Industry: Mining and Natural Resources
Product: ModelRisk
Application: Mine closure planning

A 50-year AMD bill the average could not see

An open-pit copper mine in northern Chile, four years from the end of mining at 78 kt/yr Cu cathode, posted a deterministic closure-cost provision of $185M against a regulator-required surety of 100% of expected liability. The Monte Carlo rebuild put the mean closure cost at $208M but the 95th-percentile at $324M — and, as the cost distribution below shows, the deterministic provision sits down at the 41st percentile, below both the mean and the median.


The driver of that right skew is acid-mine drainage: low-probability, high-impact pyrite-oxidation outcomes in the waste-rock dump that the deterministic linear-extrapolation cost model could not represent. The surety filing was raised by $64M; the alternative was a material chance of inadequate provisioning within 25 years. Closure-cost forecasting is a 50-year present-value problem with heavy-tailed environmental dynamics, and the deterministic NPV is almost always the wrong moment of the cost distribution.

Where acid-mine drainage actually lives

The waste-rock dump at this mine has an average sulphide content of 1.8% S, an active footprint of 2.4 km², and a pyrite-oxidation rate that depends nonlinearly on oxygen ingress, water flux, and microbial-community structure. The deterministic model assumed steady-state AMD load: 1.3 m³/min at pH 3.1, sulphate 4,800 mg/L, lime treatment cost $0.92/m³, NPV at 5% over 50 years = $42M.

The probabilistic rebuild replaced that single line with:

• AMD generation rate: LogNormal(μ = ln 1.3, σ = 0.55) m³/min — right-skewed, calibrated to 38 analogue dumps across the Atacama and northwest Argentina.
• pH evolution: mixture model — 72% probability the dump stabilises at pH 3.0-3.8 by year 15, 28% probability of acidic-flush events triggered by storms above the 1-in-30-year return period.
• Treatment unit cost: LogNormal(μ = ln 0.95, σ = 0.30) $/m³, escalating with a 2.4% real-cost-of-lime CPI.
• Treatment-plant lifetime: Weibull(k = 2.6, λ = 22) years before major refurbishment — meaning two to three plant rebuilds across the 50-year horizon.

Mean AMD-treatment NPV over 50 years = $58M; P90 = $99M; P95 = $123M. The deterministic $42M sat around P40 — a low number presented as the answer.


Closure-cost components

Total closure cost is the sum of six components, each modelled separately:

The components are not independent — a regulator-driven scope-of-work change tends to lift all six together. The model applied a Gaussian copula with ρ = 0.45 across the six lines; the correlated total has a P90 of $288M and a P95 of $324M, materially above what an independence assumption would predict.


Why Monte Carlo, not a point estimate

The deterministic provision was $185M. The Monte Carlo mean was $208M, the P95 was $324M, and the right-skew came almost entirely from the AMD tail. The deterministic answer was below both mean and median — by construction, since it modelled the central pathway only. A 50-year liability with a heavy-tailed driver requires a distributional view; anything else under-provisions the regulator's surety calculation.

Tornado: what's actually moving the closure bill


AMD treatment NPV dominates with ±$28M of spread. Waste-dump capping is second. Tailings-dam closure and regulatory-scope drift round out the top four. The bottom three components together account for less than 10% of total P10-P90 spread.

What the model changed

• Closure provision raised from $185M to $232M (mean + 0.25 σ contingency).
• Surety bond increased $64M to align with regulator's 95th-percentile expectation.
• Capital allocated to a $14M dry-stack tailings retrofit, dropping waste-dump capping P90 by $18M — net $4M expected saving.
• Long-term water-treatment plant designed for 2× nominal capacity, dropping P90 AMD-NPV by $22M for a $7M upfront cost.

ModelRisk functionality used

• Compound AMD cost model combining LogNormal generation rate, mixture-model pH evolution, LogNormal unit cost and Weibull plant-rebuild cycles into a 50-year NPV with mean $58M and P95 $123M.
• Gaussian copula across six cost components with ρ = 0.45, raising joint P95 by $19M versus an independence assumption.
• Mixture model for AMD pH trajectory — 28% probability mass on acidic-flush events that the deterministic single-pathway model could not represent.
• NPV under stochastic discounting with the long-bond yield modelled as Ornstein-Uhlenbeck around 4.5%, so present-value variability captures both cost and rate uncertainty.
• Tornado at P95 rather than mean, ranking inputs by their contribution to the tail rather than the central case — what matters for surety, not what matters for budget.

A 50-year provision sized to the deterministic mean is almost never adequate; the only honest closure number is the regulator's percentile.