2012 IR&D Annual Report

Integrity Management of Nuclear Power Plant Components Subjected to Localized Corrosion Using Time-Dependent Probabilistic Model, 20-R8267

Principal Investigators
Pavan K. Shukla
Osvaldo Pensado
Jay Fisher
Gary Burkhardt

Inclusive Dates:  11/14/11 – Current

Background — The objective of this project is to develop an adaptive-predictive probabilistic model to forecast localized-corrosion-induced pit population and pit depth distributions. Nuclear power plant (NPP) operators are required to periodically inspect components by visual and volumetric examinations to maintain integrity and ensure safety. As nuclear power plants age, however, more frequent inspections are expected to ensure component integrity. A framework to define an inspection schedule based on risk considerations is needed to keep the cost of inspection constrained without compromising safety. SwRI is developing a model to forecast localized-corrosion-induced damage of NPP components based on damage measured at a given time. For example, if a component exhibits pitting corrosion in an environment, the model will be used to estimate the distribution of pit depths as a function of time and an initial state. The model is expected to account for previous inspection data, randomness of pit generation and propagation, and pit growth rate as a function of time. The model could be used to estimate probability of component failure due to pitting corrosion, and calibrate inspection schedules so that detection of corrosion-induced degradation occurs before failure.

Approach — Model development consists of the following tasks: statistical model, experiments, and data analysis and integration. Probabilities of transition between discrete states that satisfy Kolmogorov's forward equations for a pure birth process can be used to describe the evolution of depths of a population of pits. The discrete state of a pit is defined as a pit falling in a range of depths (e.g., a pit is in state 1 if its depth falls between 0 µm and 100 µm; it is in state 2 if the depth is between 100 µm and 200 µm; and so on). Thus, pit growth is conceptualized as a pit that transitions from a state to the next. Parameters to define the transition rate between states can be obtained by measuring the average pit depth as a function of time. Experiments are being conducted with coupons and tubes made of stainless steel 316. The coupons and tubes have been placed in a tub filled with synthetic sea water. Sea water is used in some NPPs as coolant in the open-cycle cooling water system. The tubes will be inspected using a eddy current technique for pit population and their depths. One-by-one, coupons will be removed from the tub at defined intervals. When a coupon is removed from the tub, it will be inspected using laser profilometry. The eddy current method will provide a coarse measurement of pit population and pit depth distribution in tubes, representative of results that would be achieved during in-service inspections of NPP components, whereas the laser profilometer will provide more accurate measurements. The data collected from coupons will be used to estimate pit depth versus time. Both coupon and tube data will be used to estimate statistical model parameters, such as transition rates, separately for coupons and tubes. The model will be used to forecast the next pit depth distribution. At the next inspection, the model will be updated with the collected data and the next forecast will be performed.

Accomplishments — A numerical solution for the system of Kolmogorov's forward equations for a pure birth process was implemented, with non-homogeneous birth rate or transition rate to develop the model. Several dependencies for the transition rate were investigated to find a functional dependence that yields a growth rate for the average pith depth that is consistent with a time dependence empirically observed. The common growth law is of the form d = κ(t + tο)ν, where d is a reference pith depth, t is the time, tο is a reference time, and κ and ν are empirical constants. In the numerical solution, the empirical parameter ν is provided as an input to define state transition rates, and the parameter κ is used to map computer time to a physical time. Given an initial distribution of pit depths, the numerical solution can be used to forecast the distribution at a later time, preserving the relationship d = κ(t + tο)ν, where d is interpreted as the average pit depth. The experimental work has been initiated, and the data from the experiments will be fed in the model to test the adaptive-predictive forecasting approach. Specifically, later stages of the project will be devoted to track pit population and their depth with time using the model, i.e., forecast the pit population and depth distribution, inspect experimental data and compare with the model forecast, and if necessary, update the model to make next forecast. This will be repeated till a satisfactory match is found between the model forecast and experimental data.

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