Arctic FLNG Concept for Shtokman Field with Ice & Wave Load Analysis
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My Documents/Template Edited Sept. 2013
2. Ship & Offshore
Consultancy
Department of Naval Architecture, Ocean &
Marine Engineering
NM983 - Group Project - SOT
Arctic Circular-Shaped FLNG with Hydrodynamic Wave &
Ice Loading Analysis
Team Members:
Torsten Wessels (201383387)
Alexander Steinert (201388205)
Stanimir Yankov (201379385)
Chen Zeng (201375033)
Yuwei Li (201376225)
Date: May 6, 2014
3. i
Executive Summary of Overall Project
With the increasing demand of natural resources the oil and gas industry turns
more and more to the further development of the Arctic area. The region however
presents significant challenges for the safe development and production.
The present report offers a hull-concept of an Arctic FLNG-floater with improved
shape to reduce ice-loads. The analysis done in the report are adjusted to the
Shtokman field in the Russian part of the Barents Sea. The SOTCON-floater has
conical shape which has significant advantages in contrast to classical ship-shaped
constructions. Furthermore it will be compared to a SEVAN Marine Design concept
with circular shaped hull.
In the current report several tasks have been challenged. First, a parametric
analytical solution was conducted for the estimation of the ice loads on the external
hull. The purpose was to evaluate an optimal slope with regards to the load coming
from a first year ice-ridge formation. Afterwards a numerical solution was conducted
with the optimal slope.
An analytical mooring analysis was conducted as well. The mooring system con-
sists of two symmetrically stationed mooring lines. The lines are composed of three
segments – chain, wire rope and another chain. A parametric study was undertaken
in order to evaluate a resulting force from a possible displacement of the platform.
Also the behaviour of the mooring lines was observed for estimation of the optimal
segments lengths and physical properties.
The final task conducts a numerical wave analysis which utilises a wide range of
different waves and hence includes the sea-spectrum of the Shtokman field. In this
part the global response and loads on the structure due to waves of the SOTCON-
floater is calculated and compared to the SEVAN Marine Design. Here, the global
response includes the response amplitude operator (RAO) for heave, pitch and surge.
Due to symmetry roll and sway are not considered. Furthermore the cumulative
displacement due to heave and pitch in z-direction is shown. The hydrodynamic
wave load analysis considers wave pressure on the hull.
The purpose of this project is to evaluate the governing design condition in which
the floater would operate in the presented area. The results from the analysis were
therefore compared to assess whether the wave or the ice loads represent bigger
threat for the structure. Hence the external shape of the platform will be finalized
with accordance to the governing loads.
4. ii
Acknowledgements
The SOTCON-team would like to show their gratitude of a number of scholars
who helped them in reaching the final goal. The guidance and assistance of Dr.
Narakorn Srinil throughout the preparation of the presented paper were most helpful
and are much appreciated. Furthermore the members of the team also show deep
gratitude to another member of staff - Dr. Erkan Oterkus - who provided guidance
for the numerical simulations. Also without the help and constructive suggestions of
a number of Ph.D.-researchers, the progress of this project would have been slower.
Therefore, great many thanks to Dennj De Meo, Junfeng Ding, and Minglu Chen.
To all of them as a part of the department of Naval Architecture, Ocean and Marine
Engineering in the University of Strathclyde this team would like to say thank you.
7. List of Figures v
List of Figures
1.1. The seabed at the Shtokmans field. The shown area is 35x48 kilometer
according to [32]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3. Concept of the offshore processing of the Shtokman Development AG
concept [8]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1. Cross sections for models with sloped and vertical hull shape at the
waterline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2. First-year ridge model with its main geometrical parameters [12]. . . 10
2.4. Initial interaction between ice and sloping structure.[11] . . . . . . . . 15
2.5. General interaction between ice and sloping structure.[11] . . . . . . . 16
2.6. Comparation of 2D and 3D theory of ice loads.[11] . . . . . . . . . . . 17
2.7. Tendency of the horizontal and vertical ice loads with decreasing hull
inclination α. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.8. Geometry for the analytical mooring line analysis. . . . . . . . . . . . 22
2.9. Relationship between horizontal displacement and horizontal force
acting on the structure for the whole system consisting of two mooring
lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.10. Relationship between horizontal displacement and horizontal force
acting on the structure for the system consisting of only one mooring
lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1. GeniE model of vertical walls. It shows the hull plates, applied panel
load areas for and applied point loads for mass calculation of the FLNG. 28
3.2. GeniE model of SOTCON FLNG design, showing the hull mesh, panel
load areas and applied point loads for mass calculation of the FLNG. 28
3.3. Panel Model with Offbody Points in HydroD. . . . . . . . . . . . . . 30
3.4. Hydrostatic pressure distribution along the two different hull shapes. 31
3.5. Geometry of the model used for the estimation of the ice load on the
vertical wall in ANSYS with the boundary conditions of the structure. 34
3.6. Geometry of the model used for the estimation of the ice load on the
wall with 45 degrees slope in ANSYS with the boundary conditions
of the structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1. Heave RAO for the two different hull shapes. . . . . . . . . . . . . . . 37
4.2. Pitch RAO for the two different hull shapes. . . . . . . . . . . . . . . 38
4.3. Surge RAO for the two different hull shapes. . . . . . . . . . . . . . . 38
4.4. Displacement in z-direction of FLNG model with a vertical wall for
wave-period of Tp = 8s. Max: 0.063. . . . . . . . . . . . . . . . . . . 40
4.5. Displacement in z-direction of FLNG model with a sloped wall for
wave-period of Tp = 8s. Max: 0.168. . . . . . . . . . . . . . . . . . . 40
4.6. Compared displacement in z-direction of FLNG with a vertical and a
sloped wall for a wave period of 25 seconds. . . . . . . . . . . . . . . 42
4.7. Comparison of maximum hydrodynamic pressure on the different
hulls for a wave direction of 45◦
. . . . . . . . . . . . . . . . . . . . . . 44
4.8. Resulting stress on the vertical wall of the SOTCON FLNG from the
ice-ridge after the applied displacement. . . . . . . . . . . . . . . . . 46
8. List of Figures vi
4.9. Resulting stress on the sloped wall of the SOTCON FLNG from the
consolidated layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.10. Moment of the dynamic simulation showing the stresses on in the
structure after the impact of the ice ridge. . . . . . . . . . . . . . . . 49
4.11. Moment of the dynamic simulation showing the deformations on the
structure after the impact of the ice sheet. . . . . . . . . . . . . . . . 50
A.1. CAD model of adopted SEVAN Marine Design [18]. . . . . . . . . . . 55
A.2. CAD model of the SOTCON FLNG Design. . . . . . . . . . . . . . . 55
B.1. Cylindrical hull shape: Hydrodynamic Load Distribution for Wave
Period of 8 seconds for 45 degrees (Peak Period Case). . . . . . . . . 56
B.2. Cylindrical hull shape: Hydrodynamic Load Distribution for Wave
Period of 9 seconds for 45 degrees. . . . . . . . . . . . . . . . . . . . . 56
B.3. Cylindrical hull shape: Hydrodynamic Load Distribution for Wave
Period of 14 seconds for 45 degrees (Heave Resonance Case). . . . . . 57
B.4. Cylindrical hull shape: Hydrodynamic Load Distribution for Wave
Period of 25 seconds for 0 degrees (Pitch Resonance Case). . . . . . . 57
B.5. Conical hull shape: Hydrodynamic Load Distribution for Wave Period
of 8 seconds for 45 degrees (Peak Period Case). . . . . . . . . . . . . 58
B.6. Conical hull shape: Hydrodynamic Load Distribution for Wave Period
of 9 seconds for 45 degrees. . . . . . . . . . . . . . . . . . . . . . . . . 58
B.7. Conical hull shape: Hydrodynamic Load Distribution for Wave Period
of 13 seconds for 45 degrees (Heave Resonance Case). . . . . . . . . . 59
B.8. Conical hull shape: Hydrodynamic Load Distribution for Wave Period
of 19 seconds for 45 degrees (Pitch Resonance Case). . . . . . . . . . 59
9. List of Tables vii
List of Tables
1.1. Main dimensions of SOTCON FLNG. . . . . . . . . . . . . . . . . . . 6
2.1. Total horizontal and vertical ice forces for different hull inclinations. . 18
2.2. Parameters of the mooring lines in the maximum load case. . . . . . . 24
3.1. Input Values for Environmental Data and Analysis Conditions . . . . 30
3.2. Scatter diagram of the Barents Sea [5]. . . . . . . . . . . . . . . . . . 30
4.1. Overview of maximum displacement for a set of representative periods. 39
4.2. Hydrodynamic pressures for vertical wall. . . . . . . . . . . . . . . . . 43
4.3. Hydrodynamic pressures for sloped wall. . . . . . . . . . . . . . . . . 43
4.4. Comparison of hydrodynamic pressures on cylindrical to conical hull
shape. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
10. 1. Introduction and Field Information 1
1 Introduction and Field Information
This report is the final outcome of the MSc group project module at Strathclyde
University performed from January 2014 until May 2014. The aim of the group,
consisting of five members, is to perform an analysis and design of structural systems
in the Arctic region. Therefore a critical and state-of-the art review of current
developments of the oil and gas industry in Arctic waters was performed. Based on
this review, the Shtokman field in the Russian Barents Sea was chosen for further
investigations and outline of new development opportunities.
For the chosen field the environmental conditions and reservoir characteristics are
reviewed and will be used for analysis purpose in this project. Furthermore the
current field development concept of the Shtokman Development AG is presented
and the alternative production approach, based on a floating liquefaction of natural
gas concept, is introduced. The proposed FLNG design is based on the SEVAN
Marine design and is conical shaped.
For this chosen FLNG concept in the challenging region, the environmental loads
due to ice and wave loads are estimated. Analytical and numerical approaches are
used to determine the loads for the original cylindrical shaped hull form and for a
modified conical configuration. A comparison of the two cases is performed in order
to quantify the most suitable solution of the chosen field. Moreover an analytical
mooring lines analysis was performed. The mooring system consists of a detachable
buoy and two symmetrically stationed mooring lines with three segments.
1.1. Field Information
The Shtokman field, also known as Shtockmanovskoye field, is a gas and gas con-
densate field in the Russian part of the Barents Sea and was discovered in 1988 [7].
The field location is at 73◦
N and 43◦
, which is 600 km NE of Murmansk and 300
km W of Novaya Zemlya [23].
In figure 1.1 the seabed area around the Shtokmans field is shown. The water depth
around the field is between 50 and 400 m and the seabed is uneven, which will in-
fluence the pipeline design. The specific field water depth is between 320 and 340
m [6]. The reservoir is dome-shaped and spreads over 48 times 35 squarekilometers
[32].
1.1.1. Reservoir Capacities
The reservoir contains huge amounts of gas and gas condensate. The exact number
of capacity varies from 3.205 trillion cubic meter of gas and 226 million barrels of
gas condensate [7] to 3.9 trillion cubic meters of gas and 56 million tons of gas con-
densate [6].
The gas quality of the reservoir is good and contains no significant H2S or CO2.
The reservoir pressure of 210 bar Wellhead Shut-In Pressure (WHSIP) as well as
very low liquid content and a moderate reservoir temperature are positive factors
for the production [3].
11. 1.1. Field Information 2
Figure 1.1.: The seabed at the Shtokmans field. The shown area is 35x48 kilometer
according to [32].
1.1.2. Environment
The Stokman field is located in an area with harsh environment. According to
Potapov et. al. (2001) [23] waves can reach 17.5 meter and the wind speed can get
up to 38 meter per second. Furthermore during winter months ice occurs with an
average thickness of 1.2 meter. According to the Shtokman Development AG (2010)
[3] ice occurs once in 2.6 years and stays in average for up to 3 month (average: 3.3
weeks). Therefore only first-year ice can occur with, according to them, an average
thickness of 0.85 m (max. 2.0 m). Furthermore iceberg danger exists with ice ridges
keel up to 21 m depth [3].
1.1.3. Water Masses and Water Flow
The Barents Sea is influenced by different water masses and current flows. The three
main water masses are Coastal Water (CW), (North-) Atlantic Water (NAW), and
Arctic Water (AW) and the locally formed water masses are Melt Water (MW),
Bottom Water (BW), and Barents Sea Water (BSW) [17]. Figure 1.2b and 1.2a
show the different water masses, currents and characteristics of the water masses.
A combination of BSW and BW forms the water masses at the Shtokman field
and has the characteristics of low temperature and high salinity [17]. The current
velocity at the field is around 1.46m
s
[22].
During winter time, the upper 150 m of the water column is occupied by Arctic
Water. During this time ice can build-up and the formations (and also icebergs)
can drift south. During summer time the upper part of the water column of Arctic
Water is covered with Melt Water (5 to 20 meter thickness) [17]. Due to the char-
acteristics of BSW, the ice development is limited to the winter month and the time
of ice occurrence is limited due to Atlantic Water in this area.
12. 1.1. Field Information 3
(a) Overview over different water masses in
the Barents Sea [17].
(b) Different current directions bring differ-
ent water masses to the Barents Sea [17].
1.1.4. Additional Design Issues in the Barents Sea
Different water masses, current flows and ice occurrence have great influences on
design concepts for field developments in the Barents Sea (and therefore for the
Shtokman field). Nevertheless other factors can also influence concepts for this
area. One example is the polar night, which is from December to February every
year (3 month period) [3]. In this time the sun disappears completely and the whole
area is in darkness. This leads to a challenge for health, safety and environment
(HSE) and efforts must be made to face these circumstances.
Another factor which has to be considered for a design concept is the location itself.
The closest shoreline is 300 km west of the field [23]. Thus, the harsh environ-
ment conditions, polar nights and the large distance to the next harbour must be
considered together. In the case of an accident, rescue teams are not available in-
stantaneously and the necessary rescue time should be included in design concepts.
13. 1.2. Field Development Concepts 4
1.2. Field Development Concepts
The recent field development concept of the Shtokman field is a strategy established
by the Shtokman Development AG in which Gazprom, Total and Statoil is involved.
This concept is from the year 2010 and the production is scheduled to start in 2015.
This concept includes a ice-resistant ship shape floating production platform. On
this platform the processing of the gas is done. The processed gas is then exported
via two export trunklines to the onshore liquefaction plant. From this plant the
export of the liquefied natural gas is done by pipeline to the European market or
by LNG-Carrier to customers abroad. The scheme of the production concept is
illustrated in figure 1.3. It has to be stated that this sort of concept leads to large
investments of the offshore production unit, the export pipeline with a length of app.
600 km and the onshore liquefaction plant. The advantage of this concept is, that
further gas fields in the Barents Sea might be connected to the export line and will
also use the established liquefaction plant. Referring to figure 1.3 it has to be stated
that the ship-shaped production unit is turret moored, which allows a disconnection
if an iceberg is appearing. Furthermore this mooring concept, together with the
lazy-s configuration of the riser, allows operation the harsh environment.
Figure 1.3.: Concept of the offshore processing of the Shtokman Development AG
concept [8].
14. 1.3. SOTCON Shtokman Production Concept 5
1.3. SOTCON Shtokman Production Concept
In this chapter the production concept for the Shtokman field is presented. As
stated in section 1.1 the Shtokman field is a large gas field in the Russian part of
the Barents sea. Three different approaches are considered for the extraction and
production of the large amount of gas reserves.
The first concept is a fixed or floating production unit with minimum offshore pro-
cessing and an export pipeline to the Russian shore. The structure could be a fixed
steel jacket with topside or a gravity based production unit, similar to the Hibernia
structure in Canada. The export pipeline would connect the structure to an onshore
terminal at the Russian shore with a distance of around 500 km.
The fixed structure has one major disadvantage, so that it was not considered
for the further investigations. A fixed structure is not economical in a water depth
of 400 m, due to the fact that the costs of fixed structures increase exponentially
with water depth. An alternative for this type of structure in the given water depth
is a floating production unit, like a semi-submersible. Due to the harsh environ-
ment the motion characteristics of such a structure is a drawback. Furthermore a
semi-submersible has a small deck loading capacity, so that the offshore processing
is limited.
In addition to that, a pipeline with a length of 500 km is a huge cost factor in
the Arctic region. Due to environmental conditions and related off times of the
installations, pipe laying operations will take a long time. The uneven seabed is an
additional drawback, see chapter 1.1. Furthermore no onshore terminal is available
at the Russian shore until now, so further investments would be necessary.
The second approach is a sub-sea production system, similar to the Snøhvit field
in the Norwegian sea. The sub-sea production units are connected by a flow-line
to an onshore liquefaction plant. The liquefaction is done onshore and the liquefied
natural gas (LNG) is exported by LNG-Carriers. The Snøhvit field is connected
by a 140 km long pipeline, whereas the Shtokman field would need a 500 km pipe
system. With respect to the costs of such a long system and the expected issues of
multi-phase flow problems, this approach is also not evaluated as a suitable solution.
The third approach is an offshore liquefaction concept, similar to the Prelude
project from Shell. This project will start to produce LNG close to the Australian
coast in 2015 [20]. The natural gas will be extracted from the reservoir and processed
as well as liquefied offshore. The export of the LNG is achieved by shuttle tankers.
This solution is evaluated as suitable for the Shtokman field, because no pipeline
has to be constructed to the shore. In addition to that no onshore liquefaction plant
is necessary, so an export can directly be done from the LNG-FPSO. This makes
the field concept economic and feasible.
15. 1.3. SOTCON Shtokman Production Concept 6
1.3.1. SOTCON Arctic FLNG Concept
The FLNG concept is considered for the Shtokman field, thus offshore liquefaction,
storage and offloading have to be balanced by the designed system. In addition to
that the design has to withstand the environmental conditions and challenges in the
chosen Arctic region. In order to fulfil all these requirements a cylindrical shape is
chosen for the LNG-FPSO. The SOTCON design is inspired by the Goliath FPSO,
which is a SEVAN Marine design, [14]. The cylindrical shape is beneficial, because it
has good motion characteristics, which minimizes the fatigue and bending loading.
Moreover no turret or swivels are necessary, because the structure is not subjected
to weathervane due to the circular shape [14]. Furthermore the design offers a large
deck area and deck load capacity, which is necessary for complex processing and
liquefaction units.
The SOTCON FLNG is based on a concept study from SEVAN marine. The main
dimensions can be seen in table 1.1. Liquefaction is the change of the aggregate
condition of the natural gas by cooling down the gas to - 162 ◦
in order to shrink
the volume by 600 times. This allows effective storage and export of the LNG. For
the offshore liquefaction two parallel FNLG trains are chosen, which produces 2.4
million tonnes LNG per year [14]. This yields to a LNG production of approxi-
mately 15,600 m3
d
. With respect to the storage capacity of 200 000 m3
an offloading
is needed every 10 days in order to keep a buffer of around 2.5 days. This buffer is
necessary in case of unexpected complications, especially in the harsh environment.
For the LNG export an Arctic LNG-Carrier is used, which will ship between the
Shtokman field and the LNG terminal in Rotterdam, Netherlands. This carrier has
to have a storage capacity of approximately 160,000 m3
and a service speed of 21 kn
to guarantee an adjusted export schedule. A suitable reference vessel is the Arctic
Voyager, which is used for the Snøhvit concept. This vessel has a capacity of 140,000
m3
[10], so that it has to be modified in order to cope more LNG and the ice loading
in the northern Barents sea.
Hull diameter [m] 106
Main deck diameter [m] 120
Process deck diameter [m] 130
Main deck elevation [m] 37
Process deck elevation [m] 58
LNG Capacity [m3
] 200 000
Table 1.1.: Main dimensions of SOTCON FLNG.
16. 1.3. SOTCON Shtokman Production Concept 7
1.3.2. Required Analysis and Design of Structural Systems for
the SOTCON FLNG Concept
The liquefaction of natural gas on a floating production unit is a state of the art
production concept. The Shell Prelude project is the first FLNG concept, which will
start to operate in 2015. This FLNG will be operated in the Australian sea, 200 km
off the coast of Australia. This platform is designed according to the occurring en-
vironmental conditions in that specific region and is therefore designed to withstand
cyclones.
As illustrated in the previous sections the environmental conditions at the Shtok-
man field are largely different and dominated by the ice loading. Therefore another
design and analysis approach is needed in order to generate a sophisticated design
for the Arctic region.
Investigations of a series of production concepts in similar environmental regions
showed, that cylindrical shaped structures are commonly used, eg. the Goliath field
in the Norwegian Barents sea. But taking into account that this field is not sub-
jected by large ice fields it was concluded that the cylindrical hull shape has to be
improved in order to withstand the environmental loadings in the more northern
Shtokman field.
The objective of the upcoming structural analysis is to estimate environmental load-
ing on a cylindrical hull shape and a conical shaped hull. The aim is to compare the
two different loadings in order to validate the assumption, that a conical shaped hull
form is advantageous in the chosen field. Therefore analytical as well as numerical
analysis are performed to estimate the ice and wave loading on the two structures.
The expected outcome is that the wave loads will be increased for the conical shaped
hull, whereas the ice loading will decrease.
17. 2. Theoretical Models & Analytical Studies 8
2 Theoretical Models & Analytical Studies
This chapter deals with the theoretical models of the SOTCON project. Analytical
solutions for the ice loading on two different hull shapes are provided and a simplified
analytical mooring line study is performed. The results of these theoretical models
are used for validation and comparison for the numerical simulations, which are
introduced in chapter 3. Furthermore the two different hull shapes, which will be
compared in the following sections are introduced.
2.1. Conical Shaped Hull Form
The structural analysis of the project is focused on load estimation due to ice and
hydrodynamic wave loads for two different structures. The two different geometries
can be seen in figure 2.1. The hull shape, shown in figure 2.1a, is characterised by
a vertical wall at the waterline. The geometry, illustrated in figure 2.1b, has an
inclined hull at the position of the waterline. The vertical configuration is adopted
from the SEVAN Marine design. A similar shaped FPSO is operating at the Goliath
field in the Norwegian Barents Sea [14].
In order to reduce the total load on the structure and to allow a more cost efficient
and lightweight design, the hull shape is changed. In order to justify the assumption,
that the inclined configuration reduces the loads a set of analytical and numerical
analysis are performed and reported.
(a) Cross section of the model with cylindri-
cal hull shape at the water line.
(b) Cross section of the model with conical
hull shape at the water line.
Figure 2.1.: Cross sections for models with sloped and vertical hull shape at the
waterline.
It has to be noticed that enlarged drawings of the two different geometries can be
seen in the appendix A on page 55. The figure A.1 shows the vertical configuration,
whereas the figure A.2 shows the sloped version of the FLNG design.
18. 2.2. Environmental Ice Loading 9
2.2. Environmental Ice Loading
Ice can be categorized into several types with regards to the formation time or the
general geometrical parameters. A general division can be made for the formation
time to first-year ice and multi-year ice. The first-year ice is the ice that forms during
the winter and melts during the summer. The multi-year ice is the formation that
has ”survived” the summer. With the passing time the porosity of the ice decreases
and therefore its strength increases. According to the geometrical parameters a
separation of level ice, ice ridges (pressure ridges) and icebergs is possible. The level
ice is generally a sheet of ice on the water surface. Depending on the environmental
conditions, its thickness can vary. An ice ridge is a curvilinear or straight deformed
ice feature that forms when ice floes collide under pressure or shear forces. Newly
formed first-year ridges consists of randomly oriented rubble blocks both above and
below the waterline. Once the ridge has formed, water and slush between the rubble
blocks of the keel will generally begin to freeze, forming a consolidated layer. In the
Arctic areas icebergs can be formed as calving from glaciers and the weight can get
up to several hundreds tons. In the current project an assumed homogeneous model
will be used for a first-year ice ridge.
Three steps are going to be undertaken to estimate the loading from the forma-
tion. The first one conducts analytical solutions based on theoretical and statistical
analysis. The second one conducts numerical analysis for the ice load on a vertical
cylindrical structure. The last step will perform the same ice loading numerical
analysis as the second step but with a changed geometry from vertical to sloped
walls of the structure.
Several approaches and theories can be utilized to calculate the forces that a first
year ridge of sea ice would exert on an offshore structure. Different looks at the
geometry of the formation will be taken into account. The ice-ridge or a pressure
ridge is shown in figure 2.2 on page 10 has three forming parts: (1) a sail - loosely
bonded blocks of ice above the surface of the level ice; (2) a consolidated layer, which
is a comprised layer of refrozen ice. Its thickness is variable but mainly dependent
on the level ice thickness and could be up to 3 or even 4 times than the level
ice thickness; and (3) the keel, also comprised of loosely bonded blocks under the
consolidated layer. Both the consolidated layer and the keel and sail (unconsolidated
layers) can exert loads on the structure. To calculate the forces of a ridge on an
offshore structure, the usual approach is to predict the forces for each of the three
layers and sum up these individual load components. Two important assumptions
are made in this approach. First, spatial independence, which means that the failure
or breaking of one part of the ridge cannot influence another one; and second, no
temporal difference amongst the failure of each component of the ridge, which means
that the ridge fails simultaneously everywhere.
2.3. Ice loads on vertical wall
The first step in estimation of the ice loads on the structure is conducting an analyt-
ical solution. Considering the geometry of the ice formation, an approach is adopted
which summarizes the work of a number of researchers in the topic. The following
calculations are in accordance to the paper from Kazuyuki Kato [12].
19. 2.3. Ice loads on vertical wall 10
2.3.1. Parameters of the ridge and platform
For the estimation of the load from the ridge, a homogeneous body is considered.
The following figure 2.2 introduces the shape and main dimensions of the formation.
Figure 2.2.: First-year ridge model with its main geometrical parameters [12].
The ridge consists of three parts - consolidated layer, sail and keel. In figure 2.2
Hs is the sail height, Hk is the keel depth, Bs is the sail breadth, Bk is the keel
breadth, and hi is the thickness of consolidated layer. Due to the fact that the the
ridge is formed from an average level ice with thickness of 1.2m all of the parameters
can be evaluated as functions of the level ice thickness. The following formulas for
the dimensions are statistically estimated.
h0 = 1.2m (2.1)
Hs = 4.7 h0 = 4.7
√
1.2 = 5.149 m, (2.2)
Hk = 4Hs = 4 × 5.149 = 20.59 m , (2.3)
Bs = 6.3Hs = 6.3 × 5.149 = 32.44 m , (2.4)
Bk = 3.93Hk = 3.93 × 5.149 = 80.94 m , (2.5)
hi = 0.2Hk = 0.2 × 20.59 = 4.118 m . (2.6)
Due to the fact that these dimensions are statistically estimated the calculations can
be made with simplified values:
Hs = 5 m, Hk = 20 m, Bs = 30 m, Bk = 80 m and hi = 4 m
For the current analysis the structure is considered only as a cylinder with diameter
De, where
De = 106 m.
The velocity of the ridge is considered to be constant and according to the hydro-
logical data explained in [15]:
v = 2 m/s
The densities of the water(ρw) and ice(ρi) are considered to be standard and inde-
pendent on the temperature and salinity:
ρw = 1025 kg/m3
ρi = 920 kg/m3
20. 2.3. Ice loads on vertical wall 11
2.3.2. First year ice-ridge load
According to the methodology followed in the current project, the author divides the
total exerted force on the structure Fr into two components[12]. Their summation
is the resultant force.
Fr = Fc + Fks, (2.7)
In equation 2.7 Fc is the load from the consolidated layer and Fks is the load from
the unconsolidated layer.
There are two important assumptions made while using the equation 2.7. First,
the failure of both parts of the formation is spatially independent. That means
that the failure of one part does not influence the failure of the other. The second
assumption is the temporal independence, which means that the ridge is failing
simultaneously everywhere. Furthermore the unconsolidated layer would fail in the
same manner as a granular material. The consolidated layer would fail the same
way as a level ice sheet [15]. The failing mode of the ice is assumed to be crushing
due to the fact that the contact surface is normal to the velocity vector of the ice.
Load from unconsolidated layer Fks
In the presented methodology, the authors utilizes an approach proposed by Croas-
dale and Cammaert (1993) [13]. Like previously explained the statistical origin of
the approach can provide a moderate value for the unknown variables. The hereby
mentioned approach is based on the global plug failure theory of Croasdale(1980)
[4].
Fks =
BkDeHk
2
+
BkH2
k
3
γetanφ, (2.8)
In equation 2.8 φ is the angle of internal friction of the material of which the keel
and sail is consisting. In the current project a value of 35 degrees is assumed with
accordance to [12].
φ = 35◦
In equation 2.8 γe is the effective specific weight of the material defined as follows:
γe = (ρwg − ρig)(1 − nk), (2.9)
In equation 2.9 nk is the porosity of the keel. In the current project, an empirical
formula for the estimation of porosity of the keel is employed proposed by Sturkov
et al.(1997) [12].
nk = 0.09051 · ln 64.701
l
h0
, (2.10)
In equation 2.10 l is the average length of the ice fragment the ridge is consisting
of. With accordance to [12] the mean ratio of l
h0
= 3.56 can be used.
All the other variables in equation 2.8 are previously defined.
Therefore , with the utilization of the formulae 2.8, 2.9 and 2.10 the load from
the unconsolidated layer can be calculated as follows:
nk = 0.09051 · ln(64.701 · 3.56) = 0.492, (2.11)
21. 2.3. Ice loads on vertical wall 12
γe = (1025 × 9.81 − 920 · 9.81)(1 − 0.492) = 522.744
kg
m2s2
, (2.12)
Fks =
80 · 106 · 20
2
+
80 · 202
3
522.744 · tan(35◦
) = 34.944 MN, (2.13)
Load from consolidated layer Fc
As previously mentioned, the formation will fail in a crushing mode. With ac-
cordance to [26] Korzhavin equation can be utilized to evaluate the ridge load as
follows:
Fc = p · De · hi , (2.14)
In equation 2.14 Fc is the exerted force on the structure, p is the pressure from
the ice. Like previously defined De is the diameter of the structure and hi is the
thickness of the consolidated layer. To estimate the load from the consolidated layer
therefore only the estimation of the ice pressure p is required. It is defined as follows:
p = I · m · k · σc , (2.15)
In equation 2.15 I is the indentation factor, m is the shape factor, k is the contact
factor and σc is the uni-axial compressive strength. For the estimation of the com-
pressive strength σc, the relationships from Karlsson and Strindo (1985) are used
with accordance to [12].
With accordance to [12], the indentation factor is directly related to De and hi as
follows:
I = 0.54
hi
De
+ 1 = 1.02, (2.16)
The shape factor m for a cylindrical structure can be assumed as 0.9 [11].
m = 0.9, (2.17)
Also with accordance to [11], the value of contact factor k consists of two parts:
k1 - depends on the strain rate.
k2 - depends on the relative width of the structure if the strain velocity is high
enough. The strain rate and the relative width can be defined respectively as follows:
˙ε =
v
4De
= 4.72 × 10−3
(1/s) ≥ 5 × 10−4
(1/s) (2.18)
De
hi
= 26.5, (2.19)
Therefore k1 and k2 can be estimated from figures 2.3a and 2.3b with accordance
to [11]: k1 = 0.3, k2 = 0.6 Therefore with accordance to the same document [11] the
contact factor k can be estimated as follows:
k = k1 · k2 = 0.18, (2.20)
The final unknown variable in the equation 2.15, the compressive strength, is
affected by the porosity of the material. In the followed methodology the author
22. 2.3. Ice loads on vertical wall 13
(a) Plot for the estimation of the k1 coeffi-
cient
(b) Plot for the estimation of the k2 coeffi-
cient as a function of D/H ratio when
˙ε > 5 × 10−4(1/s)
utilizes an approach with an approximated equation for estimation of the compres-
sive strength σc [12]:
σr = 1.0143e−5.64n
, (2.21)
In equation 2.21 σr is the relative strength, and n is the porosity of the consolidated
layer. According to [12] the author assumes that with n = 0 the compressive strength
of the consolidated layer is identical to the same of a level ice sheet. Consequently,
σr = 1.0143.
Furthermore for the estimation of the compressive strength, an empirical formula
is used [12]:
σc0 = −7.42 − 0.1404T + 0.1458S + 11.57845ρig − 0.847
S
|T|
, (2.22)
In equation 2.22 σc0 is the reference compressive strength in MPa, T is the ice
temperature in C◦
, S is the salinity of the ice in ppt and ρig is the specific weight
of ice in gf
cm3
According to [12], the ice temperature T can vary from −10C◦
to −2C◦
. In the
current project a temperature of T = −5C◦
will be used. The salinity S is on
average S = 3.4 ppt and ρig = 0.92 gf
cm3 .
After the calculation, σc0 = 3.622 MPa
Combining the relative compressive strength σr and the level ice compressive
strength σc0, the compressive strength of consolidated layer σc is defined as follows:
σc = σr · σc0 = 1.02 · 3.622 = 3.674 MPa, (2.23)
Furthermore the ice pressure can be calculated:
p = I · m · k · σc = 0.609 MPa (2.24)
Therefore the consolidated layer force is:
Fc = p · De · hi · σc = 258.0 MN, (2.25)
23. 2.4. Parametric study for ice loads on conical shaped platform 14
Total force
Therefore the total force is estimated as the summation of consolidated and uncon-
solidated layer loads:
Fr = Fks + Fc = 34.944 + 258.0 = 292.957 MN (2.26)
Nevertheless for further calculations only the force Fc from the consolidated layer
will be used due to the fact, that the it plays the dominant role in the acting force.
2.4. Parametric study for ice loads on conical shaped
platform
Due to the harsh environment in which the platform is located it is reasonable to
consider a load reduction measure. Thus the structure will be exploited in safer
conditions. One of the ways to reduce the ice load on the structure is to adjust it
external hull shape from from cylindrical to conical.
The current chapter shows the undertaken parametric study to evaluate the reduc-
tion of the ice load on the platform with regards to the the slope of the external wall.
The consolidated layer load presents more than 90% of the total load. Also there
is very little information regarding unconsolidated layer load on conical structures.
With accordance to the analytical methodology presented in [16], the consolidated
ice load plays the major role in the overall forces. Due to these facts, in this chapter,
only consolidated layer with 4 meters thickness will be considered. Additionally, the
this load was estimated in [16] as 258.0MN. Following is the parametric study for
the load exerted on a cone with different slopes.
2.4.1. Ice and platform parameters
The thickness and velocity of the level ice are assumed to be constant:
hi = 4 m
v = 2 m
s
The densities of the water and ice - ρw ρi respectively - are considered to be
standard and independent on the temperature and salinity:
ρw = 1025 kg
m3
ρi = 920 kg
m3
As previously explained in chapter 2.1 analysis on two geometries is undertaken.
These models can be seen in figure 2.1 on page 8.
As can be seen from the figure both platforms have the same diameter De at the
waterline, where:
De = 106 m
Additionally, as its name expresses, the conical shaped platform has a downward
slope of α.
24. 2.4. Parametric study for ice loads on conical shaped platform 15
2.4.2. Consolidated layer load on conical platform
When the ice is hitting the sloped wall, buckling becomes the major ice breaking
mode instead of crushing. For simplification, first only a two-dimensional model is
considered. Next it is modified into three dimensions.
2-D theory
There are two main components of the two-dimensional ice load.
The first is the initial interaction between the ice and the structure which is shown
in the following figures 2.4.
Figure 2.4.: Initial interaction between ice and sloping structure.[11]
The parameters on the figure 2.4 represent the vertical component of the force -
V , the horizontal component of the force - H, the slope angle - α and the coefficient
of friction - µ The correlations between them can be expressed as follows:
V2D = N · sin α + µ · N · cos α (2.27)
H2D = N · cos α − µ · N · sin α (2.28)
H2D = V2D
sin α + µ · cos α
cos α − µ · sin α
(2.29)
Assuming that the ice sheet behaves as a beam, the maximum force required to
break the advancing ice V is limited by the ice bending strength σf , which is defined
according to the equation [11]:
σf =
6 · M0
b · t2
, (2.30)
In equation 2.30, b is the beam width and t is the thickness of the ice sheet. In the
current calculations, the ice can be regarded as a semi-infinite beam on an elastic
foundation. Therefore the Hetenyi’s formula according to [11] is suitable to describe
the maximum bending moment M0:
M0 =
V
β · e
π
4
· sin
π
4
(2.31)
In equation 2.31 β is a characteristic length defined as:
25. 2.4. Parametric study for ice loads on conical shaped platform 16
β =
ρw · g · b
4 · E · I
0.25
(2.32)
Combining equations 2.30, 2.31 and 2.32, leads to the ice breaking vertical force
V2D in two-dimensional case:
V2D = 0.68 · σf · b
ρw · g · t5
E
0.25
(2.33)
Furthermore with the utilization of the equation 2.29 the horizontal component
H of the force can be estimated as::
H2D = 0.68 · σf · b
ρw · g · t5
E
0.25
·
sin α + µ · cos α
cos α − µ · sin α
(2.34)
The second part of the total force is the one resulting from the force required to
push the broken ice upwards. This upwards force P can be seen on the following
figure and calculated according to equation 2.35:
Figure 2.5.: General interaction between ice and sloping structure.[11]
P =
Z
sin α
· t · b · ρi · (sin α + µ · cos α), (2.35)
In equation 2.35 Z is the highest vertical point that the ice can reach on the sloped
wall.
3-D theory
As can be seen from the following figure 2.6, the failure in the three-dimensional
theory is quite different from that of two-dimensional one. The ice failure zone
in the three dimensional case is much wider than the cone structure’s waterline
diameter.
With accordance to [13] the three-dimensional breaking force can be defined as:
H3D = H2D ·
D + π
4
· lc
D
(2.36)
In equation 2.36, H2D is defined with equation 2.34 and D is the diameter of the
cone. The last parameter lc is the characteristic length defined as:
26. 2.4. Parametric study for ice loads on conical shaped platform 17
Figure 2.6.: Comparation of 2D and 3D theory of ice loads.[11]
lc =
E · h3
12 · ρw · g · (1 − ν2)
0.25
(2.37)
In equation 2.37 ν is the Poisson’s ratio.
ν = 0.3
Assuming that:
ζ1 = sin α + µ · cos α (2.38)
ζ2 = cos α − µ · sin α (2.39)
The total ice force per unit on the cone can be calculated as:
Fx = 0.68·σf ·b
ρi · g · t5
E
0.25
·
ζ1
ζ2
·
D + π
4
· lc
D
+
Z
sin α
·t·b·ρi ·
ζ2
1
ζ2
+
ζ1
tan α
(2.40)
Calculation of the ice loads on the platform
The current design has a wall with downward slope of α, therefore, the positive
direction of the vertical axis should be downward. This allows the use of the original
formulae for breaking ice. Additionally, in equation 2.35 of ice climbing force, the
used density of the ice ρi must be modified to (ρw − ρi), due to the downward slope.
In equation 2.40, the breadth of the ice b and the diameter of the contact area D
are both equal to De.
Fx = 0.68 · σf · De
ρw · g · t5
E
0.25
·
ζ1
ζ2
·
De + π
4
· lc
De
+
Z
sin α
· t · De · (ρw − ρi) ·
ζ2
1
ζ2
+
ζ1
tan α
(2.41)
In equation 2.41 the following parameters can be assumed with accordance to [11]:
σf = 0.7 MPa
µ = 0.2
E = 8.7 GPa
27. 2.4. Parametric study for ice loads on conical shaped platform 18
g = 9.81 m
s2
ν = 0.3
Due to the fact that the slope of the proposed platform is downwards it is assumed
that the maximum vertical distance Z is the intersection point of the sloped section
adn the vertical one. From figure 2.1b, this distance Z can be calculated as:
Z = 5 · tan α (2.42)
The variable α here represents the slope angle from the horizontal plane.
The results from the parametric study for different slope angles can be seen in
following table 2.1.
Slope from the horizontal [◦
] Total horizontal force [MN] Total vertical force [MN]
(α) (Fx) (Fy)
90◦
258.0 -
70◦
131.749 20.137
60◦
59.802 20.23
45◦
30.622 20.415
30◦
18.222 20.734
20◦
12.881 21.178
Table 2.1.: Total horizontal and vertical ice forces for different hull inclinations.
2.4.3. Conclusion of analytical ice loading estimation
With accordance to section 2.3.2, the horizontal consolidated ice load on the cylin-
drical wall is 258.0MN. As seen in table 2.1 this is twice as much as the value of
the horizontal load on the sloped wall with the angle of 70◦
. Therefore the initial
assumption that the modification of the external wall from vertical to inclined is
justified. The following graph 2.7 shows the variation of the horizontal load on the
structure with regards to the slope of the external wall.
It can be seen from figure 2.7, that the horizontal ice force decreases with the
decreasing of the inclination angle from the horizontal plane.
However, the vertical ice force doe not change it value significantly from 20MN.
Due to the FLNG concept and the required capacity for storage, a slope of 45◦
is
chosen for the finalized geometry of the structure. Furthermore this value of the
slope will be used for the generation of the numerical models used for the ice and
wave analysis.
28. 2.5. Mooring system analysis 19
Figure 2.7.: Tendency of the horizontal and vertical ice loads with decreasing hull
inclination α.
2.5. Mooring system analysis
In the ice free operation-period, the structure should be designed for safe exploitation
in the standard condition. Thus the wind and wave loading must be considered as
well for proper analysis of the mooring system. In order to evaluate the critical
loading condition first the wave and wind loads are calculated. Furthermore the
wave load is compared to the previously estimated ice load. The goal is to estimate
whether the load from the combined ice and wind load is larger than the combined
wave and wind load. The first step is to calculate the wave loads. The method
applied for its estimation is utilizing the following Morison’s equation.
Fx = Fix + Fdx (2.43)
2.5.1. Wave loading
In the Morison’s equation the wave and current forces are combined into one sin-
gle force. This horizontal force acting on the structure can be divided into two
components - inertia and drag force. The inertia force can be calculated with the
integral.
Fix = cm ·
0
−h
ρ · Aw · ux (2.44)
In equation 2.44 cm is the added mass coefficient, h = 20 m is the depth of the
structure, ρ = 1.025 t
m3 is the density of the water, Aw is the projectile water plane
29. 2.5. Mooring system analysis 20
area, and ux is the wave particle acceleration in x direction. Aw is
Aw = π · c2
, (2.45)
where c = 53 m is the simplified radius of the structure.
Therefore the projectile water plane area is
Aw = π · c2
= π · 532
= 8825 m2
. (2.46)
Furthermore the added mass coefficient cm can be calculated by
cm = 1 +
Madd
M
(2.47)
where M is the submerged mass of the structure, and Madd is the added mass of the
structure in the x-direction. Their fraction is directly calculated as
Madd
M
=
ρ · π · c2
· h
ρ · π · c2 · h
= 1 . (2.48)
Hence the added mass coefficient cm is
cm = 1 + 1 = 2 . (2.49)
The wave horizontal acceleration can be estimated as
ux = 0.5 · Hw · w2
· eky
· sin(kx − wt) , (2.50)
where Hw = 11 m is the significant wave hight, w = 0.79 rad
s
is the wave frequency,
k is the wave number, and y is the position with regards to the depth. Thus,
k =
w2
g
=
0.792
9.81
= 0.064 , (2.51)
and
y = −h = −20 m . (2.52)
Therefore the wave horizontal acceleration ux is
ux = 1.22 · sin(0.064x − 0.79t) , (2.53)
and the inertia force can be estimated as
Fix = 1.138 · sin(kx − wt) . (2.54)
For sin(kx − wt) = 1 the maximum force is hence
Fix = 1.138 MN . (2.55)
The drag force can be estimated by
Fdx = 0.5 · ρ · D · cdx · ux · |ux| , (2.56)
where cdx is the drag coefficient, D = 106 m is the diameter of the structure, and
30. 2.5. Mooring system analysis 21
ux is the wave velocity. The drag coefficient is related to the shape of the structure
and for the short cylinder cdx = 1.15 [21].
Thus the drag force can be estimated as
Fdx = 1.851 MN . (2.57)
The total force exerted on the cylinder is the summation of the two forces:
Fx = Fix + Fdx = 1.138 + 1.851 = 2.989 MN . (2.58)
Compared to the calculated in the previous chapter 2.4.2 ice-load of 30.622 MN, this
force is much smaller. Therefore for the mooring system analysis the combination
of wind and ice-loads will be utilized.
2.5.2. Wind loading
For the estimation of the horizontal wind load, the basic equation can be utilized as
F = 0.5 · ρ · u2
wind · A · C · Kh , (2.59)
where ρ = 1.29 kg
m3 is the density of the air, uwind = 37 m
s
is the velocity of wind,
A is the upper windward area, C = 0.8 is the wind factor, H = 20 m is the upper
height of the platform, and Kh = 1.63 is the wind height variation coefficient with
accordance to [1].
The upper wind are A (see equation 2.60) is estimated from the geometry seen in
the appendix in figure A.2.
A = 0.5 · H · (Dup + Ddown) , (2.60)
where Dup = 146 m is the upper diameter of the platform, and Ddown = 106 m is
the lower diameter of the platform at mean water level.
Therefore the upper wind area A is
A = 2520 m2
. (2.61)
Finally the wind force exerted on the structure is estimated as
F = 2.9 MN . (2.62)
Ergo the load which will be used for the maximum displacement of the structure in
the mooring lines analysis will be the summation of the ice load calculated in the
previous chapter 2.4.2 and the wind load:
F = 2.9 + 30.622 = 33.522 MN . (2.63)
31. 2.6. Mooring line analysis 22
2.6. Mooring line analysis
In this section an analytical approach of a simplified mooring line system with two
mooring lines will be developed. The aim of this is to calculate initial parameter for,
for example, mooring line length and the distance to the touch down point (TDP).
Figure 2.8 gives an overview about the mooring line layout. As seen in the mentioned
figure, the considered mooring lines will contain three different sections to reduce for
example the submerged weight or optimise the field layout. As in chapter 1.1 stated,
the mean water depth is between 320 and 340 metres. Hence, for the mooring line
analysis 330 m is chosen. Furthermore the FPSO draught is 20 metres (see figure
2.1a in chapter 2.1). Therefore the distance between top point of the mooring line
and sea bed is 310 metres. To estimate the mooring line parameters for different
situations such as equilibrium position and different horizontaltal displacements due
to applied horizontaltal loads, basic catenary equations are used. The mooring line
composition itself depends on the water depth [19]. Here, the upper part (20 to 30
metres of water depth) chain is used. The middle part (30 to 300 metres of water
depth) spiral strand wire rope is used and the lower part (300 to 330 metres of water
depth) a chain is used again.
Figure 2.8.: Geometry for the analytical mooring line analysis.
To calculate the mooring lines the following steps are necessary:
1. Estimation of submerged weight of the mooring line composition
2. Estimation of breaking strength of the mooring line components
3. Estimation of the maximum diameters of the mooring line segments
Estimation of submerged weight
The submerged weight of the chain segment is:
wchain = 0.1875 · D2 N
m
. (2.64)
32. 2.6. Mooring line analysis 23
The submerged weight of the wire rope is:
wspiralstrand = 0.043 · D2 N
m
, (2.65)
where D is the diameter of mooring line in millimetre.
Estimation of breaking strength
The breaking strength of the chain segment is:
Fb,chain = 27.4 · (44 − 0.08 · D) · D2
N . (2.66)
The breaking strength of the wire rope segment is:
Fb,spiralstrand = 900 · D2
N . (2.67)
Estimation of the maximum diameter
The maximum diameter of each segment of the mooring line is calculated by:
T = wd + H = Fb (2.68)
where T is the top tension, and H is the horizontaltal force due to environmental
conditions. As seen in equation 2.64 and 2.65 the submerged weight depends on the
Diameter as well as the breaking strength Fb (see equation 2.66 and 2.67). Except
for the material properties of the mooring lines, the applied top tension is required to
estimate the mooring line parameters. The top tension is estimated according to the
environmental loads. As previously mentioned in the chapter 2.5 the combinatin of
the ice load and wind load will be used for the mooring line design. For simplification
of the calculations and additional safety factor a value of 35 MN will be used as for
the horizontal force. Furthermore for design load a safety factor of 1.25 is required
with accordance to[2]. The final horizontal force used in the calculations for this
case is 43.75 MN. For this situation, the entire resistance is provided by only one
mooring line. The other one is not considered due to its vertical position. Therefore
the system can be seen as a single mooring line system and evaluated by the catenary
equation:
y(x) =
H
mg
cosh
mg
H
· x −
mg
2H
· l − cosh
mg
2H
· l (2.69)
L =
2H
mg
· sinh
mgl
2H
(2.70)
Equation 2.69 is the function representing the catenary shape of the line. Equation
2.70 represents the full catenary length of the line. In both equations H is the
horizontal force, mg is the submerged weight of the line per meter length, L is the
full catenary length and l is the horizontal distance. Furthermore the relationship
between the total tension T and its vertical and horizontal components - V and H
respectively - may be used:
T =
√
V 2 + H2 (2.71)
33. 2.6. Mooring line analysis 24
The concept is to use the relationship between weight of the mooring line, tension
for the critical case and the breaking load to find out the diameter and lengths of
each mooring line part. This critical case is in the situation when the structure is
subjected to the maximum design horizontal force. The first step in the calculation
method is to estimate the depth at which the first segment of the mooring lines is
reaching. The next required parameter for the lines is the diameter for this segment.
For this to be evaluated, the maximum horizontal force previously mentioned in the
current chapter 2.6 with value of 43.75 MN is used. With the functions previously
mentioned in the chapter for the weights and breaking forces for each segments, the
equation 2.68 is solved with only variable the diameter of the segment. These steps
lead to the estimation of all other geometrical properties of the segment of the moor-
ing lines like the catenary and horizontal lengths. The next step in the calculations
is the estimation of the properties of the second segment of the mooring line. In
order to calculate it, a fictive mooring line is used which has the same properties as
the second segment and has a fictive touch down point at the bottom. Furthermore
the lengths of the lower section of the fictive mooring line are estimated. Then these
lengths are extracted from the total lengths of the fictive mooring line to find the
lengths and depths of each segment. These are further used with equation 2.68 to
calculate the diameter of the second segment. With this diameter all remaining
properties are calculated for the lowest segment and middle segment. The explained
procedure is then repeated to evaluate the diameter of the upper segment. Then
this diameter is used again for the estimation of all remaining parameters like the
catenary and horizontal length of the third segment.
The following table 2.2 represents the calculated properties for the mooring lines.
Further details about the procedure and the calculations can be seen in the attached
MathCAD file.
Mooring line parameter Unit I segment II segment III segment Total
Diameter - D [mm] 267 223 271 -
Submerged weight - w [N/m] 1.337 · 104
2.138 · 103
1.337 · 104
-
Catenary length - L
2
[m] 444.17 1575 46.55 2065.7
Depth - d [m] 30 270 10 310
Horizontal length l
2
[m] 442.81 1551 45.46 2039.3
Table 2.2.: Parameters of the mooring lines in the maximum load case.
34. 2.6. Mooring line analysis 25
2.6.1. Mooring line analysis
With the calculated parameters presented in table 2.2 the analysis of the entire
system can be conducted. As previously mentioned in chapter 2.5 the two lines
are completely identical. Further a parametric study with four cases is made to
build a relationship between the horizontal force that acts on the platform and the
horizontal displacement of the platform.
For the first situation, the platform is subjected to the max horizontal force of
43.75 MN to the left direction. Therefore as seen in table 2.2 the distance from the
platform to the left anchor is 1755 m, and the distance to the right anchor is 2039
m.
For the second case, the platform is in its equilibrium state. There is no force
exerted on it. From the first case the total horizontal distance between the two
anchors can be estimated as 3794 m. The distance then between the platform and
each anchor is 1897 m. Further the distance between each touch down point and
the anchor is 141 m.
In the third case the system is subjected to a smaller horizontal force that the
maximum one. The same equations 2.69 and 2.70 are used to find the value of
the force and the relationship between horizontal force and horizontal displacement
of the whole platform. The following figure 2.9 shows the relationship between
the force and displacement of the platform for the system with two mooring lines.
Further on figure 2.10 the same relationship can be seen for the system with just
one line. Further details about the algorithm and calculations can be seen in the
attached MathCAD file which can also be used for estimation of any displacement
with regards to the horizontal force.
The final situation is the same as the first one but in the right direction. It is
used for complete results. The distance from the platform to the left anchor is 2039
m and 1755 m to the right one.
35. 2.6. Mooring line analysis 26
Figure 2.9.: Relationship between horizontal displacement and horizontal force act-
ing on the structure for the whole system consisting of two mooring
lines.
Figure 2.10.: Relationship between horizontal displacement and horizontal force act-
ing on the structure for the system consisting of only one mooring lines.
36. 3. Numerical Analysis Methodologies 27
3 Numerical Analysis Methodologies
The current chapter covers the parts numerical wave and ice analysis. The section
about the wave analysis deals with the specific environmental wave conditions of the
Shtokman field in the Barents Sea in the ice free period. For this, the DNV GL’s
Sesam software package will be introduced which is used to create the geometry
and to perform the hydrodynamic calculations. The post-processing utilises as well
software tools of the DNV GL’s Sesam software package. These tools will also be
introduced in this chapter. The ice analysis is executed with ANSYS. The software
will be introduced further in the project. An ice- and simplified hull-model will be
utilised to estimate the load on the structure due to ice impact.
In both analysis - wave and ice - the two different hull shapes - SOTCON Design
and SEVAN Marine Design - are implemented for result comparison.
Chapter 4 will show afterwards the results of the analysis. Furthermore they will be
compared and discussed.
3.1. Wave Analysis of FLNG
The field specific environmental conditions are used to estimate the global response
and hydrodynamic loading of the FLNG hull.
For two different hull designs these two analysis are performed in order to esti-
mate and discuss the influence of the hull shape on the responses and loadings due to
waves. These results will then later be linked to the performed ice loading analysis,
which estimates the influence of the hull shape on the ice loading (see chapter 3.2).
For the wave analysis DNV GL’s Sesam software is used, which is a strength as-
sessment tool for engineering of ships and offshore structures, using finite element
methodology. The Sesam package consists of different sub-programs, whereby for
the desired analysis the GeniE and HydroD packages are sufficient. For the post-
processing the tools Postresp and Xtract are used. They are also included in the
Sesam package and are used for general response statistics and graphical animations,
respectively. These programs and work flow will be presented in more detail in the
following sections. The results of the wave analysis are presented and discussed in
chapter 4.1, followed by an outlook to the future work in chapter 4.1.7.
3.1.1. Geometrical Set-up (GeniE)
The design and analysis tool GeniE helps designers and engineers to develop con-
structions and designs. Besides the simple design part, GeniE can also be used as a
FEM software and the structural response (for example deflections) can be calculated
by applying loads like static point loads on the structure. Users can use commands
in a textual (code-commands) or graphical form and therefore GeniE provides fea-
tures for a large spectrum of needs and preferences. In the current project GeniE is
used to generate the geometries of the floating structures and to create input files
for HydroD, which are used for hydrodynamic simulations (see section 3.1.2).
To simulate the different structures (vertical wall and sloped wall) two geometries
are designed in GeniE. As mentioned in [15] the diameter at mean water level is 106
metres and the draft is 20 metres. These values are constant for both geometries. In
37. 3.1. Wave Analysis of FLNG 28
figure A.1 in the appendix A and in figure 3.1 a model with vertical walls is shown,
which is adopted from the SEVAN Marine Design. The SEVAN Marine FLNG De-
sign considers vertical walls at the water surface [18]. It is designed for the Goliath
field in Norway where the danger of ice is lower, and ice-protection is not the main
design criterion. In contrary to the SEVAN Design the SOTCON design consideres
a hull shape with a sloped wall, designed to minimise ice-loads as shown in figure
A.2 in the appendix A and in figure 3.2.
Figure 3.1.: GeniE model of vertical walls. It shows the hull plates, applied panel
load areas for and applied point loads for mass calculation of the FLNG.
Figure 3.2.: GeniE model of SOTCON FLNG design, showing the hull mesh, panel
load areas and applied point loads for mass calculation of the FLNG.
GeniE is used to generate different input files for HydroD. These files include a
panel model (T1.FEM), a structure model (T3.FEM) and a mass model (T3.FEM).
An also possible Morison model (T2.FEM) is not required for the large structure
of the SOTCON FLNG. The panel model includes the outer hull shape, where de-
tails about material and plate thickness are not necessary. To create a correct panel
model the surface, which is assumed to be exposed to water, must be defined as a
wetted surface. On this wet surface is a load case defined with a so-called ”dummy
hydrostatic pressure”. This is necessary for the panel model for hydrodynamic cal-
culations in HydroD. The second FEM file (T3.FEM) includes the structure and the
mass model. Here it is necessary to define material properties and plate thicknesses.
Furthermore even if the FLNG is floating, the structure model requires supports.
38. 3.1. Wave Analysis of FLNG 29
These supports are necessary to avoid rigid body displacements of the structure,
which would lead to singularities. The supports do not affect hydrodynamic cal-
culations [27]. The mass model requires additionally all masses so that the centre
of gravity can be estimated. As only wave loads on the hull are considered, the
exact structure will not be modelled. Therefore point loads are included to simu-
late masses of LNG cargo and topside modules, e.g. accommodation and processing
units, and other masses from not designed structure elements (stiffeners, girders,
etcetera).
3.1.2. Hydrodynamic Analysis (HydroD)
This section deals with the in section 3.1 introduced hydrodynamic analysis of the
two floating structures. In order to execute the analysis, HydroD is used, which is
designed to perform wave load and stability analysis of fixed and floating structures
[29]. Besides the hydrostatics and wave loads, the motion response for the consid-
ered structures will be computed as well.
These characteristics are computed by Wadam and presented and visualized by the
sub-program Xtract, which is also part of the Sesam package. Wadam stands for
”Wave Analysis by Diffraction and Morrison Theory” and is capable to compute
the wave-structure interaction for different kind of fixed and floating structures [30].
Due to the fact that it includes Morison and diffraction method, it is able to analyse
slender and large structures, compared to the wave length.
The designed SOTCON FLNG with a diameter of 106 meter is large compared to
the wave length and therefore the diffraction method has to be applied. In Wadam
the corresponding model is called Panel Model, which is used to calculate the hy-
drodynamic and -static forces from the potential theory. In contrast to that, if the
structure would just consist of slender components, the Morison Model must have
been applied. For that kind of model the forces and responses are determined by
the Morison‘s equation only. If the structure is a combination of large and small
components, e.g. semi-submersibles, the Composite Model is the required model.
This option applies Morison and potential theory to the structure.
Due to the fact that the considered LNG-FPSO is a large body, the Panel Model
is the appropriate choice in order to determine the required responses. The panel
model and the offbody points, which are used for free surface animations, can be
seen in figure 3.3. Thereby it has to be noticed that the model is generated and
imported from GeniE, as explained in section 3.1.1.
The analysis is in the frequency domain, because the wave potential and equations
of motion are solved in frequency domain. Thereby it has to be noticed, that time
domain analysis is usually only relevant for fixed structures.
In HydroD a WadamWizard guides the user through the analysis and requests the
required input files and information, based on predefined settings. For this case Load
Crossections and Load Transfer are selected in order to perform a load transfer cal-
culation of hydrostatic and hydrodynamic forces to a structural model. Furthermore
Offbody Points are selected, which are required for post-processing in Xtract.
In order to perform the analysis for the specific location in the Barents Sea the
corresponding environmental data has to be provided. The wave direction is set to
a range of 0 to 90 degrees in the horizontal plane, see table 3.1. This selection is
39. 3.1. Wave Analysis of FLNG 30
Figure 3.3.: Panel Model with Offbody Points in HydroD.
done with respect to the circular shape of the FLNG and main wave direction at the
Shtokman field. The considered wave period is between 3 and 40 seconds, because
this large spectrum covers the main wave periods for the regarded sea state, which
is between 3 and 24 seconds. The wave scatter diagram for the Barents sea can be
seen in table 3.2. This table illustrates that the mean peak period Tp is between 6
and 9 seconds and the significant wave height Hs is between 9 and 12 m. There-
fore the mean peak period is set to be 8 seconds and the significant wave height is
assumed to be 11 meters for the upcoming calculations. The main water depth at
the Shtokman field varies between 320 and 340 meters and therefore a depth of 330
meter is chosen for the simulation.
Wave Direction Set 0 ◦
- 90 ◦
Wave Period Set 3 sec - 40 sec
Water Depth 330 m
Table 3.1.: Input Values for Environmental Data and Analysis Conditions
Occurence Peak Period (s)
HSig(m) 3 - 5.9 6 - 8.9 9 - 11.9 12 - 14.9 15 - 17.9 18 - 20.9 TOTAL
0 - 2.9 0.01 0.05 0.06
3 - 5.9 0.02 0.97 0.45 0.03 1.5
6 - 8.9 <0.01 8.0 6.8 1.9 0.08 <0.01 16.7
9 - 11.9 15.2 48.5 13.5 8.4 0.94 0.12 81.7
TOTAL 15.3 51.5 21.3 10.7 1.1 0.13 100.0
Table 3.2.: Scatter diagram of the Barents Sea [5].
For the further calculations the peak period Tp is chosen as 8 seconds, the signif-
icant wave height Hs is chosen as 11 m.
40. 3.1. Wave Analysis of FLNG 31
3.1.3. Hydrodynamic Wave Loading Analysis
This section deals with the hydrodynamic analysis of the two different hull shapes.
The cylindrical and conical shapes are compared regarding the acting wave forces on
the outer hull. In order to perform the analysis the results of the Wadam analysis,
which are generated in the program HydroD, are applied. The results are presented
by the sub-program Xtract, which is part of the post-processing package of Sesam.
The objective of this analysis is to obtain an understanding of the two different hull
shapes on the wave loading. These findings will then be taken into account for the
global loading on the structure due to ice and waves in the Barents Sea.
The results, presented in chapter 4.1, mainly consider hydrodynamic wave loads.
Hydrostatic pressure will only be used for validation purposes. Apart from that the
hydrostatic pressure will not be taken into account.
3.1.4. Calculation of Wave Loads in Wadam
This section describes the calculation of the wave loads by using the Wadam-package.
As explained before Wadam applies the diffraction and Morison theory in order to
calculate the wave loads on a large or slender body.
The two described structures are modelled with shell elements. As described in
section 3.1.1, a wetted surface is defined on which the hydrostatic load is applied
and determined as normal pressure on the shell elements. The hydrostatic pressure
distribution can be seen in figure 3.4. The static pressure is just depended on
the draught, so that the maximum pressure is at the bottom part of the floating
structure. Due to the fact that both structures are considered at the same draught
d of 20 meters, the maximum static pressure is the same.
Pstatic = ρ · g · d = 1025 · 9.81 · 20 = 201105 N (3.1)
(a) Hydrostatic pressure distribution for the
cylindrical hull shape.
(b) Hydrostatic pressure distribution for the
conical hull shape.
Figure 3.4.: Hydrostatic pressure distribution along the two different hull shapes.
In contrast to the hydrostatic pressure the hydrodynamic pressure load calcula-
tion on the elements are performed by applying the potential theory, which is based
in the panel model. the panel pressures are then transferred into normal pressure
41. 3.2. Numerical solution for the ice loading 32
load by an internal algorithm [30].
The calculated hydrodynamic loads are affected by several components. These
loads contain the exciting forces from incidents waves and forces due to wave induced
motion [30]. Furthermore the fluctuating hydrostatic pressure forces due to the body
motion is included [30].
3.2. Numerical solution for the ice loading
In this chapter, the numerical simulation performed for the estimation of the ice
loads on the structure is described. The load is estimated for the same ice-ridge
formation as in the analytical solutions presented in the previous chapter 2.3.
The ANSYS software is used for the analysis. It utilizes the finite element method
for the calculations of the required variables like for example stresses, deformations
and loads. In the current report a static analysis is presented for the load on the
vertical part of the SEVAN Marine design with 106 m diameter. The purpose of
this simulation is to evaluate the accuracy and reliability of the generated model by
comparing it to the analytical solutions. Furthermore the numerical model will be
used to estimate the load on 45 degrees sloped wall with the same diameter of 106
m. Only the geometry will be adjust to the SOTCON concept. Furthermore the
details for the geometry and simulation are presented.
3.2.1. Structure geometry (ANSYS)
The geometry of the structure used in the simulation is the same as the one used for
the wave loading as seen on figure A.2 CAD model of the SOTCON FLNG Design.
on page 55. As explained in the previous chapter 3.1.1 regarding the wave loading
analysis two different geometries are used for the simulations as seen on the pictures.
For the model of the structure in the software are used shell elements with thickness
of 70mm. According to [24] the authors use a shell thickness of 55mm and the
complete model of the structure including stiffeners etc. In the current project the
thickness of the hull is fictive and approximated from the mentioned report including
the stiffeners. For the external hull a standard carbon steel is used with Young’s
modulus of 210GPa and Poisson’s ratio of 0.3. In order to save computational time
and due to the symmetry of the structure only half of it is modelled as seen on figure
3.5.
42. 3.2. Numerical solution for the ice loading 33
3.2.2. Ice modelling
As mentioned before the geometry of the ice formation is the same as the one used
in the analytical solutions seen in section 2.3.1. Here the main parameters will be
just mentioned again:
Hs = 5m - sail height
Hk = 20m - keel depth
Bs = 30m - sail breadth
Bk = 80m - keel breath
hi = 4m - thickness of consolidated layer
In order to represent the ice formation in the software, a mathematical formulation
for the behaviour of the material is needed. The ice is modelled with two different
elements in order to approximate the real material behaviour in the software. The ice
itself is represented with cube bulk elements with 2x2x2m dimensions. According to
[31] the use of this size for the elements of the ice is justified. The bulk elements are
modelled with linear viscoelastic material according to [9] exhibiting the properties
of both viscous material and elastic material in different conditions (like creep and
relaxation). The linear material can be used when dealing with relatively short
durations of time. Since the current project focuses on the estimation of the ice loads
from the impact, it is reasonable approximation to use the linear representation of
the material. For the bulk elements Young’s modulus of 8.7GPa is used for standard
ice formation. Furthermore to represent the viscoelastic behaviour of the material
Prony series are used to show the change of the shear and bulk moduli in time.
However due to the lack of experimental data only one step in time is used for the
change of the values of the moduli with ratio to the initial ones of 1.
At every boundary of the bulk elements cohesive elements are placed. The pur-
pose of the cohesive elements in the analysis is to simulate the paths where cracks
can propagate in the material. According to [31] these elements can be utilized.
The concept that these elements represent is that they are connected with both
elements they are adjacent to. When load is applied on the system the cohesive
elements are gradually failing. When a certain limit of the strength of the cohesive
element is reached the it is completely broken and disappears from the calculations.
Afterwards the elements in-between this cohesive element was have no connection
any more. According to [25] exponential behaviour of the cohesive elements is uti-
lized. The parameters used for the traction-separation curve for the elements are
with accordance to [31] again due to the lack of experimental data. The maximum
tensile strength of the elements is 500KPa.
The boundary conditions used in the model are as follows. All the nodes along
the lines where the structure is cut-off are fixed in all degrees of freedom due to the
fact that in reality they are part of the structure and are connected to the other
part of the structure. The top and bottom part of the structure are only free to
rotate about the X and Y axis. All other nodes from the facility are free in all
degrees of freedom. At all the nodes from the ice-formation is applied displacement
until the surface of the ice comes into contact with the structure. For this contact
to be represented and the interaction to be taken into account contact pair is used.
On the surface of the ice are attached contact elements and on the surface of the
structure - target elements.
43. 3.2. Numerical solution for the ice loading 34
The following figure 3.5 shows the geometry including the boundary conditions
of the model. After conducting the analytical solution for the estimation of the ice
Figure 3.5.: Geometry of the model used for the estimation of the ice load on the
vertical wall in ANSYS with the boundary conditions of the structure.
load as seen in chapter 2.3, it was found that in the current method of calculations
the governing part of the load is the consolidated layer load. The part of the total
load which is due to this layer is roughly 90 percent of the total force. According
to this fact and the lack of method for calculating the ridge force on a sloped wall
as explained previously, the calculations in the analytical solution were made only
for the consolidated layer. It is assumed therefore that it is behaving the same
way as a level ice-sheet. Furthermore according to the fact that the conducted
simulation is static, this is a reasonable assumption and it will not affect the result.
As seen on figure 2.7 the analytical parametric study for the estimation of the loads
on different slopes of the structure lead to the conclusion that the force on the 45
degrees slope was the smallest. Therefore the numerical solution was conducted only
for a 45 degrees slope. The geometrical set-up for this simulation can be seen on the
following figure 3.6. The solution was the same static one with applied displacement
on the ice in the direction of the structure.
44. 3.2. Numerical solution for the ice loading 35
Figure 3.6.: Geometry of the model used for the estimation of the ice load on the
wall with 45 degrees slope in ANSYS with the boundary conditions of
the structure.
3.2.3. Disadvantages and inaccuracy
Every time when utilizing software for simulations, it is important to know its extend
and accuracy. In the current model several disadvantages can be pointed out. First
cube-like elements are used for the representation of the bulk part of the ice. Due
to the fact that the cracks an propagate only along the boundaries of the blocks
(they would have a zig-zag like shape), this will lead to extra energy consumption
when breaking the block which is unrealistic. Furthermore the model is highly
mesh size dependent. Furthermore in the current project only static solution is
considered which could lead to more inaccuracy. Moreover the bulk elements are
modelled as linearly viscoelastic material. Due to the fact that in reality the material
behaviour depends on salinity, temperature etc. and is non-linear, this can lead to
more inaccuracy.
45. 4. Numerical Analysis Results 36
4 Numerical Analysis Results
This chapter deals with the results of the numerical simulations, which are in-
troduced in the previous chapter. For the numerical wave load analysis the results
of the global response, the vertical cumulative displacement and the hydrodynamic
wave loading are presented for the two hull designs, which are presented in section
2.1.
This section is followed by the presentation of the results of the numerical ice load
analysis. The ice loading for the sloped and vertical hull configuration is simulated
and discussed. In addition to that the analytical ice load estimation, seen in section
2.3, is used for the validation and comparison purpose.
4.1. Results of Wave Analysis
This section presents the results of the wave analysis, which procedure is explained
in section 3.1. The results of the global response, vertical displacement and hydro-
dynamic wave loading are established and discussed.
4.1.1. Results of Global Response
In this section the results of the global responses of the two different structures are
analysed. The heave and pitch Response Amplitude Operators (RAOs) are presented
and discussed. Furthermore the displacement for the two floaters are investigated,
using the sub-program Xtract.
Response Amplitude Operators of the two Structures
For the two different hull shapes, presented in section 3.1.1, the heave and pitch and
surge RAOs are generated by the sub-program Postresp. It is a general interactive
graphic post-processor for post-processing of responses [28]. The generated responses
are exported and then processed in Excel in order to achieve the following diagrams.
Validation of the Natural Period In order to validate the achieved results, the
natural period of the structure is estimated by fundamental equations of dynamics
of floating structures. The natural frequency of a floating structure is equal to the
heave stiffness ks divided by the mass M and added mass MAV M,Y of the structure.
ωn =
ks
M + MAV M,Y
(4.1)
Whereby the heave stiffness is
ks = ρ · g · Aw = 1.025 · 9.81 · 1062
·
π
4
= 88734 kN/m (4.2)
The Mass M is idealised for a cylinder with diameter of 106 meters and a draught d
of 20 meters
M = ρ · Aw · d = 1.025 · 1062
·
π
4
· 20 = 180907 t (4.3)
46. 4.1. Results of Wave Analysis 37
The added Mass of a vertical excited cylinder is calculated as
MADM,Y =
4
3
· ρ ·
D3
8
=
4
3
· 1.025 ·
1063
8
= 203465 t (4.4)
Substitution of these values into equation 4.1 yields to a natural frequency of 0.48
rad
sec
, which corresponds to a natural period Tn of 13.1 seconds.
Heave Response Amplitude Operators The heave RAO can be seen in figure
4.1. This diagram shows, that the heave response of the structure with the vertical
hull shape is app. 25 % greater than the response of the modified hull. The natural
frequency of the two floater is also different. The natural heave period of the vertical
shaped FLNG is 14 seconds, whereby the FLNG with sloped shape has a natural
heave period of 13 seconds.
Figure 4.1.: Heave RAO for the two different hull shapes.
47. 4.1. Results of Wave Analysis 38
Pitch Response Amplitude Operators The pitch RAO can be seen in figure 4.2.
Similar to the heave case, the response of the structure with sloped hull is approxi-
mately 25 % lower than the response of the vertical hull. Furthermore the natural
pitch period is shifted downwards. The natural period of the vertical case is around
25 seconds, whereby the natural period of the sloped case is at 19 seconds respec-
tively. The consequence of this shift will be further discussed in section 4.1.7
Figure 4.2.: Pitch RAO for the two different hull shapes.
Surge Response Amplitude Operators Figure 4.3 shows the RAO for the surge
condition. It can be seen that the amplitude for the sloped hull configuration is
higher, compared to the vertical hull shape. Furthermore it can be seen that the
natural surge period is shifted. For the vertical hull the natural period is approx-
imately 25 seconds, whereas this period is about 19 seconds for the sloped hull,
respectively. It has to be noticed that these two periods coincide with the natural
pitch periods of the two different bodies.
Figure 4.3.: Surge RAO for the two different hull shapes.
48. 4.1. Results of Wave Analysis 39
4.1.2. Results of Displacement
This paragraph has the purpose to show the resulting displacement in z-direction.
Again, the two models are compared to show the influence of the different shapes.
The displacement in z-direction includes besides heave also z-movements due to
pitch. It hence depends on different influences and the result could be amplified.
In section 4.1.1 the natural heave and pitch periods are discussed and are used to
explain the displacement behaviour. Thereby it has to be noticed that the focus in
this section lies upon the cumulative displacement.
Table 4.1 shows a set of maximum displacement for the following six periods.
1. Peak period Tp of 8 seconds
2. Heave resonance period for the sloped hull of 13 seconds
3. Heave resonance period for the vertical hull of 14 seconds
4. Pitch resonance period for the sloped hull of 19 seconds
5. Pitch resonance period for the vertical hull of 25 seconds
6. Period far away from the resonance cases of 38 seconds
Table 4.1.: Overview of maximum displacement for a set of representative periods.
Period T [sec] 8 13 14 19 25 38
Displacement vertical wall[m/m] 0.063 0.625 1.394 1.102 2.289 1.005
Displacement sloped wall [m/m] 0.168 1.216 1.279 5.723 1.009 1.002
A representative figure of the displacement due to a certain wave period can be
seen in figure 4.4 and 4.5. They show the displacement of the vertical and sloped hull
shape for the peak period of 8 seconds. This is the most common wave period for the
Shtokman field, which occurs for more than 50 %, see table 3.2. It can be seen that
the displacement of the vertical hull shape is much smaller than the displacement
of the sloped hull shape design. The difference is 0.105 [m/m] and can be explained
by the heave and pitch RAOS, shown in figure 4.1 and figure 4.2 respectively. The
pitch response is almost zero for both cases at the period of 8 seconds, so that the
increased displacement of the sloped hull design has to be explained by the heave
response of the two structures. With respect to figure 4.1 it can be seen that for a
period of 8 seconds the heave amplitude of the vertical wall is nearly zero, whereas
the amplitude of the sloped wall is approximately 0.1. This is caused due to tha
fact that the natural heave frequency of the sloped wall is shifted towards the peak
period of the sea state.
For a wave period of 13 seconds and can be seen in table 4.1, that the sloped hull
design has an increased displacement. It is nearly twice as high as for the vertical
hull shape design. Considering the heave RAO, shown in figure 4.1, it has to be
stated that both structures have nearly the same response amplitude for this wave
period. Therefore the difference is caused by the pitch response, which is illustrated
in figure 4.2. For the vertical configuration the rotation is zero, whereas the sloped
49. 4.1. Results of Wave Analysis 40
Figure 4.4.: Displacement in z-direction of FLNG model with a vertical wall for
wave-period of Tp = 8s. Max: 0.063.
Figure 4.5.: Displacement in z-direction of FLNG model with a sloped wall for wave-
period of Tp = 8s. Max: 0.168.
50. 4.1. Results of Wave Analysis 41
hull design has already a small response amplitude. This small difference in the
rotation leads to the significant difference in the displacement.
For a wave period of 14 seconds the z-displacement of the vertical wall is higher
than the z-displacement of the sloped hull design. However the pitch response of
the sloped configuration is higher, the main influence comes from the heave response
due to that wave period. It can be seen in figure 4.1 that the vertical hull design has
its peak at this position with a amplitude off appendix. 1.7, whereas the response of
the sloped design is declined and appendix 1.2. In this case the heave resonance case
of the vertical wall is dominant and leads to the increased z-displacement, compared
to the sloped wall.
The wave period of 19 seconds represents the pitch resonance case for the sloped
hull design. The difference in the cumulative z-displacement is significant and ex-
pected. Referring to figure 4.2 it can be seen that for 19 seconds the pitch response
of the vertical wall is nearly zero, whereas the sloped configuration has its peak
with a value of approximately 0.3. Besides that it has to be noticed that the heave
response has no significant influence at this period of 19 seconds, seen in figure 4.1.
However the displacement of the sloped design is very high for this wave period, it
has to be noticed that the probability of the occurrence of this wave period is very
low, see table 3.2 in section 3.1.2.
The pitch response for the vertical hull design occurs at 25 seconds. Therefore an
increased response for this design is expected and it can be seen in table 4.1 that the
cumulative z-displacement is more than twice as high as for the sloped design. Due
to the fact that there is no difference in the heave response between the two designs
for a period of 25 seconds, the main driver is the pitch response, seen in figure 4.2.
It can be seen that the response for the sloped wall is close to zero, whereas the
response of the vertical wall has its maximum at approximately 0.38. This leads to
the significant difference in the displacement.
The last comparison, for a period of 38 seconds, illustrates that for a wave period
higher than approximately 30 seconds no significant cumulative z-displacement has
to be expected. It can be seen in figure 4.1 and figure 4.2 that the response is almost
zero for both cases. The values, shown in table 4.1, show that the structure will
move with the wave and will the motion of the structure is not amplified by any
resonance phenomena.
51. 4.1. Results of Wave Analysis 42
(a) Displacement in z-direction of FLNG
model with a vertical wall for wave-period
of T = 25 seconds. Max: 2.289.
(b) Displacement in z-direction of FLNG
model with a sloped wall for wave-period
of T = 25 seconds.Max:1.009.
Figure 4.6.: Compared displacement in z-direction of FLNG with a vertical and a
sloped wall for a wave period of 25 seconds.
4.1.3. Conclusion of Global Response Analysis
As a first step of wave analysis, the global responses of two structures are compared.
As shown in the results (see section 4.1.1) the RAO peak for heave, pitch and surge
of the sloped wall option is closer to the mean wave period (Tp) of 8 seconds than of
the vertical wall option. At the first view this result could lead to the conclusion that
the vertical wall model is more suitable for the planned operation at the Shtokman
field. However, the heave and pitch amplitude is smaller for the sloped configuration
at the corresponding natural periods, as stated in section 4.1.1. Furthermore it has
to be noticed that the responses are small at the peak period of 8 seconds. As seen in
table 4.1 of section 4.1.2 the cumulative displacement in z-direction is larger at the
mean wave period, the heave resonance period (T = 13s) and the pitch resonance
(T = 19s), but smaller at the heave and pitch resonance of the vertical hull shaped
geometry (T = 14s and T = 25s, respectively).
Hence, the global response of the conical structure has positive and negative parts
and cannot be considered alone and have to be compared with the hydrodynamic
wave and ice loading.
4.1.4. Results of Hydrodynamic Loading on Cylindrical Hull
Shape
A set of representative hydrodynamic pressures is listed in table 4.2. For the mean
peak period, the natural heave frequency, natural pitch period and the period of the
maximum hydrodynamic pressure, the maximum pressure values along the hull are
obtained from the post-processing program Xtract.
It can be seen that the hydrodynamic pressure on the cylindrical hull shape with
a vertical wall has its maximum close to the peak wave period at T = 9 s. The
pressure distribution with the maximum hydrodynamic pressure of p = 17946 N
52. 4.1. Results of Wave Analysis 43
Table 4.2.: Hydrodynamic pressures for vertical wall.
Wave-period T [s] Hydrodynamic pressure p [N]
8 (peak wave) 17,037
9 (max) 17,946
14 (heave) 16,729
25 (pitch) 11,396
for this case can be seen in figure B.2 in the appendix. The hydrodynamic pressure
for the peak wave period Tp = 8 s, the heave resonance period Theave = 14 s, and
the pitch resonance period Tpitch = 25 s are shown in the appendix in figure B.1,
B.3, and B.4, respectively. Table 4.2 shows the corresponding pressures for the four
different cases. These values will be compared with the conical hull shape in section
4.1.6.
4.1.5. Results of Hydrodynamic Loading on Conical Hull Shape
Table 4.3 shows the different pressure values for the mentioned periods. Similar
to the cylindrical hull shape, the mean peak wave,the natural heave, and natural
pitch period is considered. Furthermore the period of the maximum hydrodynamic
pressure for the vertical hull shape is taken under consideration. The figures B.5,
B.6, B.7, and B.8 in the appendix show the pressure distribution on the hull for the
simulated times T = 8 s, T = 9 s, T = 13 s, and T = 19 s, respectively.
Table 4.3.: Hydrodynamic pressures for sloped wall.
Wave-period T [s] Hydrodynamic pressure p [N]
8 (peak wave) 14,917
9 (maxvertical walls) 16,792
13 (heave) 13,752
19 (pitch) 34,992
It has to be noticed that the hydrodynamic pressure for the conical hull shape
(sloped wall) is different than for a vertical wall (compare section 4.1.4). Again, the
hydrodynamic pressure is higher at T = 9 s than at the peak wave period T = 8 s
or the heave resonance period T = 13 s. However, the maximum hydrodynamic
pressure occurs at the pitch resonance period T = 19 s. Here the pressure increases
dramatically. At this point the pressure is twice as high as at T = 9 s. Furthermore
it has to be pointed out, that the maximum pressure values are directly at the
water surface for each evaluated wave period. This effect has been expected and can
be explained by the decreasing water particle velocities from the water surface to
increased water depth.
