Pit Optimisation For Minex v5.3 April 2008
Copyright © 2008 Surpac Minex Group Pty Ltd (A Gemcom Company). All rights reserved.
This This sof software are and and docu docum ment entatio ation n is propr opriet ietary ary to Surp Surpac Mine Minex x Grou Group p Pty Ltd Ltd. S urpac Minex Group Pty P ty Ltd publishes this documentation documentation for the the sole use of Minex licenses. licenses . Without written permission you may not sell, reproduce, store in a retrieval system, or transmit any part of the documentation. For such permission, or to obtain extra copies please contact your local Surpac Minex Group Office. S urpac urpac Minex Group Pty P ty Ltd Ltd Level 8 190 St Georges Terrace P erth, Western Australia Australia 6000 6000 Telep Teleph hone: one: (08 (08) 94201383 Fax: (08) 94201350 While every precaution has been taken in the preparation of this manual, we assume no responsibility for errors or omissions. Neither is any liability assumed for damage resulting from the use of the information contained herein. All brand and product names are tradem trademarks arks or registered trademarks trademarks of of their respective companies. Ab out ou t Th is Manual
This This manual nual has has bee been n desig esign ned to provid ovide e a pract actical ical guide ide to the many any use uses of of the sof software. are. The The applications contained within this manual are by no means exhaustive as the possible uses of the software are only limited by the user’s imagination. However, it will give new users a starting point and existing users a good overview by demonstrating how to use many of the functions in Minex. If you have any difficulties or questions while working through this manual feel free to contact your local S urpac urpac Minex Group Group Office. Contributors
J on Bar Barber S urpac urpac Minex Group Mittagong, New South Wales Product
Minex v5.3
Table of Contents Ab ou t Th is Doc um ent ................................................................................................................4 Overview of Pit Optimi sation .....................................................................................................5 How t he Optimizer work .............................................................................................................7 The Optimis er menu .................................................................................................................12 MNX File .................................................................................................................................................15 How coal i s valued in the opti miser ........................................................................................16 Mine or P ort............................................................................................................................................16 Extra Elements .......................................................................................................................................16 Bauxite and Alumina...............................................................................................................................17 Multiple Coal Products............................................................................................................................17 Washing Costs and Yield .........................................................................................................18 Output Grids .............................................................................................................................21 Report Points ............................................................................................................................22 Ad van ced co st s u si ng SQLs ...................................................................................................23 Steep Dip Depos its ...................................................................................................................25 System inf ormation ..................................................................................................................26
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About This Document This document describes the operation of the Gemcom Minex pit optimiser. This optimiser uses a Minex gridded seam model as its input and creates a gridded surface representing the optimum pit. Both the Minex and Whittle optimisers are based on the Lerchs Grossmann algorithms. More detailed training information is available within the software and from your local Surpac Minex Group Support Office. When the software has been installed you can see additional training resources and help documentation in the Help menu. Contact Minex support as follows: •
Call the Brisbane office +61 (07) 3036 7000
•
Send a message to
[email protected]
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Overview of Pit Optimisation
Overview of Pit Optimisation “Optimization” is a process in which something is made as effective, perfect or useful as possible. The term can be used in a general sense to mean a process where an outcome is “optimized” by the adjustment of inputs or methods. “Optimization” also has a mathematical definition: which means to find the optimal value of a function , often subject to constraints. “Optimal” in mathematical terms means one of the following: 1. 2.
Minimal – The lowest possible value. If you were to optimize total cost, you would be seeking to minimize it. Maximal – The highest possible value. If you were to optimize total profit, you would be seeking to maximize it.
air waste
ore
Figure 1: Example ore body For any ore body model (Figure 1) there are many feasible pit outlines. In fact the number of technically feasible outlines is usually very large. In this context “feasible” means that it obeys safe slope requirements. In the current context, optimum pit is the pit with the maximum dollar value where Dollar Value.is defined as: Dollar Value =Revenues - Costs Revenues can be calculated from coal tonnages, energy, pit and wash plant recoveries or yields and product price. Price is often the main unknown factor but, in order to design at all, some price must be assumed. For simplicity we assume that the costs of mining and processing are known. However costs are often not known. The dollar value of any feasible outline can be calculated by totaling revenues less costs for every cubic meter, or every block, within the outline. The optimal outline is the one with the highest dollar value. Nothing can be added to an optimal outline which will increase the value without breaking the slope constraints. Nothing can be removed from an optimal outline which will increase the value without breaking the slope constraints. In other words, we mine everything which is “worth mining”. The optimal value for a given ore body can be affected by: 1. 2.
Prices and costs. In general if the product price goes up, the optimal pit gets bigger and conversely if costs go up, the optimal pit gets smaller. Slopes. In general if we use steeper slopes, the optimal pit gets deeper.
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Overview of Pit Optimisation
So in summary the Minex optimiser, like any optimiser, generates a pit shape (here a Minex grid) that is of maximum value. A typical analysis methodology in pit optimisation is to vary sale price and study the effect on the pit. As sale price is increased, the pit will grow because more material becomes economic. This growth of pits, often termed nested pits, helps us understand the pit limits and the best path or schedule to that limit.
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How the Optimizer work
How the Optimizer work The example given here is simplistic but illustrates the main calculations involved in setting up the costs. The following premises or assumptions apply: 1. 2. 3. 4. 5. 6. 7.
A set of 3D blocks can be superimposed on the geology. These blocks can be filled with dollar value =(revenue – costs). A mining cost of $3/block is used for coal and waste. Revenue of $20/block is used. Blocks are for simplicity assumed to be coal or waste. This assumption is not correct but serves the purpose at this stage. A more detailed discussion on this point is given later in this document. Coal blocks thus have a value of $20 - $3 or $17/block. For simplicity waste mining and coal mining costs are the same.
Figure 2 shows a simple cross section and discusses optimization as a 2D section. This is simplistic as optimization works in 3D, however 2D is adequate for this discussion. The first stage of optimization is to determine the individual block values. In Figure 2 we assume blocks are 100% coal or 100% waste. The dollar values are thus $17 and -$3 for coal and waste respectively.
$0 -$3 -$3 -$3 -$3 -$3 -$3 -$3 -$3
Cost $3/block Revenue $20/block
$0 $0 $0 $0 $0 $0 $0 $0 -$3 -$3 -$3 -$3 -$3 -$3 -$3 -$3 -$3 $17 -$3 -$3 -$3 -$3 -$3 -$3 -$3 -$3 $17 -$3 -$3 -$3 -$3 -$3 -$3 -$3 -$3 $17 -$3 -$3 -$3 -$3 -$3 -$3 -$3 -$3 $17 -$3 -$3 -$3 -$3 -$3 -$3 -$3 -$3 $17 -$3 -$3 -$3 -$3 -$3 -$3 -$3 -$3 $17 -$3 -$3 -$3 -$3 -$3 -$3 -$3 -$3 $17
Geology
Block costs
Figure 2: Block values =Revenue – Cost. Following cost and revenue definition, the optimizer algorithm sums the block values vertically downwards. Mining a lower block implies the bocks above are removed. Thus to mine a coal block, all the blocks above must be mined (Figure 3).
Figure 3: Block values summed vertically. An optimum pit: 1. 2. 3.
Has the maximum value and Is break even at its limits. A larger or a smaller pit will have a smaller value compared to the optimum.
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How the Optimizer work
Lerches and Grossman (CIM 1966) developed the optimum pit algorithm to determine the pit of maximum value. The detail of their approach is not discussed here. The final result is a pit outline with maximum value for that set of costs and revenue. Figure 4 shows two pits where we assume 45 o slopes. The LHS pit has a value of $13. This is the sum of the seven columns. From left to right the columns are 0, -3, 14, 11, -6, -3, 0 =$13. The RHS pit has a value of $12. This is the sum of its columns. From left to right the columns are 0, -3, 14, 11, 8, -9,-6,-3=$12. A smaller pit shown in Figure 5 would have a value of $8 (-3,14,-3). Thus the $13 dollar pit is optimum as it has the maximum value for the cost and revenue assumptions. A smaller pit is sub optimum and a larger pit is sub optimum.
o
Figure 4 Optimum pit for 45 slopes
Figure 5: Smaller pit has a value of $8. The term “nested pits” is used frequently in optimisation. If the coal sale price increases, the optimum pit will be larger. The extra revenue makes a deeper pit economic. Using different sales prices will generate a set of optimum pits, one pit for each sale price. Thus as price increases we would get pits 1, 2, 3 and 4 as shown in Figure 6.
1
2
3
4
Figure 6: Nested Pits This sequence of pits or outlines forms a set of nested pits. Nested pits are important in strategic mine planning. Assume that the actual sale price equates to pit 4. Then mining in the sequence 1, 2, 3, 4
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How the Optimizer work
maximizes cash flow and maximizes NPV. This occurs because the smallest pit (pit 1) is optimum at the smallest sale price. Thus if the market price of $100/tonne equates to pit 4 and pit 1 is profitable at say $40, then this pit makes $60 profit per tonne. Mining pit 1 first maximizes early cash flow and thus maximizes NPV. In conclusion the optimum pit gives planners: 1. 2.
The final economic pit for a set of costs and revenues. A sequence of nested pits, which show the best mining sequence.
Minex is a seam or layered modeling system. The basis of the Minex system is a 2D grid or surface model. Figure 7 shows the 2D grids for topography and for one coal seam floor. Typically in Minex a set of floor, roof, thickness, density, energy and ash grids etc exist for each seam. These grids in combination make up a 3D geological model. The optimization process uses a 3D block model. The Minex optimizer firstly converts the 2D gridded seam model into a block model. This block model is not a resource model with waste volume, coal tonnes and grade. It is a block model of block value, where value =(revenue – cost). To build this block model, the Minex optimizer defines the extent of the block model in X Y and Z. The X, Y extents are based on the input topography surface. The vertical or Z extent is based on the maximum Z of topography and the minimum Z of the deposit or a base grid. The block size of the 3D block model is based on the grid cell size of the topography grid. Thus if the topography grid used is 100 x 100 metres in size then the optimizer blocks will be 100m x 100m x 100m in XY Z. Sub blocking in the vertical or Z dimension provides better Z accuracy and thus allows better resolution of coal seams. The Z extent of the optimizer model is taken from the topography and base grid. It can for speed reasons be useful to reduce the model size by limiting the base grid. Similarly if the economic area (in XY) is limited, then reducing the input topography will reduce the block model size and may reduce compute times. Figure 7 shows these concepts; the topography defines the block model X, Y dimension. The Z dimension comes from the topography and base seam.
Z extent n e t x e Y
X extent
Figure 7: 3D block model defined by topography and base seam or base grid. The block model stores dollar value as an integer which is equal to: Value =(Volume x revenue) – (Volume x costs) The example used below assumes the following: 1. 2. 3.
Waste mining costs is a constant of $1.47/bcm. Coal mining costs are $5/bcm. The coal sale price is $20/tonne.
Thus a 100% waste block with dimensions of 100 x 100 x 100 metres would be valued at negative $1,470,000. The value for a block is based on a scan through the centroid of each block. In section the block value is defined as illustrated in Figure 8. Here block A is assigned a value based on: 1. 2. 3.
A cost for the thickness of waste between topography and the seam W1 x $1.47 Revenue minus a cost for the coal. Thus C2 x 1.4 x 20 – C1 x 5.00 A cost for the waste below the seam W2 x 1.47
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How the Optimizer work
Using the thickness values in block A, the block value is: {- (60 x 1.47) +(5x1.4x20-5*5) – (35 x 1.47))}x (100x100) =-$246,500. Block B can be calculated as (-5x1.47+5x1.4x20-5x5-60x1.47+5x1.4x20-5x5-25x1.47) x 100 x 100=+$977,000. Now consider the base block C. Assuming the stratigraphy stops at the lowest seam then this block is assigned a value of (-10 x 1.47 +10 x 1.4 x 20 - 10 x 5) x 100 x100 = $2,153,000. The underburden of 80 metres (W7) below the basal seam is not included in the block value as it will not be mined. In Minex this cost is excluded as it is below the stratigraphy. Underburden W2 and W5 is however used to determine the value of blocks A and B respectively as these blocks are above the basal seam. In some cases this extra underburden cost can be misleading. To minimize this error the Minex optimizer uses Z sub blocking. Basically the Z block is subdivided by an integer value between 1 and 8. So if the primary block size is 100x100x100 and the Z blocking is 4 then the optimizer runs at 100x100x25.
W3=5
W1 =60m
C1=5
W4=60
W2=35m
A
W5=25
B
C2=5
C3=10 W6=10 W7=80
C Figure 8: Example block value calculation. Sub-blocking gives advantages in: 1. 2.
Accuracy and Slope definition.
Dividing blocks A, B or C into four 25m high blocks increases the resolution. These thinner blocks are more clearly either waste or coal, or more correctly are either economic or uneconomic. Sub-blocking is not always an exact division of the primary block size. For the optimizer to achieve the o required side slope sufficient block detail must exist. In Figure 9 a 45 slope can be achieved with 40 x 40 o x 10 metres blocks. However a side slope of 30 can only be achieved with 23.09 metres of vertical rise. Table 1 illustrates that the Z-sub block size is a function of the wall slope and the Z-sub blocking. The Minex optimizer will automatically calculate the appropriate Z block size based on the user input Z blocking and the user input slopes.
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How the Optimizer work
Table 1: Relationship between block size in Z and slope angle. WALL
BLOCK
OPT Z
TAN
SIZE Z
Z BLK S
SLOPE
X SIZE
BL OCK
WALL
REQD
REQD
DEGREES
MET
MET
45
40
10
1.00
40.00
4.00
40
40
8.39
0.84
33.56
4.00
35
40
7
0.70
28.01
4.00
30
40
5.77
0.58
23.09
4.00
45o
MET
30o
Figure 9: As optimizer side slope falls the Z sub block size falls to accommodate the flatter slope angle. 4 x 5.77 metre blocks up and one 40m block across equates to a 30 o slope (RHS).
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The Optimiser menu
The Optimiser menu The optimiser menu is run from the Minex 5 software. The optimiser is located at the top of the pit design option as it should logically be run as a guide to the design.
The optimiser menu is shown in Figure 10 and it is explained below.
Figure 10: Optimiser menu Table 2: Menu Parameters New parameter file name
Name of the file to store these parameters
Log file name
An output file created when the optimizer runs. This file will contain errors and result information.
Structural model
Model containing seam floor and seam thickness grids. Roof grids are not required. Must also contain topography, weathering and a base grid. The output optimizer grids are also stored in this file.
Quality model
Model containing density and energy grids. See note 1
Cost model
Waste mining and coal mining costs can be based on grids having suffixes such as WM and CM respectively. If these grids exist they will be stored in this file. See Section 6 SQL Costs.
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The Optimiser menu
Table 2: Menu Parameters Topography grid
Project topography. See note 3.
Weathering grid
Use topography if weathering is unavailable. Any coal above weathering is set to be waste. See note 3.
Base grid
Usually the basal seam floor or a maximum depth grid. For example the user may create a grid as TOPS – 200 as the base for the pit. Coal below this base would not be considered.
Seam file (.b35)
Seam B35 file used to list seams in stratigraphic order.
Density grid suffix
Usually RD
Density grid default
Usually 1.3 or 1.4. This value is used if the density grids don't exist
Washery Yield Suffix
A grid suffix such as YD. These grids will contain wash plant yield or recovery expressed as a percentage. See Section 5.
Washery yield Default
A default value used when the YD grid doesn’t exist. Yield is expressed in percent.
Sale value grid suffix
Usually SE or CV or BTU or in coal an energy value grid. The value of the coal must increase as the grid increases. Ash can't be used as a value. See note 1 and section 4.
Sale value/grade unit
Price of a SE unit. For example if SE varies from 28 to 33 and this value is 1, then sale price will be $28 to $33/tonne. See note 1
Sale value default
Energy value used if grid values don’t exist.
Sale value cutoff
Coal with less SE will be wasted. See Note 4
Minimum thickness
Coal less than this thickness will be wasted.
Pit recovery %
Allows for wastage of some coal. The lost coal is not treated as waste.
Pit slope (degrees)
Average slope for optimization.
Z sub blocks
An integer between 1 and 8 usually set at 4 or 5. The primary block size say 50x50x50 is divided to 50x50x10 for an input of 5. The optimizer may modify the Z value to meet slope inputs. So the block could be 50x50x11 or 50x50x12.7 where this combination better meets an input wall slope.
Minimum mining width
Allows trivial spotty pits to be removed. See note 5.
Waste mining cost ($/bcm)
Operating cost of mining waste. Should include drill and blast, loading and haulage.
Waste lift cost ($/bcm/m)
Extra haulage cost can be added for depth.
Waste exit elevation
Point at which waste is deemed to leave the pit rim. Depth costs are incremented to this elevation.
Waste Cost grid Suffix
Grids with the seam name and a WM suffix can be created using tools such as SQL. Refer Section 7. The optimizer will if they exist use these grids for costs.
Coal mining cost ($/bcm)
Coal mining costs expressed in $/bcm not $/tonne.
Coal lift cost ($/bcm/m)
Coal lift cost expressed in $ per bcm of coal per metre of lift to the exit elevation.
Coal exit elevation
Elevation at which coal exits pit.
Coal mining grid Suffix
Usually CM for coal Mining. These grids are expressed in $/bcm and typically are used where costs need to vary with depth or location or seam. See Section 7.
Coal wash cost ($/feed tonne)
Cost of washing coal in $/input or feed tonne. See note 6
Start discount factor
The first optimizer run will be run at this price.
End discount factor
The last optimizer run will be at this price. See note 7.
Discount step
Increments will be run between the above prices.
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The Optimiser menu
Table 2: Menu Parameters Output grid prefix
All output grids will be prefixed with this name.
Note 1: Value. The grade quality variable on which the sale price is based must increase with increasing
quality value. For example, higher values of BTU/lb or MJ /kg have higher sale values. Ash can not be used to value coal. Higher ash coal has less value than a low ash coal. If BTU/lb or MJ /kg is unavailable you could use a proxy such as (100- Ash%). See also section 4. Note 2: Output Model. To create nested pits, the first pit at say 30% of sale price is the input topography
for the second run at say 35% of sale price. To facilitate this cascading system the output optimum pit grids must be written to the input structure file. Note 3: Topography. As the optimiser block model is based on the topography grid, it is often advisable
to run on a coarser topography for optimisation. Thus optimisation may be run on a 50x50 mesh grid, while the original topography may be 5x5. If a weathering grid is unavailable then use topography. Note 4: Cutoff. All optimisers will waste coal or ore that is uneconomic. However coal below a cut-off or
market specification may have no market. Setting a cut-off will ensure coal below cut-off is wasted. Setting the cut-off to a low vale say 0, will allow the optimiser to set its own cut-off. Note 5: Minimum mining width. This option eliminates trivial pits which are less than this width in
diameter. These pits are usually uneconomic by the time a practical ramp is constructed. Using this option is not however optimal, these trivial pits are economic under the criteria given. Note 6: Wash cost. As the wash cost is measured in $/tonne it is often used to cover many other costs.
For example pit services (lighting, roads, pumps, supervision, rehabilitation etc) could be added to this figure. Note 7: End Discount factor. This value can exceed 1. For example if the value is 1.10, the coal is
valued at 110% of sale price. To complete the menu the user must decide to: •
Save
•
Save & Run or
•
Cancel.
Save will write two files in the project directory. These files are the .MNX commands which will be used by the optimiser and a .BAT file called Run_Opt.Bat that will run the MNX file. The save option should be
used when you intend to run the optimiser at the end of the day or overnight. Save & Run will create the same two files on disk as the Save option. Save & Run will immediately run the optimiser. Cancel will exit the menu and discard all entered values.
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The Optimiser menu
MNX File The MNX file is a J ob Control Language File J CL which is created using the information from the menu. The MNX file can be edited if required. A simple example file is shown below. //TER //DD SYSPRINT DSN=TRAINING.LOG ,DIS=NEW,UNIT=PACKA //DD GRDFILE DSN=MODEL.grd,DISP =OLD,UNIT=PACKA //DD QUALITY DSN=MODEL.grd,DISP =SHR,UNIT=PACKA //DD COS T DSN=cost.grd,DISP =OLD,UNIT=PACKA //DD SYS IN * //* INIT SEAMS=(SW1,SW2,AB,ST,DL,UGB,MGB1,MGB2, ULGB,LLGB,UDB,UDBS,LDBS,LDB,WGG1,WGG2, - ,) - DENSITY_DE FAULT=(1.4), - GRADE_QUALITY =(28), - YIELD_QUALITY=(80), - STRUCTURE_ DDNAME=GRDFILE, - QUALITY_ DDNAME=QUALITY - COS T_MODEL_ DDNAME=COST GRADE_P ARAMS GR ADE_CUT=18, - S ALE_PRICE=1.0, - GRADE_SUFF=SE, - DENSITY_ SUFF=RD, - YIELD_S UFFIX=YD, - DILUTION_THICK=0.0, - QUALITY _DILUTION=0.0, - YIELD_DILUTION=0.0, - MINIMUM_ THICK=0.3 WASH FEED_STOCK=0,WASH_REC=0,WASH_ COST=5 WASH FEED_STOCK=1.00,WASH_REC=1,WASH_ COST=5 WASH FEED_STOCK=100.00,WASH_REC=100,WASH_COST=5 ORE_COSTS COST_ OF_EXT=(5), - COST_ TO_P LANT=0.0, - R EFERENCE _RL=100, - COST_OF_ LIFT=0.001, - ORE_MINING_ REC=100, - COST_ GRID_S UFFIX=CM WASTE_COSTS COST_OF_ EXT=2, - R EFERENCE _RL=100, - COST_OF_ LIFT=0.001, - COST_GRID_SUFFIX=WM PIT_ PARAM SLOPE_ ANGLE=(45,45,45,45,45,45,45,45),Z_SUB=4, - MINIMUM_MINING_WIDTH=(0) COMPUTE TOP O=TOPS_ OPT, BASE =WGG2SF, WEATHER=BOW, OUTP UT_DDNAME=GRDFILE , OPT=OPT030, DESC=('Optimum pit discount 0.3','Surface 3'), FORCING_P AR=0.0,REPORT_P OINT=(10000,120000), LERC H=YES, FLOATING_ CONE=YES, CONE _CONV=2, OPTIMUM_PIT=YES, MAJ OR_CYCLES=50, SURFACE_ NUMBER_RE SET=YES, SET_SURFACE_NUMBER=3 EXIT
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THE LOG FILE CONTAINS OUTPUT REPORTS
SEAMS LISTED IN STRATIGRAPHIC ORDER.
WASHING COSTS ARE FIXED AT $5/FEED TONNE THE WASH TABLE LINES ARE DISCUSSED IN SECTION 6.
SLOPES ARE DEFINED IN 8 DIRECTIONS CLOCKWISE FR OM NORTH.
THE REPORT POINT OPTION WILL CREATE A LIST OF DATA AND COSTS AT THE XY COORDINATE ENTERED.
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How coal is valued in the optimiser
How coal is valued in the optimiser The pit optimizer uses a grade value like energy to determine the value of the coal. For example if 28kcla/kg coal is sold at $30FOB/tonne then the value could be expressed as $1.07/kcal. Thus 20kcal/kg coal would be valued at $21.42/tonne. Coal which is unmarketable, say coal below 18kcal/kg, should be wasted using the cut-off grade switch. Typical questions in optimization are: •
Should I optimize at the mine or at the port?
•
How to I optimize for extra elements?
•
What to do with bauxite and alumina?
•
What about multiple coal products?
Mine or Port It is generally best to optimize at the mine and remove the downstream costs from the optimization process. Using the above figures and downstream costs as in Table 3, coal can be considered sold at $20/tonne ($30FOB less $10 for downstream costs). •
•
FOB “Free on board” means the coal is sold free of any costs loaded on the ship. The supplier pays all costs to get it into the boat the buyer pays unloading and shipping costs. FIS “free in store” means the seller pays shipping and unloading and the coal is delivered to the buyer’s store. Table 3: Downstream costs RAIL HAULAGE
$
5.00
PORT CHARGES
$
2.00
ROY ALTIES
$
2.00
DEMURRAGE
$
1.00
TOTAL
$ 10.00
In this case the optimizer would use a sale value of 20/28 =$0.71/kcal. Optimizing at the mine makes sense as the downstream costs, while real, are not controllable by the mine. A mine can changing mining costs using contractors or larger equipment etc, but it can’t rapidly change rail port or royalty costs.
Extra Elements A typical multi element operation would be a gold copper project. Assume values such as $2000/ton for copper and $350/oz for gold and assume gold is modelled in grams/tonne and copper is modelled in %. This equates to $20.00/% copper and $11.25/gram for gold. To optimize, it is normal to create an equivalent metal grade. For example, gold could be equated to copper equivalent based on sale price. Often value or dollars is used as the common parameter. A more detailed example follows. In this case downstream costs like smelting are removed as they can’t be controlled by the mine. The sale price is Cu $1.00/lb and Au $350/oz. Both prices are reduced to account for smelting and refining costs and losses. Copper is concentrated to 25% copper and shipped and smelted for $200 per tonne of concentrate. With 4 tonnes of concentrate required per tonne of copper, this equates to $800 per tonne of copper. At a price of $1.00/lb the nett copper value is $2204.6 $800 =$1404.6/tonne or $0.639/lb. Gold also incurs a smelting and refining cost of $8.00 per ounce, reducing its price to $342/oz. Thus a gram of gold is valued at ($350-8)/31.1035 =$11.00/g Both the gold and copper incur processing losses in smelting and refining. For copper, a refining and smelting loss of 4% is incurred. This reduces the value to $0.639/lb * .96 =$0.613/lb. This equates to $1352 per tonne of copper, as copper grade is modeled in percentage terms a block is valued at
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How coal is valued in the optimiser
$13.52/% copper. Gold incurs a 5% smelting and refining loss. As 95% of the gold is realized after smelting and refining the nett value is $11.00 * .95 or $10.45/g. Because copper is modeled in percent and gold is modeled in grams, a dollar value can be determined for each block based on its metal content, the sale value of the metal and the mill recoveries. Using the mill recoveries of 85% ad 75% a variable DOLLAR can be determined as: DOLLAR
=
(Cu% x $13.52 x 0.85) +
(Aug x $10.45 x 0.75)
This variable DOLLAR is the basis for determining block values and is the main input for pit optimization.
Bauxite and Alumina In cases such as bauxite the process of refining bauxite into alumina adds value and the process of converting alumina to aluminium adds value. The average Australian 2006 export commodity values illustrate this value add: •
Bauxite averaged $22/tonne,
•
Alumina averaged $362/tonne and
•
Aluminum averaged $2974/tonne
What is measured in the ground and in the model is the bauxite or %Al or %Al2O3 and this is what needs to be optimised. In bauxite processing, the cost of caustic soda is critical and the elements that consume caustic such as silica or iron etc can be as critical in determining value as the alumina content. As with the gold copper example, some local logic is needed to determine the value based on these chemical components.
Multipl e Coal Products In this example a coal deposit creates three products. 1. 2. 3.
Coking sold at $80/tonne, Blending or middlings sold at approximately $30/tonne and Thermal sold at $50/tonne.
The coking coal is washed at a low SG and produces a coking coal of say 8% ash. The yield is approximately 50%. The reject from this wash is rewashed and produces a secondary product (middlings) with an ash of 25% and a yield of approximately 15%. The steaming coal has an ash of 13% and a yield of 70%. The steaming coal is not given a secondary wash. Grid suffixes are as follows: •
PY Primary yield of coking coal
•
SY Secondary yield of coking coal
•
PA Primary ash of coking coal
•
SA Secondary ash of coking coal
•
TY yield of thermal coal
•
TA ash of thermal coal
From an SQL point of view it is easier to have PY SY and TY for all seams with TY =0 on the coking coals and PY and SY =0 on the thermal coals. To value the coal a sales value grid can be created as: SV =80 x RD x PY/100 +50 x RD x TY/100 +50 x 0.60 x RD x SY/100 Note:
As the yields are in percentages they must be divided by 100.
As RD is used in creating the SV grid it must not be double counted. So when the optimizer is run a density default of 1.0 and a dummy RD suffix such as XX would be used.
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Washing Costs and Yield
Washing Costs and Yield The MNX file allows the user to manipulate washability data to reflect practical plant recovery. The menu doesn’t allow this flexibility as it assumes perfect plant efficiency. Users can edit the MNX file using the information given below. The fist example assumes all coal is washed with 100% recovery and a cost of $10/tonne. WASH FEED_STOCK=0,WASH_ REC=100,WASH_COST=10.000 WASH FEE D_STOCK=100.00,WASH_RE C=100,WASH_ COST=10.000 The expression WASH_FEED_STOCK refers to the value of the yield grid for the seam at that block. Say the yield grid suffix YD has a value of 70% then the actual yield used is raised to 100% as defined by the WASH_REC entries. Essentially the two entries define yield and cost and be plotted as shown in Figure 11. Here the implication is that all coal is bypassed (100% yield) and processing costs are constant at $10/tonne.
120
ACTUAL YIELD 100 L E I Y L A U T C A & T S O C
80
60
40
20
WASH COST/FEED TONNE
0 0
20
40
60
80
100
120
GRID INPUT YIELD
Figure 11: Washability Curves
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Washing Costs and Yield
In the next example, washery yield has been downgraded 5% to compensate for the slim core yield overstating true or practical yield. Costs are allowed to fall as the yield increases. This could reflect lower reject disposal costs. This example is shown in Figure 12. WASH FEED_STOCK=0,WASH_ REC=0,WASH_COST=10 WASH FEED_STOCK=5,WASH_ REC=0,WASH_COST=10 WASH FEED_STOCK=50,WASH_REC=45,WASH_COST=9 WASH FEED_STOCK=100,WASH_ REC=95,WASH_COST=8 100 90 80 70
D E L I Y L A U T C A
60 L E I Y
50 40 30 20
WASH COST/FEED TONNE
10 0 0
20
40
60
80
100
120
SLIM CORE MODELLED YIELD
Figure 12: Cost fall as yield rises and modeled slim core yield is made practical by de-rating 5%. The next example uses ASH as the feed stock (bolded below). Here the assumption is that low ash coal (below 12%) can be bypassed at 100% yield with a low cost of $3/tonne to cover crushing. Above 12.1% the recovery falls and the costs increase. Here ASH is a proxy for yield but in the syntax of the optimizer ASH is WASH_FEED_STOCK. This example is shown in Figure 13. GRADE_ PAR AMS GRADE_ CUT=0,SALE _P RICE =1, - GRADE_S UFF=SE, YIELD_SUFF=AS,DENSITY_S UFF=RD, - DILUTION_THICK=0.0,QUALITY_ DILUTION=0.0, - YIE LD_DILUTION=0,MINIMUM_THICK=0.3 WASH FE ED_ STOCK=0,WASH_R EC=100,WASH_COS T=3 WASH FE ED_ STOCK=12,WASH_ RE C=100,WASH_COS T=3 WASH FE ED_ STOCK=12.1,WASH_R EC=80,WASH_ COS T=9 WASH FE ED_ STOCK=100,WASH_RE C=0,WASH_COST=12
The washability definition must cover the range of input feed stock. So if you are using ash as the Feed stock and ash varies from 1 to 50% then this range must be defined. If you are using BTU as the feed stock and BTU varies from 5000 to 13000, then the definition must cover this range. The lines below would for example cover a BTU case WASH FEED_STOCK=0,WASH_ REC=0,WASH_COST=9 WASH FEED_STOCK=5000,WASH_REC=50,WASH_COST=9 WASH FEE D_STOCK=20000,WASH_RE C=100,WASH_COST=12
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Washing Costs and Yield
120
100
80 L E I Y
A C T U A L Y I E L D
60
40
20
WASH COST/FEED TONNE
0 0
20
40
60
80
100
120
ROM ASH
Figure 13: Wash yield and costs for an ASH feed stock
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Output Grids
Output Grids The result of the optimizer runs is usually a set of nested pits such as those shown in Figure 14. The naming convention used is a prefix and a suffix. The suffix 30, 40 110 etc represents the sale value. So the grid OPT080 represents an optimizer run at 80% of the sale price.
Figure 14: Example directory listing Each grid can be plotted in plan 3D or section. Each grid is assigned a surface number which shows the nested sequence. The colors indicate the incremental size of each nested pit. In Figure 15 the sequence is white, green blue as sale price increases.
Figure 15: Example pit with colour highlighting sequence of nested pits. When running nested pits some pits may not be economic. For example a sale price of 10% may not generate an economic pit. Similarly if using a 30% pit as the topography for a 32% pit, it is possible that there will be no additional economic material in this 2% increment. Obviously the generation of an optimum pit depends on the deposit characteristics and the costs applied. In both cases the optimizer will output the incremental grid say OP T10 or OP T32 as these grids are used as topography for the next increment.
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Report Points
Report Points The optimizer can output a report on the grids and costs at an X Y coordinate. The report point can be useful when validating a model and the costs used. The menu does not allow you to define a report point. It simply assigns a dummy coordinate of (1000,120000). You will need to edit this to be a coordinate inside your deposit. When the optimiser program runs the report point output is placed in a file with a name of the type: PitOptim_PointReportxxx07May02123519.txt Where xxx is the user id followed by the date. The contents of this file are shown below (left) and explained on the right. Processing Seam:TT23 **** Waste Layer **** Roof : 132.61 Floor: 127.94 Waste Extraction Cost: 4.62 Waste haulage Cost: 0.00 Waste haul time : 0.00 Waste to Plant : 0.00 Waste Haulage Factor : 1.00 Waste Mining Costs : -4.62 Insitu Value : -4.62 **** ORE Layer **** Roof : 127.94 Floor: 127.30 Waste Extraction Cost: 4.62 Waste haulage Cost: 0.00 Waste haul time : 0.00 Waste to Plant : 0.00 Waste Haulage Factor : 1.00 Waste Mining Costs : -4.62 Ore Density : 1.56 Ore Grade Var : 35.36 Ore Yield Var : 81.57 Ore Extraction Cost: 29.61 Ore haulage Cost: 0.00 Ore haulage time : 0.00 Ore to Plant : 0.00 Ore Haulage Factor : 1.00 Ore Mining Costs : -29.61 Tonnage of Ore : 1.56 Unit Sale Price : 35.3584 Product yield : 81.57 Sale Price : 44.87 Cost Milling : 0.00 Cost Mining : -29.61 Net Value Ore : 60.14 Insitu Value : 60.14
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1. 2.
3. 4. 5. 6. 7. 8. 9.
At this point TTIB has a cost of $4.62 so entry is minus (-4.62). The next layer is ORE or coal, note same cost $4.62 is reported. MRCOPN will only use this cost if the coal is wasted. Coal goes from 127.30 to 127.94 so its 0.64 metres thick. Density is 1.56 yield is 81.57 sale price is 35.36 so sale price per cubic metre is $44.87. The actual sale price is 2 x 44.87 =89.74/bcm (as FF =2 in this example) Coal cost is 29.61 (recall this cost is expressed as $/bcm) The final ore value is difference $89.74- 29.61) = $60.14/bcm As $60.14 is greater than 4.62 so we treat it as ore. If value was less than 4.62 then we would treat it as waste (EG low yield low price)
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Advanced costs using SQLs
Advanced costs using SQLs Minex users will be familiar with the power of grid SQL. This document presents some examples of using grid SQL to set costs for the optimizer. It doesn’t aim to train you in SQLs. Waste costs typically increase with depth. However a more complex case could involve: 1. 2.
Costs are high on the surface as waste is trucked out of pit and waste at depth is cheaper as it is back-filled and Thin waste is more expensive than thick waste. Thick waste can be mined with larger equipment.
In this case a grid with a suffix such as WM is created for each seam using an SQL. Assumptions are: 1. 2. 3.
The top 100 metres of waste material is trucked out of pit at $2.50/bcm, lower waste material is trucked in pit at $1.50/bcm. Bulldozers are used to rip thin waste less than 2 metres in thickness at $1.50/bcm. This material is then loaded by front end loader at $0.75/bcm. Thicker waste is drilled and blasted at $1.00/bcm and loaded by excavators at $0.50/bcm.
An SQL to create the WM grids would use the seam floor (SF) and seam interburden grids (IB) as input grids. A grid should be created as TOPS minus 100 (TOPS-100) and saved as TOPSm100. The IB and SF grids should exist in a merged grid so they exist everywhere. An SQL using these assumptions would read as follows: EXTERNAL TOP Sm100, SF, IB, WM ! X THIN AND DEEP SELECT X WHERE SF #NULL AND SF =TOPSm100 AND IB >= 2 IF SELECT Z WM =1.50 +1.00 WM =WM + 0.50 ENDIF
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Advanced costs using SQLs
! A THIN AND SHALLOW SELECT A WHERE SF #NULL AND SF >=TOPSm100 AND IB < 2 IF SELECT A WM =1.50 +1.50 WM =WM + 0.75 ENDIF
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Steep Dip Deposits The Minex optimizer uses a set of seams in stratigraphic order to generate the cost and revenue model. Waste below the base seam is not assigned a cost as the base seam is the logical pit floor. In steep dip cases where the pit wall slope is flatter than the seam this can cause problems. In Figure 16 the stratigraphy is A B C and the waste mining cost is $3/cubic metre. In the optimizer the waste above A, above B and above C are all assigned $3 costs. However the waste below C is not in the stratigraphic definition and is assigned a cost of $0. This can cause the pit to grow artificially in the area below the base seam. In these cases the user should introduce a new base seam below the C seam using grid manipulate. The new seam should be given a thickness of zero so there is no revenue introduced. This will then correct the optimum pit as shown in Figure 17.
3
0
3 3
A B 0
C Figure 16: Problem where seam dip is greater than wall slopes.
3
3
3 3
A B 3
C
D Figure 17: Adding seam D (with 0 thickness) corrects the problem
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System information
System information The optimizer is limited to input grids with less than 4,000,000 mesh points or a grid of 2000 x 2000 points.
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