A generalised form of Gy’s equation for gold ores – empirical evidence - R C. A Minnitt (The Australasian Institute of Mining and Metallurgy, 2017)
The two methods for calibrating the parameters K and (alpha) for use in Gy’s equation for the fundamental sampling error (FSE), the duplicate sampling analysis (DSA) and the segregation fractionalised analysis (SFA) are described in detail. A case study using identical broken reef material from a Witwatersrand-type orebody is calibrated using the DSA and SFA methods and the results are compared. Classically, the form of Gy’s equation for the FSE raises the nominal size of fragments given by dN to a power of 3. Gy’s formula is a theoretical formula applicable in the case when fragments are randomly collected one by one, which is obviously never the case. This is because the fragment shape factor (f) and the granulometric factor (g) were introduced to take care of this anomaly. More recent formulae, such as those suggested by François-Bongarçon and Lyman, are empirically based formula. A later modification of Gy’s formula raises dN to the power ? (alpha), the latter term being calibrated with the coefficient K in the DSA and SFA methods. The preferred value of ? (alpha) for low-grade gold ores used by sampling practitioners in the mining industry is 1.5. A review of calibration experiments for low-grade gold ores using the DSA and SFA methods has produced values of K that vary between 70 and 170 and values of alpha in the range 0.97 to 1.30. The average value for alpha is found to be 1, rather than 3 as originally proposed in the classic form of Gy’s equation or the industry preference for 1.5. It is suggested that for low-grade gold bearing ores, the equation for the FSE should raise dN to a power of 1. Such an equation for the variance of the combined FSE plus the grouping and segregation error, now referred to as the short-term component of the quality fluctuation error (QFE1), greatly simplifies the characterisation of gold ores, which now only requires the calibration of K for a given mass and established fragment size. The implications for the heterogeneity test from the generalised equation are that provided the fragments have been screened to within a narrow size range, any particular size will return a value for K that is acceptable for use in the sampling nomogram.CITATION:Minnitt, R C A, 2017. A generalised form of Gy’s equation for gold ores – empirical evidence, in Proceedings Eighth World Conference on Sampling and Blending , pp 331–350 (The Australasian Institute of Mining and Metallurgy: Melbourne).