Markov chain modelling of pitting corrosion in underground pipelines

Caleyo, F.; Velázquez, J. C.; Valor, A.; Hallen, J.M.

doi:10.1016/j.corsci.2009.06.014

Cited by 131 publications

(51 citation statements)

References 12 publications

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“…The pit depth distribution at 5 years was used for constructing the future pit depth distribution at 10 years, 15 years and 20 years as the pipeline wall thickness was divided into 100 states of 0.0841 mm-thick per state. The constructed pit depth distribution shown in Figure 6b indicated that the pitting rate distribution decreased with the increase in time of exposure as was concluded by other researchers [1,12]. The variation of the pitting damage ( ( ) ) and the probability parameter ( ) with time is also shown if Figures 9a and 9b respectively whereas Figure 9c shows the maximum pit depth growth with time as computed from the simulation result.…”

Section: Figure 6a: Gev Distribution Of Monte Carlo Simulated Pit Depmentioning

confidence: 61%

“…Different researchers have shown that if the initial probability distribution of the pit depth at time t0 is known, the future probability distribution of the pit depth can be estimated [ 1,6,8,12] and reliability of the pipeline established. Equation (32) is used to compute the future distribution of the pit depth (Pn (t)) [19].…”

Section: =1mentioning

confidence: 99%

“…Caleyo et al [12] has shown that the probability distribution (FD (π)) over the time interval (t, t0) at state n0 can be related to the probability density function (f (π)) according to Equation (28):…”

Section: Estimation Of the Probability Distribution Of The Corroded Pmentioning

confidence: 99%

“…Other researchers such as Bolanos-Rodriguez et al [11], Valor et al [12] and Rodriguez III et al [13] also applied non-homogenous, continuous time pure birth Markov chain modelling to estimate the pit depth distribution of pipelines by using a closed form of Kolmogorov forward equation for computation of the transition probability function whilst assuming that the pit depth follows a stochastic process. Similarly, Camacho et al [14] applied Fokker-Planck equation for transition probability function estimate of pitting corrosion of underground pipelines based on a continuous time, non-homogenous pit depth evolution and Hong [15] worked on pit initiation and growth processes by modelling pit initiation as a homogenous…”

Section: Introductionmentioning

confidence: 99%

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

Ossai

Boswell

Davies

2016

Engineering Failure Analysis

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A continuous time non-homogenous linear growth pure birth Markov model was used to predict the future pit depth distribution of internally corroded oil and gas pipelines. A negative binomial distribution was used for calculating the transition probability functions of the pit depths whilst pit depths growth was estimated for low, moderate, high and severe pitting corrosion rates using field measured data of pit depths, temperatures, CO2 partial pressures, pH and flow rates. The Markov predicted results agreed well with field measured pit depth data from X52 grade pipeline and L-80 and N-80 grades offshore well tubing.

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Section: Figure 6a: Gev Distribution Of Monte Carlo Simulated Pit Depmentioning

confidence: 61%

Section: =1mentioning

confidence: 99%

Section: Estimation Of the Probability Distribution Of The Corroded Pmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Ossai

Boswell

Davies

2016

Engineering Failure Analysis

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“…This methodology is based on the estimation of the two parameters of the Gumbel distribution. It is worth noting that it has been extended to the three-parameter Generalized Extreme Value distribution (GEV) [8][9][10][11][19][20][21][22][23][24][25][26]. The GEV distribution is expressed such that:…”

Section: Introductionmentioning

confidence: 99%

A generic statistical methodology to predict the maximum pit depth of a localized corrosion process

et al. 2011

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. This paper outlines a new methodology to predict accurately the maximum pit depth related to a localized corrosion process. It combines two statistical methods: the Generalized Lambda Distribution (GLD), to determine a model of distribution fitting with the experimental frequency distribution of depths, and the Computer Based Bootstrap Method (CBBM), to generate simulated distributions equivalent to the experimental one. In comparison with conventionally established statistical methods that are restricted to the use of inferred distributions constrained by specific mathematical assumptions, the major advantage of the methodology presented in this paper is that both the GLD and the CBBM enable a statistical treatment of the experimental data without making any preconceived choice neither on the unknown theoretical parent underlying distribution of pit depth which characterizes the global corrosion phenomenon nor on the unknown associated theoretical extreme value distribution which characterizes the deepest pits.Considering an experimental distribution of depths of pits produced on an aluminium sample, estimations of maximum pit depth using a GLD model are compared to similar estimations based on usual Gumbel and Generalized Extreme Value (GEV) methods proposed in the corrosion engineering literature. The GLD approach is shown having smaller bias and dispersion in the estimation of the maximum pit depth than the Gumbel approach both for its realization and mean. This leads to comparing the GLD approach to the GEV one. The former is shown to be relevant and its advantages are discussed compared to previous methods.

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Predicting the risk of pitting corrosion initiation of stainless steels using a Markov chain model

Brenna

Bolzoni

Lazzari

et al. 2017

Materials & Corrosion

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A probabilistic approach based on Markov chains for the assessment of pitting and crevice corrosion initiation is proposed. A Markov chain is a stochastic process that undergoes transitions from one state to another through a finite number of possible states, until a so‐called “absorbing state” from which the system has no tendency to evolve is attained. The proposed model calculates the probability to have pitting or to maintain a stable passive condition involving a large number of operating parameters related to both metal and environment: steel chemical composition (namely, the PREN index), chlorides content ([Cl−]), chloride critical threshold ([Cl−]cr), temperature, pH, fluid velocity, electrochemical steel potential, E, presence of crevices. Model and algorithms are mainly based on corrosion data collected from literature. Although the proposed model needs experimental confirmation, the simulations here presented seem acceptable, considering the engineering application of stainless steels.

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Markov chain modelling of pitting corrosion in underground pipelines

Cited by 131 publications

References 12 publications

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

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

A generic statistical methodology to predict the maximum pit depth of a localized corrosion process

Predicting the risk of pitting corrosion initiation of stainless steels using a Markov chain model

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