Cut-off grade estimation

Cut-Off grade is the minimum amount of valuable mineral in a given mining unit required to mine (or process) at a profit. Material above this grade is considered to be ore, and material below this grade is considered to be waste. Usually expressed as:

• g/t (grams per tonne)
• $/t (dollars per tonne)
•  % (percent metal)

The cut-off grade can be determined through a variety of methods, each of varying complexity. Cut-off grades are selected to achieve a certain objective, such as resource utilization or economic benefit. Dividing these objectives even further gives way to specific goals such as the maximization of total profits, immediate profits, and present value. It is important to recognize that the cut-off grade is not simply calculated to a definite answer. It is in fact a strategic variable that has major implications on mine design. The cut-off grade is adapted as the economic environment changes with regard to metal prices and mining costs, and is therefore a constantly changing.

Calculating the Cut-Off Grade

Pros and cons of each method should be added...

Break-Even and Internal

The most simplistic way to determine cut-off grade is through the break-even and internal method. This method is easy to use and involves minimal background information. It is preferred as a first estimate, and is most effective in the early planning phases of a project. The internal cut-off grade classifies material based on processing only while the break-even cut-off grade is based on mining. Both methods utilize the following formula:

$\mathbf {G=(c+m_{o}-m_{w})/(y(s-r))}$

Parameters

mo	Cost to mine ore
mw	Cost to mine waste
r	Refinery unit cost
c	Cost to process ore
y	Metal recovery
s	Unit metal sale price

For the Internal (Milling) cut-off grade, mw = mo. Material below this grade should not be processed whether or not it has already been mined.

$\mathbf {Gmill=c/(y(s-r))}$

For the Break-even (Mining) cut-off grade, mw = 0. Material below this grade should not be mined.

$\mathbf {Gmine=(c+m_{o})/(y(s-r))}$

These cut-off grades are the fastest way to classify ore and waste, however, in a more detailed analysis they should not be relied on.

Lane’s Method

Lane’s Method offers a more accurate and complex way to calculate cut-off grade. This method also requires more information, so it may not be the first choice for a preliminary calculation. Although there are many intermediate grades determined through Lane’s Method, there is ultimately only one output cut-off grade. This grade is known as the optimum cut-off grade and it is used to maximize present value. The optimum cut-off grade gives the advantage of considering discount rates and process capacities, however, these inputs are also subject to change. In the early stages of the design process the production rate and concentrator capacity have not yet been determined, therefore Lane's method is most accurate and effective during the production (operational) phase of the project.

Lane's Method was developed by Ken Lane in 1988 when he identified three distinct stages of cut-off grade application; mining, concentrating, and processing. He related these steps to the concept of Net Present Value.

Parameters

y	Recovery
C	Concentrator capacity
R	Refining capacity
f	Fixed costs
s	Sale price
c	Concentrator costs
r	Refining Costs
V	Present value
d	Discount rate

The grades; gm, gc, and gr represent the milling, concentrating and refining cut-off grades respectively.

$\mathbf {g_{m}=c/(y(s-r))}$

$\mathbf {g_{c}=c+(f+dV)/C)/(y(s-r)}$

$\mathbf {g_{r}=c/(y(s-r-(f+dV)/R))}$

The following intermediate grades relate each of the previous grades. The table below is used

$\mathbf {g_{m}c=f(Qm,Qc,gradedistribution)}$

$\mathbf {g_{r}c=f(Qr,Qc,gradedistribution)}$

$\mathbf {g_{m}r=f(Qm,Qr,gradedistribution)}$

The following grade distribution table can be used to find the average grade of the deposit, which is assumed to be the same as the mill feed. This information is used to create tables in which the grade as a function of mine, concentrator, or refining capacity is found.

Qm	Mine capacity
Qc	Concentrator capacity
Qr	Refining capacity

The median value of $G_{m}c$,$G_{r}c$, and $G_{m}r$ is the optimum cut-off grade.

Polymetallic Deposits

Polymetallic deposits are orebodies which produce or are capable of producing multiple metals. To calculate the cut-off grade of a polymetallic deposit, an equivalent cut-off grade method is used. This method uses the gross recoverable value (GRV) of each individual metal as well as an equivalent grade factor, which is a ratio of the GRV of each metal to the GRV of the metal being used for the equivalent grade. GRV is calculated by taking the product of reasonable metal price, in $/weight, and the estimated recovery of the metal.

The following formula can be used to classify the equivalent grade for a mining unit:

Failed to parse (syntax error): {\displaystyle \mathbf{G_e = g_1 + f_2g_2 + f_3g_3 +…}}

Where $G_{e}$ is equivalent grade of a specified metal (in either g/t or %, depending on the metal), $f_{n}$ is the ratio of the grade of metal n to the grade of the specified metal, and $g_{n}$ is the grade of grad of metal n.

Equivalent grade is necessary for polymetallic deposits in which the value of a block may be influenced by more than one valuable mineral. It simplifies the value of the block so that cut-off grade analysis can be performed, and a decision of whether or not to mine the block can be made.

Mineral Classification

Cut-off grades are used to determine the point at which material becomes economically valuable. Therefore, they are necessary to define the amount of ore in a deposit. The classification of ore depends entirely on cut-off grade. Increasing the cut-off grade places a stricter requirement on what can be considered ore. This decreases the amount of material that can be considered ore, and with it the reserves and life of mine. This table shows the impact of cut-off grade on mineral reserves and average grade. Note the changes in tonnage and grade as the cut-off grade changes.

Grade-Tonnage Curves

Grade-Tonnage curves are a visual representation of the impact of cut-off grades on mineral reserves. The Grade Tonnage Curve displays the size and average grade of a deposit relative to cut-off grade. As the criteria for ore classification becomes more selective, the tonnage of the deposit decreases. Conversely, as the cut-off grade is lowered, the tonnage of the deposit increases. This is simply because the standard used to distinguish between ore and waste has become less selective. As the cut-off grade increases, so too does the average grade of the ore mined.

Metal value is not the only factor affecting the profitability of a block. The presence of unwanted (often hazardous) material in a block may increase the processing cost [SME reference]

Adjusting the Cut-Off Grade

Stockpiling and blending are often used to ensure consistency of mill feed. This can affect cut-off grade since If the metal price increases, it may seem intuitive to lower the cut-off grade since the low grade material can be mined at a profit. However, the better decision is often to increase the cut-off grade instead. Processing the higher grade material will yield an increase in the amount of valuable mineral produced. This is assuming that the processing capacity does not change; only the ore being processed does. The extra product can then be sold at this increased price.

It is important not to view high grade ore as the most desirable The challenge of balancing the tactical and strategic aspects of operations is

Extraction Sequence and Variable Grade Interprocess Options

• Polymetallic Deposits & Metal Equivalencies

Selectivity and Dilution Constraints Stock Piling and Pushback Factors Opportunity Costs, Discount Rates, and NPV Equation 1:

Interprocess Options

In the case of multiple processing options, cut-off grade is used to determine which process the ore will be sent to.

$\mathbf {U_{1}(x_{c})=U_{2}(x_{c})}$

Where $U_{1}$ is the utility of sending ore to process 1, and $U_{2}$ is the utility of sending ore to process 2. Utility is defined as the value (economic or otherwise) of selecting a process.

This means that if process A is cheaper than process B, the cut-off grade for process A

Stockpiling

The ore that has not yet been processed can also have an impact on cut-off grade. In this case, blending is used to keep the process feed (ore) a consistent grade.

References

1. Thorley, Ursula. MINE 341 Lecture 10: Cutoff Grade (2013)
2. Rendu, Jean-Michel. An Introduction to Cut-Off Grade Estimation
3. Lane, Ken

External Links

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