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.

Formatted example

Figure 2 provides an example of a block model prepared and ready to be imported into MiningMath using the Marvin block model - based on data available in the MineLib1 repository.

Optional fields inside the block model are listed below:

Figure 2: Example of a block model read to be imported.

Each field related to Economic Value (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 illustrate the calculation of economic values, an example is shown based on the block with indices (IX, IY, IZ) = (17, 22, 7), highlighted in Figure 2. The calculation parameters are described in the table from Figure 3.

Figure 3: Parameters for calculating the economic values.

2. Economic Value: Calculation

2.1. Block Tonnes

  • Block Tonnes= BlockVolume x BlockDensity

  • Block Tonnes = 30 m x 30 m x 30 m x 2.68 t/m³

  • Block Tonnes = 72360.00 t

2.2. Tonnes Cu

  • Tonnes Cu = Block Tonnes x Grade Cu/100

  • Tonnes Cu = 72360 t x 0.635556/100

  • Tonnes Cu = 459.89 t


2.3. Mass Au

  • Mass Au = Block Tonnes x Grade Au

  • Mass Au = 72360 t x 0.334444 g/t

  • Mass Au = 24200.37 g

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 = [459.89 t x 0.88 x (2000 – 720)$/t] + [24200.37 g x 0.60 x (12 – 0.20)$/g] – [72360.00 t x (4.00 + 0.90)$/t]

    • Economic Value Process = $ 334,793

2.5. Economic Value Waste

    • Economic Value Waste = –Block Tonnes x Mining Cost

    • Economic Value Waste = –72360.00 t x 0.90 $/t

    • Economic Value Waste = – $65,124

Therefore, $ 334,793 will be the economic value of the block if it is sent to the process and $ -65,124 will be the economic value if it is discarded as waste. MiningMath will be responsible for defining the appropriate destination for each mined block throughout the time.

Do you want more details on how to calculate Economic Values?

The video below exemplifies the calculation process in case you have any doubts.

AVOID COMMON MISTAKES

FURTHER READING