# Polymetallic deposit cut-off grade estimation

Polymetallic deposits are classified as deposits that contain one or more mineral or metal of economic value. The economic evaluation of polymetallic deposits must be conducted on a basis of contribution from each metal. The calculation of cut-off grades for polymetallic deposits are done using utilities; the cut-off is expressed as a dollar value as opposed to a metal grade.

Calculating the metal equivalent grade of a polymetallic deposit is useful to simplify the evaluation of a block model by expressing the orebody in terms of an equivalent grade of one mineral. The calculation of equivalent grade is dependent on two factors [1]:

• The metal price of each commodity
• The process recovery of each commodity

Equivalent grade is calculated using an equivalent factor, used to convert the secondary grade distribution in terms of the primary metal grade [2]. The equivalent factor is calculated using the equation below, where the subscript 1 denotes the primary mineral.

Variable Definition
Market sale value of each metal
Sales and marketing cost of each metal
Metallurgical recovery of each metal

The average equivalent grade is then calculated using the equivalent factor and the average grade of each metal in the deposit [3]:

The equivalent grade method is not recommended when determining the cut-off grade due to the use of changing and fluctuating metal prices and recoveries [4].

### Evaluation

NSR models are useful in mine planning and mine design. NSR models evaluate the sensitivity of a project with respect to the assumptions made [4] . Evaluating profits at various cut-off grades, an optimum cut-off grade can be determined. NSR models can also be used to determine the optimum mill recovery rate, as well as help choose representative samples for metallurgical test work.

### Exploitation

NSR models provide a realistic approach to determining cut-off grades by distinguishing material that can be extracted whose value exceeds expenditures required to develop, extract and process the material. NSR models are more realistic compared to working with an arbitrary, constant cut-off grade [4].

The relationship between mill head grade and recoveries, and between mill head and concentrate grades for copper, lead and zinc were analyzed and presented in the Mining Sourcebook in 1990. The study was based on 13-32 different operations and the results are shown in the table below [4].

Based on the study, it was found that the presence of copper had a negative effect on the metallurgical characteristics of zinc and lead in mill feed. Similarly, the presence of zinc had a negative effect on the characteristics of copper in mill feed. The presence of lead was found to have no significant effect on copper recovery and grade. It was also determined that mill recoveries and concentrate grade increase with increasing mill head grades [4].

## References

1. S. McKinnon, "MINE 448 Notes: Ore Value," Kingston, 2019.
2. A. Nieto and K. Y. Zhang, "Cutoff grade economic strategy for byproduct mineral commodity operation: rare earth case study", 2013.
3. M. Osanloo and M. Ataei, "Using equivalent grade factors to find the optimum cut-off grades of multiple metal deposits," 2003.
4. R. Goldie and P. Tredger, "Net Smelter Return Models and Their Use in the Exploration, Evaluation and Explotation of Polymetallic Deposits," Geoscience Canada, pp. 159-171.
5. J.-M. Rendu, An Introduction to Cut-off Grade Estimation, Society for Mining, Metallurgy, and Exploration, Inc., 2008.
6. A. S. Hashemi, MINE 341 - Open Pit Mining: Lecture 6 - Cut off-grade, Kingston: Queen's University, 2016.