Difference between revisions of "Cut-off grade estimation"

From QueensMineDesignWiki
Jump to: navigation, search
Line 1: Line 1:
 
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.
 
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:
 
Usually expressed as:
 
* g/t
 
* $/t
  +
* %
   
Contents
 
  +
<math>\sqrt{2}</math>
 
== Calculating the Cut-Off Grade ==
   
== [[1.0 Calculating the Cut-Off Grade 1]]
 
 
=== Break-Even and Internal ===
'''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.
 
The most simplistic way to determine cut-off grade utilizes the following formula: Equation 1.
Line 51: Line 31:
   
   
1.2 Lane’s Method
+
=== 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.
 
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.
Line 79: Line 59:
 
Qr Refining capacity
 
Qr Refining capacity
   
1.3 Equivalent Grade
+
=== Equivalent Grade ===
 
The following formula can be used to classify the equivalent grade for a mining unit:
 
The following formula can be used to classify the equivalent grade for a mining unit:
 
G = g1 + f2g2 + f3g3 + …
 
G = g1 + f2g2 + f3g3 + …
Line 86: Line 66:
 
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.
 
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 ==
+
== Mineral Classification ==
 
 
   
Line 92: Line 72:
 
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.
 
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 ===
   
 
Grade-Tonnage curves are a visual representation of the impact of cut-off grades on mineral reserves.
 
Grade-Tonnage curves are a visual representation of the impact of cut-off grades on mineral reserves.
Line 101: Line 81:
   
   
== 3.0 Adjusting the Cut-Off Grade ==
+
== Adjusting the Cut-Off Grade ==
   
   

Revision as of 00:07, 4 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. Usually expressed as:

  • g/t
  • $/t
  •  %

Calculating the Cut-Off Grade

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.



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

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.

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.

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]


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