An Itô model of pit corrosion in pipelines for evaluating risk-informed decision making

Abstract

The purpose of this paper is to present a stochastic model based on the Itô differential equation to the time evolution of pit corrosion depth in nuclear power plant piping systems. The stochastic solution obtained by analytical and numerical methods (for comparison purposes) is compared to the deterministic solution, which is obtained by setting the stochastic term of the Itô equation equal to zero. The study of extended qualified useful life of nuclear power plants has two components, one deterministic and another probabilistic and one complements the other. The evaluation based on deterministic methods defines the difference between the current state and condition of the item in the qualifying phase, but does not define its probability of continuing performing its function adequately for a period longer than the one defined by its qualified life. The corrosion process is modeled by the Itô stochastic equation, which describes the time evolution of pit corrosion depth among different states. The Itô equation is determined by the knowledge of two functions known as the drift and diffusion coefficients. This work shows that these functions can be used to estimate pit corrosion depths from plant inspection data. An Itô modeling of pit corrosion can also be developed for any component of a nuclear power plant for which corrosion depth data is available. The above proposed approach provides a precise and easy way in which pit corrosion depth can be monitored over time, which is critical for developing reliability and risk-informed models for inspection and maintenance planning of corroded pipelines. The stochastic model presented is developed considering the influence of the Gaussian white noise on corrosion. The equations of the stochastic model are solved analytically based on the Itô integral. The maximum operating time of a piping before its wall reaches the minimum allowable thickness is calculated. This study uses pit corrosion depth data from the Angra I nuclear power plant.