Economic Values

1. Introduction

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.

1.1. Destinations required

MiningMath requires two mandatory destinations at least:

    • 1 Processing stream

    • 1 Waste dump

Therefore, each block must be associated with:

    • 1 Economic value for the processing plant

    • 1 Economic value for the waste dump

Notes:

  1. 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 the process instead of the waste.

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

Figure 1: Simplified flow-chart of blocks' destinations optimization.

2. Economic Value: 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 based on the block with indices (IX, IY, IZ) = (1, 1, 1), highlighted in Figure 2. The calculation parameters are described in the table from Figure 3.

Figure 2: Parameters for calculating the economic values.
Figure 3: Internal Calculator.

2.1. Block Tonnes

  • Block Tonnes= BlockVolume x BlockDensity

  • Block Tonnes = 30*30*30*[Density]



2.2. Tonnes Cu

  • Tonnes Cu = Block Tonnes x (Grade Cu/100)

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






2.3. Mass Au

  • Mass Au = Block Tonnes x Grade Au

  • Mass Au = [BlockTonnes]*[AU]

Figure 4: Block model calculations.

2.4. 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 x (2000–720))+([MassAu]*0.60*(12–0.6))–([BlockTonnes]*(4.00 + 0.90))

Figure 5: Process Economic Value calculation.

2.5. Economic Value Waste

    • Economic Value Waste =
      = –Block Tonnes x Mining Cost

    • Economic Value Waste = –[BlockTonnes]*0.9

Figure 6: Economic Value Waste calculation.

The first block in this example 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.

AVOID COMMON MISTAKES

FURTHER READING