Industry: Mining and Natural Resources Product: ModelRisk Application: Water Balance and Augmentation Strategy in Arid-Region Mining
A 10-million-tonne-per-year flotation circuit consumes roughly 18 Mm³ of process water a year, and a further 5 Mm³ in dust suppression and pond evaporation — close to 23 Mm³ of total annual demand. In the Atacama and the high Andes — where some of the world's largest copper mines sit — the rainfall record carries a coefficient of variation north of 40%, and combined catchment supply averages around 27 Mm³. The deterministic water balance returns a comfortable +4.1 Mm³ surplus. The probabilistic balance shows roughly a one-year-in-three risk of net deficit on the same operation (P10 of the annual balance is -5.1 Mm³), and — across a 10-year mine life — a 12.9% chance of at least one severe deficit year above 10 Mm³, the level at which water trucking becomes the dominant operating cost.
A high-Andes copper mine put its 10-year water-supply plan through ModelRisk to size on-site storage, evaluate a desalination option, and price the emergency-water tail honestly enough to defend in front of the community and the regulator.
Annual water availability is the sum of three sources, each with a defensible distribution family:
Demand carries:
The year-1 distribution of net balance (shown above) makes the magnitude of the swing visible. Mean balance is +4.1 Mm³ — comfortably positive. But P10 of the balance is -5.1 Mm³ — a real deficit — and the probability of a year-level deficit is 32%. That is the number the operations team needs to plan against, not the mean.
Climate is serially correlated — wet years cluster, dry years cluster. The model encodes this with an AR(1) on the regional climate shock (ρ ≈ 0.35), which is what turns a single-year deficit probability into a multi-year planning problem: it is the clustering of dry years, not any single dry year, that breaks a water plan.
The probability of any deficit sits at about 32% in every single year of the horizon, and the probability of a severe deficit (> 10 Mm³) runs around 1% per year — but these are exactly the years that drive emergency-water cost. The multi-year view is what matters: over the full 10-year mine life there is a 96.7% probability of at least one deficit year, and a 12.9% probability of at least one severe deficit year above 10 Mm³ — the headline number the regulator and the community-engagement team both wanted to hear quantified. A single-year average hides both.
Rainfall variability dominates — a LogNormal σ_log of 0.40 produces a P10-to-P90 ratio of roughly 3× on rainfall alone. Surface inflow and processing demand follow, with the demand-side levers (process improvement, dust-suppression efficiency) genuinely controllable and the supply-side ones (rainfall, recharge) not. The tornado was the input to the year's monitoring plan: two new piezometers on the aquifer, continuous rainfall telemetry at the catchment headwaters, and a reagent reformulation programme targeting a 6% reduction in processing-water intensity.
The augmentation options under evaluation:
Run both strategies under the same simulated 10-year climate:
Trucking only looks cheap per-event, but because a deficit lands in roughly one year in three, the $30/m³ delivered cost compounds: the truck-only strategy carries a mean 10-year cost of $385M, a P90 of $751M and a P95 of $892M — a tail the board would not authorise. Desal + trucking front-loads $180M of capex but then meets deficits at $1.20/m³, capping trucking exposure to the residual above 10 Mm³/yr. It wins decisively on both statistics: mean $217M, P90 $240M, P95 $279M. The point estimate alone (mean) already favours desal here; the distribution is what makes the case airtight — the P95 falls from $892M to $279M, a tail reduction no average-year balance could have surfaced or sized.
A water balance is not "supply minus demand" — it is the joint distribution of two correlated time series under a climate that does not honour deterministic averages. Monte Carlo simulation in ModelRisk, with explicit serial correlation on the climate shock, is what makes the augmentation question answerable in P10/P95 terms instead of average-year platitudes, and what lets a mining company defend its water plan in front of a regulator who has read every other mining company's deterministic claim of "we will not run dry."