Copper Porphyry Mine Optimization in Chile’s Atacama Region

Scenario

A Tier-1 copper porphyry project in northern Chile’s Atacama Desert faces steep haul distances (2.8 km average), high power costs, and stringent water-use regulations. The mine must balance ore throughput with waste stripping ratios and community water-sharing agreements — limiting processing capacity to 85,000 tpd. A revised mine plan requires recalculating the cut-off grade to maximize NPV while respecting a 12% maximum annual dilution allowance and tailings storage constraints.

Given Data

• Mining Cost: $6.20/ton (includes diesel, labor, and haulage escalation)
• Processing Cost: $11.40/ton (includes grinding, leaching, and reagent costs; elevated due to low-grade oxide-sulphide blend)
• Recovery Rate: 82.3% (lower than baseline due to increased clay content in newly exposed zones)
• Metal Price: $3.72/lb (LME 3-month forward, USD)

Calculation

The Cut-Off Grade (COG) is calculated using the standard economic cut-off formula:

$$ \text{COG} = \frac{\text{Mining Cost} + \text{Processing Cost}}{\text{Metal Price} \times \text{Recovery Rate} \times \text{Conversion Factor}} $$

Where conversion factor accounts for unit consistency: since metal price is in $/lb and COG is expressed as % Cu (i.e., lb Cu per 100 lb ore), we use:

• 1 ton (US short ton) = 2000 lb → 1% grade = 20 lb Cu/ton ore
• So, effective factor = 20 lb/ton per % grade

Rearranged for % grade: $$ \text{COG (%)} = \frac{\text{Total Cost/ton}}{\text{Metal Price ($/lb)} \times \text{Recovery Rate (decimal)} \times 20} $$

Plugging in values:

• Total cost/ton = 6.20 + 11.40 = $17.60
• Recovery rate = 0.823
• Denominator = 3.72 × 0.823 × 20 = 61.2252
• COG = 17.60 / 61.2252 ≈ 0.2874 → 0.29% Cu

Result and Decision

The calculator returned 0.29% Cu, up from the prior 0.24% cut-off. This led to reclassification of ~12.4 Mt of marginal stockpile material as waste, reducing processing load and extending leach pad life by 11 months. The updated pit shell was optimized using this COG, increasing projected mine life by 2.3 years and improving 5-year NPV by $214M (8.7%).

Lesson

Small changes in recovery rate or cost inputs disproportionately impact COG — especially in low-margin, large-scale operations. Always re-run the calculation when metallurgical testwork updates recovery estimates; a 3.7% drop in recovery lowered COG viability by 0.05% — enough to shift >10 Mt of material across economic boundaries.