Pit & Cut-off
Optimisation
Work Book
Prepared by
Norm Hanson
Whittle Consulting Pty Ltd
For
University of Queensland
Sept 2008
Worksheet 1
The Value Of Truck Load Of Ore
Calculate the value (which is Revenue - Costs) of a single truck load of ore in three example cases - 1. 50 tonnes of 2g/t Gold
2. 100 tonnes of 1 g/t Gold 3. 250 tonnes of 0.5% g/t Gold
Before you begin the calculation can you guess which is the most valuable truck load?
Costs Mining $ 1.50 Processing (CIP) $17.50 Gold Prices US$900/oz Grams Unit Prices Recoveries (CIP) 92.5%
Value = Revenue - Costs
= [(GRADE* ORE* PRICE*RECOVERY) - (ORE*COSTP)]- ROCK*COSTM)
Example 1 - 2 grams per tonne in 50 tonnes
= [(2* 50 *
PriceAu
* 92.5%) - (50 * $17.5)]- (50 * $1.50)
=
Example 2 - 1 gram per tonne in 100 tonnes
= [(1*100 *
PriceAu
* 92.5%) - (100 * $17.5)]- (100 * $1.50)
=
Example 3 - 0.5 grams per tonne in 250 tonnes
= [(0.5*250 *
PriceAu
* 92.5%) - (250 * $17.5)]- (100 * $1.50)
31.103 grams per oz 2240 lbs per tonnne
Worksheet 2
The Value with Multi-Metal, Destinations
If you have more than one metal or more than one possible
4. 250 Tonnes of 0.25% Copper & 0.5 g/t Gold from an Oxide Zone
In this example the truck could go to two different processes, a floatation (but since it is oxide ore and has lower recoveries) or SXEW (a form of heap leach with a solvent extraction)
Costs Mining $ 1.50 Processing (SXEW) $ 5.00 Processing (Floatation) $ 8.00 Gold Copper Prices US$400/oz US$1.20/lb Grams Tonnes Unit Prices Recoveries (SXEW) 65% 30% Recoveries (Floatation) 25% 75%
Value = Revenue - Costs
= [(GRADE* ORE* PRICE*RECOVERY) - (ORE*COSTP)]- ROCK*COSTM)
Example 4a - 0.5 grams Au plus 0.25% Cu per tonne in 200 tonnes to SXEW
= [(0.5*250 *
PriceAu
* 65% + 0.25%*250*
PriceCu
*30%)
- (250 * $5)]- (250 * $1.50)
Example 44b- .5 grams Au plus 0.25% Cu per tonne in 200 tonnes to flotation
= [(0.5*250 *
PriceAu
* 25% + 0.25%*250*
PriceCu
*75%)
- (250 * $8)]- (250 * $1.50)
=
31.103 grams per oz 2240 lbs per tonnne
Worksheet 3
Simple Example
Let us consider a very simple ore body which is rectangular, of constant grade, and sits beneath a horizontal topography. Let us further assume that it is of infinite length, so that we do not have to allow for end effects, and need only consider one section.
The following diagram shows such an ore body.
Surface
100 tonnes waste
500 tonnes ore
Bench Level
Using the quantities indicated in the diagram, we can easily calculate the tonnages for the eight possible pit outlines, and the following table shows these.
Tonnages for possible outlines
Pit 1 2 3 4 5 6 7 8
Ore 500 1,000
Waste 100 400 900 1,600 2,500 3,600 4,900 6,400
Total 600 1,400
If we assume that ore is worth $2.00 per tonne and that waste costs $1.00 per tonne to mine and remove, then the following table shows the value of each pit.
Pit values for ore at $2.00/T and waste at -$1.00/T
Pit 1 2 3 4 5 6 7 8
Worksheet 4
Floating Cones
Trace around the Optimal Pit
Case A
Case B
+40
+60
+200
-70
-80
-30
-20
Which Case Overmines
Which Case Undermines
-30
-80
-80
Worksheet 5
Two Dimensional L-G
To see how the Lerchs-Grossmann method works, we will use a two dimensional example. To keep the example simple we will use squares and assume a 45o slope.
As an example we can have a two dimensional model 17 blocks long by 5 blocks high. Only three blocks contain ore and they have the values shown (after mining). All other blocks are waste and have the value -1.0.
6.9 23.9 23.9
Draw the Lerch-Grossman network and determine the most profitable pit.
Structural arcs for each block
Worksheet 6
Handling Variable Slopes
Blocks whose centroid is above the desired slope line must be mined, Those below the line do not need to be mined.
Desired
Slope
1,1
2,1
3,1
etc
1,2
X
Z
How arcs can be referenced.
1, 1 > 1, 2
1, 1 > 2, 2
the third arc from 1,1 is:
Worksheet 8
The Sequence of Mining
If we have another look at our simple example pit design, we can look at the discounted cash flow and its interaction with the sequence of mining and production rates
Surface
100 tonnes waste
500 tonnes ore
Bench Level
We will use a discount rate of 10%
Top Down Mining SequencePit 1 2 3 4 5 6 7 8
Value 900 1,600 2,100 2,400 2,500 2,400 2,100 1,600 Mill Capicty 500 tpp 900 1,530 1,917 2,085 2,057 1,851 1,486 978 Mill Capicty 1000 tpp 900 1,530 1,868 2,011 1,956 1,552 1,049 449
Inner Shell First then Mining out by Shell
Pit 1 2 3 4 5 6 7 8
Value 900 1,600 2,100 2,400 2,500 2,400 2,100 1,600 Mill Capicty 500 tpp 900 1,530 1,935 2,154 2,220 2,161 2,002 978 Mill Capicty 1000 tpp 900 1,530 1,898 2,068 2,105 1,993 1,790 449
Top Down Mining is the WORST CASE NPV BEST CASE NPV
