Probabilistic and Statistical Techniques to Study the Impact of Localized Corrosion Defects in Oil and Gas Pipelines: A Review
Abstract
:1. Introduction
- Electrochemical background for the statistical modeling of localized corrosion defects. The details, background, and electrochemical concepts needed to model localized corrosion defects are explained. Similarly, the chemical and physical factors that influence the growth of corrosion defects are described. In addition, the applications of statistics are explained to better understand the electrochemical nature of the localized corrosion phenomenon.
- Estimation of corrosion defect depths and corrosion rates. Quantification of the uncertainty of the localized corrosion defect depth and rate assist in the estimation of the thickness of the wall of the pipeline with accuracy and precision and, thus, the remaining life of these structures [14,15,16]. Consequently, in this section, the use of different statistical techniques as tools for estimation is explained.
- Bayesian applications in pipeline integrity to update the probability distributions of corrosion defect characteristics (depth, length, and spatial distribution). This statistical technique can be applied to estimate the depth of the corrosion defect, corrosion rate, and the sample size required to estimate the depth of corrosion defect and other damage caused by different corrosion mechanisms [17,18,19,20]. In this section, an application that used Bayesian inference is detailed.
- Pipeline reliability estimations. Reliability analysis has become a cornerstone in pipeline integrity management to mitigate the threats provoked by different corrosion mechanisms. The reliability of corroded pipelines is usually assessed by probabilistic tools that should consider the unavoidable uncertainties associated with the sizing of corrosion defects, the pipe manufacturing process that influences the material mechanical characteristics, pipe dimensioning, and working conditions of these pipelines [16,21,22,23]. In this section, several examples of pipeline reliability estimation are shown to broadcast the scope of probability and statistics in pipeline integrity management.
- Future challenges for the application of probability and statistics in corroded oil and gas pipelines. The challenge of the application of probability and statistical techniques is discussed to motivate their use or at least gradually reduce the risk caused by corrosion defects in pipelines that transport hydrocarbons.
2. Electrochemical Background for Statistical Modeling of Localized Corrosion Defects
- Temperature. The higher the temperature, the higher the corrosion rate because of the resulting accelerated electrochemical reactions. Nonetheless, under some conditions, the effect of temperature on protective layer formation is multivariate because with a significant increase in temperature, protective films are formed faster and reduce the deterioration [42].
- pH. Frequently, the acidity or basicity of the environment has been recognized as the variable that exerts more influence on pitting corrosion deterioration [12,43]. Because the effect of pH on the corrosion rate is not completely understood and depends on the environment, it is not feasible to conclude that the relationship with the corrosion rate is always inversely proportional. In some studies, it was observed that the value of the breakdown film potential (Eb) [44] (in electrochemical techniques, breakdown potential is the surface potential at which the surface’s passive film breaks down [42]) is almost flat within a large range of pH values [45].
- Chemical composition. Some ions that encourage localized corrosion deterioration, such as halides (mainly chlorides), can form salts at low pH at the bottom of the pit [42,46]. However, other ions, such as bicarbonate, carbonate, and sulfate, discourage the growth of localized corrosion defects [42,46].
- Fluid velocity. For metals such as steel, there is a critical velocity beyond which the corrosion rate is high. It is important to remember that when the flow velocity increases, the protective layers detach from the surface, indicating that the corrosion rate increases as the velocity increases [42,47,48].
- Biological factors. Microbiologically influenced corrosion has been reported to cause approximately 40% of all internal corrosion incidents in oil pipelines [49,50]. Sulfate-reducing bacteria are recognized as the major bacteria that cause corrosion. These bacteria are anaerobic and can degrade organic compounds to produce sulfides [51].
- Metallurgical factors. Some characteristics of steel can influence the growth of localized corrosion defects, such as inclusion density, alloy composition, surface finish, grain size, and grain boundary [29].
- Dissolved gases in the environment. The fluids transmitted by oil and gas pipelines contain dissolved gases such as carbon dioxide (CO2), oxygen (O2), and hydrogen sulfide (H2S). Carbon dioxide reacts with water and leads to the formation of carbonic acid (H2CO3), which decreases the pH of the fluid, making it more aggressive and deteriorating the metal surface. Nevertheless, carbonic acid dissociates in hydrogen and bicarbonate ions, and the bicarbonate ion can reduce the corrosion rate. Therefore, the influence of carbonic acid on the corrosion rate depends on the amount present and the interaction with other ions and the physical variables involved [42,46]. Oxygen is also present in the hydrocarbons that are transmitted by pipelines and is also present in soils surrounding these structures. This means oxygen has an influence on both external and internal corrosion in pipelines because it increases corrosion rates [42]. The corrosion rate of local anodes depends on the cathode reaction; therefore, depolarization is faster with an increase in oxygen concentration at the cathode [45]. H2S is also found in oil and gas. This gas is approximately 3 times more soluble than CO2. H2S can also reduce pH, such as CO2, resulting in a higher corrosion rate [41].
3. Applications of Probabilistic and Statistical Methods to Approximate Localized Corrosion Defect Depth and Rate in Pipelines
Advances in Regression Models
4. Stochastic and Random Walk Models
5. Other Examples of the Use of Statistics in the Prediction of the Lives of Oil and Gas Pipelines
- “Probability Distribution of Pitting Corrosion Depth and Rate in Underground Pipelines: A Monte Carlo Study” by F. Caleyo et al. [15]. In this study, the probability distributions of the external-corrosion pit depth and pit growth rate were investigated in buried pipelines in a range of Mexican soils using Monte Carlo simulations. Information from previous studies [14,61] and the regression model already discussed were used to determine the best fit to the pitting depth and rate data for different future times. The distributions studied were Gumbel, Weibull, Fréchet, and generalized extreme values [86] (Gumbel, Weibull, and Fréchet distributions are special cases from generalized extreme value distribution [86]; the mathematical expression that represents GEVD is shown in the latter part of this paper). It was observed that the means, variances, and shape parameters of these distributions differ significantly between soil types, and they were not completely constant for different exposure times. These differences developed more substantially as exposure time increased. However, after long exposure times, the distribution of the corrosion rate achieved a relatively constant yet slightly decreasing mean and variance. The probabilistic corrosion rate distributions provided in this study can be used to accurately estimate the reliability evolution of oil and gas pipelines rather than reclining the conservative average pit growth rates in existing studies. The predicted probability function that describes the distribution of the pit depth, computed by Caleyo et al. [15], is as follows:
- “Stochastic Modelling of Corrosion Damage Propagation in Active Sites from Field Inspection Data” by Alamilla and Sosa [16]. In this study, the PDF of the depths of corrosion damage of pipeline systems was computed, and four models to calculate the velocities of corrosion damage at localized defects were proposed. Each of these models is described as follows:
- A model that considers the generation of corrosion defects following a Poisson process was proposed. The corrosion rate is expressed as follows:
- In the second model, it was considered that two inspections were performed in oil and gas pipelines at different time instants and the defects were identifiable in both inspection reports. In addition, the generation of corrosion defects was not considered. The corrosion rate is estimated to have less variability. In this case, the corrosion rate is represented as follows:
- Because the main disadvantage of the second model is the identification of corrosion defects in two consecutive inspections, a third model considers the PDF of the depths of corrosion defect of a pipeline system and , related to inspections in and , respectively. This third model, proposed by Alamilla and Sosa, is expressed as follows:
- The fourth model is based on Bayes’ theorem, and it is used to update the propagation function (corrosion rate function) by including new measurements from sequential inspections. The updated propagation function is expressed as follows:
- “Modelling Steel Corrosion Damage in Soil Environment” by Alamilla et al. [87]. A model to estimate the propagation of the localized corrosion damage in buried oil and gas pipelines was developed considering the physical and chemical soil characteristics. This model offers a satisfactory description of the evolution of corrosion damage and minimizes most of the inconveniences of the power law used (Equation (7)). The variability of the depths of corrosion defects was satisfactorily represented by the Gumbel PDF. The depth of the corrosion defect can be estimated as follows:
- “Stochastic Process Corrosion Growth Models for Pipeline Reliability” by Felipe Alexander Vargas Bazán and André Teófilo Beck [88]. A nonlinear model was proposed, in which the corrosion rate was studied as a Poisson square wave process. Instead of proposing a parameterized stochastic process by considering the parameters of the power-law equation as random variables, the proportionality factor of the power-law function (Equation (7)) is exhibited as a Poisson square wave process. This tolerates temporal uncertainty in the growth of corrosion defect to be characterized but continues to grow. The authors defined four models for the growth of corrosion defects. The models are listed in Table 1.
- “The Negative Binomial Distribution as a Model for External Corrosion Defect Counts in Buried Pipelines” by Valor et al. [89]. In this study, the statistical analysis of real corrosion information from 50 buried oil and gas pipelines operating in Mexico led to the conclusion that the negative binomial (NB) distribution provides a correct description of corrosion defect counts, and the authors discussed the origin of this distribution for this phenomenon. Therefore, the corrosion defect count or corrosion defect density is a random variable that is independent and identically distributed, considering the number of corrosion defects per unit area. The causes determining NB as the distribution for defect counts are associated with three processes: gamma–Poisson mixture, compound Poisson process, and Roger’s process. Unlike other studies, where the number of corrosion defects is modeled as a Poisson process, the defects are randomly distributed and do not interact with each other, and the NB distribution allows representation of cluster corrosion defects that are more realistic in buried pipelines because of the heterogeneous conditions of the soil. Here, the NB distribution is given as follows:
6. Pipeline Reliability Estimations
- Single-value corrosion rate. Valor et al. used the NACE-recommended value for the corrosion rate in pipelines, which is 0.4 mm/year [94]. This value of corrosion rate was used for each defect found in the in-line inspection to obtain future pit depths.
- Linear rate model. It is assumed that each depth of corrosion defect evolves at the same rate at any moment. The corrosion rate of the corrosion defects can be calculated using the following equation:
- Time-dependent generalized extreme value distribution (GEVD) model. This model uses a time-varying corrosion rate distribution proposed by Caleyo et al. [15], which was also discussed in the present study. Caleyo et al. showed that the localized corrosion growth rate in underground pipelines could be represented by a GEVD [86]:
- Time-independent GEVD model. This is similar to the preceding model, excluding the fact that the GEVD parameters of the GEV distribution are assumed as constants and equal to the parameters at the time of the previous inspection.
7. Bayesian Data Analysis in Corroded Oil and Gas Pipelines
8. The Future Challenge for the Application of Probability and Statistics in Corroded Oil and Gas Pipelines
- It would be interesting to study other electrochemical variables using statistical techniques. An example is the determination of whether the icorr or Epit of a steel sample in a corrosive environment exhibits stochastic behavior. This could help in determining the limits with a certain degree of confidence for some conditions where the corrosion rate could exist or the pitting potential could occur. Similarly, it would be necessary to correlate and model the pit initiation time using both electrochemical and statistical techniques for pipeline steels under aggressive environments. It is necessary to orient some studies using electrochemical impedance spectroscopy or electrochemical noise to obtain information that can help to model the pit initiation and the pit growth stochastically.
- The randomness of the pit initiation time is another parameter that should be studied and modeled. Velazquez et al. [14] determined different values of pit initiation time for each type of soil studied. In that study, the pit initiation time was found to be a regression parameter; therefore, it is considered a deterministic value. Nonetheless, determining whether this pit initiation time can also have characteristics of randomness and modeling this randomness would be applicable to estimating the remaining life of the pipeline because these corrosion defects do not initiate at the same time the pipeline makes contact with the soil.
- Further, finding a more accurate approach to determine the corrosion rate distribution in a pipeline using the information provided by consecutive in-line inspection (ILI) is worth mentioning. Many kilometers of oil and gas pipelines are inspected by ILI; however, it is difficult to determine the corrosion rate using this information because the technologies used in both inspections could be different, and the methods to calibrate the devices used differ; locating the same corrosion defects in two consecutive inspections can be a daunting task due to differences in the resolution of the devices used in each inspection, even if they are of the same technology.
- Notwithstanding the evidence that the mechanical properties of pipeline steels change because of the aging of the material, as demonstrated by González-Arévalo et al. [23], there are no studies that use real-life information of aged and corroded pipelines to estimate their reliability. This may be because it is very difficult to monitor changes in the mechanical properties of an in-service pipeline. However, this estimation can help compute the failure probability with greater accuracy.
- BDA has been used in corroded pipelines to successfully estimate the remaining life and the failure probability. However, this statistical technique is not used for other factors related to pipeline deterioration, such as coating disbondment, cathodic protection, ECDA, conditions of fluid transmission, or even stray currents. This technique can be used to study all the phenomena involved in pipeline corrosion.
- New approaches using machine learning techniques and probability concepts have been developed recently by Ossai [109]. These techniques will be widely used in years to come because they can include the independent variables that provoke the localized corrosion deterioration (temperature, chemical composition, fluid velocity, etc.) and represent the phenomenon’s stochastic nature. One advantage of these approaches is that they can manage a vast amount of data with great flexibility.
9. Conclusions
- Pitting corrosion can be studied using the knowledge of probability and statistics, both in laboratory tests (electrochemical and immersion) and in-service pipelines. In electrochemical tests, the most studied variable is the corrosion potential (Ecorr); however, there is a lack of deeper analysis of other characteristics, such as pitting or passive potential, to demonstrate their randomness. Conversely, several studies demonstrate by immersion tests the randomness of the pitting corrosion defect depth, not only in low-carbon steel (pipeline material) but also in other alloys. Usually, the deeper pitting corrosion defect depths measured after the immersion test can be fitted to a Gumbel distribution or GEVD with high confidence. For buried pipelines, the external depths of corrosion defect can also be fitted with high confidence in a GEVD.
- Regression analysis has been widely used to model the growth of localized corrosion defects with a sufficient confidence level. This type of statistical modeling has been used to predict the growth of external corrosion defects in buried pipelines and in solutions that simulate oilfield-produced water. Regression analysis is advantageous in that the physical and chemical characteristics of the environment that is in contact with the pipe can be incorporated into the model. Similarly, the initiation time of the corrosion defect can be included and a deterministic value can be obtained.
- Markov chain models have been successfully used to model the stochastic nature of localized corrosion defects in both immersion tests and oil and gas pipelines. In all cases, the Kolmogorov differential equations are the bases of the solutions in these models. These models correctly represent the shape, kurtosis, and skewness of the observed data histogram in pipeline inspections. In these models, it is also feasible to incorporate the chemical and physical characteristics of the environment in contact with the pipeline, meaning it is not only a purely mathematical model but also possible to establish a sound chemical and physical correlation between the characteristics of the corrosion defect and the properties of the environment.
- Both stochastic models and distributions fitted from observed data can be used to estimate the reliability of oil and gas pipelines. The accurate estimation of the depths of future corrosion defects drives a suitable pipeline reliability estimation, thus achieving better risk management because it is possible to channel resources at the most appropriate time.
- The Monte Carlo simulation approach was used to forecast the long-term distribution of the pitting corrosion rate and pipeline reliability estimation. This method has become quite popular because of the increasing computing power that allows complex simulations to be performed in a short time.
- Bayesian data analysis provides a useful tool for the estimation of the probability distributions of the corrosion defect depth, length, and density. This statistical method helps to estimate the conditions of the corrosion defect characteristics in oil and gas pipelines as long as there is prior information on probability distribution and some observed data in the inspections. BDA can be particularly useful in non-piggable pipelines because it is not feasible from the economic point of view to dig up an entire pipeline and carry out an inspection using a portable flaw detector. These pipelines are usually partially inspected; therefore, it is indispensable to infer the total damage of the structure. Using BDA, it is feasible to estimate the non-piggable pipeline reliability and in this way optimize resources in the maintenance plan.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- British Petroleum. Energy Outlook 2020 Edition. Available online: https://www.bp.com/content/dam/bp/business-sites/en/global/corporate/pdfs/energy-economics/energy-outlook/bp-energy-outlook-2020.pdf (accessed on 1 November 2021).
- Velázquez, J.C.; González-Arévalo, N.E.; Diaz-Cruz, M.; Cervantes-Tobón, A.; Herrera-Hernandez, H.; Hernández-Sánchez, E. Failure pressure estimation for an aged and corroded oil and gas pipeline: A finite element study. J. Nat. Gas Sci. Eng. 2022, 101, 104532. [Google Scholar] [CrossRef]
- Pootakham, T.; Kumar, A. Bio-oil transport by pipeline: A techno-economic assessment. Bioresour. Technol. 2010, 101, 7137–7143. [Google Scholar] [CrossRef]
- Bell, H.S. Petroleum Transportation Handbook, 1st ed.; McGraw-Hill: New York, NY, USA, 1963. [Google Scholar]
- CIA The World Factbook. Available online: https://www.cia.gov/the-world-factbook/ (accessed on 5 November 2021).
- Lu, H.; Iseley, T.; Behbahani, S.; Fu, L. Leakage detection techniques for oil and gas pipelines: State-of-the-art. Tunn. Undergr. Space Technol. 2020, 98, 103249. [Google Scholar] [CrossRef]
- EGIG 11th Report of the European Gas Pipeline Incident Data Group. Available online: https://www.egig.eu/reports (accessed on 15 December 2021).
- Caleyo, F.; Alfonso, L.; Alcántara, J.; Hallen, J.M. On the Estimation of Failure Rates of Multiple Pipeline Systems. J. Press. Vessel Technol. 2008, 130, 021704. [Google Scholar] [CrossRef]
- Koch, G.; Varney, J.; Thompson, N.; Moghissi, O.; Gould, M.; Payer, J. International Measures of Prevention, Application, and Economics of Corrosion Technologies Study; NACE International: Houston, TX, USA, 2016. [Google Scholar]
- Evans, U.R.; Mears, R.B.; Queneau, P.E. Corrosion-velocity and corrosion-probability. Engineering 1933, 136, 689. [Google Scholar]
- Romanoff, M. Underground Corrosion; US Government Printing Office: Washington, DC, USA, 1957.
- Aziz, P.M. Application of the Statistical Theory of Extreme Values To the Analysis of Maximum Pit Depth Data for Aluminum. Corrosion 1956, 12, 35–46. [Google Scholar] [CrossRef]
- American Petroleum Institute. API Recommended Practice 571, Damage Mechanisms Affecting Fixed Equipment in the Refining Industries, 2nd ed.; American Petroleum Institute: Washington, DC, USA, 2011. [Google Scholar]
- Velázquez, J.C.; Caleyo, F.; Valor, A.; Hallen, J.M. Predictive Model for Pitting Corrosion in Buried Oil and Gas Pipelines. Corrosion 2009, 65, 332–342. [Google Scholar] [CrossRef]
- Caleyo, F.; Velázquez, J.C.; Valor, A.; Hallen, J.M. Probability distribution of pitting corrosion depth and rate in underground pipelines: A Monte Carlo study. Corros. Sci. 2009, 51, 1925–1934. [Google Scholar] [CrossRef]
- Alamilla, J.L.; Sosa, E. Stochastic modelling of corrosion damage propagation in active sites from field inspection data. Corros. Sci. 2008, 50, 1811–1819. [Google Scholar] [CrossRef]
- Caleyo, F.; Valor, A.; Alfonso, L.; Vidal, J.; Perez-Baruch, E.; Hallen, J.M. Bayesian analysis of external corrosion data of non-piggable underground pipelines. Corros. Sci. 2015, 90, 33–45. [Google Scholar] [CrossRef]
- Valor, A.; Caleyo, F.; Alfonso, L.; Vidal, J.; Hallen, J.M. Statistical Analysis of Pitting Corrosion Field Data and Their Use for Realistic Reliability Estimations in Non-Piggable Pipeline Systems. Corrosion 2014, 70, 1090–1100. [Google Scholar] [CrossRef]
- Ogutcu, G. Pipeline Risk Assessment by Bayesian Belief Network. In Proceedings of the 6th International Pipeline Conference, Calgary, AB, Canada, 25–29 September 2006. Paper: IPC2006-10088. [Google Scholar] [CrossRef]
- Ainouche, A. Future integrity management strategy of a gas pipeline using bayesian risk analysis. In Proceedings of the 23rd World GAS Conference, Amsterdam, The Netherlands, 5–9 June 2006; Available online: http://members.igu.org/html/wgc2006/pdf/paper/add10327.pdf (accessed on 20 March 2022).
- Stephens, M.; Nessim, M. A Comprehensive Approach to Corrosion Management Based on Structural Reliability Methods. In Proceedings of the 6th International Pipeline Conference, Calgary, AB, Canada, 25–29 September 2006. Paper: IPC2006-10458. [Google Scholar] [CrossRef]
- Caleyo, F.; González, J.L.; Hallen, J.M. A study on the reliability assessment methodology for pipelines with active corrosion defects. Int. J. Press. Vessel. Pip. 2002, 79, 77–86. [Google Scholar] [CrossRef]
- González-Arévalo, N.E.; Velázquez, J.C.; Díaz-Cruz, M.; Cervantes-Tobón, A.; Terán, G.; Hernández-Sanchez, E.; Capula-Colindres, S. Influence of aging steel on pipeline burst pressure prediction and its impact on failure probability estimation. Eng. Fail. Anal. 2021, 120. [Google Scholar] [CrossRef]
- Zakikhani, K.; Nasiri, F.; Zayed, T. A Review of Failure Prediction Models for Oil and Gas Pipelines. J. Pipeline Syst. Eng. Pract. 2020, 11, 03119001. [Google Scholar] [CrossRef]
- Muhlbauer, W.K. Pipeline Risk Management Manual, 3rd ed.; Elsevier: Amsterdam, The Netherlands, 2004; ISBN 9780750675796. [Google Scholar]
- Tan, M.Y.J.; Varela, F.; Huo, Y.; Wang, K.; Ubhayaratne, I. An Overview of Recent Progresses in Monitoring and Understanding Localized Corrosion on Buried Steel Pipelines. Paper presented at the CORROSION 2020, Physical Event Cancelled, 14–18 June 2020. Paper Number: NACE-2020-15025.
- Papavinasam, S. Corrosion Control in the Oil and Gas Industry; Elsevier: Amsterdam, The Netherlands, 2014; ISBN 9780123970220. [Google Scholar]
- Peabody, A.W. Peabody’s Control of Pipeline Corrosion, 2nd ed.; Bianchetti, R.L., Ed.; NACE International: Houston, TX, USA, 2001; ISBN 978-1575900926. [Google Scholar]
- Bhandari, J.; Khan, F.; Abbassi, R.; Garaniya, V.; Ojeda, R. Modelling of pitting corrosion in marine and offshore steel structures—A technical review. J. Loss Prev. Process Ind. 2015, 37, 39–62. [Google Scholar] [CrossRef]
- Fontana, M.G. Corrosion Engineering, 3rd ed.; McGraw-Hill Book Company: New York, NY, USA, 1985; ISBN 978-0070214637. [Google Scholar]
- Agar, J.N.; Hoar, T.P. The influence of change of size in electrochemical systems. Discuss. Faraday Soc. 1947, 1, 158. [Google Scholar] [CrossRef]
- Corrosionpedia Critical Pitting Potential (Epit). Available online: https://www.corrosionpedia.com/definition/352/critical-pitting-potential-epit (accessed on 5 December 2021).
- Szklarska-Smialowska, Z. Pitting Corrosion of Metals; NACE International: Houston, TX, USA, 1986; ISBN 978-0915567195. [Google Scholar]
- Corrosionpedia Repassivation Potential. Available online: https://www.corrosionpedia.com/definition/6258/repassivation-potential (accessed on 5 December 2021).
- Caines, S.; Khan, F.; Shirokoff, J. Analysis of pitting corrosion on steel under insulation in marine environments. J. Loss Prev. Process Ind. 2013, 26, 1466–1483. [Google Scholar] [CrossRef]
- Frankel, G.S. Pitting Corrosion of Metals: A Review of the Critical Factors. J. Electrochem. Soc. 1998, 145, 2186–2198. [Google Scholar] [CrossRef]
- Böhni, H. Metastable Pitting—Occurrence and Significance for Passive Metals; Swiss Federal Institute of Technology: Zürich, Switzerland, 2002. [Google Scholar]
- Finsås Wika, S. Pitting and Crevice Corrosion of Stainless Steel under Offshore Conditions. Master’s Thesis, The Norwegian University of Science and Technology, Trondheim, Norway, 2012. [Google Scholar]
- Angal, R.D. Principles and Prevention of Corrosion; Alpha Science International Ltd.: Oxford, UK, 2010; ISBN 978-1842655290. [Google Scholar]
- Sridhar, N.; Dunn, D.S.; Seth, M. Application of a General Reactive Transport Model to Predict Environment under Disbonded Coatings. Corrosion 2001, 57, 598–613. [Google Scholar] [CrossRef]
- Craig, B.D. Practical Oilfield Metallurgy and Corrosion, 3rd ed.; Pennwell Corp: Tulsa, OK, USA, 1993; ISBN 978-0878143887. [Google Scholar]
- Papavinasam, S.; Doiron, A.; Revie, R.W. Model to Predict Internal Pitting Corrosion of Oil and Gas Pipelines. Corrosion 2010, 66, 035006. [Google Scholar] [CrossRef]
- Malik, A.U.; Ahmad, S.; Andijani, I.; Al-Fouzan, S. Corrosion behavior of steels in Gulf seawater environment. Desalination 1999, 123, 205–213. [Google Scholar] [CrossRef]
- Frankel, G.S.; Sridhar, N. Understanding localized corrosion. Mater. Today 2008, 11, 38–44. [Google Scholar] [CrossRef]
- Abood, T.H. The Influence of Various Parameters on Pitting Corrosion of 316l and 202 Stainless Steel; Department of Chemical Engineering of the University of Technology: Baghdad, Iraq, 2008. [Google Scholar]
- Velázquez, J.C.; Cruz-Ramirez, J.C.; Valor, A.; Venegas, V.; Caleyo, F.; Hallen, J.M. Modeling localized corrosion of pipeline steels in oilfield produced water environments. Eng. Fail. Anal. 2017, 79, 216–231. [Google Scholar] [CrossRef]
- Dean, S.W.; Grab, G.D. Corrosion of carbon steel by concentrated sulfuric acid. Mater. Perform. 1985, 24, 21–25. [Google Scholar]
- Panossian, Z.; de Almeida, N.L.; de Sousa, R.M.F.; Pimenta, G. de S.; Marques, L.B.S. Corrosion of carbon steel pipes and tanks by concentrated sulfuric acid: A review. Corros. Sci. 2012, 58, 1–11. [Google Scholar] [CrossRef]
- Maruthamuthu, S.; Kumar, B.D.; Ramachandran, S.; Anandkumar, B.; Palanichamy, S.; Chandrasekaran, M.; Subramanian, P.; Palaniswamy, N. Microbial Corrosion in Petroleum Product Transporting Pipelines. Ind. Eng. Chem. Res. 2011, 50, 8006–8015. [Google Scholar] [CrossRef]
- Santillan, E.-F.U.; Choi, W.; Bennett, P.C.; Diouma Leyris, J. The effects of biocide use on the microbiology and geochemistry of produced water in the Eagle Ford formation, Texas, U.S.A. J. Pet. Sci. Eng. 2015, 135, 1–9. [Google Scholar] [CrossRef]
- Liu, T.; Cheng, Y.F.; Sharma, M.; Voordouw, G. Effect of fluid flow on biofilm formation and microbiologically influenced corrosion of pipelines in oilfield produced water. J. Pet. Sci. Eng. 2017, 156, 451–459. [Google Scholar] [CrossRef]
- Shibata, T.; Takeyama, T. Stochastic Theory of Pitting Corrosion. Corrosion 1977, 33, 243–251. [Google Scholar] [CrossRef]
- Gabrielli, C.; Huet, F.; Keddam, M.; Oltra, R. A Review of the Probabilistic Aspects of Localized Corrosion. Corrosion 1990, 46, 266–278. [Google Scholar] [CrossRef]
- Lewis, C.F. Statistics—A Useful Tool For the Examination of Corrosion Data. Corrosion 1953, 9, 38–43. [Google Scholar] [CrossRef]
- Rivas, D.; Caleyo, F.; Valor, A.; Hallen, J.M. Extreme value analysis applied to pitting corrosion experiments in low carbon steel: Comparison of block maxima and peak over threshold approaches. Corros. Sci. 2008, 50, 3193–3204. [Google Scholar] [CrossRef]
- Mughabghab, S.F.; Sullivan, T.M. Evaluation of the pitting corrosion of carbon steels and other ferrous metals in soil systems. Waste Manag. 1989, 9, 239–251. [Google Scholar] [CrossRef]
- Kajiyama, F.; Koyama, Y. Statistical Analyses of Field Corrosion Data for Ductile Cast Iron Pipes Buried in Sandy Marine Sediments. Corrosion 1997, 53, 156–162. [Google Scholar] [CrossRef]
- Katano, Y.; Miyata, K.; Shimizu, H.; Isogai, T. Predictive Model for Pit Growth on Underground Pipes. Corrosion 2003, 59, 155–161. [Google Scholar] [CrossRef]
- Race, J.M.; Dawson, S.J.; Stanley, L.; Kariyawasam, S. Predicting Corrosion Rates for Onshore Oil and Gas Pipelines. In Proceedings of the 6th International Pipeline Conference, Calgary, AB, Canada, 25–29 September 2006. Paper: IPC2006-10261. [Google Scholar] [CrossRef]
- Carpenter, C. The Effect of CO2 Injection on Corrosion and Integrity of Facilities. Available online: https://jpt.spe.org/effect-co2-injection-corrosion-and-integrity-facilities (accessed on 11 December 2021).
- Velázquez, J.C.; Caleyo, F.; Valor, A.; Hallen, J.M. Technical Note: Field Study—Pitting Corrosion of Underground Pipelines Related to Local Soil and Pipe Characteristics. Corrosion 2010, 66, 016001. [Google Scholar] [CrossRef]
- Ossai, C.I. Predictive Modelling of Wellhead Corrosion due to Operating Conditions: A Field Data Approach. ISRN Corros. 2012, 2012, 237025. [Google Scholar] [CrossRef] [Green Version]
- Zakikhani, K.; Nasiri, F.; Zayed, T. A failure prediction model for corrosion in gas transmission pipelines. Proc. Inst. Mech. Eng. Part O J. Risk Reliab. 2021, 235, 374–390. [Google Scholar] [CrossRef]
- Al-Fakih, A.M.; Algamal, Z.Y.; Lee, M.H.; Abdallah, H.H.; Maarof, H.; Aziz, M. Quantitative structure-activity relationship model for prediction study of corrosion inhibition efficiency using two-stage sparse multiple linear regression. J. Chemom. 2016, 30, 361–368. [Google Scholar] [CrossRef]
- Finley, H.F.; Toncre, A.C. Extreme value statistical analysis in correlation of first leak on submerged pipeline. Mater. Prot. 1964, 3, 29–34. [Google Scholar]
- Finley, H.F. An Extreme-Value Statistical Analysis of Maximum Pit Depths and Time to First Perforation. Corrosion 1967, 23, 8387. [Google Scholar]
- Provan, J.W.; Rodriguez, E.S. Part I: Development of a Markov Description of Pitting Corrosion. Corrosion 1989, 45, 178–192. [Google Scholar] [CrossRef]
- Rodriguez, E.S.; Provan, J.W. Part II: Development of a General Failure Control System for Estimating the Reliability of Deteriorating Structures. Corrosion 1989, 45, 193–206. [Google Scholar] [CrossRef]
- Hong, H.P. Inspection and maintenance planning of pipeline under external corrosion considering generation of new defects. Struct. Saf. 1999, 21, 203–222. [Google Scholar] [CrossRef]
- Timashev, S.A.; Malyukova, M.G.; Poluian, L.V.; Bushinskaya, A.V. Markov Description of Corrosion Defects Growth and Its Application to Reliability Based Inspection and Maintenance of Pipelines. In Proceedings of the 7th International Pipeline Conference, Calgary, AB, Canada, 29 September–3 October 2008. Paper: IPC2008-64546. [Google Scholar] [CrossRef]
- Caleyo, F.; Velázquez, J.C.; Valor, A.; Hallen, J.M. Markov chain modelling of pitting corrosion in underground pipelines. Corros. Sci. 2009, 51, 2197–2207. [Google Scholar] [CrossRef]
- Parzen, E. Stochastic Processes, Classics in Applied Mathematics; Society for Industrial and Applied Mathematics (SIAM): Philadelphia, PA, USA, 1999. [Google Scholar]
- Cox, D.R.; Miller, H.D. The Theory of Stochastic Processes, 1st ed.; Chapman and Hall/CRC: Boca Raton, FL, USA, 1977; ISBN 9780412151705. [Google Scholar]
- Timashev, S.A.; Bushinskaya, A.V. Markov approach to early diagnostics, reliability assessment, residual life and optimal maintenance of pipeline systems. Struct. Saf. 2015, 56, 68–79. [Google Scholar] [CrossRef]
- Wang, H.; Yajima, A.; Liang, R.Y.; Castaneda, H. A clustering approach for assessing external corrosion in a buried pipeline based on hidden Markov random field model. Struct. Saf. 2015, 56, 18–29. [Google Scholar] [CrossRef]
- Ossai, C.I.; Boswell, B.; Davies, I. Markov chain modelling for time evolution of internal pitting corrosion distribution of oil and gas pipelines. Eng. Fail. Anal. 2016, 60, 209–228. [Google Scholar] [CrossRef] [Green Version]
- Valor, A.; Caleyo, F.; Alfonso, L.; Rivas, D.; Hallen, J.M. Stochastic modeling of pitting corrosion: A new model for initiation and growth of multiple corrosion pits. Corros. Sci. 2007, 49, 559–579. [Google Scholar] [CrossRef]
- Strutt, J.E.; Nicholls, J.R.; Barbier, B. The prediction of corrosion by statistical analysis of corrosion profiles. Corros. Sci. 1985, 25, 305–315. [Google Scholar] [CrossRef]
- Melchers, R.E. Pitting Corrosion of Mild Steel in Marine Immersion Environment—Part 2: Variability of Maximum Pit Depth. Corrosion 2004, 60, 937–944. [Google Scholar] [CrossRef]
- Velázquez-Altamirano, J.C.; Torres-Avila, I.P.; Teran-Méndez, G.; Capula-Colindres, S.I.; Cabrera-Sierra, R.; Carrera-Espinoza, R.; Hernández-Sánchez, E. A Stochastic Model and Investigation into the Probability Distribution of the Thickness of Boride Layers Formed on Low-Carbon Steel. Coatings 2019, 9, 756. [Google Scholar] [CrossRef] [Green Version]
- Amaya-Gómez, R.; Riascos-Ochoa, J.; Muñoz, F.; Bastidas-Arteaga, E.; Schoefs, F.; Sánchez-Silva, M. Modeling of pipeline corrosion degradation mechanism with a Lévy Process based on ILI (In-Line) inspections. Int. J. Press. Vessel. Pip. 2019, 172, 261–271. [Google Scholar] [CrossRef]
- van Noortwijk, J.M. A survey of the application of gamma processes in maintenance. Reliab. Eng. Syst. Saf. 2009, 94, 2–21. [Google Scholar] [CrossRef]
- Kuniewski, S.P.; van der Weide, J.A.M.; van Noortwijk, J.M. Sampling inspection for the evaluation of time-dependent reliability of deteriorating systems under imperfect defect detection. Reliab. Eng. Syst. Saf. 2009, 94, 1480–1490. [Google Scholar] [CrossRef]
- Velázquez, J.C.; van Der Weide, J.A.M.; Hernández, E.; Hernández, H.H. Statistical Modelling of Pitting Corrosion: Extrapolation of the Maximum Pit Depth-Growth. Int. J. Electrochem. Sci. 2014, 9, 4129–4143. [Google Scholar]
- Kowaka, M.; Tsuge, H. Introduction to Life Prediction of Industrial Plant Materials: Application of the Extreme Value Statistical Method for Corrosion Analysis; Originally Published in Japanese by The Japan Society of Corrosion Engineers 1984; Allerton Press: New York, NY, USA, 1994; ISBN 978-0898640731. [Google Scholar]
- Castillo, E.; Hadi, A.S.; Balakrishnan, N.; Sarabia, J.M. Extreme Value and Related Models with Applications in Engineering and Science, 1st ed.; Wiley: Hoboken, NJ, USA, 2004. [Google Scholar]
- Alamilla, J.L.; Espinosa-Medina, M.A.; Sosa, E. Modelling steel corrosion damage in soil environment. Corros. Sci. 2009, 51, 2628–2638. [Google Scholar] [CrossRef]
- Bazán, F.A.V.; Beck, A.T. Stochastic process corrosion growth models for pipeline reliability. Corros. Sci. 2013, 74, 50–58. [Google Scholar] [CrossRef]
- Valor, A.; Alfonso, L.; Caleyo, F.; Vidal, J.; Perez-Baruch, E.; Hallen, J.M. The negative binomial distribution as a model for external corrosion defect counts in buried pipelines. Corros. Sci. 2015, 101, 114–131. [Google Scholar] [CrossRef]
- Ahammed, M.; Melchers, R.E. Reliability estimation of pressurised pipelines subject to localised corrosion defects. Int. J. Press. Vessel. Pip. 1996, 69, 267–272. [Google Scholar] [CrossRef]
- Zhang, P.; Su, L.; Qin, G.; Kong, X.; Peng, Y. Failure probability of corroded pipeline considering the correlation of random variables. Eng. Fail. Anal. 2019, 99, 34–45. [Google Scholar] [CrossRef]
- Andrieu, C. Monte Carlo Methods for Absolute Beginners. Lecture Notes in Computer Science. 2004, pp. 113–145. Available online: http://nozdr.ru/data/media/biblio/kolxoz/Cs/CsLn/Advanced%20Lectures%20on%20Machine%20Learning%202003(LNCS3176,%20Springer,%202004)(ISBN%203540231226)(248s).pdf#page=120 (accessed on 1 January 2022).
- Valor, A.; Caleyo, F.; Hallen, J.M.; Velázquez, J.C. Reliability assessment of buried pipelines based on different corrosion rate models. Corros. Sci. 2013, 66, 78–87. [Google Scholar] [CrossRef]
- Race, J.M.; Dawson, S.J.; Stanley, L.; Kariyawasam, S. Development of a predictive model for pipeline external corrosion rates. J. Pipeline Eng. 2007, 6, 15–29. [Google Scholar]
- Caleyo, F.; Valor, A.; Velázquez, J.C.; Hallen, J.M. On the estimation of the probability of failure of single corrosion defects in oil and gas pipelines. In Proceedings of the Nace Corrosion Risk Management Conference, Houston, TX, USA, 23–25 May March 2016. Paper No. RISK16 -8761. [Google Scholar]
- American Society of Mechanical Engineers. Manual for Determining the Remaining Strength of Corroded Pipelines: Supplement to ASME B31 Code for Pressure Piping; American Society of Mechanical Engineers: New York, NY, USA, 1984. [Google Scholar]
- American Society of Mechanical Engineers. Manual for Determining the Remaining Strength of Corroded Pipelines: Supplement to ASME B31 Code for Pressure Piping; American Society of Mechanical Engineers: New York, NY, USA, 1991. [Google Scholar]
- American Society of Mechanical Engineers. Manual for Determining the Remaining Strength of Corroded Pipelines: Supplement to ASME B31 Code for Pressure Piping; American Society of Mechanical Engineers: New York, NY, USA, 2009. [Google Scholar]
- Ma, B.; Shuai, J.; Wang, J.; Han, K. Analysis on the Latest Assessment Criteria of ASME B31G-2009 for the Remaining Strength of Corroded Pipelines. J. Fail. Anal. Prev. 2011, 11, 666–671. [Google Scholar] [CrossRef]
- Kiefner, J.F.; Vieth, P.H. Evaluating pipe-1 new method corrects criterion for evaluating corroded pipe. Oil Gas J. 1990, 88, 56–59. [Google Scholar]
- Klever, F.J.; Stewart, G.; van der Valk, C.A.C. New developments in burst strength predictions for locally corroded pipelines. In Proceedings of the Offshore Mechanics and Artic Engineering (OMAE) Conference, Copenhagen, Denmark, 18–22 June 1995. [Google Scholar]
- Leis, B.N.; Stephens, D.R. An Alternative Approach to Assess the Integrity of Corroded Line Pipe—Part I: Current Status. Available online: https://www.onepetro.org/conference-paper/ISOPE-I-97-490 (accessed on 7 August 2016).
- Leis, B.N.; Stephens, D.R. An Alternative Approach to Assess the Integrity of Corroded Line Pipe—Part II: Alternative Criterion. Available online: https://www.onepetro.org/conference-paper/ISOPE-I-97-490 (accessed on 7 August 2016).
- Det Norske Veritas DNV-RP-F101 Corroded Pipelines. Available online: https://rules.dnvgl.com/docs/pdf/DNV/codes/docs/2010-10/RP-F101.pdf (accessed on 21 May 2012).
- American Petroleum Institute. API RP 579, Fittness-for-Service; American Petroleum Institute: Washington, DC, USA, 2007. [Google Scholar]
- Cicero, S.; Lacalle, R.; Cicero, R.; Ferreño, D. Assessment of local thin areas in a marine pipeline by using the FITNET FFS corrosion module. Int. J. Press. Vessel. Pip. 2009, 86, 329–334. [Google Scholar] [CrossRef]
- Corrosionpedia Non-Piggable Pipeline. Available online: https://www.corrosionpedia.com/definition/2817/non-piggable-pipeline (accessed on 20 December 2021).
- Kruschke, J.K. Doing Bayesian Data Analysis, 2nd ed.; Academic Press: Cambridge, MA, USA, 2015; ISBN 978-0-12-405888-0. [Google Scholar]
- Ossai, C.I. A Data-Driven Machine Learning Approach for Corrosion Risk Assessment—A Comparative Study. Big Data Cogn. Comput. 2019, 3, 28. [Google Scholar] [CrossRef] [Green Version]
Model | Characteristic | Distributions Used | Description |
---|---|---|---|
Linear random variable |
|
| It is a simple representation of the corrosion defect rate (v) as a random variable. It can be estimated as follows: |
Linear stochastic process |
|
| The authors proposed modeling the growth rate of the corrosion defect as a Poisson square wave process with stationary and independent increments (pulse heights). The pulse height and time durations are both characterized as random variables. The pulse durations are described as an exponential random variable with parameter λ. Conversely, pulse heights are represented using a gamma distribution. The following equation describes this process:
|
Nonlinear random variable |
|
| In this case, the authors used the power-law model proposed by Velázquez et al. [14] and Caleyo et al. [15] (Equation (14)). Bazán and Beck modeled considering both the proportional and exponential factors as random variables, considering the initiation time of 2.88 years. The proportionality factor is supposed to follow a gamma distribution. The exponent is supposed to follow a lognormal distribution. |
Nonlinear stochastic process |
|
| This model emerges as a combination of the nonlinear random variable model and the linear stochastic process model. The proportional factor of the power law (see Equation (14)) is represented by a Poisson square wave process, with pulse height and durations . Both exponential and gamma distributions are used to represent the arrival and new pulses and pulse intensities, respectively. Similarly, the lognormal distribution is used to represent the exponential factor of the power law. The increment in the size of corrosion defect is given as follows: |
Model and References | Authors | Expression | Bulging Factor |
---|---|---|---|
ASME B31G-1984 [96] | ASME | , , | |
ASME B31G-1991 [97] | ASME | , , | |
ASME B31G-2009 [98,99] | ASME | , | |
Modified ASME B31G [100] | ASME J.F. Kiefner P.H. Vieth | , | |
Shell-92 [101] | Shell F.J. Klever G. Steward C.A.C. van der Valk | ||
PCORR [102,103] | Batelle B.N. Leis D.R. Stephens | ||
DNV RP F101 [104] | Det Norske Veritas (Norway) BG Technology (Canada) | ||
API RP 579 [105] | API | ||
FITNET FFS [106] | European Fitness for Service Network E. Seib et al. |
Characteristic | Units | Distribution | Parameters | ||
---|---|---|---|---|---|
Depth | %PWT (pipe wall thickness percent) | GEV | 18.50 | 8.86 | 0.078 |
Length | m | GEV | 0.095 | 0.195 | 0.753 |
Defect density | Per ditch | Negative binomial | |||
0.208 | 0.21 |
Defect Characteristic | Units | Fitted Distribution | Parameters | ||
---|---|---|---|---|---|
Depth | %PWT | GEV | 17.01 | 8.02 | 0.12 |
Length | m | GEV | 0.078 | 0.086 | 1.11 |
Density | Per ditch | Negative binomial | 0.35 | 0.13 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Velázquez, J.C.; Hernández-Sánchez, E.; Terán, G.; Capula-Colindres, S.; Diaz-Cruz, M.; Cervantes-Tobón, A. Probabilistic and Statistical Techniques to Study the Impact of Localized Corrosion Defects in Oil and Gas Pipelines: A Review. Metals 2022, 12, 576. https://doi.org/10.3390/met12040576
Velázquez JC, Hernández-Sánchez E, Terán G, Capula-Colindres S, Diaz-Cruz M, Cervantes-Tobón A. Probabilistic and Statistical Techniques to Study the Impact of Localized Corrosion Defects in Oil and Gas Pipelines: A Review. Metals. 2022; 12(4):576. https://doi.org/10.3390/met12040576
Chicago/Turabian StyleVelázquez, Julio César, Enrique Hernández-Sánchez, Gerardo Terán, Selene Capula-Colindres, Manuela Diaz-Cruz, and Arturo Cervantes-Tobón. 2022. "Probabilistic and Statistical Techniques to Study the Impact of Localized Corrosion Defects in Oil and Gas Pipelines: A Review" Metals 12, no. 4: 576. https://doi.org/10.3390/met12040576