Analysis of Jackup Rig in Wet Tow Transit

ANALYSIS OF JACK-UP RIG DURING WET TOW WITH LEGS LOWERED

A THESIS submitted by

P LALITH KUMAR OE14M053

In partial fulfilment of the requirements for the award of the degree of

MASTER OF TECHNOLOGY in

OFFSHORE STRUCTURAL ENGINEERING

DEPARTMENT OF OCEAN ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY MADRAS CHENNAI - 600036 MAY 2016

T o Mom M om and Da D ad who who always always supp suppor orte ted d me me whate whateve verr path I too took

THESIS CERIFICATE

This is to certify that the thesis titled "ANALYSIS OF JACK-UP RIG DURING WET TOW WITH LEGS LOWERED", submitted by Mr. LALITH KUMAR P , to the Indian Institute of

Technology Madras, Chennai for the award of the degree of MASTER MASTER OF TECHNOLOGY in OFFSHORE STRUCTURAL ENGINEERING, is a bonafide record of the research work done

by him under my supervision in the Department of Ocean Engineering, Indian Institute of Technology Madras (IITM). The contents of this thesis , in full or in parts, have not been submitted submitte d to any other Institute or University for the award of any degree or diploma.

Date: Place: Chennai, India

Prof. R. PANNEER SELVAM

Professor and Guide Department of Ocean Engineering Indian Institute of Technology Madras

ACKNOWLEDGEMENTS

I am highly indebted to Prof. R. Panneer Selvam my mentor, philosopher and guide for his invaluable guidance, advice, encouragement and above all for his role as a teacher. His guidance has played a big role in this project from the very conception to the completion and the knowledge acquired by me in the process. His sincerity and dedication to work remains as source of inspiration to me. No words can express my deep sense of gratitude to Prof. S Nallayarasu, Co-ordinator, for his valuable suggestions, the professional way in which he arranged the project reviews and for his guidance whenever the students were in need. I am grateful to Dr. Rajiv Sharma, review panel member whose valuable inputs have been beacons guiding me along the the correct path at every stage of my project work. I am thankful to all my teachers at IIT Madras for making my post-graduate studies an invaluable learning experience, both academically and practically who put their faith in me and urged me to do better. I express my deepest gratitude towards my loving Grandma Smt. Sriranjanamma for all the sacrifices borne for me and for the emotional support throughout my life. I express my gratitude to my father Shri P Muneeswara Reddy and my mother Smt. P Parvathi for their abundant love, nurture and the most important of all providing quality education without which I wouldn't have been at this pleasant juncture in life. I am also deeply indebted to my sister P Deepika for her kind affection and support. I will always remember my friends and classmates at IIT M campus with whom I have cherished some joyous moments during my stay at the campus.

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ABSTRACT

Keywords: Jack-up Rig Wet Tow, Response Response Amplitude Operator, Operator, Lowering Legs, Bending Moments, Stresses, Safe Limits, Rig's Response, Drag Forces, Stick Leg Model, Hydrodynamic Coefficients

There is a steadily increasing demand for the use of jack-up units in deeper water and harsher environments. The deployment of jack-up rig from one drilling site to another involves either a wet tow or dry tow. Usually the latter requires the application of a specialised submersible barge whereas wet tow can be undertaken with relative ease and increased stability. Wet tow can be undertaken with legs partially submerged rather than cut in case of dry tow which introduces the possibility of distortions, defects, excessive stresses and high localised heat input due to welding.

Dry tow is performed with the legs extended above the hull and in transit there t here is a probability that it could be subjected to storm conditions and the legs has to be lowered below the hull to maintain the rig motions within acceptable level (stability and safety considerations). This will cause additional loads in the form of drag on the legs which are extended below the hull, unlike the condition with legs extended in air.

In this study several cases of wet tows are studied in which various lengths of jack-up's legs are submerged. A Typical Marathon LeTourneau 116-c jack-up rig is used to perform motion analysis with various leg drafts and indicate the safe limits up to which the legs can be lowered below the hull without overstressing it. For each wet tow case various wave headings are considered to report rigs response. For each of the different tow cases and heading, time dependent bending moments about longitudinal and transverse directions were determined at the jack house level for the portion of the leg above as well as below the hull.

For the above purpose, a simplified 'stick leg' model of a jack-up leg was adopted. the equivalent dimensions of the stick leg and cross sectional properties are derived by employing the formulas given in the ISO standard. For this model Hydrodynamic drag and mass coefficients are calculated using an equivalent drag coefficient CDe, and an equivalent mass coefficient C Me, in accordance with the ISO standard.

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TABLE OF CONTENTS

........................................... .............................. ................................ .................................. ...................... ... i ACKNOWLEDGEMENTS.............................. ABSTRACT.............. ............................. .............................. ............................... ............................... ................................ .............................. .............................. .................ii ii TABLE OF CONTENTS ............... ................................ .............................. .............................. ................................ .............................. ......................iii .......iii LIST OF TABLES ................. ................................ ................................ ................................ .................................. .................................. ...........................vi ............vi LIST OF FIGURES ............. ............................ ................................ ................................ .............................. ................................ ................................vii ...............vii ABBREVIATIONS.............. ............................. ............................... ............................... .............................. ................................. .................................xii ...............xii

................................ .............................. ............................. ............................. ................................... ................................... ....................xiii .....xiii NOTATIONS.................

CHAPTER 1 INTRODUCTION

1.1 General........... General............................ ................................ ............................... ............................... .............................. .............................. .................................... .....................1 1 1.2 jack-up rig Characteristics................ Characteristics................................. ................................ ................................ .............................. ............................. .................1 .1 1.3 Jack-up analysis and modelling................................ modelling................................................. ................................ .............................. .......................3 ........3 1.4 Types of jack-up units..................................... units.................................................... ............................. ............................... .................................. ...................6 ..6 1.4.1 Independent leg type jack up unit................................ unit..................................................... .................................... .........................6 ..........6 1.4.2 Mat type jack-up unit................................. unit................................................ .............................. ................................ .................................. .................7 7 1.5 Jack-up fatalities................................ fatalities................................................. ................................ ................................... ................................... ..........................8 ...........8 1.6 Need for the study................................... study.................................................. .............................. .................................. .................................. ......................10 .......10

CHAPTER 2 LITERATURE REVIEW

2.1 General............................ General........................................... ................................ ................................ .............................. .............................. .................................11 ..................11 2.2 Various studies on wet tow transit of jack-up jack- up rig.................................. rig................................................. ........................11 .........11 2.3 Objective Objectiv e and scope of the th e study.......... stud y......................... .............................. ................................ ................................ ..........................14 ...........14 2.4 Thesis outline................................. outline.................................................. ................................ .............................. .............................. .................................16 ..................16

iii

CHAPTER 3 ANSYS AQWA AND DESCRIPTION OF JACK-UP MODEL

3.1 General............................ General........................................... ............................... ............................... .............................. .............................. ..................................17 ...................17 3.2 Ansys AQWA suite................................ suite............................................... ................................... ................................... ............................. ......................17 ........17 3.3 Response amplitude operator.............................. operator............................................. ............................... ............................... ............................19 .............19 3.4 Description of Jack-up unit................................ unit............................................... ................................. ............................... ...........................20 ..............20 3.4.1 Deck parameters............................. parameters............................................ .............................. ................................ .............................. ...........................21 ..............21 3.4.2 Jack-up legs............................... legs............................................... ............................... .............................. .............................. .............................. ..................22 ...22 3.4.3 Spud can................................ can................................................ ............................. .............................. ................................ .............................. .....................24 ......24 3.5 Structural modelling............................... modelling.............................................. .............................. ................................ ................................ .........................29 ..........29 3.5.1 General............................ General............................................. ................................ .............................. ................................ ............................... .........................29 ...........29 3.5.2 Equivalent leg modelling............................... modelling.............................................. ................................... ................................... .......................29 ........29 3.5.3 Equations Eq uations as per pe r ISO standard.............................. standard.............................................. ............................... .............................. ....................29 .....29 3.5.4 Equivalent hydrodynamic coefficients.................. coefficients................................... ................................. ............................... ..................31 ...31 3.5.5 Equivalent diameter.............................. diameter............................................ ................................. .................................. .............................. ...................31 ....31 3.5.6 Equivalent drag coefficient............................. coefficient............................................ ................................ ................................ .........................31 ..........31 3.5.7 Equivalent mass coefficient............................. coefficient............................................ ................................ ................................ ........................32 .........32

CHAPTER 4 ANALYSIS AND RESULTS

4.1 General............................ General........................................... ................................ ................................ .............................. .............................. .................................34 ..................34 4.2 Loads on the structure.................................. structure................................................ .............................. ................................... ................................. .................34 ...34 4.2.2 Motion response................................ response............................................... .............................. ................................ ................................ .......................34 ........34 4.2.3 Response to irregular waves............................... waves............................................... ............................... .............................. ......................34 .......34 4.3 Results.............................. Results............................................. ................................ ................................ .............................. .............................. .............................. .................37 ..37 4.3.1 Response amplitude operators for legs above the hull......................................... hull.............................................37 ....37 4.3.2 Response amplitude ampli tude operators for f or 100 ft f t leg draft.......................................... draft...................................................41 .........41

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4.3.3 Response amplitude ampli tude operators for f or 200 ft f t leg draft............................................. draft...................................................44 ......44 4.3.4 Response amplitude ampli tude operators for f or 250 ft f t leg draft.......................................... draft...................................................47 .........47 4.3.5 Response amplitude ampli tude operators for f or 300 ft f t leg draft.............................................. draft...................................................50 .....50 4.3.6 response to irregular waves.............................. waves............................................. ................................ ................................ ........................55 .........55 4.4 Bending moments on legs................................ legs............................................... .............................. .............................. ................................58 .................58 4.5 Stresses in legs................................ legs................................................. ................................ .............................. ............................. ............................. ..................66 ...66 4.6 Safe limits of leg draft............................... draft.............................................. .............................. ............................... ................................... .......................69 ....69 4.7 Natural period variation................................... variation.................................................. .............................. .............................. ............................. ................70 ..70 4.7 Moment of inertia and added mass variation.......................................... variation......................................................... .......................72 ........72 4.8 Drag force and velocity v elocity variation.................................. variation................................................. ............................. ............................. ....................73 .....73

CHAPTER 5 SUMMARY AND AND CONCLUSIONS

5.1 Summary......................... Summary........................................ ................................ ................................ .............................. ............................. ............................. ...................75 ....75 5.2 Conclusions.................. Conclusions................................. .............................. .............................. ............................... ............................... .............................. ......................75 .......75 5.3 Scope for future work............................... work.............................................. ............................... .................................. ................................. ....................76 .....76

REFERENCES............................. ............................................ .............................. .............................. ................................... ................................... .....................77 ......77

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LIST OF TABLES

Table No.

Title

Page No.

1.1

Jack-ups lost in transit................................... transit.................................................. .............................. .................................. ...................08 08

3.1

Principle dimensions of hull.............................. hull.................................................. ................................... ........................21 .........21

3.3

Legs and spud can specifications..................... specifications.................................... .............................. ...............................23 ................23

4.1

Maximum response of jack-up rig in different degrees of freedom..............53 freedom..............53

4.2

Percentage change in responses in comparison with the case when full leg up............................. up............................................ ................................ .............................. .............................. .............................53 ............53

4.3

Maximum bending moment about transverse axis for 12 m wave height................................. height.............................................. .............................. .................................... ................................. ..................62 ....62

4.4

Maximum bending moment about longitudinal axis for 12 m wave height................................... height................................................ ............................. ............................... .............................. .....................63 ......63

4.5

Maximum bending moment about transverse axis for different wave heights.................................. heights............................................... .............................. .................................. ................................ ..................63 ...63

4.6

Maximum bending moment about longitudinal axis for different wave heights.................................. heights............................................... .............................. ............................... ............................. .....................64 ......64

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LIST OF FIGURES

Figure No.

Title

Page No.

1.1

"A" shape structure with a flat top and bottom.................................. bottom.............................................02 ...........02

1.2

Modes of operations when a jack-up is to operate at a location..................03

1.3

Jack-up rig being towed using tugs.................................. tugs................................................... ............................04 ...........04

1.4

Typical jack-up drilling rig profile............................... profile.............................................. ............................... ................05 05

1.5

Image of jack-up rig drilling on the platform............................. platform............................................. .................05 .05

1.6

Jack-up rig failure during transit................................ transit.................................................. .................................. ................09 09

1.7

Jack-up rig failure during wet tow................................. tow................................................ ..............................09 ...............09

2.1

A typical 3-legged jack-up rig.............................. rig............................................. .............................. ........................11 .........11

2.2

Steps involved in the study.................................. study............................................... ............................. ...........................15 ...........15

3.0

Ansys workbench GUI menu.......................... menu......................................... ................................ ..............................19 .............19

3.1

Marathon LeTorneau jack-up rig being towed.................................. towed............................................20 ..........20

3.2

Plan of hull (upper deck).............................. deck)............................................. .............................. ................................ ..................22 .22

3.3

Model of hull............................... hull................................................ ................................ ................................... .................................22 .............22

3.4

Plan of front single leg............................. leg............................................. ............................... ................................ .....................24 ....24

3.5

Plan of leeward leg............................... leg............................................... ............................... .............................. .........................24 ..........24

3.6

Spudcan detailing.................................. detailing................................................... ................................ .............................. .......................25 ........25

3.7

Spud can model in Ansys............................... Ansys.............................................. .............................. ...............................25 ................25

3.8

Front view of jack-up leg................................ leg............................................... .............................. ..............................26 ...............26

3.9

Isometric view of jack-up leg.............................. leg........................................... .............................. ...........................26 ..........26

3.10

Model of jack-up rig in Ansys with legs above the hull..............................27 hull..............................27

3.11

Model of jack-up rig with legs lowered below the hull...............................28 hull...............................28

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Figure No. 3.12

Title

Page No.

Equations for determining the effective shear area for two- dimensional structures (ISO 19905-1 ,2012).............................. ,2012).......................................30 .........30

3.13

Equations for determining the equivalent section properties of three dimensional lattice legs (ISO 19905-1,2012)................30

3.14

Flow angles appropriate to a lattice leg (ISO 19905-1,2012)..................... 19905-1,2012)......................32 .32

3.15

Drag coefficient variation using the actual leg model.................................33 model.................................33

3.16

Equivalent stick model of jack-up rig............................. rig.............................................. .............................33 ............33

4.1

Meshed image of hull.................................. hull................................................. .............................. ................................ ...................35 ..35

4.2

Meshed image of rigs leg............................... leg.............................................. .............................. ...............................35 ................35

4.3

Beam sea condition for the model........................... model.......................................... ................................ .....................36 ....36

4.4

Head sea condition for the model............................. model............................................ ................................ ....................36 ...36

4.5

Different directions of wave approach............................... approach................................................. ..........................37 ........37

4.6

Surge RAO for full leg up............................. up............................................ .............................. ............................... .................38 .38

4.7

Sway RAO for full leg up............................. up............................................ .............................. ............................... .................38 .38

4.8

Heave RAO for full leg up............................. up............................................ .............................. ...............................39 ................39

4.9

Pitch RAO for full leg up.............................. up............................................... ................................ ................................ .................39 39

4.10

Roll RAO for full leg up........................... up............................................ ................................ .............................. ...................40 ....40

4.11

Yaw RAO for full leg up.............................. up............................................. .............................. ................................ .................40 40

4.12

Surge RAO for leg draft 100 ft............................... ft.............................................. .............................. ......................41 .......41

4.13

Sway RAO for leg draft 100 ft.............................. ft............................................. .............................. ........................41 .........41

4.14

Heave RAO for leg draft 100 ft............................. ft............................................ .............................. .......................42 ........42

4.15

Pitch RAO for leg draft 100 ft................................. ft................................................. ................................ ....................42 ....42

4.16

Roll RAO for leg draft 100 ft............................... ft.............................................. .............................. .........................43 ..........43

4.17

Yaw RAO for leg draft 100 ft............................... ft.............................................. .............................. ........................43 .........43

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4.18

Surge RAO for leg draft 200 ft.............................. ft............................................... ................................ .....................44 ......44

4.19


4.20

Heave RAO for leg draft 200 ft.............................. ft............................................. .............................. ......................45 .......45

4.21

Pitch RAO for leg draft 200 ft................................ ft............................................... .............................. ......................45 .......45

4.22

Roll RAO for leg draft 200 ft............................... ft............................................ .............................. ...........................46 ..........46

4.23

Yaw RAO for leg draft 200 ft................................ ft............................................... .............................. .......................46 ........46

4.24

Surge RAO for leg draft 250 ft.............................. ft............................................. .............................. .......................47 ........47

4.25

Sway RAO for leg draft 250 ft................................ ft............................................... .............................. .....................47 ......47

4.26

Heave RAO for leg draft 250 ft.............................. ft............................................. .............................. ......................48 .......48

4.27


4.28

Roll RAO for leg draft 250 ft.................................. ft................................................. .............................. ......................49 .......49

4.29


4.30

Surge RAO for leg draft 300 ft............................... ft.............................................. .............................. ......................50 .......50

4.31


4.32

Heave RAO for leg draft 300 ft................................ ft............................................... ............................... ....................51 ....51

4.33


4.34

Roll RAO for leg draft 300 ft............................... ft............................................ .................................... ...........................52 ....52

4.35


4.36

Pitch RAO- 0 degree heading................................. heading................................................ .............................. ......................54 .......54

4.37

Roll RAO-90 degree heading................................. heading................................................ .............................. .......................54 ........54

4.38

Maximum pitch response for Hs = 20 ft for 10 sec period..........................55 period..........................55

4.39


4.40


4.41


4.42


ix

4.43

Maximum pitch response for Hs = 20 ft ............................. ............................................ ........................57 .........57

4.44

Maximum Roll response for Hs = 20 ft............................... ft.............................................. ........................57 .........57

4.45

BM above hull with legs above hull in wave of heading 135°....................58 135°....................58

4.46

BM above hull with legs above hull in wave of heading 120°....................59 120°....................59

4.47

BM above hull for jack-up rig with legs 25% below hull in wave heading 90°................................ 90°............................................... ................................ ................................ .........................59 ..........59

4.48

BM above the hull for jack-up rig with legs 25% below hull in wave of heading 135°................................... 135°.................................................. ................................ .................................60 ................60

4.49

BM below the hull for jack-up rig with legs 25% below hull in wave of heading 135°............................... 135°................................................ .................................. ................................ ..................60 ...60

4.50

BM below the hull for jack-up rig with legs 50% below hull in wave of heading 120°.................................... 120°................................................... .............................. .............................. .................61 ..61

4.51

BM above the hull for jack-up rig with legs 50% below hull in wave of heading 135°................................... 135°.................................................. .............................. .............................. ..................61 ...61

4.52

BM below the hull for jack-up rig with legs 50% below hull in wave of heading 135°.................................... 135°................................................... .............................. .............................. .................62 ..62

4.53

Variation of maximum bending moment about transverse axis for12 m wave............................ wave........................................... ............................... ................................... .................................. .................64 ..64

4.54

Variation of maximum bending moment about longitudinal axis for12 m wave............................ wave........................................... ............................... ............................... .............................. .....................65 ......65

4.55

Variation of maximum bending moment about longitudinal axis for different wave heights................................... heights.................................................... ................................ ........................65 .........65

4.56

Variation of maximum bending moment about transverse axis for different wave heights................................... heights.................................................... ................................ ........................66 .........66

4.57

Maximum stress in leg for 4 m wave............................. wave............................................ ..............................67 ...............67

x

4.58

Maximum stress in leg for 8 m wave............................... wave................................................ ............................67 ...........67

4.59

Maximum stress in leg for 10 m wave............................. wave.............................................. ............................68 ...........68

4.60


4.61


4.62

Variation of natural period vs leg draft for roll............................. roll............................................71 ...............71

4.63

Variation of natural period vs leg draft for pitch............................... pitch.........................................71 ..........71

4.64

Variation of moment of inertia vs leg draft............................. draft.............................................. .....................72 ....72

4.65

Variation of added mass vs leg draft.............................. draft............................................. ..............................73 ...............73

4.66

Variation of drag force vs leg draft............................... draft.............................................. ...............................73 ................73

4.67

Velocity variation across the front leg............................. leg............................................. ............................74 ............74

4.68

Velocity variation across the back leg............................. leg.............................................. ............................74 ...........74

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ABBREVIATIONS

API

American Petroleum Institute

ABS

American Bureau of Shipping

BM

Bending Moment

BSI

British Standards Institution

CFD

Computational fluid dynamics

DNV

Det Norske Veritas

GUI

Graphical User Interface

ISO

International Organization for Standardization

ISOPE

International Society of Offshore and Polar Engineers

JONSWAP

Joint North sea Wave Project

MARIN

Maritime Research Institute Netherlands

MODU

Mobile offshore drilling unit

MPC

Multi point constraint

MSL

Mean Sea Level (still water level)

OTC

Offshore Technology Conference

RAO

Response Amplitude Operator

SNAME

Society of Naval Architects and Marine Engineers

SPE

Society of Petroleum Engineers

VDL

Variable deck load

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NOTATIONS

A

Added mass

Aci

Area of chord

Asi

Effective shear area

c

Center to center distance between chords

CAe

Added mass coefficient

CMe

Equivalent mass coefficient

CDe

Equivalent drag coefficient

De

Equivalent diameter

Di

Reference diameter of member i

h

Bay height of rig's leg

Hs

Significant wave height

l

Leg length

li

Reference length of member i

s

Height of one bay

t

Time

T

Wave period

T p

Peak period

γ

Peak enhancement factor (default value = 3.3)

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CHAPTER 1 INTRODUCTION 1.1 GENERAL A jack-up is a self-elevating unit comprising of a buoyant hull that can be raised over the sea surface by three or more steel legs supported on the seabed. The hull contains the facilities required to carry out the mission of the unit, such as drilling, production, construction support and as service platforms for offshore operations. The industry has also started using these units for installation and servicing offshore wind farms. The hull carries also all supporting functions such as accommodation, power generation, utilities etc. Most of these units are not self-propelled and therefore are dependent upon being towed by tugs or transported on heavy lift vessels between the different locations the units shall operate. These platforms are in general the most popular type of mobile units and there are about 540 jack-ups in operation in the world by end of 2013. They originated from drilling offshore in the Mississippi area in the early 1950s and the first one was designed by R. G. LeTourneau for Zapata Drilling.

1.2 JACK-UP RIG CHARACTERISTICS A jack-up unit is composed of a hull, legs, footings, drilling package and other equipment. Hulls are mainly triangular, but other forms as rectangular, octagonal and shipshape are also present. The most common are three leg systems, whereof the legs are truss type structures with triangular or square trusses. For the shallow water, the legs may also be of tubular type. Tubular legs are less expensive than open-truss legs to fabricate, they are less stable and cannot adapt to stresses in the water as well as open-truss legs. For this reason, tubular-legged jack-ups are not used in waters exceeding a certain water depth (<75m). At the bottom part of each leg, there is an independent or spudcan supported footing or a mat supported footing. Spudcans are fitted to support the legs on the seabed. These are typical cylindrically shaped steel shoes with pointed ends, similar to a cleat. A spike in the can is driven into the ocean floor, adding stability to the unit during operations. Jack-up units with cylindrical type legs typically have a mat supported footing. A mat supported footing is generally one common footing for all the legs. The shape is formed as a rectangular, “A” shape structure with a flat top flat top and bottom, see the Fig. 1.1 for an illustration.

1

Fig. 1.1: “A” shape structure with a flat top and bottom bot tom (Morandi 1986)

Once a jack-up unit has been towed to site, the legs are jacked down to the seabed, where they continue to be jacked down into the seabed until there is adequate bearing capacity for the hull to climb out of the water. The foundations are then preloaded by filling up seawater into ballast tanks or by pre-driving the legs. The spudcan will penetrate through the soil until it has sufficient bearing capacity to carry the preload. The vertical bearing capacity will be equal to the applied preload. This preloading process will act as a proof test of the foundation by exposing it to a larger vertical load than would be expected during the design storm. After preloading, the ballast tanks are emptied and the hull is jacked clear to a predetermined distance above the still water level. This distance is called the “air gap” and is defined as the distance between the underside of the hull (keel) and still water level (MSL). Fig. 1.2 illustrates the operations of a jack-up unit from arriving at a site to be in full operation step by step from towing to the location, lowering the legs, Preloading and jacking up hull to start operating it. Fig. 1.3 shows the jack up being tow to the location and Fig. 1.4 and Fig. 1.5 depicts the jack-up rig position after complete jacking up and just before drilling in the field and in the presence of platform respectively

2

Fig. 1.2: Modes of operations when a jack-up is to operate at a location (Morandi, 1986) 1986)

1.3 JACK-UP ANALYSIS AND MODELLING Before a jack-up can operate at a given site, an assessment of its capacity to withstand a design storm, usually for a 50-year return period, must be performed. In the past, with jackups used in relatively shallow and calm waters, it has been possible to use overly simplistic and conservative jack-up analysis techniques for this assessment. However, as jack -ups have moved into deeper and harsher environments, there has been an increased need to understand jack-up behaviour and develop analysis techniques. The T he publication of the ‘Guidelines for the Site Specific Assessment of Mobile Jack-Up Jack-Up Units’ (SNAME, 1994) was an attempt by the offshore industry to standardise jack-up assessment procedures. The guidelines also detail categories of jack-up modelling sophistication based on the latest research.

3

More realistic modelling of jack-ups based upon the rel evant physical processes has been developed in a number of areas, the most significant being:



Dynamic effects



Geometric non-linearities in structural modelling



Environmental wave loading



Models for foundation response



Response to different environmental conditions



Site specific assessment

Fig. 1.3: Jack-up Rig being towed using tugs tu gs (source: http://gcaptain.com/wp-content/uploads/2013/04/dt.common.streams.StreamServer.jpeg)

4

Fig. 1.4: Typical Jack-up drilling rig Profile (Source: http://offshore-fleet.com/images/jackup-rig-01.jpg)

Fig 1.5: Image of Jack-up rig drilling on the platform (Source: http://www.offshoreenergytoday.com/wp-content/uploads/2013/02/ADTI-Hires-Energy-Endeavour-Jack-UpRig-for-N.-Sea-Drilling.jpg)

5

1.4 TYPES OF JACK-UP UNITS There are two basic types of jack-ups: 1. Independent leg type Jack-up 2. Mat type Jack-up Both types of jack-ups have a hull, float onto location, jack the legs to the ocean bottom, and then jack the hull out of the water.

1.4.1 Independent-Leg Type Jack-up Unit For the independent-leg units (usually three legs with latt ice construction), construction), “preloading” is required to drive the legs into the ocean bottom before the hull is completely jacked out of the water. During this procedure, the jack-up jack- up MODU is at risk from weather and leg “punch through”; through” ; i.e., one leg breaks through a hard crust, putting the other legs in a large bending movement. Generally, 5-ft swells and/or a combined sea of 8 ft are the maximum seas in which these units can jack out of the water. If the hull should roll, pitch, and heave to an extent that the legs come into contact with the ocean bottom, particularly if it is hard, the legs can be severely damaged.

The preload sequence is usually done in stages, with the hull never rising more than 5 ft out of the water to safeguard against having a leg punch through. If the ocean bottom is soft and consists of clay, it is not uncommon to take 7 or more sequences, with each sequence taking 7 to 12 hours. The unit’s pumps seawater into its preload tanks, adding weight to the hull and d riving the legs. After the legs are driven and the hull goes into the water, the seawater is dumped overboard and the sequence is begun again. This process occurs until the legs no longer penetrate the ocean bottom. The concept is to load the legs to a level above that which the unit will encounter in the harshest predicted environment. The newer, enhanced premium units do a single preload in which the jacking system is strong enough to jack the unit with all the preload water onboard, the basic weight of the hull, and the full transit VDL. This is a significant advantage in that a much smaller “weather “w eather window” can be acceptable to move the unit. Jack-ups are most susceptible to major damage or loss when they the y are floating.

6

1.4.2 Mat-Type Jack-up Unit The mat-type jack-up also usually consists of three legs that are cylindrical and are from 8 to 12 ft in diameter. The mat is carried just under the hull during mobilization, usually with ≈ 5 -ft gap. When the unit comes onto location, it jacks the mat down to the ocean bottom, and because of its low bearing pressure, usually under 500 to 600 psf, the unit jacks the hull out of the water without going through the preload sequence required for independent-leg units. Bethlehem Steel Corp. built most of these units from the 1950s through through the 1980s. Their key advantages advantages are that they were relatively inexpensive to build and leave no footprint at the drilling location. Unfortunately, the Mat-Type Jack-up unit also has several disadvantages: 

They are very susceptible to damage from any object on the ocean bottom.



They tow very slowly because the mat and hull are large and cr eate a lot of drag. Their mats are susceptible to being gouged by workboat propellers.



Their upper hull has limited open deck storage space.



Their legs sometimes form a wind-induced leg vibration known as vortex shedding at high winds, which can cause them to fail.



Vortex shedding is a form of severe vibration seen with smoke stacks without spoilers.



Most mat rigs have cylinders for legs and are structurally limited to shallower water wat er depths, usually less than 250 to 275 ft.



Only a few units have reached 300 ft, and these units have lat tice-type legs.

For these reasons, mat jack-ups have fallen into disfavour, although they are relatively inexpensive and for some well types are more than adequate.

1.5 JACK UP FATALITIES The rigs are susceptible to fatalities which includes Bad weather, metal fatigue, loss of towline, human error and equipment failure are all common factors leading to the loss of rigs at sea when en-route to a new location. At least 30 jack-ups alone have been lost while on tow. Listed below in Table is a selection of rigs that have sunk. The sunk. The images in Fig. 1.6 and 1.7 shows the position of rig just before sinking which occurred during wet tow.

7

Table 1.1: Jack-ups Lost in Transit (Source: http://home.ve http://home.versatel.nl/the_sims rsatel.nl/the_sims/rig/i-sunk.htm) /rig/i-sunk.htm)

Rig Name

Bohai 2

Year

Place of Occurrence

Description of Accident

25 November

Gulf of Bohai, off

In 1979, the jack-up Bohai 2 capsized

1979

China

and sank in a storm while on tow off the coast of China.

Interocean II

08 November

Southern North Sea,

After a dramatic crew rescue in 1989,

1989

UK Continental Shelf

the Interocean II sank in a North Sea storm after towline failure.

Key Biscayne

1 September 1983

Ledge Point, Western

The Key Biscayne capsized and sank

Australia

off Australia's west coast in 1983 after flooding and towline failure.

Ocean Express

15 April 1976

Gulf of Mexico

Jack-up

Another casualty of towline failure, the Ocean Express sank in 1976 during a storm in Gulf of Mexico.

Ocean Master II Jack-up

June 1977

West Africa

The Ocean Master II sank off West Africa in 1977 as a result of structural s tructural problems and bad weather

Mr. Bice Jack-up

June 1998

Gulf of Mexico

Mr Bice sank in 1998 in the Gulf of Mexico after structural failure and flooding.

Rowan Gorilla I

15 December 1988

North Atlantic

The Rowan Gorilla I was crossing the North Atlantic in 1988 when it capsized and sank after structural failure caused by bad weather.

West Gamma Jack-up

20 August 1990

German Bight, North

A storm in 1990 caused structural

Sea

failure and flooding to the West Gamma, resulting in its sinking after towline loss.

8

Fig. 1.6 : Jack up rig failure during transit (source: http://i2.wp.com/gcaptain.com http://i2.wp.com/gcaptain.com/wp-content/uploads /wp-content/uploads/2015/05/CERQ6sjW /2015/05/CERQ6sjWMAIMAI58q.jpg?resize=600%2C450)

Fig. 1.7 : Jack up rig failure during wet tow (source: http://s3-ap-southeast-2.ama http://s3-ap-southeast-2.amazonaws.com zonaws.com/media/mediaaspermontlimited/images/e aspermontlimited/images/ern/AOC_Offsh rn/AOC_Offshore_Jack-up_R ore_Jack-up_Rig_Collapse_II_ ig_Collapse_II_low.jpg) low.jpg)

9

1.6 NEED FOR THE STUDY To meet the world increasing demands for oil, exploration and exploitation have moved into deeper and deeper water and harsher environment. Today, oil companies are searching for oil in water depths up to 3000 meters and in any weather conditions ranging from typhoons to the arctic areas. Exploration has traditionally been carried out by two types of units; a floater (ship-shaped and semi-submersible units) and a jack-up (self-elevating unit) as this mission requires mobility. Together with the technological advances in drilling technology to meet the increasing water and increasing drilling depth, the equipment and the storage requirements for bulk and liquid have grown in size and weight. The units have therefore grown in similar manner.

From their introduction, the accident rate involving jack-ups has exceeded that of other offshore installations. Accidents have occurred in the past in all the four stages; during transportation, installation, operation and removal. The probability of accidents can be reduced by proper design and analysis of the structure.

The jack-up units are slender structures due to their layout. The platform deck is supported on either three or more independent moveable legs. By increasing the water depth, the structure becomes more and more susceptible to the responses as the natural periods move towards the peak of the wave energy spectrum. As a part of the development, the water depth limitations for jackups have increased by improving the structural robustness. The main objective of this work is to analyse the jack-up unit for various sea states and for different leg drafts and to investigate the limitations i.e., the safe limits up to which the leg be extended below the hull without overstressing it , purpose-built for the harsh environment in the North Sea.

10

CHAPTER 2 LITERATURE REVIEW

2.1 General This chapter presents a literature review review on Jack-up rigs. The purpose purpose is to primarily explore explore the various approaches used by researchers worldwide to better understand the modelling and behaviour of such structures. s tructures. The review r eview focuses on the static and hydrodynamic response of the structure due to various environmental considerations, such as wind, waves and current. Not much work is reported in literature on anal ysis of a jack-up with its legs lowered lower ed below hull. Emphasis is placed on modelling techniques and methods of solution. Many modelling and techniques are common to ocean engineering communities due to similarities in structural and environmental complexities. Fig. 2.1 shows the model of rig with extended cantilever performing drilling.

Fig. 2.1: A typical 3-legged jack up rig (DNV 2012)

11

2.2 Various studies on wet tow transit of Jack-up rig Dallinga et al. al. (1984) studied on Design Aspects for Transport of Jack-up Platforms which contains A method for the calculation of design data for the transport of a jack-up platform on a barge is presented. The motions as well as the internal loads and the resulting deformations are considered. With the aid of a computer. program based on three-dimensional diffraction theory the hydrodynamic characteristics of the barge are determined. The effects of forward speed and nonlinear roll damping are investigated. Also the loads in the jack-up and the dynamic hogging, sagging and torsion deformations of the barge are calculated. The above mentioned aspects of the transport are reviewed for various wave conditions including directional seas. A procedure to determine design values based on long-term statistics is proposed.

Sharples et al. (1989) studied the risks with respect to jack-up rigs into perspective by quantifying them and comparing them to other risks. Their paper contains a few risk comparisons with fixed platforms, semisubmersibles, semisubmersibles , and drill dri ll ships. Historical casualties casualt ies are used in an example to show how a change intended to make an operation safer, may result in the opposite effect. Examining risks from losses due to environmental overload, the conclusion is reached that jack-ups are very safe structures." There appears to be no jack-up, in the timeframe examined, that has been lost because of a deficiency in the calculation methods currently in use by knowledgeable knowledgeable experts.

Massie et al. (1992) performed experimental and numerical study on jack-up dynamic behaviour. The laboratory study of three principle jack-up platform models were carried out in both regular and irregular waves. The data from irregular wave tests were analysed in both the probability domain and frequency domain supported by careful error analysis. Computer simulations were carried out in the time domain using a nonlinear, dynamic, multiple degree of freedom software which includes various hydrodynamic interaction options.

Grenda et al. (1992) al. (1992) Conducted a study to investigate the dynamic response to wave loading of a typical midsized jack-up drilling rig in the elevated position. Results of the study revealed the potential for significant dynamic amplification amplificat ion of wave loads in water depths exceeding about 150 ft range. Major parameters considered considered were water depth, damping ratio and current velocity. the increase in wave-induced leg stresses due to inclusion of dynamic effects was calculated to be on the order of 20% to 150 % for the subject rig in 150 and 300 ft of water, respectively. Sensitivity to damping ratio was found to be quite high, while the effect of currents was minimal. The dynamic analysis procedure used in study incorporated a time domain simulation method with a simplified wave load model. 12

Chakrabarti et al. al. (1995) have analysed Jack-up's by modelling it as a plate model using the structural analysis computer program StruCAD 3D and the motion response has been calculated using the program NEPTUNE. Different cases of wet tow are analysed and the limits for safe tow in case of storm are found out.

Brunel et al. al. (1996) performed a study based on three dimensional hydro-elasticity theory, the responses namely displacements, distortions, bending moments, shearing forces, stresses at any position in a flexible jack-up rig structures are assessed. The transported rig is either ei ther carried dry or towed wet in a unidirectional or confused seaway. Calculated response spectra and statistical measures are illustrated to know the barge or jack-up flexibility, sea conditions, wave spreading. The rig was modelled using Timoshenko beam elements for jack up legs and thin plate elements for barge and jack-up deck.

Houlsby Houlsby et al. al. (1998) presented a two-dimensional finite element program for the non-linear dynamic analysis of offshore jack-up units under storm loading is described. The program aims to incorporate consistent and reasonable levels of approximation of all the major system parameters; this is in contrast to many previous approaches, which have tended to model some aspects of the problem in great detail while adopting a very simplified approach to others. Accurate modelling of the jack-up legs is achieved using an Eulerian formulation of beam column theory. The complex non-linear behaviour of the spudcan footings is represented by a recently developed workhardening plasticity model, which represents a considerable advance over the simple pinned footing assumption which is most frequently used for jack- up analysis. Several options for calculating wave kinematics are available, including Stokes' fifth order wave theory.

Cassidy et Cassidy et al . (2001) published paper on Analysis of Jack-up units using a Constrained NewWave methodology which is concerns with the models appropriate for the dynamic assessment of jackups, with a balanced approach taken in considering the nonlinearities in structure, foundation and wave loading. A work hardening plastic model for spud-cans on sand is used for the foundation model. The spectral content of wave loading is considered using wave theory. A method for determining short-term extreme response statistics for a sea-state using Constrained newwaves is detailed

Hunt et al. (2004) in their paper on Jack-up response to wave-in-deck loads during extreme storms paper presents the methodology and key findings of a study into the wave loads generated on a 13

typical jack-up structure. The effects of structural response to previous waves, foundation modelling complexity and hull inundation levels on maximum structural response to wave-in-deck loading were assessed by performing a number of short duration time-domain analyses. A principal finding of the study was that large horizontal and vertical wave-in-deck loads are generated during inundation, and that the jack-up effectively reacts statically to the vertical loading.

Gang and Yong (2012) dealt with the dynamic analysis of jack-up unit leg system. Analysis of three frequently used truss-type legs is conducted including X -type, reverse (rev) K -type and mixing type. In their study, detailed models are built to simulate the Jack-up unit. Multi point constraint (MPC) elements are used together with the spring elements to deal with the boundary condition. Static response analysis, dynamic response and weight, which are the key technical objects of jack-up legs are analysed and compared for three kinds of different leg through finite element analysis.

Lee and Yan (2012) carried analysis on a typical jack-up leg configuration and the investigation of the internal wave loading on jack-up legs has been performed using Computational Fluid Dynamics (CFD) methodology. Systematic parametric studies are conducted to determine the dependence between the hydrodynamic hydrodynamic load and and internal wave amplitude under different incident wave directions. Through this study, useful information on hydrodynamic load ranges of internal waves can be obtained for future jack-up design.

The following observations are drawn from the literature study: 

Various analysis are performed with varying rig configuration and their responses are analysed.



Wave loading on the jack-up legs are performed to find it s impact on legs



Limited study on wet tow analysis of rig when legs lowered.



risks associated with respect to t o jack-up rigs in transit conditions either eit her wet or dry tow.



Comparative study with respect to different sea states and with different configurations of the rig.

14

2.3 OBJECTIVE AND SCOPE OF THE STUDY The main objective of the study is to Compare the Jack up rig response when legs extended above hull and when legs are lowered below the hull and to know the influence of submerged leg length on rig’s response along with finding the limits up to which th e legs can be lowered without overstressing. The scope of the work includes: 

Modeling the Jack-up rig in Rhinoceros and import the model into Ansys workbench and give the parameters required for analysis



Above model with legs above the hull is analysed in Ansys Aqwa and the response is obtained.



Validating the results with the results published in the paper.



The legs are lowered for different drafts below the hull and the rig is analysed for each case using Ansys Aqwa and hydrodynamic hydrodynamic loads are calculated using Ansys Fluent



Bending moments on Jack up rig legs are calculated for different l eg drafts.



Finding out safe limits up to which the leg can be extended below the hull without overstressing it.

The Fig. 2.2 below depicts the process involved in the study in the order which it i s performed

Model the rig in Rhinoceros

Analyse the above model with legs above the hull using Ansys AQWA

Bending moments are calculated on the jackup rig

Import the model from rhino to ANSYS

Lower the legs for the above model and perform the analysis for each case

Study is extended for different sea states

Input various parameters required for analysis

Hydrodynamic loads on the legs are calculated

Stresses on the legs are calculated and safe limits of leg draft are found out

Fig. 2.2: Steps involved in the study

15

2.4 THESIS OUTLINE Chapter 1 Introduction: This chapter gives brief introduction about the jack-up rig characteristics, their modes of operation and different considerations in jack-up analysis and modelling which outlines the various factors to be considered. The details of different types of jack up units and the details det ails on the jack-up rigs lost during transit is also presented along with the description.

Chapter 2 Literature Review: A detailed discussion on the review of works done by various authors along with the problem definition and their mode of approach which concludes with defining the objective and scope of the study.

Chapter 3 Ansys Aqwa and Description of model: In this chapter the theoretical formulation of the jack-up rig, the parameters used in modelling along with the model used in the study is shown which includes various assumptions made and the details of the software tool used in the study is also discussed. The details of the stick model is also presented along with the considerations from ISO is detailed.

Chapter 4 Analysis and Results: This section of the thesis includes the various cases and conditions used to analyse the model in Ansys AQWA. This also includes the results obtained by analysing the rig for different cases along with the observations made during the study.

Chapter 5 Summary and Conclusions: This section briefs a summary of the study along with the observations made during the study, this is followed by conclusions from the study and future work that can be carried out is also briefed.

16

CHAPTER 3 ANSYS AQWA AND DESCRIPTION OF THE JACK UP MODEL

3.1 GENERAL In this chapter, the theoretical formulation for the analysis of Jack-up rig is presented. The details of software tool ANSYS AQWA is also included. A brief description about the graphical user interface of the software tool is given. The details of the potential flow theory used used by AQWA for solving the hydrodynamic problems are also explained.

3.2 ANSYS AQWA SUITE ANSYS AQWA contains a set of programs for hydrodynamic analysis. The software is based on potential theory approach. AQWA suite contains many models in which each model performs various functions, in all of these models AQWA Line computes the linearised hydrodynamic fluid wave loading on a floating or fixed body using 3 dimensional radiation or diffraction theories. The hydrodynamic forces are composed of radiation forces and wave excitation forces. The radiation fluid loading is due to body motions and may be calculated by investigating the radiated wave field arising from body motions. The active or wave excitation loading which includes motion is composed of diffraction forces due to the scattering of the incident wave field and Froude-Krylov forces due to the pressure field in the undisturbed incident wave. The incident wave acting on the body is assumed to be harmonic and of small amplitude compared to its length. The fluid is assumed to be ideal, incompressible and irrotational, hence potential flow theory is used. The hydrostatic fluid forces may also be calculated using AQWA-LINE and these, when combined with the hydrodynamic force and body mass characteristics, may be used to calculate the small amplitude rigid body response about an equilibrium mean position. The solution technique utilises a distribution of fluid singularities over the mean wetted surface of the body. body. It provides an engineering tool set for the investigation of the effects of wave, wind and current on floating and fixed offshore and marine structures. The programs within the AQWA Suite are as follows (AQWA manual, Release 14.5, October 2012)

AQWA-LIBRIUM - Used to find the equilibrium characteristics of a moored or freely floating body or bodies. Steady state environmental loads may also be considered to act on the body (e.g. wind, wave drift and current).

17

AQWA-LINE - Used to calculate the wave loading and response of bodies when exposed to a regular harmonic wave environment. The first order wave forces and second order wave drift forces are calculated in i n the frequency domain.

AQWA-FER - Used to analyse the coupled or uncoupled responses of floating bodies while operating in irregular waves. The analysis is performed in the frequency domain.

AQWA-NAUT - Used to simulate the real-time motion of a floating body or bodies while operating in regular or irregular waves. Non-linear Froude-Krylov and hydrostatic forces are estimated under instantaneous incident wave surface. Wind and current loads may also be considered. AQWA-DRIFT - Used to simulate the real-time motion of a floating body or bodies while operating in irregular waves. Wave frequency motions and low period oscillatory drift motions may be considered. Wind and current loading may also be applied to the body.

AQWA-WAVE - Used to transfer wave loads on fixed or floating structure calculated by AQWALINE to a finite element structure analysis package.

The analysis is done in a Workbench based editor which is a graphical interface for AQWA analyses. It is used to create the model, apply specific inputs and view results. The main analyses done on floating structures are Hydrodynamic Diffraction and Hydrodynamic Time Response. AQWA Hydrodynamic Diffraction provides an integrated environment for developing the primar y hydrodynamic parameters required for undertaking complex motions and response analyses. Three-dimensional linear radiation and diffraction analysis may be undertaken taking full account of hydrodynamic interaction effects that occur between bodies. AQWA Hydrodynamic Time Response provides dynamic analysis capabilities for undertaking global performance assessment of floating structures in the time domain. A wide range of physical connections, such as mooring lines, fenders, and articulations, can be provided to model the restraining conditions on the vessels. The image of the Workbench user interface is shown in Fig 3 below.

18

Fig. 3: Ansys Workbench Workbench GUI menu

3.3 RESPONSE AMPLITUDE OPERATOR In case of regular waves, the amplitude of structural response is generally normalised with reference to the amplitude of wave. For linear systems these normalised responses are invariant to the wave amplitude at a frequency and these are referred to as the response amplitude operator (RAO).

       

(3.1)

In case of random waves, the power spectral densities of the response and wave surface elevation are proportional to the square of their response am plitude. Hence RAO can be written as

RAO

   19

(3.2)

3.4 DESCRIPTION OF JACK-UP UNIT The jack-up jack-up unit is a “similar” design des ign as Marathon LeTorneau 116-c Class drilling unit, with 3 square legs chorded inverse K-braced truss legs, with internal span-breaker bracing and splittubular chords which have opposed racks. This rig is widely used in Mideast - Persian Gulf, AsiaPacific, Gulf of Mexico and North sea taking its usage to its very limits to work in these harsh environments. This class of rigs are capable of drilling to a maximum well depth of 35,000 feet while operating in water depths ranging from 9 to 400 feet. This rig is built according to American Bureau of Shipping and classified under A1 Self-Elevating Drilling Unit. The specification of each part of the rig is given below. Fig. 3.1 shows Marathon LeTorneau 116-c Class drilling unit being towed using tugs. This This is case of wet tow where the legs are above the hull.

Fig. 3.1: Marathon LeTorneau Jack-up rig being towed Source: http://www.foxoildrilling.com/uploads/2/6/5/8/2658531/6696877_orig.jpeg

20

3.4.1 Deck Parameters The deck is modeled as a triangular hull which essentially comprises of an upper plate and a lower plate with water tight bulkheads between the two plates. The three legs pass through the two plates. A plan of the hull is shown in Fig. 3.2 and its model as seen in Ansys Ansys is shown in Fig. 3.3. This hull is 200 ft wider and 305.3 ft longer. This hull consists of upper and lower decks which are stiffened panels and as such are modeled as beams and plates. A number of plates are supported over a grid of beams. The Table 3.1 below shows the overall details of the hull and jack-up rig principal dimensions.

Table 3.1: Principle Dimensions of hull Overall Length (ft) (ft)

305.3

Hull Length (between perpendiculars) (ft)

243.1

Hull Width (ft)

200

Hull Depth (ft)

26

Deck Area (sq. Area (sq. ft) ft)

27055

Net Tonnage Tonnage (tonnes (tonnes))

2240

Gross Tonnage (tonnes (tonnes))

7460

Load Line Draft (ft)

17

Max. water depth (ft) (ft)

350

21

Fig. 3.2: Plan of Hull-upper Deck (Rowan 2000)

Fig. 3.3: Model of hull

22

3.4.2 Jack-Up Legs Each leg of jack-up is 477.5 ft (145.54200 mts) in length (l) and is modeled as a square space truss having horizontal vertical and diagonal members. Fig 3.4 and 3.5 shows the plan of single leg, Fig. 3.8 and Fig. 3.9 shows Isometric and side views of the Jack-up legs. The horizontal, vertical and diagonal members ofthe jack-up are hollow steel tubular sections whose dimensions are tabulated below in Table 3.2. The Table 3.3 is about the detailed specifications of Legs and Spud can.

Table 3.2: Dimensions of truss leg members Member Description

Outer Diameter (mm)

Wall Thickness (mm)

Horizontal Members

750

50

Vertical Members

750

50

Diagonal members

400

40

Table 3.3: Legs and Spud can Specifications Legs

Length Overall ( 3xSquare truss) (ft)

477.5

Chord, Centerline to Centerline (ft)

30

Longitudinal Leg Spacing (ft) (ft)

129

Transverse Leg Spacing (ft)

142

Spud Can Dimensions

Spud Can – Can – Diameter Diameter (ft)

46

Height (ft)

23.8

Nominal Projected Area (sq. ft) ft)

1555

Volume (cu. ft) ft)

9788.405

23

Fig. 3.4: Plan of front single Leg

Fig. 3.5: Plan of leeward leg

The above legs are constructed using a particular type of high tensile strength steel with minimum Tensile yield strength of 689 MPa (100ksi). The cente to center dista nce (c) between chords is 9.15 m (30.01 ft) and bay height, h of 3.41 m (11.18 ft).

3.4.3 Spud Can A spudcan is the term used for the base cones on mobile-drilling jack-up mobile-drilling jack-up platform. platform. The spudcans are the inverted cones mounted at the base of the jack-up which provide stability to lateral forces on the jack-up rig when deployed into ocean-bed systems. in sand overlying clay, the installation of spudcans is often subjected to a potential punch-through hazard. This occurs when the applied load exceeds the maximum bearing resistance of the upper sand layer causing the spud can to plunge into the underlying clay. cla y. The Spudcan of Marathon LeTourneau design, class 116-c jackup rig has diameter (across flat) 14 m and height 7.3 m with bearing area of 143.6 m 2 with volume of 275 m 3. Normally spudcans are constructed using a particular type of high tensile strength steel with minimum Tensile yield strength of 689 MPa (100ksi) which are used for the construction of jack-up legs.

24

Fig. 3.6: Spud can detailing (Roper 2008)

Fig. 3.7: Spud can model in Ansys

25

Fig. 3.8: Front view of jack-up leg

Fig. 3.9: Isometric view of jack-up leg

26

Fig. 3.10: Model of Jack-up rig in ANSYS with legs above the hull

27

Fig. 3.11: Model of Jack-up rig with legs lowered below the hull

28

3.6 STRUCTURAL MODELLING

3.6.1 General There are different modelling techniques that can be used to depict jack-up units. These techniques have different applicability and limitations with respect to the units design and level of detailed checks. In this work, a jack-up unit is modelled as a so-called so- called simplified ‘barstool’ model or an equivalent model, using an equivalent stiffness model of legs and spudcans, equivalent leg hull connection springs and representative beam-element hull grillage. This model is suitable for performing the global analyses. anal yses. After Aft er performing a global analysis of the barstool bars tool model, a more detailed analysis of a single leg model may be recommended to assess the strength of leg members and leg holding system. This detailed single leg model consists of a detailed leg and is used in conjunction with the reactions at the spud can or the forces and moments in the vicinity of lower guide, obtained from the global barstool model.

3.6.2 Equivalent Leg Modelling The equivalent leg model represents both the spudcan and legs. The stiffness of a leg is characterized by the following equivalent cross sectional properties: 

Cross sectional area



Moment of inertia



Shear area



Torsional moment of inertia

The most dominating factor affecting the leg stiffness is leg bending. The shear deflection of most members is small, but it can be significant in a lattice structure. The legs in the barstool model is modelled by a series of collinear beams, where the cross sectional properties are derived by employing the formulas given in the ISO and DNV standards. The determination of stiffness for the equivalent leg model is accomplished as outlined below.

3.6.3 Equations as per ISO Standard and DNV RP C 104 The equations given in the ISO standard and DNV RP C 104 are shown in Fig. 3.12 and Fig. 3.13. Varying sizes of chords and braces along the leg can be accounted for by calculating the propertie s for each leg section and creating the equivalent leg model accordingly.

29

Fig. 3.12: Equations for determining the effective shear area for two-dimensional structures (ISO 19905-1 and DNV C104, 2012)

Fig. 3.13: Equations for determining the equivalent section properties of three-dimensional lattice legs (ISO 19905-1 and DNV C104, 2012)

30

3.6.4 Equivalent Hydrodynamic Coefficients Hydrodynamic drag and mass coefficients are calculated using an equivalent drag coefficient C De, and an equivalent mass coefficient CMe, used on a lattice leg represented by an equivalent diameter De.

In accordance with the ISO and DNV standard, these are calculated using the following procedures.

3.6.5 Equivalent Diameter The equivalent diameter of the lattice leg can be given by:

(3.3)

where, Di - reference diameter of member i li - reference length of member i (node to node) s - height of one bay

3.6.6 Equivalent Drag Coefficient The equivalent drag coefficient of the lattice leg is determined by:

(3.4)

where, CDei - equivalent drag coefficient of each individual member i, given by:

31

(3.6)

where, CDi - drag coefficient of each individual member i, related to the reference diameter

α1 - angle between flow direction and member axis β1

- angle defining the member inclination from the horizontal plane

The Fig. 3.14 below for illustration of flow angles to a lattice leg structure within one bay height.

Fig. 3.14: Flow angles appropriate to a lattice leg ( ISO 19905-1 and DNV C104, 2012) 2012)

The drag coefficient of each individual member is calculated based on the geometry. For plain tubular elements, such as internal, diagonals and horizontal elements, the individual drag coefficient is set to 1.05 (rough) and 0.65 (smooth).

3.6.7 Equivalent Mass Coefficient The equivalent inertia coefficient C Me of a lattice leg is recommended to fixed at 2.0 (smooth) and 1.80 (rough). The added mass coefficient C Ae, is defined as (C Me-1) and used in conjunction with the equivalent area of the leg, calculated by Section 3.6.3. The Fig 3.15 below shows the variation of drag force for the actual model when analysed in Fluent and Fig. 3.16 shows the stick model of the jack up rig.

32

. Fig. 3.15: Drag coefficient variation using the actual leg model

Fig. 3.16: Equivalent Stick model of Jack-up J ack-up

33

CHAPTER 4 ANALYSIS AND RESULTS

4.1 GENERAL In this chapter the type of analysis performed along with the different parameters taken for the analysis is mentioned. Brief discussion on the results obtained is also presented along with the meshed model used for analysis in Aqwa is also shown. The chapter concludes with the results of the motion response of the rig to various sea states along with the variation of bending moments in the leg and the drag force on it is also presented. The safe limit up to which legs can be lowered for different sea states is also calculated by taking the weight of leg and moment on the leg to calculate the axial and bending stresses.

4.2 LOADS ON THE STRUCTURE For afloat operations the jack-up rig must meet the stability and structural criteria prescribed by the classification societies, such as ABS. For rigs in severe storm transit condition, ABS requirement states that legs are to withstand acceleration and gravity bending moments resulting from the motions in the most severe anticipated environmental transit conditions, together with wind moments corresponding to a velocity of not less than 51.5 m/s (100 knots) and current 0.5 m/sec.

4.2.1 Motion Response The jack-up rig is modelled using equivalent stick leg and anal ysed for various cases as follows: Case 1: Full leg above the hull Case 2: Leg Draft 100 ft below the hull Case 3: Leg draft 200 ft below the hull Case 4: Leg draft 250 ft below the hull Case 5: Leg draft 300 ft below the hull

Different directions of wave approach are considered for each of the above case namely 45°, 90° (beam sea), 135°, 180° (head sea) and its responses are analysed for each case which are shown in the sections presented below along with the variation of motion response shown in each case.

34

4.2.2 Response to Irregular Waves In order to compare the responses for the various cases instead of using a single wave an irregular wave has been used represented by a spectrum. Responses of the Jack-up rig has been evaluated for a JONSWAP spectrum with a significant wave height H s of 20 ft and a peak period T m of 10 second. The Fig. 4.1 shows the meshed image of hull and Fig. 4.2 shows the meshed image of legs. The Fig. 4.3, 4.4 and 4.5 shows different directions of wave attack.

Fig. 4.1: Meshed image of hull

Fig. 4.2: Meshed image of rigs leg

35

Fig. 4.3: Beam sea condition for the model

Fig. 4.4: Head sea condition for the mode

36

Fig. 4.5: Different directions of wave approach

4.3 RESULTS 4.3.1 Response Amplitude Operators for Legs above the Hull The response amplitude operators for the case of legs above the hull are shown below in Fig. 4.6 to 4.11 for different degrees of freedom i.e., surge, sway, heave, roll, pitch, and yaw. The analysis is done by using the barstool model or the stick model of the rig in Ansys AQWA. Different directions of wave approach are considered to know the influence of the wave in different directions. Similarly in the coming sections the analysis is carried out by lowering the legs below the hull for different leg drafts and the analysis is continued. Fig. 4.6 shows the surge RAO of the rig, Fig. 4.7 shows the sway RAO, Fig. 4.8 shows the RAO in heave, Fig. 4.9 shows pitch RAO, Fig. 4.10 shows RAO for roll motion and Fig. 4.11 shows RAO for Yaw. From these graphs it can be observed that the responses of jack-up jack -up rig is higher in pitch and roll degrees of freedom and the same observation can be made in different cases of wet tow when legs are lowered presented in the sections below.

37

0.12

0.1

) t f 0.08 / t f ( O A0.06 R e g r u S0.04

0 Degree 45 Degree 90 Degree 135 Degree

0.02

0 0

5

10

15

20

25

Period (secs)

Fig. 4.6: Surge RAO for Full Leg Up

0.25

0.2

) t f / t f ( 0.15 O A R y a 0.1 w S


0.05

0 0

5

10

15

20

Period (secs)

Fig. 4.7: Sway RAO for Full Leg Up

38

25

4.5 4 3.5

) t f 3 / t f ( O2.5 A R 2 e v a e H1.5


1 0.5 0 0

5

10

15

20

25

Period (secs)

Fig. 4.8: Heave RAO for Full Leg Up

4.5 4 3.5

) t f 3 / g e d ( 2.5 O A 2 R h c t i 1.5 P


1 0.5 0 0

5

10

15

20

25

30

Period (secs)

Fig. 4.9: Pitch RAO for Full Leg Up

39

35

2.5

2

) t f / g e 1.5 d ( O A R 1 l l o R

90 deg 45 deg 135 deg 180 deg

0.5

0 0

5

10

15

20

25

30

35

Period (secs)

Fig. 4.10: Roll RAO for Full Leg Up

0.25

0.2

) t f / g e 0.15 d ( O A R 0.1 w a Y


0.05

0 0

5

10

15

20

Period (secs)

Fig. 4.11: Yaw RAO for Full Leg Up

40

25

4.3.2 Response Amplitude Operators for 100 ft. Leg Draft The response amplitude operators for the case of legs lowered below the hull by 100 ft are shown below in Fig. 4.12 to 4.17 for different de grees of freedom i.e., surge, sway, swa y, heave, roll, pitch, and yaw respectively. The response for this case is lower than the case where the legs are above.

0.14 0.12

) 0.1 t f / t f ( 0.08 O A R e 0.06 g r u S0.04


0.02 0 0

5

10

15

20

25

Period (secs)

Fig. 4.12: Surge RAO for Leg Draft 100 ft

0.14 0.12

) t f 0.1 / t f ( O0.08 A R 0.06 y a w S0.04


0.02 0 0

5

10

15

20

Period (secs)

Fig. 4.13: Sway RAO for Leg Draft 100 ft

41

25

4.5 4 3.5

) 3 t f / t f ( O2.5 A R 2 e v a e H1.5


1 0.5 0 0

5

10

15

20

25

Period (secs)

Fig. 4.14: Heave RAO for Leg Draft 100 ft

1.4

1.2

) 1 t f / g e d0.8 ( O A R0.6 h c t i P

45 Degrees 90 Degrees 135 Degrees 180 Degrees

0.4

0.2

0 0

5

10

15

20

25

30

Period (secs)

Fig. 4.15: Pitch RAO for Leg Draft 100 ft

42

35

1.6 1.4 1.2

) t f / 1 g e d ( O0.8 A R l l 0.6 o R


0.4 0.2 0 0

5

10

15

20

25

30

35

Period (secs)

Fig. 4.16: 4.16: Roll RAO for Leg Draft Draft 100 ft

0.2 0.18 0.16 0.14

) t f / g e 0.12 d ( O 0.1 A R w0.08 a Y


0.06 0.04 0.02 0 0

5

10

15

20

Period (secs)

Fig. 4.17: Yaw RAO for Leg Draft 100 ft 43

25

4.3.3 Response Amplitude Operators for 200 ft. Leg Draft The response amplitude operators for the case of legs lowered below the hull by 200 ft are shown below in Fig. 4.18 to 4.23 for different degrees of freedom i.e., for surge, sway, s way, heave, roll, pitch, and yaw respectively.

0.12

0.1

) t f 0.08 / t f ( O A0.06 R e g r u0.04 S


0.02

0 0

5

10

15

20

25

Period (secs)

Fig. 4.18: Surge RAO for Leg Leg Draft 200 ft

0.12

0.1

) t f 0.08 / t f ( O A0.06 R y a w0.04 S


0.02

0 0

5

10

15

20

Period (secs)


44

25

4.5 4 3.5

) t f 3 / t f ( O2.5 A R 2 e v a e 1.5 H


1 0.5 0 0

5

10

15

20

25

Period (secs)

Fig. 4.20: 4.20: Heave RAO for Leg Draft Draft 200 ft

0.9 0.8 0.7

) t f 0.6 / g e D ( 0.5 O A0.4 R h c t i 0.3 P


0.2 0.1 0 0

5

10

15

20

25

30

Period (secs)


45

35

0.8 0.7 0.6

) t f / g e 0.5 d ( O0.4 A R l l 0.3 o R


0.2 0.1 0 0

5

10

15

20

25

30

35

Period (secs)

Fig. 4.22: Roll RAO for Leg Draft 200 ft

0.18 0.16 0.14

) t f 0.12 / g e d 0.1 ( O A0.08 R w a Y0.06


0.04 0.02 0 0

5

10

15

20

Period (secs)

Fig. 4.23: Yaw RAO for Leg Draft 200 ft

46

25

4.3.4 Response Amplitude Operators for 250 ft. Leg Draft The response amplitude operators for the case of legs lowered below the hull by 250 ft are shown below in Fig. 4.24 to 4.29 for different de grees of freedom i.e., surge, sway, swa y, heave, roll, pitch, and yaw respectively.

0.12 0.1

) t f 0.08 / t f ( O A0.06 R e g r 0.04 u S


0.02 0 0

5

10

15

20

25

Period (secs)


0.12

0.1

) t f 0.08 / t f ( O A0.06 R y a w0.04 S


0.02

0 0

5

10

15

20

Period (Secs)

Fig. 4.25: Sway RAO for leg Draft 250 ft

47

25

4 3.5 3

) t f / t f ( 2.5 O A 2 R e v 1.5 a e H


1 0.5 0 0

5

10

15

20

25

Period (secs)


0.8 0.7 0.6

) t f / g e 0.5 d ( O0.4 A R h c 0.3 t i P


0.2 0.1 0 0

5

10

15

20

25

Period (secs)

Fig. 4.27: Pitch RAO for leg Draft 250 ft

48

30

35

0.7 0.6

) 0.5 t f / g e d ( 0.4 O A0.3 R l l o R0.2


0.1 0 0

5

10

15

20

25

30

35

period (secs)


0.18 0.16 0.14

) t f 0.12 / g e d 0.1 ( O A0.08 R w a 0.06 Y


0.04 0.02 0 0

5

10

15

20

Period (secs)

Fig. 4.29: Yaw RAO for Leg Draft 250 ft

49

25

4.3.5 Response Amplitude Operators Operators For 300 ft Leg Leg Draft The response amplitude operators for the case of legs lowered below the hull by 300 ft are shown below in Fig. 4.30 to 4.35 for different de grees of freedom i.e., surge, sway, swa y, heave, roll, pitch, and yaw respectively.

0.14 0.12

) 0.1 t f / t f ( 0.08 O A R0.06 e g r u S0.04


0.02 0 0

5

10

15

20

25

Period (secs)


0.12

0.1

) t f 0.08 / t f ( O A0.06 R y a w0.04 S


0.02

0 0

5

10

15

20

Period (secs)


50

25

4 3.5 3

) t f / t 2.5 f ( O A 2 R e v 1.5 a e H


1 0.5 0 0

5

10

15

20

25

Period (secs)


0.7 0.6

) 0.5 t f / g e d ( 0.4 O A R0.3 h c t i P0.2


0.1 0 0

5

10

15

20

25

Period (secs)


51

30

35

0.6

0.5

) 0.4 t f / g e d ( O0.3 A R l l o R0.2


0.1

0 0

5

10

15

20

25

30

35

Period (secs)


0.18 0.16 0.14

) t f 0.12 / g e d ( 0.1 O A0.08 R w a Y0.06


0.04 0.02 0 0

5

10

15

20

Period (secs)

Fig 4.35: Yaw RAO for Leg Draft 300 ft

52

25

Table 4.1 shows the maximum responses of the jack-up rig in various wet tow conditions when the legs are lowered below the hull. The reduction in response can be observed in case when the legs are lowered below the hull.

Table 4.1 Maximum Responses of Jack-up rig in Different Degrees of Freedom Full Leg up

Leg Draft

Leg Draft

Leg Draft

Leg Draft

100 ft

200 ft

250 ft

300 ft

Surge

0.122

0.111

0.108

0.107

0.096

Sway

0.21

0.14

0.11

0.108 0.108

0.104

Heave

4.131

4.05

3.864

3.77

3.33

Pitch

4.181

1.325

0.82

0.704

0.612

Roll

2.26

1.505

0.736

0.619

0.5609

Yaw

0.192

0.177

0.167

0.163

0.1562

Table 4.2 shows the percentage change in response of the jack-up rig in various degrees of freedom in comparison with the case when the legs are above the hull. Fig 4.36 and 4.37 shows the pitch and roll RAO in 0 and 90 degree direction for different leg drafts.

Table 4.2 Percentage change in responses in comparison with the case when Full Leg up Full Leg up

Leg Draft

Leg Draft

Leg Draft

Leg Draft

100 ft

200 ft

250 ft

300 ft

Surge %

-

9.016↓

11.475↓

12.295↓

21.311↓

Sway %

-

33.33↓

47.61↓

48.57↓

50.47↓

Heave %

-

1.96↓

6.463↓

8.738↓

19.389↓

Pitch %

-

68.309↓

80.387↓

83.161↓

85.36↓

Roll %

-

33.407↓

67.433↓

72.616↓

75.181↓

Yaw %

-

7.812↓

13.02↓

15.104↓

18.645↓

53

4.5 4 3.5

) 3 t f / e e 2.5 r g e d ( 2 h c t i 1.5 P

Full Leg Up Leg Draft 100 ft Leg Draft 200 ft Leg Draft 250 ft Leg Draft 300 ft

1 0.5 0 0

5

10

15

20

25

30

35

Period (secs)

Fig 4.36: Pitch RAO - 0 Degree Heading

3

2.5

) 2 t f / e e r g e 1.5 d ( l l o R 1

Full Leg Up Leg Draft 100 ft Leg Draft 200 ft Leg draft 250 ft Leg Draft 300 ft

0.5

0 0

5

10

15

20

25

Period (secs)

Fig 4.37: Roll RAO - 90 Degree Heading

54

30

35

4.3.6 Response to Irregular Waves The Fig. 4.38 to 4.42 shows the effect of varying wave period on maximum response for significant wave height of 20 ft and peak period of 10 sec. Here the peak period of the wave spectrum has been varied over a range of periods with the wave height held constant at H s= 20 ft. The graphs shown below are responses in pitch degree of freedom when the Legs are above hull for wave periods 10 - 14 seconds.

15 10

) s 5 e e r g e d 0 ( 0 h c t i -5 P

10

20

30

40

50

60

10 sec period

70

-10 -15

Period (secs)

Fig. 4.38: Maximum pitch response for Hs = 20 ft for 10 sec period

20 15 10 ) s e e r 5 g e d ( 0 h c t 0 i P

Time Period 11 sec 10

20

30

40

50

60

70

-5

-10 -15

Period (secs)


55

30 20

) s e e 10 r g e d 0 ( 0 h c -10 t i P

10

20

30

40

50

60

70

time period 12 sec

-20 -30

Time (secs)


40 30

) 20 s e e 10 r g e d 0 ( 0 h c -10 t i P-20

10

20

30

40

50

60

70

Time Period 13 sec

-30 -40

Time (secs)


40 30 20

) s e e 10 r g e 0 d ( 0 h c -10 t i P

10

20

30

40

50

60

70

Time Period 14 sec

-20 -30 -40

Period (secs)


56

The above peak responses for each case of wet tow are plotted in Fig. 4.43 for pitch and Fig. 4.44 for roll respectively. here the peak period is varied and analysis is run for each case to get the maximum response of the rig.

35 30 25 ) s e e r 20 g e d ( 15 h c t i P10

Full Leg Up Leg Draft 100 ft Leg Draft 200 ft Leg Draft 250 ft Leg Draft 300 ft

5 0 10

11

12

13

14

15

16

17

18

Period (secs)

Fig. 4.43: Maximum Pitch Response, H s=20 ft

16 14 12

) s 10 e e r g e d 8 ( l l o R 6

Leg Draft 100 ft

4

Leg Draft 300 ft

Full Leg Up

Leg Draft 200 ft Leg Draft 250 ft

2 0 10

11

12

13

14

15

16

17

Period (secs)

Fig. 4.44: Maximum Roll Response, H s=20 ft

57

18

4.4 BENDING MOMENTS ON LEGS Bending Moments are calculated for a simplified stick leg model of jack up leg. The equivalent dimensions of the stick leg were derived by analysing the detailed model of the jack-up leg. The Mass distribution and hydrodynamic coefficients were selected to match the detailed model according to ISO 19905-1. The bending moments on the leg were determined using Ansys Aqwa which considers the inertia forces due accelerations in six degrees of motion, due to gravity, wind forces on the legs above the hull and hydrodynamic forces due to wave, forward velocity on portion of leg below the hull. Simulation is carried out on the model for the three cases of wet tow :   

Jack-up legs above the hull, Jack-up legs with 25 % (36.34 m) below the hull, Jack-up legs with 50 % (72.69 m) below the hull,

Regular wave of 10 seconds period is used with wave headings of 90° (beam sea), 120°, 135°, 150°, 180° (head sea) were analysed for regular wave heights of 4 m, 8m, 10 m, 12 m, 16 m. For the portion of leg above hull, wind velocity of 51.5 m/s (100 knots) is considered. For each of the different tow cases and heading, time dependent bending moments about longitudinal and transverse directions were determined at the jack house level for the portion of legs above and below the hull. The graphs in Fig. 4.45 to Fig. 4.52 shown below are for wave height of 12 meters and for period of 10 seconds.

4

) 3 m N k 2 ( t n e 1 m o M0 g 0 n i d-1 n e B-2 -3

x10

5

5

10

15

20

25

30

35

40

45

Period (secs)

Fig 4.45: BM above hull with legs l egs above hull in wave of heading 135°

58

50

x105 5 4

) m3 N k ( t 2 n e 1 m o M0 g 0 n-1 i d n e -2 B

5

10

15

20

25

30

35

40

45

50

-3

Time (secs)

-4

Fig. 4.46: BM above hull for Jack-up with legs above hull in wave heading 120°

4000

x105

3000

) 2000 m N ( t n e 1000 m o M 0 g n i 0 d n e B-1000

10

20

30

40

50

60

-2000

Time (secs) -3000

Fig. 4.47: BM above hull for Jack-up with legs 25% below hull in wave heading 90°

59

70

2000 1500

) m1000 N k ( t 500 n e m 0 o 0 M -500 g n i d n e-1000 B

10

20

30

-1500

40

50

60

70

Time (secs)

-2000

Fig. 4.48: BM above hull for Jack-up J ack-up with legs 25% below hull in wave heading 135°

x10

4

3.5 3

) 2.5 m N 2 k ( t 1.5 n e m o 1 M 0.5 g n i d 0 n e -0.5 0 B

10

20

30

40

50

60

70

-1 -1.5

Time (secs)

Fig. 4.49: BM below the hull with legs 25% below hull in wave of heading 135°

60

80

10

x10

4

8

m N 6 k t n e 4 m o M2 g n i d 0 n e B

0

10

20

30

40

50

60

70

80

-2

Time (secs)

-4


x10

4

3

2

m N k t 1 n e m o 0 M 0 g n i d-1 n e B -2

10

20

30

40

50

60

70

Time (secs)

-3

Fig. 4.51: BM above hull with legs 50% below hull in wave of heading 135°

61

80

x10

4

10

m8 N k t 6 n e m4 o M2 g n i d 0 n e 0 B-2

10

20

30

40

50

60

70

80

-4 -6

Time (s)


Each of the above figures gives us the bending moment variation for different cases and the maximum values in each case is tabulated in Table 4.3 about transverse axis and Table 4.4 shows the values of maximum bending moment about Longitudinal axis.

8

Table 4.3: Maximum Bending Moment about Transverse Axis [x10 Nm] for 12 m wave height Heading [deg]

Leg Up

25% Leg below hull

50% Legs below hull

180

4.201

3.623

1.613

150

2.763

0.767

1.486

135

1.230

0.635

1.301

120

1.436

0.812

1.246

90

4.165

1.451

1.082

62

8

Table 4.4: Maximum Bending Moment about Longitudinal Axis [x10 Nm] for 12 m wave height Heading [deg]

Leg Up

25% Leg below

50% Leg below

180

0

0

0

150

2.016

0.754

0.456

135

2.936

1.248

0.678

120

3.897

1.506

0.798

90

5.264

1.625

0.916

The Table 4.5 shown below depicts the maximum values of bending moment about transverse axis and for different wave heights ranging from 4 m to 16 m. Similarly the Table 4.6 shows the values of maximum bending moment about longitudinal axis

Table 4.5 Maximum Bending moment about transverse axis for different wave 8

heights [x10 Nm] Wave Ht. [m]

Leg up

25 % leg below

50 % leg below

4

1.357

0.58687

0.96458

8

2.9631

1.0214

1.11621

10

3.0125

2.3145

1.4015

12

3.8156

2.8146

1.6102

16

5.1246

4.0126

1.8151

63

Table 4.6 Maximum Bending moment about Longitudinal axis for different wave heights [x108 Nm] Wave Ht. [m]

Leg up

25 % leg below

50 % leg below

4

1.90125

0.9125

0.4125

8

3.81025

1.5126

0.61256

10

4.3125

1.826

0.14586

12

5.1214

1.8026

1.102

16

7.1246

3.0126

2.10151

The variation of maximum bending moment for 12 m wave is shown in Fig. 4.53 and Fig. 4.54. These values are from Tables 4.3 and 4.4. The moments are calculated for different directions of wave approach and the maximum value is obtained for each case.

8 m7 N

8

0 16 * t n e m5 o M g4 n i d n e 3 B m u2 m i x a M1

180 deg 150 deg 135 deg 120 deg 90 deg

0 0

10

20

30

40

50

60

Leg Draft %

Fig. 4.53: Variation of Maximum bending moment about Transverse axis (12 m wave)

64

6

m N 8 05 1 * t n e 4 m o M g3 n i d n e B2 m u m1 i x a M0

180 deg 150 deg 135 deg 120 deg 90 deg

0

10

20

30

40

50

60

Leg Draft %

Fig. 4.54: Variation of Maximum bending moment about Longitudinal axis (12 m wave) The Fig. 4.55 and 4.56 shows the variation of maximum bending moment about longitudinal and transverse axis respectively for different wave heights and are plotted against the percentage of the legs lowered below the hull.

8

m7 N 8 0 6 1 * t 5 n e m o 4 M g n 3 i d n e B2 m u 1 m i x a 0 M 0

4m 8m 10 m 12 m 16 m

10

20

30

40

50

60

Leg Draft %

Fig. 4.55: Variation of Maximum bending moment about Longitudinal axis for different wave heights 65

6

m5 N 8 0 1 *4 t n e m o3 M g n i d n e2 B m u m1 i x a M

4m 8m 10 m 12 m 16 m

0 0

10

20

30

40

50

60

Leg Draft %

Fig. 4.56: Variation of Maximum bending moment about Transverse axis for different wave heights

4.5 STRESSES IN LEG The leg of jack-up rig is a latticed structure consisting of four triangular chords. The rack chord and other sectional properties may vary from elevation to elevation. Here, in this study an average cross sectional property has been assumed. Local bending moment of the chord has been ignored. The stresses in the leg at the lower guide level have been calculated with the weight of the leg as axial load and bending moment. It was mentioned earlier that from consideration of safety required to meet ABS criteria, the stresses should be limited to 80% of yield stress. This therefore can be considered as safe limit up to which legs can be lowered. Fig. 4.57 shows the stress variation for 4 m wave, Fig. 4.58 shows variation for 8 m wave, Fig. 4.59 shows variation for 10 m wave, Fig. 4.60 shows the stress variation for 12 m wave and Fig. 4.61 shows the stress variation for 16 m wave.

66

450 400 350 300

a p M250 s s e 200 r t S 150

Maximum Stress in Leg for 4 m Wave

100 50 0 0

10

20

30

40

50

60

Leg Draft in %

Fig. 4.57: Maximum Stress in leg for 4 m wave

700 600 500

a p400 M s s e 300 r t S Maximum Stress in Leg for 8 m Wave

200 100 0 0

10

20

30

40

50

60

Leg Draft in %


67

900 800 700 600

a p M500 s s e 400 r t S


300 200 100 0 0

10

20

30

40

50

60

Leg Draft in %


900 800 700 600

a p M500 s s e 400 r t S Maximum Stress in Leg for 12 m Wave

300 200 100 0 0

10

20

30

40

50

60

Leg Draft in %


68

1600 1400 1200

a 1000 p M 800 s s e r t S 600


400 200 0 0

10

20

30

40

50

60

Leg Draft in %


4.5 SAFE LIMITS OF LEG DRAFT As mentioned earlier the leg draft corresponding to 80% of yield stress can be considered as safe limit up to which legs can be lowered. From the t he above graphs it can be concluded that the le g draft corresponding to 560 MPa is considered safe for severe transit condition.

4.5-(I) 4 m Wave From the Fig. 4.57 the stresses in the leg are within the limits i.e., less than 560 MPa. Hence, for 4 m wave the legs can be lowered to the limit of 50% of the length.

4.5-(II) 4.5-(II) 8 m wave From the Fig. 4.58 the leg draft corresponding to 80% of yield stress is 45% of leg length i.e, 214.65 ft (65.5 mts) which can be considered safe for 8 m wave.

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4.5-(III) 4.5-(III) 10 m wave From the Fig. 4.59 the leg draft corresponding to 80% of yield stress is 38% of leg length i.e, 181.45 ft (55.30 mts) which can be considered safe for 10 m wave.

4.5-(IV) 4.5-(IV) 12 m wave From the Fig. 4.60 the leg draft corresponding to 80% of yield stress is 33% of leg length i.e, 157.57 ft (48.02 mts) which can be considered safe for 12 m wave.

4.5-(IV) 4.5-(IV) 16 m wave From the Fig. 4.61 the leg draft corresponding to 80% of yield stress is 25% of leg length i.e, 119.37 ft (36.38 mts) which can be considered safe for 16 m wave.

4.6 NATURAL PERIOD VARIATION The natural periods for roll and pitch of the vessel with various leg drafts are shown in Fig. 4.62 and 4.63. The plot shows that as leg draft is increased to 200 ft, the vessel's natural period becomes shorter than that with full leg up. As the leg draft is increased to 300 ft, the natural period again begins to lengthen. This behaviour is related to the changes in the moment of inertia with the leg draft as shown in Fig. 4.64. As the legs are lowered, the vessel's centre of mass is lowered which tends to reduce its mass moment of inertia which is evident from the figure which causes the vessels response to stiffen. For leg drafts up to 200 ft, the vessel motions are governed by the moment of inertia which reduces with the leg draft. below 200 ft the added mass effect of the legs tends to predominate and increases the natural period. different natural periods also imply that for different leg drafts, critical response to a given wave height will occur at different wave periods.

70

25

20

) s 15 ( d o i r e P10

Roll

5

0 0

50

100

150

200

250

300

350

Leg Draft (ft)

Fig. 4.62: Variation of Natural period vs leg draft for roll

25

20

) s 15 ( d o i r e P10

Pitch

5

0 0

50

100

150

200

250

300

350

Leg Draft (ft)

Fig. 4.63: Variation of Natural period vs leg draft for Pitch

71

4.7 MOMENT OF INERTIA AND ADDED MASS VARIATION The behaviour of moment of inertia and added mass is the governing parameter for the natural period variation. As the legs are lowered, the vessels center of mass is lowered which tends to reduce the vessels mass moment of inertia and cause the vessels response to stiffen. For leg drafts up to 200 ft, the vessel motions are governed by the moment of inertia which reduces with leg draft. Below 200 ft however ever the added mass effect of the legs tends to predominate and increases the natural period again. Fig. 4.66 shows the variation of the mass moment of inertia with respect to the leg draft. It decreases until the legs are lowered to a leg draft of 200 ft and increases thereafter. Fig. 4.65 shows the variation of added mass with respect to the leg draft and it increases monotonically.

30000

25000

) m g20000 k ( a i t r e n15000 I f o t n e m10000 o M

2

5000

0 0

50

100

150

200

250

Leg Draft (ft)

Fig. 4.64: Variation of Moment of inertia vs leg draft

72

300

350

5500000 5000000

) g k ( s 4500000 s a M d e4000000 d d A 3500000 3000000 0

50

100

150

200

250

300

350

Leg Draft (ft)

Fig. 4.65: Variation of Added mass vs leg draft

4.8 DRAG FORCE AND VELOCITY VELOCITY VARIATION VARIATION The variation of drag force on the leg is shown in Fig. 4.66 which increases with increase in leg draft which will be in additional when the legs are lowered into the sea way instead of air which acts for the part above the hull. The fig 4.67 and 4.68 4.68 shows velocity variation across the legs which can be used to know whether there is any formation of eddys on the rear part of leg. Here it can be seen that the flow does not induce any an y vortices across the legs. 35000 30000 25000

N k20000 , e c r o15000 F 10000 5000 0 0

50

100

150 200 Leg Draft (ft)

250

Fig. 4.66: Variation of drag force vs leg draft 73

300

350

Fig. 4.67: Velocity variation across the front leg

Fig. 4.68: Velocity variation across the back leg

74

CHAPTER 5 SUMMARY AND CONCLUSIONS 5.1 SUMMARY In this Thesis, hydrodynamic analysis of jack-up rig in wet tow is carried out and for each wet tow case various wave headings are considered to report rigs response. For each of the different tow cases and heading, time dependent bending moments about longitudinal and transverse directions were determined at the jack house level for the portion of the leg above as well as below the hull. The stresses at the lower guide level have been calculated with the weight of the leg as axial load and the bending moment. safe limits have been calculated for each wet tow case and are mentioned in the conclusions part below.

5.2 CONCLUSIONS The salient conclusions from the study are shown below 

The Jack-up rigs response in pitch and roll changes significantly with increase in leg draft. In sway degree of freedom it can be reduced up to 50 percent when legs are lowered to a leg draft of 300 ft and similarly in pitch and roll it can be reduced up to 85 percent and 75 percent respectively for the same leg draft of 300 ft.



The natural period plots for roll and pitch shows that as leg draft is increased to 200 ft, the vessel's natural period becomes shorter than that with full leg up. As the leg draft is increased to 300 ft, the natural period again begins to lengthen.



The above said behaviour is related to the changes in the moment of inertia. As the legs are lowered, the vessel's centre of mass is lowered which tends to reduce its mass moment of inertia which is evident from the figure which causes the vessels response to stiffen. For leg drafts up to 200 ft, the vessel motions are governed by the moment of inertia which reduces with the leg draft. Below 200 ft the added mass effect of the legs tends to predominate and increases increas es the natural period. different natural periods also imply that for different leg drafts, critical response to a given wave height will occur at different wave periods.

75



There is significant increase in Drag Force on the leg with increase in leg draft due to the hydrodynamic forces on the legs when they are submerged, which depends on vessel motion as well as wave height and period. requirement of additional powering during the tow is essential because of increase in leg's drag.



It can be observed that calculated maximum bending moments for the 25% leg below the hull case are appreciably lower than those determined for the leg completely retracted case. As the motions are also lowered nearly 68% in pitch and 33% in roll this condition can be adopted during wet tow of the jack-up rig in a very satisfactory manner.



As mentioned earlier the leg draft corresponding to 80% of yield stress can be considered as safe limit up to which legs can be lowered i.e., the leg draft corresponding to 560 MPa is considered safe for severe transit condition. The safe values of leg draft for different wave heights are calculated.

5.3 SCOPE FOR FUTURE WORK Few suggestions for future work are given below: 

The model can be analysed as a lattice structure (legs) instead of using a stick model which may dampen the response further corresponding to that of an equivalent leg model.



More case studies for different tow speeds and sea states need to be carried out for a specific tow, before a firm estimate of degree of leg submergence can be recommended with confidence.



Comparison study can be made by changing the configuration of the leg truss network. Here, rev. K type is used, this can be extended to X and mixed truss types and its effect on the jack-up's dynamic behaviour can be studied.



This can be verified through experimental study on the 'equivalent stick model' and the comparison can be brought out.

76

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2.

B. P. M. Sharpies, W. T. Bennett, Jr and J. C. Trickey (1989), Risk analysis of jack-

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9.

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11.

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13.

M.S. Williams, R.S.G. Thompson, G.T. Houlsby (1998), Non-linear (1998), Non-linear dynamic d ynamic analysis anal ysis

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O.T. Gudmestad and G. Moe (1996) Hydrodynamic coefficient for calculation of

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Analysis of Jackup Rig in Wet Tow Transit

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