NUMERICAL INVESTIGATION ON THE HYDRODYNAMIC PERFORMANCES OF A NEW SPAR CONCEPT
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
473
Ser.B, 2007,19(4):473-481
NUMERICAL INVESTIGATION ON THE HYDRODYNAMIC
PERFORMANCES OF A NEW SPAR CONCEPT*
ZHANG Fan, YANG Jian-min, LI Run-pei, CHEN Gang
State Key Laboratory of Ocean Engineering, Shanghai Jiaotong University, Shanghai 200030, China,
E-mail: jmyang@sjtu.edu.cn
(Received August 22, 2006; Revised September 28, 2006)
ABSTRACT: Recently, the spar platform concept develops Main feature of the classic spar is its
quickly in the offshore oil and gas exploitations, especially in deep-draft vertical cylinder hull, which presents
deep and ultra-deep water, owing to its benign motion excellent motion characteristics even in severe sea
performance, excellent stability and adaptation to wide range of states. However, in some sea area, where the
water depth. Many new spar concepts have been put forward
ambient deep current becomes a major factor, the
with the purpose of reducing fabrication difficulty and cost,
while meeting the requirements of exploitation in the meantime.
drag on the large cylindrical shape can be
Based on the aims mentioned above, a new spar concept was significant. In such a case, a truss spar is an
presented in this article and its hydrodynamics both in attractive alternative[5, 6]. The truss spar is also more
operating and survival conditions was studied by means of structurally efficient when substantial crude storage
numerical simulation. Basic model tests were also conducted to is not required. It consists of a top hard tank and a
calibrate the numerical approach. Following aspects are bottom soft tank separated by a truss mid-section.
highlighted: (1) new spar concept, (2) global performance of Horizontal steel plates are fitted across the truss
the spar concept and (3) mooring line analysis. bays to reduce heave motion by increasing both the
added mass and damping for the structure. In
KEY WORDS: spar platform, time-domain coupled analysis,
addition, it has a much lower drag area than the
hydrodynamic performances
classic spar mid-section so that the current and
associated mooring loads are reduced [7,8]. The cell
spar is a new design that has several physical
1. INTRODUCTION
characteristics that are different from those of the
Since the installation of Neptune production
classic and truss spars. Its upper portion is
spar platform in the Gulf Of Mexico (GOM) by
composed of six out cells surrounding a center cell
Kerr-McGee in 1996, spar technology has been
to provide the buoyancy, while the lower portion is
developed quickly in recent years[1,2]. As a deep sea
formed by extending three of the outer cells down
oil and gas exploitation facility, the spar platform
to the keel. This concept was put forward basically
has aroused broad attentions, due to its adaptation
in consideration of the reduction of fabrication
of wide range of water depth and benign motion
difficulty and cost, as the standard rolling technique
characteristics. From the first generation of classic
could be taken in.
spar, spar platform has evolved into the second
Based on the spar characteristics mentioned
generation of truss spar. A new configuration of
above, this article presents a new spar configuration
spar platform - the cell spar is presently used in
worked out by the State Key Laboratory of Ocean
Texas[3,4].
* Project supported by the Major Fundamental Research Program of Science and Technology Commission of Shanghai
Municipality (Grant No. 05DJ14001) and the National High Technology Research and Development Program of China (863 Program,
Grant No. 2006AA09A107).
Biography: ZHANG Fan (1981-),Male, Ph. D. Student474
Engineering (SKLOE) in Shanghai Jiaotong The cell-truss spar is moored in place by 9
University, intending to take advantage of both the chain-wire-chain formed mooing lines, separated
typical truss spar and cell spar. A nonlinear into 3 groups, as shown in Fig.2. Total vertical
time-domain dynamic coupled analysis program, pretension of the mooring system is approximately
named SESAM (developed by DNV software), is in 1.0×107 N.
application to the investigation of the global
performance and mooring factor of the new spar Table 1 Main particulars of cell-truss spar concept
concept. Basic experiment with a 1:100 scale model Summary of key figures In-place
is also conducted in the water basin of SKLOE to Height from keel to top (m) 170
calibrate the numerical approach.
Draft (m) 160
Free board (m) 10
2. NEW SPAR CONCEPT Diameter (m) 20
A variation of spar is designed as a concept for Length of hard tank (m) 85
the study without any commercial purpose. Features
Length of truss section (m) 80
of truss spar and cell spar are both taken into
account in the design of the new spar concept, Diameter of cells (m) 6.4
which is named as the cell-truss spar here, aiming Side length of heave plate (m) 10
to take advantage of the heave plate damping Displacement (t) 17903
feature of the truss spar to obtain satisfactory heave
Center of gravity above keel (m) 86
motion performance, while reducing manufacture
and installation difficulty by means of cell Center of buoyancy above keel (m) 107
concept[9,10]. Illustration of the cell-truss spar
concept is shown in Fig.1.
Fig.2 Mooring system of cell-truss spar
Fig.1 Illustration of cell-truss spar concept 3. HYDRODYNAMIC THEORY
It is a tough work to include a complete
The hard tank of the spar hull consists of 7 description of the numerical simulation method in
cylinders (cells) with the same diameter and length, the short space of this article. Compared to the
while the lower part is fitted with a truss section. traditional de-coupled approach, the coupling
Each bay of the truss is spanned by a horizontal effects due to the mooring and riser system will
hexagonal plate, as the hexagon shape results in typically tend to reduce the low frequency motion
large added mass without extending the edges of of the spar platforms. Some details may be found in
the plate outside the diameter of the hard tank and Ormberg et al. [11]. Briefly, in the coupled approach
lends itself to be supported efficiently on the truss mentioned here, the total loads (dynamics included)
horizontal. Fixed ballast is set at the bottom of the from the “slender body models” of mooring lines
hull in the soft tank to adjust the position of its and risers are transferred as a force into the “large
gravity center. There is a strake around the outside body” model of the floater. Irregular Wave
of hard tank to reduce Vortex-Induced-Vibration Frequency (WF) and Low Frequency (LF)
(VIV). The design water depth is 1500 m. Its main environmental loading is required to give an
particulars are shown in Table 1. adequate representation of the dynamic behavior of475
the coupled vessel/slender structures system. systems work as spring mechanisms where the
Dynamic equilibrium between the forces acting on displacement of the floater from a neutral
the floater and slender structure response is satisfied equilibrium position causes a restoring force to
at every time instant, and thus the assessment of the react to the applied loading. For the coupled
low frequency damping from the slender structure approach the finite element model of mooring lines
is not needed. consists of bar elements only, i.e., bending stiffness
All the system components are described in a and torsional stiffness are neglected. The mass
FEM-model. The governing dynamic equilibrium properties are modeled according to the reported
equation of the spatially discretized system is measures. Hydrodynamic forces are modeled by
expressed as means of the generalized Morison equation. The
numerical model includes the spring and the bare
R I ( r ,
r , t ) + R D ( r , r, t ) + R S ( r , t ) = R E ( r , r, t ) tendon and the bare riser body.
(1)
where R I , R D and R S represent the inertia,
damping and internal reaction force vectors
respectively, R E is the external load vector, r ,
r and r are the structural displacement, velocity
and acceleration vectors respectively.
The inertia force vector is expressed as
R I ( r ,
r , t ) = M ( r )
r (2)
where M is the system mass matrix that includes
structural mass, mass accounting for internal fluid Fig.3 Panel FEM of cell-truss spar
flow in pipes, and hydrodynamic mass.
The damping force vector is expressed as Coupled analysis model for the spar and
mooring system is shown in Fig. 4.
R D ( r , r, t ) = C ( r ) r (3)
where C is the system damping matrix that
includes contributions from internal structural
damping as well as hydrodynamic damping.
The internal reaction force vector R ( r , r, t )
E
is calculated based on the instantaneous state of
stress in the elements. The external load vector
accounts for the weight and buoyancy, forced
Fig.4 Coupled analysis model (Depth = 1500 m)
displacements, environmental forces and specific
forces.
5. ENVIRONMENT CONDITIONS
4 environment conditions are selected to carry
4. NUMERICAL SIMULATION
out the simulation, including: a storm condition
4.1 Hull panel
happening once in 100 years, and a operation
The hull panel is used for the calculation of
condition in GOM, and a wave extreme condition
3-D velocity potential, as shown in Fig.3. Linear
and a swell extreme condition in the West Africa.
and quadratic hydrodynamic coefficients are
Details are shown in Table 2. All sea states are
obtained from the first- and second-order analysis.
generated using the JONSWAP wave spectrum and
4.2 Mooring system modeling
NPD wind spectrum for 3 h simulation. Wave and
Mooring systems are compliant systems. They
wind directions are set to be heading (180°).
provide resistance to environmental loading by
Dynamic waves and wind in time domain are
deforming and activating reaction forces. Mooring476
generated using random selected seeds. prevailing wave frequency range and thus heave
motion is generally insignificant. This has been
proven in the GOM where the long periods prevent
6. RESULTS AND DISCUSSIONS any serious occurrence of heave resonance, and
The motion response of the spar platform, the thus induce very favorable heave response.
heave mode of which is of special interest, should However, in some other sea areas, such as in the
be adequately low to satisfy the installation of rigid West Africa, the spar platform may undergo large
risers with dry-heads[12]. The concept behind deep heave motions at resonance, up to 8-10 times of
draft floaters is their ability to reduce the first-order incident wave amplitude, as in such areas, long
heave excitation significantly. Typical natural swell condition may persist for a considerable
periods of the spars deployed in the GOM case are portion of the year.
60 s for pitch and 28 s for heave[13].
Figures 5-7 show both the numerical and
experimental results of transfer functions with
mooring lines for the surge, heave and pitch.
Predicted RAOs are in excellent agreement with
test measurements.
Fig. 7 Pitch transfer function with mooring lines
Spectral analysis results of motions and
mooring line tension (Line 3) are shown in Table 3,
where Hs is the significant value and Tz zero
crossing period. Basically, global motion responses
Fig. 5 Surge transfer function with mooring lines of the cell-truss spar platform are restrained in a
satisfactory region, that the surge amplitude should
be less 10% water depth, while heave and pitch
amplitude should be within the range of –3 m-3 m
and –10o-10o, respectively. On the other hand,
though the significant wave height represents the
energy contained in the waves, it may not have the
simple effect of linearity on motions and mooring
line tensions. From Table 3, it is known that the
minimum significant values always appear in the
operation condition in the GOM, inspiringly, which
seems to reveal that the wave period is a more
dominative factor in the relationship between
incident wave and platform response. This is
Fig. 6 Heave transfer function with mooring lines especially obvious in the heave motion.
In view of the interests on the heave motion,
For the cell-truss spar, the surge natural period Figs.8-11 show the power spectra of heave response
is above 100 s, and the heave and pitch natural in the 4 environment conditions. Model tests
periods are about 25 s and 31 s respectively. conducted in the 100 years storm in the GOM and
Calculation results show that the cell-truss spar has wave extremes in the West Africa conditions are
inherited the spar characteristics of long motion also presented. The predicted responses notably
natural periods, which is considered one of the great capture the motion features of model tests.
advantages of the spar concept[14]. In most To indicate the relationship between the
circumstances, this period is sufficiently outside the response and incident wave, wave spectrums are477
Table 2 Ocean environment conditions
Wave Wind
Environment conditions Significant Peak
γ Velocity (m/s)
wave height (m) Spectrum Period (s)
A 100 year storm in GOM 12.59 14.6 2 38.6
B Operation condition in GOM 3.96 9.0 2 38.6
C Wave extremes in West Africa 4.5 18.8 6 7.5
D Swell extremes in West Africa 1.7 25.0 6 7.1
Table 3 Spectral analysis results of motion and mooring line tension (Line 3) response
Surge Heave Pitch Line 3
Hs (m) Tz (s) Hs (m) Tz (s) Hs (o) Tz (s) Hs (kN) Tz (s)
A 15.0 39.4 1.32 29.3 5.17 31.9 345.3 17.2
B 2.65 20.5 0.016 12.9 1.33 25.9 50.6 6.1
C 7.71 56.7 2.52 39.1 3.32 54.0 195.5 33.1
D 3.75 72.9 2.92 49.1 3.1 86.2 147.7 46.2
plotted with imaginary lines in each figure as well. molecule. In most sea areas, such as the GOM, this
The largest heave motion occurs in the swell could be easily satisfied as the waves there only
extremes in the West Africa, as shown in Table 3, cause the motion of water molecule in a
though the significant wave height is the lowest comparatively thin surface layer. However, in some
among the 4 environment conditions. However, its long swell conditions, large wave length may
period is the closest one to the heave natural period, arouse the water molecule in quit deep water.
and Fig. 11 shows a notable coherence between the Instead of a relative motion, the molecule motion
excitation and response. Comparatively, waves in even transfers the wave energy directly to the heave
Fig. 9 barely arouse any heave response. plates, thus cause large amplitude of heave
resonance.
Fig.8 Heave spectrum in 100 years Storm in GOM
From a hydrodynamic point of view, the heave
plates entrap large amount of water to move with Fig.9 Heave spectrum in operation condition in GOM
them, resulting in the increase of added mass and
In the following discussions, the mean,
potential damping, while the precondition is the
standard deviation (Std) and extreme values of the
relative motion between the plates and water478
motion and mooring line tension response are which may indicate that, the resonant heave
concerned. Because there are resonant frequencies response in long-period swell condition needs
in the low frequency region, it is essential to filter adequate attention.
the responses to further explore the coupled effects To predict the mooring line tensions, total
in different frequency regions as shown in Table standard deviation is no longer than an adequate
4[15]. value. Complete time-domain simulation is an
essential process to obtain some important data,
such as extreme values, which is valuable in the
structural verification and other post-analysis.
Fig.10 Heave spectrum in Wave Extremes in West Africa
Fig.12 Statistical analysis of surge
Fig.11 Heave spectrum in Swell Extremes in West Africa
Fig.13 Statistical analysis of heave
Table 4 Frequency region
Frequency ω(rad/s) T (s)
Low Frequency (LF) ≤0.2 ≥31.4
Wave Frequency (WF) 0.2-1.5 4.2-31.4
The results of statistical analysis for cell-truss
spar motions and mooring line tensions are shown
in Tables 5-8, in which the units are m and rad for
motions and kN for tensions.
As mentioned above, for the spar platforms,
natural periods of horizontal motions are designed Fig.14 Statistical analysis of pitch
far from the wave frequency in order to reduce
first-order wave excitation, and thus the To indicate the effect of wave height and
second-order wave becomes more dominant. This is period on the motions and mooring ling tensions,
especially obvious in the surge and pitch motion, as the results of statistical analysis are plotted as bar
the LF Std in always bigger than the WF Std. Heave chart maps in Figs.12-15, in which Abs Max stands
motions seems to behave more like the WF motion, for the absolute maximum values.479
Table 5 Statistical analysis of spar motions and line tensions in 100 years in GOM
Extreme
Mean LF Std WF Std Total Std
Max Min
Surge -12.32 3.036 2.260 3.784 2.305 -27.459
Heave 0.377 0.029 0.329 0.330 1.651 -0.777
Pitch -0.434 1.061 0.772 1.312 4.048 -5.009
Line 3 1274.0 28.7 81.5 86.4 1731.2 869.6
Line 8 1074.2 24.8 70.8 75.0 1660.1 729.8
Table 6 Statistical analysis of spar motions and line tensions in operation condition in GOM
Extreme
Mean LF Std WF Std Total Std
Max Min
Surge -1.237 0.559 0.375 0.673 1.086 -3.749
Heave 0.434 0.001 0.004 0.004 0.417 0.447
Pitch -0.047 0.306 0.150 0.340 1.000 -1.057
Line 3 1188.2 3.2 13.0 13.4 1237.0 1132.7
Line 8 1167.1 5.2 21.3 22.0 1259.2 1187.0
Table 7 Statistical analysis of spar motions and line tensions in wave extremes in West Africa
Extreme
Mean LF Std WF Std Total Std
Max Min
Surge -0.493 1.502 1.229 1.941 11.489 -19.653
Heave 0.431 0.021 0.629 0.630 2.327 -1.509
Pitch -0.021 0.724 0.433 0.843 3.147 -3.077
Line 3 1184.3 12.4 47.3 48.9 1507.6 982.0
Line 8 1175.6 15.1 37.3 40.3 1377.8 926.3
Table 8 Statistical analysis of spar motions and line tensions in swell extremes in West Africa
Extreme
Mean LF Std WF Std Total Std
Max Min
Surge -0.336 0.784 0.527 0.946 2.797 -3.270
Heave 0.433 0.071 0.727 0.731 2.345 -1.532
Pitch -0.017 0.747 0.214 0.778 2.050 -2.240
Line 3 1182.8 4.3 36.6 36.9 1330.0 1046.1
Line 8 1176.7 4.5 21.4 21.9 1259.3 1105.1480
For surge and pitch motions, and line tension, frequency motions and tensions, as in many
response values in Conditions A and C is larger situations, this kind of responses have become the
than those in Conditions B and D, which shows most significant factors. For the horizontal motions,
coherence to the wave heights in Table 2. However, low frequency motion usually present a
by investigating the differential values, it may be second-order drift motion, while in vertical
concluded that, the response differences are not direction, it is often aroused by the resonance
only the representation of wave height variation. As between heave motion and long swell.
for surge motion, Abs Max value in Condition C is (3) Wave height and period both play
71.6% of that in Condition A, while the wave important roles in affecting the motion responses
significant height ratio of the two conditions is just and mooring line tensions. However, the former
35.7%. seems more influential to the horizontal motion,
while the latter to the vertical motion.
(4) Complete time-domain analysis is a
necessary method in the design process and
response prediction of spars, while the lower
frequency responses occupy a considerable part,
and traditional spectrum analysis alone may not
adequately handle such problems.
REFERENCES
[1] ZHANG Fan, YANG Jian-min, LI Run-pei et al.
Experimental investigation on hydrodynamic behavior
Fig.15 Statistical analysis of tension (Line 3)
of the geometric spar platform[J]. China Ocean
Engineering, 2006, 20(2): 213-224.
Surge response in Condition C is large than [2] AGARWAL A. K. and JAIN A. K. Dynamic behavior
that in Condition D, agreeing with the wave height, of offshore spar platforms under regular sea waves[J].
which reveals that, the significant wave height Ocean Engineering, 2003, 30: 487-516.
[3] FINN L. D., MAHER J. V. and GUPTA H. The cell
plays a remarkable role among the factors affecting spar and vortex induced vibrations[A]. 2003 Offshore
the horizontal motion. For the pitch motion and line Technology Conference[C]. Texas, USA, OTC
tension, the wave period becomes more effective, as 15244,2003.
shown in Figs.14 and 15. [4] LIM S. J., RHO J. B. and CHOI H. S. An experimental
study on motion characteristics of cell spar platform[C].
The results of heave motion exhibit a little Proceedings of the Fifteenth International Offshore
difference. Though the significant wave height in and Polar Engineering Conference. Seoul, Korea,
Condition D is only 13.5% of that in condition A, 2005, 233-237.
heave Abs Max in D is even larger than that in A. [5] DATTA I., PRISLIN I., HALKYARD J. E. et al.
In this situation, the wave period has the priority in Comparison of truss spar model test results with
numerical predictions[C]. 18th International
the design process and performance prediction of Conference on Offshore Mechanics and Arctic
spar platforms. Engineering. Newfoundland, Canada,
OMAE99/OFT-4231, 1999.
[6] WANG J., BERG S., LUO Y. H. et al. Structural design
of the truss spar – an overview[C]. Proceedings of the
7. CONCLUSIONS Eleventh International Offshore and Polar
A new cell-truss spar concept has been put Engineering Conference. Stavanger, Norway, 2001,
forward, and its global performance has been 354-361.
studied by nonlinear time-domain dynamic coupled [7] DOWNIE M. J., GRAHAM J. M. R., HALL C. et al. An
analysis. The relationship between incident wave experimental investigation of motion control devices for
truss spars[J]. Marine Structures, 2000, 13: 75-90.
and responses of motion and mooring line tensions [8] LU R. R., WANG J. J. and ERDAL E. Time domain
has been investigated as well. The following strength and fatigue analysis of truss spar heave plate[C].
conclusions have been reached: Proceedings of the Thirteenth International Offshore
(1) Basically, the new cell-truss spar concept and Polar Engineering Conference. Hawaii, USA,
2003, 272-279.
has inherited the advantages of its former [9] GROVE M. A., CONCEIÇÄO C. A. L. and
generations of spars. Its motion responses could be SCHACHTER R. D. A Concept design and
availably restrained in a satisfactory region. hydrodynamic behavior of a spar platform[C]. 22nd
(2) Enough attention should be paid to the low International Conference on Offshore Mechanics and481
Arctic Engineering.Cancun,Mexico,OMAE2003-37166, Janeiro, RJ, Brazil, OMAE2001/OFT-1352, 2001.
2003. [13] HONG Y. P., LEE D. Y., CHOI Y. H. et al. An
[10] ZHANG Fan, YANG Jian-min, LI Run-pei et al. Effects experimental study on the extreme motion responses of a
of heave plate on the hydrodynamic behaviors of cell SPAR Platform in the Heave Resonant Waves[C].
spar platform[C]. 25th International Conference on Proceedings of the Fifteenth International Offshore
Offshore Mechanics and Arctic Engineering. and Polar Engineering Conference. Seoul, Korea,
Hamburg, Germany, OMAE2006-92199, 2006. 2005, 225-232.
[11] ORMBERG H., FYLLING I. J., LARSEN K. et al. [14] THIAGARAJAN K. P., DATTA I., RAN A. Z. et al.
Coupled analysis of vessel motion and mooring and riser Influence of heave plate geometry on the heave response
system dynamics[C]. 16th International conference on of classic spars[C]. 21st International Conference on
Offshore Mechanics and Arctic Engineering. Offshore Mechanics and Arctic Engineering. Oslo,
Yokohama, Japan, 1997, 1-A: 91-100. Norway, OMAE2002-28350, 2002.
[12] TAO L., LIM K. Y. and THIAGARAJAN K. Heave [15] LIU T., CHEN X., WU J. F. et al. Global performance
motion characteristics of spar platform with alternative and mooring analysis of a truss spar[C]. Proceedings of
hall shapes[C]. 20th International Conference on the Thirteenth International Offshore and Polar
Offshore Mechanics and Arctic Engineering. Rio de Engineering Conference. Hawaii, USA, 2003, 256-263.You can also read
