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Transcript of Chapter 1 to 5
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CHAPTER 1
INTRODUCTION
1.1 GENERAL
During the last few decades, the exploration and production of offshore petroleum
reserves have progressively moved to deeper water sites around the world. Operations in 1000 to
1200 m water depth have become common and the offshore industry gears up to venture into
ultra-deepwaters of 3000 m and beyond for new finds. Traditional shallow water platforms e.g.
jack-up and jacket type drilling and production platforms, have given way to floating platforms,
which are more economical in deep waters. These platforms, such as tension leg platforms
(TLPs) and spars are kept on station using vertical tendons, which are sometimes combined with
more conventional spread mooring systems. Unlike the rigid platforms, the motion
characteristics of compliant platforms play significant role in their operations. Therefore, the
study of structural behavior and dynamic response of these platform concepts in order to
optimize their designs are presently being actively pursued in the literature.
In ultra-deepwater sites the use of seabed-mounted platforms becomes uneconomic and use
of floating platform becomes the only viable option. Numerous small oil fields have been
discovered in very deep waters. New concepts of platform construction, exploration, drilling and
production are necessary for economic development of these minimal oil fields in deepwater
locations in hostile environment. To reduce wave induced motion, the natural frequency of these
newly proposed offshore structures are designed to be far away from the peak frequency of the
force power spectra. Spar platforms are one such compliant offshore floating structure used for
deep water applications for the drilling, production, processing, storage, and offloading of ocean
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deposits. It is being considered as the next generation of deep water offshore structures by many
oil companies.
A spar platform consists of a vertical cylinder, which floats vertically in the water. Fig.1.1
shows a typical spar platform with the basic arrangements. The structure floats so deep in the
water that the wave action at the surface is dampened by the counter balance effect of the
structure weight. Fin like structures called strakes, attached in a helical fashion around the
exterior of the cylinder, act to break the water flow against the structure, further enhancing the
stability. Station keeping is provided by lateral, multi-component catenary anchor lines attached
to the hull near its center of pitch for low dynamic loading. The analysis, design and operation of
Spar platform turn out to be a difficult job, primarily because of the uncertainties associated with
the specification of the environmental loads. The present generation of Spar platform has the
following features:
a) It can be operated till 3000 m depth of water from full drilling and production to
production only,
b) It can have a large range of topside payloads,
c) Rigid steel production risers are supported at the center well by separate buoyancy cans,
d) Always stable because center of buoyancy (CB) is above the center of gravity (CG)
e) It has favorable motions compared to other floating structures
f) It can have a steel or concrete hull
g) It has minimum hull/deck interface
h) Oil can be stored at low marginal cost
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i) It has sea keeping characteristics superior to all other mobile drilling units
j) It can be used as a mobile drilling rig
k) The mooring system is easy to install, operate and relocate
l) The risers, which are normally exposed to high waves on semi-submersible, drilling units
would be protected inside the spar platform. Sea motion inside spar platform center well
would be minimum
Figure 1.2 shows three types of Spar configurations:
1. Classic Spar
2. Truss Spar
3. Cell Spar
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Fig 1.1 A typical spar platform with basic arrangements and terms
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Classic Spar Truss Spar Cell Spar
Fig 1.2 Various configurations of a spar platform
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1.2 OBJECTIVE
• The objective of the project is to develop a program which can be used to perform design
of spar platform.
• The program also includes the analysis of motion response of spar, using simplified
approach.
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CHAPTER 2
DEVELOPMENT OF SCHEME
1.3 GENERAL
The computer program starts with reading inputs, mainly wave height (Hw ), water
depth(d), Time period(T), Topside Weight (WT) from a file. Using these inputs diameter and
thickness of the spar are determined based on buoyancy requirements. Designed structure is
checked for safety against hydrostatic pressure, hoop buckling, tension and compression.
Circumferential stiffening rings are provided based on API recommendations. Total weight of
spar is calculated including weight of stiffener and topside weight. Total buoyancy is determined
from the draft and diameter of spar. Then, the hydrostatic stability check is performed in order to
ensure stable equilibrium. If the required metacentric height is not achieved, the structure is
redesigned after providing ballast. Motion response analysis is done using simplified calculation
approach. An optimized design can be achieved by running the program for different drafts to
find out corresponding response amplitude operator (RAO).The design corresponding to
minimum diameter and minimum RAO can be taken as an optimized design. A flow diagram
showing the general flow of the program is given below. Theoretical background of each step
involved in the flow diagram is explained in Chapter 3.
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1.4 FLOW DIAGRAM
Fig 2.2 Flow Diagram
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CHAPTER 3
THEORETICAL BACKGROUND
3.1 GENERAL
The procedure followed for the structural design of spar, weight estimation,
hydrostatic stability check and response prediction using simplified approach are
described here.
3.2 STRUCTURAL DESIGN
The given parameters for the structural design are the topside weight (WT), wave
height (Hw) and water depth(d). The aim is to obtain the dimensions of spar.
Initial sizing of the hull is determined by the following steps:
Initial value for the draft (Df) is assumed.
Free board is calculated as Hf = 0.6x Hw +1.5 m.
Total length of spar, Ls = Df + Hf
Ballast Weight (WB) is initially taken as zero.
Diameter is calculated from buoyancy requirements as
Thickness (t) is calculated using assumed D/t ratio.
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Check for hoop stress due to hydrostatic pressure.
Where,
fh = hoop stress due to hydrostatic pressure, MPa
p = hydrostatic pressure, MPa
SFh = safety factor against hydrostatic collapse (API RP 2A)
Fhc = critical hoop buckling stress, MPa (API RP 2A)
Multiply p with a factor of 1.25 to take into account the pressure due to wave
elevation.
Check for axial tension. The allowable tensile stress, Ft, for cylindrical members
subjected to axial tensile loads should be determined from:
Where, Fy = Yield strength (Mpa)
Check for axial compression. The allowable axial compressive stress shall be
determined from the following AISC formulas for the members with a D/t ratio equal
to or less than 60.
for
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Where,
E = Young’s Modulus of elasticity, ksi (MPa)
K = effective length factor
l = unbraced length (m)
r = radius of gyration (m)
For D/t ratio greater than 60, substitute the critical local buckling stress (Fxe
or Fxc
,
whichever is smaller) in determining Cc
and Fy
Check for local buckling:
The elastic local buckling stress, Fxe
is determined from
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Where,
C= Critical elastic buckling coefficient
D= Outside diameter(m)
t = Wall thickness (m)
The inelastic local buckling stress, Fxc
is determined from
Check for hoop buckling stresses:
Elastic hoop buckling is given by
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Where, L is the spacing between cylindrical rings
M is geometric parameter
Critical hoop buckling stress is given by
When longitudinal tensile stresses and hoop compressive stresses occur
simultaneously, the following interaction equation should be satisfied
A2+B2+2ν׀A׀B≤1.0
Where,
A reflects maximum tensile stress combination.
ν = poisson’s ratio
fa =absolute value fof axial stress,(MPa)
fb = absolute value of acting resultant bending stress,(MPa)
fh= absolute value for hoop compression,(MPa)
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SFx= Safety factor for axial tension(API RP2A).
SFh= Safety factor for hoop compression(API RP2A).
When longitudinal compressive stresses and hoop compressive stresses occur
simultaneously, the following interaction equation should be satisfied
SFx= Safety factor fort axial compression(API RP2A).
SFb= Safety factor for bending(API RP2A).
Ring Design:
Circumferential stiffening ring size may be selected on the following basis
Where,
Ic = Required moment of inertia of ring composite section
L =Ring Spacing (m)
D = Diameter (m)
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An effective width (bf) of shell equal to 1.1(Ds t )1/2 is be assumed as the flange for composite
ring section.
For flat bar stiffener minimum dimension provided is 10x76 mm.
The width (b) to Thickness(t) ratios of stiffening rings are selected in accordance with AISC
requirements.
b=tsx65/(fy)1/2
3.3 WEIGHT ESTIMATION
An initial estimate of total weight of the structure is based on Topside weight(WT), hull
weight including the weight of circumferential stiffeners and weight of ballast(WB) which is
initially taken as zero.
Weight of Hull is given by,
Weight of stiffeners is given by,
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Fig 3.3 Stiffener Details
Total Weight, W = WT + Ws +Wst+ WB
3.4 HYDROSTATIC STABILITY
Hydrostatic stability is achieved only if there is a balance between the total
downward force and buoyancy. The diameter of spar is selected in such a way as to
satisfy this condition. Also, for a floating body to be in equilibrium, metacentric height
should be greater than zero. Usually for a spar, the required matacentric height is 4-6 m.
Metacentric height is determined as follows.
Distance of centre of buoyancy from keel, KB = Df /2
Dead Weight of spar, WD = SPAR weight(Ws) + stiffener weight(Wst)
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Distance of centre of gravity from keel,
Metacentric radius, BMT=Transverse moment of inertia(I )/Displaced Volume(V)
Distance of metacentre from keel , KM=KB + BM
Metacentric height, GM = KM – KG
Where, Df= Draft of spar
Ls= Length of spar
ADF=Additional draft due to Ballast
3.5 RESPONSE PREDICTION USING SIMPLIFIED APPROACH
Simplified calculation approach is based on linear potential theory and the superposition
principle, i.e. behavior in irregular sea is modeled by linearly superposing results from regular
waves. Hydrodynamically, it is therefore sufficient to analyze a spar platform exposed to regular
sinusoidal waves. The simplified method is described by Faltinsen (1990).
3.5.1 The Hydrodynamic Problem
Assuming linear damping, the linear equations of motion for surge, heave, and pitch can
be solved in frequency domain. The damping represents the non-potential flow effects. Due to
symmetry, the waves can be assumed to propagate along the positive x-axis with no roll, sway
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and yaw-response of the spar. The heave equation of motion is uncoupled while pitch and surge
are coupled. The wave elevation and the velocity potential of incoming waves may be written:
and (3.5.1)
;
For slender structures like spar, the wavelength is much longer than the diameter i.e. D/L<0.2.
The consequence of this long wavelength assumption is that no waves are generated by the hull.
Then the diffraction problem may be solved in a simplified manner. The excitation forces are
obtained from the incoming wave potential and using analytical expressions for the added mass.
No internal flow effects are considered as the spar bottom is closed. The equations to solve are
the coupled surge/pitch equations of motion;
(3.5.2)
and the heave equation of motion;
(3.5.3)
but before the equation can be solved, all the coefficients (Aij, Bij, Cij, and Fi) have to be
determined. These coefficients are representing hydrodynamic forces and determining these
coefficients, “the hydrodynamic problem”, can be divided into two sub-problems:
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“The diffraction problem”: The forces and moments on the body when the body is fixed
and there are incoming regular waves. These hydrodynamic forces are again divided into
the Froude-Krylov forces (pressure forces and moments due to undisturbed fluid flow)
and the diffraction forces (pressure forces occurring since the body changes the pressure
field by its presence in the water).
Fi=FFK+FDIF i=1,3,5.
“The radiation problem”: The forces and moments on the body when the body is forced
to oscillate and there are no incident waves. These hydrodynamic loads are identified as
added mass, damping, and restoring terms. (Aij, Bij, Cij i, j=1, 3, 5). Note that due to the
long wavelength characteristic, there is no radiation damping, since it is assumed that no
waves are generated by the hull. Consequently Bij consist of non potential flow effects
only.
3.5.2 Hydrodynamic Forces
The heave excitation is obtained by integrating the dynamic pressure over the wetted hull
surface. The pressure is found by using Bernoulli’s equation. Formally the excitation force can
be written as:
where (3.5.4)
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n = <n1 n2, n3> is the vector normal to the body surface defined to be positive into the fluid. But
as previously mentioned a simplified approach based on a long wavelength assumption will be
applied.
a) Heave excitation force
The Froude-Krylov heave force is obtained by integrating the undisturbed fluid pressure from the
incoming wave potential over the bottom of the spar. The diffraction force is obtained in a
simplified manner as previously described.
Due to the long wavelength assumption, the diffraction term may be simplified and the integral
over the wetted surface can be replaced by the quantities at the center of the spar(x=0). This
means that structure is assumed transparent with respect to waves. Due to the normal vector of
the body surface, only the bottom surface of the spar contributes to the heave force (see figure
3.5.2)
(3.5.5)
where Td = draft of the spar
The above equation becomes:
The first term is the Froude-Krylov force while the second term is an approximation for the
diffraction force. For a spar platform, the Froude-Krylov term is an order of magnitude larger
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than the diffraction term, due to low added mass. Therefore, a spar platform does not take
advantage of the heave cancellation effect.
b) Heave added mass
The heave added mass A33 appears both in the expression for the excitation force, Equation
(3.5.5), and a mass term in the equation of motion, Equation (3.5.3). In order to solve the
equation of heave motion, it is necessary to estimate the added mass A33. Newman (1985)
calculated with the help of numerical methods, the axial added mass for a semi infinite cylinder
to be A33=2.064ρr3, where r is the radius of cylinder. For a typical spar, the free surface effects
have small influence on the heave added mass i.e. the added mass is basically an end effect. It
may be noted that 2.064 ρr3 is fairly close to the displaced mass of the hemisphere
. So for a bare cylinder, is used. See fig. 3.5.3 (a)
The added mass for a bare cylinder is low compared to the total mass of the spar, and has
therefore a relatively small effect. As mentioned earlier, when a heave plate is attached at the
bottom of the spar, the heave added mass increases and becomes significantly high. The heave
added mass for a spar + disc configuration is estimated as shown below:
The added mass of a disc oscillating along its axis approximately equal to the mass of a sphere of
water enclosing the disk (Sarpkaya, et al., 1981)
For the configuration of a cylinder with a disc attached to its base, if the diameter of the disc is
greater than that of the cylinder, there is only a part of the disc on the cylinder side producing
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added mass effect since the presence of the cylinder (see figure 3.5.3 (b)). Thus, the added mass
of a cylinder + disc configuration can be estimated by subtracting approximately the mass of the
cylindrical volume of water.
After calculations, the added mass of a cylinder + disc becomes:
(3.5.6)
c) Horizontal excitation forces
The excitation forces and total added mass for lateral motions are estimated using strip theory and the
two-dimensional added mass for a cylinder in infinite fluid.
For a two dimensional cylinder section in infinite fluid, the excitation force can be written
. The first term is the diffraction force and the second term is the Froude-Krylov
force. is the two dimensional added mass of the section, r = radius of the cylinder, and a is
the undisturbed water particle acceleration. It can be noted that this expression for the force
corresponds to the inertia term in Morrison’s equation with inertia coefficient Cm=2.
The total surge and pitch excitation forces are obtained by integrating the unit length force on
each horizontal strip along the wetted hull surface. The pitch excitation moment is taken about
VCG, see figure 3.5.1
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(3.5.7)
(3.5.8)
where z coordinate of center of gravity as shown in figure 3.5.1
The integration is to be done over the wetted length of the cylinder.
d) Horizontal added mass
The added mass coefficients Aij, i,j = 1,5 are determined by considering forced surge and pitch
oscillation of the spar, see figure 3.5.1. Under combined surge/pitch oscillations, every strip
along the hull has the acceleration . is again the vertical distance from the
strip to the vertical centre of gravity, VCG. Water cannot penetrate the spar hull, so when the
strip is accelerated by astrip, a pressure field is set up on the hull’s surface to displace the water.
The strip will “feel” a counteracting inertia force, .
The global reaction forces due to the forced oscillations (F1, RAD and F5, RAD) are obtained by
integrating the reaction force on each strip. The added mass coefficients Akj are then found based
on the definition of added mass:
(3.5.9)
(3.5.10)
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Coefficient of (- ) in the above equation is A11 and of (- ) is A15.
Also,
(3.5.11)
Coefficient of (- ) in the above equation is A51 and of (- ) is A55.
Fig. 3.5.1 Spar geometry
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Fig. 3.5.2 Forces on a spar platform
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Hemispherical fluid mass acting as heave added mass
Cylinder of diameter Ds
Fig. 3.5.3 (a) Heave added mass for cylinder
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Fig 3.5.3 (b) Added mass of a disc attached to a cylinder
3.5.3 Hydrostatic restoring forces
Since the spar is free floating, only hydrostatic terms are contributing to the restoring matrices:
and (3.5.12)
Here Aw is the waterplane area, GM is the metacentric height, and Δ is the displaced weight of
the spar.
3.5.4 Damping Effects
In general, both generation of waves (radiation damping) and viscous forces (non
potential flow effects) are contributing to the total damping of a floating body.
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In the simplified analysis it is assumed that the wave generation by the body is negligible, i.e.
there is no radiation damping. This approximation is relevant for survival conditions (long wave
periods). For shorter wave periods on the other hand, where radiation effects are more important,
damping effects have a small influence on the linear wave frequency response. Viscous damping,
which plays a crucial role in the resonant response, is an empirical input to the analysis, and is
not explicitly calculated.
In the region around resonance, which is important in this study, the radiation damping is small.
It is therefore assumed that the important damping effects are caused by viscous forces on the
platform hull, on mooring lines, on risers, and other appendices. It is believed that these drag
forces have a quadratic behavior. However, only linear damping forces are included in this
simplified linear frequency domain analysis. For simplicity, the linear damping coefficients Bii
are here calculated as ratios of the critical damping (ξ=B/Bcritical):
and (3.5.13)
The values of ζ5 and ζ3 used for the calculation of B55 and B33 are obtained from experiments.
3.5.5 Response Amplitude Operators (RAOs)
When all the coefficients (Aij, Bij, Cij and Fi) are established, the equations of motions are solved
by assuming steady state solutions oscillating with the same frequency as the excitation. The
assumed solutions are substituted into the equations of motion (3.5.2) and (3.5.3).
The motion response amplitude is complex.
Motion transfer function or response amplitude operators (RAO) are defined as the frequency
dependent steady state motion response amplitude divided by the wave elevation amplitude:
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[m/m]
[m/m] (3.5.14)
[rad/m]
Phase angles describing the phase shift between the wave elevation, at x=0, and the motion
response are defined as:
(3.5.15)
3.5.6 Solution of Equation of Motion
The floating structure dynamics can be considered as the case where the structure floating in
water is free to move in six directions when subjected to waves. The EOM will be of the form
same as for the SDOF spring mass system with damping except that instead of single direction,
the system is free to move in all six directions (Bhattacharyya, 1978). Thus the EOM is:
Where (M+A) is a 6x6 mass matrix, B is 6x6 damping matrix, C is a 6x6 stiffness matrix, and
F(t) is a 3x1 force vector. is acceleration vector, is velocity vector and is the displacement
vector for structure oscillatory motion.
Out of the 6 degrees of freedom, sway, roll, yaw are restrained in the present case. Thus only
i=1,3,5 (i=mode of motion) are the remaining degrees of freedom. Heave (i=3) is uncoupled
from surge and pitch. Surge (i=1) and pitch (i=5) are coupled. Thus, the EOM are equations 3.5.2
and 3.5.3.
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Following the same approach as for a SDOF spring-mass system, according to linear theory, the
responses of the vessel will be directly proportional to wave amplitude –‘LINEAR’- and occurs
at the same frequency as that of excitation, ω. Excitation is sinusoidal and so is the response
also.
We know
So
where is the phase shift between wave elevation and motion response.
Writing in complex form:
where is complex amplitude of vessel response in heave direction.
Also,
Substituting in EOM for heave
We get,
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Linear Transfer Function is ratio of output amplitude to input amplitude. So:
Thus,
Thus, and,
So the time series for heave response can be found out for various frequencies.
Similar procedure is to be followed for surge and pitch motion response. The final EOM become,
The above simultaneous linear equations are then solved for unknowns and .
3.5.7 Natural Periods
1. Heave Natural period
2. Pitch Natural Period
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CHAPTER 4
RESULTS & DISCUSSIONS
4.1 GENERAL
The outputs for three different trial runs for the program are presented and discussed in this
chapter. Predicted heave responses for all three trials are also plotted with respect to wave
period. A parametric study of heave response with diameter and draft as parameters is also done
in an attempt to optimize the response of the spar platform.
4.2 TRIAL 1
4.2.1 Inputs
Water Depth= 1000 m
Wave Height = 15 m
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Topside Weight = 50000 kN
4.2.2 Outputs
SPAR DATA
Diameter of spar (m) : 21.4
Thickness of spar (mm) : 71.2
Draft of spar (m) : 49.0
Free board of spar (m) : 10.5
Displacement (KN) : 1.815e+05
Dead weight of spar (kN) : 22475.02
Mass of spar (kg) : 2.312e+06
Ballast weight (kN) : 1.090e+05
Mass moment of inertia (kg/m2) : 5.349e+05
STIFFENER DETAILS
Spacing between stiffeners (m) : 4.30
Moment of inertia required (mm4) : 2.54e+10
Moment of inertia provided (m4) : 2.54e+10
Effective flange width (mm) : 1357.0
Outstand length of stiffener (mm) : 643.0
Thickness of the ring stiffener (mm) : 70.0
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Flange width of stiffener (mm) : 1283.0
Weight of stiffeners (kN) : 9653.0
STABILITY CHECK
Vertical centre of gravity of spar (m) : 20.6825
Vertical centre of buoyancy of spar (m) : 24.6680
Transverse BM (m) : 0.0153
Metacentre of the spar (m) : 24.6833
Metacentric height, GM (m) : 4.5643
Fig 4.2.1 Heave RAO plot for Trial 1
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4.3 TRIAL 2
4.2.1 Inputs
Water Depth= 300 m
Wave Height = 23 m
Topside Weight = 10000 kN
4.2.2 Outputs
SPAR DATA
Diameter of spar (m) : 12.0
Thickness of spar (mm) : 40.0
Draft of spar (m) : 40.0
Free board of spar (m) : 15.3
Displacement (kN) : 4.764e+04
Dead weight of spar (kN) : 6738.03
Mass of spar (kg) : 6.069e+05
Ballast weight (kN) : 3.090e+04
Mass moment of inertia (kg/m2) : 8.546e+04
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STIFFENER DETIALS
Spacing between stiffeners (m) : 3.0
Moment of inertia required (mm4) : 2.1e+09
Moment of inertia provided (mm4) : 2.1e+09
Effective flange width (mm) : 775.0
Outstand length of stiffener (mm) : 368.0
Thickness of the ring stiffener (mm) : 40.0
Flange width of stiffener (mm) : 453.0
Weight of stiffeners (kN) : 1727.58
STABILITY CHECK
Vertical centre of gravity of spar (m) : 15.8646
Vertical centre of bouyancy of spar (m) : 19.8628
Transverse BM (m) : 0.0062
Metacentre of the spar (m) : 19.8690
Metacentric height, GM (m) : 4.2325
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4.3.1 Heave RAO plot for Trial 2
4.4 TRIAL 3
4.4.1 Inputs
Water Depth= 500 m
Wave Height = 10 m
Topside Weight = 40000 kN
4.4.2 Outputs
SPAR DATA
Diameter of spar (m) : 16.0
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Thickness of spar (mm) : 64.0
Draft of spar (m) : 62.0
Free board of spar (m) : 7.50
Displacement (kN) : 1.275e+05
Dead weight of spar (kN) : 17506.0
Mass of spar (kg) : 1.624e+06
Ballast weight (kN) : 70000.0
Mass moment of inertia (kg/m2) : 5.506e+05
STIFFENER DETIALS
Spacing between stiffeners (m) : 3.1898
Moment of inertia required (mm4) : 1.13e+10
Moment of inertia provided (mm4) : 1.14e+10
Effective flange width (mm) : 1110.0
Outstand length of stiffener (mm) : 552.0
Thickness of the ring stiffener (mm) : 60.0
Flange width of stiffener (mm) : 752.0
Weight of stiffeners (kN) : 6493.3
STABILITY CHECK
Vertical centre of gravity of spar (m) : 27.07
Vertical centre of buoyancy of spar(m) : 31.13
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Transverse BM (m) : 0.0081
Metacentre of spar (m) : 31.1403
Metacentric height GM (m) : 4.3148
4.4.1 Heave RAO plot for Trial 3
4.4 DISCUSSIONS
The table 4.5.1 shows the results obtained after various trial runs for the following input data.
Water Depth= 500 m
Wave Height = 10 m
Topside Weight = 40000 kN
Table 4.5.1 Output for different trial runs
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Diameter(m) Draft(m) Heave RAO(m/m) Dead wt spar(KN) Wave Period(s)
15.9492 62.2644 4.975 17506.166 5.8298
16.1279 61.1333 4.986 17610.3452 5.7834
16.3375 60.0256 4.997 17779.4454 5.7381
16.5526 58.9157 5.01 17950.831 5.6925
16.7473 57.7804 5.023 18061.3342 5.645
16.9742 56.6667 5.038 18237.5735 5.598
17.2075 55.5509 5.055 18416.5486 5.5517
17.4477 54.4329 5.072 18598.4381 5.5045
17.695 53.3128 5.091 18783.4367 5.4569
17.9771 52.2107 5.111 19035.8789 5.4103
18.2402 51.0858 5.131 19227.9381 5.3618
18.5395 49.9778 5.154 19488.3131 5.3143
18.8481 48.8666 5.177 19753.1892 5.2664
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Fig 4.5.1 Heave RAO vs Diameter plot
Fig 4.5.2 Heave RAO vs Draft plot
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Fig 4.5.3 Dead Weight of spar vs Diameter plot
The data given in table 4.5.1 is represented gaphically in figures 4.5.1, 4.5.2, 4.5.3.
Figure 4.5.1 shows that heave RAO also increases as diameter increases.From the figure 4.5.3 it
is also evident that as diameter increases, dead weight of the spar also increases.So inorder to
achieve an optimised design of spar, it is better to select the minimum possible diameter.
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CHAPTER 5
CONCLUSION
A computer program which can be used to perform design of spar platform has been developed.
The program also determines the response amplitude operators (RAO) for the heave, surge and
pitch motions using simplified calculation approach. Thus, the program can be effectively used
to get an optimized design of a spar platform. The functionality of the program can be improved
by adding a module to automate the optimization part of the design process, which is presently
done manually.
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