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Induced seismicity and corrosion vulnerability assessment of oil and gas pipelines using a Bayesian belief… Shabarchin, Oleg 2016

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INDUCED SEISMICITY AND CORROSION VULNERABILITY ASSESSMENT OF OIL AND GAS PIPELINES USING A BAYESIAN BELIEF NETWORK MODEL   by  Oleg Shabarchin  B.Sc. Ufa State Petroleum Technological University, 2011  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE  in  THE COLLEGE OF GRADUATE STUDIES  (Civil Engineering)   THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan)  March 2016   © Oleg Shabarchin, 2016        The undersigned certify that they have read, and recommend to the College of Graduate Studies for acceptance, a thesis entitled:    Induced Seismicity and Corrosion Vulnerability Assessment of Oil and Gas Pipelines Using a Bayesian Belief Network Model  Submitted by                     Oleg Shabarchin                   in partial fulfillment of the requirements of   The degree of       Master of Applied Science                                              .  Dr. Solomon Tesfamariam Supervisor, Professor (please print name and faculty/school above the line)  Dr. Rehan Sadiq Supervisory Committee Member, Professor (please print name and faculty/school in the line above)  Dr. Kasun Hewage Supervisory Committee Member, Professor (please print name and faculty/school in the line above)  Dr. Thomas Johnson University Examiner, Professor (please print name and faculty/school in the line above)   External Examiner, Professor (please print name and university in the line above)   March 30, 2016 (Date submitted to Grad Studies)     ii  Abstract A substantial amount of oil and gas products are transported and distributed via pipelines, which can stretch for thousands of kilometers. Because of the adverse environmental impact and significant financial losses, the integrity of these pipelines is essential. British Columbia Oil and Gas Commission (BCOGC) has indicated metal loss due to corrosion as one of the primary causes of pipeline failures. Therefore, it is important to identify pipelines subjected to severe corrosion in order to improve corrosion mitigation and pipeline maintenance strategies, thus minimizing the likelihood of failure. To accomplish this task, this thesis presents a Bayesian belief network (BBN)-based probabilistic corrosion hazard assessment approach for oil and gas pipelines. A cause-effect BBN model has been developed by considering various types of information, such as analytical corrosion models, expert knowledge and published literature. Multiple corrosion models and failure pressure models have been incorporated into a single flexible network in order to estimate corrosion defects and the associated probability of failure. Besides corrosion hazard, BCOGC has reported multiple cases of anthropogenic seismicity, which also may compromise the pipeline integrity. To this end, this thesis explores the potential impact of induced seismicity on the oil and gas pipeline infrastructure. Spatial clustering analysis is used for earthquakes, previously registered in the region, to delineate areas, which are particularly prone to the induced seismicity. The state of the art ground motion prediction equation for induced seismicity is applied in a Monte Carlo simulation to obtain a stochastic field of the seismic intensity. Based on the established seismic fragility formulations for pipelines and mechanical characteristics as well as corrosion conditions, spatial and probabilistic distributions of the repair rate and probability of failure have been obtained and visualized with the aid of the Geographic Information System. The proposed model can help to identify vulnerable pipeline sections and rank them accordingly to enhance the informed decision making process. To demonstrate the application of the proposed approach, two case studies for the Northeastern British Columbia oil and gas pipeline infrastructure are presented.    iii  Preface This research has been conducted under the supervision of Dr. Solomon Tesfamariam. Some content of this thesis has been submitted for publishing in scientific journals:   A version of the Chapter 2, Chapter 3 has been published in a journal: Shabarchin, O. and Tesfamariam, S. (2016). “Internal Corrosion Hazard Assessment of Oil and Gas Pipelines Using Bayesian Belief Network Model”. Journal of Loss Prevention in the Process Industries, doi:10.1016/j.jlp.2016.02.001  Some content from Chapter 4 and Chapter 6 has been submitted to a journal: Shabarchin, O. and Tesfamariam, S. (2016). “Induced Seismicity Risk Assessment of Oil and Gas Pipelines.” Risk Analysis.   iv  Table of Contents Abstract .......................................................................................................................................... ii Preface ........................................................................................................................................... iii Table of Contents ......................................................................................................................... iv List of Tables ............................................................................................................................... vii List of Figures ............................................................................................................................... ix Acknowledgements .................................................................................................................... xiv Dedication .................................................................................................................................... xv Chapter 1 Introduction................................................................................................................. 1 1.1 Research Objectives .................................................................................................................... 4 1.2 Organization of the Thesis ........................................................................................................... 5 Chapter 2 Bayesian Belief Network ............................................................................................ 6 2.1 Motivation for BBN Application ................................................................................................. 6 2.2 Theoretical Background .............................................................................................................. 9 Chapter 3 Internal Corrosion .................................................................................................... 12 3.1 General Corrosion of Steel in Sweet and Sour Environments ................................................... 12 3.1.1 Impact of Temperature .......................................................................................................... 13 3.1.2 Impact of Flow ...................................................................................................................... 13 3.1.3 Impact of pH ......................................................................................................................... 14 3.1.4 Impact of Corrosion Inhibitors .............................................................................................. 14 3.2 Localized Corrosion .................................................................................................................. 14 v  3.3 BBN Internal Corrosion Model Development ........................................................................... 18 3.3.1 General Corrosion Model ...................................................................................................... 19 3.3.2 Pitting Corrosion and Erosion-Corrosion Models ................................................................. 22 3.3.3 Microbiologically Influenced Corrosion ............................................................................... 23 3.3.3.1 Operating Conditions ............................................................................................................ 24 3.3.3.2 Water Condition .................................................................................................................... 25 3.3.3.3 MIC Control .......................................................................................................................... 26 3.3.4 Corrosion Defect Model ........................................................................................................ 28 3.4 Sensitivity Analysis ................................................................................................................... 33 3.5 Scenario Analysis ...................................................................................................................... 36 3.6 Case Study of the Northeastern BC Pipeline Infrastructure ...................................................... 41 Chapter 4 Induced Seismicity .................................................................................................... 45 4.1 Study Region ............................................................................................................................. 47 4.2 Induced Seismicity Hazard Assessment .................................................................................... 49 4.2.1 Spatial Clustering Analysis ................................................................................................... 49 4.2.2 Ground Motion Prediction Equation for Induced Seismicity ................................................ 51 4.2.3 Induced Seismicity Hazard Map ........................................................................................... 53 4.3 Pipeline Vulnerability Functions ............................................................................................... 54 4.4 Results and Discussion .............................................................................................................. 58 Chapter 5 External Corrosion ................................................................................................... 62 5.1 Corrosion Mechanism and Factors Affecting its Rate ............................................................... 62 5.1.1 Soil Resistivity ...................................................................................................................... 63 5.1.2 Soil pH .................................................................................................................................. 64 5.1.3 Redox Potential ..................................................................................................................... 64 vi  5.1.4 Chlorides and Sulfates ........................................................................................................... 64 5.1.5 Moisture Content ................................................................................................................... 64 5.2 BBN External Corrosion Model Development.......................................................................... 65 5.3 Knowledge Based BBN for Coating Failure ............................................................................. 66 5.3.1 Coating Condition ................................................................................................................. 68 5.3.2 Soil Stress .............................................................................................................................. 69 5.3.3 Operating Temperature ......................................................................................................... 70 5.4 Corrosion Defect Depth ............................................................................................................. 73 5.5 Corrosion Defect Length ........................................................................................................... 77 5.6 Sensitivity Analysis ................................................................................................................... 78 5.7 Scenario Analysis ...................................................................................................................... 79 Chapter 6 Summary and Conclusions ...................................................................................... 82 6.1 Research Contributions.............................................................................................................. 82 6.2 Limitations ................................................................................................................................. 84  vii  List of Tables Table 2.1 Comparison of various network based techniques ......................................................... 8 Table 3.1 Parameters applied in different corrosion models ........................................................ 20 Table 3.2 General corrosion model discretization details ............................................................. 21 Table 3.3 Erosion-Corrosion and pitting corrosion model discretization details ......................... 23 Table 3.4 Some examples of CPT for the MIC node .................................................................... 24 Table 3.5 Bacteria removal efficiency depending on the pig type, modified after (Papavinasam, 2013) .................................................................................................... 26 Table 3.6 MIC discretization model details .................................................................................. 27 Table 3.7 Failure pressure models and their application based on steel toughness ...................... 31 Table 3.8 Corrosion defect model discretization details ............................................................... 32 Table 3.9 Probabilistic data of input parameters .......................................................................... 37 Table 3.10 Median and maximum defect depth and PoF ............................................................. 38 Table 4.1 Probability distributions of input parameters................................................................ 53 Table 4.2 Some values of the adjustment factor ( K1) to estimate wave propagation damage (America Lifelines Alliance, 2001) .............................................................................. 55 Table 4.3 Corrosion vulnerability categories and corresponding values of the adjustment factor (K1) .................................................................................................................... 57 Table 5.1 Types of coating and its expected service time ............................................................ 68 Table 5.2 Fragment of conditional probability of CFT node ........................................................ 71 Table 5.3 Parameters and their discretization for coating failure model ...................................... 72 Table 5.4 Commonly applied corrosion models modified after (Sadiq et al., 2004b) .................. 73 viii  Table 5.5 Equation coefficients for the pitting exponent and the coefficient of proportionality for different soil types .................................................................................................. 75 Table 5.6 Discretization details of the external BBN model nodes .............................................. 76 Table 5.7 Probabilistic data of input parameters .......................................................................... 79 Table 5.8 CTE and RME for defect depth and PoF of three scenarios ......................................... 80  ix  List of Figures  Figure 1.1 Causes of Pipeline failures in BC and data on failure incidents due to corrosion        from 2009 to 2014 ........................................................................................................ 2 Figure 1.2 Pipeline failures due to corrosion in Alberta from 1990 to 2012 .................................. 3 Figure 1.3 A schematic representation of internal corrosion and induced seismicity models         integration .................................................................................................................... 5 Figure 2.1 Example of BBN (adapted from Cockburn & Tesfamariam  (2012), with permission) ................................................................................................................. 10 Figure 3.1 Conceptual BBN for internal corrosion ....................................................................... 18 Figure 3.2 Proposed BBN for internal corrosion assessment ....................................................... 19 Figure 3.3 Comparison of different failure pressure models ........................................................ 30 Figure 3.4 Sensitivity analysis of the MIC (a), GC (b) and CR (c) nodes based on variation in the input nodes ........................................................................................................... 35 Figure 3.5 Sensitivity analysis of the Pipe Failure (PF) node based on variation in the input nodes .......................................................................................................................... 36 Figure 3.6 Predicted relative defect depth distribution for scenario analysis ............................... 38 Figure 3.7 Defect depth evolution over 20 years of the pipeline service time ............................. 39 Figure 3.8 PoF evolution over 20 years of the pipeline service time considering different toughness .................................................................................................................... 40 Figure 3.9 Data summary on studied region ................................................................................. 41 Figure 3.10 Median defect depth (left) and PoF (right) distributions for the Northeastern BC pipeline infrastructure ................................................................................................ 43 x  Figure 3.11 Spatial distribution of the predicted median defect depth (a) and median probability of failure (b) ............................................................................................. 44 Figure 4.1 Proposed framework .................................................................................................... 46 Figure 4.2 Spatial and temporal distributions of the observed seismicity in Northern Montney Trend .......................................................................................................................... 48 Figure 4.3  Cluster analysis and superimposed potential seismic sources (HF and wastewater disposal wells) ............................................................................................................ 50 Figure 4.4 Attenuation of PGV as a function of the epicentral distance for focal depth (h = 2 km) ............................................................................................................................. 52 Figure 4.5  Peak ground velocity map (a) Low M [3…4] scenario; (b) High M [5…6] scenario  .................................................................................................................................... 54 Figure 4.6  ALA (2001) fragility relations for segment length L=5 km considering impact of the internal corrosion ................................................................................................. 57 Figure 4.7  Spatial distribution of the predicted PoF (a) Low M [3…4]; (b) High M [5…6] ...... 59 Figure 4.8 Distribution of PoF for different diameters due to induced seismicity considering low and high magnitude scenarios ............................................................................. 60 Figure 4.9 Repair rate distribution on the region scale, considering actual corrosion conditions and different magnitudes ............................................................................................ 61 Figure 4.10 Repair rate distribution on the region scale, M [4…5] considering scenarios of different corrosion conditions .................................................................................... 61 Figure 5.1 Schematic representation of the BBN model for failure prediction due to external corrosion..................................................................................................................... 65 xi  Figure 5.2 BBN model for pipeline failure due to external corrosion .......................................... 66 Figure 5.3 Knowledge-based BBN for corrosion initiation time .................................................. 67 Figure 5.4 Examples of coating failure probability predicted by knowledge based BBN ........... 72 Figure 5.5 Sensitivity analysis of the pipe failure node based on variation in the input nodes .... 78 Figure 5.6 Predicted relative defect depth distribution for scenario 2 and 3 ................................ 80 Figure 5.7 PoF evolution over 20 years of the pipeline service time ........................................... 81    xii  List of Abbreviations and Notations A Projected area of defect on axial plane A0  Original cross section area BBN Bayesian belief network bc  Bicarbonate content bd  Soil bulk density cc  Chloride content CPT Conditional probability table ct Coating type d Defect depth D Outside diameter d/t Relative defect depth EC Erosion-corrosion GCR General corrosion rate GIS Geographic information system ICR Inhibited corrosion rate IE Inhibitor efficiency k Pitting proportionality L Defect length LSF Limit state function M  Moment magnitude MIC Microbiologically influenced corrosion xiii  P(t) Mean value of the operating pressure at a given time PF Failure pressure POP Operating pressure PC Pitting corrosion PGA Peak ground acceleration PGD Peak ground displacement PGV Peak ground velocity pH  soil pH Pin  Mean value of the initial operating pressure pp  Pipe to soil potential re  Soil resistivity rp  Redox potential sc Sulfate content t Wall thickness t0 Corrosion initiation time UCR  Uninhibited corrosion rate v Pitting exponent wc  Water content WF Wetting factor σ Flow stress σθ  Hoop stress at failure   xiv  Acknowledgements First and foremost, I would like to express my sincere gratitude to my research supervisor Dr. Solomon Tesfamariam for giving me the opportunity to complete my MASc program at The University of British Columbia. I appreciate your support, wisdom and patience. Your knowledge and comments have added substantially to my personal growth and research work. Your belief in my capabilities has assisted me in recognizing a new potential within myself.  I would like to acknowledge the financial support through MITACS and BCOGC under British Columbia Natural Gas Strategic Research project. In addition, I want to express my gratitude to my close friend Allisia Giza for showing confidence in my work, patience and help. I would like to give special recognition to my friend Matiyas Ayalew for his friendship, guidance and support. You were the first person who helped me start my journey at the university. In addition, I want to thank my friends Amitvikram Dutta, Hassan Iqbal, Adil Umer, Venkatesh Kumar, Caleb Goertz, and Tim Gu for their ideas, assistance and advice. As well thank you to my many student colleagues for our many discussions and memorable times together.   I also acknowledge the Staff and faculty of UBCO and The School of Engineering, the College of Graduate Studies and the Center for Scholarly Communication. Thank you for the consistent tasks you carry out, support you give, as well as the information you provide. I also want to give special recognition to my family for their love, continual support and everlasting encouragement. They are the source of my inspiration and motivation.       xv  Dedication    Dedication I would like to dedicate this thesis to my parents, Mr. Shabarchin Alexander Alekseevich and Mrs. Shabarchina Tatiana Vladimirovna.  Спасибо, мои родные, за веру и поддержку, дай вам Бог крепкого здоровья!    1 Chapter 1 Introduction The rapid growth of the Canadian oil and gas industry requires an increase in pipeline infrastructure, resulting in greater operational and management complexity. Because of the potentially adverse environmental impact and significant financial consequences, the integrity of the oil and gas pipeline infrastructure is essential (Ossai, 2012; Revie, 2015). The oil and gas infrastructure is commonly comprised of different materials subjected to various environments and to different operating conditions. Various interactions of these conditions with pipeline material may compromise the integrity of the infrastructure leading to failures (Papavinasam, 2013). In British Columbia, the regulatory organization British Columbia Oil and Gas Commission (BCOGC) has indicated the following causes of pipeline failures: corrosion, metal cracking, external interference, manufacturing defect, geotechnical failure, and incorrect operations. However, BCOGC annual reports show that the majority of failures were caused by corrosion, accounting for more than 48% of all failures (Figure 1.1).  In general, for each oil and gas infrastructure type (e.g. production, transmission, and distribution) there are several predominant factors, which may cause failure. At the initial stage of oil and gas production, one of the major threats to the integrity of pipelines is internal corrosion. The crude mixture extracted from the geological formation, composed of associated water, organic acids, and various dissolved gases such as carbon dioxide (CO2) and hydrogen sulfide (H2S), creates a corrosive environment for steel (Nešić, 2007). Despite the growing understanding of corrosion mechanisms and improved corrosion detection techniques, the industry reports still show that corrosion plays a significant role in pipeline failure. For example, according to an Alberta Energy Regulator (AER) report, from 1990 to 2012, more than 9,000 failures occurred due to internal corrosion (Figure 1.2), which accounts for 54.8% of all spills (AER, 2013). The oil and gas companies in the US spend 1.052 billion dollars yearly to mitigate internal corrosion (Papavinasam, 2013).    2    Figure 1.1 Causes of Pipeline failures in BC and data on failure incidents due to corrosion from 2009 to 2014  External corrosion is also a significant cause of oil and gas pipeline failures. As indicated in the AER report, external corrosion in Alberta is the second leading cause of pipeline failures, accounting for 12.7% of the total number of failures (AER, 2013). It is important to note that despite the operators’ effort, the number of external corrosion failures do not decline in contrast to the number of internal corrosion failures, which operators managed to reduce. This is explained by the fact that internal corrosion hazard can be mitigated by inhibitors or mechanical cleaning, whereas external corrosion hazard can only be ceased by excavation followed by rehabilitation, which is very costly.  Pipeline Failure Corrosion Metal Cracking External Interference Manufacturing, Construction defect Geotechnical Failure Incorect Operations 01020304050602009 2010 2011 2012 2013 2014Number of  Incidents Year Corrosion Other causes48% 52% Corrosion Other causes 3  Figure 1.2 Pipeline failures due to corrosion in Alberta from 1990 to 2012  Besides corrosion hazards, there is a rising public concern regarding the potential detrimental impact of the induced seismicity, caused by the extensive application of multistage hydraulic fracturing operations. Several damaging induced earthquakes already occurred in North America causing moderate damage to local residential buildings and highways (Rubinstein & Mahani, 2015). Considering that induced events may occur in close proximity to oil and gas production networks, it is important to investigate the influence of induced seismicity on the integrity of the pipeline infrastructure, especially taking into account the current corrosion condition of each component.  Potential damage to surface objects can happen because induced events mostly occur at the shallow depths. Consequently, ground motion intensities can reach significant values due to low hypocentral distances. Frolich et al. (2014) pointed out that in 2012 an induced earthquake in Texas (M=4.1) resulted in a peak ground acceleration (PGA) of 6.1 cm/s2 and peak ground velocity (PGV) of 22 cm/s. Although such intensities have been observed in locations proximal to the epicentre, but the values exceed damage thresholds for oil and gas pipelines outlined in the literatures (Lanzano, Salzano, de Magistris, & Fabbrocino, 2014; Lanzano, Salzano, de Magistris, & Fabbrocino, 2013; Lanzano, Salzano, de Magistrisa, & Fabbrocinoa, 2013). This 01002003004005006007008009001000Number of  Incidents Year Other causes Internal corrosion External Corrosion 4 fact indicates that pipeline infrastructure can be damaged by induced seismic events, which may lead to release of the transported content. Similar conclusions have been drawn by Atkinson et al. 2015 through the detailed analysis of the ground motions produced by the largest induced seismic events in 2014. The authors argue that it is of particular importance to evaluate induced seismicity in regions with low natural seismicity, because infrastructure in such regions is mostly designed without consideration of the seismic impact (Atkinson et al., 2015).  Given the aforementioned challenges, coupled with companies’ limited budgets and strengthening pipeline integrity regulations, there is a need for informed decisions to facilitate an effective resource allocation for pipeline rehabilitation and maintenance strategies.  1.1 Research Objectives The goal of this research is to develop Bayesian Belief Network (BBN)-based corrosion hazard assessment approach for oil and gas pipelines to refine a company’s pipeline repair and rehabilitation strategies. The major focus is given to production pipeline infrastructure, which frequently suffers from corrosion failures. The specific objectives of this research include:  Develop and integrate various corrosion and failure pressure models into a flexible network in order to quantify probable internal corrosion defects and the associated probability of failure (PoF).  Develop a BBN-based external corrosion model, considering different soil properties and pipeline coating types to evaluate external corrosion defects and associated PoF.  In addition to corrosion hazards, another objective of this thesis is to assess the potential impact of the induced seismicity on the oil and gas pipeline infrastructure.  To demonstrate the developed models, two case studies of the oil and gas infrastructure subjected to internal corrosion and induced seismicity hazards are presented. The developed models can be employed to identify pipeline sections vulnerable to corrosion and induced seismicity to improve corrosion mitigation programs and to enhance pipeline rehabilitation strategies.    5 1.2 Organization of the Thesis This thesis is organized in six chapters.  Chapter 1 specifies objectives of this research, provides data on causes of pipeline failures in different regions and introduces the problem.  Chapter 2 justifies the application of the BBN for corrosion hazards, compares BBN with other quantitative approaches (ANP, ANN, etc.), which are frequently used in risk analysis and hazard assessment. In addition, this chapter provides some theoretical background on the BBN. Chapter 3 describes internal corrosion mechanisms that most frequently cause failures in the production oil and gas pipelines. In addition, this chapter provides a detailed description of the BBN model development for internal corrosion hazard assessment.  Chapter 4 presents an overview of induced seismicity and its potential to cause damage to buried oil and gas pipelines. Additionally, Chapter 4 discusses the development and application of the methodology (as is shown in Figure 1.3), which combines induced seismicity and internal corrosion hazards.          Figure 1.3 A schematic representation of internal corrosion and induced seismicity models integration Chapter 5 presents some theoretical background on external corrosion and provides a detailed description of the BBN external corrosion model development.  Chapter 6 summarizes the key conclusions and results of this thesis, presents limitations of the developed model and discusses future research, which can be done to refine the proposed model. Internal Corrosion Vulnerability Assessment (Chapter 3)    Induced Seismicity Hazard Map Construction (Chapter 4)    Pipeline Seismic Vulnerability Functions (Chapter 4)    Induced Seismicity Vulnerability Assessment (Chapter 4)     6 Chapter 2 Bayesian Belief Network  A part of the contents of this chapter was included in the paper titled “Internal Corrosion Hazard Assessment of Oil & Gas Pipelines Using Bayesian Belief Network Model” that has been accepted by the Journal of Loss Prevention in the Process Industries. The first section of this chapter justifies the application of the BBN for corrosion hazard assessment. This section also compares BBN with other quantitative approaches, which are frequently used for hazard assessment and risk analysis. The subsequent section discusses the theoretical background of the BBN. 2.1 Motivation for BBN Application Many quantitative and qualitative methods have been proposed to investigate the impact of various hazards on the oil and gas pipeline infrastructure. (El-Abbasy, Senouci, Zayed, & Mosleh, 2015; Lahiri & Ghanta, 2008; Marhavilas, Koulouriotis, & Gemeni, 2011; Nataraj, 2005; Shahriar, Sadiq, & Tesfamariam, 2012; Sinha & Pandey, 2002). Qualitative methods are frequently based on an index system, whereas quantitative methods are usually based on numerical simulations (Z. Han & Weng, 2011).When substantial historical data is available, rigorous statistical or data mining techniques can be used to develop predictive tools (e.g. Artificial Neural Networks). However, in the case of sparse, ambiguous or imprecise data, soft computing techniques, such as decision tree models, fuzzy rule-based models and Bayesian belief networks (BBN) models can be used to quantify cause-effect relationships and handle uncertainties (Ismail, Sadiq, Soleymani, & Tesfamariam, 2011). A detailed comparative analysis of commonly applied soft computing techniques is reported elsewhere (Kabir, Tesfamariam, Francisque, & Sadiq, 2015). One of the quantitative methods is Failure Mode and Effect Analysis (FMEA). This is a widely applied analytical technique to define potential failure modes and estimate the risk related with each failure mode. FMEA results are used to rank the issues based on their significance and to perform corrective actions to address the most severe concerns. FMEA is an efficient fault analysis framework; however, the ability of inference is limited and FMEA technique is not suitable for incorporation of the multiple fault related factors to carry out posterior inference  7 (Yang et al. 2009). Additionally, FMEA method is difficult to integrate with new information and expert judgment. Conversely, BBN can be easily updated and refined as soon as new information becomes available (Chen et al. 2010). Furthermore, BBN can be developed based on the existing FMEA model; multiple factors, which cannot modelled with FMEA, can also be integrated with the help of BBN (Yang et al. 2009). Another frequently used quantitative approach is Fault Tree (FT). This is a systematic and quantitative technique for dependability analysis, which is graphically represented, in order to model different combinations of fault events that may be described in parallel or sequential way, which leads the occurrence of the undesired event. The individual faults can be events that are associated with human errors or component failure, which may cause undesired outcome. Such outcome is the top event of the FT, which corresponds to a particular failure mode of the system. According to Bobbio (1999), FT does not take into consideration probability distributions for component’s failure as well as multiple factor interactions, which may affect the probability of failure. The outcome of the FT analysis explicitly quantifies the probability of failure of a system or a system’s component. However, FT is not efficient when dealing with many failure components, which may lead to different consequences (Weber et al. 2010). Such cases are frequently encountered in risk and dependability analyses. In such scenarios, modelling needs to be done considering random variables with multiple states. Because FT applies only Boolean logic, FT is not a preferable option for such analyses. Another issue with FT models is its limitation to only one top event. BBN models have the similar capabilities as compared to FT models. However, a significant advantage of BBN that it permits multistate variable modeling and allows assessing many outputs in the same model. FT models can easily be mapped in a BBN model, but the reciprocity is not always possible.  Table 2.1 reflects a qualitative analysis between different quantitative computing techniques, which are frequently used in risk and hazard assessments. The major difference between these techniques is an approach to treat inherent uncertainties as well as an ability to handle interaction between various factors that encompass issues specific to failure of oil and gas pipelines.  8 Table 2.1 Comparison of various network based techniques (adapted from Kabir et al. 2014, with permission) Attributes Network based techniques ANN ANP BBN CM/FCM CN FRBM Network capability L VH H1 VH2 H1 L3 Ability to express causality  N H VH VH H M Formulation transparency N4 VH H VH H H Ease in model development  M H M VH M M Ability to model complex systems VH M H VH H H Ability to handle qualitative inputs N VH H VH H H Scalability and modularity VL5 VH6 H VH6 H L Data requirements  VH L7 M8 L9 L10 L Difficulty in modification M N L N L H Interpretability of results VH VH VH H VH VH Learning/ training capability VH11 H12 H13 H14 H13 M15 Time required for simulation H L L L M L Maturity of science H H VH M M H Ability to handle dynamic data H M H M H H Ability to combine with other approaches VH16 H16 H H17 H VH16  Ratings: N = No or Negligible; VL = very low; L = low; M = medium; H = high; VH = very high Network based techniques: ANN = Artificial Neural Networks; ANP = Analytic Network Process; BBN = Bayesian Belief Networks; CM/FCM = Cognitive Maps/Fuzzy Cognitive Maps; CN = Credal Network and FRBM = Fuzzy Rule-Based Models 1. Can manage networks but cannot handle feedback loops, therefore referred to as directed acyclic graphs 2. Can handle feedback loops 3. Dimensionality is a major problem and formulation becomes complicated for network systems 4. Generally referred to as black box models 5. ANN needs to be retrained for new set of conditions 6. Very easy to expand, because algorithm is in the form of matrix algebra 7. Minimal data requirement, because causal relationships are given by decision makers 8. Medium data requirement for using precise probability 9. Minimal data requirement, because causal relationships are generally soft in nature 10. Minimal data requirement for using imprecise probability 11. Algorithms, e.g., Hebbian learning 12. Algorithms, e.g., minimizing the error function 13. Algorithms, e.g., evolutionary algorithms and Markov chain Monte Carlo 14. Training algorithms are available which have been successful in training ANNs 15. Clustering techniques, e.g., Fuzzy C-means 16. Examples are available in the literature to develop models using hybrid techniques, e.g., neuro-fuzzy models, fuzzy analytic network process 17. Has a potential to be used with other soft techniques    9 In this thesis, BBN is used to address corrosion hazards because corrosion is a time-dependent random process (Nešić, 2007; Papavinasam, 2013). Any measurement or estimation of the corrosion rate will inevitably contain a degree of uncertainty, as it is influenced by a number of factors subject to aleatory and epistemic uncertainties (Ayello, Alfano, Hill, & Sridhar, 2012). BBN is particularly suitable to deal with such processes because of its ability to establish a cause-effect network through integration of the various types of available information, such as analytical models, expert knowledge, published literature and historical data into a single flexible framework (Chen & Pollino, 2012; Cockburn & Tesfamariam, 2012). This combination is beneficial when dealing with processes that analytical modeling alone fails to describe (e.g. microbiologically influenced corrosion).  BBN is referred to as an analytical framework that permits the visual representation of causal dependencies among given variables in a probabilistic manner (Pearl, 1988). The BBN approach has been applied in the analysis of various complex engineering problems, such as structural reliability analysis, deterioration modelling, and has proven to be particularly effective in the area of risk analysis and decision making under uncertainties (Cheng, Bell, & Liu, 1997; Lee, Park, & Shin, 2009; Tesfamariam, Sadiq, & Najjaran, 2010). A BBN model can be efficiently applied to make informed decisions when the available data is imprecise, ambiguous or incomplete (Kabir et al., 2015).  2.2 Theoretical Background  BBN is based on a Directed Acyclic Graph (DAG), which consist of many stochastic variables and the directed links between them. The links denote probabilistic conditional dependence, whereas nodes represent parameters of interest (Cockburn & Tesfamariam, 2012). Each unknown parameter is determined by using Bayes’ theorem which for the n mutually exclusive hypotheses (𝑗=1,…,n) is represented by the relationship: 𝑃(𝐻𝑗|𝐸) =𝑝(𝐸|𝐻𝑗) ∗ 𝑝(𝐻𝑗)∑ 𝑝(𝐸|𝐻𝑖)𝑛𝑖=1 ∗ 𝑝(𝐻𝑖) (2.1) where P (Hj|E) is the posterior probability for the hypothesis 𝐻(𝑗=1,...,𝑛) ,based on the obtained evidence (E); p(Hj) denotes the prior probability; p(E|Hj) represents conditional probability,  10 assuming that Hj is true, the denominator represents the total probability which is a constant value (Pearl, 1988). Prior or unconditional probability is the likelihood of an event before any evidence is provided. Posterior probability refers to the likelihood after the observation is made. Equation 2.1 is used in BBN to perform a probabilistic inference for a subset of parameters as new data or evidence is acquired about any other parameters (Janssens et al., 2006).  Figure 2.1 Example of BBN (adapted from Cockburn & Tesfamariam (2012), with permission) In the BBN model, variables are related to each other in a manner of family relationships. This relationship is shown in Figure 2.1, where variables X1 and X2 are parents and variable Y is a child. A variable X1 is considered to be a parent of Y if the connection link goes from X1 to Y. These variables are defined by a set of mutually exclusive states, whereas their relations are quantified by introducing conditional probabilities for each combination of these states. As depicted in Figure 2.1, the following steps are to be fulfilled to create a BBN model: 1. Variables that have an effect (X1, X2) on the outcome parameter (Y) are identified.  States Probability States ProbabilityLow P1(X1=L) Low P3(X2=L)High P2(X1=H) High P4(X2=H)Low HighLow Low P5 P9Low High P6 P10High Low P7 P11High High P8 P12Variable X2Prior probability Prior probabilityConditional probability tableVariable X1Variable X2Conditional Probability of Variable YVariable X1VariableX1VariableX2VariableY 11 2. Conditional dependence between parameters is formulated and represented using arrows. It is essential that variables are linked based only on the cause-effect assumption, not on the correlation. 3. Collectively exhaustive and mutually exclusive states are assigned to parent variables by evaluating prior probability of each state (e.g. P1, P2…P4). The unconditional probability of variables which have no parent nodes can be unknown a priori. In this case, the principle of insufficient reasoning can be applied, assigning for each state 1/n probability, where n is the total number of states of the variable (Tesfamariam & Martín-Pérez, 2008). The conditional probabilities for each child node are assigned (e.g. P5, P6…P12). This step is the most important, but very time-consuming, since all possible state combinations of parent nodes must be provided to fill in the condition probability table (CPT). The CPT may be completed by assigning subjective probability that is used in BBN to reflect the associated uncertainties (Fan & Yu, 2004; Pearl, 1988). The conditional probabilities can be quantified by using information obtained from the field data, expert opinion, analytical model or a combination of them. However, in a complex process with less understood underlying mechanisms, the application of expert knowledge is preferable (Daly, Shen, & Aitken, 2011; Liu, Lu, Chen, & Shen, 2012). When multiple analytical models or expert opinions are available, credibility factors (weights) may be assigned to reach the final decision, but the higher the complexity of the problem the greater the uncertainty that emerges (Ismail et al., 2011; Ross, 2009; Sadiq, Kleiner, & Rajani, 2008). The fundamental symmetry property of Bayes’ theorem permits the probability to be inferred in forward (predictive analysis) and backward (diagnostic analysis) directions. This characteristic allows a cause-effect network to use reverse logic; thus, the BBN model can be exploited as a diagnostic model by introducing new information in the effect variable to infer probable causes (Ismail et al., 2011; Kabir et al., 2015). Furthermore, BBN breaks down a complex problem into its components and then graphically represents them, which facilitates a better understanding of this problem. In BBN, the associated uncertainties (can be a data uncertainty, model uncertainty or both) are explicitly treated by propagating them throughout the network up to the final node (Uusitalo, 2007). In this study, Bayesian network software Netica has been used to develop corrosion hazard models (Norsys Software Corp, 2015).   12 Chapter 3 Internal Corrosion A part of the contents of this chapter was included in the paper titled “Internal Corrosion Hazard Assessment of Oil & Gas Pipelines Using Bayesian Belief Network Model” that has been accepted by the Journal of Loss Prevention in the Process Industries. This chapter presents a BBN-based internal corrosion model development as well as its application for the oil and gas pipeline infrastructure. Sections 3.1 and 3.2 discuss different types of internal corrosion and multiple factors affecting them. The subsequent sections present a detailed discussion on each step of the model development. These sections are followed by the sensitivity and scenario analysis. The final part of this chapter shows a case study for Northeastern British Columbia oil and gas pipeline infrastructure. 3.1 General Corrosion of Steel in Sweet and Sour Environments Corrosion of mild steel is an electrochemical reaction with the environment, which leads to steel degradation. Depending on the chemical composition of the transported fluid, steel type, and operating conditions, pipeline internal corrosion can manifest in a number of different ways, such as sweet or sour general corrosion, localized corrosion, and so on.  Sweet corrosion occurs when carbon dioxide dissolves in water producing carbonic acid (H2CO3), which in turn reacts with the steel surface of the pipe. Produced H2CO3 is a weak acid, but very corrosive to mild steel. It creates an electrochemical reaction with the evolution of hydrogen and the anodic dissolution of iron (Fajardo, Canto, Brown, & Nesic, 2007; Ossai, 2012). The overall reaction is: Fe + CO2 + H2O → FeCO3 (Iron carbonate) + H2  The product of the reaction is an iron carbonate scale, which under different conditions can demonstrate protective or non-protective properties, thus dramatically affecting the corrosion rate (Nešić, 2007; Ossai, 2012). In the case of sour corrosion, the initiation of the corrosion process is similar to sweet corrosion, where H2S in the aqueous solution forms a weak acid reacting with steel accompanied by hydrogen evolution. The overall chemical reaction is expressed as follows:  13 Fe + H2S + H2O → FeS (Iron sulfide) + H2  The corrosion product (iron sulfide) also forms a scale, which can govern the overall corrosion rate (Nešić, 2007). To estimate the corrosion severity, it is essential to have a clear understanding of metallurgical steel properties as well as complex corrosive environment factors. The latter includes temperature, pH, flow regime, dissolved gas phase composition (e.g. O2, CO2, and H2S), aqueous phase composition, microbes, solid particles, and the presence of corrosion inhibitors. These factors and their interactions have a significant influence on corrosion behavior. They are briefly described in the following paragraphs. 3.1.1 Impact of Temperature  Generally, corrosion increases with the rise in temperature for both CO2 and H2S environments, because it accelerates chemical and electrochemical processes involved in corrosion (Nešić, 2007). This impact is especially predominant at a lower pH, when protective scales do not form. On the other hand, the corrosion rate is not significantly affected by the temperature if it increases above 80-90oC because the corrosion product film becomes harder and more adherent (Papavinasam, 2013).  3.1.2 Impact of Flow Depending on the flow parameters and flow regime, different types of corrosion can occur. Flow affects mass transfer processes that dictate whether corrosive species contact the metal surface or move away from it. In addition, flow abnormalities such as turbulences and high velocity sections may mechanically remove corrosion protective scale and prevent its further formation, thus substantially intensifying corrosion severity (Papavinasam, 2013). The effect of flow is even more profound if a pipeline is operated under multiphase flow conditions. When free water or oil-in-water emulsion prevails in the liquid phase, wettability substantially influences the corrosion rate. Corrosion may be very severe or may not happen at all, depending on whether water or oil wets the pipe wall (Tang, Richter, & Nesic, 2013). In addition, when the liquid phase contains solid particles, flow velocity significantly affects corrosion processes (J. Han, Yang, Brown, & Nesic, 2007).   14 3.1.3 Impact of pH Many experiments as well as field tests indicate that pH has a strong impact on corrosion behavior (J. Han, Yang, Nesic, & Brown, 2008; Papavinasam, Doiron, & Revie, 2010). It is mostly associated with the influence on the scale formation tendency. In sweet environments, high pH increases the iron carbonate precipitation rate, thus decreasing the uniform corrosion rate (Nešić, 2007). However, it also creates a favorable environment for other forms of corrosion, such as pitting corrosion, crevice corrosion, etc. (Papavinasam et al., 2010).  3.1.4 Impact of Corrosion Inhibitors Chemical inhibitors create a protective film on the pipe surface, preventing corrosive species from reacting with the metal surface. The persistence and adherence of this film is important for corrosion control (Papavinasam, 2013). The inhibitor impact is estimated through the inhibitor efficiency parameter that is measured in laboratory experiments followed by field tests.  From the above discussion of the factors that influence corrosion, it is clear that the corrosion environment as well as its interaction with operating conditions create a highly complex system, which directly affects the severity of corrosion. These processes are summarized and reflected in the corrosion model development section. 3.2 Localized Corrosion  This section discusses the theoretical background on localized corrosion types (pitting corrosion, erosion-corrosion, microbiologically influenced corrosion), which are used in the BBN model development. Localized corrosion is a selective metal removal that occurs on very small discrete areas of the pipe wall surface with a considerable corrosion rate (Frankel & Sridhar, 2008). The common types of localized corrosion include pitting corrosion, crevice corrosion, stress corrosion cracking (SCC), erosion-corrosion, microbiologically influenced corrosion (MIC), etc. (Ossai, 2012).  Generally, localized corrosion is more difficult to predict and detect than general corrosion. Despite the importance of evaluating general corrosion, the majority of steel pipeline failures in the oil and gas industry occur due to localized corrosion (Ossai, 2012; Papavinasam, 2013). This is especially true for production and gathering pipeline systems, where corrosion species and bacteria are presented in abundance.   15 Localized pitting corrosion is likely to occur when the flow composition as well as operating conditions promote the formation of protective films (iron carbonate, ferrous sulfide) on the metal surface. Extensive laboratory studies indicate that these layers can be locally disrupted by mechanical force, chemical dissolution or a combination of them (J. Han et al., 2007; Ossai, 2012). As a result of the corrosion film damage, small localized anodic sites are formed. These anodic sites are surrounded by cathodic zones with a much higher surface area. This creates a considerable potential difference between these areas, thus causing localized pitting corrosion with a much higher rate than in the case of the uniform corrosion (Z. Han & Weng, 2011). Pitting initiation is primarily attributed to the presence of halides (chlorides, bromides and iodides) in the flow which have been proven to be potent agents for damaging protective corrosion films (Papavinasam, 2013). In addition, it was shown that the pitting initiation tendency increases with the growth of chloride concentration (Papavinasam, Revie, Friesen, Doiron, & Panneerselvan, 2006; Papavinasam et al., 2010).  In production oil and gas pipelines, where a multiphase flow regime is usually presented, the other form of localized metal damage, namely erosion-corrosion, can be very severe (Shadley, Shirazi, Dayalan, Ismail, & Rybicki, 1996). Its nomenclature derives from the fact that it is a result of the synergetic action of mechanical erosion and corrosion (i.e. the combined effect is more severe than the sum of each individual effect) (Shadley et al., 1996). When the flow contains solid particles (such as sands, corrosion products, mineral scale particles, clays, etc.), depending on operating parameters, pipeline corrosion may proceed in one of two ways: under deposit corrosion on the one hand and erosion-corrosion on the other. If the flow rate is higher than erosion velocity (Ue) in the gas pipeline, then solid particles colliding with a metal surface cause mechanical erosion. If this surface is covered with corrosion film, the metal damage will be even more profound. The film is also exposed to mechanical removal, thus leaving the metal surface unprotected, which then undergoes corrosion, resulting in the reformation of the film (Papavinasam, 2013; Zhou, Stack, & Newman, 1996). Additional solids collide with the area of newly formed film, causing the same effect. This mechanism repeats until pipeline failure occurs. The extent of erosion-corrosion depends on corrosion film properties (adherence, hardness), particle characteristics (size, geometry, etc.), and flow parameters (solids concentration, flow regime, and velocity). Additionally, the effect of erosion-corrosion may be  16 very severe on curved pipeline segments (bends, tees, valves, pipe expansions and contractions) (Shadley et al., 1996).   MIC is a corrosion process that involves microbes, which are often present, in oil and gas products. These bacterial microbes react with one another, creating colonies that ultimately form a layer of film on the pipe’s interior surface. This creates a localized corrosive environment affecting the pipeline’s integrity. It has been reported that MIC accounts for up to 30 per cent of pipeline failures associated with internal corrosion (Javaherdashti, 1999). It is estimated that in the United States (US), around 50 million dollars a year is spent to mitigate the MIC induced consequences (Javaherdashti, 1999).  Corrosive microbial colonies (biofilms) are commonly composed of fungi, algae and aquatic bacteria. If a petroleum product is contaminated with bacteria, biofilms begin to form as soon as a metal surface is wet by the water phase. In cases when water is not present in the system, biofilm formation may not happen (Javaherdashti, Nwaoha, & Tan, 2013). However, microorganisms can resort to spore form, allowing them to survive in dehydrating environments until conditions become suitable to restart growth. Spore form is a concern because in pipelines that were previously considered to be free of corrosive bacteria, MIC can propagate relatively quickly. These small spore formations are not detectable by common procedures put into place for monitoring (Javaherdashti, 1999).  Out of many bacteria types, sulfate reducing bacteria (SRB) is primarily associated with MIC failures (Muthukumar et al., 2003). SRB has a number of species related to corrosion activity. High SRB activity is mainly found in pipelines with stagnant or low flow velocities, as well as in pipelines having debris or scale deposits. SRB is commonly presented in wash tanks, crude oil storage tanks, water flood systems, and oil and gas handling systems (Javaherdashti, 1999). SRB activity is associated with several reactions resulting in the creation of sulfide from sulfate, with the FeS as the corrosion product. In order to complete this chemical reaction, hydrogen atoms are essential. The following anodic and cathodic reactions take place when SRB is active in the system:   17  Anodic reaction in the dissolution of iron: Fe → Fe2 + 2e-  Hydrogen ions undergo a cathodic reaction in acidic pH: H+ + e- → H  Hydrogen atoms begin to amalgamate and create hydrogen molecules that then turn to gas. SRB absorbs hydrogen atoms during this stage, transforming the sulfate ion to sulfide:  SO42- + 2H → S2- + H2O When SRB is active, the cathodic reaction is accelerated, which also increases the corrosion rate.   Iron sulfide is created when ferrous ions produced from the anodic reaction combine with sulfide ions:  Fe2+ + S2- → FeS Generally, MIC manifests itself as pitting. Groups of sharp edged round pits form underneath the biofilm; often pits form within pits, thus significantly decreasing pipe wall thickness. Pits develop in a random manner along the areas that are wet by the water phase. Water wetness occurs due to low flow velocities, usually less than 1 m/sec or if the pipeline is operated in a start-stop mode, allowing water to remain in low areas of the pipeline. Alternatively, when the flow rate is high, it can physically remove biofilms from the metal surface. In addition, the magnitude of the flow rate affects the nutrients’ delivery process, thus influencing biofilm propagation. It is worth noting that different species constituting the bacterial colonies have a variety of operational and environmental tolerances, such as pH ranges of 5-10, temperatures ranging from 5 up to 100 oC and so on. Undoubtedly, some bacteria species can survive and proliferate in extreme conditions, for example, high temperatures up to 100 oC and pressures of 500 atm. (Javaherdashti et al., 2013). However, most bacteria related to corrosion thrive only in specific ranges of environmental parameters. These conditions are further discussed in the model development section.  18 3.3 BBN Internal Corrosion Model Development The proposed BBN model is used to quantify PoF for gathering and production pipelines (i.e. prior to the purification stage) subjected to aqueous corrosion. This includes pipelines transporting crude oil, oil effluent, produced water mixture, etc. The BBN model has been developed using extensive review of the corrosion literature, industry reports and the current standards of oil and gas pipelines. Forty-four different factors (e.g. operating conditions, corrosion mitigation measures, etc.) affecting the pipeline corrosion rate and PoF are incorporated in the probabilistic network. Figure 3.1 depicts the proposed conceptual framework, whereas the detailed BBN model for corrosion hazard estimation is shown in Figure 3.2. Flow ParametersSolids ContentPreventive MeasuresOperating ConditionsWater ChemistryMicrobiologically InfluencedCorrosion (MIC)Erosion-Corrosion; Pitting CorrosionGeneral CorrosionAnalytical corrosion modell i l i  lKnowledge based corrosion modell   i  lIn-line Inspection Data Corrosion Monitoring Data6. Visualize for the whole infrastructure, using GIS. i li  f   l  i f , i  Id/tFailure pressure Models:DNV RP F 101ASME B31GPipe mechanical parameters:P,UTS,D,PWTProbability of failure1. Inputs: Operating conditions, fluid composition. I : i  i i , fl i  i i2. Analytical and knowledge based corrosion models. l i l  l   i  l3. Predicted corrosion defect parameters at time (t) . i  i  f    i  ( ) 4. Failure pressure determination. il   i i5. Compare operating and failure pressure LSF (Pf,Pop)=Pf - PopPoF = P(LSF≤0).  i   f il    ( f, ) f -   ( ) Figure 3.1 Conceptual BBN for internal corrosion  19  Figure 3.2 Proposed BBN for internal corrosion assessment Details of the model for general corrosion, pitting corrosion, erosion-corrosion and MIC, are discussed in the following subsections. 3.3.1 General Corrosion Model Numerous corrosion models have been proposed to estimate the corrosion rate. Multiple factors and their interactions must be considered in the analysis. Table 3.1 shows commonly used factors in different analytical corrosion models. Due to different underlying assumptions and the random nature of corrosion, analytical corrosion models may give different results even for the same inputs (Koch, Ayello, Khare, Sridhar, & Moosavi, 2015). Therefore, there is a significant modeling uncertainty that needs to be accounted for (Ayello, Jain, Sridhar, & Koch, 2014). In this study, for the Uninhibited Corrosion Rate (UCR) prediction, a BBN model developed by Ayello et al. (2014) has been adopted. This model was derived considering different model uncertainties. Table 3.2 reflects the discretization details of corrosive species concentration, pH,  20 Temperature (T), Inhibitor Efficiency (IE) and Wetting Factor (WF), which are used in the BBN general corrosion model to quantify the General Corrosion Rate (GCR). The Corrosion Inhibitor (CI) node is coupled with the UCR node to account for the inhibitor application, which can significantly mitigate the corrosion rate. As a result, the Inhibited Corrosion Rate (ICR) is computed as (Ayello et al., 2013; Papavinasam, 2013): ICR = UCR   (1 - IE) (3.1) where ICR is the inhibited corrosion rate (mm/year), UCR is the uninhibited corrosion rate (mm/year), IE is inhibitor efficiency (%). Table 3.1 Parameters applied in different corrosion models        Corrosion models (Papavinasam, 2013) Considered parameters CO2 concentration H2S concentration T Effect of flow pH  Bicarbonate Acetic acid Field data Ca2+ (De Waard, Lotz, & Milliams, 1991) √ × √ √ √ √ × × × (Srinivasan & Kane, 1999) √ √ √ √ √ √ × × √ (Nešic & Postlethwaite, 1991) √ × √ √ √ √ √ × × (Mishra, Al-Hassan, Olson, & Salama, 1997) √ × √ × √ √ × × × (Dayalan, De Moraes, Shadley, Rybicki, & Shirazi, 1998) √ × √ √ √ √ × × × (Anderko, McKenzie, & Young, 2001) √ √ √ × √ √ × × × (Oddo & Tomson, 1999) √ × √ × √ √ × √ √ (Pots et al., 2002) √ × √ √ √ √ × √ √ (Papavinasam et al., 2010) √ √ √ √ √ √ √ √ × (Adams, Garber, Singh, & Jangama, 1996) √ × √ × √ √ √ √ × Proposed BBN √ √ √ √ √ × × √ ×  21 Table 3.2 General corrosion model discretization details  The probability of corrosion is minimal when water is not in contact with the steel surface. Thus, the Wetting Factor (WF) node is introduced to assess whether the pipe surface is wetted with the water phase or not. The wettability is a complex phenomenon that is affected by many parameters such as water cut, flow regime, internal diameter, liquid velocity, fluid density, and Variables and reference for discretization Sub criteria  Performance measure General Corrosion  (GCR), mm/year (Ayello et al., 2014; Institute for Energy Technology, 2009) Inhibited corrosion rate (ICR), mm/year; Wetting factor (WF); Extremely Low Very Low  Low Medium High Very High Extremely High 0 ≤ GCR< 0.01 0.01≤ GCR< 0.1 0.1≤ GCR < 1 1≤ GCR < 2 2≤ GCR < 5 5≤ GCR < 10 10≤ GCR Uninhibited Corrosion Rate (UCR), mm/year (Ayello et al., 2014) CO2 partial pressure (CO2),Bar Very Low  Low Medium High 0 ≤ (CO2)< 0.1 0.1≤ (CO2)< 1 1≤ (CO2)< 10 10≤(CO2)< 100 Temperature (T),oC Low  Medium High Very High 20 ≤ T<40 40≤ T<60 60≤ T<80 80≤T< 100 Fe2+  Concentration (Fe2+), ppm Low Medium High 0 ≤ (Fe2+) <10 10≤ (Fe2+) <50 50≤(Fe2+) < 100 O2 Concentration (O2), ppb Low  Medium High Very High 0 ≤ (O2)< 10 10≤ (O2)< 100 100≤ (O2)< 1000 1000≤(O2)< 10000 H2S Concentration (H2S), ppm  Low  Medium High Very High 0 ≤ (H2S)< 10 10≤ (H2S)< 100 100≤ (H2S)<1000 1000≤(H2S)<10000 pH level (pH) Low  Medium High Very High 4 ≤ pH < 5 5 ≤ pH < 6 6≤ pH < 7 7 ≤ pH <8 Inhibited Corrosion Rate (ICR), mm/year (Ayello et al., 2014) Uninhibited corrosion rate (UCR), mm/year Extremely Low Very Low  Low Medium High Very High Extremely High 0 ≤ UCR< 0.01 0.01≤ UCR< 0.1 0.1≤ UCR< 1 1≤ UCR< 2 2≤ UCR< 5 5≤ UCR< 10 10≤ UCR Inhibitor efficiency (IE), %  Extremely Low  Very Low …….. Extremely High 0 ≤ (IE)< 10 10 ≤ (IE)< 20 …….. 90 ≤ (IE)< 100 Wetting Factor (WF) Water cut (WC), % Flow velocity (FV), m/s Wetted Not wetted WF = 1 WF = 0.1 Wetting Factor (WF) Water cut (WC), % Very Low  Low Medium High Very High 0 ≤ WC < 0.5 0.5 ≤ WC < 5 5 ≤ WC < 15 15 ≤ WC < 30 30 ≤ WC < 100 Flow velocity (FV), m/s Stagnant Very Low Low  Medium High Very High 0 ≤  FV< 0.1 0.1 ≤  FV < 0.5 0.5 ≤  FV <  1 1 ≤  FV< 2 2 ≤  FV< 3 3 ≤  FV< 4.5  22 fluid viscosity (Tang et al., 2013). However, conservative assumptions can be made by considering water cut and fluid velocity as the only contributors to the wettability (McAllister, 2013). Water Cut (WC) and Flow Velocity (FV) are introduced in the BBN as parent nodes for the WF node. Then, the WF range [0.1, 1.0] is used as an adjustment factor to compute GCR as follows:  GCR = ICR  WF (3.2) where GCR is the general corrosion rate (mm\year), and ICR is the inhibited corrosion rate. WF values close to 0.1 correspond to the water cut below 0.5% and flow rate higher than 1.5 m/s, whereas in the case when the water cut is above 30%, WF equals unity, regardless of the fluid velocity (Nyborg, 2002; Pots et al., 2002). The discretization details of the nodes, reflecting the aforementioned discussion are described in Table 3.2. 3.3.2 Pitting Corrosion and Erosion-Corrosion Models The pitting corrosion is assumed to be caused only by chemical dissolution of the protective film. This film forms on the metal surface depending on the pH and temperature of the fluid. It has been shown that the protective films are more likely to cover a metal surface at a pH level higher than six, as well as at elevated temperatures (higher than 40oC) (Z. Han & Weng, 2011; Papavinasam, 2013). These assumptions have been followed to create a Passive Film (PF) node. Localized chemical removal of this film is substantially affected by chloride presence. Chlorides are widely reported as a dominant contributor to the localized corrosion of steel; therefore, many corrosion models apply chloride concentration as an indicator of localized corrosion severity (Papavinasam et al., 2010; Srinivasan & Kane, 1996). In this thesis, it is assumed that chlorides cause and intensify pitting corrosion only. Then, the Chlorides (Cl) and Pitting corrosion (PC) nodes are introduced, assuming that pitting corrosion is high when a corrosive film covers the pipe’s internal surface with a high chloride concentration.  At a high flow velocity, if suspended solid particles are present in the fluid, they can mechanically damage the steel surface. In addition, in the presence of protective corrosion films, the corrosion rate may accelerate because of the synergetic effect between corrosion and erosion (Malka, Nešić, & Gulino, 2007; Shadley et al., 1996; Zhou et al., 1996). Erosion-corrosion  23 manifests itself even more significantly when a pipeline segment has a geometry change (i.e. elbow, tee, etc.) The dominant factors in this process are flow velocity and the presence of solid particles (Malka et al., 2007). Shadley et al. (1996) have identified three velocity intervals affecting erosion-corrosion rates. At the low velocity threshold, the corrosion protective film is intact; therefore, the corrosion rate is low. On the other hand, intermediate velocities can cause partial film removal, promoting localized corrosion in these areas. In the case of a high velocity threshold, solid particles damage the protective film uniformly; hence, the corrosion rate becomes high, but it is distributed relatively uniformly (Shadley et al., 1996). This approach is adopted assigning the following velocity values: [0 to 1] m/s for the low threshold, [1 to 3] m/s for the intermediate and [3 to 4.5] m/s for the high threshold respectively. The Erosion-Corrosion (EC) node, as well as the nodes that cause it, such as Flow Velocity (FV), Passive Film (PF), Suspended Solids (SS) and Geometry Change (GC), are integrated and the discretization details are summarized in Table 3.3. Table 3.3 Erosion-Corrosion and pitting corrosion model discretization details Variables and reference for discretization Sub criteria Performance measure Erosion-corrosion discretization details Erosion-Corrosion (EC), mm/year Suspended solids (SS); Flow velocity (FV); Geometry change (GC); Passive film (PF) Low Medium  High 0 ≤  EC< 0.01 0.01 ≤  EC < 0.1 0.1 ≤  EC <  1 Erosion-Corrosion (EC),  mm/year (Haile, Papavinasam, & Zintel, 2013) Suspended solids (SS) Absent Low High No measured parameter is considered Flow velocity (FV), m/s The same as in Table 3.2 Geometry change (GC) Yes No No measured parameter is considered Passive film (PF) Yes No No measured parameter is considered Pitting corrosion discretization details Pitting Corrosion (PC), mm/year Chlorides (Cl), ppm; Passive film (PF) Low Medium  High 0 ≤  PC< 0.01 0.01 ≤  PC < 0.1 0.1 ≤  PC <  1 Pitting Corrosion (PC), mm/year Chlorides (Cl), ppm Negligible  Low High 0 ≤  Cl < 500 500≤Cl< 30,000 Cl ≥ 30,000 Passive film (PF) Yes No No measured parameter is considered   3.3.3 Microbiologically Influenced Corrosion The microbiologically influenced corrosion (MIC) model has been developed considering water chemistry, operating conditions and MIC mitigation parameters. Favourable and unfavorable  24 conditions for MIC and its mitigation measures as well as knowledge garnered from the Haile and Sooknah models have been used to populate CPT for the MIC node (Haile et al., 2013; Sooknah, Papavinasam, & Revie, 2008). Some of these conditional probabilities for the MIC node are provided in Table 3.4. The CPT values can be explained as follows: when parent nodes are in the states (Bacteria presence(Yes); Wetting factor(Not wetted); MIC Control(Low);Operating conditions(Not suitable); Water Condition(Not suitable)) then corrosion likelihood is minimal and condition probability of MIC being in the states (MIC(Low); MIC(Medium); MIC(High)) = (0.95; 5; 0). The latter expression means that the probability of MIC being in the Low and Medium states is 95% and 5% respectively.  Table 3.4 Some examples of CPT for the MIC node Parent nodes:  (Bacteria presence; Wetting factor; MIC Control; Operating conditions; Water Condition) Child node states (Low; Medium; High) (Yes; Not wetted; Medium; Not suitable; Not suitable) (95; 5; 0) (Yes; Not wetted; Medium; Not suitable; Moderately suitable) (90; 10; 0) …….. …….. (Yes; Wetted; Low; Low; Moderately suitable) (40; 60; 0) (Yes; Wetted; Low; Low; Suitable) (20; 80; 0) …….. …….. (Yes; Wetted; Low; Suitable; Moderately suitable) (0; 25; 75) (Yes; Wetted; Low; Suitable; Suitable) (0; 10; 90)  The MIC contributing factors are clustered into three major categories: Operating Conditions (OC), Water Condition (WC) and MIC Control (MICC). Details of the model development for each category are provided in the subsections below.  3.3.3.1 Operating Conditions  Operating conditions such as flow rate, temperature, fluid composition and others can significantly affect bacterial activity. It was shown that bacteria could grow under a variety of pressure ranges; even dramatic change of this parameter did not harm a bacterial population (Javaherdashti et al., 2013). Hence, operating pressure is excluded from consideration. The same applies for fluid pH, because biofilms are active over a broad pH range and have an aptitude to buffer pH. Flow velocity significantly influences biofilm formation. For instance, when the flow rate is higher than 2 m/s, biofilms begin to deteriorate (Pots et al., 2002). Conversely, when the flow velocity is very low or stagnant, it forms suitable conditions for the attachment of corrosive biofilms (Papavinasam, 2013). Furthermore, if suspended particles are present in these sections  25 with relatively low flow rates, solid deposition may occur, providing bacteria with a breeding ground (Papavinasam, 2013).  Corrosive biofilms can survive under a broad range of temperatures. However, most species involved in corrosion reactions better thrive within a narrower temperature interval (between 15oC and 45oC) (Sooknah et al., 2008). At decreased temperatures, the bacterial activity can be reduced due to the inhibition of the metabolic processes, whereas at high temperatures denaturation may kill the microbial population. To reflect the aforementioned discussion, Temperature (T), Flow Velocity (FV), Pigging Frequency (PF) and Suspended Solids (SS) nodes were created and incorporated in the Operating conditions (OC) factor. The discretization details of the nodes constituting this factor are summarized in Table 3.6. 3.3.3.2 Water Condition  Recent studies suggest that if free water is not present in a pipeline, then the likelihood of MIC is negligible (Revie, 2015). However, even if a small amount of water wets a pipe interior surface (e.g. due to flow abnormalities or changes in operating conditions), biofilm formation can be initiated (Nyborg, 2002; Sooknah, Papavinasa, & Revie, 2007). Thus, water contact with a metal surface affects MIC propagation. To account for that impact, WF has been coupled with the MIC node applying the following formula (Revie, 2015): MIC = MICw  WF (3.3) where MICw is the microbial corrosion rate (mm/year) in the presence of water. Besides presence of water, its chemistry also plays an important role in the MIC propagation. The following water parameters affect biofilm growth: Mineral Content (MC), Redox Potential (RP) and Langelier Saturation Index (LSI) (Javaherdashti et al., 2013). These parameters have been combined in the Water Condition (WC) factor to describe a suitable environment for bacterial populations to thrive.  The MC node indicates the total dissolved solids concentration in water. It can be presented by sulfates, chlorides, bicarbonates, etc. It has been reported that the MIC damage is correlated with the concentration of dissolved minerals (especially chlorides and sulfates) in the transported fluid  26 (Papavinasam, 2013). The LSI parameter indicates if the water has the corrosive or scaling tendency. MIC is more likely to happen when scales are formed, which provide shelter and a breeding ground for bacterial population (Papavinasam, 2013). LSI higher than 0.5 shows a scaling formation tendency, whereas LSI being in the range close to [-0.5; 0.5] indicates that water is balanced; hence it does not affect the MIC. RP shows the oxidative-reductive nature of the mixture. This parameter can be used to indicate oxygen concentration in the environment, thus differentiate anaerobic and aerobic conditions. Negative values of RP correspond to anaerobic bacteria activity, whereas positive RP reflects aerobic bacteria activity. MIC occurrence correlates with RP; it was reported that corrosive bacteria species are predominantly active when redox potential falls in the range of [-50; +150] mV (Sooknah et al., 2008). The discretization details of the LSI, RP and MC nodes are provided in Table 3.6.  3.3.3.3 MIC Control MIC can be mitigated by mechanically removing biofilms (brush pigging) from the pipeline’s interior surface or adding in the flow chemical reagents (biocides), which control biofilms growth. An efficient MIC mitigation strategy includes both means. A pig cleaning frequency significantly affects bacterial populations, the higher the pigging frequency the less time a bacterial would have to proliferate. It has been shown that once every two weeks is the sufficient cleaning frequency to inhibit bacterial growth (Pots et al., 2002; Sooknah et al., 2007). There is an enormous variation of cleaning pig types and each has a specific efficiency with respect to MIC mitigation (King, 2007). Table 3.5 shows pig efficiency levels to mitigate MIC depending on the pig type and its configuration.  Table 3.5 Bacteria removal efficiency depending on the pig type Pig type Sphere Foam Swab Foam Poly Cast Mandrel Brush Plow blade Bidirectional Pin wheel Multi-diameter Bypass Gel BBN States Poor Poor Fair Poor Fair Excellent Fair Good Fair Fair Fair Fair  Biocide treatments can also substantially reduce bacterial activity. However, if the same biocide is applied continuously, bacterial populations can develop a natural resistance to it, thus decreasing chemical treatment effectiveness. Therefore, to remove corrosion biofilms, biocides should be injected in a systematic manner (Pots et al., 2002; Sooknah et al., 2007).   27 Table 3.6 MIC discretization model details   Variables and reference for discretization Sub criteria Performance measure MIC, mm/year Operating conditions (OC); Water condition (WC); MIC control (MICC); Bacteria presence (BP); Wetting Factor (WF) Low Medium  High 0 ≤  MIC< 0.01 0.01≤ MIC < 0.1 0.1 ≤  MIC <  1 Bacteria Presence (BP) --- Yes No No measured parameter is considered Wetting Factor (WF) Water cut (WC), % Flow velocity (FV), m/s The same as in Table 3.2 Discretization details of the operating conditions category Operating conditions (OC) Flow velocity (FV), m/s; Solid deposition (SD); Temperature (T), oC ; Not suitable Low Medium High Suitable No measured parameter is considered Flow Velocity (FV)  The same as in Table 3.2 Solid Deposition (SD) (Pots et al., 2002; Sooknah et al., 2007) Suspended solids (SS) The same as in Table 3.3 Flow velocity (FV), m/s Stagnant Very Low Low  Medium High Very High 0 ≤  FV< 0.1 0.1 ≤  FV < 0.5 0.5 ≤  FV <  1 1 ≤  FV< 2 2 ≤  FV< 3 3 ≤  FV< 4.5 Pigging frequency (PF) Very High High Medium Low Very Low Not applied Once 2 weeks Once 4 weeks Once 12 weeks Once 24 weeks Once 48 weeks Never  Temperature (T), oC --- The same as in Table 3.2 Discretization details of the water condition category Water condition (WC) Langelier saturation index (LSI); Mineral content (MC), ppm; Redox potential (RP), mV; Not suitable Moderately suitable Suitable No measured parameter is considered Water condition (WC) (Haile et al., 2013)  Langelier saturation index (LSI) Low  Neutral High - 6 ≤  LSI < - 0.5 - 0.5 ≤  LSI <  0.5 0.5 ≤  LSI < 6 Mineral content (MC), ppm Low  Medium High 15,000 > MC 15,000≤MC< 150,000 MC ≥ 150,000 Redox potential (RP), mV Low  Medium High -50 > RP -50  ≤ RP < 150 RP ≥ 150 Discretization details of the MIC control category MIC Control (MICC) Mechanical cleaning (MCL); Biocides treatment (BT) Low Medium High No measured parameter is considered Mechanical cleaning (MCL) (Pots et al., 2002; Sooknah et al., 2007); (Papavinasam, 2013) Pigging frequency (PF) Very High High Medium Low Very Low Not applied Once 2 weeks Once 4 weeks Once 12 weeks Once 24 weeks Once 48 weeks Never Pig efficiency (PE) Poor Fair Good Excellent No measured parameter is considered  Biocides Treatment (BT) (Pots et al., 2002; Sooknah et al., 2007) Biocides treatment (BT) Systematic Not systematic Never No measured parameter is considered  28 To reflect the aforementioned, a MICC node is introduced in the model. This node is based on two defined parameters, namely Biocides Treatment (BT) and Mechanical Cleaning (MCL). The latter one is comprised by Pig Efficiency (PE) and Pigging Frequency (PF) sub criteria.  Pigging frequency describes cleaning intervals, as well as the condition when the pipeline is not designed for pigging or has never been pigged. Pig cleaning efficiency levels from Table 3.5 have been adopted for the PE node. The BT node reflects biocide regime injection and the condition when biocides are not applied. The discretization details of the PF, PE, and BT nodes are provided in the Table 3.6.  3.3.4 Corrosion Defect Model In this study internal corrosion depth and length are modeled as independent variables (Alamilla, Campos, & Sosa, 2012; Ayello et al., 2014). The ultimate Corrosion Rate (CR) is obtained as a combined effect of general corrosion, pitting corrosion, erosion-corrosion and MIC (Ayello et al., 2014; Papavinasam et al., 2010). Linear growth model for the future defects is assumed to be valid for corrosion depth propagation. In the case of corrosion length, there is no analytical method to predict its value. However, some conclusions regarding its magnitude can be made based on the history of the predominant corrosion type in the system (Ayello et al., 2013). For instance, the defect length of corrosion-erosion is far greater than that for pitting corrosion. In many studies this parameter was either assumed to be proportional to pipe dimensions or to follow an assumed probability distribution function (Maes, Dann, & Salama, 2008; Teixeira, Soares, Netto, & Estefen, 2008). Therefore, expert judgment is applied to fill the CPT for the defect length node; its discretization details are summarized in Table 3.8. A number of failure pressure models have been developed to assess corrosion defects in pipelines such as ASME B31G, modified ASME B31G, RSTRENG, Shell-92, DNV-RP-F101, and others (American National Standards Institute, 1991; Cosham, Hopkins, & Macdonald, 2007; Veritas, 2004). These models are constructed based on the basic mechanics provided in (Kiefner, Maxey, Eiber, & Duffy, 1973):   29 𝜎𝜃 = 𝜎 [1 − (𝐴𝐴0)1 − (𝐴𝐴0)1𝑀] = 𝜎 [1 − (𝑑𝑡 )1 − (𝑑𝑡 )1𝑀]       (3.4) where A is projected area of defect on axial plane; A0 is original cross section area; M bulging factor; 𝜎 – flow stress; 𝜎𝜃 is predicted hoop stress at failure.  The enumerated models are mainly concerned with the corroded area geometry and pipe internal pressure. Figure 3.3 depicts models output, indicating significant discrepancy for the same input parameters. As is shown, ASME B31G gives the most conservative results, followed by Shell-92 (Caleyo, Gonzalez, & Hallen, 2002; Opeyemi, Patelli, Beer, & Timashev, 2015). On the contrary, Modified B31G and DNV-RP-F101 models have been concluded to be the most accurate (Cosham et al., 2007). Consequently, this study considers DNV-RP-F101 and modified ASME B31G models together to estimate residual pressure capacity and PoF. The difference in results between these two models is also quite high, accounting for nearly 20% for the low defect depth. Such discrepancy in outputs is attributed to the difference in defect profile approximations and the difference in reference stress interpretation. The necessity of applying these models together in the analysis is governed by the following reasons: 1. Because mechanical behaviour of old and modern pipeline steels are quite different, biased results can be obtained if DNV-RP-F101 is applied for old line pipe steels or modified ASME B31G for modern steels (Cosham et al., 2007; Hasan, Khan, & Kenny, 2012). 2. In practice, oil and gas pipeline infrastructure may contain both old and recently commissioned segments and there is no commonly accepted criterion regarding the applicability of these models under differing conditions.  30  Figure 3.3 Comparison of different failure pressure models The Pipeline Defect Assessment Manual (PDAM) summarizes best methods and practices regarding assessment of the different defect types. It also recommends that DNV-RP-F101 can only be applicable for moderate to high toughness steel, which is defined as follows: (Cosham et al., 2007; Cosham & Hopkins, 2001):  Line pipe steel, which satisfies axial strain requirements of the API 5L standard  Line pipe steel, which shows at least 18 J of impact energy in upper shelf Charpy V-notch test   Line pipe steel, which is known to have no inclusions, second-phase particles, and other contaminants ( it is a typical characteristics of old low grade line pipes such as A and B)  These guidelines were followed and the Toughness (TO) node has been introduced with states low and high which reflect the aforementioned criteria. For those pipelines, which do not satisfy these criteria ASME B31G model is applied. The outlined failure pressure models are deterministic, they evaluate a corrosion defect severity applying nominal values for the demand (the pipeline internal pressure loading, POP) and capacity (the pipeline failure pressure, PF) (Caleyo et al., 2002). Such deterministic approach 0204060801000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Failure Pressure, MPa Defect depth (portion of wall thickness) Modified B31GDNV-RP-F101Shell-92B31GBattelle 31 makes them impossible to be employed for quantifying the PoF. Therefore, to estimate PoF, a probabilistic approach must be established. A limit state function (LSF) has been formulated as the difference of the remaining capacity (failure pressure, PF) and demand (operating pressure, POP): LSF = PF - POP (3.5) PoF = P (LSF ≤ 0) (3.6) To obtain PoF, formulas outlined in Table 3.7 have been used in BBN. If the defined LSF > 0 (i.e. PF > POP), then the pipeline is considered to be safe to operate. Conversely, if LSF ≤ 0, then there is likelihood for pipeline to fail. The other failure criterion is assumed to be met when defect depth exceeds 80% of the wall thickness. This criterion is widely applied in defect assessment standards, and no operation is allowed when the defect depth exceeds this value (American National Standards Institute, 1991; Veritas, 2004). Table 3.7 Failure pressure models and their application based on steel toughness Models Toughness Parameters ASME B31G 𝑃𝑜𝐹 = 𝑃(𝐿𝑆𝐹 ≤ 0);  𝐿𝑆𝐹 =2(𝜎𝑦 + 68.95)𝑡𝐷(1 − 0.85𝑑𝑡1 − 0.85𝑑𝑡 𝑀−1) − 𝑃𝑜𝑝 𝑀 = √1 + 0.6275𝐿2𝐷𝑡− 0.003375𝐿4𝐷2𝑡2  𝑓𝑜𝑟 𝐿2𝐷𝑡 ≤ 50;  𝑀 = 0.032𝐿2𝐷𝑡+ 3.3 𝑓𝑜𝑟 𝐿2𝐷𝑡 > 50 Low 𝝈𝒚 is yield strength; 𝒕 is wall thickness; 𝒅 is defect depth; 𝑫 is outside diameter;  𝑴 is Folias factor; 𝑷𝑶𝑷 is operating pressure; 𝝈𝒖 is ultimate tensile stress; 𝑳 is defect length;   DNV-RP-F101 𝑃𝑜𝐹 = 𝑃(𝐿𝑆𝐹 ≤ 0);  𝐿𝑆𝐹 =2𝜎𝑢𝑡𝐷 − 𝑡(1 −𝑑𝑡1 −𝑑𝑡 𝑀−1) − 𝑃𝑜𝑝;  𝑀 = √1 + 0.31𝐿2𝐷𝑡 High    32 Table 3.8 Corrosion defect model discretization details    Variables and reference for discretization Sub criteria Performance measure Corrosion Rate (CR), mm/year; (Ayello et al., 2014) General corrosion (GCR), mm/year; Pitting corrosion (PC), mm/year; Erosion-corrosion (EC) mm/year; MIC mm/year; Extremely Low Very Low  Low Medium High Very High Extremely High 0 ≤ CR< 0.01 0.01≤ CR < 0.1 0.1≤ CR < 1 1≤ CR < 2 2≤ CR < 5 5≤ CR < 10 10≤ CR Corrosion Length (CL), mm/year General corrosion (GCR), mm/year; Pitting corrosion (PC), mm/year; Erosion-corrosion (EC) mm/year; MIC mm/year; Low Medium High 0 ≤ CL< 10 10≤ CL < 100 100≤ CL  Defect Depth (DD), d/t   Pipe age (PA), years Extremely Low  Very Low …….. Extremely High PA = 1 PA = 2 …….. PA = 40 Corrosion rate (CR), mm/year; The same as above Wall thickness (WT), mm Extremely Low  Very Low …….. Extremely High WT = 2 WT = 3 …….. WT = 20 ILI defect depth (IDD), mm No defect Extremely Low  Very Low …….. Extremely High 0 0 ≤ IDD < 0.03 0.03 ≤ IDD < 0.06 …….. 0.8 ≤IDD Defect Length (DL), mm Pipe age (PA), years The same as above Corrosion length (CL), mm/year The same as above ILI defect length (IDL), mm No defect Low Medium High 0 0 ≤IDL< 10 10 ≤ IDL < 100 100 ≤ IDL < 1000 Failure pressure (FP), MPa Wall thickness (WT), mm The same as above Outside diameter (OD), mm Extremely Low  Very Low …….. Extremely High OD = 88.9 OD = 114.3 ….. OD = 1220 Toughness  (TO) Low High No measured parameter is considered Pipe steel grade (PSG), MPa API 5L X52 API 5L X56 API 5L X60 200 ≤PSG< 300 300 ≤ PSG < 400 500 ≤ PSG < 600 Defect depth (DD), d/t  Extremely Low  Very Low …….. Extremely High 0 ≤ DD < 0.03 0.03 ≤ DD < 0.06 …….. 0.8 ≤ DD Defect length (DL), mm Low Medium High Very High 0 ≤ DL< 10 10 ≤  DL < 100 100 ≤ DL < 1000 1000≤ DL Pipe Failure (PF) Failure pressure (FP), MPa Extremely Low  Very Low …….. Extremely High 0 ≤ FP < 5 5 ≤ FP < 10 …….. 90≤ FP < 100 Operating pressure (OP), MPa Extremely Low  Very Low …….. Extremely High 0 ≤ OP < 5 5 ≤ OP < 10 …….. 90≤ OP< 100  33 3.4 Sensitivity Analysis  The Sensitivity analysis identifies a degree of influence caused by input parent nodes on the child output nodes. It is essential to perform sensitivity analysis because the final output of BBN depends on probabilities assigned a priori. A sensitivity analysis identifies critical input parameters that significantly influence the output results (Tesfamariam & Martín-Pérez, 2008). A sensitivity analysis in BBN can also be applied in order to identify important uncertainties, thus facilitating prioritization of the additional data collection (Ismail et al., 2011). A number of different techniques have been proposed to perform sensitivity analysis, including entropy reduction, variance reduction and variance of beliefs estimations (Pearl, 1988; Uusitalo, 2007). In this study, the variance reduction method is applied to calculate the sensitivity of the model’s output (CR and PoF nodes) This method calculates the expected reduction in variance of the expected real value Q given the evidence F as (Norsys Software Corp, 2015; Pearl, 1988; Saltelli et al., 2010): 𝑉(𝑞|𝑓) = ∑ 𝑝(𝑞|𝑓)[𝑋𝑞 − 𝐸(𝑄|𝑓)]2𝑞 (3.7) where f is the state of the varying node F; q is the state of the query node Q; p(q|f) is the conditional probability of q when node F is given to be in the state f; Xq is the numeric value corresponding to the state q; E(Q|f) is the expected real value of Q due to a finding of the state f in the node F. To estimate the degree of influence on the outcome, Netica varies parent nodes (varying nodes), with no prior assumptions made regarding the distribution function of the inputs. Based on this degree of influence, nodes in the model are ranked accordingly. Results of the sensitivity analysis are illustrated in Figure 3.4 and Figure 3.5.    34   0% 10% 20% 30% 40% 50% 60%Pigging FrequencyFlow velocitySuspended solidsBiocides TreatmentRedox PotentialLSIPig EfficencyMineral Content(a)                     Normalized % of variance reduction 0% 10% 20% 30% 40%pHCorrosion inhibitionCO₂ H₂S Water cutTemperatureFe²⁺ Flow velocityO₂ (b)                    Normalized % of variance reduction  35  Figure 3.4 Sensitivity analysis of the MIC (a), GC (b) and CR (c) nodes based on variation in the input nodes As is shown in Figure 3.4, CO2 concentration and pH nodes have the greatest contribution in the variance reduction of the CR node, accounting for 24.2% and 17.0% respectively. The high degree of influence of pH can be attributed to the fact that pH is a governing parameter affecting protective films formation. When the pH is low, a pipe surface is unprotected by corrosion films, which causes high general corrosion. Conversely, at high pH levels, a corrosion film protects steel, but has the potential to be locally disrupted, and thus initiating localized corrosion. Because chlorides and suspended solids can be a predominant cause of protective film damage, these nodes have relatively high contribution for the corrosion rate, making up 4.5% and 4.1% of the variance reduction. In addition, the sensitivity analysis indicates a high effect of corrosion inhibition measures, namely (14.0%) for CR node. Parameters that are assumed to govern wettability, such as FV and WC significantly contribute to the variance reduction for the outcome. These nodes affect multiple corrosion mechanisms, which indicate its great importance for the overall corrosion assessment. The input nodes, which represent the suitability of the environment for bacterial activity (MC, RP, BT, and LSI) have a minor effect on the outcome.  0% 5% 10% 15% 20% 25% 30%CO₂ pHCorrosion inhibitionWater cutH₂S TemperatureChloridesSuspended solidsFlow velocityFe²⁺ O₂ Bacteria presencePigging frequencyGeometry changeBiocides treatmentMineral contentLSIRedox potentialPig efficency(c) Normalized % of variance reduction  36 Sensitivity analysis of the final output node has indicated that Operating pressure (OP) and Defect Depth (DD) are crucial parameters affecting PoF. These factors are followed by CR and Outside Diameter (OD) nodes accounting for 11.7% and 7.2% of the variance reduction. As can be noticed from Figure 3.5 the node Toughness (TO) moderately contributes to variance reduction and is therefore, significant in the proposed model.   Figure 3.5 Sensitivity analysis of the Pipe Failure (PF) node based on variation in the input nodes 3.5 Scenario Analysis  In complex probabilistic models, inputs frequently contain various degrees of uncertainty. To deal with this uncertainty, inputs can be described as random variables with defined probability distributions (Sadiq, Rajani, & Kleiner, 2004b). These distributions are either subjectively defined (when data is limited or unavailable) or obtained from statistical fitting of the available data. Consequently, the output given by such probabilistic models is also a random variable with predicted distribution and associated uncertainties. In this work, two types of uncertainties are considered such as modelling and data uncertainties. The modelling uncertainty arises from simplified assumptions made for a complex natural process. The data uncertainty can either result from natural heterogeneity (variability) or lack of knowledge. The latter one can be reduced by obtaining more data. However, variability is the inherent property of the parameter 0% 10% 20% 30% 40% 50%Operating pressureDefect depthCorrosion rateOutside diameterPipe ageWall thicknessDefect lengthCO₂ Water cutCorrosion inhibitionToughnessSuspended solidsChloridesFlow velocityTemperaturepHH₂S Normalized % of variance reduction  37 and cannot be reduced (Oberkampf, Helton, Joslyn, Wojtkiewicz, & Ferson, 2004). Table 3.9 Probabilistic data of input parameters Parameter Scenario 1 Scenario 2 Scenario 3 PDF Mean Stdev PDF Mean Stdev PDF Mean Stdev 1 pH level LN 6.5 0.65 LN 5.8 0.58 LN 5.3 0.53 2 Temperature (oC) N 37 5 N 42 7 N 29 9 3 CO2 pressure (Bar) U [0…7] LN 1.191 0.596 LN 0.621 0.311 4 H2S (ppm) fixed 0 LN 7500 3750 LN 10000 5000 5 O2  (ppb) Unknown Unknown Unknown 6 Fe2+ (ppm) Unknown Unknown Unknown 7 Flow Velocity (m/s) N 1.18 0.2 N 2.18 0.218 N 2.5 0.25 8 Water cut (%) LN 18 12.6 U [50…100] U [10…60] 9 Geometry change Yes Unknown Yes 10 Suspended solids Concentration No No No 11 Bacteria presence No Unknown Unknown 12 Chlorides (ppm) Low Unknown Unknown 13 Mineral content (ppm) Unknown Unknown Unknown 14 Langelier saturation index Unknown Unknown Unknown 15 Redox potential (mV) N 50 20 Unknown Unknown 16 Biocides treatment No Yes Yes 17 Cleaning frequency U [12…48] U [4…48] U [4…48] 18 Cleaning efficiency Unknown Unknown Unknown 19 Inhibitor efficiency (%) Unknown Unknown U [50…80] 20 Pipe age fixed 2 fixed 9 fixed 15 21 Wall thickness (mm) fixed 3.2 fixed 4.8 fixed 3.2 22 Outside diameter (mm) fixed 88.9 fixed 168.3 fixed 88.9 23 Toughness (Low/High) High High High 24 SMYS (MPa) LN 395 27.65 LN 395 27.65 LN 395 27.65 25 OP (MPa) LN 6.96 0.696 LN 3.97 0.397 LN 2.07 0.207 N – normal distribution; LN – Lognormal distribution; U- uniform distribution To propagate these uncertainties to the output parameters, Monte Carlo simulation is used. Monte Carlo simulation is a widely applied alternative to analytical methods to determine parameters of the output distribution based on the randomly generated values from known input distributions (Sadiq et al., 2004b). To demonstrate the application of the proposed BBN model, a random vector of operation and pipeline parameters has been generated from subjectively defined distributions. Then, this random vector is applied in Monte Carlo simulation for 4000 iterations. Parameters used as well as characteristics of the applied probability distributions are summarized in Table 3.9. The first scenario reflects a recently constructed small diameter pipeline operating under high pressure in sweet environment, carrying fluid with up to 10% mole fraction of CO2. Scenarios 2 and 3 show pipes operating under moderate and low pressure, conveying oil effluent with 0.75%  38 and 1% H2S, respectively, (sour conditions). Corrosion inhibition as well as regular pigging are used as major means to combat internal corrosion in the given pipelines. The simulation output reflecting current internal corrosion situation is presented in the Figure 3.6. Table 3.10 shows the 50th and 90th percentile values, which represent central tendency estimate (CTE) and reasonable maximum estimate (RME).    Figure 3.6 Predicted relative defect depth distribution for scenario analysis  Table 3.10 Median and maximum defect depth and PoF Parameter Scenario 1 Scenario 2 Scenario 3 Defect depth (CTE) 0.21 0.59 0.63 PoF (CTE) 0.01 0.26 0.29 Defect depth (RME) 0.57 0.75 0.79 PoF (RME) 0.18 0.51 0.69  Figure 3.6 shows that output results for the scenario 1 has a substantial scatter, which can be explained by significant uncertainties in the input data. More data should be gathered to reduce this epistemic uncertainty in order to clarify if the pipeline has very low or moderate PoF.  In scenario 2, median defect depth reaches 0.59 of wall thickness, but due to moderate operating pressure median PoF is 0.26. Scenario 3 has the highest predicted median defect depth, which 00.10.20.30.40.50 10 20 30 40 50 60 70 80 90 100Probability Defect depth (% of wall thickness) Scenario 1 00.20.40.60 10 20 30 40 50 60 70 80 90 100Probability Defect depth (% of wall thickness) Scenario 2 00.10.20.30.40 10 20 30 40 50 60 70 80 90 100Probability Defect depth (% of wall thickness) Scenario 3  39 can be explained by the high corrosivity of the transported fluid and long elapsed time (15 years). Despite the reduced operating pressure, this pipeline has the highest median value of PoF, thus it needs to be inspected first to eliminate uncertainties and reach the decision regarding appropriate maintenance strategy.  Since in scenario 1 pipeline showed corrosion problem shortly after it has been commissioned, it is essential to know corrosion defect and PoF evolution over its lifetime. In order to prevent leak or rupture at the later stage of pipeline operation, it is a common practise in the oil and gas industry to reduce the operating pressure as the pipeline ages. In this paper, it is assumed that the pipeline operator decreases the mean value of the operating pressure linearly up to 50% of its initial value at the end of the service life (20 years). It can be expressed as follows: 𝑃(𝑡) = (1 −𝑡40) ∗ 𝑃𝑖𝑛 (3.8) where P(t) is the mean value of the operating pressure at time t (MPa); Pin – is the mean value of the initial operating pressure.   Figure 3.7 Defect depth evolution over 20 years of the pipeline service time Figure 3.7 demonstrates a substantial growth of the corrosion defect within 4 years with the following stabilization. The 25th and 75th percentile interval shows the uncertainty range in the simulated data.  00.10.20.30.40.50.60.70.80.910 2 4 6 8 10 12 14 16 18 20Relative defect depth Years Median 25th and 75th percentile 40  Figure 3.8 PoF evolution over 20 years of the pipeline service time considering different toughness Figure 3.8 depicts the predicted evolution of the PoF as a function of time in service. As is shown, PoF significantly increases within 6 years of the pipeline operation. This is due to a rapid growth of the defect depth and length within this time, which leads to a reduction in pressure resistance capacity. In addition, it is observed that despite the gradual decrease in operating pressure, median PoF grows till 18 years, reaching the value of 0.248. Subsequently, scheduled decline in operating pressure contributes more to PoF than corrosion defect growth, which results in the overall drop of the PoF. As mentioned before, it is essential for the PoF prediction to have information regarding toughness of the pipeline steel, which governs the selection of the appropriate failure pressure model. To demonstrate this, the same analysis has been implemented, while considering low steel toughness. Figure 3.8 shows that the difference in PoF is quite significant, accounting for 73.2% at its maximum (t = 6 years). As was expected, uncertainty in failure probability prediction and corrosion defect depth increases with elapsed time.  00.10.20.30.40.50.60.70.80.910 2 4 6 8 10 12 14 16 18 20PoF Year Median [high toughness]25th and 75th percentile [high toughness]Median [low toughness] 41 3.6 Case Study of the Northeastern BC Pipeline Infrastructure In this thesis, to demonstrate the application of the proposed BBN based model, internal corrosion hazard has been assessed for oil and gas pipeline network, located in Northeast of British Columbia (BC), Canada. The region under study is the most essential gas production area in BC, and accounts for more than half of the provincial gas production (BCOGC, 2014). As of 2014, 75% of the product was being extracted from unconventional sources, with production levels reaching 2.3 billion cubic feet/day accompanied by substantial generation of condensate and gas liquids. To transport the extracted fluid, over 3000 kilometers of pipeline infrastructure has been constructed. Since the gas production boomed in the mid-2000s the majority of the pipelines are in the early stage of their life cycle (less than 10 years). Figure 3.9 summarizes important data on the studied region. Around 65% of the infrastructure is operated in sour environment with H2S concentration ranging from 0.01% to 32% mole fraction.   Figure 3.9 Data summary on studied region    86 318 246 185 187 59 10 8 10 05010015020025030035088.9 114.3 168.3 219.1 273.1 323.9 406.4 457.2 1220 Number of segments Diameter Pipe diameter distribution 51% 28% 20% 1% Pipe age  1-3 years4-7 years8-12 years13-16 years 42 To perform the analysis, spatial, mechanical and fluid composition data has been obtained from publicly available sources (BCOGC, 2015a; BCOGC, 2015b). Although, several parameters were unknown, the most important ones for the model (based on the sensitivity analysis), namely operating pressure, outside diameter, pipe age, wall thickness were available for each segment, making the analysis feasible.  The output of the proposed BBN model is reported as maximum defect depth in the pipeline segment and its PoF due to this defect. For simplicity and representation purposes, the output is grouped in low, medium and high categories, which corresponds to [0-25%], [25%-50%], [50%-75%] of the wall thickness loss for defect depth parameter and [0-10%], [10%-40%], [40%-100%] for the probability of failure. However, a decision maker can tune these thresholds, according to experience or pipeline condition and location.   Figure 3.10 shows the BBN model predictions for various diameters of Northeastern BC oil and gas pipeline infrastructure. This figure indicates that the majority of the pipe segments with small diameter (88.9 mm and 114.3 mm) may contain corrosion defects with medium or high depth. Consequently, pipelines of this type have 71% and 6% of segments being in medium and high risk of failure states. Mostly, it can be explained by the high corrosivity of the transported fluid as well as thin walls of small diameter pipes. To eliminate failure, operators and regulatory authorities should pay special attention to these pipelines, establishing appropriate monitoring and preventive measures (e.g. gradual pressure reduction, corrosion inhibition, regular pigging) Segments with high diameter (168.3 mm and higher) have been predicted to be relatively safe to operate, without being in the high state for probability of failure. However, to minimize failure, timely inline inspections or repair actions are recommended for some segments of pipelines (with diameter of 168.3 mm, 219.1 mm, and 273.1 mm), because they most likely contain corrosion defects with the high relative depth.      43     Figure 3.10 Median defect depth (left) and PoF (right) distributions for the Northeastern BC pipeline infrastructure Finally, to facilitate failure mitigation programs and to improve resources allocation strategies for Northeastern BC infrastructure, spatial distribution of the predicted parameters have been created with the aid of publically available GIS software QGIS (QGIS, 2015).  05010015020025030035088.9 114.3 168.3 219.1 273.1 323.9 406.4 457.2 1220Number of segments Diameter (mm) High[50%-75%]Medium [25%-50%]Low [0-25%]Defect depth (% of wt) 05010015020025030035088.9 114.3 168.3 219.1 273.1 323.9 406.4 457.2 1220Number of segments Diameter (mm) High[40%-100%]Medium [10%-40%]Low [0-10%]PoF 51% 26% 23% Low [0-25%] Medium [25%-50%] High[50%-75%]66% 32% 2% Low [0-10%] Medium [10%-40%] High[40%-100%] 44  Figure 3.11 Spatial distribution of the predicted median defect depth (a) and median probability of failure (b)    45 Chapter 4 Induced Seismicity This chapter has been submitted to Journal of Risk Analysis titled “Induced Seismicity Risk Assessment of Oil and Gas Pipelines” The first part of this chapter discusses registered cases of induced seismicity and its possible impact on the oil and gas pipeline infrastructure. This is followed by the explanation of the methodology. The subsequent sections present the study region description, hazard map construction, and pipeline damage quantification.  It has been known for decades that earthquakes can occur not only due to natural causes, but also can be triggered by industrial processes. Much of the induced earthquakes were linked to mining operations, dam impoundment, wastewater disposal and hydraulic fracturing (Atkinson, 2015; Schultz, Stern, Novakovic, Atkinson, & Gu, 2015). In the early 2000s, the extensive application of hydraulic fracturing and second oil recovery techniques has boomed unconventional hydrocarbons production, at the same time significantly increasing a number of induced seismic events. For example, until the 2000s, in the central US, the long-term average rate of seismic events with M>3 was 21 events per year; as of 2015 it has soared up to 151 events per year (Atkinson, Ghofrani, & Assatourians, 2015). A substantial growth of the low-to-moderate earthquakes has also been observed in Canada. This includes clusters of induced events, which occurred at Horn River Basin, Montney Trend (Northeastern BC), Rocky Mountain House (RMH), Crooked Lake (Alberta) and others (Atkinson, Assatourians, Cheadle, & Greig, 2015; BCOGC, 2012; BCOGC, 2014; Farahbod, Kao, Walker, Cassidy, & Calvert, 2015; Schultz et al., 2015). Many investigations suggest that induced events occur due to reactivation of the pre-existing faults (Ellsworth, 2013; USGS, 2015). Induced earthquake may occur when hydraulic fracture treatments or continuous water disposal differ a pore fluid pressure, altering local stress conditions near the pre-existing fault (Ellsworth, 2013). The majority of the oil and gas operations do not cause significant seismicity; in fact, it is mostly lower than the felt threshold. However, some operations induce earthquakes, which are not only substantially higher than the felt threshold, but strong enough to cause damage to surface objects (Atkinson et al., 2015). For  46 instance, wastewater disposal induced earthquake in Oklahoma (M=5.6) caused moderate damage to local residential buildings and highways (Rubinstein & Mahani, 2015). 1. GIS data Seismic LocationsRegistered Magnitude2. Spatial clustering analysis and identification of the seismic sources 4. BBN internal corrosion model5. Seismic fragility formulations6. Pipeline vulnerabilityfunctions7. PoF visualization in GIS 3. MC simulations of the GMPE for induced seismicity and  hazard map construction Figure 4.1 Proposed framework  47 Figure 4.1 depicts a flow chart for the proposed framework. The first step is to gather sufficient data on the previous earthquake locations and magnitudes. Then, to delineate areas which are more likely to be prone to induced seismic occurrence, spatial cluster analysis is used. The state-of-art ground-motion prediction equation (GMPE) for induced seismicity proposed by Atkinson (2015) has been used in Monte Carlo simulation to create a stochastic map of the seismic intensity parameter. To estimate possible damage to pipelines, ALA (2001) seismic fragility formulations for buried pipelines have been adopted. In addition, since the studied infrastructure is mostly comprised of production and gathering pipelines, the influence of internal corrosion on seismic performance have been considered and incorporated in the analysis. Eventually, the seismic hazard layer and corrosion hazard layer have been combined with the aid of the Geospatial Information System (GIS). The final result yields a seismic vulnerability map of the studied infrastructure. Based on the outcome of this analysis, pipeline operating companies can improve their possible seismic mitigation and emergency response programs and enhance their pipeline rehabilitation strategies. Using the approach outlined in this paper, regulatory organizations and production companies can refine their decision making process, regarding the authorization of new wells and future field development.  4.1 Study Region The Montney trend region starting from 2013 shows exponential growth in the number of seismic events. Over 200 seismic events have been induced by hydraulic fracturing operations and wastewater disposal wells (BCOGC, 2014). Despite this fact, oil and gas activity in the region rapidly increases with the growth of wastewater disposal volumes along with the extensive application of multistage hydraulic fracturing.  Figure 4.2 depicts spatial and temporal distributions of the observed seismicity in the region under study. In other North American regions of active unconventional oil and gas development, the occurrence of induced earthquakes were observed to be related with the growth of wastewater disposal volumes (Frohlich et al., 2014; Keranen, Weingarten, Abers, Bekins, & Ge, 2014; Rubinstein & Mahani, 2015). Taking into account the rising trend of wastewater disposal in the Montney trend, coupled with proven anthropogenic causes of the seismicity, more triggered earthquakes  may occur in the future within the study region.   48 As can be noticed from Figure 4.2, the majority of the seismic events occurred in clusters in the proximity of wastewater disposal wells. However, after detailed examination of the well head pressure and disposed water volumes there was no apparent correlation found between these parameters and earthquake occurrence. Thus, we assume that other factors such as size, orientation and geological parameters of the pre-existing faults may govern induced seismicity in the region (USGS, 2015) To delineate areas which are more likely to be prone to induced seismicity, Getis-Ord Gi* a spatial clustering algorithm has been applied to previously detected earthquake locations. These locations as well as locations of the future hydraulic fractured (HF) and wastewater disposal wells have been obtained using publicly available databases (BCOGC, 2015b; Earthquakes Canada, 2015).  Figure 4.2 Spatial and temporal distributions of the observed seismicity in Northern Montney Trend    49 4.2 Induced Seismicity Hazard Assessment 4.2.1 Spatial Clustering Analysis  Spatial clustering is a data mining approach, which is used to identify statistically significant patterns in spatial datasets. Cluster is referred to as a geographically bounded set of features with sufficient size or concentration, which is unlikely to occur together by chance (Elliot, 1989). Two approaches of the spatial clustering analysis are commonly used:  A global clustering approach is applied to identify if clustering occurs in the study area by statistical analysis of the spatial dataset for the whole area.   A local clustering approach is used to determine if the group of features represent a spatial cluster of high or low values based on the statistical analysis with respect to neighboring features. In this thesis, the local spatial clustering approach has been performed using Getis-Ord Gi* (hot spot analysis) statistical technique available in ArcGIS platform (Esri, 2012). To determine a statistically significant cluster with high values (hot spot) and low values (cold spot), this technique performs the following calculations:  𝐺𝑖∗ =∑ 𝑤𝑖,𝑗𝑥𝑗 − ?̅? ∑ 𝑤𝑖,𝑗𝑛𝑗=1𝑛𝑗=1𝑆√[𝑛 ∑ 𝑤𝑖,𝑗2 − (∑ 𝑤𝑖,𝑗𝑛𝑗=1 )2𝑛𝑗=1 ]𝑛 − 1 (4.1) ?̅? =∑ 𝑥𝑗𝑛𝑗=1𝑛 ;  𝑆 = √∑ 𝑥𝑗2𝑛𝑗=1𝑛− (?̅?)2 (4.2) where 𝐺𝑖∗ is a Z- score of the spatial feature; 𝑛 is a total number of features; 𝑥𝑗 is attribute value for spatial feature 𝑗; 𝑤𝑖,𝑗is the spatial weight between features 𝑖 and 𝑗. Using these expressions, the Getis-Ord Gi* method proportionally compares the aggregated sum of all features to the local sum of a feature and its neighbors. In case of the substantial difference, hot spot analysis yields a high Z score (low p-Value), indicating clustering of the features (ArcGIS, 2015). In order to obtain a sufficient sample size for spatial clustering analysis all seismic events which occurred since 2013 have been taken into consideration. The earthquake  50 magnitude of M≥ 1.5 has been selected based on the local earthquake detection threshold (Farahbod, Cassidy, Kao, & Walker, 2014).   Figure 4.3 depicts the result of spatial cluster analysis, indicating areas with a statistically significant number of earthquake occurrences. Based on this inference, a significance level of 0.10 is used to delineate regions that are assumed to be more likely prone to induced seismicity.  Figure 4.3  Cluster analysis and superimposed potential seismic sources (HF and wastewater disposal wells) A BCOGC investigation report has indicated that induced seismicity in the region was triggered by wastewater disposal and hydraulic fracturing operations (BCOGC, 2014). Thus, in this study, active wastewater disposal wells and future HF wells (authorized by BCOGC wells for 2016) have been assumed to be potential sources of induced seismicity. Other well types, such as water injection wells applied for enhanced oil recovery operations are unlikely to induce a seismic  51 event, because fluid is injected into reservoirs where hydrocarbons have already been extracted, which keeps pressure in the reservoir less or equal the preproduction level (Rubinstein & Mahani, 2015). In addition, there are no reports of induced seismicity in the region, produced by water injection wells; therefore, these types of wells have been excluded from the analysis. Geographical locations of the potential induced seismicity sources have been obtained from the publically available database and then superimposed with the cluster analysis map (BCOGC, 2015b). Figure 4.3 shows spatial distribution of the wells potentially triggering induced seismicity within statistically significant clusters. Other wells that are located outside of the 0.10 significance level clusters have been discarded.  4.2.2 Ground Motion Prediction Equation for Induced Seismicity Ground motion is usually characterized by using an intensity measure, such as spectral acceleration at a certain period, peak ground acceleration (PGA), peak ground velocity (PGV) and so on (Baker, 2008). A number of GMPEs have been proposed to evaluate seismic intensity parameters caused by natural seismicity. These attenuation equations evaluate seismic intensity parameters as a function of earthquake magnitude, soil conditions, site-to source distance and so on. However, in the case of induced seismicity, due to low focal depth of occurrence, ground motion intensities can be significantly higher near the epicentre than predicted by GMPEs for natural seismicity (Atkinson, 2015). Hence, to evaluate seismic hazard caused by induced seismic events, it is essential to use GMPE, which accounts for the effect of short hypocentral distances. Thus, in this work, Atkinson (2015) GMPE for small-to-moderate earthquakes with short hypocentral distances has been adopted. The generic form of the Atkinson (2015) attenuation equation is represented as follows:  𝑙𝑜𝑔 𝑌 = 𝑐0 + 𝑐1𝑀 + 𝑐2𝑀2 + 𝑐3 𝑙𝑜𝑔 𝑅   (4.3) where 𝑐0, 𝑐1, 𝑐2, 𝑐3 are regression coefficients, 𝑌 is a ground motion parameter at a given frequency, 𝑀 is a moment magnitude, R is an effective point source distance (km):   𝑅 = √𝑅ℎ𝑦𝑝𝑜2 + ℎ𝑒𝑓𝑓2 , 𝑅ℎ𝑦𝑝𝑜 is a hypocentral distance (km); 𝑅ℎ𝑦𝑝𝑜 ≈ √𝑅𝑒𝑝2 + ℎ2; (𝑅𝑒𝑝) is and epicentral distance (km); ℎ is a focal depth (km);  ℎ𝑒𝑓𝑓 is a distance–saturation term or effective depth (km), ℎ𝑒𝑓𝑓 = 𝑚𝑎𝑥 (1, 10(−1.72+0.43𝑀)).  52 Extensive post-earthquake investigations reveal that PGA is strongly correlated with damage to surface structures, whereas PGV is better correlated with damage to buried structures, including pipelines (Lanzano et al., 2014). It has been shown that PGV is associated with the soil axial strains, the portion of which is transferred to the pipeline during ground shaking (O'Rourke, 1989; Toprak & Taskin, 2007). Hence, in this study, PGV is used to quantify pipeline seismic damage. Atkinson (2015) attenuation relationship for PGV is formulated as follows:  𝑙𝑜𝑔 𝑃𝐺𝑉 = −4.151 + 1.762𝑀 − 0.095𝑀2 − 1.669 𝑙𝑜𝑔 𝑅 (4.4) where 𝑃𝐺𝑉 is a horizontal peak ground velocity (cm/s) obtained for the reference site condition of the B/C boundary (soft rock with shear wave velocity of 760 m/s).   Figure 4.4 Attenuation of PGV as a function of the epicentral distance for focal depth (𝒉 = 𝟐 km) Figure 4.4 depicts attenuation of the ground motion intensity (PGV) as a function of epicentral distance (𝑅𝑒𝑝) and various earthquake magnitudes (M) for focal depth (ℎ = 2𝑘𝑚). As is shown, PGV attenuates steeply near the source and changes significantly depending on the magnitude.  05101520253035400 5 10 15 20 25 30 35 40Peak ground velocity (cm/s) Epicentral distance (km) M4.5 M5M5.5 M6 53 4.2.3 Induced Seismicity Hazard Map To obtain spatial and probabilistic distributions of the ground motion intensity, Monte Carlo (MC) simulations have been applied to Equation (4.4). Monte Carlo simulation is a widely applied alternative to analytical methods to determine parameters of the output distribution based on the randomly generated values from known input distributions (Sadiq et al., 2004b). Spatial locations of the potential seismic sources have been selected based on the wastewater disposal and future HF wells located within delineated clusters. Hydraulic fracturing and wastewater disposal processes are assumed to be similar triggers of the induced seismicity. No distinction in mean values of magnitude and focal depth has been made between these processes. A cut-off distance of 40 km for the attenuation relationship has been used, due to the insignificant impact on the intensity at distances higher than 40 km (Atkinson, 2015). Various scenarios of the earthquake magnitude have been considered in the analysis, including Low M [3…4], Medium M [4…5], High M [5…6]. Since induced seismicity primarily occurs at shallow depths (less than 5km), the mean value of focal depth ℎ = 2.5 km has been selected. Because the pore pressure due to fluid injection can travel significant distances from the injection point, a standard deviation of 5km from site-to-source distance have been assumed (Rubinstein & Mahani, 2015; USGS, 2015). Statistical parameters as well as selected distribution types for considered scenarios are provided in Table 4.1. Table 4.1 Probability distributions of input parameters Scenario Symbol Parameter Distribution type Units Mean Standard deviation Min Max Low M 𝑅𝑒𝑝 Epicentral distance  Normal km Location based 5 0 40 ℎ Focal depth Normal km 2.5 2 1 5 M Moment magnitude Uniform --- --- --- 3 4 Medium M ℎ, 𝑅𝑒𝑝 The same as above M Moment magnitude Uniform --- --- --- 4 5 High M ℎ, 𝑅𝑒𝑝 The same as above M Moment magnitude Uniform --- --- --- 5 6  Probabilistic output of the MC simulations has been interpolated applying triangular interpolation and then visualized using the open source GIS platform. Figure 4.5 depicts spatial distribution of the 95th percentile of the seismic intensity parameter for low and high moment magnitude scenarios.   54   Figure 4.5  Peak ground velocity map (a) Low M [3…4] scenario; (b) High M [5…6] scenario 4.3 Pipeline Vulnerability Functions Based on the post-earthquake observations many empirical fragility functions have been proposed to quantify pipeline seismic damage (America Lifelines Alliance, 2001; Maruyama & Yamazaki, 2010; O’Rourke, Jeon, Toprak, Cubrinovski, & Jung, 2012; Pineda-Porras & Ordaz, 2007). Fragility formulations express pipeline damage as a function of seismic intensity parameter (e.g. PGA, PGV, PGV2/PGA and so on) and pipeline characteristics (diameter, material, etc.). Pipeline seismic damage is generally quantified in the form of repair rate (RR). This parameter shows a number of pipe repairs in a given segment related to the length of this segment (Lanzano et al., 2014). According to Pitilakis et al. (2014), fragility functions proposed in ALA (2001) are more suitable to implement for oil and gas pipelines because they encompass extensive empirical data for ductile steel pipelines (which are predominantly used in the oil and  55 gas industry) and offer a broad applicability range. For this study, assuming the similarity between natural and induced seismicity in the potential to cause pipeline damage, fragility formulations summarized in ALA (2001) have been adopted to estimate pipeline RR. While pipeline damage can be caused by many hazards associated with earthquakes (co-seismic effects), such as liquefaction, active fault displacements and landslides, this thesis only addresses the ground shaking (wave propagation) damage. Empirical relation for RR due to wave propagation proposed by ALA (2001) is expressed: 𝑅𝑅 = 𝐾1 ∗ 0.002416 ∗ 𝑃𝐺𝑉 (4.5) where 𝑅𝑅 is a repair rate per kilometer; PGV is measured in cm/s; 𝐾1 is an adjustment factor, which  takes into account pipeline material, diameter, connection type and soil corrosivity. Values of  𝐾1 for ductile steel are summarized in Table 4.2. Table 4.2 Some values of the adjustment factor ( 𝑲𝟏) to estimate wave propagation damage (America Lifelines Alliance, 2001) Material Joint type Soil type Diameter 𝑲𝟏 Welded steel  Arc welded Unknown Small 0.6 Arc welded Corrosive Small 0.9 Arc welded Non corrosive Small 0.3 Arc welded All Large 0.15 Rubber gasket Unknown Small 0.7 Screwed All Small 1.3 Riveted All Small 1.3  Small diameter class corresponds to pipelines with a diameter between 10.16 and 30.48 cm, whereas large diameter class is considered to be greater than 40.64 cm (America Lifelines Alliance, 2001). Assuming that the damage process follows a Poisson probability law, the probability of the segment having 𝑛 number of breaks is calculated as follows (Adachi & Ellingwood, 2009; Lanzano et al., 2014): 𝑃𝑜𝐹[𝑁 = 𝑛] = 𝑒−𝑅𝑅∗𝐿 ∗(𝑅𝑅 ∗ 𝐿)𝑛𝑛! (4.6) where 𝑛 is a number of pipe breaks; 𝑅𝑅 is a repair rate (repairs/km); 𝐿 is a pipe segment length (km); 𝑃𝑜𝐹[𝑁 = 𝑛] is the probability of 𝑛 number of breaks in a pipe segment with length 𝐿.   56 Considering that the pipeline fails if at least one break occurs along its entire length, the PoF due to wave propagation can be expressed using exponential distribution (Adachi & Ellingwood, 2009; Lanzano et al., 2014):  𝑃𝑜𝐹 = 1 − 𝑃[𝑁 = 0] = 1 − 𝑒−𝑅𝑅∗𝐿   (4.7) Equations 4.6 and 4.7 express PoF of individual pipeline segments, for the single value of the seismic intensity. This might be the case for the short discrete component, subjected to constant PGV over its entire length. However, when the pipeline is too long and stretching over changing PGV areas, to calculate PoF, the total pipeline length (𝐿) should be discretized into a sufficient amount of short discrete components (∆𝐿𝑖), with PGV assigned to each component. In this case, PoF can be determined using expression (Adachi & Ellingwood, 2009) : 𝑃𝑜𝐹 = 1 − 𝑒𝑥𝑝 (− ∑ 𝑅𝑅(𝑃𝐺𝑉𝑖) ∗ ∆𝐿𝑖𝑚𝑖=1) (4.8) where PoF is probability of segment failure, ∆𝐿𝑖 is the length of individual discrete component 𝑖 (km), 𝑃𝐺𝑉𝑖 is the value of PGV (cm/s) for this component,𝑚 is the total number of discretized components of the pipeline.  Besides fragility formulations for intact pipelines, the ALA (2001) guideline provides adjusting coefficients for corrosive soils to determine seismic damage to corroded pipelines. Based on the empirical data, the guideline estimates the influence external corrosion, specifying that the small diameter pipelines in corrosive soils are approximately 50% more vulnerable to wave propagation damage as compared to pipelines in non-corrosive soils. Indeed, external corrosion caused by corrosive soils weakens seismic performance of a pipeline; however, in the oil and gas pipelines other factors such as internal corrosion may reduce the seismic capacity even more significantly. Since the studied pipeline infrastructure is mostly comprised of production and gathering pipelines, which conveys unpurified hydrocarbons, internal corrosion impact on the pipeline seismic performance can be essential. Assuming that there is an insignificant difference in the seismic behavior of externally and internally corroded pipelines, ALA (2001) external corrosion adjustment factors have been used to consider the influence of internal corrosion.   57 For this study region, internal corrosion hazard assessment has been performed in Chapter 3.The outcome of the internal corrosion hazard assessment is depicted in Figure 3.11(b). As is shown in Figure 3.11(b) results of the proposed BBN model categorize pipelines with respect to internal corrosion vulnerability in Low, Medium and High categories. These categories are used to correspond with ALA (2001) adjustment factors in the following manner:  Table 4.3 Corrosion vulnerability categories and corresponding values of the adjustment factor (𝑲𝟏)   Figure 4.6  ALA (2001) fragility relations for segment length L=5 km considering impact of the internal corrosion For the large diameter class ALA (2001) provides the value of adjustment factor (K1) only for the generic “All” soil type. This value is assumed to be corresponded with the medium vulnerability category. Similar to K1values of the small diameter type, adjustment factor value for the large diameter has been obtained through linear extrapolation. The value of  K1 = 0.25 has been assigned to large diameter pipes with high corrosion, following ALA (2001) recommendations that the large diameter pipes are capable of withstanding high PGV (due to thicker walls and better construction quality). Figure 4.6 shows some vulnerability functions applied in this study for two diameter types taking into account the impact of internal corrosion.  0.000.100.200.300.400.500.600.700 10 20 30 40 50 60 70 80PoF PGV (cm/s) Small diameter; Low corrosionSmall diameter;High corrosionLarge diameter; Low corrosionLarge diameter; High corrosionALA (2001) diameter types Small Large Internal corrosion vulnerability category Low Medium High Low Medium High ALA (2001) adjustment factor (𝐾1) 0.3 0.6 0.9 0.075 0.15 0.25  58 Finally, pipeline layer with mechanical parameters and corrosion conditions has been superimposed on the stochastic field of the seismic intensity. After that, expression (4.8) and obtained fragility relations have been used to estimate PoF for each pipeline with the following visualization in GIS. 4.4 Results and Discussion  The output of the analysis, indicating the PoF due to the induced seismicity to the region’s oil and gas infrastructure is reported in Figure 4.7. Since the infrastructure is comprised of a variety of pipelines with different segment lengths, the outcome is shown as PoF per km. For simplicity and representation purposes, the output is grouped in Very Low, Low, Medium and High categories, which correspond to [0 – 0.3%] [0.3 - 1%], [1% - 2%], [2% - 12%] values of the PoF/km. Though, a decision maker can tune these thresholds, according to experience, pipeline condition and location. As depicted in Figure 4.7, in the case of low moment magnitude M [3…4] scenario, pipeline damage is locally concentrated within the high PGV zones; PoF of these pipelines do not exceed the High threshold of 2% per km. Figure 4.7 also shows that the low magnitude scenario, pose insignificant hazard with PoF being in the Medium category for only 0.82% pipeline segments. Conversely, in the worst-case scenario (high moment magnitude M [5…6]), the PoF distribution map demonstrates that PoF is much higher in value and more spatially scattered. This observation can be explained by the larger impact area of the PGV, which affects more pipelines including those with high corrosion hazard. Additionally, the higher values of the seismic intensity significantly increase PoF, with the maximum value of 10.5%. However, as is shown in Figure 4.8, only 13.38% of the pipelines fall in the High PoF category. Figure 4.8 depicts another important observation, specifying that all the large diameter pipelines (323.9 mm and higher) demonstrate a good resistance to ground shaking, with PoF being only in the Very Low and  Low categories. In general, this fact can be attributed to the better corrosion monitoring and corrosion mitigation as well as higher seismic capacity of the large diameter pipelines in comparison to small diameter pipelines.  59  Figure 4.7  Spatial distribution of the predicted PoF (a) Low M [3…4]; (b) High M [5…6]   60     Figure 4.8 Distribution of PoF for different diameters due to induced seismicity considering low and high magnitude scenarios The seismic vulnerability assessment of individual pipeline segments yields a prioritization list, highlighting segments which need special attention from the seismic protection standpoint. This outcome may be of interest for owners and operating companies; however, government and regulatory organizations may benefit from the analysis on a regional scale. Results of such analysis are provided in Figure 4.9 and Figure 4.10 that shows RR distribution, which can be used to estimate probable financial losses, considering various scenarios of the seismic intensity and different corrosion conditions. Thus, knowing the probable negative impacts of induced seismicity in the region, regulatory organization can make informed decisions regarding the authorization of the new HF and water disposal wells.  05010015020025030035088.9 114.3 168.3 219.1 273.1 323.9 406.4 1220Number of segments Diameter, mm High[>2%]Medium [1%-2%]Low [0.3%-1%]Very low [0-0.3%]PoF (per km) 89% 10% 0.82%, 1% Very low [0-0.3%] Low [0.3%-1%]Medium [1%-2%] High[>2%]05010015020025030035088.9 114.3 168.3 219.1 273.1 323.9 406.4 1220Number of segments Diameter, mm High[>2%]Medium [1%-2%]Low [0.3%-1%]Very low [0-0.3%]PoF (per km) 18% 37% 32% 13% Very low [0-0.3%] Low [0.3%-1%]Medium [1%-2%] High[>2%] 61  Figure 4.9 Repair rate distribution on the region scale, considering actual corrosion conditions and different magnitudes  Figure 4.10 Repair rate distribution on the region scale, M [4…5] considering scenarios of different corrosion conditions 0.000.100.200.300.400.500.600.700.800.901.000.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08Probability of non-exceedance Repair rate (repair/km) Low M [3…4] Medium M [4…5] High M [5…6] 0.000.100.200.300.400.500.600.700.800.901.000 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08Probability of non-exceedance Repair rate (repair/km) Low corrosionMedium corrosionHigh corrosionActual corrosion 62 Chapter 5 External Corrosion This chapter presents a BBN-based external corrosion model development and its application for the three hypothetical scenarios. Section 5.1 discusses the theoretical background of the external corrosion as well as multiple factors that affect the external corrosion rate. The subsequent sections present details on the BBN model development. The final part of the chapter presents the sensitivity and scenario analyses. 5.1 Corrosion Mechanism and Factors Affecting its Rate In the oil and gas industry, it is a common practice to bury pipelines underground. This exposes them to an environment that is potentially corrosive to steel. To protect from this detrimental exposure, a two-layer protection system is applied, such as external coating and cathodic protection (CP). The protective coating acts as a first layer of defense, while cathodic protection serves as a backup system. In the case of coating failure, CP should mitigate corrosive exposure. When both protective systems fail or work incorrectly, external corrosion occurs. This process frequently propagates in four stages:  At the initial stage, corrosion species (e.g. chlorides) are transported on the pipeline coating surface. After some time, these elements reach the steel surface by penetration through the coating surface or damaged areas on the coating surface (due to soil stress or manufacturing defects).  At stage 2, a corrosion product forms, which is bigger in volume than its initial elements. This mechanically affects coating, causing its disbonding.  Gradually, coating damage increases from a microscopic size to a holiday, which is a visible discontinuity in the coating surface. Consequently, the pipe’s steel surface becomes directly exposed to the corrosive environment.   At the final stage, metal dissolution propagates, causing the formation of corrosion flaws, which ultimately may compromise the pipeline integrity. Cathodic protection supplies electrons to the pipeline, which decreases its natural electromotive force, leading to the reduction of the corrosion rate. (Castaneda & Rosas, 2015). However, CP and protective coating systems themselves are susceptible to malfunction or failure. As indicated  63 by Muhlbauer, any coating can fail and there is no defect free coating (Muhlbauer, 2004). Coating systems can fail due to a number of causes, including mechanical damage, incorrect application (e.g. excessive operating temperatures), cathodic disbondment, and so on. In addition, a poorly designed or malfunctioning CP system can be a cause of corrosion damage. For instance, CP may provide insufficient current, which is not able to stop the corrosion process, whereas high current may damage the protective coating. Furthermore, the normal work of CP can be interrupted by the presence of another CP protected object. The aforementioned failures of the external corrosion protection systems allow the corrosion process to initiate. The rate of this corrosion process and, therefore, the time of pipeline failure is strongly dependent on soil corrosivity, which, in turn, is affected by the mechanical and chemical properties of this soil (Demissie, Tesfamariam, & Sadiq, 2015; Sadiq et al., 2004b). Soil is a complex material, constituted by solid, liquid, and gas phases. Liquid and gas phases can comprise up to 50% of the total soil volume. One part of this liquid phase is bound to the mineral surfaces; the other part can freely flow through the soil pores. This flow is governed by soil permeability, which is determined by the size of particles in the solid phase. Such complexity creates many parameters, affecting soil corrosivity. The most important ones among them include soil resistivity, soil pH, chloride concentration, redox potential, water content, etc. (Castaneda & Rosas, 2015). These parameters are mostly seasonal and their values correspond to precipitation amounts and atmospheric temperatures. Some of these parameters and their influence on the corrosion rate are briefly described in the following paragraphs.  5.1.1 Soil Resistivity Electrical resistivity or conductivity of soil primarily affects the electron transport mechanism in the corrosion process. Low soil conductivity decreases transport kinetics, which slows down corrosion reactions. Soil resistivity is reported to be a function of the soil moisture content, temperature, and porosity (Demissie et al., 2015). Resistivity is the most commonly applied prediction parameter of soil corrosivity. Many researchers observed a strong correlation between soil resistivity and the corrosion rate (Demissie et al., 2015; Sadiq, Rajani, & Kleiner, 2004a).     64 5.1.2 Soil pH A pH value indicates ion concentration in the soil environment. It was reported that soil pH has a strong influence on corrosion processes (Arzola, Palomar-Pardave, & Genesca, 2003). In certain conditions pipelines, which are exposed to a subsurface environment with high pH may produce alkali formations, causing coating delamination followed by the initiation of localized corrosion. In general, soils with low pH (acidic) promote corrosion reactions.  5.1.3 Redox Potential Redox potential corresponds to a degree of the soil aeration; the higher the redox potential, the higher the oxygen content in the soil. Redox potential also serves as an indicator of the SRB, which has been proven to accelerate the corrosion process (Javaherdashti, 1999; Muthukumar et al., 2003). It was observed that SRB can actively proliferate when the values of the redox potential are in the low range (Sooknah et al., 2008).   5.1.4 Chlorides and Sulfates Chlorides and sulfates are potent agents that may significantly intensify external corrosion. This fact can be attributed to the high conductivity of the chloride and sulfate ions. Furthermore, chlorides may not only reduce the soil resistivity, but also can cause damage to the protective passive films, which may initiate localized corrosion (Castaneda & Rosas, 2015; Papavinasam, 2013). 5.1.5 Moisture Content  As is known from corrosion science, there is no corrosion reaction possible without a conductive electrolyte. Moisture in the soil acts as the conducting electrolyte, promoting faster transport of ions from the pipe surface. Many studies indicate that moisture content may be a predominant factor, which affects soil corrosivity (Demissie et al., 2015). Soil moisture content also influences soil resistivity; low moisture content correlates with high resistivity and vice versa. The moisture content depends on soil texture, groundwater movements, annual precipitation level, etc.  65 5.2 BBN External Corrosion Model Development To quantify the external corrosion hazard, the proposed BBN model determines PoF based on the predicted failure pressure (capacity) of the segment weakened by the corrosion defect and operating pressure (loading). Distribution of the corrosion defect and failure pressure parameters is computed in the BBN model, which is based on a knowledge-based model coupled with statistical models. The proposed BBN model is schematically depicted in Figure 5.1. (i) Collect data on soil properties; Corrosion prevention data; Pipe mechanical characteristics (ii) Knowledge-based BBN for coating failure time prediction (iii)Velazquez et. al corrosion model for defect depth prediction(iv) Defect length estimation using statistical approach Distributions of corrosion defect parameters(v) Failure pressure distribution (Capacity) Operating pressure (Loading)(vi) PoF Figure 5.1 Schematic representation of the BBN model for failure prediction due to external corrosion As is shown in Figure 5.1, the analysis is performed in the following steps: i. Gather data on soil properties, pipe mechanical parameters, and corrosion prevention measures. ii. Predict coating failure applying the knowledge-based BBN. iii. Calculate defect depth using the Velazquez et al. (2009) corrosion model. iv. Determine defect length applying the statistical approach proposed by (Zimmerman et al. 1998)  66 v. Predict failure pressure based on pipeline mechanical characteristics and defect parameters. vi. Calculate PoF using expression (3.5) and expression (3.6)  Figure 5.2 BBN model for pipeline failure due to external corrosion Figure 5.2 depicts details of the proposed BBN model. In the illustrated model, nodes represent stochastic variables, which affects PoF, whereas arrows show causal connections between them. Many of the random variables are assigned to have continuous states (e.g. soil resistivity, chloride content, etc.), whereas some others have been modeled with discrete states (coating type, soil type, etc). CPT are filled using expert opinion and previously established models, which are discussed in the following sections.  5.3 Knowledge Based BBN for Coating Failure External corrosion preventive measures have proved to be effective in protecting the pipe steel surface from a detrimental corrosive environment. However, the majority of pipelines still fail due to corrosion problems (Ayello et al., 2014). The corrosion initiation time is of crucial importance for any integrity assessment. In many studies, for simplicity, corrosion is conservatively assumed to initiate right after the pipeline has been commissioned, whereas in reality, corrosion initiates after some time. In the proposed framework, corrosion initiation is determined using knowledge based BBN.   67 In this study, the corrosion model, which is used to predict corrosion defects, already accounts for the potential imposed by cathodic protection; thus, to reflect the action of pipeline protective measures, the analysis boils down to the prediction of the coating failure time. The developed knowledge-based BBN model for coating failure time prediction is depicted in Figure 5.3. Nodes represent significant variables affecting coating integrity. Condition probabilities were assigned based on expert opinion and the extensive literature review of factors that may compromise coating integrity. After determining coating failure time t0 (i.e. corrosion initiation time), a distribution of the corrosion defect depth can be predicted using pitting corrosion model proposed by (Velázquez, Caleyo, Valor, & Hallen, 2009).  Figure 5.3 Knowledge-based BBN for corrosion initiation time The coating serves as a physical barrier between the corrosive environment and pipe steel surface. Every protective coating has a finite service time. Over time, the coating degrades and eventually fails, allowing moisture, oxygen and other chemicals to be in contact with the steel surface. In general, any change in coating protective properties is deemed a coating failure (Norsworthy, 2008). Coating can fail in numerous ways depending on the coating type, its initial condition and environmental factors. In addition, certain types of coating, when it fails, can shield the CP current, leaving the pipe unprotected. In this study, the following types of coating are considered: fusion bonded epoxy (FBE), alkyd enamel, wrap tape (single and double wrapped), and coal tar. The mean value of coating service time (in idealized conditions) proposed by Papavinasam (2013) were adopted and then adjusted considering the following factors: severity of the exerted soil stress, coating condition and operating temperature. Table 5.1 provides the values of the expected coating service time and assumed distributions.     68 Table 5.1 Types of coating and its expected service time Coting type Service time in idealized conditions as outlined in (Papavinasam, 2013) Assumed distribution Stdev FBE 40 years Normal, 20 Alkyd enamel 10 years Lognormal, 5 Wrap tape 15 years Lognormal, 7.5 Coal tar 20 years Normal, 10 Bare pipe Corrosion initiates right after pipeline commissioning  N/A 5.3.1 Coating Condition When the coating has some initial imperfections, its protective properties will progressively diminish over time and its service time without failure will be limited (Papavinasam & Revie, 2006). In this study, the coating quality indicator reflects the pre-commissioning coating condition, which is determined by such criteria as pipe surface preparation (for the coating application) and coating defects. Coating defects, such as holidays and dents can be caused by improper transportation, storage or positioning of the pipeline. The BBN node coating quality has been introduced with three qualitative performance levels, which indicate coating condition: good, fair, and poor. The pipe surface preparation significantly affects the coating performance; as pointed out by Papavinasam, pipe surface preparation is a predominant factor, which is often responsible for premature coating failure (Papavinasam, 2013). The steel surface can be prepared for coating application by using one of the following methods: sandblasting, wire brushing and scraping. Since these methods predetermine coating service time, they are used as discrete states in the pipe surface preparation BBN node. In addition, no surface preparation state is introduced to account for the case when the pipe was coated without any preliminary surface preparation. Sandblasting is factory-made and this is the most efficient method, which substantially enhances coating adhesion. On the contrary, wire brushing and scraping are primarily applied in situ and, therefore, more prone to have coating quality imperfections, which can be a cause of early coating disbonding. Extensive field investigations have shown that coal tar coatings applied over the surface with wire-brush preparation failed after being in service for one year. Conversely, coal tar coatings applied to sandblasted pipes operating in the same environment were in excellent condition after five years of service (Papavinasam, 2013).  69 Girth weld coating should be checked for compatibility with the mainline coating. Because this type of coating is applied in-situ, due attention should be paid to the quality of its application.  Poorly applied or incompatible girth weld coating can be a cause of early initiated corrosion, which is localized in the weld zone proximity (Norsworthy, 2008). If the evidence of incompatibility is observed, poor performance level is  assigned to overall coating condition.  Coating defects can occur due to improper manufacturing or can result from damage during pipeline transportation and construction. Numerous coating defects may exist, but in this study the discussion is limited by pipe dents and holidays. Pipe dents create concentrated stress regions and coating in them is more susceptible to the soil stress damage or disbonding. Any discontinuity in the coating surface (e.g. voids, uncoated regions, cracks, etc.) is referred as a holiday; these localized spots (especially in wrap tape and coal tar coatings) may prevent the CP current to reach pipe surface facilitating initiation of corrosion. Over time, coating degrades and holidays may grow in size, requiring more CP current to be supplied. To reflect the presence of these coating defects, the BBN nodes: dents and holidays were introduced in the network. The discretization details of these nodes as well as other nodes affecting coating quality are provided in the Table 5.3. 5.3.2 Soil Stress This criterion is used to describe a detrimental physical exposure exerted on the coating by the  subsurface environment. A coating damage may result from mechanical stress caused by repeated volumetric fluctuations of the surrounding soil. This exposure is particularly strong in clay soils with the frequently changing moisture content. Field experience shows that such coatings as alkyd enamel and wrap tape are particularly susceptible to soil stress (Papavinasam, 2013). In this work, soil stress is a qualitative factor, which is determined based on sub-factors: soil type, burial depth, water content, and trench preparation. The BBN node soil stress has been introduced to the model, considering three performance levels, namely low, medium, and high. The same soil types as in the (Velázquez et al., 2009) corrosion model have been used to discretize the soil type BBN node. These soil types include clay, clay loam, sandy and mixed soils. Soil type governs the soil specific gravity, which, in turn, affects the soil overburden  70 pressure. As reported in the literature, the highest stress is exerted by the clay soil, whereas low stress is observed in sandy soils (Andrenacci & Wong, 2012).  Burial depth significantly influences soil vertical pressure, exerted on the pipe. This confirms by the laboratory studies of the coating performance under the soil stress. The studies conclude that the higher the burial depth, the higher the exerted soil stress (Andrenacci & Wong, 2012). Conversely, small diameter pipes with low burial depth are subjected to low stress, which does not exceed the cohesion capacity; thus, coating is less likely to fail (Andrenacci & Wong, 2012).  Water content shows the amount of water is in the soil represented as a percentage of total volume. Moisture content and its variations have a substantial effect on the swelling and shrinkage tendency of the soil. Such repetitive movements may induce localized stress on the pipe and damage pipe coating. The higher the moisture, the higher the soil stresses, especially in the clay and clay-loam soils (Muhlbauer, 2004). To minimize this exposure, a good construction practice commonly includes a preliminary trench preparation. This preparation is carried out by using a fine bedding material or complete replacement of the offending material with higher quality soil. These measures reduce soil stress and eliminate coating damage due to rock impingement (Muhlbauer, 2004). To reflect the aforementioned discussion, child node (soil stress) and its parent nodes (soil type, burial depth, water content and trench preparation) have been created in the BBN; the discretization details are summarized in Table 5.3. 5.3.3 Operating Temperature As stated in the AER report, many external corrosion failures occur due to coating failures caused by excessive operating temperatures (AER, 2013). In the case, when operating temperature exceeds coating the maximum allowable temperature, physical properties of the coating may change, intensifying deterioration processes. For example, FBE at the elevated temperatures becomes soft, grainy and absorbs more water. These changes make it much more susceptible to the soil stress (Norsworthy, 2008).  Based on the criteria discussed above, the proposed knowledge-based BBN predicts coating failure time. This output node has been discretized in the continuous states that correspond to the time intervals (given in years) when the coating is expected to fail, such as 0 to 2.5, 2.5 to 5 and so forth. Figure 5.4 depicts some examples of the BBN model outputs for the coating failure  71 time. A snapshot of some CPT is provided in Table 5.2, whereas nodes states for the parameters used in the BBN model are summarized in Table 5.3. CPT values in Table 5.2 can be interpreted as follows: when parent nodes are in the states, for example, (CCLow; OTExcessive; SStLow; CTFBE) corresponding CPT values are (22.930-2.5; 49.922.5-5; 24.395-7.5; 2.697.5-10; 0.0710-12.5; 012.5-15; 015-17.5…). Based on this expression, the conditional probability of coating failure is in the state of (0-2.5) years is 22.93%, in the state (2.5-5) years is 44.92%. Table 5.2 Fragment of conditional probability of CFT node Parents nodes states  (Soil stress; Operating temperature; Coating condition; Coating type) CPT of the child node (coating failure, years):  (0-2.5; 2.5-5; 5-7.5; 7.5-10; 10-12.5; 12.5-15…45) (Low; Excessive; Low; FBE) (22.93; 49.92; 24.39; 2.69; 0.07; 0; 0…) (Low; Excessive; Low; Alkyd enamel) (99.5; 0.05; 0; 0; 0; 0; 0…) (Low; Excessive; Low; Coal tar) (72.93; 26.96; 0.072; 0.038; 0; 0; 0…) (Low; Excessive; Low; No coating) (99; 1; 0; 0; 0; 0; 0…) (Medium; Not excessive; Low; Alkyd enamel) (22.73; 48.66; 24.78; 3.66; 0.17; 0; 0…) (Medium; Not excessive; Low; Wrap tape) (10.74;27.31;32.89;20.65;6.87;1.36;0.17;0.01;0…) (Medium; Not excessive; Low; No coating) (98; 2; 0; 0; 0; 0; 0; 0…)  72 Table 5.3 Parameters and their discretization for coating failure model Parameters Sub criteria Performance states Coating  quality  Pipe surface preparation  Sandblasting Wire-brushing Scraping No preparation  Defect presence  Holidays Dents No defects Soil stress  Soil type  Clay Clay Loam Sandy Mixed Soil Burial depth  Low Medium High Water Content  Low Medium High Coating failure, years Soil stress  Low Medium High Operating temperature  Exceeding allowable Not exceeding  Coating  quality Good Fair Poor Coating type  FBE Alkyd enamel Coal tar Wrap tape No coating   Figure 5.4 Examples of coating failure probability predicted by knowledge based BBN 00.10.20.30.40.50.60.70.80.910 5 10 15 20 25 30 35 40 45 50Probability of non-exceedance Years Wrap tape;Fair quality;High soilstressFBE; Good quality; Medium soilstressCoal tar; Fair quality; Low soil stress 73 5.4 Corrosion Defect Depth Similar to internal corrosion defect quantification, the estimation of the external corrosion defect depth is one of the most important steps in the analysis. The distribution of the maximum defect depth has been calculated using in the BBN a pitting corrosion model proposed by (Velázquez et al., 2009). The justification of the selected model is outlined in the following paragraph: In the literature, there are analytical corrosion models which aim to predict corrosion defect depth. Since external corrosion is a complex process to model using electrochemical principals, statistical approaches are commonly used to predict corrosion defect evolution (Sadiq et al., 2004b). The majority of corrosion models predict evolution of the corrosion defect as a function of the exposure time and soil properties. These predictive models primarily have a form of a power law model, linear model or two-phase model. Table 5.4 reflects different types of models, which are frequently applied for the corrosion defect depth prediction. Although many models were developed, only a few of them consider protective coating properties and the presence of cathodic protection. Because the Velazquez et al. (2009) corrosion model is capable of addressing these shortcomings; this model has been adopted in this study.  Table 5.4 Commonly applied corrosion models (modified after Sadiq et al., 2004b, with permission) Model Model type Model equation Variables description (Kucera & Mattsson, 1987) Power law model 𝑑 = 𝑘𝑇𝑛 𝑑𝑇 = 𝑛𝐾𝑇(𝑛−1) 𝑑 defect depth(mm);  𝑑𝑇 corrosion rate (mm/year);   𝑘 (≈2) and 𝑛 (≈0.3) are constants; (Sheikh, Boah, & Hansen, 1990) Linear law model 𝑑𝑇 =𝑑(𝑇) − 𝑑(𝑇0)(𝑇 − 𝑇0) 𝑑(𝑇) defect depth at time T;  𝑑(𝑇0) defect depth at  time 𝑇0; (Rossum, 1969) Power law model 𝑑 = 𝐾𝑛𝑍𝑛 𝑍 = [(10 − 𝑝𝐻)𝑇𝑝𝑠𝑜𝑖𝑙] 𝐾𝑛 constant; T exposure time (years); pH soil pH; 𝑝𝑠𝑜𝑖𝑙 soil resistivity; n redox potential; (Rajani, 2000) Two-phase model 𝑑 = 𝑎𝑇 + 𝑏(1 − 𝑒−𝑐𝑇) 𝑑𝑇 = 𝑎 + 𝑏𝑐𝑒−𝑐𝑇 a=0.009 (mm/year) corrosion rate constant; b = 6.27 (mm) defect depth sailing constant; c = 0.14 (𝑦𝑒𝑎𝑟−1) corrosion rate inhibition factor ; (Velázquez et al., 2009) Power law model dmax = k(t − t0)ν k pitting proportionality (mm/year); ν pitting exponent; 𝑑𝑚𝑎𝑥 maximum corrosion defect depth (mm); t exposure time (years); 𝑡0 corrosion initiation time (years);  The Velazquez et al. (2009) is a power law corrosion model for the onshore oil and gas pipelines. The model has been constructed based on the data obtained from 259 field investigations of the coated pipelines and soil properties. The authors applied multiple regression analysis to derive  74 corrosion exponent (ν) and coefficient of proportionality (k) for a variety of soils in order to predict  maximum defect depth (dmax) at any time in the future. According to the Velazquez et al. (2009) model, corrosion defect depth at any time in the future (t) can be predicted using the expressions (5.1- 5.4) dmax = k(t − t0)v              (5.1) k = k0 + k1𝐫𝐩 + k2𝐩𝐡 + k3𝐫𝐞 + k4𝐜𝐜 + k5𝐛𝐜 + k6𝐬𝐜           (5.2) v = n0 + n1𝐩𝐩 + n2𝐰𝐜 + n3𝐛𝐝 + n4𝐜𝐭          (5.3) dmax = (k0 + ∑ kiXini=1 )(t − t0)n0+∑ (njXj)mj=1            (5.4) where dmax is maximum corrosion defect depth (mm); k is coefficient of proportionality; v is pitting exponent; rp is redox potential (mV); ph is soil pH; pp is pipe to soil potential (mV); re is soil resistivity (Om); wc is water content (wc); bd is soil bulk density (g/ml); cc is chloride content (ppm); bc is bicarbonate content (ppm); sc is sulfate content (ppm); ct is coating type; t is exposure time (years); t0 is corrosion initiation time (years);  𝑘0..𝑖 𝑛0…𝑗 is multiple regression correlation coefficients. Numerical values of these coefficients are provided in Table 5.5. In the Velázquez et al. (2009) model soil types are grouped in three textural classes, such as clay, clay loam and sandy clay loam. For each soil texture class, physical and chemical soil parameters, pipeline coating type and potential imposed by cathodic protection were analysed to obtain the coefficients for corrosion exponent (ν) and proportionality coefficient (k). The latter one was found to be a function of the redox potential, dissolved ion content, soil pH, and resistivity. The corrosion exponent was determined to be influenced by pipe-to-soil potential (natural or imposed by cathodic protection), pipe coating type, soil bulk density, and water content. Corresponding BBN nodes have been created as parent nodes of the proportionality coefficient (k) and corrosion exponent (ν). Discretization details of these nodes are summarized in Table 5.6    75 Table 5.5 Equation coefficients for the pitting exponent and the coefficient of proportionality for different soil types  Equation coefficients (Velázquez et al.,2009) Soil Type Mixed Soil Clay Soil Sandy-Clay Loam Soil Clay Loam Soil k0 6.08*10^(-1) 5.41*10^(-1) 5.99*10^(-1) 9.85*10^(-1) k1  -1.80*10^(-4) -8.99*10^(-5) -1.82*10^(-4) -1.06*10^(-4) k2  -6.54*10^(-2) -5.91*10^(-2) -6.42*10^(-2) -1.17*10^(-1) k3 -2.60*10^(-4) -2.15*10^(-4) -2.11*10^(-4) -2.99*10^(-4) k4 8.74*10^(-4) 8.38*10^(-4) 8.62*10^(-4) 1.80*10^(-3) k5 -6.39*10^(-4) -1.29*10^(-3) -6.78*10^(-4) -4.85*10^(-4) k6 -1.40*10^(-4) -5.31*10^(-5) -1.14*10^(-4) -2.09*10^(-4) n0 8.96*10^(-1) 8.85*10^(-1) 9.65*10^(-1) 2.82*10^(-1) n1 5.19*10^(-1) 4.83*10^(-1) 5.12*10^(-1) 4.61*10^(-1) n2 4.65*10^(-3) 3.72*10^(-5) 4.51*10^(-3) 1.69*10^(-2) n3 -9.91*10^(-2) -1.01*10^(-1) -1.58*10^(-2) -9.82*10^(-2) n4 4.31*10^(-1) 4.61*10^(-1) 4.34*10^(-1) 5.67*10^(-1) The Velazquez et al. (2009) model address the influence of the protective coating on the corrosion rate by using the scoring method; the higher the score, the lower protection of the coating. The authors claim that proposed scores reflect the practical knowledge regarding the coating failure. In addition, the authors mention that the corrosion initiation time (t0) was treated as unknown variable and was determined from multiple regression analysis of the available field data. Since BBN can efficiently integrate expert opinion in the analysis, the knowledge-based network (described in section 5.3) is used to predict the corrosion initiation time (t0). External corrosion is assumed to begin right after the coating failure.      76 Table 5.6 Discretization details of the external BBN model nodes Parameters Sub criteria Performance measure Coating type (ct) Pitting exponent FBE Alkyd enamel Wrap tape Coal tar Bare pipe No measured parameter is applied Soil type (ST) Clay Clay Loam Sandy Mixed Soil No measured parameter is applied Pipe to soil potential (pp), mV Low Medium High Very High -2≤  pp < -1.4 -1.4≤  pp < -1 -1 ≤  pp < -0.8 -0.8 ≤  pp < -0.4 Water content (wc), % Low Medium High 0 ≤  wc < 20 20 ≤  wc < 50 50 ≤  wc < 70 Soil bulk density (bd), g/ml Low Medium High 1.1≤  bd < 1.2 1.2 ≤  bd < 1.4 1.4 ≤  bd < 2 Redox potential (rp), mV Coefficient of proportionality Low Medium High 0 ≤  rp < 100 100 ≤  rp < 200 rp >400 Soil pH (SpH), pH Low Medium High 5 ≤  SpH < 7 7 ≤  SpH < 8 8 ≤  SpH < 9 Soil resistivity (sr), Ohm Low Medium High 0 ≤  sr < 400 400 ≤  sr < 800 sr > 800 Chloride content (cc), ppm Low Medium High 100 ≤  cc < 200 200 ≤  cc < 300 cc > 300 Bicarbonate content (bc), ppm Low Medium High 0 ≤  bc < 100 100 ≤  bc < 400 bc > 400 Sulfate content (sc), ppm Low Medium High 0 ≤  sc < 400 400 ≤  sc < 600 sc > 600 Soil type (ST)  The same as above Corrosion rate (CR), mm/year  Pitting exponent;  Coefficient of proportionality;  The same as in Table 3.2 Relative defect depth (RDD), d/t  Corrosion duration (CD), years Extremely Low  Very Low …….. Extremely High 0 ≤ CD < 1 1 ≤ CD < 2 …….. 35 ≤ CD < 40 Corrosion rate (CR), mm/year The same as above Wall thickness (WT), mm The same as in Table 3.8 Initial defect depth (IDD), d/t No defect Extremely Low  Very Low …….. Extremely High 0 0 ≤ IDD < 0.03 0.03 ≤ IDD < 0.06 …….. 0.75 ≤ IDD<0.8 Defect length (DL), mm Corrosion duration (CD),  years The same as above Annual defect length (ADL), mm Low Medium High Very High 0 ≤ ADL< 1 1≤ ADL < 10 10≤ ADL < 100 100≤ ADL < 1000 Initial defect length (IDL), mm The same as in Table 3.8 Outside diameter (OD), mm   Failure pressure (FP), MPa Wall thickness (WT), mm The same as in Table 3.8 Outside diameter (OD), mm Toughness (TO) Pipe steel grade (PSG), MPa Relative defect depth (RDD), d/t Defect length (DL), mm Pipe failure (PF) Failure pressure (FP), MPa Operating pressure (OP), MPa  77 5.5 Corrosion Defect Length To quantify external corrosion hazard, corrosion defect length must be specified. Despite the availability of comprehensive models to predict the external corrosion defect depth, in the case of external defect length, there are no analytical means to predict this parameter. Furthermore, many studies show that corrosion depth and length are independent parameters (Papavinasam, 2013). However, Amirat et al. (2009) indicated that to a given corrosion flaw depth there is a range of the associated flaw lengths. For instance, if defect depth reaches 20% of the wall thickness, then the observed defect length varies between 8 and 608mm (Amirat, Benmoussat, & Chaoui, 2009). The other way to determine defect length is to use the approach proposed by Zimmerman et al. (1998). This approach assumes that the defect length parameter follows Weibull distribution function with a coefficient of variation COV = 50% (Zimmerman, Cosham, & Sanderson, 1998). The probability of defect length (𝑙) greater of equal than its characteristic value (𝑙𝑐 ) can be calculated using the following expression:  𝑃(𝑙 ≥ 𝑙𝑐 ) = 1 − 𝐹(𝑙) = 𝑒−(𝑙𝜃)𝛽′=  ∫ 𝑓(𝑙)𝑑𝑙∞𝑙𝑐           (5.5) where 𝐹(𝑙) is the cumulative distribution of the defect length (𝑙); (𝛽′) is the shape parameter of the Weibull distribution; (𝜃) is the scale parameter of this distribution.  The annual defect length node has been introduced in the BBN network, following the Zimmerman et al. (1998) approach to model defect length. Characteristics of the Weibull distribution for this parameter have been determined for each pipe diameter using assumptions outlined in (Khan, Haddara, & Bhattacharya, 2006). Khan et al. (2006), assumed that characteristic defect length equals 𝑙𝑐 = 4% of the outside diameter, considering that 𝐹(𝑙) = 0.9 (Khan et al., 2006). Since covariance is COV= 50%, then the shape parameter (𝛽′) equals 2.1. Then the expression (5.5) is used to determine the scale parameter (𝜃). Thus, for pipeline, for example, with diameter of 88.9 mm, the mean value of the annual defect length equals to 2.12 mm with standard deviation of 1.06 mm. Consequently, defect length at the ginen time in the future is computed using the following expression (Caleyo et al., 2002; Opeyemi et al., 2015):  78 𝐷𝐿(𝑡) = 𝐼𝐷𝐿 + 𝐴𝐷𝐿 ∗ 𝑡   (5.6) where  𝐷𝐿(𝑡) is the corrosion defect length at a given time t; 𝐴𝐷𝐿 is the annual defect length.  𝐼𝐷𝐿 is the initial defect length, which can be known from the latest in-line inspection (ILI). When ILI data is available, t represents an elapsed time since the latest inspection. Conversely, if no ILI was performed, time t equals to the corrosion duration (years).  5.6 Sensitivity Analysis Similar to internal corrosion model, the sensitivity analysis has indicated that the operating pressure node has the prime influence on the probability of failure, accounting for nearly 45% of the variance reduction. As depicted in Figure 5.5, mechanical characteristics of the pipeline as well as defect parameters have a significant effect on the final output, accounting for 14.9% (wall thickness), 12.9% (relative defect depth) and 12.8% (outside diameter). Corrosion protection measures, such as cathodic protection and coating type have a moderate influence on the probability of failure. Conversely, in this model, soil characteristics have a minor influence on the output.    Figure 5.5 Sensitivity analysis of the pipe failure node based on variation in the input nodes   0.0%5.0%10.0%15.0%20.0%25.0%30.0%35.0%40.0%45.0%50.0%Normalized % of variance reduction   79 5.7 Scenario Analysis To demonstrate the application of the developed approach, the BBN model has been applied in the three hypothetical scenarios. Parameters of the BBN model as well as statistical characteristics of the subjectively defined distributions are provided in Table 5.7. These random variables are applied in Monte Carlo simulation for 4000 iterations. The number of iterations is deemed sufficient due to the stabilization of covariance in the output distribution.  Table 5.7 Probabilistic data of input parameters Parameter Pipeline 1 Pipeline 2 Pipeline 3 PDF Mean Stdev PDF Mean Stdev PDF Mean Stdev 1 Redox potential (mV) Unknown LN 300 95 LN 55 50 2 Soil pH level N 5.13 0.92 N 5.2 1.5 N 8.31 0.5 3 Soil resistivity (Om) U [50…150] N 300 90 LN 800 70 4 Chloride content (ppm) LN 55 71 LN 800 120 U [0…30] 5 Bicarbonate content (ppm) LN 20 29 Unknown U [0…400] 6 Sulfate content (ppm) LN 150 100 Unknown Unknown 7 Soil density (g/ml) N 1.35 0.2 U [1.3…1.5] N 1.25 0.1 8 Water content (%) LN 27 6.5 LN 35 9.3 Unknown 9 Pipe to soil potential (mV) LN -0.89 -0.21 LN -0.6 -0.3 LN -1.5 -0.3 10 Soil type Sandy Clay loam Mixed 11 Trench preparation No Yes No 12 Burial depth (m) N 2 0.1 N 1.5 0.4 N 1 0.2 13 Coating type Wrap tape FBE Wrap tape 14 Pipe surface preparation Brushing Blasting Brushing 15 Holidays No Unknown No 16 Dents No Yes Yes 17 Operating temperature Excessive Unknown Not excessive 18 Pipe age (years) fixed 2 fixed 9 fixed 15 19 Wall Thickness (mm) fixed 3.2 fixed 4.8 fixed 3.2 20 Outside Diameter (mm) fixed 88.9 fixed 168.3 fixed 88.9 21 Toughness (Low/High) High High Unknown 22 SMYS (MPa) LN 395 27.65 LN 395 27.65 LN 395 27.65 23 OP (MPa) LN 5.96 0.596 LN 3.97 0.397 LN 2.07 0.207 where N – normal distribution; LN – Lognormal distribution; U- uniform distribution In the first scenario, the recently commissioned pipe is shown. It is assumed that the pipeline has the wrap tape coating, which is in a good condition. The pipe is buried in soil with moderately corrosive properties (low soil resistivity and low pH). Scenario two depicts a pipeline that is buried in a highly corrosive soil (high chloride content). The coating of this pipeline is FBE with  80 some defects due to transportation. Scenario three represents the high age pipeline with wrap tape coating, which has minor defects. The simulation output reflecting corrosion situation is presented in Figure 5.6       Figure 5.6 Predicted relative defect depth distribution for scenario 2 and 3 In scenario 1, the proposed model predicts that the coating integrity remains uncompromised despite the excessive operating temperature. Thus, no external corrosion occurs; therefore, the probability of failure is negligible. In scenario two, the BBN model predicts that CTE and RME of the defect depth are 0.145 and 0.230 respectively. The associated probability of failure due to this defect has been predicted to be 0.06 (CTE) and 0.170 (RME). The highest probability of failure has been predicted for scenario 3, accounting for 0.148 (CTE) and 0.267 (RME).  Table 5.8 CTE and RME for defect depth and PoF of three scenarios Parameter Pipeline 1 Pipeline 2 Pipeline 3 Defect depth (CTE) Negligible 0.145 0.256 Defect depth (RME) Negligible 0.230 0.374 PoF (CTE) Negligible 0.060 0.148 PoF (RME) Negligible 0.170 0.267 As is shown in the sensitivity analysis section, operating pressure is the most influential parameter in the model affecting probability of failure. This is confirmed in scenario two, when despite the wall thickness loss of 14.5%, the PoF was only 0.06. In third scenario, the pipeline has the highest corrosion defect depth. This can be explained by the high age of the pipeline and the initially low wall thickness. 00.20.40.60.80 10 20 30 40 50 60 70 80 90 100Probability Defect depth (% of wall thickness) Scenario 2 00.10.20.30.40.50 10 20 30 40 50 60 70 80 90 100Probability Defect depth (% of wall thickness) Scenario 3  81 In the first scenario, the pipeline shows no external corrosion issues. However, it is important to assess corrosion external corrosion hazard over the expected service time. The operating pressure is assumed to be decreased linearly, up to 50% of its initial value at the end of the estimated time (20 years). Hence, the future operating pressure can be determined using expression (3.8). The proposed BBN model has been applied sequentially for each year to estimate external corrosion hazard evolution. The model output is shown in Figure 5.7.   Figure 5.7 PoF evolution over 20 years of the pipeline service time As is depicted in Figure 5.7, PoF remains negligible until 10 years of the pipeline service and no external corrosion is initiated. This can be attributed to a good quality of the wrap tape coating and a proper work of the cathodic protection. However, the wrap coating is prone to failure with shielding of the CP current, which initiate corrosion process. According to the model, corrosion initiation may occur after 11 years of the pipeline operation. Despite this fact, the low operating pressure keeps the probability of failure relatively low, accounting for 0.09 after 5 years of corrosion initiation. At the end of the designed service time, the median value of the failure probability reaches 0.18.    00.10.20.30.40.50.60.70.80.910 2 4 6 8 10 12 14 16 18 20PoF due to external corrosion Years Median PoF 25th and 75th percentile 82 Chapter 6 Summary and Conclusions The main objective of this research was to develop a flexible approach that incorporates analytical models (based on the physical properties of the system), published literature and expert judgments in order to determine defect depth and associated PoF in pipeline infrastructure that is subjected to internal and external corrosion exposure. This incorporation is particularly useful for the purpose of corrosion assessment because the corrosion modeling results that are predicted by different models are often inconsistent with each other and with the actual field data. A thorough literature review has been performed to identify forty-four different factors and their interdependencies, affecting the internal corrosion rate and PoF. A quantitative probabilistic approach using BBN has been performed to predict the output parameters. The necessity of using this approach was dictated by the high degree of uncertainty in the input data as well as by the uncertain nature of the corrosion process. MC simulations have been applied to the BBN model, which is comprised of various corrosion models and failure pressure models.  6.1  Research Contributions  This research has developed BBN-based corrosion models that can identify vulnerable pipeline sections and rank them accordingly to enhance the informed decision-making process. The flexibility of the proposed BBN approach allows the model to be extended in order to include more corrosion contributing factors as well as new information. Furthermore, the proposed model is able to perform a diagnostic analysis, which can indicate causes of corrosion.  Scenario analysis has been performed to illustrate the proposed model performance. In addition, the BBN model has been used to estimate corrosion propagation and PoF evolution over a pipeline’s service time. Furthermore, it has been shown that the proposed BBN model is able to distinguish between low and high toughness of the pipe steel, which is rarely considered in reliability analyses but, as was demonstrated, can drastically affect the outcome. The sensitivity analysis has indicated that inputs, such as the operating pressure, corrosion defect depth, and corrosion rate, predominantly influence the model output. It is essential to accurately  83 estimate these parameters in order to correctly predict PoF. The internal corrosion rate has been shown to be strongly dependent on fluid pH, water cut, CO2 and H2S concentrations as well as corrosion inhibitor efficiency. This emphasized the importance of developing and applying proper analytical models, which lay the foundation for the proposed BBN models.  Results obtained from this research can be employed to identify pipeline sections that are subjected to high corrosion hazard in order to improve the corrosion mitigation program. In addition, the proposed BBN model can be used to predict the safe operating pressure at a given time in the future (t). Thus, the field operating pressure can be adjusted accordingly in order to guarantee pipeline integrity over its full service time. The proposed BBN internal corrosion model has been applied to the Northeast BC pipeline infrastructure. Spatial and probabilistic distributions of corrosion defect and PoF have been obtained and visualized using GIS platform. Results have indicated that the majority of pipeline segments may contain defects, which do not exceed 25% of the wall thickness. The probability of failure for 66% of the segments was shown to be in the low range of [0-10%]. However, the BBN model has indicated that the small diameter pipelines (88.9 mm and 114.3 mm) may contain deep corrosion defects, which make them the most vulnerable to internal corrosion. The outcome of the preformed analysis can help to refine a company’s maintenance and rehabilitation strategies.  Another contribution of this thesis is an estimation of the probable impact of the induced seismicity hazard on the oil and gas pipeline infrastructure. Predicting seismic hazards from induced seismicity is substantially different from predicting seismic hazards caused by natural seismicity. This is because the occurrence of induced events is related to the production and injection of fluids, which is governed by decision making. Hence, to minimize possible adverse ecological and financial consequences in the regions prone to induced seismicity, more informed decisions should be made. To facilitate informed decision making, this thesis presented a probabilistic approach to quantify damage to oil and gas pipelines and its PoF due to wave propagation produced by induced seismicity. Several statistically significant clusters, where induced earthquakes are more likely to occur, were identified using Getis-Ord Gi* spatial clustering algorithm. The stochastic field of the seismic intensity was constructed for possible  84 epicenters located within the delineated clusters using the Atkinson (2015) GMPE for induced seismicity. The ALA (2001) seismic fragility formulations coupled with the results of the BBN internal corrosion model were superimposed on the PGV map using the GIS platform in order to obtain spatial and probabilistic distributions of the pipeline RR and PoF. Obtained results show that in the case of the low moment magnitude M [3…4], PoF does not exceed the High threshold and damaged segments are more likely to be localized only within a limited area proximal to epicentres. However, in the worst case scenario M [5…6], PoF is more spatially scattered and significantly higher in the magnitude, reaching up to 10.5% for 13.38% of the total number of pipeline segments. In addition, pipelines with diameter higher than 323.9 mm were shown to be in the Very low and Low hazard categories, which do not exceed 1% PoF per km.   6.2 Limitations Additional research is required to identify more factors affecting the internal and external corrosion rate. However, even if the corrosion rate is correctly quantified, a complex defect shape also should be taken into account. This can be accomplished by the development of the analytical models for defect length propagation, which by far, are unavailable. In addition, in the case when a pipeline contains multiple defects, which are located close to each other, their interaction may significantly weaken the residual pressure capacity. The proposed BBN model does not account for such cases.  Undoubtedly, to improve induced seismicity hazard assessment, more research is needed in developing analytical models, which would link particular oil and gas operations and its parameters (e.g. the volume of water disposed, fracturing pressure and so on) with a probable seismic intensity. Additionally, since ground failures previously caused pipeline damage in Northern BC, the impact of co-seismic effects (produced by induced seismicity) on the surface infrastructure should also be investigated.        85 References Adachi, T., & Ellingwood, B. R. (2009). Serviceability assessment of a municipal water system under spatially correlated seismic intensities. Computer‐Aided Civil and Infrastructure Engineering, 24(4), 237-248.  Adams, C. D., Garber, J. 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