The inventory equations are calibrated against four independent OpenMC depletion campaigns and verified by three independent tests (a blind test + two out-of-envelope real designs) — across the full SMR operating-power range (≤300 MWe ≈ ≤1000 MWth) the equation-to-code deviation never exceeds 1.5%.
The equations compute the core inventory correctly across the entire SMR definition band — from 100 up to 1000 MWth (≈300 MWe equivalent) of operating power: the calibration comes from four designs spanning 100–530 MWth; the IRIS test carries validity to the top of the band. In every test the predictions were pinned BEFORE the run (pre-registered) — no tuning to the outcome.
Calibrated Effective Yields
4 campaigns · ENDF/B-VII.1 chain · coefficient band ±1%
Effective yields deviate from pure U-235 yields because part of the fissions in burnt fuel come from Pu-239 (a +15% correction for I-131). That the coefficient band stays within ±1% although the four designs use three different fuel-management schemes is the numerical proof that saturated inventory depends on power alone.
| Nuclide | y (U-235 thermal) | y_eff (calibrated) | Coefficient |
|---|---|---|---|
| Xe-133 | 0.0661 | 0.0694 | 2.166×10¹⁵ Bq/MWth |
| I-131 | 0.02878 | 0.0331 | 1.032×10¹⁵ Bq/MWth |
| I-133 | 0.0670 | 0.0689 | 2.151×10¹⁵ Bq/MWth |
| Cs-137 | — | 0.0615 | 1.21×10¹¹ Bq/(MWth·EFPD) |
Calibration Campaigns — Equation vs OpenMC
EOC equilibrium core · four designs · spot checks
| Campaign | Nuclide | Equation (Bq) | OpenMC (Bq) | Ratio |
|---|---|---|---|---|
| FLEXBLUE 530 MWth | Xe-133 | 1.148×10¹⁸ | 1.143×10¹⁸ | 1.004 |
| FLEXBLUE 530 MWth | I-131 | 5.47×10¹⁷ | 5.43×10¹⁷ | 1.008 |
| FLEXBLUE 530 MWth | Cs-137 | 6.93×10¹⁶ | 6.95×10¹⁶ | 0.997 |
| NuScale 200 MWth | Xe-133 | 4.33×10¹⁷ | 4.35×10¹⁷ | 0.996 |
| NuScale 200 MWth | Cs-137 | 2.74×10¹⁶ | 2.74×10¹⁶ | 1.000 |
| mPower 530 MWth | I-133 | 1.140×10¹⁸ | 1.136×10¹⁸ | 1.004 |
| mPower 530 MWth | Cs-137 | 7.96×10¹⁶ | 7.99×10¹⁶ | 0.997 |
| ACP100 385 MWth | I-131 | 3.97×10¹⁷ | 3.98×10¹⁷ | 0.998 |
| ACP100 385 MWth | Cs-137 | 5.51×10¹⁶ | 5.50×10¹⁶ | 1.002 |
Blind Test & Out-of-Envelope Extrapolation
OpenMC / equation ratio · predictions pinned before the run
| Nuclide | VSMR-300 (blind · 300 MWth) | CAREM-25 (↓ 100 MWth) | IRIS (↑ 1000 MWth) |
|---|---|---|---|
| Xe-133 | 0.998 | 0.994 | 0.998 |
| I-131 | 1.002 | 0.999 | 1.003 |
| I-133 | 0.999 | 0.996 | 0.997 |
| Cs-137 | 1.005 | 1.015 | 0.987 |
CAREM-25 sits below the envelope on five axes (including a hexagonal lattice); IRIS sits above it in power, core height and core age (a 1000 MWth integral PWR — the thermal equivalent of the SMR definition threshold). The Cs-137 deviations at the two ends are two faces of one mechanism: the calibrated y_eff embeds the decay loss of ~1100–1240-day irradiations; for short irradiation the correction is smaller (CAREM +1.5%), for long it grows (IRIS −1.3%) — the single-parameter (1−e^(−λT))/(λT) ratio predicts 0.9875 for IRIS, measured 0.9873. The I-133 row is covered by the method; it is not yet carried by the dispersion engines.