Industry: Mining and Natural Resources
Product: ModelRisk
Application: Environmental impact assessment

Pricing the regulatory tail of a copper-mine EIA

The deterministic EIA the operator filed showed a 22 g/m³ peak PM10 concentration at the nearest village — comfortably below the 50 g/m³ daily limit, and the basis on which the permit was granted. The Monte Carlo rerun told a different story: the daily-max concentration averages 18 g/m³ but carries a 99th-percentile of 152 g/m³, and puts a 7.9% probability on at least one day above the 50 g/m³ limit each year. One bad-day exceedance is enough to trigger a 30-day cease-operations order under most Latin American air-quality codes. That gap — between a tidy average and a fat-tailed reality — is exactly what probabilistic environmental impact assessment is built to close.

The operator — a 140 kt-Cu/yr open-pit in Chile's Atacama with a 1.7 km transport buffer to the nearest village — rebuilt three EIA components in ModelRisk: dust plume dispersion, dry-season water demand against the local catchment yield, and end-of-life rehabilitation cost across a 1,800 ha disturbance footprint.


Where the dust plume actually lives

Gaussian-plume dispersion at the village receptor depends on emission rate Q (truck haul × moisture × dust-suppression efficacy), wind speed u, and Pasquill stability class. The deterministic filing used annual-average values: Q = 12 g/s, u = 4.2 m/s, neutral stability. That returned the comfortable 22 g/m³.

The probabilistic rebuild used distributions calibrated to two years of on-site met-tower data:

• Emission rate Q: LogNormal(μ = ln 12, σ = 0.45) g/s — right-skewed because suppression-truck downtime and dry-pile loading events drive a long tail.
• Wind speed u: Weibull(k = 1.9, λ = 4.8) m/s, with a heavy probability mass at low wind speeds (calm, plume-trapping conditions).
• Stability class: discrete (A 5%, B 12%, C 18%, D 40%, E 15%, F 10%) — F-class stable nights are the regulatory-exceedance regime.

A naïve Normal on wind speed would have buried the calm, stable-night tail entirely. Sampling the joint distribution 50,000 times, the daily-max PM10 concentration distribution has mean 18 g/m³, median 8 g/m³, P90 = 43 g/m³, P99 = 152 g/m³ — a textbook right-skew where most days are quiet and a handful of inversion-trapped nights carry the regulatory risk. The model puts 7.9% probability on at least one 50 g/m³ exceedance per year, against a regulator's implicit tolerance of roughly 1.5%.

Water balance against a drought-prone catchment

The mine's process plant requires 3.8 ML/day. The local catchment yields a long-term-average 4.6 ML/day, but yield is gamma-distributed (shape 3.2, scale 1.45) and serially correlated — dry spells cluster (AR(1) ρ = 0.80 on the daily climate driver). The deterministic EIA reported a comfortable 0.8 ML/day average buffer. The Monte Carlo found that in any given year there is a 9.8% probability of at least 30 consecutive days where catchment yield falls below process demand — a sustained-deficit, water-trucking and community-relations event the annual average simply cannot see.

Tornado: what actually moves the rehabilitation bill

Rehabilitation cost for the 1,800 ha disturbance was modelled as LogNormal across four cost lines (re-contouring, soil cap, native revegetation, infrastructure removal), with a Bernoulli switch for a 35% probability of stricter post-2030 closure rules adding 22% to the bill. Mean closure cost = $196M; median = $191M; P90 = $250M; P95 = $272M.


Why Monte Carlo, not a point estimate

The deterministic EIA pencilled a $145M rehabilitation provision and a 22 g/m³ peak plume — both comfortable, both wrong. The probabilistic model showed an expected rehabilitation cost 35% higher, a daily-exceedance probability over five times the implicit regulatory tolerance, and a 9.8% chance of a sustained 30-day water deficit and community-relations conflict. None of those three numbers can be read off a deterministic spreadsheet.

What the model changed

• Suppression-truck fleet upsized from four to six units; emission-rate σ in the rebuild drops from 0.45 to 0.30 and the modelled daily-exceedance probability falls below 2%.
• Rehabilitation provision raised from $145M to $215M (between mean and P95), with a $50M contingency reserve sized against the regulatory-change scenario.
• Aquifer-recharge well-field commissioned to buffer the ~10%-probability sustained-deficit tail; expected community-conflict cost falls from $4.2M/yr to $0.7M/yr.

ModelRisk functionality used

• Gaussian-plume sampling with Weibull wind, LogNormal emission rate and discrete stability class — produced the 7.9% exceedance figure that drove the suppression-fleet decision.
• Gamma-distributed catchment yield with first-order serial correlation, surfacing the 9.8% probability of a 30-day sustained deficit.
• Bernoulli regulatory-change switch layered over LogNormal cost components — the 35%-probability scenario lifts the mean closure bill to $196M and the P95 to $272M.
• Tornado on the rehabilitation bill ranking the four cost lines plus the regulatory switch, identifying revegetation unit cost and the regulatory scenario as the top two drivers.
• Joint-output reporting combining plume exceedance, water-deficit and rehabilitation distributions into a single "Expected Environmental Cost" figure for the board paper.

What looked like a compliant EIA at 22 g/m³ was actually an 8%-probability shutdown risk — and the only honest answer to "how much should we provision?" is a distribution, not a number.