Note: Descriptions are shown in the official language in which they were submitted.
i ~1()7S(~9~
METHOD AND APPARATUS FOR STABILIZATION
OF A FLOATI~G SEMI-SU~MERSIBLE STRUCTURE
Semi-submersible floating platforms are required in
various typeq of offshore operations, including scientific
surveys and oil and gas drilling and production. In use a
stable platform is desired. However, wave motion produces sub-
~tantial unde-~irable oscillatory platform displacement including
heave (vertical linear displacement), roll (angular displacement
about a longitudinal axis), and pitch (angular displacement about
a transverse axis). In heavy seas, it is particularly desirable
to reduce hea~e in order to achieve platform stability.
Since a semi-submersible floating platform is a re~onant
system, undeæirable oscillatory platform displacement is greatly
i increased in response to seas having wave periods substantially
equal to the resonant period of the platform (such wave period~
often being referred to herein as resonant wave periods). Thus,
heave displacement at resonant wave periods may be several times
~ greater than the maximum heave displacement for comparable wave
i height at other non-resonant wave periods.
Methods and apparatus suggested in the past for minimizing
undesirable o~cillatory motion of a floating platform typically
- 20 require exertion of very large control forces of a type not
economically generated to counteract the very large disturbing
forces exerted on the platform by wave motion. Much smaller and
more economically generated control forces would be required in
the case of a semi-submersible platform, which is also resonant
r at longer, less commonly occurring wave periods. However, a
semi-submersible platform may still be subject to seriou~ heave
displacement at shorter, commonly occurring non-resonant wave
28 periods. Moreover, design considerations for decreasing this
'1 ~
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heave displacement of those shorter non-resonant wave periods
also tend to make the platform resonant at shorter, more common-
ly occurring wave periods.
In accordance with one aspect of this invention there
is provided a semi-submersible floating structure for use in a
body of water, comprising a deck; column means attached to the
deck and disposed for partial submersion in the water; pontoon
means attached to the column means and disposed for total
` submersion in the water; the column means and the pontoon means
10 supporting the deck above the surface of the water; and damp-
ing control means, including one or more control force tanks
mounted outboard of the column means and in communication with
the water, for exerting on the structure a damping control force
that is a function of the rate of change of at least one dis-
placement component of undesirable motion of the structure
caused by wave motion of the water.
In accordance with another aspect of this invention
there is provided a system for stabilizing a vessel having
` floatation means, said system comprising one or more tanks,
F 20 having open access to the water, mounted on the outboard
surfaces of the floatation means at a point where the ambient
surface of the water approximately intersects the floatation
means; said tanks being selectively supplied with air in such
magnitudes and phases as are required to develop control
forces for stabilizing the motion of the vessel in varying
water conditions; said control forces being developed solely
by the selective supply of air to said tanks.
In accordance with another aspect of this invention
there is provided a method of applying control forces for
30 stabilizing a vessel having a floatation member, said method
comprising the step of applying selectively variable control
forces to the outboard surface of the floatation member at a
~ -2-
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point ~here said floatation ~lember approximately intersects
the ambient surface of the water.
By way of added explanation, in accordance with princi-
ples of the present invention, in certain of its aspects, methods
and apparatus are disclosed for decreasing the magnitude of the
undesirable displacement of a floating structure such as a semi-
submersible platform by applying to the platform a damping con-
trol force that is a function of the vertical velocity (i.e., the
rate of change of the vertical linear displacement) of the plat-
form. This velocity damping technique permits the displacement
magnitude of the semi-submersible platform to be greatly decreased
- at resonant wave periods by the application of a relatively small
~ and economically generated damping control force. Accordingly,
- it also permits design of a semi-submersible platform having sub-
stantially decreased displacement magnitude at shorter non-
resonant wave periods even though the platform may then be reson-
ant at shorter wave periods. Thus, in accordance with further
principles of the present invention, methods and apparatus are
- also disclosed for substantially reducing the displacement magni-
tude`of the platform at shorter non-resonant wave periods.
~- Figure 1 is a perspective view of a conventional semi-
submersible platform of the type presently used in offshore drill-
ing operations.
Figure 2 is a graph illustrating the heave response of a
conventional semi-submersible platform, such as ~at shown in
Figure 1, as a function of wave period and the heave response of
an improved semi-submersible platform embodying principles of the
present invention, such as that shown in Figure 15, as a function
of wave period.
Figure 3 is a diagrammatic representation of the forces
exerted by waves on a pontoon and associated columns of a
- 2a -
` ~075092
conventional semi-~ubmersible platform, such as that shown in
Figure l.
Figure 4 is a graph illustrating the heave response of
a conventional semi-submersible platform, such as that shown in
Figure l, as a function of wave period both with and without
velocity damping.
Figure 5 shows an arrangement for hydrostatic velocity
damping a semi-submersible platform in accordance with one
embodiment of the present invention.
Figure 6 i~ a block diagram of a closed loop control
system for the arrangement of Figure 5.
Figure 7 shows an exempl~ry form of the vertical velocity
sensor of Figure 6.
Figure 8 shows an alternative arrangement for hydrostatic
velocity damping a semi-submersible platform in accordance with
another embodiment of the present invention.
: Figure 9 is a block diagram of a closed loop control
~ystem for the arrangement of Figure 8.
Figure lO ~hows a further arrangement for hydrostatic
velocity damping a semi-submersible platform in accordance with
another embodiment of the present invention.
Figures llA and llB are croæs-sectional diagrams illus-
trating the principles of operation of a control force tank for
hydrostatic velocity damping a semi-submersible platform in
accordance with another embodiment of the present invention.
Figure 12 is a partially cutaway top view of a portion
of a semi-submersible platform equipped with the control force
tank of Figures llA and llB.
Figure 13 is a perspective view of a semi-submersible
platform equipped with four control force tanks of the type shown
in Figures llA and llB.
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Figure 14 is a function diagram of the control force tank
of Figures llA and llB in a dynamic motion suppression control
system.
Figure 15 is a perspective view of an improved semi-
submersible platform in accordance with another embodiment of the
present invention.
Figure 16 is a graph illustrating heave forces on the
- improved semi-submersible platform of Figure 15.
Figures 17 and 18 are diagrammatic end views of improved
semi-submersible platforms in accordance with other embodiments
of the present invention.
Figures l9A and 19B are diagrammatic top and side view ,
respectively, of an improved semi-submersible platform in accord-
ance with still another embodiment of the present invention.
As shown in Figure 1, a semi-submersible platform of the
type presently uQed for offshore oil drilling operations comprises
a deck 13 supported above the water surface 19 by four hollow
vertically-extending columns 15 and two horizontally-extending
pontoons 17, each of which interconnects two of the columns.
Although only four columns are shown, additional columns may be --
interposed between columns 15 along each pontoon 17. The pon-
toons 17 and portions of the columns 15 are submerged below the
water surface 19. Iypically deck 13 is about 200 feet square
and each of the colwmns 15 and pontoons 17 has a cross-sectional
area of abou' 800 square feet. Pontoons 17 extend beyond the
columns 15 a distance E that is typically less than about 40 feet.
Operational draft of the platform is 50 to 70 feet. In the
presence of disturbing waves, oscillatory forces act on columns
15 and pontoons 17 to cause platform heave. The heave amplitude
is a function of wave period (i.e., the time between wave crests
as measured from a stationary point).
-- 4 --
~ ~75092
Figure 2 illustrates a typical heave response curve 21 for
the platform of Figure 1. Curve 21 is approximately the same for
beam and head-on waves. The vertical axis represents the absolute
value of the ratio of heave amplitude to wave amplitude measured
at a given wave amplitude (such as 15 feet), while the horizontal
axis represents wave period in seconds. Thuc, for a given wave
period, the heave amplitude is equal to the corresponding value
on curve 21 multiplied by the wave amplitude. curve 21 is the
resultant of two principal components corrected for the drag
effects of platform geometry. These two components are the
response to the oscillatory forces exerted by the waves on the
bottoms of the columns and the response to the oscillatory forces
acting on the pontoons.
For certain wave periods the column force is opposite to
the pontoon force. These forces are illustrated in FigUre 3
where a side view of a semi-submersible platform such as that
shown in Figure 1 is diagrammatically represented in the presence
of large waves 26. As a wave crest 32 passes, the dynamic pres-
sure created by the wave decreases with depth. For a pontoon of
a given vertical dimension D there will be a dynamic pressure
differential Fp acting downwardly on the pontoon in opposition
to the upward forces Fc on columns lS.
Curve 21 indicates that platform heave varies substantially
as a function of wave period. In particular, maximum heave occurs
at platform resonance designated by region R. In the resonance
region, upward forces Fc acting on the column bottoms dominate.
Minimum heave occurs at points B and C. At point C the upward
column forces Fc and downward pontoon forces Fp cancel, although
29 the net force is not zero because of the presence of small platform
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.
drag forces. At point B the column and pontoon forces Fc and Fp
also cancel and tend toward zero net force. A smaller heave maxi-
mum occurs at region P, where the downward forces Fp acting on the
pontoons dominate. The magnitude of the heave maximum at region P
is about 0.4 of the wave amplitude, while the magnitude of the
heave maximum at region R is about 2.0 times as great as
the wave amplitude. Thus, the platform heave may be 4 feet in
seas where the wave period is about 12 seconds and the wave height
is 10 feet, but may be as much as 20 feet in seas where the wave
height is the same and the wave period is about 18 seconds.
Serious heave problems are caused by the heave maximum at
region P because it occurs at more commonly encountered wave
periods. However, design considerations for reducing the heave
maximum at region P tend to move the larger heave maximum at
region R to shorter wave periods of less than 18 seconds. This
has heretofore been unde~irable since wave periods of less than
18 seconds are more likely to occur, and the platform is there-
fore more likely to be subject to waves at its then lowered
resonant period. However, by applying to the platform an oscil-
latory damping force that is a function of and in phase oppositionto the heave velocity of the platform in accordance with the prin-
ciples of the present invention, resonant oscillatory platform
heave may be effectively and economically reduced to acceptable
levels by the exertion of a relatively small force. The platform
may then also be redesigned in accordance with the principles of
the present invention to reduce non-resonant oscillatory heave to
acceptable levels.
The effects of velocity damping and the significance of
-` applying a force that is a function of and in phase opposition to
velocity, as distinguished, for example, from a force that is a
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~075092
function of displacement or acceleration, may be understood by
considering the following basic equation of oscillatory motion
of a damped resonant system:
mx + c~ + kx = PO sin ~t Eq. (1)
where x, x, and ~ are displacement, velocity and acceleration,
respectively, k is the coefficient of restitution (or spring
constant), c is the coefficient of damping, m is the system mass,
PO is the peak amplitude of the exciting force, ~ is the frequency
of variation of the disturbing force, and t is time. After
dividing through by m Equation (1) may be written
~ + px + rx s Fo sin ~t Eq. (2)
where p is equal to c/m, r is equal to k/m and Fo is equal to
PO/m. From Equation (2) it may be shown that the system displace-
ment may be defined as
Fo sin (~t-~)
x ~(r ~2) + p2 ~2~1/2 Eq. (3)
where iS the phase angle. The system velocity may be expressed
as
- Fo ~ cos (~t - )
; t(r-~2)2 + p2 2~1/2 Eq. (4)
From Equation (2) the damping force may be defined as
p~ cos (~t- )
px = F -~ Eq. (5)
At resonance r-w is equal to zero and the phase angle
is 90. Thus, Equation (5) may be rewritten as
:; ~
px = Fo 2P 2 1/2 cos (~t-~/2) = Fo sin ~t Eq. (6)
Equation (6) states that the damping force px is equal
to the exciting force Fo sin ~t at resonance. In other words,
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:107509Z
..
all other forces acting on the platform, the inertia due to mass
and acceleration, and the spring force due to the spring constant
and its displacement, have no net effect upon the platform (being
.~.
mutually equal and opposite at resonance). Accordingly, if a
damping force is provided as a function of and in phase opposition
to the platform velocity, it will effectively oppose the wave-pro-
duced disturbing force. It can be seen from Equation (5) that at
other frequencies the amplitude of the damping force px will not
be Fo sin ~t but will be smaller because the term (r-~2)2 is not
then zero and is always positive. Thus, the damping force has a
ma~imum amplitude exactly where it i8 most beneficial, namely at
resonance, and a lesser amplitude at other frequencies.
From inspection of Equation (6) it can be seen that if a
sinusoidal force proportional to the velocity of platform heave
at resonance is generated, it will be exactly equal to the sinu-
~oidal, wave-produced disturbing force acting on the platform.
- Further, the damping force px (the product of the system velocity
and the damping coefficient) has a constant peak value at reso-
, . .
, nance regardless of the damping coefficient. Thus, if one in-
creases the damping coefficient p, the velocity x concomitantly --
decreases and vice versa so that the product of the two remains
constant. In the systems described herein, the fixed peak value
of the damping force at resonance will exist as long as the mag-
~ nitude of the force required to be exerted in opposition to the
disturbing force remains within the limits of the forces avail-
able from the force generating system.
Figure 4 illustrates an experimentally obtained heave
response curve 50 of a scale model of the semi-submersible plat-
form of the type shown in Figure 1 with very small amounts of
~ 30 damping such as is achieved by virtue of platform drag and an
i,~
-- 8 --
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.. - , ,
" 1075092
experimentally obtained heave response curve 52 of the same scale
model with velocity proportional damping applied thereto. The
vertical axis represents the absolute value of heave amplitude
for unit wave amplitude (taken to be fifteen feet for purposes
of the experiment), and the horizontal axis represents wave period
in seconds. Curve 52 is based on 50% critical damping. Critical
- damping is the amount of damping that causes a resonant system,
when displaced from a rest position, to tend to return to the rest
position, approaching such position as an asymptote and just
barely avoiding an opposite sense displacement. Mathematically
a damped harmonic system such as described in Equation (1) is
critically damped if c2 = 4 mk. From Figure 4 it may be seen
that by employing velocity proportional damping the maximum plat-
form heave amplitude at the 18-second resonant wave period is
significantly reduced from more than twice the wave amplitude to
about 0.1 of the wave amplitude. Moreover, the sm2ller maximum
platform heave amplitude at the 12-13 seconds non-resonant wave
period is reduced from about 0.4 of the wave amplitude to less
than 0.25 of the wave amplitude.
In Figure 4, damping forces in tons per column of a four
column platform such as that shown in Figure 1 and for a wave
height of 15 feet are shown below the horizontal axis for certain
; wave periods. It may be seen that damping forces of quite readily
available and economically feasible magnitude may be applied to
achieve the considerably diminished heave response curve 52. At
the 18 second wave period of platform resonance a peak damping
force of about 24 tons per column is employed to achieve the
illustrated decrease in heave amplitude. This 24 ton peak damp-
- ing force will vary sinusoidally with the sinusoidal variation
of heave velocity and wave force during a wave period of 18 seconds.
1075092
At the 12-13 seconds non-resonant wave period a peak damping
force of about 86 tons per column i5 employed to achieve the
illustrated decrease in heave amplitude. It may be noted that
such forces are quite feasible since in a platform of the type
shown in Figure 1 with an increased column diameter o~ 40 feet,
a 50 ton force may be exerted by a change in actual water level
within the column o~ approximately 1.5 feet from a mean water
level.
Referring to Figure 5, there is shown an active hydro-
10 static system for velocity damping a semi-submersible platform
such as that shown in Figure 1. This system employs air pressure
for moving sea water so as to maintain the actual water level
above or below a mean water level by an amount that is always
proportional to the vertical velocity of the platform. It is
located in one of the columns 15 which in this case is open at
its bottom. Preferably an identical system is provided in each
column of the platform. Lower and upper transverse bulkheads 56
and 58, water level 64, and a vertical bulkhead 60 divide a lower
portion of column 15 into three chambers 62, 66, and 68 containing
20 air (or some other gas). An air pump 70, preferably a Roots type
(a high capacity low pressure blower), has an intake conduit 72
that communicates with chamber 62 via a valve 78 and a conduit 74
and with chamber 68 via a conduit 76. Pump 70 also has an exhaust
conduit 80 that communicates with chamber 62 via a valve 86 and a
conduit 82 and with chamiber 66 via a conduit 84. Water level in
the ballast tank formed by the open bottora of column 15 is con-
trolled by air pressure in chamber 62. A ballast water level
sensor 88 in the lower end of column 15 furnishes a ballast signal
indicating the amount of ballast water aboard the platform and,
30 hence, the magnitude of the anti-heave force exerted.
-- 10 --
1075092
In the illustrated arrangement air is always pumped in the
same direction, normally maintaining a relatively higher pres~ure
in chamber 66 and a relatively lower pressure in chamber 68. If
valve 86 is opened, high pressure air from chamber 66 enters cham-
ber 62 and forces water out of the ballast tank thereby increasing
the vertical upward force on the platform. If valve 78 is opened,
air from chamber 62 enters the lower pressure chamber 68 thereby
drawing water into the ballast tank and providing a component of
downward vertical force. If, for example, the water level 64 is
10 at a depth of about 70 feet and the pressure in chamber 62 is about
45 pounds per square inch (about the pressure of the ambient water),
chamber 66 will then have a pressure of about 55 pounds per square
inch, and chamber 68 will have a pressure of about 35 pounds per
square inch. This arrangement helps to decrease the work required
from pump 70, which is caused to run constantly at a fixed speed
and in but one direction to maintain this pressure differential
in chambers 66 and 68. Although pump 70 is shown located at a
position above the water surface 71, it may be located at other
places such as in the wall 60 between chambers 66 and 68 or, for
20 easy access, on the platform deck. It is preferably run at a
fairly constant power level determined by sea conditions, running
at higher levels in higher seas and at lower levels in lower seas.
A closed loop control system, such as that illustrated in
Figure 6, is employed to opPrate valves 78 and 86. This system
includes a vertical velocity sensor 90 for sensing the vertical
heave velocity of the platform and generating a signal proportional
thereto. Vertical velocity sensor 90 may comprise any one of a
number of conventional types such as an acceleration sensing
device the output of which is integrated to provide a velocity
30 signal or a vertical displacement sensing device the output of
-- 11 --
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which is differentiated to provide a velocity signal. Such a
vertical displacement sensing device, as illustrated in Figure 7,
comprises a cable 92 that is fixed at one end to a weight 94 on
the sea bottom, that extends upwardly over a sheave 96 on the
platform deck 13, and that is fixed at its other end to the plat-
form deck 80 that rotation of the sheave shaft is directly pro-
portional to vertical heave displacement of the platform.
Rotation of the sheave shaft drives the arm of a potentiometer 98
to provide on a lead 100 an output signal that is directly pro-
portional to vertical platform displacement. This output signalis differentiated by a differentiating circuit 102 to provide on
an output lead 104 a velocity signal that i directly proportional
to the first derivative of platform displacement (i.e., platform
velocity) and that has a sense or polarity determined by the
direction (up or down) of the platform displacement.
-; As shown in Figure 6, the velocity signal on lead 104 is
fed to a gain controlling circuit 106 which provides one input
to a difference circuit 108. A ballast signal on a lead 110 from
ballast water level sensor 88 of Figure 5 provides the other input
to difference circuit 108. This ballast signal is proportional to
the amount the actual water level is above or below a mean water
level (or to the volume of the water above or below the mean
water level) for a ballast tank of constant cross section and has
a ~ense or polarity determined by whether the actual water level
is above or below the mean water level. Difference circuit 108
- provides an output difference signal that is proportional to the
algebraic difference between the two inputs thereto. This dif-
ference signal is amplified by an amplifier 112 and fed to a
sense circuit 114 which provides an output signal on lead 116 or
118 as determined by the sense or polarity of the difference
- 12 -
~07509~
signal from difference circuit 108. The output signal on lead
116 or 118 is fed to valve controller 120 or 122, respectively,
for controlling valve 78 or 86, respectively, so that water level
in the ballast tank is changed in a sense to diminish the dif-
ference signal from difference circuit 108. The output signals
fed to valve controllers 120 and 122 need not be proportional to
the difference signal from difference circuit 108 since the
control circuit may operate in a conventional on/off servo loop
fashion.
; 10 Assuming that at a given instant platform heave motion
is upward, a damping force of the appropriate direction is pro-
duced if the actual water level in the ballast tank is higher
than the mean water level (positive) by an amount that is pro-
portional (for linear damping) to the upward (positive) platform
velocity. If the actual water level is not high enough, the
positive platform velocity signal is greater than the positive
ballast signal and a positive difference signal is produced by
difference circuit 108 causing sense circuit 114 to operate valve
controller 120. This opens valve 78 to lower the pressure in
chamber 62 and draw more water into the ballast tank until the
amount of water therein above the mean water level is proportional
to the sensed platform velocity whereupon the difference signal
become-~ zero and valve 78 is closed. If the actual water level
in the ballast tank is too high and the platform velocity is
positive, the difference signal is then negative (the larger
positive ballast signal is algebraically subtracted from the
smaller positive velocity signal) causing sense circuit 114 to
operate valve controller 122. This opens valve 86 to increase
the pressure in chamber 62 and drive more water from the ballast
tank until the difference signal again becomes zero. The control
- 13 -
" 1075092
system operates similarly for downward platform heave motion
` where the water level in the ballast tank is lower than the mean
water level.
In Figure 8 there is shown an alternative hydrostatic
stabilization system for use in one or more columns 15 of a semi-
submersible platform such as that shown in Figure 1 to exert an
anti-heave force proportional to the sensed vertical heave velocity
of the platform. Each column 15 in which the system is placed is
again open at its bottom to the ambient sea water and provided
with upper and lower transverse bulkheads 128 and 130 which, to-
gether with water level 136, divide the lower portion of column
15 into chambers 132 and 134. A,ballast water level sensor 138
; mounted within chamber 134 operates in the same manner as ballast
water level sensor 88 of Figure 5. An air pump 140, suitably
mounted in or near column 15 and preferably above the ambient
water level 142, has a first duct 144 that communicates with
chamber 132 and a second duct 146 that communicates with chamber
134. In this system the average air pressure is the same in
chambers 132 and 134 and is equal to the ambient pressure of the
20 Qea water outside of column 15 at the same depth as the mean water
level in chamber 134. This minimizes the work required of pump
140, which is capable of pumping air in either direction. Pump
140 is employed to raise or lower the air pressure in chamber 134
and accordingly to lower or raise the water level therein to ob-
tain the required damping force.
As shown in Figure 9, the control system for controlling
pump 140 comprises a vertical velocity sensor formed of a vertical
heave sensor 150 for providing an output signal (with a magnitude
proportional to displacement and with a sense or polarity deter-
30 mined by the direction of displacement) and of a differentiator152 for differentiating that output signal to feed a signal
-- 14 --
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proportional to heave velocity to a gain controller 154. The
effective damping coefficient of the system is readily varied by
changing the gain of gain controller 154. A servo controller,
which functions as a difference circuit 156 receiving one input
from gain controller 154 and another input from the balla~t water
level sensor 138, operates a servo motor 158 in one direction or
another depending upon the sense of the algebraic difference be-
tween those two input signals. Servo motor 158 drives pump 140
in one direction or another so as to change the water level 136
as required to maintain the anti-heave force exerted by the
ballast water proportional to the sensed heave velocity of the
platform in substantially the sa~e manner as described in con-
nection with Figure 6.
Although the systems described herein produce anti-heave
damping forces that are a linear function of (i.e., in phase
opposition and proportional to) the heave velocity of the plat-
form (Newtonian damping), anti-heave damping forces that are a ~--
non-linear function of heave velocity may also be employed to
~ advantage. For example, the anti-heave damping force may be,2 20 made proportional to the square of the sensed velocity, in which
case relatively small damping is provided at low velocities and
exceedingly large damping is provided at higher velocities. The
anti-heave damping force may also be made directly proportional
to velocity for predetermined magnitudes of velocity above or
below which the damping force generator becomes saturated (i.e.,
~ is unable to or will not generate any further increased damping
-~ force).
Referring to Figure 10, there is shown an active hydro-
static platform stabilization system that is preferred in many
situations. This system employs a ballast tank 250 mounted in a
column 15 substantially at the level 252 of the water in which
.
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1075092
the platform is floating and provided with a water filled con-
duit 254 extending to the bottom of the column and opening to
the ambient water. A reversible pump 256 is connected at one
side to ambient atmosphere via a conduit 258 and is connected
at the other side to ballast tank 250 via a conduit 2 60. Thus,
in this arrangement no separate pressurized air chamber is
needed to decrease the load on the pump. Pump 256 may be con-
trolled by a control system identical to that shown in Figure 9.
As previously described, pump 256 is controlled in response to
10 the difference between the sensed platform heave velocity and the
volume of water in ballast tank 250 relative to a mean volume as
detected by a ballast sensor 262
Referring to Figures llA and llB, there is shown still
another active hydrostatic platform stabilization system that
can be added externally to an existing platform such as that shown
in Figure 1 to achieve advantages of the present invention without
' altering the internal structure of the platform and without
changing the passive response characteristics of the platform,
that can be used with lower cost air pumps, and that does not
20 require the use of accumulators for storage of pressurized air.
This sy~tem comprises a tank 10 open at its bottom to the water
and mounted on a column of the platform at a location where the
ambient water level approximately bisects the side of the tank as
indicated at 11. A blower 12 comprising, for example, a centri-
fugal or some other low-pressure, high-volume blower provides air
pressure to a chamber 18 of the tank in such magnitudes and phases
as are needed to suppress the motion of the platform. The air
flow demands upon the blower are only those required to develop
damping control forces. As illustrated in Figure lL~, to provide
30 a downward damping control force air is drawn out of chamber 18
-- 16 --
10750g~
through a valve 14 and exhausted to the atmosphere at a valve 20.
Conversely, as illustrated in Figure llB, to provide an upwardly
directed damping control force air is drawn in from the atmosphere
at a valve 16 and blown into chamber 18 via a valve 22. From time
to time, the water level in tank 10 for downwardly directed con-
trol forces is higher than the ambient water level while for up-
wardly directed control forces it is below that of the ambient
water level. If valves 14, 16, 20, and 22 are opened, the water
level in tank 10 is permitted to rise and fall in response to the
varying pressure of waves at the base of the tank. Thus, addition
of such tanks does not change the passive response characteristics
- of the platform.
As shown in Figure 12, where a portion of the platform
deck 13 has been cut away for clarity, tank 10 is secured to the
outboard periphery of a column 15. Tank 10 can be of any shape
which is compatible with the particular column design of the plat-
form. For the cylindrical column 15, tank 10 is crescent shaped
and takes on the appearance of a fender at the water level of the
column.
In Figure 13, there is shown a semi-submersible platform
having a tank 10 secured to each of its four columns 42 between
its deck 40 and its pontoons 44. Although tanks 10 may be of any
shape, they must be large enough to develop sufficient control
forces at each position to stabilize the platform. For typical
platforms of approximately 40,000 square feet, tanks 10 each
having a cross-sectional area of approximately 250 square feet and
pressurized up to 6 pounds per square inch will provide the re-
quired amount of damping control force. The tanks 10 should also
be designed so that the bottoms thereof will be submerged in the
varying surface conditions of the water where they will be used.
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The valves and blowers for tanks 10 may be controlled by
a dynamic control system of the type shown in Figure 6. In such
a system, as shown in Figure 14, a remote unit (RU) 46 may provide
command signals to the valves and blowers which thereupon direct
air preæsure to develop the damping control forces necessary to
stabilize the platform. Remote unit (RU) 46 also receives feed-
back signals which inform an on-line computer of the real-time
status of the pressure in tanks 10 while the computer is per-
forming mathematical operations to suppress the motion of the
platform.
.. . .. .
Some of the active hydrostatic stabilization systems
described above, or the ballast ~ank portions thereof, may be
incorporated in the pontoons of the platform rather than the
columns. Other systems, such as active hydrodynamic and passive
systems may also be employed for generating a velocity-proportional
damping force that effectively counteracts heave oscillation at
platform resonance. Such a passive system may comprise a tensioned
cable that is secured at one end on the sea bottom, that passes
over a sheave mounted on a piston supported by a cylinder secured
to the platform deck, and that is secured at the other end to the
platform deck. The cylinder, which is filled with oil below the
piston and provided with a vented air mass above the piston, is
connected via a conduit having a flow restrictive orifice to a
pressurized oil reservoir. As the platform rises in the presence
of a disturbing wave, the piston tends to move downwardly in the
cylinder but is restrained in part by the restriction of the flow
of oil from the cylinder to the reservoir. Thus, the piston acts
between the sheave and the tensioned cable to increase the tension
in the cable and exert an increased downward force upon the up-
wardly moving platform. This increased downward force due to the
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:` 1075~92
restrictive orifice is a function of the upward velocity of the
platform. As the platform moves downwardly, tension in the cable
is decreased and pressurized oil in the reservoir tends to move
the piston upwardly to oppose this decrease in cable tension.
However, flow of oil from the reservoir to the cylinder is also
restricted, and the downward force exerted on the platform by the
tensioned cable and the pressurized oil is therefore decreased.
This provides a net upward component of force that is in oppo- -
' sition to the downward heave motion and that is also a function
of the vertical velocity of the platform. The anti-heave damping
forces generated by this passive system may be made a linear or a
non-linear function of velocity depending on the type of restric-
~- tive orifice employed between the piston and the oil reservoir.
- The above-disclosed systems for providing anti-heave
damping control forces as a function of vertical heave velocity
permit the design of a semi-submersible platform having a -Qhorter
natural period of heave than is normally acceptable. Such a ~ -
design is characterized by relatively larger column cross sections
and relatively ~maller pontoon cross sections. For such a design
there is less heave motion at wave periods substantially shorter
than the natural heave period, and the platform has a larger
variable deck load capacity. In addition, the platform has
smaller roll and pitch motions due to the decreased pontoon size
relative to the column size. Roll and pitch motions may be
-. further decreased by deploying the above-disclosed systems at
each of the four corner columns of the platform and by employing
them to additionally generate control forces for suppressing the
vertical motion of each column individually as a function of
29 vertical column velocity.
, -- 19 --
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,
A platform employing any of the above-disclosed
~` stabilization systems for damping undesirable oscillatory heave
motion at the resonant wave period of the platform may still
undergo excessive heave motion at non-resonant wave periods due
to the smaller heave maximum at region P of heave response curve
21 in Figure 2. In accordance with another aspect of the present
invention, Figure 15 illustrates an improved semi-submersible
; platform design that substantially reduces heave response in the
region P of curve 21. In this improved semi-submersible platform
design a deck 41 is supported by four columns 43, 45, 47 and 49
and by pontoons 51 and S3 of non-uniform cross section that inter-
connect the lower ends of columns 43, 45 and 47, 49, respectively,
and that are submerged below the water line. For example, pontoon
" 51 has portions 57 and 59 that extend outboard of columns 43 and
45 by a distance L and a portion 55 that extends inboard of those
columns and that has a smaller cross section and, hence, a smaller
displacement volume per unit length than the outboard portions 57
and 59. The inboard and outboard portions of pontoon 53 are
similarly configured.
It has been found that for a column diameter of 40 feet
and a column center to column center spacing of 200 feet, effec-
tive reduction of platform heave in the region P of curve 21 in
Figure 2 occurs when each pontoon has an inboard portion 55 of
26 feet ln diameter and outboard portions 57 and 59 each of 34
feet in diameter, when the centers of the two columns connected
to each pontoon are located inboard from the ends of the pontoon
by about 1/4 of the over-all length of the pontoon, and when the
distance L by which the outboard portions of each pontoon extend
beyond the respective columns is about 80 feet. The total length
of each pontoon should be on the order of 400 feet.
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It should be understood that the pontoons may have other
shapes and dimensions than those described above. In general, a
platform structure has a reference point about which sectors of
; the structure are disposed. Within each sector a portion of the
length of a pontoon is allocatable to all columns attached to the
pontoon in that sector. In accordance with the present invention,
the pontoon design should be such that for long waves having a
wave period of, for example, 20 seconds the effective center of
dynamic force acting on the allocated portion Df a pontoon within
a sector will be outboard of the center of gravity of the column
displacement associated with that sector. This may be done by
lengthening or increasing the diameter of the outboard portions
of the pontoons. In Figure 15, the reference point for the plat-
form is designated by point 31 and the sectors correspond to the
four quadrants of the surface of deck 41. The center of gravity
of column 45 located in one sector is at its longitudinal axis,
and the effective center of dynamic force acting on the pontoon
portion A allocatable to column 45 and located in the same sector
is disposed outboard of the center of gravity of column 45 along
the longitudinal axis of pontoon 51. If an additional column 33
is interposed between columns 43 and 45 (and also between columns --
47 and 49), the longitudinal one-half portion 35 of column 33 is
allocatable to the one-half portion A of pontoon 51. In this
configuration the center of gravity of column 45 and the one-half
portion 35 of column 33 is intermediate the longitudinal axes of
columns 33 and 45 along pontoon 51. The effective center of
dynamic force acting on pontoon portion A is still disposed out-
board of the center of gravity of column 45.
Figure 16 illustrates heave force as a function of wave
period for the semi-submersible platform of Figure 15 as a wave
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- 1075092
.
crest passes neglecting the effects of small drag forces acting
on the platform. Curve 61 represents aggregate wave force acting
on the columns, while curve 63 represents aggregate ~orce acting
on the pontoons. The resultant of these two curves is shown as
curve 65. It can be seen that curve 65 has a negative hump (indi-
cating net downward force on the platform) having a maximum in the
- region P' at a wave period of about 13 seconds.
`` As can be understood by reference to Figure 3, the dif-ferent portions of the pontoons contribute unequally to the total
dynamic pontoon force when analyzed with respect to a wave crest
; appearing at the center of the piatform. In particular, the in-board portions contribute more dynamic force per unit volume be-
cause they are at the wave crest,while the outboard portions con-
tribute less dynamic force per unit volume because they are
located near the wave troughs. The force contribution of the
portion of the pontoon at a distance of l/4 wavelength from the
wave crest is zero. With the pontoon configuration shown in
Figure 15, pontoon displacement inboard of the columns is less
than pontoon displacement outboard of the columns. Thus, in the
` 20 presence of a wave the inboard portions of the pontoons contribute
a smaller portion of the total dynamic pontoon force than if the
pontoons were of uniform cross section over the entire lengths
thereof. In addition, the pontoon length and configuration cause
wave forces acting on the different portibns of the pontoons to
be out of phase. Consequently, in the presence of a wave crest
~ total dynamic pontoon force is diminished thereby reducing heave
.~ in the region P'.
A heave response curve 39 for a semi-submersible platform
such as that shown in Figure 15 is illustrated in Figure 2 for
comparison with the heave response curve 21 for a conventional
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semi-submersible platform of the type shown in Figure 1. This
comparison illustrates the substantial improvement in heave
response for short non-resonant wave periods in the range of
about 9-15 seconds (in this range externally generated damping
forces can be less efficiently applied than at the resonant wave
period of about 18 seconds). For the conventional platform of
Figure 1, heave response for a 13-second wave period is 0.4.
Thus, vertical platform displacement due to thirty-foot waves is
twelve feet (an intolerably large displacement which would pro-
hibit use of the platform in oil drilling operations). In con-
trast the heave response for the same wave period is less than
0.2 for the improved platform of Figure 15 giving a vertical
displacement of less than six feet due to thirty-foot waves.
This displacement is within an acceptable range for offshore
drilling operations. The heave response curve 39 for the im-
proved platform of FigUre 15 is achieved in the presence of head-
on and stern-on waves. Heave response for quartering waves was
found to be slightly greater, although still substantially less
than that for a platform of conventional design.
Further improvement in platform heave response to beam
waves may be achieved, as shown in Figure 17, by employing a
platform having a deck 69 supported by two columns 73 attached to
a pontoon 77 and by two columns 75 attached to a pontoon 79 and
having its pontoons arranged so that the centerlines 81 and 83
thereof are shifted laterally outward by a distance S from
the centerlines 85 and 87, respectively, of the columns associated
with those pontoons. Thus, the effective center of dynamic force
(and for axially symmetrical pontoons, the effective center of
displacement volume) of each pontoon is located outboard of the
center of its associated columns. The offset distance S between
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:
each pontoon centerline and the corresponding column center i~
preferably about 12-15 feet for the column and pontoon dimenaions
given above with respect to Figure 15. Pontoons offset in this
manner produce dynamic forces which are more out of phase with
respect to a reference in the center of the platform and with
respect to each other than those produced by the arrangement of
Figure 15 thereby reducing the total dynamic pontoon force in
the presence of beam waves.
FigUre 18 illustrates another platform for achieving
improved heave response in the presence of beam waves. In this
case a deck 91 is supported hy two columns 93 attached to a pon- -
toon 97 and by two columns 95 at~ached to a pontoon 99. Columns
93 and 95 are tilted outwardly a sufficient distance to achieve
the same results as provided by offset distance ~ described above.
The portion of each column below the water line 101 acts as a pon-
~` toon because it has entirely submerged upper and lower surfaces
subject to dynamic wave forces as illustrated by the exemplary
increment of column volume 103.
Figures 19A and l9B illustrate a platform which incorpo-
rates outwardly skewed pontoons 115 to achieve reduced heave
i response in the presence of waves from any direction (e.g.,
head-on, stern-on, quartering, and beam waves). In this case a
deck 111 is supported by four columns 113 each attached to a
pontoon 115 extending diagonally outward in alignment with a
diagonal axis 117 of the deck to shift the effective center of
dynamic pontoon force 121 outboard of the centerline 119 of the
respective column by a distance S'. Columns 113 may be disposed
vertically or tilted outwardly in alignment with diagonal axes
117. In this arrangement the dynamic pontoon forces become more
out of phase with respect to a reference at the center of the
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platform and with respect to each other thereby reducing the
total dynamic pontoon force and improving heave re~ponse in the
3 presence of waves from any direction.
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