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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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. Example.jpg

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