Stochastic process corrosion growth models for pipeline reliability

Markov chain modelling for time evolution of internal pitting corrosion distribution of oil and gas pipelines

“…Although any positive random distribution can be used for realizing the pulse heights [26], Gamma distribution [26] as well as Gumbel distribution [25] have been used for estimating variables in PSWP by other authors, however, lognormal distribution is employed in this work because the best fitting distribution of the field data followed a lognormal distribution. In order to estimate the time of pitting initiation process (tint) using the procedure shown in Figure 3, a 5000 run random numbers simulation was carried out using the minimum and maximum values of the operating variables and the maximum pit depths for the corrosion categories shown in Table 2 as boundary conditions.…”

“…If the deterministic corroded pit growth in this work is assumed to follow a linear random model which have been used by researchers to model different kinds of physical systems including pipelines deterioration [26,[35][36][37][38], then the progression of the deterministic pit depth ( ( )) will be of the form shown in Equation (23).…”

“…Since the magnitude and duration of the generated pulses from the PSWP follow a Poisson distribution with the duration of individual pulses being independently exponentially distributed [25][26], the excepted pipeline failure time (tfail) can be computed as the cumulative simulated times for which the cumulative simulated pit depth ( ) is equivalent to 100% of the pipe-wall thickness of the pipeline.…”

“…In order to estimate the time of pitting initiation process (tint) using the procedure shown in Figure 3, a 5000 run random numbers simulation was carried out using the minimum and maximum values of the operating variables and the maximum pit depths for the corrosion categories shown in Table 2 as boundary conditions. By assuming that the maximum pit depth and operating parameters follows a lognormal distribution as earlier stated, the best fit distributions were obtained from the simulated data whilst a Poisson Square Wave Process (PSWP) shown in Figure 4 was used to calculate the pit depth growth with time using the relationship shown in Equation (37) [26].…”

“…Bazán and Beck [26] also used Poisson square wave process to model external pitting corrosion of underground pipelines and concluded that power model gave a more conservative estimate of the future corrosion wastage than random linear model after comparing the results with field inspection data.…”