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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
Technische Universiteit Delft
Technische Universiteit Delft
PETRONAS, Maleisië
ISBN 9789085704218
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), parentsinlaws (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 Malaysianowned 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
i
at the Peninsular Malaysia Operation (PMO): Tn. Hj. Muhammad Bidon, Mr. Mohd
Zaini Ismail, Mr. Wan Mohd Shafrizal Wan Mohd Yusof, Mr. Adli Budiman
[email protected], Mr. Mohd Shahrustami Mohd Nadzeri, Mrs. Noorhidayah Mahamud,
Mrs. Noraini Wahab, and Ms. Phong Soo Kwan.
I am indebted to many of my exUTP 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.
ii
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 timevariant processes, making the pipeline as a timedependant 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 ‘inhouse 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 inhouse 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 reliabilitybased 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 fluidstructure 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
fluidstructure interactions. The present work illustrates interesting results when those
theories are validated with pipeline data from the field. The updated knowledge from
this fluidstructure 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 reliabilitybased
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
Offshorepijpleidingen, 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 offshorepijpleidingen. 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 offshorepijpleidingen 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 ontwerpnormen of co
des. Hoewel ontwerpcodes 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 belastingsvariabelen toegepast, welke zich
onderscheidt van de toepassing met veiligheidscoëfficiënten volgens de standaard ont
werpnormen.
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 offshorepijpleidingen die aan corrosie onderworpen zijn, en later
optimale corrosie onderhoudsstrategieën te ontwikkelen. Het proefschrift is gericht op het
ontwikkelen van de zogenaamde een ‘inhouse 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
ontwerpnormen 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 ontwerpnormen. Deze beperking heeft de vele onzekerheden van het sys
teem zichtbaar gemaakt.
Aan het begin van deze proefschrift worden de onzekerheden in corrosieinspectie 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 inhouse model te ontwikkelen, wat een
beter beeld geeft van corrosie in vergelijking met de bestaande failurepressure 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 ontwerpnormen.
In deze proefschrift wordt ook de nadruk gelegd op corrosie onderhoudsstrategieën in
pijpleidingen. Onderhoud van corrosie wordt normaal gesproken uitgevoerd door het
vrijgeven van corrosie remmers 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 ontwerpnormen 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 ‘reliabilitybased 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 corrosiegroei 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 vloeistofconstructie 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 offshorepijpleidingen, dicht bij de kust,
wordt veroorzaakt door dergelijke vloeistofconstructie interacties. Het huidige werk illu
streert interessante resultaten wanneer deze theorieën worden gevalideerd met pijpleiding
gegevens uit het veld. De huidige kennis van deze vloeistofconstructie 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 corrosiescenario'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 (‘reliabilitybased 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 CO
2
Corrosion 47
3.2.1 Electrochemistry of CO
2
Corrosion..................................................... 47
3.2.2 Forms of Corrosion ............................................................................. 48
3.2.3 Parameters Affecting CO
2
Corrosion .................................................. 51
3.3 Summary on CO
2
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 TimeVariant 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 Conclusions117
x
Chapter 6 System Reliability for Corroded Pipelines 119
6.1 Introduction119
6.2 Reliability Per Pipeline Section 119
6.3 Length Effects on System Reliability of Pipelines 122
6.3.1 Correlation Distance, d
corr
................................................................. 124
6.4 Conclusions129
Chapter 7 ReliabilityBased Maintenance Model 131
7.1 Introduction131
7.2 Overview of Model131
7.3 Modelling Principles132
7.3.1 Forensic Evidence ............................................................................. 132
7.3.2 InputOutput Model ......................................................................... 134
7.3.3 Benchmarking................................................................................... 134
7.4 Model Parameter Selection137
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 Conclusions152
Chapter 8 Spatial Corrosion Prediction 153
8.1 Introduction153
8.2 Theories on FluidStructure Interactions 153
8.3 Validation of Theories Using Field Data157
8.3.1 Environmental Conditions ................................................................ 157
8.3.2 External Interferences....................................................................... 159
8.3.3 External Corrosions .......................................................................... 160
8.4 Discussions161
8.4.1 Longitudinal Section Check .............................................................. 161
8.4.2 Cross Section Check ......................................................................... 162
8.4.3 Results Interpretation....................................................................... 165
8.5 Conclusions169
Chapter 9 Conclusions and Recommendations 171
Appendix I 175
Appendix II 177
References 179
List of Publications 189
xi
xii
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.
14
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 mileslong 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 7,000square
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 knockeffect 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
impact
corrosion
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 checkup of existing pipelines is the most important preven
tive measure to insure safety and longterm 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 ‘downtime’ will result but,
importantly, assets will underperform during ‘uptime’.
• 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 remodified 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 worsecase 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). Semiquantitative (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
Strength Load
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 worstcase pipeline sce
nario. Herein the scenarios are ranked to identify the most likely failure mechanisms.
C
o
n
s
e
q
u
e
n
c
e
o
f
F
a
i
l
u
r
e
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 riskbased 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 inline
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 uptodate 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 reliabilitybased 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 Malaysianowned 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 reliabilitybased maintenance model using approaches like fo
rensic evidence and benchmarking, through which inhouse 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 5LX65, 2000,
6981 corrosion defects.
Chapter 4 Chapter 5 Chapter 6
28” x 128.9 km Gas Pipeline,
Type API 5LX65, 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 counterchecking 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 Buckinghamπ 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 (inhouse) 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 d m 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 x a = = (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 d m 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
2 Theories on Probability Methods
(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 modelsspecifically, 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 x
F x e
m s
m s
 
= (2.9)
• Fréchet or Extreme Value Type II distribution,
(( )/ )
( ; , , )
x
F x e
a
m s
m s a

 
= for x > μ, (2.10)
• Weibull or Extreme Value Type III distribution,
for x < μ, (2.11)
( ( )/ )
( ; , , )
x
F x e
a
m s
m 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
2 Theories on Probability Methods
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 threeparameter model
that combines the Gumbel, Fréchet, and Weibull maximum extreme value distributions.
It has the following cumulative distribution function:
1/
( ; , , ) exp 1
x
F x
x
m
m s x x
s

ì ü
ï ï
é ù æ ö
ï ï

÷ ï ï ç
ê ú
÷ =  + ç í ý
÷
ê ú ç
÷ ï ç ï
è ø
ê ú ï ï
ë û
ï ï î 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 subfamilies 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
causeandeffect 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 meanvalue 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) (x
i
,
y
i
), i = 1, ..., n, where x
i
is an independent variable and y
i
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 y
i
’ and can be written as,
'
1 1 2 2
( , ) ....
i o i i k ik
f x y x x x b b b b b = = + + + + +e (2.14)
for each i, where β
o
, β
1
,…., β
k
are constant regression coefficients that must be estimated
from the observed data (x
i1
, x
i2
, …, x
ik
).
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 x a 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 (Yx)= 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
2 Theories on Probability Methods
' '
( ) E Y x x a 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 i
r y y = 
i
. (2.17)
(x
i
, y
i
)
'
i i
y 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 LeastSquares method of estimation. The ‘leastsquares’ 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 leastsquares 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 leastsquares fall into two categories: linear or ordinary least squares and nonlinear
least squares, depending on whether or not the residuals are linear in all unknowns. The
linear leastsquares occurs in statistical regression analysis; it has a closedform solution.
The nonlinear 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 leastsquares 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 (y
i
’) formulated from an observed data sets (x
i
, y
i
). Rephrase the
equation into a matrix form,
y’=Xβ (2.18)
where y’ is a vector y’= {y
1
’, y
2
’, .., y
n
’}, in which each y’ is given by equation (2.14)
(predicted values), β is a vector of the regression coefficients β = {β
o
, β
1
,.., β
k
}, 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 ù
ê ú
ê ú
ê
=
ê
ê ú
ê ú
ê ú
ë û
k
ú
ú
2
The conditional variance of Y for given values x
i1
, x
i2
,…., x
ik
is assumed to be constant
for any i,
Var (Y x
i1
, x
i2
,…., x
ik
)= σ
2
(2.20)
The leastsquares method finds its optimum when the sum, ∆, of squared residuals
2
1
n
i
i
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,
2
2
1 1 2 2
1
ˆ ˆ ˆ ˆ
[ ... ] 0
n
i o i i k ik
i o
y x x x b b b b
b
=
¶D
=      =
¶
å
2
2
1 1 1 2 2
1 1
ˆ ˆ ˆ ˆ
[ ... ] 0
n
i i o i i k ik
i
x y x x x b b b b
b
=
¶D
=     
¶
å
= (2.22)
…..
2
2
1 1 2 2
1
ˆ ˆ ˆ ˆ
[ ... ] 0
n
ik i o i i k ik
i k
x y x x x b b b b
b
=
¶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,
X
T
Xβ = X
T
y (2.23)
37
2 Theories on Probability Methods
where y= {y
1
, y
2
, .., y
n
} is the observed values of Y and T is the transpose.
Premultiplying both sides of equations (2.23) by the inverse of the matrix X
T
X, we
obtain the solutions for the leastsquares estimates of the regression coefficients as,
1
ˆ
(X X) X y
T T
b

=
(2.24)
where is a (k+1) vector, ={β
o
, β
1
,.., β
k
}, with which we obtain the multiple
regression equations, in matrix form,
ˆ
b
ˆ
b
'
ˆ
y =Xb
(2.25)
In scalar form, the above equation represents a set of k multiple regression equations,
'
,
1
ˆ ˆ
k
i j ij
j
y b b
=
= +
å
x with i = 1, 2, …, n and j = 1, 2, …, k. (2.26)
where and
ˆ
o
b
ˆ
j
b are the components of . An unbiased estimate of conditional vari
ance of Y for given values of X
1
, X
2
, …., X
k
is,
ˆ
b
1 2
' 2
2
2 1
/ , ,..
( )
1 1
k
n
i i
i
Y x x x
y y
S
n k n k
=

D
= =
   
å
(2.27)
in which y
i
’
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. Lag1 scatterplot of residuals
7. DurbinWatson
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 sumofsquares terms,
2.3.5 Statistics
In statistics, the coefficient of determination, (Rsquared value, R
2
) is the explanatory
power of the regression used to judge the goodness of the predicted model to the ob
served data. The R
2
the proportion of variance ‘accounted for’, ‘expl
2
1
STR SSE
R
SST SST
= =  (2.28)
with,
as sum of squares, error
2
1
ˆ
n
i
i
SSE e
=
=
å
n
2
1
( )
i
i
SST y y
=
= 
å
as sum of squares, total (2.29)
2
1
i
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 R
2
is 1.
2.4 RELIABILITY ANALYSIS
n = sample size (number of observations)
S
It is important to keep in mind that a high R
2
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 sumofsquar 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 21. 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
2 Theories on Probability Methods
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
• Semiprobabilistic 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 sim
idealizing (linearising) a failure surface
Level I
ad) 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 availa
and 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 RSplane 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
relati
2
40
2.4. Reliability Analysis
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 (P
f
) is then
given by,
Pr( 0) Pr( )
f
P Z R = £ = ³S (2.32)
The reliability is the probability Pr(Z>0) and is therefore the complement of the prob
ability of failure,
Pr( 0) 1
f
Z > = P
(2.33)
The probability of failure can also be translated into another form,
( )
( )
(
1
2 2 2
R S
f
S R
P
m m
b
s s
é ù
 
ê ú
= F = F 
ê ú
ê ú
+
ê ú
ë 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,
( )
1 Z
f
Z
P
m
b
s

= = F (2.35)
with Φ
1
(P
f
) 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 (P
f
) 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
2 Theories on Probability Methods
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 P
f
computation for Level III is based on mathematical formulation of the subset of the
probability space. Herein, the joint probability density function f
R,S
(R,S) of the strength
and load is known and its corresponding P
f
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 S
P f R S dRdS
¥
¥ ¥
=
ò ò
(2.37)
If the strength is given by R=R(X
1
, X
2
, ..., X
m
) and the load by S=S(X
m+1
, X
m+2
, ..., X
n
),
the reliability function is a function of variables i,
Z = R–S = Z(X
1
, X
2
, ..., X
n
) (2.38)
If the strength and load are statistically independent,
Pr( ) ( ) ( ) ( ) ( )
S
f R s
P R S f R f S dR dS F S f S
¥ ¥
¥ ¥ ¥
æ ö
÷ ç
÷
ç = < = =
÷
ç
÷
÷ ç
è ø
ò ò ò
(2.39)
Or,
1 2
1 2 1 2
0
... ( ) ( )... ( ) ..
n
f X X X n
Z
P f X f X f X dX dX
<
»
òò ò
n
dX (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
2.4. Reliability Analysis
dS
dR
Strength, R
Strength, R
+
+ ++
+ +
+
+
+
++
+
+
++
+
+
+
+
+
++
+
+
+
+
+
+
+
+
+
+
+ +
+
+
+
++
+
+
+
+
+
+
+
+
Z < 0
+
+
+
++
Load, S Load, 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
2 Theories on Probability Methods
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 E
i
denotes failure of component i, then the failure of a series system is the event of,
1 2
...
s
E E E E = È È È
m
)
)
2
(2.41)
For a simple series system that contains two components, the probability of component
E
1
or component E
2
is given by,
( ) ( ) (
1 2 1 2 f
P P E E P E P E = È = +
( ) ( ) (
1 2 1
P E P E P E E = +  Ç
( ) ( ) ( )
( ) 1 2 1 2
P 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
...
s
E 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
, ... ....
f
P P E P E E P E E E P E E E

=
1 n 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 leastsquares method in choosing the best re
liability model to describe the scenarios of interests. The leastsquares 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
LMoments, the Bayesian method and others.
45
2 Theories on Probability Methods
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 CO
2
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 CO
2
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 (CO
2
) in water. The sour corrosion, on the other hand, containing or caused
by hydrogen sulphide (H
2
S) or another acid gas. This thesis is dedicated to pipelines
concerned with the CO
2
corrosions only, which is in accordance to the nature of corro
sions observed in the Peninsular Malaysia pipeline operation.
3.2.1 Electrochemistry of CO
2
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
→ H
2
(3.2)
2H
2
CO
3
+ 2e
→ H
2
+ 2HCO
3

(3.3)
and finally the overall reaction is then represented by,
Fe + CO
2
+ H
2
O → FeCO
3
+ H
2
(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
Crevice
General
corrosion
Intergranular
corrosion
Pitting
corrosion
Stress corrosion
cracking
Selective
leaching 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
3 Theories on Corrosions
Other forms of corrosion can be classified as crevice, galvanic, intergranular, velocity or
microbiallyinduced 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 metaltometal
and metaltononmetal 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 grainboundary 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.
Microbiallyinduced
corrosion (MIC)
Caused or promoted by microorganisms or living organisms,
e.g. sulphatereduced bacteria (SRB), algae or fungi.
Often associated with the presence of tubercles or slimy organic
substances.
50
3.2. Background on CO2 Corrosion
3.2.3 Parameters Affecting CO
2
Corrosion
CO
2
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 CO
2
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 CO
2
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 FeCO
3
and various types of scales (Figure 3.4) typically rich in calcium
(CaCO
3
, CaSO
4
, 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 CO
2
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 CO
2
is its partial pressure (P
CO2
). An increase in P
CO2
leads to
an increase in the corrosion rate. However, when high pH is also presence, high P
CO2
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 CO
2
. The HAc is however, a
weak acid, in which iron acetate’s solubility is so much higher than iron carbonate’s,
51
3 Theories on Corrosions
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 threephase
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
3.2. Background on CO2 Corrosion
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 topofline 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
3 Theories on Corrosions
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 lowgrade 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 9099% 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 icelike 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 CO
2
CORROSION MODELS
There have been various mathematical modelling strategies applied in estimating CO
2
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 32.
Table 3.2 General form of corrosion pit models
Model Equation Parameters
Power model d = kT
n
d = depth of corrosion pit (mm)
k = constant
n = constant
T = exposure time (yr)
Twophase model d = aT + b(1e
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
3 Theories on Corrosions
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 CO
2
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 CO
2
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.
Semiempirical 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 semiempirical 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
(σ
h
) acting on a pipeline. For this, consider a unit length (1 m long) pipeline containing
fluids with external diameter (D
o
), internal diameter (D
i
), wall thickness (t), internal
pressure (p
i
), and external pressure (p
o
), 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.
p
o
(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,
2
o o h i i
p D t p D s + = (3.5)
Arranging equation (3.5),
2
i i o o
h
p D p D
t
s

= (3.6)
Equation (3.6) gives the mean circumferential stress exactly, whatever the diameterto
thickness (D/t) ratio. There are various versions of equation (3.6) and the most widely
used is the Barlow formula, given by,
2
i
h
p D
t
s = (3.7)
D
o
D
i
p
i
t t
p
o
σ
h σ
h
p
i
57
3 Theories on Corrosions
The above formula was derived by neglecting the external pressure term p
o
D
o
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
andready way of allowing for the small variation of hoop stress through the wall thick
ness (Palmer and King, 2008). Rearranging equation (3.7),
2
h
i
t
p
D
s
= (3.8)
It can be said that that,
,
i
t
p f
D
s
æ 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 thicknesstodiameter (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
t
p PF f A
D
s
æ ö
÷ ç = =
÷
ç ÷
è
h
ø
(3.10)
Batelle developed a semiempirical 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 NG18 equation and is given by,
1
.2.
1
1
flow
o
o
A
t
A
PF
A
D
A M
s
é ù
 ê ú
ê
= ê
ê ú

ê ú
ê ú
ë û
ú
ú
(3.11)
where, A
o
=dt, M is Folias bulging factor, σ
flow
is flow stress, and d is maximum corrosion
depth. Note that the σ
h
term has been replaced by σ
flow
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, σ
flow
,
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), σ
flow
is a concept proposed in the 1960s to measure the
strength of steel in the presence of a defect. The NG18 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 σ
flow
has been proposed for several modifications, as listed below,
σ
flow
= 1.1 SMYS
σ
flow
= 1.15 SMYS
σ
flow
= 0.5 (SMYS+SMTS)
σ
flow
= SMYS + 68.95 MPa (or 10 ksi)
σ
flow
= 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 NG18 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
3 Theories on Corrosions
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
NG18
NG18
a
SMYS + 68.95 MPa
rectangle (dl)
2 4
1 0.6275 0.003375
l l
Dt Dt
æ ö æ ö
÷ ÷ ç ç
÷ ÷ +  ç ç
÷ ÷
ç ç
÷ ÷ ç ç
è ø è ø
ASME B31G NG18 1.1 SMYS parabolic (2/3dl) 2
1 0.8
l
Dt
æ ö
÷ ç
÷ + ç
÷
ç
÷ ç
è ø
Modified B31G NG18 SMYS + 68.95 MPa arbitrary (0.85dl) 2 4
1 0.6275 0.003375
l l
Dt Dt
æ ö æ ö
÷ ÷ ç ç
÷ ÷ +  ç ç
÷ ÷
ç ç
÷ ÷ ç ç
è ø è ø
RSTRENG NG18 SMYS + 68.95 MPa river bottom profile 2 4
1 0.6275 0.003375
l l
Dt Dt
æ ö æ ö
÷ ÷ ç ç
÷ ÷ +  ç ç
÷ ÷
ç ç
÷ ÷ ç ç
è ø è ø
SHELL 92 NG18 SMTS rectangle (dl) 2
1 0.8
l
Dt
æ ö
÷ ç
÷ + ç
÷
ç
÷ ç
è ø
LPC NG18 SMTS rectangle (dl) 2
1 0.31
l
Dt
æ ö
÷ ç
÷ + ç
÷
ç
÷ ç
è ø
DNVRPF101 NG18 SMTS rectangle (dl) and
river bottom profile
2
1 0.31
l
Dt
æ ö
÷ ç
÷ + ç
÷
ç
÷ ç
è ø
PCORRC
New
b
SMTS rectangle (dl) c
b
The basic equation of the PCORRC partwall NG18 failure criterion is,
1 1
,
1 1
1 1
o
o
A d
A t
d A
M M t A
q
s s s
é ù æ ö é ù æ ö
÷ ç ê ú ÷ ç ê ÷ ç ÷ ç ÷
ê ú ç ÷
ê ç ÷÷ ÷ ç ç
è ø è ø
ê ú
ê ú
= =
ê ú
ê ú
æ ö æ ö
ê ú
÷ ÷ ê ú ç ç
÷ ÷  ç ç ê ú
÷ ÷ ê ú
ç ç ÷ ç ÷÷ ç è ø ê ú
ê ú è ø
ë û
ë û
ú
ú
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 1
d l
t t
Rt
q
s s
 é ù æ ö é ù
æ ö æ ö æ ö ÷ ç ê ú
ê ú÷ ÷ ÷ ÷ ç ç ç ç
÷ ÷ ÷ ÷ =     ê ç ç ç ç ê ú÷ ÷ ÷ ÷ ç ç ç ç ÷ ÷ ÷ ÷ ç ç ç ê ú
ç è ø è ø ê ú è ø ÷÷ ç
è ø ê ú ë û
ë 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).
60
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 RPF101 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 fullscale 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 springloaded 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
3 Theories on Corrosions
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 nonintelligent 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 pickup 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
3.5. Corrosion Inspection, Maintenance and Control
Brushes of the pig
clean
Pig
Pipe wall
pipe wall
Debris 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 onethird 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
3 Theories on Corrosions
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 nonintrusive 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
3.5. Corrosion Inspection, Maintenance and Control
• 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 metalloss/corrosion devices, the
65
3 Theories on Corrosions
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
Metalloss/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 CO
2
corrosion and are
not particularly suited for situations with appreciable amounts of H
2
S. 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 5LX65
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.
70
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.
1019%; 299
2029%; 52
3039%; 22
4049%; 5
<10%; 483
<10%
1019%
2029%
3039%
4049%
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)
N
u
m
b
e
r
o
f
d
e
f
e
c
t
s
< 10%
1019%
2029%
3039%
4049%
Figure 4.3 Number of defects along the longitudinal distance of pipeline as recorded at one
IP inspection year
71
4 Corrosion Data Analysis
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
Longitudinal pipeline distance (km)
D
e
f
e
c
t
d
e
p
t
h
(
%
)
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
Longitudinal pipeline distance (km)
R
e
m
a
i
n
i
n
g
p
i
p
e
l
i
n
e
w
a
l
l
t
h
i
c
k
n
e
s
s
(
m
m
)
Allo wable remaining wall thicknes s , 12.96 mm
No minal wall 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
1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
0 10 20 30 40 50 60 70 80 90 100 110 120 130
Longitudinal pipeline distance (km)
O
'
c
l
o
c
k
o
r
i
e
n
t
a
t
i
o
n
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 fluidstructure 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 straightforward. 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.
73
4 Corrosion Data Analysis
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 yaxis 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 xaxis 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 metastable, stable and superstable 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 ‘superstable’ 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
4.3. Statistical Interpretation on Corrosion Data
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
F
r
e
q
u
e
n
c
y
o
f
d
a
t
a
M e ax. extrem
values
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
4 Corrosion Data Analysis
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, nonparametric 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 nonparametric 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
nonparametric 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
76
4.3. Statistical Interpretation on Corrosion Data
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 (CO
2
).] 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
4 Corrosion Data Analysis
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 (CO
2
) 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.
78
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 TimeVariant 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 timevariant proc
ess, making the pipeline a timedependant 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 timedependant structure can be visualised in Figure
4.11, a work by Estes et al. (2004) who studied timedependant 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)
79
4 Corrosion Data Analysis
In the case where loadings are nonstationary, 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)
80
4.4. Importance of Statistical Analysis on Corrosion Data
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 timevariant 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 8year 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
4 Corrosion Data Analysis
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 inline 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.
82
4.4. Importance of Statistical Analysis on Corrosion Data
(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+∆x. 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.
83
4 Corrosion Data Analysis
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
4.4. Importance of Statistical Analysis on Corrosion Data
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 d
d 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. σ
ε
= 0.23, 0.18,….) can be simulated,
~ (0, N
e
e (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 i
d d e = (4.3)
' x
i i
d 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
4 Corrosion Data Analysis
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.
86
4.4. Importance of Statistical Analysis on Corrosion Data
+
=
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
87
4 Corrosion Data Analysis
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
88
4.4. Importance of Statistical Analysis on Corrosion Data
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)
R
e
l
i
a
b
i
l
i
t
y
I
n
d
e
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
4 Corrosion Data Analysis
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 timedependant structure and corro
sion is a timevariant 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 straightforward. 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 timevariant 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 NG18 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 NG18 criterion was done by
Ahammed and Melchers (1996). A multiplying factor, m
f
was introduced into the equa
tion which is usually taken as between 1.10
10
and 1.15
10
.
1 /
2
1 /( )
f o
t d t
Z m SMYS P
D d tM
−
=
−
¸ ¸
(
−
(
(5.1)
Pandey (1998) has applied flow stress, σ
flow
coefficient of 1.15, thus resulting below equa
tion,
1 /
2.3
1 /( )
o
t d t
Z SMYS P
D d tM
−
=
−
¸ ¸
(
−
(
(5.2)
Ahammed (1998) and De Leon and Macías (2005) applied a different σ
flow
into their equa
tion, given by,
0 0
0 0
1 [ ( )] /
2( 68.95)
1 [ ( )] /
d
o
d
d R T T t t
Z SMYS P
D d R T T tM
¦ − + −
= +
´
− + −
¹ )
¹
−
`
(5.3)
with d=d
o
+R
d
(TT
o
) and l=l
o
+R
L
(TT
o
)
Teixeira et al. (2008) developed their model based on the results of a series small scale
experiments and 3D nonlinear finite element analysis of the burst pressure of intact and
corroded pipelines. Their model parameters were simplified using the Buckinghamπ
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 0.4
1.1* *2
[1 0.9435( / ) ( / ) ]
o
SMYS t
Z 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),
P
o
= applied/operating pressure,
d
o
= defect depth measured at time T
o
,
l
o
= defect longitudinal length measured at time T
o
,
T= any future time,
T
o
= time of last inspection,
R
d
= radial corrosion rate (=Δd/ΔT), and
R
L
= 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.
94
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. FitnessforService (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
5 Reliability Assessment on Corrosions
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
96
5.3. Dimensionless Limit State Function Model
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 Buckinghamπ 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 5LX65 mentioned earlier.
Figure 5.2(a) below proves a linear relationship between them. Both variables were posi
tively correlated with R
2
value of 0.39. This value may seem low even though good cor
97
5 Reliability Assessment on Corrosions
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 R
2
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 R
2
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 5LX65
98
5.3. Dimensionless Limit State Function Model
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
1.3
3.3
l
d
w
= (unit mm) (5.5)
In order to check the goodness of this equation, the correlation between d
predicted
and d
ob
served
was carried out using the leastsquares method (defined in Section 2.3.3) with the
corresponding R
2
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
5 Reliability Assessment on Corrosions
(a)
(b) (c)
Figure 5.3 Results obtained from multivariate regression analysis for pipeline API 5LX65
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
0.8
1.9
l
d
w
= (unit mm) (5.6)
The R
2
value between the d
predicted
and d
observed
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
5.3. Dimensionless Limit State Function Model
(a)
(b) (c)
Figure 5.4 Results obtained from multivariate regression analysis for pipeline API 5LX65
containing external defects (a) Comparison between predicted and observed data (b) Histo
gram of the standardised residual (c) Residuals scatterplot
Buckinghamπ Theorem
The Buckinghamπ 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
5 Reliability Assessment on Corrosions
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 (P
b
), 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 (P
b
) data are not
possible to be measured from the field. The P
b
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 P
b
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, flatbottomed 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, flatbottomed 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
5.3. Dimensionless Limit State Function Model
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, P
b
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
inghamπ theorem addressed their dependency as,
) , , , , , , (
1
w l d t D P SMTS f
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 (73 = 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
P
f
b
, , ,
2
π
(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 0.0104
b
P 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 (P
o
) with the SMTS.
0.8442 0.0545 0.0104
o
P t d l
Z
D 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
103
5 Reliability Assessment on Corrosions
probability of failure, P
f
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
t
p f A
D
s
æ ö
÷ ç =
÷
ç ÷
è ø
The equation explains that the internal pressure (p
i
) of a corroded pipeline can with
stand is a function of a wall thicknesstodiameter (t/D) ratio, pipeline strength (or
stress, σ
h
) 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 thicknesstodiameter (t/D) in equation 5.10
gives an estimate on the design parameters of the pipeline (Figure 5.5). The defect
depthtowall thickness (d/t) ratio represents the amount of wall losses as measured from
the pipeline cross section view (Figure 5.5). The defect longitudinal lengthto
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
5.3. Dimensionless Limit State Function Model
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 cutopen, 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
5 Reliability Assessment on Corrosions
Owing to this, this section introduces the Bootstrap method as a tool to treat parame
ters (α
1,
α
2,
α
3
) uncertainty of the dimensionless LSF model rewritten below,
1 2 3
o
P t d l
Z
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 (x
1
*, x
2
*,..., x
B
*), each consisting of n
data values drawn with replacement from x.
2. Evaluate the bootstrap corresponding to each bootstrap sample [θ*(b)=f(x
b
*) 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 α
1
, α
2
and α
3
are presented in Figure 5.7 to Figure 5.9. Two types of plots were prepared, namely his
togram and normal quantilecomparison (QQ) 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 α
1
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 α
1
value of the dimen
sionless LSF model is acceptable. Histograms for α
2
and α
3
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 α
2
and α
3
could be represented by the (i) QQ plot and
(ii) confidence intervals of the distribution. From the QQ 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.
106
5.3. Dimensionless Limit State Function Model
The 95% confidence intervals for α
2
was [0.0705, 0.0365] and α
3
was [0.0174, 0.0040],
respectively. Recall that the mean value for α
2
calculated using the leastsquare method
was 0.0545 while α
3
was 0.0104. Therefore confidence intervals of the bootstrap esti
mates were in the range of the mean values given by the leastsquare method.
In summary, the parameter’s uncertainties for α
1,
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 QQ 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
leastsquare 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.
107
5 Reliability Assessment on Corrosions
Figure 5.7 Histogram and normal quantilecomparison plots for bootstrap replications of α
1
Figure 5.8 Histogram and normal quantilecomparison plots for bootstrap replications of α
2
Figure 5.9 Histogram and normal quantilecomparison plots for bootstrap replications of α
3
108
5.3. Dimensionless Limit State Function Model
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 (P
o
) 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 (P
f
) 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 (P
o
). 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
109
5 Reliability Assessment on Corrosions
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
P
o
Operating pressure MPa Normal 1430 1.43.0
In the first comparison, the probability of failures (P
f
) 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 DNVRPF101, Modified ASME B31G, Shell 92 and
RSTRENG models. The figure illustrates the behaviour of P
f
under varying pipeline op
erating pressures (P
o
); a term that has been made dimensionless by dividing it with the
specified minimum tensile strength (SMTS) term.
Figure 5.11 Probability of failure (P
f
) computed for all models under varying
operating pressures
110
5.3. Dimensionless Limit State Function Model
It was found that P
f
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 DNVRPF101 models. The Modified
ASME B31G model falls under the ‘old’ model category while the DNVRPF101 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 fullscale 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 DNVRPF101 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
RPF101 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 wellreferred 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 P
f
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 P
f
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. NG18 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
5 Reliability Assessment on Corrosions
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 (P
f
) 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 (P
f
) and reliability index. The relationship be
tween β and P
f
is unique (Sing et al., 2007) that P
f
decreases with increasing values of β.
Typical values of β lie between 1 and 4 which corresponds to P
f
ranging from the order
of 15% to 0.003%. Nevertheless, a change in β can not be readily correlated to a change
in P
f
because their relationship is highly nonlinear (Sing et al., 2007). The choice be
tween using β or P
f
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.
112
5.3. Dimensionless Limit State Function Model
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 (P
o
). 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 5LX65 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 (P
f
=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, P
o
(MPa)
R
e
l
i
a
b
i
l
i
t
y
I
n
d
e
x
,
β
14.8
3.8
Figure 5.13 Reliability index for pipeline API 5LX65 computed using
the dimensionless LSF model
Table 5.3 Design and operating parameters for pipeline API 5LX65
based on PETRONAS (2009)
Parameters Pressure
(MPa)
Design Pressure, P
design
14.65
Maximum Allowable Operating Pressure, MAOP 12.40
Maximum Inlet Operating Pressure, P
i(max)
10.50
Minimum Inlet Operating Pressure, P
i(min)
0.75
113
5 Reliability Assessment on Corrosions
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 (P
b
) data
sets taken from the DNV Technical Report (1995). It is a comprehensive report that
114
5.3. Dimensionless Limit State Function Model
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 P
b
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 P
b
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 P
b
data for every single corrosion defect in
the field. Tests on real corrosion are more preferable than the machined grooves defects.
Once the P
b
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.
d
max
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
115
5 Reliability Assessment on Corrosions
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 interfield pipelines, for instance.
The interfield 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 undersized 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) rearrange them into another set of Buckinghamπ 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 straightforward 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 casetocase 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
5 Reliability Assessment on Corrosions
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 0.0104
o
P t d l
Z
D t w SM
− −
(
     
= −
(
  
\ . \ . \ .
(
¸ ¸
TS
Load Resistance
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
∆x =L/n
Figure 6.1 A pipeline with length L divided into n sections (not to scale)
If the same pipeline API 5LX65 (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, reapply other random variables as displayed in Table 52, but
this time fix the operating pressure to be 18 MPa (for example).
The calculations resulted in probability of failure (P
fi
) 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 51 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 P
f
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 P
f
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)
D
e
f
e
c
t
d
e
p
t
h
,
d
(
%
)
Section 1 Section 2 Section 3
P
f1
= 7.8 x 10
3
P
f3
= 5.6 x 10
3
P
f2
= 4.4 x 10
3
P
f4
= 6.7 x 10
3
Section 4
P
f
= 1.3 x 10
2
Figure 6.2 Comparison in probability of failure between sectional and individual pipeline
of pipeline API 5LX65
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)
D
e
f
e
c
t
d
e
p
t
h
,
d
(
%
)
P
f
= 5.6 x 10
2
P
f
= 6.7 x 10
2
Figure 6.3 Probability of failure computed at sections of interests of pipeline API 5LX65
121
6 System Reliability for Corroded Pipelines
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 ∆x between the two points considered.
122
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+∆x is described by,
( ) ( )
2
,
corr
x
d
R x R x x e r
æ ö
D
÷ ç
÷ ç 
÷
ç
÷÷ ç
è ø
é ù
+D =
ë û
(6.1)
with x as a characteristics under consideration, ∆x as distance between two points (in
time) which is known as the distance lag and d
corr
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 d
corr
. The d
corr
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 ith section is beta, β (for i=1,
2,…n),
( ) (
i
P F b = F  ) (6.2)
and that β is given by,
2 2
R S
Z
R S
m m m
b
s
s s

=
+
Z
= (6.3)
Then the overall failure probability is given by,
( ) ( ) ( ) ( ) ( )
2
1
1 2
1
i
P F n
r
b b b b
r
ì ü æ ö
ï ï
 ÷ ï ç
ï
÷
ç
= F  +  F   F  F 
í ÷
ç
÷
ï ï ç
÷ ç 
è ø ï ï
ï ï î þ
ï
ï
ý
(6.4)
Since
( ) ( )
2
2
1
max and and and 1
corr
x
d
i i j i
j i
corr
x
P F F P F F e
d
r
æ ö
D
÷ ç
÷ ç
÷
ç
÷÷ ç
è ø

<
æ ö
D
÷ ç
÷ = = »
ç
÷
ç
÷ ç
è ø
 ,
as well as,
2
2
1 2
corr
x
d
r
æ ö
D
÷ ç
÷ = 
ç
÷
ç
÷ ç
è ø
, whereas
1
( )
2 2
u
u f
p
= + for small u.
Therefore ( ) ( )
1
1
corr
n x
P F
d
b
b
p
ì ü
ï ï  D
ï ï
= F  + +
í ý
ï ï
ï ï î þ
(6.5)
123
6 System Reliability for Corroded Pipelines
Since
( )
 1
and
corr corr
L n L L
x n
n nd d
b b
p p
D = ¥ ,
Therefore, ( ) ( ) 1
f
corr
L
P P F
d
b
b
p
ì ü
ï ï
ï ï
= = F  + +
í ý
ï ï
ï ï î þ
(6.6)
which is independent of the number of sections n and P
f
is previously addressed as prob
ability of failure.
6.3.1 Correlation Distance, d
corr
Equation (6.6) can only be successfully achieved with the preselection of the correct d
corr
.
The d
corr
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 x r
é
+D
ë
ù
û
, 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
d
e
æ ö
D
÷ ç
÷ ç 
÷
ç
÷÷ ç
è ø
and can be calculated
manually once d
corr
is known.
Brief guidelines to aid readers on the procedures required to obtain d
corr
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 (n
1
, n
2
,… n
n
) of a pipeline, through which the
size/distance ∆x can be determined.
2. Compute the average values of corrosion depths at each section n
i
i.e. d
1
, d
2
,… d
n
.
3. Solve for autocorrelation function values for d
1
, d
2
,… d
n
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 ∆x.
6. Take a value for d
corr.
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 d
corr
until they conform to each other very well.
Basically, equation (6.1) is solved simply using trials and errors on different values of
d
corr
. The best choice for a d
corr
value is when the sum of squares, errors (SSE) (equation
124
6.3. Length Effects on System Reliability of Pipelines
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 5LX65 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 d
corr
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, d
corr
Scenario Number of
sections, n
∆x
(km)
Sum of squares, errors,
SSE
Correlation distance,
d
corr
(km)
1 13 10 0.034 85
2 128 1 2.424 65
While choosing the correct d
corr
value for pipeline candidate API 5LX65, 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 (∆x) 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, d
corr
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, d
corr
of 65 to 85
km.
125
6 System Reliability for Corroded Pipelines
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
1 2 3 4 5 6 7 8 9 10 11 12 13
Pipeline section
M
e
a
n
,
S
t
a
n
d
a
r
d
d
e
v
i
a
t
i
o
n
(
m
m
)
Mean
Standard deviation
Figure 6.4 Statistics (mean and standard deviation) for pipeline subdivided into 13 sections
Number of sections = 13
Correlation distance, d
corr
= 85 km
Sum of squares, error = 0.034

0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 2 3 4 5 6 7 8 9 10 11 12 13
Pipeline section
A
u
t
o
c
o
r
r
e
l
a
t
i
o
n
( )
2
x
d
e
D

( )
( ) , R x R x x r
é ù
+ D
ë û
Figure 6.5 Autocorrelation functions for pipeline subdivided into 13 sections
126
6.3. Length Effects on System Reliability of Pipelines
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
0 10 20 30 40 50 60 70 80 90 100 110 120
Pipeline section
M
e
a
n
(
m
m
)
Figure 6.6 Statistics (mean) for pipeline subdivided into 128 sections
Pipeline sections = 128
Correlation distance = 65 km
Sum of squares, error = 2.424
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 11 21 31 41 51 61 71 81 91 101 111 121
Pipeline sections
A
u
t
o
c
o
r
r
e
l
a
t
i
o
n
( )
2
x
d
e
D

( )
( ) , R x R x x r
é ù
+ D
ë û
Figure 6.7 Autocorrelation functions for pipeline subdivided into 128 sections
127
6 System Reliability for Corroded Pipelines
For the sake of illustration, the remaining analysis of this section assumed a correlation
distance, d
corr
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
(d
corr
) 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
d
corr
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 5LX65
with and without the length effects
128
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 (P
f
) 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 P
f
) 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 (d
corr
) 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
RELIABILITYBASED 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 costeffective 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 reliabilitybased 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 reliabilitybased maintenance model is closely integrated by three impor
tant principles, namely (1) forensic evidence, (2) inputoutput model, and (3) bench
marking. The model is designed using the ideology of forensic science while its structure
adapted the so called inputoutput model. The outcomes from both principles will be in
a form of a model describing historical corrosion development of a particular pipeline.
7 ReliabilityBased 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 reliabilitybased 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 inhouse 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 wellproven 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
ReliabilityBased
Maintenance Model
Structure
O n ptimizatio
Technique
Forensic Evidence
InputOutput Model
Benchmarking
132
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 reliabilitybased 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 reliabilitybased maintenance model
Facts and physical
evidence
Conclusions
Analysis
Optimise corrosions
P
ap es
robabilistic
proach
Sources toward + Mechanisms
against + Managerial aspects
133
7 ReliabilityBased Maintenance Model
7.3.2 InputOutput Model
The structure of the reliabilitybased maintenance model relies on a metaphor adopted
from an inputoutput model, as illustrated in Figure 7.3:
SYSTEM
Input
Output
Figure 7.3 An inputoutput 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 inputoutput structure of the reliability basedmaintenance model was
then translated by,
Pipeline characteristics,
flows, environment, and
maintenance strategy
PIPELINE
Corrosions
Figure 7.4 Input–output framework for the reliabilitybased 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
noncompetitor companies within the same in
dustry or technological area.
• Generic benchmarking: Comparison of own processes against the best
processes around, regardless of industry.
135
7 ReliabilityBased Maintenance Model
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 reliabilitybased 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 reliabilitybased 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.
137
7 ReliabilityBased Maintenance Model
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
opencircuit 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 insitu 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 reliabilitybased 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 (parame
done 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.
A
probabilistically. 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.
S
Obeying 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.
T
dency 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.
T
proposed 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
7 ReliabilityBased Maintenance Model
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 sat
Table 73 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 5LX65
Diameter: 16 inch
Wall thickness: 19.1 mm
Length: 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
T
eration. It comprised data on the amount of oil/condensate (O, unit kL/day), gas (G,
unit km
3
/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
1000
2000
3000
4000
5000
6000
7000
1

J
a
n
2
6

J
a
n
2
3

F
e
b
2
6

M
a
r
2
2

A
p
r
2
0

M
a
y
1
4

J
u
n
9

J
u
l
3

A
u
g
3
0

A
u
g
2
4

S
e
p
2
4

O
c
t
1
8

N
o
v
1
4

D
e
c
Time (dd/mm/yyyy)
O
i
l
/
C
o
n
d
e
n
s
a
t
e
,
W
a
t
e
r
(
k
L
/
d
a
y
)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
G
a
s
(
k
m
3
/
d
a
y
)
Oil/Condensate
Water
Gas
Figure 7.7 Trend of oil/condensate, gas and water as captured
in pipeline API 5LX65 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 b
bit fluctuated with time but by average the trend seemed to be rationally increased.
The behaviours of these profiles could not be straightforward 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
7 ReliabilityBased Maintenance Model
(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 R
2
value. The R
2
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 CO
2
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 reliabilitybased maintenance model,
d = O
0.2339
G
0.0934
WC
0.3768
CI
0.0007
(7.1)
The goodness of the above equation (model) was checked using the leastsquares method
once again and the correlation between d
predicted
and d
observed
produced an R
2
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 reliabilitybased maintenance model
which utilized an inputoutput 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 ReliabilityBased Maintenance Model
7.6 CORROSION OPTIMIZATION TECHNIQUES
7.6.1 Interpreting Past Maintenance Practice
Recall that the reliabilitybased 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 nondetection 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 nondetection 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.
144
7.6. Corrosion Optimization Techniques
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
1

j
a
n
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a
n
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9

j
a
n
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f
e
b
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f
e
b
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m
r
t
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6

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a
p
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r
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m
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j
u
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s
e
p
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o
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o
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n
o
v
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d
e
c
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7

d
e
c
3
1

d
e
c
Time
C
o
r
r
o
s
i
o
n
I
n
h
i
b
i
t
o
r
(
p
p
m
)
Figure 7.10 Corrosion inhibitor practice carried out in year 2009
0
20
40
60
80
100
120
140
1Feb 6Feb 11Feb 16Feb 21Feb 26Feb
C
o
r
r
o
s
i
o
n
i
n
h
i
b
i
t
o
r
(
p
p
m
)
0
20
40
60
80
100
120
140
1Apr 6Apr 11Apr 16Apr 21Apr 26Apr
(a) February (b) April
0
20
40
60
80
100
120
140
1Jul 6Jul 11Jul 16Jul 21Jul 26Jul 31Jul
C
o
r
r
o
s
i
o
n
i
n
h
i
b
i
t
o
r
(
p
p
m
)
0
20
40
60
80
100
120
140
1Sep 6Sep 11Sep 16Sep 21Sep 26Sep
(c) July (d) September
Figure 7.11 Corrosion inhibitor practice at different months of year 2009
145
7 ReliabilityBased Maintenance Model
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
P
r
o
b
a
b
i
l
i
t
y
P ro bability 0.87 0.75 0.82 0.89 0.94 0.93 0.97 0.97 0.97 0.96 0.87 1.00
1 2 3 4 5 6 7 8 9 10 11 12
Figure 7.12 Probability of nondetection 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 reliabilitybased 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
146
7.6. Corrosion Optimization Techniques
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 nondetection 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 straightforward 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
147
7 ReliabilityBased Maintenance Model
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 dayt = % corrosion growth at dayt
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
148
7.6. Corrosion Optimization Techniques
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
a
Wall loss
b
Cumulative corrosion growth =
Cumulative inhibitor requirement
c
Inhibitor
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
a
Original wall thickness is 0.8 cm.
b
Assume 30 days as ending period of corrosion growth.
c
Implicit computation based on physics of corrosion of Valor et al. (2010)
Table 7.5 Proposed corrosion inhibitor (CI) practice for optimizing the reliabilitybased
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
149
7 ReliabilityBased Maintenance Model
0
5
10
15
20
25
30
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Time(day)
C
o
r
r
o
s
i
o
n
i
n
h
i
b
i
t
o
r
(
C
I
)
r
e
l
e
a
s
e
d
(
%
)
Physics of corrosion as in Valor et al. (2010)
Uniformly CI practice
Periodically CI practice
Figure 7.14 Monthly distributions of two proposed corrosion inhibitor (CI) practices
0
2
4
6
8
10
12
14
16
1Jan 30Jan 28Feb 29Mar 27Apr 26May 24Jun 23Jul 21Aug 19Sep 18Oct 16Nov 15Dec
C
o
r
r
o
s
i
o
n
I
n
h
i
b
i
t
o
r
(
C
I
)
(
p
p
m
)
Time (ddmm)
Uniformly CI practice
Periodically CI practice
141
36
83
79
96
130
118
39
95
78
79
75
107
95
127
Figure 7.15 Annual (2009) overview of proposed corrosion inhibitor (CI) practices
150
7.6. Corrosion Optimization Techniques
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 reliabilitybased 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 75 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
151
7 ReliabilityBased Maintenance Model
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 reliabilitybased 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 inhouse 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 inhouse 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 fluidstructure 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 fluidstructure 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 fluidstructure interactions using actual
data from the field.
8.2 THEORIES ON FLUIDSTRUCTURE 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 JarnoDruaux 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
Vortices
Vortices
(a) (Lévêque, 2011) (b) (Information Services & Technology, 2011)
Figure 8.2 Vortex simulation at the vicinity of a circular structure
154
8.2. Theories on FluidStructure 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) nondissipated 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 JarnoDruaux et al. (1995) (Adapted from Zhao et al., 2006)
155
8 Spatial Corrosion Prediction
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).
156
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 fluidstructure 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 5LX65. The unburied
offshore pipeline transports gas from a shallow water of approximately less than 70 m to
onshore.
157
8 Spatial Corrosion Prediction
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 5LX65
(b)
Figure 8.6 Study area (a) Peninsular Malaysia (Source: Google map), and (b) Shoreline of
Kerteh with pipeline layouts (Source: Hydrographical map)
158
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 (BrinkKjaer et al.,
1986). Detailed descriptions on the environmental conditions of the South China Sea are
given in Morton and Blackmore (2001) and BrinkKjaer et al. (1986).
Figure 8.7 Surface currents of the South China Sea in (a) winter and (b) summer.
(Adapted from BrinkKjaer et al., 1986)
According to the 100year 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 crossflow 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
8 Spatial Corrosion Prediction
report was found to mention that the area has been experiencing nutrient pollution
caused by the agricultural runoff 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 DNVOSF101 (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.
160
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.
161
8 Spatial Corrosion Prediction
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)
D
e
f
e
c
t
d
e
p
t
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
Longitudinal distance (km)
N
u
m
b
e
r
o
f
d
e
f
e
c
t
s
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'clock
26
8%
2 o'clock
17
5%
3 o'clock
5
2%
4 o'clock
16
5%
5 o'clock
14
5%
6 o'clock
22
7%
7 o'clock
16
5%
8 o'clock
14
5%
9 o'clock
22
7%
10 o'clock
25
8%
11 o'clock
63
21%
12 o'clock
66
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
8 Spatial Corrosion Prediction
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 fluidstructure 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/soilstructure 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 5LX65.
Mustaffa and Van Gelder (2010) have also showed another near shore pipeline of type
API 5LX60 agreed well to the results of API 5LX65.
3
10
3
6
Sea bed
Pipeline
Waves
Currents
I
II
III
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
8 Spatial Corrosion Prediction
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 chisquare (χ
2
) 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 chisquare (χ
2
) 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 (H
o
) and al
ternative hypothesis (H
a
). 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,
H
o
: O’clock position and longitudinal distance are independent
H
a
: 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) * ( 1 DF 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 (χ
2
*,0.05
) based
on the chisquare 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 (E
r,c
) and the chisquare
test (χ
2
) statistic. The corresponding equations for these parameters are given below,
,
( * )/
r c r c
E n n = n
2
,
(8.2)
2
, ,
[( ) / ]
r c r c r c
O E E c = S  (8.3)
where n
r
is the number of observations from level r of o’clock positions, n
c
is the number
of observations from level c of longitudinal distance, n is the number of observations in
the sample and O
r,c
is the observed frequency count when o’clock position is r and longi
tudinal distance is c.
Table 8.4 Data sets for chisquare 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 E
r,c
could be computed as,
E
1
,
1
= (8*68)/ 108 = 3.02
E
1
,
2
= (8*26)/ 108 = 1.16
E
1
,
3
= (8*14)/ 108 = 0.62
E
2
,
1
= (34*68)/ 108 = 21.41
E
2
,
2
= (34*26)/ 108 = 8.19
E
2
,
3
= (34*14)/ 108 = 4.41
E
3
,
1
= (47*68)/ 108 = 29.59
E
3
,
2
= (47*26)/ 108 = 11.31
E
3
,
3
= (47*14)/ 108 = 6.09
E
4
,
1
= (9*68)/ 108 = 5.67
E
4
,
2
= (9*26)/ 108 = 0.75
E
4
,
3
= (9*14)/ 108 = 1.17
E
5
,
1
= (10*68)/ 108 = 6.30
E
5
,
2
= (10*26)/ 108 = 2.41
E
5
,
3
= (10*14)/ 108 = 1.30
167
8 Spatial Corrosion Prediction
Finally, the chisquare test (χ
2
) statistic could be obtained as,
χ
2
= (33.02)
2
/3.02 + (11.16)
2
/1.16 + (40.62)
2
/0.62 +
(1721.41)
2
/21.41 + (118.19)
2
/8.19 + (64.41)
2
/4.41 +
(3429.59)
2
/29.59 + (1111.31)
2
/11.31 + (26.09)
2
/6.09 +
(55.67)
2
/5.67 + (30.75)
2
/0.75 + (11.17)
2
/1.17 +
(96.30)
2
/6.30 + (02.41)
2
/2.41 + (11.30)
2
/1.30
= 34.79
Since the chisquare test statistic (χ
2
) 34.79 exceeds the critical value (χ
2
*,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/soilstructure 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 soilstructure 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 fluidstructure interactions between external flows (waves and/or
currents) and circular cylinders (pipelines). The hydrodynamics of vortex flows pro
duced in the fluidstructure 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 fluidstructure 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 fluidstructure interactions as
169
8 Spatial Corrosion Prediction
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 reliabilitybased 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 Buckinghamπ 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 outsource data sets but
only to utilize field data. Nevertheless, the fact that burst pressure (P
b
) 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
P
b
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 (P
f
) 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 P
f
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 inputoutput 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 actionreaction 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 timevariant process like corrosion.
APPENDIX I
Burst Test Data Set
(Extracted from DnV Technical Report, 1995)
D t SMTS d l w P
b
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 LengthScale Effect on System Reliability of
Pipelines, Reliability Engineering and System Safety, to be submitted.
Mustaffa, Z., A Framework on ReliabilityBased 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)
DataDriven Risk Based Maintenance Optimization of Petroleum Pipelines Subjected to Cor
rosion, the 21
st
International Offshore and Polar Engineering Conference (ISOPE), Vol 1, pp.
122129.
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 29
th
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 20
th
International Offshore and Polar Engineering
Conference (ISOPE), Vol 4, pp. 625632.
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 19
th
International Offshore
and Polar Engineering Conference (ISOPE), Vol 4, pp. 653658.
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Marine Pipelines Inspection Data Using Probabilistic Approach, the 7
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International Probabil
istic Workshop (IPW), pp. 451464.
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. 19.
INDEX OF NOTATION AND ABBREVIATIONS
Symbol Description
α
Intercept of linear regression
equation
β
β
Slope of linear regression equa
tion
Reliability index
β
o
, β
1
,.
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
∆
∆x
Sum of squared residuals
Distance between two points
η
Corrosion rate
σ
flow
Flow stress
π
π
Buckinghamπ parameter
Pi = 3.142
θ* Parameter uncertainty
χ
2
Chisquare test statistics
a Final pitting rate of constant
A Projected corroded area
A
o
=dt
b Pitting depth scaling constant
c Corrosion rate inhibition factor
c Number of levels of longitudi
nal distance
CaCO
3
Calcium carbonate
CO
2
Carbon dioxide
CO
3

Carbonate ion
C.O.V Coefficient of variation
d Corrosion defect depth
D Pipe diameter
d
o
Defect depth measured at time
T
o
d
corr
Correlation distance
e Electron
e
E
i
E
s
Distance between the sea bed
and the lower part of the pipe
line
Failure of component i
Failure of system
E
r,c
Expected frequency count
when o’clock position is r and
longitudinal distance is c
Fe Iron
FeCO
3
Iron carbonate
Fe
++
Iron ion
f
x
PDF of X
f
R,S
Joint probability function of R
and S
F
x
CDF of X
g Acceleration of gravity
HAc Acetic acid
H
+
Hydrogen ion
H
a
Alternative hypothesis
H
o
Null hypothesis
H
2
Hydrogen
H
2
O
Water
H
2
S
Hydrogen sulphide
k Constant
l Corrosion defect longitudinal
length
l
o
Defect longitudinal length
measured at time T
o
L Length of pipeline
M Folias/bulging factor
m
f
Coefficient
n Constant
n
n
Number of observations in the
sample
Number of pipeline sections
n
r
Number of observations from
level r of o’clock positions
n
c
Number of observations from
level c of longitudinal distance
O
r,c
Observed frequency count
when o’clock position is r and
longitudinal distance is c
P
CO2
CO
2
partial pressure
P
corr
Allowable corroded pipe pres
sure
P
b
Burst pressure
P
f
Probability of failure
P
o
Applied/operating pressure
r Residuals
r Number of levels of o’clock po
sitions
R Strength
R
d
Radial corrosion rate
R
L
Longitudinal corrosion rate
R
2
Coefficient of determination
S Load
T Exposure time
T Any future time
T Wave period
T
o
Time of last inspection
t Pipe wall thickness
U Velocity
w Corrosion defect circumferen
tial width
x Realization of X
x
1
* 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 Fitnessforservice
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 Microbiallyinduced 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 Sulphatereduced 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 Topofline 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 5LX65..................................... 98
Figure 5.3 Results obtained from multivariate regression analysis for pipeline
API 5LX65 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 5LX65 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 cutopen, showing
defect as seen from plan view (not to scale) ................................... 105
Figure 5.7 Histogram and normal quantilecomparison plots for bootstrap
replications of α
1
............................................................................. 108
Figure 5.8 Histogram and normal quantilecomparison plots for bootstrap
replications of α
2
............................................................................. 108
Figure 5.9 Histogram and normal quantilecomparison plots for bootstrap
replications of α
3
............................................................................. 108
Figure 5.10 Degree of sensitivity of dimensionless LSF variables ....................... 109
Figure 5.11 Probability of failure (P
f
) computed for all models under varying
operating pressures ......................................................................... 110
Figure 5.12 Probability of failure (P
f
) computed for all limit state functions
under varying operating pressures................................................ 112
197
Figure 5.13 Reliability index for pipeline API 5LX65 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 5LX65 ................................... 121
Figure 6.3 Probability of failure computed at sections of interests of pipeline
API 5LX65.................................................................................... 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 5LX65 with and without the length effects........................... 128
Figure 7.1 Framework of the reliabilitybased maintenance model ...................... 132
Figure 7.2 Investigation pyramid for the reliabilitybased maintenance model .... 133
Figure 7.3 An inputoutput model of a system.................................................... 134
Figure 7.4 Input–output framework for the reliabilitybased 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
5LX65 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 nondetection 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 JarnoDruaux 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 BrinkKjaer 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 5LX65 based on
PETRONAS (2009)........................................................................ 113
Table 6.1 Comparison between two scenarios for the computation of correlation
distance, d
corr
................................................................................... 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
reliabilitybased 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 chisquare 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
riskbased 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, 19
th
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 Buckinghamπ 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 Buckinghamπ stelling kan worden gebruikt om een betere beschrijving van cor
rosie parameters te geven. (dit proefschrift)
4. De doeltreffendheid van corrosieremmers 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.