DESIGN OF A FLOATING, PRODUCTION, STORAGE, AND OFFLOADING ...alexandersevert.weebly.com/uploads/5/2/8/2/52821231/2.019_final... · DESIGN OF A FLOATING, PRODUCTION, STORAGE, AND OFFLOADING

DESIGN OF A FLOATING, PRODUCTION,

STORAGE, AND OFFLOADING VESSEL FOR

OPERATION IN THE GULF OF MEXICO

2.019 Design of Ocean Systems

Massachusetts Institute of Technology

Judy Hsiang and Alexander Severt

Contents

List of Figures iii

List of Tables v

1 Abstract 1

2 Introduction 1

3 General Arrangement and Overall Hull Design 2

4 Weight, Buoyancy, and Stability 44.1 Intact Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44.2 Damaged Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

5 Strength and Structural Design 6

6 Hydrodynamic Loads and Seakeeping Analysis 76.1 FPSO Properties and Testing Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76.2 WAMIT Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86.3 Seakeeping Performance and Possible Improvements . . . . . . . . . . . . . . . . . . . . . . . 9

7 Mooring System Design 117.1 Steady Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127.2 Tension vs. Displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127.3 Slowly-Varying Forces and Motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

8 Cost Estimation 14

9 Conclusion 15

Appendices 17

Appendix A FPSO Parameter Summary 17

Appendix B Compartment Volumes, Geometries, and Locations 21

Appendix C GZ Curves for Three Different Loading Conditions 25

Appendix D Damaged Compartment Arrangements 27

Appendix E Transverse Cross Sections with Girder Layout 31

Appendix F Stresses, Shear Forces, and Moments for 3 Loading Conditions 33

Appendix G Extreme Conditions 36

Appendix H Stresses, Shear Forces, and Moments for Extreme Conditions 37

Appendix I Added Mass and Damping Coefficients 39

Appendix J Wave Excitation Forces 41

Appendix K Response Amplitude Operators 43

i

Appendix L Output Functions 45

ii

List of Figures

1 FPSO Examples: (left) Marlim Sul - a traditional FPSO design with external turret mooringsystem. (right) Sevan Voyageur - circular FPSO vessel. . . . . . . . . . . . . . . . . . . . . . . 2

2 JONSWAP Spectrum for 1-year wave and 100-year wave conditions . . . . . . . . . . . . . . . 83 Catenary Mooring Line Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Tension in a Catenary Mooring Line as Function of Displacement . . . . . . . . . . . . . . . . 135 Catenary Mooring Line at Average Steady Load Position . . . . . . . . . . . . . . . . . . . . 136 Sketch of FPSO — plan view . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Lines Drawing of FPSO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 Hydrostatics Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Perspective view of FPSO design generated in Rhino. . . . . . . . . . . . . . . . . . . . . . . 2010 Stability curve for 90% Cargo Oil, 50% SLOP, 0% SWB . . . . . . . . . . . . . . . . . . . . . 2511 Stability curve for 50% Cargo Oil, 50% SLOP, 0% SWB . . . . . . . . . . . . . . . . . . . . . 2512 Stability curve for 0% Cargo Oil, 0% SLOP, and SWB as necessary. . . . . . . . . . . . . . . 2613 Damaged Condition 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2714 Damaged Condition 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2715 Damaged Condition 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2816 Damaged Condition 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2817 Damaged Condition 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2918 Damaged Condition 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2919 Damaged Condition 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2920 Damaged Condition 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3021 Damaged Condition 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3022 Damaged Condition 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3023 Cross section of bow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3124 Cross section of internal turret. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3125 Cross section at midship. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3226 Cross section of stern. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3227 Stresses for 90% Cargo Oil, 50% SLOP, 0% SWB . . . . . . . . . . . . . . . . . . . . . . . . . 3328 Shear forces and moments for 90% Cargo Oil, 50% SLOP, 0% SWB . . . . . . . . . . . . . . 3329 Stresses for 50% Cargo Oil, 50% SLOP, 0% SWB . . . . . . . . . . . . . . . . . . . . . . . . . 3430 Shear forces and moments for 50% Cargo Oil, 50% SLOP, 0% SWB . . . . . . . . . . . . . . 3431 Shear forces and moments for 0% Cargo Oil, 0% SLOP, and SWB as necessary. . . . . . . . . 3532 Shear forces and moments for 0% Cargo Oil, 0% SLOP, and SWB as necessary. . . . . . . . . 3533 Extreme Hogging condition: Full ballast condition, 0% cargo oil with a troichoidal wave with

the crest centered amidships and same length as the vessel. . . . . . . . . . . . . . . . . . . . 3634 Extreme Sagging condition: 98% oil cargo with a troichoidal wave with the trough centered

amidships and the same length as the vessel. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3635 Stresses for extreme hogging conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3736 Shear forces and moments for extreme hogging conditions. . . . . . . . . . . . . . . . . . . . . 3737 Stresses for extreme sagging conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3838 Shear forces and moments for extreme sagging conditions. . . . . . . . . . . . . . . . . . . . . 3839 Added mass and damping coefficients for light ship conditions in heave, roll, and pitch motion. 3940 Added mass and damping coefficients for full ship conditions in heave, roll, and pitch motion. 4041 Wave excitation forces for light ship conditions in heave, roll, and pitch for 0◦ and 45◦ incident

wave headings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4142 Wave excitation forces for full ship conditions in heave, roll, and pitch for 0◦ and 45◦ incident

wave headings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4243 RAO for fully loaded ship with 0◦ and 45◦ incident wave headings. . . . . . . . . . . . . . . . 4344 RAO for light ship with 0◦ and 45◦ incident wave headings. . . . . . . . . . . . . . . . . . . . 4445 Motion output spectrum for fully loaded ship in the 1-year wave condition. . . . . . . . . . . 45

iii

46 Motion output spectrum for fully loaded ship in the 100-year wave condition. . . . . . . . . . 4647 Motion output spectrum for light ship in the 1-year wave condition. . . . . . . . . . . . . . . 4748 Motion output spectrum for light ship in the 100-year wave condition. . . . . . . . . . . . . . 48

iv

List of Tables

1 Principle Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Hull Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Estimate of full ship weights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Hydrostatics information for three different loading conditions. . . . . . . . . . . . . . . . . . 55 Metacentric heights for different damaged conditions. . . . . . . . . . . . . . . . . . . . . . . . 66 Section Modulus and Area Moment of Inertia for Different Cross Sections . . . . . . . . . . . 67 Wave Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Properties of Hull Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Estimated Natural Frequencies/Periods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 810 Natural Frequency for Various Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 911 Significant Amplitude for Various Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 1012 Approximate Material and Labor Cost for Basic Construction in Millions of Dollars . . . . . 15

v

1 Abstract

The objective of this report is to analyze, research, model, and design a Floating, Production, Storage,

and Offloading vessel (FPSO) capable of surviving the weather conditions found in the Gulf of Mexico.

This design covers different aspects of the ship, including hull size, shape, displacement, empty and loaded

draft, as well as accounting for the natural heave, pitch, and roll periods. The vessel is required to fulfill all

ABS and MARPOL requirements for a steel vessel carrying oil. Environmental data from the test site was

analyzed to find the wind, wave, and current forces that the ship can endure both in regular and extreme

cases. The ship is able to keep production capability in conditions of the one year storm and is able to survive

the 100-year storm conditions. Mooring systems were then analyzed after the ship design was completed.

This design project uses a barge shape for preliminary geometry and dimensions that are adjusted to

reach specific conditions which must be satisfied. These conditions include safe and efficient hull design,

matching production, storage, and offloading, recognizing the impact of hull deflections, and matching the

mooring system to motions and loads. Several software applications, including Rhinoceros, ORCA 3D, and

POSSE were used to determine final geometry and dimensions, as well as evaluate the performance of the

finals design.

Through numerical analysis and software simulations, we have designed a FPSO vessel that is capable

of operating in the Gulf of Mexico during calm and stormy seas. The vessel is stable enough to handle the

forces and moments caused by either environment, as well as different damage conditions. The design also

has an internal mooring system that stabilizes the FPSO’s position over the well during production. Building

the vessel to our design specifications in a US shipyard would cost approximately $3.2 billion.

2 Introduction

The design of an FPSO allows the offshore oil and gas industry to have an easier mechanism for the

processing of hydrocarbons and storage of oil. Most FPSOs are easy to install and do not need a pipeline

system to export the oil. The vessel receives hydrocarbons from deep sea oil wells, processes them, and

stores the oil until it is offloaded onto a tanker. Once a well has been depleted, the vessel can just move to

a new location. Production of oil in offshore locations has been a reality since the late 1940s. Originally,

all of these offshore locations sat on the seafloor, but as oil exploration expanded to deeper waters, floating

structures became more common. With 50 years of technological improvements, designers of FPSOs have

constructed many different designs. Shown in Figure 1 are two very different designs. On one hand, there

1

is the Marlim Sul1, a traditional FPSO similar to a large barge. On the other hand, some designs are a bit

more creative, such as the second FPSO, Sevan Voyageur2, which is a circular vessel. Each design has it’s

own advantages and disadvantages; for our FPSO, we will go with a more traditional design.

Figure 1: FPSO Examples: (left) Marlim Sul - a traditional FPSO design with external turret mooringsystem. (right) Sevan Voyageur - circular FPSO vessel.

3 General Arrangement and Overall Hull Design

The design of this FPSO was based off of a barge of length - 300 m, breadth - 60 m, and molded depth -

30 m. With the exception of the bow and stern, the hull is essentially a large rectangular prism. This design

has three rows of tanks, a 4 m deep double bottom, 2 m double sides, an internal turret, and a cambered

main deck. Two tank rows and an external mooring systems were also considered for alternative designs.

A three row tank arrangement was chosen over two rows because the extra longitudinal bulkhead provides

additional structural stability. With respect to roll, the three tank arrangement provides more hydrostatic

stability than the two row arrangement. Lastly, an internal mooring system was chosen instead of an external

system because it is easier to maintain and has less vertical motion (due to pitch). To accommodate the

internal turret, the ship’s length was increased to 330 m. Other principle dimensions are shown in Table 1.

Outlined in Figure 6 are 7 center cargo oil tanks and 5 pairs of identical side cargo tanks within our

double-hull design. One pair of side cargo tanks holds an equivalent volume of oil as a single center tank.

This volume also coincides with the production volume for a single day. By designing the tanks in this

1http://www.offshore-technology.com/projects/marlim2http://www.sevanmarine.com/index.php/component/content/article/41/16-fpso-sevan-voyageur

2

Table 1: Principle Dimensions

Final DimensionTotal Length (L) 330 mBreadth (B) 64 mMolded Depth (D) 32.15 m

manner, the ship has minimal internal free surfaces after each production day. The arrangements of the

tanks is designed such that the center tanks are filled first, followed by transverse pairs of side cargo tanks.

The minimized internal free surfaces and the tank fill-order contribute to better hydrodynamic stability.

On the opposite sides on the internal turret, as well as in front of, are separate sets of ballast tanks. In

addition, there are pairs of ballast tanks on opposite sides of the two aftmost center cargo tank. The double-

hull layout was used due to the requirement of ballast volume, as well as it helped with stability analysis.

The breadth and molded depth of our design were increased to accommodate the 4 m double bottom and

2 m double side. These dimensions were specifically chosen to meet the ballast volume requirements set by

the ABS Steel Vessel Rules Part 5A for Double Hull Tankers Sections 5.2-5.4 and the MARPOL Annex I

Regulation 24 environmental guidelines, as well as help with stability.

The internal turret mooring system was chosen for its lower level of maintenance and the lower induced

pitch moment by the mooring cable forces. Based on known mooring systems currently used, our design

allows for a maximum mooring diameter of 30 m. But, to do this design, the total hull length needed to be

lengthened to accommodate the extra space needed for the turret. The hull ratios, shown in Table 2, are all

comparable to similar FPSO designs. A detailed lines drawing of our design is shown in Figure 7. We have

also included a detailed table outline, in Appendix B, with all of the compartments’ volumes, geometries,

and locations.

Table 2: Hull RatiosL/B 5.16B/D 1.99L/D 10.26

After forming the hull shape in Rhinoceros3, the FPSO’s buoyancy and stability were tested using ORCA

3D4. For waterlines ranging from 3 m to 32 m at 1m increments, a hydrostatics table, shown in Figure 8, was

created that outlines many important features. These features include displacements, waterline surface areas,

longitudinal center of buoyancy, and much more. Some aspects that we found were that many coefficients,

3Rhinoceros (Version 5.0) [Software]. Robert McNeed & Associates, 2012.4Orca3D (Version 1.3.1) [Software]. DRS Technologies, Inc., July 2013.

3

such as the block coefficient, are very close to 1. If you draw a box around the submerged part of the ship,

the block coefficient is the ratio of the box volume occupied by the ship. Thus, since the majority of our

ship is box shaped, our coefficient should be approximately 1. All of the aspects outlined in this table are

strictly based on the geometrical properties of our design.

4 Weight, Buoyancy, and Stability

Many of the other parameters in our design are based off of approximate percentages of the total displace-

ment gathered from many other similar FPSO designs. After preliminary sizing of the vessel, and knowing

how much cargo oil we need to be able to carry, we can calculate these weights. An outline of our full ship

loads are shown in Table 3.

Table 3: Estimate of full ship weights.Approximate Percentage of

Total Displacement Weight Position ExtentsCargo oil 75 301,392 mt 60m to 300mHull structure 15 52,000 mt 0m to 330mProduction platform 7 32,000 mt 80m to 270mMoorings/risers 3 10,000 mt 270m to 300mAccommodations 5 20,000 mt 0m to 20m

Once we have these approximate values, we can find a vertical and longitudinal center of gravity (VCG

and LCG respectively). These values are necessary to calculate the stability of our design. The VCG was

determined to be approximately 11 m and the LCG was about 160 m. For this stability analysis, the

largest righting arm produced by the application of a wind moment was .034 m. Since this is three orders of

magnitude smaller than the heeling righting arms for the vessel, the wind moment is assumed to be negligible

for the rest of the analysis.

4.1 Intact Stability

To predict how our design will respond in different loading conditions, we used the US Navy’s Program

of Ship Salvage Engineering (POSSE 5.1 )5 to apply different loading conditions. We used three conditions,

which included 0%, 50%, and 90% cargo oil capacity. Table 4 shows the hydrostatics information for

three loading conditions, including total displacement, trim angle, horizontal and vertical center of gravity

locations, and metacentric heights. In addition to this table, graphs showing the GZ stability curves for the

5POSSE 5 (Version 5.1.134) [Software]. Herbert-ABS Software Solutions, LLC., 2014.

4

three loading conditions can be found in Appendix C. From this data we need to confirm that our design

meets the standards sets by MARPOL Annex I Regulation 25A on intact stability. First, the maximum

righting arm (GZ) must occur at an angle of heel of at least 25circ. Next, the righting lever arm shall be

at least 0.20 m at an angle of heel equal to or greater than 30circ. Also, the initial metacentric height,

measured at an angle of heel of 0circ, shall be not less than 0.15 m. Lastly, the area under the righting lever

curve shall not be less than 0.055 m·rad up to an angle of heel of 30circ and not less than 0.09 m·rad up to

40circ. Our analysis shows that these requirements are satisfied for all conditions.

Table 4: Hydrostatics information for three different loading conditions.

Condition Displacement(MT) Trim Angle(◦) VCG(m-BL) LCG(m-AP) GM(m)50% SLOP, 0% SWB

- 90% Cargo Oil 481,924 0.08F 12.70 160.59F 11.94- 50% Cargo Oil 291,532 0.07A 10.96 160.46F 21.91

0% SLOP, SWB as needed- 0% Cargo Oil 218,131 0.07F 6.71 163.47F 32.55

4.2 Damaged Stability

Using POSSE again, our design was tested to see if it would still have sufficient stability in the case where

a compartment was damaged for some unforeseen reason. According to MARPOL Annex I Regulation 25, to

analyze side damage, we must assume that we have damaged 15 m intervals along the length of the ship. To

satisfy this requirement, we have damaged neighboring compartments and analyzed the heeling angle that

results from the damage. Assuming the ship is at 50% capacity and proceeding along the length, we damaged

10 pairs of side compartments; which specific compartments are damaged in each damaged condition are

outlined in Appendix D. We have outlined, in Table 5, the various GM values for each damaged condition.

MARPOL has given a set of requirements that we must satisfy for damaged stability. The angle of heel due

to unsymmetrical flooding shall not exceed 25◦. Also, the area under the curve within this range shall not

be less than 0.0175 m·rad up to the maximum heeling angle. Last, The final waterline, taking into account

sinkage, heel and trim, shall be below the lower edge of any opening through which progressive flooding

may take place. Comparing the POSSE outputs with the MARPOL regulations, we found that our ship

sufficiently satisfy all of the damage stability requirements.

5

Table 5: Metacentric heights for different damaged conditions.

Damaged GM(m) Heeling Angle Corresponding FigureCondition (◦) in Appendix D

1 20.78 1.20 132 20.37 2.63 143 19.73 3.80 154 19.87 3.45 165 19.95 3.36 176 19.99 3.31 187 20.01 3.31 198 20.00 3.38 209 20.11 2.85 2110 21.04 0.68 22

5 Strength and Structural Design

To ensure that our design can withstand the loads that it will be subject to, we needed to outline where

we would place the structural girders. In Appendix E, we have included various cross-sectional views of

our design that show the girder placement. The section modulus values for the various cross sections are

included in Table 6. These values of the section modulus satisfy the ABS safety criterion.6

Table 6: Section Modulus and Area Moment of Inertia for Different Cross SectionsSection Modulus Top (m3) Bottom (m3) Ixx (m4) Iyy (m4) Ixy (m4)Bow 24.25 21.69 271.9 673. -2.305E-13Turret 51.22 59.37 884.6 3287 3.567E-12MidShip 61.26 73.29 1073 3346 2.802E-12Stern 39.07 39.33 532.5 1762 1.289E-13

To ensure a stable ship, three wave conditions were tested: still-water, a 1-year wave, and a rare 100-year

wave. The characteristics of these waves are outlined in Table 7. In still-water, we analyzed the strength

of our ship at the three loading conditions. We need to ensure that the section moduli satisfy the ABS

requirements. Graphs showing the bending moment and shear stress measurements are shown in Appendix

F. In a 100-year wave, we analyzed extreme sagging and hogging conditions. Illustrations for these scenarios

and the corresponding stress graphs are included in Appendix G and H respectively. Knowing the maximum

sagging and hogging moments and dividing by the section modulus in the different sections, we can calculate

the maximum stress. This stress needs to be less than the admissible stress of 17.5 kN/cm2, as per ABS

requirements. Using the approximations given by ABS Rules for Building and Classing FPSOs Part 5A and

Part 3-2-1 Section 3.5-3.7.3), we find that our FPSO does satisfy these constraints.

6American Bureau of Shipping. ”Rules for Building and Classing: Steel Vessels Part 3”. 2012

6

Table 7: Wave ConditionsCharacteristic 1-Year Wave 100-Year WaveWind Speed [m/s] 15.0 40.0Current Speed [m/s] 1.2 1.5Significant Wave Height [m] 4.0 12.0Peak Wave Period [s] 10.0 14.0

6 Hydrodynamic Loads and Seakeeping Analysis

6.1 FPSO Properties and Testing Conditions

We have summarized the ship’s basic properties into Table 8. Our analysis will be carried out using both

light ship (0% loading) and full loaded ship (100% loading) conditions.

Table 8: Properties of Hull DesignLight ship Full ship

Center of Gravity [m] 6.71 12.70Draft [m] 10.88 23.37Mass [MT] 218,131 481,924

Given the two wave characteristics mentioned above, we used a JONSWAP (Joint North Sea Wave

Observation Project) spectrum through our calculations to find the ship’s response the each wave condition.

A graph showing these spectrums for the two wave condition is shown in Figure 2. In the 1-year wave case,

there is a much wider spectrum with a lower peak, compared to the high and thin spectrum for the 100-year

wave condition.

An approximation for the natural period in heave motion and natural period in pitch are given by

Tnh = 2π

√CBT

Cwg

(1 + 0.4

B

T

)(1)

Tnp = 2π

√12TL2 R2 + B

4

g, (2)

ωn = 2πf =2π

T(3)

where CB is the block coeffiecent, Cwg is the waterplane coefficient, and R is the radius of gyration. Using

the properties in Table 8 and Equations (1) - (3), we were able to approximate the natural frequencies and

periods for the light ship and full ship. These values,shown in Table 9, will serve as response benchmarks

for comparison to models and simulations.

7

Figure 2: JONSWAP Spectrum for 1-year wave and 100-year wave conditions

Table 9: Estimated Natural Frequencies/PeriodsCondition Natural Frequency [rad/s] Natural Period [s]Light Ship

- Heave 0.526 12.9- Pitch 0.658 9.5

Full Loaded Ship- Heave 0.458 13.7- Pitch 0.570 11.0

6.2 WAMIT Analysis

In order to calculate the various forces and motions of the ship under the different conditions, we used a

program called WAMIT. WAMIT is a state of the art tool used for analyzing wave interactions with offshore

structures and vessels. Inputting the ship properties, we were able to determine added mass, damping

coefficients for a range of frequencies (with periods from 5 seconds to 25 seconds). These values are shown

in Appendix I. There, a relatively flat curve with a spike at one frequency can be seen. Our analysis has

guided us to believing that these peaks are occurring due to our interior mooring system, which we will go

into more detail with later on.

Next, WAMIT calculated wave excitation forces over the same range of frequencies with two incident

8

wave heading angles of 0 (following sea) and 45 (quartering stern sea) degress. Graphs showing this force as

a function of frequency are shown in Appendix J. In these figures, there are several additional peaks, which

we believe are also due to our mooring system.

WAMIT also estimates the resonance amplitude operators (RAO) over a range of frequencies for the

different conditions previously outlined. The RAOs are transfer functions that characterize the effect that a

sea state will have on the motion of a ship through the water. These functions are shown versus frequency

in Appendix K. The relative maximums within these functions are the natural frequencies. These values are

shown in Table 10. All of these WAMIT calculations help us analyze the ship’s frequency response.

Table 10: Natural Frequency for Various ConditionsCondition Natural Frequency [rad/s] Natural Period [s]Light Ship

- 0 Degree Heading- Heave 0.5129 12.3- Pitch 0.5845 10.7


Full Loaded Ship- 0 Degree Heading

- Heave 0.4760 13.2- Pitch 0.5236 12.0


Now that we have the sea spectrum and the transfer function, we can use the Wiener–Khinchine relation

to find the spectrum that characterizes the motion of the ship. We have shown these spectrum in Appendix

L. For the spectrum of different conditions, we can use statistical analysis to understand the ship’s motion.

The variable we are going to compute is the significant motion amplitude for each of the different conditions,

outlined in Table 11.

6.3 Seakeeping Performance and Possible Improvements

When we analyzed the response spectrum for our ship we noticed an extra natural frequency occurring.

After consulting the literature, we have come to the conclusion that the extra peak is coming from an

additional natural frequency due to the sloshing of water within our interior mooring system. These extra

peaks are mainly prevalent in a 45◦ heading, where the frequency bump into each other. This analysis was

given that our mooring system was essentially an empty cavity. With the installation of the mooring system,

9

Table 11: Significant Amplitude for Various ConditionsCondition Significant Amplitude Significant Height

1-Year Wave 100-Year WaveLight Ship

- 0 Degree Heading- Heave (m) 0.1334 2.7574- Roll (rad) 0.0000 0.0000- Pitch (rad) 0.0023 0.0594


Full Loaded Ship- 0 Degree Heading

- Heave (m) 0.1412 1.1288- Roll (rad) 0.0001 0.0002- Pitch (rad) 0.0031 0.0224


the resulting forces would be decreased due to less volume for sloshing. This extra frequency does not

dramatically alter our ship’s final response, but it is something that we found very interesting and specific

to our design.

The estimated natural frequencies of response for the light ship and full ship conditions fell within the

range of the calculated natural frequencies for incident wave headings of 0◦ and 45◦. Based on our results

from WAMIT, for both light ship and full capacity conditions, the lowest natural frequencies are in heave

with a 0◦ incident wave heading and the highest frequencies in pitch with a 45◦ incident wave heading. For

1-year wave heights, the heave displacement is approximately 18 of the significant wave amplitude for light

and full ship loading conditions. For 100-year wave heights and full capacity, the heave displacement of our

FPSO is 1.2 m or 10%· of the significant wave amplitude for 0◦ incident wave headings and 2.1 m or 18% of

the significant wave height for 45◦ incident waves. All of these values are small compared to the surrounding

significant wave amplitude of 12 m.

The best way to combat further movement is to incorporate a mooring system, as we will do later in

this paper. Another possibility is to increase the moment of inertia, either through increasing the number

of bulkheads or thickness of steel.

10

7 Mooring System Design

We developed a preliminary mooring system based on the steady wind, current, wave loads and motions,

as well as wave-frequency and slowly-varying loads and motions. The mooring system will consist of 12 lines

placed in groups of 3 (3◦ spacing between lines of the same group) with a group in each of the 4 cardinal

directions. The legs of the system will consist of 2500 m of cable and 250 m of chain securing the system to

the sea bottom.

For this analysis we considered a full loaded ship condition in a 100-year survival environment as was

mentioned previously in the hydrodynamic loads and seakeeping section. Our analysis is based on the worst

case scenario, in which there is one mooring line in the head sea condition. Shown in Figure 3 is a depiction

of a single catenary mooring line changing as the displacement varies.

Figure 3: Catenary Mooring Line Design

11

7.1 Steady Loads

The steady loads that will be acting on our design include forces due to wind, currents, and waves. They

use the wave characteristics, as well as our ship’s design parameters, to calculate a rough estimate of the

mean steady force. The first of these forces is characterized by the Equation (4), where ρair is the density

of air, V is the speed of the wind, Ap is the approximate transverse area of the ship above the water level,

and CD is the coefficient of drag.

Fwind =1

2ρairV

2ApCD (4)

Next, the current force is shown in Equation (5), where ρwater is the density of water, U is the speed of

the current, As is the submerged transverse area, Swet is the submerged surface area of the ship, and Cf is

the coefficient of friction.

Fcurrent =1

2ρwaterU

2(AsCD + SwetCf ) (5)

Lastly, the forces due to the steady wave drifting load is summed up using Equation (6), where (F1(ωj)ζ2a

) is

the wave drift force transfer function outputted from WAMIT and Aj is the amplitude of the wave component

with frequency ωj .

Fwave =

N∑j=1

(F1(ωj)

ζ2a

)A2j (6)

The sum of these three forces give us a value for our average steady loads, which came out to approximately

5.4 million newtons. This value will be used in the next section.

7.2 Tension vs. Displacement

The next step in our mooring system design, was to take the characteristics of a typical catenary line

and find what the tension would be on the line as the ship varied by a fixed distance. A graph of the tension

as a function of the displacement is shown by the load-excursion relation in Figure 4. We have also plotted

the mean steady forces acting on the ship.

The point at which these two lines cross is the equilibrium position of our ship under steady forces, and

that value is -48.2 m. Knowing that this point is the equilibrium, the shape of our catenary line at this point

12

Figure 4: Tension in a Catenary Mooring Line as Function of Displacement

is shown in Figure 5. One thing to notice is that in this scenario, the line is rather taut. In a standard case,

where there is more than one mooring line, this steady load tension would be spread out across the various

lines and thus would lead to a more slack line.

Figure 5: Catenary Mooring Line at Average Steady Load Position

13

7.3 Slowly-Varying Forces and Motions

Along with the steady forces acting on our ship, we also accounted for slowly varying wave forces. These

can be accounted by using the spectrum associated with the 100-year wave. The slowly varying motion of

our ship acts similar to how a mass reacts to a spring and damper system. The tension in the line has

a corresponding spring constant, which is equal to the slope of the load excursion relation at the steady

equilibrium position. Once we have the spring constant we can estimate the surge natural frequency that

comes from this force. The helps us understand how the ship will oscillate around the steady equilibrium

position.

From the natural frequency, we can calculate the slowly-varying force, the spectrum of slowly-varying

motion, and then the significant distance that the ship will travel. The significant distance is the average

of the one-third highest distances that come from the spectrum of slowly-vary motion. Our design has

a significant distance of 36 m. At the outstretched extent of this oscillation, we can follow where this

displacement puts us on the load excursion relation. At a displacement of -12.1 m, the tension in the line

would be nearly 16 million newtons.

To understand how this tension will react in our system, it is important to look at the breaking force

of the mooring line. According to International Association of Classification Societies (IACS) Requirements

Concerning Mooring, Anchoring and Towing Section A1.4, the breaking force of a spiral stranded mooring

line, is about 19 million newtons.7 This means our mooring system falls under the 1.1 safety factor required

by the IACS for survival. A key take away from this analysis is to remember that this is a worst case scenario;

in the worst wave condition, all of the forces lined up in the same direction, and all but one of the mooring

lines snapped, our design still fits within the safety criterion.

8 Cost Estimation

The cost of an FPSO is heavily dependent on the shipyard in which it is built. We will do our analysis

assuming, our ship is built in the United States. Our estimation of cost is based off of a naval vessel in

which the approximate percentages of the different system’s weight were already known. We have outlined

the sections, the corresponding percentages, approximate material and labor cost in Table 12.

Summing this very rough, preliminary estimate we obtain an amount of $3.2 billion for basic construction.

The largest percentage of weight is from the structure of the ship, which includes the steel plating, girders,

7International Association of Classification Societies, ”Requirements Concerning MOORING, ANCHORING AND TOW-ING”, 2014. http://www.iacs.org.uk/document/public/Publications/Unified requirements/PDF/UR A pdf148.PDF

14

Table 12: Approximate Material and Labor Cost for Basic Construction in Millions of DollarsSystem Percentage Material Cost Labor CostStructures 61.4 $204 $42Propulsion 5.5 $458 $2Electrical Generation & Distribution 3.3 $344 $322Electronics & Navigation 1.4 $236 $43Auxiliary Systems 13.5 $558 $139Outfit & Furnishings 14.9 $618 $295

deck plating, etc. The expensive systems include everything else besides the main structure of the ship. The

labor intensive system installation is the most expensive cost in designing an FPSO.

9 Conclusion

History tells us that the demand for Floating, Production, Storage, and Offloading vessels is increasing

due to its ability to access remote locations. These vessels provide a method to operate in remote locations

and severe environmental conditions that many other offshore structures can’t handle. The FPSO vessel

doesn’t require the pipeline necessary to transport cargo oil to a land based terminal.

Our final FPSO design is a double-hulled, interior mooring system, barge shaped steel vessel. The vessel’s

particular dimension include a length of 330 m, a breadth of 64 m and a depth as 32 m from keel. The size and

placement of our cargo oil tanks assist in the daily process of loading and limit the amount of hydrodynamic

variability associated with free surface movement. The design proved to be a stable vessel in all operating

conditions. The shear and wave induced moment of the vessel was analyzed in POSSE. To simplify the

structure of the vessel, it was modeled as a beam. The model was subjected to worst case scenarios for

hogging and sagging. The shear and wave induced moment were within the proper stress bounds.

The stability analysis, also done in POSSE, shows that the intact and damaged stability for a fully loaded

vessel passes ABS regulations. For intact stability, the maximum angle of inclination of our design was found

to be less than 25◦, satisfying all conditions of a stable vessel. The damaged stability minimums were also

met. Using the RAO input from WAMIT and the JONSWAP wave spectrum with wave characteristics, the

hydrodynamics of the ship were determined. The heave displacement for the vessel was found to be 1.1 m

for 0◦ heading, and 2.1 m for a 45◦ heading. The pitch and roll were found to be negligible. Because of the

hydrodynamics of the vessel and the environment within which it operates, the offloading will be done in a

symmetric configuration. Taking into account the day to day and severe wave conditions, it was concluded

that an internal turret would be the optimal mooring system solution. This applies less bending moment to

15

our ship which is ideal.

Our design incorporates a unique interior mooring system, easy loading process, and low ship movement

in heave, pitch and roll. If we can decrease the cost of construction, this design will prove to turn a profit

and become an FPSO that can be modeled after in the future.

16

Appendix A FPSO Parameter Summary

The following parameters include design decisions as well as calculated properties.

Length 330 m

Beam 64 m

Depth 32.15 m

Total Displacement 400,000 metric tons

Cargo Oil Weight 301,392 metric tons

Light Ship Weight 52,000 metric tons

Production Platform 32,000 metric tons

Moorings/Risers Weight 10,000 metric tons

Internal Turret maximum diameter 30 m

Double Bottom Salt Water Ballast Volume 76,800 m3

2 Double Side Salt Water Ballast Volume 36,000 m3

Additional Salt Water Ballast Tank Volumes 100,000 m3

Percentage of Salt Water Ballast/Cargo Oil Volumes 52.78%

Figure 6: Sketch of FPSO — plan view

17

Figure 7: Lines Drawing of FPSO

18

Figure 8: Hydrostatics Table

19

Figure 9: Perspective view of FPSO design generated in Rhino.

20

Appendix B Compartment Volumes, Geometries, and Locations

Cargo Tanks

Tank Name Volume LCG VCG TCG Aft Fwd Below Above Port Star

COT-060C 26592 75F 17.08 0 60F 90F 2 32.15 15P 15S

COT-090C 26592 105F 17.08 0 90F 120F 2 32.15 15P 15S

COT-120C 26592 135F 17.08 0 120F 150F 2 32.15 15P 15S

COT-150C 26592 165F 17.08 0 150F 180F 2 32.15 15P 15S

COT-180C 26592 195F 17.08 0 180F 210F 2 32.15 15P 15S

COT-210C 26592 225F 17.08 0 210F 240F 2 32.15 15P 15S

COT-240C 26592 255F 17.08 0 240F 270F 2 32.15 15P 15S

COT-120P 13296 135F 17.08 22.5P 120F 150F 2 32.15 30P 15P

COT-150P 13296 165F 17.08 22.5P 150F 180F 2 32.15 30P 15P

COT-180P 13296 195F 17.08 22.5P 180F 210F 2 32.15 30P 15P

COT-210P 13296 225F 17.08 22.5P 210F 240F 2 32.15 30P 15P

COT-240P 13296 255F 17.08 22.5P 240F 270F 2 32.15 30P 15P

COT-TurretP 13296 285F 17.08 22.5P 270F 300F 2 32.15 30P 15P

COT-120S 13296 135F 17.08 22.5S 120F 150F 2 32.15 30S 15S

COT-150S 13296 165F 17.08 22.5S 150F 180F 2 32.15 30S 15S

COT-180S 13296 195F 17.08 22.5S 180F 210F 2 32.15 30S 15S

COT-210S 13296 225F 17.08 22.5S 210F 240F 2 32.15 30S 15S

COT-240S 13296 255F 17.08 22.5S 240F 270F 2 32.15 30S 15S

COT-TurretS 13296 285F 17.08 22.5S 270F 300F 2 32.15 30S 15S

Salt-Water Ballast Tanks


bottom tank - center - 60 2400 40.00F 1 0.00P 20.00F 60.00F 0 2 15P 15S




21





bottom tank - center - 270 1800 255.00F 1 0.00S 240.00F 270.00F 0 2 15P 15S

bottom tank - center - 300 1800 285.00F 1 0.00S 270.00F 300.00F 0 2 15P 15S

bottom tank - center - 320 1089 309.12F 1.04 0.00P 300.00F 320.00F 0 2 15P 15S

bottom tank - port - 60 1280 40.00F 1.02 23.01P 20.00F 60.00F 0 2 32P 15P









bottom tank - star - 60 1280 40.00F 1.02 23.01S 20.00F 60.00F 0 2 15S 32S









side tank - port - 30 1499 17.09F 18.71 31.00P 0 30.00F 0 32.01 32P 30P

side tank - port - 60 1860 45.00F 16.5 30.99P 30.00F 60.00F 0 32.01 32P 30P





22






side tank - star - 30 1499 17.09F 18.71 31.00S 0 30.00F 0 32.01 30S 32S

side tank - star - 60 1860 45.00F 16.5 30.99S 30.00F 60.00F 0 32.01 30S 32S









SWB-060P 13568 75.00F 17.08 22.50P 60.00F 90.00F 2 32.15 30P 30S

SWB-090P 13568 105.00F 17.08 22.50P 90.00F 120.00F 2 32.15 30P 30S

SWB-060S 13568 75.00F 17.08 22.50S 60.00F 90.00F 2 32.15 15S 30S

SWB-090S 13568 105.00F 17.08 22.50S 90.00F 120.00F 2 32.15 15S 30S

SWB-FC 13568 307.50F 17.08 0 300.00F 315.00F 2 32.15 30P 15P

SWB-FP 6784 307.50F 17.08 22.50P 300.00F 315.00F 2 32.15 15P 15S

SWB-FS 6784 307.50F 17.08 22.50S 300.00F 315.00F 2 32.15 15S 30S

Slop Tanks


SLOP-55C 4523 57.50F 17.08 0 55.00F 60.00F 2 32.15 15P 15S

SLOP-55P 2261 57.50F 17.08 22.50P 55.00F 60.00F 2 32.15 30P 15P

SLOP-55S 2261 57.50F 17.08 22.50S 55.00F 60.00F 2 32.15 15S 30S

Miscellaneous Tanks

23


Forward Void 18671 320.40F 18.09 0.00P 315.00F 328.00F 0.06 32.14 30P 30S

Aft Void 89583 29.83F 18.01 0.00S 0 55.00F 2 32.15 30P 30S

Interior Mooring 28935 285.00F 16.08 0 270.00F 300.00F 0 32.15 15P 15S

24

Appendix C GZ Curves for Three Different Loading Conditions

Figure 10: Stability curve for 90% Cargo Oil, 50% SLOP, 0% SWB

Figure 11: Stability curve for 50% Cargo Oil, 50% SLOP, 0% SWB

25

Figure 12: Stability curve for 0% Cargo Oil, 0% SLOP, and SWB as necessary.

26

Appendix D Damaged Compartment Arrangements

Figure 13: Damaged Condition 1


27



28




29




30

Appendix E Transverse Cross Sections with Girder Layout

Figure 23: Cross section of bow.

Figure 24: Cross section of internal turret.

31

Figure 25: Cross section at midship.

Figure 26: Cross section of stern.

32

Appendix F Stresses, Shear Forces, and Moments for 3 Loading

Conditions

Figure 27: Stresses for 90% Cargo Oil, 50% SLOP, 0% SWB

Figure 28: Shear forces and moments for 90% Cargo Oil, 50% SLOP, 0% SWB

33

Figure 29: Stresses for 50% Cargo Oil, 50% SLOP, 0% SWB

Figure 30: Shear forces and moments for 50% Cargo Oil, 50% SLOP, 0% SWB

34

Figure 31: Shear forces and moments for 0% Cargo Oil, 0% SLOP, and SWB as necessary.

Figure 32: Shear forces and moments for 0% Cargo Oil, 0% SLOP, and SWB as necessary.

35

Appendix G Extreme Conditions

Figure 33: Extreme Hogging condition: Full ballast condition, 0% cargo oil with a troichoidal wave with thecrest centered amidships and same length as the vessel.

Figure 34: Extreme Sagging condition: 98% oil cargo with a troichoidal wave with the trough centeredamidships and the same length as the vessel.

36

Appendix H Stresses, Shear Forces, and Moments for Extreme

Conditions

Figure 35: Stresses for extreme hogging conditions.

Figure 36: Shear forces and moments for extreme hogging conditions.

37

Figure 37: Stresses for extreme sagging conditions.

Figure 38: Shear forces and moments for extreme sagging conditions.

38

Appendix I Added Mass and Damping Coefficients

Figure 39: Added mass and damping coefficients for light ship conditions in heave, roll, and pitch motion.

39

Figure 40: Added mass and damping coefficients for full ship conditions in heave, roll, and pitch motion.

40

Appendix J Wave Excitation Forces

Figure 41: Wave excitation forces for light ship conditions in heave, roll, and pitch for 0◦ and 45◦ incidentwave headings.

41

Figure 42: Wave excitation forces for full ship conditions in heave, roll, and pitch for 0◦ and 45◦ incidentwave headings.

42

Appendix K Response Amplitude Operators

Figure 43: RAO for fully loaded ship with 0◦ and 45◦ incident wave headings.

43

Figure 44: RAO for light ship with 0◦ and 45◦ incident wave headings.

44

Appendix L Output Functions

Figure 45: Motion output spectrum for fully loaded ship in the 1-year wave condition.

45

Figure 46: Motion output spectrum for fully loaded ship in the 100-year wave condition.

46

Figure 47: Motion output spectrum for light ship in the 1-year wave condition.

47

Figure 48: Motion output spectrum for light ship in the 100-year wave condition.

48

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