Polymetallic deposit cut-off grade estimation

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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.


Calculation of Equivalent 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
p Market sale value of each metal
s Sales and marketing cost of each metal
y 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].

Example Calculation

An example for a polymetallic deposit can be seen below. Assume a selling price of $2,500, $2,400 and $6,500 per tonne of zinc, lead and copper, respectively. For this example, the selling cost has been chosen to be 5% of the selling price, and metallurgical recoveries are all 90%. A grade of 6, 3 and 0.5 percent by mass of zinc, lead and copper is used, respectively.

Calculation of Cut-off Grade Using Net Smelter Return (NSR)

Net Smelter Return is a measure of the value of ore and is defined as the proceeds from the sale of mineral products, after deducting transportation and treatment costs. A NSR model of a mineral deposit serves two main purposes [4]:

  • Provides a common denominator for comparison of assays from polymetallic deposits
  • Provides awareness of economic factors that determine the value of the ore

In addition, NSR models considers the three typical stages of mining operations: the mining stage, the treatment stage, and the refining stage. For a polymetallic deposit, it is recommended to examine two NSR cut-off values [1]:

  • Mine (external) cut-off NSR
  • Mill (internal) cut-off NSR

NSR of Deposit

In the case of a deposit with n metals of economic value, the NSR of one metric ton is calculated as:

Variable Definition
x Grade of each metal in deposit
r Process recovery of each metal
R Refining cost of each metal
p Smelting recovery of each metal
V Market sale value of each metal
K Metric tons of material required to produce one metric ton of concentrate
Cs Smelter cost per ton of concentrate
Ct Transportation costs per ton of concentrate

In the case of small or complex polymetallic deposits, it may be considered to ship a bulk concentrate resulting in a lower net smelter return, as opposed to operating the equipment required to separate the minerals [4]. Polymetallic projects such as McArthur River, Australia and Red Dog, Alaska have benefited from bulk lead-zinc concentrates.

Utility of Ore and Waste

The utility of sending one metric ton of material to the processing plant, and the utility of sending one metric ton to the dump, are written as:

Variable Definition
MO Mining cost per tonne of ore
PO Processing cost per tonne of ore
OO Overhead cost per tonne of ore

Processing costs and recoveries can vary based on geological characteristics such as mineralogy, hardness, clay content, and degree of oxidation, depending on the location of the deposit [5].

Mine (external) Cut-off NSR

The mine cut-off NSR is described as material that does not need to be mined [6]. The breakeven NSR cut-off value is therefore calculated by equating the utility of ore and waste, as shown below:

Mill (internal) Cut-off NSR

The mill cut-off NSR is described as the material that must be mined but can either be sent to the waste dump or processed as ore [5]. The mill cut-off value is the difference between the mine operating cost and the mining cost.

Application of NSR Models

NSR models can be used to economically evaluate a polymetallic deposit at the exploration stage, evaluation stage, as well as the exploitation stage.


In the exploration stage, the main use for NSR models is to evaluate and compare polymetallic drill-hole intersections [4]. For example, two drill-hole intersections, 53B and 58, from the Louvicourt project, Quebec in 1989 are shown below.

Drill-hole 53B and 58 from the Louvicourt project, Quebec, 1989. [4]

The two drill-holes contained copper, zinc, gold and silver. To evaluate and compare the economic value, both drill-holes were calculated in terms of NSR; the NSR of 53B and 58 were $57.27/tonne and $64.55/tonne, respectively [4].


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.


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].

Grades and Recoveries of Copper, Lead and Zinc Concentrates

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].

1990 study of the relationship between mill head grades, recoveries, and concentrate grades of copper, lead, and zinc. [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].


  1. 1.0 1.1 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. 4.00 4.01 4.02 4.03 4.04 4.05 4.06 4.07 4.08 4.09 4.10 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. 5.0 5.1 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.
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