MiningMath

MiningMath

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5. Calculator stage

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Note: Using the internal calculator is not a required step for creating scenarios and optimizing your model. It is only required if you don’t have economic values or if you need to derive new fields not present in the original data.

By using the calculator you can define new fields based on your imported values. Any calculation can be done in the Function tab.

Internal calculator to define economic value.

Example

The most common use of the calculator is to create new economic values. You can learn more about destinations required in the explanation below.

MiningMath does not require pre-defined destinations ruled by an arbitrary cut-off grade. Instead, the software uses an economic value for each possible destination and for each block. The average grade that delineates whether blocks are classified as ore or waste will be a dynamic consequence of the optimization process.

Therefore, MiningMath requires at least two destinations: 1 processing stream and 1 waste dump. Therefore, each block must be associated with:

  • 1 Economic value for the processing plant
  • 1 Economic value for the waste dump

MiningMath can determine the best destination option during optimization without the user pre-setting it. If you don’t have economic values defined in your model, you can use the example below as a guide to calculate them.

Note: Even blocks of waste might have processing costs in the economic values of the plant. Therefore, non-profitable blocks would have higher costs when sent to process instead of waste.

Note: If you have any material that should be forbidden in the plant, you can use economic values to reduce the complexity and runtime, as mentioned here.

The definition of economic values involves considering factors such as the destination of the block, grades, recovery, mining cost, haul costs, treatment costs, blasting costs, and selling price.

An example of the calculation is provided with the calculation parameters listed below.

Description Cu (%) Au (PPM)
Recovery
0.88
0.6
Selling price (Cu: $/t, Au: $/gram)
2000
12
Selling cost (Cu: $/t, Au: $/gram)
720
0.2
Processing cost ($/t)

                  4

Mining cost ($/t)
                 0.9
Discount rate (%)
                 10
Dimensions of the blocks in X, Y, Z (m)
          30, 30, 30

Block Tonnes

  1. Block Tonnes = BlockVolume * BlockDensity

  2. Block Tonnes = 30*30*30*[Density]

Tonnes Cu

  1. Tonnes Cu = Block Tonnes x (Grade Cu/100)

  2. Tonnes Cu = [BlockTonnes]*([CU]/100)

Mass Au

  1. Mass Au = Block Tonnes x Grade Au

  2. Mass Au = [BlockTonnes]*[AU]

Economic Value Process

  1. Economic Value Process =
    [Tonnes Cu x Recovery Cu x (Selling Price Cu – Selling Cost Cu)] +
    [Mass Au x Recovery Au x (Selling Price Au – Selling Cost Au)] –
    [Block Tonnes x (Processing Cost + Mining Cost)]

  2. Economic Value Process = ([TonnesCu]* 0.88 * (2000–720)) + ([MassAu] * 0.60 * (12 – 0.2)) – ([BlockTonnes] * (4.00 + 0.90))

Economic Value Waste

  1. Economic Value Waste = –Block Tonnes x Mining Cost

  2. Economic Value Waste = –[BlockTonnes] * 0.9

The block in the example above would generate -299,880$ if sent to the process, and –55,080.1$ if discarded as waste. Therefore, this block might go to waste, since it would result in less loss than when it is processed. MiningMath defines the best destination regarding the set of constraints throughout the time, thus this decision is a lot more complex than the example above in most cases.

Tip: You can use the calculator to define multiple economic values. For example, what if the selling price or selling cost of Cu varies? These alternative scenarios can be evaluated later on with the help of our decision tree. To learn more about the calculator click here.

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