system reliability assessment of offshore pipelines · 2015-09-23 · intan fadzilah and their two...

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System Reliability Assessment of Offshore Pipelines

Proefschrift

ter verkrijging van de graad van doctor

aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben,

voorzitter van het College voor Promoties,

in het openbaar te verdedigen op woensdag 19 oktober 2011 om 12:30 uur

door

Zahiraniza MUSTAFFA

Master of Science in Water Resources Engineering

geboren te Perak, Maleisië

Dit proefschrift is goedgekeurd door de promotor:

Prof. drs. ir. J.K. Vrijling

Copromotor:

Dr. ir. P.H.A.J.M. van Gelder

Samenstelling promotiecommissie:

Rector Magnificus,

Prof. drs. ir. J.K. Vrijling,

Dr. ir. P.H.A.J.M. van Gelder,

Prof. ir. dr. M. F. Nuruddin,

Prof. ir. T. Vellinga,

Prof. dr. ir. C. van Rhee,

Prof. dr. ir. M. A. Gutiérrez,

Mr. M. S. Ayob,

voorzitter

Technische Universiteit Delft, promotor

Technische Universiteit Delft, copromotor

Universiti Teknologi PETRONAS, Maleisië

Technische Universiteit Delft



PETRONAS, Maleisië

ISBN 978-90-8570-421-8

Copyright © 2011 by Zahiraniza Mustaffa, Hydraulic Engineering Section, Faculty of Civil Engineering and Geosciences, Delft University of Technology, The Netherlands.

All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by means, without prior permission from the author and publisher.

Printed in the Netherlands by WÖHRMANN PRINT SERVICE

Cover layout: Nik Shahman Nik Ahmad Ariff (NSA Design); [email protected]

Cover image: Farhan Iqbal Mohd Yusof

For my Ammar, for his innocent sacrifice

ACKNOWLEDGEMENT

It would not have been possible to write this doctoral thesis without the help and support of the kind people around me, to only some of whom it is possible to give particular mention here. It is a pleasure to thank those who made this thesis possible.

Above all, I owe my deepest gratitude to my husband Dr. Mohd Fadzil Hassan for his personal support and great patience at all times. My parents (Tn. Hj. Mustaffa Mohd Ariffin & Pn. Hjh. Zaharah Mohamad Zin), parents-in-laws (Tn. Hj. Hassan Abdullah & Pn. Hjh. Fatimah Khamis), brother (Ahmed Muzairee) and sister (Maria Hani) have given me their prayers and unequivocal support throughout, as always, for which my mere expression of thanks likewise does not suffice.

This thesis would not have been possible without the full support of my promotor, prof. drs. ir. Han Vrijling. His continuous trust and confidence are highly acknowledged. I am heartily thankful to my supervisor, dr. ir. Pieter van Gelder, whose encouragement, guidance, and support have enabled me to develop an understanding on the subject Probabilistic Design. His kindness, understanding, and friendship have been truly in-valuable on both academic and personal levels, for which I am extremely grateful.

I wish to express my outmost appreciation to my PhD examination committee members: (i) Prof. Ir. Dr. Muhd Fadhil Nuruddin, Dean of Engineering of Universiti Teknologi PETRONAS (UTP), Malaysia, (ii) Mr. Mohd Sapihie Ayob, Principal Engineer (Structural Mechanics) of PETRONAS Group Technical Solution, Technology & Engineering Division (PGTS), Malaysia, (iii) prof. ir. Tiedo Vellinga, professor in Ports and Waterways (TU Delft), (iv) prof. dr. ir. Cees van Rhee, professor in Dredging Technology (TU Delft), and (v) prof. dr. ir. Miguel A. Gutiérrez, professor in Reliability of Structures and Processing (TU Delft). Your comments and recommendations during the reviewing process of the thesis are highly acknowledged.

I would like to acknowledge the major financial support provided by the Universiti Teknologi PETRONAS (UTP), Malaysia. I owe sincere and earnest thankfulness to the management of UTP, especially to the Rector Datuk Dr. Zainal Abidin Hj. Kassim, and the Head of Department of Civil Engineering, Assoc. Prof. Ir. Dr. Shahir Liew Abdulllah. Supplementary financial support awarded by the Schlum-berger Foundation is indeed highly appreciated as well.

It is an honour for me to collaborate with the Malaysian-owned oil and gas company, the Petroliam Nasional Berhad (PETRONAS). It has been a great experience to be working with representatives from the PETRONAS Carigali Sdn. Bhd. (PCSB), namely, Ir. Mohd Ashri Mustapha and Mr. Zaini Roslan, as well as the PCSB engineers

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at the Peninsular Malaysia Operation (PMO): Tn. Hj. Muhammad Bidon, Mr. Mohd Zaini Ismail, Mr. Wan Mohd Shafrizal Wan Mohd Yusof, Mr. Adli Budiman Zaidin@Ziden, Mr. Mohd Shahrustami Mohd Nadzeri, Mrs. Noorhidayah Mahamud, Mrs. Noraini Wahab, and Ms. Phong Soo Kwan.

I am indebted to many of my ex-UTP students who are presently PETRONAS engineers: Engr. Nuzul Izani Mohammed and Engr. Haniza Haron whom I consulted for professional opinion and expert judgement in the technical aspects of this research.

I must show my admiration to the people involved in the thesis cover preparation: Engr. Farhan Iqbal Mohd Yusof, for his technical but artistic credibility in capturing the image of the pipelines, and Mr. Nik Shahman Nik Ahmad Ariff (NSA Design), for his creative sense of touch in designing the layout of the thesis cover. I am also very thank-ful to drs. Mariette van Tilburg as well as dr. ir. Pieter van Gelder for their assistance in the translation work of this thesis.

I would like to express my sincere gratitude to de Groot’s family: Ing. Gert, Mw. Intan Fadzilah and their two beautiful princesses, Aisha Nur Sofia and Fatima Zahra Maria. I will always remember their generosity and encouragement which con-tributed to the prolonged motivation to survive in this foreign country.

I am most grateful to my very best friend Dr. Bilkiss B. Issack in Edmonton, Canada for her never ending support and true friendship in the last ten years. Not to forget Dr. Saied Saiedi, a person who always motivates me in every aspect of life. My four years working experience with him have equipped me with what it needs to have to face this challenging journey; not only as a PhD student, but also as a mother and wife. I thank him for that.

Amongst my fellow postgraduate students in the Department of Hydraulic Engineering, special thanks to my officemates Mr. Gholamreza Shams, ir. Alex Dawotola, Mr. Hu Zhan and ir. Cornelis van Dorsser for sharing good inputs in this doctoral research, as well as their great sense of humour.

Last, but by no means the least, I thank to all my Malaysian communities in Delft for their support and encouragement throughout. Special mention to my PhD sisters Wan Mazlina, Siti Mariam and Wan Nurul Karimah for their great sisterhoods. The occasional meetings have definitely promoted good social environment and at the same time added more spices in life.

I offer my regards and blessings to all of those who supported me in any respect during the completion of the project. For any errors or inadequacies that may remain in this doctoral work, of course, the responsibility is entirely my own.

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SUMMARY

Offshore pipelines, a complex civil engineering system, comprising up to a total length of thousands of kilometres, have been the most practical and low price means of transport-ing hydrocarbon in the offshore oil and gas industry. As the structure operates with time, it is exposed to many types of defects. Corrosion has been one of the biggest threats to offshore pipelines. The World Corrosion Organisation (2010) for example, highlighted an estimated $2.2 trillion annual cost of corrosion worldwide (3 to 4 % of gross domestic product (GDP) of industrialized countries). Leakage from corrosion fail-ures lead to oil spill in the sea water and this is something intolerable and has become one of the greatest public attentions and concerns.

Corrosions deteriorate the structural strength and integrity of a pipeline. Their growth evolves with time, spreading in size and increasing in quantities. It is then said that cor-rosions are time-variant processes, making the pipeline as a time-dependant structure and so does its reliability. In addition to that, corrosions in offshore pipelines are ran-dom, unique, complicated and describing these are not something straight forward. Cor-rosion development is proportionally influenced by its surrounding environment and pipeline operational systems, in which their characteristics cannot always be described by deterministic approaches as in the design standards or codes. Even though design codes have helped avoid unnecessary repairs and replacements, the excessive conservatism of the codes continues to cause some unnecessary repairs. Probabilistic methods are then seemed to be the best approaches to deal with corrosions. The methods have been fre-quently used in the design of civil structures such as dikes, storm surge barriers, bridges, hydraulic structures, buildings, etc. The methods are represented by statistical distribu-tion functions of the strength and load variables which distinguishes from the application of safety coefficients as in the design standards.

Obeying to the fact that corrosion can never be stopped from occurring in pipeline sys-tems, the best way to tackle the problem is to critically deal with it. The main intention of this thesis is to identify, apply and judge the suitability of the probabilistic methods in evaluating the system reliability of offshore pipelines subjected to corrosion, and later to optimise corrosion maintenance strategies. The thesis is aimed at developing the so called an ‘in-house model’ which is entirely based on historical data or events. Using

iii

knowledge of forensic evidence as an aid, the work involved retracing historical processes and activities, and applying this information as evidence to correlate certain relation-ships that lead to corrosion development in the pipeline. It is assumed that creating in-house models is one of the best options to determine pipeline’s compatibility with the ex-isting design standards or codes. Reason being, those standards which are experimen-tally or numerically based are restricted to parameters or laboratory set ups where the works have been carried out. In reality, neither reservoir conditions and characteristics, nor pipeline operations completely comply with the rules stated in the design standards. This limitation has then exposed the system to many types of uncertainties.

Uncertainties produced in the corrosion inspection and maintenance tool are addressed at the beginning of the thesis. The dependencies among corrosion parameters are prob-abilistically evaluated. As corrosion grows deeper, the defect length and width will also expand to certain extend, obeying to the correlations that exist among them. The in-sights from this analysis is then used to develop an in-house model which provides better representation of corrosion shapes compared to the existing failure pressure models. The so called dimensionless limit state function model provides an easier approach to assess the reliability of corroded pipeline subjected to internal pressure without actually de-pending on the design standards.

Also highlighted in this thesis are corrosion maintenance strategies in the pipelines. Maintaining corrosion is normally carried out by releasing corrosion inhibitor into the pipeline. It is important to highlight that the effectiveness of the maintenance works is something that cannot be directly measured from the design standards too. In this the-sis, the effectiveness of the past maintenance practice carried out by the pipeline opera-tors is proposed to be checked by mean of reliability-based maintenance model. This model is governed by factors that contribute to corrosion and also those against its de-velopment. Treating this model as a benchmark, the past maintenance practice can be proposed to be improved in any ways, which consequently leads to optimization in the system. The present work proposes several approaches to carry out the work in order to optimise or control corrosion growth. The approach which utilizes corrosion physics seems to provide favourable results.

Not only has become the magnitude of corrosion the interest of the thesis, but also their occurrence in space. The spatial analysis can be investigated using theories on hydrody-namics involving fluid-structure interactions between the external flows and circular cyl-inders placed close to the wall. In the present case, the circular cylinder placed close to the wall mimics an offshore pipeline laid on the sea bed. External corrosions formed in offshore pipelines placed close to the shore are assumed to be partly contributed by such fluid-structure interactions. The present work illustrates interesting results when those theories are validated with pipeline data from the field. The updated knowledge from this fluid-structure interaction is hoped to be given more attention by the industry and perhaps to be incorporated into the current subsea pipeline designs.

iv

Outcomes from this thesis are beneficial to the oil and gas industry in many ways. Not only minimizing cost impact, but also educating and providing valuable knowledge to pipeline operators. The dimensionless limit state function model for instance, offers a simpler and straight forward approach for which pipeline operators can interpret corro-sion characteristics easily. The model is applicable to many corrosion scenarios that take place in the pipeline. Not only the probability of failure can be computed for the whole pipeline segment, but also at any pipeline sections of interests. The reliability-based maintenance model will alert pipeline operators with the way maintenance has been car-ried out in the past. Proper optimization techniques related to corrosion inhibitor re-leased can be proposed from here, allowing operators to act according to their present available resources and techniques. It is hoped that illustrations provided in this thesis are applicable to other civil engineering structures of similar concerns.

Zahiraniza Mustaffa

October 2011, Delft

v

SAMENVATTING

Offshore-pijpleidingen, een complex civiel technisch systeem van soms een totale lengte van duizenden kilometers, zijn het meest praktische en goedkoopste middel van transport van koolwaterstoffen in de offshore olie- en gas industrie. Echter, na verloop van tijd blijkt dat dit systeem onderhevig kan zijn aan vele defecten. Corrosie is een van de grootste bedreigingen voor de offshore-pijpleidingen. De Wereld Corrosie Organisatie (2010) benadrukt dat de jaarlijkse kosten aan corrosie wereldwijd naar schatting 2200 miljard dollar bedragen (3 tot 4% van het bruto binnenlands product (BBP) van de ge-industrialiseerde landen). Corrosie in pijpleidingen hebben lekkages van olie in het zee-water tot gevolg; dit is onaanvaardbaar en is een belangrijk onderwerp van publieke aan-dacht en bezorgdheid geworden.

Corrosie verslechtert de constructieve sterkte en integriteit van een pijpleiding. Corrosie evolueert met de tijd mee, zich verspreidend in grootte en stijgend in omvang. Er kan gesteld worden dat corrosie een tijdsafhankelijk proces is, waardoor de pijpleiding een tijdsafhankelijke constructie wordt en, ten gevolge daarvan, dit ook geldt voor de be-trouwbaarheid van de constructie. Bovendien is corrosie in offshore-pijpleidingen wille-keurig, uniek en gecompliceerd, en is er geen eenduidige beschrijving van dit proces mo-gelijk. Het ontstaan van corrosie wordt in belangrijke mate beïnvloed door de omgeving en de operationele systemen van de pijpleidingen; hierdoor kunnen de specifieke eigen-schappen niet altijd worden beschreven in termen van standaard ontwerp-normen of co-des. Hoewel ontwerp-codes hebben bijgedragen aan het voorkomen van onnodige repara-ties en vervangingen, blijft het conservatisme van de codes nog steeds de oorzaak van onnodige reparaties. Probabilistische methoden lijken de beste benaderingswijze te zijn voor het probleem van corrosie. Probabilistische methoden zijn veelvuldig gebruikt in het ontwerp van civiele constructies zoals dijken, stormvloed keringen, bruggen, en overi-ge waterbouwkundige constructies en gebouwen, enz. In deze methoden wordt statisti-sche verdelingen van functies van sterkte- en belastings-variabelen toegepast, welke zich onderscheidt van de toepassing met veiligheidscoëfficiënten volgens de standaard ont-werp-normen.

Uitgaande van het feit dat corrosie nooit voorkomen kan worden in pijpleidingsystemen, volgt dat de beste manier om het probleem aan te pakken is om er kritisch mee om te

vi

gaan. Het belangrijkste doel van dit proefschrift is het identificeren, toepassen en oorde-len over de geschiktheid van probabilistische methoden bij de evaluatie van de systeem-betrouwbaarheid van offshore-pijpleidingen die aan corrosie onderworpen zijn, en later optimale corrosie onderhoudsstrategieën te ontwikkelen. Het proefschrift is gericht op het ontwikkelen van de zogenaamde een ‘in-house model’, die volledig is gebaseerd op histori-sche gegevens of gebeurtenissen. Met behulp van de kennis van forensische techniek, zijn historische processen en activiteiten geanalyseerd en is deze informatie vervolgens toege-past als bewijs van de correlatie tussen bepaalde eigenschappen die tot corrosie-ontwikkeling in de pijplijn leiden. Er is van uitgegaan dat het creëren van interne model-len een van de beste opties is om de compatibiliteit van de pijpleiding met de bestaande ontwerp-normen of -codes te bepalen. De reden hiervoor is dat de normen die experimen-teel of numeriek gebaseerd zijn, beperkt worden door parameters en laboratorium criteria waar de experimenten zijn uitgevoerd. In werkelijkheid voldoen noch reservoir voorwaar-den en kenmerken noch de pijpleiding bedrijfsvoering aan de standaard regels zoals ge-noemd in de ontwerp-normen. Deze beperking heeft de vele onzekerheden van het sys-teem zichtbaar gemaakt.

Aan het begin van deze proefschrift worden de onzekerheden in corrosie-inspectie en on-derhoud behandeld. De onderlinge afhankelijkheden tussen alle variabelen zijn volgens probabilistische methoden geëvalueerd. Als corrosie dieper groeit, zullen de lengte en breedte zich ook uitbreiden, volgens de reeds bestaande correlaties. De inzichten uit de-ze analyse worden vervolgens gebruikt om een in-house model te ontwikkelen, wat een beter beeld geeft van corrosie in vergelijking met de bestaande failure-pressure modellen. Het zogenaamde ‘dimensionless limit state function model’ biedt een eenvoudigere aan-pak voor het beoordelen van de betrouwbaarheid van gecorrodeerde pijpleidingen, on-derworpen aan interne druk, onafhankelijk van de bestaande ontwerp-normen.

In deze proefschrift wordt ook de nadruk gelegd op corrosie onderhoudsstrategieën in pijpleidingen. Onderhoud van corrosie wordt normaal gesproken uitgevoerd door het vrijgeven van corrosieremmers in de pijpleidingen. Over het algemeen onderschat men onvoorziene zaken, zoal menselijke interventie, die ook een impact hebben op de onder-houdsstrategie. Het is belangrijk om te benadrukken dat de doeltreffendheid van de on-derhoudswerkzaamheden niet rechtstreeks met behulp van ontwerp-normen gemeten kan worden. In deze dissertatie wordt voorgesteld om de doeltreffendheid van de voorafgaan-de onderhoudspraktijken, uitgevoerd door de pijpleiding exploitant /beheerder, uit te voeren volgens het ‘reliability-based maintenance model’. In dit model worden zowel de factoren die corrosie veroorzaken als de factoren die corrosie tegen gaan gecombineerd. Deze proefschrift stelt verschillende benaderingen voor om de werkzaamheden te opti-maliseren en corrosie-groei onder controle te houden. Deze fysische aanpak van corrosie lijkt gunstige resultaten op te leveren.

Niet alleen is de omvang van corrosie, maar ook de ruimtelijke variabiliteit van corrosie, van belang in deze proefschrift. De ruimtelijke analyse kan worden onderzocht met be-hulp van theorieën uit de hydrodynamica; namelijk de vloeistof-constructie interacties

vii

viii

tussen de externe stromen en circulaire cilinders dicht bij de wand. In de onderhavige zaak, de circulaire cilinder dicht bij de muur geplaatst bootst een offshore pijpleiding ge-legd op de zeebodem. De circulaire cilinder lijkt op pijplijn in de onderhavige zaak. Het is de veronderstelling dat externe corrosie in offshore-pijpleidingen, dicht bij de kust, wordt veroorzaakt door dergelijke vloeistof-constructie interacties. Het huidige werk illu-streert interessante resultaten wanneer deze theorieën worden gevalideerd met pijpleiding gegevens uit het veld. De huidige kennis van deze vloeistof-constructie interactie krijgt hopelijk meer aandacht van de industrie en wordt wellicht opgenomen in de huidige on-derzeese pijpleiding ontwerpen.

Resultaten van deze proefschrift zullen in vele opzichten gunstig zijn voor de olie- en gas industrie: niet alleen het minimaliseren van onkosten, maar ook het informeren en verstrekken van waardevolle kennis aan pijpleiding exploitanten. Het ‘dimensionless li-mit state function model’ bijvoorbeeld, biedt een eenvoudiger en heldere benadering waarmee de pijpleiding exploitanten corrosie eigenschappen gemakkelijk kunnen interpre-teren. Het model is van toepassing op veel corrosie-scenario's die in de pijplijn plaats-vinden. Niet alleen de kans op falen voor de gehele pijpleiding kan worden berekend, maar ook belangrijke secties van een pijpleiding kunnen onder de loep genomen worden. Het op betrouwbaarheid gebaseerde model (‘reliability-based maintenance model’) geeft informatie aan pijpleiding exploitanten over de wijze waarop onderhoud in het verleden is uitgevoerd. Juiste optimalisatie technieken, gerelateerd aan ingevoerde corrosieremmers, kunnen hiermee voorgesteld worden, en geven de mogelijkheid aan exploitanten om vol-gens de beschikbare middelen en technieken te handelen. Hopelijk kunnen de illustraties in deze proefschrift van toepassing zijn op andere civiel – technische constructies met een vergelijkbare problematiek.

Zahiraniza Mustaffa

Oktober 2011, Delft

CONTENTS

Acknowledgement i

Summary iii

Samenvatting vi

Contents ix

Chapter 1 Introduction 13 1.1 Background----------------------------------------------------------------------------------- 13 1.2 Motivation ------------------------------------------------------------------------------------ 19

1.2.1 Pipeline Codes and Standards ............................................................ 19 1.2.2 Probabilistic vs. Traditional (Deterministic) Approach ...................... 20

1.3 Fundamentals of Study -------------------------------------------------------------------- 23 1.3.1 Problem Statement............................................................................. 23 1.3.2 Objectives........................................................................................... 24 1.3.3 Study Approach.................................................................................. 24 1.3.4 Scientific and Social Relevance ........................................................... 25

1.4 Outline of Thesis---------------------------------------------------------------------------- 26

Chapter 2 Theories on Probabilistic Methods 29 2.1 Introduction ---------------------------------------------------------------------------------- 29 2.2 Elements of Probability ------------------------------------------------------------------- 29

2.2.1 Uncertainties....................................................................................... 30 2.2.2 Random Variables and Probability Distributions ............................... 30 2.2.3 Extreme Value Distributions .............................................................. 33

2.3 Regression Analysis ------------------------------------------------------------------------ 34 2.3.1 Background......................................................................................... 34 2.3.2 Models ................................................................................................ 35 2.3.3 Model Parameter Estimates................................................................ 36 2.3.4 Analysis of Residuals .......................................................................... 38 2.3.5 Statistics ............................................................................................. 39

2.4 Reliability Analysis ------------------------------------------------------------------------- 39 2.4.1 Reliability of Element ......................................................................... 39 2.4.2 Limit State, Strength and Load.......................................................... 40

2.4.3 Calculation Methods........................................................................... 41 2.4.4 Reliability of Systems ......................................................................... 43

2.5 Conclusions----------------------------------------------------------------------------------- 45

Chapter 3 Theories on Corrosion 47 3.1 Introduction ---------------------------------------------------------------------------------- 47 3.2 Background on CO2 Corrosion----------------------------------------------------------- 47

3.2.1 Electrochemistry of CO2 Corrosion..................................................... 47 3.2.2 Forms of Corrosion ............................................................................. 48 3.2.3 Parameters Affecting CO2 Corrosion .................................................. 51

3.3 Summary on CO2 Corrosion Models --------------------------------------------------- 55 3.4 Corrosion Defect Assessment Methods ------------------------------------------------ 56 3.5 Corrosion Inspection, Maintenance and Control ------------------------------------ 61

3.5.1 Introduction........................................................................................ 61 3.5.2 Pig’s Philosophy ................................................................................. 62 3.5.3 Pig Trap System................................................................................. 63 3.5.4 Unpiggable Pipelines .......................................................................... 63 3.5.5 Lost Pigs............................................................................................. 64 3.5.6 Intelligent Pigs.................................................................................... 65

3.6 Conclusions----------------------------------------------------------------------------------- 66

Chapter 4 Corrosion Data Analysis 69 4.1 Introduction ---------------------------------------------------------------------------------- 69 4.2 An Overview on Intelligent Pigging Data--------------------------------------------- 69 4.3 Statistical Interpretation on Corrosion Data----------------------------------------- 73

4.3.1 Initial Distribution.............................................................................. 75 4.3.2 Extreme Value Distribution................................................................ 77

4.4 Importance of Statistical Analysis on Corrosion Data----------------------------- 79 4.4.1 Corrosion as a Time-Variant Process.................................................. 79 4.4.2 Discrepancies in Corrosion Data......................................................... 82 4.4.3 Statistical Treatment to Corrosion Data............................................. 84

4.5 Conclusions----------------------------------------------------------------------------------- 90

Chapter 5 Reliability Assessment on Corrosions 93 5.1 Introduction ---------------------------------------------------------------------------------- 93 5.2 Overview on Limit State Function Models ------------------------------------------- 93 5.3 Dimensionless Limit State Function Model ------------------------------------------ 95

5.3.1 Background of Model.......................................................................... 95 5.3.2 Development of Model ........................................................................ 97 5.3.3 Model Validation .............................................................................. 109 5.3.4 Target Reliability.............................................................................. 112 5.3.5 Advantage......................................................................................... 114 5.3.6 Limitation......................................................................................... 114 5.3.7 Recommendation .............................................................................. 116

5.4 Conclusions----------------------------------------------------------------------------------117

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Chapter 6 System Reliability for Corroded Pipelines 119 6.1 Introduction ---------------------------------------------------------------------------------119 6.2 Reliability Per Pipeline Section --------------------------------------------------------119 6.3 Length Effects on System Reliability of Pipelines ---------------------------------122

6.3.1 Correlation Distance, dcorr ................................................................. 124 6.4 Conclusions----------------------------------------------------------------------------------129

Chapter 7 Reliability-Based Maintenance Model 131 7.1 Introduction ---------------------------------------------------------------------------------131 7.2 Overview of Model-------------------------------------------------------------------------131 7.3 Modelling Principles-----------------------------------------------------------------------132

7.3.1 Forensic Evidence ............................................................................. 132 7.3.2 Input-Output Model ......................................................................... 134 7.3.3 Benchmarking................................................................................... 134

7.4 Model Parameter Selection --------------------------------------------------------------137 7.4.1 Facts about Water in Pipeline .......................................................... 137 7.4.2 Model Variables Selection................................................................. 139

7.5 Model Development -----------------------------------------------------------------------140 7.5.1 Pipeline Candidate ........................................................................... 140 7.5.2 Regression Analysis .......................................................................... 140

7.6 Corrosion Optimization Techniques ---------------------------------------------------144 7.6.1 Interpreting Past Maintenance Practice ........................................... 144 7.6.2 Optimizing Future Maintenance Practice ......................................... 146

7.7 Conclusions----------------------------------------------------------------------------------152

Chapter 8 Spatial Corrosion Prediction 153 8.1 Introduction ---------------------------------------------------------------------------------153 8.2 Theories on Fluid-Structure Interactions --------------------------------------------153 8.3 Validation of Theories Using Field Data ---------------------------------------------157

8.3.1 Environmental Conditions ................................................................ 157 8.3.2 External Interferences....................................................................... 159 8.3.3 External Corrosions .......................................................................... 160

8.4 Discussions-----------------------------------------------------------------------------------161 8.4.1 Longitudinal Section Check .............................................................. 161 8.4.2 Cross Section Check ......................................................................... 162 8.4.3 Results Interpretation....................................................................... 165

8.5 Conclusions----------------------------------------------------------------------------------169

Chapter 9 Conclusions and Recommendations 171

Appendix I 175

Appendix II 177

References 179

List of Publications 189

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Index of Notation and Abbreviations 191

List of Figures 195

List of Tables 201

Curriculum Vitae 203

Chapter 1

INTRODUCTION

1.1 BACKGROUND

The oceans of planet Earth have been the medium in which life first appeared and later exploited by men for transportation and fisheries activities. These traditional uses of oceans, however, have expanded to include the exploitation of hydrocarbons (petroleum) below the sea bed as early as 1850s, when the first exploration drilling was carried out from over a few feet (69 ft) of water in California. That was the beginning of the oil in-dustry. Other early discoveries of oil were later observed in Pakistan (1886), Peru (1869), India (1890) and Dutch East Indies (1893) (Hassan, 2008). The development of the Gulf of Mexico as an offshore area started in 1930s with oil first being produced in 1938 from a timber platform in 14 ft of water. The offshore industry began a technically more challenging phase when the North Sea was first explored as a potential offshore area in the early 1960s (Patel, 1995). Since then the pace of oil exploration and produc-tion in shallow water has gradually increased to deepwater with the exploration phase started in 1975 while production began twenty years later. The deepwater industry de-fines deepwater as depth at +3000 ft (900 m) while ultra deepwater as +7000 ft (2100 m). The exploration of deepwater at present day is approximately approaching 10,200 ft (3100 m) and production at 8000 ft (2400 m) (Nergaard, 2005).

The development of an offshore industry is proportionally related to the development of offshore pipelines as well. As the industry expands towards deeper water depths, the pipelines are required to undergo improvement in material designs simply to withstand changes in the new environments. The transport of crude oil is performed at both ele-vated temperatures and high pressures, approaching up to 90°C and pressures up to 170 bar. Because of these requirements, not to mention the long distances typically involved, oil and gas transportation steel pipes have been considered the optimal means of trans-port (Barbey, 2006). Steel pipes on the other hand, can suffer from two kinds of corro-sion: from inside due to chemicals in the oil, or from outside due to wet and/or salty en-

1 Introduction

vironmental conditions. Since these pipes are not buried and are exposed to severe cli-mate conditions including humidity, and in the presence of everyday oxygen will eventu-ally causes steel corrosion.

Corrosion in Pipelines

Corrosion is defined as the chemical or electrochemical reaction between a material, usu-ally a metal, and its environment that produces deterioration of the material of the ma-terial and its properties. The corrosion occurs because of the natural tendency for most metals to return to their natural state for example, iron in the presence of moist air will revert to its natural state, iron oxide. Corrosion, however, is not an easily detectable process, even when using such advanced technologies as acoustic emissions and flux leak-age scanning (Barbey, 2006). Moreover, pipeline operators find it difficult to regularly check pipelines of tremendous length and with pipes of large diameter, which are fre-quently laid in not easily accessible places. Besides corrosions, the pipelines are also ex-posed to hazards like extreme weather conditions, collision with vessels, trawl impact and pipeline span, as sketched in Figure 1.1.

Figure 1.1 Different types of pipeline hazards

Collisions with vessels

Extreme weather

Spanning Trawl impact

Corrosions

SEABED

WATER LEVEL

PIPELINE

TO ONSHORE

OFFSHORE PLATFORM

Internal and external corrosion are together one of the major causes of pipeline failures. The severity of corrosion has been statistically reported to ensure its impact and degree of threads. The Committee on the Safety of Marine Pipelines (1994) for instance, had made compilation of causes of pipeline failures in the USA, with results as shown in Figure 1.2 and Table 1.1. The figure reveales that corrosion gives the highest threat (49%), followed by other hazards (25%), maritime activities (14%) and natural forces (12%). When compared between an oil and gas pipeline, the latter has 32% higher ten-dency towards corrosions, as reported in Table 1.1.

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1.1. Background

Maritime

activities

14%

Natural

forces

12%

Other

25%

Corrosion

49%

Figure 1.2 Pipeline failures, by reported cause, as compiled by the Committee on the Safety of Marine Pipelines (1994)

Table 1.1 Reported failure causes, by product carried, as compiled by the Committee on the Safety of Marine Pipelines (1994)

Percentage of failures attributed to each category of cause in:

Reported cause Oil lines Gas lines Corrosion 48 80 Maritime activities 14 12 Natural forces 14 8 Other/unknown 24 30 Total: 100 100

Incident data from the Office of Pipeline Safety in the USA for the year 2001 attributes 29% of incidents in liquid pipelines, and 19% of incidents in gas pipelines, to corrosion (Cosham et al., 2007).

Corrosion Consequences

Consequences due to corrosion have known to be one of the major concerns and have been given serious attention not only among pipeline operators, but also the public. The impact of corrosions towards environmental, economic, safety and technological will be briefly highlighted in the remaining paragraphs.

Environmental Effect

Leakage from corrosion failures lead to oil spill. Oil spill in the ocean (Figure 1.3a) has been one of the greatest public attentions and concerns. The oil spillage from the Druz-hba pipeline in year 2006 for instance, has dramatically highlighted the problems of pipe-

15

1 Introduction

line corrosion. Druzhba, the world’s longest oil pipeline in fact one of the biggest oil pipeline networks in the world, was built in the 1960s to pump oil some 4,000 km from the eastern part of the European Russia to points in Ukraine, Belarus, Poland, Hungary, Slovakia, Czech Republic, and Germany. This oil spill incident encountered by Russia is an example of an environmental catastrophe that significantly affects international po-litical reputations and affairs.

More recently in 2010, an oil spill taken place in the Gulf of Mexico was greatly endan-gering an unseen world of amazing sea creatures on the bottom of the Gulf. One of the major concerns among the scientists was that the oil spill would reach a major ocean current that could carry it through the Florida Keys and up the East Coast. In addition to that, researchers worried that miles-long underwater plumes of oil from the oil spill could poison and suffocate sea life across the food chain, with damage that could endure for a decade or more. Air samples from Louisiana reveal that levels of airborne chemi-cals has far exceeded what is considered safe for human exposure. An over 7,000-square-mile wildlife ‘dead zone’ located in the center of the Gulf of Mexico has grown from be-ing a curiosity to a colossus over the past two decades, and scientists are now concerned that the recent oil spill and other emerging chemical threats could widen the zone even further (Figure 1.3b).

(a) (b)

Figure 1.3 Oil spill disasters (a) Extinguished efforts to control a Deepwater Horizon rig that caught fire and finally sank in April 2010 in the USA (Kedrosky, 2011) (b) Concerned re-

searchers and scientists investigating the 2010 oil spills in the Gulf of Mexico (The Most Im-portant News, 2011)

Economic Effect

The International Pipeline and Offshore Contractors Association (IPLOCA) was formed in Paris in 1966 by companies active in the international pipeline construction industry. IPLOCA is bringing the pipeline owners, engineers and contractors together to establish essential standards for safety planning and procedures. The entire industry should be working under common standards. More and more stringent legislation is coming into

16

1.1. Background

effect and indeed pressure from various environmental quarters are putting intense pres-sures on oil companies to deal with the way pipelines are maintained. This is obviously going to affect the amount that needs to be spent, with the knock-effect that higher oil prices may occur (Harkin, 2006). The costs involved with a pipeline being out of action are not just aligned with the oil that’s flowing through it, but also essentially linked with the processing that occurs in the refineries. Closing down a pipeline also means closing down production facilities and the short to medium term effect of this will surely be re-flected in oil prices (Harkin, 2006). Some major oil companies have recently incurred significant fines due to the leakage of some pipelines in environmental sensitive areas. If leakage problem continues, it will be perceived as showing lack of commitment by the oil companies to sort the problems out.

Safety Effect

Piper Alpha oil rig disaster has been known as the worst oil rig accident in history. The Piper Alpha platform was a North Sea oil production platform operated by Occidental Petroleum (Caledonia) Ltd. The platform began production in 1976, first as an oil plat-form and then later converted to gas production. An explosion and resulting fire de-stroyed it on July 6, 1988, killing 167 men, with only 59 survivors. Two crewmen on a rescue boat also perished and 30 bodies were never recovered. This event laid the foun-dation for the worst oil rig accident in history. Total insured loss was about £1.7 billion. At the time of the disaster the platform accounted for approximately ten percent of North Sea oil and gas production, and was the worst offshore oil disaster in terms of lives lost and industry impact.

Pipeline Failure

Figure 1.4 Fault tree analysis for offshore pipeline

Corrosion may not seem to be the cause of accident to the Piper Alpha disaster, but the consequences of leak or burst pipelines should never be under estimated. With reference to an illustration in Figure 1.1 earlier, a fault tree analysis can be prepared as shown in

OR gate

AND gate

Spanning

Collisions with vessels

Storm/Hurricane

Mud slide

Corrosion Extreme Weather Third Party Impact

External Internal Dropped objects

Trawl impactcorrosion corrosion

17

1 Introduction

Figure 1.4 above. Despite the independency of each hazard towards failure, as given by the ‘OR’ gate, care should be taken when a combination effect is likely to occur. For in-stance, a moderate corrosion may become a bigger threat in the presence of extreme weather condition or third party impact. Agreeing to these potential impacts, corrosion loss control should also obey to the basic laws for the management of safety (Brown, 1995).

Technological Effect

The economic consequences of corrosion affect technology. A great deal of the develop-ment of new technology is held back by corrosion problems because materials are re-quired to withstand, in many cases simultaneously, higher temperatures, higher pres-sures, and more highly corrosive environments. The selection of offshore pipeline material should be able to resist corrosion types like sulfide stress corrosion and microbiological corrosion. In many of these instances, corrosion is a limiting factor preventing the devel-opment of economically or even technologically workable systems.

Corrosion Control and Maintenance

Costs for maintaining corrosion represent a significant portion of operating budgets in the offshore industry, particularly when ageing structures like pipeline is involved. Mod-ern approaches to maintenance management are designed to minimize these costs and to improve reliability and availability of the structure. The maintenance and protection approaches, however, are restricted to several obstacles like geographical location, acces-sibility (due to terrain), and method and techniques of construction (some pipelines are over 50 years old) (Harkin, 2006). The maintenance of pipelines should be well planned to comply with the nature of the product the external environment, operating conditions with regards to rate and substance of the flow of product. Maintenance should be a regular occurrence and planned inspections need to be carried out on a regular basis (Barbey, 2006). The regular check-up of existing pipelines is the most important preven-tive measure to insure safety and long-term service life. Although periodic inspection and preventive maintenance are required to minimize cost of corrosion, these routine in-spections are visual in nature and hence are subjective and limited to exposed areas. The following are the consequences of poor maintenance practices and/or inadequate in-vestment in the maintenance function:

• Reduced production capacity: Not only an increase in ‘down-time’ will result but, importantly, assets will under-perform during ‘up-time’.

• Increased production costs: Whenever assets are not performing at optimal level, real cost and opportunity cost penalties are incurred.

• Lower quality products and services: The ultimate consequence will be customer dissatisfaction and probably lost sales.

• Safety hazards: Failures can lead to loss of life, injuries and major financial losses.

18

1.2. Motivation

Questions arise among pipeline operators on the possible solutions to tackle corrosion problems. Pray (2006) and Harkin (2006) in their interviews addressed several examples of new and advanced technologies in the R&D to improve corrosion problems, which in-volved development in tools (remote condition monitoring systems), instrumentations (better gas leaks detector), methods (e.g. new ‘hot tapping’ method), materials (rein-forced thermoplastic pipe) as well as IT (major advances in hardware and software).

1.2 MOTIVATION

1.2.1 Pipeline Codes and Standards

The petroleum industry has been widely evolved throughout the globe since the begin-ning of its first exploration in 1850s until the present day. The formation of IPLOCA in 1966 for example, signifies the widespread active participation from the international pipeline construction companies. Statistics prepared by the Central Intelligence Agency (CIA) in 2010 showed that oil accounts for a large percentage of the world’s energy consumption; ranging from 32% for Europe and Asia, and up to 53% for the Middle East. Other geographic regions’ consumptions are South and Central America (44%), Africa (41%), and North America (40%). The world consumes 30 billion barrels of oil per year, with developed nations being the largest consumers. Figure 1.5 exhibits the distribution of oil and natural gas reserves among the world's 50 largest oil companies.

Figure 1.5 Distribution of oil and natural gas reserves among the world's 50 largest oil companies. (Wikipedia: Petroleum Industry, 2011)

19

1 Introduction

Pipeline codes and standards were developed to provide guidance on the design, con-struction and operation of pipelines, but the use of codes can be confusing since there are numerous available and different countries have different national standards and codes for best practice (Alkazraji, 2008). This becomes the drawbacks for some developing countries which are lack of capabilities to develop their own codes. The available stan-dards and codes were then re-modified to suit the new environment of the developing countries. Quite often this transformation is feasible and that pipeline operations can still be carried out smoothly. However, utilizing out source design standards and codes can never be 100% guaranteed to represent the exact conditions or scenarios of other countries, especially when involving different environmental and reservoir conditions. This is because the design standards developed earlier were mostly prepared by means of experimental and/or numerical works. The variables or parameters in the laboratory works could be easily controlled depending on the needs of studies but this is definitely not the case in real applications. How can one be too sure that his pipeline is not overd-esigned? Therefore, discrepancy on this aspect remains as an issue among pipeline op-erators and answers to this are yet to be discovered.

1.2.2 Probabilistic vs. Traditional (Deterministic) Approach

Oil and gas pipelines are vulnerable to a whole variety of threats throughout operational life, particularly corrosion, which eventually compromise pipeline integrity. Corrosion re-liability evaluation, an important aspect in pipeline integrity management, can be been carried out by means of either traditional (deterministic) or probabilistic approaches. The latter, however, may seem to be less favourable when knowledge about it is still not well understood among industries.

Traditionally, the evaluations of safety and adequacy of engineering systems were ex-pressed in terms of safety margins and safety factors to compensate for uncertainties in loading and material properties and inaccuracies in geometry and theory (Singh et al., 2007). The use of precisely defined point design (single) values represents not what an engineer needs to accomplish, but rather what is convenient to numerically solve, assum-ing inputs that are known precisely (Singh et al., 2007). The safety factor accounts for the condition of future, the engineer’s judgement, and the degree of conservatism incor-porated into the parameter values and say little about safety but nothing about reliabil-ity (Singh et al., 2007). The traditional or commonly referred to as deterministic ap-proach considers the worse-case scenarios to determine the load and capacity of a sys-tem, as shown in Figure 1.6. In most cases, such safety margins and factors are seldom based on any mathematical rigor or true knowledge of the underlying risk and results in an overdesign (Singh et al., 2007). Consequently, this leads to designs that are more ‘heavy’ and costly and even result in greater safety or reliability.

The probabilistic approach used in the reliability evaluation is a logical extension of the traditional approach. It deals with many uncertainties that are common to the data (random variables) employed. Both the strength (R) and load (S) can take on a wide

20

1.2. Motivation

range of values by explicitly incorporating uncertainty in system parameters. The ap-proach treats both random variables in the form of probability density functions (will be explained in Chapter 2) rather than considering each input parameter as an average value, as what has been assumed in the deterministic approach. Figure 1.7 illustrates the contradiction of these definitions.

Figure 1.6 Traditional (deterministic) approach of safety analysis considered in engineering

system (Adapted and modified from Singh et al., 2007)

(a) Deterministic (b) Probabilistic

Figure 1.7 Comparison in load and strength from two different methods

The deterministic assessment can be approached either qualitatively and/or semi-quantitatively. The traditional deterministic approach to the assessment of pipeline cor-rosion risks is typically based on the judgement of ‘competent engineering personnel’ as the paradigm for identifying risk (Lawson, 2005). Semi-quantitative (deterministic) methods essentially substitute the analytic of science for the fallible judgement of ‘com-petent personnel’, with the explicit notation that scientific treatment provides a superior basis for reliable prediction (Lawson, 2005). The outputs from the qualitative assess-ment for instance, yield a curve that shows how the ‘risk’ of failure increases with time.

Probability Safety Factor, Reliability Unknown

Load Strength

StrengthLoad σ

μ

Strength

Probability

Load

Random variables Probability of

failure

21

1 Introduction

The pipeline operator simply chooses the level of risk that is acceptable and the devises a strategy to deal with those risks. This approach merely segments the output risks as ei-ther high, medium or low; a strategy for managing is devised based on the selection of an appropriate time interval to allow reasonable prospect of detecting deterioration before the pipeline corrosion allowance is exceeded, or no longer complies with the code (Law-son, 2005). The final result would be in the form of a ‘risk matrix’ (Figure 1.8), defined by probability of failure and the consequence of failure for the worst-case pipeline sce-nario. Herein the scenarios are ranked to identify the most likely failure mechanisms.

Con

sequ

ence

of Fa

ilure

High

High consequence &

Probability of failure

Medium

Low

Low

Medium

High

Probability of Failure

Figure 1.8 Risk matrix applied in the qualitative risk assessment

The deterministic approach has the distinct advantage of simplicity and the capability of being applied to an entire pipeline or collection of pipelines relatively easily. On the other hand, the disadvantages of deterministic method as reported by Vrijling et al. (2006) are given below:

1. Unknown how safe the structure is.

2. No insight in contribution of different individual failure mechanisms.

3. No insight in importance of different input parameters.

4. Uncertainties in variables cannot be taken into account.

5. Uncertainties in the physical models cannot be taken into account.

Lawson (2005) has essentially made a critique between the deterministic and probabilis-tic methods on a 16.1 km long and 14 inch a main export line in the North Sea. The de-terministic approach which used risk matrix with target probabilities for high and conse-quence of failure for normal, predicted failure probabilities between time period of 8.5 and 13 years. On the other hand, the probabilistic assessment of risks indicated that pipeline inspections may be extended beyond that suggested by the deterministic as-sessment. This welcomes the opportunity to defer expenditure on pipeline inspections to a later date. The probabilistic assessment overcomes the seemingly arbitrariness of se-lecting contingencies in the deterministic method. A corrosion management strategy should be risk-based and should take account of all aspects of asset maintenance, corro-sion rate activity, historical and future operational parameters and the management and business requirements (Lawson, 2005).

22

1.3. Fundamentals of Study

Uncertainties either directly or indirectly introduced in pipeline operations can be easily incorporated into the probabilistic assessment. Uncertainty reality is now becoming a significant research interest. For example, Koornneef et al. (2010) has recently assessed and reviewed impacts of uncertainties from meteorological conditions, operating conditions (pipeline pressure, temperature) pipeline geometries (length, diameter) etc. Uncertainties caused by environmental parameters governed by waves, water levels or even discharges have been previously acknowledged in works involving other coastal structures like Mai Van et al. (2009c), Van Gelder and Mai Van (2008), Van Gelder et al. (2008a), Van Gelder et al. (2008b) and many more. Some typical measuring instruments like turbine meters, rotary meters, diaphragm etc. are prone to uncertainties as well. The uncertainty of a measuring system includes uncertainties of its measuring instruments (Bluvshtein, 2007). The inaccuracies of pipeline sensor’s datasets has been acknowledged and studied by Olufemi et al. (2009). Particularly for corrosion inspection, the in-line inspection (ILI) tools such as the Magnetic flux leakage (MFL) has been also considered as source of uncertainties (Maes and Salama, 2008).

Not much extensive work has been carried out using probabilistic approach on offshore pipelines. There are a list of work by Ahammed and Melchers (1996), Pandey (1998), Ahammed (1998), De Leon and Macías (2005), Teixeira et al. (2008), but these are re-stricted to assessing corrosions in pipelines, which in return provides reliability towards possible future operating time. There are still a lot more to learn about corrosions in pipelines using probabilistic approaches, especially when treating the structure as a sys-tem. This is something that is lacking and should be further exploited. Literatures claimed that the probabilistic method is intensive, time consuming and can be very com-plex. Nevertheless, it may be effectively mirrors pipeline operations, provides a superior basis upon which to manage risk and would therefore likely maximise both safety and business performance (Lawson, 2005).

1.3 FUNDAMENTALS OF STUDY

1.3.1 Problem Statement

Impacts of corrosions and solutions overcoming the problems have been briefly described in the first section of this chapter. The advanced R&D technologies reported are indeed thrilling, but still require a lot of investment in costs and efforts. By and large these ad-vanced technologies will consequently arrive to one ‘root’ problem: uncertainties. The uncertainties, however, can best be treated probabilistically, and this has been fairly ex-plained in Section 1.2.2 earlier.

Section 1.2.1 on the other hand, has addressed the difficulties in understanding the com-patibility between the adapted design standards/codes and actual environments and op-erating conditions of developing countries. There is a need in investigating an approach

23

1 Introduction

that could be used for this purpose and probabilistic approaches are believed to be able to provide answers to such problem.

Corrosion control or maintenance in pipelines (introduced in Section 1.1) is the key as-pect that should be well planned and operated. Proper optimization of maintenance will be able to improve the pipeline system, and at the same time avoiding unnecessary re-pairs that have direct cost impacts. Applying up-to-date technologies and/or techniques may not be easily implemented especially those which require expert users. Special trainings should then be prepared for the local operation staffs to start utilizing the new systems. Unfortunately, this will become a problem for some areas in the world that are lacking of computer skills. Instead of improving pipeline operations through mainte-nance, the advanced R&D may then become another restriction to carry out the work. This then paved the idea to look into a simpler but reasonable approach to optimise maintenance in pipelines, one of which will be discovered in the present work.

1.3.2 Objectives

With reference to the problem statements highlighted in the previous section, the frame-work of this thesis was prepared to fulfil below objectives:

• to analyse and interpret corrosions (characteristics) as random variables, allowing them to be treated as another source of uncertainties

• to develop a reliability model for corroded pipelines

• to analyse the reliability of pipelines as a system

• to optimise present maintenance practice using a reliability-based maintenance model

• to spatially predict corrosions

1.3.3 Study Approach

The framework of this thesis was fully developed using the knowledge of probabilistic methods. The analyses utilized data at several offshore pipelines located in Peninsular Malaysia. Offshore activities in this region have started in 1968 and mostly controlled by external experts. The Malaysian-owned oil and gas company, the Petroliam Nasional Berhad (PETRONAS) was later established in 1974 (Hassan, 2008). No severe offshore pipeline accidents have been reported in the region since operations but corrosions re-main as one of the hazards to the pipelines.

24

1.3. Fundamentals of Study

A summary on candidate pipelines utilized in different chapters of the thesis is given in Figure 1.9. It illustrates the pipeline properties (diameter, length, dominated product, type, and commissioning year) coupled with total number of corrosion defects (as re-ported from a specific time of inspection). Also mentioned in the figure is the type of corrosion studied in each chapter; the internal or external corrosions, both measured with respect to the pipeline wall.

Figure 1.9 Brief illustration on candidate pipelines utilized in different chapters of the thesis

1.3.4 Scientific and Social Relevance

The scientific relevance of this research can be addressed as:

1. an extension of current corrosion data analysis and interpretation using probabil-istic approaches,

2. a development of a reliability model for corroded pipelines with the inclusion of a more comprehensive corrosion defect parameters,

3. an investigation of pipeline length effects towards pipeline system reliability,

4. a development of a reliability-based maintenance model using approaches like fo-rensic evidence and benchmarking, through which in-house corrosion control prac-tice can be optimised for future operations,

5. an investigation of probabilistic spatial (external) corrosion prediction in pipelines with the aid of theories on hydrodynamics around circular cylinder placed closed to wall.

16” x 6.9 km Crude Oil Pipeline, Type API 5LX-65, 2000, 6981 corrosion defects.

Chapter 4 Chapter 5 Chapter 6

28” x 128.9 km Gas Pipeline, Type API 5LX-65, 1999,

861 corrosion defects.

Internal External

Chapter 8 Chapter 7

Internal Internal External Internal External

25

1 Introduction

The social relevance of this research can be classified as:

1. an investigation of pipeline conditions subjected to corrosions in Peninsular Ma-laysia, results from which can be used to understand interactions between local offshore environment and pipeline operating conditions, and

2. an illustration on the suitability of probabilistic methods for counter-checking the compatibility of the adapted design standards and codes, especially for a develop-ing country like Malaysia.

1.4 OUTLINE OF THESIS

This thesis is prepared in two parts. The first part deals with theoretical basis of prob-abilistic approaches and theories on corrosions. The former will be presented in Chapter 2 and contains all the methods used in the thesis. The latter will be the content of Chapter 3 and allows readers to get acquainted with some basic existing theories about corrosions. Understanding corrosion and its physics is necessary so that factors influenc-ing its development can be properly addressed.

The second part of the thesis exhibits the analysis and computation sections which util-ized data from case studies of Peninsular Malaysia pipeline operations. Chapter 4 illus-trates how corrosion data set can be analysed and interpret probabilistically. Herein, corrosion parameters are treated as random variables and this will be the basis assump-tion applied in all calculations for the remaining Chapters 5 to 8.

Chapter 5 attempts to adapt the well known Buckingham-π theorem when developing the reliability model for corroded pipelines, through which better corrosion defect shape and presentation can be incorporated. While doing so, the model allows better estimate for reliability computation and consequently expands and improves several existing mod-els. This favourable outcome will be proven at the end section of the chapter.

Chapter 6 will further investigate the capability of the model developed in Chapter 5 by investigating the effect of pipeline lengths. This ideology is simply tested knowing that the effect is significant for other similar structure that is also arrayed in series, for exam-ple the dikes system. Understanding pipeline length effects towards reliability is impor-tant so that the pipeline sections can be operated in a more effective manner.

Chapter 7 exhibits a new approach in determining the effectiveness of present corrosion maintenance practice. With the aid of three important principles, past information on pipeline operation can be modelled and exploited to achieve an optimum corrosion prac-tice. It is believed that improvement can be done on present (in-house) corrosion man-agement to control corrosion development without really applying a more sophisticated technology or tool to carry out the work.

26

1.4. Outline of Thesis

27

Not much concerns have been given to predict corrosion in space, thus Chapter 8 tries to investigate the possibility of doing so by applying knowledge on hydrodynamics of circu-lar cylinder placed close to the wall which is resemblance to pipelines laid on sea bed. It will be shown later that simple statistics can be applied to achieve this. Inputs from this chapter could be used to enhance theories on hydrodynamics surrounding an unburied offshore pipeline closed to the sea bed.

Chapter 9 provides conclusion and recommendation of the thesis. This includes remarks on the suitability of the proposed probabilistic approaches in assessing corrosions in off-shore pipelines. The limitation of the present work will also be highlighted. The rec-ommendation presented are hoped to be further improved and incorporated in future re-searches on similar topic.

Chapter 2

THEORIES ON PROBABILISTIC METHODS

2.1 INTRODUCTION

This chapter contains the methodology of the thesis. Probabilistic methods will be fully utilized throughout the analysis. The methods, however, are too broad to be discussed in one single chapter. Thus this chapter does not intent to discuss thoroughly about the whole concept in probabilistic methods but to briefly introduce those related to the pre-sent work. The basic ideas about probabilistic methods will be covered when discussing about elements of probability. Following this, readers will be introduced to regression and correlation analysis, which is known as one of the basic techniques used in statistics. Knowledge on reliability analysis will be presented the last after which readers have developed some basic sense about probabilistic methods.

2.2 ELEMENTS OF PROBABILITY

The use of probabilistic methods for the purpose of improving designs has the advantage that it provides a complete framework for the safety analysis, in which the actual prob-ability of failure and not some empirical safety rule is used as a measure of the perform-ance of a design (Plate, 1993). Yen and Tung (1993) described that the reliability analy-sis involves two major steps:

1. identify and analyse the uncertainties of each of the contributing parameters, and

2. combine the uncertainties of the random variables to determine the overall reli-ability of the structure.

By all means the above description is a bit too informative for a layman to digest. Nev-ertheless, it is worth somehow to capture and remember some basic words that seem to be the roots in probabilistic methods, some of which will be discussed in the remaining paragraphs.

2 Theories on Probability Methods

2.2.1 Uncertainties

Design of structures are subjected to uncertainties due to randomness of natural phe-nomena, data sample limitations and errors, modelling reliability and operational vari-ability. Uncertainties in decision and risk analysis can primarily be divided in two cate-gories (Van Gelder, 2000):

1. uncertainties that stem from variability in known (or observable) populations and therefore represent randomness in samples (inherent uncertainty), and

2. uncertainties that come from basic lack of knowledge of fundamental phenomena (epistemic uncertainty).

It is not possible to reduce inherent uncertainties but epistemic uncertainties may change as knowledge increases (Van Gelder, 2000). Analyzing uncertainties is essential as it is the prerequisite for reliability analysis.

2.2.2 Random Variables and Probability Distributions

If the outcomes of an experiment are uncertain, one speaks of a random variable (Vrijling et al, 2006). The term ‘experiment’ is used here in a general case. A random variable is a mathematical vehicle for representing an event in analytical (numerical) terms (Ang and Tang, 2007). The value of a random variable may be defined within a range of pos-sible values. Yet, there is frequently a degree of consistency in the factors governing the outcome that exhibits a statistical regularity (Singh et al., 2007), which is expressed through a probability distribution defined on the probability space.

Probability distributions which are typically defined in terms of the probability density function (PDF) is a fundamental concept in statistics that are used both in a theoretical and practical level. A PDF of an absolutely continuous random variable is a function that describes the relative chance for this random variable to occur at a given point in the observation space. Some typical PDF used are uniform distribution, normal distri-bution, log normal distribution, weibull distribution, gamma distribution and many more, which are described in more details in Ang and Tang (2007) for instance. Each PDF is normally characterized by mean (μ), standard deviation (σ) or coefficient of variation (C.O.V) values. The mean is a measure of average while the standard devia-tion and coefficient of variation describe the dispersion of a random variable. However, the C.O.V which is the ratio of standard deviation to the mean offers a normalized measure useful and convenient for comparison and for combining uncertainties of differ-ent variables (Tung and Yen, 1993).

Besides the probability density function, other types of probability functions are briefly listed below and further descriptions pertaining to them can be found from other pub-lished resources. The cumulative distribution function (CDF) is the probability that the variable takes a value less than or equal to x. That is,

( ) Pr[ ]F x X x a= £ = (2.1)

30

2.2. Elements of Probability

For a continuous distribution, this can be expressed mathematically as,

( ) ( )x

F x f dm m-¥

= ò (2.2)

For a discrete distribution, the CDF can be expressed as,

0

( ) ( )i

F x f i=

= å (2.3)

The percent point function (PPF) is the inverse of the cumulative distribution function or quantile function. For this reason, the PPF is also commonly referred to as the inverse distribution function. That is, for a distribution function we calculate the probability that the variable is less than or equal to x for a given x. For the PPF, we start with the probability and compute the corresponding x for the cumulative distribution. Mathe-matically, this can be expressed as,

Pr[ ( )]X G a£ = a (2.4)

Or alternatively,

( ) ( ( ))x G G F xa= = (2.5)

The cumulative hazard function is the integral of the hazard function. It can be inter-preted as the probability of failure at time x given survival until time x.

( ) ( )x

H x h dm m-¥

= ò (2.6)

This can alternatively be expressed as,

( ) ln(1 ( ))H x F x= - - (2.7)

Survival functions are most often used in reliability and related fields. The survival func-tion is the probability that the variate takes a value greater than x.

( ) Pr[ ] 1 )( )S x X x F x= > = - (2.8)

Graphical presentations of the above probability functions are illustrated in Figure 2.1. The graphs were plotted based on corrosion defect depth (d, measured in %) data, fitted using a lognormal distribution function.

31


(a) Histogram and probability density function (PDF) (b) Cumulative density function (CDF)

(c) Quantile function (d) Cumulative hazard function

(e) Survivor function

Figure 2.1 Different types of probability distribution functions plotted based on corrosion de-fect depth (d, measured in %); with best fit taken from a lognormal distribution function.

32

2.2. Elements of Probability

2.2.3 Extreme Value Distributions

Extreme events of natural phenomenon involving the maximum and minimum values have always been the subject of interest in engineering. It is concerned with the largest and smallest values from a sample of population. Recall that a sample of population can be characterized by its own probability distribution function, known as initial distribu-tion. Similarly, the extreme values may also be modelled as random variables with re-spective extremeal (extreme) probability distributions. The smallest values of the data population can be described by the lower tail (left tail) while the largest values are por-trayed by the upper tail (right tail). Such distributions and their associated parameters have special characteristics that are unique to the extreme values (Ang and Tang, 1984). The central portion of the initial distribution has little influence on the asymptotic form of the extremal distribution; the extremal parameters, however, will depend on the form of the extremal distribution (Ang and Tang, 1984).

A complete discussion on statistics of extremes can be referred to Ang and Tang (1984) for instance. The present section does not attempt to critically review on this matter but it is important to at least understand that the extreme value theory states that there are only three types of distributions that are needed to model the maximum or minimum of the collection of random observations from the same distribution. In other words, if you generate N data sets from the same distribution, and create a new data set that in-cludes the maximum values from these N data sets, the resulting data set can only be described by one of the three models-specifically, the Gumbel, Fréchet, and Weibull dis-tributions. These models, along with the Generalised Extreme Value distribution, are widely used in risk management, finance, insurance, economics, hydrology, material sci-ences, telecommunications, and many other industries dealing with extreme events. In this thesis, however, emphasize will only be given to those concerned with corrosions.

The cumulative distribution functions of the three extreme value distribution functions are given by:

• Gumbel or Extreme Value Type I distribution, ( )/( ; , ) e xF x e m sm s - -= (2.9)

• Fréchet or Extreme Value Type II distribution,

(( )/ )( ; , , ) xF x eam sm s a

-- -= for x > μ, (2.10)

• Weibull or Extreme Value Type III distribution,

for x < μ, (2.11) ( ( )/ )( ; , , ) xF x eam sm s a - - -=

with σ >0, α>0. μ, σ and α are the shape, scale, and location parameters, respectively. The Gumbel distribution is unbounded (defined on the entire real axis) and its shape does not depend on the distribution parameters. The Fréchet distribution is bounded on the lower side (x > 0) and has a heavy upper tail. When α = 1, Weibull distribution re-duces to the Exponential model, when α = 2, it mimics the Rayleigh distribution and

33

http://www.mathwave.com/articles/extreme-value-distributions.html#evd_gumbel

http://www.mathwave.com/articles/extreme-value-distributions.html#evd_frechet

http://www.mathwave.com/articles/extreme-value-distributions.html#evd_weibull

http://www.mathwave.com/articles/extreme-value-distributions.html#evd_gev


when α = 3.5, it resembles the Normal distribution. The Gumbel and Fréchet models are commonly relate to maximum, while the Weibull model relates to minimum.

Generalised Extreme Value Distribution

The Generalised Extreme Value (GEV) distribution is a flexible three-parameter model that combines the Gumbel, Fréchet, and Weibull maximum extreme value distributions. It has the following cumulative distribution function:

1/

( ; , , ) exp 1x

F x

xm

m s x xs

-ì üï ïé ùæ öï ï- ÷ï ïçê ú÷= - + çí ý÷ê úç ÷ï ç ïè øê úï ïë ûï ïî þ

for 1+ξ(x − μ)/σ > 0, (2.12)

where m is the location parameter, σ > 0 the scale parameter and the shape Î x Î parameter. The shape parameter ξ governs the tail behaviour of the distribution. When fitting the GEV distribution to sample data, the sign of the shape parameter ξ will usu-ally indicate which one of the three models best describes the random process you are dealing with. The sub-families defined by ξ=0, ξ>0 and ξ<0 correspond to the Gumbel, Fréchet and Weibull families, respectively.

2.3 REGRESSION ANALYSIS

2.3.1 Background

When there are two (or more) random variables involved in an experiment, relationships may presence between (among) the variables. In the presence of randomness, the rela-tionship between the two variables will not be unique; given the value of one variable, there is a range of possible values of the other variable (Ang and Tang, 2007). There-fore, the relationship between these variables requires probabilistic description and the regression analysis technique is one of the common statistical methods applied. The regression analysis is one of the basic techniques and sometimes labeled as the ‘mother of all statistical techniques’.

The regression analysis includes any techniques for modelling and analyzing several variables, when the focus is on the relationship between a dependant variable and one (or more) independent variable(s). The technique helps one to understand how the typical value of the dependant variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. One variable may cause the other one to behave in a certain way and thus necessary to estimate this causation so that we are able to predict one from the other. The mean and variance are the typical measures describing such probabilistic relationship.

34

2.3. Regression Analysis

2.3.2 Models

The regression analysis can be described using either linear or nonlinear relationship. The linear or nonlinear relationship obtained from a regression analysis does not necessarily represent any causal relation between the variables i.e. there may not be any cause-and-effect relationship between the variables (Ang and Tang, 2007).

The simplest regression model is the bivariate one, in which there is one response or de-pendant variable, and one predictor or independent variable, and the relationship be-tween the two is (normally) represented by a straight line. It is normally called the sim-ple linear regression model and given by,

y = α + βx + ε (2.13)

where α is the intercept, β is the slope and ε is the error or residuals. The sign of β de-scribes whether the relationship is positive or negative. Because reality is rarely linear, this model is at best a linear approximation of the true relationship. Therefore, there is always some error left in the above model, some variation in y which is not explained by x and which is probably due to the influence of other variables or to sampling error.

Multivariate regression analysis on the other hand, is a form of statistics encompassing the simultaneous observation and analysis of more than one statistical variable. When the mean-value function is assumed to be linear, the resulting analysis is called multiple linear regression analysis. Suppose a simple data set consists of n points (data pairs) (xi, yi), i = 1, ..., n, where xi is an independent variable and yi is a dependant variable whose value is found by observation. Assume the predicted model function for the multiple regression analysis has the form f(x, β) or yi’ and can be written as,

'1 1 2 2( , ) ....i o i i k ikf x y x x xb b b b b= = + + + + + e (2.14)

for each i, where βo, β1,…., βk are constant regression coefficients that must be estimated from the observed data (xi1, xi2, …, xik).

In the real engineering world, variables are not always adequately described by linear models and nonlinear relationship will become more appropriate instead. The nonlinear regression is usually based on an assumed nonlinear function of the mean value of the dependant variable, Y, as a function of the independent (or control) variable X, with cer-tain undetermined coefficients that must be evaluated on the basis of the observed data (Ang and Tang, 2007). The simplest type of nonlinear functions for the regression of Y on X is,

( ) (E Y x g xa b= + ) (2.15)

where g(x) is a predetermined nonlinear function of x, for example polynomial, exponen-tial or logarithmic functions. It normally coupled with a constant conditional variance, Var (Y|x)= constant, or a conditional variance that is a function of x. Quite often the new variable (x’) are created and defined as a function of x’= g(x), then equation (2.15) becomes,

35


' '( )E Y x xa b= + (2.16)

The above equation is now as the same mathematical form as the linear regression equa-tion (2.14) earlier.

2.3.3 Model Parameter Estimates

Some examples of regression analysis models (equations) have been briefly described in the previous section. Recall that the objective of the analysis is to simply fit a line between the observed data points, as illustrated in Figure 2.2. But how can we get the best possible line that best represents the overall trend of the data? One of the ways to achieve this is by controlling the error or residual terms in the models. With reference to Figure 2.2, a residual (r) of a random variable i is defined as the difference between the value predicted by the model (y’) and the actual value (y) of the dependant variable,

'i ir y y= - i . (2.17)

(xi, yi)

'i iy y−

++

++

+++

+++

+

+

++

+

+

+

++++

+

y’=α +βx

y

x

Figure 2.2 Scattergram of two random variables x and y

Controlling the error or residual term can be done by finding a formula that minimizes the sum of all the distances between the actual values and predicted values. In statistics, a method in minimizing the sum of the squared values of the prediction errors is known as the Least-Squares method of estimation. The ‘least-squares’ means that the overall solution minimizes the sum of the squares of the errors made in solving every single equation. Thus, the objective consists of adjusting the parameters of a model function to best fit a data set. The least-squares method corresponds to the maximum likelihood estimate (MLE) criterion if the experimental errors have a normal distribution and can also be derived as a method of moments (MOM) estimator. Both MLE and MOM, however, will not be discussed in this thesis.

The least-squares fall into two categories: linear or ordinary least squares and non-linear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares occurs in statistical regression analysis; it has a closed-form solution. The non-linear has no closed solution and is usually solved by iterative refinement; at

36

2.3. Regression Analysis

each iteration the system is approximated by a linear one, thus the core calculation is similar in both cases (Ang and Tang, 2007).

The application of least-squares method in determining a best regression model will be described from this point onwards. A linear multivariate regression analysis model as in equation (2.14) earlier will be chosen to illustrate the example. Descriptions presented herein are adapted from Ang and Tang (2007). Recall that equation (2.14) is actually a predicted equation (yi’) formulated from an observed data sets (xi, yi). Rephrase the equation into a matrix form,

y’=Xβ (2.18)

where y’ is a vector y’= {y1’, y2’, .., yn’}, in which each y’ is given by equation (2.14) (predicted values), β is a vector of the regression coefficients β = {βo, β1,.., βk}, and X is an n by k+1 matrix,

X (2.19)

11 12 13

21 22 23

1 2

1

1

. . . .

1 n n n

x x x

x x x

x x x

é ùê úê úê= êê úê úê úë ûk

úú

2

The conditional variance of Y for given values xi1, xi2,…., xik is assumed to be constant for any i,

Var (Y| xi1, xi2,…., xik)= σ2 (2.20)

The least-squares method finds its optimum when the sum, Δ, of squared residuals

2

1

n

ii

r=

D =å (2.21)

is a minimum. The minimum of the sum of squares is found by setting the gradient to zero, which can be written as,

22

1 1 2 21

ˆ ˆ ˆ ˆ[ ... ] 0n

i o i i k ikio

y x x xb b b bb =

¶D= - - - - - =

¶ å

22

1 1 1 2 211

ˆ ˆ ˆ ˆ[ ... ] 0n

i i o i i k iki

x y x x xb b b bb =

¶D= - - - - -

¶ å = (2.22)

…..

2

21 1 2 2

1

ˆ ˆ ˆ ˆ[ ... ] 0n

ik i o i i k ikik

x y x x xb b b bb =

¶D= - - - - -

¶ å =

Equation (2.22) comprises k+1 equations with the k+1 unknown regression coefficients. Again, in matrix notation, the set of equations (2.22) may be written as,

XTXβ = XTy (2.23)

37


where y= {y1, y2, .., yn} is the observed values of Y and T is the transpose.

Premultiplying both sides of equations (2.23) by the inverse of the matrix XTX, we obtain the solutions for the least-squares estimates of the regression coefficients as,

1ˆ (X X) X yT Tb -= (2.24)

where is a (k+1) vector, ={βo, β1,.., βk}, with which we obtain the multiple regression equations, in matrix form,

b b

' ˆy =Xb (2.25)

In scalar form, the above equation represents a set of k multiple regression equations,

',

1

ˆ ˆk

i j ijj

y b b=

= +å x with i = 1, 2, …, n and j = 1, 2, …, k. (2.26)

where and ob ˆjb are the components of . An unbiased estimate of conditional vari-

ance of Y for given values of X1, X2, …., Xk is,

b

1 2

' 22

2 1/ , ,..

( )

1 1k

n

i ii

Y x x x

y yS

n k n k=

-D

= =- - - -

å (2.27)

in which yi’ is given by equation (2.26).

2.3.4 Analysis of Residuals

Analysis of residuals should be carried out after determining the corresponding regres-sion coefficients (β) of the best fit model. The residuals are examined with the aid of graphs and statistics as well. Some frequently used residuals tests are listed below (Meko, 2009):

1. Time series plot of residuals

2. Scatterplot of residuals against predicted values

3. Scatterplot of residuals against individual predictors

4. Histogram of residuals

5. Act of residuals

6. Lag-1 scatterplot of residuals

7. Durbin-Watson

8. Portmanteau test

Chapter 5 of the thesis will exhibit two types from the above residual checks, namely the scatterplot of residuals against individual predictors and histogram of residuals. In the

38

2.4. Reliability Analysis

former, the residuals are assumed to be uncorrelated with the individual predictors. Vio-lation of these assumptions would be indicated by some noticeable pattern of dependence in the scatterplots i.e. nonlinear relationship, and might suggest transformation of the predictors (Meko, 2009). For the latter check, the residuals are assumed to be normally distributed with a population mean of zero. Accordingly, the histogram of the residuals should resemble a normal PDF. If this is true, it can be said that the different error terms cancel each other and have no aggregate influence on the data. If the error terms seem to go more in one direction than another (skewness), then it is likely that the model is missing something important and that there is a bias in the data.

ained’, or ‘de-scribed’ by regressions. It is computed from the sum-of-squares terms,

2.3.5 Statistics

In statistics, the coefficient of determination, (R-squared value, R2) is the explanatory power of the regression used to judge the goodness of the predicted model to the ob-served data. The R2 the proportion of variance ‘accounted for’, ‘expl

2 1STR SSE

RSST SST

= = - (2.28)

with,

as sum of squares, error 2

1

ˆn

ii

SSE e=

= å

n2

1

( )ii

SST y y=

= -å as sum of squares, total (2.29)

2

1i

i=

ˆ( )n

SSR y y= -å as sum of squares, regression

ST = SSR + SSE (2.30)

es erms. If the regression is ‘perfect’, all residuals are zero, SSE is zero, and R2 is 1.

2.4 RELIABILITY ANALYSIS

n = sample size (number of observations)

S

It is important to keep in mind that a high R2 does not always imply the goodness of the regression in terms of fitting the observed data. The judgement is also coupled with the relative sizes of the sum-of-squar t

2.4.1 Reliability of Element

In structural design, the level of safety in each design component may be evaluated in several ways, as given in Table 2-1. Level I method have been used as the common prac-tice in the present days when designing a structure. It offers values of partial safety fac-

39


tors for the most common strength and load parameters, as shown in Figure 1.7 in Chapter 1 earlier. Level II and III on the other hand, are formed by knowledge of prob-bility and reliability theory concepts.

Table 2.1 Safety levels applied in structural design

n

a

Safety level Descriptio• Deterministic method • Should not be applied

Level 0

Level I

(safety factor) to

• Semi-probabilistic approach • Also known as load resistance factored design • Standard design procedures (codes and guidelines)

Utilizes a single partial coefficient • represent an uncertainty variable

• Design strength < design load x safety factor Level I

ad) is approximated by a

plified by

I • Approximations of the full probabilistic approach Each variable (strength and lo• standard normal distribution

• Probability of failure computation is simidealizing (linearising) a failure surface

Level Iad) is defined by its own

eated based on the knowledge of (joint)

urface which requires numerical

ble were, the calculations would be

overwhelming

II • Full probabilistic approach (more advanced) Each variable (strength and lo• probability density functions All variables are tr• distribution Utilizes the exact failure s• integration or simulation

• Information needed for this method is not always availaand even if they

bility function and normally addresses as the limit state function (Z) equation given by,

(2.31)

onship between the two parameters can be described from the RS-plane of Figure .3.

2.4.2 Limit State, Strength and Load

The state just before failure occurs, is a limit state (Vrijling et al., 2006). The reliability is the probability that this limit state is not exceeded. The limit state can be used to define relia

Z R S= -

where, R is the strength or more generally the resistance to failure and S is the load or that which is conducive to failure (‘solicitation’) (Vrijling et al., 2006). Recall that the R and S are both addressed as random variables or probability density functions here. The relati2

40


Strength, R

Load, S

Z < 0

Z > 0

Z = 0

Figure 2.3 Failure space as a function of basic variables

The limit state is described by Z=0. Failures takes place when the failure surface falls in the region of Z<0 while Z>0 is a survival region. The probability of failure (Pf) is then given by,

Pr( 0) Pr( )fP Z R= £ = ³ S (2.32)

The reliability is the probability Pr(Z>0) and is therefore the complement of the prob-ability of failure,

Pr( 0) 1 fZ > = -P (2.33)

The probability of failure can also be translated into another form,

( )

( )(1

2 2 2

R Sf

S R

Pm m

bs s

é ù- -ê ú

= F = F -ê úê ú+ê úë û

) (2.34)

with μ and σ as previously described by the mean and standard deviation. The term Φ is a notation describing the cumulative distribution function (CDF) for the standard normal distribution i.e. N(0, 1). The reliability index, β can be written as,

( )1Zf

Z

Pm

bs

-= = -F (2.35)

with Φ-1(Pf) known as the inverse of the standard normal probability distribution func-tion. The reliability index is a measure of the reliability of an engineering system that reflects both the mechanics of the problem and the uncertainty in the input variables (Sing et al., 2007).

2.4.3 Calculation Methods

Recall that Level III as described in Section 2.4.1 is mainly originated from probabilistic approaches, thus the probability of failure (Pf) computed in equation (2.32) may be solved in many ways. Some of the numerical integration approaches include analytical approximation methods like First Order Reliability method (FORM) and Second Order

41


Reliability Method (SORM) or simulation method like Monte Carlo Simulation (MCS) etc. The FORM and MCS methods will be applied in the thesis. Before pursuing to the description of the two methods, it is important to first understand the general mathe-matical formulation describing the strength and load terms.

Descriptions presented in this section are adapted from Vrijling et al. (2006). The Pf computation for Level III is based on mathematical formulation of the subset of the probability space. Herein, the joint probability density function fR,S(R,S) of the strength and load is known and its corresponding Pf is calculated by means if integration,

,

0

( , )f R S

Z

P f R S dR<

= òò dS

R s dS

(2.36)

Since Z<0 when R<S, then

, ( , )S

f R SP f R S dR dS¥

-¥ -¥

= ò ò (2.37)

If the strength is given by R=R(X1, X2, ..., Xm) and the load by S=S(Xm+1, X m+2, ..., Xn), the reliability function is a function of variables i,

Z = R–S = Z(X1, X2, ..., Xn) (2.38)

If the strength and load are statistically independent,

Pr( ) ( ) ( ) ( ) ( )S

f R sP R S f R f S dR dS F S f S¥ ¥

-¥ -¥ -¥

æ ö÷ç ÷ç= < = =÷ç ÷÷çè øò ò ò (2.39)

Or,

1 21 2 1 20... ( ) ( )... ( ) ..

nf X X X nZ

P f X f X f X dX dX<

» òò ò ndX (2.40)

The First Order Reliability method (FORM) comprises a number of approximate meth-ods in which the failure boundary is linearized and probability distributions are trans-formed into standard normal distributions. The probability of failure is then calculated by converting the original hyperplane failure surface into the tangential and quadratic approximation (refer Figure 2.4a). If the failure surface is not linear, it is approximated by tangent hyperplane. Furthermore, if the variables are not normally distributed, they have to be transformed into standard normal variables. Finally, if the variables are sto-chastically dependant, a transformation to independent variables is needed using the Rosenblatt transformation.

42


dS

dR

Strength, R Strength, R

++++

++

+

+

+

++

+

+

++

+

+

++

+++

+

+

++

++

+

+ +

+ ++

+

++

++

+

+

++

+

++

+

Z < 0 +

+

+ ++

Load, SLoad, S

Z < 0

•

(a) Numerical integration (b) Monte Carlo simulation

Figure 2.4 Illustration of numerical integration and Monte Carlo sampling (Adapted and modified from Korving, 2004)

The Monte Carlo simulation (MCS) method (Figure 2.4b) is simpler and straightforward method that does not require the model to be linear as in FORM, but computationally demanding. It is a numerical process of repeatedly calculating a mar empirical operator in which the variables within the operator are random or contain uncertainty with pre-scribed probability distributions (Ang and Tang, 2007). It is a class of computational algorithms that rely on repeated random sampling to compute their results. It should be emphasized that the numerical solution obtained by one repetition (or run) of a MCS, with a given sample size, may be slightly different when repeated by another repetition of the same sample size (Ang and Tang, 2007). The accuracy of the solution obtained through MCS will improve with the sample size.

The Monte Carlo simulation uses the possibility of drawing random numbers from a uni-form probability density function between zero and one. Because of their reliance on repeated computation of random numbers, these methods are most suited to calculation by a computer and tend to be used when it is unfeasible or impossible to compute an exact result with a deterministic algorithm. The method is useful for modelling phenomena with significant uncertainty in inputs.

2.4.4 Reliability of Systems

A system can be defined as ‘a group of elements or processes with a common objective (Vrijling et al., 2006). Many physical systems composed of multi components and the re-liability of multicomponent system will be a function of the redundancy of the system (Ang and Tang, 1984). A system may be redundant or nonredundant. When a system is redundant, the components can either be (i) participating e.g. sharing loads (active redundancy) or (ii) inactive and become activated only when some of the active compo-nents have failed. Details on this aspect can be referred to Ang and Tang (1984).

43


Care should be taken when dealing with multi components because the cause of failure at one component may trigger other components as well. The multicomponent system can be classified as connecting either in series or parallel.

Series System

Systems that are composed of components (elements) connected in series (Figure 2.5) are such that the failure of any one or more of these components constitutes the failure of the system; such systems, therefore, have no redundancy and are also known as ‘weakest link’ systems (Ang and Tang, 1984). In other words, the reliability or safety of the sys-tem requires that none of the components fail.

1 2 3 n - 2 n n - 1

Figure 2.5 Representations of series system

If Ei denotes failure of component i, then the failure of a series system is the event of,

1 2 ...sE E E E= È È È m

)

)2

(2.41)

For a simple series system that contains two components, the probability of component E1 or component E2 is given by,

( ) ( ) (1 2 1 2fP P E E P E P E= È = +

( ) ( ) (1 2 1P E P E P E E= + - Ç

( ) ( ) ( ) ( )1 2 1 2P E P E P E P E E= + - 1 (2.42)

Equation (2.40) shows that the probability of failure of the system is not only a function of the individual probabilities of failure of the components, but also of a conditional probability. The statistical dependence of the failure of the elements is therefore of im-portance (Vrijling et al., 2006).

Parallel System

Systems that are composed of components (elements) connected in parallel (Figure 2.6) are such that the total failure of the system requires failures of all components; in other words, if any one of the components survives, the system remains safe (Ang and Tang, 1984). The parallel system is an obvious example of a redundant system.

44

2.5. Conclusions

n -1

n

2

1

Figure 2.6 Representations of parallel system

The failure of an n component system is described by,

1 2 ...sE E E E= Ç Ç Ç m (2.41)

The probability of n components in parallel system is given by,

( ) ( ) ( ) ( )1 2 1 3 2 2, ... ....fP P E P E E P E E E P E E E -= 1n n (2.42)

2.5 CONCLUSIONS

Theories presented in this chapter are the main probabilistic approaches used in this the-sis. The probabilistic method itself is too broad to be discussed. Thus, descriptions pre-sented earlier were rather simplified and straight forward, intentionally prepared to suit the content of this thesis. Further and detailed descriptions pertaining to any of these approaches are recommended to refer back to their original texts or other published lit-eratures.

The probabilistic method is all about dealing with random variables and uncertainties. Thus readers have been fairly acquainted to random variables and their associated prob-ability functions at the beginning of this chapter. Theories on extreme values were pre-sented too, which its application to corrosions in pipelines will be later illustrated in Chapter 4.

Two major frameworks of this thesis were developed from the knowledge of regression analysis, which will be shown in Chapter 5 and 7 later. While carrying out these proce-dures, the analysis mostly dependant on the least-squares method in choosing the best re-liability model to describe the scenarios of interests. The least-squares method is consid-ered as one of the popular classical estimation methods among engineers because it gives lower probabilities underdesign (Van Gelder, 2000). Detailed theoretical backgrounds on this method will not be described in this thesis but readers are advised to refer to Van Gelder (2000) who has made good comparison between many other estimation methods such as Method of Moment (MOM), Maximum Likelihood Estimate (MLE), Method of L-Moments, the Bayesian method and others.

45


46

Simulations on random variables in Chapter 5, 6 and 7 were mainly carried out using ei-ther the Monte Carlo simulation method (MCS) or First Order Reliability method (FORM). When nonlinear equations needed to be used, the MCS method is more pref-erable.

Chapter 3

THEORIES ON CORROSION

3.1 INTRODUCTION

Some basic theories on corrosions will be introduced in this chapter. It is important to allow readers to get acquainted with the physics on corrosions before actually dealing with them in the remaining chapters of this thesis. It is well acknowledged that theories on corrosions cover a broad range of themes and areas. The processes involved are com-plicated but for the sake of presentation, illustrations given in this section is restricted to the interests of the thesis. Background on CO2 corrosion will be highlighted at the be-ginning. Herein, topics on electrochemistry of corrosion, forms of corrosion and factors governing them will be reported. A brief overview of corrosion models will also be in-cluded, followed by corrosion defect assessment models. Maintenance on corrosion will be later presented to conclude the chapter.

3.2 BACKGROUND ON CO2 CORROSION

Corrosions are normally classified into two categories; the sweet and sour corrosions. The sweet corrosion is defined as the deterioration of metal caused by contact with car-bon dioxide (CO2) in water. The sour corrosion, on the other hand, containing or caused by hydrogen sulphide (H2S) or another acid gas. This thesis is dedicated to pipelines concerned with the CO2 corrosions only, which is in accordance to the nature of corro-sions observed in the Peninsular Malaysia pipeline operation.

3.2.1 Electrochemistry of CO2 Corrosion

Corrosion is the chemical or electrochemical reaction between a material, usually a metal, and its environment that produces deterioration of the material of the material and its properties (Baboian, 2005). In the most common use of the word, this means electrochemical oxidation of metals in reaction with an oxidant such as oxygen. The cor-

3 Theories on Corrosions

rosion occurs because of the natural tendency for most metals to return to their natural state; e.g., iron in the presence of moist air will revert to its natural state, iron oxide. The electrochemical process involves anodic dissolution of iron and cathodic evolution of hydrogen. A typical anodic oxidation that produces dissolved ionic product, for example for iron metal is given by,

Fe → Fe++ + 2e⎯ (3.1)

while the cathodic reactions are described by,

2H+ + 2e⎯ → H2 (3.2)

2H2CO3 + 2e⎯ → H2 + 2HCO3- (3.3)

and finally the overall reaction is then represented by,

Fe + CO2 + H2O → FeCO3 + H2 (3.4)

3.2.2 Forms of Corrosion

In general, corrosions can be observed either at the internal or external side of the pipe-line wall. Figure 3.1 provides samples of internal corrosions observed in pipelines. The evolvement of external corrosions also behaves in the same way but at the opposite side of the pipeline wall. Analyses in this thesis utilized both types of corrosion, and this has been briefly introduced in Section 1.3.3.

An experimental view of corrosion can be seen from a micro scale laboratory work car-ried out by Rivas et al. (2008), as shown in Figure 3.2. It is visible from the figure that the shape of corrosion pit is governed by several length scale parameters. The shapes of corrosion, however, may be difficult to characterize. Typically, it will have an irregular depth profile and extend in irregular pattern in both longitudinal and circumferential di-rections (Cosham et al., 2007), as visualised in Figure 3.1 as well. One of the important parameters is the depth (d), which is proportionally measured with respect to its thick-ness. The spread of corrosion can be further described by means of its longitudinal length (l) and circumferential width (w) (Figure 3.2). Detail description on these length scale parameters will be presented in Chapter 5 later on.

48

3.2. Background on CO2 Corrosion

(a) (b) (c)

Figure 3.1 (a)(b) Examples of pipeline failures due to internal corrosions (Institute for En-ergy Technology, 2011) (c) Sketch on irregular length, width, and depth of a typical corrosion

defect (Adapted from Cosham et al., 2007)

(a) Plan view (b) Cross section view

Figure 3.2 Laboratory illustrations on pit corrosions (Adapted and modified from Rivas et al., 2008)

d

w

l

CreviceGeneral corrosion

Intergranular corrosion

Pitting corrosion

Stress corrosioncracking

Selectiveleaching Velocity affected

Figure 3.3 Different forms of corrosion developed on a particular metal surface (Adapted and modified from Freeman, 2002)

All corrosion reactions are electrochemical in nature and depend on the operation of elec-trochemical (living) cells at the metal surface, which results in different forms of corro-sion. There are no clear definitions of different types of corrosion defects (Cosham et al., 2007). The simplest and perhaps most widely used recognized definitions are the general and pitting corrosions.

49


Other forms of corrosion can be classified as crevice, galvanic, intergranular, velocity- or microbially-induced corrosions, or even stress corrosion cracking and selective leaching as schematically shown in Figure 3.3. Brief explanation pertaining to these corrosions is presented in Table 3.1. The rate, extent, and type of corrosive attack that can be toler-ated in an object vary widely, depending on the specific application and initial design Freeman (2002).

Table 3.1 Types of corrosion with their characteristics

Corrosion Characteristics

General (Uniform) corrosion

Defined as corrosion with a length and width greater than three times the uncorroded wall thickness. Uniform thinning of metal surface that proceeds without appre-ciable localized attack. Corrosion rate is assumed constant over the period of time.

Localized (Pitting) corrosion

Defined as corrosion with a length and width less than or equal to three times the uncorroded wall thickness. A form of extremely localized corrosion that leads to the creation of small holes in the metal. Thickness is reduced locally.

Crevice corrosion Occurs in spaces to which the access of the working fluid from the environment is limited, e.g. slots and in gaps at metal-to-metal and metal-to-nonmetal interfaces, especially at critical joining sur-faces.

Galvanic corrosion Occurs when two dissimilar conducting materials (metallic or nonmetallic) are in electrical contact. One metal corrodes preferentially to another when both metals are in electrical contact and immersed in an electrolyte.

Intergranular corro-sion

A form of corrosion where the boundaries of crystallites (grains) of the material are more susceptible to corrosion than their insides. Caused by environmental interactions or metallurgical changes in the grain-boundary regions during manufacturing or service expo-sure.

Stress corrosion cracking (SCC)

An unexpected sudden failure of normally ductile metals subjected to a tensile stress in a corrosive environment, especially at elevated temperature in the case of metals.

Selective leaching Removal of one element or phase from a solid alloy which results in an altered matrix usually consisting of a porous mass. Also known as dealloying, and when referring to the noble metals, it is also called parting.

Velocity affected corrosion

Depends on the relative velocity between the water and the metal surface. Water corrosivity can be dramatically increased by dissolved gases, acids, salts, strong bases, entrained abrasives, high tem-perature, fluctuating pressure, cavitation, or impingement.

Microbially-induced corrosion (MIC)

Caused or promoted by microorganisms or living organisms, e.g. sulphate-reduced bacteria (SRB), algae or fungi. Often associated with the presence of tubercles or slimy organic substances.

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3.2.3 Parameters Affecting CO2 Corrosion

CO2 corrosion in pipeline is affected by many factors with some of these are highlighted in this section.

Effect of Water Chemistry

Water chemistry is known to be one of the most influential parameters affecting CO2 cor-rosion. The specification can vary from very simple, with only a few carbonic species present, as is the case with condensed water in gas pipeline, to very complex with nu-merous species found, for example, in formation water emerging together with crude oil (Nešić, 2007).

Dissolved CO2 that contains in water, hydrates to form carbonic acid. It dissociates two steps in the electrochemical reactions to give a hydrogen ion and carbonate ion. These salts can precipitate if their solubility is exceeded which result in the formation of iron carbonate FeCO3 and various types of scales (Figure 3.4) typically rich in calcium (CaCO3, CaSO4, etc.). This scale or sometimes referred to as protective scale precipitates at the steel surface and slows down the corrosion process by (i) presenting a diffusion barrier for the species involved in the corrosion process, or (ii) covering (inhibiting) a portion of the steel surface. When acting as a barrier (Figure 3.5) to CO2 corrosion, scales can reduce the general corrosion rate (Li et al., 2008). The protection ability of the scale is closely related to the scale morphological characteristics (Li et al., 2008), es-pecially its precipitation rate (Nešić, 2007).

Another influence of the CO2 is its partial pressure (PCO2). An increase in PCO2 leads to an increase in the corrosion rate. However, when high pH is also presence, high PCO2 re-sults to an increase in bicarbonate and carbonate ion concentration and a higher super-saturation (Nešić, 2007), which then accelerates precipitation and scale formation.

Corrosion rate and scale are proportionally influenced by water temperature and pH (Nyborg, 2002; Nešić, 2007). Corrosion rate steadily increases with temperature with temperature, and this is the case at low pH when precipitation of iron carbonate (or an-other salt) or protective scale does not occur. On the other hand, when solubility of iron carbonate is exceeded, typically at higher pH, high temperature accelerates the kinetics of precipitation and protective scale formation, which also result in the decrease in corro-sion rate.

Water also carries organic acids, particularly the acetic acid (HAc) which can accelerate corrosion problem further. The HAc has recently been recognized as a major factor in premature pipeline failure causing either generalised or centralized corrosion (Nafday, 2004). It dissociates in the same manner to that of the CO2. The HAc is however, a weak acid, in which iron acetate’s solubility is so much higher than iron carbonate’s,

51


making scale formation by iron acetate not readily to occur. Even though it was specu-lated that the presence of organic acids impairs the protectiveness of iron carbonate films, there is no strong evidence that the former change the solubility of the latter (Nešić, 2007).

Figure 3.4 Different types of scales formed in pipelines (Adapted from Bufton and Cochran, 2008)

Figure 3.5 Laboratory work by Nešić, and Lee (2003) showing a cross section of a steel specimen including an iron carbonate scale acting as a barrier to corrosion

(Adapted from Nešić, and Lee, 2003)

Effect of Flow

Most pipelines or flowlines carrying oil and gas are operating under two or three-phase flow conditions, with the common ones being stratified, slug and annular flows, as given in Figure 3.6. In the liquid phase, water and oil can flow separated or mixed with either phase being continuous with the other flowing as a dispersed phase. Different flow pat-terns lead to a variety of steel surface wetting mechanisms which greatly affect corrosion (Nešić, 2007). Multiphase flow results in large fluctuations of mass transfer rates and

52


surface shear stress which can lead to removal of protective scales and/or inhibitors (Nešić, 2007). Jepson et al. (1997) suggested that the Froude number is important for characterizing the effect of multiphase flow on corrosion. [Froude number is interpreted as the ratio of the inertial to gravity forces in the flow in the form of a dimensionless quantity U(gL)−½, where U is a characteristic velocity of flow, g is the acceleration of gravity, and L is a characteristic length.] Hong et al. (2002) has proven that slug flow occurs at high turbulence and high Froude numbers which could easily damage and wash away the inhibitor film from the metal surface, thus leading to low corrosion resistance. Hausler and Schmitt (2004) reported that there exist a relationship between fluid veloc-ity and corrosion inhibitor concentration for equal corrosion rate, thereby opening the possibilities of corrosion inhibition at ever higher flow rates, albeit with higher inhibitor concentrations.

Figure 3.6 Different flow regimes that may present in multiphase flows (Adapted from Zhou, 1993)

Effect of Condensation

Certain multiphase flows may exhibit a gas dominated system. Water vapour condensa-tion takes place on the upper part of the internal pipe wall of wet gas pipelines, as shown in Figure 3.7. This normally occurs when the transported natural gas starts to cool down. Quite often this scenario is related to the top-of-line corrosion (TLC). If the condensation rate is high, plenty of acidic water flows down the internal pipe walls lead-ing to a very corrosion situation (Nešić, 2007). The condensing water is unbuffered with low pH, but can become rapidly saturated or supersaturated with corrosion products, giving rise to an increased pH and possibility for iron carbonate film formation (Nyborg, 2002). The composition of the condensing phase is subjected to the composition of salts and crude oil in the liquid at the bottom (Smith and de Waard, 2005). The TLC is pri-marily concern in the first few kilometres of wet gas pipelines with relatively high inlet temperatures (Nyborg, 2002) and can often result in a corrosion peak further along the pipeline route, as the temperature of the gas decreases (Alkazraji, 2008).

53


Figure 3.7 Water vapour condensation of internal pipeline wall

If the pipeline tends to be over- or undersized due to unexpected changes in the products transported in it, the pipeline may become unstable and cause terrain slugs inside the pipeline. Unstable flow may impact pipeline mechanical integrity by causing pipeline vi-bration and excessive corrosion (Guo et al., 2005). Interested readers are advised to re-fer to Nešić et al. (2004) for depth discussions on how the flow regime is actually pre-dicted and how the hydrodynamics properties affect the corrosion rate.

Effect of Corrosion Inhibitor

A corrosion inhibitor is a chemical compound that, when added to a liquid or gas, decreases the corrosion rate of a metal or an alloy. Inhibitors are released into the pipeline from a solution or dispersion. They can be applied through batch treatments, formation squeezes, continuous injections or a slug between two pigs (Bai and Bai, 2005). Corrosion inhibitors reduce the corrosion process by either (Bai and Bai, 2005):

i. increasing the anodic or cathodic polarization behaviour,

ii. reducing the movement or diffusion of ions to the metallic surface, or

iii. increasing the electrical resistance of the metallic surface.

Engineers normally select a combination of low-grade material and corrosion inhibitor, and hope that the useful life of the structure is appropriately extended. This practice is proven to be viable, provided that inhibitor performance has been assessed predictably. Describing the effect of corrosion inhibitors is not a straightforward task (Nešić, 2007). The effectiveness of corrosion inhibitors is affected by a number of environmental, physical and metallurgical parameters, which may include but not limited to fluid composition, quantity of water, and flow regime. Failures occur under the most aggressive conditions, be it due to flow intensity, pH, metallurgy or the combination of high pressure and temperature (Hausler, 2005). These variables interact with each other in unpredictable nonlinear fashion, and moreover, such interactions are inhibitor specific (Hausler, 2005). The effectiveness can be achieved when the system is properly understood. If the correct inhibitor and quantity is selected then it is possible to achieve as high as 90-99% efficiency. The inhibitor efficiency normally increases with an increase

54

3.3. Summary on CO2 Corrosion Models

in inhibitor concentration. It is important to understand that adding ‘new’ chemical to an existing corroding system requires compatibility, chemical and thermal stability, and in some cases physical stability as well.

Glycol and methanol may be regarded as a special case of inhibition to prevent hydrates from forming. Hydrates compose crystalline compounds of water and light hydrocarbon molecules which look like ice-like solid crystals, as shown in Figure 3.8. When gly-col/methanol is released at a higher dosage, they can be used to control corrosion. They dilute the water phase which leads to a decreased activity of water, and also act as dry-ing agent which reduces water condensation rate at the top of the line. Their concentra-tion becomes smaller with distance into the pipeline.

Figure 3.8 Example of hydrates formed in pipelines (Adapted from Bufton and Cochran, 2008)

3.3 SUMMARY ON CO2 CORROSION MODELS

There have been various mathematical modelling strategies applied in estimating CO2 corrosion models for pipelines. The basic form of these models can be either power, two-phase or linear models (Lee at al., 2006), which are listed in Table 3-2.

Table 3.2 General form of corrosion pit models

Model Equation Parameters Power model d = kTn d = depth of corrosion pit (mm)

k = constant n = constant T = exposure time (yr)

Two-phase model d = aT + b(1-e-cT) d = depth of corrosion pit (mm) a = final pitting rate of constant (mm/yr) b = pitting depth scaling constant (mm) c = corrosion rate inhibition factor (yr-1) T = exposure time (yr)

Linear model d = ηT d = depth of corrosion pit (mm) η = corrosion rate (mm/yr) T = exposure time (yr)

55


The models are normally used in simple corrosion prediction exercise but quite often en-gineers tend to refer to more complicated mathematical models. This is because, apply-ing as simple as (Nešić, 2007) a linear model (even if it is multivariable) is doubted to

describe well the highly nonlinear processes occurring in the CO2 corrosion. Nešić (2007) who recently made a thorough review on different strategies the predictive models have employed in order to account for the complex processes underlying the CO2 corrosion, has classified them into arbitrarily three broad categories based on how firmly they are grounded in theory. The following are the summary prepared by the author to each group:

Mechanistic models are the most direct translation of our knowledge of the underlying processes into mathematical functions. They are the hardest ones to construct and have the largest potential to help engineers in various stages of the design, operations and control operations.

Semi-empirical models, which have a limited amount of inbuilt understand-ing, rely on correction factors to perform well. These factors come in the form of arbitrary functions developed on spares experimental data sets and have dubious interactions. While being significantly easier to develop than mechanistic models, the capability of semi-empirical models to extrapolate is questionable.

Empirical models consisting or arbitrary mathematical functions of varying complexity, can have reasonable or even excellent interpolation capabilities but have to be treated with utmost caution when used to predict outside they calibration range.

Some of these models have been made commercialised by the name of de Waard, Cas-sandra, Norsok, Cormed, Lipucor, Hydrocor, KSC, Tulsa, Predict, SweetCor, Corpos, Ohio, ULL, Dream, OLI and ECE models (Nyborg, 2002). Interested readers are rec-ommended to refer to the work by Nyborg (2002) who had critically reviewed the per-formances of these commercialised models by comparing them to a field data set. Note that it is not the intention of the present work to either elaborate or present the respec-tive equations to the above categories because their contribution to the present work is considered to be minor. Nevertheless, the above reasoning will become good arguments for the analysis in Chapter 7 later on.

3.4 CORROSION DEFECT ASSESSMENT METHODS

This section provides an overview of the best practices for the assessment of corrosion in pipelines. Ultimately, the engineer has to decide whether a pipeline containing a re-ported defect is fit for the intended pressure or whether it needs repair (Alkazraji, 2008). Failure pressure (PF) models have been developed for this purpose and widely used to estimate the remaining strength of corroded pipelines subjected to internal pressure.

56

3.4. Corrosion Defect Assessment Methods

The PF model (equation) was originated from the circumferential stress or hoop stress (σh) acting on a pipeline. For this, consider a unit length (1 m long) pipeline containing fluids with external diameter (Do), internal diameter (Di), wall thickness (t), internal pressure (pi), and external pressure (po), as shown in Figure 3.9(a). The idea is to de-termine the force that the internal pressure induces in the wall by considering the equi-librium of everything within the circumscribing rectangle drawn in Figure 3.9(b). Half the pipe and half the contents are redrawn in Figure 3.9(b) as a free body diagram. The rectangle is bounded by the diameter, two tangents at the point where the diameter in-tersects the outside surface, and a tangent parallel to the diameter. The stress compo-nents that act across the boundaries of different parts of the rectangle are known as the hoop stress.

po

(a) (b)

Figure 3.9 Circumferential stress in a pipeline pressurized internally and externally (Adapted and modified from Palmer and King, 2008)

The resultant force in the vertical direction must be zero, thus the equilibrium equation becomes,

2o o h i ip D t p Ds+ = (3.5)

Arranging equation (3.5),

2i i o o

h

p D p D

ts

-= (3.6)

Equation (3.6) gives the mean circumferential stress exactly, whatever the diameter-to-thickness (D/t) ratio. There are various versions of equation (3.6) and the most widely used is the Barlow formula, given by,

2i

h

p D

ts = (3.7)

Do

Di

pi

tt

po

σh σh

pi

57


The above formula was derived by neglecting the external pressure term poDo in equation (3.6). Internal pressure from the contained fluid is the most important loading a pipe-line has to carry (Palmer and King, 2008). D is normally taken as the outside diameter which is obviously larger than the inside parameter. This can be interpreted as a round-and-ready way of allowing for the small variation of hoop stress through the wall thick-ness (Palmer and King, 2008). Rearranging equation (3.7),

2 hi

tp

D

s= (3.8)

It can be said that that,

,i

tp f

Dsæ ö÷ç= ÷ç ÷è h ø

(3.9)

The above equation implies that the internal pressure of an intact (no defect) pipe can withstand is a function of a wall thickness-to-diameter (t/D) ratio and its strength (or stress).

For the case of a pipeline with corrosion defects, equation (3.9) can be modified by incor-porating the defect projected area (A) term into the equation. The same principle was applied when developing the failure pressure (PF) model; a model used for the assess-ment of remaining strength in a pipeline subjected to corrosions. Generally, the basic PF model can be expressed as,

, ,i

tp PF f A

Dsæ ö÷ç= = ÷ç ÷è h ø

(3.10)

Batelle developed a semi-empirical equation for the remaining strength of corroded pipe-lines in early 1970 (Maxey et al., 1971; Kiefner and Duffy, 1971; Kiefner, 1974). The equation has been called the NG-18 equation and is given by,

1.2.

11

flow o

o

At A

PFADA M

sé ù

-ê úê

= êê ú-ê úê úë û

úú (3.11)

where, Ao=dt, M is Folias bulging factor, σflow is flow stress, and d is maximum corrosion depth. Note that the σh term has been replaced by σflow here. Several modifications have been made to the above parameters depending on the available test data sets and study techniques. These involved:

1. flow stress, σflow,

2. defect profile or projected corrosion area, A, and

3. geometry correction factor (also referred to as the Folias factor, or the bulging correction factor, M).

58

3.4. Corrosion Defect Assessment Methods

The flow stress (strength), σflow is a concept proposed in the 1960s to measure the strength of steel in the presence of a defect. The NG-18 equation here assumes that fail-ure is due to a flow stress dependent mechanism and can, therefore be described by the tensile properties like yield strength or ultimate tensile strength (Cosham et al., 2007). The σflow has been proposed for several modifications, as listed below,

σflow = 1.1 SMYS

σflow = 1.15 SMYS

σflow = 0.5 (SMYS+SMTS)

σflow = SMYS + 68.95 MPa (or 10 ksi)

σflow = x.SMYS, where x = 0.90, 1.0 or 1.1

where, SMYS and SMTS is Minimum Specified Yield Stress and Specified Minimum Tensile Strength, respectively.

The projected corrosion area, A has also undergone several propositions, namely,

A = dl (rectangle)

A = 2/3dl (parabolic)

A = 0.85dl (approximate average of rectangle and parabolic)

A = ‘exact’ calculation

with l as the defect longitudinal length.

The geometry correction factor which is also referred to as the Folias factor, or the bulg-ing correction factor, M developed by Folias (1964) to account for the stress concentra-tion that is caused by radial deflection of the pipe surrounding a defect.

Table 3.3 provides a summary of the available PF models used to compute the remaining strength of corroded pipelines. All models were developed based on the NG-18 equation. Also given in the table is the bulging factor, M equation for each model. Detailed dis-cussions and comparison on the theories and development of the PF models have been carried out by Cosham et al. (2007), BjØrnØy and Marley (2001) and Cronin (2000), for instance. Their works involved critical comparison between the performances of all as-sessment methods, and these will not be repeated in here.

59


Table 3.3 Design standards on the assessment of corrosion in pipelines (Adapted from Cosham et al., 2007)

Method Basic equation

Flow stress Defect shape Bulging factor

NG-18

NG-18a

SMYS + 68.95 MPa

rectangle (dl)

2 4

1 0.6275 0.003375l l

Dt Dt

æ ö æ ö÷ ÷ç ç÷ ÷+ -ç ç÷ ÷ç ç÷ ÷ç çè ø è ø

ASME B31G NG-18 1.1 SMYS parabolic (2/3dl) 2

1 0.8l

Dt

æ ö÷ç ÷+ ç ÷ç ÷çè ø

Modified B31G NG-18 SMYS + 68.95 MPa arbitrary (0.85dl) 2 4

1 0.6275 0.003375l l

Dt Dt


RSTRENG NG-18 SMYS + 68.95 MPa river bottom profile 2 4

1 0.6275 0.003375l l

Dt Dt


SHELL 92 NG-18 SMTS rectangle (dl) 2

1 0.8l

Dt


LPC NG-18 SMTS rectangle (dl) 2

1 0.31l

Dt


DNV-RP-F101 NG-18 SMTS rectangle (dl) and river bottom profile

2

1 0.31l

Dt


PCORRC Newb SMTS rectangle (dl) c

b The basic equation of the PCORRC part-wall NG-18 failure criterion is,

1 1

,11 11

o

o

A dA t

dAMM tA

qs s s

é ùæ ö é ùæ ö÷çê ú ÷çê÷-ç ÷-ç÷ê úç ÷ê ç÷÷ ÷ç çè ø è øê ú ê ú= =ê ú ê úæ ö æ öê ú÷ ÷ê úç ç÷ ÷--ç çê ú÷ ÷ê úç ç ÷ç÷÷ç è øê ú ê úè ø ë ûë û

úú where, M is bulging factor and s is flow stress.

c The basic equation for PCORRC failure criterion is,

0.5

1 1 exp 0.16 1d l

t tRtqs s

-é ùæ öé ùæ öæ ö æ ö ÷çê úê ú÷÷÷ ÷ççç ç ÷÷÷ ÷= - - - -ê ççç çê ú÷÷÷ ÷ççç ç ÷÷÷ ÷ç ççê úçè ø è øê úè ø ÷÷çè øê úë ûë û

.d

ú

The above assessment methods can be further classified into two categories (Stephens and Francini, 2000):

1. The ‘old’ methods: empirically calibrated criteria that have been adjusted to be conservative for almost all corrosion defects, irrespective of the toughness of the line pipe (these criteria are variously based on the yield strength, the flow stress, or ultimate tensile strength).

2. The ‘new’ methods: plastic collapse criteria that are only appropriate for blunt defects in moderate to high toughness line pipe (these criteria are based on the ultimate tensile strength).

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3.5. Corrosion Inspection, Maintenance and Control

The ‘old’ methods like ASME B31G (or modified B31G and RSTRENG) were predomi-nantly developed and validated through full scale tests on older line pipe steels while the ‘new’ methods such as the DNV RP-F101 and PCORR through tests on modern, high toughness, line pipe steels (Cosham et al., 2007). Therefore each method was biased to-wards the type and toughness of the steels. Then, the difference between the behaviour of both categories can largely be attributed to the general increase in the toughness of line pipe, due to improvement in steel production and technological advances. Because of the ‘old’ methods demonstrate greater scatter than the ‘new’ methods when compared to the (relevant) published full-scale test data, the ‘new’ methods are more accurate (Cosham et al., 2007).

It is also important to highlight here that the models in Table 3.3 are basically determi-nistic, in which the equations are mostly governed by safety factors. The factors of safety are not well understood due to lack of appropriate experimental data (Cronin, 2000). Safety factors are normally represented by certain ‘fix’ numbers which may not be directly applicable to describe other scenarios.

With the evolvement in study techniques, the finite element method (FEM) has recently been proposed as a less conservative method of assessment (Chouchaoui and Pick, 1993; Fu and Kirkwood, 1995) yet it has been validated for simple corrosion geometries. Fur-ther, the cost and expertise necessary to conduct such analyses prohibit their general use. BjØrnØy and Marley (2001) later concluded that reliability methods will become more common in the future and part of this evolvement will be presented in the remain-ing chapters of the thesis.

3.5 CORROSION INSPECTION, MAINTENANCE AND CONTROL

3.5.1 Introduction

Pigging in the maintenance of pipelines refers to the practice of using pipeline inspection gauges or pigs to perform various operations without stopping the flow of the product in the pipeline. The name pig was originally applied to scrapers which were devices driven through the pipeline by the flowing fluid trailing spring-loaded rakes to scrape wax off the internal walls (Cordell and Vanzant, 2003). The rakes made a characteristic loud squealing noise, hence the name ‘pig’ has been widely used ever since. Pipeline pigs are inserted into and travel throughout the length of a pipeline driven by a product flow. They were originally developed to remove deposits which could obstruct or retard flow through a pipeline. Their occurrence usually does not interrupt production, though some product can be lost when the pig is extracted.

61


Today pigs are used during all phases in the life of a pipeline for many different reasons, with some of which as addressed below Mohammed et al. (2009):

Separation of products Internal inspection

Cleaning out deposits and debris Gas removal

Gauging the internal bore Pipe geometry measurements

Location of obstructions Coating of internal bore

Meter loop calibration Corrosion inhibition

Liquids' removal Improving flow efficiency

Generally, the type of pig to be used and its optimum configuration for a particular task in a particular pipeline should be determined based upon several criteria, which include:

The purpose:

• Type, location, and volume of the substance to be removed or displaced in conventional pigging applications,

• Type of information to be gathered from an intelligent pig run,

• Objectives and goals for the pig run.

The line contents:

• The contents of the line while pigging,

• Available vs. required driving pressure,

• Velocity of the pig.

Characteristics of the pipeline:

• The minimum and maximum internal line sizes,

• Maximum distance pig must travel,

• Minimum bend radius, and bend angles,

• Additional features such as valve types, branch connections, and the elevation profile.

Depending on the functionality, the non-intelligent pig can be classified into mandrel, foam, solid cast or spherical pigs, as summarized in Mohammed et al. (2009).

3.5.2 Pig’s Philosophy

The philosophy of pig cleaning is illustrated in Figure 3.10 below. A solid interface formed between the pipe wall and the pig sealing element which imparts a cleaning ac-tion on the pipe wall. This can be further enhanced by the addition of brushes, scrapers, or even more aggressive tools to the pig. For lines where ferrous debris is expected, magnets attached to the pigs can add a pick-up action for removal of magnetic debris. The turbulence within the fluid flow will hold any small, solid debris in suspension, effec-tively sweeping it out of the line. The use of bypass ports through the pig can aid this sweeping effect. Waxes and sludges tend to adhere to the pig brushes and scrapers and are generally ‘ploughed’ through the line.

62


Brushes of the pig clean

Pig Pipe wall

pipe wallDebris removed

due to turbulence

Figure 3.10 Pig cleaning philosophy

3.5.3 Pig Trap System

The pig has to be placed in a proper pig trap system (Figure 3.11) in order to provide a safe manner and without flow interruption; the means to either insert and launch a pig into a pipeline or receive and retrieve a pig from a pipeline. A pig is released from the upstream (pig launcher) and received at the downstream (pig receiver) of the pipeline.

Figure 3.11 Placing a pig in the pig trap system (United Kingdom Society for Trenchless Technology, 2011; PETRONAS Technical Standard, 1998)

3.5.4 Unpiggable Pipelines

There has been range of pigs designed and manufactured according to the present needs. Today’s generation of inspection pigs are much more versatile in their ability to pig the unpiggable pipelines. However, it is still believed that over one-third of the world's pipe-lines are still considered unpiggable for various reasons such as (Harkin, 2006):

• Changes in the diameter of the pipeline restricting the size and type of pig that can be used.

• The size, type and location of valves and other AGI systems.

• The insertion of various types of fittings such at ‘T’ sections

• Pipeline bend restrictions

• Various other pipeline configurations.

63


Harkin (2006) who has shared good remarks and opinions on this issue commented that these new generation of inspection pigs are now being used to carry out pipeline inspec-tions on pipelines constructed in the last 10 years or so, but still find it incredibly diffi-cult (if not impossible) to pig the older, more important lines as far as potential failure is concerned. The author believed the older lines were constructed without enough consid-eration to preventative maintenance programs. What is needed is a way of pigging what was previous thought as unpiggable! Harkin (2006) further informed that there are a number of pig manufacturers who now claim they have such pigs at the industry’s dis-posal with some companies able to insert hot taps in pipelines where it was thought im-possible. This concept brings a whole new and vastly improved method of preventative maintenance and inspection programs. However, the author also reminded that whilst these new techniques may be the next generation of inspection methods, there will still be some restrictions due to obstructions occurred from road and water crossings.

3.5.5 Lost Pigs

The pigs may have seemed as the most ‘human trusted friends’ in pipeline operation so far, but quite often pigs do provide ‘troubles’ to pipeline operators. A pig sometimes ex-periences difficult time to find its way ‘home’ and consequently lost in the pipelines, as shown in a comedic illustration in Figure 3.12. One of the reported incidents involving pig lost can be referred to Lino et al. (2006). The incident happened when a mandrill pig was unable to be detected at the pig receiver. Six recovery operations were conducted within nine months to search for the lost pig. Strategies needed to be well planned with maximum priority given to the avoidance of accidents to personnel and/or the environ-ment, and any interruption whatsoever to production. Obeying to these rules, the first strategy was to adopt non-intrusive techniques.

Figure 3.12 Pig lost in pipeline (StarTrak Pipeline Technologies, Inc., 2011)

When a pig got stuck in a pipeline, the pipeline operations are exposed to production dangers like (Lino et al., 2006):

• Wax accumulation — in regular pigging routines, wax accumulation is controlla-ble. However, disruption to a cleaning routine could create a significant wax ac-cumulation.

64


• Water accumulation — in addition to wax removal, pigging removes water. A disruption to the cleaning routine could create a significant accumulation of water which could, in turn, create a pipeline blockage.

• Pipeline erosion — an increase in flow velocity in the specific location of the lost pig could amplify the erosion factor and cause further damage to the pipeline.

The search for the lost pig by Lino et al. (2006) reached to an end when the pig was lo-cated 20 km farther away from the launcher. The pig that was broken into parts was then investigated to identify the causes of failures. Based on the examination and analy-sis of all pig components, Lino et al. (2006) concluded that the pig could be dismantled:

1. due to a valve misalignment,

2. caused by a dent in the sector of pipeline between the launcher and valve sta-tion,

3. as a result of inadequate construction whereby, the pig was unable to support the operational loads, or

4. from an operational failure during the launching.

3.5.6 Intelligent Pigs

In the oil and gas pipelines, the in line inspection (ILI) tool or smart/intelligent pigs (IP) are used to provide an overview (mapping) of the condition of a corroded pipe. Focus from this point onwards will be given to this type of tool. The IP as shown in Figure 3.13, is a tool that is extensively used to carry out inspection and maintenance works on corroded pipelines. It is a tool that has been proven for its benefits, expanding capabili-ties and legislative requirements. Corrosion maintenance using the IP has received nu-merous attentions in the present world because of enhancement in technology. Neverthe-less, it is costly and disruptive activity. A sample of specifications and requirements for IP inspection has been comprehensively addressed in Shell International Exploration and Production (2005).

Figure 3.13 Some examples of pigging tools (Pigging Products & Services Association, 2011)

Data gathered by this type of tool will be analysed by the pipeline operators to deter-mine and report on the condition of the line. Although the two most common require-ments are for geometry/diameter measurement and for metal-loss/corrosion devices, the

65


information which can be provided by these intelligent pigs covers a much wider range of inspection and troubleshooting needs which include:

Diameter/geometry measurements Photographic inspection

Curvature monitoring Crack detection

Pipeline profile Wax deposition measurement

Temperature/pressure recording Leak detection

Bend measurement Product sampling

Metal-loss/corrosion detection Mapping

With regards to metal loss/corrosion detection, not only the defect geometrical parame-ters that are reported, but also its orientation as measured from the pipeline cross sec-tion and along longitudinal pipeline distance. This will be further elaborated in Chapter 4 later on. The IP records any internal or external metal loss of pipeline wall as it is re-leased from the pig launcher and received at the pig receiver of the pipeline.

Maintenance using the IP tool is only carried out at only certain intervals during pipe-line operation life. Although continuous improvements are being made to the accuracy of IP, the defects are sometimes under or over reported in size, which is likely due to the following reasons:

Pigs cannot detect all defects, all of the time.

Pigs measurements have associated errors.

Pigs cannot discriminate between all defects.

The simple defect assessments (e.g. estimated repair factor, ERF) provided by pig-ging companies may not be appropriate for all defects and all pipelines.

Defect location accuracies of pigs vary and have errors.

3.6 CONCLUSIONS

Discussions presented in this chapter are primarily related to type CO2 corrosion and are not particularly suited for situations with appreciable amounts of H2S. The main inten-tion is to allow readers to get acquainted with some theories on corrosions, particularly those that will be utilized in the analysis sections of the thesis.

Water has shown to be one of the major threats to pipelines exposed to corrosion. Whether extracted directly from the wells or condensed through the transported natural gas, controlling water in pipeline is not an easy task to carry out. Its occurrence in the pipeline is proportional to the forms of corrosion evolved from it. Together with other

66

3.6. Conclusions

67

operating parameters like temperature and pressure, compositions in water expedite the development of other products like scales and hydrates. Even though protective scale is considered handy in controlling corrosion penetration through the pipe wall, these prod-ucts affect the pipeline operation and flow assurance in one way or another. Pigging as well as the use of corrosion inhibitor for instance, are then required to be carried out in order to manage the problem. These theories indirectly provide answers to the problem statement of Chapter 7. In addition to that, intelligent pigging will be given special at-tention in Chapter 4, through which analysis are focused on understanding and interpret-ing the outputs of that inspection tool. Chapter 8 will also benefits from the ability of the tool to report on corrosion orientation, allowing spatial corrosion to be predicted.

Stopping corrosion development by all means is impossible, thus it is compulsory to monitor the remaining strength of the corroded pipelines for controlling failures from taken place. Theories on design standards or codes pertaining to this aspect have been fairly presented, as well as the governing parameters associated to them. Analysis pre-sented in Chapter 5 and 6 will be judging the goodness of these standards with emphasis given particularly to corrosion defect shapes.

As addressed earlier, theories on corrosions cover a broad range of themes and areas which are not thoroughly covered in this chapter. Nevertheless, theories presented herein have provided appropriate and sufficient information to enable readers to further appre-ciate discussions presented in the remaining content of this thesis.

Chapter 4

CORROSION DATA ANALYSIS

4.1 INTRODUCTION

Chapter 3 has acquainted the readers to corrosions in offshore pipelines. Also mentioned in the chapter was the capability of an intelligent pigging (IP) tool to record corrosion data set. An IP contractor will then analyse the data set and prepare the outcomes. These outcomes are more or less qualitative as the IP data sets are simply translated in the form of graphical presentations. These graphs are somehow plotted in certain stan-dard and typical ways. An overview of these graphical presentations is presented at the beginning of this chapter in order to provide understanding on how corrosion measured data set are normally presented. Statistics are applied later to the original measured data set, to understand its capability to extract and interpret some useful information about corroded pipelines.

4.2 AN OVERVIEW ON INTELLIGENT PIGGING DATA

In general, the graphical presentations of corrosion measured data sets of a particular pipeline are aimed at summarizing the defect distributions in the longitudinal distance and cross section of the pipeline, as shown in Figure 4.1(a) and (b), respectively. They are concerned with the magnitude and location (orientation) of the defects. The magni-tude of defect is given by depth of penetration (mm) or amount of wall loss with respect to pipeline wall thickness (%) while the location can be described by two means, namely (i) distance as measured along the pipeline longitudinal view (Figure 4.1a), and (ii) ori-entation as described by the o’clock position with respect to pipeline cross section view (Figure 4.1b). These implicitly represent descriptions on corrosion development in space. The count of defects at an IP inspection time corresponds to its frequency of occurrence of that particular time. Descriptions about corrosion development in time can be made by comparing the frequency of defects at different IP inspection times.

4 Corrosion Data Analysis

Flow

y

0

3 o’clock

6 o’clock

0/12 o’clock

9 o’clock

x (km)

(a) Longitudinal view (b) Cross section view

Figure 4.1 Corrosion defect distributions as captured by an intelligent pigging (IP) tool

Examples of some typical graphical presentations of corrosion data sets captured at one IP inspection time (i.e. 2007) will be discussed here. This section, however, is only con-cerned about describing the data sets in space. An example of corrosion development in time will be explained in Section 4.4 later on. For this, a pipeline candidate which is still in operation located at Kerteh, Terengganu, the east coast of Peninsular Malaysia was chosen. Its properties and corrosion characteristics as shown in Table 4.1 would be used throughout the analysis.

Table 4.1 Pipeline properties and corrosion characteristics

Type: API 5LX-65 Diameter: 28 inch Nominal wall thickness: 16.2 mm Length: 128.9 km Year of installation: 1999 IP inspection year: 2007 Type of defects: Internal and external corrosions Number of defects: 861 defects

Any pipeline operator would be interested to know the amount of wall losses that have occurred in their pipelines. It is wise to describe it according to categories on the sever-ity level of defects. For instance, Figure 4.2 presents five categories of defects for the above pipeline, namely defects with wall loss <10%, 10 to 19%, 20 to 29%, 30 to 39% and 40 to 49%. The figure would provide a quick glance of the distribution and the main highlight would be the greatest percentage of wall loss i.e. the 40 to 49% category with total of 5 defects. This information would alert the pipeline operators on any possi-ble threats to the pipeline.

Next, the concern would be looking at how these defect categories spread along the lon-gitudinal distance of the pipeline. This would give some ideas on the location of some de-fects of interests. Figure 4.3 was prepared for this purpose.

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4.2. An Overview on Intelligent Pigging Data

The figure indirectly explained that not all defect categories were observed throughout the pipeline length, especially for defects with higher percentages. ‘New born’ defects (<10%) were expected to grow along the pipeline length and a similar trend was also ob-served for defects of 10 to 19%. The rest of the categories could be explored the same way. However, this figure was limited to the fact that only the numbers of defect were plotted. To avoid this, another type of graphical presentation is needed.

10-19%; 299

20-29%; 52

30-39%; 22

40-49%; 5

<10%; 483

<10%

10-19%

20-29%

30-39%

40-49%

Figure 4.2 Number of defects according to categories as recorded at one IP inspection year

0

10

20

30

40

50

60

<10 10 20 30 40 50 60 70 80 90 100 110 120

Longitudinal pipeline distance (km)

Num

ber

of def

ects

< 10%

10-19%

20-29%

30-39%

40-49%

Figure 4.3 Number of defects along the longitudinal distance of pipeline as recorded at one IP inspection year

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Quite often pipeline operators are more interested with the amount of wall losses meas-ured with respect to the pipeline wall, rather than the longitudinal or circumferential orientations. Thus, data on corrosion defect depth (d) would be given more priority compared to the longitudinal length (l) or circumferential width (w) (recall Figure 3.2). Figure 4.4 below provides information on the parameter d along the pipeline. It could be obviously seen now where the higher percentage of defect occurred. Agreeing to the trend in Figure 4.3 earlier, the area of defects less than 20% seemed to be more occupied. Figure 4.5 could also be a representation of d which was in the form of a remaining wall loss rather than percentage. One of the advantages of using this figure is that one could see the variation in wall loss with respect to the nominal wall thickness and allowable remaining wall thickness.

0

20

40

60

80

100

0 10 20 30 40 50 60 70 80 90 100 110 120 130


Def

ect

dep

th (

%)

Figure 4.4 Corrosion depth, d (%) distribution along the pipeline

0

2

4

6

8

10

12

14

16

18

0 10 20 30 40 50 60 70 80 90 100 110 120 130


Rem

aini

ng p

ipel

ine

wal

l th

ickn

ess

(mm

)

Allo wable remaining wa ll thicknes s , 12.96 mm

No mina l wa ll thicknes s , 16.20 mm

Figure 4.5 Remaining wall thickness (mm) distribution along the pipeline

72

4.3. Statistical Interpretation on Corrosion Data

Last but not least, the spread of defects from the cross section view could be prepared by making use of the o’clock information reported by the IP. Note that the 6 o’clock orien-tation is a point when the pipeline touches the sea bed. Figure 4.6 is a common way of presenting the data set with longitudinal pipeline distance acting as the x- axis and o’clock orientation plotted at the y- axis.

0:00

1:002:00

3:004:00

5:006:00

7:008:00

9:0010:00

11:0012:00

13:00

0 10 20 30 40 50 60 70 80 90 100 110 120 130


O'clo

ck o

rien

tati

on

Figure 4.6 Corrosion defects mapping along the circumference (o’clock orientation) length

of pipeline

The above figure could also be used to indentify colonies of defects (given by boxes), from which localised effects might have taken place. Localised effects are likely to occur due to:

i. nature of flow in the pipeline,

ii. existence of a certain structure, like clamp,

iii. deformations caused by excessive forces, like dent or bend, and,

iv. interaction with surrounding environment, like platform which permits com-plicated fluid-structure interactions (typically for external corrosions).

4.3 STATISTICAL INTERPRETATION ON CORROSION DATA

The previous section has described several common ways of presenting the IP data sets, which are fairly easy and straight-forward. This section endeavours the likelihood of ap-plying statistical methods to the data set in order to implicitly extract valuable informa-tion that has been captured by the IP about that corroded pipeline.

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Instead of looking at individual data i.e. corrosion at a particular location in the pipe-line, statistics interpret the data set as a whole (sample) and the results will be in the form of sample distributions. To do this, a sample data needed to be selected first, for example the defect corrosion depth, d measured in % (recall Figure 3.2). For simple sta-tistical presentation, Figure 4.7 was prepared.

Figure 4.7 Simple statistical representation of corrosion data

Two histograms were coupled with the scattered data, each at the x- and y- axis. The distribution of d could be read along the longitudinal pipeline length as given by the x- axis. Indirectly this plot resembles the plot in Figure 4.3. Defects at each kilometre were counted and summed. Peaks in the histogram corresponded to higher frequent of occurrence, thus requiring critical investigation to be carried out at those points.

On the other hand, the histogram placed on the y-axis represented frequency of occur-rence determined by the magnitude of wall losses (measured in %). It is more interesting to analyse corrosion distribution from this point of view, thus the remaining section will be focused on this matter instead of the distribution given by the x-axis earlier. For each defect size (%), the data were counted and summed as well. High peaks were noticed for smaller defect sizes (<20%, for example) while low values would be expected for larger defect sizes (>40%). Recall that this pipeline has been in operation for almost ten years, so the defect distribution could be classified under different categories. Melchers (2008) for example, who studied on long term pitting corrosion, has defined three categories based on exposure time, namely meta-stable, stable and super-stable pits. The meta-stable pits are conventionally taken to be those that are not necessarily initiated imme-diately upon first exposure but will certainly ‘die’ or stop growing in depth eventually. The stable pits on the other hand, continue to increase in depth with time. A new cate-gory of pits, the so called ‘super-stable’ pits was defined to denote the category of stable pits that are initiated immediately upon first exposure and then grow in depth at the fastest possible rate consistent with material and environmental constraints (Melchers, 2008). In a work by Laycock et al. (2003) on the other hand, two populations of pits

74


could be observed with time; one of shallow pits with smaller propagation rates and sec-ond of pits that propagate with fast rates that nevertheless decrease with time.

It is now certain that different defect categories could be captured from a statistical rep-resentation of corrosion data. The categories are able to describe characteristics of cor-rosion development. Statistics could explicitly translate this into two types of distribu-tion namely, initial and extreme value distributions. The former is also known as the parent distribution of the original sample population and the latter is simply a portion taken at the tails of the initial distribution. The upper tail (right tail) refers to maxi-mum extreme values while the low tail (left tail) denotes minimum extreme values. Figure 4.8 below exhibits this illustration.

Mean

Fre

quen

cy o

f dat

a

M e ax. extremvalues

Min. extreme values

Data

Figure 4.8 Illustration of initial and extreme values (minimum and maximum) of a typical normal distribution function of a histogram

In the context of corrosion development, deepest pits which are also the oldest pits will always belong to the right tail of the distribution whereas the ‘new born’ pits will be lo-cated at the left tail. The occurrence of defects will be more concentrated at the central portion of the initial distribution where the mean values lies. Detail explanation on ini-tial and extreme value distributions will be presented in the next section.

4.3.1 Initial Distribution

The goal of this section is to find a good distributional model for corrosion data as cap-tured by the IP tool. Once a good distributional model has been determined, various aspects pertaining to its characteristics can be computed. Data in engineering world, specifically for reliability analysis do not typically follow a normal distribution. Other probability density functions may be more suitable and reasonable instead. A parametric method as described by Ang and Tang (1984) based on a specific distributional model of

75


the data is preferred if the data can be shown to follow a specific distribution. However, it is important to verify that the distributional assumption is indeed valid. If the distri-butional assumption is not justified, then the conclusions drawn from the model may not be valid. Otherwise, non-parametric methods (techniques that do not rely on a specific distribution) are frequently recommended for developing confidence intervals for failure data. One problem with this approach is that sample sizes are often small due to the expense involved in collecting the data, and non-parametric methods do not work well for small sample sizes (Ang and Tang, 1984).

The nature of corrosions in pipeline is random and not straight forward to be described. By default, there should not be any specific distributional models to describe it. The non-parametric method seems to suit corrosion scenarios better provided the corrosions is known to be a major threat to the pipeline. Thus, it can be assumed that the sample size is large enough for the analysis. On the other hand, the development of corrosion with time is something that can be speculated.

For instance, a ‘young’ pipeline (age approximately less than half of the design life) may experience corrosions that are heavily concentrated at the left tail of an initial distribu-tion, in which the percentages of wall losses are small but large in quantities. Figure 4.9 is an example of corrosions computed by an IP tool in year 2007, which represents an 8-year old pipeline in operation. Recall that the corrosion parameter d can either be de-scribed by depth of penetration (mm) or amount of wall loss with respect to pipeline wall thickness (%). The actual corrosion data set was plotted in the form of a histogram first and later several probability density functions were assigned to find the best fit for the data. The lognormal distribution function with parameter estimates μ as 2.01 and σ as 0.74 fitted well to the data sets. It is a heavily right tailed distribution function. More corrosion with magnitude less than 10% could be noticed from the figure, obeying to the hypothesis mentioned earlier. Shallow corrosion pits were just taken place in the pipeline; unstable (Melchers, 2008) and smaller propagation rates (Laycock et al., 2003).

Figure 4.9 An example of probability density function of corrosion depth, d (%) measured with respect to pipeline wall thickness

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4.3.2 Extreme Value Distribution

The extreme values of corrosion pit depth are normally applied to pits corrosion. It is a form of corrosion where the electrochemical attack on a metal surface is localized, with the extremes of corrosion occurring at relatively few sites on a surface (Scarf and Lay-cock, 1996). Extreme pits can often be regarded as the largest of a very large number of pits, even if this fact is not noted and no further measurements made. The focus on deepest pits is natural in two senses: first, it is the deepest pits that lead to failure; and second, measuring deep pits is relatively easy, whereas pit measurement techniques that involve measuring very small pits are laborious and contain ambiguities (McNeil, 1988).

The depth of the deepest pit on a specimen is the upper tail of the distribution of depths of all pits on that specimen (Haynie, 2005). Values in the upper tail which comprises the highest total wall loss represent low structural resistance to the pipeline because they have altered the original design strength of the structure. There has been work on extreme values for pits corrosions even though not all were specifically on pipelines. These works, however, were experimental and could only be conducted for a short period of time. A number of researchers (Aziz, 1956; Elderidge, 1957; Finley, 1967) have used the extreme value methods of Type I (Gumbel) to predict extreme pit depths. The con-ventional approach for predicting pits corrosions is to collect data for pits over a number of nominally identical surfaces, order the data in some way and then to represent it on a Gumbel plot. The trend of the data on the Gumbel plot is taken to permit extrapola-tion, usually for longer exposure periods or greater area of plate (Melchers, 2008). Gen-erally, in pitting corrosion experiments only the maximum pit observed in each block (coupon) is measured and recorded (Rivas et al., 2008). Melchers (2005) proposed that this standard approach to using Gumbel distribution is not valid because the underlying population of pit depths typically used in the analysis is not homogeneous. Melchers (2008) then tried to apply the extreme value Type II (Fréchet) to analysis extremes. He focused on the sulphate reduction bacteria (SRB) attack on corrosions in a predominantly anaerobic condition which seemed to be one of the major sources for long term corrosion failure. He concluded that pitting process changes with exposure time and eventually becomes controlled by the rate of bacterial metabolism. [Corrosions dominated by the SRB, however, are beyond the scope of interest of this thesis because the present work only concentrated with those dominated by the carbon dioxide (CO2).] The Fréchet distribution was found to provide a better estimate for this corrosion scenario compared to Gumbel. The Type III (Weibull) on the other hand, has not attracted much attention compared to the Type I earlier and was only reported by Haynie (2005). Even though the pits were assumed to be independent, even with some dependency (due to the inter-action between growing pits), the Gumbel distribution can be justified to describe the pit depth of the extreme values very well (Rivas et al., 2008).

The above literatures on extreme values were somewhat limited to corrosion pits, whereas corrosions reported from the field comprise random shapes like general (GENE), axial grooving (AXGR), axial slotting (AXSL), circumferential grooving (CIGR), circum-ferential slotting (CISL) and pinhole (PINH); parts of which have been briefly discussed

77


in Section 3.2.2 earlier. Not much attention has specifically been given to corrosions in pipelines. Nevertheless the above hypotheses on corrosion pits were applied to the field data for the sake of getting some insights about the matter. For this, corrosion data in Figure 4.9 was refitted using the Generalized Extreme Values (GEV) distribution (recall Section 2.3.3). Comparisons were made between probability density functions of GEV and lognormal distribution, as shown in Figure 4.10(a). The shape (ξ), scale (σ) and lo-cation (μ) parameters of the GEV distribution were 0.18, 4.61 and 6.57, respectively. By definition, when the shape parameter is larger than zero (ξ >0), the distribution can be grouped into Fréchet models. For a better view on the extreme values, Figure 4.10(b) which corresponds to a probability plot could be used instead. In this case, the extreme values were approximated by corrosion depth, d larger than 30%. It is interesting to ob-serve how the (GEV) Fréchet model provides better fitting for the extreme values com-pared to the lognormal fit. Nevertheless, a significant different could be observed be-tween the data and both fittings when d was larger than 40%.

(a) (b)

Figure 4.10 An example of extreme value distribution of corrosion depth, d (%) measured with respect to pipeline wall thickness

Interpreting the outcomes of this preliminary analysis was not something straightforward when compared with literatures reported earlier. The literatures particularly dealt with corrosion pits, whereas field data are mostly governed by random corrosion shapes. When Melchers (2008) speculated that Fréchet models provide better fitting for corrosion pits dominated by sulphate reduction bacteria (SRB), the present analysis which was en-tirely caused by the carbon dioxide (CO2) seemed to agree to the same rule as well. The aspects of dependency and homogeneity of the corrosion defects developed in pipelines also seemed to contradict with the above literatures. There is then no direct comparison between the extreme values on corrosion pits and those developed in pipelines. The sto-chastic process of corrosions do not seem to fully obey with works carried out in the laboratory, as what have been done in the past literatures. There are still a lot to learn about the extreme values of corrosions in pipelines, a subject of which are recommended to be further explored.

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4.4. Importance of Statistical Analysis on Corrosion Data

4.4 IMPORTANCE OF STATISTICAL ANALYSIS ON CORROSION DATA

Section 4.3 has shown some possible approaches to ‘treat’ corrosion data sets statisti-cally. This section will further elaborate the importance of applying such approaches. Two scenarios will be highlighted to illustrate this concern, namely (i) corrosion as time-variant processes, and (ii) discrepancies in corrosion data.

4.4.1 Corrosion as a Time-Variant Process

Corrosions deteriorate the structural strength and structural integrity of a pipeline. Their growth evolves with time, spreading in size and increasing in quantities. It is a time dependent mechanism and depends on the local environment within or adjacent to the pipeline (Cosham et al., 2007). It is then said that corrosion is a time-variant proc-ess, making the pipeline a time-dependant structure as well as its reliability. Recall that the shape of a corrosion pit is normally addressed using three common length scale pa-rameters, namely the defect depth (d), longitudinal length (l) and circumferential width (w), as illustrated in Figure 3.2. In probabilistic methods, these parameters are inter-preted as a sample and the results are described in the form of probability functions (re-fer Chapter 2). The probability density function (PDF) is the most common probability function applied to corrosion data sets.

A simple philosophy to describe a time-dependant structure can be visualised in Figure 4.11, a work by Estes et al. (2004) who studied time-dependant reliability of steel miter gates and girders on locks and dams. They demonstrated that losses due to corrosions caused the actual (bending) stress to increase with time, resulting in increments in prob-ability of failure as well. Once the stress approaches its designed yield stress, failure be-comes more likely to occur.

Figure 4.11 Decrease in reliability over time as reduced section loss causes an increase in the bending stress on the girders (Adapted from Estes et al., 2004)

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In the case where loadings are non-stationary, Melchers (2005) has made a realization for the loading (given by notation Q) and resistance (denoted by R), as displayed in Figure 4.12. It is a comprehensive diagram describing the interaction between load and resis-tance with time, thus making them stochastic processes Q(t) and R(t). The diagram was coupled with the parameters’ probability density functions. Regardless of the non-stationary loadings, it is interesting to note the decreasing pattern of strength with time, as a result of corrosion attacks. This decreasing pattern promotes higher tendency of upcrossing events to take place, which corresponds to a condition when the load of a structure is greater than resistance.

Figure 4.12 Realization of a continuous random load process Q(t) and the potential exceedence of the deteriorating structural resistance R(t) (Adapted from Melchers, 2005)

Figure 4.13 Experimental works by Rivas et al. (2008) showing the growth of pit depth over time at different exposure times (Adapted from Rivas et al., 2008)

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Rivas et al. (2008) and Valor et al. (2010) focused on experimental investigations on cor-rosion pits growth with time. It can be seen from Figure 4.13 that the probability den-sity function of the pits ‘moves’ to the right over time in the direction of increasing pit depth, while the standard deviation increases, making the distribution wider. This is an indication of the stochastic character of the pitting corrosion process (Rivas et al., 2008). Increment in pit depths is directly proportional to the actions of resulting forces and pressures onto the structure. The works by Rivas et al. (2008) and Valor et al. (2010) could be used to support ideologies of Estes et al. (2004) and Mechers (2005) earlier. These have provided sufficient theories to assess impacts of corrosions to other structures like pipelines. Nevertheless experimental prediction should be coupled with some evi-dence from the field.

Figure 4.14 Historical corrosion development in an offshore pipeline at different times of operation

The time-variant process of corrosion pits as observed in the experiments was validated with data from the field. For this, an offshore pipeline with properties as displayed in Table 4.1 was chosen once again. The pipeline suffers from both internal and external corrosions. Two IP records on corrosion checks taken in 2004 and 2007, which represents a 5- and 8-year old pipeline, respectively, were compared. [For the sake of simplicity, only the length scale depth (d) measured in % (percentage of wall losses with respect to pipeline wall thickness) was chosen for illustration.] The IP surveys revealed an incre-ment in defects from 162 defects to 307 defects within those 3 years of operation. When applying statistical properties to the data, the 2004 IP was best characterized by a Weibull distribution while lognormal distribution for the 2007 IP, as shown in Figure 4.14. From the figure, it can be seen that the probability distribution function for the 2004 IP has shifted to the right over time in the direction of increasing defect depth, while the standard deviation increases. This ‘movement’ might not be clearly visualized

81


from the figure, but the difference in the mean value showed an increment of almost twice as much during the three year period of operation. The standard deviation exhib-ited wider spreads in the 2007 IP, indicating a more disperse data measured from the mean. Corrosions have evolved to depths larger than 20%, approaching nearly 40% of the pipeline wall thickness. Statistical information portrayed in Figure 4.14 implicitly describes corrosion evolvement in the pipeline.

Figure 4.14 has shown the progress of corrosions in time which was in good agreement with theories by Rivas et al. (2008) and Valor et al. (2010) earlier. They have direct im-pacts towards pipeline operating stresses (hoop stress, longitudinal stress etc.). When its durability becomes weaker, the probability of failure and thus reliability will be affected as well. For a pipeline approaching its design life, it is speculated that the probability distribution function of corrosions would continue to change with respect to their statis-tical parameter mean and standard deviation. A young pipeline produces smaller (corro-sion) mean value and more concentrate about its mean (less dispersion) while an older pipeline exhibits larger mean as well as larger dispersion. As a pipeline continue to op-erate, corrosions evolve in magnitude (defect becomes deeper) with new born defects forming concurrently. This results in a larger sample size with more dispersion in the data set.

4.4.2 Discrepancies in Corrosion Data

The importance and significance of the intelligent pigging (IP) tool in pipeline engineer-ing have been fairly addressed. Corrosion maintenance using the IP tool has received numerous attentions in the present days because of enhancement in technology. Outputs from the IP have been very useful to pipeline operators, allowing them to understand, manage, and maintain their pipelines. Despite the tool is prone to measuring inaccura-cies, its outcomes have always been fully trusted and directly applied for further analy-sis.

There has not been much reported work related to probabilistic estimate on measure-ment uncertainties of corrosion inspection tools like the intelligent pigging. Bea et al. (2002) is one of the examples who looked into the discrepancies of an inspection tool ty-pe magnetic flux leakage (MFL) in a gas pipeline. The authors compared data recorded by the MFL with direct measurements on some recovered sections that was in-line in-strumented. The uncertainties associated with the measurement ranged from 35% (for smaller pit depths) to 25% (for larger pit depths). The sensitivity of the tool along the pipeline length was also captured, as shown in Figure 4.15(a) while the bias of the actual and measured corrosion depth is given in Figure 4.15(b). The discrepancies observed were indeed significant.

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(a) (b)

Figure 4.15 Systematic error observed in pipeline inspection tools (Note: 1 mil ≈ 0.025 mm) (Adapted from Bea et al., 2002)

The IP tool is considered as a trusted primary source in providing information about corrosions in a pipeline. The accuracy of the tool, however, remains as an issue among pipeline operators. When dealing with measurement uncertainties, the probabilistic method seems to be one of the best approaches to deal with such problem (Van Gelder, 2000). One of the factors that undermine the advantages of using the IP is its measure-ment tolerances. A particular IP tool provider measures the corrosion defect size at cer-tain given tolerances. Quite often the tolerances vary for corrosion defect depth (d), lon-gitudinal length (l) and circumferential width (w). At 80% probability of detection for example, Table 4.2 illustrates various tolerances for different corrosion types. The table also provides comparison between two different tool providers, namely tool provider A and B. The tolerances given by both providers are significant, for instance the general corrosion has defect depth (d) of ±0.23t for provider A while ±0.10t for tool provider B.

Now, assume tool provider A carries out the corrosion maintenance work for a particular pipeline in year x while tool provider B for year x+Δx. It can be said that it is almost impossible to directly compare the corrosion development of that pipeline within those years of operation. Unfortunately, it is somehow common for any IP tool providers not to quantitatively incorporate these tolerances when reporting the graphical defect pres-entations (as given in Section 4.2 earlier). The tolerances are normally addressed qualita-tively as one of the IP tool design parameters only.

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Table 4.2 Comparisons in IP tool tolerances at 80% probability of detection of two tool providers

Defect length scale parameter

Corrosion type Tool provider A Tool provider B

General metal loss ±0.23t ±0.10t

Pitting ±0.24t ±0.20t

Axial grooving ±0.12t ±0.15t

Depth, d

Circumferential ±0.23t ±0.15t

General metal loss ±8.8 mm ±20 mm

Pitting ±22.4 mm ±15 mm

Axial grooving ±9.6 mm ±25 mm

Longitudinal length, l

Circumferential ±12.8 mm ±20 mm

General metal loss ±38.4 mm ±20 mm

Pitting ±32 mm ±15 mm

Axial grooving ±33.6 mm ±25 mm

Circumferential width, w

Circumferential ±40 mm ±20 mm

Note: t is wall thickness of the pipe.

Recall that maintenance using the IP tool is only carried out depending on the necessity, thus limiting the work to be carried out at only certain intervals during pipeline opera-tion. Problem arises when two (or more) corrosion measured data sets need to be com-pared in order to develop a historical trend of corrosion development in a particular pipeline. This can be avoided if using the same tool for the whole life operation of the pipeline, thus the uncertainties are said to be uniform in time.

However, this is not always the case due to the following reasons:

i. pipeline inspection is subjected to demand and necessity,

ii. the choice of the tool provider (contractor) to carry out inspection work depends on the availability, experiences and price offered, and

iii. improvement in technology has attracted new designs for IP.

4.4.3 Statistical Treatment to Corrosion Data

The earlier discussions have acknowledged that the accuracy of an intelligent pigging (IP) tool is important and should not be taken for granted. One of the attempts made in this thesis was to judge the likelihood of tackling the problem statistically. The idea was to propose an approach that is able to integrate tolerance or measuring uncertain-ties into the primary (original) data sets reported from the tool.

84


This will somehow reduce the difficulties to correlate magnitude of corrosion develop-ment at different IP years and eventually provide better information on the corrosion historical trends of a particular pipeline.

Assume that the primary measured data sets of an IP tool is the corrosion defect depth parameter (d) measured in % (percentage of wall losses with respect to pipeline wall thickness). From this point onwards, d is described as data sets without measuring un-certainties (error). For the sake of simplicity, also assume that the random variables of sample d follow a lognormal distribution,

~ ( ,d dd LN m s )

)s

i

i

(4.1)

with μ and σ as mean and standard deviation, respectively. The lognormal distribution was simply chosen to show that corrosion data should be represented by positive real numbers, where distributions like lognormal, Weibull,..etc. can fit so well to describe this behaviour.

Let’s furthermore assume the measuring uncertainties provided by the tool as a source of error (ε) or noise to the data. A normal distribution with μ of 0 and σ equal to the tol-erance value reported in Table 4.2 (i.e. σε = 0.23, 0.18,….) can be simulated,

~ (0,N ee (4.2)

It is proposed that the ‘new’ simulated corrosion data sets with error (d’) to be formu-lated by two means, namely additive or multiplicative models. The algorithms for the additive and multiplicative models between the measured and noise data sets are given by equation 4.3 and 4.4, respectively,

' +i id d e= (4.3)

' xi id d e= (4.4)

for i equal to 1, 2,…, n. The formulation of these models is based on pair wise-interactions and the procedures can be simulated using the Monte Carlo simulation as described in Section 2.4.3 earlier.

To illustrate equations 4.3 and 4.4, measured data sets without error (d) for IP year 2007 of pipeline candidate presented in Figure 4.14 was applied once again. Suppose the IP tool tolerance was set to be 0.23t. The corresponding simulated corrosion data sets with error (d’) will be computed based on the two proposed models.

It is noteworthy to understand that when introducing some Gaussian (normal) er-ror/noise to a distribution and given that the error is centered, the resulting distribution shall have the same mean as the original one and only the standard deviation may change (Anonymous, 2011).

85


Hypothetically, it is expected that the mean value of d’ not to deviate much from d, but the standard deviation of d’ should exhibit larger dispersion than d. A larger standard deviation indicates that the data points are further from the mean value. The inclusion of noise makes the simulated data more disperse and scatter compared to the measured data. The performances of equations 4.3 and 4.4 were literally checked in compliance with this hypothesis as well.

With errors generated from N(0,0.23), results for d’ computed using the additive model (equation 4.3) are given in Figure 4.16. Descriptive statistics pertaining to this formula-tion are also provided in Table 4.3. The mean value of d’ (=9.86) was found to be in good agreement with the d (=9.82) data sets, while the standard deviation of the former exhibits slightly larger spread compared to the latter.

The multiplicative model (equation 4.4), on the other hand, revealed certain limitation when formulated using the same error variables of N(0,0.23). Multiplying sets of random variables with this error function would lead to impractical answers. As a suggestion to avoid this limitation, the generation of random variables for the errors was proposed to be modified to a lognormal distribution function characterized by LN(0,0.23). Note that the error distribution of LN(0,0.23) could be literally presented with another normal dis-tribution of N(1,0.23). There seemed to be good improvement using this revision, as seen in Figure 4.17 and Table 4.4; with mean value of d’ so close to d and expected dis-persion in the former compared to the latter.

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+

=

Figure 4.16 Corrosion data sets computed through the additive model with error, ε~N(0,0.23)

Table 4.3 Descriptive statistics of the measured and simulated corrosion data sets computed through the additive model with error, ε~N(0,0.23)

Measured data, d(without error)

Simulated data, d’ (with error)

Mean (μ) 9.82 9.86

Standard deviation (σ) 8.27 8.37

Coefficient of variation (C.O.V) 0.84 0.85

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x

=

Figure 4.17 Corrosion data sets computed through the multiplicative model with error, ε~N(1,0.23)

Table 4.4 Descriptive statistics of the measured and simulated corrosion data sets computed through the multiplicative model with error, ε~N(1,0.23)

Measured data, d

(without error) Simulated data, d’

(with error)

Mean (μ) 9.82 9.84

Standard deviation (σ) 8.27 9.39

Coefficient of variation (C.O.V) 0.84 0.95

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To summarize, this section looks into the response of incorporating measuring errors of an intelligent pigging (IP) tool through the use of additive and multiplicative models. The proposed approach, either the additive or multiplicative model, allows the corrosion data not to deviate much from the measured mean value, but to make it more disperse and scatter. This has been proven from the outcomes shown earlier. A wider range of up to 15% could be expected when using the two proposed models for the selected pipe-line.

Table 4.5 Comparison in the performance of additive and multiplicative models, as measured using reliability index (β) parameter

Simulated Corrosion Data (with tolerances)

Operating Pres-sure

(MPa)

Measured Data (without toler-

ances) Additive Model

Multiplicative Model

12 5.38 5.39 5.34 14 4.24 4.25 4.22 16 3.23 3.24 3.23 18 3.24 2.35 2.36 20 1.55 1.55 1.58 22 0.84 0.84 0.89 24 0.20 0.20 0.28

0

1

2

3

4

5

6

7

10 12 14 16 18 20 22 24

Operating Pressure, P o (MPa)

Rel

iabi

lity

Inde

x

Data without error

Data with error (additive model)Data with error (multiplicative model)

Figure 4.18 Graphical comparison in the performance of additive and multiplicative models, as measured using reliability index (β) parameter

89


The reliability index parameter given by equation (2.35) is used to illustrate the influence of the corrosion data sets with the inclusion of tool tolerances. [Detailed descriptions about reliability index will be given in Section 5.3.4 later]. The response of new (simu-lated) corrosion data sets towards the reliability index are displayed in Table 4.5, and graphically shown in Figure 4.18. Apparently, results showed no significance deviation between the simulated and measured data sets. Regardless of this insignificance, the idea of applying either the additive or multiplicative model when incorporating uncer-tainties of an inspection tool should be acknowledged. It is not right to simply arrive to a conclusion that the measuring errors of an IP tool have no direct impact towards the reliability of the pipeline. Note that the analyses presented herein are limited to the choice of tolerance value (%) of the IP tool and corrosion data itself, for which other sce-narios might experience different outcomes. The proposed framework may be applied to other types of measurement tools which are exposed to uncertainties and require proper reliability computations.

4.5 CONCLUSIONS

The purpose of this chapter was to acquaint readers with corrosion data sets as reported by the intelligent pigging (IP) inspection tool. Several typical graphical presentations of the data set which are normally prepared by the tool operators were first presented. The data were extracted and plotted along the longitudinal distance of the pipeline as well as its cross section. Severe defects could be easily traced this way because most of the time pipeline operators are keen in dealing with severe defects rather than ‘new born’ de-fects.

The corrosion data were then treated as a sample of random variables. The characteris-tics of all defects formed in the whole pipeline length could be presented as the initial distribution function. This provides some ideas on the behaviour of their growth and spread at that particular time of inspection. Obeying to the fact that defects with higher wall loss have always become the major threat, they could be further analysed us-ing the extreme value distribution functions.

It may not be of great interest among pipeline operators to analyse the corrosion meas-ured data set statistically. On the other hand, it is something that should not be taken for granted after knowing that pipeline is actually a time-dependant structure and corro-sion is a time-variant process. Neglecting the two may underestimate the reliability of the pipeline especially when computing the historical trends of corrosion development in that pipeline.

Measuring error or uncertainties in the IP tool was highlighted at the end of the chapter. In reality the IP tool was designed to allow certain tolerances. This is practically ac-ceptable because no tools can ever provide the most accurate readings.

90

4.5. Conclusions

91

However, this has become a drawback when different IP tools were used for a particular pipeline during its lifetime. Since the typical graphical presentations of the corrosion measured data sets do not quantitatively incorporate these tolerances, comparing two IP events would not be something straight-forward. Owing to this limitation, the statistical approaches seemed to be more reasonable to be applied instead. The tolerances can be described as a source of error or noise to the random variable samples. Representing the defects for this purpose could be done through simulations. The proposed approach can be used as an aid in providing better insights on corrosion time-variant processes of a pipeline at different years.

Chapter 5

RELIABILITY ASSESSMENT ON CORROSIONS

5.1 INTRODUCTION

In this chapter, the first attempt in checking the suitability of using probabilistic ap-proaches in assessing reliability of corroded offshore pipelines is presented. The attempt was made based on the present assessment methods that are deterministic oriented. Several unfavourable rules about one of the corrosion parameters were reconsidered and given special attention in this section. This has allowed the shape of the defect to be represented in a dimensionless way. The goodness of the probabilistic model was judged by comparing it with other models.

5.2 OVERVIEW ON LIMIT STATE FUNCTION MODELS

In the present days, the probabilistic approaches become important when assessing the reliability of pipeline subjected to corrosions. One of the common ways used by past re-searchers was to integrate the existing failure pressure (PF) models with the load pa-rameter into the limit state function (LSF) model. Theories on LSF have been intro-duced in Section 2.4.2 earlier. The past LSF models were mostly modified from the PF models originated from the NG-18 criterion, as described in Section 3.4. In these mod-els, the strength/resistance (R) term of equation 2.31 has been aggressively studied by Ahammed and Melchers (1996), Pandey (1998), Ahammed (1998), De Leon and Macías (2005) and Teixeira et al. (2008), for instance. All models, however, assumed the same parameter for the load (S) term, represented by the operational loading exerted by the transported hydrocarbon in the pipeline.

This section onwards presents past LSF models used in the assessment of corrosions in offshore pipelines. The assessment is made to check the remaining strength of the struc-

5 Reliability Assessment on Corrosions

ture, for which its response towards operational loads can then be predicted. One of the earlier attempts to introduce uncertainties into the original NG-18 criterion was done by Ahammed and Melchers (1996). A multiplying factor, mf was introduced into the equa-tion which is usually taken as between 1.1010 and 1.1510.

1 /21 /( )f o

t d tZ m SMYS P

D d tM

−= −

− (5.1)

Pandey (1998) has applied flow stress, σflow coefficient of 1.15, thus resulting below equa-tion,

1 /2.31 /( ) o

t d tZ SMYS P

D d tM

−= −

− (5.2)

Ahammed (1998) and De Leon and Macías (2005) applied a different σflow into their equa-tion, given by,

0 0

0 0

1 [ ( )] /2( 68.95)1 [ ( )] /

do

d

d R T T ttZ SMYS P

D d R T T tM

− + −= + − + −

− (5.3)

with d=do+Rd(T-To) and l=lo+RL(T-To)

Teixeira et al. (2008) developed their model based on the results of a series small scale experiments and 3D non-linear finite element analysis of the burst pressure of intact and corroded pipelines. Their model parameters were simplified using the Buckingham-π theorem, following the approach applied earlier by Netto et al. (2005) for the design of pipeline buckle arrestors. The multivariate regression analysis was then used to create equation below,

1.6 0.41.1* *2 [1 0.9435( / ) ( / ) ] o

SMYS tZ d t l D P

D = −

− (5.4)

with SMYS = Minimum Specified Yield Stress, d = corrosion defect depth, l = corrosion defect longitudinal length, t = pipe wall thickness, D = pipe outer diameter,

M= Folias/bulging factor (as in Modified ASME B31G), Po= applied/operating pressure, do= defect depth measured at time To, lo= defect longitudinal length measured at time To, T= any future time, To= time of last inspection, Rd= radial corrosion rate (=Δd/ΔT), and RL= longitudinal corrosion rate (=Δl/ΔT).

There are other works involving LSF development as reported by Ahammed and Melchers (1994, 1995, 1997), Guan and Melchers (1999), Caleyo et al. (2002), Lee et al. (2003, 2006), Lee et al. (2005), Santosh et al. (2006), Khelif et al. (2007) and many more.

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5.3. Dimensionless Limit State Function Model

Since most of these works were either for onshore or buried pipelines, it is not the inten-tion of the present work to further deliberate about them.

5.3 DIMENSIONLESS LIMIT STATE FUNCTION MODEL

5.3.1 Background of Model

Motivation

This thesis proposes another LSF model that can be used to determine the reliability of offshore corroded pipelines subjected to internal pressure. The so called dimensionless LSF model was mainly developed using probabilistic approaches. The proposed model, however, has the advantage of presenting a better estimate of corrosion shapes as com-pared to other reported models. This ideology was supported to the fact that the IP tool is capable to report not only the defect depth (d) and longitudinal length (l) pa-rameters, but also the circumferential width (w). The aim was to utilize information provided by the IP into a single equation as much as possible. Unlike in the present days, the current assessment practices use a single simple corrosion geometry and the corrosion circumferential width (w) is not considered (Fu and Kirkwood, 1995). The longitudinal extent of a corroded area is the most important length parameter for the burst strength under internal pressure loading (Cosham et al., 2007). Defects in this orientation have been reported to be the most severe since it alters the hoop stress distribution and pro-motes bulging.

Concurrently, Chouchaoui and Pick (1994), Fu and Kirkwood (1995) and Batte et al. (1997) have shown that the influence of corrosion circumferential width (w) to failures was not that significant. Circumferential defect acting alone may not harm much of the pipeline remaining strength. However, defects in the circumferential direction would be-come more important when poor longitudinal stresses resulted from pipe bending pres-ence (Chouchaoui and Pick, 1994 and Cosham et al., 2007). The circumferential extent of damage is only become priority when depth of the corrosion is greater than 50% of the original pipe wall thickness and the circumferential extent is greater than 1/12 (8.33%) of the circumference (Escoe, 2006).

The importance of w may be partially explained when looking at the way a colony of de-fects interact. Fitness-for-Service (FFS) approach, for instance, provides rules to de-scribe interaction among corrosion defects. The FFS is basically conducted by first iden-tifying and assessing single critical defects and later doing the same to the interacting de-fects. One commonly used rule in this approach is that adjacent defects are considered to interact if the spacing (i.e. the longitudinal or circumferential direction) between the defects is less than the respective dimension (i.e. length or width) of the smaller defect (Hopkins, 1992). The composite depth of that colony of defects is described by the

95


maximum depth while the longitudinal length and circumferential width is given by the dimensions of an enveloping rectangle.

The interaction among defects is still not well defined. When it is conservative to as-sume that all of a cluster of adjacent defects interact (Cosham et al., 2007), BjØrnØy and Marley (2001) concluded that there are unlimited combinations of interaction of defects. Li et al. (2009) has studied the effect of correlation of corrosion defects and it was re-vealed that the assumption of independent corrosions defects lead to conservative results. The BjØrnØy and Marley (2001) suggested the assessment should be based upon sound engineering judgement because the interaction is very complex and require more precise and accurate interaction rules. The above hypothesis has paved the basic ideology of the present work which will be described in the next paragraph.

Importance of Model

A corrosion defect that forms in a pipeline will spread and develop in size with time. Its growth is described by the d, l and w dimensions. It is believed the spread in those di-mensions might follow certain relationships. For example, when d grows deeper, the length of l and w will also expand to certain extend, obeying to the correlations that ex-ist among them. Each defect interacts with each other in certain correlations as well, so no defects should be left out. Probabilistic approaches are the best way to investigate this phenomenon, not experimental or numerical works. The experimental and numeri-cal were normally carried out for certain sizes of defects but the probabilistic method in this study is taking into account all defects that form in the pipeline.

Case Study

The dimensionless LSF model deals with internal corrosion defects in offshore pipelines only, where IP inspection is possible to carry out. The equation is governed by the cor-rosion defect shapes, design parameters as well as burst and pressure operating pressures. A similar pipeline candidate to that in Chapter 4 was applied once again. However, fo-cused was only given to internal corrosions only. 554 internal corrosion defects of various types were reported by the IP during the maintenance work. Descriptive statistics of the corrosion data is as shown in Table 5.1. The wall losses were calculated up to 30% of the actual wall thickness.

Table 5.1 Descriptive statistics of corrosion defects

Variables Symbol Description Unit

Distribution Mean Standard deviation

d Depth mm Weibull 1.90 1.16 l Longitudinal length mm Exponential 32.64 23.52 w Circumferential

width mm Gamma 36.76 33.17

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5.3.2 Development of Model

This section describes the methodologies used to develop the present dimensionless LSF model with parts of the discussions can be referred to Mustaffa et al. (2009). The corro-sion measured data set was first tested using the regression analysis methods. After un-derstanding the correlation in the data, important data were selected and included in the LSF equation using the Buckingham-π theorem. The uncertainties in the model were then checked using the Bootstrap method. Finally, the equation was carried out for sen-sitivity analysis check.

Bivariate Regression Analysis

Detailed explanation about regression analysis has been presented in Section 2.3 earlier. The method allows us to understand which among the independent variables are related to the dependant variable, and to explore the forms of these relationships. In this con-text, the corrosion defect parameters d, l and w were the variables of interest. Their de-pendency and relationship between each other were first investigated using the simplest model, known as the bivariate regression analysis. The bivariate regression analysis looks at two variables at a time, see if there is a significant relationship between them, and estimate the exact magnitude of this relationship. One variable may cause the other one to behave in a certain way and thus necessary to estimate this causation so that we are able to predict one from the other.

Figure 5.1 presents an overview on how the analysis would be carried out. The depend-ency between variable d and l is indirectly supported by detail explanation in Section 5.2.1 earlier. Since the variable l is more significant than w, the next dependency check will be coupling them together. Concurrently the analysis between d and w can be car-ried out. This completes the bivariate regression analysis. Judgement whether to pro-ceed to multivariate regression analysis depends upon the results of the bivariate regres-sion analysis, as given by the broken red line in the figure.

w

Negatively correlated Proven by literatures

l

Positively correlated

d

Figure 5.1 Proposed hypothesis for the development of the model

The first step was to identify the dependency between variables l and w using the bivari-ate regression using IP data taken from pipeline type API 5LX-65 mentioned earlier. Figure 5.2(a) below proves a linear relationship between them. Both variables were posi-tively correlated with R2 value of 0.39. This value may seem low even though good cor-

97


relation could be noticed for smaller defects (l and w < 100 mm). Since the measured data were analysed in its original condition without being filtered for any outliers, the presence of larger defects (l and w > 100 mm) has resulted in the low R2 value. Regard-less of this, the analysis has agreed to the fact that the l and w did reveal strong correla-tion between each other, which means the defect growth in its longitudinal orientation did affect the growth in the circumferential orientation (Mustaffa et al., 2009).

The dependency between variable d and w was next to be checked. Figure 5.2(b) pre-sents the correlation of both variables. The results showed good correlation with nega-tively correlated. The R2 value for this correlation was measured to be 0.25. Indeed this value is small and less preferable. However, it should be noted that this behaviour was once again caused by the occurrence of several larger defects (w>100 mm) among smaller defects. The reasoning provided in earlier paragraph thus applies to this scenario as well.

(a) Defect longitudinal length, l vs. defect circumferential width, w

(b) Defect depth d vs. defect circumferential width, w

Figure 5.2 Bivariate regressions for pipeline API 5LX-65

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It is obvious that scatter trends did present in the above plots. From Figure 5.2(b) for example, certain groups of defect (say w>150 mm, or d>4 mm) seemed to exhibit certain trends in the plot as compared to the concentrated population at smaller defects. This behaviour was mostly governed by the size of the defects. It is important to highlight here that the dependency check (regression analysis) in this chapter does not concern about classifying defects according to specific forms like corrosion general (uniform), pit-ting, crevice, galvanic, etc., but to simply assume all defects as a group of random vari-ables. The intention was to allow each defect parameter (say d) to ‘interact’ with its re-spective length scale parameters (say l and w) probabilistically. There are still a lot to understand about the degree of dependency in these variables regardless of their sizes. When two parameters have proven to be strongly correlated, the next step was to judge the level of dependency when all variables were tested together. This could be carried out using the multivariate regression analysis which will be discussed in the next section.

Multivariate Regression Analysis

The aim of the multivariate regression analysis was to examine the degree of dependency for all defect variables d, l and w. Several regression models were tested which involved linear and nonlinear equations. The corrosion defect depth, d was selected as the inde-pendent (criterion) variable because its geometry is proportional to the pipeline wall thickness. Vertical penetration caused by d through the pipeline wall has greater poten-tial for leakage (failure) as compared to the spread of defects in either circumferential or longitudinal direction. Thus the variables l and w were classified as the dependant (pre-dictor) variables.

The best model to describe the dependency for the three corrosion defect variables was the nonlinear model as given by equation (5.5),

0.4

1.33.3

ld

w= (unit mm) (5.5)

In order to check the goodness of this equation, the correlation between dpredicted and dob-

served was carried out using the least-squares method (defined in Section 2.3.3) with the corresponding R2 value of 0.75, as shown by Figure 5.3(a). This value is statistically very good and acceptable, which reveals that most of the data were correlated between each other. Analysis on residuals (defined in Section 2.3.4) should also be conducted to fur-ther validate the goodness of the selected model. The residuals are examined with the aid of scatterplot of histogram of residuals and residuals against individual predictors (de-fined in Section 2.3.4), as shown in Figure 5.3(b) and Figure 5.3(c), respectively. The residuals were uncorrelated, with no noticeable pattern of dependency as observed in Figure 5.3(c). This is favourable which shows the absence of bias in the data sets. The residuals plot as seen from the histogram exhibited a normal distribution function, with mean value of 0, interpreting that the predicted samples closely resembled to those of the observed samples.

99


(a)

(b) (c)

Figure 5.3 Results obtained from multivariate regression analysis for pipeline API 5LX-65 containing internal defects (a) Comparison between predicted and observed data (b) Histo-

gram of the standardised residual (c) Residuals scatterplot

Apparently, the multivariate regression analysis for the above pipeline has granted an easy and reliable way to combine d, l and w into one equation. To support this hypothe-sis, another corrosion scenario was tested. Similar pipeline with 307 external corrosion defects were analysed and the results, as shown in Figure 5.4, were compared with Figure 5.3 obtained earlier. Several regression models were tested and the best fit was found to be the nonlinear model as well, given in equation (5.6),

0.6

0.81.9

ld

w= (unit mm) (5.6)

The R2 value between the dpredicted and dobserved was 0.79, which was also statistically very good and acceptable. This outcome has affirmed results established in the earlier inter-nal corrosion scenario. The two findings from multivariate regression analysis have ac-knowledged the fact that w is highly dependant upon d and l.

100


(a)

(b) (c)

Figure 5.4 Results obtained from multivariate regression analysis for pipeline API 5LX-65 containing external defects (a) Comparison between predicted and observed data (b) Histo-

gram of the standardised residual (c) Residuals scatterplot

Buckingham-π Theorem

The Buckingham-π theorem is a key theorem in the dimensional analysis techniques. The theorem loosely states that if we have a physically meaningful equation involving a certain number, n, of physical variables, and these variables are expressible in terms of k- independent fundamental physical quantities, then the original expression is equivalent to an equation involving a set of p = n − k dimensionless variables constructed from the original variables: it is a scheme for dimensionless (Chakrabarti, 1994). This provides a method for computing sets of dimensionless parameters from the given variables, even if the form of the equation is still unknown. The method also guides us to select the most significant parameters describing the characteristics of the scenario under investigation while omitting the less ones.

101


Interested readers are recommended to refer to book chapter on Dimensional Analysis from any Hydraulics or Fluid Mechanics books for further discussion about this method. For offshore structures in particular, Chakrabarti (1994) is one of the good references on this matter. Discussion herein will first be given on how to create the strength (R) term of the dimensionless LSF model. For the assessment of a corroded pipeline, the impor-tant parameters required to compute its remaining reliability are:

1. corrosion geometry

2. operating pressure

3. burst pressure

Also needed in the assessment are the design parameters:

4. pipeline geometry (diameter and wall thickness)

5. strength

From the above list, seven parameters has been selected in this study, namely *burst pressure (Pb), specified minimum tensile strength (SMTS), pipeline wall thickness (t), di-ameter (D), corrosion depth (d), corrosion longitudinal length (l) and corrosion circum-ferential width (w). Note that some of the parameters are similar to those developed in Section 5.2. It is assumed that the failure in the proposed model is governed by plastic collapse (plastic flow), for which the flow stress is controlled by the SMTS parameter.

*Burst Test

It is important to highlight here that the burst pressure (Pb) data are not possible to be measured from the field. The Pb represents the strength of a corroded pipe at which it starts to burst (fail). A burst test ex-periment is normally conducted in the laboratory to generate Pb data sets. The tests can be planned at a small or full scale, which may also involve either real or artificial corrosion defects. The artificial defects are machined pits, grooves and patches, blunt, flat-bottomed defects with a uniform profile. Most tests were predominantly longitudinal orientated and subjected to internal pressure; and only small number of tests con-ducted for axial and/or bending loads under internal pressure, and on circumferential and helical defects (Cosham et al. 2007).

Cosham et al. (2007) has prepared a good summary on available full scale burst tests on real and artificial corrosion defects. The artificial de-fects are machined pits, grooves and patches, blunt, flat-bottomed defects with a uniform profile. Out of the 343 burst tests reported, only 157 tests are considered reliable for the case of longitudinally orientated corrosion subject to internal pressure. The Det Norske Veritas (DNV) Technical Report (1995) has also compiled burst tests conducted at four institu-tions, namely American Gas Association (AGA), NOVA, British Gas and University of Waterloo.

102


Out of the 151 data sets reported, only 31 were considered suitable to represent the present corrosion characteristics in this thesis (refer Ap-pendix I).

In the recent development, Pb data sets can be produced numerically with the aid of the finite element method (FEM). This new approach is indeed favourable when the burst test experiments are unlikely to be conducted.

Next, the selected physical variables, n were counted as seven parameters and the Buck-ingham-π theorem addressed their dependency as,

),,,,,,(1 wldtDPSMTSf b=π (5.7)

Note that by default, the dimensional analysis technique describes the ‘independent fundamental physical quantities’, k as three, namely mass, length and time (Chakrabarti, 1994). Therefore, the dimensionless variables, p was then computed by the n−k expres-sion which resulted in four parameters (7-3 = 4). Equation (5.7) could then be refined by making it dimensionless according to their units, as given below,

=

w

l

t

d

D

t

SMTS

Pf b ,,,2π (5.8)

The dependency between the four dimensionless parameters in Equation (5.8) was later formulated using the nonlinear multivariate regression analysis and a nonlinear model was chosen to best describe the parameters, as given in equation (5.9). This is the equa-tion representing the remaining strength (R) of the corroded pipeline. The R is one im-portant term required for the LSF equation.

0.8442 0.0545 0.0104bP t d l

SMTS D t w

− − =

(5.9)

Reliability Computation

Section 2.4.1 earlier has presented the common form of a LSF equation, Z. To complete the Z equation, the load (S) term needed to be included as well. Since the R term in equation 5.9 was made dimensionless, the S term was also made dimensionless by divid-ing the maximum allowable operating pressure (Po) with the SMTS.

0.8442 0.0545 0.0104oPt d l

ZD t w SM

− − = TS

− (5.10)

This is the finalized dimensionless LSF equation (model) proposed to be used in the reli-ability assessment of corrosions in offshore pipelines. By referring to equation (2.24), the

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probability of failure, Pf of the above equation could be computed using the Monte Carlo simulation (MCS) method.

Physical Meaning

The physical meaning of the proposed model in equation 5.10 closely conformed to the mechanics of corroded pipelines subjected to internal pressure. For this, equation (3.10) is referred to once again, and is given below:

, ,i h

tp f A

Dsæ ö÷ç= ÷ç ÷è ø

The equation explains that the internal pressure (pi) of a corroded pipeline can with-stand is a function of a wall thickness-to-diameter (t/D) ratio, pipeline strength (or stress, σh) and the projected corrosion area (A). Recall that the proposed model in this chapter was intentionally developed to provide a better description about corrosion shape. This has direct implication towards the parameter A. Arguments about corro-sion shape have been briefly presented in the first part of Section 5.3.1, part of which can be proven by the designated parameters shown in Table 3.1. Corroded area has been ar-gued from as simple shape as a rectangular (dl) to parabolic (2/3 dl) and average of rec-tangular and parabolic (0.85 dl) shapes. Concerns on this aspect will remain as one big issue among pipeline operators and researchers even until today.

The corrosion shape which is governed by the parameter A was exploited in a different way in this chapter. It was characterized by means of dimensionless corrosion parame-ters. The proposed dimensionless LSF model was designed to provide better visual views of the corrosion shape. The expression wall thickness-to-diameter (t/D) in equation 5.10 gives an estimate on the design parameters of the pipeline (Figure 5.5). The defect depth-to-wall thickness (d/t) ratio represents the amount of wall losses as measured from the pipeline cross section view (Figure 5.5). The defect longitudinal length-to-circumferential width (l/w) ratio allows description on the size or spread of the defect, as seen from a plan view (Figure 5.6). A plan view resembles a pipeline that is cut open. Thus this equation is comprehensive enough to illustrate the physical layout of a cor-roded pipeline.

104


d

Figure 5.5 Pipeline design parameters and corrosion length scales, as seen from the longitu-dinal view of pipeline (not to scale)

(a) (b)

Figure 5.6 Pipeline design parameters and corrosion length scales (a) Cross section view of pipeline, and (b) Part of pipeline cut-open, showing defect as seen from plan view (not to

scale)

Parameter Uncertainty of Regression Models

Recall that the dimensionless limit state function (LSF) model was created based on the multivariate regression analysis method. The method is exposed to parameter uncer-tainty when limited numbers of data are taken into account. The fewer data applied in the analysis, the larger the parameter uncertainty. A parameter of a distribution func-tion is estimated from the data and thus can be considered a random variable (Van Gelder, 2000). Parameter uncertainty can then be determined by the probability distri-bution function (PDF) of the parameter. Data about a random variable can be updated with the help of expert judgement (Van Gelder, 2000). Quite often the bootstrap method is used to judge parameter’s uncertainty.

t

D

l

w d

l

w

105


Owing to this, this section introduces the Bootstrap method as a tool to treat parame-ters (α1, α 2, α 3) uncertainty of the dimensionless LSF model rewritten below,

1 2 3

oPt d lZ

D t w SMT

α α α = S

− (5.11)

Efron (1979) is one of the earlier discussions on the bootstrap method, followed by sev-eral more work in the coming years and recently (Efron and Tibshirani, 1994) has been widely referred to. To illustrate the method, a simple bootstrap algorithm reported by Van Gelder (2000) is presented below:

1. Select B independent bootstrap samples (x1*, x2*,..., xB*), each consisting of n data values drawn with replacement from x.

2. Evaluate the bootstrap corresponding to each bootstrap sample [θ*(b)=f(xb*) for b=1,2,...,B].

3. Determine the parameter uncertainty by the empirical distribution function of [θ*].

It is actually a procedure that involves choosing random samples with replacement from a data set and analyzing each sample the same way. The bootstrapped samples of the observed data are normally generated with the aid of MATLAB programming language for (normally) 1000 random values. It is assumed that if a set of random samples could be repeated many times on data that come from the same source, the maximum likeli-hood estimates of the parameters would be approximately follow a normal distribution.

The results of the bootstrap estimates for parameter uncertainty checks of α1, α2 and α3 are presented in Figure 5.7 to Figure 5.9. Two types of plots were prepared, namely his-togram and normal quantile-comparison (Q-Q) plots. It may be difficult to state the de-gree of dispersion from these plots, so the measure of dispersion relative to the central value would be more appropriate instead. Dispersions which can be either large or small is more meaningful if measured relative to the central value (Ang and Tang, 2007). For this purpose, coefficient of variation (C.O.V) should be used particularly for positive mean values. It is a nondimensional measure of dispersion or variability by dividing the standard deviation to the mean value.

By referring to Figure 5.7, parameter α1 could be very well approximated by normal dis-tribution with mean value of 0.8442 and C.O.V of less that 1%. This means that the degree of dispersion is so small, which is preferable. Thus the α1 value of the dimen-sionless LSF model is acceptable. Histograms for α2 and α3 were normally distributed as well but it is not meaningful to describe their dispersion using the C.O.V because of their negative means value. In a real world application, negative C.O.V is less favour-able. Nevertheless, variability in α2 and α3 could be represented by the (i) Q-Q plot and (ii) confidence intervals of the distribution. From the Q-Q plot of Figure 5.8 and Figure 5.9, it can be seen that the bootstrap estimates appeared closely to normality (described by the broken line). This is indeed acceptable.

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The 95% confidence intervals for α2 was [-0.0705, -0.0365] and α3 was [-0.0174, -0.0040], respectively. Recall that the mean value for α2 calculated using the least-square method was -0.0545 while α3 was -0.0104. Therefore confidence intervals of the bootstrap esti-mates were in the range of the mean values given by the least-square method.

In summary, the parameter’s uncertainties for α1, α 2, α 3 have been tested using the boot-strap method. The analyses were carried out to see whether the bootstrapped samples might follow a normal distribution. Other than the histogram, the Q-Q plot or confi-dence interval could be used to measure the degree of dispersion relative to the central value (mean). Results from the bootstrap method were compared to those from the least-square method. In this analysis, both methods agreed to each other very well. Therefore, the coefficients of the dimensionless LSF model were valid thus making the equation to be acceptable as well.

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Figure 5.7 Histogram and normal quantile-comparison plots for bootstrap replications of α1



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Sensitivity Analysis

Sensitivity analysis is the study of how the variation (uncertainty) in the output of a mathematical model can be apportioned, qualitatively or quantitatively, to different sources of variation in the input of the model (Saltelli et al., 2008). Figure 5.10 shows the sensitivities of the failure criterion of equation (5.10), with respect to changes in the variables. A positive sensitivity indicates that an increase in a variable results in an in-crease in the failure criterion and positively contributes to reliability.

w , 0.2

l , -0.2

P o , -6.2

d , -0.8

D , -12.6

t , 14.6

SMTS , 5.7

Figure 5.10 Degree of sensitivity of dimensionless LSF variables

It can be seen that the diameter (D) and wall thickness (t) were the most important variables in the reliability estimates of corroded pipelines. The t variable in particular, needs to be strong and thick enough to avoid leakage caused by corrosions, followed by the strength of the pipeline material i.e. SMTS. The operating pressure (Po) which showed negative sensitivity implied that the structure would be prone to failure when higher loads exerted to it.

5.3.3 Model Validation

This section attempts to validate the dimensionless LSF model with (i) pressure failure (PF) models for corroded pipelines (described in Section 3.4) and (ii) past literatures on LSF models (described in Section 5.2). As mentioned earlier, the dimensionless LSF equation (equation 5.10) leads to the computation of the probability of failure (Pf) for corroded pipelines, for which the reliability of the structure to operate with time can be predicted. The comparison can be carried out in many ways but the present work only investigated the effects under varying pipeline operating pressures (Po). Apart from the statistical properties of the corrosion defects presented in Table 5.1 earlier, other random variables required for equation (5.10) is as given in Table 5.2.

Note that it was not the intention of the present work to distinguish the best model to determine the reliability of corroded pipelines while carrying out the comparison works. Discussion in this section is meant at measuring the goodness and performance of the

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dimensionless LSF model compared to other models. The closest behaviour of the pre-sent model towards certain models is assumed to be able to reveal similar characteristics or physics in them. Since the PF models have been widely accepted in the industry, any similarities between the models should be fairly acknowledged.

Table 5.2 Random variables of pipeline characteristics

Variables Symbol Description Unit

Distribution Mean Standard deviation

D Diameter mm Normal 711.2 21.3 t Nominal wall

thickness mm Normal 16.2 0.81

SMTS Specified minimum tensile strength

MPa Normal 530.9 37.2

Po Operating pressure MPa Normal 14-30 1.4-3.0

In the first comparison, the probability of failures (Pf) of the dimensionless LSF model were compared with the PF models for corroded pipelines, as shown in Figure 5.11. The PF models were represented by the DNV-RP-F101, Modified ASME B31G, Shell 92 and RSTRENG models. The figure illustrates the behaviour of Pf under varying pipeline op-erating pressures (Po); a term that has been made dimensionless by dividing it with the specified minimum tensile strength (SMTS) term.

Figure 5.11 Probability of failure (Pf) computed for all models under varying operating pressures

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It was found that Pf increased as loads increased. This is true because as higher loadings exerted to the pipeline, its capability to withstand the load decreases and thus prone to failure. All models were in good agreement with this fact. However, some models seemed to be either over or underestimated from one another. Lee et al. (2002) and Caleyo et al. (2007) for example, have previously looked into these models’ discrepancies. Since those arguments were beyond the scope of interest of the present work, they will not be further discussed.

Instead, the aim was to visually determine the closest behaviour that the dimensionless LSF model could agree to. The figure depicts that the dimensionless LSF model was bounded by the Modified ASME B31G and DNV-RP-F101 models. The Modified ASME B31G model falls under the ‘old’ model category while the DNV-RP-F101 model is the ‘new’ model (Cosham et al, 2007). Recall Section 3.4 on descriptions pertaining to the old and new models. The ‘old’ methods was predominantly developed and validated through full scale tests on older line pipe steels while the ‘new’ methods through tests on modern, high toughness, line pipe steels. Therefore each method was biased towards the type and toughness of the steels. Then, the difference between the behaviour of both categories can largely be attributed to the general increase in the toughness of line pipe, due to improvement in steel production and technological advances. Because of the ‘old’ methods demonstrate greater scatter than the ‘new’ methods when compared to the (relevant) published full-scale test data, the ‘new’ methods are more accurate (Cosham et al., 2007). Despite the preference towards the ‘new’ models, the approximate methods used in the DNV-RP-F101 model to assess corrosion could be argued too. The most conservative idealisation is a rectangular profile (Cosham et al., 2007). The Modified ASME B31G on the other hand, assumes an arbitrary profile with a 0.85 factor in the equation.

When speaking about model preference between the Modified ASME B31G and DNV-RP-F101 models, there is no straight forward answer to this, but having said that, it is indeed favourable to observe the dimensionless LSF model plot (in Figure 5.11) lies be-tween the two models. Hypothetically, the proposed model exhibits and behaves in the approximate characteristics of the two well-referred models.

In the second comparison, the performance and goodness of the dimensionless LSF model was compared with past literatures on LSF models as introduced in Section 5.2 earlier. Once again, the behaviour of Pf under varying pipeline operating pressures was investigated. Figure 5.12 provides the comparison of all models and similar trend to that in Figure 5.11 was observed. The Pf increased as loads increased. Results from the fig-ure showed a pleasant surprise with the dimensionless LSF model having the least ten-dency to failure compared to other models. Explaining the discrepancies in these models was not something straight forward. While Ahammed and Melchers (1996), Pandey (1998), Ahammed (1998), and De Leon and Macías (2005) were originated from the same background i.e. NG-18 criterion, Teixeira et al. (2008) was developed using different ap-proach. Nevertheless, the choice of safety factors in the first four models did influence

111


the performance of the models. The safety factor which is normally described by a single number has restricted the equations to be somewhat deterministic in nature. The models in Section 5.2 include safety factors and should not be used directly in a probabilistic analysis (Anonymous, 2009). Contradiction of interests may present is such work and it is beyond the scope of the present work to further elaborate about the matter.

Figure 5.12 Probability of failure (Pf) computed for all limit state functions under varying operating pressures

5.3.4 Target Reliability

Theories on reliability index, β has been briefly presented in Section 2.4.2. Its applica-tion will be illustrated in this section. It is noteworthy to first understand the relation-ship between the probability of failure (Pf) and reliability index. The relationship be-tween β and Pf is unique (Sing et al., 2007) that Pf decreases with increasing values of β. Typical values of β lie between 1 and 4 which corresponds to Pf ranging from the order of 15% to 0.003%. Nevertheless, a change in β can not be readily correlated to a change in Pf because their relationship is highly nonlinear (Sing et al., 2007). The choice be-tween using β or Pf as a measure of design risk is a matter of convenience. The probabil-ity of failure appears more physically meaningful but awkward to use when the value be-comes very small, and it carries the negative implication of failure. The reliability index, on the other hand, is a more convenient number to report.

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Besides the probability of failures, reliability indices were also computed for the present dimensionless LSF model under varying loads. Figure 5.13 was prepared which illus-trates the performance of the model with respect to operating pressure (Po). Reliability indices ranging from 0 to 6 were obtained with the increment of pressures from 12 MPa up to 24 MPa. Having this figure, the target reliability level can then be estimated for the pipeline candidate type API 5LX-65 subjected to corrosions. For this, a report by Skjong et al. (1995) is referred. The authors have made compilations on target reliability levels for offshore structures from several design codes. Among all codes, the target reli-ability level given by Eurocode 1 (1993) seemed to best suit the present case. The code defined an annual target reliability level of 3.8 (Pf=0.72 x 10-4) for an ultimate limit state. By projecting this value in the reliability plot of Figure 5.13, the corresponding operating pressure was known to be 14.8 MPa. When compared with the pipeline’s de-sign and operating pressures (Table 5.3), this outcome was in good agreement with each other. Moreover, the present model allows an extra (design) pressure of 1% to be ex-erted into the pipeline.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

12 13 14 15 16 17 18 19 20 21 22 23 24

Operating Pressure, Po (MPa)

Rel

iabilit

y In

dex

, β

14.8

3.8

Figure 5.13 Reliability index for pipeline API 5LX-65 computed using

the dimensionless LSF model

Table 5.3 Design and operating parameters for pipeline API 5LX-65 based on PETRONAS (2009)

Parameters Pressure (MPa)

Design Pressure, Pdesign 14.65 Maximum Allowable Operating Pressure, MAOP 12.40 Maximum Inlet Operating Pressure, Pi(max) 10.50 Minimum Inlet Operating Pressure, Pi(min) 0.75

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5.3.5 Advantage

The previous section has proven that the dimensionless LSF model is reasonable and ac-ceptable when compared to the performance of other models. The model also provides advantages which can be classified into several groups, as presented below:

Computation

The model is simpler and straightforward compared to the lengthy LSF as reported by past literatures. Thus less simulation time is required to carry out the analysis.

Corrosion Characteristic

There have been many arguments on the corrosion shapes assumed by the design stan-dards. Corroded area has been argued from as simple shape as a rectangular (dl) to parabolic (2/3 dl) and average of rectangular and parabolic (0.85 dl) shapes. Even until today, one can never be too sure of the assumptions made in those standards. Knowing this, it may be rationale to apply the dimensionless corrosion parameters without making any assumptions on the shapes. The proposed dimensionless LSF model is able to pro-vide a visual view of defects with respect to the pipeline original geometry. While the expression (t/D) corresponds to the original geometry of the pipeline, the (d/t) term represents the wall loss that has taken place from a cross section view. The (l/w) term is important to describe the size/spread of the defect, as seen from a plan view. Thus this equation is comprehensive enough to illustrate the physical layout of a corroded pipeline.

Spatial Reliability Analysis

The fact that this equation was developed in a probabilistic way, all input parameters are treated as random variables and thus no single value (or safety factor) will be used but to apply the probability density function (PDF) instead.

A pipeline can be several kilometres long and the level of corrosion attack varies accord-ing to the location, space and factors contributing to it. The dimensionless LSF model is capable to analyse any sections of interests so long its corrosions PDF is known (exam-ples of this will be discussed in Chapter 6). This leads to a more optimised and economi-cal reliability analysis.

5.3.6 Limitation

The following paragraphs highlight some limitations of the proposed dimensionless LSF model.

Burst Pressure Database

The dimensionless LSF model was partially developed using the burst pressure (Pb) data sets taken from the DNV Technical Report (1995). It is a comprehensive report that

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covers a wide range of defect sizes. The corrosion defects in this analysis, however, fall under the shallow (d/t < 0.30), short (l/D < 0.20) and broad (w/t > 0.50) type of corro-sions (Fu and Kirkwood, 1995). Therefore, the Pb data sets taken from the technical re-port had to be selected accordingly. This has restricted the model to be only applied to those defect categories. Nevertheless, for the sake of presentation, the model has been proven to be applicable and reasonable.

For classes of defects other than those incorporated in the model, the Pb data set needs to be further expanded. This can be done using either experimental or numerical studies be-cause it is not possible to obtain or generate Pb data for every single corrosion defect in the field. Tests on real corrosion are more preferable than the machined grooves defects. Once the Pb data set is complete, the model can be regenerated following similar steps described earlier. The dimensionless parameters will remain the same; the difference can only be noticed in the nonlinear equation coefficients.

Complete Corrosion Profile

The failure pressure (PF) models of Section 5.2 follow simple approximations to the ex-act corroded area, which was based on the maximum longitudinal length (l) and the maximum depth (d) of the defect (Figure 5.14). These are the default defect parameters measured by the intelligent pigging (IP) tool. Corrosion, however, typically has an ir-regular profile. Therefore, a complete corrosion profile at other than the maximum value could not be taken into account. This is a limitation not only to the PF models, but also to the proposed dimensionless LSF model (equation 5.10). Nevertheless, incorporat-ing the parameter w into the equation has enabled the defect to be visually seen from all views i.e. plan, longitudinal and cross sections. These have provided at least a whole view of the defect rather than the longitudinal section only as illustrated in the PF mod-els.

dmax t

Figure 5.14 Cross section view of corrosion defect at pipeline wall (not to scale)

Pipelines in Operation

The dimensionless LSF model was formulated for corroded pipelines that has been oper-ating and experiencing corrosion attacks. It does not compute corrosion growth rate (normally addressed in mm/yr) of a particular pipeline. Nevertheless, the probability distribution functions (PDF) of the corrosion characteristics (d, l, w) as reported by the intelligent pigging at present time could provide some insights on future corrosion devel-

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opment. This requires some probabilistic judgement when looking at the type of PDF coupled by its mean and standard deviation.

The dimensionless LSF model can also be applied to new pipelines provided future corro-sion development can be properly forecasted. This once again requires good knowledge and judgement on probabilistic approaches.

5.3.7 Recommendation

The proposed framework presented in this chapter depends on the availability of corro-sion database of a particular pipeline. Quite often this can be achieved when dealing with trunkline; a type of pipeline used to convey hydrocarbon products to the shore or Floating Production Storage and Offloading (FPSO). This type of pipeline is normally long and is designed to be pigged. A good pipeline system is designed to cater the needs for pigging activities in order to sustain the performance of the structure. A piggable pipeline is a pipeline that is designed to allow a standard inspection tool to negotiate it, which requires basically a more or less constant bore, sufficiently long radius bends and traps to launch and receive the pigs (Schmidt, 2004). As shown in the present context, pigging activity through the use of an intelligent pigging (IP) tool is capable to report corrosion patterns inside the pipeline.

Unpiggable Pipelines

It is quite common for unpiggable pipelines to take place in an offshore pipeline system. This has been the case for old pipelines or even some inter-field pipelines, for instance. The inter-field pipelines are used in the same reservoir field. Thus, they can be short, and may or may not be designed for pigging activities. The unpiggable pipelines by definition are those not designed like the piggable ones. There are plenty individual rea-sons, why a pipeline can not be negotiated by standard inspection tools (Schmidt, 2004): over- or under-sized valves, repair sections in a different size, short radius or mitred bends etc.

In the absence of corrosion database as what might have been the case for unpiggable pipelines, the proposed model can still be applied so long the corrosion shape (database) are captured and reported. It has been shown that other alternative tools called the re-motely operated vehicles (ROV) are capable to also provide information on the pipeline wall thickness, for which the thickness depletion subjected to corrosions can be implicitly measured. An ROV operates outside the pipeline. It is a tethered underwater vehicle, which are very common in the offshore hydrocarbon industries. It is unoccupied, highly manoeuvrable and operated by a person aboard a vessel. It is linked to the ship by a tether (sometimes referred to as an umbilical cable), a group of cables that carry electri-cal power, video and data signals back and forth between the operator and the vehicle. Some commercial ROVs that are capable of measuring the wall thickness are the under-

116

5.4. Conclusions

water ultrasonic testing tools, underwater radiography testing, and long range ultrasonic test, for instance.

Assuming that each ROV has its own format on reporting corrosions, the framework of the model development (Section 5.3.2) needs to be modified accordingly in order to suit the outcomes of that ROV. In short, (i) the corrosion parameters (d, l or w) need to be identified and to (ii) re-arrange them into another set of Buckingham-π theorem (gov-erned by corresponding load and strength terms), and later (iii) to formulate the corre-sponding dimensionless LSF model using the nonlinear multivariate regression analysis. The final outcome would be another dimensionless LSF term with different coefficients resulted from the corrosion parameters reported by the ROV.

5.4 CONCLUSIONS

Corrosion in offshore pipelines is a representation of uncertainties as they are random, unique and not straight-forward to be described. Although corrosions prediction has al-ways based on their science and physics, we should always admit that their occurrence is somewhat complicated and very much depends on their operating environment and sur-roundings. Their characteristics cannot always be described by the design standards. It is believed that there is no single solution as proposed in any corrosion models that suit all corrosions, thus if possible their analysis may wise be tackled on a case-to-case basis.

Experimental and numerical techniques have been the common methods applied in the past to create a model (equation) to assess the remaining strength of corroded pipelines. Among the governing parameters involved are the corrosion defect depth (d) and longi-tudinal length (l). The defect circumferential width (w) on the other hand, was reported to be less significant. This assumption has been widely agreed even though those studies were conducted for certain sizes of defects, whereas in reality the corrosions are definitely beyond those limits.

Corrosions grow and evolve in three main orientations, namely vertical, longitudinal and circumferential. As one component expands in one direction, the other two will also be affected accordingly. Relationships do presence in these interactions. Describing them would best be described by the multivariate regression analysis, part of probabilistic ap-proaches. While doing so, the role of w could be relooked into. The idea was not to ne-glect or omit any less significant parameters as done in the current design standards be-cause their correlation between each other can never be guaranteed to be any less impor-tant.

117


118

By utilizing more corrosion parameters (d, l and w) to describe corrosion shape, one is looking at a more detail description about its shape as well as addressing its interaction with the surrounding environment. Having them together in an expression was assumed to be able to provide a better estimate on the defect’s characteristics. By making those parameters dimensionless, the equation provides proper visualization from not only the cross section, but also the longitudinal and plan view.

The so called dimensionless limit state function (LSF) model was simpler and straight-forward. Thus less simulation time is required to carry out the analysis. Favourable re-sults were obtained after validating it with other design standards and past literatures on LSF models. Implicitly, it has been probabilistically proven that all defect parameters do correlate with each other. It is then wrong to assume that probabilistic approaches have no value at all, especially in the reliability assessment of corroded pipelines. The field is yet to be further explored with part of it will be presented in the remaining chap-ters.

Chapter 6

SYSTEM RELIABILITY FOR CORRODED PIPELINES

6.1 INTRODUCTION

This chapter intends to demonstrate the application of the reliability model of corroded pipelines as proposed in Chapter 5. Pipelines are structures operating in series and this provides great advantages to the model. It will be shown later that the model has broad applications, through which three of its applications will be highlighted in this chapter, namely (i) reliability per pipeline section, and reliability for total pipeline system (ii) with, and (iii) without the inclusion of length effects.

6.2 RELIABILITY PER PIPELINE SECTION

In the previous examples in Chapter 5, the pipeline was treated as a single structure but in reality it comprises many subsections, as casted and sized according to manufacturer’s scope of designs. Most of the time pipeline operators are more concerned about certain pipeline sections which are exposed to bigger threats, as compared to the whole structure alone. Dealing with certain pipeline section of interests seemed to be more economical too.

In conjunction to the development of the reliability model of corroded pipelines i.e. di-mensionless limit state function (LSF) model in Chapter 5 earlier, it is the interest of the present section to further expand its capability and potential, especially when dealing with sectional analysis. Recall that the model as given by equation (5.10) is,

0.8442 0.0545 0.0104oPt d l

ZD t w SM

− − = − TS

LoadResistance

6 System Reliability for Corroded Pipelines

This model suits the reliability computation for sectional pipelines very well. Reason be-ing, the model can easily takes into account defects distributions (statistical properties of parameter d, l and w) at separate pipeline sections. This can be done by first assuming a pipeline of length L is schematised into n sections by,

L

Δx =L/n

Figure 6.1 A pipeline with length L divided into n sections (not to scale)

If the same pipeline API 5LX-65 (as in Chapter 5) were to be tested, and that the pipe-line was divided into four sections, the corresponding corrosion defects’ statistical prop-erties for each section could be determined, as displayed in Appendix II. Now, to con-tinue with the calculation, re-apply other random variables as displayed in Table 5-2, but this time fix the operating pressure to be 18 MPa (for example).

The calculations resulted in probability of failure (Pfi) for each section i of the whole pipeline length as portrayed in Figure 6.2. For comparison, the probability of failure for the whole pipeline length with corrosion defect properties as given in Table 5-1 was also included in the figure. It is interesting to notice that different failure values were ob-served at each section. In general the sectional pipelines would fail in the order of 10-3 which corresponds to probability of 1/1000 per year per pipe. Section 1 with the highest magnitude of failure seemed to be the earliest to fail, followed by sections 4, 3 and finally 2. When comparing these outcomes with failure computed from the whole pipeline length, it was obvious that the latter produced the fastest to fail with Pf of 10

-2 (1/100). This is true as the higher the defects considered in a certain reliability calculation, the higher the corresponding probability of failure too. The single pipeline length has taken into account all defects as a lump sum value whereas dividing into sections enabled the defects to be fairly distributed. The failure probabilities were distributed throughout the pipeline section in the same manner as well.

Despite sectional pipeline with similar lengths, the reliability model of corroded pipelines could also be applied to any pipeline distances; so long the defect characteristics could be interpreted statistically. The same pipeline candidate as shown in Figure 6.3 for exam-ple, portrays clusters or groups of defects concentrated at several different locations along the pipeline length. Once their defects’ statistical properties were known, the Pf could be computed following the same steps as described earlier.

120

6.2. Reliability Per Pipeline Section

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100 110 120 130

Longitudinal distance (km)

Def

ect

dep

th, d

(%)

Section 1 Section 2 Section 3

Pf1 = 7.8 x 10-3 Pf3 = 5.6 x 10

-3Pf2 = 4.4 x 10-3 Pf4 = 6.7 x 10

-3

Section 4

Pf = 1.3 x 10-2

Figure 6.2 Comparison in probability of failure between sectional and individual pipeline of pipeline API 5LX-65

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100 110 120 130


Def

ect

dept

h, d

(%

)

Pf = 5.6 x 10-2

Pf = 6.7 x 10-2

Figure 6.3 Probability of failure computed at sections of interests of pipeline API 5LX-65

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6.3 LENGTH EFFECTS ON SYSTEM RELIABILITY OF PIPELINES

Recall that a system as cited by Vrijling et al. (2006) in Chapter 2 is defined as a group of elements or processes with a common objective. When speaking about system reli-ability of pipelines, one is referring to the whole structure for which elements and proc-esses have relations amongst each other. When a complete pipeline is installed, the sub-sections are interconnected to each other which resemble to an operation of system in se-ries, as described in Section 2.4.4.

A pipeline system may be exposed to more than one types of failure as well, but in this context the system reliability is only concerned with failures subjected to corrosion threat. Even though corrosions in pipelines have been widely studied using probabilistic approaches, the potential effect of spatial correlation of corrosion defects (in sections of a pipeline) on its failure probability has not received much attention. De Leon and Macías (2005) may be one of the first to look at this aspect but their work simply assumed sev-eral degrees of spatial correlation coefficient (of 0, 0.2, 0.4, 0.6, 0.8, and 1.0) for the cor-rosion in determined sections of a pipeline. In reality, the correlation should not be simply assumed as other factors, one of which will be elaborated in the next paragraph, may contribute to the degree of correlation for pipelines aligned in series.

A structure like pipeline which is arrayed in series may promote sectional length effects. Studies on the effect of sectional length for structures operating in series have been pre-viously carried out, for instance in flood sea defence structures (Van Gelder et al., 2008; Mai Van, 2010). It is then interesting to investigate the length effects to another struc-ture like pipelines and its consequences towards the overall probability of failure of the structure.

Herein, the procedures to carry out the length effects analysis to pipeline systems were adapted from reliability analysis applied to flood sea defence structures and systems as reported in Van Gelder et al. (2008) and Van Gelder and Vrijling (2006), with the follow-ing assumptions:

1. The pipeline system with total length, L can be divided into n number of sections with n dependant on the correlation distance.

2. The influence of failure mode i.e. corrosions equally contribute to the total prob-ability of failure of a pipeline section.

3. Pipeline system has uniformly cross section throughout its length, L.

With reference to Figure 6.1 once again, the pipeline system that has uniform cross sec-tion comprises n sections of certain length. The strength, R at every pipeline section of a system in series can be described as random variables and the strengths at two adja-cent sections are assumed to be correlated. The degree of correlation depends, amongst other factors, on the distance Δx between the two points considered.

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6.3. Length Effects on System Reliability of Pipelines

In statistics, the relation between the correlation and the distance can be described by a correlation function. A common form of autocorrelation function, ρ describing strengths at location x and x+Δx is described by,

( ) ( )2

, corr

x

dR x R x x eræ öD ÷ç ÷ç- ÷ç ÷÷çè øé ù+D =ë û (6.1)

with x as a characteristics under consideration, Δx as distance between two points (in time) which is known as the distance lag and dcorr as correlation distance or sometimes re-ferred to as fluctuation scale. Within a statistically homogeneous length of a pipeline, the number of pipeline sections is identified with lengths equal to the dcorr. The dcorr is defined as the distance over which the statistical properties of the reliability function are assumed totally correlated.

In this context, the parameter x is described by corrosion depth (d) measured in millime-tre (mm) or percentage (%). Corrosion development in a particular pipeline section is assumed to be proportionally related to the corresponding pipeline strength.

To continue the analysis, the reliability index for the i-th section is beta, β (for i=1, 2,…n),

( ) (iP F b= F - ) (6.2)

and that β is given by,

2 2

R S

ZR S

m m mb

ss s

-=

+Z= (6.3)

Then the overall failure probability is given by,

( ) ( ) ( ) ( ) ( )2

11 2

1iP F n

rb b b b

r

ì üæ öï ï- ÷ï çï ÷ç= F - + - F - - F - F -í ÷ç ÷ï ïç ÷ç -è øï ïï ïî þ

ïïý (6.4)

Since ( ) ( )2

2

1max and and and 1corr

x

di i j i

j icorr

xP F F P F F e

dr

æ öD ÷ç ÷-ç ÷ç ÷÷çè ø-<

æ öD ÷ç ÷= = » ç ÷ç ÷çè ø- ,

as well as, 2

2 1 2corr

x

dr

æ öD ÷ç ÷= - ç ÷ç ÷çè ø, whereas

1( )

2 2

uuf

p= + for small u.

Therefore ( ) ( )1

1corr

n xP F

d

bb

p

ì üï ï- Dï ï= F - + +í ýï ïï ïî þ (6.5)

123


Since ( )- 1

andcorr corr

L n L Lx n

n nd d

b bp p

D = ¥ ,

Therefore, ( ) ( ) 1fcorr

LP P F

d

bb

p

ì üï ïï ï= = F - + +í ýï ïï ïî þ (6.6)

which is independent of the number of sections n and Pf is previously addressed as prob-ability of failure.

6.3.1 Correlation Distance, dcorr

Equation (6.6) can only be successfully achieved with the pre-selection of the correct dcorr. The dcorr can be determined using equation (6.1) by satisfying both the left (LHS) and right (RHS) hand sides of the equation. The LHS of the equation is denoted by the term ( ) ( ),R x R x xr é +Dë ùû , which corresponds to an autocorrelation function. This standard statistical function can be computed using commercial statistical programming lan-guages. Particularly for the present case, the LHS term was solved using the MATLAB

command. The RHS term, on the other hand, is given by

2

corr

x

de

æ öD ÷ç ÷ç- ÷ç ÷÷çè ø and can be calculated manually once dcorr is known.

Brief guidelines to aid readers on the procedures required to obtain dcorr using equation (6.1) are presented below. [Recall that the parameter x is described by corrosion depth (d) measured in millimetre (mm) or percentage (%).]

To solve LHS term

1. Identify the number of sections (n1, n2,… nn) of a pipeline, through which the size/distance Δx can be determined.

2. Compute the average values of corrosion depths at each section ni i.e. d1, d2,… dn.

3. Solve for autocorrelation function values for d1, d2,… dn at each pipeline section using standard statistical command in MATLAB.

4. Store the results for comparisons later on.

To solve RHS term

5. Stick to the assumptions in Step (1) for the values of n and Δx.

6. Take a value for dcorr.

7. Manually calculate the RHS term. Store the results.

8. Compare results in Step (4) with those in (7). Repeat Steps (6) to (8) for another value of dcorr until they conform to each other very well.

Basically, equation (6.1) is solved simply using trials and errors on different values of dcorr. The best choice for a dcorr value is when the sum of squares, errors (SSE) (equation

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2.21) is minimized. If graphical plots were to be used to carry out this task, the two graphs representing the LHS and RHS equations of equation (6.1) should be fitted close to each other.

Details pertaining to the above procedures will be elaborated herein using pipeline can-didate API 5LX-65 once again. Two scenarios involving two different numbers of sec-tions (n) were identified, as given in Table 6.1. A random trial value of dcorr was then se-lected for each scenario and applied into equation (6.1). Following this, the LHS and RHS equations should be plotted in a single graph and compared. Visually comparing the goodness of the two may not be easy, so the SSE should be used instead. A smaller SSE is always preferable.

Table 6.1 Comparison between two scenarios for the computation of correlation distance, dcorr

Scenario Number of sections, n

Δx (km)

Sum of squares, errors, SSE

Correlation distance, dcorr (km)

1 13 10 0.034 85 2 128 1 2.424 65

While choosing the correct dcorr value for pipeline candidate API 5LX-65, it was interest-ing to notice the effect of ‘number of sections’ towards the autocorrelation functions. Figure 6.5 and Figure 6.7 are referred to provide better view on this aspect. Selecting smaller number of sections (scenario 1) led to a more or less consistent pattern. This was because the defects have been grouped at reasonable intervals (Δx) for which their corresponding mean values lies within small gap, ranging from 1.0 to 1.6 mm as in Figure 6.4. This then promoted to fairly ‘smooth’ autocorrelation functions, as can be seen from Figure 6.5. On the other hand, large number of sections (scenario 2) tend to picture the actual corrosion distribution of the whole pipeline length, for which any sig-nificant or insignificant i.e. extremes defect characteristics would be taken into account, disabling them to be simply ignored (through averaging). The mean values computed in scenario 2 (Figure 6.6) seemed to fall within 0 to 2.6 mm, larger than those obtained from scenario 1. The corresponding auto correlation functions would then result in fluc-tuates and ‘peaky’ trend (Figure 6.7).

One would be in favour of scenario 1 when looking at the smaller SSE value of 0.034. Smaller error values describe both RHS and LHS equations of equation (6.1) are in bet-ter agreement to each other. Nevertheless, the SSE value scenario 2 could also be fairly accepted. It is not wrong to propose correlation distance, dcorr for pipeline structure of certain range values, as what have been proposed for other structures like flood defence system (Vrouwenvelder and Vrijling, 1987). Thus a structure like pipeline with similar characteristics is proposed to be represented with a correlation distance, dcorr of 65 to 85 km.

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ndar

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m)

MeanStandard deviation

Figure 6.4 Statistics (mean and standard deviation) for pipeline subdivided into 13 sections

Number of sections = 13

Correlation distance, dcorr = 85 km

Sum of squares, error = 0.034

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elat

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Figure 6.5 Autocorrelation functions for pipeline subdivided into 13 sections

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Figure 6.6 Statistics (mean) for pipeline subdivided into 128 sections

Pipeline sections = 128

Correlation distance = 65 km

Sum of squares, error = 2.424

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Figure 6.7 Autocorrelation functions for pipeline subdivided into 128 sections

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For the sake of illustration, the remaining analysis of this section assumed a correlation distance, dcorr of 85 km. This value was then applied to equation (6.6) to complete the length effects analysis procedures. Different loadings were applied to the reliability model of corroded pipelines or dimensionless limit state function (LSF) equation, which resulted in different failure probabilities, as displayed in Figure 6.8 below. For compari-son, the previous results (computed in the absence of sectional length effects) taken from Figure 5.9 and 5.12 earlier were also included in the figure.

The figure depicts that a pipeline reliability model with the influence of length effects produces higher probability of failure. This result showed that the correlation distance (dcorr) parameter of a statistically homogeneous length of a pipeline subjected to corro-sion failure has significance impact towards the reliability of the structure. The choice of dcorr has allowed the statistical properties of the reliability function to be totally corre-lated. The correlations herein have been acknowledged and considered into the reliabil-ity calculation. Even thought the failure threat seems larger than the one without (length effects), it may lead to a safe and better prevention towards failure.

Figure 6.8 Comparison in probability of failure as determined from pipeline API 5LX-65 with and without the length effects

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6.4. Conclusions

129

6.4 CONCLUSIONS

The outcomes of this chapter are useful in a way they provide different options to pipe-line operators in managing their corroded pipelines. Depending on the concerns and limitations (budget, manpower, resources etc.), they may apply one of the proposed ap-proaches to determine the reliability of the structure. Tackling the problem by means of dividing the pipeline into sections may seem to be economical and practical if the threat is considered to be moderate.

Results showed that the probability of failure (Pf) for sectional pipelines is smaller com-pared to one section covering the whole pipeline length. A cluster of defects interacting together may provide more threats to the pipeline.

When the reliability for the whole pipeline length becomes a major concern, it is sug-gested to carry out the analysis with the inclusion of length effects because the method seems to provide the worst scenario (higher Pf) compared to the one without. Reason being, corrosions in pipelines aligned in series are believed to be correlated with each other and this can be described probabilistically using an autocorrelation function. Through the correlation distance (dcorr) parameter, the analysis enabled pipelines to be divided into sections for which the statistical properties of the reliability function are to-tally correlated.

Chapter 7

RELIABILITY-BASED MAINTENANCE MODEL

7.1 INTRODUCTION

The ultimate goal of a crude oil production system is to generate revenue for the owners. To achieve this, the production facilities and pipeline infrastructure are properly moni-tored to ensure theirs system integrity. Corrosions, however, will always be the main threats to system integrity because water (especially) can never be stopped from entering the pipeline. Obeying to this fact, the maintenance activity towards corrosion control is the only aspect that can be exploited. Corrosion control through the use of corrosion inhibitor is known as the most cost-effective methods for imparting corrosion protection in a system. Care should be taken when using this method as Horsup et al. (2007) de-scribed it as ‘I put it in, but where does it go?’ The fate of corrosion inhibitor in a pipe-line system is still a big issue in the industry. The effectiveness of the maintenance prac-tice should be examined and this will be the highlight in this chapter.

7.2 OVERVIEW OF MODEL

The reliability-based maintenance model was developed for the purpose of creating a cor-rosion model that represents interactions between the environments, operations and pipeline itself. The model is not meant at forecasting corrosions as normally done by other corrosion models (as described in Section 3.3), but to be used as an aid for the im-provement of future maintenance practices in a pipeline.

The proposed reliability-based maintenance model is closely integrated by three impor-tant principles, namely (1) forensic evidence, (2) input-output model, and (3) bench-marking. The model is designed using the ideology of forensic science while its structure adapted the so called input-output model. The outcomes from both principles will be in a form of a model describing historical corrosion development of a particular pipeline.

7 Reliability-Based Maintenance Model

Model optimization can then be carried out through benchmarking. An overview of this integration can be seen in Figure 7.1 and details pertaining to these principles will be further described in Section 7.3.

Ideology

Figure 7.1 Framework of the reliability-based maintenance model

It is necessary to understand that no single (hydrocarbon) reservoir can be said to be 100% homogeneous to another reservoir and so thus the operating conditions. Then no specific design standard can best suit a particular pipeline. The same goes to the mechanism to carry out certain corrosion maintenance practices. The practice at the field is subjected to human intervention and does not entirely obey to the designated procedures as in the design standards. Owing to this, independent in-house investigation should be carried out from time to time and an illustration of this will be presented in the following sections.

7.3 MODELLING PRINCIPLES

7.3.1 Forensic Evidence

Forensic science (often shortened to forensics) is the application of a broad spectrum of sciences to answer questions of interest to a legal system. In simpler words, the term forensics is mostly related to courts. It is the application of engineering principles and methodologies to answer questions of fact which are usually associated with accidents, crimes, catastrophic events, degradation of property, and various types of failures. It deals with retracing processes and procedures leading to certain accidents. A forensic engineer relies mostly upon the actual physical evidence found at the scene, verifiable facts related to the matter, and well-proven scientific principles. These pieces of evi-dence are used to reconstruct an event that has taken place.

The phrase forensic evidence may seem to be misleading when applied to the context of this chapter if the legal definition is to be used. Note that the proposed modelling

Reliability-Based Maintenance Model

Structure

O n ptimizatioTechnique

Forensic Evidence

Input-Output Model

Benchmarking

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7.3. Modelling Principles

principles have no relation to any legal aspects. The present analysis only tries to adapt the ideologies for which forensics activities are carried out, which will be briefly elabo-rated in this paragraph. Recall that forensic science deals with retracing processes and procedures which lead to an accident. The retracing process results in important pieces of evidence. Scientific methodologies and principles are then applied to interpret the physical evidence and facts of the investigation. The application of scientific method in the reconstruction of accidents or failures according to Noon (2001) allows an event to be ‘experimentally’ duplicated or reconstructed. The experiments are conducted for vari-ables of interest until they are not obscured by other effects which are acting simultane-ously. The variables would simply be changed and combined until the ‘right’ combina-tion is found that faithfully reconstructs the event (Noon, 2001). When the actual event is experimentally duplicated, it can then be said that the reconstruction of the failure has been solved.

The reliability-based maintenance model proposed in this thesis attempts to tackle corro-sion problems in the pipelines using the above ideologies of forensic evidence. The term ‘accident’ is assumed to be addressed by means of corrosions, even though corrosion failures might not have taken place in the pipeline system. Corrosion historical devel-opment will be ‘experimentally’ duplicated and reconstructed, and this can be done by collecting appropriate pieces of evidence associated to the event in the past. Probabilis-tic methodologies will be applied to the evidence to trace possible relationships in it. Several variables will be chosen to represent this relationship. For this, two forms of fo-rensic evidence will be proposed, namely those contribute to corrosion and those against its development. Implicitly the proposed model wishes to speculate the reasons for cor-rosions to continuously evolve even though safety measures have been extensively carried out in a particular pipeline. It is known that one of the more rewarding aspects of foren-sic science practice is the opportunity to make recommendations on the basis of an inves-tigation (Carper, 2001). It will be shown later that the collected evidence was capable to highlight some ‘weakness points’ of the past corrosion mitigation strategy in the pipeline, in which these results would become handy for model optimization later on. To suit the present interest, the basic structure of forensic science needs to be translated, as given in Figure 7.2.

Figure 7.2 Investigation pyramid for the reliability-based maintenance model

Facts and physical evidence

Conclusions

Analysis

Optimise corrosions

P ap es robabilistic

proach

Sources toward + Mechanisms against + Managerial aspects

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7.3.2 Input-Output Model

The structure of the reliability-based maintenance model relies on a metaphor adopted from an input-output model, as illustrated in Figure 7.3:

SYSTEMInput Output

Figure 7.3 An input-output model of a system

An input of a system will result in certain output. Assume the system as a structure, in this case a pipeline; represented by the characteristics of materials, geometry and strength.

The input to the pipeline is the flow itself, symbolized by transported hydrocarbons (coupled with operating conditions). Note that the hydrocarbon is influenced by the reservoir and sea water properties. In addition to that, corrosion mitigation strategy such as the release of corrosion inhibitor can also be considered as part of the input pa-rameters.

The output from the system in this case is assumed to be corrosion, represented by the corrosion defect depth, d (unit %) parameter.

The above metaphor has paved the assumption that the shape and characteristics of a particular corrosion defect is actually representing the interactions between the pipeline’s characteristics (materials, geometry, strength), flows (transported hydrocarbons), envi-ronment (sea water, reservoir properties), and maintenance strategy (corrosion inhibitor). The proposed input-output structure of the reliability based-maintenance model was then translated by,

Pipeline characteristics, flows, environment, and maintenance strategy

PIPELINE Corrosions

Figure 7.4 Input–output framework for the reliability-based maintenance model

7.3.3 Benchmarking

Benchmarking is the first and foremost tool for improvement, achieved through compari-son with other organisations recognized as the best within the area (Andersen and Pet-tersen, 1996).

134

7.3. Modelling Principles

Xerox Corporation who launched benchmarking in the early 1970s defined benchmarking as “the search for industry best practices which lead to superior performance” (Wireman, 2010). At that time the benchmarking technique was mainly used for two purposes (Andersen and Pettersen, 1996):

1. To ‘wake up’ the organisation and show that improvements were necessary

2. To motivate the organisation for improvement and to show that improvements could be made (by referring to others who had made it).

A more operation definition of benchmarking is described by:

“Benchmarking is the process of continuous measuring and comparing one’s business processes against comparable processes in leading organisations to obtain information that will help the organisation identify and implement improvement (Andersen and Pettersen, 1996).”

There are different types of benchmarking available depending on the purpose and aim of the practice. They can be classified into two categories (Andersen and Pettersen, 1996):

I. Compare what?

• Performance benchmarking:

Comparison of performance measures (often fi-nancial, but also operational) for the purpose of determining how good one’s own company is compared to others.

• Process benchmarking: Comparison of methods and practices for per-forming business processes for the purpose of learning from the best improve one’s own proc-esses.

• Strategic benchmarking: Comparison of the strategic choices and disposi-tions made by other companies for the purpose of collecting information to improve one’s own stra-tegic planning and positioning.

II. Compare against whom?

• Internal benchmarking:

Comparison between departments, units, subsidi-aries, or within the same company or organisa-tion.

• Competitive benchmarking: Direct comparison of own performance/results against the best real competitors.

• Functional benchmarking: Comparison of processes or functions against non-competitor companies within the same in-dustry or technological area.

• Generic benchmarking: Comparison of own processes against the best processes around, regardless of industry.

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The benchmarking categories can be also combined to give the highest benefits, as given by below matrix,

Table 7.1 Matrix of benchmarking (Adapted from Andersen and Pettersen, 1996)

Internal

benchmarking Competitive

benchmarking Functional

benchmarking Generic

benchmarking

Performance benchmarking

Process benchmarking

Strategic benchmarking

Relevance/Value: High Medium Low

Following the two principles introduced earlier, model optimization could be carried out based on the outputs of the reliability-based maintenance model. The model which was developed based on past information (evidence) would now be used as a benchmark for optimization. Once the past corrosion maintenance practices are properly understood, future practice can be planned to optimise (or minimize) corrosion growth in the pipe-line. Herein the benchmarking process was carried out by combining the process and in-ternal benchmarking (as highlighted in Table 7.1). Although the two combinations ap-peared with a ‘medium’ score according to Andersen and Pettersen (1996), they reflect the most to the scenario under investigation. Reason being, the model was developed in view to highlight the managerial aspects of the past corrosion mitigation strategy in the pipeline, which was in line with the definition of process benchmarking. Also, when comparing the past performance for the betterment of future maintenance practice, this imitates the internal benchmarking process nicely.

The model was expected to be able to improve human intervention of the pipeline opera-tors. This supports well by the fact that benchmarking can cause a change of the atti-tude and behaviour of people (Yam et al., 2000). Experience suggests that in actual field situations it is not necessary the equipment design that is deficient, but operational as-pects may not be adequately addressed (PETRONAS Technical Standard, 2010).

For illustration, the benchmarking processes on maintenance management in the power plant carried out by Yam et al. (2000) are as presented in Table 7.2 below. Several modifications were made to suit the proposed reliability-based maintenance model, which are also given in the table.

136

7.4. Model Parameter Selection

Table 7.2 Steps for benchmarking procedures

No. Adapted from Yam et al. (2000) Amendments to suit proposed model

1. Identifying the key maintenance per-formance variables that need to be benchmarked.

Corrosion mitigation strategy through the application of corrosion inhibitor.

2. Selecting good information sources for benchmarking.

Data selection as described in Section 7.4.2.

3. Collecting and measuring maintenance data.

Brief description of collected data as de-scribed in Section 7.5.1.

4. Normalizing and adjusting the collected and measured maintenance information to a meaningful data set.

Developing a benchmark model as reported in Section 7.5.2 onwards.

5. Analyzing the maintenance data against other organisations that are known to be superior performers in the world.

6. Changing and improving the mainte-nance performances.

Optimizing the benchmark model using several proposed maintenance practices as illustrated in Section 7.6.

7.4 MODEL PARAMETER SELECTION

7.4.1 Facts about Water in Pipeline

One of the stages involved when developing an oil field is to investigate and determine the amount of hydrocarbon reserves in the reservoir. A typical reservoir comprises not only gas and oil, but also water, as illustrated in Figure 7.5. A reservoir engineer whose task is to develop an oil field, prepares a production profile using reservoir simulations. The production profiles, as shown in Figure 7.6, define how the oil, water, and gas flowrates change with time for the whole field life. The information from the profiles is one of the prerequisites for the design of pipeline sizing. A typical production profile il-lustrates the oil flowrate reaching a maximum in a short period of time and staying at the maximum flowrate for a few years before starting to decline. Only oil and gas are produced in the initial production of a well. Water may not be produced for the early stage of production. Often carbon dioxide and water are pumped down the well to en-hance the oil and gas production at the later stage of the production period. Once water is breaking through, the water flowrate tends to increase rapidly and stays at the maxi-mum flowrate for some time before starting to decline (Guo et al., 2005). If successful pressure maintenance programs are utilized, water production may not decline much for the whole field life.

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Platform

Mixture of gas/oil/water

Water level Well

Gas

Oil Water

Reservoir

Well to the reservoir

Sea bed

Figure 7.5 An overview of hydrocarbon operation and reserves

Figure 7.6 Typical oil, water, and gas production profiles

(Adapted from Guo et al., 2005)

Fluid and water compositions are not always favourable in the pipeline. Reason being, their mutual effects will trigger corrosion to take place. These have been critically pre-sented in Section 3.2.3 earlier. Sea water contains high salt concentrations and is very corrosive. The dissolved gases in water, such as oxygen, hydrogen sulfide, carbon diox-ide, would significantly increase the water’s corrosivity. In addition, interactions be-tween the cations (calcium, magnesium, and barium) and anions (sulfate, carbonate, and bicarbonate) of the produced water will form scales (refer Figure 3.4).

A corrosion inhibitor is a chemical compound that, when added to a liquid or gas, de-creases the corrosion rate of a material, typically a metal or an alloy. A pipeline is dosed continually with a corrosion inhibitor in order to mitigate against any corrosion that could occur where water accumulations develop in the line. It acts as a film on a metal surface that either provides physical protection against corrosive attack or reduces the

138

7.4. Model Parameter Selection

open-circuit potential difference between local anodes and cathodes and increases the po-larization of the former. The corrosion inhibitor is said to be only efficient when it could present in the water phase and reach the pipe wall. The presence of solids like scales can interfere with the corrosion inhibitor in several ways (Achour et al., 2008). When scales developed on the pipe wall, they constitute an extra physical layer that the inhibitor has to overcome in order to get to the surface (Achour, 2007). These solids will also absorb the active components of the inhibitor and may cause under dosage of the inhibitor. Horsup et al. (2007) in their work concluded that production variables such as tempera-ture, brine salinity, oil composition and the presence of other production chemicals can all impact on in-situ inhibitor availability. Even though corrosion mitigation strategies are developed to control corrosion development, the main task is to stop water from en-tering the pipeline, which is definitely impossible.

7.4.2 Model Variables Selection

ters) for the reliability-based maintenance model was

ll selected variables were treated as random variables and analyses were carried out

ection 7.4.1 in particular has described the significance of water in a pipeline system.

he effect of multiphase flows (as described in Section 3.2.3) has also implied the ten-

he corrosion inhibitor (CI) was also selected as another governing parameter for the

The selection of variables (paramedone in accordance to the principles presented in Section 7.3. The selection was based on the sources contribute to corrosion and mechanism to fight against it.

Aprobabilistically. The corrosion defect depth, d (unit %) parameter was chosen as the dependant variable in the model (recall Section 2.3.1), while descriptions about the asso-ciated independent variables will be highlighted in the remaining paragraphs.

SObeying to the fact that water can never be completely drained from a pipeline, the best way to tackle corrosion problem is to critically deal with it. Water (W) or water cut (WC) was treated as one of the important parameters in the proposed model to promote corrosion. The parameter WC (unit %) was chosen over W (unit kL/day) because it is the ratio of water produced compared to the volume of total liquids produced, making it more appropriate to be used.

Tdency for water to be ‘trapped’ into the system. Therefore, the transported hydrocar-bons either oil/condensate (O) or gas (G) needed to be included in the proposed model as well. The ‘interaction’ between the O and G variables was assumed to be able to provide some insights on the possibility of water detection using the probability of occur-rences of oil and gas in the pipeline.

Tproposed model. The use of CI as corrosion mitigation strategy is known to be one of the most effective methods in the present days. Nevertheless, there have been a lot of is-sues pertaining to CI. Even though the practice has become ubiquitous, the industry

139


lacks a comprehensive knowledge of what actually happens to corrosion inhibitor mole-cules when added into a system (Horsup et al., 2007). Lack of CI availability, or sys-temic under dosing, remains a major problem for oil and gas industry in the UK where many operators still struggle with this issue (Marsh and Duncan, 2009). The works on measuring the effectiveness of CI were mostly experimental based. However, variables or parameters in the laboratory could be easily controlled but not in the case of real appli-cations. With regards to these issues, having CI as a parameter in the proposed model would be one of the attempts to tackle the problem probabilistically.

7.5 MODEL DEVELOPMENT

7.5.1 Pipeline Candidate

ellite to a mother platform with characteristics as given in

Table 7.3 Pipeline properties and corrosion characteristics

A pipeline connecting a satTable 7-3 below was chosen as a candidate pipeline in this chapter. It was built to transport crude oil extracted from a reservoir to processing facilities located at the mother platform. The pipeline transported not only the oil/condensate, but also signifi-cant amount of gas and water. It was the intention of the present work to select a crude pipeline that has not been processed yet, as this represented the actual amount of flows directly extracted from the well.

Type: API 5LX-65 Diameter: 16 inch Wall thickness: 19.1 mmLength: 6.9 km Year of commission: 2000 Type of defects: Internal and external corrosions Number of defects: 6981 defects

he measured data sets were taken from year 2009, which represents a nine year old op-

7.5.2 Regression Analysis

Section 5.3.2 has illustrated the application of bivariate and multivariate regression analyses in determining the dependency between variables. The independent variable is

Teration. It comprised data on the amount of oil/condensate (O, unit kL/day), gas (G, unit km3/day), water (W, unit kL/day) or water cut (WC, unit %) transported in the pipeline. Records on corrosion inhibitor practice (CI, unit ppm) in the pipeline system were also adopted into the analysis.

140

7.5. Model Development

somewhat related to dependant variables in certain forms of relationships. In this chapter, once again the dependency among variables d, O, G, WC and CI were determined using the regression analysis techniques. Knowing how theories on O, G and WC of a particular reservoir change with time (as described in Section 7.2.1), it was important to first determine whether certain trends might exist in the data sets, thus Figure 7.7 was prepared to illustrate these relationships.

0

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eb

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ar

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ater

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Figure 7.7 Trend of oil/condensate, gas and water as captured in pipeline API 5LX-65 for year 2009

The figure has g correlation did presence in the data. e in Figure 7.7 increased

ut the trend for oil/condensate seemed to be the opposite. Gas profile was a

proven trends did exist in each variable with time, thus stron It can be said that the water profil

with time bbit fluctuated with time but by average the trend seemed to be rationally increased. The behaviours of these profiles could not be straight-forward compared to profiles as shown in Figure 7.6 earlier if the nine year old operation were to be used as a reference point. The production profiles in Figure 7.6 were only illustrations for a short term reservoir operation. Nevertheless, the increment in water and gas profiles and decrement in oil/condensate speculated that the reservoir was approaching to its end stage of operation.

141


(a)

(b)

(c)

Figure 7.8 Bivariate regression analyses for (a) defect depth and oil/condensate, (b) defect depth and gas and (c) defect depth and water

142

7.5. Model Development

Since it was the interest of the present work to investigate corrosion defect d, the next step to carry out was to apply the bivariate analysis between variable d and variables O, G and WC. The analyses resulted in graphs as displayed in Figure 7.8. The purpose of the bivariate analysis was to have some rough estimation on the likelihood to obtain relationships in the data. It could be seen from the figures that certain relationships did present in each set of variables regardless of the dispersions observed. Also included in each figure was the corresponding regression R2 value. The R2 value for the regression between d and G in particular seemed to be very small. Its contribution to the outcome of the work at this moment was not too significant as this preliminary result was meant at reporting possible estimates on the relationships observed. Nevertheless the above analysis could be improved using multivariate regression analysis for all variables. Ap-plying as simple as a linear model (even if it is multivariable) is doubted to describe well the highly nonlinear processes occurring in the CO2 corrosion (Nešić, 2007). Moreover, the performance of corrosion inhibitors is highly influenced by the unpredictable nonlinear fashion of operating variables like flow intensity, pH, metallurgy, high pressure and temperature (Hausler, 2005) of the pipeline. Thus, a nonlinear model as given below was chosen to represent the reliability-based maintenance model,

d = O 0.2339 G -0.0934 WC 0.3768CI -0.0007 (7.1)

The goodness of the above equation (model) was checked using the least-squares method once again and the correlation between dpredicted and dobserved produced an R2 value of 0.82, as shown in Figure 7.9. This high percentage revealed that most data were correlated between each other; implicitly acknowledged the proposed approaches used to carry out the analysis. It can then be said that the proposed reliability-based maintenance model which utilized an input-output model and forensic evidence ideology has been probabilisti-cally proven and acceptable as another mean of describing corrosions phenomenon.

Figure 7.9 Comparison between predicted and observed data

of multivariate regression analysis equation

143


7.6 CORROSION OPTIMIZATION TECHNIQUES

7.6.1 Interpreting Past Maintenance Practice

Recall that the reliability-based maintenance model as given by equation (7.1) allows corrosion defect depth (d) to be described as a function of water cut (WC), oil (O), gas (G) and corrosion inhibitor (CI). Also recall that the model was developed based on the CI practice that has taken place for a period of one year (2009 data). It could then be said that the model was based on an annual pipeline performance or event. This section will now introduce the ability of the model to be used as a benchmark in describing the goodness of CI performance that has been carried out in the past for maintaining the pipeline.

Describing the effect of corrosion inhibitors is not a straightforward task (Nešić, 2007). In this thesis, the performance of the maintenance practice was assumed to be probabilisti-cally described by the coefficient associated with the CI parameter in equation (7.1). Particularly for the 2009 CI data sets, the coefficient seemed to be very small with a value of -0.0007, even closer to 0. This small coefficient was then required to be looked into more details and a plot as shown in Figure 7.10 was prepared to illustrate such be-haviour. It could be seen from the figure that the amount of monthly CI practice varied significantly and inconsistent each month. Indeed this is practically acceptable as the monthly volume of CI to be released in the pipeline is subjected to the outcomes from the fluid compositions contained in the pipeline. However, it was not the intention of the present work to deliberate about this aspect. The present analysis was only concerned at addressing the occurrence or detection of CI in the pipeline during 2009 period of opera-tion. Figure 7.10 also revealed that data seemed to occupy 0 ppm values the most, which related to the absence or non-detection of CI in the pipeline system. Peaks only occurred at selected days. For better visualization, the figure was enlarged (for example) to four different months, as shown in Figure 7.11. The frequency of CI release in these four months obviously did not seem to follow any specific daily trends as well. Following this, the 2009 probability of CI non-detection trend in the pipeline was computed, as given by Figure 7.12. By average all data were found to be larger than probability of 0.8 which implied as very poor daily detection of CI in the pipeline.

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7.6. Corrosion Optimization Techniques

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Figure 7.11 Corrosion inhibitor practice at different months of year 2009

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1 2 3 4 5 6 7 8 9 10 11 12

Figure 7.12 Probability of non-detection of corrosion inhibitor (CI) in pipeline for year 2009

Figure 7.10 to Figure 7.12 agreed to the fact that there was no specific monthly release practice carried out in the pipeline. At most time the pipeline was free from the pres-ence of CI. The occurrence of peaks in Figure 7.10 for example, has proven the likeli-hood of releasing the inhibitor in large quantity at selected days. The practice seemed to be more concerned at complying with the needs of monthly targeted CI volume to be re-leased in the pipeline without really worrying much on the mechanism or approaches to carry out the work.

Coming back to the model proposed in equation (7.1), the reasonings presented in earlier paragraphs have direct impact to the very small value of coefficient associated with the CI parameter. When no specific rules or relationships present in the data sets of CI, then the corresponding correlation became poor. The effectiveness of the maintenance practice could be judged through this way as well. This indirectly provides useful infor-mation to the pipeline operators on the effect of their corrosion maintenance practice to-wards controlling corrosion development.

7.6.2 Optimizing Future Maintenance Practice

The reliability-based maintenance model based on the 2009 data will now be treated as a benchmark model for the optimization of future corrosion maintenance practice in the pipeline. This allows the present model to be further expanded. The variables driven by the nature are assumed to be ‘unchangeable’ but those governed by human activity is the one to be further improved. The variable CI would then become the main parameter to be exploited while other variables d, WC, O and G were assumed to follow similar char-acteristics to that in the original measured data. Reason being, reservoir characteristics

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and the amount of flows extracted into the pipeline were assumed to be governed by the same forces. Even if the magnitudes of each variable appear to change up to certain ex-tend in the immediate coming years (say 2010 or 2011), the degree of relationship or cor-relation embedded among variables were more or less consistent to that in year 2009, thus the bivariate regression analyses would once again result in the same answers.

In conjunction with the idea to exploit the CI variable in the proposed model, it is also important to highlight how human operational activities have direct impact towards cor-rosion maintenance and mitigation programs in the pipelines. Powell and Islam (2004) for instance, were one of a few works reporting on this impact. Their paper contrasts the corrosion monitoring programs at two crude oil and natural gas production fields which was based on extensive personal experiences at the facilities of both producers. From the comparison of both field operators, they concluded the quality of the monitor-ing program is directly related to the ability to identify potential corrosive conditions, and to implement appropriate corrosion mitigation programs, thus reducing the incidents of leaks and maintaining the integrity of the production systems. The corrosion mitiga-tion programs in this context were proportionally influenced by the quality or goodness of pipeline operators. High uptime of the corrosion injection system is critically depend-ant on the people element, particularly during operation (PETRONAS Technical Stan-dard, 2010). By adopting these findings into the present analysis, the CI practice of the present model which involved human intervention, was required to be further investi-gated.

Changing or improving the CI practice could be done in many ways. In this chapter, however, the modifications were made based on the weakness observed in the past, par-ticularly on the way the maintenance practice was carried out. The main intention of the present work was to promote more inhibitor into the pipeline, thus improving the frequency of CI occurrence in Figure 7.10 to Figure 7.12. Note that the total monthly volume of inhibitor was kept as in the original measured data sets (no change in quan-tity), but to properly distribute it instead. It was suggested that the performance of cor-rosion inhibitor is dependant on exposure time (Hong et al., 2002). Hong et al. (2002) also experimentally showed that the inhibitor becomes good corrosion protection by forming more compact inhibitor films on the metal surface at longer exposure time. Ow-ing to this, the present work suggested the inhibitor to be present in the pipeline on daily basis. The aim was to improve the probabilities of CI non-detection as computed in Figure 7.12 to become as small as possible, thus allowing more time of CI exposure to the pipeline.

Releasing the right and reasonable amount of CI into the pipeline on daily basis is not something straight-forward as it requires proper judgement and justification. In order to come out with a more realistic reasoning, the present work utilized knowledge from the physics of corrosion itself. Proper understanding on how corrosion grows with time is important in order to relate how long CI is required to stay in contact with the pipeline inner surface. Several recent experimental works that indirectly reported the physics of

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pitting corrosion development in time were considered in the analysis, namely Rivas et al. (2008), Caleyo et al. (2009) and Valor et al. (2010). Corrosion development was de-scribed by means of probability distribution functions in these works.

Figure 7.13 Pit growth as described by immersion time (Adapted from Valor et al., 2010)

Experimental results by Valor et al. (2010) on corrosion development within 30 days are as presented in Figure 7.13 above. It is interesting to note how corrosion pit grows each day even though the increment is considered to be so small. Thus it is wrong to assume corrosion daily growth as a stagnant or passive process with time. These outcomes are important as they could be implicitly applied to predict the likelihood for corrosion in-hibitor requirement in the pipeline. The proportion of inhibitor to be released on daily basis could be computed from this hypothesis as well. For instance, the present work suggested that the amount of CI to be released at a certain day (t) to be proportionally obey to the increment of corrosion growth of that same day, which can be simply ex-pressed as,

% corrosion inhibitor at day-t = % corrosion growth at day-t

Following this ideology, Table 7.4 was prepared by considering physics of corrosion growth when estimating inhibitor requirement in the pipeline. The framework was pre-pared based on a monthly practice since the CI total volume at the field was revised on a monthly basis as well. From the table, the physics of corrosion showed that higher CI (26%) needed to be released at the beginning of the month followed by moderate quan-tity throughout the remaining days/weeks.

Note that the experimental work by Valor et al. (2010) was carried out using a ‘new’ metal coupon which resembles a brand new pipeline. Since the pipeline candidate in the present work was not a newly installed pipeline, the actual amount of CI requirement was somewhat prorated accordingly. No specific rules of thumb were required to carry out such computations; so long the values were within the range provided, the selection

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should be said to be acceptable. For the sake of illustration, the so called periodically CI practice as given in Table 7.5 were chosen to suit a nine year old pipeline in operation.

Table 7.4 Monthly corrosion inhibitor requirement as determined from

experimental work by Valor et al. (2010)

Time Corrosion pit

depth

aWall loss bCumulative corrosion growth =

Cumulative inhibitor requirement

cInhibitor

require-

ment

(days) (μm) (%) (%) (%)

1 32.8 0.4 26 26

3 47.0 0.6 37 11

7 72.9 0.9 57 20

15 94.9 1.2 74 17

21 105.9 1.3 83 9

30 127.9 1.6 100 17 aOriginal wall thickness is 0.8 cm. bAssume 30 days as ending period of corrosion growth. cImplicit computation based on physics of corrosion of Valor et al. (2010)

Table 7.5 Proposed corrosion inhibitor (CI) practice for optimizing the reliability-based maintenance model

Time CI practice as in

physics of corrosion

Periodically CI

practice

Uniformly

CI practice

(days) (%) (%) (%)

1 26 10 3.33

3 11 15.5 6.66

7 20 30 13.33

15 17 28 26.66

21 9 12 20

30 17 4.5 30

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Besides the periodically practice, the present work also proposed another approach of corrosion maintenance called the uniformly CI practice, which was also included in Table 7.5. This practice was somewhat easier to be implemented in which constant daily amount of 3.33% inhibitor should be released into the pipeline throughout the month. Information in Table 7.5 could also be expanded in the form of Figure 7.14. The figure provides an overview on the monthly distributions of CI fractions (%) for each day in a month. Figure 7.15 on the other hand, illustrates the CI consumption (ppm) for the whole year. The total monthly volume of inhibitor as reported in the (original) meas-ured data sets was also included in the figure. The main intention of the proposed prac-tices was to allow CI to be presence in the pipeline every day even in small quantity be-cause the physics of corrosions have showed that the defect does evolve in daily basis.

The two proposed CI practices could now be considered as input parameter to the vari-able CI of the reliability-based maintenance model. There would be two ‘new’ CI meas-ured data sets for year 2009, each represented by the uniformly and periodically CI prac-tices. By inserting each new data set to the benchmark model, one could simulate its corresponding corrosion defect depth, d. The Monte Carlo simulation technique was ap-plied to carry out the simulation. The benchmark model in equation (7.1) was regener-ated which resulted in the corresponding new model:

d = O 0.2410 G -0.1083 WC 0.3878 CI 0.0078 (7.2)

d = O 0.2363 G -0.0977 WC 0.3798 CI 0.0012 (7.3)

with equation (7.2) for the uniformly CI practice and equation (7.3) for the periodically CI practice. The analysis was actually speculating what could possibly happen to the corrosions in the pipeline if the practice was to be done in a different way, assuming that information related to other parameters O, G and WC remained as in the original data sets. Utilizing past information but exploiting one of the parameters would be one of the reasonable approaches towards model optimization. In order to appreciate the above models, Table 7-5 illustrates the expected corrosions in the pipeline from the optimiza-tion procedures involving the past information (benchmark model) and two proposed CI practice models. Results in the table seemed to favour in the periodically practice better with the smallest mean corrosion value of 12.98%. This outcome was indeed favourable. The uniformly practice resulted in small improvement compared to the present data sets.

Table 7.6 Comparison in simulated mean corrosion depth, d for all models

Models Corrosion depth, d (%) (mm) Benchmark model 14.15 2.70 Uniformly CI practice model 14.08 2.69 Periodically CI practice model 12.98 2.48

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152

It is important to highlight here that each millimetre or inch of pipeline wall thickness depletion is considered to be a big threat to the oil and gas industry which finally may lead to failure. Failures associated to offshore pipeline leakage are something intolerable. There is proportional cost impact related to corrosions. Thus being able to ‘save’ every micro metre of pipeline wall will be highly acknowledged. In the above corrosion simula-tion results for example, it could be speculated that the periodically CI practice model will be able to sustain the wall structure better and that the maximum corrosion threat may only be achieved at later years compared to the other two models. The model could then result in less repair or failure costs.

7.7 CONCLUSIONS

The reliability-based maintenance model introduced in this chapter was meant at model-ling past information on corrosion maintenance strategy and allowing it to be exploited for optimization. The model was actually doing a probabilistic check on the effectiveness of the past maintenance approaches. In the absence of neither reliable deterministic nor probabilistic corrosion models that utilizes maintenance strategy as one of the governing parameters, the analysis has to rely on in-house information instead.

Optimizing corrosion inhibitor (CI) usage in the pipeline could be done in many ways. The present work simply applied knowledge from physics on corrosion growth to estimate the exposure time required for inhibitor to be in contact with the pipeline wall. The main intention was to allow inhibitor to be present in the pipeline on daily basis.

Cost impact on the optimised CI practice models were not critically elaborated in this chapter. Nevertheless, the advantage of simulating smaller percentage of corrosion mag-nitude (through the periodically CI practice model) has fairly answered its response to-wards the repair or maintenance costs associated to corrosion failures. The work can be further improved by incorporating costs related to the operational or energy costs, espe-cially those involving chemical injection pumps.

It is important to highlight here that the maintenance optimization approaches explained in this chapter are advisable to be applied to an annual operations or events which re-quire in-house annual quality assurance check. Unfortunately, looking at the availability of the data sets, only the 2009 production profiles could be modelled. Knowing that the production profiles of a particular reservoir change with time, the life cycle cost estimate could not be directly applied to the model. Nevertheless the present model could be used for immediate future years which may have similar reservoir contents or characteris-tics. The future maintenance practice could then be planned based on past information of the operational systems.

Chapter 8

SPATIAL CORROSION PREDICTION

8.1 INTRODUCTION

Recent discoveries in fluid-structure interactions between the external flows and circular cylinders placed close to the wall have added new values to the hydrodynamics of unbur-ied offshore pipelines placed on a seabed. The hydrodynamics of waves and/or currents introduced vortex flows surrounding the pipeline. Herein, external corrosions formed in offshore pipelines are assumed to be partly contributed by these fluid-structure interac-tions. Thus it is the intention of this chapter to highlight spatial consequences from such interactions. The present work tends to validate theories from experimental and numeri-cal studies carried out by previous researchers on fluid-structure interactions using actual data from the field.

8.2 THEORIES ON FLUID-STRUCTURE INTERACTIONS

A structure like pipeline placed in shallow waters behaves under the influence of waves and/or currents. Due to the complexity of the sea floor contours coupled with the inter-actions between the environmental effects like winds, tides, waves and currents and the shore area, it may be difficult to simply assume the most dominant flow that governs the area of interests. It may be wise in some cases to consider both effects.

Zhao et al. (2006) and Qi et al. (2006) have demonstrated the significance of vortex for-mations surrounding a circular cylinder placed on a wall. Emphasis were given to fluid-structure interactions between the external flows (current and/or waves) and unburied pipelines placed in shallow waters. The studies were looking at the response under dif-ferent vertical distances between the wall and the cylinder. The analysis in this chapter, however, was restricted to those very close to the wall (with vertical distance between the wall and the lower part of the cylinder very close to zero), resembling a pipeline laid

8 Spatial Corrosion Prediction

on the sea bed. Numerical simulations of the wave action on a horizontal circular cylin-der using the finite element method were carried out by Zhao et al. (2006). Also com-puted were the wave force coefficients and velocity fields and these were later verified with results reported by Jarno-Druaux et al. (1995). Studies by Qi et al. (2006) on the other hand, dealt with understanding vortex characteristics exerted by cross flows around a horizontal circular cylinder.

All works conformed well to the fact that when a horizontal circular cylinder is near a wall, the presence of the wall changes the symmetric flow. In the context of offshore en-gineering, the cylinder and wall represent pipeline and sea bed, respectively. The hydro-dynamics of wave and/or current around the pipeline can result in the generation of sheet vortices. A vortex, as shown in Figure 8.1 can be seen in a spiraling motion of water around a center of rotation. As the flow moves over the cylinder, the water deforms, rotates and because of the relatively high velocity, shears and forms a vortex. A group of vortex is called vortices, as illustrates in Figure 8.2, and they contain a lot of energy in the circular motion of the water. These vortices are not stable and shed alter-nately around the pipeline. The high velocity exerted by the vortex is capable to erode the external surface metal of the pipeline, in which this common scenario is also known as external corrosions.

Flow direction New starting vortex

Vortex street

New circulation

Figure 8.1 Vortex formation surrounding a circular structure

VorticesVortices

(a) (Lévêque, 2011) (b) (Information Services & Technology, 2011)

Figure 8.2 Vortex simulation at the vicinity of a circular structure

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8.2. Theories on Fluid-Structure Interactions

For pipelines very close to the sea bed with a given ratio e/D of 0.09 (approximately 0), Zhao et al. (2006) reported that both the wave crest and through produced vortex flows to the cylinder. [Here e denotes the distance between the sea bed and the lower part of the pipeline and D is the pipe diameter.] They numerically predicted the streamlines at different moments in one wave period, T. From their observations, vortex would form whenever the wave crest and through passed over the cylinder, even though these hap-pened at different moments in a single T. The locations of these vortices, however, dif-fered from each other, in which the one formed by the wave crest would take place at the downstream section of the cylinder while the other one developed upstream it. Once a vortex formed by the wave crest at t/T=0 s as show in Figure 8.3, it would undergo sev-eral phases of development accordingly: (i) increased in size and velocity (until t/T=0.25 s), (ii) reduced in velocity, and partially dissipated (t/T=0.33 s), (iii) non-dissipated vor-tex converted to the upstream, (iv) another vortex formed by wave through at the up-stream section (t/T=0.65 s) and (v) vortex at the downstream section was weaker than downstream due to cancellation effect (t/T=0.8 s). Due to high velocities in the vortex, the upper part of the cylinder for both upstream and downstream sections was believed to be prone to material loss.

Upstream Downstream

Wave crest effect

Wave trough effect

(a) (b)

Figure 8.3 Streamlines near circular cylinder at various values of t/T (shown by the number in the circle) for e/D = 0.1. (a) Numerical work by Zhao et al. (2006) (b) Experimental work

by Jarno-Druaux et al. (1995) (Adapted from Zhao et al., 2006)

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With the aid of a particle image velocimetry probe, similar vortex formation was also visualised by Qi et al. (2006). Since this work only involved cross flows and e/D was equal to 0, the location of the vortex was only limited to the downstream section of the cylinder and no flow passed under the cylinder, as shown in Figure 8.4. This huge vortex has a diameter larger than the cylinder and comprised many small vortices. These vor-tices, however, were unstable and could instantly move further downstream. Neverthe-less, they dissipated with time. It could be speculated then that the downstream section of the cylinder, especially the upper part prone to vortex activities. In the case of a pipeline in particular, such vortex activities would lead to material loss i.e. corrosions would take place.

Downstream

Figure 8.4 Vortex at downstream section of circular cylinder at e/D=0. (Here T denotes time taken by the particle image velocimetry probe to capture images, x and y are the hori-

zontal and vertical distances measured from the cylinder, respectively) (Adapted from Qi et al., 2006)

It is now understood that velocities of the flows play a significant role in the fluid-structure interactions. Previous work by Melchers (2005) amply explains how water ve-locity influences the degree of metal loss or corrosion. The author summarized contribu-tions to corrosion loss at different water velocities for sea water temperature of 20°C. Even though the work was meant for early corrosion loss, it could still provide some ba-sic ideas on the proportional impact of corrosion loss at different magnitudes of velocity. It was concluded that the higher the velocity, the greater the corrosion loss. An over-view of the results is presented in Figure 8.5. For instance, a high velocity with magni-tude of 0.45 m/s was found to give the highest corrosion loss compared to other remain-ing velocities, thus this finding can be used to support ideologies of Zhao et al. (2006) and Qi et al. (2006).

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8.3. Validation of Theories Using Field Data

Figure 8.5 Effect of water velocity on early corrosion loss (Adapted from Melchers, 2005)

8.3 VALIDATION OF THEORIES USING FIELD DATA

Theories on fluid-structure interactions presented earlier have shown the hydrodynamics of vortex in flows around a pipeline placed close to sea bed. Such interactions can be in-terpreted in many ways but it is of interest of the present work to represent this scenario from the external corrosions point of view. In order to apply this hypothesis to external corrosions, there is a need to validate it using field data. For this, an offshore pipeline containing external corrosions placed on sea bed in shallow water was chosen. Detailed descriptions about this pipeline will be presented in the next section. Simple statistical calculations were applied to summarize the external corrosion characteristics of the pipe-line.

Theories proposed by Zhao et al. (2006) and Qi et al. (2006) were compared with the field data. The authors’ works were taken to represent as the models while the pipeline candidate from the field as the prototype. It is important to highlight here about simili-tude and scaling considerations between the models and the prototype. For simplicity purpose, the analysis was not intended to consider the similitude and scaling effects but rather focus on the prediction of the spatial consequences. The idea was to look into spatial effects of corrosions on the external surfaces of the pipeline prototype by making use of knowledge obtained from those theoretical models. Direct scaling up of the mod-els’ size and characteristics would lead to certain underestimations of the expected proto-type, which was contradicted to the available information provided by the current field data.

8.3.1 Environmental Conditions

Once again the pipeline candidate applied in Chapters 4, 5 and 6 will be used in this analysis. Recall that it is a 28” diameter steel pipeline type API 5LX-65. The unburied offshore pipeline transports gas from a shallow water of approximately less than 70 m to onshore.

157


The site was at Kerteh, Terengganu, the east coast of Peninsular Malaysia, about 130 km in the South China Sea (5°50’30”N, 104°07’30”E). Figure 8.6(a) shows the location of the pipeline area, circled near Kerteh while Figure 8.6(b) provides an overview of pipelines layout near Kerteh shore line. Also provided in the latter was sea bed contours of the surrounding area.

(a)

(b)

Kerteh, Terengganu

Pipeline API 5LX-65

(b)

Figure 8.6 Study area (a) Peninsular Malaysia (Source: Google map), and (b) Shoreline of Kerteh with pipeline layouts (Source: Hydrographical map)

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8.3. Validation of Theories Using Field Data

Kerteh is a monsoon region, thus experiencing a monsoonal climate created by the influ-ences of the Southwest Monsoon in summer (Figure 8.7b) and the Northeast Monsoon in winter (Figure 8.7a). The latter is stronger than the former (Morton and Blackmore, 2001). The typhoons originated from tropical waters far to the east of Peninsular Ma-laysia and only at rare occasions have they came close to the site (Brink-Kjaer et al., 1986). Detailed descriptions on the environmental conditions of the South China Sea are given in Morton and Blackmore (2001) and Brink-Kjaer et al. (1986).

Figure 8.7 Surface currents of the South China Sea in (a) winter and (b) summer. (Adapted from Brink-Kjaer et al., 1986)

According to the 100-year return periods, the given current velocity, significant wave height and periods were 0.36 m/s, 5.3 m and 11.6 s, respectively. Water temperature is measured to be 27°C. The surface current directions within the area are as provided in Figure 8.7 and can reasonably applied to this particular site as surface currents are generally restricted to the upper 400 meters of the ocean. As addressed earlier in Mor-ton and Blackmore (2001) earlier, the dominant current direction would be in winter (Figure 8.7a), acting at a cross-flow direction to the pipeline.

8.3.2 External Interferences

Preliminary understanding of the surrounding activities near the pipeline area is neces-sary to ensure the site is free from other external interferences or threats. As reported in Nadzeri (2009), the area was free from anchor drags, vessel collisions and dropped ob-jects interferences. The area was not affected by sand erosions as well. No free span ex-ceeding the maximum allowable length was observed. Damaged caused by wave impact (splash zone) present in the pipeline but mostly taken place at the first 500 m pipeline distance as measured from the shore line.

Marine habitats such as the mangroves and seagrass beds were not found to occupy the area but coral reefs were more likely to be found in a very shallow water (~15 m). No

159


report was found to mention that the area has been experiencing nutrient pollution caused by the agricultural run-off or sewage pollution in coastal regions and oil pollution at offshore oil fields (Nadzeri, 2009). These effects, however, have only been investigated qualitatively and the relationship between nutrient levels and increased corrosion has not been quantified (Melchers, 2005).

8.3.3 External Corrosions

The pipeline was installed in 1999 and has been in operation for more than ten years. It was assumed that any defects taken place during within this period was more or less stable with the exclusion of early year defects (resulted from installation etc.). Emphasis was only given to external corrosion as its formation is mainly governed by the interac-tions between the external flows and pipeline itself.

Note that DNV-OS-F101 (2000) divides a pipeline into two sections, namely Zone 1 and 2, as sketched in Figure 8.8. The Zone 1 is the middle area that excludes 500 m upstream and downstream of the pipeline, leaving Zone 2 to cover those excluded sections.

500 m

Pipeline

500 m

Zone 1 Zone 2 Zone 2

Kerteh Platform

Figure 8.8 Longitudinal layout of the pipeline (not to scale)

A total of 307 external corrosion defects of various types were reported by the intelligent pigging (IP) tool in Zone 1 with length of 128.9 km. It was assumed that this long pipe-line has provided sufficient length to the analysis, making some predominant spatial and localized effects like marine growth and sand blasting to be reasonably ignored. Thus corrosions formation along the pipeline was only subjected to the reactions between the external flows and pipeline surface. The minimum, average and maximum wall losses were 4, 15 and 42%, respectively, calculated with respect to the actual wall thickness.

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8.4. Discussions

8.4 DISCUSSIONS

Recall that the IP tool is able to provide corrosion defect parameters in the form of pipe-line defect depth (d), longitudinal length (l) and circumferential width (w) as well as its orientation and location. The orientation is normally addressed as o’clock position with respect to pipeline cross section. Herein, spatial corrosion prediction makes use of the defect parameter d as measured from the o’clock position.

There are two stages involved in the spatial corrosion prediction analysis, namely the longitudinal and cross section checks. In the present work, the latter is assumed to be dependant on the former. This is because only uniform corrosion distribution is fa-vourable in the longitudinal section check. Without this distribution, results obtained from the cross section check will be less meaningful. Field data as introduced in Section 8.3 will be tested for illustrations on the above checks.

8.4.1 Longitudinal Section Check

Graphical presentations as shown in Figure 8.9 and Figure 8.10 provided examples of a longitudinal check in a pipeline. Note that distance of 0 km and 130 km referred to lo-cations of platform (pig launcher) and Kerteh shoreline (pig receiver), respectively. Figure 8.9 revealed that the corrosions were developed almost uniformly throughout the longitudinal length of the pipeline. Most defects were concentrated around defect depths of 20% with some severe defects approaching 40%.

Figure 8.10 provided evident that most points along the 128.9 km pipeline were filled with corrosions, with no significant empty gaps observed. An average of 20 defects could be seen at each tenth km pipeline length with high concentration observed at the first 30 km (distance from the platform). Despite this high value, in general it could be said that there was consistent occurrence of corrosions throughout the pipeline length. The rule of having uniform corrosion distribution is now achieved. This indirectly explained that the whole pipeline length was almost free from specific spatial or localized effects. Thus the corrosion could be assumed to be mainly influenced by the hydrocarbon prod-ucts transported in the pipeline.

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0

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h (%

)

Figure 8.9 Longitudinal section check in a pipeline showing defect depth (%) distributions

0

10

20

30

40

50

60

10 20 30 40 50 60 70 80 90 100 110 120 130


Num

ber

of d

efec

ts

Figure 8.10 Longitudinal section check in a pipeline showing number of defects

8.4.2 Cross Section Check

When uniform corrosion development was assured along the longitudinal pipeline dis-tance, the next step of the analysis was to understand the orientation of each defect with respect to the cross section of the pipeline, as shown in Figure 8.11. Also given in the figure was an overview of clock wise orientation, as the IP device reports each defect with respect to its o’clock position in the pipeline. From here, the corrosions were ana-lysed according to their o’clock positions and a summary of this can be found in Table 8.1 and Figure 8.12.

162

8.4. Discussions

Figure 8.11 Cross section view of a pipeline with details of o’clock orientation as reported by the IP

The pie chart shows that high concentration of defects (>20%) were found at 11 and 12, while moderate concentration (>7%) were at 1, 6, 9 and 10 and o’clock positions. Higher percentage of occurrence at certain pipeline o’clock position indirectly tells the higher tendency for that location towards failure.

Table 8.1 Number of defects at each o’clock position in the pipeline

O’clock position 1 2 3 4 5 6 7 8 9 10 11 12 Number of defects 26 17 5 16 14 22 16 14 22 25 63 66

1 o'clock268%

2 o'clock175%

3 o'clock5

2%

4 o'clock165%

5 o'clock145%

6 o'clock227%

7 o'clock165%

8 o'clock145%

9 o'clock227%

10 o'clock258%

11 o'clock63

21%

12 o'clock66

22%

Figure 8.12 Pie chart on defect distributions at individual o’clock positions

Preliminary results presented here are valuable as they enable one to conduct proper en-gineering precautions or maintenances to those locations only. Tackling the problem based on individual o’clock position of the pipeline, however, does not seem to be very economical and practical way to do. For instance, the usual form of external corrosion protection for offshore pipelines is by cathodic protection using sacrificial anodes. It normally consists of a zinc or aluminium bar cast about a steel tube and welded on to the pipeline. In the case of spatial corrosion prediction based on individual o’clock

7

1

4

5

11

10

9 3

6

12

2

Waves

Pipeline

Sea bed

Currents

8

163


position, it does not seem practical to weld every single point of concerns. It may be wise then to further expand the individual o’clock position as a group or region in order to investigate spatial corrosion prediction.

The spatial corrosion prediction defined the so called ‘region’ when representing the in-teractions between each o’clock position in space. The attempt was to group individual o’clock position based on regions. It is important to highlight here, however, that there are various ways to define the regions and this is subjected to many arguments. In this present work, the regions were proposed by incorporating the ideologies obtained from studies presented in Section 8.2 earlier.

The pipeline was divided into three unsymmetrical regions, as shown in Figure 8.13. Re-gion I which was bounded from the 10 to <3 o’clock positions was proposed to conform the fluid-structure interactions mainly governed by waves. Knowing that currents prone to mostly affected the downstream sections of the pipeline, Region II was proposed and bounded from the 6 to <10 o’clock positions. The remaining o’clock positions were cov-ered by Region III. Even though Region III was not highlighted in any reported works but it was simply adopted to cater for sea bed/soil-structure interactions.

Figure 8.13 The proposed regions for spatial corrosion prediction

Table 8.2 and Figure 8.14 provide summaries of defects taken place at each region. It can be seen that Region I occupied 64% of the pipeline area followed by Region II with 24% and Region III with 11%. Detailed discussion on each region is given in the next section.

The idea of dividing a pipeline cross section into regions seemed to be more realistic so far. Recall that the above examples utilized a pipeline candidate of type API 5LX-65. Mustaffa and Van Gelder (2010) have also showed another near shore pipeline of type API 5LX-60 agreed well to the results of API 5LX-65.

3

10

3

6Sea bed

Pipeline

Waves

Currents

I

IIIII

164

8.4. Discussions

Table 8.2 Summary of defects taken place at each region

Region O’clock positions Total defects I � 10, 11, 12, 1, 2 and <3 197 II � 6, 7, 8, 9 and <10 74 III � 3, 4, 5 and <6 35

Region I, 197, 65%

Region II, 74, 24%

Region III, 35, 11%

Figure 8.14 Pie chart on defect distributions based on proposed regions

8.4.3 Results Interpretation

Spatial corrosion prediction from this section onwards will be based on external corro-sions as grouped by Region I, II and III. Interpreting these results was not something straight forward as the actual hydrodynamics that take place at the vicinity of the pipe-line could be very complicated. Nevertheless, the explanation provided here will be en-tirely based on theories of hydrodynamics involving vortex characteristics.

Region I

When waves travel over the pipeline from the upstream to downstream sections, the area which covers Region I will be mostly affected by vortices. This complied well with the highest percentage of 64% obtained from Region I. Table 8.3 provides a summary of number of defects that occurred at certain pipeline lengths. Apparently the 11 and 12 o’clock positions contributed to the most occurrences of defects. This was indeed ex-pected after knowing how waves travel over the pipeline. The top of the pipeline has greater tendency to be ‘touched’ as the waves travel over it, with the 11 and 12 o’clock positions as points on top part of a pipeline which prone to waves’ activities.

165


Table 8.3 Number defects based on o’clock position in Region I

0 ≤ x ≤ 30 km 30 < x ≤ 60 km 60 < x ≤ 90 km 90 < x ≤ 128 km 10 o’clock 8 4 6 7 11 o’clock 34 12 11 6 12 o’clock 47 4 7 7 1 o’clock 9 4 4 9 2 o’clock 10 4 2 1

Note: x is a point at any locations along the longitudinal distance of the pipeline

Figure 8.9, Figure 8.10, and Table 8.3 earlier revealed that the first 30 km (as measured from the pig launcher location) seemed to experience more corrosions compared to other remaining lengths of the pipeline. Due to the limitation of the database, it was unlikely to verify the actual underwater condition within the vicinity of the pipeline. Neverthe-less, statistics allow to check for dependency between the o’clock position and longitudi-nal pipeline distance. The dependency check for Region I at the first 30 km was carried out using the chi-square (χ2) test of independence. It was used to determine the presence of any significant association between the variables o’clock positions and longitudinal pipeline distance. In other words, the method investigates whether corrosion develop-ment was associated with its location along the pipeline.

The procedures to carry out the chi-square (χ2) test could be simplified into four steps, namely,

1. state the hypothesis,

2. set the rejection criteria,

3. compute the test statistic, and

4. interpret results of null hypothesis.

For the first step, two hypotheses were prepared, namely a null hypothesis (Ho) and al-ternative hypothesis (Ha). The former assumes that there is no association between the two variables while the latter speculates that there is an association between the two variables. Herein the hypotheses were addressed as,

Ho: O’clock position and longitudinal distance are independent

Ha: O’clock position and longitudinal distance are dependant

For the second step, the rejection criteria requires two important parameters namely, de-gree of freedom (DF) and predetermined level of significance (confidence level). The pre-determined level of significance was assumed to be 0.05 (95% confidence level) while DF can be determined using below equation,

( 1) * ( 1DF r c= - - ) (8.1)

166

8.4. Discussions

where r is the number of levels of o’clock positions and c is the number of levels of longi-tudinal distance. Using the information presented in Table 8.4, r was counted to be 5 while c was 3, thus the resulting DF based on equation (8.1) was computed as 8. Having DF as 8 and predetermined level of significance as 0.05, the critical value (χ2

*,0.05) based on the chi-square distribution table was set to be 15.51.

To continue with the third step, it was also required to compute the expected frequency count when o’clock position is r and longitudinal distance is c (Er,c) and the chi-square test (χ2) statistic. The corresponding equations for these parameters are given below,

, ( * )/r c r cE n n= n2

,

(8.2) 2

, ,[( ) / ]r c r c r cO E Ec = S - (8.3)

where nr is the number of observations from level r of o’clock positions, nc is the number of observations from level c of longitudinal distance, n is the number of observations in the sample and Or,c is the observed frequency count when o’clock position is r and longi-tudinal distance is c.

Table 8.4 Data sets for chi-square test for independence for Region I at the first 30 km of pipeline length

0 ≤ x ≤ 10 km 10 < x ≤ 20 km 20 < x ≤ 30 km Row total 10 o’clock 3 1 4 8 11 o’clock 17 11 6 34 12 o’clock 34 11 2 47 1 o’clock 5 3 1 9 2 o’clock 9 0 1 10 Column total 68 26 14 108 Note: x is a point at any locations along the longitudinal distance of the pipeline

The Er,c could be computed as,

E1,1= (8*68)/ 108 = 3.02

E1,2= (8*26)/ 108 = 1.16

E1,3= (8*14)/ 108 = 0.62

E2,1= (34*68)/ 108 = 21.41

E2,2= (34*26)/ 108 = 8.19

E2,3= (34*14)/ 108 = 4.41

E3,1= (47*68)/ 108 = 29.59

E3,2= (47*26)/ 108 = 11.31

E3,3= (47*14)/ 108 = 6.09

E4,1= (9*68)/ 108 = 5.67

E4,2= (9*26)/ 108 = 0.75

E4,3= (9*14)/ 108 = 1.17

E5,1= (10*68)/ 108 = 6.30

E5,2= (10*26)/ 108 = 2.41

E5,3= (10*14)/ 108 = 1.30

167


Finally, the chi-square test (χ2) statistic could be obtained as,

χ2 = (3-3.02)2/3.02 + (1-1.16)2/1.16 + (4-0.62)2/0.62 +

(17-21.41)2/21.41 + (11-8.19)2/8.19 + (6-4.41)2/4.41 +

(34-29.59)2/29.59 + (11-11.31)2/11.31 + (2-6.09)2/6.09 +

(5-5.67)2/5.67 + (3-0.75)2/0.75 + (1-1.17)2/1.17 +

(9-6.30)2/6.30 + (0-2.41)2/2.41 + (1-1.30)2/1.30

= 34.79

Since the chi-square test statistic (χ2 ) 34.79 exceeds the critical value (χ2*,0.05) of 15.51,

the null hypothesis should be rejected, thus there is a statistically significant association between o’clock position and longitudinal distance at the first 30 km distance of the pipeline.

It is important to highlight here, however, that the above conclusion was entirely based on statistics computation in the absence of underwater inspection reports. It was also recommended to conduct site investigations and later to make comparison with the above findings.

Region II

Region II was proposed to allow for hydrodynamics exerted by currents originated from the upstream section. Early studies speculated that the downstream section of the pipe-line would experience high vortex activities (Qi et al., 2006). Field data seemed to agree well to this hypothesis when representing this scenario onto external corrosion impacts. About 24% of the corrosions were obtained from the analysis. Being the second largest region to be affected with corrosions, this outcome could be reasonably well accepted as the pipeline was placed in a shallow water condition which allowed waves action to be-come the dominant environmental factor.

Region III

Region III which was assumed to be governed by the sea bed/soil-structure interactions produced the least threat to external corrosions with only 11%. Apparently vortex for-mation at the upstream section of the pipeline caused by the wave trough effect resulted in mild effect towards corrosion too. It was not the interest of the present work to de-bate much neither on soil characteristics nor soil-structure interactions because their con-tributions to the outcomes of this analysis were considered to be minor.

Region Boundary Identification

It may be of concern to understand how the boundaries of each region were identified. This was actually based on qualitative judgement but still subjected to theories of fluids-

168

8.5. Conclusions

structure interactions presented at the beginning of this chapter. The work involved ex-panding the coverage of pipeline circumferential width to certain extent until the theories related to its coverage were reasonably complied. For instance, to decide whether the 10 o’clock position (i.e. downstream section of pipeline) was the best boundary for Region I and II was entirely based on how the flows ‘move’ in that section. Knowing (from theo-ries) that the downstream section of the pipeline should have mutual impacts from the waves and currents, then the 10 o’clock position was chosen simply to allow more effects from the currents because waves’ actions have been originated from the top part of the pipeline as well. For the sake of some simple quantitative computations, interested read-ers are advised to refer to Mustaffa and van Gelder (2010).

8.5 CONCLUSIONS

This chapter utilized actual field data to validate earlier theoretical (experimental and numerical) works on fluid-structure interactions between external flows (waves and/or currents) and circular cylinders (pipelines). The hydrodynamics of vortex flows pro-duced in the fluid-structure interactions were assumed to result in external corrosions on the pipeline walls. This work critically analysed the spatial consequences of corrosions by considering the defect orientations measured from the cross section of the pipeline. It was proposed to describe the corrosions distributions by regions, instead of analyzing it individually. Using expert judgements based on principles of the theoretical works, the region was defined by expanding the coverage of pipeline circumferential width to certain point.

Results from this analysis conformed well to both theories on waves and currents but the former was found to give higher impact to the pipeline probably because the structure was placed in a shallow water condition which was mostly governed by waves. Certain section of the pipeline experienced higher corrosion concentrations. It was unlikely to conduct thorough investigation on this aspect due to limitations in the field data set. This then restricted the work to be carried out based on statistics only, thus it was then subjected for improvements especially when site investigations are possible to carry out.

Two new values were added to the fluid-structure interactions between waves and/or currents and pipelines in the proposed region. It was found that (i) each o’clock position (as measured with respect to pipeline cross section) would have consistent and uniform corrosions development throughout the whole pipeline length, but (ii) more corrosions should be expected for areas governed by waves, which was mainly dominated by the 11 and 12 o’clock positions.

The analyses have proven that the idea of interpreting vortex characteristics using exter-nal corrosions on pipelines could be well accepted. A more complicated probabilistic ap-proach, however, may be required for other aspects of fluid-structure interactions as

169


170

briefly highlighted in Mustaffa et al. (2009). The updated knowledge from this fluid-structure interaction is hoped to benefit the industry and constructively incorporated into the current subsea pipeline designs.

Chapter 9

CONCLUSIONS AND RECOMMENDATIONS

The title of this thesis, System Reliability Assessment of Offshore Pipelines, portrays the application of probabilistic methods in assessing the reliability of these structures. The main intention of this thesis is to identify, apply and judge the suitability of the prob-abilistic methods in evaluating the system reliability of offshore pipelines subjected to corrosion. The analysis was first emphasized on interpreting corrosion data as random variables and probabilistic functions, through which uncertainties of the corrosion inspection tool could be taken into account. The reliability of the pipeline was initially studied by treating the structure as an independent unit. The analysis was further elaborated for pipelines arrayed as a series system of units, with the consideration of length effects. A framework for the reliability-based maintenance model was also developed in this thesis, aiming at optimizing the pipeline system operations. Herein, the analysis was mainly focused on improving the practice of releasing corrosion inhibitors into the pipeline. The use of inhibitors is considered to be the most applied maintenance practice among pipeline industries because of its simple mechanism to fight against corrosions. Last but not least, the thesis also looked into interpreting corrosions in space using theories on hydrodynamics.

Chapter 2 and 3 have fairly introduced readers to some basic theories pertaining to the main theme of this thesis. While the former describes the methodology that will be util-ized throughout the thesis, the latter acquaints some basic knowledge on corrosions in pipelines. Without doubts the two themes are too broad to be discussed. Thus, descrip-tions presented were rather simplified and straight forward, intentionally prepared to suit the content of this thesis.

When speaking about maintaining structural reliability, quite often people tend to think of sophisticated ways and apply the most updated technologies to achieve it. It has not been much attention, however, to look into the primary source of the measured data set for which the reliability computation relied on. Inspection tools can be considered as a primary mean that provides direct information to the end users on defects encountered

9 Conclusions and Recommendations

by any civil engineering structures. The tools are designed to allow tolerances, in which these could be a source of uncertainties. Tolerances given by the tools have been quali-tatively addressed as design standards and not quantitatively accounted for when pre-senting the end results of the measured data set. This scenario can be seen in an intelli-gent pigging (IP) tool, a tool that records internal and external corrosion defects devel-oped in a pipeline. The present work is aiming at illustrating some possible implications of ignoring the tolerances of an IP. Herein, the tolerances or noise are described by normally distributed random variables. Using simple mathematics, data of the noise could be incorporated into the measured data sets, allowing ‘new’ data sets to be prob-abilistically simulated. Comparisons have been made between the measured and simu-lated data sets and descriptive statistics of the two have implicitly highlighted the influ-ence of the IP tool tolerance. The proposed framework is simple and straight forward but its implications towards sustainability and reliability should not be taken for granted. Synchronizing the IP data sets should be the first step to consider so that bet-ter estimates on historical corrosion development of a particular pipeline can be achieved. These were the topics of Chapter 4.

Chapter 5 exhibits the possibilities of incorporating a more detailed description of corro-sion shape into a single equation/model. The so called reliability model for corroded pipelines was simply developed using a dimensionless limit state function (LSF) model. The intention to promote the Buckingham-π method as the most suitable method to carry out the analysis has been acknowledged when results from the proposed framework (model) have been fairly justified with the design codes and past literatures. In terms of reliability performance, the proposed model was bounded by the two most referred Modi-fied ASME B31G and DNV models. This indirectly describes the present model having similar characteristics to the two, which is indeed favourable. Implicitly, results from this chapter supports the idea of not to ignore any less important defect parameters (particularly defect circumferential width, w) because it has been proven that the pa-rameters (including defect depth, d and longitudinal length, l) do correlate with each other statistically. As one component expands in one direction, the other two will also be affected accordingly. Relationships do presence in these interactions. It is then wrong to assume that probabilistic approaches have no value at all, especially in the reli-ability assessment of corroded pipelines.

Since probabilistic modelling deals with random variables, so the goodness of the reliabil-ity model for corroded pipelines of Chapter 5 is subject to the goodness of the field data set. As much as possible, the analysis tried not to rely on other out-source data sets but only to utilize field data. Nevertheless, the fact that burst pressure (Pb) data used in that model cannot be directly obtained from the field, the analysis was then relied on burst data sets reproduced either experimentally or numerically. This model uncertainty may affect the performance of the proposed model to certain extend unless the simulated Pb data sets conformed well to the present corrosion characteristics reported from the field.

172

173

The applications of the reliability model for corroded pipelines are highlighted in Chapter 6. The model acts as a solver to pipeline operators when different corrosion scenarios needed to be tackled. From multiple pipeline sections to a single (whole) length; or even from one defect to clusters of defects; the reliability of the structure can be computed easily so long the corrosion characteristics can be statistically determined. Results showed that the probability of failures (Pf) for a pipeline cuts into several sections would be smaller compared to one section covering the whole pipeline length. In addition, a cluster of defects interacting together might provide more threats to the pipeline. The model also speculated reliability estimates when the pipeline length effect was considered in the analysis. The Pf for pipeline with length effects was expected to be higher than the one without. Probabilistic methods have proven that correlations do exist among these corroded pipeline sections. Apparently when acting as one system is series, the structure has the tendency to promote more danger to the environment.

Chapter 7 was designed using three important principles. There have been some con-cerns among pipeline operators, especially in a developing country like Malaysia about the goodness or suitability of the adapted design standards or codes to the present envi-ronment and operating conditions. There is a need in conducting a compatibility check between those proposed in the design standards and the actual situations. The absence of available resources and expertise has always been blamed for not being able to carry out the work. This should not be the case in the present time anymore because the knowledge from forensic evidence has allowed the problem to be appreciated in another aspect, provided good and reliable measured data sets are available. Valuable informa-tion can be digged up, extracted, investigated and become answers to the problems, simi-larly to what is known as ‘causes and effects’. In the context of pipeline systems experi-encing corrosions, ideologies of forensic evidence can be used to provide better under-standing on the development of corrosions as well as mechanisms to fight against them. Obeying to the fact that water can never be avoided from entering the pipeline, which resulted in corrosion formation, one of the common ways applied to fight corrosion is through the use of corrosion inhibitor. Care should be taken when applying this, know-ing the effectiveness of corrosion inhibitor in the real world application is still not certain and remain as a big issue. Consequently, the only thing left to do is to look at the main-tenance practice to release the inhibitor into the pipeline.

Chapter 7 has identified several governing factors for the development of the reliability-based maintenance model, amongst which are the transported hydrocarbon and water it-self. This could be achieved using the input-output model. Through benchmarking, cor-rosions were simulated from the model using the Monte Carlo simulation method. It is important to highlight here that the proposed model can be used as an aid to monitor the effectiveness of the present corrosion inhibitor practice. When applied to present field data set from Malaysia pipeline operations, the outcomes revealed that the practice of releasing inhibitor in the pipelines did not seem to follow specific trends, but to simply fulfil the total targeted monthly amount. Indeed this result has welcomed the idea to further exploit other approaches of inhibitor practice, aiming at optimizing the system operation and at the same time minimizing corrosion development. This thesis proposes

173

9 Conclusions and Recommendations

174

the release of inhibitor to be conducted according to physics of corrosions itself. This is because theories on corrosion physics showed that corrosions evolve every day even with micro meter increments! If the metaphor of the action-reaction law of Newtons’ law of motion were to be ‘applied’ in this context, factors expediting corrosion process should be counter parted by mechanisms fighting against it too. This hypothesis was then translated into ‘time domain’ of corrosion growth which eventually triggered the idea of simulating corrosion based on uniformly and periodically inhibitor released practices. Results showed an improvement in corrosion magnitude (as measured in corrosion depth, d mm or %) if either one of the two practices were to be replaced with the current practice in the field.

Cost implication towards the above proposed optimization techniques could not be criti-cally illustrated due to the limitation of the research database. Nevertheless, the advan-tage of simulating smaller percentages of corrosion magnitude has fairly answered its re-sponse towards the repair or maintenance costs associated to corrosion failures. It is rec-ommended that matters associated with costs to be further supported by means of cost benefit analysis (CBA), or other suitable analysis. In addition to that, if the total life cycle cost (TLCC) were to be carried out for pipeline systems, the analysis will not be straight forward. This is due to the varying reservoir production profiles with time which are proportionally related to pipeline operation systems. The TLCC can only be carried out with complete past information and reliable future predictions data.

Spatial corrosion prediction was the topic of interest of Chapter 8. It is interesting to see how simple statistic approaches could be applied to speculate corrosion formation in space. Theories on hydrodynamics of waves/currents near circular cylinder were applied to support the analysis of pipelines placed close to the sea bed. Vortex activities at the vicinity of the cylinder were assumed to imitate activities surrounding a pipeline which result in the formation of external corrosions. Even though the analysis presented involved simple statistics, the hydrodynamics theories on vortices conformed well to field data on pipelines experiencing external corrosions placed closed to the shore. It has helped to provide some preliminary insights about corrosion prediction in space. This field should be further explored probabilistically especially to cater the complicated fluid-structure interactions. Better descriptions on this aspect will lead to proper reliability estimate on pipelines subjected to external corrosions, which is also a continuation of the model proposed in Chapter 5.

The proposed frameworks in this thesis are simple and straight forward but their im-plications towards sustainability and reliability of pipeline system operations are highly acknowledged. The frameworks have proven to be able to provide better esti-mate for a time-variant process like corrosion.

APPENDIX I

Burst Test Data Set (Extracted from DnV Technical Report, 1995)

D t SMTS d l w Pb

No. (mm) (mm) (MPa) (mm) (mm) (mm) (MPa)

1 508 6.4 517 3.01 103 102 12.5

2 508 6.4 517 2.94 205 204 9.8

3 508 6.4 517 3.37 205 394 8.45

4 610 12.34 471 4.94 152 574 18.45

5 324 5.93 432 4.68 47 43 13.49

6 324 6.07 432 4.01 59 53 14.29

7 324 5.84 432 3.91 33 21 16.29

8 324 5.99 432 4.67 26 20 15.36

9 324 6 432 4.38 29 30 16.09

10 324 6.07 432 2.91 41 34 16.95

11 324 5.58 432 4.41 35 31 13

12 324 6.14 432 2.39 29 24 15.78

13 324 6.16 432 4.5 37 30 14.29

14 324 5.95 432 4.17 39 27 15.57

15 324 6.02 432 1.99 50 24 16.12

16 324 6.4 432 3.23 20 19 16.64

17 324 6.01 432 3.6 19 19 16.22

18 324 6.3 432 3.57 20 19 15.95

19 324 6.31 432 3.73 20 20 14.16

20 324 6.16 432 3.73 20 20 18.85

21 324 6.27 432 3.76 20 20 19.13

22 324 6.25 432 3.79 20 20 19.27

23 324 6.18 432 3.75 20 20 19.44

24 324 6.45 432 3.05 21 22 15.81

25 324 6.4 432 3.72 39 20 13.87

26 324 6.45 432 3.79 20 21 14.84

27 324 6.35 432 3.72 20 21 15.53

28 324 6.27 432 3.77 20 21 17.61

29 324 6.29 432 3.79 72 21 15.11

30 324 6.24 432 3.79 72 21 15.67

31 324 6.16 432 3.7 20 20 15.25

176

APPENDIX II

Descriptive Statistics of Corrosion Defects (Corrosion defects for pipeline sections with n=4)

Pipeline length (km)

0 to 30

30 to 60

Defect

parameters Section 1 2

PDF Weibull (2.02, 1.58) Lognorm (1.17, 1.03)

Mean 1.37 1.02

d

Std. dev. 0.70 0.74

PDF Lognorm (33.91, 15.74) Expon (39.99)

Mean 33.54 39.99

l

Std. dev. 13.40 33.70

PDF Weibull (0.62, 27.31) Lognorm (42.83, 32.66)

Mean 32.88 43.03

w

Std. dev. 31.69 33.25

177

178

Continue…

Pipeline length (km)

60 to 90

90 to 128

Defect

parameters Section 3 4

PDF Weibull (1.55, 1.51) Weibull (1.76, 1.14)

Mean 1.36 1.12

d

Std. dev. 0.90 0.65

PDF Lognorm (28.77, 16.96) Expon (32.16)

Mean 28.71 32.16

l

Std. dev. 17.03 25.83

PDF Weibull (0.84, 34.24) Weibull (1.07, 37.14)

Mean 36.18 36.57

w

Std. dev. 38.93 28.37

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LIST OF PUBLICATIONS

Mustaffa, Z., Van Gelder, P.H.A.J.M. and Hashim, A.M., An Insight in Spatial Corrosion Predic-tion, International Journal of Pressure Vessels and Piping, submitted.

Mustaffa, Z., Van Gelder, P.H.A.J.M. and Dawotola, A.W., A Framework in Dealing with Uncer-tainties of Corrosion Inspection Tools, Measurement, submitted.

Dawotola, A.W., Trafalis, T.B., Mustaffa, Z., Van Gelder, P.H.A.J.M. and Vrijling, J. K., Risk Based Maintenance of a Cross Country Petroleum Pipeline System, Journal of Pipeline Sys-tems Engineering and Practice, submitted.

Mustaffa, Z., Van Gelder, P.H.A.J.M., Shams, G. and Dawotola, A.W., A Dimensionless Ap-proach for the Reliability Assessment of Corrosions in Pipelines, Reliability Engineering and System Safety, submitted.

Mustaffa, Z. and Van Gelder, P.H.A.J.M., The Length-Scale Effect on System Reliability of Pipelines, Reliability Engineering and System Safety, to be submitted.

Mustaffa, Z., A Framework on Reliability-Based Maintenance Model, Reliability Engineering and System Safety, to be submitted.

Mustaffa, Z., Measuring the Effectiveness of Corrosion Maintenance in Pipelines, International Journal of Pressure Vessels and Piping, to be submitted.

Dawotola, A.W., Trafalis, T.B., Mustaffa, Z., Van Gelder, P.H.A.J.M. and Vrijling, J. K. (2011) Data-Driven Risk Based Maintenance Optimization of Petroleum Pipelines Subjected to Cor-rosion, the 21st International Offshore and Polar Engineering Conference (ISOPE), Vol 1, pp. 122-129.

Mustaffa, Z. and Van Gelder, P.H.A.J.M. (2010) Supporting New Insight in Pipeline Hydrody-namics Using Stochastic Approaches on External Corrosion Damage, the 29th International Conference on Ocean Mechanics and Arctic Engineering (OMAE).

Mustaffa, Z. and Van Gelder, P.H.A.J.M. (2010) A Review and Probabilistic Analysis of Limit State Functions of Corroded Pipelines, the 20th International Offshore and Polar Engineering Conference (ISOPE), Vol 4, pp. 625-632.

Mustaffa, Z, Van Gelder, P.H.A.J.M. and Vrijling, J. K. (2009) A Discussion of Deterministic vs. Probabilistic Method in Assessing Marine Pipeline Corrosions, the 19th International Offshore and Polar Engineering Conference (ISOPE), Vol 4, pp. 653-658.

Mustaffa, Z., Shams, G. and Van Gelder, P.H.A.J.M. (2009) Evaluating the Characteristics of Marine Pipelines Inspection Data Using Probabilistic Approach, the 7th International Probabil-istic Workshop (IPW), pp. 451-464.

Mustaffa, Z., Shams, G., Van Gelder, P.H.A.J.M. and Vrijling, J. K. (2008) Risk Assess-ment on Aging Marine Pipelines: A Probabilistic Approach, International Conference on Environment (ICENV), pp. 1-9.

INDEX OF NOTATION AND ABBREVIATIONS

Symbol Description

α Intercept of linear regression equation

β

β

Slope of linear regression equa-tion

Reliability index

βo, β1,. Regression coefficients

ε Error of linear regression equa-tion

σ Scale parameters of PDFs

α, λ Location parameters of PDFs

μ, ξ Shape parameters of PDFs

μ Mean

σ Standard deviation

Δ

Δx

Sum of squared residuals

Distance between two points

η Corrosion rate

σflow Flow stress

π

π Buckingham-π parameter

Pi = 3.142

θ* Parameter uncertainty

χ2 Chi-square test statistics

a Final pitting rate of constant

A Projected corroded area

Ao =dt

b Pitting depth scaling constant

c Corrosion rate inhibition factor

c Number of levels of longitudi-

nal distance

CaCO3 Calcium carbonate

CO2 Carbon dioxide

CO3- Carbonate ion

C.O.V Coefficient of variation

d Corrosion defect depth

D Pipe diameter

do Defect depth measured at time To

dcorr Correlation distance

e Electron

e

Ei

Es

Distance between the sea bed and the lower part of the pipe-line

Failure of component i

Failure of system

Er,c Expected frequency count when o’clock position is r and longitudinal distance is c

Fe Iron

FeCO3 Iron carbonate

Fe++ Iron ion

fx PDF of X

fR,S Joint probability function of R and S

Fx CDF of X

g Acceleration of gravity

HAc Acetic acid

H+ Hydrogen ion

Ha Alternative hypothesis

Ho Null hypothesis

H2 Hydrogen

H2O Water

H2S Hydrogen sulphide

k Constant

l Corrosion defect longitudinal length

lo Defect longitudinal length measured at time To

L Length of pipeline

M Folias/bulging factor

mf Coefficient

n Constant

n

n

Number of observations in the sample

Number of pipeline sections

nr Number of observations from level r of o’clock positions

nc Number of observations from level c of longitudinal distance

Or,c Observed frequency count when o’clock position is r and longitudinal distance is c

PCO2 CO2 partial pressure

Pcorr Allowable corroded pipe pres-sure

Pb Burst pressure

Pf Probability of failure

Po Applied/operating pressure

r Residuals

r Number of levels of o’clock po-sitions

R Strength

Rd Radial corrosion rate

RL Longitudinal corrosion rate

R2 Coefficient of determination

S Load

T Exposure time

T Any future time

T Wave period

To Time of last inspection

t Pipe wall thickness

U Velocity

w Corrosion defect circumferen-tial width

x Realization of X

x1* Bootstrap realization of X

X’ Realization of X’

y Realization of Y

Y’ Realization of Y’

Z Limit state function

192

Symbol Description

AGA American Gas Association

AXGR Axial grooving

AXSL Axial slotting

CDF Cumulative distribution func-tion

CI Corrosion inhibitor

CIGR Circumferential grooving

CISL Circumferential slotting

DF Degree of freedom

DNV Det Norske Veritas

ERF Estimated repair factor

FFS Fitness-for-service

FORM First order reliability method

G Gas

GENE General

ILI In line inspection tool

IP

IQR

LHS

Intelligent pigging

Interquantile range

Left hand side

LSF Limit state function

MCS Monte Carlo simulation

MIC Microbially-induced corrosion

MFL

MLE

MOM

Magnetic flux leakage

Maximum Likelihood Estimate

Method of Moment

O

RHS

Oil/condensate

Right hand side

SCC Stress corrosion cracking

SMTS Specified minimum tensile strength

SMYS Minimum specified yield stress

SORM Second order reliability method

SRB Sulphate-reduced bacteria

SSE Sum of squares, error

SSR Sum of squares, regression

SST Sum of squares, total

PDF Probability density function

PF Failure pressure

PINH Pinhole

PPF Percent point function

TLC Top-of-line corrosion

W Water

WC Water cut

LIST OF FIGURES

Figure 1.1 Different types of pipeline hazards ...................................................... 14 Figure 1.2 Pipeline failures, by reported cause, as compiled by the Committee

on the Safety of Marine Pipelines (1994).......................................... 15 Figure 1.3 Oil spill disasters (a) Extinguished efforts to control a Deepwater

Horizon rig that caught fire and finally sank in April 2010 in the USA (Kedrosky, 2011) (b) Concerned researchers and scientists investigating the 2010 oil spills in the Gulf of Mexico (The Most Important News, 2011) ..................................................................... 16

Figure 1.4 Fault tree analysis for offshore pipeline ............................................... 17 Figure 1.5 Distribution of oil and natural gas reserves among the world's 50

largest oil companies. (Wikipedia: Petroleum Industry, 2011).......... 19 Figure 1.6 Traditional (deterministic) approach of safety analysis considered in

engineering system (Adapted and modified from Singh et al., 2007) 21 Figure 1.7 Comparison in load and strength from two different methods............. 21 Figure 1.8 Risk matrix applied in the qualitative risk assessment ........................ 22 Figure 1.9 Brief illustration on candidate pipelines utilized in different chapters

of the thesis ...................................................................................... 25 Figure 2.1 Different types of probability distribution functions plotted based on

corrosion defect depth (d, measured in %); with best fit taken from a lognormal distribution function. .................................................... 32

Figure 2.2 Scattergram of two random variables x and y ..................................... 36 Figure 2.3 Failure space as a function of basic variables ...................................... 41 Figure 2.4 Illustration of numerical integration and Monte Carlo sampling

(Adapted and modified from Korving, 2004).................................... 43 Figure 2.5 Representations of series system.......................................................... 44 Figure 2.6 Representations of parallel system....................................................... 45 Figure 3.1 (a)(b) Examples of pipeline failures due to internal corrosions

(Institute for Energy Technology, 2011) (c) Sketch on irregular length, width, and depth of a typical corrosion defect (Adapted from Cosham et al., 2007) ................................................................ 49

Figure 3.2 Laboratory illustrations on pit corrosions (Adapted and modified from Rivas et al., 2008) .................................................................... 49

Figure 3.3 Different forms of corrosion developed on a particular metal surface (Adapted and modified from Freeman, 2002) ................................... 49

Figure 3.4 Different types of scales formed in pipelines (Adapted from Bufton and Cochran, 2008) .......................................................................... 52

Figure 3.5 Laboratory work by Nešić, and Lee (2003) showing a cross section of a steel specimen including an iron carbonate scale acting as a barrier to corrosion (Adapted from Nešić, and Lee, 2003) ................ 52

Figure 3.6 Different flow regimes that may present in multiphase flows (Adapted from Zhou, 1993) .............................................................. 53

Figure 3.7 Water vapour condensation of internal pipeline wall ........................... 54 Figure 3.8 Example of hydrates formed in pipelines (Adapted from Bufton and

Cochran, 2008) ................................................................................. 55 Figure 3.9 Circumferential stress in a pipeline pressurized internally and

externally (Adapted and modified from Palmer and King, 2008) ..... 57 Figure 3.10 Pig cleaning philosophy ..................................................................... 63 Figure 3.11 Placing a pig in the pig trap system (United Kingdom Society for

Trenchless Technology, 2011; PETRONAS Technical Standard, 1998)................................................................................................. 63

Figure 3.12 Pig lost in pipeline (StarTrak Pipeline Technologies, Inc., 2011)....... 64 Figure 3.13 Some examples of pigging tools (Pigging Products &

Services Association, 2011)............................................................... 65 Figure 4.1 Corrosion defect distributions as captured by an intelligent pigging

(IP) tool ........................................................................................... 70 Figure 4.2 Number of defects according to categories as recorded at one IP

inspection year.................................................................................. 71 Figure 4.3 Number of defects along the longitudinal distance of pipeline as

recorded at one IP inspection year ................................................... 71 Figure 4.4 Corrosion depth, d (%) distribution along the pipeline ....................... 72 Figure 4.5 Remaining wall thickness (mm) distribution along the pipeline .......... 72 Figure 4.6 Corrosion defects mapping along the circumference (o’clock

orientation) length of pipeline ......................................................... 73 Figure 4.7 Simple statistical representation of corrosion data .............................. 74 Figure 4.8 Illustration of initial and extreme values (minimum and maximum)

of a typical normal distribution function of a histogram .................. 75 Figure 4.9 An example of probability density function of corrosion depth, d (%)

measured with respect to pipeline wall thickness.............................. 76 Figure 4.10 An example of extreme value distribution of corrosion depth, d (%)

measured with respect to pipeline wall thickness.............................. 78 Figure 4.11 Decrease in reliability over time as reduced section loss causes an

increase in the bending stress on the girders (Adapted from Estes et al., 2004) ...................................................................................... 79

196

Figure 4.12 Realization of a continuous random load process Q(t) and the potential exceedence of the deteriorating structural resistance R(t) (Adapted from Melchers, 2005) ........................................................ 80

Figure 4.13 Experimental works by Rivas et al. (2008) showing the growth of pit depth over time at different exposure times (Adapted from Rivas et al., 2008)............................................................................. 80

Figure 4.14 Historical corrosion development in an offshore pipeline at different times of operation............................................................... 81

Figure 4.15 Systematic error observed in pipeline inspection tools (Note: 1 mil ≈ 0.025 mm) (Adapted from Bea et al., 2002) ................................. 83

Figure 4.16 Corrosion data sets computed through the additive model with error, ε~N(0,0.23) ............................................................................. 87

Figure 4.17 Corrosion data sets computed through the multiplicative model with error, ε~N(1,0.23) ..................................................................... 88

Figure 4.18 Graphical comparison in the performance of additive and multiplicative models, as measured using reliability index (β) parameter ......................................................................................... 89

Figure 5.1 Proposed hypothesis for the development of the model....................... 97 Figure 5.2 Bivariate regressions for pipeline API 5LX-65..................................... 98 Figure 5.3 Results obtained from multivariate regression analysis for pipeline

API 5LX-65 containing internal defects (a) Comparison between predicted and observed data (b) Histogram of the standardised residual (c) Residuals scatterplot.................................................... 100

Figure 5.4 Results obtained from multivariate regression analysis for pipeline API 5LX-65 containing external defects (a) Comparison between predicted and observed data (b) Histogram of the standardised residual (c) Residuals scatterplot.................................................... 101

Figure 5.5 Pipeline design parameters and corrosion length scales, as seen from the longitudinal view of pipeline (not to scale)............................... 105

Figure 5.6 Pipeline design parameters and corrosion length scales (a) Cross section view of pipeline, and (b) Part of pipeline cut-open, showing defect as seen from plan view (not to scale) ................................... 105

Figure 5.7 Histogram and normal quantile-comparison plots for bootstrap replications of α1 ............................................................................. 108



Figure 5.10 Degree of sensitivity of dimensionless LSF variables ....................... 109 Figure 5.11 Probability of failure (Pf) computed for all models under varying

operating pressures ......................................................................... 110 Figure 5.12 Probability of failure (Pf) computed for all limit state functions

under varying operating pressures................................................ 112

197

Figure 5.13 Reliability index for pipeline API 5LX-65 computed using the dimensionless LSF model................................................................ 113

Figure 5.14 Cross section view of corrosion defect at pipeline wall (not to scale)115 Figure 6.1 A pipeline with length L divided into n sections (not to scale) ......... 120 Figure 6.2 Comparison in probability of failure between sectional and

individual pipeline of pipeline API 5LX-65 ................................... 121 Figure 6.3 Probability of failure computed at sections of interests of pipeline

API 5LX-65 .................................................................................... 121 Figure 6.4 Statistics (mean and standard deviation) for pipeline subdivided into

13 sections ...................................................................................... 126 Figure 6.5 Autocorrelation functions for pipeline subdivided into 13 sections.... 126 Figure 6.6 Statistics (mean) for pipeline subdivided into 128 sections ............... 127 Figure 6.7 Autocorrelation functions for pipeline subdivided into 128 sections .. 127 Figure 6.8 Comparison in probability of failure as determined from pipeline

API 5LX-65 with and without the length effects........................... 128 Figure 7.1 Framework of the reliability-based maintenance model ...................... 132 Figure 7.2 Investigation pyramid for the reliability-based maintenance model .... 133 Figure 7.3 An input-output model of a system.................................................... 134 Figure 7.4 Input–output framework for the reliability-based maintenance model134 Figure 7.5 An overview of hydrocarbon operation and reserves........................... 138 Figure 7.6 Typical oil, water, and gas production profiles (Adapted from Guo

et al., 2005) .................................................................................... 138 Figure 7.7 Trend of oil/condensate, gas and water as captured in pipeline API

5LX-65 for year 2009 ...................................................................... 141 Figure 7.8 Bivariate regression analyses for (a) defect depth and oil/condensate,

(b) defect depth and gas and (c) defect depth and water ............... 142 Figure 7.9 Comparison between predicted and observed data of multivariate

regression analysis equation............................................................ 143 Figure 7.10 Corrosion inhibitor practice carried out in year 2009 ...................... 145 Figure 7.11 Corrosion inhibitor practice at different months of year 2009.......... 145 Figure 7.12 Probability of non-detection of corrosion inhibitor (CI) in pipeline

for year 2009................................................................................... 146 Figure 7.13 Pit growth as described by immersion time (Adapted from Valor et

al., 2010)......................................................................................... 148 Figure 7.14 Monthly distributions of two proposed corrosion inhibitor (CI)

practices ......................................................................................... 150 Figure 7.15 Annual (2009) overview of proposed corrosion inhibitor (CI)

practices ......................................................................................... 150 Figure 8.1 Vortex formation surrounding a circular structure ............................ 154 Figure 8.2 Vortex simulation at the vicinity of a circular structure.................... 154

198

199

Figure 8.3 Streamlines near circular cylinder at various values of t/T (shown by the number in the circle) for e/D = 0.1. (a) Numerical work by Zhao et al. (2006) (b) Experimental work by Jarno-Druaux et al. (1995) (Adapted from Zhao et al., 2006) ........................................ 155

Figure 8.4 Vortex at downstream section of circular cylinder at e/D=0. (Here T denotes time taken by the particle image velocimetry probe to capture images, x and y are the horizontal and vertical distances measured from the cylinder, respectively) (Adapted from Qi et al., 2006)............................................................................................... 156

Figure 8.5 Effect of water velocity on early corrosion loss (Adapted from Melchers, 2005)............................................................................... 157

Figure 8.6 Study area (a) Peninsular Malaysia (Source: Google map), and (b) Shoreline of Kerteh with pipeline layouts (Source: Hydrographical map) ............................................................................................... 158

Figure 8.7 Surface currents of the South China Sea in (a) winter and (b) summer. (Adapted from Brink-Kjaer et al., 1986).......................... 159

Figure 8.8 Longitudinal layout of the pipeline (not to scale).............................. 160 Figure 8.9 Longitudinal section check in a pipeline showing defect depth (%)

distributions ................................................................................... 162 Figure 8.10 Longitudinal section check in a pipeline showing number of defects 162 Figure 8.11 Cross section view of a pipeline with details of o’clock orientation

as reported by the IP ..................................................................... 163 Figure 8.12 Pie chart on defect distributions at individual o’clock positions...... 163 Figure 8.13 The proposed regions for spatial corrosion prediction...................... 164 Figure 8.14 Pie chart on defect distributions based on proposed regions............ 165

LIST OF TABLES

Table 1.1 Reported failure causes, by product carried, as compiled by the Committee on the Safety of Marine Pipelines (1994) ....................... 15

Table 2.1 Safety levels applied in structural design .............................................. 40 Table 3.1 Types of corrosion with their characteristics......................................... 50 Table 3.2 General form of corrosion pit models ..................................................... 55 Table 3.3 Design standards on the assessment of corrosion in pipelines

(Adapted from Cosham et al., 2007) ................................................ 60 Table 4.1 Pipeline properties and corrosion characteristics .................................. 70 Table 4.2 Comparisons in IP tool tolerances at 80% probability of detection of

two tool providers............................................................................. 84 Table 4.3 Descriptive statistics of the measured and simulated corrosion data

sets computed through the additive model with error, ε~N(0,0.23) .. 87 Table 4.4 Descriptive statistics of the measured and simulated corrosion data

sets computed through the multiplicative model with error, ε~N(1,0.23) ....................................................................................... 88

Table 4.5 Comparison in the performance of additive and multiplicative models, as measured using reliability index (β) parameter ............................ 89

Table 5.1 Descriptive statistics of corrosion defects ............................................... 96 Table 5.2 Random variables of pipeline characteristics....................................... 110 Table 5.3 Design and operating parameters for pipeline API 5LX-65 based on

PETRONAS (2009)........................................................................ 113 Table 6.1 Comparison between two scenarios for the computation of correlation

distance, dcorr................................................................................... 125 Table 7.1 Matrix of benchmarking (Adapted from Andersen and Pettersen,

1996)............................................................................................... 136 Table 7.2 Steps for benchmarking procedures..................................................... 137 Table 7.3 Pipeline properties and corrosion characteristics ................................ 140 Table 7.4 Monthly corrosion inhibitor requirement as determined from

experimental work by Valor et al. (2010) ....................................... 149 Table 7.5 Proposed corrosion inhibitor (CI) practice for optimizing the

reliability-based maintenance model ............................................... 149 Table 7.6 Comparison in simulated mean corrosion depth, d for all models ....... 151 Table 8.1 Number of defects at each o’clock position in the pipeline ................. 163

202

Table 8.2 Summary of defects taken place at each region................................... 165 Table 8.3 Number defects based on o’clock position in Region I ........................ 166 Table 8.4 Data sets for chi-square test for independence for Region I at the

first 30 km of pipeline length.......................................................... 167

CURRICULUM VITAE

The author of this thesis, Engr. Zahiraniza Mustaffa, was born on August, 22, 1978 in Perak, Malaysia. She obtained her Bachelor of Engineering (Hons.) in Civil Engineering from the Universiti Teknologi Malaysia (2000) and Master of Science in Water Resources Engineering, from the University of Alberta, Canada (2003). Her earlier backgrounds are Hydraulics and Hydrology. She develops herself as an expert in risk-based modeling, probabilistic mechanics and optimization techniques through her PhD research at the Faculty of Civil Engineering and Geosciences of Delft University of Technology (TU Delft), The Netherlands (Apr 2007- Oct 2011), under the supervision of assoc. prof. dr. ir. P.H.A.J.M van Gelder (TU Delft) and promotor prof. ir. J.K. Vrijling (TU Delft). The PhD research was fully funded by the Universiti Teknologi PETRO-NAS (UTP) and partly by the Schlumberger Foundation. Being under the auspices of the Petroleum National Company in Malaysia (PETRONAS), her work on probabilistic assessment of ageing offshore pipelines has widespread opportunities for application, and may attract the interest of specialists in stochastic methods and offshore engineering. Zahiraniza is a Graduate Member of the Board of Engineer Malaysia (BEM) and Insti-tute of Engineer Malaysia (IEM). Upon completion of her PhD studies, she will continue her service as a lecturer at the Universiti Teknologi PETRONAS in Malaysia.

PROPOSITIONS Pertaining to the thesis

System Reliability Assessment of Offshore Pipelines

By

Zahiraniza Mustaffa

Delft, 19th October 2011

1. The existence of many uncertainties in pipeline engineering supports the logic of applying probabilistic approaches in the design and the assessment of these struc-tures. (this thesis)

2. Inspection of pipelines with pigging tools can increase the pipeline’s reliability

without a structural improvement of the system.

3. The Buckingham-π theorem can be used to provide a better description of corro-sion parameters. (this thesis)

4. The effectiveness of corrosion inhibitors is still subject to ambiguities and should

be of major concern. (this thesis)

5. Human attitude and intervention do influence the efficiency in pipeline mainte-nance operations. (this thesis)

6. First check if maintenance procedures are correctly applied before going to new

engineering solutions.

7. Forensic cases can benefit from using probability theory.

8. The thesis of a PhD research does contribute to individual knowledge but the contribution to collective knowledge in industry is still lacking.

9. Doing a PhD while being a single mother to a son can be very challenging but it

is actually a complementary factor towards the success of a PhD study.

10. The four seasons in a temperate country where one can look forward to the next season inspires science and art more than in a tropical area.

These propositions are regarded as opposable and defendable, and have been approved as such by the supervisor prof. drs. ir. J.K. Vrijling.

204

205

STELLINGEN Behorende bij het proefschrift

Systeem Betrouwbaarheids Beoordeling van Offshore Pijpleidingen

Van

Zahiraniza Mustaffa

Delft, 19 Oktober 2011

1. Het bestaan van vele onzekerheden in de techniek van pijpleidingen ondersteunt de logica van de toepassing van probabilistische benaderingen in het ontwerp en de beoordeling van deze constructies. (dit proefschrift)

2. Inspectie van pijpleidingen met “pigging” gereedschap kan de betrouwbaarheid van

de pijpleiding verhogen zonder een constructieve verbetering van het systeem. 3. De Buckingham-π stelling kan worden gebruikt om een betere beschrijving van cor-

rosie parameters te geven. (dit proefschrift) 4. De doeltreffendheid van corrosie-remmers is nog steeds onderworpen aan dubbel-

zinnigheden en moet een belangrijk punt van aandacht zijn. (dit proefschrift) 5. Menselijk gedrag en interventies hebben invloed op de efficiëntie van de onder-

houdswerkzaamheden van pijpleidingen. (dit proefschrift) 6. Controleer eerst of onderhoudsprocedures correct worden toegepast voordat tot

nieuwe technische oplossingen wordt overgegaan. 7. Forensische gevallen kunnen profijt hebben van het gebruik van een probabilistische

benadering. 8. Het proefschrift van een PhD onderzoek draagt bij aan individuele kennis maar een

bijdrage aan de collectieve kennis in de industrie ontbreekt nog steeds. 9. Promoveren als alleenstaande moeder van een zoon kan zeer uitdagend zijn, maar is

in feite een aanvullende factor op weg naar het succes van een PhD studie. 10. De vier seizoenen in een land met een gematigd klimaat, waar men kan uitkijken

naar het volgende seizoen, zijn een grotere bron van inspiratie voor de wetenschap en de kunsten dan een tropisch klimaat.

Deze stellingen worden opponeerbaar en verdedigbaar geacht en zijn als zodanig goedge-keurd door de promotor prof. drs. ir. J.K. Vrijling.

system reliability assessment of offshore pipelines · 2015-09-23 · intan fadzilah and their two...

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