MiningMath

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A unique approach to maximizing NPV

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Economic Values

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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.

Destinations required

MiningMath requires two mandatory destinations at least:

Therefore, each block must be associated with:
  • 1 Economic value for the processing plant

  • 1 Economic value for the waste dump

  • 1 Processing stream

  • 1 Waste dump

Notes:
  • 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.

  • 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.

Animation (click to see): Simplified flow-chart of blocks' destinations optimization.

Calculation

Each field related to Economic Value (Process/Waste) must report the value of each block as a function of its destination (Process or Waste in this example), grades, recovery, mining cost, haul costs, treatment costs, blasting costs, selling price, etc. The user is not required to pre-set the destination, as the software will determine the best option during the optimization.

To calculate the Economic Values you can use MiningMaths’s internal calculator, available at the “Function” option inside the “Model” tab. To illustrate the calculation of economic values, an example is shown below. The calculation parameters are listed in Table 1.

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

Table 1: Parameters for calculating the economic values.

Figure 1: Internal Calculator.
Block Tonnes
  • Block Tonnes = BlockVolume * BlockDensity

  • Block Tonnes = 30*30*30*[Density]

Figure 2: Block model calculations.
Tonnes Cu
  • Tonnes Cu = Block Tonnes x (Grade Cu/100)

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

Figure 3: Block model calculations.
Mass Au
  • Mass Au = Block Tonnes x Grade Au

  • Mass Au = [BlockTonnes]*[AU]

Figure 4: Block model calculations.
Economic Value Process
  • 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)]

  • Economic Value Process = ([TonnesCu]* 0.88 * (2000–720)) + ([MassAu] * 0.60 * (12 – 0.6)) – ([BlockTonnes] * (4.00 + 0.90))

Figure 5: Process Economic Value calculation.
Economic Value Waste
  • Economic Value Waste = –Block Tonnes x Mining Cost

  • Economic Value Waste = –[BlockTonnes] * 0.9

Figure 6: Economic Value Waste calculation.

The example block in Figures 4-6 would generate -299,880$ if it is 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 prejudice than when it is processed. MiningMath defines the best destination regarding the set of constraints throughout the time, thus this decision a lot more complex than the example above in most cases.

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