AN OVERVIEW AND VALIDATION OF THE FITNESS-FOR-SERVICE ASSESSMENT PROCEDURES FOR LOCAL THIN AREAS. A Thesis. Presented to

Transcription

1 AN OVERVIEW AND VALIDATION OF THE FITNESS-FOR-SERVICE ASSESSMENT PROCEDURES FOR LOCAL THIN AREAS A Thesis Presented to The Graduate Faculty of the University of Akron In Partial Fulfillment of the Requirements for the Degree Masters of Science Mechanical Engineering J.L. Janelle December, 2005

2 AN OVERVIEW AND VALIDATION OF THE FITNESS-FOR-SERVICE ASSESSMENT PROCEDURES FOR LOCAL THIN AREAS J.L. Janelle Thesis Approved: Accepted: Advisor Dr. Paul Lam Department Chair Dr. Celal Batur Committee Member Dr. Jiang Zhe Dean of College Dr. George K. Haritos Committee Member Dr. Xiaosheng Gao Dean of the Graduate School Dr. George R. Newkome Date ii

3 ABSTRACT In today s petroleum refining industry, aging infrastructure is a primary concern when considering replacement costs and safe operation. As vessels, piping, and tankage age in service, they are subjected to various forms of degradation or damage that may eventually comprise structural integrity. An engineering or Fitness-For-Service (FFS) assessment is required to evaluate structural integrity and safely extend the life of damaged equipment. Guidelines for performing a FFS assessment have been documented in API RP 579. The goal of API 579 is to ensure the safety of plant personnel and the public while aging equipment continues to operate, provide technically sound Fitness-For-Service assessment procedures for various forms of damage, and help optimize maintenance and operation of existing facilities while enhancing long-term economic viability. The procedures in API 579 (2000 release) provide computational methods to assess flaws that are found in in-service equipment caused by various damage mechanisms. The focus of this study is to review the technical basis for the Fitness-For-Service assessment procedures for general and local metal loss. Extensive validation of these procedures along with additional development is presented. The conclusions of the study are recommended as the best practices to be included in future versions of API 579. The specific objectives for the study are as follows: Objective 1: Validate the API 579 Section 5 LTA rules in addition to the validation in WRC 465. The validation includes comparison of the API 579 methodology to other industry method and to a database of full scale tests. Objective 2: Develop new or improve upon the existing methodology to increase the accuracy of the assessment procedures and eliminate some of the limitations. iii

4 Objective 3: Standardize the safety margin between MAWP and failure pressure for industry analysis methods and different Design Code margins on allowable stress. Objective 4: Improve the existing rules for LTAs subject to supplemental loading (circumferential extent of the LTA). This study is part of a series of WRC Bulletins that contain the technical background to the assessment procedures in API 579: WRC 430 Review of Existing Fitness-For-Service Criteria for Crack-Like Flaws WRC 465 Technologies for the Evaluation of Erosion/Corrosion, Pitting, Blisters, Shell Out-of-Roundness, Weld Misalignment, Bulges, and Dents in Pressurized Components WRC CCC An Overview and Validation of The Fitness-For-Service Assessment Procedures for Crack-Like Flaws in API 579 (not complete as of this printing) WRC 471 Development of Stress Intensity Factor Solutions for Surface and Embedded Cracks in API 579 WRC 478 Stress Intensity and Crack Growth Opening Area Solutions for Through-Wall Cracks in Cylinders and Spheres WRC MMM An Overview of the Fitness-For-Service Assessment Procedures for Weld Misalignment and Shell Distortions in API 579 (not complete as of this printing) WRC PPP An Overview of the Fitness-For-Service Assessment Procedures for Pitting Damage in API 579 (not complete as of this printing). This study represents a significant improvement to the current techniques available in the public domain for the analysis of Local Thin Areas. Information is also included that can be used to standardize the different LTA analysis techniques available in industry. However, further research, development and testing is required to further increase the accuracy of LTA analysis methods. The shortcomings of the assessment procedures are discussed as well as areas for future research. iv

5 TABLE OF CONTENTS Page LIST OF TABLES... LIST OF FIGURES... xii xiv CHAPTER I. INTRODUCTION Industry Needs Flaw Types and Damage Mechanisms in API General Corrosion and Local Thin Areas (LTAs) Need for Standardized Assessment... 3 II. LTA ASSESSMENT AND VALIDATION OVERVIEW Introduction Acceptance Criteria Overview Linear Elastic Allowable Stress Classification Non-linear Elastic-Plastic Stress Criteria Remaining Strength Factor Original LTA Assessment Methodology LTA Development and Validation Work Introduction Kiefner, et al Stephens, Bubenik, Leis, et al Coulson, Worthington v

6 2.4.5 Mok, Pick, Glover, Hoff Chell Hopkins, Jones, Turner, Ritchie, Last Kanninen, et al Chouchaoui, Pick Valenta, et al Zarrabi, et al Sims, et al Batte, Fu, Vu, Kirkwood Fu, Stephens, Ritchie, Jones ASME Section XI Class 2 and 3 Piping Current In-Service Inspection Codes III. API 579 METAL LOSS ASSESSMENT PROCEDURES Introduction Multi-Level Assessment Procedure Inspection Data Requirements Point Thickness Readings Critical Thickness Profiles Assessment of General Metal Loss Overview Applicability and Limitations Metal Loss Away from Structural Discontinuities Assessment with Point Thickness Readings Assessment with Critical Thickness Profiles Metal Loss at Major Structural Discontinuities Assessment of Local Metal Loss Overview Applicability and Limitations vi

7 3.5.3 Assessment Procedure Circumferential Stress Direction Overview API 579 Section 5, Level 1 Assessment API 579 Section 5, Level 2 Assessment Assessment Procedure Longitudinal Stress Direction Overview API 579 Section 5, Level 1 Assessment API 579 Section 5, Level 2 Assessment Non-Cylindrical Shells Overview Spherical Shells and Formed Heads Conical Shells Elbows API 579 Advanced Assessment of Metal Loss Overview Assessment with Numerical Analysis API 579, Level 3 Assessment (Lower Bound Limit Load) Plastic Collapse Load Comparison of General and Local Metal Loss Remaining Life Evaluation Overview Thickness Approach MAWP Approach IV. LTA ASSESSMENT PROCEDURES FOR CIRCUMFERENTIAL STRESS Introduction Calculation of Undamaged MAWP Calculation of Undamaged Failure Pressure vii

8 4.4 Calculation of Damaged MAWP and Damaged Failure Pressure Thickness Averaging Assessment Overview API 510 Assessment (Method 8) API 653 Assessment (Method 9) API 579 Section 4, Level 1 and Level 2 Assessment (Methods 25 and 26) ASME B31.G Assessment Overview Original ASME B31.G Assessment (Method 7) Modified B31.G Assessment, 0.85dl Area (Method 4) Modified B31.G Assessment, Exact Area (Method 6) RSTRENG Method (Method 5) PCORR Assessment (Method 20) API 579 Assessment Overview API 579, Level 1 Assessment (Method 1) API 579, Level 2 Assessment, Effective Area (Method 2) API 579, Level 2 Assessment, Exact Area (Method 3) API 579 Hybrid 1, Level 1 Assessment (Method 14) API 579 Hybrid 1, Level 2 Assessment (Method 15) API 579 Hybrid 2, Level 1 Assessment (Method 16) API 579 Hybrid 2, Level 2 Assessment (Method 17) API 579 Hybrid 3, Level 1 Assessment (Method 18) API 579 Hybrid 3, Level 2 Assessment (Method 19) API 579 Modified, Level 1 Assessment (Method 27) API 579 Modified, Level 2 Assessment (Method 28) Chell Assessment viii

9 Overview Chell Assessment (Method 12) Modified Chell Assessment (Method 13) British Gas Assessment Overview British Gas Single Defect Analysis (Method 10) British Gas Complex Defect Analysis (Method 11) BS 7910 Assessment BS 7910, Appendix G Assessment, Isolated Defect (Method 21) BS 7910, Appendix G Assessment, Interacting Flaws (Method 22) Kanninen Assessment (Method 23) Shell Theory Assessment (Method 24) Janelle Method Janelle Level 1 Assessment (Method 29) Janelle Level 2 Assessment (Method 30) V. VALIDATION OF LTA ASSESSMENT PROCEDURES FOR CIRCUMFERENTIAL STRESS Introduction Validation Databases New LTA Analysis Methods API 579 Hybrid Assessment Procedures New Folias Factor Development for Hybrid Methods Modified API 579, Level 2 Folias Factor for Long Flaws Janelle Method Statistical Validation of LTA Methodology Using a Failure Ratio Summary of Validation Results VI. ALLOWABLE RSF FOR DIFFERENT DESIGN CODES Introduction ix

10 6.2 Design Codes for Pressurized Equipment Margin of MAWP to Failure Pressure per Design Code Allowable RSF Results VII. LTA ASSESSMENT PROCEDURES FOR LONGITUDINAL STRESS Introduction Kanninen Assessment Method Thickness Averaging API API API 579 Assessment Methods API 579 Section 5, Level 1 Analysis API 579 Section 5, Level 2 Analysis Modified API 579 Section 5, Level 2 Analysis Janelle, Level 1 Analysis Janelle. Level 2 Analysis VIII. VALIDATION OF LTA ASSESSMENT PROCEDURES FOR LONGITUDINAL STRESS Introduction Validation Databases Summary of Validation Results IX. LTA PROCEDURES FOR HIC DAMAGE Introduction Subsurface HIC Damage Surface Breaking HIC Damage X. LTA PROCEDURES FOR EXTERNAL PRESSURE XI. CONCLUSIONS AND RECOMMENDATIONS Introduction LTA Assessment Procedures for Circumferential Stress x

11 Recommended Methods for Circumferential Stress Allowable Remaining Strength Factors Recommended Methods for Longitudinal Stress Further LTA Assessment Development Material Toughness Effects Stress Triaxiality from LTAs Rules for LTAs Near Structural Discontinuities XII. NOMENCLATURE XIII. TABLES XIV. FIGURES REFERENCES xi

12 LIST OF TABLES Table Page 1 Stress Classification Examples of Stress Classification Thickness Averaging for In-Service Inspection Codes Section Properties for Computation of Longitudinal Stress in a Cylinder with a LTA LTA Assessment Methods Validation Cases for the Undamaged Failure Pressure Calculation Method Parameters for a Through-Wall Longitudinal Crack in a Cylinder Subject to a Through-Wall Membrane and Bending Stress LTA Database 1 Case Descriptions LTA Database 2 Case Descriptions LTA Database 3 Case Descriptions LTA Database 4 Case Descriptions FEA Results for a Cylindrical Shell with a LTA FEA Results for a Spherical Shell with a LTA API 579 Folias Factor Values for a Cylinder and a Sphere Cases Omitted from Statistics Stress Limits Based on Design Codes Stress Limits Based on Design Codes MAWP Ratio vs. Allowable Stress for ASME Section VIII, Division 1 (Pre 1999) and ASME B31.1 (Pre 1999) MAWP Ratio vs. Allowable Stress for ASME Section VIII, Division 1 (Post 1999) and ASME B31.1 (Post 1999) xii

13 20 MAWP Ratio vs. Allowable Stress for ASME Section VIII, Division 2 and ASME B MAWP Ratio vs. Allowable Stress for the New Proposed ASME Section VIII, Division MAWP Ratio vs. Allowable Stress for CODAP MAWP Ratio vs. Allowable Stress for AS 1210 and BS MAWP Ratio vs. Allowable Stress for ASME B31.4 and ASME B31.8, Class 1, Division MAWP Ratio vs. Allowable Stress for ASME B31.8, Class 1, Division MAWP Ratio vs. Allowable Stress for ASME B31.8, Class MAWP Ratio vs. Allowable Stress for ASME B31.8, Class MAWP Ratio vs. Allowable Stress for ASME B31.8, Class MAWP Ratio vs. Allowable Stress for API MAWP Ratio vs. Allowable Stress for API Geometry Parameters for the Circumferential Extent Validation Cases Circumferential Extent Validation Results x iii

14 LIST OF FIGURES Figure Page 1 Logic Diagram for the Assessment of General or Local Metal Loss in API Logic Diagram for the Assessment of Local Thin Areas in API Coefficient of Variation for Thickness Reading Data (a) Small Variability in Thickness Profiles and the COV (b) Large Variability in Thickness Profiles and the COV Examples of an Inspection Grid to Define the Extent of Metal Loss Damage Establishing Longitudinal and Circumferential Critical Thickness Profiles from an Inspection Grid (a) Inspection Planes and Critical Thickness Profile (b) Critical Thickness Profile (CTP) Longitudinal Plane (Projection of Line M) (c) Critical Thickness Profile (CTP) Circumferential Plane (Projection of Line C) Critical Thickness Profiles for Isolated and Multiple Flaws (a) Isolated Flaw (b) Network of Flaws Zone for Thickness Averaging in a Nozzle LTA to Major Structural Discontinuity Spacing Requirements in API Example of a Zone for Thickness Averaging at a Major Structural Discontinuity Level 1 Assessment Procedure for Local Metal Loss I Cylindrical Shells (Circumferential Stress) Determination of the RSF for the Effective Area Procedure (a) Subsection for the Effective Area Procedure (b) Minimum RSF Determination Exact Area Integration Bounds Supplemental Loads for a Longitudinal Stress Assessment Assessment Locations and Parameters for a Longitudinal Stress Assessment (a) Region of Local Metal Loss Located on the Inside Surface (b) Region of Local Metal Loss Located on the Outside Surface Longitudinal Stress, Level 1 Screening Curve BG Depth Increment Approach x iv

15 17 Table Curve 3D Fit of the Shell Theory Folias Factor Comparison Between Analysis Methods and FEA Trends for a Cylinder with a LTA D Solid FEA Model Geometry of a Cylinder for λ = Axisymmetric FEA Model Geometry of a Cylinder for λ = Table Curve 2D Fit of the Modified API 579 Folias Factor Comparison of the Old API 579 Folias Factor to the Modified Folias Factor and the Original Folias Factor Screening Curve for the Circumferential Extent of an LTA Comparison of the Old API 579 Level 1 Screening Curve to the Modified API 579 Folias Factor Level 1 Screening Curve Axisymmetric FEA Model Geometry of a Sphere for λ = Comparison Between Analysis Methods and FEA Trends for a Sphere with a LTA Table Curve 3D Plot of the Janelle Method RSFA vs. MAWP Ratio for ASME Section VIII, Division 1 (Pre 1999) and ASME B31.1 (Pre 1999) for the Modified API 579 Assessment (Method 28) RSFA vs. MAWP Ratio for ASME Section VIII, Division 1 (Post 1999) and ASME B31.1 (Post 1999) for the Modified API 579 Assessment (Method 28) RSFA vs. MAWP Ratio for ASME Section VIII, Division 2 and ASME B31.3 for the Modified API 579 Assessment (Method 28) RSFA vs. MAWP Ratio for the New Proposed ASME Section VIII, Division 2 for the Modified API 579 Assessment (Method 28) RSFA vs. MAWP Ratio for CODAP for the Modified API 579 Assessment (Method 28) RSFA vs. MAWP Ratio for AS 1210 and BS 5500 for the Modified API 579 Assessment (Method 28) RSFA vs. MAWP Ratio for ASME B31.4 and ASME B31.8, Class 1, Division 2 for the Modified API 579 Assessment (Method 28) RSFA vs. MAWP Ratio for ASME B31.8, Class 1, Division 1 for the Modified API 579 Assessment (Method 28) RSFA vs. MAWP Ratio for ASME B31.8, Class 2 for the Modified API 579 Assessment (Method 28) RSFA vs. MAWP Ratio for ASME B31.8, Class 3 for the Modified API 579 Assessment (Method 28) x v

16 38 RSFA vs. MAWP Ratio for ASME B31.8, Class 4 for the Modified API 579 Assessment (Method 28) RSFA vs. MAWP Ratio for API 620 for the Modified API 579 Assessment (Method 28) RSFA vs. MAWP Ratio for API 650 for the Modified API 579 Assessment (Method 28) Maximum Bending Factor as a Function of the Radius to Thickness Ratio Screening Curve for the Circumferential Extent of a LTA Longitudinal Stress Folias Factor Subsurface HIC Damage (a) Subsurface HIC Damage Actual Area (b) Subsurface HIC Damage Area Modeled as an Equivalent Rectangle Surface Breaking HIC Damage (a) Surface Breaking HIC Damage Actual Area (b) Surface Breaking HIC Damage Area Modeled as an Equivalent Rectangle Idealized Geometry for a LTA Subject to External Pressure x vi

17 CHAPTER I INTRODUCTION 1.1 INDUSTRY NEEDS Most US design codes and standards for pressure containing equipment do not adequately address degradation and damage during operation. In the pressure vessel and pipeline industries, surface flaws are major limiting factors of vessel or pipe life, and this type of degradation due to age and aggressive environment eventually threatens the structural integrity of equipment. Replacing vessel and piping equipment is expensive, making it cost effective and desirable to operate slightly damaged equipment. For corrosion beyond a specified limit or other damage mechanism like cracking, a Fitness-For-Service (FFS) assessment is required. A FFS assessment is a quantitative engineering evaluation to determine the structural integrity of equipment containing a flaw or damage. The American Petroleum Institute (API) Recommended Practice (RP) 579 [1] is a comprehensive document for evaluating common flaws and damage in pressure vessels, piping, and tankage. The guidelines presented in API 579 may also be used in other industries as long as the applicability and limitations for an assessment are satisfied. API 579 is intended to supplement and expand upon the requirements in the inspection codes NBIC [2], API 510 [3], API 570 [4], and API 653 [5]. The goals are to ensure an acceptable margin of safety, provide accurate remaining life predictions, and help optimize maintenance and inspection for damaged equipment still in operation. The focus of this study is to further develop and validate the rules for assessing metal loss or corrosion damage in API

18 1.2 FLAW TYPES AND DAMAGE MECHANISMS IN API 579 Various types of flaws can occur in piping systems and pressure vessels due to environmental and in-service factors. API 579 addresses the following geometric flaws and damage mechanisms: Brittle Fracture: Brittle fracture is the susceptibility of a material to form crack-like flaws or experience a catastrophic failure typically at lower temperatures. General Metal Loss: General metal loss is a uniform reduction in wall thickness caused by corrosion and is one of the simplest defects to assess. Local Metal Loss: Local metal loss or Local Thin Areas (LTAs) are similar to general metal loss. The geometry of these defects is more complex than general metal loss and includes most types of isolated metal loss that can occur in pipe and vessel walls. Pitting: Pitting corrosion is closely related to local metal loss and is characterized by large numbers of small pits in a given area of pipe or vessel wall. The damage can be assessed with the same rules that are provided for LTAs with a few additional requirements. Blisters and Laminations: Blisters most often appear in equipment that is in some form of hydrogen service. Hydrogen molecules impregnate the steel, forming high-pressure bubbles of hydrogen gas or blisters in the vessel wall. Laminations occur during the steel plate manufacturing process and are a plane of non-fusion in the interior of the steel plate. Blisters may also be evaluated with the analysis methodology provided for LTAs with additional requirements. Weld Misalignment and Shell Distortion: Weld misalignment is an offset of plate centerlines that occurs in the longitudinal or circumferential weld joints of vessels during the vessel fabrication process. Shell distortion usually occurs during fabrication and is the result of improperly rolled shell plates. 2

19 Crack-Like Flaws: Crack-like flaws can have widely varying geometry and are caused by multiple mechanisms. Rules are provided for analyzing crack-like flaws as they are, or grinding them out and treating them like a LTA. Creep Damage: Creep damage occurs mostly in high temperature service and is a relation between time, temperature, stress, and excessive strain. This damage can also lead to cracks and crack growth. Dents and Gouges: Dents and gouges are forms of damage usually resulting from mechanically cold working a material. These defects are similar to shell distortions and LTAs respectively, but additional requirements must be met to prevent brittle fracture. 1.3 GENERAL CORROSION AND LOCAL THIN AREAS (LTAS) Local thin areas appear in several different geometries. The first is isolated areas of general corrosion. These "patches" of corrosion are areas of isolated uniform corrosion in a pipe or vessel wall and are characterized by a non-varying flaw thickness profile. Areas of local metal loss are similar to general metal loss but may have extreme variations in the flaw thickness profile. Isolated pits are another classification of local thin area that have a circular shape and are usually smaller than areas of general corrosion. Combinations of general metal loss, local metal loss, and pitting can give rise to an infinite number of local thin area geometries. General pitting, blisters, and gouges can also be thought of as local thin areas and assessed using similar analysis methods. Likewise, a crack-like flaw may be ground out and the resulting groove evaluated like a LTA. With many types of common defects being classified as local thin areas, the importance of finding a reliable analysis method is evident. 1.4 NEED FOR STANDARDIZED ASSESSMENT Currently there are twenty-five different methods compiled in this study for analyzing local thin areas in pipes and vessels. These analysis methods all have roots in various industries, codes, and standards. In industry, at least five of these methods are actively used in Fitness-For- 3

20 Service assessments today. This can make communication difficult between parties using different assessment procedures, and some parties may be using methods with low accuracy or reliability. Depending on the assessment code that is used, assessment results may vary drastically. One standardized set of analysis guidelines is needed to eliminate confusion regarding which method should be used. The focus of this study is to find the most statistically accurate and reliable method currently available and to validate the guidelines in API

21 CHAPTER II LTA ASSESSMENT AND VALIDATION OVERVIEW 2.1 INTRODUCTION Determining the Fitness-For-Service or safe operating pressure of corroded equipment is not yet an exact science. As such, assessment accuracy is extremely important. In an attempt to improve reliability, researchers have implemented test programs involving full-scale burst tests and finite element analysis of corroded pipes and vessels. With the data collected from test programs, many different methods and acceptance criteria for analyzing LTAs have evolved. The questions are: which of these methods are the most accurate and can the accuracy be further improved? In an attempt to answer these questions, large databases of burst tests and finite element analysis have been compiled in this study from various sources. The cases in each database are analyzed with each of analysis methods available in the public domain and some newly developed methods. Statistical analysis of the various Fitness-For-Service assessment methods will provide the best gage for measuring the accuracy of each method. Alterations to the current API 579 Fitness-For-Service guidelines will be recommended based on the findings of this study. The current procedures for inspection and analysis of an LTA from the document are presented in later sections. The assessment methods in API 579 will be validated and compared to all other closed formed methods presented in this study. The validated assessment methods will be used with various construction codes, and code based assessment guidelines will be developed and included in API 579. This will allow standardized assessment of components designed to different construction codes. 5

22 2.2 ACCEPTANCE CRITERIA Overview Depending of the type of mechanical analysis being performed, different acceptance criteria have been developed for various failure modes to insure safety in a given design. For example, a primary concern in the design of a vacuum tower is buckling of the shell wall due to external pressure. To prevent this type of failure, structural stability criteria have been developed for use with buckling analysis for equipment with large compressive stresses. There are other types of acceptance criteria such as fatigue initiation used to evaluate components subject to cyclical loading, and similarly, creep-fatigue initiation criteria used for components exposed to cyclical loading in the creep regime. One of the most widely used acceptance criterion is stress criteria. Stress criteria are limits placed on stresses generated in a given component due to geometry, loading, damage (such as an LTA), or other conditions and is based on material properties of the component at a given temperature. The two types of stress criteria that are relevant to a LTA assessment are linear elastic stress classification and non-linear elastic-plastic stress evaluation. A separate approach for evaluating a LTA is the Remaining Strength Factor (RSF) criteria. With the RSF approach, the load carrying capacity of a damaged component is compared to the load carrying capacity of the undamaged component to calculate a reduction in strength. Either linear elastic stress or RSF criteria are used for the closed form assessment procedures presented in this report. Non-linear elastic-plastic stress criteria is most commonly used for advanced (numeric) analysis of a LTA, but other criteria for fatigue, buckling, creep, or any other failure mode may also be used Linear Elastic Allowable Stress Classification For LTAs a quantity known as stress intensity can be computed and compared to an allowable value of stress intensity. Stress intensity is a measure of stress derived from a yield criterion. Two yield criteria to establish stress intensity are recommended by API 579. Maximum 6

23 yield stress intensity is equal to twice the maximum shear stress which is equal to the difference between the largest and smallest principle stress as follows: S = 2τ max = max σ1 σ2, σ2 σ3, σ3 σ1 (1) The other yield criterion is maximum distortion energy. This is the preferred criteria and is also known as the Von Mises equivalent stress. 1 S = σvon Mises = σ1 σ2 + σ2 σ3 + σ3 σ1 2 ( ) ( ) ( ) (2) Determination of structural integrity is based on a comparison between calculated stress intensity and the allowable stress intensity of the material. There are five stress intensity categories based on location and origin of the stress field. The five categories and their associated limits along with the tri-axial stress limits are shown in Table 1. Examples of stress classification based on component, location, and loading is provided in Table 2. Establishment of the allowable stress intensity for structural integrity comparison is based on the design code used to construct the component. A detailed description of the design codes and associated allowable stress intensities can be found in Paragraph Non-linear Elastic-Plastic Stress Criteria Non-linear elastic-plastic stress criteria typically provide a better prediction of safe load carrying capacity for a component. Traditional linear elastic stress classification and allowable stress criteria make only a rough estimate of failure loads because they ignore non-linear phenomenon that may occur in component failure. Non-linear elastic plastic analysis takes into account geometric, material, and combined non-linearity directly, to develop plastic collapse loads. Plastic collapse loads are defined as the maximum load where material response is elastic-plastic including strain hardening and large displacement effects. Closed form solutions for plastic collapse loads are not readily available, so numerical techniques such as Finite Element Analysis (FEA) may be used to obtain a solution. The calculated stress intensity for limit 7

24 or plastic collapse loads can be compared to allowable stress intensities to determine a component s structural integrity. The concept of plastic collapse load can be used to develop a simplified strength factor for LTAs called the Remaining Strength Factor Remaining Strength Factor The Remaining Strength Factor (RSF) has been introduced to define the acceptability for continued service of components containing a flaw in terms non-linear elastic plastic stress criteria. For a LTA analysis, plastic collapse loads can be calculated using FEA or full scale burst tests. The RSF was originally proposed by Sims [6] to evaluate LTAs and is defined as: { Collapse Load of Damaged Component} { Collapse Load of Undamaged Component} RSF = (3) Acceptance criteria can be established using the RSF in combination with traditional code formulas, elastic stress analysis, limit load theory, or elastic-plastic analysis, depending on complexity of the assessment. The RSF is the value calculated by many of the assessment procedures presented in API 579. Each of the LTA assessment methods presented in this study has been reworked in terms of the RSF where possible for ease of comparison. Detailed procedures for calculating the RSF for each analysis method are found in Paragraphs 4.6 through The RSF can be used to calculate either the failure pressure or the Maximum Allowable Working Pressure (MAWP) of damaged components. The calculation for determining the failure pressure of damaged equipment is: Pf = P RSF (4) 0 The MAWP is slightly different and can be calculated using the RSF and an allowable RSF as follows: RSF MAWP = MAWP for RSF < RSF 0 a RSFa (5) 8

25 MAWP = MAWP0 for RSF RSFa (6) In a Fitness-For-Service assessment, the calculated RSF is compared to an allowable value. If the calculated RSF is greater than the allowable, the component may be returned to service. If the calculated RSF is less than the allowable, the component may be derated using Equation (5). The recommended value for the allowable remaining strength factor that is currently in API 579 is 0.9 for equipment in process services. This value can be overly conservative or un-conservative based on the design code used in construction, type of loading, or consequence of failure. One of the objectives of this study is to standardize the amount of conservatism in the determination of a damaged MAWP for different design codes and assessment methods. This will be achieved by tuning the allowable RSF so that a fixed margin on MAWP to failure pressure is maintained regardless of design code. 2.3 ORIGINAL LTA ASSESSMENT METHODOLOGY Before specific LTA assessment procedures were developed, regions of metal loss in were assessed using thickness averaging techniques. The origins of this method are unclear, although some guidelines still use these procedures which have been shown to be greatly conservative. To improve the assessment techniques for corroded pipelines, additional criteria was developed in the late 1960 s and early 1970 s through research sponsored by Texas Eastern Transmission Corporation and the AGA pipeline research committee. The criterion was incorporated into ASME B31.4 and B31.8 piping design codes and is commonly referred to as the B31.G [7] assessment criteria. The B31.G criteria are based on a fracture mechanics relationship developed by the AGA NG-18 Line Pipe Research Committee. The relationship was introduced by Maxey [8] and is based on a Dugdale plastic zone model, a Folias [9] bulging factor for a through wall crack in a cylindrical shell, and a flaw depth to thickness relationship. A series of corroded pipe burst tests were performed by Kiefner [10] to demonstrate the relationship between the remaining strength of pipes with and without LTAs. The B31.G method is the 9

26 foundation for most of the local thin area assessments that are currently in use. Details of the original B31.G calculation procedure are presented in Paragraph LTA DEVELOPMENT AND VALIDATION WORK Introduction Since initial development of local thin area assessment in the late 1960 s, many other groups and individuals have conducted research related to this topic. Twenty-five analysis methods developed by various authors are contained in this study for general LTAs, and many more methods exist for analyzing specific cases. In addition to new development work, much effort has gone into validating the existing methods and comparing the methods to determine which is the most accurate. The following paragraphs have a brief summary of the validation and development work that is available in the public domain Kiefner, et al Kiefner [11], [12], [13], [14], [15], [16], [17] has published multiple papers with other authors on the subject of local thin area assessments for pipes. Contained in the papers from the late 1960 s and early 1970 s is the basis for most of today s assessment procedures, in addition to a large number of corroded pipe burst test cases that were used to validate the developed methodology. Kiefner also contributed to the development of techniques that improved upon the basic procedure, including the RSTRENG [18] (see Paragraph 4.7) method and software analysis tool. 10

27 2.4.3 Stephens, Bubenik, Leis, et al Bubenik [19] showed that finite element analysis can be used to predict the load carrying capacity of corroded pipes. Comparisons between FEA and over 80 burst tests showed that failure stresses were well over yield. It was also concluded that load redistribution is dependent on geometry and strain hardening and is more significant for small deep corroded regions than for large corrosion regions. Stephens [20] conducted research with full scale testing and FEA on the failure of corroded pipe subjected to internal pressure and axial loading. For pipe defects subjected only to internal pressure, defect width was of secondary importance to defect length and depth. For pipe defects subject to combined axial and pressure loads, defect width is significant, and results indicated that axial loads increased the combined von Mises stress in the pipe, resulting in lower failure pressure. Interaction of separated defects was also examined. The interaction of separated defects is dependant on the defect size. Small defects have small interaction length and large defects have large interaction lengths. Axial spaced defects increase the stresses when compared to an isolated defect, which may decrease failure pressure. Circumferentially spaced defects decrease the stresses when compared to an isolated defect, which may increase failure pressure. This study was also used in the development of PCORR. The PCORR analytic model uses traditional finite element analysis applied to local thin areas in pipelines. Stephens [21] compared some of the prominent LTA assessment methods to determine the most accurate method. Methods used in the comparison were B31.G, modified B31.G, RSTRENG, Chell, Kanninen, Ritchie, Sims, and API 579. Conclusions showed the API 579 method to have the least variability. The modified B31.G, RSTRENG, and Chell methods also had small variability. Stephens [22], [23], [24], [25], [26] has investigated the fundamental mechanisms driving failure of pipeline corrosion defects. The research involved three phases: development of an analytic model known as PCORR, comparative evaluation of material and defect geometry variables controlling failure, and development of a simple closed form failure assessment 11

28 method. A parametric study with PCORR was used to identify variables that influence failure in moderate to high toughness pipe. The variables are ranked according to the magnitude of their influence as follows: 1. Internal pressure 2. Vessel or pipe diameter 3. Flaw depth and wall thickness 4. Ultimate material strength 5. Defect Length 6. Defect shape and characteristics 7. Yield strength and strain hardening characteristics 8. Defect Width 9. Fracture toughness The authors observed that pipes with low material toughness may fail at stresses below ultimate stress. This could be caused by crack initiation at the base of corrosion defects, resulting in failure pressures below the fully ductile prediction. PCORR was also used to develop a closed form solution for analyzing corrosion defects. The method is fully described in Paragraph 4.8 and is called the PCORR Assessment Method Coulson, Worthington Coulson and Worthington [27], [28] examined spirally oriented local thin areas and the interaction spacing between adjacent local thin areas. A full-scale burst test program was used in the study. Axial oriented flaws were compared to spiral flaws of equal length, and it was found that the spirally oriented flaws were less severe. A factor was developed that scaled the severity of spiral flaws to axial flaws of equal length. Failure pressure for spiral flaws is determined by calculating the failure pressure of an equivalent axial flaw and multiplying the result by the spiral factor. Additionally, general rules for the interaction of adjacent defects were developed as follows: 12

29 Flaws may interact in the axial direction if the separation between them is less than or equal to the length of the shortest flaw. Flaws may interact in the circumferential direction if the separation between them is less than or equal to the width of the narrowest flaw. Spiral flaws may interact if the separation between them along the spiral direction is less than or equal to the length. Spiral flaws separated by at least 12 inches normal to the spiral direction are not expected to interact. For the assessment of interacting flaws, assessment of the individual components is also necessary. The burst tests to verify these rules consisted of four spiral flaw tests, two axial flaw tests, three axial spaced flaw tests, one spirally spaced flaw test, and two circumferentially spaced flaw tests. Further validation of this method was performed by British Gas Mok, Pick, Glover, Hoff Mok, Pick, Glover, and Hoff [29], [30] examined the effects of long external corrosion by expanding on the work by Coulson and Worthington. Their objective was to develop a less conservative approach for evaluating long and long spiral flaws. Using previous tests and FEA analysis, the authors developed a burst pressure criterion for those types of flaws based on an orientation angle with respect to the circumferential plane of a cylindrical shell Chell In the original B31.G assessment methodology, a Folias factor is calculated based on a nondimensional length parameter for the LTA. The Folias factor is used with the flaw profile to calculate a surface correction factor and subsequent acceptance criterion. Chell [31] developed 13

30 an alternate form for the surface correction factor for LTA assessments. Details of the Chell surface correction factor are presented in Paragraph Hopkins, Jones, Turner, Ritchie, Last Hopkins and Jones [32] performed experimental tests to examine long flaws, interactions of slots, interaction of small and moderate size flaws, and short deep flaws contained in a larger shallow flaw. The experiments were performed in 24 inch pipe and included the following tests. Long slots: 4 cases Ring slots: 4 cases Short flaws and pits: 9 cases Interaction of medium flaws: 9 cases Short, deep flaws in a larger shallow flaw: 6 cases Jones, Turner, and Rithcie [33] performed FEA tests to examine plane stress failures (infinite length flaw) in 36 inch pipe. The authors were able to show that the failure sequence for the flaws were as follows. Yielding of the thinned section Full plastic behavior of the thinned section. Bending stresses exceeding yield develop in the undamaged section adjacent to the thinned section. Ductile failure occurs in the thinned section Ritchie and Last [34] developed a calculation procedure to calculated the failure pressure of a corroded shell based on the original B31.G equations. The authors modified the procedure to remove some of the conservatism and take into account ultimate strength and strain hardening for the damaged component. 14

31 2.4.8 Kanninen, et al Kanninen [35], [36], [37], [38] and others developed methodology to analyze the failure of LTAs subject to supplemental loading. As part of the research, full scale failure tests were performed to study the behavior of a LTA defect in a cylindrical shell that fails due to an applied net section bending moment. The assessment methodology developed by Kanninen is the bases for the evaluation of the circumferential (longitudinal stress) profile of a LTA. The details of his assessment method are presented in Paragraphs 4.13 and Chouchaoui, Pick Chouchaoui and Pick [39], [40], [41], [42], [43], [44] investigated the behavior of isolated or closely spaced corrosion flaws oriented circumferentially or longitudinally in pipe. The study included full scale burst tests and FEA of the test cases. For isolated flaws, it was shown that the B31.G and RSTRENG methods result in reasonable characterization of the damage. It was also concluded that longitudinally aligned pits within a certain spacing decreases the failure pressure of the pipe Valenta, et al Valenta [45], [46] developed a Finite Element Analysis model and a theoretical model for evaluating corrosion defects in gas transmission pipelines. The models were compared to the B31.G assessment and experimental verification. It was concluded that the FEA model would more accurately predict failure in corroded gas transmission pipelines than the ASME B31.G assessment method. 15

32 Zarrabi, et al Zarrabi [47] has presented methodology for assessing the integrity of cracked, eroded, or corroded vessels, tubes, or pipe. The methodology involves Finite Element models of cylindrical shells with part through rectangular slots. Plastic collapse pressures from the FEA are reported for a wide range of shells and slots through the use of non-dimensional parameters. Zarrabi [48] has developed methodology for assessing locally thin boiler tubes. By using elastic-plastic Finite Element Analysis models of boiler tubes with local thinning, a procedure is presented to calculate primary stress in the thinned section. The primary stress combined, material properties of the boiler tube, and operating conditions are used to calculate the creep and plastic lives of the boiler tube Sims, et al Sims [49], [50] was responsible for developing the RSF acceptability criterion for LTAs as described in Paragraph In addition the authors reviewed existing methodology and developed modified rules for evaluating LTAs and groove-like flaws Batte, Fu, Vu, Kirkwood Batte, Fu, Vu, and Kirkwood [51], [52] undertook a British Gas group sponsored project to improve the assessment of corroded pipelines, resulting in the BG assessment methods. Included in that study are numerous full-scale pipe burst tests and FEA models. The burst tests were performed on high strength steel pipes with machined single or adjacent local thin areas. The full scale burst tests were reproduced with FEA models and the numeric results were compared to the actual results. The BG methods are presented in Paragraph 4.11 and the databases are presented in Paragraph

33 Fu, Stephens, Ritchie, Jones Fu, Stephens, Ritchie, Jones [53] are the authors of the most current publication from the Pipeline Research Council. In the document, the original B31.G, modified B31.G, RSTRENG, and British Gas (BG) closed form methods for assessing local thin areas are compared. The study did not include the methodology currently in API 579. The cases are validated with full scale tests which are included in Database 1 and Database 3 of this report. The study recommends using the B31.G method for analyzing low toughness pipes and the RSTRENG and BG methods for high toughness pipes based on statistical analysis of the burst pressures predicted by the different methods. The BG methods (10 and 11) presented in this report have been expanded on to include methodology for analyzing groups of closely spaced local thin areas. Some spacing criteria is presented, but the method is still largely empirical. 2.5 ASME SECTION XI CLASS 2 AND 3 PIPING The ASME Section XI [54], [55], [56], group on pipe flaw evaluation is currently developing requirements for analytical evaluation of pipe wall thinning. The evaluation involves two separate assessments for a LTA in a pipe, elbow, or reducer. The first assessment is a thickness evaluation to determine if the minimum wall thickness is acceptable for internal pressure loads. The second is a stress evaluation to determine if primary and secondary loads cause stress that exceeds the material allowable limits specified by the code of construction. 2.6 CURRENT IN-SERVICE INSPECTION CODES Current in-service inspection codes for pressure vessels, piping, and tankage in the refinery and petrochemical industries contain assessment guidelines to evaluate LTAs. Although these rules have been in existence for many years, they are empirically based and do not have a sound technical background that is required to extend current limitations. A summary of the existing rules for the API 510, API 653, API 570, and NBIC inspection codes is shown in Table 3. These 17

34 rules are based on average measured thickness data over a prescribed length. The advantages and limitations of thickness averaging are discussed in Chapter 3. As an alternative, the inservice inspection codes provide an option for evaluation by stress analysis. In this option, assessment results are evaluated using the ASME Boiler and Pressure Vessel Code, Section VIII, Division 2, Appendix 4 (Hopper diagram). This option provides flexibility in the analysis but becomes difficult to apply because the categorization procedure in Appendix 4. However, results may be arbitrary due to stress classification with the Hopper diagram. 18

35 CHAPTER III API 579 METAL LOSS ASSESSMENT PROCEDURES 3.1 INTRODUCTION The Fitness-For-Service (FFS) assessment procedures proposed in API 579 were developed to provide a standardized assessment methodology for inspectors, plant engineers, and engineering specialists. The rules include classification, limitations, and acceptance criteria for different types of metal loss. The option to calculate a derated MAWP based on the extent of damage is also provided. The procedures are valuable for extending the life of damaged equipment, setting inspection intervals, or determining the remaining life of damaged equipment. Most in-service inspection codes and standards use a thickness averaging procedure to evaluate areas of metal loss. API 579 includes modified thickness averaging rules as well as specific LTA analysis methodology to be consistent with the inspection standards. Therefore, metal loss is divided into two categories in API 579. General metal loss includes regions of corrosion or erosion that have uniform or non-uniform remaining thickness. The rules for evaluating general metal loss are presented in Section 4 of API 579. Local Metal Loss includes regions of metal loss that have a non-uniform thickness and more detailed assessment rules are used to provide an accurate result. The rules for evaluating local metal loss are presented in Section 5 of API 579. The difference between general and local metal loss assessments has to do with the amount and type of data that is required for the assessment. For general metal loss, point thickness readings or detailed thickness profiles are required. For local metal loss, detailed thickness profile information, which involves thickness readings and their spacing, is required. 19

36 The assessment procedures for general metal loss in API 579 are based on a thickness averaging approach similar to other existing codes and provide a suitable result when applied to uniform metal loss. For local areas of metal loss, the thickness averaging approach may still be used; however, the results will be overly conservative. For these cases, the API 579 assessment procedures for local metal loss can be used to reduce the conservatism in the analysis. The local metal loss rules may also be used to evaluate general metal loss, but the amount of inspection data and complexity of the analysis is greater. The distinction between general and local metal loss is difficult to make without detailed knowledge of the metal loss profile, so the rules in API 579 have been structured to provide consistent results between the two methods. It is recommended that a simpler general metal loss assessment be initially performed for either type of metal loss. If the results are not satisfactory, an assessment using the local metal loss rules can be used for a less conservative estimate. 3.2 MULTI-LEVEL ASSESSMENT PROCEDURE Three levels of assessment are provided in API 579 for each flaw and damage type. In general, each assessment level has a balance between degree of conservatism, the amount of information required to perform the assessment, the skill of the personnel performing the assessment and the complexity of the analysis. A logic diagram is included in each section to illustrate how these assessment levels are interrelated. The overall logic diagram for assessing general or local metal loss is shown in Figure 1, and the logic diagram for evaluating local metal loss specifically is shown in Figure 2. Level 1 is the most conservative, but is easiest to use. Practitioners usually proceed sequentially from a Level 1 to a Level 3 assessment (unless otherwise directed by the assessment techniques) if the current assessment level does not provide an acceptable result or a clear course of action cannot be determined. A general overview of each assessment level and its intended use are described below: Level 1: The assessment procedures included in this level provide conservative screening criteria that require a minimum amount of inspection or component information. 20

37 The Level 1 assessment procedures are intended for use by either plant inspection or engineering personnel. Level 2: The assessment procedures included in this level provide a more detailed evaluation that is less conservative than those from a Level 1 assessment. In a Level 2 assessment, inspection information similar to that required for a Level 1 assessment is required; however, more detailed calculations are used in the evaluation. Level 2 assessments are intended for use by plant engineers or engineering specialists experienced and knowledgeable in performing FFS assessments. Level 3: The assessment procedures included in this level provide the most detailed evaluation that produces results that are less conservative than those from a Level 2 assessment. In a Level 3 assessment additional inspection and component information is typically required, and the recommended analysis is based on numerical techniques such as finite element analysis. The Level 3 assessment procedures are intended for use by engineering specialists experienced and knowledgeable in performing FFS evaluations. 3.3 INSPECTION DATA REQUIREMENTS Point Thickness Readings (PTR) There are two inspection techniques that may be used when characterizing a region of metal loss. Point Thickness Readings (PTR) are a random sampling of thickness measurements in a corroded region. PTR are only suitable for assessments where the variation in thickness readings is statistically small. The test for significance in the variability is based on the Coefficient of Variation (COV) of the thickness reading population. The COV is defined as the standard deviation of a sample divided by the mean of a sample. As shown in Figure 3, if the COV of the thickness reading population is small, then the variability in thickness readings is small. Alternatively, if the variability in thickness readings is large, so is the COV. If the COV of the thickness reading population minus the Future Corrosion Allowance (FCA) is less than 10%, 21

38 then the general metal loss is defined to be uniform and the average thickness can be computed directly from the population of thickness readings. If the COV is greater than 10%, then the use of thickness profiles is required to determine the average thickness. PTR data may only be used for an API 579 Section 4 general metal loss assessment. As recommended in API 579, if point thickness readings are used in an assessment, the assumption of general metal loss should be confirmed considering the following: A minimum of 15 thickness readings is recommended unless the level of NDE utilized can be used to confirm that the metal loss is general. In some cases, additional readings may be required based on the size of the component, the construction details utilized, and the nature of the environment resulting in the metal loss. Additional inspection may be required such as visual examination, radiography or other NDE methods Critical Thickness Profiles (CTP) The other technique for characterizing metal loss is by using a Critical Thickness Profile (CTP). If possible, it is recommended that CTPs are always used for the assessment of metal loss. They are required for a detailed API 579 Section 5 local metal loss assessment and may also be used for an API 579 Section 4 general metal loss assessment. In addition the CTPs are better for inspections records if continued damage is expected. If the COV test for point thickness readings is greater than 10%, then the general metal loss is defined to be non-uniform and the use of thickness profiles is required. An inspection grid covering the region of metal loss is typically required to determine the extent of the damage. Examples of inspection grids used to map the metal loss damage on a cylinder, cone, and elbow are shown in Figure 4. Once the inspection grids have been established and the thickness readings are taken, the Critical Thickness Profiles (CTPs) can be determined. The CTPs in the longitudinal and circumferential directions are required for the assessment. The process to establish the CTP is shown in Figure 5. The longitudinal and circumferential CTPs are found by taking the lowest readings along the 22

39 lines designated by M i and C i, respectively, as noted in the figure. This establishes the maximum metal loss or minimum thickness readings in the region of damage by using a "river bottom" approach. Once the minimum thicknesses along all of the lines identified with M i and C i lines are taken, these values are projected onto longitudinal and circumferential planes, respectively, to form the CTP in these directions as shown in Figure 5. In the figure, the dimension s is the length of the longitudinal CTP and the dimension c is the length of the circumferential CTP. The spacing of the CTPs is the spacing of the thickness grid in the longitudinal and circumferential directions. This process can be used for both isolated and multiple flaws as shown in Figure ASSESSMENT OF GENERAL METAL LOSS Overview The API 579 Section 4 assessment procedures can be used to evaluate uniform and nonuniform metal loss on the outside diameter or inside diameter of a component. The results obtained for general metal loss may be overly conservative for flaws with significant thickness variations. To account for this, an initial screening can be performed using general metal loss guidelines, and an additional assessment may be performed using local metal loss guidelines if the component does not meet the general metal loss criteria. Two procedures for evaluating general metal loss away from structural discontinuities are provided based on the type of inspection data available. One procedure uses Point Thickness Readings (PTR) and the other uses Critical Thickness Profiles (CTP). Point thickness readings should be used in assessments where variance in thickness readings is small. Critical thickness profiles are suited to handle all types of assessment. It is recommended that CTPs be used whenever possible. Acceptability for both methods is determined from a strength criterion dictated by the original construction code, and each has criteria to ensure against leakage. If the strength criterion is not satisfied, rules are provided to determine the MAWP of pressurized components or the maximum fill height for atmospheric storage tanks. Procedures are also 23

40 provided to establish an inspection interval based on a remaining life assessment, or to specify a future corrosion allowance for continued operation. A different procedure is required for metal loss at structural discontinuities. Structural discontinuities include nozzles and branch connections, axisymmetric discontinuities such as stiffening rings, piping systems which have thickness interdependency, or any other structural component that affects the shell stiffness in the region of metal loss. The current assessment methodology defines a zone of interaction between the shell and discontinuity. Acceptance for the region of metal loss is established by determining an average thickness for each component in the interaction zone and using the average thickness with the original design code equations for each component and the interdependency of the two Applicability and Limitations The following are the limitations and applicability for the Level 1 and Level 2 assessment procedures specified in API 579. The component must be designed and constructed in accordance with a recognized code or standard. This insures construction to a standard quality level and requires normal scheduled inspections. The component must not be operating in the creep range. The assessment guidelines presented here have not been validated for these conditions, although they may be applicable. Accumulated creep strains usually become concentrated in reduced stiffness regions. Stiffness reduction is a function of wall thickness, flaw geometry, material properties, and load conditions. These effects have not yet been addressed, so this type of assessment may not be conservative for these conditions. The region of metal loss must have relatively smooth contours without notches, crack-like flaws, or other locations of stress concentration. Notches and other areas of stress concentration may lead to cracking or brittle fracture, which is not considered in this type of assessment. Similarly, the material of the component must have sufficient material 24

41 toughness. The local metal loss rules do not apply to materials that may be embrittled due to temperature or operating environment The component is not subject to cyclic service. Fatigue screening guidelines in API 579 are separate from a general LTA assessment. The cut-off for cyclic service in API 579 is 150 cycles. These limitations result in an acceptable level of conservatism when performing this type of assessment. Limitations based on loading conditions are also included. Internal pressure, maximum fill height, or supplemental loads must be governed by equations that relate the load to a required wall thickness. A summary of load limitations in API 579 for each assessment level are given as follows. Level 1 assessments are applicable to internal or external pressure only Level 2 assessments may have internal or external pressure and/or supplemental loading from weight and occasional loads Level 3 assessment can be performed when any of the above limitations are not satisfied or for any load conditions Metal Loss Away from Structural Discontinuities Assessment with Point Thickness Readings The acceptance criteria for metal loss can be determined once the average and minimum thicknesses have been established. The Level 1 Assessment criteria are shown below. t FCA t (7) am mm min t FCA t (8) lim Where the minimum permissible thickness for pressure vessels and piping is lim [ ] t = max 0.5 t, 0.10 inches (9) min 25

42 and the minimum permissible thickness for tanks is lim [ ] t = max 0.6 t, 0.10 inches (10) min The Level 2 Assessment criteria are shown below. t FCA RSF t (11) am mm lim a min t FCA t (12) The minimum permissible thickness, t lim, is evaluated using Equations (9) and (10). If the component fails the above criteria, a damaged MAWP can be determined by substituting the average thickness back into the original design equations as long as the minimum thickness requirement is satisfied. For example, for a cylindrical shell subjected to internal pressure, the MAWP could be determined as follows using a typical design equation. ( tam FCA) ( ) 1 σ a MAWP = RSF R t FCA a am (13) The Level 1 calculation does not include the allowable RSF. The MAWP with inclusion of the allowable RSF may not be higher than the original calculated MAWP Assessment with Critical Thickness Profiles To perform a thickness averaging assessment with CTPs, the length for thickness averaging, L, is computed using the following equations. L= Q Dt min (14) 2 1 R t Q = Rt RSF a R t FCA 0.5 am t = (16) tmin (15) 26

43 The Q factor is actually derived from the API 579, section 5 assessment rules for regions of local metal loss and can be thought of as a conservative screening method for local metal loss. A remaining strength factor based on the remaining thickness ratio and the flaw length is calculated as follows: Rt RSF = M t ( R ) t (17) M t λ 2 = (18) λ = l (19) Dt R t t FCA t mm = (20) min In the above equations, l is the length of the local thin area based on the CTP. By setting the RSF equal to the allowable RSF and solving for l, conservative screening criteria can be derived which relates the length for thickness averaging to the remaining thickness ratio as follows: λ = l (21) Dt M t RSF l = Dt a = 1 Rt 1 R 2 l Dt t 2 (22) (23) Solving for l or the length for thickness averaging yields: 27

44 2 1 R t l = 1.262Dt 1 Rt 1 RSF a (24) Setting l equal to L and factoring out Q yields the following: L = Q Dt (25) 2 1 R t Q = Rt 1 RSF a 0.5 (26) When the thickness averaging rules are applied to an area of metal loss that is an actual LTA, the length for thickness averaging will be small because a small R t ratio produces a small Q value. This small length for thickness averaging when centered on the minimum thickness reading will produce a small average thickness that subsequently results in a small or conservative MAWP. The rules of API 579 have been structured to direct the user to the LTA assessment procedures for these cases. Alternatively, when the LTA has a high remaining thickness ratio, the value of Q becomes larger thus increasing the length for thickness averaging. When this longer length is centered on the minimum thickness reading value, a large average thickness and corresponding MAWP will result. This MAWP will approach the value that would be obtained using the LTA assessment procedures. The consistency in the rules is guaranteed because the length for thickness averaging given by Equation (14) is derived by substituting RSF a for RSF in equation (35) and solving for l; the resulting value of l is then set to the length for thickness averaging, L. After the length for thickness averaging, L, is determined, the assessment is completed based on the relative values of s and L: s > L the local metal loss assessment rules can be used for the evaluation s < L the general metal loss rules are used for the evaluation 28

45 When using the general metal loss rules, the average thickness for both the meridional and circumferential planes must be considered. The average thickness in the meridional direction, t s am, is determined by averaging the thickness readings within the dimension s over the length L, and the average thickness is in the circumferential direction, t c am, is determined by averaging the thickness readings within the dimension c over the length L. The minimum thickness is based on the minimum thickness reading in the grid. In a Level 1 assessment, t am = t s am for cylindrical shells because the only loading permitted is internal pressure. For spheres and formed heads, the average thickness is taken as t am =max[t s am, t c am]. In a Level 2 assessment, t s am and t c am are used directly in the analysis to account for supplemental loads. For cylindrical shells, the acceptance criterion for the average thickness is the same as specified in Paragraph except Equation (11) is replaced with the following equations. t FCA RSF t (27) s am c am a a C min t FCA RSF t (28) L min For spherical shells and formed heads the assessment criterion is identical to the cylindrical shell methodology. The only difference is how t min is calculated. If the component fails the specified criteria, a damaged MAWP can be determined as described in Paragraph Metal Loss at Major Structural Discontinuities One advantage the general metal loss rules have over the local metal loss rules is that they allow the assessment of metal loss at structural discontinuities. Examples of structural discontinuities include local erosion and/or corrosion at vessel nozzle and piping branch connections, internal tray support rings, stiffening rings, conical shell transitions, and flanges. In the current edition of API 579, general and local areas of metal loss at structural discontinuities are evaluated by determining an average thickness within a thickness averaging zone, and using 29

46 the thickness with the original construction code design rules to determine acceptability for continued service. Design rules for components at a major structural discontinuity typically involve satisfying a local reinforcement requirement (e.g. nozzle reinforcement area), stress requirement based upon a given load condition, geometry, and thickness configuration (e.g. flange design). These rules typically have a component with thickness that is dependent upon the thickness of another component. To evaluate components with thickness interdependency, the MAWP should be computed based upon the average measured thickness minus the future corrosion allowance including the thickness required for supplemental loads for each component using the equations in the original construction code. The calculated MAWP should be equal to or exceed the design MAWP. The average thickness of the region can be obtained as follows for components with thickness interdependency as described in API 579. Nozzles and branch connections: The average measured thickness is determined as the average of the thickness readings taken within the nozzle reinforcement zone as shown in Figure 7. Axisymmetric Structural Discontinuities: Determine L using Equation (14) and L v based on the type of structural discontinuity as shown in Figures 8 and 9. The average thickness is computed based on the smaller of these two distances. If L < L v, the midpoint of L should be located where the wall thickness is equal to t mm to establish a length for thickness averaging unless the location of t mm is within L/2 of the zone for thickness averaging. In this case, L should be positioned so that it is entirely within L v to compute the average thickness. Piping Systems: Piping systems have thickness interdependency because of the relationship between the component thickness, piping flexibility, and the resulting stress. For straight sections of piping, determine L using the procedure described above and compute the average thickness to represent the section of pipe with metal loss in the piping analysis. For elbows or bends, the thickness readings should be averaged within the bend and a single thickness used in the piping analysis (i.e. to compute the flexibility 30

47 factor, system stiffness and stress intensification factor). For branch connections, the thickness should be averaged within the reinforcement zones for the branch and header, and these thicknesses should be used in the piping model (to compute the stress intensification factor). An alternative assumption is to use the minimum measured thickness to represent the component thickness in the piping model. This approach may be warranted if the metal loss is localized; however, this may result in an overly conservative evaluation. 3.5 ASSESSMENT OF LOCAL METAL LOSS Overview The local metal loss assessment rules are used to evaluate regions of metal loss resulting from erosion/corrosion, mechanical damage such as grooves and gouges, blend ground areas used to remove crack-like flaws, and the damage associated with pitting and blisters. The local metal loss assessment rules may only be used with CTP data. These procedures use the concept of an RSF for acceptance criteria, and contain separate rules for evaluating the longitudinal and circumferential stress direction of a flaw in cylindrical shells. The local metal loss rules are divided into rules for evaluating the circumferential stress direction or longitudinal profile of an LTA and the longitudinal stress direction or circumferential profile of an LTA. The circumferential stress assessment is used to evaluate LTAs in equipment subject to internal pressure only where circumferential stresses dominate. The longitudinal stress assessment is used to evaluate LTAs in equipment subject to internal pressure and supplemental loads that may cause the longitudinal stresses to effect the flaw behavior. As in the rules for general metal loss, two levels of assessment are provided. 31

48 3.5.2 Applicability and Limitations The applicability and limitations of Level 1 and Level 2 local metal loss assessment procedures have the same limitations as those described for general metal loss in Paragraph In addition, the following limitations must be satisfied for an API 579 Section 5 LTA assessment. A Level 1 assessment may only be used for components subject to internal pressure A Level 2 assessment may only be used for components subject to internal pressure or cylinders subject to internal pressure and supplemental loads The length of a LTA may not exceed the following limitation for a Level 2 assessment. l Dt (29) The assessment must be performed using CTP inspection data. PTR inspection data may not be used. The assessment may not be used to evaluate components subjected to external pressure. Local metal loss rules are currently limited to flaws that meet the following minimum wall thickness criteria. The minimum measured wall thickness may not be less than 20% of the original wall thickness or less than 0.1 inches R t FCA mm t = (30) tmin R 0.2 (31) t t FCA 0.10 inches (32) mm The local metal loss may not be near a structural discontinuity. If an LTA fails the following criterion, the rules provided for analyzing regions of general metal loss near a structural discontinuity in Paragraph may be used. Lmsd 1.8 Dt (33) min 32

49 The assessment is currently limited to the following components: cylindrical, conical, spherical, elliptical, and torispherical shell sections away from structural discontinuities or junction and head attachment locations. (See Paragraph 3.5.5) The assessment for longitudinal stress is only applicable to cylindrical shell sections Assessment Procedure Circumferential Stress Direction Overview Due to geometry and loading of cylindrical shells, different assessment criteria are provided in API 579 based on the stress direction. For most LTAs in cylindrical shaped shells, the circumferential direction is limiting because hoop stresses are typically twice that of longitudinal stresses. As a result, almost all LTA research and development has been concentrated on the circumferential stress direction. This approach is valid for most cases where only pressure loading is evaluated. If supplemental loads are included in the assessment, then the longitudinal stress direction should be taken into consideration. Two levels of assessment are provided for regions classified as local metal loss. The region of metal loss is approximated as a simple rectangular section encompassing the critical thickness profile for a Level 1 assessment. Level 2 uses an iterative process that slices the critical thickness profile of the region of metal loss into subsections. Each subsection is evaluated, and acceptance is based on the limiting subsection. These assessment methods may also be applied to groove-like flaws and gouges. Additional geometric limitations are required for groovelike flaws, and additional material limitations are required for gouges API 579 Section 5, Level 1 Analysis A Level 1 assessment is based on a simple rectangular approximation for the area of metal loss. This method may be overly conservative for flaws with significant variations in the critical 33

50 thickness profile or for groups of flaws that are closely spaced. The following procedure is presented in API 579 for the Level 1 local metal loss assessment. Step 1: Determine the critical thickness profile as described in Paragraph Step 2: Determine the minimum required thickness. For a cylinder, the minimum required thickness for the circumferential stress direction is: t min PR = c SE 0.6P (34) Step 3: Check the restrictions covered in Paragraph Step 4: Calculate an RSF as follows: Rt RSF = M R t t FCA ( R ) t mm t = (36) tmin (35) M t λ 2 = (37) λ = l (38) Dt The above equations can be represented in graphical form by plotting the metal loss damage parameter against the remaining thickness ratio. The resulting plot is shown in Figure 10. This plot can be considered as a failure assessment diagram for local metal loss. The MAWP for the damaged component may also be calculated using the RSF and Equations (5) and (6) API 579 Section 5, Level 2 Assessment In the Level 2 assessment, the remaining strength of an LTA is evaluated using an incremental approach. The length limitation for an LTA can be expressed in terms of lambda as follows. 34

51 λ 5.0 (39) If the above limitation is satisfied, then the RSF can be computed using the following steps. The procedure is also presented in a standard format in Paragraph Steps 1 3: Use the same procedure as Steps 1 3 detailed in Paragraph Step 4: Implement the incremental procedure as follows: Rank the thickness readings in ascending order based on metal loss. As shown in Figure 11, set the initial evaluation starting point, s 1, as the location of maximum metal loss, this is the location in the thickness profile where t mm is recorded; subsequent starting points should be in accordance with the ranking in Step 1. At the current evaluation starting point, subdivide the thickness profile into a series of subsections. The number and extent of the subsections should be chosen based on the desired accuracy and should encompass the variations in metal loss. For each subsection, compute the Remaining Strength Factor using the following equation where the term A i is the area of metal loss associated with s i (see Figure 12). The bulging factor for a cylindrical shell given by Equation (41) is based on the original work by Folias. RSF i i A 1 i Ao = i 1 A 1 i i M t Ao (40) M i t i 2 i 4 ( λ ) ( λ ) i 6 i ( λ ) ( ) ( λ ) = (41) A = st (42) i o i min 35

52 i A i le i ls ( ) = d x dx (43) Step 5: Determine the minimum value of the Remaining Strength Factor, RSF i, for all subsections (see Figure 11). This is the minimum value of the Remaining Strength Factor for the current evaluation point. Step 6: Repeat Steps 3 through 5 of this calculation for the next evaluation point which corresponds to the next thickness reading location in the ranked thickness profile list. Step 7: The Remaining Strength Factor to be used in the assessment, RSF, is the minimum value determined for all evaluation points. Step 8: The MAWP for the damaged component may also be calculated using the RSF and Equations (5) and (6) Assessment Procedures Longitudinal Stress Direction Overview Pressure vessels and piping are frequently subjected to significant axial and bending loads as well as internal pressure. At this point there are no industry-accepted criteria for performance of blunt defects under combined pressure and axial loads. To address this shortcoming, a simple beam bending formulation is used to evaluate the longitudinal stress in cylinders due to supplemental loads. Rules to evaluate net-section loads on cylindrical shells and pipes using conventional elastic bending theory are provided in API 579. It is assumed in the methodology that plane sections remain plane and that the pipe does not ovalize or distort during bending. Section properties of net cross-sectional area and section modulus are computed based upon uniform depth metal loss in the circumferential plane. In the event that the longitudinal stress is compressive, a buckling check is also performed. Supplemental loads applicable to a Level 2 assessment are shown in Figure 13. A level 1 assessment is a graphical representation of the Level 2 assessment procedure with 36

53 supplemental loads set to zero (internal pressure only). For a Level 2 assessment, two load cases, weight and weight plus thermal, must be considered. The weight case includes load controlled loads. The weight plus thermal case includes displacement controlled loads. Acceptability is established by satisfying the von Mises equivalent stress criteria for two critical stress locations on the cylinder cross section. The von Mises stress was used based on the observation of full scale burst tests that ruptured due to a net section bending moment. It was observed that flaws under the same loads failed differently depending on if the flaw was on the tension or compression side of the pipe. The phenomenon follows the von Mises bi-axial stress envelope. The points A and B are the critical assessment locations as shown in Figure 14. Circumferential regions of non-uniform metal loss can be analyzed by bounding the area of metal loss with a rectangular area. This method insures conservative results; for less conservative results, a Level 3 assessment is required API 579, Section 5, Level 1 Assessment The current API 579 Section 5, Level 1 assessment for the circumferential extent of a LTA is a graphical procedure based on two parameters. The first parameter in the ratio of the circumferential flaw length to the cylinder diameter and the second is the remaining thickness ratio. The screening curve was developed using the Level 2 rules with the following assumptions: The circumferential extent of the LTA can be approximated with a rectangular area The component was designed correctly with an allowable stress equal to two-thirds yield. One-half of this stress was allocated for the longitudinal stress due to pressure and onehalf was allocated to a bending moment that causes maximum tension on the LTA. All other end loads are assumed to be equal to zero. The graph is based on the maximum controlling radius to thickness ratio that varied from 5 to 1000 in the analysis. The curve is based on an allowable remaining strength factor of

54 The actual curve was generated by back calculating remaining strength factors of 0.9 with a range of circumferential flaw to diameter ratios and remaining thick ratios. The Level 1 screening curve is shown in Figure API 579, Section 5, Level 2 Assessment The Level 2 assessment procedure for longitudinal stress can be used to determine the acceptability of the circumferential extent of a flaw in a cylindrical or conical shell subject to pressure and/or supplemental loads. These types of loads may result in a net section axial force, bending moment, torsion, and shear being applied to the cross section of the cylinder containing the flaw. Supplemental loads will result in longitudinal membrane, bending, and shear stresses acting on the flaw, in addition to the longitudinal and circumferential (hoop) membrane stress caused by pressure. The supplemental loads should include loads that produce both load-controlled and displacement-controlled effects. Therefore, the net section axial force, bending moment, torsion, and shear should be computed for two load cases; weight and weight plus thermal. The weight load case includes pressure effects, weight of the component, occasional loads from wind or earthquake, and other loads, which are considered as load-controlled. The weight plus thermal load case includes the results from the weight case plus the results from a thermal case which includes the effects of temperature, support displacements, and other loads which are considered as displacement-controlled. Longitudinal stresses are calculated using an elastic bending model for a beam with cylindrical cross section subject to axial force and bending moment. The circumferential extent of the flaw is approximated with a rectangular box bounding the circumferential critical thickness profile. The cylinder section modulus in the beam equations is then modified to exclude the bounding box area in the longitudinal stress calculation. Circumferential stresses are calculating using a code equation with an increase in stress based on the RSF calculated to account for bulging effects generated by the LTA. The API 579, Section 5, Level 2 assessment for the 38

55 circumferential stress direction as shown in Paragraph is used to calculate the RSF. The Level 2 assessment procedures are as follows: Step 1: For the circumferential inspection plane being evaluated, approximate the circumferential extent of metal loss on the plane under evaluation as a rectangular shape. for a region of local metal loss located on the inside surface, f o mm 2( ) D = D t FCA (44) and for a region of local metal loss located on the outside surface: f i mm 2( ) D = D + t FCA (45) The circumferential angular extent of the region of local metal loss is: c 180 θ = D π f ( θ in Degrees) (46) Step 2: Compute the section properties of a cylinder with and without a region of local metal loss using the equations in Table 4. Step 3: Compute the maximum section longitudinal membrane stress for both the weight and weight plus thermal load cases considering points A and B in the cross section: ( MAWP ) A w σ lm = r + + Am Af Am Af y I A X A x ( y + b)( MAWP ) A + M + M F A r w x y IY (47) ( MAWP ) B w σ lm = r + + Am Af Am Af y I B X A x ( y + b)( MAWP ) A + M + M F B r w x y IY (48) A B σ = max σ, σ (49) lm lm lm 39

56 Step 4: Evaluate the results as follows. The following relationship should be satisfied for either a tensile and compressive longitudinal stress for both the weight and weight plus thermal load cases: σ σ σ + σ + 3τ Hσ (50) cm cm lm lm ys with, σ cm MAWP r D i = EL RSF Do Di (51) M T τ = + 2( t + tf ) A A d V A A m f (52) The elastically calculated von Mises stress must be satisfied for both the weight and weight plus thermal load cases for positions on the cross section defined by x and y (see Figure 14). The critical points that are required to be check are labeled A and B in the figure. For the weight case, H = 0.75, and for the weight plus thermal case, H = 1.5. The value H = 0.75 is established considering a RSF a = 0.9 factor applied to a two-thirds factor that is typically applied to the yield stress to establish a design stress value for a load-controlled stress (H = 0.9x0.67 ~ 0.75). For the weight plus thermal case, a margin of two is typically applied to the yield stress. The value of H = 1.5 represents an allowable stress reduction factor that is typically applied to a weight plus thermal load case. This reduction was included to compensate for possible elastic follow-up that can occur in some structures because of a significant localized change in stiffness. Step 5: If the maximum longitudinal stress computed in Step 4 is compressive, then this stress should be less than or equal to the allowable compressive stress or the allowable tensile stress, whichever is smaller. When using this methodology to establish an 40

57 allowable compressive stress, an average thickness representative of the region of local metal loss in the compressive stress zone should be used in the calculations. Step 6: If the longitudinal membrane stress computed in Step 3 does not satisfy the requirements of Step 4, then the MAWP and/or supplemental loads should be reduced, and the evaluation repeated. If the metal loss in the circumferential plane is composed of several distinct regions, then a conservative approach is to define a continuous region of local metal loss that encompasses all of these regions. If this assumption is too conservative or the metal loss has significant variability making the rectangular approximation for the remaining thickness too conservative, a numerical procedure such as the Monte Carlo integration method may be used to compute the section properties Non-Cylindrical Shells Overview Non-cylindrical shells include spherical shells, formed heads, conical shells, and elbows. Very little technical development and experimental validation has been performed for flaws in components with these types of geometry. The assessment procedure for non-cylindrical shells is based on the procedure for cylindrical shells with minor modifications Spherical Shells and Formed Heads The Level 1 assessment procedure for spherical shells and formed heads is the same procedure used in an API 579, Section 5, Level 1 assessment for cylindrical shells. The Level 2 assessment uses the API 579, Section 5, Level 2 assessment for cylindrical shells with a different Folias factor. The Folias factor for a spherical shells and formed heads replaces Equation (41) in the API 579, Section 5, Level 2 assessment for cylindrical shells and is from the original work by Folias [57] and is defined as follows. 41

58 M t ( λ ) ( λ ) 2 ( λ) ( λ) = (53) The LTA assessment procedures for formed heads in API 579 are limited to LTAs occurring within the 0.8D center zone of the head. The minimum required thickness and maximum allowable working pressure for spherical heads is defined as follows. t min PR = c 2SE 0.2P (54) MAWP 0 = 2SEtc R + 0.2t c c (55) The minimum required thickness and maximum allowable working pressure for elliptical heads within the center zone of the head is defined as follows. t min PDc K = 2SE 0.2P (56) MAWP 0 = 2SEtc KD + 0.2t c c (57) K = R R R (58) 2 3 ell ell ell The minimum required thickness and maximum allowable working pressure for torispherical heads within the center zone of the head is defined as follows. t min PC rc = 2SE 0.2P (59) 2SEtc MAWP0 = C + 0.2t rc c (60) 42

59 The procedures outlined in Paragraphs and to calculate RSFs for a Level 1 and 2 can be used in conjunction with the above equations to evaluate spherical shells and formed heads Conical Shells The LTA assessment procedures for conical shells are the same as those used for cylinders. However, in the assessment procedures, the minimum required thickness is based on the equations in the original construction code for conical shells, and the inside diameter to be used in the assessment is specified to be the diameter at the center of the LTA. The minimum required thickness and maximum allowable working pressure for conical shells is defined as follows. t min PD = c 2cosα 0.6 ( SE P) (61) MAWP 0 = 2SEtc cosα D + 1.2t cosα c c (62) The procedures outlined in Paragraphs and to calculate RSFs for a Level 1 and 2 can be used in conjunction with the above equations to evaluate conical shell sections Elbows Bubenik and Rosenfeld [58] studied the effects of an LTA on the strength of an elbow with analytical and experimental methods. It can be concluded from the results of the study that LTAs in an elbow can be evaluated using the assessment procedures for a cylindrical shell if the Lorenz factor is included in the analysis. The Lorenz factor is the ratio of the elastic membrane stress at a point on the circumference of an elbow to the membrane stress in a cylindrical shell with the same inside diameter and thickness. The Lorenz factor is defined as follows. 43

60 L f Rb sinθ L + Rm 2 = Rb + sinθ L Rm (63) In the above equation, θ L = 0 0, correspond to the crown position on the elbow, θ L = 90 0 corresponds to the extrados of the elbow, and θ L = corresponds to the intrados of the elbow. Bubenik indicates that a conservative estimate of the failure stress for an LTA in an elbow can be computed as follows. σ fail A 1 σ flow t A loc o = L f t 1 A 1 Mt A o (64) The term t loc in the above equation is the local wall thickness in the elbow before corrosion and t is the nominal wall thickness of the elbow. The effects of local variation in the elbow wall thickness from forming are neglected; therefore, in Equation (64), t loc /t = 1.0. The Lorenz factor is included in the LTA assessment procedure by using the minimum required thickness as follows. t min = PDo MA σ ae + c 2 + PY L f (65) 3.6 API 579 ADVANCED ASSESSMENT OF METAL LOSS Overview A Level 3 assessment is API 579 is considered and advanced assessment of metal loss. Finite element analysis is the typical method for quantifying stress in a component for a Level 3 assessment; however, other numerical methods may be employed. Linear elastic stress analysis with appropriate stress classification or non-linear elastic-plastic stress analysis to calculate 44

61 collapse loads may be used. Non-linear stress analysis will more accurately duplicate actual behavior like the redistribution of stress due to plasticity or creep which are considered directly in the analysis. Linear elastic analysis tends to under predict strain ranges at fatigue sensitive points, while non-linear analysis will more accurately represent actual strain ranges and the accumulation of inelastic strains. Components that are subject to external pressure or large compressive stresses should also be evaluated for structural stability and buckling. Additional procedures for components subject to cyclic loading are also provided in API 579, Appendix B. When formulating a finite element model for a Level 3 assessment, thickness data can be mapped directly onto two or three dimensional continuum elements as applicable. Alternately, shell elements with different thicknesses may be used to approximate an LTA. Mesh densities and application of loads and boundary conditions vary between applications and must be applied using engineering experience. Special considerations must be taken into account if there are significant supplemental loads and structural discontinuities affecting the region containing the flaw. Flexibility and stress distribution in these locations may be affected by the location and distribution of metal loss, may cause a reduction in calculated plastic collapse loads, and cause difficulty in relating to the original design specifications Assessment with Numerical Analysis For a non-linear stress analysis, structural integrity can establish for a component by taking two-thirds of the plastic collapse load. The plastic collapse load can be determined using the following two criteria taken directly from API 579. Global Criteria: A global plastic collapse load is established by performing an elasticplastic analysis of the component subject to the specified loading conditions. The plastic collapse load is the load which causes overall structural instability. Local Criteria: A local plastic collapse load is a measure of the local failure in the vicinity of the flaw as a function of the specified loading conditions. Local failure can be defined 45

62 in terms of a maximum peak strain in the remaining ligament of the flaw. One recommendation is to limit the peak strains at any point in the model to 5%. Alternatively, a measure of local failure can also be established by placing a limit on the net section stress in the remaining ligament of the flaw when material strain hardening is included in the analysis. In addition, the operational requirements of the component (i.e. local deformation); constraint effects related to the hydrostatic stress, material ductility, the effects of the environment; and the effects of localized strain which can result in zones of material hardness that may be subject to damage from the environment should be considered. An alternate method to determine structural integrity of a component may be used in place of calculating plastic collapse loads. Applied loads in a finite element analysis may be increased by a multiplier, and the stability of the component with respect to the loads can be determined with non-linear elastic-plastic FEA and the global and local criteria. This procedure is referred to as Load and Resistance Factor Design (LRFD) API 579, Level 3 Assessment (Lower Bound Limit Load) The following procedure for performing a Level 3 assessment using LRFD for a volumetric flaw is provided in API 579 and is also known as the lower bound limit load. The procedure may be modified based on specific application, component configuration, material properties, and loading conditions. It is not applicable to cyclic loading conditions. Step 1: Develop a finite element model of the component including all relevant geometry characteristics. The mesh used for the finite element analysis should be designed to accurately model the component and flaw geometry. In addition, mesh refinement around areas of stress and strain concentrations should be included. Based on the experience of the Engineer performing the analysis, the analysis of one or more finite element models may be required to ensure that an accurate description of the stress and 46

63 strains in the component is achieved. This type of model evaluation is particularly important for non-linear analysis. Step 2: Define all relevant loading conditions including pressure, supplemental loads and temperature distributions. Step 3: An accurate representation of material properties should be included in the finite element model. An elastic-plastic material model with large displacement theory should be used in the analysis. The Von Mises yield function and associated flow rule should be used if plasticity is anticipated. Material hardening or softening may be included in the analysis if the material stress-strain curve is available. If hardening is included in the plastic collapse load analysis, it should be based upon the kinematic hardening model, or a combined kinematic and isotropic model. Step 4: Determine the load to be used in the analysis by applying a load multiplier of 1.5 to the actual load. If the component is subject to multiple loads, all of the actual loads should be proportionally scaled with the same multiplier. Step 5: Perform an elastic-plastic analysis. If convergence is achieved in the solution, the component is stable under the applied loads, and the global criteria described above is satisfied. Otherwise, the load as determined in Step 4 should be reduced and the analysis repeated. Note that if the applied loading results in a compressive stress field within the component, buckling may occur, and the effects of imperfections, especially for shell structures, should be considered in the analysis. Step 6: Review the results of the analysis in the areas of high strain concentrations and check the failure parameter chosen to categorize local failure. If the local criteria are not satisfied, the applied loads should be reduced accordingly. Step 7: If the global and local criteria are satisfied, the component is suitable for continued operation subject to the actual loads used in the assessment. Step 8: A check for shakedown should be made if the component is to remain in-service during multiple start-up and shutdowns. This check can be made by removal and re- 47

64 application of the actual load. A few cycles of this load reversal may be necessary to demonstrate shakedown. If significant incremental plastic strains occur during this load cycling (ratcheting), the permissible operating load should be reduced; otherwise, shakedown has occurred Plastic Collapse Load An alternate Level 3 procedure for analyzing a LTA is by using FEA to directly calculate a RSF. The method is known as the plastic collapse load and can be calculated with the following procedure. Step1: Develop a FEA model as described in Step 1 of Paragraph for both the undamaged and damaged geometry of the component. Step 2: Define all relevant loading conditions including pressure, supplemental loads and temperature distributions. Step 3: Include elastic-plastic material properties with kinematic hardening in the FEA models. Step 4: Perform an elastic-plastic analysis for each model with increasing load increments. The load increment that causes instability (no convergence) in the analysis is the plastic collapse load for the component. Step 5: Compare the plastic collapse load of the damaged component to the undamaged component to determine the RSF. The RSF can be used with Equations (5) and (6) to calculate a safe operating pressure or loading condition. Step 6: Rerun the analysis of the damaged component at the safe operating pressure or loading condition and performs Steps 6 8 in Paragraph

65 3.7 COMPARISON OF GENERAL AND LOCAL METAL LOSS The differences between the API 579 assessment procedures for general and local metal loss can be summarized as follows: The general metal loss rules for Level 1 and Level 2 assessments are based on establishing an average thickness. The average thickness is then used with Code rules to determine acceptability for continued operation. Rerates, if required, are based on the Code rules using the average thickness. The local metal loss rules for Level 1 and Level 2 assessments are based on establishing a Remaining Strength Factor. The RSF is then used to determine acceptability for continued operation. Rerates, if required, are based on the Code rules for determining the MAWP and the RSF. The general metal loss rules for Level 1 and Level 2 assessments can be based on point thickness readings (subject to a restriction on the variability in the thickness reading data) or critical thickness profiles. The local metal loss rules for Level 1 and Level 2 assessments are based on critical thickness profiles. The Level 2 assessment procedures for general and local metal loss when applied to corrosion and/or erosion at local structural discontinuities are currently the same and use the general metal loss rules. New Level 2 local metal loss assessment procedures are currently being developed. The Level 3 assessment procedures for general and local metal loss are currently the same. Numerical analysis using elastic-plastic stress analysis techniques is recommended for the assessment. As previously stated, the general and local metal loss rules have been structured to provide consistent results. If the general metal loss rules are applied to an LTA and the assessment results produce a conservative answer, the same LTA can be re-evaluated with the local metal loss rules. The resulting answer will typically be less conservative. Therefore, it is recommended 49

66 by API 579 that regions of corrosion/erosion be evaluated initially with the general metal loss rules, followed by an assessment using the local metal loss rules. 3.8 REMAINING LIFE EVALUATION Overview API 579 includes procedures for estimating the remaining life for components subject to continued corrosion or degradation. Rules to evaluate the current integrity of a component are provided by general and local metal loss assessments. However, a remaining life assessment can be used to calculate a rough estimate to actual time of failure. This type of assessment is valuable in determining an inspection interval, in service monitoring, or urgency of repair. Two procedures can be used to evaluate reaming life, one based on component thickness and the other based on maximum allowable working pressure Thickness Approach Minimum required thickness based on in service conditions, thickness data from inspection, and an estimated corrosion rate can be used to estimate remaining life of a component. This method is applicable for components that do not have thickness interdependency and may be non-conservative when applied to components with this configuration. The remaining life can be estimated as follows: R life t Kt C am am = (66) rate for components with interdependent thickness, the MAWP approach should be used. 50

67 3.8.3 MAWP Approach The MAWP approach for determining remaining life was proposed by Osage [59] and is applicable to all types of pressurized components, including those with thickness interdependency. It also ensures that design pressure is not exceeded during operation as long as the future corrosion rate is correctly estimated. The following procedure for the MAWP approach is taken directly from API 579. Step 1: Determine the metal loss of the component, t loss, by subtracting the average measured thickness at the time of the last inspection, t am, from the nominal thickness, t nom. Step 2: Determine the MAWP for a series of increasing time increments using an effective corrosion allowance and the nominal thickness in the computation. The effective corrosion allowance is determined as follows: CAe = tloss + Crate time (67) Step 3: Determine the remaining life from a plot of MAWP versus time. The time at which the MAWP curve intersects the design MAWP for the component is the remaining life of the component. Step 4: Repeat the Steps 1, 2 and 3 for each component. The equipment remaining life is taken as the smallest value of the remaining lives computed for each of the individual components. 51

68 CHAPTER IV LTA ASSESSMENT PROCEDURES FOR CIRCUMFERENTIAL STRESS 4.1 INTRODUCTION This section contains a compilation of the LTA assessment methods published in the public domain for evaluating the circumferential stress direction in cylindrical shells. All the methods in this section will be used in the statistical validation to determine the most reliable method. A complete summary of all the methods provided in Table 5. Each method is assigned a number, and the method number will be used to identify each in the statistical analysis results. Where possible, the methods have been converted to a standard calculation format for ease of comparison. Methods are presented in their original form and then recast into the standard calculation form whenever possible. For assessment of flaws governed by the circumferential stress direction only, methods for assessment include the original and modified B31.G methods, the Battelle method, the API 579 methods and hybrids, the Chell based methods, the British Gas methods, and the BS 7910 methods. The modified API 510 and API 653 thickness averaging methods and the Kanninen method are included, but are applicable to both the circumferential and longitudinal stress direction. 4.2 CALCULATION OF UNDAMAGED MAWP For the calculation of MAWP of an undamaged component, the following general equation is used unless otherwise specified: MAWP 0 = σ t a R + 0.6t 52 (68)

69 Different design codes may use different design equations for the MAWP, but the differences result in a negligible change in the MAWP calculation. Where a specific design code has the largest impact on calculated MAWP is in the allowable stress basis. The allowable stress can be significantly different for different design codes, leading to a large variation in the safety margin between the calculated MAWP and the calculated failure pressure. The non-uniform margin on calculated MAWP is addressed in later sections by varying the allowable remaining strength factor. 4.3 CALCULATION OF UNDAMAGED FAILURE PRESSURE The estimated undamaged failure pressure is calculated using methodology developed and validated by Svensson [60]. The method is an internal pressure to inner and outer bore strain relationship for a material that has the following stress-strain relationship. σ σε n = 0 (69) The variables n and σ 0 are parameters to define the true stress true strain curve for the material. For a thick wall cylinder, the following relationship between pressure and the material stress-strain curve is as follows. The 1 and 2 locations are the inner radius and outer radius, respectively. ε 2 n ε P= σ dε (70) 0 3ε ε 1 e 1 The formulation for a thick walled sphere is as follows. ε 2 n ε P= σ dε (71) 0 1.5ε 1 e ε1 For the condition where the pressure is at the strain based failure pressure, the following conditions must be satisfied. 53

70 dp = 0 dε1 (72) n 3ε1 ε 1 e = 2 ε2 R o 3ε1 ( e ) 1 1 R i log 1 ( 1 ε R o ε = e e ) 3 R i 2 (73) (74) For a given true stress-strain curve, the above equations can be solved using various numerical techniques to calculate the inner and outer strain values and evaluate the integral to determine burst pressure. The following simplified solution can be derived for a thin wall cylinder, but for the calculations in this study, the thick wall solution is always used. P f t n = 2 σ 0 n 1 Ri e + n ( 3) (75) For spheres, the simplified solution is as follows. P f σ t n = 0 Ri e n 2 3 n+ 1 n (76) The thick walled formulation for a cylindrical shell was compared to FEA to validate the accuracy. The FEA models were run with non-linear geometry and an elastic-plastic true stressstrain curve. The results from the FEA and the above methodology are almost identical. The validation cases and results are shown in Table 6. 54

71 4.4 CALCULATION OF DAMAGED MAWP AND DAMAGED FAILURE PRESSURE All the analysis methods presented here have been recast in terms of a standard calculation format where applicable in order to provide a standard means for comparison of the methods. Conversion to the format does not change the values calculated by each method; it only rearranges the variables to be consistent between all the methods. The standard format consists of evaluating an LTA by calculating certain factors with the following steps: Step 1: Calculate flaw area and original area. The procedure for calculating the flaw area will vary from method to method. The original area is always the undamaged component thickness times the length of the LTA. For methods that have an incremental approach, the area calculation will be referred to as the effective area. The effective area involves subdividing a LTA into sections centered on the deepest point on the critical thickness profile in order to prevent an un-conservative result for highly irregular profiles (See Figures 11 and 12). For a LTA that is very long, but with only one very deep location, this prevents the severity of the damage from being averaged out over the length of the flaw. The following equations are used to calculate the areas for the different methods. A0 = t l (undamaged area) (77) A= d l (rectangular area) (78) 2 A = d l (parabolic area) (79) 3 A = 0.85d l (equivalent area) (80) l 0 ( ) A = d x dx (exact area) (81) 55

72 ( e s) i i i A = t l l (effective undamaged area) (82) ( e s) i i i A = d l l (effective rectangular area) (83) i A i le i ls ( ) = d x dx (effective area) (84) Step 2: Calculate the lambda (λ) non-dimensional geometry factor and the Folias factor, M t. The Folias factor is based on lambda and both vary between methods. Step 3: Calculate the surface correction factor, M s based on area ratio and the Folias factor. There are two forms of M s as shown below. M s A 1 1 A0 Mt = A 1 A0 (B31.G) (85) M s 1 = A A A A M 0 0 t (Chell) (86) Step 4: Calculate an RSF. The RSF is usually calculated as follows. 1 RSF = (87) M s Step 5: Calculate the final MAWP for the corroded component using Equations (5) and (6). The failure pressure for the corroded component can be calculated with the following equation. f 0 ( ) P = P RSF (88) 56

73 This procedure is used with every method presented in this chapter where applicable. Each method is presented in its original format and the standard format whenever possible. 4.5 THICKNESS AVERAGING ASSESSMENT Overview Thickness averaging is the simplest method used to evaluate LTAs and was developed to provide a reasonable result for areas of general metal loss based on the average thickness of the region. The method is not accurate for complex areas of metal loss and will produce the most conservative results of all the methods. The thickness averaging methods do not conform to the standard calculation format described in Paragraph API 510 Assessment (Method 8) The API 510 assessment methodology consists of averaging thickness readings over a specified length and comparing the average thickness to limiting thickness. The average measured thickness, t am, is determined by averaging the thickness readings over the following lengths: D L min =, 20 inches when D 60 inches 2 (89) D L min =, 40 inches when D > 60 inches 3 (90) The required strength check is as follows: t CA t (91) am min An additional check is made on the minimum measured thickness: 57

74 t CA 0.5t (92) mm min A MAWP and failure pressure can be calculated using the design equations and average measured thickness over the specified region as follows. σ atam MAWP = R t am (93) P f = σ utstam R + 0.6t am (94) API 653 Assessment (Method 9) The API 653 assessment methodology consists of averaging thickness readings over a specified length and comparing the average thickness to limiting thickness. The average measured thickness, t am, is determined by averaging the thickness readings over the following length: L = max 3.7 Dtmm, 40.0inches (95) The required strength check is as follows: t CA t (96) am min An additional check is made on the minimum measured thickness: t CA 0.6t (97) mm min A MAWP and failure pressure can be calculated using the design equations and average measured thickness over the specified region with Equations (93) and (94). 58

75 4.5.4 API 579, Section 4 Level 1 and 2 Assessment (Methods 25 and 26) The API 579, Section 4 Level 1 and Level 2 assessment for general regions of metal loss is also a variation of the thickness averaging methodology and is presented in Paragraphs and III respectively. These methods are used as screening criteria for a local metal loss assessment. They were never meant to actually be used in the assessment of local metal loss, but are still included in the statistical comparison of the LTA assessment methods. Like the other thickness averaging methods, a MAWP and failure pressure can be calculated using the design equations and average measured thickness over the specified region with Equations (93) and (94) 4.6 ASME B31.G ASSESSMENT Overview The B31.G assessment method was designed to more accurately assess corrosion in pipe lines and is included in ASME B31 Codes for Pressure Piping. The procedure was developed based on full-scale burst tests of defected pipes. Mathematical expressions were developed semi-empirically and based on fracture mechanics principles. The original method is a combination of a Dugdale plastic zone size model, a Folias analysis of an axial crack in a pressurized cylinder, and an empirically established flaw depth to pipe thickness relationship. The original B31.G method has evolved over time with the addition of new burst tests and data. Methods 4, 5, 6, and 7 in are the original B31.G method and its modifications including the RSTRENG method Original ASME B31-G Assessment (Method 7) The original B31-G LTA assessment method was first presented in the following form. 59

76 2 d 1 3 t P' = 1.1P 2 d t M for 2 l 20 Dt (98) P' 1.1P 1 d = t for 2 l 20 Dt > (99) By inspection, it is evident that the remaining strength factor and allowable remaining strength factor can be written as follows RSF = (100) a 2 d 1 3 t RSF = 2 d t M for 2 l 20 Dt (101) RSF 1 d = t for 2 l 20 Dt > (102) From this, an original allowable RSF of (1/1.1) is specified. Since the surface correction factor defined in the standard format is equal to one over the RSF, the surface correction factor can be written as follows. M s 2 d t M = 2 d 1 3 t for 2 l 20 Dt (103) M s 1 = d 1 t for 2 l 20 Dt > (104) 60

77 The surface correction factor can be converted to areas by multiplying the LTA depth and original thickness by the length of the LTA. The area of metal loss is assumed to be rectangular with respect to the maximum depth and length of the LTA. The surface correction factor can be rewritten as follows. M s A 1 1 A M 1 A 0 0 = A for 2 l 20 Dt (105) In Equation (105), the undamaged area and parabolic damaged area are calculated using Equations (77) and (79). M s 1 = A 1 A 0 for 2 l 20 Dt > (106) In Equation (106), the undamaged area and rectangular damaged area are calculated using Equations (77) and (78). The original form of the Folias factor was presented as follows. M l = + Dt 1/2 (107) The Folias factor and the dimensional limits can be converted to the non-dimensional parameter, lambda, as follows. λ = l (108) Dt l Dt λ = (109) 2 M t 2 = λ (110) 61

78 2 l Dt 20 becomes λ 5.75 (111) 2 l Dt > 20 becomes λ > 5.75 (112) The original B31.G equations can be recast in terms of the standard format and calculated with the following steps. Step 1: Calculate the undamaged area and parabolic damaged area using Equations (77) and (79). The defect area is a parabolic estimate based on the maximum depth and total length of the defect. Step 2: Calculate λ and the Folias factor, M t. l λ = (115) Dt o M t 2 = λ for 5.75 λ (116) Step 3: Calculate the B31.G surface correction factor, M s. M s A 1 1 A0 Mt = A 1 A0 for λ 5.75 (117) M s 1 = A 1 A 0 for λ > 5.75 (118) Step 4: Calculate the RSF as described in Paragraph 4.4. Step 5: Calculate new MAWP and failure pressure as described in Paragraph

79 4.6.3 Modified B31-G Assessment, 0.85dl Area (Method 4) The modified B31-G, 0.85 dl Area method is essentially the same as the original. The difference between the two methods is in estimation of defect area and calculation of the Folias factor. The Folias factor for this method was developed by the American Gas Association (AGA). The original presentation of this method is as follows: d P' = P 1 + t σ d 1 ys t M (119) By inspection, the following is apparent from the above equation = 1+ RSF a σ ys (120) d RSF = t d t M (121) The RSF can be written in terms of a surface correction factor and areas in the same manner as the original B31.G method. In the modified B31.G method, the Folias factor is slightly different and is written as follows. M l l = 1+ 2 Dt 4 D t 2 2 1/2 for 2 l 50 Dt (122) M 2 l = for Dt 2 l 50 Dt > (123) The Folias factor equations can be rewritten using lambda in place of l 2 /Dt as follows. 63

80 l Dt λ = (124) 2 M λ λ 2 4 t = for 9.1 λ (125) M t 2 = λ for 9.1 λ > (126) The allowable remaining strength factor is different from the original B31.G method and is dependant on the material properties. It can be written as follows. RSF a = σ ys σ ys (127) The Modified B31.G, 0.85 dl area method can be calculated in terms of the standard format as follows. Step 1: Calculate the undamaged area and equivalent damaged area using Equations (77) and (80). Step 2: Calculate λ and the Folias factor, M t. l λ = (128) Dt o M λ λ 2 4 t = for 9.1 λ (129) M t 2 = λ for 9.1 λ > (130) Step 3: Calculate the B31.G surface correction factor, M s, using Equation (85) in Paragraph 4.4. Step 4: Calculate the RSF as described in Paragraph 4.4. Step 5: Calculate new MAWP and failure pressure as described in Paragraph

81 4.6.4 Modified B31-G Assessment, Exact Area (Method 6) The exact area modified B31.G method is exactly the same as the 0.85dl method, except for the defect area calculation. The defect area is more accurately calculated by numerically integrating the defect profile. The same procedure detailed in Modified B31.G Assessment, 0.85dl Area can be used with the following modifications. Step 1: Calculate the undamaged area and exact damaged area by numerically integrating the defect profile using Equations (77) and (81). Step 2: Calculate λ and the Folias factor, M t, with equations (128), (129), and (130). Step 3: Calculate the B31.G surface correction factor, M s, using Equation (85) in Paragraph 4.4. Step 4: Calculate the RSF as described in Paragraph 4.4. Step 5: Calculate new MAWP and failure pressure as described in Paragraph RSTRENG METHOD (METHOD 5) The RSTRENG method differs from other B31.G methods in that it is an iterative calculation. The flaw profile is divided into sections as described in Step 1 and an RSF is calculated based on the current section. The advantage of the iterative approach is that very deep locations in an otherwise shallow flaw are not averaged out over the length of the defect. The final RSF is equal to the lowest value calculated for all the section iterations. The lambda and Folias factors along with the surface correction factor are the same as described for the B31.G modified 0.85dl assessment. The current API 579 Level 2 assessment method is based on the RSTRENG iterative procedure. Step 1: Starting with the deepest location in the critical thickness profile, partition the LTA into i sections. Calculate the effective undamaged area and effective damaged area for each section using Equations (82) and (84). Step 2: Calculate λ and the Folias factor, M t for each section. 65

82 i i ( le ls) i λ = (131) Dt o ( ) ( ) i i i t i M = + λ λ for λ 9.1 (132) M i t i ( λ ) 2 i = for λ > 9.1 (133) Step 3: Calculate the B31.G surface correction factor, M s, for each section. M i s i A 1 1 i i A0 Mt = i A 1 i A0 (134) Step 4: Determine the minimum remaining strength factor as follows for all the sections: RSF i 1 = (135) i M s RSF RSF RSF RSF 1 2 i = min,,..., (136) Step 5: Calculate new MAWP and failure pressure as shown in Paragraph PCORR ASSESSMENT (METHOD 20) The PCORR method was developed by Battelle as part of ongoing research into the fundamental mechanisms driving failure of pipeline corrosion defects. The focus was to derive a more analytical, as opposed to empirical, method for predicting failure of general and complex LTAs. A finite element analysis tool called PCORR was developed to aid in the research. The procedure presented here is the final closed form model for the failure of blunt defects in pipelines that are general in nature and that can be applied to critical defect problems in the 66

83 pipeline industry. The method is only applicable to high toughness steels, so its flexibility is limited. The original Battelle method was designed to predict the failure pressure of damaged pipe and was originally presented as follows. P d 2t d l = σ uts 1 1 exp D t Rt * (137) By inspection, the failure pressure for an undamaged component, and the RSF can be separated as follows. P 0 2t = σ uts and D d RSF = 1 1 exp t l Rt * (138) Since this method is designed to calculate a failure pressure, no allowable RSF is needed. This method does not use the Folias factor or surface correction factor in the calculation, but an equivalent Folias factor can be derived using the definition of the surface correction factor in terms of rectangular area and the definition of lambda as follows. λ = i l D t ( d) or l Rt * λ 2 = (139) M s d t Mt 1 = = = RSF d 1 d l t 1 1 exp t * Rt (140) Substituting lambda in the above equation and solving for the Folias factor yields the following equation. M t d 1 1 exp t = exp ( λ ) ( λ ) (141) 67

84 The Battelle assessment method can be calculated in the API 579 format with the following steps: Step 1: Calculate the undamaged area and rectangular damaged area using Equations (77) and (78). Step 2: Calculate λ and the Folias factor, M t. λ = i l D t ( d) (142) M t d 1 1 exp t = exp ( λ ) ( λ ) (143) Step 3: Calculate the B31.G surface correction factor, M s, using Equation (85) in Paragraph 4.4. Step 4: Calculate the RSF as described in Paragraph 4.4. Step 5: Calculate new MAWP and failure pressure as described in Paragraph API 579 ASSESSMENT Overview The current API 579 Level 1 and 2 assessments for regions of local metal loss are presented in Paragraphs and These assessments are shown below in the standard calculation format as methods 1 and 2. Method 3, as shown in Paragraph 4.9.4, is a modified version of the API 579 Section 5, Level 2 assessment that calculates the exact area of metal loss instead of using the effective area iterative procedure. Three hybrid assessments based on API 579 assessment methodology are also included in this section. All of the Level 1 assessments use the rectangular area formulation. 68

85 4.9.2 API 579 Section 5, Level 1 Analysis (Method 1) Step 1: Calculate the undamaged area and rectangular damaged area using Equations (77) and (78). Step 2: Calculate λ and the Modified B31.G Folias factor, M t. l λ = (144) Dt i M t 2 = λ (145) Step 3: Calculate the B31.G surface correction factor, M s, using Equation (85) in Paragraph 4.4. Step 4: Calculate the RSF as described in Paragraph 4.4. Step 5: Calculate new MAWP and failure pressure as described in Paragraph API 579 Section 5, Level 2 Assessment, Effective Area (Method 2) The API 579, Level 2 effective area method is identical to RSTRENG (method 5) except the Folias factor has been modified. The level 2 assessment differs from level 1 by the area calculation and Folias factor. Step 1: Starting with the deepest location in the critical thickness profile, partition the LTA into i sections. Calculate the effective undamaged area and effective damaged area for each section using Equations (82) and (84). Step 2: Calculate λ and the Folias factor, M t. i i ( le ls) i λ = (146) Dt i 69

86 M t = i 2 i 4 ( λ ) ( λ ) i 6 i ( λ ) ( )( λ ) (147) Step 3 Step 5: See the Modified B31-G Assessment, Effective Area RSTRENG method, Steps 3 through 5 in Paragraph API 579 Section 5, Level 2 Assessment, Exact Area (Method 3) The same procedure detailed in can be used with the following modifications in steps: Step 1: Calculate the undamaged area and exact damaged area by numerically integrating the defect profile using Equations (77) and (81). Step 2: Calculate λ and the Folias factor, M t. l λ = (148) Dt i M t = λ λ ( ) λ λ (149) Step 3: Calculate the B31.G surface correction factor, M s, using Equation (85) in Paragraph 4.4. Step 4: Calculate the RSF as described in Paragraph 4.4. Step 5: Calculate new MAWP and failure pressure as described in Paragraph API 579 Hybrid 1, Level 1 Assessment (Method 14) The API 579 Hybrid 1 assessment follows the same procedure as the current API 579 assessments. The λ factor and surface correction factor calculation from the Chell method in Paragraph have been substituted into the assessment as well as the B31.G Folias factor. 70

87 Step 1: Calculate the undamaged area and rectangular damaged area using Equations (77) and (78). Step 2: Calculate the Chell λ and B31.G Folias Factor, M t. πl λ = (150) 4 Dd i M t 2 = λ (151) Step 3: Calculate the Chell surface correction factor, M s, using Equation (86) in Paragraph 4.4. Step 4: Calculate the RSF as described in Paragraph 4.4. Step 5: Calculate new MAWP and failure pressure as described in Paragraph API 579 Hybrid 1, Level 2 Assessment (Method 15) The Level 2 Hybrid 1 assessment is identical to the Level 1 assessment except the effective area procedure is used. Step 1: Starting with the deepest location in the critical thickness profile, partition the LTA into i sections. Calculate the effective undamaged area and effective rectangular damaged area for each section using Equations (82) and (83). Step 2: Calculate the Chell λ and Folias Factor, M t, for each increment. ( le ls) i i π i λ = (152) 4 Dd i M i t i = ( λ ) 2 (153) Step 3: Calculate the Chell surface correction factor, M s, for each increment. 71

88 M 1 = A A 1 1 i + i i A0 A0 Mt i s i i (154) Step 4 Step 5: See the Modified B31-G Assessment, Effective Area RSTRENG method, Steps 4 and 5 in Paragraph API 579 Hybrid 2, Level 1 Assessment (Method 16) Hybrid 2 is identical to Hybrid 1 except that a depth dependant lambda and the BG Folias factor is used. The Level 1 assessment is as follows. Step 1: Calculate the undamaged area and rectangular damaged area using Equations (77) and (78). Step 2: Calculate λ and British Gas Folias factor, M t. l λ = (155) Dd i M t 2 = λ (156) Step 3: Calculate the Chell surface correction factor, M s, using Equation (86) in Paragraph 4.4. Step 4: Calculate the RSF as described in Paragraph 4.4. Step 5: Calculate new MAWP and failure pressure as described in Paragraph API 579 Hybrid 2, Level 2 Assessment (Method 17) The Level 2 Hybrid 2 assessment is identical to the Level 1 assessment except the effective area procedure is used. 72

89 Step 1: Starting with the deepest location in the critical thickness profile, partition the LTA into i sections. Calculate the effective undamaged area and effective damaged area for each section using Equations (82) and (84). Step 2: Calculate λ and the British Gas Folias factor, M t, for each increment i i ( le ls) i λ = (157) Dd i M i t i = ( λ ) 2 (158) Step 3: See API 579 Hybrid 1, Level 2 Assessment, Step 3 in Paragraph Step 4 Step 5: See the Modified B31-G Assessment, Effective Area RSTRENG method, Steps 4 and 5 in Paragraph API 579 Hybrid 3, Level 1 Assessment (Methods 18) Hybrid 3, like hybrid 2, uses different equations for λ, M t, and M s. The depth dependant lambda and Chell surface correction factors are used. A new Folias factor has been developed based on actual test data and is incorporated into the method. The details of the new JO Folias factor are presented in Paragraph Step 1: Calculate the undamaged area and rectangular damaged area using Equations (77) and (78). Step 2: Calculate λ using Equation (155) and the JO Folias factor, M t. M t d = λ λ t (159) Step 3 Step 5: See API 579 Hybrid 1, Level 1 Assessment, Steps 3 through 5. 73

90 API 579 Hybrid 3, Level 2 Assessment (Method 19) The Level 2 Hybrid 3 assessment is identical to the Level 1 assessment except the effective area procedure is used. Step 1: Starting with the deepest location in the critical thickness profile, partition the LTA into i sections. Calculate the effective undamaged area and effective damaged area for each section using Equations (82) and (84). Step 2: Calculate λ using Equation (157) and the JO Folias factor, M t, for each increment M t i d λ λ λ i ( ) = t (160) Step 3: See API 579 Hybrid 1, Level 2 Assessment, Step 3 in Paragraph Step 4 Step 5: See the Modified B31-G Assessment, Effective Area RSTRENG method, Steps 4 and 5 in Paragraph API 579 Modified, Level 1 Assessment (Method 27) The modified API 579 methods are identical to the current API 579 methods except that the Folias factor has been modified to include very long flaws (no lambda limitation). The details of the modified API 579 Folias factor are presented in Paragraph The Level 1 assessment can be calculated as follows. Step 1: Calculate the undamaged area and rectangular damaged area using Equations (77) and (78). Step 2: Calculate λ and the Janelle Folias factor, M t. l λ = (161) Dt i 74

91 M λ λ λ 2 3 t = λ 5 λ + ( 4 6 ) λ ( ) ( ) ( ) ( ) λ λ λ λ (162) Step 3: Calculate the B31.G surface correction factor, M s, using Equation (85) in Paragraph 4.4. Step 4: Calculate the RSF as described in Paragraph 4.4. Step 5: Calculate new MAWP and failure pressure as described in Paragraph API 579 Modified, Level 2 Assessment (Method 28) The API 579 Modified Level 2 assessment uses the effective area instead of the rectangular area and can be calculated as follows. Step 1: Starting with the deepest location in the critical thickness profile, partition the LTA into i sections. Calculate the effective undamaged area and effective damaged area for each section using Equations (82) and (84). Step 2: Calculate λ and the Janelle Folias factor, M t. i i ( le ls) i λ = (163) Dt i i i 2 i 3 ( ) ( ) ( ) i 4 i 5 4 i 6 ( λ ) ( λ ) + ( )( λ ) 5 i 7 i 8 i ( )( λ ) ( )( λ ) ( )( λ ) 10 i 10 ( )( λ ) M = λ λ λ + t (164) Step 3 Step 5: See the Modified B31-G Assessment, Effective Area RSTRENG method, Steps 3 through 5 in Paragraph

92 4.10 CHELL ASSESSMENT Overview In the Chell method, a different surface correction factor is introduced into the original B31.G assessment method. Like the original B31.G method, the Chell surface correction factor was originally developed to analyze crack like flaws. The Chell surface correction factor behaves better for deep flaws than the surface correction factor introduced in B31.G. The surface correction factors differ as follows: M s d 1 1 t Mt = d 1 t (B31.G) (165) M s 1 = d d t t Mt (Chell) (166) The Chell surface correction factor is a more analytical solution than the empirically based original surface correction factor and is derived by treating a cylinder with metal loss as two separate cylinders. The area of metal is assumed to be a rectangle encompassing the area of metal loss. Cylinder 1 is equal to the undamaged cylinder. Cylinder 2 has the radius of cylinder 1 with thickness equal to the depth of the area of metal loss. The failure pressures of cylinders 1 and 2 are calculated as follows. P cylinder1 f σ R t uts = (167) P cylinder 2 f σ R d t t uts = (168) 76

93 Subtracting the failure pressures for cylinder 2 from cylinder 1 will yield the failure pressure for a cylinder with thickness equal to the minimum measured thickness of the original cylinder containing the flaw as follows: P σ R σ R d = t t t tmm uts uts f (169) The failure pressure for cylinder 2 containing the flaw is calculated based on the Folias factor as follows: P flaw f σ utsr d 1 = t t Mt (170) By adding the failure pressure for the cylinder with minimum measured thickness and the failure pressure for cylinder 2 containing the flaw, the failure pressure for the original cylinder with the flaw can be calculated as follows. P = P + P (171) tmm flaw f f f P f σutsr σutsr d σutsr d 1 = + t t t t t Mt (172) P σ R = (173) t 0 uts f P f 0 d d 1 = Pf 1 + t t Mt (174) By definition, the failure pressure for a cylinder containing a flaw is equal to the undamaged failure pressure multiplied by a remaining strength factor. d d 1 RSF = 1 + t t Mt (175) 77

94 1 RSF = (176) M s M s 1 = d d t t Mt (177) It can be shown that as the solution approaches a through wall flaw (d = t), the Chell surface correction factor goes to infinity while the B31.G surface correction factor is simply equal to the Folias factor. This causes better behavior with the Chell surface correction factor for deep flaws. Also, an alternate lambda parameter has been derived from the Chell work Chell Assessment (Method 12) The Chell assessment method can be calculated with the following steps: Step 1: Calculate the undamaged area and exact damaged area by numerically integrating the defect profile using Equations (77) and (81). Step 2: Calculate the Chell λ and the B31.G Folias factor, M t. πl λ = (178) 4 Dd i M t λ 2 = (179) Step 3: Calculate the Chell surface correction factor, M s, using Equation (86) in Paragraph 4.4. Step 4: Calculate the RSF as described in Paragraph 4.4. Step 5: Calculate new MAWP and failure pressure as described in Paragraph

95 Modified Chell Assessment (Method 13) The modified Chell uses a D/t dependent Folias factor and an effective area calculation. The Chell procedure can be used with the following modifications. Step 1: Starting with the deepest location in the critical thickness profile, partition the LTA into i sections. Calculate the effective undamaged area and effective rectangular damaged area for each section using Equations (82) and (83). Step 2: Calculate the Folias factor as follows, where A mm, and A mb are functions that are defined by the ratio of the diameter to the thickness. The below factors were developed based on a through wall crack like flaw in a cylinder. ( ),( ) MT = Max Amm + Amb Amm Amb (180) The parameters A mm and A mb are evaluated using the information in Table 7 with λ computed from the following equation: 1.818l λ = (181) R t i Step 3: Calculate the Chell surface correction factor, M s, using Equation (86) in Paragraph 4.4. Step 4: Calculate the RSF as described in Paragraph 4.4. Step 5: Calculate new MAWP and failure pressure as described in Paragraph BRITISH GAS ASSESSMENT Overview LTA defects are separated into two categories in the British Gas methods: single defects and complex defects. A single defect is defined as an isolated pit or area of general corrosion. Complex defects are groups of pits or general corrosion. The single defect analysis can be used 79

96 as a lower bound for complex defect analysis. The same basic equations for assessment are used by both analysis methods. A Folias factor that was developed based on finite element test cases is used to calculate the RSF. The finite element test cases of single, semi-elliptical shaped defects based on varying d/t and lambda were used. The FEA models were then used to develop a new Folias factor by curve fitting the results. To develop the BG Folias factor, the following base equation was used. M t l = 1+ C Dt B (182) Initially, C and B were allowed to vary in the curve fit, but based on the B31.G form of this equation, B was set to two. For the final curve fit of the FEA results, a best fit of C=0.31 was derived and the final equation is as follows: M t l = Dt 2 (183) The complex defect analysis uses the same equations to calculate an RSF. The only difference is the defect is broken into about fifty different depth increments and the geometric variables are based on all the included defects. An RSF is calculated at each depth increment, and the worst case RSF is the final result similar to the effective area approach. Interaction rules are provided to determine whether a flaw can be treated as a single defect or a complex defect. A flaw can be treated as a single defect if the depth of the flaw is less than 20% of the wall thickness or if the following equations are satisfied. 3 t φ > 360 (184) π D s > 2 Dt (185) 80

97 Phi is the circumferential spacing between defects, and s is the longitudinal spacing between defects. If the longitudinal defect spacing is less than the limit, the defects will interact if the following conditions are satisfied. d 1 dl 11+ dl t t l + l + s 1 2 > d1 1 dl 11+ dl tq 1 tq12 l1 + l2 + s (186) d 1 dl 11+ dl t t l + l + s 1 2 > d2 1 dl 11+ dl tq 2 tq12 l1 + l2 + s (187) Q = + l Dt 2 (188) Q = + l Dt 2 (189) + + = + Dt 1 2 Q l l s 2 (190) British Gas Single Defect Analysis (Method 10) The British Gas method for the single defect was originally presented in the following form. P f d 1 = P t 0 d 1 1 tq (191) 81

98 l Q = Dt 2 (192) Q is the British Gas Folias factor and the RSF is calculated as follows. d 1 RSF = t d 1 1 tq (193) The RSF is in terms of the surface correction factor and can be simply recast in terms of rectangular areas. The British Gas Folias factor can be written in terms of lambda with the following relationship. 2 2 l λ = Dt (194) M t λ 2 = (195) The British Gas single defect analysis can be calculated as follows in terms of the standard format. Step 1: Calculate the undamaged area and rectangular damaged area using Equations (77) and (78). Step 2: Calculate the British Gas Folias factor, M t, based on λ. l λ = (196) Dt o M t λ 2 = (197) Step 3: Calculate the B31.G surface correction factor, M s, using Equation (85) in Paragraph 4.4. Step 4: Calculate the RSF as described in Paragraph

99 Step 5: Calculate new MAWP and failure pressure as described in Paragraph British Gas Complex Defect Analysis (Method 11) The British gas complex defect analysis uses an iterative process to calculate failure pressure. The method divides a complex LTA into several depth increments as shown in Figure 16. At each increment, failure pressure is calculated for the total LTA, each individual LTA that may be formed based on the depth increment, and the interaction of individual LTAs. A minimum failure pressure is obtained at each depth increment, and the minimum failure pressure for the LTA is most limiting result for all the increments. Since the complex defect analysis is iterative, it is difficult to put it in terms of the standard format. For this reason, it is presented in its original format, except for the calculation of the Folias factor. Step 1: Calculate the failure pressure for a defect free section of pipe and the average depth of the LTA with numerically integrated area. P 0 = 2tσ uts ( D t) (198) d ave A = (exact area) (199) l Step 2: Calculate the failure pressure for the total defect. l λ = (200) Dt o M t λ 2 = (201) 83

100 P total dave 1 t = P o dave 1 1 t Mt (202) Step 3: Select the number of depth increments to partition the LTA and calculate the incremental depth based on the maximum depth and number of increments. d j d # inc max = (203) Step 4: For each depth increment, calculate the average depth of the patch. d patch A patch = (exact area) (204) l total Step 5: Calculate the failure pressure of the patch. P patch d patch 1 t = P o d patch 1 1 t Mt (205) Step 6: Determine the number of pits and calculate the average depth of each individual LTA. i = # individual LTA' s (206) d i A ilta, = (exact area) (207) l i Step 7: Determine the equivalent thickness for each individual LTA. t e = P patch D ( 2σ uts + Ppatch ) for i= N d l < A (208) j i patch i= 1 84

101 te = t for i= N d l A (209) j i patch i= 1 Step 8: Determine the equivalent average depth of each individual LTA. ( ) d = d t t (210) ei i e Step 9: Calculate the failure pressure of each individual LTA. li λ i = (211) Dt e M ti = λ (212) 2 i P i = d ei 1 2t t eσ uts e D t e d ei 1 1 te Mti ( ) (213) Step 10: Calculate the overall length of the interacting individual LTAs. i= m 1 l = l + l + s ( ) (total length of LTAs plus spacing) (214) nm m i i i= n Step 11: Calculate the average depth of the interacting LTAs. d enm, = i= m i= n l dl nm ei i (215) Step 12: Calculate the failure pressure of the interacting LTAs. l λ nm nm = (216) Dt e 85

102 M nm = λ (217) 2 nm P nm = denm, 1 2t t eσ uts e e denm, 1 1 te Mtnm ( D t ) (218) Step 13: Determine the final failure pressure and RSF for the LTA. (,,, ) P = MIN P P P P (219) f total patch i nm P f RSF = (220) P 0 Step 14: Repeat Steps 4 through 13 for each depth increment. The failure pressure for this assessment is the minimum pressure obtained for all the depth increments BS 7910 ASSESSMENT The BS 7910 flaw assessment guide uses the British Gas research as its basis for the assessment of local areas of metal loss. Like British Gas, the assessment of local metal loss is based on classifying a flaw as either a single defect or complex or interacting defect. The interactions rules are exactly the same as presented in the British Gas method BS 7910, Appendix G Assessment, Isolated Defect (Method 21) The BS 7910 assessment for a single flaw is exactly the same as the British Gas single flaw assessment procedure presented in Paragraph

103 BS 7910, Appendix G Assessment, Interacting Flaws (Method 22) The BS 7910 assessment for interacting defects uses the BS 7910 isolated defect procedure for each isolated flaw and for all combination of isolated flaw interaction. Unlike the British Gas complex defect assessment, the BS 7910 procedure is no longer iterative. The BS 7910 flaw assessment procedure is as follows: Step 1: Calculate the failure pressure (P1, P2,, P N ) for each of the N isolated defects using the procedure presented for British Gas Single Defect Analysis. Step 2: Calculate the failure pressure for all combinations of the isolated defects using the procedure presented for British Gas Single Defect Analysis and the following equations for flaw length and depth. i= m 1 l = l + l + s ( ) (221) nm m i i i= n d nm = i= m i= n l dl nm i i (222) Step 3: Calculate the failure pressure for the combined defects. (,,...,, ) P = MIN P P P P (223) f 1 2 N nm Step 4: Calculate the MAWP. The f c factor is based on the original design factor. MAWP = f P (224) c f 4.13 KANNINEN ASSESSMENT (METHOD 23) The Kanninen method was developed by the Southwest Research Institute to analyze corroded areas in pipes subject to large axial stress. Large longitudinal stresses can be generated due to end forces and bending moments applied to a pipe in addition to pressure 87

104 loads. The methods presented above focus on pressure loading only, where failure is a function of the circumferential stress. In the Kanninen method, large longitudinal stress is accounted for by computing an equivalent stress based on circumferential and longitudinal stress and comparing it to material ultimate stress for failure or allowable stress for MAWP. The Circumferential stress is compute based on the load conditions and increased with an RSF factor due to the corroded region. The RSF is calculated using a Folias factor derived from shell theory. The longitudinal stress is calculated based on the load conditions and cross sectional properties of the corroded region. The Kanninen method can be calculated as follows. Step 1: Calculate the undamaged area and exact damaged area by numerically integrating the defect profile using Equations (77) and (81). Step 2: Calculate the shell theory Folias factor, M t. η = 1 d (225) t α = l ( d) D t (226) M t = 4 ( 1 η )( coshα sinhα sinα cosα) / η ( cosh α cos α) + 2 2η ( coshα sinhα sinα cosα) + 5/ η ( cosh α cos α) coshα sinα + sinhα cosα + 5/2 2η coshα cosα + 2 η ( sinhα cosα coshα sinα) (227) Step 3: Calculate the B31.G surface correction factor, M s, using Equation (85) in Paragraph 4.4. Step 4: Calculate the RSF as described in Paragraph

105 Step 5: Calculate the equivalent von Mises stress with the following equations. Z = I x D f + y 2 (228) σ = pd M x lm1 4t + Z (229) σ = pd M x lm2 4t Z (230) σ = 1 pd cm RSF 2t (231) σ = σ σ σ + σ (232) 2 2 eq1 cm cm lm1 lm1 σ = σ σ σ + σ (233) 2 2 eq2 cm cm lm2 lm2 σ = max σ, σ (234) eq eq1 eq2 Step 6: Calculated the MAWP and failure pressure by varying the pressure in the above equations until the calculated equivalent von Mises stress is equal to the material allowable stress or material ultimate stress, respectively SHELL THEORY ASSESSMENT (METHOD 24) The shell theory method follows the standard format and uses the shell theory Folias factor presented in the Kanninen method. The shell theory Folias factor has been curve fit using Table Curve 3D as shown in Figure 17. The shell theory method can be calculated with the following steps: 89

106 Step 1: Calculate the undamaged area and exact damaged area by numerically integrating the defect profile using Equations (77) and (81). Step 2: Calculate the shell theory Folias factor, M t. η = 1 d (235) t α = l ( d) D t (External Flaw) (236) M t = η α η α ηα η α η α ηα (237) Step 3: Calculate the Chell surface correction factor, M s, using Equation (86) in Paragraph 4.4. Step 4: Calculate the RSF as described in Paragraph 4.4. Step 5: Calculate new MAWP and failure pressure as described in Paragraph JANELLE METHOD The Janelle method does not involve the calculation of a Folias Factor or surface correction factor. Instead, the RSF is calculated directly from non-dimensional parameters. The development of the Janelle method is described in Paragraph The Level 1 assessment is based on the rectangular defect area, and the Level 2 assessment is based on the effective area Janelle Level 1 Assessment (Method 29) The Level 1 Janelle assessment can be calculated with the following steps. Step 1: Calculate the undamaged area and rectangular damaged area using Equations (77) and (78). Step 2: Compute the Remaining Strength Factor using the following equations. 90

107 l λ = (238) Dt i Z = A A (239) Z 1.0 = λ (240) ( ) RSF = Z Z 1 Z (241) Step 3: Calculate new MAWP and failure pressure as shown in Step 5 of Paragraph Janelle Level 2 Assessment (Method 30) The Level 2 Janelle assessment can be calculated with the following steps. Step 1: Starting with the deepest location in the critical thickness profile, partition the LTA into i sections. Calculate the effective undamaged area and effective damaged area for each section using Equations (82) and (84). Step 2: For each subsection, compute the Remaining Strength Factor using the following equations. i i ( le ls) i λ = (242) Dt i 91

108 Z 1.0 = A i A i 1 i (243) Z 1.0 = λ i 2 i (244) ( ) RSF = Z Z 1 Z i i i i (245) Step 3: Determine the minimum remaining strength factor as follows for all the sections: = (246) 1 2 i RSF min RSF, RSF,..., RSF Step 4: Calculate new MAWP and failure pressure as shown in Step 5 of Paragraph

109 CHAPTER V VALIDATION OF LTA ASSESSMENT PROCEDURES FOR CIRCUMFERENTIAL STRESS 5.1 INTRODUCTION This section contains details of the procedures used to validate the LTA analysis methods presented in Paragraphs 4.5 through 4.15 as well as the theory behind the newly developed analysis methods. The analysis methods were verified by comparing calculated results for a given method to full-scale burst tests and non-linear FEA. Close to one thousand full-scale burst tests and non-linear FEA models were used in the validation. A computer program was used to evaluate each test case with each analysis method and calculate associated statistics. The most accurate assessment method was determined based on the statistical analysis. 5.2 VALIDATION DATABASES There are four separate databases of burst test and FEA cases, which are organized based on their primary source. The cases in the four databases are assigned by numbering convention. Database 1 contains cases numbered from 1 to Similarly, Database 2 cases are numbered from 2000 to 2999, Database 3 cases are 3000 to 3999, and Database 4 cases are 4000 to A complete listing of the databases and their sources are shown in Tables 8, 9, 10, and 11. LTA Database 1: LTA Database 1 is a collection of burst test cases from two primary sources. Cases and are summarized in Kiefner [61], and Cases are summarized in Kiefner [62]. There is also a spreadsheet compiled by Battelle that has a summary of all 222 cases. The cases were compiled and used to develop and 93

110 validate the RSTRENG analysis method. A case by case summary of LTA Database 1 is shown in Table 8. LTA Database 2: The full scale burst tests in LTA Database 2 are from Connelly [63]. These burst tests were also correlated with finite element analysis by Depadova [64]. The 58 LTA tests were performed using two retired pressure vessels. Approximately 30 LTAs were created in each vessel, and the pressure tests were run until leaks occurred. Defects included internal and external LTAs in the shell and heads. A case by case summary of LTA Database 2 is shown in Table 9. The cases in this database were not used in the LTA validation. The vessels were pressurized to the point of plastic deformation multiple times and the results obtained from the test are not consistent with the other databases. LTA Database 3: The burst test cases for local thin areas found in LTA Database 3 are from a British Gas Linepipe Group Sponsored Project reported by Fu [65]. The tests were designed and performed for the development of the British Gas analysis methods. These cases are actual burst tests performed for the project. A case by case summary of LTA Database 3 is shown in Table 10. LTA Database 4: LTA Database 4 is composed of the finite element testing done as part of the British Gas Linepipe Group Sponsored Project performed in conjunction with the test cases in LTA Database 3. In order to determine a failure or burst pressure for the FEA cases, the models were run to the ultimate tensile stress for the material. These cases were reported by Fu [66]. A case by case summary of LTA Database 4 is shown in Table NEW LTA ANALYSIS METHODS New assessment procedures are incorporated in this study in an attempt to improve assessment accuracy. Two approaches were taken. The Hybrid methods were developed based on existing analysis methods. Desirable characteristics were taken from the existing 94

111 methods and combined to develop hybrid methods. The basis for these hybrids is the API 579 format with alterations to the Folias factor and surface correction factor. Hybrids one and two have the best attributes of existing methods combined into a new method. Hybrid three is similar, except that a new Folias factor was derived and included in the method. The new proposed API 579 (Janelle) method was derived directly from actual burst test data and FEA simulation. In the method, the Folias factor and surface correction factor equations are eliminated. The RSF is calculated directly based on the area of metal loss and a non-dimensional length parameter. In addition to developing completely new analysis methods, new Folias factors were developed for the API 579 method to eliminate the limitation on the length of a flaw that may be analyzed. Most of the current Folias factors do not behave appropriately for very long flaws and result in non-conservative evaluations. The new factors were developed based on the original Folias data and by comparison to FEA API 579 Hybrid Assessment Procedures Methods 14 through 19 presented in Paragraph through are newly developed assessment procedures designed to improve upon existing methods. There are three hybrid methods, each with a level one and two assessment. Rectangular area calculations are used in the Level 1 assessment, and the effective area is used in the Level 2 assessment. In all of the hybrids, the B31.G surface correction factor calculation is replaced with the Chell surface correction factor. The API Folias factor is used for Hybrid 1, the British Gas Folias factor is used in Hybrid 2, and a newly developed Folias factor is used in Hybrid 3. The details for development of the new Folias factor are presented in Paragraph The hybrid methods were statistically more accurate than the original API 579 method in the validation process and are not recommended for use. 95

112 5.3.2 New Folias Factor Development for Hybrid Methods The new Folias factor was developed based on a curve fit of the burst test cases. The data points for all the LTA analysis cases were plotted three dimensionally using d/t, lambda, and RSF for the axes. The Chell surface correction factor was used for the fit as follows. d d 1 RSF = 1 + t t Mt (247) The new factor was derived by picking an equation form for the Folias factor M t, and curve fitting that equation to the LTA test cases. The first form chosen was similar to the one derived by British Gas and has the following form. Mt n = C λ (248) 0 l λ = (249) Dd i The values of C 0 and n were derived based on a curve fit using the Table Curve 3D software and the resulting equation was as follows. M t λ = (250) The accuracy of the above equation was not a significant improvement in the predicted RSF. A second Folias factor form was chosen with a direct d/t dependence that is lacking in other forms of the Folias factor. This form was defined as follows. n3 n1 n2 d t = λ + 1λ M C C t (251) The initial curve fit resulted in the following equation. M t d = λ λ 96 t (252)

113 Based on the results of the curve fit, n1 was set to 0.5, n2 was set to 1.0, and n3 was set to 1.5. The equation was refit for C 0 and C 1 with the following final result. M t 0.5 d = λ λ t 1.5 (253) It was determined during the validation process that accuracy was not improved with the above Folias factor, and it is not recommended for use Modified API 579, Level 2 Folias Factor for Long Flaws One of the limitations with the current API 579 assessment of local metal loss is a restriction on the length of a LTA that can be analyzed. The current version of the document has the following length limitation. λ 5.0 > l Dt (254) The limitation reflects the fact that the Folias factor and corresponding RSF calculation do not approach the proper bound as a flaw becomes very long. As a flaw increases in length, the RSF should approach the ratio of the remaining thickness to the undamaged thickness. The current Folias factor does not approach this limit fast enough, resulting in slightly higher RSFs and an un-conservative result. The reason this occurs, is because the data for the development of the original Folias factor only went out to a lambda value of 8. For longer flaws, a linear extrapolation was used, and the assumption that the function remains linear was not accurate. The actual trend for the Folias Factor should approach a very large value as the length of the flaw approaches the following limit based on shell theory. lmax = 20 DT λ = 15 (255) A matrix of axisymmetric and 3D solid FEA models was developed to further investigate the behavior of long flaws. The models included non-linear geometry effects and an elastic-plastic 97

114 material model with kinematic hardening. In all cases, the collapse load calculated for a model containing a flaw was compared to the collapse load of an undamaged model to obtain the RSF for the flaw. The RSF trend with respect to the flaw length is shown in Figure 18 and the FEA details and calculated RSF values are shown in Table 12. Typical geometries for the 3D solid and axisymmetric models are shown in Figures 19 and 20 respectively. In the figure, the current API 579 Folias factors do not follow the trend of the FEA. The original Folias data (to a lambda of 8) was refit and extrapolated to follow the trend of the FEA results as shown in the figure. For lambda values greater than 30, a lambda of 30 should be used in the calculation. The curve fit for the modified Folias factor is shown in Figure 21 and the resulting equation is as follows. M λ λ λ 2 3 t = λ 5 λ + ( 4 6 ) λ ( ) ( ) ( ) ( ) λ λ λ λ (256) For LTAs that have a lambda less than 8, the results of the analysis are identical when using the old or new Folias factor (see Figure 22). Almost all of the cases in the LTA database fall into that category. The results for LTAs with lambda greater than 8 are slightly more conservative with the new Folias factor and approach the limiting value much quicker than the old Folias factor. The new Folias factor will be recommended to replace the existing API 579, Level 2 factor, and the length limitation for the analysis will be removed as the results will no longer be un-conservative for long flaws. A new Level 1 screening curve was also developed with the modified Folias factor and is shown in Figure 23. A comparison between the new screening curve and the old screening curve is shown in Figure 24. The FEA procedure used to investigate long flaws in cylindrical shells was repeated for a spherical shell. The geometry and RSF calculations for the FEA cases are shown in Table 13. A typical geometry for the axisymmetric model is shown in Figure 25. The trends of the FEA and the current API 579 Folias factor for spheres are shown in Figure 26. Based on the trends, the current API 579 Folias factor is applicable to flaws that extend up to the entire inside 98

115 circumference of the shell. The API 579 Folias factor for spherical shells is shown in Equation (53). Tabular data for the cylindrical and spherical shell Folias factors is shown in Table Janelle Method The Janelle method is a departure from the previous methodology and does not include the calculation of the Folias factor or surface correction factor. Instead, the RSF for a given LTA is calculated directly from a non-dimensional LTA length parameter and metal loss damage factor. The RSF formulation is a direct data fit of the actual burst tests and FEA simulations. This method has slightly better scatter statistics than the other methods because it is a curve fit of the actual database cases, but the greatest advantage is how the function is bounded. The function approaches and RSF of 1.0 as the length or depth approaches 0.0, and the RSF approaches the ratio of remaining thickness to undamaged thickness as the length approaches infinity. The curve fit derived from the Table 3D program is shown in Figure 27. This method will be recommended to replace the API 579, Level 2 assessment in a future release of the document. The resulting equations from the fit are as follows. Z = A A (257) Z 1.0 = λ (258) RSF = Z Z ZZ (259) 99

116 5.4 STATISTICAL VALIDATION OF LTA METHODOLOGY USING A FAILURE RATIO In order to validate the analysis methods in this study, comparisons between the methods and actual test cases are required. Pressure ratio assessment is the main tool for determining the statistical accuracy of each LTA analysis method. The failure ratio is defined as follows: Actual Failure Pressure Failure Ratio = Predicted Failure Pressure (260) The actual failure pressure can be obtained two ways. Full-scale vessel or pipe specimens that contain an LTA can be pressurized to failure, or non-linear elastic plastic finite element models of an LTA can be generated and loaded to failure conditions. The predicted failure pressure is calculated with the methods provided in this study. For each of the cases in the database, the ratio is calculated. Statistical analysis based on the calculations is used to quantify the accuracy of each analysis method at calculating these ratios. Databases 1, 3, and 4 were used for the validation and omitted cases are shown in Table 15. All the cases in the databases were analyzed using a computer program that included all the analysis methods and statistics were generated for each method. For the computer program, the inside diameter, shell or pipe thickness, allowable stress ratios based on yield and ultimate stress, an allowable RSF, yield and ultimate stresses, actual failure pressure, and the longitudinal defect profile are required input data. The program output for each method included the calculated failure pressure, calculated MAWP, ratio of calculated failure to actual failure, ratio of calculated MAWP to actual failure, and statistics of the ratios based on all the database cases. The most desirable method is the one with the least amount of scatter in the failure ratio calculations, or the one with the smallest standard deviation. The analysis methods with statistical data are shown in Table 16. Scatter in the data can be attributed to physical phenomenon that can occur with LTAs. Material toughness plays a major role in determining the failure pressure of a damaged component. Most of the methods presented here do not directly consider material toughness in the analysis. Those that make an attempt to include toughness effects, have considered 100

117 materials with very high toughness which is not applicable to many cases that can be found in industry. Another phenomenon that affects the failure of corroded components is triaxial stresses. A high state of triaxiality has been shown to have a significant effect on failure. These conditions can be generated from jagged or non-uniform profiles of metal loss. Methods like the British Gas method, which are solely based on cases with smooth metal loss profiles, do not take this effect into consideration. 5.5 SUMMARY OF VALIDATION RESULTS Based on the statistical results in Table 16, the new Janelle Method (Method 30) is the most accurate. It has a mean failure ratio of nearly 1.0 and the lowest standard deviation of any of the other methods. The most accurate of the old methods are API 579 and modified API 579, Level 2 effective and exact area methods (Methods 2, 3, and 28) and the RSTRENG effective and exact area methods (Methods 5 and 6). The methods that use the effective area are considered superior because they protect against highly irregular metal loss profiles. The Janelle and modified API 579 methods (Methods 28 and 30) do not have a limitation on the length of a flaw that may be analyzed, so have less limitations than the other methods. The modified API 579, Level 2 (Method 28) is recommended for current use. The Janelle Method (Method 30) is recommended to replace the current method in the next release of API

118 CHAPTER VI ALLOWABLE RSF VALUES FOR DIFFERENT DESIGN CODES 6.1 INTRODUCTION Local thin areas are phenomena appearing in a wide variety of field equipment, from pressure vessels to piping to large storage tanks. Based on the type of equipment, different design codes are used in construction. Since the LTA assessment procedures presented are meant for use with most types of equipment, effects of the design code must be taken into consideration. Each design code has different factors to determine allowable material stresses. Using the different values for allowable stress will have no effect on calculating the failure pressure or failure ratio. The difference is in calculating the MAWP; some methods may be too conservative for a certain design code. In this section an allowable RSF vs. MAWP margin will be developed for various design codes. 6.2 DESIGN CODES FOR PRESSURIZED EQUIPMENT All of the following design codes provide a maximum allowable stress, which is calculated from material yield and ultimate stresses as follows: f ys yield stress = (261) allowable stress f uts ultimate stress = (262) allowable stress 102

119 σ = Min F σ, F σ (263) a ys ys uts uts Actual yield and ultimate stresses or minimum values may be used in VCESage, and for the analysis presented here, actual measured stress values from material testing were used. The design code will have no effect on the failure ratio calculation, but does contribute to the MAWP ratio. Some design codes may be over-conservative for calculating the MAWP ratio, allowing for a reduction in the allowable RSF factor. The objective is to determine which allowable RSF best matches each design code. A summary of the design codes and their allowable stresses can be found in Table 17. ASME Section VIII, Division I and Division II [67], [68], [69]: ASME Section VIII design codes cover the fabrication rules for all types of pressure vessels. Section VIII is subdivided into three divisions. Divisions I and II are addressed in this study and described below. Division III is alternate rules for high pressure vessels and not considered in this study. Division I contains the general rules for constructing pressure vessels or design by rule. Division II is the alternate rules for pressure vessel fabrication. Division II is more restrictive in the choice of materials than Division I. It also permits higher design stress intensity values to be used in the range of temperatures over which the design stress intensity value is controlled by the ultimate or yield strength. More detailed design procedures and complete examination, testing, and inspection are required. ASME B31.1, B31.3, B31.4, and B31.8 [70], [71], [72], [73], [74]: The ASME B31 design codes cover all types of piping. ASME B31.1 covers the design, fabrication, and inspection of power piping associated with steam boilers. This type of piping is usually found in electrical power generation stations, industrial plants, institutional plants, geothermal heating systems, and heating and cooling systems. The B31.3 code covers the design, fabrication, and inspection of process piping that is found in refinery and petrochemical plants. This code was formerly referred to as the refinery and chemical plant piping code. It is used in the design of piping that is found in petroleum refineries, 103

120 chemical, pharmaceutical, textile, paper, semiconductor, and cryogenic plants, and related processing plants and terminals. The ASME B31.4 design code covers pipeline transportation systems for liquid hydrocarbons and other hydrocarbons. It is used to design piping for transporting products which are predominantly liquid between plants and terminals and within terminals, pumping, regulating, and metering stations. The B31.8 design code deals with gas transportation and distribution systems. It is used for the design of piping transporting products which are predominately gas between sources and terminals including compressor, regulating, and metering stations and gas gathering pipelines. The code assigns design factors according to pipe classification. The design factor is selected based on five piping location classes described in B31.8. They are location class 1, division 1 and division 2, and location class 3, class 4, and class 5. This code uses yield stress along with the design factor for steel piping system design requirements. The yield times the design factor, F, is essentially the allowable stress used in design. The steel pipe design formula presented is written as: 2St P= ( F E T) (264) D API 620 and API 650 [75], [76]: The design and construction of large, welded, low pressure storage tanks is detailed in API 620. These types of tank include fieldassembled storage tanks that contain petroleum intermediates (gases or vapors) and finished products including other liquid products commonly handled and stored by the various branches of industry. Tank temperature must be less than 250 F and tank gas or vapor space pressure may not exceed 15 psi. API Standard 650 covers the design of welded steel storage tanks of various sizes and capacities. CODAP [77]: CODAP is the French design code for fired or unfired pressure vessels, similar to the ASME Section VIII Codes. AS 1210 [78]: AS 1210 is the Australian design code for fired or unfired pressure vessels, similar to the ASME Section VIII Codes. 104

121 BS 5500 [79]: BS 5500 is the British Standard design code for pressurized vessels, similar to the ASME Section VIII Codes. 6.3 MARGIN OF MAWP TO FAILURE PRESSURE PER DESIGN CODE To determine the margin, or safety factor on working pressure compared to failure pressure, the MAWP ratio is used. The MAWP ratio is defined as: Actual Failure Pressure MAWP Ratio = Predicted MAWP (265) The actual failure pressure is determined from a full scale burst test or numeric FEA simulation. The predicted MAWP for the damaged component is a function of the analysis methods in Paragraphs 4.5 through 4.15 and the material allowable stress. Since each Code has a different formulation for allowable stress, the margin between MAWP and failure pressure can vary. The allowable RSF is used to set a desired margin on MAWP to failure pressure. The database cases are run with allowable RSFs of 0.7, 0.75, 0.8, 0.85, 0.9, and 0.95, and 1.0 for each of the design codes in Paragraph 6.2. The lower 95% prediction interval on MAWP ratio is used to determine the margin on MAWP for each design code. The statistical analysis results for each method and each design code are shown in Tables 18 through ALLOWABLE RSF RESULTS With the data in Tables 18 through 30, a margin of calculated MAWP to failure pressure can de derived for any of the methods described in Paragraphs 4.5 through 4.15 and any of the design codes described in Paragraph 6.2. The allowable RSF vs. the MAWP to failure margin based on the 95% prediction interval are shown in Figures 28 through 40 for the modified API 579, Level 2 assessment (Method 28). Similar plots can be derived for any assessment method by graphing the data points in the tables. 105

122 CHAPTER VII LTA ASSESSMENT PROCEDURES FOR LONGITUDINAL STRESS 7.1 INTRODUCTION The LTA assessment procedures for longitudinal stress presented in this section are based on work done by Southwest Research and Kanninen. The research at Southwest was done to incorporate effects from thermal expansion and supplemental loads into an LTA assessment. Full scale burst tests subject to internal pressure and four point bending were performed to evaluate the increased longitudinal stress. The Kanninen method presented in Chapter 4 was the conclusion of this research. 7.2 KANNINEN ASSESSMENT METHOD The Kanninen method is presented in Paragraph 4.13 and was included in the circumferential stress methods to evaluate its accuracy at predicting failure for flaws dominated by circumferential stress (internal pressure only). 7.3 THICKNESS AVERAGING The thickness averaging methods are applicable to both the circumferential and longitudinal stress directions for evaluating regions of metal loss. The methods are presented in LTA Assessment Procedures for Circumferential Stress. 106

123 7.3.1 API 510 This method is presented in Paragraph API 653 This method is presented in Paragraph API 579 ASSESSMENT METHODS API 579 Section 5, Level 1 Analysis This method is presented in Paragraph The screening curve is shown in Figure API 579 Section 5, Level 2 Analysis This method is presented in Paragraph Modified API 579 Section 5, Level 2 Analysis The following modifications to the API 579, Section 5, Level 2 longitudinal stress assessment have been made to improve the assessment. The worst case stress conditions including effects from both longitudinal and circumferential weld joint efficiency can be calculated with the following modifications. Equations (266), (267), (268), (269), and (270) should replace Equation (50) in the original method. σ eq Hσ (266) ys σ = max σ, σ (267) eq eq1 eq2 107

124 σ 2 2 A A σ cm σcmσ lm σ lm 2 eq1 = + + 3τ Ec EcEl El (268) σ 2 2 B B σ cm σcmσ lm σ lm 2 eq1 = + + 3τ Ec EcEl El (269) E C = E = 1.0 (Corroded region not on a weld) (270) L The shell theory Folias factor presented by Kanninen has been curve fit and incorporated into the analysis per the following modifications. Equations (271), (272), (273), and (274) replace the RSF calculation in the original method. A 1 A0 RSF = A 1 B A 0 (271) B = η α η α ηα η α η α ηα (272) η = 1 d (273) t α = l ( d) D t (274) Janelle, Level 1 Analysis The following methodology was used to develop an improved screening curve for the circumferential extent of a local thin area (LTA). The assumptions used to develop the curve were: 108

125 The LTA must pass the longitudinal extent screening curve. If it does, the worst case RSF for the longitudinal extent of the LTA is equal to the allowable RSF (typically 0.9). The longitudinal RSF is set to the allowable RSF for the screening curve. The loads on the component are internal pressure plus a supplemental net section bending moment. All other supplemental loads are assumed to be negligible. If the component is known to have a negligible supplemental bending moment, the No Bending Moment screening curve may be used; otherwise, the Maximum Bending Moment screening curve must be used. The equivalent stress criteria must be satisfied for the moment tension and compression side, an internal or external LTA, and at locations A and B. Location A is the center of the LTA with respect to the cylinder cross section and point B is the edge of the LTA with respect to the cylinder cross section. The additional longitudinal tension or compression stress is limited to 40% of the material allowable stress based on a radius to thickness ratio of 10 (see Figure 41). The following equations from API 579 were used to generate the screening curve: S σ σ σ + σ + τ (275) a cm cm lm lm 3 RSFa In generating the screening curve, the circumferential stress is assumed to be the worst case that could pass the longitudinal LTA extent screening curve. It is assumed that the circumferential stress due to pressure is equal to the material allowable stress and the remaining strength factor for the longitudinal extent of the LTA is equal to the allowable remaining strength factor. This results in a circumferential stress equal to the allowable stress divided by the allowable remaining strength factor. The torsion stress is assumed to be zero. S a σ cm =, 0 RSFa τ = (276) 109

126 Substituting the assumptions in (276) into Equation (275) and solving, results in the acceptance criteria shown in Equation (279). 2 S S S σ + σ RSF RSF RSF a a 2 a lm lm a a a (277) σ 2 lm Sa RSF a σ lm 0 (278) σ lmrsfa 0 1 (279) S a Equation (280) is the formulation for longitudinal stress from API 579 (equations for the section properties are shown in Table 4). σ AB, lm Aw FT ( ) C MAWP + + A s m Af Am A M f = E y c AB, xab, FTy + ( y + b)( MAWP) Aw + M x + M y I x I y (280) To generate the screening curve it is assumed that the weld joint efficiency, E c, is equal to 1, and there is no additional axial force or out of plane bending moment acting on the cylinder. The maximum allowable working pressure stress is equal to the material allowable stress. E = 1, F = 0, M = 0, c T y 2St MAWP = a (281) D The stress from the in plane net section bending moment is assumed to be equal to the allowable stress multiplied by a bending factor, B F. MD x = B F S a 2I x M x 2I x S a F = B (282) D 110

127 Substituting in (281) and (282) into Equation (280) results in the final formulation for longitudinal stress shown in Equation (283). σ y AB, C Aw 2Sat AB, 2Sat 2IxSa lm = Ms + ( y+ b) Aw + BF Am Af D I x D D (283) Using the acceptance criteria in Equation (279), two conditions for acceptance must be checked. The first criterion is for the tensile side of the cylinder with respect to the applied bending moment. Assuming additional tensile longitudinal stress from the moment results in the acceptance criteria shown in Equation (284). C Aw 2t yab, 2t 2Ix RSFaM s + ( y + b) Aw + BF 1 Am Af D I x D D (284) The second criterion is for the compressive side of the cylinder with respect to the applied bending moment. Assuming additional compressive longitudinal stress from the moment results in the acceptance criteria shown in Equation (285). Aw 2t yab, 2t 2Ix + ( y+ b) Aw BF 0 Am Af D I x D D (285) Since the circumferential remaining strength factor cancels out on the compression side, the acceptance criteria is based more on a bending moment limitation as opposed to limitations on the LTA dimensions. The bending moment limitation is a function of the radius to thickness ratio (ROT). The maximum bending factor, B F, was calculated for ROTs varying between 10 and 1000 using an iterative procedure and Equation (285). The ROT of 10 was most limiting, and based on the calculations, a maximum B F of 0.4 (see Figure 41) was used to generate the screening curve with a maximum bending moment included. The screening curve varies based on the ROT for given cylinder. Screening curves using ROTs of 10 to 500 were generated. The ROT of 10 was the most conservative and used as the basis for the final screening curves. The screening curve was generated by setting values of 111

128 lambda ranging from 0 to 18 and solving for the minimum remaining thickness ratio using the acceptance criteria in Equations (284) and (285). For a cylinder with an ROT of 10, lambda is equal to 18 for an LTA that extends all the way around the circumference of the cylinder. Two separate circumferential screening curves are generated to set the bounds for the possible loading between the no supplemental load case and the maximum permissible bending moment load case. The two resulting screening curves are shown in Figure Janelle, Level 2 Analysis An alternate method for evaluating the longitudinal stress direction of local thin areas has been developed based on the full-scale tests presented by Kanninen. This method is designed for use in conjunction with the API 579 circumferential stress assessment for regions of local metal loss. This method incorporates the Folias bulging factor into the calculation of circumferential stress and longitudinal stress and uses a von Mises equivalent stress criteria. The Folias factor for circumferential stress is taken from the API 579, Section 5, Level 2 assessment. The equation for the longitudinal stress bulging factor is derived from curve fitting data presented by Folias for determining bulging effects with circumferentially oriented cracks in cylindrical shells. The influence of the Folias factor on longitudinal stress is much less than the influence on circumferential stress, but may have a significant effect on an equivalent stress calculation. The Folias factor for longitudinal stress is graphically represented in Figure 43. For flaws with no additional supplemental loads effecting longitudinal stress (pressure only), longitudinal stress is ignored and equivalent stress is not calculated. In some cases, the addition of supplement loads may result in equivalent stresses that are less than those that would be obtained for the pressure only case. For this scenario, supplemental loads may be ignored, as the circumferential stress solution will be more conservative. This can be used as a screening technique for determining the influence of supplemental loads on an LTA. 112

129 The first step in the procedure involves calculating the longitudinal stress in the flawed region of the cylinder. Longitudinal stress due to an applied bending moment is calculated based on the damaged cross section of the cylinder. This stress is added to the normal longitudinal pressure stress. The combined bending and pressure stress is multiplied by a circumferential bulging factor presented by Folias to determine the total longitudinal stress. An acceptable range is given for the longitudinal stress. If the calculated longitudinal stress is within the specified range, it can be ignored and the assessment may be performed per the API 579 Level 2 circumferential stress assessment. If the calculated longitudinal stress is outside the acceptable range, the assessment must be performed using the von Mises equivalent stress acceptance criteria. The longitudinal stresses in the given range may be ignored because equivalent von Mises stresses calculated with these values will be below stresses calculated with the circumferential assessment method. The alternate longitudinal stress assessment can be performed as follows (See Figures 13 and 14): Step1: Calculate the section properties as shown in Table 4 and the equations in Step 1 of Paragraph Step 2: Calculate the circumferential stress using the following equations: l λ L = (286) Dt L M t = λ λ ( ) λ λ (287) M L s 1 d 1 L M t t = d 1 t (288) 1 RSFL = (289) L M S 113

130 σ cm P D i = RSFL E L Do Di (290) Step 3: Calculate the longitudinal stress with following equations: c λ C = (291) Dt M C t 2 4 ( λc) ( λc) ( λ ) ( λ ) = C C (292) M C s 1 d 1 C M t t = d 1 t (293) σ lm, A AP w FT C + + A S m Af Am A M f = EC ya xa Fy T + ( y+ b) AP w + M X + M Y I I X Y (294) σ lm, B AP w FT C + + A S m Af Am A M f = EC yb xb Fy T + ( y+ b) AP w + M X + M Y I I X Y (295) σ = max σ, σ lm lm, A lm, B (296) Note: For the validation, F T and Step 4: Calculate the torsional stress M Y are set to zero in equations (294) and (295). 114

131 M T τ = + 2( + ) A A t t tf mm V A A m f (297) Note: For the validation, M T and V are set to zero in equation (297). Step 5: Calculate the von Mises equivalent stress: σ = σ σ σ + σ + τ (298) eq, A cm cm lm, A lm, A 3 σ = σ σ σ + σ + τ (299) eq, B cm cm lm, B lm, B 3 σ = max σ, σ (300) eq eq, A eq, B Step 5: The following conditions indicate failure or acceptability: σ eq σ (failure) (301) uts σ eq σ (acceptable) (302) a Failure pressure and MAWP can also be calculated by setting the equivalent stress equal to the ultimate stress or allowable stress respectively, and solving for the pressure. The maximum allowable moment can also be calculated in the same fashion as follows. These equations are valid if net section bending is the only supplemental load. C 2 2 M s σ eq M x t Z P = R 1 1 M M M M 2 4 L L C C ( s ) s s + ( s ) (303) 2 Z 2 PR L 2 1 L C 1 C 2 x = σ eq C ( s ) s s + ( s ) Ms t 2 4 M M M M M (304) 115

132 CHAPTER VIII VALIDATION OF LTA ASSESSMENT PROCEDURES FOR LONGITUDINAL STRESS 8.1 INTRODUCTION The Janelle assessment methodology for the longitudinal stress direction of an LTA described in Paragraph was validated with full scale burst tests. The full scale tests cases were pressurized to a fixed value, then four point bending was applied until the pipe failed. The loads at failure were used to calculate an equivalent stress at failure using the assessment methodology. The calculated stress was compared to actual measured ultimate stress for the pipe material. For the test cases available, there was only a small amount of error between calculated stress at failure and the material ultimate stress. 8.2 VALIDATION DATABASES Unfortunately, data for only five full scale burst tests was available to validate the assessment methodology. The tests were performed by Southwest Research on 48 inch diameter X65 pipe and have properties that are shown in Table 31. The flaws in the pipe were machined patches on the pipe OD used to simulate metal loss. Each pipe contained 2 machined flaws, one on the tension side from bending, and one on the compression side. Additional tests were performed by Southwest for 20 inch diameter X52 pipe, but complete data for use in validation was unable to be obtained. Additional test cases should be used to further validate the methodology whether they are actual test cases or Finite Element Analysis simulations. 116

133 8.3 SUMMARY OF VALIDATION RESULTS The assessment methodology was used to calculate the equivalent stress for the flaws on the tension and compression sides of the pipe tests. The equivalent stress that was calculated for the side that actually experienced failure was compared to material actual ultimate stress to verify the accuracy of the methodology. The actual failures occurred on the compression side when the calculated equivalent stresses were significantly higher on that side than the tension side and vice versa. The actual calculated values are shown in Table 32. For the five test cases, calculated equivalent stresses at failure were very close to the material ultimate strength. It can be concluded that the von Mises equivalent stress criteria with the presented method for calculating stresses in local thin areas is a good predictor of actual behavior. If this is true, stresses caused by other forms of supplemental loading should be able to be handled the same way as an applied bending moment. Additional tests should be performed to confirm these findings. 117

134 CHAPTER IX LTA PROCEDURES FOR HIC DAMAGE 9.1 INTRODUCTION HIC damage is characterized by stepwise internal cracks that connect adjacent hydrogen blisters on different planes in the metal, or to the metal surface. Externally applied stress is not required for the formation of HIC. In steels, the development of internal cracks (sometimes referred to as blister cracks) tends to link with other cracks by a transgranular plastic shear mechanism because of internal pressure resulting from the accumulation of hydrogen. The linkup of these cracks on different planes in steels has been referred to as stepwise cracking to characterize the nature of the crack appearance. HIC is commonly found in steels with high impurity levels that have a high density of large planar inclusions, and/or regions of anomalous microstructure produced by segregation of impurity and alloying elements in the steel. The effect of HIC damage is to produce a weakened zone within a plate. This weakening effect can be characterized by using an RSF factor. RSF factors need to be developed for both subsurface and surface breaking HIC damage. In the case of surface breaking HIC damage, the Folias bulging factor needs to be included in the RSF solution. 9.2 SUBSURFACE HIC DAMAGE The RSF for subsurface HIC damage (see Figure 44) can be derived from the definition of the remaining strength factor, or 118

135 L Collapse Load Of The Damaged Component = = (305) D RSF L UD Collapse Load Of The Undamaged Component The collapse loads of the damaged and undamaged plate can be estimated using lower bound limit load theory. The lower bound limit load for the damaged plate section is given by the following equations where D H is a measure of HIC damage: ( 2 ) L = L t+ A A D σ (306) D H H H ys or ( 2 ) L = L t+ st A D σ (307) D H H H ys L t L s A D t σ H D = 2 H + H ys (308) Finally H L = t 2L + s 1 A D st σ D H H ys (309) The lower bound limit load for the undamaged plate section is referenced to the minimum required wall thickness per the applicable code is: ( ) L = t L + s σ (310) D min 2 H ys Combining Equations (309) and (310): AH t 2LH + s 1 DH st RSF = min, 1.0 tmin ( 2LH + s) (311) If the actual area is approximated as a rectangle with dimensions s and w H, the expression for the RSF becomes: 119

136 wh t 2LH + s 1 DH t RSF = min, 1.0 tmin ( 2LH + s) (312) In the above equations for the RSF, the region of the undamaged plate that is assumed to strengthen the HIC damaged area is: LH = 8t (313) The minimum function in the above equations is required because the RSF is indexed to t min. Therefore, if t min is small relative to the plate thickness t, and the reduced strength of the HIC damaged area approaches the strength of undamaged plate, the RSF can be computed to be greater than 1.0 indicating that the plate thickness above t min can adequately reinforce the damaged area located below t min. If the RSF is indexed to the full plate thickness, then the expressions for the RSFs shown above become: AH 2LH + s 1 D st RSF = ( 2L + s) H H (314) or wh 2Lh + s 1 D t RSF = ( 2L + s) h H (315) 9.3 SURFACE BREAKING HIC DAMAGE For surface breaking HIC damage (see Figure 45), the bulging factor needs to be considered in the RSF. By inspection of Equation (311), the RSF factor can directly be written as: 120

137 wh 1 D H tmin RSF = 1 w H 1 D H M t t min (316) or in terms of a damaged area: AH 1 D H A0 RSF = 1 A H 1 D H M t A o (317) where Ao = st (318) min Note that when there 100% HIC damage, then D H = 1.0, and the RSF factor becomes: wh 1 tmin RSF = 1 w H 1 M t t min (319) The remaining thickness ratio, R t, is: R t t t w w 1 t t t mm min H H = = = (320) min min min then Rt RSF = M t [ R ] t (321) which is the expression used for an LTA. 121

138 Note that in the above formulation, the parameter, L H, is set to zero. This is consistent with current LTA assessment methodologies. The modified API Folias factor as shown in Equation (256) should be used in the above equations. 122

139 CHAPTER X LTA PROCEDURES FOR EXTERNAL PRESSURE The methodology for this analysis is presented by Rajagopalan [80] and supported by Esslinger [81]. It utilizes a step-wise approach for shells that have abrupt changes in thicknesses. The overall buckling pressure of a cylinder made of lengths at varying thicknesses can be calculated from the following equation: L L L L Ln = (322) P P P P P e e e e e n The parameters L and P e n are the unsupported length and buckling pressures of the overall vessel, respectively, and L n and P e n represent the unsupported lengths and the buckling pressures of each of the individual shell courses in the vessel, respectively. The following assessment procedure can be used to evaluate cylindrical shells subject to external pressure. If the flaw is found to be unacceptable, the procedure can be used to establish a new MAWP. STEP 1: Determine the CTP and the parameters in Paragraph STEP 2: Subdivide the CTP in the longitudinal direction using a series of cylindrical shells that approximate the actual metal loss (see Figure 46). Determine the length and thickness of each of these cylindrical shells and designate them t i and L i. STEP 3: Determine the allowable external pressure of each of the cylindrical shells defined in STEP 2 using (t i FCA) and L i, designate this pressure as P e i. Methods for determining the allowable external pressure are provided in Appendix A. 123

140 STEP 4: Determine the allowable external pressure of the actual cylinder using the following equation: MAWP r = n i= 1 n i= 1 L i L P i e i (323) STEP 5: If MAWP r > MAWP, then the component is acceptable for continued operation. If MAWP r < MAWP, then the component is not acceptable for continued operation and the allowable MAWP is MAWP r. 124

141 CHAPTER XI CONCLUSIONS AND RECOMMENDATIONS 11.1 INTRODUCTION This section contains a summary of the validation results for existing and new methods for evaluating the longitudinal and circumferential extent of an LTA. Recommendations for use are made for the methods that correlate the most accurately with actual full scale burst tests of damaged shells. In addition, data is provided so that a margin on MAWP to failure pressure can be calculated based on various design codes. Finally, additional areas requiring more research and validation are outlined LTA ASSESSMENT PROCEDURES FOR CIRCUMFERENTIAL STRESS Recommended Methods for Circumferential Stress Of the existing methods for analyzing LTAs that are currently in use, the API 579, Level 2 and RSTRENG methods based on an effective area procedure correlate the best to actual test data. The statistical analysis is presented in Table 16, and those two methods most accurately predict the burst pressure of a damaged shell with the least amount of scatter in the results. The drawback with these methods is that they do not approach the proper limits. For example, as the length of an LTA becomes very long, the RSF is not necessarily calculated to be the ratio of remaining thickness to undamaged thickness. To correct the problem, the modified Folias factor should be used in conjunction with these methods. The new Folias factor does not change the results of the analysis for LTAs that have a lambda value less than 8 (see Figures 21 and 22). 125

142 However, for longer flaws it is more conservative and approaches the proper bound. The modified Folias factor is incorporated into Methods 27 and 28. It is recommended that Method 27 replace the current API 579, Level 1 assessment and Method 28 replace the current API 579 Level 2 assessment. The new Janelle method was developed based on the actual test data and correlates even better with full scale test results than any of the other methods. It also mathematically approaches the bounds of the problem with the proper trends (see Figure 27). It is recommended that the method eventually replace the current methods in API 579 in a future release of the document Allowable Remaining Strength Factors Any desired margin of calculated MAWP to failure pressure can de derived for the methods described in Paragraphs 4.5 through 4.15 and the design codes described in Paragraph 6.2 with the data presented in Tables 18 through 30. It is recommended that the tables which correlate to the method published in the current or future releases of API 579 be included and referenced in the document. This will allow a user to calculate whatever safety margin of MAWP to actual failure is desired for the API 579 methodology RECOMMENDED METHODS FOR LONGITUDINAL STRESS The Kanninen method, and similarly the API 579 modified method for evaluating flaws with longitudinal stress do not give accurate results for cases where circumferential stress is dominant. However, these methods do address loading conditions that result in flaws dominated by longitudinal stresses. For local thin areas where supplemental loads or thermal expansion may cause larger longitudinal stress, it is recommended that the LTA be first evaluated using an assessment method for circumferential stress. If the flaw is acceptable for the circumferential stress assessment, then it should be evaluated using a method that addresses flaws dominated by longitudinal stresses. 126

143 The Janelle method, which is a modified version of the Kanninen and API 579 methodology is recommended for use when evaluating the circumferential extent of an LTA. The method correlates much better to actual full scale burst tests as described in Paragraph 8.3 and is recommended for use in future releases of API FURTHER LTA ASSESSMENT DEVELOPMENT Material Toughness Effects The material toughness of a shell with a LTA can influence the load carrying capacity of the component for medium and low toughness steels. A LTA is a natural stress concentration site and may have large triaxial stresses. The stress concentration in combination with the irregular geometry of the LTA may result in fracture before plastic collapse. For high toughness steels, this is likely not an issue as most failures due to a LTA type defect will be mostly a ductile failure. However, for low toughness steels, the stress concentration at the deepest point of a LTA may cause micro cracks to form and result in brittle fracture contributing to the failure. This type of failure occurs at a lower stress level than a purely ductile failure. A criterion to evaluate the susceptibility of a damaged component to experience a fracture failure should be developed for LTA type defects. A criterion for crack extension in a cylindrical shell has been developed by Hahn [82]. A similar procedure for LTAs should be developed for inclusion in a later release of API 579. In terms of stress, a modified stress calculation could be developed to include the material fracture toughness and the remaining strength factor to account for susceptibility of low toughness steels to brittle fracture. The calculation would include a factor based on toughness as follows. σ ( ) = RSF f K σ (324) cal mat m 127

144 Stress Triaxiality from LTAs The current analysis methods do not directly take into account the magnitude of triaxial stress that can result from a local defect like an LTA. Typically, as the triaxiality increases the toughness of the material decreases. This can result in a greater chance of fracture for highly triaxial stress fields. The new proposed Section VIII, Division 2 Code will have a check and limitation on the magnitude of triaxial stress fields to reduce the chance of fracture. This type of criteria could be a good additional screening check for LTAs to help avoid that failure mode Rules for LTAs Near Structural Discontinuities By far the most limiting criteria that must be satisfied in order to perform a FFS assessment of a LTA is the distance to the nearest structural discontinuity. This distance is based on the shell theory attenuation distance that stresses due to a global discontinuity die out along the shell length. In API 579, the limiting distance is set to the following value. Lmsd = 1.8 Dt (325) In API 579, any attachment or change in shell geometry that creates a local stress field is classified as a structural discontinuity. In reality there are two different types of discontinuity. The first type is a global discontinuity, like a conical shell transition. The distance required for the additional stress to die out along the shell for this type of discontinuity is on the order of magnitude calculated by Equation (325). The other type of discontinuity is a local structural discontinuity, like a nozzle attachment. The distance required for the additional stress to die out along the shell for this type of discontinuity is on the order of plate thicknesses, not the length specified in Equation (325). For local discontinuities, the limiting distance is extremely conservative. Research is currently underway to modify this limitation in API

145 CHAPTER XII NOMENCLATURE Unless otherwise cited in the text, the variables used in this report are shown below: A = Area of metal loss A o = Original metal area A a = Effective cross-sectional area for a cylinder with metal loss A f = Cross-sectional area of the region of local metal loss A m = Cylinder or pipe metal cross-section A t = Mean area to compute torsion stress for the region of the cross section without metal loss A tf = Mean area to compute torsion stress for the region of the cross section with metal loss A w = Effective area of cylinder or pipe cross section on which pressure acts B F = Bending Factor. This value is used to determine the additional longitudinal compression or tension stress caused by the net section bending moment as a factor of the material allowable stress. i.e. a bending factor of 0.4 results in addition longitudinal stress equal to 40% of the material allowable stress. b = Location of the centroid of area A w, measured from the x x axis c = Circumferential extent of the flaw C rate = Corrosion or metal loss rate 129

146 CA e = Equivalent corrosion allowance d = Depth of metal loss damage D = Mean diameter D i = Inside diameter of the cylinder D o = Outside diameter of the cylinder E C = Weld joint efficiency for circumferential stress (longitudinal weld joints) E L = Weld joint efficiency for longitudinal stress (circumferential weld joints) F = Applied section axial force determined for the weight or weight plus thermal load case F d = Design factor F ys = Yield stress factor F uts = Ultimate tensile stress factor FCA = Future corrosion allowance H = Load factor. For the weight case, H=0.75, and for the weight plus thermal case H=1.5. The H factor is based on an allowable RSF of 0.9, a F ys of 2/3, and a factor of two for the weight plus thermal load case I x = Moment of inertia of the cross section with the region of local metal loss about the y axis I y = Moment of inertia of the cross section with the region of local metal loss about the y axis I X = Moment of inertia of inertia of the cross section with the region of local metal loss about the x -axis I Y = Moment of inertia of inertia of the cross section with the region of local metal loss about the y -axis 130

147 K = Fracture toughness l = LTA length L = Length for thickness averaging L f = Lorenz factor L msd = Distance from the flaw to the nearest structural discontinuity M b = Net-section bending moment M = Surface correction factor s M = Folias through-wall bulging factor for a crack-like flaw t M = Applied net-section torsion determined for the weight or weight plus thermal load T case M x = Applied section bending moment determined for the weight or weight plus thermal load case about the x-axis M y = Applied section bending moment determined for the weight or weight plus thermal load case about the y-axis MA = Mechanical allowances MAWP = Maximum allowable working pressure of damaged component MAWP 0 = Maximum allowable working pressure of undamaged component P = Pressure P 0 = Failure pressure of undamaged component P f = Failure pressure of damage component Q = Shape factor to determine the length for thickness averaging R b = Radius of the pipe bend R i = Inside radius R life = Component remaining life 131

148 R m = Mean Radius R t = Remaining thickness ratio RSF = Calculated Remaining Strength Factor for a given flaw RSF a = Allowable Remaining Strength Factor s = Spacing between flaws t = Current wall thickness of the component t am = Average measured thickness C t am = Average measured thickness in the circumferential direction L t am = Average measured thickness in the longitudinal direction t lim = Minimum permissible thickness t loss = Metal loss computed as the difference between the furnished thickness and the thickness at the time of an inspection t min = Minimum required wall thickness of the shell containing a flaw C t min = Minimum required wall thickness based on applied circumferential stresses L t min = Minimum required wall thickness based on applied longitudinal stresses t mm = Minimum measured wall thickness t nom = Nominal thickness T = temperature derating factor V = Applied net-section shear force determined for the weight or weight plus thermal load case x = Distance along the x-axis to a point on the cross section where the bending stress is to be computed y = Distance from the x x stress is to be computed axis to a point on the cross section where the bending 132

149 y = Location of the neutral axis Y = ASME B31 y-factor adjustment for temperature Z c = Section modulus of the corroded pipe cross section λ = Shell metal loss damage parameter σ a = Allowable stress σ cm = Maximum circumferential stress, typically the hoop stress from pressure loading σ fail = Failure stress for the weight and weight plus thermal load case, as applicable σ flow = Material flow stress σ lm = Maximum longitudinal membrane stress computed for both the weight and weight plus thermal load cases σ uts = Material ultimate tensile stress σ ys = Material yield stress τ = Maximum shear stress in the region of local metal loss for the weight and weight plus thermal load case θ L = Circumferential position on an elbow where the stress is to be computed 133

150 CHAPTER XIII TABLES Table 1 Stress Classification Stress Category Description Value Average value across the thickness of a section General Primary Membrane Produced by internal pressure and other mechanical Stress Intensity, (P m ) loads ks m Excludes all secondary and peak stresses Local Primary Membrane Stress Intensity, (P L ) Primary Membrane (general or local) Plus Primary Bending Stress Intensity, (P L + P b ) Primary Plus Secondary Stress Intensity, (P L + P b + Q) Primary Plus Secondary Plus Peak Stress Intensity, (P L + P b + Q + F) Average value across the thickness of a section Produced by internal pressure and other mechanical loads Excludes all secondary and peak stresses Stress intensities exceeding 1.1Sm do not extend in the meridional direction more than Highest value across the thickness of a section Produced by internal pressure and other mechanical loads Excludes all secondary and peak stresses Highest value at any point across the thickness of a section Produced by internal pressure and other mechanical loads and general thermal effects Effects of gross structural discontinuities but not local discontinuities are included Highest value at any point across the thickness of a section Produced by internal pressure and other mechanical loads and general and local thermal effects Effects of gross structural discontinuities and local discontinuities are included Used in fatigue calculation Rt 1.5kS m 1.5kS m Notes 1. S m is the allowable stress. 2. k is equal to 1.0 for design loads and equal to 1.2 for design loads plus wind or pressure loads. 3. S a is the allowable alternating stress established from a design fatigue curve based on a specified number of cycles. 4. In addition to the stress classification acceptance criteria, a triaxial stress limit, ( σ σ σ ) loads. + + S, is applied to prevent ductile fracture. This limit is based on primary m 3S m S a 134

151 Table 2 Examples of Stress Classification Vessel Component Location Origin of Stress Type of Stress Classification Any shell including cylinders, cones, spheres and formed heads Cylindrical or conical shell Shell plate remote from discontinuities Near nozzle or other opening Any location Shell distortions such as out-ofroundness and dents LTA Center region LTA Periphery LTA Near nozzle or other opening Any section across entire vessel Junction with head or flange LTA Tank bottom courseto-shell junction Internal pressure Axial thermal gradient Net-section axial force and/or bending moment applied to the nozzle, and/or internal pressure Temp. difference. Between shell and head Internal pressure Internal pressure Internal pressure Net-section axial force and/or bending moment applied to the nozzle, and/or internal pressure Net-section axial force, bending moment applied to the cylinder or cone, and/or internal pressure Internal pressure Liquid Head General membrane Gradient through plate thickness Membrane Bending Local membrane Bending Peak (fillet or corner) Membrane Bending Membrane Bending Membrane Bending Membrane Bending Local membrane Bending Peak (fillet or corner) Membrane stress averaged through the thickness; stress component perpendicular to cross section Bending stress through the thickness; stress component perpendicular to cross section Membrane Bending Membrane Bending P m Q Q Q P L Q F Q Q P m Q P m P b P L Q (2) P L Q F P m P b P L Q P L Q 135

152 Table 2 Examples of Stress Classification (Continued) Dished head or conical head Flat head Perforated head or shell Nozzle Cladding Any Crown Knuckle or junction to shell Center region Junction to shell Typical ligament in a uniform pattern Isolated or atypical ligament Cross section perpendicular to nozzle axis Nozzle wall LTA Nozzle wall Any Any Internal pressure Internal pressure Internal pressure Internal pressure Pressure Pressure Internal pressure or external load or moment External load or moment Internal pressure Differential expansion Internal pressure Differential expansion Radial temperature distribution [note (3)] Any Any Any Membrane Bending Membrane Bending Membrane Bending Membrane Bending Membrane (average through cross section) Bending (average through width of ligament., but gradient through plate) Peak Membrane Bending Peak General membrane (average. across full section). Stress component perpendicular to section Bending across nozzle section General membrane Local membrane Bending Peak Membrane Bending Peak General membrane Local membrane Bending Peak Membrane Bending Equivalent linear stress [note (4)] Nonlinear portion of stress distribution Stress concentration (notch effect) P m P b P L (1) Q P m P b P L Q (2) P m P b F Q F F P m P m P m P L Q F Q Q F P m P L Q F F F Q F F 136

153 Table 2 Examples of Stress Classification (Cont.) Notes: 1. Consideration must also be given to the possibility of wrinkling and excessive deformation in vessels with large diameter-to-thickness ratio. 2. If the bending moment at the edge is required to maintain the bending stress in the center region within acceptable limits, the edge bending is classified as P b, otherwise, it is classified as Q. 3. Consider possibility of thermal stress ratchet. 4. Equivalent linear stress is defined as the linear stress distribution which has the same net bending moment as the actual stress distribution. 137

154 In-Service Inspection Codes API 510 Table 3 Thickness Averaging for In-Service Inspection Codes Summary Of Metal Loss Rules The average measured thickness, t am, is determined by averaging the thickness readings over the following lengths: D L min =, 20 inches when D 60 inches 2 D L min =, 40 inches when D > 60 inches 3 strength check is as follows: tam CA tmin An additional check is made the minimum measured thickness: t CA 0.5t mm min The required An alternative, the corrosion and/or erosion can be analyzed using stress analysis techniques with the results evaluated using principles of the ASME Boiler and Pressure Vessel Code, Section VIII, Division 2, Appendix IV is permitted API 570 ASME B31G Stress analysis evaluated using the principles of the ASME Boiler and Pressure Vessel Code, Section VIII, Division 2, Appendix IV Methodology included in API 510 API 653 The average measured thickness, t am, is determined by averaging the thickness readings over the following length: L = max 3.7 Dtmm, 40.0inches The required strength check is as follows: tam CA tmin An additional check is made the minimum measured thickness: tmm CA 0.6tmin An alternative, the corrosion and/or erosion can be analyzed using stress analysis techniques with the results evaluated using principles of the ASME Boiler and Pressure Vessel Code, Section VIII, Division 2, Appendix IV is permitted NBIC The assessment is the same as that required by API

155 Table 4 Section Properties for Computation of Longitudinal Stress in a Cylinder with an LTA X 2 X m LX f LX ( ) 2 I = I + A y I A y + y I = I I Y Y LY π I X = Iy = Do Di 64 I LX = 3 R d 4 4 ( ) d d d 2sin θ 1 + sin cos 2 3 θ + θ θ + 2R R 4R θ d sin θ d d R θ ( 2 d R) R 6R I LY d d d = R d 1 + sin cos 2 3 2R R 4R ( θ θ θ) y LX 2Rsinθ d 1 = 1 + 3θ R 2 d R ( D D ) c ( D D ) 0.5π + + At = 8 A a π = D 4 2 i π Am = Do Di ( ) i o i o 139

156 Table 4 Section Properties for Computation of Longitudinal Stress in a Cylinder with an LTA (Continued) For A Region of Local Metal Loss Located on the Inside Surface θ Af = Df Di 4 Aw = Aa + Af 2 2 ( ) 1 sinθ y = 12 A x A = ( Df Di ) m A Do ya = y + 2 Do xb = sinθ 2 Do yb = y + cosθ 2 1 sinθ Df b = 12 A + A D R = f 2 d = 3 3 ( Di ) a ( Df Di) 2 ( Do Df ) t = 2 c Do + D Atf = 8 ( f ) f f For A Region of Local Metal Loss Located on the Outside Surface θ A = D D 4 A 2 2 ( ) f o f w = A a 1 sinθ y = 12 A x A = y A 0.0 = y+ D 2 f 3 3 ( Do Df ) m A Df xb = sinθ 2 Df yb = y+ cosθ 2 b = 0 D R = o 2 d = ( Do Df ) 2 ( Df Di) t = 2 c Di + D Atf = 8 ( f ) f 140

157 Table 5 LTA Assessment Methods Method Description 1 API-579 Section 5, Level 1 Analysis B31.G surface correction, rectangular area, API level 1 Folias factor 2 API-579 Section 5, Level 2 Analysis B31.G surface correction, effective area, API level 2 Folias factor 3 API-579 Section 5, Level 2 Analysis B31.G surface correction, exact area, API level 2 Folias factor 4 Modified B31-G Method B31.G surface correction, 0.85dl area, AGA Folias factor 5 Modified B31-G Method (RSTRENG) B31.G surface correction, effective area, AGA Folias factor 6 Modified B31-G Method B31.G surface correction, exact area, AGA Folias factor 7 Original B31-G Method B31.G surface correction, parabolic area, B31-G Folias factor 8 Thickness Averaging API 510, 8 th Edition 9 Thickness Averaging API 653, 2 nd Edition 10 British Gas Single Defect Method B31.G surface correction, exact area, BG Folias factor 11 British Gas Complex Defect Method B31.G surface correction, exact area, BG Folias factor 12 Chell Method Chell surface correction, exact area, B31-G Folias factor 13 Osage Method Chell surface correction, effective area, D/t dependent Folias factor 14 API-579, Level 1, Hybrid 1 Analysis Chell surface correction, rectangular area, API level 1 Folias factor 15 API-579, Level 2, Hybrid 1 Analysis Chell surface correction, effective area, API level 2 Folias factor 16 API-579, Level 1, Hybrid 2 Analysis Chell surface correction, rectangular area, BG Folias factor 17 API-579, Level 2, Hybrid 2 Analysis Chell surface correction, effective area, BG Folias factor 18 API-579, Level 1, Hybrid 3 Analysis Chell surface correction, rectangular area, JO Folias factor 19 API-579, Level 2, Hybrid 3 Analysis Chell surface correction, effective area, JO Folias factor 20 Battelle Method B31.G surface correction, rectangular area, Battelle Folias factor 21 BS 7910, Appendix G (Isolated Defect) B31.G surface correction, rectangular area, BG Folias factor 22 BS 7910, Appendix G (Grouped Defects) B31.G surface correction, rectangular area, BG Folias factor 23 Kanninen Equivalent Stress B31.G surface correction, rectangular area, shell theory Folias factor 24 Shell Theory Method Chell surface correction, exact area, shell theory Folias factor 141

158 Table 5 LTA Assessment Methods (Continued) 25 Thickness Averaging API 579, Level 1 26 Thickness Averaging API 579, Level 2 27 Modified API-579 Section 5, Level 2 Analysis B31.G surface correction, rectangular area, Modified API Folias factor 28 API-579 Section 5, Level 2 Analysis B31.G surface correction, effective area, Modified API Folias factor 29 Janelle Method rectangular area 30 Janelle Method effective area 142

159 Table 6 Validation Cases for the Undamaged Failure Pressure Calculation Method Outside Diameter (in) Thickness (in) Failure Pressure from FEA (psi) Failure Pressure from Svensson Method (psi) Error Between Methods % % % % Outside Diameter (in) ID Equivalent Plastic Strain from FEA ID Equivalent Plastic Strain from Svensson Method OD Equivalent Plastic Strain from FEA OD Equivalent Plastic Strain from Svensson Method Notes: Table 118 The yield stress for the material model used in the FEA and Svensson method was psi. Table 118 The ultimate stress and corresponding plastic strain for the material was psi and in/in. 3. The strain hardening coefficient for the material was

160 Table 7 Parameters for a Through-Wall Longitudinal Crack in a Cylinder Subject to a Through- Wall Membrane and Bending Stress Ri t 3.0 A mm Parameter C 0 C 1 C 2 C 3 C 4 C E E E E E E-04 A mb 5.0 A mm A mb 10.0 A mm A mb 20.0 A mm A mb 50.0 A mm A mb A mm E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-04 A mb E E E E E E-04 Notes: Table 118 The equations to determine the coefficients are shown below. A = C + C + 2 mm C + 3 C + 4 C + 0 1λ 2λ 3λ 4λ C5λ. 2 C C C A = 0 + 1λ+ 2λ mb C λ+ C λ + C λ Table 118 Interpolation may be used for intermediate values of Ri t. Table 118 The solutions can be used for cylinders with 3 R t 100 Ri t Ri t = 3 and for R t i > 100 use the solution for R t i other than those provided is recommended. Table 118 Crack and geometry dimensional limits: λ If λ > 12.5 i < 3 use the solution for ; for Ri t = 100. Interpolation for values of, then use the following solutions. If λ exceeds the permissible limit, then the following equations can be used: A mm = L NM λ ( 10 ) λ λ ( 10 ) λ c h O QP 05. A mb = λ ( 10 ) λ ( 10 ) λ λ c h 144

161 Table 8 LTA Database 1 Case Descriptions Case Number , 52-78, , 79-81, Description These tests were performed by the Texas Eastern Transmission Corporation and are described in Reference 1-3. This group of tests involved burst tests of corroded pipe samples removed from service and fabricated into endcapped vessels. Only six different specimens were used to generate the 25 cases; leaks were repaired and the vessel tested again. These cases are another group of tests performed for the Texas Eastern Transmission Company. Details and discussion of these tests can be found in References 1-4, 1-5, and 1-6. The six pressure vessel tests were fabricated from samples of corroded pipe. These cases are burst tests conducted with PRC funding. All the cases are pressure vessel tests fabricated from line-pipe samples contributed by several pipeline operators. These cases are burst test results produced by independent pipeline operators. The tests are corroded pipes fabricated into end-capped vessels. These cases are investigations of service failures by pipeline operators. As such, the longitudinal stress in the pipe is unknown. These cases represent burst tests performed by various pipeline operators. The specimens are corroded pipe removed from service and fabricated in pressure vessels. Case 89 involves internal corrosion; the rest have external corrosion. These cases are burst tests of end-capped pipe samples performed for Nova. The defects in these test are machined, corrosion simulating, notches of significant width (>1 ). Cases and 102 were spirally oriented notches. Cases were single longitudinally oriented notches. Cases 100 and 101 had pairs of longitudinally oriented notches on the same axial line, separated by different amounts. Cases 103 and 104 involved pairs of parallel, overlapping, longitudinally oriented notches, separated circumferentially by small multiples of the wall thickness. Case 105 is a defect free control case pressurized to failure. More details of these cases can be found in References1-7 and 1-8. There are some discrepancies between the original data and the data found in Reference 1-1 and 1-2. Original values were used. Cases are pipe samples removed from service that had internal pitting. Testing on these cases was performed in a special rig that allowed pressurization of the pipe without axial stress. Defects were mostly isolated pits less than 3 in axial length. Case 107 gave an anomalous result as it was discovered that a fatigue crack had extended the pit. Cases can be found in Reference 1-9. There are some discrepancies between the original data and the data found in Reference 1-1 and 1-2. Original values were used. These cases are a variety of machined, corrosion simulating notches. Case 118 is a defect free control case. Cases 119 and 124 contain long, single, longitudinally oriented notches. Case 120 contains two longitudinally oriented slots of different lengths and depths; one on the side of the pipe and one on the other side of the pipe. Cases 121 and 122 had bands of material of differing sizes removed around the complete circumference in two locations along the axis of the sample. Case 123 contains two different sized rectangular patches of removed metal each on opposite sides of the pipe. All cases were pressurized to failure. Failures were all ruptures 145

162 Case Number Case Number Description occurring at one defect. Table 8 LTA Database 1 Case Descriptions (Continued) Description These cases were presented by British Gas researchers and can be found also in Reference They include various machined defects to simulate corroded pipe. Cases are a series of single notch defects designed to evaluate the effect of flaw length. The flaws were narrow, behaving more like a crack than a pit-like flaw. Cases involve tests with closely spaced notches to monitor defect interaction. Cases involve tests with closely spaced round pits. Cases are tests to address the behavior of patches of missing metal and their interactions with each other and with rounded pits. Cases contain short flaws within longer flaws or areas of reduced wall thickness. Cases 132, 141, and 143 are omitted from the statistical analysis due to lack of information. These cases are part of an experiment carried out at Southwest Research Institute and reported in Reference Metal loss in these cases was simulated by machining away 25-50% of the wall thickness over rectangular areas of various sizes. Two identical areas of metal loss were created with 180 degrees of circumferential separation between the two. This was done so that one defect would be in compression while the other was in tension for an applied bending moment. The tests were subjected to various combinations of internal pressure and bending moments. These cases were performed at the University of Waterloo and can be found in References 1-12, 1-13, and These burst tests were conducted on pipes containing various arrays of electrochemically machined pits. Longitudinal, circumferential, and spiral defect arrays were used. Some tests were run using a special apparatus that eliminated axial stress in the test case. Most of these cases are failures and burst tests of corroded pipe in and removed from service. Cases 188 and 190 are hydrostatic failures of corroded pipe. Cases 189, 191, 195, and 214 are ductile mode in-service failures of corroded pipe. Cases , , and 215 are burst tests of corroded pipe samples previously removed from service. Cases 196 and 197 are brittle mode in-service failures of corroded pipe. Cases and are omitted from the statistical analysis due to lack of information. These cases are additional cases found in Reference 1-1 and on the compiled spreadsheet. Case 217 is omitted from the statistical analysis due to lack of information. 146

163 Table 9 LTA Database 2 Case Descriptions Case Number Description These cases are from test vessel #1. Cases are longitudinal defects in the shell. Case 2004 is a circumferential defect in the shell. Case 2005 is a defect in the shell to head weld. Cases are defects located in the elliptical heads of the vessel. Cases are defects in and around the nozzles of the vessel. Cases are axial defects in the shell. Cases are external axial defects in the shell These cases are from test vessel #2. Cases , , and are longitudinal defects in the shell. Case 2030 is a circumferential defect in the shell. Case 2031 is a defect in the shell to head weld. Cases are defects in the elliptical heads of the vessel. Cases and are defects around the nozzles of the vessel. Cases are external axial defects in the shell. Cases are omitted from the statistical analysis due to lack of information. Table 10 LTA Database 3 Case Descriptions Case Number Description These cases are machined isolated pit defects. Cases are external pits and cases are internal pits These cases contain machined groove defects. Cases and are external grooves and cases are internal grooves , These cases contain machined patches that simulate areas of general corrosion. Cases and are external general defects and cases are patches of internal corrosion This case is a defect free control case These cases are machined circumferential defects. Cases 3058 and 3061 are areas of external general corrosion. Cases 3059 and 3062 are external grooves. Cases 3060 and 3063 are external slots These cases contain adjacent deep pit defects These cases have multiple adjacent deep pit defects. Case 3069 has 4 connected pits, and case 3070 has 3 adjacent pits These cases contain adjacent areas of machined general corrosion patches These cases contain machined pits in areas of machined general corrosion. Cases 3075 and 3076 have two pits in an area of general corrosion. Cases 3077 and 3078 have one pit in an area of general corrosion. 147

164 Table 11 LTA Database 4 Case Descriptions Case Number Description These cases are FEA models of corroded pipe. Diameter, thickness, defect length, depth, and width have all been varied These cases are defect free FEA control cases These cases are FEA models of corroded pipe with decreased material yield stress These cases are FEA models of corroded pipe with increased material yield stress These cases are FEA models of deep corrosion pits These cases are FEA models of axially adjacent corrosion pits of various dimensions These cases are FEA models of axially adjacent general areas of corrosion of varying parameters These cases are repeats of cases , except that the defect length has been changed These cases are FEA models of corrosion pits contained within an area of general corrosion These cases are FEA models of undamaged validation cases. 148

165 FEA Model Type 3D Solid Axisymmetric Solid Table 12 FEA Results for a Cylindrical Shell with a LTA LTA Length (in) Lambda, λ Failure Pressure (psi) RSF Infinite Infinite Infinite Infinite Notes 1. The FEA models were run with non-linear geometry and elastic-plastic material properties. 2. The geometry used for the models was a standard 24 inch pipe (inside diameter of inches and thickness of inches) 3. The LTA is a rectangular area of metal loss with depth of inches. 4. For the 3D models, the flaw length in the circumferential direction was a 60 degree arc. 149

166 FEA Model Type Axisymmetric Solid Table 13 FEA Results for a Spherical Shell with a LTA LTA Length (in) Lambda, λ Failure Pressure (psi) RSF Infinite (148.44) Infinite (63.6) Notes 1. The FEA models were run with non-linear geometry and elastic-plastic material properties. 2. The geometry used for the models was a sphere with inside diameter of inches and thickness of inches. 3. The LTA was modeled as a circular area of metal loss with diameter equal to the LTA Length and uniform depth of inches. 150

167 Lambda, λ Table 14 API 579 Folias Factor Values for a Cylinder and Sphere Folias Factor, M t, for a Cylindrical Shell 151 Folias Factor, M t, for a Spherical Shell

168 Table 14 API 579 Folias Factor Values for a Cylinder and Sphere (Continued) Lambda, λ Folias Factor, M t, for a Cylindrical Shell ( ) λ ( ) ( ) λ + ( ) ( ) Folias Factor, M t, for a Spherical Shell Notes 1. The equation for the cylindrical shell is as follows. If λ is greater than 30, use a λ value of 30 in the calculation. 2 3 M t = λ λ λ λ λ λ λ λ 2. The equation for the spherical shell is as follows. The λ value is only limited by the inside circumference of the shell. M t ( λ ) ( λ ) 2 ( λ) ( λ) =

169 Table 15 Cases Omitted from Statistics Case Numbers Reason 132, 141, 143 The length of the flaw is unknown The failure pressure or bending moment of the test is unknown , 217 No information is known regarding these cases The defect depth is unknown. 26, 36-37, 40-41, 45, 49-50, 52, 62, 79, 83, 85, 189, 195, , 2010, 2019, , , 3023, , , These cases have a remaining thickness over original thickness ratio of less than 0.2. The statistical analysis results obtained from these cases will skew the data as cases with less than 20% of the original wall thickness are not practical applications for the various analysis methods presented here. 107 Case 107 gave an anomalous result as it was discovered that a fatigue crack had extended the pit. Database 2 105, 118, 1005, The cases in this database were not used in the LTA validation. The vessels were pressurized to the point of plastic deformation multiple times and the results obtained from the test are not consistent with the other databases. These cases are defect free control cases, and are not included in the statistical analysis. 153

170 Method 1 - API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor 2 - API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, API level 2 Folias factor 3 - API-579 Section 5, Level 2 Analysis - B31.G surface correction, exact area, API level 2 Folias factor 4 - Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor 5 - Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor 6 - Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor 7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor 8 - Thickness Averaging - API 510, 8 th Edition 9 - Thickness Averaging - API 653, 2 nd Edition 10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor 11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor 12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor Table 16 Failure Ratio Statistics for Method Validation Mean Failure Ratio Failure Ratio Standard Deviation Failure Ratio Upper 95% Prediction Limit Failure Ratio Lower 95% Prediction Limit

171 Table 16 Failure Ratio Statistics for Method Validation (Continued) Method 13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor 14 - API 579, Level 1, Hybrid 1 Analysis - Chell surface correction, rectangular area, API level 1 Folias factor 15 - API 579, Level 2, Hybrid 1 Analysis - Chell surface correction, effective area, API level 2 Folias factor 16 - API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor 17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor 18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor 19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor 20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor 21 - BS 7910, Appendix G (Isolated Defect) - B31.G surface correction, rectangular area, BG Folias factor 22 - BS 7910, Appendix G (Grouped Defects) - B31.G surface correction, rectangular area, BG Folias factor 23 - Kanninen Equivalent Stress - B31.G surface correction, rectangular area, shell theory Folias factor Mean Failure Ratio Failure Ratio Standard Deviation Failure Ratio Upper 95% Prediction Limit Failure Ratio Lower 95% Prediction Limit

172 Table 16 Failure Ratio Statistics for Method Validation (Continued) Method 24 - Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor 25 - Thickness Averaging - API 579, Level Thickness Averaging - API 579, Level Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 29 - Janelle Method, Level 1 - rectangular area 30 - Janelle Method, Level 1 - effective area Mean Failure Ratio Failure Ratio Standard Deviation Failure Ratio Upper 95% Prediction Limit Failure Ratio Lower 95% Prediction Limit

173 Table 17 Stress Limits Based on Design Codes Design Code Equipment F ys F uts ASME Section VIII, Divison 1 (pre 1999) Pressure Vessels 2/3 1/4 ASME Section VIII, Divison 1 (post 1999) Pressure Vessels 2/3 1/3.5 ASME Section VIII, Division 2 Pressure Vessels 2/3 1/3 New Proposed ASME Section VIII, Division 2 Pressure Vessels 2/3 1/2.4 EN13445 Pressure Vessels 2/3 1/2.4 CODAP Pressure Vessels 1 1/3 AS 1210 Pressure Vessels 2/3 1/2.35 BS 5500 Pressure Vessels 2/3 1/2.35 ASME B31.1 (pre 1999) Power Piping 2/3 1/4 ASME B31.1 (post 1999) Power Piping 2/3 1/3.5 ASME B31.3 Process Piping 2/3 1/3 ASME B31.4 Liquid Piping ASME B31.8, Class 1, Division I Gas Piping 4/5 1 ASME B31.8, Class 1, Division II Gas Piping ASME B31.8, Class 2 Gas Piping 3/5 1 ASME B31.8, Class 3 Gas Piping 1/2 1 ASME B31.8, Class 4 Gas Piping 2/5 1 API 620 API 650 Atmospheric Storage Tanks Low-Pressure Storage Tanks 3/5 3/10 2/3 2/5 157

174 Table 18 MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (pre 1999) and ASME B31.1 (pre 1999) Method Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit 1 - API Section 5, Level Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor API Section 5, Level Analysis - B31.G surface correction, effective area, API level 2 Folias factor API Section 5, Level Analysis - B31.G surface correction, exact area, API level 2 Folias factor Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor Modified B31.G Method (RSTRENG) B31.G surface correction, effective area, AGA Folias factor Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor

175 Table 18 MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (pre 1999) and ASME B31.1 (pre 1999) (Continued) Method 7 Original B31.G Method B31.G surface correction, parabolic area, B31-G Folias factor 8 Thickness Averaging API 510, 8 th Edition 9 Thickness Averaging API 653, 2 nd Edition 10 British Gas Single Defect Method B31.G surface correction, exact area, BG Folias factor 11 British Gas Complex Defect Method B31.G surface correction, exact area, BG Folias factor 12 Chell Method Chell surface correction, exact area, B31-G Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

176 Table 18 MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (pre 1999) and ASME B31.1 (pre 1999) (Continued) Method 13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit API 579, Level 1, Hybrid Analysis - Chell surface correction, rectangular area, API level 1 Folias factor API 579, Level 2, Hybrid Analysis - Chell surface correction, effective area, API level 2 Folias factor API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor 17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor 18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor

177 Table 18 MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (pre 1999) and ASME B31.1 (pre 1999) (Continued) Method 19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor 20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit BS 7910, Appendix G (Isolated Defect) B31.G surface correction, rectangular area, BG Folias factor BS 7910, Appendix G (Grouped Defects) B31.G surface correction, rectangular area, BG Folias factor Kanninen Equivalent Stress B31.G surface correction, rectangular area, shell theory Folias factor Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor

178 Table 18 MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (pre 1999) and ASME B31.1 (pre 1999) (Continued) Method 25 - Thickness Averaging - API 579, Level Thickness Averaging - API 579, Level Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 29 - Janelle Method, Level 1 - rectangular area 30 - Janelle Method, Level 1 - effective area Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

179 Table 19 MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (post 1999) and ASME B31.1 (post 1999) Method Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit 1 - API Section 5, Level Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor API Section 5, Level Analysis - B31.G surface correction, effective area, API level 2 Folias factor API Section 5, Level Analysis - B31.G surface correction, exact area, API level 2 Folias factor Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor

180 Table 19 MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (post 1999) and ASME B31.1 (post 1999) (Continued) Method 7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor 8 - Thickness Averaging - API 510, 8 th Edition 9 - Thickness Averaging - API 653, 2 nd Edition 10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor 11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor 12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

181 Table 19 MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (post 1999) and ASME B31.1 (post 1999) (Continued) Method 13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit API 579, Level 1, Hybrid Analysis - Chell surface correction, rectangular area, API level 1 Folias factor API 579, Level 2, Hybrid Analysis - Chell surface correction, effective area, API level 2 Folias factor API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor 17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor 18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor

182 Table 19 MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (post 1999) and ASME B31.1 (post 1999) (Continued) Method 19 API 579, Level 2, Hybrid 3 Analysis Chell surface correction, effective area, JO Folias factor 20 Battelle Method B31.G surface correction, rectangular area, Battelle Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit BS 7910, Appendix G (Isolated Defect) B31.G surface correction, rectangular area, BG Folias factor BS 7910, Appendix G (Grouped Defects) B31.G surface correction, rectangular area, BG Folias factor Kanninen Equivalent Stress B31.G surface correction, rectangular area, shell theory Folias factor Shell Theory Method Chell surface correction, exact area, shell theory Folias factor

183 Table 19 MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (post 1999) and ASME B31.1 (post 1999) (Continued) Method 25 - Thickness Averaging - API 579, Level Thickness Averaging - API 579, Level Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 29 - Janelle Method, Level 1 - rectangular area 30 - Janelle Method, Level 1 - effective area Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

184 Table 20 MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 2 and B31.3 Method Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit 1 - API Section 5, Level Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor API Section 5, Level Analysis - B31.G surface correction, effective area, API level 2 Folias factor API Section 5, Level Analysis - B31.G surface correction, exact area, API level 2 Folias factor Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor

185 Table 20 MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 2 and B31.3 (Continued) Method 7 Original B31.G Method B31.G surface correction, parabolic area, B31-G Folias factor 8 Thickness Averaging API 510, 8 th Edition 9 Thickness Averaging API 653, 2 nd Edition 10 British Gas Single Defect Method B31.G surface correction, exact area, BG Folias factor 11 British Gas Complex Defect Method B31.G surface correction, exact area, BG Folias factor 12 Chell Method Chell surface correction, exact area, B31-G Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

186 Table 20 MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 2 and B31.3 (Continued) Method 13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit API 579, Level 1, Hybrid Analysis - Chell surface correction, rectangular area, API level 1 Folias factor API 579, Level 2, Hybrid Analysis - Chell surface correction, effective area, API level 2 Folias factor API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor 17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor 18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor

187 Table 20 MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 2 and B31.3 (Continued) Method 19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor 20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit BS 7910, Appendix G (Isolated Defect) B31.G surface correction, rectangular area, BG Folias factor BS 7910, Appendix G (Grouped Defects) B31.G surface correction, rectangular area, BG Folias factor Kanninen Equivalent Stress B31.G surface correction, rectangular area, shell theory Folias factor Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor

188 Table 20 MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 2 and B31.3 (Continued) Method 25 - Thickness Averaging - API 579, Level Thickness Averaging - API 579, Level Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 29 - Janelle Method, Level 1 - rectangular area 30 - Janelle Method, Level 1 - effective area Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

189 Table 21 MAWP Ratio vs. Allowable RSF for New Proposed ASME Section VIII, Division 2 Method Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit 1 - API Section 5, Level Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor API Section 5, Level Analysis - B31.G surface correction, effective area, API level 2 Folias factor API Section 5, Level Analysis - B31.G surface correction, exact area, API level 2 Folias factor Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor

190 Table 21 MAWP Ratio vs. Allowable RSF for New Proposed ASME Section VIII, Division 2 (Continued) Method 7 Original B31.G Method B31.G surface correction, parabolic area, B31-G Folias factor 8 Thickness Averaging API 510, 8 th Edition 9 Thickness Averaging API 653, 2 nd Edition 10 British Gas Single Defect Method B31.G surface correction, exact area, BG Folias factor 11 British Gas Complex Defect Method B31.G surface correction, exact area, BG Folias factor 12 Chell Method Chell surface correction, exact area, B31-G Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

191 Table 21 MAWP Ratio vs. Allowable RSF for New Proposed ASME Section VIII, Division 2 (Continued) Method 13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit API 579, Level 1, Hybrid Analysis - Chell surface correction, rectangular area, API level 1 Folias factor API 579, Level 2, Hybrid Analysis - Chell surface correction, effective area, API level 2 Folias factor API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor 17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor 18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor

192 Table 21 MAWP Ratio vs. Allowable RSF for New Proposed ASME Section VIII, Division 2 (Continued) Method 19 API 579, Level 2, Hybrid 3 Analysis Chell surface correction, effective area, JO Folias factor 20 Battelle Method B31.G surface correction, rectangular area, Battelle Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit BS 7910, Appendix G (Isolated Defect) B31.G surface correction, rectangular area, BG Folias factor BS 7910, Appendix G (Grouped Defects) B31.G surface correction, rectangular area, BG Folias factor Kanninen Equivalent Stress B31.G surface correction, rectangular area, shell theory Folias factor Shell Theory Method Chell surface correction, exact area, shell theory Folias factor

193 Table 21 MAWP Ratio vs. Allowable RSF for New Proposed ASME Section VIII, Division 2 (Continued) Method 25 - Thickness Averaging - API 579, Level Thickness Averaging - API 579, Level Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 29 - Janelle Method, Level 1 - rectangular area 30 - Janelle Method, Level 1 - effective area Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

194 Method Table 22 MAWP Ratio vs. Allowable RSF for CODAP Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit 1 - API Section 5, Level Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor API Section 5, Level Analysis - B31.G surface correction, effective area, API level 2 Folias factor API Section 5, Level Analysis - B31.G surface correction, exact area, API level 2 Folias factor Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor

195 Table 22 MAWP Ratio vs. Allowable RSF for CODAP (Continued) Method 7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor 8 - Thickness Averaging - API 510, 8 th Edition 9 - Thickness Averaging - API 653, 2 nd Edition 10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor 11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor 12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

196 Method 13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor Table 22 MAWP Ratio vs. Allowable RSF for CODAP (Continued) Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit API 579, Level 1, Hybrid Analysis - Chell surface correction, rectangular area, API level 1 Folias factor API 579, Level 2, Hybrid Analysis - Chell surface correction, effective area, API level 2 Folias factor API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor 17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor 18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor

197 Method 19 API 579, Level 2, Hybrid 3 Analysis Chell surface correction, effective area, JO Folias factor 20 Battelle Method B31.G surface correction, rectangular area, Battelle Folias factor Table 22 MAWP Ratio vs. Allowable RSF for CODAP (Continued) Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit BS 7910, Appendix G (Isolated Defect) B31.G surface correction, rectangular area, BG Folias factor BS 7910, Appendix G (Grouped Defects) B31.G surface correction, rectangular area, BG Folias factor Kanninen Equivalent Stress B31.G surface correction, rectangular area, shell theory Folias factor Shell Theory Method Chell surface correction, exact area, shell theory Folias factor

198 Table 22 MAWP Ratio vs. Allowable RSF for CODAP (Continued) Method 25 - Thickness Averaging - API 579, Level Thickness Averaging - API 579, Level Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 29 - Janelle Method, Level 1 - rectangular area 30 - Janelle Method, Level 1 - effective area Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

199 Method Table 23 MAWP Ratio vs. Allowable RSF for AS 1210 and BS5500 Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit 1 - API Section 5, Level Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor API Section 5, Level Analysis - B31.G surface correction, effective area, API level 2 Folias factor API Section 5, Level Analysis - B31.G surface correction, exact area, API level 2 Folias factor Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor

200 Table 23 MAWP Ratio vs. Allowable RSF for AS 1210 and BS5500 (Continued) Method 7 Original B31.G Method B31.G surface correction, parabolic area, B31-G Folias factor 8 Thickness Averaging API 510, 8 th Edition 9 Thickness Averaging API 653, 2 nd Edition 10 British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor 11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor 12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

201 Table 23 MAWP Ratio vs. Allowable RSF for AS 1210 and BS5500 (Continued) Method 13 Osage Method Chell surface correction, effective area, D/t dependent Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit API 579, Level 1, Hybrid Analysis Chell surface correction, rectangular area, API level 1 Folias factor API 579, Level 2, Hybrid Analysis Chell surface correction, effective area, API level 2 Folias factor API 579, Level 1, Hybrid 2 Analysis Chell surface correction, rectangular area, BG Folias factor 17 API 579, Level 2, Hybrid 2 Analysis Chell surface correction, effective area, BG Folias factor 18 API 579, Level 1, Hybrid 3 Analysis Chell surface correction, rectangular area, JO Folias factor

202 Table 23 MAWP Ratio vs. Allowable RSF for AS 1210 and BS5500 (Continued) Method 19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor 20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit BS 7910, Appendix G (Isolated Defect) B31.G surface correction, rectangular area, BG Folias factor BS 7910, Appendix G (Grouped Defects) B31.G surface correction, rectangular area, BG Folias factor Kanninen Equivalent Stress B31.G surface correction, rectangular area, shell theory Folias factor Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor

203 Table 23 MAWP Ratio vs. Allowable RSF for AS 1210 and BS5500 (Continued) Method 25 - Thickness Averaging - API 579, Level Thickness Averaging - API 579, Level Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 29 - Janelle Method, Level 1 - rectangular area 30 - Janelle Method, Level 1 - effective area Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

204 Table 24 MAWP Ratio vs. Allowable RSF for ASME B31.4 and ASME B31.8, Class 1, Division 2 Method Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit 1 - API Section 5, Level Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor API Section 5, Level Analysis - B31.G surface correction, effective area, API level 2 Folias factor API Section 5, Level Analysis - B31.G surface correction, exact area, API level 2 Folias factor Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor

205 Table 24 MAWP Ratio vs. Allowable RSF for ASME B31.4 and ASME B31.8, Class 1, Division 2 (Continued) Method 7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor 8 - Thickness Averaging - API 510, 8 th Edition 9 - Thickness Averaging - API 653, 2 nd Edition 10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor 11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor 12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

206 Table 24 MAWP Ratio vs. Allowable RSF for ASME B31.4 and ASME B31.8, Class 1, Division 2 (Continued) Method 13 Osage Method Chell surface correction, effective area, D/t dependent Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit API 579, Level 1, Hybrid Analysis Chell surface correction, rectangular area, API level 1 Folias factor API 579, Level 2, Hybrid Analysis Chell surface correction, effective area, API level 2 Folias factor API 579, Level 1, Hybrid 2 Analysis Chell surface correction, rectangular area, BG Folias factor 17 API 579, Level 2, Hybrid 2 Analysis Chell surface correction, effective area, BG Folias factor 18 API 579, Level 1, Hybrid 3 Analysis Chell surface correction, rectangular area, JO Folias factor

207 Table 24 MAWP Ratio vs. Allowable RSF for ASME B31.4 and ASME B31.8, Class 1, Division 2 (Continued) Method 19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor 20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit BS 7910, Appendix G (Isolated Defect) B31.G surface correction, rectangular area, BG Folias factor BS 7910, Appendix G (Grouped Defects) B31.G surface correction, rectangular area, BG Folias factor Kanninen Equivalent Stress B31.G surface correction, rectangular area, shell theory Folias factor Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor

208 Table 24 MAWP Ratio vs. Allowable RSF for ASME B31.4 and ASME B31.8, Class 1, Division 2 (Continued) Method 25 - Thickness Averaging - API 579, Level Thickness Averaging - API 579, Level Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 29 - Janelle Method, Level 1 - rectangular area 30 - Janelle Method, Level 1 - effective area Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

209 Table 25 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 1, Division 1 Method Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit 1 - API Section 5, Level Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor API Section 5, Level Analysis - B31.G surface correction, effective area, API level 2 Folias factor API Section 5, Level Analysis - B31.G surface correction, exact area, API level 2 Folias factor Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor

210 Table 25 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 1, Division 1 (Continued) Method 7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor 8 - Thickness Averaging - API 510, 8 th Edition 9 - Thickness Averaging - API 653, 2 nd Edition 10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor 11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor 12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

211 Table 25 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 1, Division 1 (Continued) Method 13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit API 579, Level 1, Hybrid Analysis - Chell surface correction, rectangular area, API level 1 Folias factor API 579, Level 2, Hybrid Analysis - Chell surface correction, effective area, API level 2 Folias factor API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor 17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor 18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor

212 Table 25 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 1, Division 1 (Continued) Method 19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor 20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit BS 7910, Appendix G (Isolated Defect) B31.G surface correction, rectangular area, BG Folias factor BS 7910, Appendix G (Grouped Defects) B31.G surface correction, rectangular area, BG Folias factor Kanninen Equivalent Stress B31.G surface correction, rectangular area, shell theory Folias factor Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor

213 Table 25 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 1, Division 1 (Continued) Method 25 Thickness Averaging API 579, Level 1 26 Thickness Averaging API 579, Level 2 27 Modified API 579 Section 5, Level 1 Analysis B31.G surface correction, rectangular area, Modified API Folias factor 28 Modified API 579 Section 5, Level 2 Analysis B31.G surface correction, effective area, Modified API Folias factor 29 Janelle Method, Level 1 rectangular area 30 Janelle Method, Level 1 effective area Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

214 Method Table 26 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 2 Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit 1 API Section 5, Level Analysis B31.G surface correction, rectangular area, API level 1 Folias factor API Section 5, Level Analysis B31.G surface correction, effective area, API level 2 Folias factor API Section 5, Level Analysis B31.G surface correction, exact area, API level 2 Folias factor Modified B31.G Method B31.G surface correction, 0.85dl area, AGA Folias factor Modified B31.G Method (RSTRENG) B31.G surface correction, effective area, AGA Folias factor Modified B31.G Method B31.G surface correction, exact area, AGA Folias factor

215 Table 26 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 2 (Continued) Method 7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor 8 - Thickness Averaging - API 510, 8 th Edition 9 - Thickness Averaging - API 653, 2 nd Edition 10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor 11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor 12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

216 Table 26 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 2 (Continued) Method 13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit API 579, Level 1, Hybrid Analysis - Chell surface correction, rectangular area, API level 1 Folias factor API 579, Level 2, Hybrid Analysis - Chell surface correction, effective area, API level 2 Folias factor API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor 17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor 18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor

217 Table 26 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 2 (Continued) Method 19 API 579, Level 2, Hybrid 3 Analysis Chell surface correction, effective area, JO Folias factor 20 Battelle Method B31.G surface correction, rectangular area, Battelle Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit BS 7910, Appendix G (Isolated Defect) B31.G surface correction, rectangular area, BG Folias factor BS 7910, Appendix G (Grouped Defects) B31.G surface correction, rectangular area, BG Folias factor Kanninen Equivalent Stress B31.G surface correction, rectangular area, shell theory Folias factor Shell Theory Method Chell surface correction, exact area, shell theory Folias factor

218 Table 26 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 2 (Continued) Method 25 - Thickness Averaging - API 579, Level Thickness Averaging - API 579, Level Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 29 - Janelle Method, Level 1 - rectangular area 30 - Janelle Method, Level 1 - effective area Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

219 Method Table 27 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 3 Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit 1 - API Section 5, Level Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor API Section 5, Level Analysis - B31.G surface correction, effective area, API level 2 Folias factor API Section 5, Level Analysis - B31.G surface correction, exact area, API level 2 Folias factor Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor

220 Table 27 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 3 (Continued) Method 7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor 8 - Thickness Averaging - API 510, 8 th Edition 9 - Thickness Averaging - API 653, 2 nd Edition 10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor 11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor 12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

221 Table 27 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 3 (Continued) Method 13 Osage Method Chell surface correction, effective area, D/t dependent Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit API 579, Level 1, Hybrid Analysis Chell surface correction, rectangular area, API level 1 Folias factor API 579, Level 2, Hybrid Analysis Chell surface correction, effective area, API level 2 Folias factor API 579, Level 1, Hybrid 2 Analysis Chell surface correction, rectangular area, BG Folias factor 17 API 579, Level 2, Hybrid 2 Analysis Chell surface correction, effective area, BG Folias factor 18 API 579, Level 1, Hybrid 3 Analysis Chell surface correction, rectangular area, JO Folias factor

222 Table 27 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 3 (Continued) Method 19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor 20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit BS 7910, Appendix G (Isolated Defect) B31.G surface correction, rectangular area, BG Folias factor BS 7910, Appendix G (Grouped Defects) B31.G surface correction, rectangular area, BG Folias factor Kanninen Equivalent Stress B31.G surface correction, rectangular area, shell theory Folias factor Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor

223 Table 27 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 3 (Continued) Method 25 Thickness Averaging API 579, Level 1 26 Thickness Averaging API 579, Level 2 27 Modified API 579 Section 5, Level 1 Analysis B31.G surface correction, rectangular area, Modified API Folias factor 28 Modified API 579 Section 5, Level 2 Analysis B31.G surface correction, effective area, Modified API Folias factor 29 Janelle Method, Level 1 rectangular area 30 Janelle Method, Level 1 effective area Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

224 Method Table 28 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 4 Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit 1 API Section 5, Level Analysis B31.G surface correction, rectangular area, API level 1 Folias factor API Section 5, Level Analysis B31.G surface correction, effective area, API level 2 Folias factor API Section 5, Level Analysis B31.G surface correction, exact area, API level 2 Folias factor Modified B31.G Method B31.G surface correction, 0.85dl area, AGA Folias factor Modified B31.G Method (RSTRENG) B31.G surface correction, effective area, AGA Folias factor Modified B31.G Method B31.G surface correction, exact area, AGA Folias factor

225 Table 28 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 4 (Continued) Method 7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor 8 - Thickness Averaging - API 510, 8 th Edition 9 - Thickness Averaging - API 653, 2 nd Edition 10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor 11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor 12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

226 Table 28 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 4 (Continued) Method 13 Osage Method Chell surface correction, effective area, D/t dependent Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit API 579, Level 1, Hybrid Analysis Chell surface correction, rectangular area, API level 1 Folias factor API 579, Level 2, Hybrid Analysis Chell surface correction, effective area, API level 2 Folias factor API 579, Level 1, Hybrid 2 Analysis Chell surface correction, rectangular area, BG Folias factor 17 API 579, Level 2, Hybrid 2 Analysis Chell surface correction, effective area, BG Folias factor 18 API 579, Level 1, Hybrid 3 Analysis Chell surface correction, rectangular area, JO Folias factor

227 Table 28 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 4 (Continued) Method 19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor 20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit BS 7910, Appendix G (Isolated Defect) B31.G surface correction, rectangular area, BG Folias factor BS 7910, Appendix G (Grouped Defects) B31.G surface correction, rectangular area, BG Folias factor Kanninen Equivalent Stress B31.G surface correction, rectangular area, shell theory Folias factor Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor

228 Table 28 MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 4 (Continued) Method 25 Thickness Averaging API 579, Level 1 26 Thickness Averaging API 579, Level 2 27 Modified API 579 Section 5, Level 1 Analysis B31.G surface correction, rectangular area, Modified API Folias factor 28 Modified API 579 Section 5, Level 2 Analysis B31.G surface correction, effective area, Modified API Folias factor 29 Janelle Method, Level 1 rectangular area 30 Janelle Method, Level 1 effective area Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

229 Method Table 29 MAWP Ratio vs. Allowable RSF for API 620 Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit 1 API Section 5, Level Analysis B31.G surface correction, rectangular area, API level 1 Folias factor API Section 5, Level Analysis B31.G surface correction, effective area, API level 2 Folias factor API Section 5, Level Analysis B31.G surface correction, exact area, API level 2 Folias factor Modified B31.G Method B31.G surface correction, 0.85dl area, AGA Folias factor Modified B31.G Method (RSTRENG) B31.G surface correction, effective area, AGA Folias factor Modified B31.G Method B31.G surface correction, exact area, AGA Folias factor

230 Table 29 MAWP Ratio vs. Allowable RSF for API 620 (Continued) Method 7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor 8 - Thickness Averaging - API 510, 8 th Edition 9 - Thickness Averaging - API 653, 2 nd Edition 10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor 11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor 12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

231 Method 13 Osage Method Chell surface correction, effective area, D/t dependent Folias factor Table 29 MAWP Ratio vs. Allowable RSF for API 620 (Continued) Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit API 579, Level 1, Hybrid Analysis Chell surface correction, rectangular area, API level 1 Folias factor API 579, Level 2, Hybrid Analysis Chell surface correction, effective area, API level 2 Folias factor API 579, Level 1, Hybrid 2 Analysis Chell surface correction, rectangular area, BG Folias factor 17 API 579, Level 2, Hybrid 2 Analysis Chell surface correction, effective area, BG Folias factor 18 API 579, Level 1, Hybrid 3 Analysis Chell surface correction, rectangular area, JO Folias factor

232 Method 19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor 20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor Table 29 MAWP Ratio vs. Allowable RSF for API 620 (Continued) Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit BS 7910, Appendix G (Isolated Defect) B31.G surface correction, rectangular area, BG Folias factor BS 7910, Appendix G (Grouped Defects) B31.G surface correction, rectangular area, BG Folias factor Kanninen Equivalent Stress B31.G surface correction, rectangular area, shell theory Folias factor Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor

233 Table 29 MAWP Ratio vs. Allowable RSF for API 620 (Continued) Method 25 Thickness Averaging API 579, Level 1 26 Thickness Averaging API 579, Level 2 27 Modified API 579 Section 5, Level 1 Analysis B31.G surface correction, rectangular area, Modified API Folias factor 28 Modified API 579 Section 5, Level 2 Analysis B31.G surface correction, effective area, Modified API Folias factor 29 Janelle Method, Level 1 rectangular area 30 Janelle Method, Level 1 effective area Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

234 Method Table 30 MAWP Ratio vs. Allowable RSF for API 650 Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit 1 API Section 5, Level Analysis B31.G surface correction, rectangular area, API level 1 Folias factor API Section 5, Level Analysis B31.G surface correction, effective area, API level 2 Folias factor API Section 5, Level Analysis B31.G surface correction, exact area, API level 2 Folias factor Modified B31.G Method B31.G surface correction, 0.85dl area, AGA Folias factor Modified B31.G Method (RSTRENG) B31.G surface correction, effective area, AGA Folias factor Modified B31.G Method B31.G surface correction, exact area, AGA Folias factor

235 Table 30 MAWP Ratio vs. Allowable RSF for API 650 (Continued) Method 7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor 8 - Thickness Averaging - API 510, 8 th Edition 9 - Thickness Averaging - API 653, 2 nd Edition 10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor 11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor 12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

236 Method 13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor Table 30 MAWP Ratio vs. Allowable RSF for API 650 (Continued) Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit API 579, Level 1, Hybrid Analysis - Chell surface correction, rectangular area, API level 1 Folias factor API 579, Level 2, Hybrid Analysis - Chell surface correction, effective area, API level 2 Folias factor API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor 17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor 18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor

237 Method 19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor 20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor Table 30 MAWP Ratio vs. Allowable RSF for API 650 (Continued) Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit BS 7910, Appendix G (Isolated Defect) B31.G surface correction, rectangular area, BG Folias factor BS 7910, Appendix G (Grouped Defects) B31.G surface correction, rectangular area, BG Folias factor Kanninen Equivalent Stress B31.G surface correction, rectangular area, shell theory Folias factor Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor

238 Table 30 MAWP Ratio vs. Allowable RSF for API 650 (Continued) Method 25 - Thickness Averaging - API 579, Level Thickness Averaging - API 579, Level Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 29 - Janelle Method, Level 1 - rectangular area 30 - Janelle Method, Level 1 - effective area Allowable RSF Mean MAWP Ratio MAWP Ratio Standard Deviation MAWP Ratio Upper 95% Prediction Limit MAWP Ratio Lower 95% Prediction Limit

239 Table 31 Geometry Parameters for the Circumferential Extent Validation Cases Case Pipe OD (in) Pipe thickness (in) Axial extent of the flaw (in) Circumferential extent of the flaw (in) Flaw depth (% of wall thickness) % % % % % Table 32 Circumferential Extent Validation Results Case Pressure at Failure (psi) Moment at Failure (in-lb) Failure Side Material Ultimate Strength (psi) Tension Side Equivalent Stress (psi) Compression Side Equivalent Stress (psi) Error in calculated stress Compression % Tension % Compression % Compression % Tension % 223

240 CHAPTER XIV FIGURES Determine tmin (see Appendix A) Locate Regions of Metal Loss on the Equipment Assessment Using Thickness Profiles? Yes No Take Point Thickness Readings and Use Additional NDE to Confirm General Corrosion Determine Inspection Plane(s) and Take Thickness Profile Data Determine tmm, tam and COV from the Thickness Data Determine tmm and L Determine CTP's in the Longitudinal and Circumferential Directions Determine s, c, and tam for the CTP's Determine Average Thickness, tam, within the Zone for Thickness Averaging, see Paragraph Yes Type B or C Component? No Yes Evaluate the MAWP Using a Section 4 Level 2 or 3 Assessment Assessment Using Thickness Profiles? Yes No COV > 10%? No Yes Obtain Thickness Profiles? No Levell 3 Assessment? Yes No Is s<=l? No Yes Longitudinal or Meridonal Extent of Metal Loss is Acceptable Cylinder, Cone No or Elbow? Assessment Complete Yes Use tam for Calculations Evaluation Option: Evaluate Circumferential Extent of Metal Loss Using Section 5, Level 1 Conservative Approach Thickness Averaging Stress Analysis Localized Metal Loss Use tam=tmm for Calculations Determine tam Using Thickness Data Within Length L Evaluate Using a Level 3 Assessment Evaluate Using Section 5 Evaluate Using Section 4, Level 1 or Level 2 Assessment Figure Assessment Procedure To Evaluate A Component With Metal Loss Using Part 4 and Part 5 Figure 1 Logic Diagram for the Assessment of General or Local Metal Loss in API

241 Obtain Equipment Data No Perform Level 1 Assessment? Yes No Equipment Is Acceptable per Level 1 Criteria? Rerate Equipment? No Yes Yes Yes Remaining Life Acceptable per Level 1 Criteria? Perform Rerate per Level 1 Criteria to Reduce Pressure and/or Temperature No Perform a Level 2 Assessment? No Yes No Equipment is Acceptable per Level 2 Criteria? No Rerate Equipment? Yes Perform a Level 3 Assessment? Yes No Yes Perform Rerate per Level 2 Criteria to Reduce Pressure and/or Temperature No Remaining Life Acceptable per Level 2 Criteria? Yes Equipment Acceptable per Level 3 Assessment? No Yes No Rerate Equipment? Remaining Life Acceptable per Level 3 Criteria? No Yes Yes Repair, Replace, or Retire Equipment Perform Rerate per Level 3 Criteria to Reduce Pressure and/or Temperature Return the Equpiment to Service Figure 2 Logic Diagram for the Assessment of Local Thin Areas in API

242 t avg Uniform Metal Loss t COV = t sd /t avg t sd t sd t avg Thickness (a) Small Variability in Thickness Profiles and the COV t avg Uniform Metal Loss t COV = t sd /t avg t sd t sd t avg Thickness (b) Large Variability in Thickness Profiles and the COV Figure 3 Coefficient of Variation for Thickness Reading Data 226

243 CL C L Metal Loss Metal Loss C1 C2 C3 C1 C2 C3 M1 M2 M3 M1 M2 M3 M3 Cylindrical Shell Conical Shell M1 Extrados C2 C3 M1 M2 M3 C L C1 Metal Loss Intrados Elbow or Pipe Bend Figure 4 Examples of an Inspection Grid to Define the Extent of Metal Loss Damage 227

244 M5 C1 C2 C3 C4 C5 C6 C7 M4 M3 M2 M1 C C L Line M - path of minimum thickness readings in the longitudinal direction Line C - path of minimum thickness readings in the circumferential direction Cylindrical Shell (a) Inspection Planes and the Critical Thickness Profile S t t min (b) Critical Thickness Profile (CTP) - Longitudinal Plane (Projection of Line M) t mm c t t c t mm (c) Critical Thickness Profile (CTP) - Circumferential Plane (Projection of Line C) Figure 5 Establishing Longitudinal and Circumferential Critical Thickness Profiles from an Inspection Grid 228

245 Flaw S Path of Maximum Metal Loss t t min Thickness Profile t mm (a) Isolated Flaw S Flaw 2 Flaw 1 t t min Thickness Profile (b) Network Of Flaws Figure 6 Critical Thickness Profiles for Isolated and Multiple LTAs 229

246 RSF a C L Nozzle Reinforcement Zone t n Reinforcing Pad L no t e Shell d i t v L ni L v L v Nozzle with a Reinforcement Element Notes: 1. Lv = max di, ( di 2 + tn + tv) (zone for thickness averaging in the horizontal direction). 2. Lno = min 2.5 tv, ( 2.5tn + te ) (zone for thickness averaging in the vertical direction on the outside of the shell). 3. Lni = min[ 2.5 tv, 2.5tn ] (zone for thickness averaging in the vertical direction on the inside of the shell). 4. tv, tn, teare the furnished vessel, nozzle and reinforcing pad thicknesses, respectively. 5. is the current inside diameter. Lower 95% Ratio - Calculated MAWP to Actual Failure Figure 7 Zone for Thickness Averaging in A Nozzle 230

247 Stiffening Ring L 1 msd Nozzle L 4 msd Flaw Pipe Support L 2 msd L 3 msd Conical Transition Notes: 1. For the example shown above, the minimum distance to a major structural discontinuity is: L min msd Lmsd, Lmsd, Lmsd, L msd 2. Typical major structural discontinues associated with vertical vessels are shown in this figure. 3. For horizontal drums, the saddle supports would constitute a major structural discontinuity and for a spherical storage vessel, the support locations (shell-to-leg junction) would constitute a major structural discontinuity. The location of the flaw from these support locations would need to be considered in determining L msd as well as the distances from the nearest nozzle, piping/platform support, conical transition, and stiffening ring. 4. The measure of the minimum distances defined in this figure is from the nearest edge of the region of local metal loss to the nearest weld of the structural discontinuity. Figure 8 LTA to Major Structural Discontinuity Spacing Requirements in API

248 C L Small End Cylinder t S Cone R S L v Zones for Thickness Averaging - Small End L v L v t C R L Large End Cylinder L v Zones for Thickness Averaging - Large End t L Notes: 1. Lv = 0.78 RStS (thickness averaging zone for the small end cylinder). 2. Lv = 0.78 RStC (thickness averaging zone for the small end cone). 3. Lv = 1.0 RLtC (thickness averaging zone for the large end cone). 4. Lv = 1.0 RLtL (thickness averaging zone for the large end cylinder). 5. ts, tc, tlare the furnished small end vessel, cone, and large end vessel thicknesses, respectively. 6. R, R are the small end and large end vessel inside radii, respectively. S L Figure 9 Example of a Zone for Thickness Averaging at a Major Structural Discontinuity 232

249 ACCEPTABLE R t UNACCEPTABLE λ Figure 10 Level 1 Assessment Procedure for Local Metal Loss in Cylindrical Shells (Circumferential Stress) 233

250 s i+3 s i+2 s i+1 s i s 2 s 1 t t min Cross Hatched Area - A i A i o - Area Within Box (a) Subsection for the Effective Area Procedure RSF i Minimum RSF S i (b) Minimum RSF Determination Figure 11 Determination of the RSF for the Effective Area Procedure 234

251 l i d(x) dx t l s i l e i Figure 12 Exact Area Integration Bounds 235

252 A Circumferential Plane t V M y F M T p Di 2 Ri M T F M x M x M y V A M y Region Of Local Metal Loss c t θ θ Di 2 F M x M T P Section A-A Figure 13 Supplemental Loads for a Longitudinal Stress Assessment 236

253 y,y Metal Loss t mm A B θ θ y Lx x x Df 2 y x x Do 2 Di 2 t (a) Region Of Local Metal Loss Located on the Inside Surface y,y Metal Loss θ A θ B t mm y Lx Df 2 x x y x x Do 2 Di 2 t (b) Region Of Local Metal Loss Located on the Outside Surface Figure 14 Assessment Locations and Parameters for a Longitudinal Stress Assessment 237

254 Circumferential LTA Screening Curve RSF a = t mm /t nom c/d m Figure 15 Longitudinal Stress, Level 1 Screening Curve l total dpatch d j d e,i d i t e l i s i Current Depth Increment, d j Figure 16 BG Depth Increment Approach 238

255 Figure 17 Table Curve 3D Fit of the Shell Theory Folias Factor D Solid FEA Axisymmetric FEA Current API 579 Level 1 Current API 579 Level 2 Modified API 579 Level 1&2 0.8 RSF Lambda, λ Figure 18 Comparison Between Analysis Methods and FEA Trends for a Cylinder with a LTA 239

256 Figure 19 3D Solid FEA Model Geometry of a Cylinder for λ = 5 Figure 20 Axisymmetric FEA Model Geometry of a Cylinder for λ = 5 240

257 folias Rank 17 Eqn 6007 y=a+bx+cx^2+dx^3+ex^4+fx^5+gx^6+hx^7+ix^8+jx^9+kx^(10) r^2=1 DF Adj r^2=1 FitStdErr= e-08 Fstat= e+19 a= b= c= d= e= f= g= h= e-05 i= e-07 j= e-08 k= e lam Figure 21 Table Curve 2D Fit of the Modified API 579 Folias Factor Current API 579 Level 2 RSTRENG Original Folias Data Proposed API 579 Level 1&2 Folias Factor, M t Lambda, λ Figure 22 Comparison of the Old API 579 Folias Factor to the Modified Folias Factor and the Original Folias Data 241

258 R t λ l Rt Screening Curve Equations = 0.2 for λ RSF a RSF a Rt = RSFa 1.0 for < λ < 20.0 Mt Mt Rt = 0.90 for λ Figure 23 Screening Curve for the Circumferential Extent of an LTA 242

259 R t Proposed Level 1&2 Remaining Strength Factor Current Level 2 Remaining Strength Factor λ l Figure 24 Comparison of the Old API 579 Level 1 Screening Curve to the Modified Folias Factor Level 1 Screening Curve 243

260 Figure 25 Axisymmetric FEA Model Geometry of a Sphere for λ = Axisymmetric FEA Current API RSF Lambda, λ Figure 26 Comparison Between Analysis Methods and FEA Trends for a Sphere with a LTA 244