Challenges of Oshore LNGTransfer

vorgelegt vonDiplom-Ingenieur Florian Sprenger

aus Berlin

von der Fakultat V Verkehrs- und Maschinensystemeder Technischen Universitat Berlin

zur Erlangung des akademischen Grades

Doktor der Ingenieurwissenschaften Dr.-Ing.

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr.-Ing. Andres Cura HochbaumBerichter: Prof. Dr.-Ing. Gunther F. ClaussBerichter: Prof. Dr.-Ing. Paul Uwe Thamsen

Tag der wissenschaftlichen Aussprache: 05.12.2012

Berlin 2012

D 83

Acknowledgement

This thesis was inspired by my research work for the project MPLS20 Maritime Pipe Loading System 20 at the Ocean Engineering Division ofTechnical University of Berlin. I wish to express my gratitude to all thepeople that encouraged me to work on this topic and supported me over thelast years.

First of all, I would like to thank Prof. Dr.-Ing. Gunther Clauss for hisexcellent technical and personal support. With his enthusiasm, experience inocean engineering and faith in me he always provided pathbreaking advice,valuable motivation and great freedom for my research work. Many thanksalso to my second promoter Prof. Dr.-Ing. Paul Uwe Thamsen who took timeand interest in my work despite his immense work load as vice president ofthe Technical University of Berlin as well as to the chairman of the doctorialcommittee, Prof. Dr.-Ing. Andres Cura Hochbaum.

I would like to thank my colleagues from the Ocean Engineering Divi-sion, namely Daniel Testa, Matthias Dudek and Marco Klein, for a uniquelycooperative, pleasant and entertaining working atmosphere. Special thanksgo to my friend, room mate and research partner Sascha Kosleck, who wasalways receptive for working related as well as private issues and who sharedcreative, productive, stressful and relaxing phases with me during the lastsix years. During my time in the team, Kornelia Tietze was always a cheerfuland irreplaceable support for all the administrative issues I am greatlyindebted to her. From the technical sta that built and equipped the shipmodels, I would like to thank namely Manfred Berndt and Haiko de Vries.Special thanks of course also to the team of graduate assistants for theirpersistent and reliable support during the model testing series.

Since I would not have been able to work on this exciting topic withoutthe funding of the research project MPLS20, I want to express my grat-itude to the German Federal Ministry of Economics and Technology andalso to Project Management Julich. Furthermore, I want to thank the in-volved project partners IMPaC Oshore Engineering, Nexans Deutschlandand Brugg Pipe Systems for their support.

But I owe the greatest debt of gratitude to my beloved wife Miriam, whoencouraged me and supported me with patience and sympathy through theentire working process of this thesis. I appreciate the energy she committed

ACKNOWLEDGEMENT iv

to compensate my mental and physical absence in the daily family life withour two wonderful daughters Paula and Mia. Last but not least I would liketo thank my parents Lieselotte and Bernhard Sprenger who always stoodbehind me and believed in me.

Florian Sprenger

Berlin, Dezember 2012

Abstract

Developing maritime gas elds in deep water by Floating Liqueed NaturalGas (FLNG) concepts poses demanding technical challenges. So far, nosystems are in operation but projects in the design or construction phaseare characterized by a oating terminal barge that produces, liquees andstores natural gas at the oshore location. Frequently operating shuttletankers are moored either alongside (side-by-side) or at the stern of theterminal (tandem) to receive the cryogenic liqueed cargo.

During the ooading procedure, which takes 18 to 24 hours in changingenvironmental conditions, the transfer system has to tolerate the occurringrelative motions between the terminal and the tanker. Gradually changinglling levels and free surface eects inside the tanks signicantly inuencethe seakeeping behavior of the LNG carrier.

Methods and research results published so far encompass experimentaland numerical analyses of individual aspects of the complex hydrodynamicproblem related to oshore LNG transfer. Well known work includes thedetermination of pressure peaks on tank walls caused by violent sloshing orexemplary reproductions of coupling eects between resonant internal uidmotions and wave-induced vessel motions. However, available results aremostly based on idealized conditions (two-dimensional setups, model testingwith fresh water instead of LNG) where relevant hydrodynamic eects areobserved to some extend but their consequences on the extrapolation of datato full scale operations is not fully comprehended. Due to these restrictions,most of the results obtained by current standard approaches are defectiveor at least incomplete.

In this thesis, the rst validated holistic numerical method, which cap-tures all hydrodynamic aspects that are relevant during ooading opera-tions is presented. By in-depth studies on the basis of this approach, thebackground of the occurring phenomena can be fully comprehended, whichallows accurate extrapolation of results from model scale to full scale. Com-bining the introduced method and the gained background knowledge is acritical prerequisite for the conduction of trustworthy feasibility studies andthe determination of operational ranges for FLNG projects. The selectedlinear potential theory based procedure is capable to excellently reproduceseakeeping characteristics as well as internal uid motions. The entire cal-

ABSTRACT vi

culation process is exemplarily demonstrated for the MPLS20 system in theHaltenbanken region.

By detailed numerical investigations, it is revealed for the rst time thatthe dierences between natural tank modes and sloshing-related maximumvalues in the respective motion response amplitude operators (RAO) areattributed to the ratio of rigid body mass to added mass. Here, hydrody-namic coupling of dierent degrees of freedom are a crucial factor. The mostimportant consequence from this nding is that in contrast to the well-established practice results obtained from model tests with fresh waterlling inside the tanks cannot be extrapolated to full scale operations withLNG.

Comprehensive three-dimensional analyses reveal for the rst time thatfor LNG carriers, signicant uid sloshing and body motions occur perpen-dicular to the direction of excitation. This phenomenon is caused by asym-metries of the submerged hull geometry as well as asymmetric mass distri-bution. This observation leads to the conclusion that commonly publishedidealized two-dimensional approaches are inadequate for the prediction ofthe motion behavior of vessels with partially lled tanks.

Kurzfassung

Die Erschlieung maritimer Gaslagerstatten in groen Wassertiefen durchsogenannte Floating Liqueed Natural Gas (FLNG) Konzepte stellt eine an-spruchsvolle technische Herausforderung dar. Derzeit sind noch keine der-artigen Systeme in Betrieb, verschiedene in der Planungs- oder Baupha-se bendliche Projekte zeichnen sich jedoch stets durch eine schwimmendeTerminalbarge aus, die das Gas von der Lagerstatte fordert, verussigt undzwischenspeichert. Regelmaig verkehrende Flussiggastanker machen entwe-der langsseits (side-by-side) oder am Heck des Terminals (tandem) fest undubernehmen das tiefkalte, verussigte Gas.

Wahrend dieser 18 bis 24 Stunden dauernden Verladeprozedur muss dasTransfersystem den aus den vorherrschenden Umweltbedingungen resultie-renden Relativbewegungen zwischen Terminal und Tanker standhalten. Ins-besondere das Bewegungsverhalten des Tankers wird hierbei durch die sichkontinuierlich andernden Fullstande und freien Flussigkeitsoberachen inden Ladetanks signikant beeinusst.

Bisher veroentlichte Forschungsergebnisse und Methoden umfassen dieexperimentelle und numerische Analyse von Teilaspekten der komplexen hy-drodynamischen Gesamtproblematik einer Oshore LNG-Verladeprozedur,z.B. die Ermittlung von Druckspitzen auf Tankwande durch Sloshing-Eekteoder die exemplarische Reproduktion von Kopplungseekten zwischen re-sonanten Fluidbewegungen in den Ladetanks und den seegangsinduziertenSchisbewegungen. Hierbei werden jedoch stets idealisierte Bedingungen an-genommen (zweidimensionale Betrachtungen, Modellversuche mit Wasseranstelle von LNG) und relevante hydrodynamische Phanomene zwar teil-weise beobachtet, ohne jedoch deren Einuss auf die Extrapolation von Er-gebnissen auf die Groausfuhrung vollstandig zu verstehen. Dadurch sindviele der durch heutige Standardverfahren ermittelten Resultate unbrauch-bar bzw. unvollstandig.

Mit dieser Arbeit liegt erstmals ein validiertes, ganzheitliches nume-risches Verfahren vor, welches die relevanten hydrodynamischen Aspekte, diewahrend des Verladevorgangs auftreten, vollstandig berucksichtigt. Vertie-fende Untersuchungen auf Basis dieses Verfahrens tragen zum grundlegendenVerstandnis der auftretenden Eekte bei, wodurch eine fehlerfreie Ergeb-nisextrapolation vom Modell auf die Groausfuhrung ermoglicht wird. Die

KURZFASSUNG viii

vorgestellte Methode in Kombination mit dem erlangten Hintergrundwis-sen kann als vertrauenswurdige Ausgangsbasis fur Machbarkeitsstudien undEinsatzgrenzenbestimmungen von FLNG-Projekten herangezogen werden.Es zeigt sich, dass das gewahlte lineare, auf Potentialtheorie beruhende Ver-fahren sowohl im Hinblick auf die Bewegungscharakteristika unter Einussvon freien Flussigkeitsoberachen als auch auf die Fluidauslenkungen in denTanks hervorragende Ergebnisse liefert. Der gesamte Analysevorgang wirdexemplarisch fur das MPLS20-System in der Haltenbanken-Region durch-gefuhrt.

Vertiefende numerische Untersuchungen zeigen erstmals, dass die Die-renzen zwischen Tankresonanzfrequenzen und den durch internes Sloshingverursachten Maxima der entsprechenden Bewegungsubertragungsfunktio-nen vom Verhaltnis der Festkorpermasse zur hydrodynamischen Masse desSchies abhangen. Hierbei ist die hydrodynamische Kopplung zwischen Be-wegungsfreiheitsgraden ein ausschlaggebender Faktor. Die wichtigste Schluss-folgerung aus dieser Beobachtung ist, dass Ergebnisse aus Modellversuchenoder Simulationen mit Wasser in den Ladetanks aufgrund unterschiedlicherVerhaltnisse von fester zu ussiger Masse und damit unterschiedlichenVerschiebungen der Maxima entgegen des oftmals praktizierten Vorge-hens nicht auf den realen Betrieb mit LNG extrapoliert werden konnen.

Durch umfassende dreidimensionale Analysen kann auerdem erstmalsgezeigt werden, dass bei Flussiggastankern aufgrund von Asymmetrien inder Geometrie des Unterwasserschies sowie in der Massenverteilung Tank-sloshing und dadurch induzierte, nicht zu vernachlassigende Starrkorperbe-wegungen senkrecht zur Angrisrichtung der erregenden Wellenkrafte auf-treten. Diese Beobachtung lasst den Schluss zu, dass durch eine oftmalsin der Literatur anzutreende idealisierte, zweidimensionale Betrachtungder Problemstellung keine vollstandigen Aussagen uber das Bewegungsver-halten von Schien mit teilgefullten Tanks zu treen sind.

Contents

Acknowledgement iii

Abstract v

Kurzfassung vii

List of Figures xiii

List of Tables xv

1 Introduction 1

1.1 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Marine Natural Gas Exploitation . . . . . . . . . . . . . . . . 2

1.2.1 Liquefaction Facilities . . . . . . . . . . . . . . . . . . 4

1.2.2 Reception Facilities . . . . . . . . . . . . . . . . . . . . 5

1.2.3 Cryogenic Transfer Technologies . . . . . . . . . . . . 8

1.3 The MPLS20 Project . . . . . . . . . . . . . . . . . . . . . . . 9

1.4 State-of-the-Art . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4.1 Sloshing . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4.2 Multi-Body Eects . . . . . . . . . . . . . . . . . . . . 17

1.4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 17

2 Description of the Numerical Method 21

2.1 Potential Theory . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2 Hydrodynamic Forces and Motions . . . . . . . . . . . . . . . 25

2.3 Internal Tank Eects . . . . . . . . . . . . . . . . . . . . . . . 26

2.4 Operational Limitations . . . . . . . . . . . . . . . . . . . . . 31

2.5 Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3 Hydrodynamic Challenges 37

3.1 Initial Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2 Sloshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.3 Coupling of Sloshing and Ship Motions . . . . . . . . . . . . . 45

3.3.1 Validation of the Numerical Method . . . . . . . . . . 47

CONTENTS x

3.3.2 Discussion I: Frequency Shifts . . . . . . . . . . . . . . 513.3.3 Discussion II: Asymmetries . . . . . . . . . . . . . . . 62

3.4 Multi-Body Analysis . . . . . . . . . . . . . . . . . . . . . . . 683.5 Stochastic Analysis . . . . . . . . . . . . . . . . . . . . . . . . 80

3.5.1 Worst Case Identication . . . . . . . . . . . . . . . . 813.5.2 Determination of the Operational Range . . . . . . . . 84

3.6 Excursion I: Exemplary Variations . . . . . . . . . . . . . . . 893.7 Excursion II: Mooring Analysis . . . . . . . . . . . . . . . . . 93

4 Conclusions & Consequences 99

Bibliography 110

Nomenclature 111

A Input Data for Numerical Calculations 119

B The Dynamic Magnication Factor 125

List of Figures

1.1 World energy demand (source: International Energy Agency,2008) and capital expenditure on FLNG facilities (source:Douglas Westwood Limited, 2009) . . . . . . . . . . . . . . . . 2

1.2 Current concepts for marine natural gas liquefaction (source:Shell, 2009 and Flex LNG, 2009) . . . . . . . . . . . . . . . . 4

1.3 Current concepts for marine LNG reception and regasica-tion (source: Business Wire, 2009, Excelerate Energy, 2009,www.marinelog.com, 2008 and TORP LNG, 2010) . . . . . . 6

1.4 Cryogenic transfer technologies (source: FMC Technologies,2010 and Bluewater, 2010) . . . . . . . . . . . . . . . . . . . 8

1.5 Loading procedure with the MPLS20 system in tandem con-guration (source: IMPaC Oshore Engineering, 2010) . . . 9

1.6 Prismatic tank with characteristic dimensions . . . . . . . . . 11

2.1 Cuboid tank restoring coecients . . . . . . . . . . . . . . . . 27

2.2 Cuboid tank added mass . . . . . . . . . . . . . . . . . . . . . 29

2.3 Tank surface deections for odd and even modes . . . . . . . 30

2.4 Pierson-Moskowitz versus JONSWAP spectra . . . . . . . . . 32

2.5 Probability density distribution of the maximum wave height 34

2.6 Exemplary roll decay measurement . . . . . . . . . . . . . . . 36

3.1 Discretization of the FLNG terminal and the LNGC . . . . . 37

3.2 Decrease of initial stability due to free uid surfaces . . . . . 39

3.3 Example of numerical sloshing mode determination from ab-solute values of a22,T . . . . . . . . . . . . . . . . . . . . . . . 40

3.4 Cuboid tank with characteristic dimensions . . . . . . . . . . 41

3.5 Comparison of numerical and analytical cuboid tank reso-nance frequencies . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.6 Comparison of numerical and analytical prismatic tank reso-nance frequencies . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.7 Coupling of sloshing and ship motions: motivation . . . . . . 45

3.8 Onboard camera captures of sloshing motions . . . . . . . . . 46

3.9 Equipment of the LNGC model for validation tests . . . . . . 47

LIST OF FIGURES xii

3.10 Validation of the numerical method: Body motions with 30%lling height . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.11 Validation of the numerical method: Internal uid motionsfor = 90 . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.12 Validation of the numerical method: Internal uid motionsfor = 180 . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.13 Comparison of roll motion and internal tank surface elevations 52

3.14 Schematic backtracing of the rst transverse sloshing peak shift 54

3.15 Comparison of surge motion and internal tank surface elevations 56

3.16 Schematic backtracing of the rst longitudinal sloshing peakshift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.17 Comparison of the roll and surge motion RAOs for 30% freshwater and LNG lling . . . . . . . . . . . . . . . . . . . . . . 59

3.18 Comparison of the rst sloshing mode and the motion re-sponse peaks . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.19 Comparison of the rst sloshing mode and the yaw responsepeaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.20 Internal surface elevations in tank 4 . . . . . . . . . . . . . . 63

3.21 Internal surface elevations in all four tanks . . . . . . . . . . . 64

3.22 Elimination of the asymmetries of the original LNGC hull intwo steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.23 Comparison of surge, roll and uid motions for three geome-try variants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.24 Validation of the numerical method: Further body motionswith 30% lling height . . . . . . . . . . . . . . . . . . . . . . 67

3.25 Approach of the LNGC to the Mooring Bay of the FLNGterminal in three steps (source: IMPaC Oshore Engineering,2010) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.26 Relevant motion RAOs of LNGC and FLNG terminal for theapproach phases ( = 180) . . . . . . . . . . . . . . . . . . . 71

3.27 Convention for the relative motions of the coupling points ofthe LNG transfer pipe (source: IMPaC Oshore Engineering,2010) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

3.28 Translatory relative motions of the coupling points of theLNG transfer pipe for 30% LNG lling height and all inci-dent wave angles . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.29 Rotatory relative motions of the coupling points of the LNGtransfer pipe for 30% LNG lling height and all incident waveangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

3.30 Translatory relative motions of the coupling points of theLNG transfer pipe for selected incident wave angles and allLNG lling heights . . . . . . . . . . . . . . . . . . . . . . . . 78

xiii LIST OF FIGURES

3.31 Rotatory relative motions of the coupling points of the LNGtransfer pipe for selected incident wave angles and all LNGlling heights . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

3.32 Relative x-motion amplitudes from the worst case analysiswith respect to the lling height . . . . . . . . . . . . . . . . 82

3.33 Relative z-motion amplitudes from the worst case analysiswith respect to the lling height . . . . . . . . . . . . . . . . 83

3.34 Relative x- and z-motion amplitudes from the worst case anal-ysis with respect to the lling height and the incident waveangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

3.35 Scheme for the determination of the tolerable sea states forthe worst case relative x- and z-motion . . . . . . . . . . . . . 86

3.36 Determination of the resulting limiting parameter and feasiblesea states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.37 Exemplary annual downtime for the Haltenbanken region . . 883.38 Discretization of the LNGC with MOSS type tanks . . . . . . 893.39 Comparison of selected LNGC motion RAOs for prismatic

and spherical tanks . . . . . . . . . . . . . . . . . . . . . . . . 903.40 Relative motions between the coupling points of the LNG

transfer pipe for side-by-side and tandem conguration . . . . 913.41 Surface elevation in the gap between FLNG terminal and

LNGC in side-by-side conguration (image source: Capt. MarkScholma) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.42 Illustration of the FLNG turret mooring layout . . . . . . . . 933.43 Static conguration of a single mooring line . . . . . . . . . . 943.44 Excursion vs. exciting forces and stiness depending on pre-

tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 953.45 Mean drift forces on the FLNG terminal in regular waves . . 963.46 Slowly-varying wave drift forces and surge drift motions of

the FLNG terminal . . . . . . . . . . . . . . . . . . . . . . . . 97

LIST OF FIGURES xiv

List of Tables

1.1 Countries participating in the worldwide natural gas trade . . 31.2 Main dimensions of the MPLS20 vessels . . . . . . . . . . . . 101.3 Dimensions of the LNGCs prismatic tanks . . . . . . . . . . 11

3.1 Dimensions of the cuboid tank . . . . . . . . . . . . . . . . . 413.2 Turret mooring line characteristics of the FLNG terminal . . 943.3 Mean excursion and stiness characteristics for the FLNG

terminal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 963.4 Signicant and maximum slow-drift excursions of the termi-

nal in surge direction . . . . . . . . . . . . . . . . . . . . . . . 98

A.1 Input data for calculations with one detached cuboid tank . . 121A.2 Input data for calculations with one detached prismatic tank 122A.3 Input data for single-body calculations . . . . . . . . . . . . . 123A.4 Input data for multi-body calculations . . . . . . . . . . . . . 124

LIST OF TABLES xvi

Chapter 1

Introduction

1.1 Outline

This thesis provides a holistic numerical approach covering and explainingall relevant hydrodynamic challenges related to oshore LNG transfer.

At rst, an overview on the LNG market, operating and proposed liq-uefaction and reception facilities as well as cryogenic transfer technologiesis provided in section 1.2. The MPLS20 concept, which is characterizedby a LNG carrier moored to a Mooring Bay at the stern of a FLNG intandem conguration is introduced in section 1.3. All exemplary investiga-tions are based of this concept and the involved vessels. In the literaturereview section 1.4, an overview on published approaches and methods to in-vestigate sloshing-induced structural loads, coupling eects between internaltank sloshing and vessel motions in waves as well as hydrodynamic eectsof multi-body arrangements for two vessels at close proximity is given. Itis pointed out which issues of oshore LNG transfer are covered by thesemethods and which aspects require the research work that is presented inthis thesis.

The theoretical background to the numerical approach that is chosen forthe investigation of the identied aspects is provided in chapter 2. Here, abrief summary on the basics of linear potential theory including internaltank eects and the forces and motions in waves given. In addition, thebasic concept of the classical spectral stochastic analysis and some aspectsof modeling nonlinear viscous damping eects in a linear numerical modelcomplete this chapter.

In the main part of this thesis, the hydrodynamic challenges of oshoreLNG transfer are presented. The impact of free uid surfaces on the initialstability of a vessel is discussed in section 3.1, followed by a description ofresonant sloshing in detached rectangular and prismatic tanks in section 3.2.In the next step, a vessel equipped with four equivolumetric prismatic tanksis considered in section 3.3. Subsequent to the validation of the numerical

1.2. MARINE NATURAL GAS EXPLOITATION 2

method by model test data, it is analyzed in detail how the presence ofliquid cargo of variable lling height inuences the seakeeping behavior ofthe vessel. Two phenomena are investigated in detail: The frequency shift ofthe sloshing peak (cf. section 3.3.2) and the occurrence of asymmetric eects(cf. section 3.3.3). From now on, the LNGC is not considered alone, but theMPLS20 ooading procedure including the presence of the FLNG terminalis taken into account in section 3.4, where the approach and transfer phaseare analyzed, including the relative motions between the coupling pointsof the cryogenic transfer pipe for various incident wave angles and tanklling heights. On the basis of this four-dimensional data, an exemplarydetermination of the operational range of the system for the Haltenbankenregion is conducted with given limiting relative motions between the twovessels (cf. section 3.5). Finally, two excursions indicate further aspectsthat should be considered in the analysis of oshore LNG transfer systems.

Conclusions of the presented work along with consequences for the in-vestigation of oshore LNG transfer systems are provided in chapter 4.

1.2 Marine Natural Gas Exploitation

For several decades, natural gas was merely a byproduct of oil production orwas even combusted through are booms. Today, its importance as energysource is undoubted and the demand for natural gas is continuously grow-ing (see Fig 1.1, left and International Energy Agency (2010)). Currently,there are 26 onshore export or liquefaction facilities worldwide for naturalgas, situated in 15 countries while 18 countries worldwide are importingLNG (Liqueed Natural Gas) by 60 on- and oshore regasication facilities(cf. Tab. 1.1). Approximately 65 marine liquefaction terminal projects and181 regasication terminal projects have currently been either proposed orare under construction (The California Energy Commission (2012)). More

Figure 1.1: World energy demand from 1980 2030 by source (left) andcapital expenditure on import and liquefaction FLNG facilities from 2005 2016 (right)

3 1. INTRODUCTION

Table 1.1: Countries participating in the worldwide natural gas trade withthe respective start up dates (The California Energy Commission (2012))

country status start up date

Algeria exporting 1971Australia exporting 1989Belgium importing 1972Brunei exporting 1987China importing 2006Dominican Republic importing 2003Equatorial Guinea exporting 2007Egypt exporting 2004France importing 1972Greece importing 2000India importing 2004Indonesia exporting 1977Italy importing 1971Japan importing 1969Malaysia exporting 1983Mexico importing 2006Nigeria exporting 1999Norway exporting 2007Oman exporting 2000Portugal importing 2003Puerto Rico importing 2000Qatar exporting 1997South Korea importing 1986Spain importing 1969Taiwan importing 1990Trinidad & Tobago exporting 1999Turkey importing 1992United Arab Emirates exporting 1977United Kingdom importing 2005United States of America im-/exporting 1971/1969

1.2. MARINE NATURAL GAS EXPLOITATION 4

and more large natural gas elds in remote oshore locations are planned tobe exploited. Until a few years ago, the challenge to develop these resourceswas not accepted and no technology i.e. oating processing and lique-faction plants was available. This attitude has changed and today, moreand more companies attempt to participate in this rapidly growing market(see also Fig. 1.1, right).

Since the transport of natural gas via pipelines is not economic withincreasing distance, dierent Floating Liqueed Natural Gas (FLNG) solu-tions have been developed: Most of these concepts comprise of an oshoreterminal that produces, stores and periodically transfers the liqueed gas toshuttle tankers which call at special deepwater ports or other regasicationfacilities close to or on-shore. Liquefaction of natural gas requires cryogenicconditions of -162C and reduces the volume to 1/600th. Since the energydensity increases by the factor 600 at the same time, LNG is a hazardouscargo. In the following, an overview on currently existing and proposedconcepts for marine natural gas liquefaction and regasication concepts andtechniques is provided (without this survey being claimed to be exhaustive).

1.2.1 Liquefaction Facilities

Until today, no oshore liquefaction facilities are operating, but the progressof several projects is considerable (see Douglas Westwood Limited (2010)).All concepts feature large turret-moored terminal barges.

In July 2009, Shell Gas & Power Developments BV signed a contractwith Technip and Samsung Heavy Industries, forming a consortium to de-velop, construct and install several oating liquefaction terminals (referredto as FLNG terminals in the following) within the next 15 years (Gilmourand Deveney (2010)). An impression of the 480 m long and 75 m wide ter-minal vessel, which is designed for side-by-side ooading is shown in Fig. 1.2

Figure 1.2: Current concepts for marine natural gas liquefaction byShell/Technip (left) and Flex LNG (right)

5 1. INTRODUCTION

(left). The rst application for this concept will be o the coast of West-ern Australia, where Shells Prelude and Concerto gas elds are situated.Further potential FLNG projects in this region are the Sunrise and Browseelds.

Founded in 2006, Flex LNG is specialized in developing solutions for o-shore LNG production. In co-operation with Samsung Heavy Industries, theFlex LNG Producer (LNGP) was developed (see Fig. 1.2, right and Pastooret al. (2009)). This 336 m long and 50 m wide liquefaction terminal vessel isconnected to the gas eld via a turret buoy system by APL AS. Shuttle carri-ers can be loaded either in side-by-side or in tandem conguration. In April2011, Flex LNG had signed agreements with InterOil Corporation (IOC),Pacic LNG Operations Ltd. (PacLNG), Liquid Niugini Gas (LNGL) andSamsung Heavy Industries for the Gulf LNG project in Papua New Guinea.From mid 2014 on, LNGP1 is scheduled to be moored alongside a jetty andproduce natural gas from the Elk and Antelope onshore gas elds in theEastern Papuan Basin northwest of Port Moresby.

Further eorts in oshore liquefaction development are made by SBMOshore, who propose a LNG FPSO (LNG Floating Production, Storageand Ooading) terminal for side-by-side as well as tandem ooading. Hav-ing signed a contract with Petrobras, SBM plans to install a LNG FPSOin the Campos Basin o the Brazilian coast. Due to the sea conditions inthis region, it will be operating in tandem conguration. In July 2011, SBMOshore signed a contract with PTT FLNG Ltd. and PTTEP Australasiato develop an FLNG terminal for the exploitation of the Cash/Maple, Oliverand Southern gas elds o the Australian north coast in the Timor Sea from2016 on.

Norwegian Hoegh LNG also developed a LNG FPSO terminal for tandemooading with exible hoses and side-by-side ooading with three rigidarms two for LNG and one for LPG (Liqueed Petroleum Gas) whichreceived an approval in principle from DNV in June 2009.

1.2.2 Reception Facilities

In contrast to the liquefaction facilities, there is already some progress visiblein oating LNG reception facilities.

The rst solution that was realized is the Energy Bridge principle, de-veloped by the Texas based company Excelerate Energy. Until today, atotal of eight Energy Bridge Regasication Vessels (EBRV) is in operation.The concept is suitable for both, ship-to-shore transfer (GasPort) as wellas oshore transfer (Gateway). In both cases, a conventional LNG carrieris moored side-by-side to an EBRV which regasies the LNG. In case ofGasPorts, shore-based loading arms transfer the gas into the downstreamdelivery infrastructure, while for oshore Gateways, cone-shaped STL buoys(Submerged Turret Loading, see Fig. 1.3, top right) are applied to transfer

1.2. MARINE NATURAL GAS EXPLOITATION 6

Figure 1.3: Current concepts for marine LNG reception and regasicationby Aker Solutions (Adriatic LNG, top left), Excelerate Energy (ExcelerateEnergy Bridge, top right), Golar LNG (Golar Spirit FSRU, bottom left) andTORP LNG (HiLoad System, bottom right)

the gas via pipelines to the onshore infrastructure (Cook (2006)). World-wide, Excelerate currently operates four GasPorts (Teesside/Great Britainsince 2007, Baha Blanca/Argentina since 2008, Mina Al-Ahmadi/Kuwaitsince 2009 and GNL Escobar/Argentina since 2011) as well as one Gateway(Northeast Gateway, since 2008 o the coast of Massachusetts) the GulfGateway o the coast of Louisiana was in operation since 2005 but will bedecommissioned in 2012.

The second type of marine LNG reception facility that is already op-erating is Adriatic LNG, built by Aker Solutions for Exxon Mobil. Since2008, conventional LNG carriers are calling at this GBS terminal (GravityBased Structure), situated 15 km o Porto Levante in the Adriatic Sea (seeFig. 1.3, top left). LNG is transferred in side-by-side conguration to theGBS, where the regasication process takes place. Subsequently, the gas istransferred to the Italian mainland via pipelines.

Golar LNG is specialized in converting former LNG carriers into so-called FSRUs (Floating Storage and Regasication Unit), which can eitheroperate oshore or in harbours (see Fig. 1.3, bottom left). In both scenarios,LNG ooading is conducted in side-by-side conguration with rigid loadingarms. Two harbour-based FSRUs are currently operating for Petrobras in

7 1. INTRODUCTION

Brazil (Golar Spirit in Pecem and Golar Winter in Rio de Janeiro, bothsince 2009) and a third unit, Golar Freeze is in service for the Dubai SupplyAuthority (DUSUP) since late 2010 in Jebel Ali/Dubai. Golar Frost, the rstoshore unit is currently under conversion for the Toscana LNG project andis scheduled to operate from late 2012 on o Livorno in the MediterraneanSea. Golar LNGs second oshore FSRU Khannur is currently also underconversion and will operate for the West Java LNG project 15 km oshorein the Jakarta Bay in Indonesia.

Norwegian Hoegh LNGs current portfolio in reception facilities com-prises deepwater ports, FLNG units and FSRUs. Two deepwater ports inthe U.S. the already ocially licensed Neptune Deepwater Port o thecoast of Massachusetts and Port Dolphin o Florida as well as Port Merid-ian o the English west coast are planned. Similar to the Energy Bridgeprinciple, these ports will feature SRVs (Shuttle Regasication Vessel) incombination with STL buoys. Together with Gaz de France-Suez, HoeghLNG is developing a FSRU for side-by-side ooading for the Triton LNGproject in the Adriatic Sea. In June 2009, Hoeghs LNG FPSO concept re-ceived an Approval in Principle from DNV. This FLNG receiving facilityis designed to transfer liqueed gas oshore to shuttle carriers in side-by-side (three rigid loading arms for LNG, two for LPG) as well as tandemconguration (exible pipes).

While most of the technological solutions for oshore LNG ooadingproposed so far are based on vessel-to-vessel transfer with rigid loading armsor exible hoses, Torps HiLoad system is a completely dierent approach.The problematic scenario of two large vessels interacting at close proximityin rough seas is avoided by a L-shaped frame mounted to the carrier vesselwhere it is held in position by friction forces (see Fig. 1.3, bottom right).HiLoad can be used in combination either with a regasication terminal atgreat distance (Bienville Oshore Energy Terminal in the Gulf of Mexico,currently under review) or alone (planned for the Esperanza project o thecoast of California). In the latter case, the carrier is moored to a buoy andHiLoad itself regasies and transfers the cargo to the mainland via pipelines.For sheltered shallow water regions, Torp has developed the EasyLNG sys-tem, which consists of a barge with regasication plants for ooading inside-by-side conguration.

Currently almost all oil and gas companies are trying to participate inthis new, dynamic oshore LNG market with their own technologies andconcepts. To name a few among them, Bluewater, Sevan Marine, MossMaritime or Saipem are also proposing FLNG solutions. ExxonMobil plansto design a FLNG terminal for the BlueOcean project o the coast of NewJersey, and Norwegian Framo Engineering part of the OCT consortium(Oshore Cryogenic Transfer) proposes a FLNG system for tandem load-ing, which features an A-frame in combination with a crowfoot-mooringarrangement. Japanese INPEX have also developed large side-by-side oper-

1.2. MARINE NATURAL GAS EXPLOITATION 8

ated FLNG units (length 500 m, breadth 82 m) for two projects o northernAustralia Ichthys LNG and Abadi LNG.

1.2.3 Cryogenic Transfer Technologies

The design of the cryogenic transfer system and the related motion capabili-ties are the central boundary condition for the operational range of the entireFLNG system. The two transfer congurations tandem and side-by-side are characterized by specic transfer technologies. For side-by-side trans-fer, FMC Technologies rigidMarine Loading Arms are currently state-of-theart (see Fig. 1.4, left). They have been designed by FMC to handle rela-tive motion amplitudes between the two vessels of 1.0 m in longitudinal,2.0 m in transverse and 1.2 m in vertical direction. Due to these limita-tions, side-by-side transfer with rigid loading arms is currently possible onlyfor calm waters to moderate sea states as for the Adriatic Sea, where theAdriatic LNG GBS is equipped with this technology.

In tandem conguration, the coupling points for the cryogenic transfersystem are typically located at the bow of the carrier and the stern of theterminal, instead of midships as for the side-by-side conguration. Sincethis implies larger relative motions that have to be handled, aerial or oat-ing exible pipes instead of rigid arms have to be used. Dutch Bluewaterdeveloped a cryogenic transfer pipe of 8 to 16 inner diameter for aerialapplications (see Fig. 1.4, right), but so far only a prototype was built. TheOCT consortium (Oshore Cryogenic Transfer), led by Norwegian FramoEngineering, also developed an oshore transfer system for LNG in tandemconguration - which is not in operation until today (Frohne et al. (2008)).

In order to develop a save and ecient oshore LNG transfer systemthat exceeds the capabilities of the state-of-the-art technologies, the re-

Figure 1.4: Cryogenic transfer technologies: rigid loading arms by FMCTechnologies for side-by-side conguration (left), prototype of exible cryo-genic hoses by Bluewater for tandem ooading (right)

9 1. INTRODUCTION

search project MPLS20 Maritime Pipe Loading System 20 was fundedby the German Federal Ministry of Economics and Technology (BMWi) in2007. The system developed by the MPLS20 consortium consisting of Nex-ans Deutschland, Brugg Pipe Systems, IMPaC Oshore Engineering andTechnical University of Berlin (TU Berlin) is presented in the following sec-tion.

1.3 The MPLS20 Project

Within the framework of the joint research project MPLS20, an innovativeoshore transfer system between a turret-moored FLNG terminal barge anda LNG shuttle carrier in tandem conguration has been developed and an-alyzed. The proposed transfer system consists of a generic FLNG terminaldesign with the new Mooring Bay concept, a modied standard LNG car-rier (LNGC) and the approach and handling system for the developed 16transfer pipes (see Fig. 1.5, Hoog et al. (2009a) and Hoog et al. (2009b)).The FLNG terminal (for main dimensions see Tab. 1.2) features a wave at-tening bow and provides a cargo loading capacity of up to 280,000 m3 LNGin ve independent SPB tanks (Self-supporting, Prismatic, IMO Type B)which are sloshing-proof and oer a at deck. The LNGC (for main dimen-sions see Tab. 1.2) is equipped with four membrane tanks and is slightlymodied compared to todays standards, as one additional and speciallydesigned receiving manifold is placed at the bow deck area. This bow man-ifold completely enters the Mooring Bay at the stern of the terminal whenthe LNGC is moored for cargo transfer, signicantly reducing the free spanlengths of the transfer pipes compared to crude oil transfer techniques. Thedistance between the bow of the LNGC and the stern of the FLNG is 10 min this conguration. The bow deck area accommodates standard anchor

Mooring Bay

offshore tugs

FLNG terminal

LNG carrier

approach and handling system

loading bridge

header

transfer pipes

Wings

Figure 1.5: Illustration of the loading procedure with the MPLS20 system intandem conguration showing the overall arrangement (left) as well as theMooring Bay concept (right)

1.3. THE MPLS20 PROJECT 10

Table 1.2: Main dimensions of the MPLS20 vessels

Parameter FLNG terminal LNGC

Length over all, LOA [m] 360 (+ 40 Mooring Bay) 282Breadth, BV [m] 65 42Draft, DV [m] 12 12Height, HV [m] 33 26Displacement, V [m3] 275,087 103,921Loading capacity, VL [m

3] 280,000 133,880

winches and if necessary chain stoppers as well as Quick ReleaseHooks (QRH) for mooring. Due to active ballasting, the LNGC as well asthe FLNG terminal operate at a constant draft of 12 m.

For safe and fast loading/ooading procedures, a corrugated, vacuuminsulated transfer pipe of 16 inner diameter for cryogenic liquids has beendeveloped which signicantly exceeds currently existing pipe diametersand hence transfer rates.

The mooring system features the patented 40 m long Mooring Bay,built of two Mooring Wings which are xed to the FLNG terminal sternat starboard and portside, respectively. This concept allows safe loading inharsh seas and even ice conditions (see Hoog et al. (2012)). The mooringof the LNGC results in a symmetrical arrangement of six moorings eachoperated by load adequate winches and heave compensation systems. Thearrangement provides a unique solution to stop the incoming vessel in a con-trolled manner at the required position right below the loading bridge as theLNGC is actively pulled into the Mooring Bay. A rail-mounted movableloading crane bridges the Mooring Bay from one wing to the other allow-ing simultaneous handling of up to six transfer pipes by means of a header.In addition, the crane accommodates the cargo transfer anges which arelocated high above the wings weather decks so that handling, draining andpurging of the exible pipes can be carried out in a safe, ecient and reliableway. For coupling of the transfer pipes to the LNGC bow manifold, stan-dard Quick Connect/Disconnect Couplers (QCDCs) and Emergency ReleaseCouplers (ERCs) are used.

The MPLS20 vessels provide the basis for all investigations presented inthis work and are denoted by the abbreviations LNGC and FLNG terminalin the following chapters. The LNGC features four equivolumetric prismatictanks with a total capacity of 133,880 m3 and the characteristic dimensionsgiven in Fig. 1.6 and Tab. 1.3. The subsequent sloshing analyses are con-ducted with these tanks, where the standard case is 30% lling height. Thekey results of the MPLS20 project are published by Frohne et al. (2010).

11 1. INTRODUCTION

Length

Height

Breadth

1

2

3

4

Figure 1.6: Numerical discretizationof the LNGCs prismatic tank withcharacteristic dimensions

Length, LT [m] 38.3

Breadth, BT [m] 35.8

Height, HT [m] 26.1

1 4.65

2 5.0

3 4.65

4 8.0

Volume, VT [m3] 33,470

Table 1.3: Dimensions of theLNGCs prismatic tanks

1.4 State-of-the-Art

Oshore ooading of LNG from a oating terminal vessel to a oatingLNGC is a delicate and challenging procedure. Due to its high energy den-sity, LNG is an extremely hazardous cargo and safe transfer operations re-quire detailed knowledge on all involved hydrodynamic eects, which are

Structural loads on tank walls caused by sloshing eects in partiallylled tanks,

Modied seakeeping behavior of the LNGC caused by sloshing in par-tially lled tanks and

Modied seakeeping behavior due to multi-body eects.

In the subsequent paragraphs, methods and approaches to analyze theseissues that have been published so far are compiled.

1.4.1 Sloshing

Free uid surfaces in moving containers with related resonant sloshing phe-nomena pose a problem not only in marine applications. In fact, extensiveresearch work on sloshing in aircraft and rocket fuel tanks has been pub-lished since the 1960s. After several accidents, especially NASA researchershave studied the inuence of free uid surfaces in fuel tanks on the dy-namic stability of rockets. Among several publications, the important andpathbreaking report by Abramson (1966) should be mentioned.

In marine applications, sloshing may even be desired specially de-signed antiroll tanks on ships act as liquid damping systems that help re-ducing roll motion amplitudes (see SNAME (1989a)). Similar system areinstalled in very tall buildings to decrease wind-induced oscillations.

1.4. STATE-OF-THE-ART 12

Due to its dangerous impact, undesired or uncontrolled sloshing in ma-rine applications is a eld of extensive research work. Recently, Faltinsenand Timokha (2009) compiled a comprehensive book covering a wide rangeof issues related to marine sloshing. A comprehensive review of existingapproaches to the sloshing problem was published by Ibrahim (2005).

Wave-induced vessel motions excite liquid motions inside large partiallylled cargo tanks, as they are typical for cargo ships carrying oil, chemicals,liquid food, LNG or LPG. Unlike tanks for LNG transport, the large cargotanks for LPG, oil, chemicals and liquid food transport are subdivided bybulkheads with openings to reduced the eective tank dimension for sloshingmotions. LNG tanks are classied into non-freestanding tanks (membranetanks, e.g. Technigaz Mark III and Gaz Transport NO96) and freestandingtanks (e.g. MOSS tanks or IHI SPB). Due to safety regulations, no weldingis allowed on the internal tank barriers which have to withstand extremetemperatures and pressure. Therefore, all LNG tank types feature large,clean volumes without any subdividing internal structures like bulkheadsand are particularly prone to violent sloshing eects.

The inuence of these sloshing motions is extremely strong for excitationsin the vicinity of the rst natural frequency of the tank. In general two majorissues are caused by marine sloshing eects: structural problems due to highpressure on the tank walls and altered seakeeping behavior of the vessel duecoupling eects of sloshing and ship motions.

Structural Loads

Local pressure peaks occur especially at discontinuous locations of the innertank walls, i.e. corners, chamfers etc. In order to investigate structural loadsdue to sloshing, model tests can be conducted. Common setups consistof single small scale tanks (1:20 to 1:70) mounted to hexapods that allowmotions in six degrees of freedom. Pressure sensor clusters are installed tomeasure loads at dierent positions on the tank walls. Apart from dicultiesin measuring the pressure peaks that are extremely localized in space andtime, scaling becomes an issue since hydroelastic eects may couple pressureand structural responses (see Graczyk and Moan (2009)).

Typical measurements of pressure distributions along vertical tank wallsin space and time are shown by Repalle et al. (2010a) for a rectangular tankmounted to a hexapod. Further investigations by Repalle et al. (2010b)showed the inuence of the sampling rate and model test duration on theimpact pressure measurements. It is recommended to select a sample rate of40 kHz and measure the impact pressure for 10 min under regular sinusoidalconditions.

Local impact loads due to sloshing can also be calculated by numericalmethods. Some recommendations and comparisons between basic potentialtheory, RANSE solvers and experimental data regarding pressure and sur-

13 1. INTRODUCTION

face elevation is provided by Thiagarajan et al. (2011). Since numerical anal-yses of these transient phenomena require an exact reproduction of the liquidfree surface in combination with eects such as spray and entrapped air inthe vicinity of the tank walls, RANSE-based (Reynolds-Averaged Navier-Stokes Equation) approaches provide an appropriate and popular method.Several well-known CFD solvers were proven to be capable of capturing pres-sure impacts on internal walls of moving tanks. Alternatively, Raee et al.(2009) presented a numerical approach to simulate two-dimensional slosh-ing ows by applying the SPH (Smooth Particle Hydrodynamics) method, ameshless, purely Lagrangian approach where the uid is represented by ran-domly distributed particles. This approach was also selected by Pakozdi(2008), who adapted the standard SPH method to a smoothed SPH methodby implementing various time integration approaches, a new denition forintroducing density as well as a moving least square method in order toinvestigate the nonlinear eects of two-dimensional sloshing in box-shapedtanks. However, the vast majority of publications include analyses of sepa-rate tanks, that are not mounted to a vessel moving in waves, hence directcoupling is often not considered.

Sames et al. (2002) showed two-phase ow simulation results for rectan-gular and cylindrical tanks obtained with a nite volume method based onthe commercial solver COMET, where the interphase was tracked with theHigh Resolution Interface Capturing scheme (HRIC). The predicted pressureat dierent tank wall positions showed good agreement with experimentaldata from the EUROSLOSH research project.

Schreier and Paschen (2008) investigated sloshing inside a prismatic tankwith the commercial CFD solver ANSYS CFX. Two interesting phenomenawere found: The occurrence of local high pressure peaks at low lling heightsis related to ows along the tank walls towards discontinuities such as knuck-les, leading to abrupt changes of the direction of the uid momentum. Athigh lling levels, very low pressures may occur, that last signicantly longerand aect larger tank wall areas. These observations are related to tank roofeects. Further studies by Schreier et al. (2009) revealed the importance oftransient eects such as the sudden encounter of a LNGC with partiallylled tanks with a steep wave. Pressure impacts were found to be severaltimes higher as compared to harmonic excitation at resonance.

A RANSE/VOF (Volume of Fluid) method based on the commercialsolver FLUENT was used by Rakshit et al. (2008) to conduct two-dimensionalstudies in order to investigate the inuence of varying lling height andsway excitation frequency on the impact pressure. Three-dimensional simu-lations with FLUENT to predict sloshing pressure in a prismatic tank werepresented by Rhee (2004). The comparison with experimental data showedgood agreement on unstructured as well as structured grids at low llinglevels. The implementation of a suitable turbulence model was consideredto be critical in order to capture violent liquid motions correctly.

1.4. STATE-OF-THE-ART 14

The capability of MARINs volume of uid (VOF) solver COMFLOWto simulate local, short-term pressure peaks was investigated by Huijsmanset al. (2004). Experimental pressure measurements and high-speed videocaptures are compared to numerical results for a rectangular tank exposed toforced harmonic roll motions. It was found that it is dicult to capture suchextremely local (in space and time) impacts numerically with reasonablecomputational eort. But improvements to the code gave better resultsin the following years: The importance of taking into account two phasesand furthermore of modeling the compressibility of the air phase correctlywas shown by Wemmehove et al. (2007). The improved numerical codeCOMFLOW was validated by pressure measurements from sloshing modeltests at a scale of 1:10. In order to track the free surface accurately, animproved volume of uid method (iVOF) was applied. It was also shownthat articial viscous damping of the air phase related to rst-order upwinddiscretization leads to underestimated wave heights especially close to tankwalls if the cells are not ne enough.

Peric and Zorn (2005) and Peric et al. (2007) were among the rst topresent an integrated method based on the commercial solver STAR-CCMthat is capable to simulate the entire process at once: In a transient three-dimensional simulation, the wave-induced motions of a LNG carrier withpartially lled tanks are calculated, taking account of the bidirectional cou-pling eects between free uid motions in the cargo tanks and vessel motions.In the same computational procedure, it is possible to obtain local pressureson the internal tank walls. However, due to the high computational eortof this method, only selected cases such as extreme wave encounters can beanalyzed in time domain.

The importance of structural response analyses of internal tank wallsand foundations under sloshing conditions is shown by Graczyk and Moan(2009). The insulation of a Technigaz Mark III tank typically consists ofplywood and foam layers covered with a thin metallic membrane that areattached to the tank steel plates. A nite element method is developedto investigate the exibility and resulting stresses in the insulation layers.It is shown that dierent layers contribute dierent modes to the overallresponse, e.g. plywood modes are relevant for short load durations whereassteel plate modes become relevant for longer load durations.

Local pressure impacts and their structural eects are not covered by thework presented in this thesis. Instead, the focus of research lies on couplingeects of internal tank sloshing and vessel motions. Individual parts of thisaspect of the marine sloshing problem have also been studied by severalresearchers, and the discussion whether numerical methods for investigatingsloshing have to be non-linear or a linear approach is sucient is still vivid.

15 1. INTRODUCTION

Seakeeping

In order to simulate the coupling process, Rognebakke and Faltinsen (2001)validated a numerical procedure where a linear strip theory approach forcalculating ship motions is coupled to an adaptive nonlinear multimodalmethod as well as to a linear method to predict internal sloshing with two-dimensional model tests using a rectangular ship section equipped withtwo box-shaped internal tanks. The model is allowed only to perform swaymotions and is exposed to regular beam seas. It was found that for smallto medium sloshing amplitudes linear theory shows good agreement withexperiments while for stronger sloshing motions, the nonlinear multimodalapproach is capable of predicting associated shiftings in the natural sloshingmodes. In order to extend the applicability of the adaptive multimodalmethod for irregular waves Rognebakke and Faltinsen (2003) introduced aconvolution formulation with a retardation function to the coupled equationsof motion.

Molin et al. (2002) proposed a linear modal approach (except for qua-dratic viscous roll damping and internal tank damping formulations) basedon Pricipias code DIODORE to account for coupling eects between slosh-ing and ship motions. For validation purposes, a barge model was equippedwith two rectangular tanks and was exposed to beam seas. Vessel motionsas well as internal uid motions were measured for altogether six dierentlling level combinations and wall roughnesses. Except for very low llinglevels where nonlinear eects are dominant, good agreement of linear theoryand model tests was achieved. Also, the rst even sloshing mode, which wasobserved during experiments could not be reproduced by the linear theorysince even modes are not directly coupled to the motion of the vessel. Fur-ther experiments by Molin et al. (2008) with the same barge model includedthe systematical analysis of roof impact for at and chamfered tank roofgeometries with dierent airgaps and wave heights. A general damping ofsloshing eects on ship motions was observed for roof impacts, but varyingairgaps lead to almost identical results despite dierent roof impact intensi-ties. For moderate sloshing and roof impact good agreement of linear theoryand model tests was observed.

A linear potential theory method that takes into account coupling ofinternal free uid surface eects and ship motions is introduced by Malenicaet al. (2003) and was found to give good results in comparison with Molinsbarge model tests.

Bunnik and Veldman (2010) also used Molins benchmark data to com-pare results obtained by a linear diraction tool and a hybrid analysismethod where the wave induced ship motions are determined by the lin-ear tool which is coupled to MARINs CFD solver COMFLOW. The resultspresented for the hybrid approach showed slightly better agreement withthe experimental data than the purely linear calculations.

1.4. STATE-OF-THE-ART 16

The description of the state-of-the-art in sloshing analyses at BureauVeritas published by Zalar et al. (2006) and Zalar et al. (2007) reveals thatthe standard analysis procedure is based on the linear potential theory in-house code HYDROSTAR. When correct modeling of the free surface con-tour inside the tanks is required, a hybrid approach based on the couplingof HYDROSTAR for seakeeping and the CFD code FLOW-3D for internaluid motions is applied.

American Bureau of Shipping (ABS) also published a number of papersrelated to the coupling of sloshing and seakeeping. Lee et al. (2005) pre-sented a numerical approach where the ship motions are calculated by apotential theory approach based on MARINs PRECAL and the uid mo-tions inside the tanks are computed by the nite-element method SLOFE2Din time domain. It was found that despite increasing LNGC and tank sizeswith corresponding sloshing loads, current safety regulations are still conser-vative. Instead of SLOFE2D, Kim et al. (2006) and Lee et al. (2007) coupleda RANSE based solver with PRECAL to account for internal tank sloshingin time domain. Results are compared to model tests data as well as re-sults obtained by a potential theory approach in frequency domain for both,external and internal ow computations. It was found that time domainresults agree well with simulations and frequency domain results predict alleects at least qualitatively. Analyses of a LNGC and a FLNG terminalin side-by-side conguration obtained with the same hybrid approach werepresented by Lee et al. (2008). Finally, Kim and Shin (2008) proposed a fre-quency domain approach to take account of coupled seakeeping for LNGCat forward speed. In all ABS publications, experimental results from thejoint-industry project SALT (Seakeeping of structures Aected by LiquidTransient) obtained at MARIN have been used for validation.

In the framework of the project SALT, model tests with a moored FPSOand a free oating LNG carrier have been conducted. As reported by Gail-larde et al. (2004), comparison of roll motion RAOs obtained by the potentialtheory code DIODORE and model tests showed good agreement. Some dis-crepancies for internal uid surface elevations and resulting tank forces areshown.

Chen (2005) and Chen et al. (2007) proposed a set of methods thatis suitable for analyzing all hydrodynamic issues related to oshore FLNGterminal design. Apart from a newly introduced second-order middle-eldformulation for drift load and low-frequency wave load analyses, it is statedthat the majority of eects in coupled sloshing/vessel motion analyses iscovered by linear theory (except for resonant phenomena) where modiedcoecients for stiness, added mass and if dissipation is to be considered for damping have to introduced to the equations of motion.

Finally, the method proposed by Newman (2005), which is based onthe linear potential theory code WAMIT (Wave Analysis at MassachusettsInstitute of Technology) is the basis for all analyses presented within this

17 1. INTRODUCTION

work. A detailed description of the theoretical background for this methodis given in the following chapter.

1.4.2 Multi-Body Eects

Two or more bodies oating in proximity in waves experience interactions,since each structure induces scattering (deection and reection of the in-cident wave eld) and radiation (wave generation caused by the movingstructure) wave elds. One of the rst publications related to these eectsis by Ohkusu (1976), who derived the coupled equations of motion and hy-drodynamic coupling forces for a ship oating close to a simplied oshorestructure and achieved good agreement of model test data and calculations.For larger structures that have to be discretized, van Oortmerssen (1979)extended the three-dimensional panel method to enable the investigation ofmultiple oating and hydrodynamically interacting bodies.

An alternative approach for axisymmetric structures is the multiple-scattering method, which solves the scattering problem for each body inthe presence of other bodies by applying Grafs theorem to expand the re-spective potential of one body to the local coordinate systems of the otherbodies. This method was applied by Chakrabarti (1999) to determine inter-actions between various structures in waves.

Newman (2001) presented the capabilities of the linear potential theorycode WAMIT to take into account scattering and radiation eects leadingto rst and second order hydrodynamic interactions as well as resonanteects between two vessels. On the basis of WAMIT calculations, Claussand Jacobsen (2004) investigated the hydrodynamic interaction between alarge oating crane vessel and a barge during the lift-o procedure from thebarge deck in frequency domain and proposed the F2T approach to transferthe relative motions between the two vessels to time domain.

In this thesis, the multi-body problem (interaction and relative motionsbetween FLNG terminal and LNGC in tandem conguration) is also solvedon basis of the linear potential theory code WAMIT.

1.4.3 Summary

For multi-body analyzes, reliable and validated methods such as potentialtheory or multiple-scattering theory for axisymmetric bodies are available.For all multi-body calculations in this thesis, WAMIT is used, which is basedon linear potential theory.

Sloshing in partially lled internal tanks causes high pressure peaks withrelated structural loads on tank walls especially in the region of geomet-rical discontinuities. In order to avoid damage and leakage, these eectshave to be studied in detail. Typically methods include model tests wherethe sloshing-induced pressure peaks are measured for a detached tank (fresh

1.4. STATE-OF-THE-ART 18

water lling) moving in six degrees of freedom on a hexapod. In the pub-lished numerical investigations, the two-phase ow in detached tanks arecommonly analyzed by RANS methods, in some studies the SPH formula-tion is applied. However, the structural issues associated with tank sloshingare not covered by this thesis.

Instead, the focus lies on coupling eects between internal tank sloshingand the seakeeping behavior of the LNGC. Due to safety reasons, model testsare exclusively conducted with fresh water lling instead of LNG. Validatednumerical methods that cover the coupling eects include linear, nonlin-ear and hybrid approaches such as the modal method, multimodal method,potential theory and RANS based methods. From the available publishedstudies, it becomes clear that so far, idealized setups were considered. Themodel tests by Rognebakke and Faltinsen (2001), Molin et al. (2002) andMolin et al. (2008), that are widely used for validation purposes were con-ducted with rectangular tanks mounted to a rectangular barge hull. Theyhave to be considered as two-dimensional model tests. Published numeri-cal studies also cover ship-shaped LNGC hulls but focus on two-dimensionalresponses in beam seas ( = 90). An actual three-dimensional numericalapproach that covers and explains all hydrodynamic inuences during anoshore ooading procedure is not available so far.

In order to analyze oshore operations where coupling between uidsloshing and vessel motions has to be considered, idealized assumptions andfresh water results are not meaningful. This is an explicit consequence ofthe two main phenomena that have not been explained or even identiedby the research work published so far, but are investigated in detail in thisthesis:

the shift of the resonant motion peak related to the rst natural slosh-ing mode and

the occurrence of asymmetric uid and vessel motion responses forsymmetric excitations.

Bunnik and Veldman (2010) explicitly mentioned the shift of the resonantresponse peak, but simply attributed it to the large variations in tank addedmass in this frequency range, which is no satisfactory explanation of thisphenomenon. Observations and investigations of the asymmetric responseshave not been published at all so far.

For the rst time, a holistic approach that covers all relevant hydrody-namic eects for oshore ooading procedures, including multi-body inter-action as well coupling of internal tank sloshing and vessel motions in de-pendency of the incident wave angle and the tank lling height is presentedin this thesis. The proposed procedure eventually reduces this complexfour-dimensional problem to a single curve that characterizes the ooadingprocedure in terms of tolerable sea states (combinations of signicant wave

19 1. INTRODUCTION

height Hs and zero-upcrossing period T0). The theoretical background forthe numerical method is provided in the following chapter 2.

1.4. STATE-OF-THE-ART 20

Chapter 2

Description of the NumericalMethod

This chapter provides the theoretical background for the proposed holis-tic approach to assess oshore LNG transfer operations. At rst, a briefoverview on the basics of potential theory is given, followed by the deter-mination of linear hydrodynamic forces and motions and an explanation ofthe inuence of internal free uid surfaces on the hydrodynamic coecientsin the equation of motion. Finally, the equations for the spectral stochasticanalysis are compiled and the inclusion of viscous damping eects in thelinear model is discussed.

The emphasis of the analyses presented in this thesis lies on dynamiceects caused by free uid surfaces and multi-body interactions. The inves-tigations and results focus on rst order motions, i.e. motions that cannotbe compensated by moorings. Eects of the six lines between LNGC andFLNG terminal are neglected, the same applies for the turret mooring ofthe FLNG terminal, which is only briey addressed by an excursion on slowdrift motion amplitudes due to second order wave forces. All results pre-sented are valid for a water depth of 100 m. The numerical calculationsare conducted in frequency domain, and are based on the specially adoptedradiation-diraction panel code WAMIT (Wave Analysis at MassachusettsInstitute of Technology, WAMIT Inc. (2006)), which is a linear potentialtheory approach (see Newman (1977), Clauss et al. (1992) and Thamsenand Siekmann (2009)). The subsequent brief explanations provide the the-oretical background of the numerical method.

2.1 Potential Theory

In this section, the ow around an arbitrarily shaped body in an ideal uidwith free surface in restricted water depth is considered. The structureis exposed to long-crested waves (incident wave eld) characterized by the

2.1. POTENTIAL THEORY 22

wave frequency , the wave number k and the wave amplitude a (i.e. thewave height H = 2 a). The ow domain of interest is denoted by Vand is bounded by the sea bed SB, the wetted body surface Sb and thefree water surface Sf (z = 0 represents the still water level). The fareld boundary S is assumed to be a vertical circular cylinder. For thegeometrical description of the structure, a cartesian coordinate system isused with the positive z-axis pointing upwards and orthogonal to Sf andthe positive x-axis pointing in the direction of wave propagation. A denedpoint on the body surface is described by the position vector r (note thatunderlined parameters represent vectors and column matrices, respectively)and the normal vector n always out of the uid domain.

A structure is considered to be hydrodynamic compact, if its characteris-tic dimension D is greater than 20% of the wave length L (i.e. D/L > 0.2).Incident waves are signicantly altered by these structures. In this case, theforces resulting from scattering and radiation (together: diraction) of theincident waves can not be neglected. Since viscous eects play a minor rolewhen analyzing hydrodynamical compact structures (Exception: Viscouseects considerably contribute to the damping of roll motions), excitationforces, added masses and potential damping can be calculated using poten-tial theory.

The ow potential (in the domain V ) around the body has to beknown. It has to satisfy Laplaces dierential equation:

(i) Laplaces equation in V

= 0 (2.1)

which is derived from the condition that the ow has to be irrotational

v = () = 0 (2.2)

and also has to satisfy the continuity equation (written here for in-compressible uids):

T v = ux

+v

y+

w

z= 0. (2.3)

Furthermore, the following conditions on the boundaries of V have to betaken into account for deriving :

(ii) Linearized, generalized free surface condition for z = 0, i.e. at the stillwater level Sf

z

2

g = 0; (2.4)

the hydrodynamic pressure at the free surface equals the atmo-spheric pressure; no particle leaves the wave contour

23 2. DESCRIPTION OF THE NUMERICAL METHOD

(iii) Bottom condition for z = d, i.e. on the sea bed SB at water depth d

z= 0; (2.5)

no ow through the sea bed(iv) Body condition on the wetted body surface Sb

sTn =

n. (2.6)

the component of the uid motion normal to the body surface equalsthe respective body motion component, i.e. there is no ow throughthe wetted body surface

The necessity of boundary conditions (2.4), (2.5) and (2.6) is obvious. Butthese conditions alone are not sucient for a well-dened description of theproblem. No boundary condition describing the far eld of V in great dis-tance to the body has been set up so far. Hence, it is not dened whetherthe generated waves propagate away from or towards the body. Mathemati-cally speaking, both cases are possible. But from the physical point of view,a perpetuum mobile would be created if the diraction and radiation wavespropagate towards the body that generated them. Therefore, an additionalcondition is required in order to model the problem:

(v) Sommerfeld radiation condition:

limR

R

(jR

ikj)= 0 j = 1, ..., 7 (2.7)

where R is the radius of the uid domain. Assuming a linear problem, thetotal potential is dened as a superposition of various wave systems andtheir potentials, respectively (Newman (1977)):

= 0 +6

j=1

j +7 (2.8)

The potential 0 describes the incident wave eld, i.e. the undisturbed waveow of the far eld. Usually, this potential is known, e.g. from the linearwave theory (see Clauss et al. (1992)):

0 =a g

cosh[k(z + d)]

sinh(kd)cos() (2.9)

where the wave number k can be derived from the dispersion relation

=kg tanh(kd) (2.10)

2.1. POTENTIAL THEORY 24

The scattering potential 7 describes the wave eld caused by scattering i.e. the reection and deection of the incident waves by the structure.The radiation wave eld due to body motions in six degrees of freedomj [1, 6] is described by a sum of altogether six potentials. When thebody moves in direction j, it generates a wave eld with the correspondingpotential j . These six potentials can be split into the six center of gravityvelocities of the body s = (s1, s2, ..., s6) and the corresponding local bodypotentials j

j = sjj j = 1, 2, ..., 6 (2.11)

where j denotes the translatory motions surge (1), sway (2), and heave(3) as well as the rotatory motions roll (4), pitch (5) and yaw (6). Allpotentials that solve the hydrodynamic problem have to satisfy Laplacesequation (2.1) as well as boundary conditions (2.4) to (2.6). For a well-dened solution, potentials j (j = 1,2,. . . , 6) and 7 additionally have tosatisfy the Sommerfeld radiation condition (2.7).

The boundary problem briey stated above is solved by applying Greenssecond identity

V

[(G)G()] dV =S

(G

nG

n

)dS (2.12)

to derive integral equations for the radiation and diraction potentials onthe body boundary. The Green function G(x, ) is referred to as the wavesource potential the velocity potential at the point x due to a point sourceof strength -4 located at the point .

The solution that for the local radiation body potentials j gives

2j(x) +

Sb

j()G(x, )

ndSb =

Sb

G(x, )j()

ndSb j = 1, ..., 6.

(2.13)The corresponding solution for the scattering potential 7 is

27(x) +

Sb

7()G(x, )

ndSb =

Sb

G(x, )7()

ndSb (2.14)

The potential of the incident wave eld 0 and the scattering potential 7are combined in the total diraction potential D. For this potential, anintegral equation with simplied right-hand side can be set up:

2D(x) +

Sb

D()G(x, )

ndSb = 40(x) (2.15)

In WAMIT, body surfaces have to be discretized by a nite number ofquadrilaterals or panels. The radiation as well as the diraction velocitypotentials are assumed to be constant over each panel.

25 2. DESCRIPTION OF THE NUMERICAL METHOD

2.2 Hydrodynamic Forces and Motions

The total dynamic force acting on a submerged body in waves results fromthe integration of the dynamic pressure over the wetted body surface Sb:

F dyn =

Sb

pdyn ndSb (2.16)

where the dynamic pressure is dened according to Bernoullis equation

pdyn = t

(2.17)

and can thus be split into three components in analogy to the potential (cf. Eq. (2.8)):

pdyn = 0

t+

7t

+

6j=1

sjj

(2.18)

resulting in internal and external (or excitation) forces:

F dyn = Sb

(0t

+7t

)ndSb

Fex, excitation force

Sb

sjjndSb

Fint,dyn, dynamic internal force

(2.19)where the dynamic internal force is depending on the added mass aij andpotential damping coecients bij :

Sb

nij dSb = aij ibij (2.20)

Forced changes in a bodys buoyancy, e.g. induced by varying submergeddepths z, lead to a hydrostatic restoring force, which is the second internalforce component to be considered:

F int,stat = gSb

n z dSb = C s (2.21)

According to Newtons second law, the equilibrium of internal and externalforces on the submerged body nally gives the equation of motion, fromwhich the body motion sj can be determined:

6j=1

[2 (mij + aij) + ibij + cij] sj = fex,j (2.22)In the following, the relevant hydrodynamic coecients to solve this equa-tion are briey introduced:

2.3. INTERNAL TANK EFFECTS 26

added mass/potential damping: The added mass aij as well as thepotential damping bij are evaluated from the local body potentials jwith the following relation, already introduced in Eq. (2.20):

aij ibij =

Sb

nij dSb (2.23)

restoring coecients: hydrostatic restoring cij is exclusively related toheave, roll and pitch motions (except for external moorings).

C =

0 0 0 0 0 00 0 0 0 0 00 0 c33 c34 c35 00 0 c43 c44 c45 c460 0 c53 c54 c55 c560 0 0 0 0 0

where

c33 = g

Sb

n3dSb

c34 = c43 = g

Sb

yn3dSb

c35 = c53 = gSb

xn3dSb

c44 = g

Sb

y2n3dSb + gzb mgzg

c45 = c54 = gSb

xyn3dSb

c46 = gxb +mgxgc55 = g

Sb

x2n3dSb + gzb mgzg

c56 = gyb +mgyg(2.24)

2.3 Internal Tank Eects

The introduced numerical method is capable of capturing the eects of cou-pling between internal liquid motions and rigid body motions of the LNGC.

27 2. DESCRIPTION OF THE NUMERICAL METHOD

The computational domain consists of an external and a specied numberof internal uid domains, which constitute one global boundary surface butthe respective potentials are independent and do not inuence each other.For the internal tank domain, diraction eects are neglected (no incidentwaves, no scattering) and according to the formulation in Eq. (2.11), thevelocity potential of each tank gives (Newman (2005)):

T = i

6j=1

sj T,j (2.25)

where sj is the body motion in the jth direction and T,j the corresponding

local tank potential.At rst, hydrostatic parameters are evaluated separately for the hull (atits actual draft but without the inuence of the liquid cargo in the massmatrix) and the tanks. Subsequently, restoring coecients, added mass anddamping are combined as follows:

restoring coecients:Free uid surfaces can be considered as a reduction of the vessels wa-terplane area. Contributions from the tanks are added to the restoringcoecients of the hull, e.g. the total heave restoring coecient becomesc33 = c33 +

c33,T . The calculation of the tank restoring coecients

is analogous to Eq. (2.24), with =T being the density of the internaluid. Due to the inverse orientation of the uid boundaries, there isno positive restoring force for the tanks, hence the respective contri-butions are negative and reduce the total restoring coecients. As

-3 -2 -1 0 1 2 3

x 109

0

20

40

60

80

100

c33,T

[kg/s2], c

44,T[kg m

2/s

2], c

55,T[kg m

2/s

2]

filli

ng h

eig

ht [%

]

c33,T

c44,T

c55,T

Figure 2.1: Cuboid tank restoring coecients c33,T , c44,T and c55,T dependingon the lling height

2.3. INTERNAL TANK EFFECTS 28

shown in Fig. 2.1 for a cuboid tank (length 38.3 m, width 35.8 m,height 26.1 m), the negative magnitudes of the restoring coecientsincrease with increasing lling height except for c33,T which remainsconstant for all lling conditions. The eect of multiple cargo tanksmounted to a ship hull is exemplarily calculated for the heave restor-ing coecient of the MPLS20 LNGC: The hull restoring coecientin fresh water ( = 998.2 kg

m3) is c33 = 9.59 107 kgs2 and each of

the four prismatic tanks (with 30% fresh water lling) contributesc33,T = 1.34 107 kgs2 , resulting in a total heave restoring coecientc33 = c33 + 4 c33,T = 4.23 107 kgs2 . added mass coecients:Added mass eects can be observed when submerged bodies are sub-jected to a transient pressure eld caused by relative accelerationsbetween uid and structure. In the case of internal tanks, this also in-cludes relative accelerations between tank walls and the internal uid.The respective coecients are evaluated globally by integration of thepressure force over the total wetted body surface, including tank wallswhere is replaced by T (see Eq. (2.23)). Only the coecients forthe vertical modes heave, roll and pitch require special adaptations,because a ctitious hydrostatic contribution (WAMIT Inc. (2006))has to be considered. This adaptation takes into account that the freesurface eects on the restoring coecients are evaluated with respectto the global origin and not to the local centroid of the free surfacearea as in the classical hydrostatic approach. For example, the heaveadded mass contribution from the internal tank domain becomes:

a33,T = T

ST

n3 T,3 dST = TT + 12

c33,T (2.26)

where the last term is canceled out by the hydrostatic restoring coef-cient for very low wave frequencies, i.e. there is no tank contributionfor the limit 0. The added mass characteristics of a tank alonegive information on the odd natural modes. All even modes, like thesecond sloshing mode, are caused by non-linear wave-wave interactionand are therefore not computable by the chosen linear potential theoryapproach (Malenica et al. (2003)). But since the free surface elevationsinside the tank are symmetric for even modes (see Fig. 2.3), there areno coupling eects with the ship motions, i.e. they are not relevant inthis context anyway. In Fig. 2.2, a11,T and a22,T are calculated for adetached cuboid tank (length 38.3 m, width 35.8 m, height 26.1 m),showing the rst and third longitudinal and transverse mode for ex-emplary lling heights of 10%, 20% and 30%. In the frequency rangebelow the rst mode, the added mass caused by the pressure of the

29 2. DESCRIPTION OF THE NUMERICAL METHOD

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-5

-4

-3

-2

-1

0

1

2

3

4

5x 10

8

[rad/s]

a11,T

[kg

]

10% Filling height

20% Filling height

30% Filling height

1 modest

FEX FPFEX FP

3 moderd

longitudinal sloshing

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-4

-3

-2

-1

0

1

2

3

4x 10

8

[rad/s]

a22,T

[kg

]

1 modest

3 moderd

FEX FPFEX FP

transverse sloshing

Figure 2.2: Characteristics of the added masses a11,T (top) and a22,T (bot-tom) of the detached cuboid tank for exemplary lling heights of 10%, 20%and 30%

2.3. INTERNAL TANK EFFECTS 30

i=1 i=2

i=3 i=4

no

de

an

tin

od

e

an

tin

od

e

no

de

no

de

an

tin

od

e

an

tin

od

e

an

tin

od

e

an

tin

od

e

an

tin

od

e

an

tin

od

e

an

tin

od

e

no

de

no

de

no

de

an

tin

od

e

an

tin

od

e

an

tin

od

e

an

tin

od

e

an

tin

od

e

no

de

no

de

no

de

no

de

odd modes even modes

Figure 2.3: Schematic visualization of the tank surface deections at the rstfour sloshing modes

accelerated uid is positive (exemplarily indicated by the green areabelow the added mass for 30% lling height), while a phase shift inthe uid motions for the frequency range above the rst mode resultsin negative added mass eects (exemplarily indicated by the red areabelow the added mass for 30% lling height). This eect is illustratedby a simplied system with indicated directions of forces for a excitedpartially lled container. Identical observations can be made for allother odd modes.

damping coecients:The moving walls of the internal tanks generate waves in the internaluid. Since these waves are trapped and cannot propagate away fromthe system, no radiation with associated energy dissipation occurs.Therefore, the potential damping contribution of the internal tanks iszero.

According to Faltinsen and Timokha (2009), the natural transverse slosh-ing frequency of the ith mode for a rectangular tank is given by an expressionbased on the dispersion relation:

r,i =

g

i

BTtanh

(i

BThf

)(2.27)

31 2. DESCRIPTION OF THE NUMERICAL METHOD

where the respective lling height inside the tank is denoted by hf and thetank width by BT . The natural frequency is not dependent on the densityof the uid inside the tank. For prismatic tanks with chamfered bottom,Faltinsen and Timokha (2009) proposed a correction factor:

(r,ir,i

)2= 1

12

sinh2(i2BT

) 21 sin2

(i1BT

)i sinh

(2ihBT

) (2.28)

giving the percentaged deviation compared to rectangular tanks. r,i is thecorrected natural frequency of the ith mode for prismatic tanks. The excita-tion of the lowest natural frequency of the liquid motion and its impact andcoupling with ship motions is of primary interest. The wave lengths insidethe tanks related to the rst mode (i = 1) are about twice the respectivecharacteristic tank dimension, i.e. 2BT for = 90 and 2LT for = 180,with a node in the tank center.

2.4 Operational Limitations

Due to the design and material properties of the transfer pipes, the crucialparameter for oshore ooading procedures is the relative motion of thecoupling points of the LNG transfer system, i.e. the relative motion betweenFLNG terminal and LNGC. Once a maximum tolerable relative motion am-plitude is established, the operational range of the FLNG system can bedetermined based on a linear stochastic approach.At rst the type of spectrum and associated range of peak periods has to bedened. Typical standard spectra include the Pierson-Moskowitz spectrum(Pierson and Moskowitz (1964)), e.g. the formulation recommended by theITTC

S() = 490H2s

T 4P 5e 1955

T4P

4 (2.29)

which can be applied for analyses in the North Atlantic Ocean region. Forthe North Sea region, the JONSWAP spectrum which accounts for the oc-currence of steeper waves can be applied, e.g. the formulation by Houmband Overik (1976) which was extended by Wichers (1979) in order to ensureidentical spectral areas hence identical signicant wave heights:

S() = H2s4p5

e54 [

p ]

4

B() (2.30)

2.4. OPERATIONAL LIMITATIONS 32

where

=0.313

F ()with

{F = 1 for = 1F = 1.52 for = 3.3

B() = e (p)

2

222p

=

{0.07 for p0.09 for > p

The coecient represents the ratio of maximum values of JONSWAP toPierson-Moskowitz spectra i.e. for = 1, both spectra are identical. Atypical value for the North Sea is = 3.3. The spectral shapes resultingfrom Eqs. (2.29) and (2.30) with = 3.3 are exemplarily compared forHs = 1 m and Tp = 10 s in Fig. 2.4. Alternatively, sea spectra can be setup in dependency of the zero-upcrossing period T0, which is related to thepeak period by T0 = Tp/1.285.

Once a set of suitable sea state spectra with an associated range of peakperiods is established, the stochastic analysis begins with the determinationof the desired response spectra Sj(, Tp) by multiplying the sea state spec-tra by the squared absolute value of the RAO of the jth mode sj,a()/a(the procedure is illustrated for motions but can be applied analogously to

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.05

0.1

0.15

0.2

0.25

0.3

0.35

[rad/s]

S(

) [m

2s]

Pierson-Moskowitz

JONSWAP ( = 3.3)

Figure 2.4: Exemplary comparison of a Pierson-Moskowitz and a JONSWAPspectrum ( = 3.3), both for Tp = 10 s and Hs = 1 m.

33 2. DESCRIPTION OF THE NUMERICAL METHOD

velocities, accelerations, forces):

Sj(, Tp) = |sj,a()a

|2 S(, Tp) (2.31)

From the area enclosed by these response spectra, signicant double ampli-tudes are determined:

(2sj,a)s(Tp) = 4

0

Sj(, Tp)d (2.32)

Division by the signicant wave height gives the desired signicant RAO. Forpredened maximum tolerable parameters, tolerable signicant wave heightsare calculated in dependency of the peak periods (assuming a statisticalvalue of 1.86 for the ratio of tolerable maximum relative motions to tolerablesignicant relative motions):

Hs,tol(Tp) = (2si,a)s,tolHs

(2si,a)s(Tp)(2.33)

These limiting sea states can be transferred to a wave scatter diagram of therespective operational location. With the known frequencies of occurrencefor each combination of Hs and Tp (or alternatively T0), the operationalrange or the annual downtime in days can be determined.

Excursion: Statistical Maximum Values

Theoretically, the wave height distribution of a narrowband sea spectrum ischaracterized by the Rayleigh distribution

R(H) =2 H

H2RMSe H2

H2RMS (2.34)

with the root mean square of the heights of all N waves

HRMS =

1N

Nj=1

H2j (2.35)

Since the signicant wave height is the mean value of the 33% highest waves,it can be identied as the center of the area enclosed by the Rayleigh distri-bution above the limit H33:

Hs =

H33

H R(H)dH

H33

R(H)dH

= 3

H33

2 H2

H2RMSe H2

H2RMS (2.36)

2.4. OPERATIONAL LIMITATIONS 34

This integral has to be solved numerically and yields

Hs 2 HRMS (2.37)

Assuming the maximum wave to be the wave height that is exceededonce in the chosen observation period, its probability of exceedance is

P (H Hmax) = 1 R(Hmax) = e H

2max

H2RMS =

1

N(2.38)

Solving Eq. (2.38) for Hmax gives

Hmax = HRMSln(N) (2.39)

Substituting Eq. (2.37) nally gives the relation of Hmax to Hs

Hmax = Hs

ln(N)

2(2.40)

Typically, a standard value of N = 1000 waves is chosen which representsa three-hour storm with a mean wave period of 10 s. The standard relationis therefore

Hmax = 1.86 Hs (2.41)

0 0.5 1 1.5 2 2.5 3 3.50

0.5

1

1.5

2

2.5

3

3.5

4