CAPÍTULO 4. PRESENTACIÓN Y DISCUSIÓN DE RESULTADOS
4.1 Matriz de codificación de resultados
Overview
To generate an optimal pit for a ore deposit where the net value of each block in the model must be calculated automatically by the Pit Optimiser from given sale prices and costs. As an
additional requirement, the resultant optimal pit must have wall slope angles of no greater than 45 degrees around the entire wall of the pit.
Requirements
The data files required for this exercise are: gold.mdl, topo1.dtm, topo1.str
These files are located in the dem/training/pitopt directory where Surpac Vision has been installed.
Getting started
Set your current working directory to be the directory containing the files to be used for this exercise. To do this, left click with the mouse on the directory in the navigator and then right click to pop up a menu. Select Set As Work Directory from this menu.
Display the block model menu by right clicking with the mouse at the end of the main menu bar (to the right of the Help menu). When discussing any block model functions in this tutorial, they will be referred to from this menu.
Open the block model file gold.mdl by selecting this file from the navigator with the left mouse button and while holding down this button, dragging the mouse pointer into the graphics viewport.
The block model status item should appear at the bottom of the Surpac window as shown below:
From the Block model menu, select Summary. This will display a form summarising the properties of the block model and should appear as follows:
The important features of the block model to note are the user block size of 20m x 20m x 20m and that four levels of sub-blocking have been allowed making the minimum possible block size 5m x 5m x 5m.
In addition, it can be seen from the list of attributes that we are dealing with an ore deposit where the background value of gold is -99.00 and there is also an ore_type attribute that classifies the different ore materials in the model by an integer value.
From the information in the block model, it can be seen that there is no attribute containing the net value for each block and so the Pit Optimiser will have to automatically calculate it.
Press Apply on the form to close it.
From the Block model menu, select Display, to display the entire block model. The following form should appear:
Fill in the form as displayed above and press Apply to draw the model with block faces. The model should be centred in the graphics viewport as the Rescale option has been checked and should look similar to the image below:
To get a better indication of where the ore deposit is located in the block model, a graphical constraint can be added to display only the blocks where the gold value is greater than zero.
From the Constraints menu, select New graphical constraint, enter the information as shown below and Apply the form.
The block model is displayed as shown below:
Colouring the blocks by the gold grades shows the quality distribution throughout the deposit. The gold grades for this deposit range from values of 0.02 to 15.24. In this example, the gold grades will be coloured by the range 0,16,2:
From the Display menu, select Colour model by attribute, enter the information as shown below and Apply the form.
Press Apply to colour the model using the above grade range.
The block model should appear as shown below:
Rotate the constrained block model around to gain familiarity with the deposit.
The object of this exercise is to generate the base of the pit for this deposit that will return the most profit at a given sale price.
Before entering the pit optimisation parameters, we must set the units that will be used when specifying the maximum allowable slope angles for the optimal pit. The two options available are decimal degrees or gradients. For this exercise, we will choose decimal degrees.
From the Customise menu, select Default preferences, then click on the Coordinate System/Units tab pane as highlighted in the image below.
From the Block model menu, select Pit optimisation. The following form will appear prompting you to enter the name of the parameters file.
The parameters file is a file created to store all the pit optimisation parameters that are entered on the next form so that on subsequent runs of the pit optimisation it is possible to redisplay all the parameter values that were previously entered. Modifications can then be made to these parameters and the pit optimiser can be run again. All modifications will be saved back to the parameter file.
The parameter file has a .pop extension. Enter in gold_$unit for the parameter file name for this example.
Press Apply to display the Pit Optimiser parameters form.
As can be seen above, the form is made up of five different tab panes labelled Ore Type, Mining Costs, Slopes, Vertical Limits and Optimisation.
Parameters for each of these tab panes should be entered in the order they appear and are discussed in the following pages:
Ore Type
This tab pane is used to identify whether a block is an ore block or a waste block. It also tells the Pit Optimiser whether it has to calculate the net value for each block or whether the value is already stored in the model.
If you click on the down arrow button on the Method combo box, you will see there are three different methods available - $/unit, $/mass and $/volume.
Select $/unit from the Method combo box.
For this exercise, the $/unit option from the Method combo box has been selected as this is the only method that automatically calculates the net value for each block given sale prices, milling and mining costs. For this method, the sale price must be stated in dollars per unit of ore (e.g.
$/g). The other two methods, $/mass and $/volume, require the net value for each block to be already calculated.
Each of the three different methods is discussed in detail below:
$/unit
With this method, the net value for each block is automatically calculated from the sale price, milling costs and mining costs that will be defined later for each ore type in the model. The sale price for the ore must be expressed in monetary units per unit of ore where the unit of ore is the same unit of measurement as the quality measurement of the ore.
For example, if grades for the ore material to be mined are measured in grams per tonne (g/t), the unit of measurement would be a gram and hence, sale prices need to be expressed as dollars per gram ($/g).
Alternatively, if grades for the ore material to be mined are measured in percentages (%), the unit of measurement would be a percent and hence, sale prices need to be expressed as dollars per percent of ore ($/percent).
It is important to note that using this method to define the sale price, the net value for each block does not have to be calculated and stored in the model before running the pit optimisation. The Pit Optimiser will automatically calculate the net value for each block from the sale prices, mining costs and milling costs that have been assigned for each different ore type.
$/mass
To use this method, the block model must contain an attribute that stores the net value for each block. This must be calculated prior to performing the optimisation and must be expressed in monetary terms per mass unit of material within a block (e.g. dollars per tonne).
The net value for a block can be calculated using the Attributes – Maths function, if the sale price, mining costs and milling costs are all stored as attributes in the model. As mentioned earlier, the net value for a block is calculated as follows:
Net Value = Sale Price – (Mining Costs + Milling Costs)
If any additional costs need to be factored in, they too can be added into the calculation.
To use this method, the specific gravity for each different ore type must be known in order for the Pit Optimiser to work with mass units.
This method assumes the net value assigned to each block is correct and any blocks with a negative or zero value are waste and air blocks respectively, and any blocks with a positive value are ore blocks. Special care must be taken when calculating the net value for each block as any errors will result in an incorrect optimal pit being generated for the deposit.
$/volume
Similarly, the $/volume method requires a net value attribute to be stored in the model. The net value must be expressed in monetary terms of per volume unit (e.g. dollars per cubic metre). This method only uses volumes to determine the optimal pit for the deposit.
Ore Type
If you click on the down arrow on the Ore Type combo box, you will only be able to select one of the integer attributes that are stored in the model.
Select the ore_type attribute from the Ore Type tab pane.
The Ore Type attribute is an integer attribute that classifies each block as belonging to a
particular ore type. Each different ore type is assigned a unique integer and different sale prices, costs and recovery properties can be defined for each different ore type. The Ore Type attribute can be assigned using the Attributes – Maths (MC – add link) function from the block model menu.
In our block model, the Ore Type attribute is called ore_type and each block has been given an ore_type value of one. This means that all the blocks in the model are ore blocks (not waste) and therefore will be processed by the Pit Optimiser. In reality, only a portion of blocks in the model are actually part of the ore deposit and hence the Pit Optimiser will use the Sale Price Curves (discussed later) to determine if a block is really an ore block or is actually waste.
Select the ore_type attribute from the Ore Type combo box. Next to this combo box is a button labelled Populate Tables. This button relates to the Sale Price Curves and Milling Cost Curves tab panes at the bottom of the Ore Type tab pane and is used to populate the Ore Type combo box in these tab panes. It looks at the ore_type attribute and displays all the possible unique integer values assigned to this attribute into the combo box for selection.
SG (Optional)
The SG field is an optional field and should be left blank if there is no specific gravity field in the model. For this exercise, leave this field blank.
If the specific gravity / density for each block in the model is stored as an attribute, this attribute should be selected here so that tonnages for the ore can be calculated.
For this exercise we will leave this field blank and assign a default SG for gold later when defining the Sale Price Curves...
Grade
If you click the down arrow on the Grade combo box, all the possible real, float and integer attributes in the model will be listed.
Select the gold attribute from this list.
The Grade field is used to specify the quality attribute in the model for the material being mined or the material that determines whether an ore block classified by the Ore Type attribute (MC – add link) is to be treated as ore or waste given grade cutoffs for this attribute. The grade cutoffs are defined when setting up the Sale Price Curves (discussed later).
In this exercise, the attribute of concern is the gold attribute. Select gold from the Grade combo box on the Ore Type tab pane.
Yield
If you click the down arrow on the Yield combo box, all the real, float and integer attributes in the model will be listed.
It is possible to factor in different process plant recoveries depending on a Yield attribute. For example in a gold deposit, it could contain the percent of oxide ore in each ore block, and the mill recovery would increase as the oxide content increased.
If you are modelling processing recovery on the input grade to the mill and/or the ore type, or are using a fixed recovery, then you should choose the same attribute you selected for the grade attribute, or leave it blank. By default it will be set as equal to the grade attribute.
Select the gold attribute from the Yield combo box on the Ore Type tab pane to indicate the gold grade will be used to model our milling recovery.
Sale Price Curves
To work out the sale price for each ore block in the model so the Pit Optimiser can calculate its net value, mathematical curves can be set up for each ore type.
For complex pricing structures, several grade cutoffs can be used to define different sale prices for different qualities of the ore. The sale price for each block will be linearly interpolated from the curve given its quality value.
Ore Type
Click on the Populate Tables button to list all the different ore types in the model in the Ore Type combo box in the Sale Price Curves tab pane. These values are taken from the Ore Type field located to the left of the Populate Tables button.
Select 1 from the Ore Type combo box.
The Ore Type field will allow you to set up a sale price curve for a particular ore type in the model.
For this exercise, we will set up a price curve for Ore Type 1. Note that this is the only value available to choose from because the ore_type attribute in our block model considers every block to be an ore block.
Sale Price
Enter in a value of $23.00 for the Sale Price of the ore material after it has been extracted and processed through the mill.
This is where the sale price for a particular ore type is entered. The sale price must be expressed in terms of monetary units per unit of ore material.
In this example, the grades have been measured in grams per tonne (g/t) and so the units used to specify the sale price is per gram.
A value of $23.00 for the Sale Price indicates the price is $23.00 for a gram of gold.
If the grade has been measured in % metal per tonne, and the metal value was $10,000/tonne, then the sale price would be $ value of one percent metal per tonne ie 1% x $10,000 = $100.
Note a grade of 3% would be stored in the grade attribute as a value of 3 and not 0.03 in order for the above example to work correctly.
Grade Cutoff
Enter a value of 0.0 for the Grade Cutoff of the ore material to indicate the sale price specified in the previous field only applies to blocks which have a grade value above 0.0. Any block with a value below 0.0 will be treated as waste.
The Grade Cutoff value applies to the Grade attribute described above. The value entered in this field represents the lowest grade that must be satisfied in order for the Sale Price to apply. For example you may specify that any block with a grade of less than 0.01 g/t should have a sale value of $0
In our example, we will say any block with a gold grade value greater than or equal to 0.0 is considered to be part of the ore resource. The optimiser will still determine if an ore resource block should be treated as an ore block or as a waste block, by calculating the respective value of the block when considered as ore and then as waste.
Default SG
Specify a default specific gravity for Ore Type 1 to be a value of 2.5. This default value will apply to any block that does not have an SG value specified in the SG (Optional) field that was
discussed above.
The Default SG value for each different ore type can be specified in this field. This value will apply to all blocks that do not have an SG specified by the attribute selected in the SG (Optional) field.
As we did not specify an SG field, all ore blocks will have an SG value of 2.5.
Recovery (%)
The last field to define for the Sale Price Curve is the mining recovery percentage. This recovery percentage is applied to the block tonnage to determine the proportion of the ore material that is recovered from the mine for milling. The remainder of the ore is lost and has no value.
Enter in a value of 100.0 % in the Recovery (%) field to indicate that 100 % of all ore blocks with an Ore Type of 1 are recovered during mining.
For this exercise, it is assumed 100 % of the ore is recovered for the mill after mining.
Sale Price Curve Definition
The Sale Price Curve defined implies any block with a gold grade value of greater than or equal to 0.0 will be sold for $23.00 per gram and 100 % of this ore will be recovered after mining for processing in the mill. All blocks that have a gold grade value of less than zero will be treated as waste blocks and will have a sale price of $0.00 per gram associated with it. Essentially, a constant sale price curve has been defined.
More than one entry can be made for each different ore type defining different sale prices and recovery values for different grade cutoffs. This will result in a cost curve being formulated and the sale price for each grade value will be linearly interpolated if it falls between the two cutoff values. The next exercise will show an example of a complex sale price curve.
So far, the Ore Type tab pane should appear as follows:
Now the milling cost curves can be defined. Left click on the Milling Cost Curves tab pane on the Ore Type tab pane to display the table where the milling cost curves are defined for each ore type.
The following information is required to set up a milling cost curve:
Ore Type
Select 1 from the Ore Type combo box. The values in the combo box should have already been populated when the Populate Tables button was pressed when the Sale Price Curves were being defined.
The Ore Type combo box is used to select the ore type for which a milling cost curve is to be defined. We will set up a Milling Cost Curve for Ore Type 1.
Mill Grade
Enter in a Mill Grade of 0.0 to define a milling cost associated with any ore blocks that have a mill
Enter in a Mill Grade of 0.0 to define a milling cost associated with any ore blocks that have a mill