Failure Assessment on Effects of Pressure Cycle Induced Fatigue on Natural Gas Pipelines

Transcription

1 Failure Assessment on Effects of Pressure Cycle Induced Fatigue on Natural Gas Pipelines Hugo Filipe Barros de Oliveira Dias Thesis to obtain the Master of Science Degree in Materials Engineering Supervisor: Prof. PhD Alberto Eduardo Morão Cabral Ferro Co-supervisor: Eng. Carlos Alberto Pires Sousa Examination Committee: Chairperson: Prof. PhD Maria de Fátima Reis Vaz Supervisor: Prof. PhD Alberto Eduardo Morão Cabral Ferro Member of the Committee: Prof. PhD Pedro Miguel Gomes Abrunhosa Amaral November 214

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3 Make big plans, aim high in hope and work let your watchword be order and your beacon beauty iii Burnham

4 Acknowledgments Firstly, I would like to thank my parents for all the support through the years and for making available resources for doing this work. Without them my education and growth as a person and a professional would not been possible. Secondly, I would like to acknowledge REN Redes Energéticas Nacionais, in particular to Chief Operating Officer, Engineer, João Conceição, for allowing me to take an academic internship for concluding my Masters. Furthermore, at REN-Gasodutos, I would like to express my gratitude to my co-supervisor Engineer Carlos Pires Sousa for the reception within the company and for making resources available to me, as I needed them. Moreover, I would like to recognize all people that were in a way connected with this work, namely, the Area Managers Rui Marmota, Paulo Ferreira and Ferreira Marques and Engineers David Gil, João Marrazes and João Teixeira Santos. Thirdly, I would like to recognize my supervisor PhD Alberto Ferro to put up with me since my second year in the University, and for the assistance and care through the work. Also, I would like to acknowledge PhD Ricardo Baptista for his help in this work. Without his advices, several results present in this work would not be possible. Finally, I would like to express my deeply gratitude to all my friends from Instituto Superior Técnico and other places for the friendship and for helping me to have great times. iv

5 Resumo A probabilidade de falha de uma estrutura pode ser minimizada através de uma avaliação de integridade que permita adoptar correctamente as acções mitigadoras e preventivas necessárias. O objectivo desta dissertação é avaliar se os gasodutos de transporte de gás natural estão sujeitos ao perigo de falha devido ao agravamento de defeitos graças à fadiga causada por ciclos de pressão. Estes ciclos de pressão podem ser originados pela alteração da filosofia de injecção de gás natural na rede no Terminal de Gás Natural Liquefeito, em Sines, tendo como objectivo a redução de custos maximizando as emissões nos períodos de tarifa reduzida. Os ciclos de pressão foram simulados no software SIMONE e os valores resultantes utilizados em ensaios de fadiga, na avaliação de integridade baseada nas normas BS 791 e API 579 e modelação numérica através do software Abaqus/CAE. Os resultados obtidos confirmaram que os gasodutos não têm perigo de falhar devido a fadiga provocada pelos ciclos de pressão, em situações em que não haja intervenção de terceiros. Os tempos estimados de falha rondariam os 15 a 2 anos. Foi também realizado um estudo probabilístico para prever a falha de um gasoduto com um defeito (semi-elipse), cuja probabilidade de fractura foi aproximadamente Palavras-chave: Fadiga; FEM; Fitness-for-Purpose; Gasoduto; Ciclo de Pressão; Aço X7; XFEM v

6 Abstract The probability of pipeline failure can be minimized if structural integrity is assessed and necessary prevention and mitigation measures appropriately taken.the goal of this work is to evaluate if natural gas pipelines are subjected to failure when cracks are activated by pressure cycle induced fatigue. Pressure cycles can be originated by modification of the natural gas send out philosophy in the liquefied natural gas terminal, in Sines, aiming for a operation cost reduction boosting emissions on low tariff periods. Send out cycles were simulated with software SIMONE and the resulting values were used in fatigue tests, in the integrity assessment studies through procedures BS 791 and API RP 579 and in numerical modelling of crack growth with software Abaqus/CAE. The results obtained confirmed that natural gas pipelines do not have danger to fail under pressure cycle induced fatigue, with high amplitudes whenever third party activities are not involved. Predicted times to failure ranged from 15 to 2 years. A probabilistic study was also carried out in order to predict the failure of a pipeline with one defect (semi-ellipse), whose probability of failure was found to be around Keywords: Fatigue; FEM; Fitness-for-Purpose; Pipeline; Pressure Cycle; X7 Steel; XFEM vi

7 Index Acknowledgments... iv Resumo... v Abstract... vi Index... vii List of Figures... ix List of Tables... xi Abbreviations... xii List of Symbols... xiii Chapter 1 Introduction Context Objective and Scope Thesis Outline... 3 Chapter 2 Overview Portuguese Natural Gas System Natural Gas Transmission Network Underground Gas Storage Liquefied Natural Gas Terminal... 7 Chapter 3 Fundamental Concepts Review on Fracture Mechanics Linear Elastic Fracture Mechanics Elastic-Plastic Fracture Mechanics Reviews on Fatigue Failure Concepts of Pipeline Mechanics Developments of high strength steels for pipelines Chapter 4 Pressure Cycle Simulation vii

8 4.1 Introduction SIMONE Simulation Conclusions Chapter 5 Experimental Testing and Results Introduction Mechanical characterization Fatigue characterization Conclusions Chapter 6 Numerical Modelling Introduction The Finite Element Method XFEM framework Models and Results K and J Estimation Values J-Based Failure Assessment Diagram Conclusions... 4 Chapter 7 Integrity Assessment and Structural Reliability Introduction Empirical Methods Fitness-for-Purpose Approach for Integrity Assessment Structural Reliability Models and Results Fitness-for-Purpose for Integrity Assessment Structural Reliability Conclusions Chapter 8 Final Remarks and Future Work Final Remarks viii

9 8.2 Future Work... 6 References Appendix I Natural Gas Transmission Network II Pressure cycle profiles and gas flow for different scenarios III API 5L X7 Steel Euro Pipe Certificate... 7 IV Assessment Procedure to Evaluate a Pipeline with Crack-Like Flaws V Methodology for Crack Growth Analysis List of Figures Figure 1-1 Causes of failure of Natural Gas pipelines around the world, from 2 to 212. [2] [3]... 2 Figure 2-1 LNG Terminal at Sines. [5]... 7 Figure 2-2 Comparison of the use of NG and LNG, through the years. [5]... 7 Figure 3-1 Effect of fracture toughness on the governing failure mechanism. [1]... 8 Figure 3-2 a) Real and ideal crack tension behavior. b) Stress field around the crack. [13]... 9 Figure 3-3 a) A 2D contour integral and b) a 2D closed contour integral. [14]... 1 Figure 3-4 Contour integral for general three dimensions crack front. [14] Figure The damage tolerance approach to design. [1] Figure 3-6 (a) S-N curve with fatigue limit. [15] (b) Clam Shell fatigue crack surface. [15] Figure 3-7 Random Load Spectrum. [9] Figure 3-8 Crack length increase with number of cycles. [15] Figure 3-9 Different regions of the a N vs K plot. [17] Figure 3-1 Pipeline Stresses under Internal Pressure. [18] Figure Evolution of line pipe steel grades. [2] Figure 4-1 Gas Flow during a week for the Scenario 1 (highest nomination) and 2 (lowest nomination) Figure 4-2 Scenario 1: Pressure Cycle Profiles, during a week Figure 4-3 Scenario 2: Pressure Cycle Profiles, during a week Figure 4-4 Pressure Range for: (a) Scenario 1 (b) Scenario Figure 4-5 Pressure Range for real-time profiles Figure 5-1 Steps to obtain specimens. [22] [23] Figure 5-2 Stress-strain curve: a) Longitudinal Direction; b) Radial/Transverse direction ix

10 Figure 5-3 Schematically representation of the compact specimen. [24] Figure 5-4 Detail of the camera attached to the machine (Left). Crack propagation (Right) Figure 5-5 Crack length vs. Number of cycles Figure 5-6 Fatigue crack growth rate: a) Specimen 1; b) Specimen Figure 5-7 Details from the specimen after the fatigue failure Figure 5-8 Stages I and II of fatigue crack propagation. [25] Figure 6-1 A body with a crack with a fixed boundary subjected to a load. [1] Figure 6-2 (a) Mesh with a crack. (b) Mesh without a crack. The circle numbers are the element numbers. [29] Figure 6-3 (a) An arbitrary crack in a mesh. (b) Local coordinate axes for two crack tips. [27]33 Figure 6-4 Scenario 1: (a) Schematic representation (b) ABAQUS models (FEM-Contour Integral and XFEM) Figure 6-5 Scenario 2: (a) Schematic representation (b) ABAQUS models (FEM-Contour Integral and XFEM) Figure 6-6 Single Edge Notched Testing simulated with: (a) FEM (b) XFEM Figure 6-7 Scenario 1: K and J parameters as a function of the Load. Values are for a = 2mm Figure 6-8 Scenario 1: K and J parameters as a function of the crack length. Values are for P= 15 MPa Figure 6-9 Center-cracked Tensile Plate simulated with XFEM Figure 6-1 Scenario 2: K and J parameters as a function of the: (a) Load. (b) Crack Length. Values are for a = 2 mm and for P = 15MPa Figure 6-11 (a) Quadratic curve-fit to the J results in the elastic range. (b) Infer the elastic J trend using the curve fit Figure 6-12 Finding the intersection of the J total /J elastic ratio and the result curve Figure 6-13 J-Based Failure Assessment Diagram Figure 7-1 Failure Stress for cracked pipelines Figure 7-2 Schematically comparison between fracture condition differences in two geometrical configurations, representing the concept of transferability. [32] Figure 7-3 Fracture Toughness on Geometric Shape relationship. [33] Figure 7-4 FAD Diagram defining regions of safeness for the structure. [17] Figure 7-5 Possible flaws in pipe: Axial oriented surface flaws ((a) Internal (c) External); Circumferential oriented surface flaw ((b) Internal (d) External) and (e) Through-Wall flaw in a pipeline. [17] [35]... 5 Figure 7-6 Failure Assessment Diagram (BS791): (a) Level 1; (b) Level x

11 Figure 7-7 Failure Assessment Diagram (BS 791) - Level 1 Assessment (a) Internal flaws (b) External Flaws Figure Failure Assessment Diagram (BS 791) - Level 2 Assessment (a) Internal flaws (b) External Flaws Figure 7-9 Leak before Breakage analysis for points that are unsafe for Level 2 Assessment Figure 7-1 Failure Assessment Diagram (BS791) Fatigue Assessment (a) Level 1 (b) Level Figure Leak before Breakage analysis Figure 7-12 Remaining Life in-service in function with the crack depth Figure 7-13 API 579 Level 2 Assessment for growing crack Figure 7-14 Probability of Detection of a defect Figure 7-15 Probability of Failure over the years Figure 7-16 Different FAD curves using different procedures Figure A-1 Gas Flow during February 26 th to March 4 th, Figure A-2 Gas Flow during September 21 st to September 27 th, Figure A-3 Gas Flow during March 22 nd to March 28 th, Figure A-4 Pressure Cycle Profiles, during February 26 th to March 4 th, Figure A-5 Pressure Cycle Profiles, during September 21 st to September 27 th, Figure A-6 - Pressure Cycle Profiles, during March 22 nd to March 28 th, List of Tables Table 2-1 Available capacity for commercial purposes of relevant points. [5]... 6 Table 3-1 Mechanical Properties for some API 5L Steel Grades. [21] Table 4-1 Total LNG Terminal gas nominations for two scenario studies Table 4-2 Description of real-time profiles Table 5-1 Specimen Dimensions for Tensile Testing Table 5-2 Results obtained from the tensile testing Table 5-3 Specimen Dimensions for Fatigue Crack Growth Testing Table 5-4 Fatigue Crack Propagation Test results Table 7-1 Trunckline L12 Pipeline dimensions for different classes Table 7-2 Flaw characterization. [35] [17] Table 7-3 Remaining life in-service of the case 2 scenario Table 7-4 Input parameters for POF analysis xi

12 Abbreviations API American Petroleum Institute SMYS Specified Minimum Yield Strength ASME ASTM American Society of Mechanical Engineers American Society of Testing and Materials, now ASTM International SSY TMCP small scale yielding Thermo Mechanical Controlled Process BSI British Standards Institute TSO Transmission System Operator EPFM Elastic Plastic Fracture Mechanics UGS Underground Gas Storage ERSE Energy Services Regulatory Authority XFEM Extended Finite Element Method FAD Failure Assessment Diagram FEA Finite Element Analysis FEM Finite Element Method FFP Fitness-for-Purpose FORM First Order Reliability Method GRMS Gas Regulation and Metring Station HRR Hutchinson, Rice and Rosegreen IST Instituto Superior Técnico LEFM Linear Elastic Fracture Mechanics LNG Liquefied Natural Gas MCS Monte-Carlo Simulation NG Natural Gas NGTN Natural Gas Transmission Network OPEX Operating Expenditure PFM Probabilistic Fracture Mechanics PIMS Pipeline Integrity Management System POD Probability of Detection PSF Partial Safety Factor REN Redes Energéticas Nacionais SCADA Supervisory Control and Data Acquisition POF Probability of Failure SINTAP Structural Integrity Assessment Procedures for European Industry SMTS Specified Minimum Tensile Strength xii

13 List of Symbols B Specimen thickness a Crack depth C Paris s law constant a i Initial crack depth D Outer diameter of the pie a c Critical crack depth E Young s modulus a f Crack depth at failure F Reference stress geometric factor c Half of the crack length J J-Integral m Paris s Law material constant K Stress intensity factor n Outward normal to Γ K ef Effective stress intensity factor n RO Ramberg-Osgood strain hardening coefficient K I Stress intensity factor at mode I q Notch sensitivity factor K II Stress intensity factor at mode II r Crack tip radius K IC Fracture toughness t Thickness K r Toughness ratio Γ Arbitrary path Enclosing the Crack Tip K th Threshold value for the Stress intensity factor ΔK Stress intensity factor range L Length of the pipe Δσ Stress range L r Load ratio Φ Probability density function L r p Primary load ratio α RO Ramberg-Osgood constant L r max Maximum cutoff value β Minimum distance to the limit state funciton M Folia s factor ε True strain N Number of cycles ε H Hoop strain N f Fatigue life ε L Longitudinal strain P Internal pressure ε ref Reference strain P f Probability of failure σ True stress R Outer radius of the pipe σ f Failure stress S r Load ratio σ H Hoop stress W Compact specimen parameter σ L Longitudinal stress W s Strain energy σ ref Reference stress Y Geometrical shape factor σ u Ultimate tensile stress xiii

14 σ th σ y σ θθ σ σ ρ θ ν a N (r, θ) Fatigue limit stress Yield Stress Opening stress ahead of the crack Far-field applied axial stress Flow stress Paris law s integration constant Angle of propagation Poisson s ratio Fatigue crack growth rate Polar co-ordinate system, origin located at the crack tip xiv

15 Chapter 1 Introduction 1.1 Context Natural gas (NG) is poised to capture a larger share of the world s energy demand. Although NG has been a part of the energy landscape since the Industrial Revolution, what is new and changing is the new role of this unique resource in the global energy mix. NG is shifting from a regional and often marginal fuel to becoming a focal point of global energy supply and demand. NG will increasingly complement wind and other renewable energy sources, particularly in power generation acting as a solid back up for these sources intermittence. It is anticipated that gas will grow by more than a third over its current global consumption by 225 [1]. Gas growth is accelerating, in part, because the infrastructure networks that connect supply and demand are becoming more diverse and expanding around the world but mainly boosted by new supply options like shale gas. NG requires networks to link sources of production to the various locations where it will be used. Liquefied Natural Gas (LNG) plays an important role by linking overseas producers and consumers and also as security of supply by offering several choices of suppliers. One defining characteristic of pipeline networks is that they become more valuable with size as more entities join the network. These characteristics facilitate the development of adjacent networks, uncovering hidden opportunities to create value as new links are established. Thus, the NG pipeline industry is starting to implement comprehensive integrity management practices to meet the demands of new regulatory imperatives and public interests. These new demands require formal integrity management planning programs to be developed and applied where pipeline failures could affect High Consequence Areas. A formal integrity management plan, in particular, the so called Pipeline Integrity Management System (PIMS) incorporates some process for identifying threats to pipeline s integrity. Once such threats are identified, the pipeline operator shall characterize the degree of risk associated with the threat as a means of prioritizing responses, identify suitable methods to assess the presence of the threat, and develop appropriate mitigations. Interest has arisen regarding fatigue as one such possible integrity threat. Figure 1-1 shows other possible threats regarding pipeline failure around the world. Yet, just a small part is due to induced fatigue as the use of pressure cycling operation to improve energy efficiency is far from being applied. Moreover, as the need for energy increases and the natural gas market rises in flexibility, the need for optimizing and reduction of costs plays a big role in every decision. Any innovation regarding efficiency needs to be supported with a structural integrity assessment, especially if it involves changes in nominal flow conditions required, in order to ensure network life cycle, public safety and environmental protection. Catastrophic failure of any structure can be avoided if structural integrity is assessed and necessary safety protocols are developed accordingly. 1

16 3% 24% 15% 1% 6% 7% 23% 8% 3% 5% 5% 3% Damage by Others Welds Construction Joints Pipeline Others Valve Fitting Overpressure External Corrosion Internal Corrosion Third Party Activities Natural Hazards Figure 1-1 Causes of failure of Natural Gas pipelines around the world, from 2 to 212. [2] [3] Therefore, the structural integrity of pipelines commences with good design and construction practices, which will eliminate most of the potential failure modes. Additionally, as pipelines can operate in hostile environments they are constantly threatened by defects and damage that occur in-service. These in-service defects are the major cause of pipeline failures; therefore to understand and control structural integrity, in -service defects must be understood and controlled. 1.2 Objective and Scope Natural Gas is mostly transported in pipelines. The larger of these pipelines are called transmission pipelines. In the Portuguese Natural Gas System, there are two main entries, one in Campo Maior, through the Maghreb-Europe Gas Pipeline, with a fix capacity contract with the Algerian supplier and another via LNG Terminal in Sines. To provide a more energy efficient process, aiming for energy reduction in both cost and environmental, certain changes have to be made in the Terminal. One of them can be adjusting the consumption profile of NG injected in the network. This can be done by the rational use of the rotating equipment, not only for promoting a system operation at maximum efficiency but also for avoiding successive starts and stops from the equipment, is the focal point for the adequacy of periods of higher flow rate emission of NG for the Natural Gas National Transmission Network (NGTN). It also promotes a usage of high power consumption equipment in periods whose electricity tariff is lower. These adjustment of the injection profile in the network, could lead to mechanical problems, in particular fatigue, as the pressure cycle will be higher in the material. There are little to none information about pressure cycle induced fatigue in NG pipelines, especially because generally these failures happen where the pressure cycle is not significant or by other damages, as shown in Figure 1-1. The study is going to be focus on the trunckline 12 that goes from Sines to Setubal. This line is the chosen location because in Sines, is where it is located the LNG Terminal and major cycle impacts will occur over the line immediately downstream. Due to the fact that the NG that enters through the Maghreb-Europe Gas Pipeline is a fix capacity contract, it is in the LNG Terminal that a more efficient process can occur. Therefore this study 2

17 aims to evaluate the degree of exposure to failure from defects that could grow by pressure cycle induced fatigue. Moreover, the work has the following goals: Modelling the fatigue crack growth using finite element analysis (FEA); Assessing the integrity of the structure by the means of Failure Assessment Diagram (FAD) methods; Producing recommendations to implement the proposed changes. The expectation is that such assessments will identify growing defects due to fatigue so that they can be repaired or removed before they reach sizes that will cause failures at normal operating stress levels. 1.3 Thesis Outline In chapter 1, it is expressed the goals of this thesis and where it is inserted. In chapter 2, the Natural Gas National System is described from its assets and areas. Chapter 3 reviews fracture mechanics concepts, in particular concepts of Linear Elastic Fracture Mechanics (LEFM), Elastic Plastic Fracture Mechanics (EPFM) and Fatigue Failure. Pressure Cycle Profiles were simulated and they are described in chapter 4. Due to the fact that the change of nominal flow condition will induce fatigue in the structure, several methods were conducted in order to infer the behaviour of the structure. Chapter 5 is reserved for laboratory tests and analysis of its results. Specimens were subjected tensile and fatigue crack growth tests. Numerical Modelling using a Finite Element Analysis software ABAQUS is used to predict some parameters (K and J) and the failure of the pipeline in chapter 6, using both contour integral techniques and Extended Finite Element Method (XFEM). Integrity Assessment and Structural Reliability are evaluated in chapter 7. Procedures for assessing the Fitness-For- Purpose (FFP) have developed since the late 196's and two of the most commonly used are the recommended practice for assessing fitness-for-service published by the American Petroleum Institute (API) in API RP 579 and the guidance for the assessment of defects metallic structures published by British Standards Institute (BSI) in BS 791. Both methods imply the use of the Failure Assessment Diagram method to evaluate if a structure is in risk of collapse or if the structure is safe. On the other hand, in order to infer how long a pipe can remain inservice, probability of failure of a component with crack-like flaws was calculated, using analytical, First-Order Reliability Methods (FORM) and Monte-Carlo Simulation (MCS). This thesis ends with chapter 8 containing a summary that gives an overview of the main concepts covered in preceding chapters of the document, as well, discussing the results obtained by the different methods applied and future work to be done. 3

18 Chapter 2 Overview This chapter tries to make an overview of the Portuguese Natural Gas System, mostly the Natural Gas Transmission Network, the Underground Gas Storage (UGS) and the LNG Terminal, in order to put this work on the context of REN. 2.1 Portuguese Natural Gas System NG transmission pipeline are designed, built and operated to well established standards and laws, because NG can pose a significant hazard to surrounding population and environment. The combination of good design, materials and operating practices has ensured that transmission pipelines have a good safety record. Besides safety and compliance with codes and legislation, pipelines must ensure security of supply, delivering its products in a continuous manner, to satisfy the shippers and the end users and also ensure cost effectiveness. REN Gasodutos is one of the companies which are part of the REN Group [5] and it is the single Portuguese Transmission System Operator (TSO) [4], whereby it is responsible for the operation of the high pressure transmission system. REN Gasodutos is also responsible for performing the Global Technical Management of the National Natural Gas Transmission System, as Gas System Manager [5]. REN Gasodutos seeks to integrate the operation of the different infrastructures of the Portuguese Natural Gas System, while ensuring public service obligations related to security of supply, in terms of monitoring the establishment and maintenance of security gas reserves by commercialization companies, as well as providing open, transparent and non-discriminatory third party access to NG infrastructures. The preparation of an integrated proposal for the development planning of the Portuguese Natural Gas System and its corresponding submission to the National Energy Directorate, which occurs every three years, is also an important task of the Gas System Manager. As a TSO, REN Gasodutos is responsible for monitoring the balance between NG demand and supply, and checking it against available, in order to ensure an efficient and cost-effective use of NG infrastructures. A checking mechanism has been implemented, linking scheduling and assignment processes, with a view to ensure the overall feasibility of the system. From a technical perspective, REN Gasodutos offers the market all available capacity over a given period of time, by managing pressure levels as well as performing residual system balancing between intakes and offtakes, in order to maintain the transmission system's integrity, while providing a reliable service to shippers. The natural gas activities listed below are subject to economic regulation by the National Regulator Agency (NRA/ERSE) [4]: Natural gas high-pressure transmission network through REN Gasodutos; 4

19 Overall technical management of the Portuguese Natural Gas System through REN Gasodutos; Reception, storage and regasification of LNG through REN Atlântico; Underground gas storage through REN Armazenagem; Supplier switching management process through REN Gasodutos. These companies have been public service concession holders since 26 with a licence for a period of 4 years [4]. REN's natural gas infrastructures include the Natural Gas Transmission Network, the LNG Terminal in Sines and the Underground Gas Storage facilities (5 caverns and 1 gas station) in Carriço. Furthermore, there is currently in progress a project for the implementation of a compression station to be implemented in Carregado [6] Natural Gas Transmission Network REN Gasodutos operates the NGTN, feeding, at high pressure, a set of consumers with different consumption needs. Among the various consumers are included Combined Cycle Power Plants, Distribution Network Operators and Industrial clients. The NGTN is geographically developed around two main trunk axes: The main trunk line running from South to North from the Sines LNG Terminal to Valença do Minho, which provides the supply of natural gas to the country's most densely populated areas. There are three important branch lines connected with this main trunk line, namely the pipeline that supplies the region of Lisbon, the pipeline that interconnects the transmission system with the underground storage facilities of Carriço and the pipeline that supplies gas to the central region of the country up to Viseu and Mangualde. The transmission line between the central point of the main trunckline, located in the region of Leiria-Pombal and Campo Maior, at the eastern border between Portugal and Spain. It also branches off to the underground storage facilities of Carriço, as well as an important branch line connected with this transmission line, namely the pipeline that supplies gas to the interior region of the country up to Guarda. There are two Interconnection Points between the Portuguese and the Spanish Gas Systems, namely Campo Maior/Badajoz in eastern Portugal, and Valença do Minho/Tuy in the northern point of the main trunk line. The different NGTN lines are divided by lots, comprising a main pipeline with many ramifications associated, called branch lines. At the end of 213, the NGTN consisted of the following infrastructures [7]: km of high-pressure gas pipelines; 65 junction stations for pipeline branching; 46 block valve stations; 5 industrial consumer junction station; 5

20 84 gas pressure regulating and metering stations; 2 custody transfer stations. Supervised from a state-of-the-art National Dispatch Centre, using redundant fibre-optic technology telecommunication systems, the NGTN connects the gas pipeline stations with the LNG Terminal and the UGS facility at Carriço. All systems are equipped with digital communication, especially with regard to the monitoring and registering of network input and output flows. This allows for the best practices to be adopted both in relation to information quality and supervision response. Most of the lines of NGTN are piggable 1, however there are currently 8 branch lines non-piggable due to physical impossibility of the infrastructure. Those lines have been inspected by indirect assessment by analysing the data from cathodic protection and other inspection methods, particularly by guided wave technology. As far as capacities per day, the NGTN sends out over 7 GWh per day of natural gas to the system, as observed in Table 2-1. Table 2-1 Available capacity for commercial purposes of relevant points. [5] Available Capacity for Commercial Purposes of Relevant Points GWh per day Mm 3 (n) per day Input Sines (LNG Terminal) Carriço (UGS - withdrawal) Campo Maior Valença do Minho Output Sines (LNG Terminal) Carriço (UGS - injection) Campo Maior Valença do Minho Outputs by GRMS (total) Underground Gas Storage The UGS facilities include the gas station and the gas caverns. The gas station comprises several process sections that are used according to the operation mode of the facilities: In injection mode: reception of natural gas from the pipeline, metering and compression into the caverns; In withdrawal mode: pressure reduction of the gas coming from the caverns, dehydration, metering and delivery into the pipeline. 1 Pigging refers to the practice of using devices known as pigs to perform cleaning, inspecting and maintenance operations on a pipeline. This is done without stopping the flow of the product in the pipeline 6

21 Twh The gas caverns are built via a controlled leaching process of the existing salt dome formation at the average depth of 12 metres [5]. Currently there are five caverns in operation. The five operational gas caverns have a combined storage capacity of GWh (around 265 Mm 3 ) [4]. The gas station has a nominal injection capacity of 11 m 3 (n)/h and a nominal withdrawal capacity of 3 m 3 (n)/h [4]. Expansion of the infrastructure of NG underground storage is currently under way and additional caverns are scheduled to come on stream in the future Liquefied Natural Gas Terminal The LNG Terminal is operated by REN Atlântico and is located in the industrial area of Sines port. The Terminal receives methane carriers from different LNG liquefaction plants around the world and stores the unloaded LNG in cryogenic tanks, from where it is pumped through openrack vaporizers and sent out into the natural gas transmission system. Figure 2-1 LNG Terminal at Sines. [5] The facilities can receive and dock ships with capacities ranging from 35 to 21 m 3 of LNG, corresponding to 24 to 1 45 GWh, respectively [5]. There are two storage tanks that have a combined storage capacity of 24 m 3 of LNG and a third one that have 15 m 3 of storage capacity. These tanks make possible the NG injection capacity into the NGTN of 19 GWh/day to 38 GWh/day [5] NG LNG Figure 2-2 Comparison of the use of NG and LNG, through the years. [5] 7

22 Fundamental Concepts Chapter 3 Fracture mechanics denotes the applied mechanics framework needed for characterizing the behaviour of cracked components under applied loads. Its objective is to characterize the local deformation around a crack tip, in order to predict how crack will affect the components behaviour. [8] The fracture process is related with nonlinear deformation, as the zone where the fracture process takes place, is the region around the crack tip where dislocation motions occur. The zone size is characterized by the number of grain sizes for brittle fracture or by either inclusion or second phase particle spacing for ductile fracture. Different theories have been advanced to describe the fracture process in order to developed predictive capabilities, like Linear Elastic Fracture Mechanics, Elastic-Plastic Fracture Mechanics. [12] The main goal of this chapter it is to do a quick theoretical review of some concepts that are going to be used through the work, mainly, J-integral, stress intensity factor and fatigue failure. 3.1 Review on Fracture Mechanics For engineering materials, such as metals, there are two primary modes of fracture, brittle and ductile. In the first one, the cracks spread very rapidly with little or no plastic deformation. Ductile fracture on the other hand has three stages, void nucleation, growth and coalescence. In this mode, the crack moves slowly and is accompanied by a large amount of plastic deformation. The crack will not grow unless the applied load is increased. Figure 3-1 Effect of fracture toughness on the governing failure mechanism. [1] Consider a cracked plate that is loaded to failure. Figure 3-1 is a schematic plot of failure stress in function of the fracture toughness (K Ic ). For low toughness materials, brittle fracture is the governing failure mechanism, and critical stress varies linearly with K Ic. At high toughness values, LEFM is no longer valid, and failure is governed by the flow properties of the material. At intermediate toughness levels, there is a transition between brittle fracture under linear elastic conditions and ductile overload. Nonlinear fracture mechanics bridges the gap between LEFM and collapse [1]. 8

23 3.1.1 Linear Elastic Fracture Mechanics Modern fracture mechanics was originated by Griffith studies in the 192s when he successfully showed that fracture in glass occurs when the strain energy release resulting from crack growth is greater than the surface energy. [11] In 1948, Irwin extended Griffith s strain energy release rate criterion to include metals by accounting for the energy absorbed during plastic flow around the flaw. [12] By 196, the fundamental principles of linear elastic fracture mechanics were in place. LEFM is used to predict material failure when response to the load is elastic and the fracture response is brittle. LEFM uses the strain energy release rate, G, or the stress intensity factor, K, as a fracture criterion [1]. Considering a homogeneous linear-elastic material, Irwin derived expressions which describes the stress distribution in the region in front of the crack of a plate in tensile loading. These expressions are shown below. K I σ x = 2πr [cos θ 2 (1 sen θ 2 sen 3θ )] (3.1) 2 σ y = K I 2πr [cos θ 2 (1 + sen θ 2 sen 3θ 2 )] (3.2) τ xy = K I 2πr [sen θ 2 cos θ 2 cos 3θ 2 ] (3.3) These equations describe the stress concentration in the crack tip region in function of the toughness. However, they represent a singularity for r = where σ. As the r is getting smaller, the local stress increases, reaching the yield strength of the material. a) b) Figure 3-2 a) Real and ideal crack tension behavior. b) Stress field around the crack. [13] This situation leaves the crack tip inside a region of plastically deformed material, where stress relived and linear solutions are not the most acceptable. Several models were purpose to correct the effect of the plasticized zone. All of them considered a bigger effective length of the crack than the true crack length, as a form of minimized the effect of the plastic zone in the stress field and in the elastic unloading. Though, these models have limited application due to the fact that the plastic zone radius must be inside the region of the solid where the elastic 9

24 solutions are valid. Finally, LEFM is especially adequate to fragile failure, where the response of the material is mostly linear-elastic until the instability Elastic-Plastic Fracture Mechanics Elastic-Plastic Fracture Mechanics is an alternative developed for the study of the behaviour of non-linear materials and exhibit considerable plasticity in the crack tip of a flaw, i.e., materials under large-scale or general yielding conditions. EPFM had its beginnings in 1961, when Wells noticed that initially sharp cracks in high toughness materials were blunted by plastic deformation. Wells proposed the use of the distance between the crack faces at the deformed tip to measure fracture toughness [1]. The stretch between the crack faces at the blunted tip is known as the crack tip opening displacement. In 1968 Rice developed another EPFM parameter called the J-integral. It describes the elastic-plastic deformation around the crack tip to be nonlinear elastic. The J-integral was shown to be equivalent to G for linear elastic deformation and to the crack tip opening displacement for elastic-plastic deformation. During the same year, Hutchinson Rice, and Rosengreen showed that J was also a nonlinear stress intensity parameter, for materials whose mechanical behaviour is described by the Ramberg- Osgood equation [1]. ε = σ + α ε y σ RO ( σ n RO ) (3.4) y σ y The J-integral can be used as an elastic-plastic or fully plastic crack growth fracture parameter, much like K is used as an elastic fracture parameter. (a) (b) Figure 3-3 a) A 2D contour integral and b) a 2D closed contour integral. [14] J-Integral characterizes the stress field and its fracture conditions in the neighbourhood of the crack. For virtual crack advance in the plane of a three dimensions fracture, the energy release rate is given by: J = lim Γ n H q Γ Γ (3.52) where Γ is the contour around the crack tip, Γ is the arc increment on Γ, n is the outward normal to Γ, q is the unit vector in the virtual crack extension direction. H is defined according to: H = WI σ du dx (3.63) 1

25 The strain energy can be defined as: ε W s = σ ij ε ij (3.74) The two dimensions J-Integral can be extended to a three dimensional crack front where the J is defined point wise with respect to a parametric variable along the crack front. In three dimensions, the energy release for a unit segment of crack advance over a finite segment of the crack front,j, is defined as: J = V [H q x u + (f ) q ] V x (3.85) Figure 3-4 Contour integral for general three dimensions crack front. [14] 3.2 Reviews on Fatigue Failure Fracture mechanics often plays a role in life prediction of components that are subject to time dependent crack growth mechanisms such as fatigue. The rate of cracking can be correlated with fracture mechanics parameters such as the stress-intensity factor, and the critical crack size for failure can be computed if the fracture toughness is known. Damage tolerance, as its name suggests, entails allowing subcritical flaws to remain in a structure. Repairing flawed material or scrapping a flawed structure is expensive and is often unnecessary. Fracture mechanics provides a rational basis for establishing flaw tolerance limits. Consider a flaw in a structure that grows with time (e.g., a fatigue crack) as illustrated schematically in Figure 3-5. The initial crack size is inferred from nondestructive examination, and the critical crack size is computed from the applied stress and fracture toughness. 11

26 Figure The damage tolerance approach to design. [1] Normally, an allowable flaw size would be defined by dividing the critical size by a safety factor. The predicted service life of the structure can then be inferred by calculating the time required for the flaw to grow from its initial size to the maximum allowable size. Fatigue is a process of structural degradation caused by fluctuations of stress cycles. Stresses are typically amplified locally by structural discontinuities, geometric notches, surface irregularities, defects, or metallurgical non-homogeneities. Fatigue may occur in three sequential stages, the formation of a crack, called initiation, the stable incremental enlargement of the crack in service, called propagation and the rapid instable fracture. Initiation of fatigue occurs at microstructure-scale nucleation sites within the material such as inclusions, pores, or soft grained regions, or as they become generated through micro void coalescence by the straining process. The presence of macro-scale stress concentrators enhances crack nucleation as the process of progressive localized permanent structural change occurring in material subjected to conditions which produce fluctuating stresses and strains at some point or points. (a) (b) Figure 3-6 (a) S-N curve with fatigue limit. [15] (b) Clam Shell fatigue crack surface. [15] The fatigue behavior of a material is generally described by the Wöhler curve or S-N curve, which plots the stress amplitude against the number of cycles to failure. For materials with a fatigue limit, the S-N curve will advance towards a horizontal asymptote at the level σ = σ th. When a fatigue limit does not exist, the fatigue strength or endurance limit is defined as the value for failure after a specified high typically 1 6 number of cycles [1]. The initiation 12

27 process described above causes the formation of a crack in otherwise sound, un-cracked metal. As load cycles accumulate, initiation is followed by propagation or enlargement of the crack in service. Fatigue fracture surfaces frequently exhibit prominent concentric features, such as those shown in Figure 3-6 (b) [9]. The crack surface shows two distinct markings on two different scales. At a macroscopic scale, so-called clamshell markings also called beach marks can be seen. They are the result of irregularities in the growth of the fatigue crack, due to changes in loading conditions. Propagation necessarily concerns a crack that is already present, so it is most useful to consider propagation in terms of parameters related to fracture mechanics. The crack-tip stress intensity is an expression of the theoretical stress at the tip of a crack, derived from LEFM. K = Yσ πa (3.9) where Y is the geometry factor and a the crack length. The geometry factor accounts for the crack s configuration and its orientation in the plate. The geometry factor may change as the flaw enlarges. The service stresses fluctuate over a range, σ, so the fluctuation in stressintensity is: ΔK = YΔσ πa (3.1) A typical operating pressure spectrum for a natural gas pipeline may look something like what is shown in Figure 3-76 (b). Typically the largest cyclical component is seasonal, which means it occurs once per year. The pressure signal is stochastic, meaning it consists of an apparently random mix of signal amplitudes. [15] Figure 3-7 Random Load Spectrum. [9] Although the load spectrum is already much more realistic than the harmonic loading with constant frequency and amplitude, practical loading is mostly random. Prediction of fatigue life is only possible after this random load is transferred into a harmonic load spectrum, with known frequencies and amplitudes. Several experiments have shown that the crack length is an exponential function of the number of cycles [9]. This means that crack growth is very slow until the final stage of fatigue life, where a relative short number of cycles will result in fast crack growth leading to failure. The initial fatigue crack length seems to be a very important parameter for the fatigue life. 13

28 Figure 3-8 Crack length increase with number of cycles. [15] For an initially undamaged material, it takes N i cycles to initiate a crack by dislocation movement and void coalescence. The initial crack forms at this fatigue crack initiation life. Moreover, in most cases it is so small that it cannot be detected. In this stage I, crack growth is provoked by shear stresses and involves slip in a single crystallographic slip plane. After N i cycles, in stage II of crack growth, crack propagation is faster and it is provoked by tensile stresses and involves plastic slip on multiple slip planes at the crack tip, resulting in striations. The crack growth is now much faster and after N f, its length is a f and after a few cycles a c is reached and failure occurs. For higher stress amplitudes, the crack growth will be faster. N r N f = 1 N N f (3.11) To predict the fatigue life of structures, crack growth models have been proposed, which relate a N to stress amplitude or maximum stress, which can be expressed by the stress intensity factor, where stresses are low. Microstructural models relate the crack grow rate to microstructural parameters, such as the distance between striations. The Paris Law is the simplest fatigue crack growth law [13]. The equation has the form: a N = C( K)m (3.12) where C and m are material constants, K the stress intensity factor range and a the fatigue crack growth rate. In this model, the crack growth rate is independent of the stress ratio and, if K > K th,, crack growth occurs. For low and high values of K, Paris law does not describe accurately the crack growth rate. For K K th, the lower limit, a crack grows extremely slowly, hampered by the roughness of the crack faces. For still smaller values of K, the crack growth is extremely small but not completely zero. For high values of K, crack growth is much faster than predicted by the Paris law. Paris law can be integrated analytically, where it increases from a i to a f and N goes from N i to N f. The result N f N i can be represented as a function of a f with a i as parameter or vice versa. The fatigue life is reached, when the crack length becomes critical. N 14

29 σ m N f N i = Β m C( π) m (1 m 2 ) a (1 m 2 ) [1 ( a (1 m 2 ) i ) ] f (3.13) a f where β and m are material constant, σ is the stress range, a i is the crack initial length and a f is the crack final length (when the structure fails). Figure 3-9 Different regions of the a N vs K plot. [17] The final stage of fatigue crack growth occurs when the crack-growth rate accelerates under the influence of ductile tearing or cleavage and the crack grows to such size that failure can occur at the next applied load cycle. 3.3 Concepts of Pipeline Mechanics Pipelines must be able to withstand a variety of loads. However, buried pipelines are essentially restrained elements, as the displacement of the pipe is restricted by the soil around it. [18] Thus, for buried pipelines, the major stress is caused by the internal pressure and this hoop stress is usually the major design consideration. Figure 3-1 Pipeline Stresses under Internal Pressure. [18] Typically for calculation purposes pipelines are considered to be in a bi-axial state called plane stress. The active stresses considered are shown in Figure 3-1.The hoop stress, σ H, acts 15

30 around the circumference of the pipe and the longitudinal stress, σ L, is directed along the long axis of the pipe. In general, there is a third stress, a shear stress, which could be acting on the edges of the above unit section, but this is not normally significant and is usually neglected in calculations of transmission pipelines. Pipelines with diameter to wall thickness ratios greater than 2, typical of transmission pipelines, are considered thin-walled as the distribution of normal stress perpendicular to the surface is essentially uniform throughout the wall thickness. [15] For isotropic materials, the relationship between stress and strain under plane stress conditions is expressed as: ( ε H εl ) = 1 E [ 1 ν ν 1 ] (σ H σl ) (3.14) The hoop stress is the normal stress on a longitudinal plane through the pipe centreline resulting from internal forces resisting the gas pressure force, and it goes as: σ H = PD 2t (3.15) where P is the internal pressure, D the outer diameter of the pipe and t the wall thickness of the pipeline. 3.4 Developments of high strength steels for pipelines In order to improve transportation capacity, the demand for large diameter pipes lead to fabrication of steels with higher strength accompanied with sufficient toughness and ductility, even when operating in harsh environments. High Strength Steels used in pipelines follow API 5L Specifications for Line Pipe and they vary from API 5L Grade A25 to API 5L Grade X12. They possess highly refined grain and high cleanliness and are characterized by the low sulphur content and reduced amount of detrimental second phases such as oxides, inclusions and pearlite. Figure Evolution of line pipe steel grades. [2] 16

31 The determining factor responsible for mechanical property improvement for currently used high strength steels relies in the Thermo Mechanical Controlled Processing (TMCP) routes followed by accelerated cooling [2]. High strength steels are designed to provide better mechanical properties and/or greater strain capacity to sustain imposed plastic deformation. In fact, higher strength line pipe steels tend to have lower uniform elongation, resulting in a lower deformability. This is obviously an opposite trend regarding to what is desired for high strength pipelines. Also for strain-based design applications must have sufficient toughness and high deformability as well as higher strain hardening. This means a lower yield to tensile ratio and a higher uniform elongation [16]. The chemical composition of high strength steel may vary depending on what mechanical property requirements are needed. Generally, they have manganese content up to 2. wt% in combination with very low carbon content (<.1 wt% C) and minor additions of alloying elements such as niobium, vanadium, titanium, molybdenum and boron, allowing pressures till 2 MPa. [2] The main function of the alloying additions is strengthening of the ferrite through grain refinement, solid solution and precipitation hardening. Solid solution hardening is closely related to the alloy element content, whilst precipitation hardening and grain refinement depend on the interaction between chemical composition and TMCP. Thus, each individual element coupled with the cooling rate will determine the type and volume fraction of phases that will form in given steel processed under given conditions. Table 3-1 shows some properties of the different API 5L Steel Grades, normally used on pipelines. Table 3-1 Mechanical Properties for some API 5L Steel Grades. [21] Steel Grade SMYS (MPa) SMTS (MPa) Yield to Tensile Ratio Elongation min. (%) A B X X X X X From the table, it is possible to infer that the values of yield strength and tensile strength increase as the steel grade increases, the minimum uniform elongation of the material is reduced as the grade gets higher and the Yield to Tensile Ratio increases as the steel grade increases, as well. 17

32 Chapter 4 Pressure Cycle Simulation 4.1 Introduction In this chapter, different emission profiles to be injected to the network, according to a certain value of nomination 2, will be simulated. The aim is to have high amplitudes in order to evidence a more pronounced pressure cycle, so creating a more favourable fatigue failure. While companies do their best to estimate demand for NG, it is nearly impossible to predict the exact quantity a given facility will consume. Pipelines and utilities require industrial companies to utilize nomination and balancing programs to manage gas flow and minimize operational imbalances. The concept of physical quantity of gas starts to take place. The LNG Terminal operation is highly conditioned on the needs of the NG Portuguese system, especially those conducted by the electricity market and LNG global market. This constraint has not allowed a proper rationalization of distribution. Moreover, the low nominations, especially on weekends, make the daily NG optimization profile difficult for the Dispatching Centre. 4.2 SIMONE Simulation For the purpose of the study, two scenarios of nominations were chosen. The first one it is expected to induce pressure cycle profiles with large amplitudes and the second with low amplitudes. These two cases are trying to emulate the reality. The nomination values are divided by days (as notice in Table 4-1) and they are divided by hours, as shown in Figure 4-1. Table 4-1 Total LNG Terminal gas nominations for two scenario studies. Periods Scenario 1 Scenario 2 Saturday (m 3 (n)) Sunday m 3 (n)) Monday to Friday m 3 (n)) There are considered only two entries of NG in the network, namely, through Campo Maior (from Maghreb-Europe Gas Pipeline) and through the LNG Terminal. The other two entries presented in section 2, through Valença do Minho and UGS, are not considered due to the fact that Valença do Minho has a limited capacity and the flow rates are really low, and for simplification purposes, there is no injection or withdraw from UGS. 2 A request for a physical quantity of gas under a specific purchase, sales or transportation agreement or for all contracts at a specific point. 18

33 Saturday (::) Saturday (3::) Saturday (6::) Saturday (9::) Saturday (12::) Saturday (15::) Saturday (18::) Saturday (21::) Sunday (::) Sunday (3::) Sunday (6::) Sunday (9::) Sunday12::) Sunday (15::) Sunday (18::) Sunday (21::) Monday (::) Monday (3::) Monday (6::) Monday (9::) Monday (12::) Monday (15::) Monday (18::) Monday (21::) Tuesday (::) Tuesday (3::) Tuesday (6::) Tuesday (9::) Tuesday (12::) Tuesday (15::) Tuesday (18::) Tuesday (21::) Wednesday (::) Wednesday (3::) Wednesday (6::) Wednesday (9::) Wednesday (12::) Wednesday (15::) Wednesday (18::) Wednesday (21::) Thrusday (::) Thrusday (3::) Thrusday (6::) Thrusday (9::) Thrusday (12::) Thrusday (15::) Thrusday (18::) Thrusday (21::) Friday (::) Friday (3::) Friday (6::) Friday (9::) Friday (12::) Friday (15::) Friday (18::) Friday (21::) Presure (MPa) Saturday (::) Saturday (3::) Saturday (6::) Saturday (9::) Saturday (12::) Saturday (15::) Saturday (18::) Saturday (21::) Sunday (::) Sunday (3::) Sunday (6::) Sunday (9::) Sunday12::) Sunday (15::) Sunday (18::) Sunday (21::) Monday (::) Monday (3::) Monday (6::) Monday (9::) Monday (12::) Monday (15::) Monday (18::) Monday (21::) Tuesday (::) Tuesday (3::) Tuesday (6::) Tuesday (9::) Tuesday (12::) Tuesday (15::) Tuesday (18::) Tuesday (21::) Wednesday (::) Wednesday (3::) Wednesday (6::) Wednesday (9::) Wednesday (12::) Wednesday (15::) Wednesday (18::) Wednesday (21::) Thrusday (::) Thrusday (3::) Thrusday (6::) Thrusday (9::) Thrusday (12::) Thrusday (15::) Thrusday (18::) Thrusday (21::) Friday (::) Friday (3::) Friday (6::) Friday (9::) Friday (12::) Friday (15::) Friday (18::) Friday (21::) Gas Flow (m 3 (n)) 1,E+6 8,E+5 6,E+5 Scenario 1 - LNG Terminal Scenario 1 - Campo Maior Scneraio 2 - LNG Terminal Scneraio 2 - Campo Maior 4,E+5 2,E+5,E+ Figure 4-1 Gas Flow during a week for the Scenario 1 (highest nomination) and 2 (lowest nomination). It is observed above, that the biggest gas flow entry variations are through the LNG Terminal. This situation happens due to the fact that the work has the goal to study the influence of the gas flow variations in the trunckline closest to the Terminal (L12). However, due to fix contract capacities, other locations have to be taking in account, namely, Tapada (L4), Bidoeira (L25) and Frielas (L129). Also, these are considered the most mechanically requested locations after Sines (L12). The gas flow values are the inputs to the software SIMONE 3 for simulating the pressure cycle profiles within the pipelines. The maximum projected working pressure (84 bar) and the minimum pressure in every single distribution point in the network (5 bar) were used as boundaries conditions. Moreover, a static initial state was used in order to have the first iteration for the simulation to start. This is also beneficial because, it allows for a better comparison between results and different nominations, i.e., it was set an initial value for the send out pressure in the Terminal in order to create conditions where all cases could be compared. 9, 8, 7, 6, 5, SINES TAPADA BIDOEIRA FRIELAS Figure 4-2 Scenario 1: Pressure Cycle Profiles, during a week. 3 SIMONE (SIMulation and Optimization of Networks) is the Europe leading integrated standard software package in simulating and optimizing gas flows in pipeline systems. It is developed by the SIMONE Research Group with the collaboration and cooperation of German company LIWACOM Informationstechnik GmbH. This software allows real-time functions and SCADA integration interface. 19

34 Saturday (::) Saturday (3::) Saturday (6::) Saturday (9::) Saturday (12::) Saturday (15::) Saturday (18::) Saturday (21::) Sunday (::) Sunday (3::) Sunday (6::) Sunday (9::) Sunday12::) Sunday (15::) Sunday (18::) Sunday (21::) Monday (::) Monday (3::) Monday (6::) Monday (9::) Monday (12::) Monday (15::) Monday (18::) Monday (21::) Tuesday (::) Tuesday (3::) Tuesday (6::) Tuesday (9::) Tuesday (12::) Tuesday (15::) Tuesday (18::) Tuesday (21::) Wednesday (::) Wednesday (3::) Wednesday (6::) Wednesday (9::) Wednesday (12::) Wednesday (15::) Wednesday (18::) Wednesday (21::) Thrusday (::) Thrusday (3::) Thrusday (6::) Thrusday (9::) Thrusday (12::) Thrusday (15::) Thrusday (18::) Thrusday (21::) Friday (::) Friday (3::) Friday (6::) Friday (9::) Friday (12::) Friday (15::) Friday (18::) Friday (21::) Presure (MPa) 9, 8, 7, 6, 5, SINES TAPADA BIDOEIRA FRIELAS Figure 4-3 Scenario 2: Pressure Cycle Profiles, during a week. As expected, the highest variations are present in Sines for both scenarios. Also, these two scenarios were compared with typical real life profiles. These profiles were chosen to cover all behaviours that happen every day in the network. A small description of them is shown in Table 4-2 and the Gas Flow and Pressure Profile can be shown in Appendix II. Table 4-2 Description of real-time profiles. Week Dates Nomination (GWh) Description 1 February 26 th to March 4 th, 211 >1 This week reflects a time of high consumption of NG, where the off take of the two main entries was high, especially from the Terminal. This week is an example of a typical week September 21 st where the NG that is inputted in the network 2 to September 7-8 comes from Campo Maior as the main entry 27 th, 213 but the LNG market is also favourable for the LNG Terminal off take. This week reflects the actual situation of the NGTN system. The consumption of the 3 March 22 nd to March 28 th, network is low. Due to the fix contract capacity from the Maghreb-Europe Pipeline, the NG that comes through that entry almost can fulfil all needs of the Market. The LNG Terminal is running in low yield s and everything that it is send off from it, it is consumed in Chaparral 4. 4 Delivery points where several companies are located like Repsol YPF Petrochemicals, E.D.P.Thermal Power Plant, SELL Gasoline Blending, Petrogal Oil Refinery, and others.this delivery point is located 7 km from the LNG Terminal. 2

35 Number of Cycles Number of Cycles Number of Cycles Number of Cycles per week Number of Cycles per week Even the more aggressive scenario (Week 1 - February 26 th to March 4 th, 211) has lower pressure range amplitudes than the scenario 1. For this reason, and because the goal of the study is to try to make an assessment of the worst case possible that could happen to the pipeline, the scenario 1 is going to be chosen for doing the fatigue testing, integrity assessment and for modelling the crack propagation, as the worst case scenario that can happen. This can be observed in Figure 4-4 and Figure PI2 129.PI12 4.PI2 128.PI PI2 4.PI2 129.PI PI2 (a) Pressure Range (MPa) (b) Pressure Range (MPa) Figure 4-4 Pressure Range for: (a) Scenario 1 (b) Scenario 2. 2 (a) 15 1 BIDOEIRA 25.PI2 TAPADA 4.PI2 2 (b) BIDOEIRA 25.PI2 5 SINES 128.PI2 FRIELAS 129.PI12 15 TAPADA 4.PI2 SINES 128.PI2 <ΔP<5 5<ΔP<1 Pressure Range (bar) 1 5 FRIELAS 129.PI (c) BIDOEIRA 25.PI2 TAPADA 4.PI2 SINES 128.PI2 FRIELAS 129.PI12 <ΔP<5 5<ΔP<1 1<ΔP<15 Pressure Range (bar) 5 Legend: (a) March 22 nd to March 28 th, 214 (b) September 21 st to September 27 th, 213 Pressure Range (bar) (c) February 26 th to March 4 th, 211 Figure 4-5 Pressure Range for real-time profiles. 21

36 4.3 Conclusions Nowadays, the fix capacity contract with the Algerian supplier is almost enough to supply the NGTN. However, as the economy increases (as expected), the need for more NG to be injected to the network is going to happen. In this situation, a flexible LNT Terminal is the answer to fulfil all distribution points at a lower rate, than the one of the fix contract. For the organization, an optimized profile emission leading to a more energy efficient process, aiming for energy reduction in both cost and environmental is essential. These profiles would reflect high amplitudes each cycle, therefore, subjecting the pipeline to a higher exposure of fatigue, as these fluctuations would vary the hoop stress level in the pipeline. The LNG Terminal has several equipment that can rationally use, as they can follow a rotation program within the company. This leads not only for promoting a system operation at maximum efficiency but also for avoiding successive starts and stops from the equipment, is the focal point for the adequacy of periods of higher flow rate emission of NG for the NGTN. Two nomination scenarios were considered to create pressure cycle profiles within the pipe. Scenario 1 proposed the highest amplitudes of both. The results obtained were focused on Sines and the line L12 due to the fact that it is the closest to the Terminal, so it would be the most mechanically request point in the network. These scenarios allowed to understand that it would be possible to save power and cost by day using optimized emission profiles, by sending out the maximum gas flow during the times of the day that the electricity tariffs are lower and using minimum injection rates, during the times when the electricity tariffs are higher. For the LNG Terminal, it would correspond on a cost saving per year of 5-1% in operating expenditure (OPEX). 22

37 Chapter 5 Experimental Testing and Results 5.1 Introduction This chapter describes the laboratory activities carried out to mechanically characterize and to determine the fatigue resistance characteristics of the material. The experimental results will be used in modelling and in the applied integrity assessment methods, in order to determine the integrity of a pipeline in the presence of pressure cycle induced fatigue. Test specimens were cut from an 28 inch (711.1 millimetres) steel pipe, 12.9 millimetres thick. This component had already been in-service in trunkline L3 close to Monforte, Portugal and it is made of API 5L grade X7 steel from EUROPIPE (Certificate can be observed in Appendix III). In order to obtain specimens for all experimental activities, the component went through the following steps, as represented in Figure 5-1: 1. Removing the high density polyethylene (HDPE) coating from the outside; 2. Remove the sprayed epoxy resin from the inside; 3. Flattening the surface; 4. Extract specimens for the different experiments. Figure 5-1 Steps to obtain specimens. [22] [23] 5.2 Mechanical characterization Due to the dimensions and geometry of the piece, it was difficult to extract cylindrical specimens. So, flat specimens were obtained instead. These specimens were extracted from two different directions of the piece and their dimensions are shown in Table 5-1. Tensile testing was carried out in the laboratories of the Escola Superior de Tecnologia of the Instituto Politécnico de Setubal. An Instron 1432 machine, with a load cell of 1 kn and with a crosshead speed of.2 mm/min was used. The elongation was measured by the means of a 23

38 Stress (MPa) Stress (MPa) extensometer that was connected to the specimen. No standard was followed in order to do this test. Table 5-1 Specimen Dimensions for Tensile Testing. Thickness (mm) Width (mm) Height (mm) Longitudional Radial / Transverse Raw experimental data were extracted to an excel sheet in order to be analysed. Stress-strain curves, obtained from the recorded data, are shown in Figure ,1,2,3 Strain Engineering Curve True Curve Engineering Curve True Curve,1,2,3 Strain a) b) Figure 5-2 Stress-strain curve: a) Longitudinal Direction; b) Radial/Transverse direction. Table 5-2 resumes the important stress and strain experimental data points and ratios. The standard API 5L Specification for Line Pipe, define minimum values for mechanical resistance for different steel grades, in the rolling direction. For the API 5L Grade X7 steel, the standard define a specified minimum yield strength (SMYS) of 485 MPa and a tensile strength (SMTS) of 57 MPa, as seen in Table 3-1. Table 5-2 Results obtained from the tensile testing. Properties Direction Longitudinal Radial / Transverse Young s Modulus (GPa) Yield Strength (MPa) Ultimate Tensile Strength (MPa) Yield-to-Tensile Ratio Uniform Elongation (%)

39 The results obtained are in accordance with the standard API 5 L and with the certificate of the pipe. It can be also perceived that in the radial / transverse direction, the values are higher than the longitudinal direction. This difference occurs due to the fact that the radial direction is the rolling direction when the steel plates are being fabricated, and the process induces strength mechanisms in the steel, making the results in this direction higher than the longitudinal direction. 5.3 Fatigue characterization For fatigue characterization, compact specimen were used (Figure 5-3) and their dimensions are shown in Figure 5-3 Schematically representation of the compact specimen. Table 5-3. The standard ASTM E647 Measure of Fatigue Crack Growth Rates was followed for carrying out the tests. Figure 5-3 Schematically representation of the compact specimen. [24] Table 5-3 Specimen Dimensions for Fatigue Crack Growth Testing. Dimensions Specimen 1 Specimen 2 Specimen 3 W (mm) B (mm) A camera was attached to the Universal Testing Machine (Instom 1432) in order to record crack propagation and a frequency of 12 Hz. Pictures were treated after in order to infer the fatigue crack growth rate with the increase of the number of cycles. The results for specimen 3 are not presented due to the fact that they were not valid according to the Standard. The results are presented in Figure 5-5, Figure 5-6 and in Table

40 a/ N (m/cycle) a/ N (m/cycle) Crack length (m) a b c d Figure 5-4 Detail of the camera attached to the machine (Left). Crack propagation (Right).,18 Specimen 1 Specimen 2,15,12,9,E+ 1,5E+4 3,E+4 4,5E+4 6,E+4 Number of cycles Figure 5-5 Crack length vs. Number of cycles. a) 15 ΔK (MPa m 1/2 ) b) 1,E-5 1,E-5 ΔK (MPa m 1/2 ) ,E-6 1,E-6 1,E-7 1,E-7 1,E-8 1,E-8 Figure 5-6 Fatigue crack growth rate: a) Specimen 1; b) Specimen 2. Table 5-4 resumes the most important results of the tests. The surfaces of the cracked specimens were observed on a stereoscope. The specimens fail for over 55 cycles. The values of the threshold of the stress intensity factor, which determinates whether a crack is able to propagate, are a fairly high value. However, once the amplitude of the applied load is larger than the threshold value, the crack grows at an extremely fast rate, imposing a great threat to the pipeline integrity. Details of the resulting surface failure are shown on Figure

41 Table 5-4 Fatigue Crack Propagation Test results. Specimen Material parameter, C Material parameter, m Number of cycles to fail K th (MPa) Fast Fracture Fatigue Crack Propagation Crack Initiation Figure 5-7 Details from the specimen after the fatigue failure. It is noticeable three main regions, crack initiation (stage I), fatigue crack propagation (stage II) and then an area where the final fracture occurs (stage III). Figure 5-8 Stages I and II of fatigue crack propagation. [25] 27

42 In the first region, the fatigue crack propagates along high shear stress planes (45 degrees), as it can be seen schematically in Figure 5-8, as the crack propagates until it is decelerated by a microstructural barrier such as grain boundaries, which cannot accommodate the initial crack growth direction. This kind of steel has a lot of microstructural barriers due to grain refinement in the TMCP. The smooth region observed in Figure 5-7 is the region where stage II takes place (region where Paris Law is acceptable), as the crack propagation develops in a more linear way. This situation happens when K increases as a consequence of crack growth and slips starts to develop in different planes close to the crack tip. While it is noticeable that stage I is orientated 45 degrees in relation to the applied load, propagation in stage II is perpendicular to the load direction. Because it was not possible to use a scanning electron microscope, it was not possible to see the presence of surfaces ripples (striations). Their formation is due to successive blunting and re-sharpening of the crack tip. Finally, when observing Figure 5-7 it is possible to see a region of total unstable crack growth as K approaches K IC. The beach marks can be seen, as well, as a result of successive arrests or decrease in the rate of fatigue crack growth due to a temporary load drop, or due to an overload that introduces a compressive e residual stresses field ahead of the crack tip. The final fracture presents a fibrous and irregular aspect, as the fracture, in this case, is ductile. 5.4 Conclusions The results obtained in the tensile test shows that the pipe fulfils the minimum requirements of the API 5L Standard, as both yield and tensile strength are higher than the minimum specified values. As far as the fatigue tests are concerned, the specimens fail for over 55 cycles. The values of the threshold of the stress intensity factor, which determinates whether a crack is able to propagate, are a fairly high value. However, once the amplitude of the applied load is larger than the threshold value, the crack grows at an extremely fast rate, imposing a great threat to the pipeline integrity. The Paris s law parameters obtained compared with other works are slightly higher. [22] This behaviour might be explained by the high frequency used during the tests. 28

43 Numerical Modelling 6.1 Introduction Chapter 6 This chapter has the goal to represent models in finite element commercial software of a pipeline with a crack, in order to evaluate K and J parameters to be used on integrity assessment and to validate the experimental results, as well. The FEA is widely recognize as a good tool to solve fracture mechanics problems and the usage of Abaqus/CAE 5 as a finite element analysis software is due to the fact that it allows the implementation of XFEM for evaluating fracture mechanics parameters The Finite Element Method Consider the domain Ω in Figure 6-1. The domain is bounded by the boundary Λ that consists of four sets; Λ t with a prescribed traction t, Λ u with prescribed displacements and two traction-free crack surfaces A c + and A c [26]. Figure 6-1 A body with a crack with a fixed boundary subjected to a load. [1] The equilibrium equations and boundary conditions are (for contact-free crack surfaces) [27]: σ + b = in Ω (6.1) σ n = t on Λ t (6.2) + σ n = on A c (6.3) σ n = on A c (6.4) u = u press on Λ u (6.5) 5 SIMULIA Abaqus FEA (formely ABAQUS) is a software suite for finite element analysis and computeraided engineering, from Dassault Systemes. There are five core products on Abaqus product suite, Abaqus/CAE, Abaqus/Standard, Abaqus/Explicit, Abaqus/CFD and Abaqus/Electromagnetic. Abaqus/CAE or Complete Abaqus Envirnment, is used to model and analysis of mechanical components and preprocessing assemblies and visualizing the finite element analysis result. 29

44 And the corresponding weak form 6 is σ: ( δν) Ω = t δνdγ + b δνdω Λ t Λ (6.6) which holds for arbitrary test functions δν. Although the weak formulation has always the same form, the element quality 7 depends on the constitutive relations, as well of the selected shape forms. Respecting the elasticity theory, tension obeys: σ xx σ yy σ zz σ xy [ σ xz σ yz] = D ε xx ε yy ε zz 2ε xy 2ε xz 2ε yz] [ (6.7) Being D given by 1 1 E(1 ν) 1 D = (1 + ν)(1 ν) (1 ) 1 2 2(1 ) 1 2 2(1 ) (6.8) Where σ ij and ε ij are the tension and strain components. In the finite elemento method, the actual continuum or body of solid is represented by an assemblage of subdivisions called elements. These elements are regarded as interconnected at specified joints called nodes or nodal points. The nodes are usually placed on the boundaries where adjacent elements are considered to be connected. It is necessary to assume that the variation of field variable inside a finite element can be approximated by a simple function because the actual variation of the field variable, such as displacement, stress, pressure or velocity, inside a continuum is not known. These approximated functions, which are also called interpolation models, are characterized as the values of the field variables at the nodes. When field equations, such as 6 A week form states the condition that the solution must satisfy in an integral sense, wherea a strong form of the governing equations along with boundary conditions states the conditions at every point over a domain that a solution must satisfy. 7 Element quality is always relative, as the local parametric coordinate system is assumed for each element type and how well physical coordinate systems, both element and global, match the parametric dictates element quality. 3

45 equilibrium equations, for the whole continuum are created, the new unknowns become the nodal values of the field variables. However, the nodal values of the field variable can become known values by solving the field equations, which are generally composed of matrix equations. Once these are known, the field variable throughout the assemblage of elements is clarified by the approximated functions. This orderly step-by-step process is always followed for the solution of a general continuum problem in the same manner as in Abaqus/CAE [27]. Although FEM can be used to compute fracture mechanics parameters such as K and the J- integral, it is currently not possible to directly carry out automatic crack growth simulation in finite element software such as Abaqus/CAE [8]. The region around the crack front has to be continuously re-meshed and a ring of rosette-like elements has to be constructed around the crack tip in order to compute J-integral and to predict the crack propagation angle. Automatic crack propagation is only available under certain conditions for finite element software where crack propagation path is pre-defined. The extended finite element method surpasses disadvantages associated with the meshing of crack surfaces existing FEM XFEM framework The extended finite element method is an extension of the conventional finite element method based on the concept of partition of unity [26], i.e. the sum of the shape functions must be unity. It was developed by Ted Belytschko and collaborators in Using the partition of unity concept, XFEM adds a priori knowledge about the solution in the finite element space and makes it possible to model discontinuities and singularities independently of the mesh. This makes it a very attractive method to simulate crack propagation since it is not necessary to update the mesh to match the current geometry of the discontinuity and the crack can propagate in a solution-dependent path. In XFEM, enrichment functions connected to additional degrees of freedom are added to the finite element approximation in the region where the crack is located in the mesh to include the discontinuities and singularities. These enrichment functions consist of the asymptotic crack tip functions that capture the singularity at the crack tip and a discontinuous function that represent the gap between the crack surfaces [28]. To explain how the discontinuous functions are added to the FE approximation, a simple twodimensional crack is illustrated [2]. Consider the case of a crack in a mesh with four elements, where the crack is placed on the element boundary, seen in Figure 6-2. The finite element approximation for the mesh is 1 u h (x) = φ i (x)u i i=1 (6.9) where φ i is the shape function for node i, u i is the displacement vector at node i and x is the position vector. Define k and l as k = u 9 + u 1, l = u 9 u (6.1) 31

46 i.e. k lie in between u 9 and u 1 and l is half the distance between u 9 and u 1. Figure 6-2 (a) Mesh with a crack. (b) Mesh without a crack. The circle numbers are the element numbers. [29] Now, u 9 and u 1 can be expressed in terms of k and l as u 9 = k + l, u 1 = k l (6.11) Adding these expressions into equation (6.9) yields 8 u h (x) = φ i u i + k(φ 9 + φ 1 ) + l (φ 9 + φ 1 )H(x) i=1 (6.12) where the discontinuous sign/jump function H(x) is introduced as 1, x > H(x) = { 1, x < (6.13) Now, φ 9 + φ 1 can be replaced by φ 11 and k by u 11 and the finite element approximation can be expressed as 8 u h (x) = φ i (x)u i + φ 11 u 11 + lφ 11 H(x) i=1 (6.14) The first two parts on the right-hand side are the standard finite element approximation, and the third part is the additional discontinuous jump enrichment. Equation (6.14) shows that the finite element approximation of a crack in a mesh, as in Figure 6-2, may be interpreted as a mesh without a crack and an additional discontinuous enrichment. Discontinuous asymptotic crack tip functions are added to the nodes that surround the crack tip [26], as illustrated in Figure 6-3 to capture the singularity. If the tip does not end at an element boundary, the crack tip functions also describe the discontinuity over the crack surfaces in the element containing the crack tip. Thus, in total, there are two types of enrichments, the asymptotic crack tip functions to describe the crack tip and the jump function to describe the rest of the crack. The nodes are enriched with the jump function when their supports are fully intersected by a crack whereas the element nodes surrounding the crack tip are enriched with the crack tip functions. The circled nodes are enriched with the jump function and the squared ones are enriched with the crack tip functions. 32

47 Figure 6-3 (a) An arbitrary crack in a mesh. (b) Local coordinate axes for two crack tips. [27] The total formulation of XFEM can now be derived. Let all the nodes in the mesh be defined by the set S, the nodes surrounding the crack tip by the set S c and the nodes whose supports are cut by the crack (excluding the nodes in S c ) be defined by S h. The finite element approximation now reads u h (x) i = φ I (x) [u I + H(x)a I + ψ i (x)b I ] I S i=1 4 (6.15) where u I is the nodal displacement vector, the a I nodal enriched degree of freedom vector that with the jump function H(x) represent the gap between the crack surfaces and b I i the nodal enriched degree of freedom vector that with the crack tip functions ψ i (x) represent the crack tip singularity Crack growth propagation Various criteria have been proposed to predict the angle at which a crack will propagate, which include the maximum tangential stress criterion, the maximum principal stress criterion, the maximum energy release rate criterion, the minimum elastic energy density criterion and T- criterion [3]. The crack propagation angles predicted by these criteria are slightly different but all have the implication that K II = at the crack tip as the crack extends. The maximum tangential stress criterion is chosen for the current study due to be one of the most criterions used on XFEM studies [27]. The stress field around the crack tip of a homogeneous, isotropic linear elastic material can be expressed as: σ θθ = 1 2πr cos 1 2 θ (K Icos θ 3 2 K IIsinθ) (6.17) where θ and r are polar coordinates centered at the crack tip in the plane orthogonal to the crack front. The crack propagation direction can be obtained using the condition σ θθ θ = : θ = cos 1 ( 3K II 2 + K I 4 + 8K I 2 K II 2 K I 2 + 9K II 2 ) (6.17) 33

48 Where the crack propagation angle is measured with respect to the crack plane and θ = represents the crack propagation in the straight-ahead direction Crack growth magnitude Two common approaches have been used when modeling quasi-static crack growth within the XFEM framework. The first approach is to assume a constant crack growth increment [26] and simply update the crack geometry in a constant manner. The crack growth increment commonly used in literature is.1. The second option is to use an external criteria to predict the increment of crack growth. Paris Law [16] is used in our case where we can find the increment of crack growth to take the form given below where C is the Paris Law constant, m is the Paris Law exponent, N is the number of elapsed cycles. The mixed mode correction for Paris Law [31] takes the form: m 4 Δa = CN ( K 4 2 I + 8K II ) (6.17) 6.2 Models and Results K and J Estimation Values In order to obtain mechanical properties to ensure that the laboratory results and the integrity assessments procedures are similar, two scenarios were modelled with Abaqus/CAE. In first one the defect is placed prependicular to the direction of the pipe. So the longitudional stresses are the most critical stresses. In the second scenario, the defect is placed along the direction of the pipe, thus hoop stresses are the critical stresses. (a) (b) FEM Model r σ L σ L 2a σ L σ L 2πr W XFEM Model Figure 6-4 Scenario 1: (a) Schematic representation (b) ABAQUS models (FEM-Contour Integral and XFEM) 34

49 (a) (b) FEM Model σ H r σ H σ H 2a 2πr W σ H XFEM Model Figure 6-5 Scenario 2: (a) Schematic representation (b) ABAQUS models (FEM-Contour Integral and XFEM) In scenario 1 (Figure 6-4), the pipeline can be aproximated to a single edge notched tensile plate (SENT), in order to be exported to Abaqus/CAE models and in scenario 2 (Figure 6-5), to a center-cracked tensile plate (CCT) Scenario 2 (Figure 6-5). The numerical calculation of J and K (Mode I) was carried out. The results were obtained using XFEM and Contour Integral techniques. For both cases, the numbers of contours were 5. This parameter controls the number of element rings around the crack tip that construct the contour domains for the contour integral calculation. The contour integral calculation is the most important aspect in stationary crack analysis since it gives the measure to assess critical crack size. (a) Figure 6-6 Single Edge Notched Testing simulated with: (a) FEM (b) XFEM. (b The stress intensity factors in Abaqus/CAE are calculated along the crack front for a finite number of positions, so called contour integral evaluation points. These points are chosen 35

50 K I (MPa.m 1/2 ) J (kpa.m) K I (MPa.m 1/2 ) J (kpa.m) automatically by Abaqus/CAE where the crack front intersects the element boundaries. Several contour integral calculations are performed at each evaluation point for all specified element rings. The elements surrounding the crack tip element constitute the first partial contour domain. The next partial contour domain contains the first domain and the next element ring directly connected to the first contour domain. Each subsequent contour domain is built up by adding the next element ring to the previous contour domain. Theoretically, the contour integral calculation is independent of the size of the contour domain as long as the crack faces are parallel. But, because of the approximation with a finite element solution, K and J for the different element rings will vary and should converge as the domain is increased. Therefore the first element ring was discarded in the analyses because of their large deviation. The results can be observed below, for example, for a crack depth of a = 2mm FEM (KI) XFEM (KI) Literature (KI) FEM (J) XFEM (J) 3,E+3 2,5E+3 2,E+3 1,5E+3 1,E+3 5,E+2,E Load (MPa) Figure 6-7 Scenario 1: K and J parameters as a function of the Load. Values are for a = 2mm FEM (KI) XFEM (KI) Literature (KI) FEM (J) XFEM (J) Crack length (mm) 1,6E+5 1,4E+5 1,2E+5 1,E+5 8,E+4 6,E+4 4,E+4 2,E+4,E+ Figure 6-8 Scenario 1: K and J parameters as a function of the crack length. Values are for P= 15 MPa. Figure 6-9 shows the crack propagating through the model representing scenario 2 (CCT simulation). The results can be observed in Figure 6-1. It is notice that the values obtained by the second scenario are lower than those obtained for the first scenario (SENT simulation). 36

51 K I (MPa.m 1/2 ) J (kpa.m) K I (MPa.m 1/2 ) J (kpa.m) Figure 6-9 Center-cracked Tensile Plate simulated with XFEM FEM (KI) XFEM (KI) Literature (KI) FEM (J) XFEM (J) FEM (KI) XFEM (KI) Literature (KI) FEM (J) XFEM (J) Load (MPa) (a) Crack length (mm) (b) Figure 6-1 Scenario 2: K and J parameters as a function of the: (a) Load. (b) Crack Length. Values are for a = 2 mm and for P = 15MPa J-Based Failure Assessment Diagram From the values obtained, through Abaqus/CAE, an assessment based on J-integral will be carried out, in order to know which ratios a/w put the structure in danger of failure, this is, how long can a crack grow until the structure is in danger of failure/collapse. This assessment will be done using values obtained by the SENT simulation. This choice reflects how the applied load is risky for the structure and the values are higher when there is a crack placed on the edge, which means, for the model proposed, cracks longitudinal to the applied load are far more risky for a structure than those that the circumferential oriented. This observation is also confirmed when doing the integrity assessment by the means of standards/recommended practices. The J- 37

52 J (kpa.m) J (MPa.m) based Failure Assessment Diagram can be started adjusting a curve to the results from the Abaqus/CAE simulation. A quadratic curve fit is expected since J is proportional to K which is linear in the elastic range. This situation can be observed in Figure The elastic J trend is computed using the curve-fit and compared to the several next J curves to confirm that the results are in the elastic range and that the curve-fit is valid. In a typical elastic-plastic analysis without a crack, the initial load increments can be large since equilibrium convergence is expected. However, for an elastic-plastic fracture analysis with a crack several small load increments are needed at the beginning of the analysis to ensure that J results will be in the elastic range. The maximum load must be high enough to create yielding at the crack front, which is usually a much higher than the operating or design load. The curve fit is used to extrapolate and infer the elastic J trend for higher load increments (Figure 6-11). 3 2 Curve fit Computed J J total J elastic 4 1 y =,286x 2 R² = Load (MPa) Load (MPa) (a) (b) Figure 6-11 (a) Quadratic curve-fit to the J results in the elastic range. (b) Infer the elastic J trend using the curve fit. The nominal load value is obtained using the material specific FAD equation evaluated at L r = 1. When the material specific FAD curve equation is evaluated at L r = 1, it takes this form given by: J total J elastic L r =1 = 1 +.2E + σ y E σ y (7.26) 2,5 2 Material Specific Value = 2.4 J total /J elastic 1,5 1,5 σ nominal = 93.8 MPa Load (MPa) Figure 6-12 Finding the intersection of the J total/j elastic ratio and the result curve. 38

53 The reference stress geometric factor, F, is defined as the ratio of the yield strength to the nominal stress obtained at L r = 1. F = σ y σ nominal Lr =1 (7.27) The nominal load value is obtained from the intersection point in Figure 6-12 and it gives the reference stress that satisfies the material specific FAD equation at L r = 1. The reference stress and L r can be computed for analysis increment to obtain the analysis specific and material specific values. The reference stress, at each load increment is given by: The FAD curve is obtained by using: σ ref = Fσ i (7.28) L r = σ ref σ y = Fσ i σ y (7.29) K r = J elastic J total (7.3) Where J total are the elastic-plastic analysis J results, and the J elastic values were obtained from the curve-fit to the first few result increments in the elastic range. The maximum cutoff value is given by: L r max = σ y + σ T σ y (7.31) The evaluation points are computed using the stress intensity from the elastic analysis and the reference stress at the given load. L r and K r values are computed using the equations (7.2) and (7.3). The J-based FAD can be shown below. The points are representative of the ratio a/w, which represents how much a structure is cracked. 1,6 a/w=17% a/w=33% a/w=5% a/w=67% a/w=83% 1,2 K r,8,4,2,4,6,8 1 1,2 L r Figure 6-13 J-Based Failure Assessment Diagram. 39

54 6.4 Conclusions Fracture mechanics parameters, K and J values were obtained for two models, which tried to emulate cracks in a structure that are parallel or perpendicular to the applied load. Two techniques were used in order to obtain those values. Contour integral FEM is a technique well accepted for fracture mechanics problems. However, in order to improve computational time and to not be limited to the re-meshing of the model for each instance, XFEM was used as well. It was noticeable that XFEM gives values for K close to those obtained by contour integral FEM or by the literature, in both SENT and CCT plates. However, comparing these representations, the values are higher when there is a crack placed on the edge, which means, for the model proposed, cracks longitudinal to the applied load are far more risky for a structure than those that the circumferential oriented. This situation is also confirmed when integrity assessment is done by the use of standards/ recommended practices. In terms of J values, XFEM and contour integral FEM values are in the same order of magnitude, although the second one as always higher values than the first one. The same behaviour from the SENT and CCP plates is observed when estimating J as for K values. With those values, a J-based FAD was created to predict the failure of a structure using the crack depth to thickness of the component ratio. Like it was concluded and validated with the use of FFP practices, only ratio over 7% are suitable of being in a danger zone. Note that mixed modes of failure were presented on the J-based FAD. 4

55 Normalized Faillure Stress (σ f /σ) Chapter 7 Integrity Assessment and Structural Reliability 7.1 Introduction Pipelines have quality patterns that have to be ensured. However reception quality controls are not enough to ensure the quality of the pipeline itself. During installation, mounting and operation incidents can occur that originate defects. The goal of this chapter is to predict wheatear the component must be repaired, replaced or remediate and to predict the remaining life of the component, even with defects Empirical Methods In 196s, the Battelle Laboratories developed a failure criterion for crack like defects in thinwalled pipelines, known as the NG18 equations. The failure stress (due to internal pressure) takes the form of: 1 a σ f = σ t 1 a t ( 1 (7.1) M ) where σ is the flow stress and M is the Folias Factor. The flow stress is an empirical concept that tries to represent, trough a single parameter, the strain hardening behaviour of an elasticplastic material. It is defined by: σ = σ y + σ u 2 (7.2) The Folias Factor represents the stress concentration due to the formation of a perturberance in the pipe wall in the bulging region, due to internal pressure and tries to quantify the magnification of the stress at the crack tip. 1,2 1,8,6,4,2 a/t=.2 a/t=.4 a/t=.6 a/t= Crack size (2c/(R t) 1/2 ) Figure 7-1 Failure Stress for cracked pipelines. 41

56 Figure 7-1 shows the normalized failure stress as a function of the normalized crack size, for various ratio a/t. This representation permits to evaluate allowed defects in the material in a simply manner. Empirical methods are considered safes because they are based on conservative premises. However their application to thin walled pipelines made of steels with different yield to tensile ratios and in higher strength steels, like the X7, X85 or the X1, is limited because experimental data is limited. Thus, propagation of cracks can occur due a combination of plastic deformation and ductile failure and NG18 equations do not take that in account Fitness-for-Purpose Approach for Integrity Assessment Real scale fracture tests are extremely costly and difficult to carry out. Thus, small scaled specimens are used, in laboratory to test fracture mechanics behaviour. This similarity of the stress-strain field between the specimen and the real scale structure. This allows correlating laboratory test results to cracked structures real conditions. Figure 7-2 Schematically comparison between fracture condition differences in two geometrical configurations, representing the concept of transferability. [32] Every testing standard to evaluate the fracture toughness of the material is elaborated to provide a high degree of plastic constraint in the crack tip, in order to produce more conservative values of toughness. Usually, thin wall tubular structures present a low level of plastic constraint as the thin wall does not favour a plane strain state. Moreover, pressurized tubes like pipelines are mainly subjected to bending momentums, which hampers the formation of tri axel strain states. The struggle to transfer results from the laboratory to real scale configurations is illustrated in Figure 7-3. This graph presents qualitatively the effect of plastic constraint on the determined fracture toughness value for a specific geometrical configuration. Thus, it is easy to understand that the failure behaviour of cracked structures depends heavily on the shape and loading of the structure itself. To overcome these difficulties, the scientific community, the industry and the regulatory organizations have joined efforts to develop analytical methods and engineering procedures to assess the integrity of structures. 42

57 Figure 7-3 Fracture Toughness on Geometric Shape relationship. [33] Nowadays, it is consensus that every polycrystalline metallic structure contains defects, but does not mean that they put the structure in risk of integrity [34]. The fitness-for-purpose approach is based in fracture mechanics analysis and its objective is to evaluate the impact caused by a defect in the performance of a certain structure [34]. A FPP approach presents a tremendous economic potential. It is possible to define safe operation conditions and even extend the structure s life cycle. Natural gas, Petroleum and Nuclear industries motivated the establishment of procedures for these approach. The most used are the BS791 from British Standard Institute [35], the API RP 579 from the American Petroleum Institute [17] and the R6 Procedure from the Nuclear Fuels & Co. from United Kingdom (former Central Electricity Generating Board) [36]. None of these approaches embraces all evaluation techniques. In fact, there is divergence in the results obtained by the different methods, as they use different formulations. Even so, specific methods are used in specific areas. The R6 Procedure is used more often in the electrical generation sector. The recommended practice API RP 579 is mostly used in the chemical industry, and in the petroleum and gas industries the BS791 approach is the one most in focus Failure Assessment Diagram Method Regions of safe and unsafe operation of the structure are defined in a 2D space. The vertical axis is the toughness ratio, K r, which is the ratio between the stress intensity factor applied and the fracture toughness of the material (equation 7.3). The horizontal axis presents the stress ratio, as the ratio between the applied stress and a reference stress (equation 7.4). When the stress applied in equal to the reference stress, the structure starts to collapse plastically [36]. K r = K I K IC (7.3) L r = σ σ ref (7.4) Two modes of failure are represented in this diagram; the vertical axis coincides with the total fragile failure and the horizontal axis, with the likelihood of plastic collapse. In the transition region between failure modes, there is a mixed elastic-plastic failure mode. The FAD appears 43

58 for the first time in the original R6 Procedure, as the interpolation curve for both mechanisms is obtained by the strip yield model, purposed by Dugdale. This model proposes a solution for a plain strain problem of a crack in an infinite plate with an elastic-plastic material subjected to tensile stresses [36]. Considering the plasticity effect on the crack tip, an effective stress intensity factor is defined as: K ef = σ y πa [ 8 1 πσ 2 ln sec ( )] π2 2σ y (7.5) For the model to be able to describe the failure of a structure while the stress applied approaches its collapse stress, the yield strength must be replaced by the collapse stress in equation 7.5. To obtain the FAD curve it is necessary to normalize the effective K by the elastic K (equation 7.6) and re-write equation 7.5 making its crack size independent, as observed in equation 7.7. K I = σ πa (7.6) K ef K I = σ c σ [ 8 1 πσ 2 ln sec ( )] π2 2σ c (7.7) After simplifying the equation and resolve it for K r and L r, the equation of the curve for the diagram is: K r = L r [ π 2 ln sec (πl r 2 )] (7.8) Figure 7-4 FAD Diagram defining regions of safeness for the structure. [17] Figure 7-4 shows a FAD proposed by the R6 procedure, defining regions of safe operation for a structure. The evaluation procedure consists in determining the coordinates of a point (L r, K r ) for the structure in study. Another advantage for using the FAD approach is the possibility to evaluate the actual situation of the structure and to the locus of the failure, while the stress applied or the defect present in the structure is increasing. This characteristic allows predicting how far the failure has progressed and which is the dominant mode of failure or plastic instability [36]. The conceptual simplicity of the FAD makes it useful and easy to apply. However, the critical step is to obtain values for K r and L r.each procedure has its specific formulation and the determination of some parameters is not trivial. 44

59 7.1.3 Structural Reliability For structural reliability analysis assessment of a component failure, a deterministic description is necessary. Instead, for statistical analysis is requires computing the Probability of Failure (POF) from the scatter of the random input quantities. Probability Fracture Mechanics (PFM) deals with the assessment of the reliability of structures containing crack-like defects in terms of probabilities attributed to a certain failure event. It is well accepted that certain parameters involved in fracture mechanics analysis are probabilistically distributed variables. Material properties always exhibit scatter, crack sizes are statistical variables and loadings may also be random [8]. Given the input variables x = (x 1, x 2,, x N ) with defined Probability Density Function (PDF), f(x 1 ) f(x N ), the POF is defined as: P f = f X1 (x 1 ) f XN (x N )d(x 1 ) d(x N ) (7.9) g(x 1,,x N The failure function g(x 1,, x N ) divides the domain of the variables into two parts: { Failure Domain g(x 1,, x N ) Safe domain g(x 1,, x N ) > The integration has to be carried out over the failure domain g(x 1,, x N ). For simplicity, variables are assumed to be stochastically independent for the POF calculation [37]. The failure criterion is based on the Failure Assessment Diagram, whereas the limit state equation g(x 1,, x N ) can be broken down into two separate functions, according to: g FAD (X) = (K r ρ)k IC K I, &L r L r max (7.1) g Lr max(x)l r max L r, &L r > L r max (7.11) Most of the cases, the detection of defects in pipelines is carried out using intelligent pigs, as part of the normal operation and maintenance program. During inspections, not all defects can be identified due to the sensitivity of the equipment. The process of inspection and repair of a pipeline at a given time interval will change the anticipated distribution of crack depths and length because some of the detected cracks will be repaired. The exact distribution will depend upon the repair strategy adopted, the frequency of inspection and the sensitivity of the pig. The remaining cracks will not lead to failure but those missed by the inspection tool might cause gas leakage of the pipeline. Probability of Detection (POD) is defined as: P D/a = 1 e λa (7.12) Hence, if the detectable depth of the pig follows the exponential distribution function, both the average detectable size and the standard deviation equal to1/λ. Detected defects only represent part of the overall defect population. The PDF of the undetected cracks is: f UD (a) = P ND(a)f(a) P ND (a)da (7.13) 45

60 In the pipeline industry, it is customary to define the POF per kilometre length of pipeline [8]. The failure probability is valid for pipelines with exactly one crack of random size, as given in equation 7.9. If there is more than one crack in the system and they are assumed to be independent, the cumulative POF per km of pipe length can be obtained as: P f total = 1 (1 P f ) q (7.14) The actual number of cracks of flaws is normally unknown in advance. However, it can be shown that the number of flaws per component is a Poisson-distributed random variable [19]. Therefore, the probability of having exactly q cracks is given by: P q = kq q! ek (7.15) Thus, the cumulative POF per km of pipe length for multiple cracks takes the form: P f total = 1 kq q! ek (1 P f ) q q= = 1 e kp f kp f (7.16) The POF can be evaluated by numerical integration, the First Order/Second Order Reliability Method (FORM/SORM), and by Monte-Carlo Simulation (MCS) [8]. The analytical method is rarely used, as multi-dimensional integration becomes very difficult to solve if a system includes more than three variables. The FORM/SORM is often used to account the uncertainty in limit state models and it is widely used for evaluating P f in structure reliability analysis. Nevertheless, when inspection programme of non-normal variables is involved, the predicted value becomes unreliable and it is difficult to estimate the error. On the other hand, MCS is a simple and reliable method for simulation of a complex system but it suffers from expensive computational cost due to the large number of samples required when the POF is very low Analytical Method If there are fewer than three variables, the analytical method may be used to calculate the POF. By using numerical integration P f can be obtained. For example, if only crack length and crack depth are modelled as random variables, equation (7.9) becomes: P f = f(a)f(2c) d(a)d(2c) (7.17) g(a,2c) Where f(a), f(2c) denote the PDF of the crack depth and the crack length, which are assumed stochastically independent First/Second-Order Reliability Method The FORM/SORM is a combination of both analytical and approximate methods [39]. Based upon the reliability theory, a random event function can be approximated by a linearized form about the design point in the standard normal space. In the probabilistic analysis, all variables 46

61 are treat as stochastic with independent mean values and standard deviations. The failure probability P f can be obtained by: P f = Φ( β) = 1 Φ(β) (7.19) Where Φ(β) = β 1 exp (u2 2π ) du. Although FORM/SORM is easy to implement, in some cases, 2 the result converges very slowly or oscillates about one solution without convergence. Another limitation of using FORM/SORM is that the random parameters and limit state functions must be continuous [39] Monte-Carlo Simulation The MCS is a simple method based on the fact that the failure probability integral can be regarded as a mean value in a stochastic process [37]. By generating a large number G of independent repetitions, the POF can be therefore estimated as the quotient of the failure G f counts, to the number of simulations performed in conjunction with the limit state formulations, which is given as follows: P f = G G f (7.2) In contrast to FORM/SORM, MCS allows the details of the physical failure mechanics to be preserved without linearization of the failure surface. In addition, other non-normal variable distributions can be readily accommodated in the analysis. Another big advantage of MCS is that it always converges if the sample size is large enough. However, the main disadvantage for the use of MCS is that it is not very efficient compared with FORM/SORM. The major contribution to the POF are in a small part of the whole integration interval but the MCS samples in a much large region, as the accuracy of MCS heavily depends on the number of samples used in the simulation [37]. 7.2 Models and Results In order to evaluate the behaviour of the methods applied, several crack dimensions were tested to represent the geometrical shape and size of the flaw, form an elliptical shape to a circumferential shape, leading to three cases considered: Case 1 - Theoretical points, considering two ratios: t/r =.1, representing thin-walled pipelines; t/r =.25, representing thick-walled pipelines. Also, several crack depth to thickness ratios (a/t =.1, a/t =.5 and a/t =.8,) were considered, meaning that the crack is growing in the direction of the thickness. The ratio a/t =.8 is considered because several standards consider that the critical crack depth is 8% of the thickness of the material component. [33] [16] [35] [34] 47

62 Case 2 Larger acceptable defects resulting from hydraulic testing In this case, no geometrical ratios are considered. Instead, the dimensions from Table 7-1 were used. These values are representative of the truckline L12. This pipeline is the closest to the LNG Terminal, where the change of the gas send out will happen there. Table 7-1 Trunckline L12 Pipeline dimensions for different classes. External Diameter (in.) Material Class Wall Thickness (mm) Minimum testing Pressure on Plant (MPa) Crack Depth (mm) I API 5L Grade X7 II III I API 5L Grade X7 II III I API 5L Grade X7 II III Table 7-1 also shows the crack depth resulting from on plant hydraulic testing. Pressure testing has long been an industry-accepted method for validating the integrity of pipelines. This integrity assessment method can be both a strength test and a leak test. Selection of this method shall be appropriate for the threats being assessed. ASME B31.8 contains details on conducting pressure tests for both post-construction testing and for subsequent testing after a pipeline has been in service for a period of time. The Code specifies the test pressure to be attained and the test duration in order to address defined threats. Case 3 Known crack dimension with remaining life assessment. Whereas in Case 2, cracks were static, in this case, cracks will grow every time a fatigue load cycle is completed. This evaluation reports only to Level 2 Assessment. According to Paris Law (Equation 3.31): Δa = C K m (7.22) 48

63 a n+1 = a n + Δa (7.23) Equivalent equations apply for the second axis of the semi-ellipse. Also, if equation 7.22 and 7.23 are combined: Δa = C(Y σ πa i ) m (7.24) This equation is used to calculate the size increment of a specific defect when a certain stress range is applied. The remaining life is also computed. For the Paris s equation, the remaining life is the following: 2 m 2 m 2 (a c 2 a i 2 ) N f = (7.25) (2 m) C (Y σ πa i ) m Fitness-for-Purpose for Integrity Assessment As stated in section 7.1.2, the fitness-for-purpose approach is based in fracture mechanics and has an objective to evaluate the impact caused by a defect in the performance in service of a certain structure. Two procedures have been used, the API RP 579 and the BS 791. Although the first one in more used in chemical industries, some Fitness-in-Service approaches are used with other standards (like ASME B31.8) in REN. The use of both procedures allows a better understanding of the FFP approaches and to compare both results. Crack-like flaws are planar flaws, which are predominantly characterized by a length and depth [17]. They may either be embedded or surface breaking. Examples of real crack-like flaws include planar cracks, lack of fusion and lack of penetration in welds, sharp groove due to localized corrosion, and branch type cracks associated with environmental cracking [17]. Table 7-2 shows the approximations of an ideal and an actual flaw. Flaw characterization rules allow existing or postulated crack geometry to be modeled by a geometrically simpler one in order to make the actual crack geometry more amenable to fracture mechanics analysis. The rules used to characterize crack-like flaws are necessarily conservative and intended to lead to idealized crack geometries that are more severe than the actual crack geometry they represent. These characterization rules account for flaw shape, orientation and interaction [35]. Table 7-2 Flaw characterization. [35] [17] Actual Ideal Through-wall Flaw 49

64 Actual Ideal Surface Flaw Embedded Flaw In this study, surface cracks (internal and external) oriented axially and circumferentially to the pipe were considered. Through-wall cracks were also assessed for leakage-before-break analysis. The schematic representations of the pipe with the cracks can be found below, on Figure 7-5. (a (b (c (d (e Figure 7-5 Possible flaws in pipe: Axial oriented surface flaws ((a) Internal (c) External); Circumferential oriented surface flaw ((b) Internal (d) External) and (e) Through-Wall flaw in a pipeline. [17] [35] 5

65 The part through-wall depth of a flaw can be considerably more difficult to estimate than the length. Either a default value or a value based on detailed measurements may be used for the flaw depth in an assessment [35]. If no information is available about the depth of the flaw, a conservative assumption is to consider that the flaw penetrates the wall (e.g.,a = t). In pressurized components, an actual through-wall flaw would most likely lead to leakage, and thus would not be acceptable in the long term. However, if it can be shown that a through- wall flaw of a given length would not lead to brittle fracture or plastic collapse, then the component should be acceptable for continued service with a part-through-wall flaw of that length [17]. Additional special considerations may be necessary for pressurized components containing a fluid where a leak can result in auto refrigeration of the material near the crack tip, or other dynamic effects. Flaw depths smaller than the full wall may be assumed if justified by service experience with the type of cracking observed BS 791 Procedure The FFP assessment of this procedure was carried out concerning fracture mechanics by loading and fatigue. Two levels of safeness were considered. Case 1 The same points used in the empirical methods were used to validate the concept. The results can be seen in Figure 7-6, for the two levels of safeness. K r 1,2,8,4,2,4,6,8 1 S r (a) t/ri=.1 (int/axi) t/ri=.25 (int/axi) t/ri=.3 (int/axi) t/ri=.25 (int/circ) t/ri=.3 (int/circ) t/ri=.1 (ext/axi) t/ri=.25 (ext/axi) t/ri=.3 (ext/axi) t/ri=.1 (ext/circ) t/ri=.25 (ext/circ) t/ri=.3 (ext/circ) t/ri=.1 (t-wall) t/ri=.25 (t-wall) t/ri=.3 (t-wall) K r 1,2,8,4,2,4,6,8 1 1,2 L r (b) t/ri=.1 (int/axi) t/ri=.25 (int/axi) t/ri=.3 (int/axi) t/ri=.25 (int/circ) t/ri=.3 (int/circ) t/ri=.1 (ext/axi) t/ri=.25 (ext/axi) t/ri=.3 (ext/axi) t/ri=.1 (ext/circ) t/ri=.25 (ext/circ) t/ri=.3 (ext/circ) t/ri=.1 (t-wall) t/ri=.25 (t-wall) t/ri=.3 (t-wall) Figure 7-6 Failure Assessment Diagram (BS791): (a) Level 1; (b) Level 2. The following conclusions can be obtained analysing the FAD: Internal cracks are more dangerous for the structure than external cracks; Considering the same cracks for thin and thick-walled pipelines, it is notice that thickwalled have much more resistance to failure than the thin-walled pipes; Axial cracks are more prone to failure than circumferential cracks; 51

66 Comparing the two levels, it is noticeable that Level 1 assessment is more conservative than Level 2 as in the first level, more technical concepts are not applied, giving points in the FAD that are less safer than level 2 assessment. Case 2 This case uses values from Table 7-1, related with the larger acceptable defects for a pipeline after the hydraulic test. The pipe dimensions considered are the same as the pipes used in trunckline L12. The results can be seen in Figure 7-7. As referred, due to the conservatism of Level 1 Assessment, all points are observed in the unsafe region of the FAD and the following conclusions can be made: Circumferential cracks are more prone to brittle fracture than the cracks oriented axially; The lower the class of the pipeline, less suitable is to plastic collapse; The higher the diameter of the pipeline, more unsafe it is; Mostly all points represented are in a region that both brittle fracture and plastic collapse occurs. K r 2 1,5 1,5,2,4,6,8 1 S r (a) (int/axi) D2-CI (int/axi) D2-CII (int/axi) D2-CIII (int/axi) D28-CI (int/axi) D28-CII (int/axi) D28-CIII (int/axi) D32-CI (int/axi) D32-CII (int/axi) D32-CIII (int/circ) D2-CI (int/circ) D2-CII (int/circ) D2-CIII (int/circ) D28-CI (int/circ) D28-CII (int/circ) D28-CIII (int/circ) D32-CI (int/circ) D32-CII (int/circ) D32-CIII K r 2 1,5 1,5,2,4,6,8 1 S r (b) (ext/axi) D2-CI (ext/axi) D2-CII (ext/axi) D2-CIII (ext/axi) D28-CI (ext/axi) D28-CII (ext/axi) D28-CIII (ext/axi) D32-CI (ext/axi) D32-CII (ext/axi) D32-CIII (ext/circ) D2-CI (ext/circ) D2-CII (ext/circ) D2-CIII (ext/circ) D28-CI (ext/circ) D28-CII (ext/circ) D28-CIII (ext/circ) D32-CI (ext/circ) D32-CII (ext/circ) D32-CIII Figure 7-7 Failure Assessment Diagram (BS 791) - Level 1 Assessment (a) Internal flaws (b) External Flaws. Due to their unsafeness for Level 1, Level 2 Assessment was made, and it can be inferred that: All points represented for internal cracks are in the safe region; External cracks, oriented axially, are unsafe for higher diameters, meaning that is needed to repair, remove or remediate the component with these cracks. A part from these, it is possible to consider the crack as trough-walled ones and do a break before leak analysis with these points (Figure 7-9). It is possible to see that all points are in the safe zone. However, for the 32 inches pipes, representative points are really close to the limit curve, meaning that special attention is needed using pipes with these types of cracks. 52

67 K r 1,2,8,4,4,8 1,2 L r (a) (int/axi) D2-CI (int/axi) D2-CII (int/axi) D2-CIII (int/axi) D28-CI (int/axi) D28-CII (int/axi) D28-CIII (int/axi) D32-CI (int/axi) D32-CII (int/axi) D32-CIII (int/circ) D2-CI (int/circ) D2-CII (int/circ) D2-CIII (int/circ) D28-CI (int/circ) D28-CII (int/circ) D28-CIII (int/circ) D32-CI (int/circ) D32-CII (int/circ) D32-CIII 1,2,8 K r,4,4,8 1,2 L r (b) (ext/axi) D2-CI (ext/axi) D2-CII (ext/axi) D2-CIII (ext/axi) D28-CI (ext/axi) D28-CII (ext/axi) D28-CIII (ext/axi) D32-CI (ext/axi) D32-CII (ext/axi) D32-CIII (ext/circ) D2-CI (ext/circ) D2-CII (ext/circ) D2-CIII (ext/circ) D28-CI (ext/circ) D28-CII (ext/circ) D28-CIII (ext/circ) D32-CI (ext/circ) D32-CII (ext/circ) D32-CIII Figure Failure Assessment Diagram (BS 791) - Level 2 Assessment (a) Internal flaws (b) External Flaws 1,2 K r 1,8,6,4,2,2,4,6,8 1 1,2 L r (ext/axi) D2-CI (ext/axi) D28-CI (ext/axi) D28-CII (ext/axi) D28-CIII (ext/axi) D32-CI (ext/axi) D32-CII (ext/axi) D32-CIII Figure 7-9 Leak before Breakage analysis for points that are unsafe for Level 2 Assessment. Using Paris Law, it is possible to determine the remaining life of a structure with those type of cracks. That information is shown in Table 7-3. Table 7-3 Remaining life in-service of the case 2 scenario. External Diameter (in) Class Wall Thickness (mm) Crack Depth (mm) Remaining years in-service I II III I II III I II III

68 Case 3 This last case is concerned with the growth of a crack with known dimension over the load cycles. Starting with a crack depth of.1 mm, the assessment is carried out till the crack reaches 6 mm. Figure 7-1 shows the results obtained, for the two assessment levels considered. When the crack depth reaches certain value, the point is placed in the unsafe zone, meaning that the structure has to be repaired, remediated or replace. A LFB analysis was made for these points. The result was that crack depth above 4 mm have a big probability of leakage and/or, eventually, failure. An interesting observation is that internal cracks oriented axially fail easier than external ones. The evaluation for the remaining life of the component was made according to the previous results and, as it can be seen in Figure 7-12, the bigger the crack depth, the lower is the remaining years in-service of the component. 2 1,5 Int/axi Int/Circ Ext/Axi Ext/Circ 2 1,5 Int/Axi Int/Circ Ext/Axi Ext/Circ K r 1 K r 1,5,5,2,4,6,8 1 S r,4,8 1,2 L r (a) (b) Figure 7-1 Failure Assessment Diagram (BS791) Fatigue Assessment (a) Level 1 (b) Level 2. 1,2 1 Through-Wall K r,8,6,4,2,2,4,6,8 1 1,2 L r Figure Leak before Breakage analysis. 54

69 Remaining Years of Service ,1,2,3,4,5,6 Crack Depth (m) Figure 7-12 Remaining Life in-service in function with the crack depth API 579 Procedure Case 3 was re-calculated according with the API RP 579 procedure, in order to study the differences between both FFP predictions. The results obtained dispear a more conservative predition. Pipes are more prone to fail than in the BS 791 prediction. API RP 579 is a more conservative procedure because it does not require so many material properties. It is not needed to re-estimate the other cases due to the fact that all results would be higher than those obtained with the BS 791. Nevertheless, as before, axial oriented cracks are more unsafe than circumferential flaws, and internal defects are riskier than external ones. 2,5 K r 2 1,5 1 Int/Axi Ext/Axi Int/Circ,5,2,4,6,8 1 1,2 L r p Figure 7-13 API 579 Level 2 Assessment for growing crack Structural Reliability This study will also be carry out for the dimensions of trunckline L12 pipes, mostly for 28 inch pipelines due to the fact that they are the most used diameter in that line. The cracks to be analysed are assumed to be longitudinal and circumferentially oriented as the maximum hoop stress is normal to the orientation of the flaw, the cases where brittle fracture and fatigue failure are most likely to occur. 55

70 Table 7-4 Input parameters for POF analysis. Parameter Average Standard Deviation Distribution type Pipe Diameter (𝒎𝒎) 711 Fixed Thickness (𝒎𝒎) 11.1 Fixed Initial Crack Depth (𝒎𝒎) Log-normal Initial Crack Length (𝒎𝒎) Log-normal Pressure (𝑴𝑷𝒂) Normal Fracture Toughness (𝑴𝑷𝒂 𝒎) Normal Yield Strength (𝑴𝑷𝒂) Normal Tensile Strength (𝑴𝑷𝒂) Normal Analytically, the POF is equal to For calculating the POD, the parameter 𝜆 can be defined, assuming that; the minimum detectable depth for the pig is.2 𝑚𝑚 and the probability of detecting a defect depth of 3% of the thickness is 9%.. Thus, 𝜆 takes the following value, for each class: P𝐷 = 1 𝑒 𝜆(𝐷𝑒.2).9 = 1 𝑒 𝜆(𝑡.3.2) λ= ln(1.9) 𝑡.3.2 This also implies that the average detectable depth is 1/𝜆 +.2, in this case, 𝑚𝑚. Figure Probability of Detection 7-14 shows the detection probability function for the 28 inches diameter pipe. 1% 75% 5% D28CI D28CII D28CIII 25% %,5 1 1,5 Crack depth (mm) 2 2,5 3 Figure 7-14 Probability of Detection of a defect. As observed, a higher value of crack depth leads to a higher probability of detection. The behaviour is similar for 2 and 32 inch diameter pipes used in trunckline L12. 56

71 Probability of failure If the same analysis is made for multiple cracks, the resulting POF is , considering 1 cracks per kilometre. In terms of POF over the years, it is clear that, there is going to be bigger cracks with time so it is normal that the POF will increase, as seen in Figure % 75% 5% 25% % Number of Years Figure 7-15 Probability of Failure over the years. The POF with MCS is also computed. With this method, random numbers were generated to be inside the limit state function. The POF given is The result is in good agreement with the analytical solution as the difference is below 2%. Also, using FORM, the POF is with β = Conclusions Several FFP approaches were used in order to predict the behaviour of crack-like defect in pipelines. The cracks were considered to be internal and external to the surface of the pipe. Both BS 791 and API 579 can be used to access defects, and as observed, the results on both documents are different. Due to conservatism, Level 1 Assessment for BS 791 and API RP 579 is not a reliable technique to infer if the structure is in danger of fail or not. However if used in in-field inspection, it could be a great method to know, with few calculations, if the flaw is going to be dangerous or not. From observing the graphs, it can be assumed that both circumferential and axially oriented cracks have both fracture mechanisms but the first one is brittle fracture dominant and the seconds is plastic collapse dominant. The FFP approaches done confirm that the most critical flaws are the longitudinal interior cracks and they are the ones that the manufactures have to be more careful and they cannot be repaired in-service. In terms of fatigue, the remaining life for the pipes in trunckling L12 according with the maximum crack depth allowed are around 4 to 5 years until failure. However, it has to be stated that these values are for initial cracks with a great amount of penetration in the wall thickness and generally, the initial cracks are much smaller, leading to more than 2 years inservice life. The results obtained by assess the structure by the BS 791 and the API 579 procedures are similar, although in the second one presents points with higher safety factors, resulting in more conservative values, i.e., points more prone to fail in the FAD. The FAD curve itself change with the level of assessment that is made but especially with the procedure that it is followed. 57

72 1,5 BS 791 Level 1A BS 791 Level 2A BS 791 Level 2B API 579 Level 1 API 579 Level 2 API 579 Level 3 SINTAP FITNET R6 Procedure 1 K r,5,2,4,6,8 1 1,2 L r Figure 7-16 Different FAD curves using different procedures. Figure 7-16 shows different curves for different procedures and although all curves are similar, some are more conservative than others. Note that the maximum Load ratio also is changing. The structural reliability analysis was done, assuming a certain known crack distribution. POF is strongly dependent on the distribution of the defects in the pipeline, in particular the crack depth. Other properties like yield strength, tensile strength and fracture toughness affects the value of the POF. The value of POF is relatively low and there were a good agreement between the three methods applied (analytical, FORM and MCS). As supposed the bigger the crack, higher the probability of detection of the same crack. However, the sensitivity depends on which inspection tool is used, and this can be a focal point in order to prevent some cracks to propagate catastrophically. 58

73 Chapter 8 Final Remarks and Future Work 8.1 Final Remarks The service demand for products transported through pipelines are inherently non-stationary. As a result, operating pressure levels vary from time to time. Variations in operating pressure produce variations in the hoop stress level in the pipeline, and can thus cause metal fatigue that could eventually lead to failure in service of the structure. Generally, the fatigue life of a properly designed sound structure is quite long. Typically, millions of normal service-stress fluctuations are required for a failure to occur. In a pipeline the number of very large stress cycles (i.e., pressure cycles) is usually on the order of tens to hundreds of cycles per year, so one might expect that the potential for a pressure-cycle-induced fatigue failure in any pipeline would be insignificant. However, those variations on pressure cycle do not mean high amplitudes each cycle. The goal of this thesis is to infer the degree of exposure of a pipeline to fatigue induced by high amplitude pressure cycles (2-3 bar). Nowadays, the fix capacity contract with the Algerian gas supplier is almost enough to supply the NGTN. However, as the economy activity increases (as expected), the need to inject NG in the network is going to occur. In this situation, a flexible LNT Terminal is the answer to fulfil all distribution points at a lower rate, than the one of the fix contract. For REN, an optimized profile emission leading to a more energy efficient process, aiming for energy reduction in both cost and environmental impact is essential. The LNG Terminal has several facilities that can be used rationally, as they can follow a rotation program within the company. This leads not only to the promotion of operating at maximum efficiency but also to avoid successive starts and stops of the equipment. This the focal point for the adequacy management of periods of higher flow rate emission of NG to the NGTN. Scenarios that create different pressure cycle profiles within the pipe were simulated. These scenarios allow understanding that it would be possible to daily save power and cost using optimized emission profiles. Sending out the maximum gas flow during hours of lower electricity tariffs and using minimum injection rates, during day hours of higher electricity tariffs, induce a 5-1% cost saving per year in the LNG Terminal. The results obtained, through fatigue tests, numerical modelling and integrity assessment using fitness-for-purpose approaches concluded that, in normal operational conditions, the pipe would not fail due to pressure cycle induced fatigue. The carried out approaches confirmed that the most critical flaws are longitudinal interior cracks and those that manufactures must be more aware as they cannot be repaired inservice. In terms of fatigue, the remnant life for the pipes in truckling L12, according with the maximum crack depth allowed, is around 4 to 5 years. This is a convenient observation as the normal period of concession is 4 years. However, it must be stated that these values are consider initial cracks with a great amount of penetration in the wall thickness and generally, the initial cracks are much smaller, leading to more than 2 years in-service life. This matches 59

74 reality as pipelines with more than 1 years old are still operative, as stated before in England and in The Netherlands). Structural reliability analysis was carried out, assuming a certain known crack distribution. POF is strongly dependent on the distribution of the defects in the pipeline, in particular the crack depth. Other properties like yield strength, tensile strength and fracture toughness affects the value of the POF. The value of POF is relatively low and there was good agreement between the three methods applied (analytical, FORM and MCS). As predicted the bigger the crack, the higher the probability of detection of the same crack. However, sensitivity depends on the inspection tool used, and this can be a focal point in order to prevent some cracks to propagate catastrophically. Nevertheless, a structure like a pipeline can have long usage time, as NG is not very corrosive for because before being injected in the structure, certain corrosive elements, particularly Sulphur, are extracted from the fluid. In order to guaranty the integrity, security, operability and increasing life of the NG transportation system, a Pipeline Integrity Management System may be implemented as a part of a methodology of Management Assets. Almost 9% of the assets cost of the NGTN are buried pipelines, so it is necessary to obtain equilibrium between security, maintenance costs and reliability. Implementing PIMS would benefit greatly REN. The main benefits are intangible and are related with the decrease of the probability of failure and accidents in the infrastructure, thus, reducing NG supply interruption, human related damages (injuries and death), damage in third-party infrastructures, civilian responsibility, negative impact in the image of the company, environmental impacts, OPEX costs and costs associated with the repair of the structure and loss of NG. 8.2 Future Work For future work, more tests should be made in order to have a better sample of results, resulting in a more trustworthy study. Also, the study should be extended to off plane cracks (cracks that are not perpendicular or parallel to the applied load) in order to understand the relationship between crack propagation angle and the applied load. Modelling should be also carried out for curved structures in order to confirm the results obtained by the FFP approaches. As far as Structural Reliability is concerned, a more in-depth analysis of the POF should be carried out for cases where other distributions of cracks are used, as well to validate the concept with the data from intelligent pigs. Different inspection and repair criteria should be available in the simulation whereby an optimal maintenance strategy can be obtained by comparing different combinations of inspection and repair procedures. The simulation provides not only data on the probability of failure but also the predicted number of repairs required over the pipeline life thus providing data suitable for economic models of the pipeline management. 6

75 References [1] P. C. Evans and M. F. Farina, The Age of Gas & The Power of Networks, General Electric Company, USA, 213. [2] U. C. Nneke e O. E. Anisijj, Analysis of Pipeline Failures in the Oil and Gas Industries, IMENCS, 212. [3] EGIG, Gas Pipeline Incidents Eighth Report, EGIG, Holland, 211. [4] REN, [Online]. Available: [Accessed 2 February 214]. [5] REN, Anual Report, REN, Portugal, 213. [6] REN-Gasodutos, Manual de Construção: Gasodutos e Estações, REN, Portugal, 27. [7] REN-Gasodutos, Implementação do Sistema de Gestão de Integridade de Gasodutos (PIMS), REN, Portugal, 213. [8] L. Zhang, Failure Assessment of Thin-walled Structures with Particular Reference to Pipelines, USA: WIT Press, 21. [9] P. J. Schreurs, Fracture Mechanics, Eindhoven University of Technology, 212. [1] T. L. Anderson, Fracture Mechanics: Fundamentals and Applications, 3 ed., USA: Taylor & Francis, 25. [11] A. A. Griffith, The Phenomena of Rupture and Flow in Solids, Philosophical Transactions of the Royal Society of London, vol. 221, pp , [12] R. N. Quillen, J-Integral Finite Element Analysis of Semi-Elliptical Surface Cracks in Flat Plates with Tensile Loading, Master of Science Thesis, Tennessee Technological University, 25. [13] G. Walter, R. Reuter e S. Piascik, Fatigue and Fracture Mechanics: 33rd Volume, USA: ASTM STP 1417, 23. [14] F. Oliveira, Crack Modelling with the extended Finite Element Method, Master of Science Thesis, Instituto Superior Técnico, 213. [15] T. H. Courtney, Mechanical Behavior of Materials, Second ed., USA: McGrow-Hill, 199. [16] P. Paris, M. Gomes e W. Anderson, A rational analytic theory of fatigue, The Trend in Engineering, vol. 13, pp. 9-14, [17] Ameican Petroleum Institute, API 579 (Fitness-for-service), USA: Ameican Petroleum Institute, 27. [18] M. Barker Jr., Design Methodology to Address Frost Heave Potential, Alaska Gasline Development Corporation, 211. [19] P. Hopkins, The Structural Integrity of Oil and Gas Transmission Pipelines, Penspen Group, UK, 22. [2] D. Belato, W. De Waele, D. Vanderschueren and S. Hertelé, Latest Developments in Mechanical properties and Metallurgical Features of High Strength Line Pipe Steels, 61

76 Soete Laboratory, 213. [21] American Petroleum Institute, API 5L (Specification for line pipe), USA: Ameican Petroleum Institute, 28. [22] L. Barbosa, Efeito da Espessura na Tenacidade à Fratura e no Crescimento de Trinca por Fadiga em um Aço do Tipo API 5L-X7, Master of Science Thesis, Universidade Federal de Ouro Preto, 212. [23] E. Hippert Jr., Investigação Experimental do Comportamento Dúctil de Aços API-X7 e Aplicação de Curvas de Resistência para Previsão de Colapso em Dutos, Doctor of Engineering Thesis, Universidade de São Paulo, 24. [24] ASTM International, ASTM E647 (Measure of fatigue crack growth rates), USA: ASTM International, [25] G. Totten, "Failure Analysis of Heat Treated Steel Components," Advanced Materials & Processes, vol. 1, pp , May 28. [26] N. Moes, J. Dolbow e T. Belytschko, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, vol. 46, pp , [27] A. Yazid, N. Abdelkader e H. Abdelmadjid, A state-of-the-art review of the XFEM for computational fracture mechancs, Applied Mathematical Modelling, vol. 33, n.º 12, pp , December 29. [28] M. Léven, Stationary 3D crack analysis with Abaqus XFEM for integrity assessment of subsea equipment, Master of Science Thesis: Chalmers University of Technology, 212. [29] T. Belytschko, R. Gracie e G. Ventura, A Review of Extended/Generalized FInite Element Methods for Material Modelling, International Journal for Numerical Methods in Engineering, vol. 65, pp , 29. [3] C. Shih e R. Asaro, Elastic-plastic analysis of cracks on bimaterial interfaces: Part I - small scale yielding, Journal of Applied Mechanics, vol. 55, pp , [31] K. Tanaka, Fatigue crack propagation from a crack inclined to the cyclic tension axis, Engineering Fracture Mechanics, vol. 6, pp , [32] J. L. Janelle, An Overview and Validation of the Fitness-for-Service Assessment Procedures for Local Thin Areas, Master of Science Thesis, University of Akron, 25. [33] X. J., Z. L. Zhang, E. Ostby, B. Nyhus e D. B. Sun, Constraint effect on the ductile crack growth resistance of circumferenrially cracked pipes, Engineering Fracture Mechanics, vol. 77, pp , 21. [34] Brite Euram Programme, SINTAP: Structural Integrity Assessment Procedure. Final Revision Project BE , Brüssel, Belgium, [35] British Standard Institution, BS 791 (Guide on Methods for Assessing the Acceptability of Flaws in Metallic Structures), UK,

77 [36] British Energy Generation, R6, Revision 4: Assessment of the Integrity of Structures Containing Defects, UK: British Energy Generation, 2. [37] K. Zhang e R. A. Adey, Predicting the Probability of Failure of Gas Pipelines including Inspection and Repair Procedures, 21. [38] P. Dillström, ProSINTAP - A Probabilistic Program for Safety Evaluation, SINTAP, Sweden, 29. [39]. C. Annis, FORM/SORM and g-functions, 28. [4] A. M. Pereira, D. Gil, J. Pereira, R. Costa and T. Salvado, Manual do Despacho, REN- Gasodutos, 28. [41] GIIGNL, LNG Custody Transfer Handbook, Third ed., 21. [42] M. A. Santos, Estudo do comportamento dinâmico da rede nacional de transporte de gás natural, MsC thesis, Instituto Superior Técnico, 21. [43] J. E. Ramirez, Characterization of High Strength Steel Weld Metals: Chemical Composition, Microstructure and Nonmetallic Inclusions, Welding Journal, 28. [44] J. Gray, An independent view of linepipe and linepipe steel for high strength pipelines: How to get pipe that's right for the job at the right price, Microalloyed Steel Institute, 22. [45] C. M. Spinelli e L. Prandi, High Grade Steel Pipeline for Long Distance Projects at Intermiate Pressure, PTC, 212. [46] D. Langley, C. Killmore, F. Barbaro e J. Williams, Steel - meeting the needs of an evolving linepipe industry, BlueScope Steel, 21. [47] M. Madia, H. Riesch-Oppermann, U. Zerbst e S. Beretta, A new full probabilistic framework for the structural integrity assessment of structures containing cracks, 27. [48] S. Rahman, M. Gao e R. Krishnamurthy, API 579 G-factors for K Calculations and Improvements for Assessment of Crack-like Flaws in Pipelines, 13th International Conference on Fracture, Beijing, China, 213. [49] W. Gabauer, The Determination of Uncertainties of Ramberg-Osgood Parameter (from a Tensile Test), Austria: SM&T, 2. [5] C. F. Shih e J. W. Hutchinson, Fully Plastic Solutions and Large Scale Yielding Estimates dor Plane Stress Crack Problems, vol. 98, Jornal of Engineering Materials and Technology, 1976, pp [51] M. J. McNary, Implementation of the extended finite elemet method (XFEM) in the ABAQUS software package, Georgia Institute of Technology: MSc Thesis, 29. [52] S. Vethe, Numerical Simulation of Fatigue Crack Growth, Norwegian University of Science and Technology, June 212. [53] [Online]. Available: IE/toughness.html. [Accessed 8 November 214]. [54] Erichsen, [Online]. Available: 63

78 preparation. [Accessed 8 November 214]. [55] S. Courtin, C. Gardin, G. Bézine e H. Ben Hadj Hamouda, Advantages of the J-Integral approach for calculating Stress Intensity Factors when using the commerical Finite Element software ABAQUS, Engineering Fracture Mechanics, vol. 72, pp , 25. [56] Y. Bai, Pipeline and Risers, First ed., vol. 3, Elsevier Ocean Engineering Book Series, 21. [57] J. Xu, Z. L. Zhang, E. Ostby, B. Nyhus e D. B. Sun, Effects of ccrack depth and specimen size on ductile crack growth of SENT and SENB specimens for fracture mechanics evaluation of pipeline steels, International Journal of Pressure Vessels and Pipping, vol. 86, pp , 29. [58] E. S. Folias, An axial crack in a prssurized cylindrical shell, International Journal of Fracture Mechanics, vol. 1, pp , [59] J. R. Sims, B. F. Hantz e K. E. Kuehn, A bais for the fitness for service evaluation of thin areas in pressure vessels and storage tanks, ASME Pressure Vessels & Piping Conference, vol. 233, pp , [6] ABAQUS Inc., ABAQUS/Standard user's manual 6.13, USA, 213. [61] Y. J. Kim e D. J. Lim, Reference stress based approach to predict failure strength of pipes with local wall thining under single loading, Journal of Pressure Vessel Technology, vol. 126, pp , 24. [62] P. S. Lam e R. L. Sindelar, Comparison of Fracture Methodologies for Flaw Stability Analysis of Storage Tanks, USA: Westinghouse Savannah River Company, 24. [63] K. W. Hansen, Phase Transformation Study of X7 Steel by EBSD during In Situ Heating and Quenching, Master of Science Thesis, Norwegian University of Science and Technology, 212. [64] Enagas, Anual Report, Enagas, Spain, 213. [65] ASTM International, ASTM E8 (Tension Testing of Mettalic Materials), USA: ASTM International, 29. [66] Z. Z. Du, Extended Finite Element Method (XFEM) in ABAQUS, ABAQUS Inc., USA, 21. [67] C. Tripple e G. Thrwald, Using the failure assessment diagram method with fatigue crack growth to determine leak-before-rupture, em 212 SIMULIA Customer Conference, USA, 212. [68] American Society of Mechanical Engineers, ANSI/ASME B31G (Manual for determining the remaining strength of corroded pipelines), USA: American Society of Mechanical Engineers, [69] American Society of Mechanical Engineers, ANSI/ASME B31.8S (Managing system 64

79 integrity of gas pipelines), USA: American Society of Mechanical Engineers, 21. [7] American Society of Mechanical Engineers, ANSI/ASME B31.8 (Gas trasmission and distribution piping systems), USA: American Society of Mechanical Engineers, 212. [71] K. Escoe, Piping and Pipelines Assessment Guide, USA: Elsevier, 26. [72] G. Pluvinage, Pipe-defect assessment based on the limit analysis, failure assessment diagram and subcritical crack growth, Fizyko-Khimichna Mekhanika Materialiv, vol. 42, pp , 26. [73] B. L. Low, Roles of FORM, system-form, SORM and RSM in geotechnical reliability analysis, em 5th Asian-pacific Symposium of Structural Reliability And Its Applications, Japan, 28. [74] J. R. Rice, Mechanics of crack tip defeormation and extension by fatigue, fatigue crack propagation, USA: ASTM STP 415, [75] H. Takashima, T. Mimaki e Y. Hagiwara, Reliability analysis of spherical tank by Monte Carlo simulation, Journal of Fracture Mechanics, vol. 5, pp , [76] G. A. Antaki, Piping and Pipeline Engineering: Design, Construction, Mainetenance, Integrity and Repair, USA: Taylor&Francis, 25. [77] S. Eren, I. Hadley e K. Nikbin, Differences in the Assessment of Plastic Collapse in BS791:25 and R6/FITNET FFS Procedures, em Proceedings of the ASME 211 Pressure Vessels and Piping Division Conference, Baltimore, USA, 211. [78] A. Ahmed, extended Finite Element Method (XFEM) - Modeling arbitary discontinuities and Failure analysis, Master of Science Thesis, Università degli Studi di Pavia, 29. [79] S. Hosseini, Assessment of Crack in Corrosion Defects in Natural Gas Transmission Pipelines, Master of Science Thesis, University of Waterloo, 21. [8] M. Hovdelien, Impact Against Offshore Pipelines, Master of Science Thesis, Norwegian University of Science and Technology, 212. [81] C. Holtam, Structural Integrity Assessment of C-Mn Pipeline Steels Exposed to Sour Environments, Doctor of Engineering Thesis, Loughborough University, 21. [82] J. Rostum, Statistical Modelling of Pipe Failures in Water Networks, Doctor of Engineering Thesis, Norwegian Univeristy of Science and Technology, 2. [83] M. Houssain, Modelling of Fatigue crack Growth with Abaqus, Doctor of Engineering Thesis, University of South Carolina, 29. [84] B. Bedairi, Numerical Failure Pressure Prediction of Crack-in-Corrosion Defects in Natural Gas Transmission Pipelines, Master of Science Thesis, University of Waterloo, 21. [85] V. Verderaime, Illustrated Structural Application of Universal First-Order Reliability Method, NASA, Alabama, USA, [86] P. Dillström, M. Bergman, B. Brickstad, W. Zang, I. Sattari-Far, P. Andersson, G. Sund, L. Dahlberg e F. Nilsson, A combined deterministic and probabilistic procedure for safety 65

80 assessment of components with cracks - Handbook, Sweden: Swedish Radiation Safety Autority, 28. [87] Nuclear Science and Technology, J-Integral Measurements on Various Typer of Specimens in AISI 34 S.S., Luxembourg: Commision of The European Communities, [88] G. Pluvinage, M. Allouti, C. Schmitt e J. Capelle, Assessment of a gouge, a dent or a dent plus a gouge, in a pipe using limit analysis or notch fracture mechanics, Journal of Pipeline Engineering, vol. 1, pp ,

81 Appendix I Natural Gas Transmission Network 67

82 Gas Flow (m 3 (n)) Gas Flow (m 3 (n)) Gas Flow (m 3 (n)) II Pressure cycle profiles and gas flow for different scenarios Gas Flow 8 6 AS_S CTS_7_E TERMINAL_L2 4 2 Figure A-1 Gas Flow during February 26 th to March 4 th, AS_S CTS_7_E TERMINAL_L2 Figure A-2 Gas Flow during September 21 st to September 27 th, AS_S CTS_7_E TERMINAL_L Figure A-3 Gas Flow during March 22 nd to March 28 th,

83 Pressure (MPa) Pressure (MPa) Pressure (MPa) Pressure Cycles 8 7,5 7 6,5 6 5, PI2 4.PI2 128.PI2 129.PI12 Figure A-4 Pressure Cycle Profiles, during February 26 th to March 4 th, ,5 7 6,5 6 5, PI2 4.PI2 128.PI2 129.PI12 Figure A-5 Pressure Cycle Profiles, during September 21 st to September 27 th, ,5 7 6,5 6 5, PI2 4.PI2 128.PI2 129.PI12 Figure A-6 - Pressure Cycle Profiles, during March 22 nd to March 28 th,

84 III API 5L X7 Steel Euro Pipe Certificate 7

85 IV Assessment Procedure to Evaluate a Pipeline with Crack-Like Flaws 71

86 72