Economic Values
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:
1 Processing stream and its respective economic value
1 Waste dump and its respective economic value
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.
Simplified flow-chart of blocks’ destinations optimization.
Insider version
MiningMath insider version allows for the setting of economic values per period. Check all MiningMath versions here.
As you can see, in the Production tab, a new Economic Values option is enabled. You can use it to assign different economic values for each defined range.
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 ($/t) | 0.9 | |
Discount rate (%) | 10 | |
Dimensions of the blocks in X, Y, Z (m) | 30, 30, 30 | |
Table 1: Parameters for calculating the economic values.
Block Tonnes
Block Tonnes = BlockVolume * BlockDensity
Block Tonnes
= 30*30*30*[Density]
Tonnes Cu
Tonnes Cu = Block Tonnes x (Grade Cu/100)
Tonnes Cu
= [BlockTonnes]*([CU]/100)
Mass Au
Mass Au = Block Tonnes x Grade Au
Mass Au
= [BlockTonnes]*[AU]
Economic Value Process
Economic Value Process =
[Tonnes Cu x Recovery Cu x (Selling Price Cu – Selling Cost Cu)] +
[Mass Au x Recovery Au x (Selling Price Au – Selling Cost Au)] –
[Block Tonnes x (Processing Cost + Mining Cost)]Economic Value Process
= ([TonnesCu]* 0.88 * (2000–720)) + ([MassAu] * 0.60 * (12 – 0.2)) – ([BlockTonnes] * (4.00 + 0.90))
Economic Value Waste
Economic Value Waste = –Block Tonnes x Mining Cost
Economic Value Waste
= –[BlockTonnes] * 0.9
The example block in Figures 4-6 would generate -299,880$ 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.
Other costs and revenues
The economic value calculation is based solely on the values assigned to the blocks. However, if you need to incorporate additional costs and revenues, our economic functions are fully customizable. You can easily model them using our built-in calculator.
Alternatively, you can also use scripts to work with formulas in CSV format. The Labs section provides some custom-built apps that could be useful for that.
