Small-break LOCA re-analysis: a 187 K margin built on an unqualified CHF correlation
Your consultancy is supporting the periodic safety review of a three-loop 1000 MWe PWR. The licensee has re-analysed a 25 mm equivalent-diameter cold-leg small-break LOCA using a revised critical heat flux correlation and a reduced accumulator pressure of 4.2 MPa (down from 4.5 MPa). The new best-estimate calculation gives a peak cladding temperature (PCT) of 1290 °C against the 1477 °C acceptance limit; the previous analysis gave 1020 °C. Peak local oxidation is 9% and core-wide oxidation 0.4%. The maximum PCT occurs about 40 s after loop-seal clearing, when bundle mass flux is approximately 150 kg/m²·s. The vendor's CHF correlation was validated for mass flux 500–3000 kg/m²·s and pressure 3–16 MPa; the transient spends about 90 s below 300 kg/m²·s. The licensee argues that 187 K of margin is sufficient and no further work is needed. The review meeting is in two weeks and the licensee wants the PSR chapter closed.
1. Does the revised analysis demonstrate compliance with the ECCS acceptance criteria? Set out what you would require before the PSR chapter is closed.
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Short answer: not demonstrated on the evidence presented - the margin exists, but its basis is not established.
On the face of the numbers the internationally applied ECCS criteria appear met:
- PCT 1290 °C vs 1477 °C → nominal margin 187 K, i.e. 12.7% of the limit.
- Peak local oxidation 9% vs 17%; core-wide oxidation 0.4% vs 1%.
- Coolable geometry and long-term cooling are not addressed in the summary at all.
Acceptance is about the demonstration, not just the number. Before closing the chapter I would require:
- Correlation qualification. The PCT occurs inside the 90 s window where mass flux is below the correlation's validated range. A non-conservative CHF prediction at low flow raises PCT directly; the calculation is therefore least qualified exactly where the answer is set.
- Uncertainty treatment. Confirm that 187 K exceeds the calculated uncertainty band - ideally a best-estimate-plus-uncertainty result at 95/95, not a nominal value.
- Break-size screening. The 4.5 → 4.2 MPa accumulator change alters refill and loop-seal clearing. Re-screen break sizes; a smaller break can be limiting for PCT.
- The other criteria. Local oxidation and core-wide oxidation must come from the same qualified calculation, and coolable geometry/long-term cooling must be explicitly shown.
Recommendation: do not close the chapter. Ask first for a CHF sensitivity case and a BEPU run; both can be produced within the two-week window if the input decks exist.
2. The reviewer notes that the CHF correlation is applied outside its validation range during a low-flow period. Explain why this matters and set out the options.
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Why it matters. CHF correlations are empirical fits to a database with a stated range of mass flux, pressure, quality and geometry. At 150 kg/m²·s the flow is likely stratified or inverted-annular rather than the high-velocity annular flow of the validation set, and the limiting mechanism shifts from departure from nucleate boiling to dryout. Extrapolating a DNB-type correlation into that regime can be non-conservative by tens of percent in CHF, which translates directly into a higher PCT. Because the maximum PCT occurs 40 s after loop-seal clearing, inside the invalid window, the 1290 °C result rests on the least defensible part of the calculation. The licensee's '187 K is enough' argument uses that margin to absorb an unquantified model error, which is not sound.
Options, in order of preference:
- Re-run with a correlation or look-up table validated at low mass flux across the full expected range and compare PCT.
- If no validated correlation exists, apply a demonstrably conservative CHF multiplier derived from separate-effect data or from the previously licensed correlation, and show PCT remains below the limit.
- Justify from first principles that sustained dryout cannot occur - e.g. show rewetting or that the low-flow period is short compared with the bundle heat-up time - supported by sensitivity studies.
- At minimum, report the PCT sensitivity to CHF (e.g. ±20%) in the PSR chapter so the margin is seen in context.
Option 1 or 2 is what I would insist on before signing the chapter.
3. The regulator asks for a best-estimate-plus-uncertainty (BEPU) approach. Describe how you would structure it and what the outcome would mean for the claimed margin.
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Structure:
- Select the uncertain inputs: CHF multiplier, decay heat (±5%), gap conductance, accumulator pressure and water volume, break area and discharge coefficient, initial power, ECCS injection temperature, and two-phase drag in the loop seals.
- Assign defensible distributions from data or from code validation - not arbitrary uniform ranges.
- Propagate by Monte Carlo or by order statistics. For a one-sided 95/95 tolerance with an unknown distribution, 59 runs suffice; 93 runs give two-sided 95/95. Verify convergence and identify dominant contributors by rank regression or scatter plots of PCT against each input.
- Report the 95th-percentile PCT as the licensing result.
Interpretation. If the nominal PCT is 1290 °C and the 95/95 value is, say, 1420 °C, the demonstrated margin is 57 K, not 187 K. That may still be compliant, but it changes the conclusion about whether further work is needed and it is the number that should appear in the safety case. If the 95/95 value exceeds 1477 °C, the analysis fails and the licensee must change the ECCS configuration, re-optimise injection, or apply compensatory measures. The regulator should be told which of these applies before the chapter is closed, and the result should be traceable to the input distributions and the code version used.