CA1075092A - Method and apparatus for stabilization of a floating semi-submersible structure - Google Patents
Method and apparatus for stabilization of a floating semi-submersible structureInfo
- Publication number
- CA1075092A CA1075092A CA269,450A CA269450A CA1075092A CA 1075092 A CA1075092 A CA 1075092A CA 269450 A CA269450 A CA 269450A CA 1075092 A CA1075092 A CA 1075092A
- Authority
- CA
- Canada
- Prior art keywords
- water
- platform
- vessel
- control
- column
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired
Links
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- G05D1/02—Control of position or course in two dimensions
- G05D1/0206—Control of position or course in two dimensions specially adapted to water vehicles
- G05D1/0208—Control of position or course in two dimensions specially adapted to water vehicles dynamic anchoring
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B63—SHIPS OR OTHER WATERBORNE VESSELS; RELATED EQUIPMENT
- B63B—SHIPS OR OTHER WATERBORNE VESSELS; EQUIPMENT FOR SHIPPING
- B63B1/00—Hydrodynamic or hydrostatic features of hulls or of hydrofoils
- B63B1/02—Hydrodynamic or hydrostatic features of hulls or of hydrofoils deriving lift mainly from water displacement
- B63B1/10—Hydrodynamic or hydrostatic features of hulls or of hydrofoils deriving lift mainly from water displacement with multiple hulls
- B63B1/107—Semi-submersibles; Small waterline area multiple hull vessels and the like, e.g. SWATH
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B63—SHIPS OR OTHER WATERBORNE VESSELS; RELATED EQUIPMENT
- B63B—SHIPS OR OTHER WATERBORNE VESSELS; EQUIPMENT FOR SHIPPING
- B63B39/00—Equipment to decrease pitch, roll, or like unwanted vessel movements; Apparatus for indicating vessel attitude
- B63B39/02—Equipment to decrease pitch, roll, or like unwanted vessel movements; Apparatus for indicating vessel attitude to decrease vessel movements by displacement of masses
- B63B39/03—Equipment to decrease pitch, roll, or like unwanted vessel movements; Apparatus for indicating vessel attitude to decrease vessel movements by displacement of masses by transferring liquids
Abstract
Abstract of the Disclosure A semi-submersible floating platform having a deck supported above water by four partially-submerged main columns attached to the deck and by two totally-submerged pontoons each attached to a different pair of the main columns is provided with a damping control system for suppressing undesirable motion of the platform caused by wave motion. This damping control system includes a velocity sensor for sensing the velocity of at least one of heave, roll, and pitch components of the undesirable motion of the structure and further includes control apparatus for exert-ing on the platform a damping control force that is a function of and in phase opposition to the sensed velocity. The control apparatus includes one or more ballast tanks in communication with the water and apparatus for driving water from or drawing water into each ballast tank as a function of the sensed velocity.
Each ballast tank may be included within an associated column or pontoon of the platform and may be provided with a ballast sensor for sensing the actual volume of water within the ballast tank relative to a mean volume of water therein. In this case, the control apparatus may include apparatus responsive to the velocity sensor and each ballast sensor for driving pump apparatus to vary the actual volume of water within each ballast tank relative to the mean volume of water therein as a function of the sensed velocity. Alternatively, each ballast tank may be mounted on the outboard surface of an associated column of the platform at approxi-mately the location where the ambient water level intersects the column. In this case, the control apparatus may include pump apparatus for varying the air pressure in each ballast tank as a function of the sensed velocity to drive water from or draw water into each ballast tank. Although the damping control apparatus is especially effective for suppressing undesirable motion of the platform at wave periods substantially equal to the resonant period of the platform, it is also effective at other wave periods. Suppression of undesirable motion at such other wave periods may also be achieved by modifying the geometry of the columns and/or pontoons which are apportionable in sectors about a reference point of the platform. This may be accomplished, for example, by altering the cross-sectional area of the pontoons along the length thereof or by otherwise modifying the pontoons so that the portion thereof in each sector has an effective center of dynamic pontoon force that is disposed outboard of the ef-fective center of displacement volume of the associated portion of the columns in the same sector.
Each ballast tank may be included within an associated column or pontoon of the platform and may be provided with a ballast sensor for sensing the actual volume of water within the ballast tank relative to a mean volume of water therein. In this case, the control apparatus may include apparatus responsive to the velocity sensor and each ballast sensor for driving pump apparatus to vary the actual volume of water within each ballast tank relative to the mean volume of water therein as a function of the sensed velocity. Alternatively, each ballast tank may be mounted on the outboard surface of an associated column of the platform at approxi-mately the location where the ambient water level intersects the column. In this case, the control apparatus may include pump apparatus for varying the air pressure in each ballast tank as a function of the sensed velocity to drive water from or draw water into each ballast tank. Although the damping control apparatus is especially effective for suppressing undesirable motion of the platform at wave periods substantially equal to the resonant period of the platform, it is also effective at other wave periods. Suppression of undesirable motion at such other wave periods may also be achieved by modifying the geometry of the columns and/or pontoons which are apportionable in sectors about a reference point of the platform. This may be accomplished, for example, by altering the cross-sectional area of the pontoons along the length thereof or by otherwise modifying the pontoons so that the portion thereof in each sector has an effective center of dynamic pontoon force that is disposed outboard of the ef-fective center of displacement volume of the associated portion of the columns in the same sector.
Description
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 ~ -2-107509~
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.
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).
~ ~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 .
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 : .
.,:
~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, :107509Z
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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,~
.
.. - , , " 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.
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.
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 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 ~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 " 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 ~075092 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 .
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 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.
~075092 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 :` 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 --, 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.
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 .
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 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 :
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 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.
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 ~
.
t :
..
. . .
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 ~ -2-107509~
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.
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).
~ ~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 .
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 : .
.,:
~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, :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,~
.
.. - , , " 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.
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.
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 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 ~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 " 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 ~075092 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 .
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 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.
~075092 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 :` 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 --, 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.
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 .
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 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 :
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 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.
Claims (26)
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:
1. 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 sub-mersion in the water; the column means and the pontoon means 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 displacement component of undesirable motion of the structure caused by wave motion of the water.
2. A semi-submersible floating structure as in claim 1 wherein the damping control means includes control means for driving water from or drawing water into each control force tank as a function of the velocity of at least one displace-ment component of the undesirable motion of the structure.
3. A semi-submersible floating structure as in claim 2 wherein each control force tank includes valve means disposed above the ambient surface of the water, the valve means being operable when open for allowing the water level in the control force tank to rise and fall freely and being operable when closed for allowing the air pressure in the control force tank above the surface of the water therein to be varied.
4. A semi-submersible floating structure as in claim 3 wherein the control means includes pump means for varying the air pressure in each control force tank; and means for control-ling the pump means and the valve means to vary the air pressure in each control force tank as a function of the velocity of at least one displacement component of the undesirable motion of the structure to drive water from or draw water into each control force tank.
5. A semi-submersible floating structure as in any of the preceding claims 1, 2 or 3 wherein each control force tank conforms to a contour of the column means and is mounted on an outboard surface of the column means at a location where the ambient surface of the water intersects the column means.
6. A semi-submersible floating structure as in claim 1 wherein the column means includes four main columns attached to the deck adjacent to four corner portions thereof; the pontoon means includes two pontoons each attached to a different pair of those main columns; and the damping control means includes a separate control force tank for each of those main columns.
7. A semi-submersible floating structure as in claim 6 wherein the damping control means includes control means for driving water from or drawing water into each control force tank as a function of the velocity of at least one displacement component of the undesirable motion of the structure.
8. A semi-submersible floating structure as in claim 7 wherein each control force tank includes valve means disposed above the ambient surface of the water, the valve means being operable when open for allowing the water level in the control force tank to rise and fall freely and being operable when closed for allowing the air pressure in the control force tank above the surface of the water therein to be varied.
9. A semi-submersible floating structure as in claim 8 wherein the control means includes pump means for varying the air pressure in each control force tank; and means for control-ling the pump means and the valve means to vary the air pressure in each control force tank as a function of the velocity of at least one displacement component of the un-desirable motion of the structure to drive water from or draw water into each control force tank.
10. A semi-submersible floating structure as in any of the preceding claims 6 7 or 8 wherein each control force tank conforms to the contour of an associated one of those main columns and is mounted on the outboard surface of the associated main column at a location where the ambient surface of the water intersects that main column.
11. A system for stabilizing a vessel having floata-tion means, said system comprising one or more tanks, having open access to the water, mounted on the outboard surfaces of the floatation means at a Location 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.
12. A system for stablizing a vessel as in claim 11 wherein the tanks include controllable vents at a location above the ambient surface of the water to allow the water level in the tank to rise and fall freely when open, and to form a pressurization chamber above the surface of the water in the tanks when closed.
13. A system for stabilizing a vessel as in claim 11 wherein access of the tanks to the water is adequate to allow for varying surface conditions of the water.
14. A system for stabilizing a vessel as in claim 11 wherein the tanks have a shape conforming to the contours of the floatation means at the point where the floatation means approximately intersects the ambient surface of the water.
15. A system for stabilizing a vessel as in claim 11 wherein the water flow into and out of the tanks is con-trolled solely by the air supplied to the tanks.
16. A system for stabilizing a vessel as in claim 15 wherein the water flow into and out of the tanks is con-trolled solely by the air supplied to the portion of the tank above the surface of the water therein.
17. A system for stabilizing a vessel as in claim 11 wherein the floatation means includes at least one of the vertical columns of a semi-submersible platform.
18. A system for stabilizing a vessel having floata-tion means as in claim 11 wherein said system is effec-tive for stabilizing pitch and roll motions of the vessel.
19. A system for stabilizing a vessel having floata-tion means as in claim 11 wherein said system is effective for stabilizing heave motion of the vessel.
20. A method of-applying control forces for stabiliz-ing 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 location where said floatation member approxi-mately intersects the ambient surface of the water.
21. The method of applying control forces for sta-bilizing a vessel as in claim 20 further including the steps of mounting one or more tanks, having open access to the water to outboard surfaces of the port and star-board sides of the vessel at a location where the ambient surface of the water approximately intersects the floata-tion means so that the surface of the water approximately bisects the vertical dimension of the tanks; and selec-tively supplying air to the tanks 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.
22. A method for stabilizing a vessel as in claim 20 wherein the floatation member includes at least one of the vertical columns of a semi-submersible platform.
23. A method of applying control forces for sta-bilizing a vessel having a floatation member as in claim 20 wherein said system is effective for stabilizing pitch and roll motions of the vessel.
24. A method of applying control forces for sta-bilizing a vessel having a floatation member as in claim 20 wherein said system is effective for stabilizing heave motion of the vessel.
25. A semi-submersible floating structure according to Claim 9 wherein each control force tank conforms to the contour of an associated one of those main columns and is mounted on the outboard surface of the associated main column at a location where the ambient surface of the water intersects that main column.
26. A semi-submersible floating structure as in Claim 4 wherein each control force tank conforms to a contour of the column means and is mounted on an outboard surface of the column means at a location where the ambient surface of the water intersects the column means.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA272,132A CA1092901A (en) | 1976-01-19 | 1977-02-18 | Method and apparatus for stabilization of a floating semi-submersible structure |
Applications Claiming Priority (3)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US64999776A | 1976-01-19 | 1976-01-19 | |
| US73100676A | 1976-10-08 | 1976-10-08 | |
| US05/731,007 US4112864A (en) | 1976-10-08 | 1976-10-08 | Heave stabilization of semi-submersible platforms |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1075092A true CA1075092A (en) | 1980-04-08 |
Family
ID=27417834
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA269,450A Expired CA1075092A (en) | 1976-01-19 | 1977-01-11 | Method and apparatus for stabilization of a floating semi-submersible structure |
Country Status (6)
| Country | Link |
|---|---|
| JP (1) | JPS52111191A (en) |
| AU (1) | AU2124677A (en) |
| CA (1) | CA1075092A (en) |
| DE (1) | DE2701605A1 (en) |
| FR (1) | FR2338183A1 (en) |
| NL (1) | NL7700462A (en) |
Families Citing this family (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| NL7811837A (en) * | 1978-12-04 | 1980-06-06 | Varitrac Ag | STABILIZATION SYSTEM OF A CRANE TOOLS. |
| DE3471910D1 (en) * | 1983-04-28 | 1988-07-14 | Mobil Oil Corp | Wide based semi-submersible vessel |
| JPS59192933U (en) * | 1983-06-09 | 1984-12-21 | 三井造船株式会社 | Semi-submerged offshore structure |
| JPS6095395U (en) * | 1983-12-08 | 1985-06-28 | 三井造船株式会社 | Semi-submerged offshore structure |
| FR2881102B1 (en) | 2005-01-21 | 2007-04-20 | D2M Consultants S A Sa | STABILIZED FLOATING SUPPORT |
| FR2970696B1 (en) * | 2011-01-25 | 2013-02-08 | Ideol | ANNULAR FLOATING BODY |
Family Cites Families (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| NL288939A (en) * | 1900-01-01 | |||
| DE828067C (en) * | 1945-01-04 | 1952-01-14 | Friedrich Kompe | Non-lurching body |
| US3835800A (en) * | 1968-02-13 | 1974-09-17 | Santa Fe Drilling Co | Twin hull semi-submersible derrick barge |
| US3886886A (en) * | 1974-02-28 | 1975-06-03 | Global Marine Inc | Passive ship motion stabilization system with active assist for high amplitude motions |
| CA1058208A (en) * | 1974-06-10 | 1979-07-10 | John B. Wright | Pharmaceutical n,n'(phenylphenylene) dioxamic acid derivatives |
| US3916811A (en) * | 1974-08-29 | 1975-11-04 | Sun Oil Co Pennsylvania | Tide compensation system |
-
1977
- 1977-01-11 CA CA269,450A patent/CA1075092A/en not_active Expired
- 1977-01-12 AU AU21246/77A patent/AU2124677A/en not_active Expired
- 1977-01-17 FR FR7701207A patent/FR2338183A1/en active Pending
- 1977-01-17 DE DE19772701605 patent/DE2701605A1/en not_active Withdrawn
- 1977-01-18 NL NL7700462A patent/NL7700462A/en not_active Application Discontinuation
- 1977-01-19 JP JP483377A patent/JPS52111191A/en active Granted
Also Published As
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| AU2124677A (en) | 1978-07-20 |
| JPS6257558B2 (en) | 1987-12-01 |
| DE2701605A1 (en) | 1977-07-21 |
| NL7700462A (en) | 1977-07-21 |
| FR2338183A1 (en) | 1977-08-12 |
| JPS52111191A (en) | 1977-09-17 |
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