Reserves Uncertainty Calculator: P90, P50, and P10 by Monte Carlo

Ask five geologists for the porosity of an undrilled prospect and you will get five defensible numbers. That is not a failure of geology, it is the honest state of knowledge before the bit finds out for sure. Deterministic volumetrics hide that honesty behind a single number; probabilistic volumetrics put it on the table. Instead of one STOIIP, you get a distribution, and the industry convention is to quote three points off it: P90 for the volume you are 90 percent confident of exceeding, P50 for the median, and P10 for the upside case with only a 10 percent chance.

How this calculator works

Each of the seven volumetric inputs gets a low, best, and high estimate from you, which defines a triangular probability distribution: zero likelihood at the extremes, peak likelihood at the best guess. The calculator then runs 20,000 trials, each time drawing an independent random value for every input and computing:

Recoverable = 7758 x Area x Thickness x NTG x Porosity x (1 - Sw) x RF / Bo

with area in acres, thickness in feet, and the result in stock tank barrels (7758 is the barrels in one acre-foot). Sorting the 20,000 outcomes gives the full distribution; the histogram below the results shows its shape with the three P-values marked.

Reading the output

• P90 is what a cautious lender would credit; P50 is the planning basis; P10 is what the exploration manager pitches
• The mean usually sits above the P50 because multiplying uncertain inputs skews the distribution to the right
• The P10 to P90 ratio is a one-number uncertainty gauge: under 2.5 suggests a well-appraised asset, above 5 says exploration territory
• If the ratio surprises you, look at which single input range is widest; that is almost always where the leverage is

The independence caveat, stated honestly

This tool samples every input independently, and reality is not always so tidy. Porosity and water saturation are usually negatively correlated (better rock holds less water), and area and thickness can be linked through the trap geometry. Ignoring positive correlations tends to understate the spread, while ignoring the porosity-Sw anticorrelation tends to overstate it, so the errors partially offset but not reliably. Commercial packages handle correlated sampling; for screening work, the standard defense is to keep input ranges honest rather than surgically precise, and to remember that the biggest volumetric errors in industry history came from optimistic single values, not from imperfect correlation matrices.

One more convention worth knowing: reserves reporting frameworks like SPE PRMS map P90, P50, and P10 loosely onto proved, proved plus probable, and proved plus probable plus possible for producing assets, but the mapping carries regulatory baggage and commercial tests. Treat the numbers from a screening tool like this as geologic potential, not bookable reserves.

Related Calculators and Reference

The deterministic version of this arithmetic lives in the STOIIP / GIIP calculator, the recovery factor range can be grounded with the recovery factor calculator, and the Bo range with the Bo and solution GOR calculator. For the reporting framework behind P90/P50/P10, the SPE page on the Petroleum Resources Management System is the authoritative source.