# Difference between revisions of "Cut-off grade estimation"

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+ | 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. |
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+ | g/t |
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+ | % |
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+ | $/t |
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+ | Usually expressed as: |
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+ | Contents |
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+ | == [[1.0 Calculating the Cut-Off Grade 1]] |
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+ | '''1.1 Break-Even and Internal 1 |
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+ | 1.2 Lane’s Method 2''' |
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+ | 1.3 Equivalent Grade 3 |
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+ | 2.0 Mineral Classification 4 |
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+ | 2.1 Grade-Tonnage Curves 4 |
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+ | 3.0 Adjusting the Cut-Off Grade 5 == |
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+ | [[== 1.0 Calculating the Cut-Off Grade ==]] |
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+ | == 1.1 Break-Even and Internal |
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+ | The most simplistic way to determine cut-off grade utilizes the following formula: Equation 1. |
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+ | G=(c+m_o-m_w)/(y(s-r)) |
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+ | Table 1: Basic Cut-Off Grade Parameters |
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+ | mo cost to mine ore |
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+ | mw cost to mine waste |
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+ | r refinery unit cost |
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+ | c cost to process ore |
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+ | y metal recovery |
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+ | s unit metal sale price |
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+ | For the Internal (Milling) cut-off grade, mw = mo. This is simplified in Equation 2. Material below this grade should not be processed whether or not it has already been mined. |
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+ | G_Mill=c/(y(s-r)) |
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+ | For the Break-even (Mining) cut-off grade, mw = 0. This is simplified in Equation 3. Material below this grade should not be mined. |
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+ | G_Mine=(c+m_o)/(y(s-r)) |
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+ | 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. |
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+ | 1.2 Lane’s Method |
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+ | 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. |
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+ | Table 2: Lane’s Method Cut-Off Grade Parameters |
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+ | y Recovery |
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+ | C Concentrator capacity |
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+ | R Refining capacity |
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+ | f Fixed costs |
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+ | s Sale price |
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+ | c Concentrator costs |
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+ | r Refining costs |
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+ | V Present value |
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+ | d Discount rate |
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+ | <math>g_m=c/(y(s-r))</math> |
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+ | g_c=(c+(f+dV)/C)/(y(s-r)) |
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+ | g_r=c/(y(s-r-(f+dV)/R)) |
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+ | gmc = f(Qm,Qc,gradedistribution) |
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+ | grc = f(Qr,Qc,gradedistribution) |
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+ | gmr = f(Qm,Qr,gradedistribution) |
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+ | Qm Mine capacity |
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+ | Qc Concentrator capacity |
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+ | Qr Refining capacity |
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+ | 1.3 Equivalent Grade |
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+ | The following formula can be used to classify the equivalent grade for a mining unit: |
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+ | G = g1 + f2g2 + f3g3 + … |
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+ | |||

+ | <math>G = g1 + f2g2 + f3g3 + …</math> |
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+ | This 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. |
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+ | == 2.0 Mineral Classification == |
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+ | |||

+ | |||

+ | 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. |
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+ | 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. |
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+ | 2.1 Grade-Tonnage Curves |
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+ | Grade-Tonnage curves are a visual representation of the impact of cut-off grades on mineral reserves. |
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+ | [[File:Example.jpg]] |
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+ | Figure 1: An Example Grade-Tonnage curve (J.M. Rendu) |
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+ | 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] |
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+ | == 3.0 Adjusting the Cut-Off Grade == |
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+ | |||

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+ | Stockpiling and blending are often used to ensure consistency of mill feed. This can affect cut-off grade since |
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+ | 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. |
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+ | Extraction Sequence and Variable Grade |
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+ | Interprocess Options |
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+ | *Polymetallic Deposits & Metal Equivalencies |
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+ | Selectivity and Dilution Constraints |
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+ | Stock Piling and Pushback Factors |
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+ | Opportunity Costs, Discount Rates, and NPV |
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+ | Equation 1: |
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+ | Interprocess Options |
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+ | In the case of multiple processing options |
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+ | U1G1 = U2G2 utility |
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+ | This means that if process A is cheaper than process B, the cut-off grade for process A |

## Revision as of 12:36, 3 February 2015

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. g/t % $/t Usually expressed as:

Contents

== [[1.0 Calculating the Cut-Off Grade 1]]
**1.1 Break-Even and Internal 1**
1.2 Lane’s Method 2
1.3 Equivalent Grade 3
2.0 Mineral Classification 4
2.1 Grade-Tonnage Curves 4
3.0 Adjusting the Cut-Off Grade 5 ==

[[== 1.0 Calculating the Cut-Off Grade ==]]

== 1.1 Break-Even and Internal

The most simplistic way to determine cut-off grade utilizes the following formula: Equation 1. G=(c+m_o-m_w)/(y(s-r)) Table 1: Basic Cut-Off Grade 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. This is simplified in Equation 2. Material below this grade should not be processed whether or not it has already been mined. G_Mill=c/(y(s-r)) For the Break-even (Mining) cut-off grade, mw = 0. This is simplified in Equation 3. Material below this grade should not be mined. G_Mine=(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.

1.2 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.

Table 2: Lane’s Method Cut-Off Grade 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

g_c=(c+(f+dV)/C)/(y(s-r))

g_r=c/(y(s-r-(f+dV)/R))

gmc = f(Qm,Qc,gradedistribution) grc = f(Qr,Qc,gradedistribution) gmr = f(Qm,Qr,gradedistribution) Qm Mine capacity Qc Concentrator capacity Qr Refining capacity

1.3 Equivalent Grade The following formula can be used to classify the equivalent grade for a mining unit: G = g1 + f2g2 + f3g3 + …

**Failed to parse (syntax error): {\displaystyle G = g1 + f2g2 + f3g3 + …}**
This 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.

## 2.0 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.

2.1 Grade-Tonnage Curves

Grade-Tonnage curves are a visual representation of the impact of cut-off grades on mineral reserves.

Figure 1: An Example Grade-Tonnage curve (J.M. Rendu) 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]

## 3.0 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.

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 U1G1 = U2G2 utility This means that if process A is cheaper than process B, the cut-off grade for process A