Probabilistic Model of Cumulative Damage in Pipelines Using Markov Chains

This paper presents a probabilistic model of cumulative damage based on Markov chains theory to model propagation of internal corrosion depth localized in a hydrocarbons transport pipeline. The damage accumulation mechanism is unit jump type, depending on the state. It uses a shock model based on Bernoulli trials and probabilities to remain in the same state or the next one. Data are adjusted to Lognormal distribution and proven with a Kolmogorov-Smirnov test. The vector obtained from multiplying the initial state vector with the transition matrix was developed and the system of equations to find each transition probability with a single inspection report was solved. In order to calculate propagation of internal corrosion after inspection, an exponential equation was proposed and a parameter was adjusted to the data. Time to expected failure was obtained by adding the time expected in each damage state. Each time step was adjusted to real time.