Calculate Cut-off Grades
Pit Optimisation uses the following formula to calculate a cut-off grade for the processing methods, rock parameters, and elements defined on the Pit Optimiser form.
Tonnage into the mill per tonne mined is:
| Mining_dilution * Mining_recovery |
The amount of product into the mill per tonne mined is:
| Elmnt_grade * Mining_recovery |
Where Elmnt_grade is the grade in the ground.
The grade input to the mill is:
| (Elmnt_grade * Mining_recovery)/(Mining_dilution * Mining_recovery) = Elmnt_grade/Mining_dilution |
The mill recovery is:
| [(Elmnt_grade/Mining_dilution - Threshold)/(Elmnt_grade/Mining_dilution)] * Mill_recovery = [(Elmnt_grade - Threshold * Mining_dilution)/Elmnt_grade] * Mill_recovery |
The amount of product produced per tonne mined is:
| Elmnt_grade * Mining_recovery * [(Elmnt_grade - Threshold * Mining_dilution)/Elmnt_grade] * Mill_recovery = (Elmnt_grade - Threshold * Mining_dilution) * Mining_recovery * Mill_recovery |
The revenue per tonne mined is:
| (Elmnt_grade - Threshold * Mining_dilution) * Mining_recovery * Mill_recovery * Elmnt_price |
The main processing cost per tonne mined is:
| Mining_dilution * Mining_recovery * Process_cost * PCAF |
The element processing cost per tonne mined is:
| Elmnt_grade * Mining_recovery * Elmnt_cost |
The selling cost per tonne mined is:
| (Elmnt_grade - Threshold * Mining_dilution) * Mining_recovery * Mill_recovery * Elmnt_sell_cost |
If the material is processed, the cash flow per tonne is therefore:
| (Elmnt_grade - Threshold * Mining_dilution) * Mining_recovery * Mill_recovery * Elmnt_price - Mining_dilution * Mining_recovery * Process_cost * PCAF - Elmnt_grade * Mining_recovery * Elmnt_cost - (Elmnt_grade - Threshold * Mining_dilution) * Mining_recovery * Mill_recovery * Elmnt_sell_cost = (Elmnt_grade - Threshold * Mining_dilution) * Mining_recovery * Mill_recovery * (Elmnt_price - Elmnt_sell_cost) - Mining_dilution * Mining_recovery * Process_cost * PCAF - Elmnt_grade * Mining_recovery * Elmnt_cost |
If the material is rejected, the rehabilitation cost per tonne mined is:
| Rehab_cost |
Since the decision to process or not is made while the material is still in the ground, Mining_dilution and Mining_recovery do not have an effect on the rehabilitation cost.
In order to calculate a theoretical cut - off, we equate the cash flow per tonne (calculated above), plus the rehabilitation cost per tonne, to zero.
| (Elmnt_grade - Threshold * Mining_dilution) * Mining_recovery * Mill_recovery * (Elmnt_price - Elmnt_sell_cost) - Mining_dilution * Mining_recovery * Process_cost * PCAF - Elmnt_grade * Mining_recovery * Elmnt_cost + Rehab_cost = Zero |
We then take the necessary steps to solve this equation for Elmnt_grade and bring the Elmnt_grade items together on one side of the equation:
| Elmnt_grade * Mining_recovery * Mill_recovery * (Elmnt_price - Elmnt_sell_cost) - Elmnt_grade * Mining_recovery * Elmnt_cost = Threshold * Mining_dilution * Mining_recovery * Mill_recovery * (Elmnt_price - Elmnt_sell_cost) + Mining_dilution * Mining_recovery * Process_cost * PCAF - Rehab_cost |
Divide through by Mining_recovery:
| Elmnt_grade * Mill_recovery * (Elmnt_price - Elmnt_sell_cost) - Elmnt_grade * Elmnt_cost = Threshold * Mining_dilution * Mill_recovery * (Elmnt_price - Elmnt_sell_cost) + Mining_dilution * Process_cost * PCAF - Rehab_cost/Mining_recovery |
Give Elmnt_grade a single multiplier:
| Elmnt_grade * [Mill_recovery * (Elmnt_price - Elmnt_sell_cost) - Elmnt_cost] = Mining_dilution * Process_cost * PCAF + Threshold * Mining_dilution * Mill_recovery * (Elmnt_price - Elmnt_sell_cost) - Rehab_cost/Mining_recovery |
Divide through by the Elmnt_grade multiplier:
| Cut - Off =[Mining_dilution * Process_cost * PCAF + Threshold * Mining_dilution * Mill_recovery * (Elmnt_price - Elmnt_sell_cost) - Rehab_cost/Mining_recovery] / [Mill_recovery * (Elmnt_price - Elmnt_sell_cost) - Elmnt_cost] |
Or:
| Cut - Off = [Threshold * Mining_dilution * Mill_recovery * (Elmnt_price - Elmnt_sell_cost)] / [Mill_recovery * (Elmnt_price - Elmnt_sell_cost) - Elmnt_cost] + [Mining_dilution * Process_cost * PCAF - Rehab_cost/Mining_recovery] / [Mill_recovery * (Elmnt_price - Elmnt_sell_cost) - Elmnt_cost] |
If we remove the optional values (Mining_dilution, Mining_recovery, Threshold, Elmnt_sell_cost, Rehab_cost and Elmnt_cost) this simplifies to:
| Cut - Off = (Process_cost * PCAF)/(Mill_recovery * Elmnt_price) |