| Vose Software

Industry: Oil and Gas Exploration
Product: ModelRisk
Application: Reservoir Management — STOOIP, Recoverable Reserves, and EOR Decisions


When a P50 STOOIP of 100 MMstb Is Bracketed by a P10 of 57 and a P90 of 163

STOOIP distribution — SPE PRMS P10/P50/P90 framing

The SPE Petroleum Resources Management System asks for reserves to be booked as P10/P50/P90 — the low, best, and high estimates. The framework exists for a single reason: subsurface uncertainty is irreducible, and a single deterministic STOOIP number is therefore a fiction. Yet many mature-field reservoir-management decisions — infill drilling, enhanced oil recovery (EOR), and abandonment timing — are still made against that fictional single number.

A multinational operator with a mature onshore basin asset rebuilt its reserves and EOR-decision workflow in ModelRisk. The volumetric distribution above tells the story: a P50 STOOIP of 100 MMstb is bracketed by a P10 of 57 and a P90 of 163 — close to a factor-of-three spread that the deterministic mid-case (101 MMstb) had collapsed to a single number. With the full distribution in hand, the team could finally test a WAG (water-alternating-gas) EOR project against the range of subsurface outcomes rather than the point estimate — and stage the capital commitment accordingly.

Volumetric uncertainty: one formula, six uncertain inputs

The volumetric STOOIP equation is

\[ \text{STOOIP} = \frac{7758 \cdot A \cdot h \cdot \phi \cdot (1 - S_w) \cdot (N/G)}{B_o} \;\;\text{(stb)} \]

with every term except the conversion constant 7758 carrying real uncertainty:

  • Area \(A\) — Triangular(2,200; 2,800; 3,600) acres, with bounds from 3-D seismic interpretation envelopes.
  • Net thickness \(h\) — Triangular(70; 110; 160) ft from well-log correlation across 23 control wells.
  • Porosity \(\phi\) — Beta(7, 18) scaled to [0, 0.4], mean ≈ 0.11. Beta is the right choice for a fraction bounded on [0, 1]; the legacy Normal allowed simulated draws below 0% and above 40% porosity, both physically impossible.
  • Water saturation \(S_w\) — Uniform(0.20, 0.45), reflecting limited core data and no clear central tendency in the heterogeneous reservoir.
  • Net-to-gross \(N/G\) — Triangular(0.55, 0.72, 0.88).
  • Formation volume factor \(B_o\) — Triangular(1.18, 1.28, 1.42).

Crucially, porosity \(\phi\) and permeability \(k\) are jointly correlated (ρ ≈ 0.55, calibrated to core data) using a Gaussian copula. Permeability is itself LogNormal because of its multi-order-of-magnitude range. Independent sampling of \(\phi\) and \(k\) — the textbook default — generated impossible combinations (high \(\phi\) with negligible \(k\)) that distorted the recovery-factor distribution downstream.

The STOOIP distribution in SPE PRMS format

Reading the distribution that opened this study, the simulation produces a P10 of about 57 MMstb, P50 of 100 MMstb, P90 of 163 MMstb, and mean near 106 MMstb. The deterministic "mid-case" computed term-by-term (the spreadsheet legacy) lands at 101 MMstb — close to the P50 — but the spread around it is the number that drives reserves-booking and capital decisions. The right-skew comes principally from porosity, area, and the porosity-permeability correlation flowing through to recovery factor.

What actually drives STOOIP uncertainty

Tornado: drivers of STOOIP uncertainty

Porosity is the single largest driver of STOOIP spread, followed by net thickness and area. Net-to-gross, water saturation, and \(B_o\) are second-tier. The ranking pointed the next subsurface-data dollar at core analysis to tighten porosity — a multi-well coring program with an expected porosity sigma reduction from 0.04 to 0.02. The model showed this would compress the P10-P90 STOOIP spread by roughly 25%, with a corresponding tightening of the booked-reserves range — a value-of-information case that justified the \$8M coring spend on its own.

Subsurface parameter correlations matter for the right reasons

Subsurface-parameter correlation matrix (modeled)

The modeled correlation matrix imposes physically realistic structure: porosity and permeability move together (a realized Pearson correlation of about 0.39 on the matrix, from a rank-correlation target of 0.55 in the copula), and recovery factor co-varies strongly with permeability (≈ 0.73) because high-perm rock drains more completely. Setting these off-diagonals to zero — the legacy assumption — produces a recoverable-reserves distribution with the right mean but the wrong tails: the joint events "high \(\phi\), low \(k\), high RF" and "low \(\phi\), high \(k\), low RF" appear in the independent sample but are physically improbable, and they fatten both tails. The EOR-decision NPV is itself sensitive to the tail shape, so the correlation structure feeds directly into the next chart.

The EOR decision: positive across the distribution, but front-loaded in capex

A WAG EOR project, capex \$250M, was projected to lift the recovery factor by Triangular(4%, 8%, 16%) — roughly 9% of STOOIP in additional recoverable reserves. The economic comparison:

EOR decision: incremental NPV distribution comparison

  • Primary-only NPV: mean ≈ \$4.26B, P10 ≈ \$1.24B, P(NPV<0) ≈ 0%.
  • Primary + WAG EOR (net of \$250M capex): mean ≈ \$6.63B, P10 ≈ \$2.17B, P(NPV<0) ≈ 0%.

The mean uplift is about \$2.4B, and crucially the P10 lifts too — by roughly \$0.9B — because the incremental EOR barrels are worth more than the modest \$250M capex even in the low-side reservoir cases. The two CDFs barely cross: EOR beats primary-only in 99.8% of futures. This is not a marginal coin-flip; on expected-value grounds the EOR project is clearly accretive, and the deterministic P50 comparison ("EOR adds NPV") understated rather than overstated the case.

What the distribution does sharpen is the timing question. The EOR uplift correlates with the same uncertain inputs that drive primary recovery — when the reservoir disappoints, the EOR uplift disappoints in step — so the spread of the EOR case is wider than the primary case even though its floor is higher. The decision the team took was therefore conditional on information, not on sign: approve the EOR engineering and procurement spend (\$45M) now, defer the major capex commitment (\$205M) by 18 months until the first phase of infill-well data tightens the porosity distribution. Re-running the simulation with a tighter porosity sigma showed the P10 NPV improvement from waiting was roughly \$300M — more than enough to justify the time-value loss.

What changed

  • EOR commitment staged: \$45M of pre-commitment spend approved, \$205M deferred 18 months pending infill-well data.
  • Reserves booked at P10/P50/P90 (57/100/163 MMstb) — SPE PRMS-compliant rather than a single 100 MMstb figure — with the audit committee preferring the explicit range for external reporting.
  • \$8M coring program approved specifically to tighten the porosity distribution, the input the tornado identified as the largest single mover.
  • Abandonment-timing model rebuilt on the same engine: the P50 expected end-of-life year is 2042, but the P10 is 2034 and the P90 is 2049 — driving the contingency provisioning for plugging and abandonment.

ModelRisk Functionality Used

  • Volumetric STOOIP calculation with six independent random inputs and a Gaussian copula linking porosity and permeability (ρ = 0.55) — the correlation that legacy spreadsheets routinely omit.
  • Beta porosity distribution with shape parameters fitted to 23-well core data, replacing the Normal that allowed impossible negative and >40% draws.
  • LogNormal permeability spanning the realistic three-order-of-magnitude range and correlated with porosity rank.
  • Conditional decision branching that re-runs the same engine under a "wait 18 months and tighten porosity" branch versus a "commit now" branch — producing the \$300M P10 NPV improvement from staging.
  • SPE PRMS P10/P50/P90 output formatting that fed directly into the external reserves filing, replacing the single-number legacy filing.

Subsurface uncertainty does not collapse to a single number — and the field decisions that ride on it (EOR, infill, abandonment) are richer if the uncertainty is preserved. ModelRisk is what keeps the P10 and the P90 in the conversation alongside the P50, and what turns a "go" or "no-go" EOR decision into "go now for \$45M, decide the rest in 18 months" — a richer answer that the deterministic comparison cannot produce.