Ural State Mining University, Ekaterinburg, Russia
V. Z. Kozin, Doctor of Engineering Sciences, Professor, Dean of the Mining and Mechanical Faculty, gmf.dek@ursmu.ru
A. S. Komlev, Doctor of Engineering Sciences, Professor, Department of Mineral Processing, tails2002@inbox.ru

The influence of native gold particle size on the allowable discrepancy of the commodity balance is considered based on fire assay results. Individual coarse gold grains can cause several-fold variations in the gold mass fraction in analyzed samples, necessitating the exclusion of such results as exceeding permissible deviations. Anomalous assay results contain valuable information both on gold particle size and the amount of coarse gold. Formulas are presented that allow calculating the actual gold particle size and the proportion of coarse gold grains in the ore based on anomalous results, covering single assays, assays of two parallel samples, and data processing according to accepted algorithms. Processing a large number of routine assays at a processing plant enables estimation of probable systematic error and calculation of mass fraction underestimation effects over an extended control period. Examples of calculating coarse gold grain sizes at an operating processing plant are provided. With analytical sample size requirements (–0.071 mm), gold grains of 0.37 mm and larger may be included in the samples. The relative underestimation of the average gold mass fraction in the ore for one month was found to be 5.2 %, and in the tailings by 1.3 %, which would change the allowable commodity balance discrepancy by (+5.2 %) and (–1.3 %), respectively.
The research was supported by the Ministry of Science and Higher Education of the Russian Federation in accordance with state assignment No. 0833-2023-0004 for Ural State Mining University.

1. Kozin V. Z. Sampling of mineral raw materials at processing plants. Ekaterinburg: UGGU Publishing House, 2021. 202 p.
2. Lokonov M. F., Petrova M. I., Reyngardt E. P. Methodology for sample preparation for analysis of ore containing intermetallic compounds of platinum group metals. Obogashchenie Rud. 1971. No. 2. pp. 43–47.
3. Dominy S. C., Platten I. M., Glass H. J., Purevgerel S., Cuffley B. W. Determination of gold particle characteristics for sampling protocol optimisation. Minerals. 2021. Vol. 11. pp. 1109–1155. DOI: 10.3390/min11101109
4. Cherkasova M. V., Arsentiev V. A., Ustinov I. D. On the mechanism of intensification of fine grinding of metallic powder materials. Obogashchenie Rud. 2023. No. 2. pp. 16–23.
5. Cherkasova M. V., Samukov A. D., Cuksov M. P., Arsentiev V. A. Analysis of methods for intensification of fine dry grinding of powder materials. Obogashchenie Rud. 2021. No. 6. pp. 41–47.
6. Kozin V. Z., Komlev A. S. Compatibility of discrete and continuous sampling in sampling theory. Gornyi Informatsionno-analiticheskiy Byulleten. 2025. No. 1-1. pp. 145–154. DOI: 10.25018/0236_1493_2025_11_0_145

7. Jean-Sebastian D., Esbensen K. H. Revisiting Pierre Gy’s formula (TOS) – A return to size-density classes for applications to contaminated soils, coated particular aggregated and mixed material systems. Analytica Chimica Acta. 2022. Vol. 1193. pp. 1–21. DOI: 10.1016/j.aca.2022.339227
8. Nikitenko E. M., Evtushenko M. B., Yushina T. I. Improvement of fire assay analysis of ores from the Degdekanskoye deposit. Obogashchenie Rud. 2019. No. 1. pp. 34–38.
9. Panshin A. V., Makavetskas A. R., Shekhirev D. V. Automated mineralogical analysis for processing operations. Obogashchenie Rud. 2013. No. 1. pp. 40–43.
10. Shibanova E. V. Estimation of gold and silver particle size in geological samples using high temporal resolution scintillation atomic emission analysis. Analitika i Kontrol. 2010. Vol. 14, No. 4. pp. 186–200.
11. Kotova O. B., Ozhogina E. G. Integration of modern methods of mineralogical analysis for refractory ores and mining wastes. Materials of the International Conference "Modern Problems of Complex and Deep Processing of Natural and Non-traditional Mineral Raw Materials (Plaksin's Readings – 2023)". Moscow: Sputnik+ Publishing House. pp. 49–52.
12. Sona M., Dube J.-S. Sampling particulate matter for analysis – Controlling uncertainty and bias using the theory of sampling. Analytica Chimica Acta. 2021. Vol. 1185. DOI: 10.1016/j.aca.2021.338982
13. Svensmark B. Extensions to the Theory of Sampling l. The extended Gy’s formula, the segregation paradox and fundamental Sampling uncertainty (FSU). Analytica Chimica Acta. 2021. Vol. 1187. DOI: 10.1016/j.aca.2021.339127
14. Stupakova E. V. Application of the random error formula of the reduction operation for choosing the technology of preparing a plant's reference material. Materials of the XXX International Scientific and Technical Conference "Scientific Foundations and Practice of Processing Ores and Technogenic Raw Materials". Ekaterinburg. 2025. pp. 72–75.
15. Stupakova E. V. Calculation and optimization of sample preparation flowsheets. Izvestiya Vuzov. Gornyi Zhurnal. 2023. No. 6. pp. 60–67. DOI: 10.21440/0536-1028-2023-6-60-67
16. Lepilova I. V. Preparation of samples from coarse-grained products taking into account the heterogeneity of sampled arrays. Materials of the XXX International Scientific and Technical Conference "Scientific Foundations and Practice of Processing Ores and Technogenic Raw Materials". Ekaterinburg, 2025. pp. 75–80.
17. Shemetov P. A. Quality management of ore flow during cyclic-flow technology for mining complex-structured deposits. Gornyi Zhurnal. 2002. Special Issue. pp. 80–83.
18. Yudin E. V., Sapunov R. V. Closing the metals balance based on X-ray spectral analysis data. Materials of the XXVIII International Scientific and Technical Conference "Scientific Foundations and Practice of Processing Ores and Technogenic Raw Materials". Ekaterinburg: FortDialog Publishing House LLC, 2023. pp. 398–402.
19. Standard Instruction for Compiling a Commodity Balance of Minerals at Processing Plants of the Ministry of Non-ferrous Metallurgy of the USSR. Moscow: Ministry of Non-ferrous Metallurgy of the USSR, 1968. 6 p.
20. Napier-Munn T. J., Whiten W. J., Faramarzi F. Bias in manual Sampling of rock particles. Minerals Engineering. 2020. Vol. 153. DOI: 10.1016/j.mineng.2020.106260
21. Komlev A. S. Issues of changing the regulatory framework for sampling processing plant products. Materials of the XXX International Scientific and Technical Conference "Scientific Foundations and Practice of Processing Ores and Technogenic Raw Materials". Ekaterinburg, 2025. pp. 63–72.