeneity test is very accurate, but applies only to a single size fraction in the spectrum of comminuted materials. The calculation of gold grain sizes using this method appears to be too small and does not conform with the results from detailed mineralogical studies. The factors K and alpha derived using the duplicate series analysis, are appropriate for use across a wide spectrum of comminution sizes and also provide realistic gold grain sizes, comparable with the equivalent circular diameter of gold grains identified in mineralogical studies of the ores.