The invention is related to the field of vessels, such as vessels for offshore construction, drilling, pipe and/or cable laying, or diving support, that are provided with a moon pool. In particular, the vessel is a monohull vessel, such as a ship.

A moon pool provides an opening in a hull of the vessel to allow access to the water below the bottom surface of the hull. Usually, the moon pool is located at or near the centre of the hull of the vessel.

It is noted that the moon pool can for example be used to lower equipment, for instance a remotely operated vehicle (ROV), an umbihcal or tether, flexible pipes, cables or drilhng equipment, such as drilling pipes or mining pipes, into the water from the vessel and/or to raise equipment from the water. Through the moon pool, drilling assembly and/or other

assemblies can thus be passed, for instance while a well is being drilled, completed, or abandoned.

The moon pool can be formed by a walled passage or hole in the hull of the vessel. Often, said walled hole has a substantially tubular shape, e.g. formed as a tube with a substantially rectangular cross-section, or as a substantially cylindrical tube. The passage formed by the moon pool normally extends in a substantially vertical direction between deck and bottom of the vessel and can then for instance have a substantially horizontal cross section having a substantially rectangular or square shape.

Vessels provided with a moon pool are often used as an offshore construction vessel or a drillship, e.g. a vessel which can be arranged for drilling, especially deep sea drilling, and which vessel preferably can sail with its own locomotive power.

Although a moon pool can be a very advantageous feature of a vessel, especially of an offshore construction vessel or a drillship, when performing work on location, the moon pool can also be disadvantageous during saihng, for instance in terms of sailing performances.

A disadvantage of a moon pool may be that both during transit and during stationary operation of a vessel provided with such a moon pool, said vessel can experience moon pool water motion, for example water moving in a piston mode, when the water inside the moon pool heaves up and down more or less like a sohd body, and/or water moving in a sloshing mode, which can be considered as back and forth motion of water between substantially vertical walls of the moon pool. The moon pool water motion mainly depends on the main dimensions of the moon pool at deck level, the moon pool's local geometry, the moon pool's draught and, in case of a vessel in transit, on the vessel's speed. During transit, the moon pool oscillations may start as a piston mode and can transform to a sloshing mode in specific cases, for example depending on a moon pool's draught and/or a moon pool's length, and both modes can increase the mean flow resistance of the vessel, can slow down the vessel, can increase fuel consumption, can exert an oscillatory load on a propulsion system of the vessel. In a stationary mode of the vessel, however, both the piston mode and the sloshing mode can be induced by incoming waves. The piston mode as well as the sloshing mode can cause vortex induced vibrations in the vessel and can induce slamming loads to the vessel's structure which both are undesirable for the crew and the vessel. Moon pool water motion in a piston mode can occur for example when a water column in the moon pool, which can be excited by the waves and/or the heave motion of the vessel, enters in resonant condition with the natural mode of the wave spectrum of the incoming waves. This moon pool piston mode water motion can create hazardous situations in stationary positions as well, for example causing water to flow over the vessel's deck, and may imply that operations need to be ceased.

Different solutions have been proposed to counteract moon pool water motion, such as piston motion and/or sloshing, and/or negative effects thereof. Such solutions include for example preventing water flow from entering the moon pool and/or directing a flow from the moon pool by providing a chamfer on the trailing wall of the moon pool. Another type of solutions comprises adapted moon pool shapes to suppress water motion, or installing damping systems inside the moon pool, as for example choke decks or linings, having the disadvantage that these structures may protrude into the moon pool and may be damaged by, or may damage, equipment that passes through the moon pool. Furthermore, many devices have been proposed to temporarily close off the moon pool, e.g. by means of a hd positioned near the bottom of the hull of the vessel. However, mounting or dismounting the moon pool devices may involve complicated, dangerous and/or time-consuming operations. An important drawback of most of these solutions is that they have been tailored to counteract the water motion effects of a vessel in transit, and not to water motion in moon pools of a vessel during stationary operations.

Publication WO 2015028609 discloses a semi-submersible, having two hulls, and an operation draught which can be located at 17 m. In one of the columns of the semisubmersible a cavity is provided for launching subsea equipment such as an ROV. The cavity is provided with wave dampening means. By changing the cross-section of the cavity, water waves that are present in the cavity are decreased.

A drawback of the wave dampening means of WO 2015028609 is that it is specifically designed for a semi-submersible, being distinct from a monohull ship, having a relatively long cavity and suitable only for ROV- operations. Further, the proposed wave dampening means decrease the available operational area of the moon pool. Additionally, the wave dampening means have been tailored to decrease the water waves in the cavity, due to turbulence or frictional losses, which still may affect the operation of the equipment passing through the moon pool. An object of the present disclosure is to provide vessel having a moon pool that obviates at least one of the above mentioned drawbacks. It is an object of the invention to alleviate or solve at least one of the

disadvantages associated with one or more prior art vessels having a moon pool, especially one or more disadvantages mentioned above, and/or to obtain advantages over said prior art vessels. In particular, the invention aims at providing a vessel including a moon pool, which is able to reduce significantly piston mode water motion in the moon pool's vessel, especially during stationary operations of the vessel. It is another object of the invention to provide a vessel with a moon pool, having a design which is relatively simple, relatively sturdy, relatively error insensitive, relatively cheap, and or relatively easy and/or economic to use.

To this aim, there is provided a vessel according to the features of claim 1. In particular, the vessel comprises a single hull having a bottom surface and a deck, wherein said vessel is provided with a moon pool extending from said bottom surface of the hull in an upward direction through the hull, having a main moon pool draught. Preferably, the vessel is a monohull drillship. A monohull ship has a significantly different motion behavior than a semi-submersible, e.g. it is less stable. Thus a ship typically requires a larger main moon pool cross-sectional area, in particular a cross- sectional area at a waterline of the moon pool to limit risks of damaging equipment passing or extending through the moon pool during operation. A cavity in a column of a semi-submersible may be suitable for ROV- operations only and not for drilling operations, allowing a relatively small cross -sectional area and a relatively long length. In a ship a ratio between a longitudinal length of the moon pool and the main moon pool draught can vary between about 0.8 and about 4, whereas such a ratio for a semi- submersible is typically around 0.5.

At least part of a lower end of said moon pool is adapted to provide a virtual moon pool draught different from the main moon pool draught, such that a moon pool's piston mode eigenfrequency is shifted, in particular away from a main peak in a wave spectrum of incoming waves, and preferably outside the wave spectrum of said incoming waves. Or in case the piston mode is induced by another phenomenon, such as the heave motion or transit motion of the vessel, the moon pool's piston mode eigenfrequency is to be shifted away from a main peak in a wave spectrum of the piston mode inducing phenomenon. The main moon pool draught is generally measured from the lower end of the moon pool to the waterline when the vessel is in use. The approximate theoretical piston mode eigenfrequency of a, for example rectangular, moon pool is given by the formula:

with com : piston mode eigenfrequency

g : gravity constant

dm : moon pool draught

Sm : moon pool area at deck level

c : constant

As the moon pool's piston mode eigenfrequency, i.e. the

eigenfrequency of the water column present in the moon pool and oscillating in a piston mode, mainly depends on the moon pool draught, a real or virtual change in the moon pool draught can shift the moon pool's piston mode eigenfrequency away from a main peak in the wave spectrum of a piston mode inducing phenomenon such as incoming waves, and preferably outside the wave spectrum of incoming waves, such that the chance for the oscillating water column to enter into resonant condition significantly decreases, thus advantageously avoiding unwanted amplification of water motion in the moon pool. The virtual moon pool draught can be made larger or smaller than the main moon pool draught, depending on the wave spectrum which is present during use of the vessel. A larger moon pool draught implies a lower moon pool's eigenfrequency, thus a larger moon pool's natural period, and vice versa.

Contrary to prior art wave dampening means, the solution according to the invention maintains the available main moon pool operational cross-sectional area and provides for an increased cross- sectional area at a bottom side of the moon pool. Also, contrary to the prior art wave dampening means, that act on waves already occurring in the moon pool, the proposed solution according to the invention aims at preventing the occurrence of piston mode water motion in the moon pool at the original main moon pool eigenfrequency. By providing such an increased cross -sectional area at a bottom side of the moon pool, a virtual draught is created that is different from the main moon pool draught resulting in a shift of the piston mode eigenfrequency. Furthermore, the increased cross- sectional area at a bottom side of the moon pool providing for a recess extending outwardly and downwardly with respect to the main moon pool, provides for normal flow behavior at a flow separation at virtual draught level, so no additional vortices or contraction of water flow is intended.

Contrary to prior art dampening means that interfere with the flow behavior, inducing additional vortices or wave expansion, according to the invention, the flow behavior at the flow separation point at the hull level does not interfere with moon pool behavior at the virtual draught level.

In a preferred embodiment, at least part of the lower end of said moon pool can be provided with a recess in direct fluid connection with the moon pool, such that a height of said a recess, measured from the hull's bottom surface to a top side of said recess, determines said virtual moon pool draught. As the virtual moon pool draught is measured from the top side of said recess to the waterline when the vessel is in use, the virtual moon pool draught can be obtained by reducing the main moon pool draught with the height of said recess. The presence of such a recess in direct fluid connection with the moon pool relieves the pressure in the moon pool, provided the recess is not closed off from the moon pool by, for example, a moon pool's side creating a separate chamber next to the moon pool rather than a recess. The relief in the moon pool's pressure causes the moon pool's piston mode eigenfrequency to shift away from the eigenfrequency linked to the main moon pool draught. The moon pool's eigenfrequency can shift towards an eigenfrequency depending on a virtual moon pool draught, which is measured from a waterline, when the vessel is in use, to a top side of the recess. Said virtual moon pool draught will thus be smaller than the main moon pool draught, causing the moon pool's eigenfrequency to shift towards a higher value. An additional advantage of a higher moon pool's piston mode eigenfrequency is that the inception speed, i.e. the vessel's speed at which moon pool water oscillations can start to occur during transit, rises.

Therefore, it is possible to provide a recess determining a moon pool's virtual draught such that the shift in the moon pool's piston mode

eigenfrequency is high enough to obtain an inception speed that is higher than a regular speed of the vessel in transit, preventing piston mode oscillations to occur due to the transit of the vessel.

Advantageously, the recess at a lower end of the moon pool defines an opening in the hull having a larger cross-sectional area than a main moon pool area. The main moon pool cross-sectional area may be defined by dimensions, such as radius or length and width, of the moon pool extending between a deck level and the recess. The recess, at a lower end of the moon pool, defines an opening in the hull that has a larger area than the main moon pool area. Preferably, the dimensions of the main moon pool, more preferably the dimensions defining the cross-sectional area of the moon pool, such as radius or longitudinal length and transversal width, remain constant over the height of the moon pool between a deck and the recess. Preferably, the occurrence of vertical waves, due to the water entering into piston mode, inside of the moon pool is avoided.

In a more preferred embodiment, a connection between the top side of said recess and the moon pool's side wall can be substantially formed as an edge, preferably a relatively sharp edge. Such a connection may serve relatively well as a flow separation point, and improves the demarcation of the virtual draught. It is preferred that the connection is formed as an edge that is sharp enough to obtain flow separation, but the connection may also be slightly rounded-off or chamfered, for example with a rounding radius in a range of 1 - 50 cm, preferably 5 - 10 cm, to better protect equipment which is lowered and/or raised in the moon pool, and which could

accidentally hit the edge and get damaged, or damage the edge. The rounding-off of the edge should however be such that the flow separation function can be maintained.

It is also preferred that the top side of said recess is at a

substantially right angle with a side wall of said moon pool. A right angle can provide a relatively sharp edge improving flow separation.

In an advantageous embodiment, the top side of said recess can be substantially in parallel with the hull's deck. In this way, the height of said recess may not substantially vary over said recess, leading to a clear virtual draught, which can also be defined by the difference between the main moon pool draught and said recess's height.

Preferably, the top side of said recess may be located under the waterline during use of the vessel, in order to ensure a relief of pressure in the moon pool. A top side of the recess which is located flush with, or above, the waterline during use of the vessel, results in a virtual moon pool draught equal to the main moon pool draught, so that there is no shift of the moon pool's eigenfrequency.

It may be preferred that said moon pool is a substantially round or oval moon pool having a single side wall. Substantially round moon pools can for example be found on drilling vessels provided with a turret mooring system. Alternatively, said moon pool may be a substantially rectangular moon pool having four side walls. A substantially rectangular moon pool has the advantage that it can be built and inserted into the vessel's hull relatively easy.

In a preferred embodiment, a lower end of at least a first side wall of said moon pool is provided with a first recess, and a lower end of at least a second side wall of said moon pool is provided with a second recess, said first and said second recess preferably having a same recess height. A single recess in the lower end of a single wall of the moon pool already has an effect on the moon pool's eigenfrequency. However, this effect is enhanced when the lower end of a second side wall is provided with a second recess. The first and second side walls can for example be adjacent side walls, or alternatively, can be opposing side walls. In the latter case, the first side wall can for example be a leading wall seen in a direction of transit of the vessel, and the second wall a trailing wall. Or the first and second walls can be a side wall on the vessel's starboard side and the vessel's port side. The recess in the lower end of a side wall can extend along part of the side wall, or along an entire width of said side wall. In case of adjacent side walls, the first recess in the first side wall may for example run into the second recess in the second side wall continuing the recess in the corners between the side walls, and may connect over the full width of the recess.

In a most preferred embodiment, the lower end of said moon pool can be entirely provided with a recess, preferably having a substantially equal height along said recess. A recess along the entire perimeter of the moon pool's lower end can cause a most effective shift in eigenfrequency. In case of a substantially rectangular moon pool, a first recess on a first side wall may for example run into a second recess on an adjacent second side wall such that a single and continuous recess around the moon pool's lower end is obtained, thus further reducing obstruction of the flow from the moon pool and/or relieving pressure in the moon pool.

In an advantageous embodiment, a recess's back wall connecting a recess's top side with the bottom surface of the hull is substantially in parallel with the at least one side wall of the moon pool. Such a back wall provides a recess with an optimal shape without decreasing the vessel's carrying capacity. Moreover, such a recess's back wall is easier to construct in the hull than an inclined back wall.

In a more advantageous embodiment, a ratio of a recess's width, measured from a moon pool's side wall to a recess's back wall, to the height of the recess is comprised within the range of 0.25 - 1.5, preferably between 0.5— 1. A larger recess height results in an increased shift in

eigenfrequency. For a given height, a larger width of the recess can enhance the effect. However, a too wide recess may be disadvantageous for the vessel's capacity, or may be impractical to implement in the vessel's construction. Therefore, the above-mentioned ratio can provide optimal dimensions for the recess to result in a sufficient shift in eigenfrequency with a relatively small effort to adapt the construction of a vessel's hull structure.

It may also be advantageous that at least part of a recess's back wall connecting a recess's top side with the bottom surface of the hull is inclined. For example, a recess in a leading side wall and or a trailing side wall seen in a vessel's transit direction may be inchned in order to decrease the vessel's resistance when in transit, thus reducing power and fuel consumption. The inclination may for example be chosen such that the recess still widens up towards the hull's bottom surface. Contrary to the connection between the moonpool's side wall and the top side of the recess, where a sharp edge is preferred, the transition or connection between the top side of the recess and the back wall of the recess may for example be fluent or roundecl-off, as may be the case for the connection between the back wall of the recess and the hull's bottom surface.

In an alternative embodiment of the invention, a vessel may be provided wherein at least part of the lower end of the moon pool is provided with at least one wall structure element of which an extension under the hull's bottom substantially in parallel with the at least one side wall of the moon pool is adjustable to provide a virtual moon pool draught different from the main moon pool draught, such that a moon pool's piston mode eigenfrequency is shifted. Instead of providing a virtual moon pool draught which is smaller than the main moon pool draught, an extension of the moon pool under the hull's bottom surface by at least one wall structure element can increase the moon pool's virtual draught and can cause the eigenfrequency to decrease, or the moon pool's natural period to increase. This may be preferred to avoid resonance in certain circumstances depending on the wave spectrum present at a vessel's location. Extension of the at least one wall structure element can for example be adjusted to the desired shift in eigenfrequency, or said at least one wall structure element can for example be entirely retracted, for example during transit of the vessel. The at least one wall structure element can comprise for example a single plate per side wall, a tubular structure including interconnected plates, a telescopically extendable wall structure element, a telescopically extendable tubular sleeve, etc. This feature of an extendable and adjustable wall structure element can also be combined with a recess. In that case, the at least one wall structure element can partly or entirely close off a recess, for example when an increase in eigenfrequency is more preferred than a decrease to avoid resonance.

In an advantageous embodiment of the invention, the virtual moon pool draught can be adjustable. This can be the case for the moon pool provided with a recess having an adjustable height and/or width. This can also be the case for a moon pool provided with at least one extendable wall structure element, which can for example be telescopically adjustable. A moon pool of which the virtual draught is adjustable can be optimally adapted to the circumstances in order to shift the moon pool's piston mode eigenfrequency away from a peak in a wave spectrum which can potentially induce resonance thus amplifying water motion in the moon pool.

The vessel is preferably a vessel suitable for offshore operations, such as construction, drilling, pipe or cable laying, diving support. Such vessels spend quite a lot of time in a stationary mode while performing operations, a reduction in piston mode resonance can result in a significant increase in operational time and improve safety of the operations.

Further, the invention relates to a method for shifting a moon pool's piston mode eigenfrequency of a moon pool of a single hull vessel, by providing the moon pool with a recess at a lower end thereof to provide a virtual moon pool draught different from the main moon pool draught, wherein the recess defines an opening in the hull having a larger area than a main moon pool area. By providing such a recess the area of the moon pool at a lower end thereof, i.e. near a bottom of the hull, becomes larger than the cross-sectional area of the main moon pool extending between a deck of the hull and the recess. Preferably, the dimensions of the main moon pool, more preferably the dimensions defining the cross-sectional area of the moon pool, such as radius or longitudinal length and transversal width, remain constant over the height of the moon pool between a deck and the recess.

The present invention will be further elucidated with reference to figures of exemplary embodiments. Corresponding elements are designated with corresponding reference signs.

Figure 1 shows a schematic cross-section along a vessel's longitudinal centre line of a prior art vessel, which vessel is provided with a moon pool; Figure 2 a shows a schematic cross-section along a vessel's longitudinal centre line of part of a first embodiment of a vessel according to the invention, which vessel is provided with a moon pool;

Figure 2b shows a schematic bottom view of part of the first embodiment of the vessel of Figure 2a;

Figure 3 shows a plot of the wave energy of a typical wave spectrum and a plot of the response amplitude operator of the water level elevation inside a moon pool without and with a recess;

Figure 4a shows a schematic cross-section along a vessel's longitudinal centre line of part of a second embodiment of a vessel according to the invention, which vessel is provided with a moon pool;

Figure 4b shows a schematic bottom view of part of the second embodiment of the vessel of Figure 4a;

Figure 5a shows a schematic cross-section along a vessel's longitudinal centre line of part of a third embodiment of a vessel according to the invention, which vessel is provided with a moon pool;

Figure 5b shows a schematic bottom view of part of the third embodiment of the vessel of Figure 5a;

Figure 6a shows a schematic cross-section along a vessel's longitudinal centre line of part of a fourth embodiment of a vessel according to the invention, which vessel is provided with a moon pool;

Figure 6b shows a schematic transversal cross-section of the vessel of Figure 6 a;

Figure 6c shows a schematic bottom view of part of the fourth embodiment of the vessel of Figure 6a;

Figures 7a and 7b show a schematic cross-section along a vessel's longitudinal centre line of part of a fifth embodiment of a vessel according to the invention, which vessel is provided with a moon pool; Figures 8a and 8b show a schematic cross-section along a vessel's longitudinal centre line of part of a sixth embodiment of a vessel according to the invention, which vessel is provided with a moon pool.

Figure 1 shows a schematic cross-section along a vessel's longitudinal centre line 21 of a prior art vessel, which vessel is provided with a moon pool. The vessel 1 can have a bow 3a at a front side la of the vessel 1 and a stern 3b at a rear side lb of the vessel 1, and the vessel 1 can substantially extend in a longitudinal direction from said bow 3a towards said stern 3b. The vessel 1 is a single hull ship, preferably a drillship.

The moon pool 2 may provide an opening 2 in the hull 3 of the vessel 1 to allow access to the water 4 below the bottom surface 5 of the hull 3. Usually, the moon pool 2 is located at or near the centre 3c of the hull 3 of the vessel 1. Additionally or alternatively, the moon pool 2 can be formed by a walled passage 2 or hole 2 in the hull 3 of the vessel 1 and may for instance have a substantially tubular shape. The passage 2 formed by the moon pool 2 may extend in a substantially vertical direction 6 and can then for instance have a substantially horizontal cross section having a

substantially round shape or a substantially rectangular shape, such as for instance a substantially square shape. Since the moon pool 2 can be of a substantially tubular design, horizontal cross sections at different height levels may have substantially the same form and substantially the same dimensions.

The moon pool 2 may have a substantially upwardly extending front wall 2a and/or a substantially upwardly extending rear wall 2b. The respective wall 2a, 2b may extend substantially transversally to the longitudinal direction of the vessel 1 and/or may extend substantially vertically. The length, also named height, of the moon pool 2, extending between a deck level and the bottom of the hull, may depend on the height of the vessel, but, as an example, a length of the moon pool 2 may be about 17 m or about 18 m, for example between about 12 m to about 23 m. Further, in case of a substantially rectangular moon pool, the moon pool 2 may comprise two side walls 2c, 2d, which may for instance extend substantially vertically and/or substantially in the longitudinal direction of the vessel 1.

It is noted the vessel 1 may be arranged such that the moon pool 2 can during use be located at the waterline 4a e.g. such that the front wall 2a, rear wall 2b and side walls 2c, 2d thereof are partly extending above and partly extending below said waterline 4a. The main moon pool draught 7 is generally measured from from the lower end 8 of the moon pool 2 to the waterline 4a when the vessel is in use. Further, it is noted that the moon pool 2 can be a so called open moon pool, which is open to the air above, such that the moon pool 2 is not formed as an airtight chamber in the vessel 1, but is at least partly open, preferably at least partly open at or near a top side of the moon pool 2. The main moon pool draught 7 corresponds with the submerged length of the moon pool 2, having a constant cross-sectional area over its length, as shown in figure 1.

Figure 2a shows a schematic cross-section along a vessel's longitudinal centre line 21 of part of a first embodiment of a vessel 1 according to the invention, which vessel 1 is provided with a moon pool 2, and Figure 2b shows a schematic bottom view of part of the first

embodiment of the vessel of Figure 2a. At least part of a lower end 8 of said moon pool 2 is adapted to provide a virtual moon pool draught 11 different from the main moon pool draught 7, such that a moon pool's piston mode eigenfrequency is shifted. In this embodiment, at least part of the lower end 8 of said moon pool 2, in this case a moon pool's front wall 2a and a moon pool's rear wall 2b, is provided with a recess 9 in direct fluid connection with the moon pool 2, such that a height H of said a recess 9, measured from the hull's bottom surface 5 to a top side 10 of said recess 9, determines said virtual moon pool draught 11. More specifically, a lower end 8 of at least a first side wall 2a of said moon pool 2 is provided with a first recess 9a, and a lower end 8 of at least a second side wall 2b of said moon pool 2 is provided with a second recess 9b, said first and said second recess 9a, 9b preferably having a same recess height H. The virtual draught 11 is measured from the top side 10 of said recess 9 to the waterline 4a when the vessel 1 is in use, or by reducing the main moon pool draught 7 with the height H of said recess 9. The width W of a first recess 9a and the width of a second recess 9b may, but need not, be equal. Said width W is measured from a moon pool's side wall, for example 2a, to a recess's back wall 17. It is also possible to adapt only (part of) one side wall's lower end 8 of a moon pool 2, for example by providing a recess 9, for example only a front or rear wall 2a, 2b, or only a side wall 2c, 2d. It is also possible to adapt two adjacent side walls, for example 2a, 2c, or two opposing side walls, for example a moon pool's side wall on port and starboard side 2c, 2d. Instead of providing a recess, also an extension of part of a moon pool's side wall may be provided (see Figures 7- 8). An entire moon pool's side wall 2a, 2b, 2c or 2d can be adapted as in the embodiment of Figures 2a and 2b, or, alternatively, only part of a moon pool's side wall 2a, 2b, 2c or 2d can be adapted. In case of providing a lower end 8 of a moon pool 2 with a recess 9, as shown in Figures 2a and 2b, a connection between the top side 10 of said recess 9 and the moon pool's side wall 2a, 2b, 2c or 2d is substantially formed as an edge 12, preferably a relatively sharp edge 12. The edge 12 can be slightly rounded-off to prevent damage to equipment to be raised and/or lowered in the moon pool 2, but should remain sufficiently sharp to provoke flow separation. The top side 10 of said recess 9 is preferably at a substantially right angle with a side wall 2a, 2b, 2c or 2d of said moon pool 2, while the top side 10 of said recess 9 can be substantially in parallel with the hull's deck 13. During use of the vessel, the top side 10 of said recess 9 is preferably located under the waterline 4a.

Figure 3 shows a plot of the wave energy of a typical wave spectrum and a plot of the response amplitude operator or transfer function of the water level elevation (or free surface elevation) inside a moon pool without and with a recess. The continuous line 14 represents a typical wave spectrum of incoming waves, which may induce piston mode water motion in the moon pool. Moon pool water motion in a piston mode can occur for example when a water column in the moon pool, which can be excited by the waves and/or the heave motion of the vessel, enters in resonant condition with the natural mode of the wave spectrum of the incoming waves. The response amplitude operator of the water elevation inside a prior art moon pool, i.e. without any adaptations at its lower end, is given by the peak 15 in Figure 3, and falls within the wave spectrum 14 of incoming piston mode inducing waves. Therefore, it is highly probable that the water motion in the moon pool enters in resonant condition causing a potentially dangerous amplification of the piston mode water motion in the moon pool. However, by providing a moon pool according to the invention, wherein at least part of a lower end of said moon pool is adapted to provide a virtual moon pool draught different from the main moon pool draught, such that a moon pool's piston mode eigenfrequency, or natural wave period, is shifted, in particular away from a main peak in the typical wave spectrum 14 of incoming waves, and preferably outside the wave spectrum 14 of said incoming waves, it is possible to prevent the water in the moon pool 2 from entering in resonant condition. In Figure 3, peak 16 represents the response amplitude operator of the water elevation inside a substantially rectangular moon pool provided with a continuous recess along a lower end 8 of the four side walls, 2a, 2b, 2c and 2d. The peak 16 clearly falls outside the wave spectrum 14 of piston mode inducing incoming waves, thus highly reducing or even avoiding the risk of an amplification of the piston mode water motion in the moon pool 2. An additional advantage of a lower natural moon pool period is that the wave height associated with that period is usually lower as well, such that even if there is a resonant condition of the oscillating water column in the moon pool, the resonance amplitude may be lower. Figure 4a shows a schematic cross-section along a vessel's longitudinal centre line 21 of part of a second embodiment of a vessel according to the invention, which vessel is provided with a moon pool, while Figure 4b shows a schematic bottom view of part of the second embodiment of the vessel of Figure 4a. In this second embodiment, the vessel 1 is provided with a substantially round moon pool 2 having a single side wall 2a, as can be seen in Figure 4b. To enhance the effect of the moon pool's piston mode eigenfrequency shifting, it is preferred to increase the length of the lower end adaptation, preferably providing an entire length of the moon pool's lower end 8 with a virtual moon pool draught adaptation, such as a recess 9. In the embodiment of Figure 4a, the recess 9 has a substantially equal height H along the recess 9, thus providing a clear virtual draught of the moon pool 2. Moreover, a recess's back wall 17 connecting a recess's top side 10 with the bottom surface of the hull 5 is substantially in parallel with the at least one side wall 2a of the moon pool 2.

In most vessels suitable for offshore operations, such as offshore construction, drilling, pipe and/or cable laying, the moon pool is a

substantially rectangular moon pool 2 having four side walls 2a, 2b, 2c, 2d. Figure 5a shows a schematic cross-section along a vessel's longitudinal centre line 21 of part of a third embodiment of a vessel according to the invention, which vessel is provided with a substantially rectangular moon pool. Figure 5b shows a schematic bottom view of part of the third embodiment of the vessel of Figure 5a. Contrary to the embodiment of Figures 2a and 2b, the embodiment of Figures 5a and 5b shows a moon pool 2 of which the lower end 8 is entirely provided with a recess 9, having a substantially equal height H along said recess 9. As shown in the bottom view of Figure 5b, the recess 9 along one side wall, for example 2a, runs into a recess of an adjacent side wall 2c and/or 2d, continuing in the corners between the side walls so that a single recess 9 along the entire lower end 8 of the moon pool 2 is obtained providing a moon pool providing a greater shift in eigenfrequency than a moon pool having a recess per side wall.

Another factor influencing the effectiveness of the shift in the piston mode eigenfrequency is the width W over height H ratio of the recess 9. The ratio of a recess's width W, measured from a moon pool's side wall for example 2a, to a recess's back wall 17, to the height H of the recess 9 is comprised within the range of 0.25 - 1.5, preferably between 0.5 - 1, as in Figure 5a, in which the ratio is 2/3. For example, simulations have been performed with a main moon pool draught 7 of 11 m, and with recesses of 5,5mx5,5m and of

5,5mx7,5m, respectively having a W/H ratio of 1 and of 2/3. The simulations showed that both recesses of W/H ratio of 1 and of 2/3 were performing good, but that the ratio of 2/3 performed somewhat better.

Other ratios W/H are possible and also provide a shift in piston mode eigenfrequency in various degrees, with a higher ratio providing a higher shift, approximately hmited by the theoretical shift, but requiring an increasing effort combined with a decreasing gain in shift. The choice for a given width and/or height of the recess 9 may therefore also depend on other factors, such as the vessel's dimensions and/or the vessel's use, and/or the hull's construction feasibility, with the above-mentioned ratio being a compromise between sufficient effect and feasibility. An optimal height ratio of the recess with respect to the main moon pool draught may be between approximately 10 - 90 %, preferably between about 40 - 80 %. In the example above, with a main moon pool draught of 11 m and a recess height of 7,5 m, the ratio of 7,5/11 is 68%. The height of the recess is preferably such that the water line remains in the main moon pool area, instead of retracts to the recess area. The water line in the recess area would cause undesired slamming motions. Having the water line in the main moon pool area 11, provides for the virtual draught resulting in the shift of the eigenfrequency of the piston mode with respect to the original main moon pool. The vessel provided with a moon pool according to the present invention intends to decrease the occurrence of piston mode water motion in the moon pool, especially during stationary operations of the vessel.

However, the vessel is also going to be in transit before and after stationary operations, during which transit other adaptations of the moon pool may be required to improve the vessel's performance. Figure 6a shows a schematic cross-section along a vessel's longitudinal centre line 21 of part of a fourth embodiment of a vessel according to the invention, which vessel is provided with a moon pool. Figure 6b shows a schematic transversal cross-section of the vessel of Figure 6a, and Figure 6c shows a schematic bottom view of part of the fourth embodiment of the vessel of Figure 6a. In this fourth

embodiment, the lower end 8 of the moon pool 2 has been adapted such as to find a compromise between optimal stationary conditions and transit requirements. In particular, the lower end 8 of the moon pool 2 is provided with a continuous recess 9 along the four side walls 2a, 2b, 2c and 2d. As shown in Figure 6b, the recesses 9 in the side walls 2c and 2d are of a similar construction as the recess in the embodiments of Figures 2a or 5a, i.e. having a top side 10 of said recess 9 substantially in parallel with the hull's deck 13 and recess's back wall 17 connecting a recess's top side 10 with the bottom surface of the hull 5 substantially in parallel with the side wall 2c and/or 2d of the moon pool 2. Along the entire lower end 8 of the moon pool 2, a connection between the top side 10 of said recess 9 and the moon pool's side wall 2a, 2b, 2c, 2d is substantially formed as an edge 12, which is advantageous for a good flow separation, and the top side 10 of said recess 9 is at a substantially right angle with a side wall 2a, 2b, 2c, 2d of said moon pool 2. The shape of the connection 18 between a recess's back wall 17 and a recess's top side 10 being of minor importance to the

effectiveness of a virtual moon pool draught, said connection 18 can be formed as a sharp edge, but need not, and can also be rounded-off, but preferably such that not more than 20% of the recess's original volume is lost by the rounding off, with the original volume being the volume of a recess with a sharp connection 18. In order to improve the water flow in the moon pool 2 during transit of the vessel 1, at least part of a recess's back wall 17 connecting a recess's top side 10 with the bottom surface 5 of the hull may be inclined. As a non-limiting example, the recess 9 in at least one of a leading and/or a trailing side wall 2a, 2b of the moon pool 2 of the vessel in the embodiment represented in Figures 6a-6c comprises a sloping wall 19 forming a, preferably sharp, edge 12 with the moon pool's side wall 2a or 2b but providing a smooth transition with the bottom surface 5 of the vessel's hull. The width W of the recess 9' with a sloping wall 19 may preferably be larger than the width W of the recess 9 along side walls 2c and 2d. Such a recess 9, along the entire lower end 8 of the moon pool 2, but having a different geometry along the different side walls of the moon pool 2, can provide a good compromise between differing requirements for a vessel in transit and for stationary operations of a vessel 1.

Figures 7a and 7b show a schematic cross-section along a vessel's longitudinal centre line 21 of part of a fifth embodiment of a vessel according to the invention, which vessel is provided with a moon pool. This fifth embodiment provides an alternative adaptation of a lower end 8 of a moon pool 2. In particular, at least part of the lower end 8 of the moon pool 2 is provided with at least one wall structure element 20 of which an extension under the hull's bottom substantially in parallel, and preferably in hne, with the at least one side wall 2a, 2b, 2c, 2d of the moon pool 2 is adjustable to provide a virtual moon pool draught different from the main moon pool draught, such that a moon pool's piston mode eigenfrequency is shifted. Instead of providing a virtual moon pool draught 11 that is shorter than the main moon pool draught 7, the at least one wall structure element 20 can provide a virtual moon pool draught 11 that is longer than the main moon pool draught 7, thus causing a shift of the eigenfrequency which is opposite to the shift caused by a recess. Figure 7a shows the at least one wall structure elements 20 in a retracted position such that the main moon pool draught 7 is not modified, which can for example be useful during transit of the vessel 1. Figure 7b shows the at least one wall structure elements 20 in an extended position such that the main moon pool draught 7 is modified to a virtual moon pool draught 11. The at least one wall structure element 20 can comprise for example a single plate on only one side wall, a single plate per side wall, a tubular structure including interconnected plates, at least one telescopically extendable wall structure element, as in Figure 7b, or a telescopically extendable tubular sleeve. The at least one wall structure element 20 can be actuated by actuating means, for example mechanically with a rack-and-pinion system, or for example by hydraulic cylinders or by electrical actuators. The at least one wall structure element 20 can also be guided by guiding means. Said actuating means as well as said guiding means do preferably not protrude into the moon pool, and may for example be located in an enclosure behind a moon pool side wall.

Figures 8a and 8b show a schematic cross-section along a vessel's longitudinal centre line 21 of part of a sixth embodiment of a vessel according to the invention, which vessel is provided with a moon pool. In the embodiment of Figures 8a and 8b, the feature of an extendable and adjustable wall structure element 20 is combined with a recess 9. In that case, the at least one wall structure element 20 can partly or entirely close off a recess 9, for example when an increase in eigenfrequency is more preferred than a decrease to avoid resonance. Figure 8b shows a

telescopically extendable structure 20, be it a plate structure or a tubular structure, whereas Figure 8a shows a non-telescopically extendable structure, both in an extended position. The virtual moon pool draught 11 is preferably adjustable, which is made possible via the extendable and adjustable wall structure elements 20 in line with a moon pool's side wall. In combination with a recess, as shown in Figures 8a - 8b, the virtual moon pool draught 11 is adjustable between a virtual draught 11' measured from the water level 4a to the edge 12, which is smaller than the main moon pool draught 7, to a virtual moon pool draught 11" measured till the utmost extension of the wall structure element 20, which is a virtual draught that is larger than the main moon pool draught.

For the purpose of clarity and a concise description, features are described herein as part of the same or separate embodiments, however, it will be appreciated that the scope of the invention may include

embodiments having combinations of all or some of the features described. It may be understood that the embodiments shown have the same or similar components, apart from where they are described as being different.

In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word 'comprising' does not exclude the presence of other features or steps than those listed in a claim. Furthermore, the words 'a' and 'an' shall not be construed as limited to 'only one', but instead are used to mean 'at least one', and do not exclude a plurality. The mere fact that certain measures are recited in mutually different claims does not indicate that a combination of these measures cannot be used to an advantage. Many variants will be apparent to the person skilled in the art. All variants are understood to be comprised within the scope of the invention defined in the following claims.

List of references

1 Vessel

2 Moon pool

2a Moon pool's front wall

2b Moon pool's rear wall

2c Moon pool's side wall

2d Moon pool's side wall

3 Hull

3a Bow

3b Stern

4 Water

4a Waterline

5 Bottom surface of the hull

6 Vertical direction

7 Main moon pool draught

8 Lower end of moon pool

9 Recess with height H and width W

10 Top side of recess

11 Virtual moon pool draught

12 Edge

13 Hull's deck

14 Typical wave spectrum of incoming waves

15 Response amplitude operator of the water elevation inside a prior art moon pool

16 Response amplitude operator of the water elevation inside a moon pool according to the invention

17 Back wall of recess

18 Connection

19 Sloping wall Wall structure element

Vessel's longitudinal centre line