NUMERICAL INVESTIGATION ON THE HYDRODYNAMIC PERFORMANCES OF A NEW SPAR CONCEPT

 
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        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. Student
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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 of
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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. Mooring
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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 are
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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 water
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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.
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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               1105.1
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     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.

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