Statistical Methods for Darlington Steam Generator Tube Fitness-for-service Assessments

Abstract

OPG has developed Fitness-For-Service Guidelines (FFSG) for steam generator tubes. The main objectives of the FFSG are to provide reasonable assurance that tube structural integrity is maintained, and to provide reasonable assurance that there are adequate margins between estimated accumulated dose and applicable site dose limits for consequential leakage. When tube degradation is detected, a series of mandatory, consecutive periodic assessments of the steam generator tubes are required. The condition monitoring (CM) assessment provides a current and backward-looking assessment of the entire population of tubes, including validation and/or adjustment of predictive methods based on service experience and comparison with the previous operational assessment. A forward-looking operational assessment (OA) of fitness-for-service of the entire population of tubes in the reactor unit is performed to demonstrate that the acceptance criteria will be satisfied during the next evaluation period. The operational assessment considers the projected future condition of the tubes based on the inspection results and the predicted flaw growth rates. The statistical methods used to obtain predictions for the tube fretting in the Darlington station will be presented. Initially, predictions were based only on the growth of the observed fret indications. Random growth based on the gamma distribution, with parameters estimated from the observed data, was assumed. Together with this model, a statistical test called the critical limit fret depth (CLFD) was developed to determine whether the prediction model was still appropriate, as part of the CM assessment. After several years of successful application of the model, a failure of the CLFD test was observed during the Darlington Unit 1 2004 outage. This prompted a review of the predictive methodology that resulted in a model for OA assessments with the following components: (i) growth of existing fret indications; (ii) estimation of the number of new fret indications; (iii) estimation of the fret size of new fret indications; and (iv) integration of the different predictions. The growth model for existing fret indications is still based on the gamma distribution, but the population of frets was divided into several subpopulations based on contact size length and whether or not the frets are located in an area identified at greater risk of fretting. The model to estimate the number of new fret indications is based on a negative binomial distribution. The model to estimate the size of the new fret indications is also based on the gamma distribution, but with different parameters than those used to for growth of existing fret indications. The predictions from the different fret subpopulations are then integrated to determine the upper bound number of frets exceeding the applicable structural integrity limits. The predicted consequential leak rate for frets at risk of leaking is also estimated, using inputs from OPG's Steam Generator Tube Test Project, for comparison against the maximum allowable consequential leakage rate.