Industry: Mining and Natural Resources Product: ModelRisk Application: Mineral Reserve Estimation
A single percentage-point swing in copper recovery moves the NPV of a 180-million-tonne polymetallic project by roughly $200 million. A 0.05% absolute drop in head grade — well inside the standard deviation of any infill drilling program — moves it by twice that. The JORC and NI 43-101 codes both demand that reserve estimates carry a confidence label (Proved / Probable / Possible), but the deterministic mid-case still routes capital, debt covenants, and stream financing decisions in most pre-feasibility work. The mid-case is the wrong number to defend in front of a bank credit committee.
A copper-gold-molybdenum project in the high Andes — 180 Mt nominal at 0.65% Cu, 0.35 g/t Au, 180 ppm Mo, 18-year mine life — was re-estimated in ModelRisk so that every line on the reserve statement carried an explicit P10/P50/P90, and every line on the financial model carried its full posterior over NPV. The point of the exercise is that the reserve is a curve, not a number: 80,000 Monte Carlo trials put recovered copper at P10 617 kt (Proved), P50 898 kt (Probable) and P90 1,304 kt (Possible), and the single-line 994 kt that had been carried for two years turns out to sit at the 64th percentile of that distribution.
Grade distributions inside a porphyry are right-skewed: a long tail of high-grade intercepts mixed with a thick body of low-grade halo. A Normal fit on Cu grade systematically understates both the upside and the downside, and produces negative grades in any honest simulator. The block model was fit instead with a LogNormal per metal:
Tonnage carried a separate LogNormal (mean 180 Mt, σ_log 0.18) reflecting block-model boundary uncertainty in a deposit with significant faulting. Recovery for each metal was modelled as a Beta, the only family that respects the 0-1 bound a recovery must obey: Cu mean 85% ± 5%, Au 70% ± 10%, Mo 60% ± 8%. Mining dilution (Triangular 5% / 10% / 15%) and ore loss (Triangular 3% / 7% / 12%) entered the geological mass balance directly — dilution adds waste tonnes at zero grade, which lowers head grade by 1/(1+d) before milling.
1/(1+d)
Stacking these inputs through a Monte Carlo of 80,000 trials produces the full posterior over recovered copper shown above. The classification reads directly off the CDF: P10 ≈ 617 kt of recovered copper underpins the Proved category, P50 ≈ 898 kt the Probable, P90 ≈ 1,304 kt the Possible. The deterministic mid-case — naïvely 180 Mt × 0.65% × 85% = 994 kt — sits between Probable and Possible and is taken in many in-house spreadsheets as "the reserve." The probabilistic view says it is the 64th percentile of a wide distribution.
The deterministic financial model returned a tidy NPV of roughly $870 million at $8,500/t Cu, $2,000/oz Au and $45,000/t Mo. The probabilistic NPV looks very different:
Mean NPV ($890M) is comparable to the deterministic number, but the distribution carries a long left tail, and the probability of a negative NPV is about 30% — a number the point estimate cannot show. P10 NPV is about -$950M; P90 (≈$2,930M) is roughly three times the mean. A bank looking at this curve underwrites differently from a bank looking at a single bolded number on slide nine.
Sensitivity ranking confirmed where the year's drilling and metallurgical budget should go.
Copper price and copper grade dominate, with the grade tornado leg almost the same size as the price leg — the project is roughly as exposed to its drilling programme as to the LME. Recovery is third, ahead of unit OPEX and capex overrun. Mining dilution and the gold-plus-moly by-product credit close out the chart. The verdict for the year's budget: $6.4M to infill drilling in the central high-grade zone, $2.1M to additional locked-cycle flotation testwork on the transitional ore, and a price-hedge framework brought to the board for the first two years of production.
Stress-testing copper price ±20% (matching the rough LME band of the last decade):
At Cu = $6,800/t the project's mean NPV falls to roughly $225M and P(NPV < 0) climbs to about 46% — a reserve that should be classified Probable at best, with development gated on hedge or stream. At Cu = $10,200/t the curve shifts far enough right that the mean NPV roughly doubles to about $1,660M and the bulk of the distribution clears the breakeven line — full Proved-and-Probable conversion is defensible. The reserve statement therefore carries a copper-price assumption attached, not a single number defended as "the reserve."
grade / (1 + d)
Mineral reserve estimation is not a number — it is the conditional distribution of recoverable metal given the drill record, the metallurgy, and the price deck the project will actually live through. Monte Carlo simulation in ModelRisk is what makes that conditional distribution computable, classifiable under JORC, and defensible in front of the people writing the cheques.