A study on hull shape optimization for TLP by

using optimization algorithm

(最適化アルゴリズムを用いた TLP 浮体形状最適化に関する研究)

杉田 年男
Contents
1 Background .................................................................................................................. 9
1.1. Floating Offshore Production Facilities .............................................................. 9
1.2. History and trend of TLPs ................................................................................. 14
1.3. TLP hull shape ................................................................................................... 17
1.3.1. Conventional TLP (CTLP) .......................................................................... 18
1.3.2. MOSES TLP ................................................................................................ 19
1.3.3. SeaStar TLP ................................................................................................ 20
1.3.4. Extended TLP (ETLP) ................................................................................ 21
1.4. TLP hull design and sizing ................................................................................ 22
1.1.1 Global Performance ........................................................................................ 22
1.1.2 Structural Integrity ........................................................................................ 23
1.1.1 Transportation and installation ..................................................................... 24
1.1.2 Topside Support and Integration Method...................................................... 24
1.1.3 Drilling Operation .......................................................................................... 24
1.1.4 Riser and well bay layout ............................................................................... 24
1.1.5 Constructability .............................................................................................. 24
2 Purpose of this Study ................................................................................................. 25
3 Methodology – Sizing Strategy .................................................................................. 27
3.1 Conventional Hull Sizing Method ..................................................................... 27
3.2 Sizing Strategy ................................................................................................... 28
3.3 Criteria ............................................................................................................... 28
3.4 Optimization Algorithm ..................................................................................... 30
3.4.1 Adaptive Simulated Annealing Method......................................................... 31
3.4.2 Real-coded Genetic Algorithm ........................................................................ 32
3.4.3 Steepest Gradient Method ............................................................................. 33
3.4.4 Program Test................................................................................................... 33
4 Methodology - Calculation Mesh ............................................................................... 39
4.1 Conventional TLP – Circular Column ............................................................... 40
4.2 Conventional TLP – Rectangular Column ........................................................ 43
4.3 MOSES SSIP TLP –Rectangular Column ......................................................... 46
4.4 MOSES SSIP TLP – Circular Column .............................................................. 49
4.5 Classic MOSES TLP........................................................................................... 52
5 Methodology - Hydrodynamic Calculation ................................................................ 55
5.1 Flow Field around a Floating Body ................................................................... 55
5.2 Integral Equation for the velocity potential ...................................................... 57

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 5.3 Numerical solution of Integral equation ........................................................... 58
5.4 Free-Surface Green Function ............................................................................ 59
5.5 Hydrodynamic force ........................................................................................... 63
5.6 Kochin Function and Wave Drift Forces ........................................................... 64
5.7 Motion Equation for TLP ................................................................................... 65
5.7.1 Motion Equation for TLP ............................................................................... 65
5.7.2 Mass matrix .................................................................................................... 66
5.7.3 Damping matrix ............................................................................................. 67
5.7.4 Restoring Matrix ............................................................................................ 67
5.7.5 External force ................................................................................................. 72
5.8 Maximum Response Calculation ....................................................................... 72
5.9 Program Verification .......................................................................................... 75
6 Methodology - Global Performance Calculation ....................................................... 80
6.1 Global Parameters.............................................................................................. 80
6.2 Mean Condition Calculation .............................................................................. 81
6.2.1 Restoring Forces ............................................................................................. 82
6.2.1.1 Tendon and TTR Restoring Forces ............................................................. 82
6.2.1.2 SCR Restoring Forces ................................................................................. 83
6.2.1.3 Hydrostatic Forces ...................................................................................... 85
6.2.2 Environmental Forces .................................................................................... 86
6.2.2.1 Drag Force Coefficient ................................................................................ 86
6.2.2.2 Current Coefficient Calculation ................................................................. 88
6.2.2.3 Wind Coefficient Calculation ...................................................................... 89
6.3 Wave-frequency Motion Calculation.................................................................. 89
6.4 Low-frequency Motion Calculation.................................................................... 89
6.4.1 Wind Induced Motion ..................................................................................... 89
6.4.2 Wind Spectrum ............................................................................................... 90
6.4.3 Variable Wave Drift Force Induced Motion ................................................... 91
6.5 Maximum/Minimum Value Calculation ............................................................ 91
6.6 Program Verification .......................................................................................... 92
7 Methodology - Global Structure Calculation ............................................................ 97
7.1 Section Properties .............................................................................................. 98
7.2 Correspondence .................................................................................................. 98
7.3 Spring Boundary corresponding Tendon stiffness ............................................ 99
7.4 Matrix Method .................................................................................................. 100
7.4.1 Element Stiffness Matrix ............................................................................. 101

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 7.4.2 Coordinate Conversion and Global Stiffness Matrix .................................. 102
7.4.3 Calculation of Section Forces ....................................................................... 105
7.4.4 Distributed Load ........................................................................................... 106
7.5 Load Cases ........................................................................................................ 107
7.5.1 Static Loads .................................................................................................. 107
7.5.2 Wave Loads ................................................................................................... 107
8 Methodology - Weight Calculation .......................................................................... 109
8.1 Scantling Calculation ....................................................................................... 109
8.1.1 Plating ........................................................................................................... 109
8.1.2 Stiffener ........................................................................................................ 110
8.2 Weight estimation ............................................................................................ 111
9 Calculation Result .................................................................................................... 113
9.1 Calculation Condition ...................................................................................... 113
9.2 GoM Pre-2005 condition (Case 1) .................................................................... 115
9.3 GoM Post-2005 condition (Case 2) ................................................................... 116
9.4 GoM Post-2005 condition (Case 3) ................................................................... 117
10 Discussion............................................................................................................. 118
10.1 Comparison with an existing TLP hull shape ................................................. 118
10.2 Pre v.s. Post Hurricane Condition ................................................................... 119
10.3 Hash v.s. Mild Environment ............................................................................ 120
10.4 Comparison with hydrodynamic optimization result ..................................... 121
10.5 Optimization process for GoM pre-2005 .......................................................... 122
10.6 Optimization process for GoM post-2005 ........................................................ 126
10.7 Optimization process for Southeast Asian Condition ..................................... 129
10.8 Study on Criteria – Pre-2005 condition ........................................................... 132
11 Conclusion ............................................................................................................ 140
12 Acknowledgement ................................................................................................ 141
Reference ......................................................................................................................... 142

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Figures
Figure 1-1 Components of a TLP [1-1] ...................................................................... 10
Figure 1-2 Production Semi [1-2] .............................................................................. 11
Figure 1-3 Truss SPAR [1-3] ...................................................................................... 11
Figure 1-4 Ship-shaped FPSO [1-4] .......................................................................... 12
Figure 1-5 TLP and water depth [1-7]....................................................................... 14
Figure 1-6 Distribution of TLPs [1-7] ........................................................................ 16
Figure 1-7 TLP Hull configurations [1-1].................................................................. 17
Figure 1-8 Brutus TLP [1-8] ...................................................................................... 18
Figure 1-9 Brutus TLP System Schematic [1-8] ....................................................... 18
Figure 1-10 Classic MOSES TLP [1-4] ...................................................................... 19
Figure 1-11 MOSES SSIP TLP [1-4] ......................................................................... 20
Figure 1-12 SeaStar Platform [1-11] ......................................................................... 20
Figure 1-13 Bigfoot E-TLP model [1-12] ................................................................... 21
Figure 1-14 Global Performance Parameters ........................................................... 23
Figure 3-1 Conventional Sizing Method ................................................................... 27
Figure 3-2 Flow Chart of Hull Optimization Program ............................................. 28
Figure 3-3 Simulated annealing Method 1 (Left; f(x,y), Right; g(x,y)) .................... 32
Figure 3-4 Simulated annealing Method 1 (Left; f(x,y), Right; g(x,y)) .................... 35
Figure 3-5 Simulated annealing Method 2 g(x,y) ..................................................... 35
Figure 3-6 Genetic Algorithm 1 (Left; f(x,y), Right; g(x,y)) ...................................... 36
Figure 3-7 Genetic Algorithm 2 g(x,y) ....................................................................... 36
Figure 3-8 Steepest Gradient Method 1 (Left; f(x,y), Right; g(x,y)) ......................... 37
Figure 3-9 Steepest Gradient Method 2 g(x,y) .......................................................... 38
Figure 4-1 Main dimensions of Conventional TLP – Circular Column ................... 40
Figure 4-2 Quarter Panel Model for CTLP ............................................................... 41
Figure 4-3 Full Panel Model for CTLP ...................................................................... 41
Figure 4-4 Structural Beam Model for CTLP ........................................................... 42
Figure 4-5 Main dimensions of Conventional TLP – Rectangular Column............. 43
Figure 4-6 Quarter Panel Model for CTLP (Rectangular Column).......................... 44
Figure 4-7 Full Panel Model for CTLP (Rectangular Column) ................................ 44
Figure 4-8 Structural Beam Model for CTLP (Rectangular Column)...................... 45
Figure 4-9 Main dimensions of MOSES SSIP TLP –Rectangular Column ............. 46
Figure 4-10 Quarter Panel Model for MOSES SSIP ................................................ 47
Figure 4-11 Full Panel Model for MOSES SSIP ....................................................... 47
Figure 4-12 Structural Beam Model for MOSES SSIP ............................................ 48

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Figure 4-13 Main dimensions of MOSES SSIP TLP –Circular Column .................. 49
Figure 4-14 Quarter Panel Model for MOSES SSIP (Circular Column) ................. 50
Figure 4-15 Full Panel Model for MOSES SSIP (Circular Column) ........................ 50
Figure 4-16 Structural Beam Model for MOSES SSIP (Circular Column) ............. 51
Figure 4-17 Main dimensions of Classic MOSES TLP ............................................. 52
Figure 4-18 Quarter Panel Model for Classic MOSES ............................................. 53
Figure 4-19 Full Panel Model for Classic MOSES ................................................... 53
Figure 4-20 Structural Beam Model for Classic MOSES ......................................... 54
Figure 5-1 Flow Field around a Floating Body [5-1] ................................................ 55
Figure 5-2 Method used for Green Function [5-1] .................................................... 60
Figure 5-3 TLP element coordinate [5-5] .................................................................. 70
Figure 5-4 Catenary line coordinate [5-5] ................................................................. 72
Figure 5-5 Wadam Calculation model ....................................................................... 75
Figure 5-6 Surge motion RAO (Upright) ................................................................... 76
Figure 5-7 Surge motion RAO (Offset) ...................................................................... 76
Figure 5-8 Sway motion RAO (Upright) ................................................................... 76
Figure 5-9 Sway motion RAO (Offset) ....................................................................... 76
Figure 5-10 Heave motion RAO (Upright) ................................................................ 76
Figure 5-11 Heave motion RAO (Offset) ................................................................... 76
Figure 5-12 Roll motion RAO (Upright) .................................................................... 76
Figure 5-13 Roll motion RAO (Offset) ....................................................................... 76
Figure 5-14 Pitch motion RAO (Upright) .................................................................. 77
Figure 5-15 Pitch motion RAO (Offset) ..................................................................... 77
Figure 5-16 Yaw motion RAO (Upright) .................................................................... 77
Figure 5-17 Yaw motion RAO (Offset) ....................................................................... 77
Figure 5-18 Tendon tension RAO (Upright) .............................................................. 77
Figure 5-19 Tendon tension RAO (Offset) ................................................................. 77
Figure 5-20 Tendon tension RAO (Upright) .............................................................. 77
Figure 5-21 Tendon tension RAO (Offset) ................................................................. 77
Figure 5-22 Tendon tension RAO (Upright) .............................................................. 78
Figure 5-23 Tendon tension RAO (Offset) ................................................................. 78
Figure 5-24 Wave drift force Fx (Upright) ................................................................ 78
Figure 5-25 Wave drift force Fx (Offset) ................................................................... 78
Figure 5-26 Wave drift force Fy (Upright) ................................................................ 78
Figure 5-27 Wave drift force Fy (Offset) ................................................................... 78
Figure 5-28 Wave drift force Mz (Upright)................................................................ 78

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Figure 5-29 Wave drift force Mz (Offset) ................................................................... 78
Figure 6-1 Schematic of Catenary Line Shape ......................................................... 83
Figure 6-2 Wind and current loading on the platform ............................................. 86
Figure 6-3 Drag force on rectangular cross section (DNV-RP-C205) ....................... 87
Figure 6-4 DeepC analysis model .............................................................................. 92
Figure 6-5 Offset value comparison .......................................................................... 93
Figure 6-6 Setdown value comparison ...................................................................... 93
Figure 6-7 DeepC time history of up-wave tendon tension ...................................... 94
Figure 6-8 DeepC spectrum of up-wave tendon tension........................................... 94
Figure 6-9 DeepC time history of down-wave tendon tension ................................. 95
Figure 6-10 DeepC spectrum of down-wave tendon tension .................................... 95
Figure 7-1 Beam Structural Model and Hydrodynamic Panel Model ..................... 97
Figure 7-2 Section view of Pontoon and Column ...................................................... 98
Figure 7-3 Correspondence between panels and beams ........................................... 99
Figure 7-4 Spring Boundary corresponding to Tendons ......................................... 100
Figure 7-5 Coordinate Conversion [7-1] .................................................................. 103
Figure 8-1 Compartment assumption for CTLP ..................................................... 111
Figure 8-2 Weight Calculation Method ................................................................... 112
Figure 9-1 Topside Model ......................................................................................... 114
Figure 10-1 Comparison with an existing TLP....................................................... 118
Figure 10-2 Comparison between Pre- and Post-Hurricane Hull Shape............... 119
Figure 10-3 Comparison of Hull Shape for hash and mild environment............... 120
Figure 10-4 Comparison with hydrodynamic optimization result ......................... 121
Figure 10-5 Column diameter v.s. Hull total weight (Case 1) ................................ 122
Figure 10-6 Column distance v.s. Hull total weight (Case 1) ................................. 123
Figure 10-7 Pontoon breadth v.s. Hull weight (Case 1) .......................................... 123
Figure 10-8 Pontoon height v.s. Hull weight (Case 1) ............................................ 124
Figure 10-9 Draft v.s. Hull weigh (Case 1) .............................................................. 124
Figure 10-10 Column Height v.s. Hull weight (Case 1) .......................................... 125
Figure 10-11 Column diameter v.s. Hull weight (Case 2)....................................... 126
Figure 10-12 Column distance v.s. Hull weight (Case 2) ....................................... 126
Figure 10-13 Pontoon width v.s. Hull weight (Case 2) ........................................... 127
Figure 10-14 Pontoon Height v.s. Hull weight (Case 2) ......................................... 127
Figure 10-15 Draft v.s. Hull weight (Case 2) .......................................................... 128
Figure 10-16 Column Height v.s. Hull weight (Case 2) .......................................... 128
Figure 10-17 Column diameter v.s. Hull weight (Case 3) ...................................... 129

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Figure 10-18 Column distance v.s. Hull weight (Case 3) ....................................... 129
Figure 10-19 Pontoon width v.s. Hull weight (Case 3) ........................................... 130
Figure 10-20 Pontoon Height v.s. Hull weight (Case 3) ......................................... 130
Figure 10-21 Draft v.s. Hull weight (Case 3) .......................................................... 131
Figure 10-22 Column Height v.s. Hull weight (Case 3) .......................................... 131
Figure 10-23 Criteria 1, 2, & 3 (Case 1) .................................................................. 132
Figure 10-24 Ballast Amount Condition (Case 1) ................................................... 133
Figure 10-25 Installation Stability Condition (Case 1) .......................................... 133
Figure 10-26 Quayside stability Condition (Case 1)............................................... 134
Figure 10-27 Deck post location Condition (Case 1) ............................................... 134
Figure 10-28 Airgap Condition (Case 1) .................................................................. 135
Figure 10-29 Tendon Pretension Condition (Case 1) .............................................. 135
Figure 10-30 Natural Period Condition (Case 1) .................................................... 136
Figure 10-31 Max Offset Condition (Case 1)........................................................... 137
Figure 10-32 Minimum Tendon Tension Condition (Case 1) .................................. 137
Figure 10-33 Airgap Condition (Case 1) .................................................................. 138
Figure 10-34 Tendon Strength Condition (Case 1) ................................................. 138
Figure 10-35 Hull strength Condition (Case 1) ...................................................... 139

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Tables
Table 1-1 Comparison of Floating Production Unit .................................................. 13
Table 1-2 TLP Technology evolution [1-1] ................................................................. 15
Table 3-1 Geometry criteria (criteria 1) .................................................................... 29
Table 3-2 Hull Sizing criteria (criteria 2) .................................................................. 29
Table 3-3 Design criteria (criteria 3) ......................................................................... 30
Table 3-4 Variable, objective function and constraint condition .............................. 30
Table 3-5 Optimization result (ASA) ......................................................................... 34
Table 3-6 Optimization result (GA) ........................................................................... 35
Table 3-7 Optimization result (SGM) ........................................................................ 37
Table 5-1 Nondimensionalization of Mass Matrix .................................................... 66
Table 5-2 Nondimensionalization of Damping Matrix ............................................. 67
Table 5-3 Nondimensionalization of Restoring Matrix............................................. 67
Table 5-4 Nondimensionalization of External Force ................................................ 72
Table 6-1 Effective shape coefficient (DNV-RP-C205) .............................................. 88
Table 6-2 Reduction Factor for finite length (DNV-RP-C205) .................................. 88
Table 6-3 Global performance comparison ................................................................ 96
Table 7-1 Section Properties ...................................................................................... 98
Table 7-2 Member ID definition ................................................................................ 99
Table 7-3 Symbols for matrix method formulation ................................................. 100
Table 7-4 Load Cases ............................................................................................... 107
Table 8-1 Structural Members for Conventional TLP ............................................ 111
Table 9-1 Environmental Condition ........................................................................ 113
Table 9-2 Topside Condition..................................................................................... 113
Table 9-3 Riser Condition ........................................................................................ 114
Table 9-4 Calculation result for GoM pre-2005 (Case1) ......................................... 115
Table 9-5 Calculation result for GoM post-2005 (Case 2)....................................... 116
Table 9-6 Calculation Result for Southeast Asian Condition (Case 3) .................. 117
Table 10-1 Comparison with an existing TLP ........................................................ 118
Table 10-2 Comparison between Pre- and Post-Hurricane Hull Shape ................ 119
Table 10-3 Comparison between Pre- and Post-Hurricane Hull Shape ................ 120
Table 10-4 Comparison with hydrodynamic optimization result ........................... 121

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1 Background
Tension leg platform (TLP) is an offshore platform, which is tethered by tendon pipes
and has small heave, roll and pitch motions. Currently more than twenty TLPs have
been installed and most of them are operated as oil production, drilling or wellhead
platforms. Originally, TLPs are installed mainly at Gulf of Mexico and North Sea, but
now their installation locations are becoming more global, such as West Africa, South
America, and Southeast Asia, due to recent oil discoveries in these areas. To design the
hull shape, usually past design experience or some of empirical factors are utilized, but
now it is becoming more important to find optimized hull shape suitable for each
environment condition, which any past designed TLP hasn’t experienced. This study
proposes practical system to design hull shape at initial stage by utilizing optimization
algorithms and shows it has better performance than previous studies, wide range of
application, and practical calculation efficiencies.

1.1. Floating Offshore Production Facilities

Offshore production facilities for oil production have two major types; fixed and
floating type. Most of the offshore facilities are categorized in the following categories;

 Fixed Type Jacket Structure

MOPU
GBS
Compliant Tower
 Floating Type FPSO, FSO
Semi-Submersible
TLP
SPAR

Jacket structures, Mobile Offshore Production Unit (MODU), Gravity Base Structure
(GBS), and Compliant Tower belong to the fixed type. These structures have less motion
than floating types, but these facilities are subject to the restriction of water depth. TLP,
Semi-Submersible, SPAR and F(P)SO are categorized as floating type. Characteristics
of these floating structures are explained in the following pages. Comparison of each
floating type is shown in Table 1-1.

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 [Tension Leg Platforms]
TLP consist of hull, Topsides, tendons, risers, pile and foundation (See Figure 1-1).
Typically the hull of TLP consists of columns and pontoons. Because TLP has very small
heave, roll and pitch motion, dry completion, drilling operation and workover from the
platform are applicable. Normally, top tension risers (TTR) are used as production,
drilling or workover risers and Steel catenary risers (SCR) are used as oil/gas export
risers. Because of the difficulty to design tendons for deep water, the applicable water
depth is limited. The current deepest record is 1,425m (Magnolia TLP).

Figure 1-1 Components of a TLP [1-1]

[Semi-Submersibles]
Semi-Submersibles are used for oil production platform, as well as drilling rig, crane
vessel and offshore support vessel (OSV). Semi-submersibles consist of columns and
pontoons (Figure 1-2). Typically production semi-submersibles tend to have ring
pontoon, while others (drilling, crane vessel and OSV) have twin pontoons. Columns
provide sufficient hydrostatic stability. Sometimes production Semi-submersible
platforms are converted from drilling semi-submersible rigs. Semisubmersibles are
moored by conventional mooring legs, which consist chain, wire rope or polyester rope
and can operate in wide range of water depth. The motions of Semisubmersibles are
relatively small, but not as small as TLP or SPAR. Typically dry completion is not
applicable at this moment.

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 Figure 1-2 Production Semi [1-2]

[SPAR]
Single Point Anchor Reservoir (SPAR) has small motion and dry completion is
applicable. SPAR has variations; Classic SPAR, Truss SPAR (Figure 1-3) and Cell SPAR.
Unlike TLPs, SPAR is hydrostatically stable and has conventional catenary or taut
mooring legs. Topside of SPAR has to be integrated at offshore, after launching hull into
water and making it vertical. Motion of SPAR is small because its natural period is
longer than wave period to avoid resonance, but consideration is needed when it’s
installed in swell dominant area.

Figure 1-3 Truss SPAR [1-3]

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[FPSO,FSO]
F(P)SO stands for Floating (Production) Storage Offloading unit. FPSO has storage
tanks and offloading system (Figure 1-4). Sales oil is exported by shuttle tankers. Most
of the FPSOs are ship shaped, and can be converted from used tankers. Mooring
systems are either single point mooring (SPM) or spread mooring. For single point
mooring, turret system is used and it allows vessel to weathervane. Mooring legs are
conventional catenary lines or taut lines. FPSO has relatively large motion and
basically it’s not suitable for hash environment. Some of FPSO has disconnectable
turret mooring system to evacuate from heavy weather. Normally flexible risers are
used for FPSOs. Sevan FPSOs [1-5] have cylindrical hull and don’t need turret system.

Figure 1-4 Ship-shaped FPSO [1-4]

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 Table 1-1 Comparison of Floating Production Unit
FPSO, FSO Semi TLP SPAR
Number of units FPSO 164
41 24 20
in Service* FSO 93
Small Small
Motion Large Small (Heave, Roll, (Heave, Roll,
Pitch) Pitch)

Storage O N/A N/A N/A*

Pipeline/ Pipeline/ Pipeline/

Shuttle Tanker/
Export Connected to Connected to Connected to
Pipeline
nearby unit nearby unit nearby unit
Topside
Yard Yard Yard/Offshore* Offshore
integration
New built/ New built/
Construction New built New built
Conversion Conversion
Completion Wet Tree Wet Tree* Wet/Dry Tree Wet/Dry Tree
Drilling/
N/A O O O
Workover
CTLP, Classic SPAR,
Ship-Shaped, MOSES, Truss SPAR,
Hull Type
Sevan, SeaStar, Cell SPAR,
ETLP
* As of 2014 [1-6]
* AASTA Spar (under construction) will have storage capacity.
* Topsides of Mini-tlp is integrated at offshore

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 1.2. History and trend of TLPs
First TLP is Hutton TLP which is installed at Hutton field in North Sea in 1984. After
that, more than twenty TLPs have been fabricated and installed, and they have been
updating the deepest records (Figure 1-5). R. D’Souza and Rajiv Aggarwal [1-1]
categorized history of TLP construction into the following three phases;
Phase I 1984 - 1995 Pioneering
Phase II 1996 - 2001 Innovation and Standardization
Phase III 2002 - Present Commoditization and Globalization
Now we are in Phase III and the technology for TLP is well matured and proven.

Figure 1-5 TLP and water depth [1-7]

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Table 1-2 TLP Technology evolution [1-1]

15
Figure 1-6 Distribution of TLPs [1-7]

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 1.3. TLP hull shape
TLP hull shapes are categorized into the following four types;
 Conventional TLP (C-TLP)
 MOSES TLP
 SeaStar TLP
 Extended TLP (E-TLP)
These TLPs are all field proven. The plan view of each type is shown in Figure 1-7.

Figure 1-7 TLP Hull configurations [1-1]

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 1.3.1. Conventional TLP (CTLP)
Conventional TLP is the most common type of TLP hull shape. Usually it consists of
four columns connected by four pontoons. Figure 1-8 and Figure 1-9 shows configuration
of Brutus TLP as a typical example of CTLP. Column is not necessarily circular, so West
Seno TLP has squared column [1-9].

Figure 1-8 Brutus TLP [1-8]

Figure 1-9 Brutus TLP System Schematic [1-8]

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 1.3.2. MOSES TLP
MOSES stands for Minimum Offshore Surface Equipment System. Classic MOSES
TLP and MOSES SSIP TLP fall into this category. Unlike conventional TLPs, MOSES
has cross-shaped pontoon, not ring pontoon.
Classic MOSES TLP is regarded as mini-TLP, which doesn’t have hydrostatic stability
for wet-tow or installation to minimize the hull steel structure. Classic MOSES TLP is
suitable for relatively small oil fields. Prince TLP, MarcoPolo TLP, and Shenzi TLP
belong to Classic MOSES TLP.
Oveng/Okume and Ebano belong to MOSES SSIP. MOSES SSIP TLP has hydrostatic
stability for wet-tow and installation, and enables us to reduce offshore integration cost.

Figure 1-10 Classic MOSES TLP [1-4]

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 Figure 1-11 MOSES SSIP TLP [1-4]

1.3.3. SeaStar TLP

SeaStar has single column with three pontoons. Tendons are connected at the end of
pontoon. Production risers are located at the center of the column. SeaStar is also
categorized as mini-tlp, and Topsides is integrated at offshore using floating crane.
Morpheth, Allegheny, Typhoon, Matterhorn, Neptune [1-10] are categorized as SeaStar
TLP.

Figure 1-12 SeaStar Platform [1-11]

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 1.3.4. Extended TLP (ETLP)
Extended TLP (ETLP) has similar hull shape as conventional TLP, but there are
extended structure on each column and tendon porches are connected to the structure.
This makes roll and pitch motion performance better. Kizomba A, Kizomba B, Magnolia,
Papa Terra, and Bigfoot (Figure 1-13) belong to ETLP.

Figure 1-13 Bigfoot E-TLP model [1-12]

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 1.4. TLP hull design and sizing
This subsection summarizes the key point to decide hull dimensions from a design
point of view. Typical hull sizing method is described in the reference [1-13][1-14].
Typically offshore platform project has the following phases;
1. Conceptual Study Phase
2. FEED (Front End Engineering Design) Phase
3. Fabrication and Installation Phase
4. Operation Phase
Major design works are mainly done at Phase 1-3, and are categorized into the
following three stages;
1. Conceptual Design
2. Basic Design
3. Detail Design
Main purpose of conceptual study is concept selection and feasibility study. The basic
study gives main design parameters and cost estimation. The detail design is mainly for
fabrication. This study focus on the conceptual design and basic design.
At the beginning stage of designing TLPs, hull main dimension should be decided. This
hull main dimension has a large impact on the later works. If good optimized hull
design is carried out at initial stage, less design changes and reworks will happen
through project. The following subsection explains what is needed to consider when
designing TLPs.

1.1.1 Global Performance

Global performance shows statics and dynamics of the platform under the site
environment conditions. Criteria of global performance parameters (Such as Min/Max
Tendon tension, Airgap, Offset/Set-down) (Figure 1-14) are defined in API RP 2T. Heave,
roll and pitch natural period should be smaller than 4.5 sec in order to avoid resonance
with waves. The tendon pretension ratio is calculated dividing total tendon pretension
by hull displacement. Pretension provides horizontal restoring force of the platform and
avoids too much horizontal offset. For Gulf of Mexico, pretension ratio varies from 15%
to 35%.

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 Figure 1-14 Global Performance Parameters

1.1.2 Structural Integrity

The structural strength is required as per class requirement. Global strength is the
strength of platform main members like columns and pontoons. Normally global finite
element analysis (FEA) with hydrodynamic loads is carried out to evaluate global
strength. Local strength is defined in equations specified in classification society rules.
Buckling strength and fatigue life are also evaluated as per class requirement.

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 1.1.1 Transportation and installation
Depending on the situation, TLP is transported either by dry-tow or wet-tow, and
installed at site. Proper hydrostatic stability should be kept during wet-tow, installation
or quay-side condition. Normally, the draft is restricted at quayside and during inshore
tow.

1.1.2 Topside Support and Integration Method

Typically, Topsides are integrated at offshore for mini-TLPs and at fabrication yard
for other TLPs. At offshore, Topside is lifted by offshore crane vessel and mated with
hull. At fabrication yard, Topside is mated with hull at quayside or floating dock.
Depending of the sizes, sometimes Topside is separated into several modules and
integrated to hull.

1.1.3 Drilling Operation

Drilling facilities are installed either permanently or temporally. If the temporarily
method, like Tender Assist Drilling (TAD) or modular platform drilling is applied, total
platform weight during severe environment conditions is reduced and this makes
platform performance better because TLP can maintain high pretension. For TAD
operation, deck height is limited for operability and tender assist vessel is moored to
TLP with proper clearance with TLP.

1.1.4 Riser and well bay layout

Hull should provide proper space for riser arrangement so that the hull, mooring leg
and riser will not clash each other. Conventional TLP has relatively large spaces for
riser arrangement. Mini TLPs has smaller space for risers and need keel guide to avoid
clash of riser and hull.

1.1.5 Constructability
Some TLPs have squared column for constructability, although square column has
larger wind and current drag force than circular column. All MOSES TLPs and West
Seno TLP have squared column. Column shell does not need to be formed to circular and
connection between column and pontoon become simple. It also gives better equipment
and piping arrangement.

24
2 Purpose of this Study
As explained in previous section, now TLPs technologies are matured and proven, and
they are being installed globally and subject to various environments. When the hulls of
TLPs are designed for these environments, engineers face the following problems;

1. It takes lots of time and effort to find optimized hull shape within limited amount
of time and resources.
2. Normally past project data is utilized to find the good starting point, but it is not
always applicable because design condition is not always similar.
3. Empirical factors such as pretension ratio, pontoon/column ratio, and volumetric
weight factor is utilized to extrapolate hull shape from past experience, but this is
also not useful when there is not enough supporting data.
4. The design process can be simplified by focusing on one governing criteria, but only
if governing criteria is obvious.

Clauss, and Birk carried out hull shape optimization with utilizing optimization
algorithm [2-1]. They optimized TLP hull shape by minimizing tendon tension response.
Birk et al. carried out optimization of TLP hull by maximizing tendon fatigue life [2-2].
Lee and Lim also carried out hull shape optimization by maximizing tendon fatigue life
with considering second order forces [2-3, 2-4].

1. These preceding works are focusing on hydrodynamic response or tendon fatigue

life and set these to objective function. However, these are not always governing
criteria for TLP hull shape.
2. In these preceding studies, initial hull shape must be input and the objectives of
these optimizations are to improve hull shape.
3. Only in-place conditions are considered in these preceding studies, but hull
shape is also governed by construction, transportation, and installation criteria.

Based on the above issues, the purpose of this study is as follows;

- Develop hull optimization system that can find the optimized TLP hull shape.
This system has more practical approach than preceding works: The platform
weight and tendon weight are objective function to be minimized and design
criteria are constraint condition.
- Compare the result with existing units for verification

25
- Compare with the result of hydrodynamic optimization
- Study application of TLPs to several environment condition

26
3 Methodology – Sizing Strategy

3.1 Conventional Hull Sizing Method

The conventional hull sizing is carried out by engineers in several disciplines as
follows.
 Naval Architects
 Structural Engineers
 Mooring Engineers
 Outfitting Engineers
 Hull System Engineers
 Electrical & Instrument Engineers

Naval architects take care of weight control, hydrostatic stability, hydrodynamic and
global performance analysis. Structural engineer check the structural integrity of the
hull. Mooring engineer check the strength of the tendons. Hull system and E&I
engineer check if there is enough space to arrange the piping and equipment. First
initial hull shape and tendon size are estimated by past project data or engineer’s
experience. Then, weight and center of gravity information is passed to naval architect
who carries out hydrodynamic analysis. Hydrodynamic coefficients are passed to naval
architect who is in charge of global performance. Hydrodynamic loads and inertia loads
are passed to structural engineers. Then tendon tension data is handed over to mooring
engineers. Each engineer checks the criteria in charge and if there is problem, hull
shape is revised and they do the same process again.

Figure 3-1 Conventional Sizing Method

27
 3.2 Sizing Strategy
The flow chart in Figure 3-2 shows the framework of the hull sizing program. The hull
sizing work is modeled as multivariable minimization problem with multiple constraint
conditions. The program finds an optimized solution that meets the criteria at basic
design stage, and then generates necessary design data for further design development.

Figure 3-2 Flow Chart of Hull Optimization Program

3.3 Criteria
There are three types of criteria in the program;
 Geometry criteria (criteria 1)
 Hull sizing criteria (criteria 2)
 design criteria (criteria 3)
As hydrodynamic and structure analyses consume a large amount of computation
time, geometry criteria and hull sizing criteria are checked prior to the analysis so as to

28
improve the efficiency of the optimization process. Geometry criteria (criteria 1) are
summarized in the table 2.

Table 3-1 Geometry criteria (criteria 1)

Geometry Criteria Column dia.<Column distance
Geometry Criteria Column dia.>Pontoon width
Geometry Criteria Draft>Pontoon height
Geometry Criteria Column height>Draft

Hull sizing criteria (criteria 2) are summarized in the table 3. Deck support locations
have to be consistent with column locations. Column height has to meet minimum air
gap criteria set. The metacentric height (GM) for the installation condition must
remain positive and adequate. If the hull shape does not meet these criteria at any step,
the program will skip the hydrodynamic and structure analysis and put a penalty in the
extended objective function.

Table 3-2 Hull Sizing criteria (criteria 2)

Ballast Amount >5% of displacement
GM for installation >2.0m
GM for quayside draft >2.0m
Deck post location On column
Airgap estimation >1.5m
Tendon pretension ratio 5% - 50%

The following Table 4 shows design criteria (criteria 3), which include global
performance criteria and strength criteria. Global performance criteria are in line with
API RP 2T. Strength criteria are in accordance with ABS MODU rule [8-1].

29
 Table 3-3 Design criteria (criteria 3)
Operating Extreme Survival
[Global performance]
Max. Offset (% Water Depth) < 10% <12% <14%
Airgap >1.5 m >0m
Min. Tendon Tension >0 N
Max. Tendon Tension API 2T 9.6.2.3 Pipe Strength
[6-1]
[Structural strength]
Axial Stress 0.6y 0.8y 1.0y
Shear Stress 0.4y 0.53y y

3.4 Optimization Algorithm

Table 1 shows variable, objective function and constraint condition in the sizing system.
The hull dimension (column and pontoon size) and tendon size are defined as variables.
Design conditions such as metocean data, topside and riser properties are constant
parameters. The objective function is the sum of hull and tendon weight. The constraint
conditions are design criteria such as global performance and strength.

Table 3-4 Variable, objective function and constraint condition

x Variables Hull Dimension
Tendon Size
f x Objective function Hull and Tendon Weight
g i x   0 Constraint condition Initial Criteria
Global Performance Criteria
Strength Criteria

The criteria are incorporated into objective function using penalty function method
[3-1] and the extended objective function is expressed in Eq. (3-1). i is the penalty
coefficient of constraint condition i. Starting from an initial value, i is increased
successively until the variables meet all the criteria and optimized solution converges.

f  x   f  x     Maxg  x ,0
i
i i (Eq. 3-1)

30
 3.4.1 Adaptive Simulated Annealing Method
One of the optimization method used in this study is Simulated Annealing Method
(SA)[3-2]. This method is applicable for multi-variable and non-linear global
optimization problem. This optimization method mimics the physical process of
annealing in metallurgy. The minimum energy state can be found by cooling down the
temperature slowly. In this program, extended objective function at step k is defined as
energy Ek.

E k  f  x k  (Eq. 3-2)

At the initial step, xk is generated from uniform random number. Then variables xk+1
are generated from random numbers which follow the normal distribution expressed in
Eq. (3-3). (Adaptive Simulated Annealing (ASA)[3-2]). ui is the uniform random number.

x x y , (Eq. 3-3)

1 1
y 1 1 (Eq. 3-4)
2

x ∈ , (Eq. 3-5)

The Eq. (3-6) shows the probability of acceptance of xk+1. If Ek+1 is smaller than or
equal to Ek, xk is always replaced by xk+1. In the other case, xk is replaced by xk+1
depending on the probability shown in Eq. (3-6).

 1 E k 1  E k
 
hk x k    E  Ek  (Eq. 3-6)
exp  k 1  E k 1  E k
  Tk 


This generation of xk+1, judgment of the acceptance and replacement of xk are repeated
enough times until Ek reaches equilibrium at temperature Tk. The Eq. (3-7) shows
cooling schedule. After the Ek reaches equilibrium at temperature Tk, the temperature
for the next step Tk+1 is calculated from the following equation. D is the dimension of
variable.

31
 /
T (Eq. 3-7)

Then new equilibrium Ek+1 will be searched at temperature Tk+1. This process is
repeated until temperature became cool enough and variable xk converges.

3.4.2 Real-coded Genetic Algorithm

Figure 3-3 Simulated annealing Method 1 (Left; f(x,y), Right; g(x,y))

Genetic Algorithm (GA) [3-3][3-4] is also popular method for optimization of non-linear
and multi-variable problem. This method mimics natural selection process. In this study,
real coded genetic algorithm is adopted. Figure 3-3 shows the concept of genetic
algorithm. Genetic operator is expressed as follows;

, , ,⋯ (Eq. 3-8)

x ∈ , (Eq. 3-9)

Each individual has a genetic operator and are evaluated based on objective function
value. Every generation has a certain number of individuals. Couples of individuals are
selected based on the objective value number. Better objective function value means
higher probability to be selected. Then, couples are crossed over. If couple has value a

32
and b in genetic operator, the genetic operators of the next generation are decided by the
following equations, using normal random number N.

(Eq. 3-10)

m (Eq. 3-11)
2

d a b (Eq. 3-12)

0, (Eq. 3-13)

The generated new individuals are mutated by certain probability. Using normal
random number, mutation is operated as follows;

, (Eq. 3-14)

The genetic operators of best few individuals are preserved to the next generation as
elites. These operations are done by generation and the best individual at the last
generation is the optimized solution.

3.4.3 Steepest Gradient Method

Steepest Gradient Method (SGM) [3-5][3-6] is a simple algorithm. At every step,
objective function and its gradient are calculated, and the search is always going to
steepest directions.  is step size.

, , , (Eq. 3-15)

∂
, (Eq. 3-16)
,

This step size, should be selected properly, otherwise program cannot find minimum
value. This method tends to converge to local extremal values.
3.4.4 Program Test
To study the performance of optimization program, minimum values of the following
functions are calculated by ASA, GA and SGM. This function f is simple, but g has lots
of local extremals.

, 10 (Eq. 3-17)

33
 , 5 5 5 (Eq. 3-18)

The minimum value of this function is as follows.

0, 0 10 (Eq. 3-19)

0, 0 10 (Eq. 3-20)

The convergence condition is shown in the following equation;

10 (Eq. 3-21)

10 (Eq. 3-22)

[ASA]
The Table 3-5 shows the program test result. Figure 3-4 and Figure 3-5 show the
optimization route.

Table 3-5 Optimization result (ASA)

Calculation
function run x y f
Time (sec)
f Run1 0.0002330 0.0024870 -9.9999938 0.078
f Run2 0.0004813 -0.0007605 -9.9999992 0.093
f Run3 -0.0005818 -0.0013593 -9.9999978 0.078
g Run1 0.0001260 0.0000473 -9.9999988 0.076
g Run2 -0.0001402 0.0003340 -9.9999917 0.071
g Run3 0.0000699 0.0001404 -9.9999984 0.085

34
 Figure 3-4 Simulated annealing Method 1 (Left; f(x,y), Right; g(x,y))

Figure 3-5 Simulated annealing Method 2 g(x,y)

[GA]
The Table 3-6 shows the program test result. Figure 3-6 and Figure 3-7 show the
optimization route. The points shows the generated all the individuals for each run.

Table 3-6 Optimization result (GA)

Calculation
function run x y f
Time (sec)
f Run1 0.0001154 -0.0003790 -9.9999998 0.046
f Run2 0.0010711 -0.0020444 -9.9999947 0.047
f Run3 -0.0000290 -0.0026327 -9.9999931 0.023

35
g Run1 -0.0001913 -0.0003227 -9.9999911 0.068
g Run2 -0.0003235 0.0001053 -9.9999927 0.071
g Run3 -0.0001101 0.0001312 -9.9999981 0.097

Figure 3-6 Genetic Algorithm 1 (Left; f(x,y), Right; g(x,y))

Figure 3-7 Genetic Algorithm 2 g(x,y)

36
[SGM]
The Table 3-7 shows the program test result. Figure 3-8 and Figure 3-9 show the
optimization route. Program was kept running until it converges to the solution by
changing initial values for each run. For simple function, SGM can calculate solution
very quickly, but when the function has lots of local extremes, SGM cannot calculate the
solution.

Table 3-7 Optimization result (SGM)

Calculation
function run x y f
Time (sec)
f Run1 0.0000134 -0.0001275 -10.0000000 0.013
f Run2 -0.0000012 0.0000004 -10.0000000 0.013
f Run3 -0.0000000 0.0000000 -10.0000000 0.013
g Run1 0.0000009 -0.0000009 -10.0000000 0.111
g Run2 0.0001295 -0.0000000 -9.9999989 0.096
g Run3 0.0000012 0.0000005 -10.0000000 0.136

Figure 3-8 Steepest Gradient Method 1 (Left; f(x,y), Right; g(x,y))

37
Figure 3-9 Steepest Gradient Method 2 g(x,y)

38
4 Methodology - Calculation Mesh
The auto-meshing program for the followings hull types are prepared for this study.
 Conventional TLP – Circular Column
 Conventional TLP – Rectangular Column
 MOSES SSIP TLP – Circular Column
 MOSES SSIP TLP – Rectangular Column
 Classic MOSES TLP

Each hull type has the following calculation mesh.

 Quarter Panel model
This is used for hydrodynamic calculation.
 Full panel model
This is used for mapping of hydrodynamic pressure load.
 Structural Beam model
This is used for strength calculation.

39
4.1 Conventional TLP – Circular Column

Figure 4-1 Main dimensions of Conventional TLP – Circular Column

40
Figure 4-2 Quarter Panel Model for CTLP

Figure 4-3 Full Panel Model for CTLP

41
Figure 4-4 Structural Beam Model for CTLP

42
4.2 Conventional TLP – Rectangular Column

Figure 4-5 Main dimensions of Conventional TLP – Rectangular Column

43
Figure 4-6 Quarter Panel Model for CTLP (Rectangular Column)

Figure 4-7 Full Panel Model for CTLP (Rectangular Column)

44
Figure 4-8 Structural Beam Model for CTLP (Rectangular Column)

45
4.3 MOSES SSIP TLP –Rectangular Column

Figure 4-9 Main dimensions of MOSES SSIP TLP –Rectangular Column

46
Figure 4-10 Quarter Panel Model for MOSES SSIP

Figure 4-11 Full Panel Model for MOSES SSIP

47
Figure 4-12 Structural Beam Model for MOSES SSIP

48
4.4 MOSES SSIP TLP – Circular Column

Figure 4-13 Main dimensions of MOSES SSIP TLP –Circular Column

49
Figure 4-14 Quarter Panel Model for MOSES SSIP (Circular Column)

Figure 4-15 Full Panel Model for MOSES SSIP (Circular Column)

50
Figure 4-16 Structural Beam Model for MOSES SSIP (Circular Column)

51
4.5 Classic MOSES TLP

Figure 4-17 Main dimensions of Classic MOSES TLP

52
Figure 4-18 Quarter Panel Model for Classic MOSES

Figure 4-19 Full Panel Model for Classic MOSES

53
Figure 4-20 Structural Beam Model for Classic MOSES

54
5 Methodology - Hydrodynamic Calculation
In this section, hydrodynamic calculation method is explained and the calculation
result of the program is compared with commercial software for verification.
Explanation of the hydrodynamic calculation is based on the reference
[5-1][5-2][5-3][5-4].

5.1 Flow Field around a Floating Body

Flow field surrounded by the floating body which oscillates in the wave is described in
this section. Water depth is assumed to be infinity.

Figure 5-1 Flow Field around a Floating Body [5-1]

Fluid field is surrounded by, wetted surface of floating body SH, free-surface SF, sea
bottom SB, control surface at infinity S∞. Assuming these boundary conditions are all
linear and adopting potential theory, the governing equation is expressed as follows;

[L] Φ 0 0 (Eq. 5-1)

Φ Φ
[SF] 0 0 (Eq. 5-2)

Φ
[SB] 0 (Eq. 5-3)

55
 Φ
[SH] ∙ (Eq. 5-4)

Φ
[A] 0, Φ 0 0 (Eq. 5-5)

Incident wave is assumed coming from the β direction (β radians counter-clockwise

from x-axis). The amplitude of incident wave is defined as ζ. Assuming the flow field is
periodically varying at the angular frequency ω driven by incident wave as external
force, the velocity potential which meet (5-6) - (5-7) is expressed as follows;

Φ , , (Eq. 5-6)

, , , , , , , , (Eq. 5-7)

is the velocity potential of incident wave and if the water depth can be assumed as
infinity, is as follows. (K=ω2/g);

ϕ (Eq. 5-8)

is the scattering potential. ( j=1-6 ) are the radiation potential caused by the
j-mode motion ( j=1; Surge, j=2; Sway, j=3; Heave, j=4; Roll, j=5; Pitch, j=6; Yaw ) of
floating body. Xj is the complex j-mode motion amplitude of floating body. These
velocity potential satisfy the following equation;

[L] ϕ 0 0 (Eq. 5-9)

ϕ ϕ
[F] 0 0 (Eq. 5-10)

ϕ
[B] 0 (Eq. 5-11)

ϕ
[A] (Eq. 5-12)

56
 0 (Eq. 5-13)

nj is the j component of the normal vector and positive direction is from surface to fluid
internal.

, ,
(Eq. 5-14)
, ,

5.2 Integral Equation for the velocity potential

By applying Green’s integral law, the velocity potential takes the following form. G is
the Green function. P is the point on surface of floating body and Q is the arbitrary
point.

;
ϕ ; (Eq. 5-15)

As the right hand of (4 15) is 0 on any boundary except SH, is expressed as follows;

1 ;
ϕ
2
(Eq. 5-16)
; 1~6

Assuming water depth is large, the free-surface Green function takes the following
form.

1 1 1
G ; , (Eq. 5-17)
4

r (Eq. 5-18)

r (Eq. 5-19)

57
 G , 2 , (Eq. 5-20)

X (Eq. 5-21)

Y (Eq. 5-22)

5.3 Numerical solution of Integral equation

Boundary element method is adopted in this section. By modeling the surface of
floating body as number N of panel, the integral equation can be discretized as follows.

2πϕ , ∆

(Eq. 5-23)
, Δ
1~
4

1 1
D (Eq. 5-24)

1 1
S (Eq. 5-25)

Free-surface Green function is calculated as follows;

G ; , (Eq. 5-26)

G ; 2 (Eq. 5-27)

G , , (Eq. 5-28)

∂G
, (Eq. 5-29)

∂G 1
G , (Eq. 5-30)
√

58
 For diffraction problem, can be expressed as follows;

ϕ (Eq. 5-31)

(Eq. 5-32)

(Eq. 5-33)

(Eq. 5-34)

(Eq. 5-35)

5.4 Free-Surface Green Function

Assuming the water depth is large, and flow field is varying at the angular frequency
of ω the equations which free-surface green function has to satisfy is expressed as
follows;

(Eq. 5-36)

0 (Eq. 5-37)

→0 →0 (Eq. 5-38)

The numerical method to calculate the free-surface Green functions is as follows.

Depending on the values of X and Y, calculation methods varies considering its precision
and efficiency;
(A) X=0
(B) Y=0
(C) Y > 1.7 X and Y < 7.5
(D) 0.25 X < Y < 1.7 X and R < 14
(E) Y < 0.25 X and R < 14
(F) Others

59
 Figure 5-2 Method used for Green Function [5-1]

(A) X=0

R 0, (Eq. 5-39)

R 0, 0 (Eq. 5-40)

(B) Y=0

R ,0 (Eq. 5-41)
2

R ,0 1 (Eq. 5-42)
2

(C) Y > 1.7 X and Y < 7.5

4 (Eq. 5-43)
R ,
!

60
 2 4 (Eq. 5-44)
R ,
! 1 !

2 2 ! 2 1
F 2 (Eq. 5-45)

1 1
F 0, (Eq. 5-46)

(D) 0.25 X < Y < 1.7 X and R < 14

R , , (Eq. 5-47)

, (Eq. 5-48)
! 2

R , , (Eq. 5-49)

, ′ 1 (Eq. 5-50)
! 2

1 1
I (Eq. 5-51)

I 1 (Eq. 5-52)

nI 1 I 1 2 (Eq. 5-53)

1
I′ (Eq. 5-54)
1

1
I′ 1 (Eq. 5-55)
1

nI′ 1 2I′ I′ 2 (Eq. 5-56)

1

(E) Y < 0.25 X and R < 14

R , , (Eq. 5-57)

61
 , log
2
(Eq. 5-58)
1 1
, ,
2 ! 2 1 !

R , , (Eq. 5-59)

, log
2

H 1 (Eq. 5-60)
2 2
1 1
, ,
2 ! 2 1 !

U , (Eq. 5-61)
2

2 1
U , , (Eq. 5-62)
2 2

U , (Eq. 5-63)
3

2
U , , (Eq. 5-64)
2 1 2 1

V , (Eq. 5-65)
2

2 1
V , , 2 ,
2
(Eq. 5-66)

V , (Eq. 5-67)
3

2
V , , 2 ,
2 1
(Eq. 5-68)

2 1

(F) Others

62
 1
R , (Eq. 5-69)

P 1,
(Eq. 5-70)
P 2 1 1

1
R , (Eq. 5-71)

Q 1, 3
(Eq. 5-72)
Q 2 1 1

5.5 Hydrodynamic force

Extracting the periodic-varying terms from linearized Bernoulli’s pressure equation,
the following equation is obtained.

p , , , , , , , , , (Eq. 5-73)

, , , , (Eq. 5-74)

, , , , (Eq. 5-75)

, , (Eq. 5-76)

For radiation problem, the i component of the fluid force is expresses as follows. Aij is
the added mass coefficient and Bij is the potential damping coefficient induced by the
i-mode motion.

, ,

ρ (Eq. 5-77)

, , (Eq. 5-78)

63
 , , (Eq. 5-79)

For diffraction problem, the i component of the fluid force is expresses as follows. Ei is
the wave exciting force acting along i direction.

, ,
(Eq. 5-80)
ρgζ , ,

5.6 Kochin Function and Wave Drift Forces

Kochin function for each mode of the fluid motion is expressed as follows;

,
(Eq. 5-81)
∆ 1~6

,
(Eq. 5-82)
∆

Assuming the floating body is double (x- y-) symmetrical, the can be expressed as
follows;

(Eq. 5-83)

(Eq. 5-84)

This Kochin function has the following relation to the wave exciting force and potential
damping coefficient.

64
 , (Eq. 5-85)

∗
, , (Eq. 5-86)
4

Wave drift force and moment are expressed as follows by using Kochin function.

| , | (Eq. 5-87)
8

| , | (Eq. 5-88)
8

1 ∗
, ,
8
(Eq. 5-89)
1
′ ,
2

, , , (Eq. 5-90)

5.7 Motion Equation for TLP

5.7.1 Motion Equation for TLP
In addition to added mass coefficient, wave damping coefficient and wave exciting force
(those are described in previous subsection), mass coefficient, viscous damping
coefficient, hydrodynamic restoring coefficient and tendon-and-TTR restoring coefficient
constitute the motion equation of TLP. The motion equation takes the form of linear
simultaneous complex equation. This equation is usually converted to non-dimensional
form and solved.

(Eq. 5-91)

In this section, each coefficient and external force matrix can be described. The hull
geometry of TLP is assumed to be symmetrical about x- and y-axis.

65
 - Mass Matrix
o Platform Mass Matrix
o Platform Added Mass Matrix
o Tendon and Riser Mass Matrix
- Damping Matrix
o Wave Damping Matrix
o Viscous Damping Matrix
- Restoring Matrix
o Hydrostatic Restoring Matrix
o Tendon Restoring Matrix
o TTR Restoring Matrix
o SCR Restoring Matrix
- External Force
o Wave Exciting Force

5.7.2 Mass matrix

Mass matrix consists of the following components;

Table 5-1 Nondimensionalization of Mass Matrix

1~3 4~6
1~3
4~6

Mass matrix consists of the following components;

0 0 0
0 0 0
0 0 0
(Eq. 5-92)
0
0
0

Added Mass Matrix consists of the following components;

0 0 0 0
0 0 0 0
0 0 0 0 0
(Eq. 5-93)
0 0 0 0
0 0 0 0
0 0 0 0 0

66
 5.7.3 Damping matrix
Damping matrix can be non-dimensionalized by the following parameters;

Table 5-2 Nondimensionalization of Damping Matrix

1~3 4~6
1~3 /
4~6

Potential Damping Matrix consists of the following components;

0 0 0 0
0 0 0 0
0 0 0 0 0
(Eq. 5-94)
0 0 0 0
0 0 0 0
0 0 0 0 0

Viscous Damping Matrix consists of the following components;

0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0
(Eq. 5-95)
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0 0

2 i 3~5 (Eq. 5-96)

5.7.4 Restoring Matrix

Restoring matrix can be non-dimensionalized by the following parameters;

Table 5-3 Nondimensionalization of Restoring Matrix

1~3 4~6
1~3 /
4~6

Hydrostatic Restoring Matrix consists of the following components;

67
 0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0
(Eq. 5-97)
0 0 0 0
0 0 0 0
0 0 0 0 0 0

(Eq. 5-98)

(Eq. 5-99)

(Eq. 5-100)

(Eq. 5-101)

(Eq. 5-102)

Tendon and TTR Restoring Matrix consists of the following components [5-5]. T is
static tendon tension, L is tendon length, and  is tendon stiffness. Tx, Ty, Tz are x, y,
z-component of static tendon tension. (x1, y1, z1) is tendon connection point coordinate,
and (x2, y2, z2) is tendon bottom coordinate.

(Eq. 5-103)

(Eq. 5-104)

(Eq. 5-105)

(Eq. 5-106)

(Eq. 5-107)

(Eq. 5-108)

68
 (Eq. 5-109)

(Eq. 5-110)

(Eq. 5-111)

(Eq. 5-112)

(Eq. 5-113)

(Eq. 5-114)

(Eq. 5-115)

2 (Eq. 5-116)

(Eq. 5-117)

(Eq. 5-118)

(Eq. 5-119)

(Eq. 5-120)

2 (Eq. 5-121)

(Eq. 5-122)

(Eq. 5-123)

2 (Eq. 5-124)

69
 (Eq. 5-125)

(Eq. 5-126)

(Eq. 5-127)

Figure 5-3 TLP element coordinate [5-5]

SCR Restoring Matrix consists of the following components [5-5]. Sh is horizontal

spring constant, Sv is vertical spring constant, and  is horizontal angle of the line. Px,
Py, Pz are x, y, z-component of pretension.

0
0
0 0
(Eq. 5-128)

(Eq. 5-129)

(Eq. 5-130)

(Eq. 5-131)

70
 (Eq. 5-132)

(Eq. 5-133)

(Eq. 5-134)

(Eq. 5-135)

(Eq. 5-136)

(Eq. 5-137)

(Eq. 5-138)

(Eq. 5-139)

(Eq. 5-140)

(Eq. 5-141)

(Eq. 5-142)

(Eq. 5-143)

(Eq. 5-144)

(Eq. 5-145)

(Eq. 5-146)

(Eq. 5-147)

71
 (Eq. 5-148)

(Eq. 5-149)

(Eq. 5-150)

Figure 5-4 Catenary line coordinate [5-5]

5.7.5 External force

Wave exciting forces can be non-dimensionalized by the following parameters;

Table 5-4 Nondimensionalization of External Force

1~3 /
4~6

Wave exciting consists of the following components;

(Eq. 5-151)

5.8 Maximum Response Calculation

Motion, velocity, and accelerate response at point (x, y, z) are calculated from RAO by
using the following equations.

72
Point Motion

X  X 1  zX 5  yX 6 (Eq. 5-152)

Y  X 2  xX 6  zX 4 (Eq. 5-153)

Z  X 3  yX 4  xX 5 (Eq. 5-154)

Velocity

U x  i  X 1  zX 5  yX 6  (Eq. 5-155)

U y  i  X 2  xX 6  zX 4  (Eq. 5-156)

U z  i  X 3  yX 4  xX 5  (Eq. 5-157)

Acceleration

Ax   2  X 1  zX 5  yX 6  (Eq. 5-158)

Ay   2  X 2  xX 6  zX 4  (Eq. 5-159)

Az   2  X 3  yX 4  xX 5  (Eq. 5-160)

Tendon tension response is calculated by the following equation. XT is motion response

at tendon connection point.
 
T  n  X T (Eq. 5-161)

 1
n
L

x 2  x1 , y 2  y1 , z 2  z 1  (Eq. 5-162)

Standard deviation x of a response X() is calculated by the following equation.

 x2   X  2 S  d (Eq. 5-163)

73
 S() is irregular wave spectrum. In this study, the following JONSWAP spectrum is
used as irregular wave model;
 
  /  p 1 2 
g 2    p  4
 exp  
S  = 5 exp   
2 2 
 
 (Eq. 5-164)
     
2
 Hs p2  1
= 

(Eq. 5-165)
 4 g  0.065  0.135
0.803

0.07 for    p
=  (Eq. 5-166)
0.09 for    p

2
 p= (Eq. 5-167)
Tp

=1.25 (Eq. 5-168)

The maximum response at short term sea states are calculated as follows.

X max  2 ln N  x (Eq. 5-169)

N=1000 is used for short term maximum response calculation.

74
 5.9 Program Verification
For verification, the result of this hydrodynamic calculation module was compared
with commercial software. As commercial software, Wadam in DNV Sesam Software
Package was used. The calculation condition is as follows;
Hull Type Conventional TLP
Main Dimension
Column Diameter 20 m
Column Distance 60 m
Pontoon Width 10 m
Pontoon Height 10 m
Draft 30 m
Mass Properties
Mass 36000 MT
VCG 15 m-WL
Tendon Properties
Pretension 13,000 kN each
Axial Stiffness 19,800 kN/m each
Length 1,000m
TTR Properties
Pretension 1,000 kN each
Axial Stiffness 1,000 kN/m each
Length 1,050 m
Offset/Setdown (-71m, -71m, -5m)

Figure 5-5 Wadam Calculation model

The calculated Response Amplitude Operators (RAOs) are in the Figure 5-4 – 5-27.

75
Figure 5-6 Surge motion RAO (Upright) Figure 5-7 Surge motion RAO (Offset)

Figure 5-8 Sway motion RAO (Upright) Figure 5-9 Sway motion RAO (Offset)

Figure 5-10 Heave motion RAO (Upright) Figure 5-11 Heave motion RAO (Offset)

Figure 5-12 Roll motion RAO (Upright) Figure 5-13 Roll motion RAO (Offset)

76
 Figure 5-14 Pitch motion RAO (Upright) Figure 5-15 Pitch motion RAO (Offset)

Figure 5-16 Yaw motion RAO (Upright) Figure 5-17 Yaw motion RAO (Offset)

Figure 5-18 Tendon tension RAO (Upright) Figure 5-19 Tendon tension RAO (Offset)

Figure 5-20 Tendon tension RAO (Upright) Figure 5-21 Tendon tension RAO (Offset)

77
Figure 5-22 Tendon tension RAO (Upright) Figure 5-23 Tendon tension RAO (Offset)

Figure 5-24 Wave drift force Fx (Upright) Figure 5-25 Wave drift force Fx (Offset)

Figure 5-26 Wave drift force Fy (Upright) Figure 5-27 Wave drift force Fy (Offset)

Figure 5-28 Wave drift force Mz (Upright) Figure 5-29 Wave drift force Mz (Offset)

78
79
6 Methodology - Global Performance Calculation

6.1 Global Parameters

The main purpose of the global performance calculation is to calculate the following key
global performance parameters [6-1][6-2];
- Maximum Offset
- Maximum Setdown
- Maximum Tendon Tension
- Minimum Tendon Tension
- Maximum Tendon Bottom Angle
- Minimum Airgap
- Maximum Acceleration

The frequency domain calculation is used to calculate the above parameters. The
frequency domain calculation has the following frequency range.
- Mean Condition (Constant)
- Low Frequency (Over 30 sec. period)
- Wave Frequency (From 4 sec. to 30 sec. period)
- High Frequency (Less than 4 sec. period)

The following environmental effects are considered in this calculation;

- Wave
- Wind
- Current
- Tide, Storm Surge and Subsidence

The conditions considered in this analysis are as follows;

- Intact Condition
- Tendon Damaged Condition
- Tendon Flooded Condition
- Compartment Damaged Condition

80
 6.2 Mean Condition Calculation
The mean condition is calculated by the balance of forces and moments. The following
restoring forces and their derivations are to be calculated;
 Hydrostatic Force
 Tendon Restoring Force
 TTR Restoring Force
 SCR Restoring Force
The following mean environmental forces are counted as external forces;
 Wind Force
 Current Force
 Wave Drift Forces
 Viscous Drift Force
 Tide, Storm Surge and Subsidence
The 6-DOF of force and moment balance is described as follows. fr is restoring forces
and fe is external forces.

(Eq. 6-1)

, , , , , , , , , , 0 (Eq. 6-2)

, , , , , , , , , , 0 (Eq. 6-3)

, , , , , , , , , , 0 (Eq. 6-4)

, , , , , , , , , , 0 (Eq. 6-5)

, , , , , , , , , , 0 (Eq. 6-6)

, , , , , , , , , , 0 (Eq. 6-7)

The linear iteration method is used to solve the force balance equation and obtain the
six degree of hull position;

(Eq. 6-8)
′

(Eq. 6-9)
′

81
 (Eq. 6-10)
′

(Eq. 6-11)
′

(Eq. 6-12)
′

(Eq. 6-13)
′

6.2.1 Restoring Forces

6.2.1.1 Tendon and TTR Restoring Forces
Tendon and TTR tensions are described as follows. L0i is initial length of the Tendon
and TTR line and L is line length at the vessel position.

T λ (Eq. 6-14)

′ ′ ′ (Eq. 6-15)

The fairlead positions in global coordinate system which the vessel position is taken
into account are calculated as follows;

′ y φ (Eq. 6-16)

′ y z θ (Eq. 6-17)

′ x ϕ (Eq. 6-18)

6-DOF of forces working on the vessel are described as follows;

′
F (Eq. 6-19)

′
F (Eq. 6-20)

′
F (Eq. 6-21)

M F y F z (Eq. 6-22)

M F z F x (Eq. 6-23)

82
 M F x F y (Eq. 6-24)

The derivations of those forces are to be calculated as follows;

∂F ′
λ 1 (Eq. 6-25)

∂F ′
λ 1 (Eq. 6-26)

∂F ′
λ 1 (Eq. 6-27)

∂M
λ 1 (Eq. 6-28)

∂M
λ 1 (Eq. 6-29)

∂M
λ 1 (Eq. 6-30)

6.2.1.2 SCR Restoring Forces

SCRs (Steel Catenary Risers) are to be calculated by using catenary line theory. The
axial and bending stiffness and deformation are neglected and unit weight per line
length is assumed to be uniform.

Figure 6-1 Schematic of Catenary Line Shape

The vertical force Tvi and horizontal force Thi of catenary line i are described as follows;

T ws (Eq. 6-31)

83
 T wa (Eq. 6-32)

The unit weight per line length is expressed as wi, length of the catenary line is
expressed as si and ai is catenary parameter. The line length si and horizontal
separation yQ are calculated by using the following equations;

s 2 (Eq. 6-33)

y a cosh 1 (Eq. 6-34)

The total length of the line (from anchor point to fairlead point) is calculated by the
following equation;

2 a cos 1 L (Eq. 6-35)

This total length must be constant. By using this condition, the catenary parameter a is
calculated by Newton method (suffix i is not presented);

2 a cos 1 L L 0 (Eq. 6-36)

2
′ cos 1
(Eq. 6-37)
2

(Eq. 6-38)
′

The forces and moment acting at the fairlead point are as follows;
′
F wa (Eq. 6-39)

′
F wa (Eq. 6-40)

F w 2 (Eq. 6-41)

M F y F z (Eq. 6-42)

M F z F x (Eq. 6-43)

M F x F y (Eq. 6-44)

84
The differential of those forces and moments are as follows;
∂F w

(Eq. 6-45)

∂F w

(Eq. 6-46)

∂F wz w z a
(Eq. 6-47)
z z 2 z z 2

∂M y

2 2
(Eq. 6-48)

∂M

x (Eq. 6-49)

2 2

∂M

(Eq. 6-50)

6.2.1.3 Hydrostatic Forces

The hydrostatic restoring forces acting on the vessel are as follows;

F ρgAz (Eq. 6-51)

M ρg mgz (Eq. 6-52)

85
 M ρg mgz (Eq. 6-53)

The differential of those components are expressed as follows;

∂F
ρgA (Eq. 6-54)

∂M
ρg mgz (Eq. 6-55)

∂M
ρg mgz (Eq. 6-56)

6.2.2 Environmental Forces

The environmental forces considered in the mean environmental conditions are;
- Steady Wind
- Steady Current
- Mean Drift Forces
- Tide, Storm Surge and Subsidence
In this section, drag force coefficient calculation, wind and current force calculation
and wave drift forces calculation are explained.

Figure 6-2 Wind and current loading on the platform

6.2.2.1 Drag Force Coefficient

According to DNV-RP-C205 [6-2], drag force is calculated by the following equation;

86
 1
(Eq. 6-57)
2
If the members are not solid (like truss structure), the drag force is calculated by the
following equation.  is the solidity ratio and Ce is the effective drag coefficient.
1
(Eq. 6-58)
2
If the member is a cylinder, the drag coefficient is calculated as follows. Delta is the
roughness parameter.

0.65 Δ 10
29 4 Δ
10 Δ 10 (Eq. 6-59)
20
1.05 Δ 10

If the member is a smooth rectangular, the drag coefficient is calculated as follows.

2 sinα (Eq. 6-60)

1 cosα 2 (Eq. 6-61)

1.5 cosα 2 (Eq. 6-62)

1.0 0.10 (Eq. 6-63)

4.3 13 0.10 0.25 (Eq. 6-64)

0.35 0.25 (Eq. 6-65)

Figure 6-3 Drag force on rectangular cross section (DNV-RP-C205)

87
The following effective shape coefficient Ce is used in the calculation.

Table 6-1 Effective shape coefficient (DNV-RP-C205)

Effective Shape Coefficient Ce
Solidity Ratio
Flat-side Circular Sections
members 4.2 10 4.2 10
0.10 1.9 1.2 0.7
0.20 1.8 1.2 0.8
0.30 1.7 1.2 0.8
0.40 1.7 1.1 0.8
0.50 1.6 1.1 0.8
0.75 1.6 1.5 1.4
1.00 2.0 2.0 2.0

The effect of the finite length is considered in the calculation. The following reduction
factors are applied in the drag force coefficient calculation.

Table 6-2 Reduction Factor for finite length (DNV-RP-C205)

A – Circular Cylinder – subcritical flow
B – Circular Cylinder – Supercritical flow
C – Flat plate perpendicular to flow
l/d 2 5 10 20 40 50 100
A 0.58 0.62 0.68 0.74 0.82 0.87 0.98
B 0.80 0.80 0.82 0.90 0.98 0.99 1.00
C 0.62 0.66 0.69 0.81 0.87 0.90 0.95

6.2.2.2 Current Coefficient Calculation

The current speed distribution in vertical direction is considered. If the current speed
data are available at certain positions in vertical direction, the current distributions are
assumed to be linear among data points. Total force acting on a Morison member is as
follows;
1
f (Eq. 6-66)
2

(Eq. 6-67)

88
This equation is discretized as follows;
1
f
2

1
(Eq. 6-68)
6

1
6

6.2.2.3 Wind Coefficient Calculation

Wind distribution is reproduced by using the model equation (2-63). Reference point of
the data is normally located at 10m height from mean sea water level (z10=10m). Total
force acting on a Morison member is as follows;
1
f (Eq. 6-69)
2

(Eq. 6-70)

This equation is discretized as follows;

1
f
2

1 1
(Eq. 6-71)
2 2 1

1
2 2 1

6.3 Wave-frequency Motion Calculation

As mentioned in section 6, the wave-frequency motion is calculated by the following
equation. For global performance calculation, the effect of the offset/setdown is
considered in in each matrix.

M ij +Aij xwi  Bij +C ij  x wi +K ij +S ij x wi=E i (Eq. 6-72)

6.4 Low-frequency Motion Calculation

6.4.1 Wind Induced Motion
For wind induced motion, the following motion equation is used for calculation.

89
 M +A x
ij ij li  Blij xli+K ij+Sij xli=2CU (Eq. 6-73)

C is the wind coefficient and U is mean wind velocity.

6.4.2 Wind Spectrum

API wind spectrum [6-4] is expressed as follows. f is frequency and U(z) is 1-hour mean
wind speed at z metes above water line.
 2 z 
S  f =
F
(Eq. 6-74)
f 1  1.5F 5 / 3
  z 
0.125

0.15U z   for z  zS

  zS 
 z =  0.275 (Eq. 6-75)
 0.15U z  z  for z  zS
 z 
  s
f
F= (Eq. 6-76)
fp
U z 
f p= (Eq. 6-77)
z

  0.025, z=10, z s  20 (Eq. 6-78)

ISO wind spectrum [6-5] is expressed as follows. f is frequency and U0 is 1-hour mean
wind speed at z metes above water line. z is height above water line.
2 0.45
U   z 
320 0   
S  f =  10   10  (Eq. 6-79)

1  f 
5
n 3n
m

2
 0.75
 z 3 U  (Eq. 6-80)
f m  172 f    0 
 10   10 

n  0.468 (Eq. 6-81)

90
 6.4.3 Variable Wave Drift Force Induced Motion
For the low frequency motion due to variable wave drift force, the following motion
equations are used.
Hi  H j
M +A x
ij ij dij  Bij +Cij  x dij+K ij+S ij xdij= (Eq. 6-82)
2
Newman’s approximation [3-4] is used for the external force term. By solving this
motion equation, quadratic transfer function is obtained.

6.5 Maximum/Minimum Value Calculation

Wave, wind, and variable wave drift force induced responses are multiplied with each
external force spectrum. These response spectra are combined and filtered for each
frequency ranges;
High Frequency Range: Period < 4 sec
Wave Frequency Range: 4 sec < Period < 30 sec
Low Frequency Range: 30 sec < Period
The standard deviation of the response is calculated as follows by using empirical
calibration factors , , and .

=  H 2   W 2   L 2 (Eq. 6-83)

Maximum and minimum value is calculated as follows. Pmax is peak factor for
maximum response and Pmin is peak factor for minimum.

X max=X mean  Pmax (Eq. 6-84)

X min=X mean  P min  (Eq. 6-85)

For maximum and minimum tendon tension calculation, the following margins are
considered.
Pile misalignment margin 2 feet
Tendon weight margin 3%
Tendon buoyancy margin 3%

91
 6.6 Program Verification
For verification, the result of this global performance calculation module was
compared with commercial software. As commercial software, DeepC in DNV Sesam
Software Package was used.

Figure 6-4 DeepC analysis model

Hull and Tendon/Riser conditions are the same as section 5. The environmental
loading is as follows;
Significant Wave Height 19 m
Mean Wind Speed 55 m/s
Surface Current Speed 2.7 m/s
Sea Level +0.8 m
Environmental Load Direction Collinear toward SW (225deg)

92
 Figure 6-5 Offset value comparison

Figure 6-6 Setdown value comparison

93
Figure 6-7 DeepC time history of up-wave tendon tension

Figure 6-8 DeepC spectrum of up-wave tendon tension

94
 Figure 6-9 DeepC time history of down-wave tendon tension

Figure 6-10 DeepC spectrum of down-wave tendon tension

[GP Comparison]
The following table shows calculated global performance result. Although, program is
frequency domain calculation, and DeepC is time-domain calculation, the similar result
was obtained.

95
 Table 6-3 Global performance comparison
Program DeepC
Mean Offset 81m 79m
Max. Offset 102m 99m
Max. Tendon Tension 27,761 kN 28,562 kN
Min. Tendon Tension 8,652 kN 5,983kN

96
7 Methodology - Global Structure Calculation
In this analysis, the hull and topside members are modeled by beam elements. The
benefits of this beam-model structural analysis are (1) simple and fast overview, (2)
quick verification for shell element FEM analysis and (3) better understanding for
physical phenomena by decomposing stress into each component. However, the effect
such as local deformation, hoop stress, stress concentration, shear delay and so on are
not included in the calculation result. These effects should be considered separately
with another method.
To model the hull with beam element, the section properties of each hull girder
member (such as Pontoon, Column and so on) are to be properly calculated.
Correspondence between elements in panel model and beam elements in structural
model is also necessary to transfer the hydrostatic and hydrodynamic pressure to the
beam element.

Figure 7-1 Beam Structural Model and Hydrodynamic Panel Model

97
 7.1 Section Properties
In order to calculate the stiffness and stresses, section properties of the hull girder
members are to be calculated correctly. Longitudinal members (shell plates, bulkheads
and stiffeners) are counted in the section properties. Section area, moment of inertia,
section modulus and shear area are required to be inputted.

Figure 7-2 Section view of Pontoon and Column

Table 7-1 Section Properties

Symbol Unit Description
A m2 Section Area
Iyy m4 Second moment of area about y-axis
Izz m4 Second moment of area about z-axis
Ixx m4 Torsional second moment of area
Zyy m3 Section Modulus about y-axis
Zzz m3 Section Modulus about z-axis
K m3 Torsional Section Modulus
Ay m2 Shear Area in y-direction
Az m2 Shear Area in y-direction

7.2 Correspondence
Correspondence matrix is to be prepared to transfer the panel pressure loads to beam
element. The panels which are surrounding the beam are hired as corresponding panels.
There are “dummy rigid beams” which do not have the relation to the panels. These
beams are defined to transfer the force from beam to beam.

98
 Figure 7-3 Correspondence between panels and beams

Table 7-2 Member ID definition

Section ID Member
1 Dummy Rigid Beam
2 Column
3 Node
4 Pontoon

7.3 Spring Boundary corresponding Tendon stiffness

Spring boundary conditions which x-, y-, z-stiffness are same as tendons’ stiffness are
set on the tendon fairlead points. These boundary work as tendons, and help to avoid
rigid-body motions.

99
 Figure 7-4 Spring Boundary corresponding to Tendons

7.4 Matrix Method

Matrix method [7-1] is used to calculate the force and moment in the grillage structure.
This method is based on beam theory with small deformation and each element consists
of 2 nodes.

Table 7-3 Symbols for matrix method formulation

Symbol Unit Description
E Pa Young’s Modulus
G Pa Shear Modulus
A m2 Section Area of the element
Iy m4 Second moment of area about y-axis
Iz m4 Second moment of area about z-axis
K m4 St. Venant Torsional constant
l m Length of the element

100
 Pxi N Axial Force at node i
Qyi N Shear Force at node i
Qzi N Shear Force at node i
Mxi Nm Moment about x at node i (torsion moment)
Myi Nm Moment about y at node i
Mzi Nm Moment about z at node i
ui m Displacement in x-direction at node i
vi m Displacement in y-direction at node i
wi m Displacement in z-direction at node i
xi rad Angular displacement about x-axis at node i
yi rad Angular displacement about y-axis at node i
zi rad Angular displacement about z-axis at node i

7.4.1 Element Stiffness Matrix

The relation of stiffness and displacement in each mode is expressed as follows.

Axial Compression

1 1
(Eq. 7-1)
1 1

Bending about z axis

12 .
6 4 (Eq. 7-2)
12 6 12
6 2 6 4
Bending about y axis
12 .
6 4 (Eq. 7-3)
12 6 12
6 2 6 4
Torsion

1 1
(Eq. 7-4)
1 1

Element stiffness matrix takes the following form.

101
 .
12
0
12
0 0

0 0 0
6 4
0 0 0
6 4
0 0 0 0

0 0 0 0 0
12 6 12
0 0 0 0 0
12 6 12
0 0 0 0 0 0

0 0 0 0 0 0 0 0
6 2 6 4
0 0 0 0 0 0 0
6 2 6 4
0 0 0 0 0 0 0 0

(Eq. 7-5)

7.4.2 Coordinate Conversion and Global Stiffness Matrix

The local element coordinate values are transferred to global coordinate by using the
coordinate conversion matrix T.

102
 Figure 7-5 Coordinate Conversion [7-1]

(Eq. 7-6)

Each component is as follows;

(Eq. 7-7)

(Eq. 7-8)

(Eq. 7-9)

103
If   0 Then

1
(Eq. 7-10)

1
(Eq. 7-11)

Else if   0 Then

(Eq. 7-12)
0

(Eq. 7-13)
0

The global stiffness matrix is as follows;

(Eq. 7-14)

KG is calculated as follows;

(Eq. 7-15)

.
(Eq. 7-16)

104
 7.4.3 Calculation of Section Forces
By solving the global stiffness matrix, displacements are obtained, and then section
forces are calculated as follows;

(Eq. 7-17)

12 6 12 6 (Eq. 7-18)

12 6 12 6 (Eq. 7-19)

(Eq. 7-20)

6 4 6 2 (Eq. 7-21)

6 4 6 2 (Eq. 7-22)

(Eq. 7-23)

12 6 12 6 (Eq. 7-24)

12 6 12 6 (Eq. 7-25)

(Eq. 7-26)

6 2 6 4 (Eq. 7-27)

6 2 6 4 (Eq. 7-28)

105
 7.4.4 Distributed Load
Distributed loads are applied as equivalent point load on the nodes. The equivalent
point loads are calculated by the following equation;

′ 2 (Eq. 7-29)
6

′ 7 3 (Eq. 7-30)
20

′ 7 3 (Eq. 7-31)
20

′ (Eq. 7-32)

′ 3 2 (Eq. 7-33)
60

′ 3 2 (Eq. 7-34)
60

′ 2 (Eq. 7-35)
6

′ 3 7 (Eq. 7-36)
20

′ 3 7 (Eq. 7-37)
20

′ (Eq. 7-38)

′ 2 3 (Eq. 7-39)
60

′ 2 3 (Eq. 7-40)
60

106
 7.5 Load Cases
The following table summarizes the basic load cases applied on the model.

Table 7-4 Load Cases

ID Name
LC1 Static Loads Hydrostatic Load
Self Weight
LC2 Wave Loads Hydrodynamic Load
Inertia Load

7.5.1 Static Loads

Hydrostatic load is transferred to the beam element as distributed line load or point
load. Self-weight of the hull is modeled as line load for each hull girder member. Topside
self-weight is modeled as point load at Topside COG point with dummy beams
connected each node to the COG point.

7.5.2 Wave Loads

Hydrodynamic load is transferred to the beam element as distributed line load or point
load in complex number format (which means phase information is included). Inertia
load of the hull is modeled as complex-number line load for each hull girder member.
Topside inertia load is modeled as complex-number point load at Topside COG point
with dummy beams connected each node to the COG point.
Steepness of design wave has a limitation according to DNV-RP-C103
Column-Stabilized Units [7-2]. Wave steepness is defined by;
2
S (Eq. 7-41)

The combination of wave height and wave period that are considered should imply a
value of steepness that is less than the following limit;
1
6
7
S 1 (Eq. 7-42)
6
0.93
7 36

The wave height and period combinations on the steepness limit are given by;

107
 0.22 6
S 6 (Eq. 7-43)
0.6
4.5 36

108
8 Methodology - Weight Calculation
In this section, scantling calculation and weight estimation method is described.
8.1 Scantling Calculation
8.1.1 Plating
For the designated permanent ballast tank boundary structures and external shell
plating, the following expression (per paragraph 3-2-2/9.3 of ABS MODU2008 Rules
[8-1]) governs:

sk
t 2.5
254
(Eq. 8-1)
s
2.5 mm
150

t = plate thickness (mm)

s = spacing of stiffeners (mm)
k = factor based on aspect ratio of panel
= 3.075√ 2.077 / 0.272
= 1.0
α = Aspect ratio of the panel (longer side/shorter side)
q = 235/Y
Y = specified minimum yield strength of material (N/mm2)
h = greatest of the following distances (m) from the lower edge of plate to:
i. a point representing the design draft is used;
ii. a point located two-thirds of the distance from top of tank to the top
of overflow;
iii. a point located 0.91 m above the top of the tank.

For areas subject to wave immersion, a minimum design head of 6.1 m is required.
For all other subdivision boundary structures (such as internal watertight bulkheads
and flats in void spaces), the following expression (per paragraph 3-2-2/7.3 of ABS
MODU2008 Rules) is used:

t 1.5
(Eq. 8-2)
s
2.5 mm
200

109
 8.1.2 Stiffener
For stiffeners on the designated permanent ballast tank boundary structures and
external shells, the following expression (per paragraph 3-2-2/9.5 of ABS MODU2008
Rules [8-1]) for minimum scantling was used:

SM (Eq. 8-3)

f = 7.8
c = 0.9 For stiffeners having clip attachments to deck or flat at to
the ends or having such attachments at one end with the
other end supported by girders.
= 1.00 for stiffeners supported at both ends by girders
h = Greatest of the distances (m) from the middle of l to the same point to
which h for plating is measured (1-1).
s = spacing of stiffeners (m)
l = length (m) between supports, where brackets are fitted at shell, deck or
bulkhead supports, and the brackets are in accordance with 3-2-2/Table
2 of ABS MODU2008 Rules and have a slope of approximately 45 deg,
the length l may be measured to a point on the bracket located at a
distance from the toe equal to 25% of the length of the bracket.

For stiffeners on all other subdivision boundary structures (such as column internal
watertight bulkheads and flats in void spaces), the following expression (per paragraph
3-2-2/7.5 of ABS MODU2008 Rules) for minimum scantling were used:

SM (Eq. 8-4)

f = 7.8
c = 0.56 For stiffeners having clip attachments to deck or flat at to
the ends or having such attachments at one end with the
other end supported by girders.
= 0.60 for stiffeners supported at both ends by girders
h = Greatest of the distances (m) from the middle of l to the same point to
which h for plating is measured (1-2). where the distance is less than 6.1
m, h is to be taken as 0.8 times the distance in m plus 1.22.

110
Other parameters are defined similarly to those in previous expression

8.2 Weight estimation

The weight is estimated from the calculated scantling with applying factors for
transverse and tertiary members.

Figure 8-1 Compartment assumption for CTLP

Table 8-1 Structural Members for Conventional TLP

Structure Member
Pontoon Bottom Plate/Stiffener/Transverse
Inboard Shell Plate/Stiffener/Transverse
Outboard Shell Plate/Stiffener/Transverse
Top Plate/Stiffener/Transverse
Center Bulkhead Plate/Stiffener/Transverse
Node Bottom Plate/Stiffener/Transverse
Outer Shell Plate/Stiffener/Transverse
Inner Bulkhead Plate/Stiffener/Transverse
Access Shaft Bulkhead Plate/Stiffener/Transverse
Flat Plate/Stiffener/Transverse
Column 1 Outer Shell Plate/Stiffener/Transverse
Inner Bulkhead Plate/Stiffener/Transverse
Access Shaft Bulkhead Plate/Stiffener/Transverse
Flat Plate/Stiffener/Transverse
Column 2 Outer Shell Plate/Stiffener/Transverse

111
 Inner Bulkhead Plate/Stiffener/Transverse
Access Shaft Bulkhead Plate/Stiffener/Transverse
Flat Plate/Stiffener/Transverse
Column 3 Outer Shell Plate/Stiffener/Transverse
Inner Bulkhead Plate/Stiffener/Transverse
Access Shaft Bulkhead Plate/Stiffener/Transverse
Column Top Plate/Stiffener/Transverse

On top of this structural weight, user-input outfitting, machinery, consumables, and

weight margins are included in the total weight. Total weight, center of gravity and
moment of inertia are calculated.

Figure 8-2 Weight Calculation Method

112
9 Calculation Result
9.1 Calculation Condition
The program is tested for the following environmental conditions. There are three
environmental data;
 Gulf of Mexico metocean condition before the hurricane attack in 2005
(pre-2005)[9-1]
 Gulf of Mexico metocean condition after the hurricane attack in 2005 (post-2005)
[9-2]
 A Southeast Asian environmental condition
These environmental data are summarized in Table 9-1. The total of hull outfitting,
equipment and piping weights) is assumed to be 2,000MT. Topside and riser conditions
are summarized in Table 9-2 and 9-3.

Table 9-1 Environmental Condition

Case 1 Case 2 Case 3

GoM GoM (Post-2005) Southeast Asia

Extreme Extreme Operating Extreme Survival Operating Extreme Survival

Return Period 100yr 1yr 100yr 1000yr 1yr 100yr 1000yr

Wave height Hs 12.2m 10.0m 15.8m 19.8m 5.8m 7.6m 9.1m

Peak period Tp 14.2s 13.0s 15.4s 17.2s 12.5s 14.1s 15.4s

Wind Speed Vw 39.9m/s 33m/s 48m/s 60m/s 18.9m/s 22.6m/s 25.8m/s

Current Speed Vc 1.7m/s 1.7m/s 2.4m/s 3.0m/s 1.4m/s 1.8m/s 2.0m/s

Water level L 0.9m 0.4m 0.6m 0.8m 0.42m 0.55m 0.66m

The calculation condition for topside is as follows;

Table 9-2 Topside Condition

Topside weight 20,000MT
Topside vertical center of gravity 10 m from BOS
Footprint 65 m x 65 m
Total Height 20 m
Structure See figure 9-1
Beam 1200x500x25x50
Pillar/Brace1000x25

113
 Figure 9-1 Topside Model

The followings are the riser properties;

Table 9-3 Riser Condition

TTR
Number 10
Pretension 1,000 kN for each
Stiffness 1,000 kN/m for each
Length 1050 m
SCR
Number 4
Pretension 3,000 kN for each
Fairlead Angle 15 deg

114
 9.2 GoM Pre-2005 condition (Case 1)
The calculation results of the GoM Pre-2005 by ASA and GA are summarized in the
table below. Hull total weight was both about 14,000MT and tendon pretension was
about 21%-22%. Optimization result of GA and ASA matched well.

Table 9-4 Calculation result for GoM pre-2005 (Case1)

ASA GA

Hull Shape

Column diameter 21.2 m 21.0 m

Column distance 67.2 m 61.8 m
Pontoon breadth 9.3 m 6.7 m
Pontoon height 8.7 m 10.3 m
Draft 23.5 m 26.3 m
Column height 47.3 m 48.0 m
Hull weight 14,153MT 13,920MT
Pretension Ratio 22% 21%

115
 9.3 GoM Post-2005 condition (Case 2)
The calculation results of the GoM Post-2005 by ASA and GA are summarized in the
table below. Hull total weight was both about 18,000MT and tendon pretension was
about 37%. Column height was 58m for both.

Table 9-5 Calculation result for GoM post-2005 (Case 2)

ASA GA

Hull Shape

Column Diameter 24.7 m 23.2 m

Column Distance 65.2 m 70.5 m
Pontoon breadth 8.5 m 11.4 m
Pontoon height 8.2 m 7.4 m
Draft 24.4 m 25.0 m
Column height 57.8 m 59.8 m
Hull weight 17,425MT 17,903MT
Pretension Ratio 29% 29%

116
 9.4 GoM Post-2005 condition (Case 3)
The calculation results of the Southwest Asian condition by ASA and GA are
summarized in the table below. Hull total weight was both about 12,650MT and tendon
pretension was about 20%. Column height was 36m-38m.

Table 9-6 Calculation Result for Southeast Asian Condition (Case 3)

ASA GA

Hull Shape

Column Diameter 21.3 m 23.0 m

Column Distance 60.9 m 61.8 m
Pontoon breadth 6.6 m 8.7 m
Pontoon height 13.8 m 11.0 m
Draft 21.9 m 18.0 m
Column height 38.0 m 35.6 m
Hull weight 12,658MT 12,678MT
Pretension Ratio 21% 20%

117
10 Discussion
10.1 Comparison with an existing TLP hull shape
The followings are the comparison of case 1 with an existing TLP (Brutus TLP).
Similar hull proportion was obtained. Hull weight of the calculation result was slightly
smaller than Brutus TLP.

Table 10-1 Comparison with an existing TLP

Brutus TLP GoM pre-2005 (ASA)
Column Diameter 20 m 21.2 m
Column Distance 60 m 67.2 m
Pontoon Width 11 m 9.3 m
Pontoon Height 7 m 8.7 m
Draft 25 m 23.5 m
Column Length 51 m 47.3 m
Hull Steel Weight 12,900 MT 12,153MT
Hull Total Weight 14,153MT

Brutus TLP GoM pre-2005 (ASA)

Figure 10-1 Comparison with an existing TLP

118
 10.2 Pre v.s. Post Hurricane Condition
The following table and graph shows the comparison of pre- and post-Hurricane
condition. Column height of post-Hurricane condition became much larger than
pre-Hurricane condition. As a result, hull weight of post-Hurricane was 23% larger.

Table 10-2 Comparison between Pre- and Post-Hurricane Hull Shape

GoM Pre-2005 (ASA) GoM Post-2005 (ASA)
Column Diameter 21.2 m 24.7 m

Column Distance 67.2 m 65.2 m

Pontoon Width 9.3 m 8.5 m

Pontoon Height 8.7 m 8.2 m

Draft 23.5 m 24.4 m

Column Length 47.3 m 57.8 m

Hull Total Weight 14,153MT 17,425MT

Pretension Ratio 22% 29%

GoM Pre-2005 GoM Post-2005

Figure 10-2 Comparison between Pre- and Post-Hurricane Hull Shape

119
 10.3 Hash v.s. Mild Environment
This is the comparison between hash (GoM post-Hurricane) and mild (SE Asia)
environment condition. The column became significantly shorter in mild condition. This
is because of airgap criteria. The optimized hull weight has 38% difference between two
conditions.

Table 10-3 Comparison between Pre- and Post-Hurricane Hull Shape

GoM Post-2005 (ASA) Southeast Asia (ASA)
Column Diameter 24.7 m 21.3 m
Column Distance 65.2 m 60.9 m
Pontoon Width 8.5 m 6.6 m
Pontoon Height 8.2 m 13.8 m
Draft 24.4 m 21.9 m
Column Length 57.8 m 38.0 m
Hull Weight 17,425MT 12,658MT
Tendon Pretension Ratio 29% 21%

GoM Post-Hurricane (ASA) Southeast Asia (ASA)

Figure 10-3 Comparison of Hull Shape for hash and mild environment

120
 10.4 Comparison with hydrodynamic optimization result
This result shows the effect of selected objective function. Objective function was set
to tendon tension RMS, and optimized hull shape was calculated by applying
post-Hurricane condition. Initial criteria were considered into this calculation. As a
result, pontoon height became significantly shallow and draft became significantly deep.
The final hull weight was 23% larger.

Table 10-4 Comparison with hydrodynamic optimization result

Weight Minimum Response Minimum
Column Diameter 24.7 m 21.1 m
Column Distance 65.2 m 70.4 m
Pontoon Width 8.5 m 18.1 m
Pontoon Height 8.2 m 3.1 m
Draft 24.4 m 42.3 m
Column Length 57.8 m 69.3 m
Hull Weight 17,425MT 21,358 MT

Weight Minimum Response Minimum

Figure 10-4 Comparison with hydrodynamic optimization result

121
 10.5 Optimization process for GoM pre-2005
The following Figures show the process of optimization. The red and black lines show
how the variables were optimized by each process for pre-2005 condition. The green dots
represent the area constrained by criteria 1, as these dots are generated by uniform
random numbers and screened by criteria 1. The light-blue dots show the area
constrained by criteria 2. The blue points are also generated by random numbers and
screened by criteria 3 to see the effect of each constraint condition. Hull dimensions of
existing TLPs (Brutus TLP, Auger TLP) are also plotted in the same graph for
comparison.

Figure 10-5 Column diameter v.s. Hull total weight (Case 1)

122
Figure 10-6 Column distance v.s. Hull total weight (Case 1)

Figure 10-7 Pontoon breadth v.s. Hull weight (Case 1)

123
Figure 10-8 Pontoon height v.s. Hull weight (Case 1)

Figure 10-9 Draft v.s. Hull weigh (Case 1)

124
Figure 10-10 Column Height v.s. Hull weight (Case 1)

125
 10.6 Optimization process for GoM post-2005
The following Figures show the process of optimization for post-2005 condition.

Figure 10-11 Column diameter v.s. Hull weight (Case 2)

Figure 10-12 Column distance v.s. Hull weight (Case 2)

126
Figure 10-13 Pontoon width v.s. Hull weight (Case 2)

Figure 10-14 Pontoon Height v.s. Hull weight (Case 2)

127
 Figure 10-15 Draft v.s. Hull weight (Case 2)

Figure 10-16 Column Height v.s. Hull weight (Case 2)

128
 10.7 Optimization process for Southeast Asian Condition
The following Figures show the process of optimization for Southeast Asian condition.

Figure 10-17 Column diameter v.s. Hull weight (Case 3)

Figure 10-18 Column distance v.s. Hull weight (Case 3)

129
Figure 10-19 Pontoon width v.s. Hull weight (Case 3)

Figure 10-20 Pontoon Height v.s. Hull weight (Case 3)

130
 Figure 10-21 Draft v.s. Hull weight (Case 3)

Figure 10-22 Column Height v.s. Hull weight (Case 3)

131
 10.8 Study on Criteria – Pre-2005 condition
The following chart shows region governed by each criteria. The green, light blue and
blue points are representing the territory to meet geometry criteria, hull sizing criteria
and design criteria. This graph is plotted by generating random number and evaluating
each criterion.

Figure 10-23 Criteria 1, 2, & 3 (Case 1)

The following plots show the territories of each hull sizing constraint condition.
Intersection of these is the hull sizing criteria.
 Ballast amount (>5% of displacement)
 Installation stability (GM>2m)
 Quayside stability (GM>2m)
 Deck post location
 Airgap estimation
 Tendon pretension (5% -50% of displacement)

132
 Figure 10-24 Ballast Amount Condition (Case 1)

Figure 10-25 Installation Stability Condition (Case 1)

133
Figure 10-26 Quayside stability Condition (Case 1)

Figure 10-27 Deck post location Condition (Case 1)

134
 Figure 10-28 Airgap Condition (Case 1)

Figure 10-29 Tendon Pretension Condition (Case 1)

135
 The following plots show the territories of each design constraint condition.
Intersection of these is the design criteria.
 Natural period (<4.5s)
 Max offset (<10%-14% of water depth)
 Minimum Tendon Tension(>0)
 Airgap (>0)
 Tendon strength
 Hull strength

Figure 10-30 Natural Period Condition (Case 1)

136
 Figure 10-31 Max Offset Condition (Case 1)

Figure 10-32 Minimum Tendon Tension Condition (Case 1)

137
 Figure 10-33 Airgap Condition (Case 1)

Figure 10-34 Tendon Strength Condition (Case 1)

138
Figure 10-35 Hull strength Condition (Case 1)

139
11 Conclusion
TLP is an offshore platform which has very small motions due to the mooring by
tendons. Recently TLPs are being installed on more global locations and TLPs are
started to be subject to various type of environment condition. This trend causes lots of
difficulty to design the optimized hull shape of TLPs, when we cannot utilize past
experience for these new design condition.
In this study, optimization algorithm is utilized for hull shape optimization. Preceding
works also utilize optimization algorithm, but they are not suitable for initial hull
design. In section 2, the following goals are set.
- Develop hull optimization system that can find the optimized TLP hull shape. This
system has more practical approach than preceding works: The platform weight and
tendon weight are objective function to be minimized and design criteria are constraint
condition.
- Compare the result with existing units for verification
- Compare with the result of hydrodynamic optimization
- Study application of TLPS to several environment condition

The hull sizing system developed in this study has the following characteristics;
- Objective function is hull and tendon weight, and constraint conditions are design
criteria including global performance, strength, and initial screening criteria.
- This system can find optimized hull shape without using any empirical parameters
or without input initial hull shape.
- This hull sizing system can find optimized hull shape in few hours, while it takes
few weeks to carry out hull sizing with conventional method.

This system was tested for specific design conditions and the following points are found;
- Calculated hull shape was in line with existing TLP and the program is practically
useful.
- Post hurricane condition requires larger tendon pretension and column height. As a
result, the hull weight increased by 23%.
- For SE Asia, column length becomes significantly shorter, and weight can be
reduced accordingly.
- Comparing between the weight and tension response for objective function, objective
function of tension response gives significantly smaller pontoon height and deeper
draft, and the hull weight also become larger. This means hydrodynamic
optimization doesn’t necessarily give the good solution.

140
12 Acknowledgement
I appreciate generous support and instruction from Professor Hideyuki Suzuki. I
received continuous support from MODEC TLP group, so I’m deeply grateful to the
group members.

141
Reference
Section 1
[1-1] R. D’Souza, and Rajiv Aggarwal, The Tension Leg Platform Technology - Historical
and Recent Developments, OTC-24512
[1-2]E.F.H. Lim, and B.F. Ronalds, Evolution of the Production Semisubmersible, SPE
Annual Technical Conference and Exhibition SPE-63036
[1-3] Anil K. Sablok, and Steven Alexander Barras, Spar Technology- Developments in
Deepwater spar installation, Offshore Technology Conference, 4-7 May, Houston, Texas,
OTC-20234
[1-4] MODEC Inc. website: http://www.modec.com/index.html
[1-5] Tangvald, T.B., Goliat Field Development Circular Fpso in Harsh Environment,
2009-035 OMC Conference Paper – 2009
[1-6] IMA, 2015 Jan FPS Outlook Report
[1-7] Mustang and Offshore Magazine, Worldwide survey of TLPs, TLWPs, 2010
[1-8] R. M. Rainey, Brutus Project Overview “Challenges and Results”, OTC-13990
[1-9] Stephen B. Wetch, and Peter G. Wybro, West Seno: Facilities Approach,
Innovations and Benchmarking, OTC-16521
[1-10] Stephen E. Kibbee, and David C. Snell, New Directions in TLP Technology,
OTC-14175
[1-11] Stephen E. Kibbee et al., Morpeth SeaStar Mini-TLP, OTC-10855
[1-12] Jun-Ho Song et al., Introduction of Hull Construction for Big Foot E-TLP,
ISOPE-I-13-049
[1-13] A.G. Grant, S. Sircar, and L. A. Nikodym, A systematic Procedure for Developing
Optimum TLP Configuration, OTC-6570
[1-14] R. D. Larrabee, S. B. Hodges, B. E. Cox, and R. Gonzalez, Concept Selection and
Global Sizing of Mars TLP, OTC8369

Section 2
[2-1] Clauss, G., and Birk, L., 1996, “Hydrodynamic shape optimization of large offshore
structures”, Applied Ocean Research, 18(4), pp.157-171.
[2-2] Birk, L., Clauss, G., and Lee, J.Y., 2004, “Practical application of global
optimization to the design of offshore structures”, Proceedings of 23th International
Conference on Offshore Mechanics and Arctic Engineering, Vancouver, British
Columbia, Canada.
[2-3] Lee, J.Y., and Lim, S.J., 2008, “Hull form optimization of a tensioned leg platform
based on coupled analysis”, Proceedings of 18th International Offshore and Polar

142
Engineering Conference, Vancouver, British Columbia, Canada.
[2-4] Lee, J.Y., Koo, B.J., and Clauss, G., 2007, “Automated design of a tension leg
platform with minimized tendon fatigue damage and its verification by a fully coupled
analysis”, Ship Technology Research, Vol.54 No.1, pp. 11-27.

Section 3
[3-1] Fiacco, A.V., and McCormick, G. P., 1968, Non-linear Programming, Sequential
Unconstrained Minimization Technique, John Wiley, New York.
[3-2] Ingber, L., 1993, “Simulated Annealing: Practice versus Theory”, Mathematical
and Computer Modeling, 18, 11, pp.29-57.
[3-3] Hitoshi Iba, Identeki Algorithm no kiso, Ohmu-sha, Tokyo
[3-4] Hitoshi Iba, Excel de Manabu Identeki Algorithm, Ohmu-sha, Tokyo
[3-5] Hirokazu Anai, Suri Saitekika no Jissen Guide, Kodan-sha, Tokyo
[3-6] Keiji Kawamo, Hiroshi Hasegawa, and Masaaki Yokoyama, Saitekika Riron no
Kiso to Ouyou, Korona-sha, Tokyo

Section 5
[5-1] Nihon Zosen Gakkai Kaiyoukougaku-Iinkai Seinou-bukai, 2003, Futai no Ryuutai
Rikigaku, Seizando , Tokyo
[5-2] Matao Takagi and Shinichi Arai, Senpaku Kaiyou-kouzoubutsu no Taiha Riron,
Seizan-do, Tokyo
[5-3] Masashi Kashiwagi, Hydrodynamics of a Floating Body in Waves, Ouyou-suri 11(3),
198-208, 2001-09-14
[5-4] Newman, J.N., 1977, Marine Hydrodynamics, The MIT Press, Cambridge,
Massachusetts
[5-5] Det Norske Veritas, 2008, SESAM user manual Wadam.

Section 6
[6-1] American Petroleum Institute, 2010, Recommended Practice for Planning,
Designing and Constructing Tension Leg Platforms, 3rd Edition (API RP 2T)
[6-2] American Petroleum Institute, 2008, Design and Analysis of Stationkeeping
Systems for Floating Structures, 3rd Edition (API RP 2SK)
[6-3] Det Norske Veritas, 2007, Environmental Conditions and Environmental Loads
(DNV-RP-C205)
[6-4] American Petroleum Institute, 2014, Planning, Designing, and Constructing Fixed
Offshore Platforms—Working Stress Design (API RP 2A-WSD)

143
[6-5] ISO, 2005, Petroleum and natural gas industries -- Specific requirements for
offshore structures - Part 1: Metocean design and operating considerations (ISO
19901-1).

Section 7
[7-1] Fujii, D., 2005, Excel de toku san-jigen kenchikukouzou kaiseki, Maruzen, Tokyo
[7-2] Det Norske Veritas, 2012, Column-Stabilized Units (DNV-RP-C103)

Section 8
[8-1] Amerian Bureau of Shipping, 2013, Rules for building and classing mobile offshore
drilling unit

Section 9
[9-1] American Petroleum Institute, 2007, Interim Guidance on Hurricane Conditions in
the Gulf of Mexico (API 2INT-MET)
[9-2] Richard D’Souza et al. A Comparison of Pre- and Post-2005 Sanctioned Gulf of
Mexico Tension Leg, Semisubmersible, and Spar Floating Platforms, OTC-25442

144