U.S. patent number RE30,590 [Application Number 06/034,318] was granted by the patent office on 1981-04-28 for vertically moored platform.
This patent grant is currently assigned to Standard Oil Company (Indiana). Invention is credited to Kenneth A. Blenkarn.
United States Patent |
RE30,590 |
Blenkarn |
April 28, 1981 |
**Please see images for:
( Certificate of Correction ) ** |
Vertically moored platform
Abstract
This invention relates to a structure floating on a body of
water. Three or more spar buoy-type floats support the structure
above the water. The structure is connected to anchors in the floor
of the body of water by .[.elongated members such as.]. large
diameter pipe .Iadd.for example.Iaddend.. There are no other
anchoring connections in the system. Each spar buoy has a unique
structure so that vertical forces and overturning moments on the
floating structure are minimized. .[.The spar buoys have a buoyancy
means having a volume of two parts..]. g The buoy of each spar buoy
has a volume of two parts. The first part can be defined as
resulting from a straight, vertical, prismatic shape which runs the
entire vertical length of the .[.buoyancy means..].
.Iadd.buoy.Iaddend.. The volume of this prismatic portion comprises
between about 40 and 80 percent of the total displacement. The
.[.buoyancy means have a second or.]. .Iadd.second part has an
.Iaddend.auxiliary volume of displacement which runs considerably
less than the vertical length of the prismatic portion. This
critical arrangement of buoyancy between these two parts as taught
in this invention minimizes mooring forces imposed on the vertical
elongated members, such as occur to react forces on the structure
due to passing waves.
Inventors: |
Blenkarn; Kenneth A. (Tulsa,
OK) |
Assignee: |
Standard Oil Company (Indiana)
(Chicago, IL)
|
Family
ID: |
26689937 |
Appl.
No.: |
06/034,318 |
Filed: |
April 30, 1979 |
Related U.S. Patent Documents
|
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
|
754628 |
Aug 28, 1968 |
|
|
|
Reissue of: |
017485 |
Mar 9, 1970 |
03648638 |
Mar 14, 1972 |
|
|
Current U.S.
Class: |
114/265;
405/202 |
Current CPC
Class: |
B63B
21/502 (20130101); B63B 35/4413 (20130101); B63B
2035/442 (20130101) |
Current International
Class: |
B63B
35/44 (20060101); B63B 21/00 (20060101); B63B
21/50 (20060101); B63B 035/00 (); B63B
035/44 () |
Field of
Search: |
;114/265,264,293
;405/203,224,225,202 ;175/7 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Basinger; Sherman D.
Attorney, Agent or Firm: Gassett; John D.
Parent Case Text
CROSS-REFERENCE TO RELATED APPLICATION
This application is a continuation-in-part application of copending
application Ser. No. 754,628, entitled "Vertically Moored
Platforms," filed Aug. 28, 1968, Kenneth A. Blenkarn and now
abandoned.
Claims
I claim:
1. A floating structure having limited lateral movement for use in
a body of water which comprises:
a working deck;
buoyancy means for supporting said working deck, said buoyancy
means including a plurality of slender vertical float members;
anchor means in the floor of the body of water;
horizontally spaced-apart, parallel, elongated members
interconnecting the said buoyancy means and said anchor means
whereby said deck is maintained parallel to and at a substantially
constant angle with reference to the horizontal;
each said vertical float member of said buoyancy means having
prismatic volume resulting from a straight, vertical, prismatic
shape which runs the entire vertical length of the buoyance means,
the volume of the prismatic portion comprising between about 40
and80 percent of the total displacement of the buoyancy means, and
the structure having an auxiliary buoyancy portion having a volume
of displacement between about 20 and about 60 percent of the total
displacement of the buoyancy means, said auxiliary volume being
placed below the trough of an expected maximum wave;
said platform and buoyancy means being free of any anchoring
connection with the water bottom other than said parallel elongated
members.
2. A structure as defined in claim 1 in which the volume of the
prismatic portion comprises between about 40 and about 60 percent
of the total displacement of the buoyancy means.
3. A structure as defined in claim 1 in which the ratio h.sub.max
/H is about 0.8 in which h.sub.max is the height of an expected
maximum wave and H is the still water draft.
4. A structure as defined as claim 3 in which the still water draft
is between about 75 feet and about 150 feet.
5. A structure as defined in claim 1 in which the structure is so
designed so as to have a still water draft between about 75 feet
and about 150 feet.
6. An apparatus as defined in claim 1 including pivotal means
connecting the lower ends of said elongated members with said
anchor means and additional pivotal means connecting the upper ends
of said elongated members with said buoyance means.
7. An apparatus as defined in claim 1 including horizontal fins
attached to the lower portion of said buoyancy means.
8. An apparatus as defined in claim 7 including means to move said
horizontal fins about a horizontal axis.
9. An apparatus as defined in claim 1 in which said elongated
members are tubular members.
10. An apparatus as defined in claim 1 including cross bracing
between the vertical float means, said cross bracing being
restricted to the areas below the still water line.
11. A floating structure for use in the body of water having an
expected maximum wave which comprises:
a deck;
buoyancy means rigidly supporting said deck, said buoyancy means
including at least three slender, vertical float members, each such
float member having two parts, the first part resulting from a
straight, vertical, prismatic shape which runs the entire vertical
length of the vertical float member, the volume of the prismatic
portion comprising between about 40 and about 80 percent of the
total displacement of the vertical float member, and an auxiliary
portion exterior said prismatic portion and, comprising between
about 20 and about 60 percent of the total displacement of the
buoyancy means below still water, said auxiliary portion being
placed below the trough of the expected maximum wave;
anchor means at the bottom of said body of water;
an elongated member connecting each said vertical float member and
said anchor means, said elongated members being parallel;
said structure being free of any anchoring connection with the
water bottom other than said parallel elongated members.
12. A structure as defined in claim 11 in which the volume of the
prismatic portion of the vertical float member is between about 45
and 65 percent of the total displacement of the vertical float
member and the auxiliary portion exterior of said prismatic portion
comprises between about 55 and about 35 percent of the total
displacement of the buoyancy means below still water.
13. An apparatus as defined in claim 11 including pivotal means
connecting the lower ends of said elongated members with said
anchor means and additional pivotal means connecting the upper ends
of said elongated members with said buoyancy means.
14. An apparatus as defined in claim 11 in which said elongated
members are tubular members.
15. A structure as defined in claim 11 in which the ratio h.sub.max
/H is about 0.8 in which h.sub.max is the expected maximum wave
height and H is the still water draft.
16. A structure as defined in claim 11 with a ratio h.sub.max /H
that is between about 0.65 and about 1.00 where h.sub.max is the
expected maximum wave height and H is the still water draft.
17. A floating structure for use in a body of water having an
expected maximum wave height h.sub.max which comprises:
a deck;
buoyancy means rigidly supporting said deck, said buoyancy means
providing a total still water displacement B and including at least
one slender vertical float member having a still water draft H,
comprising two parts, the first part resulting from a straight
prismatic shape which runs the entire vertical length of the
vertical float member and an auxiliary portion exterior to said
prismatic portion having an overall vertical length L, said
auxiliary portion being placed below the trough of the expected
maximum wave, for which the shape of the slender, vertical float
member is defined by a value of r, said parameter r being the ratio
of the maximum radius of the auxiliary portion to the radius of the
prismatic portion, which value r is Equations (32) through
(34);
anchor means at the bottom of said body of water;
elongated member interconnecting each said slender vertical float
member and said anchor means, if there is more than one vertical
float member, the said elongated members associated therewith are
parallel;
said structure being free of any anchoring connection with the
water bottom other than said elongated member.
18. A structure as defined in claim 17 in which the ratio
(h.sub.max /H) is about 0.8.
19. A structure as defined in claim 17 in which the ratio h.sub.max
/H is between about 0.65 and about 1.00.
20. A structure as defined in claim 17 in which said elongated
members are tubular members.
21. A structure as defined in claim 17 in which there are at least
three slender vertical float members and an elongated member
connecting each said slender vertical float member and said anchor
means, said elongated members being parallel; said structure being
free of any anchoring connecting with the water bottom other than
said elongated members.
22. A structure as defined in claim 21 in which the ratio h.sub.max
/H is between about 0.65 and about 1.00.
23. A structure as defined in claim 22 in which the ratio h.sub.max
/H is about 0.8.
24. A structure as defined in claim 17 in which r is between about
r.sub.3 and r.sub.4.
25. A floating structure for use in a body of water and having an
expected maximum wave height h.sub.max which comprises:
a deck;
buoyancy means rigidly supporting said deck, said buoyancy means
providing a total still water displacement B and including at least
one slender vertical float member, said vertical float member
having a still water draft H, comprising two parts, the first part
resulting from a straight prismatic shape which runs the entire
vertical length of the vertical float member and an auxiliary
portion exterior to said prismatic portion having an overall
vertical length L, said auxiliary portion being placed below the
trough of the expected maximum wave, for which the shape of the
slender, vertical float member is defined by a value of r, said
parameter r being the ratio of the maximum radius of the auxiliary
portion to the radius of the prismatic portion, which value r is
between about [r.sub.1 -(0.3341 kips/ft..sup.2)(H.sup.2 /B)] and
about [r.sub.2 +(34.41 kips/ft.)(H/B)] where r.sub.1 is determined
from equations (20) through (22) and r.sub.2 is determined from
equations (23) through (25);
anchor means at the bottom of said body of water;
an elongated member interconnecting each said vertical float member
and said anchor means, if there is more than one vertical float
member, the said elongated members associated therewith are
parallel;
said structure being free of any anchoring connection with the
water bottom other than said parallel elongated members.
26. An apparatus as defined in claim 25 including pivotal means
connecting the lower ends of said elongated members with said
anchor means and additional pivotal means connecting the upper ends
of said elongated members with said buoyancy means.
27. An apparatus as defined in claim 25 in which said elongated
members are tubular members.
28. A structure as defined in claim 25 in which there are at least
three slender vertical float members and an elongated member
connecting each said slender vertical float members and said anchor
means, the said elongated members associated therewith being
parallel;
said structure being free of any anchoring connected to the water
bottom other than said elongated members.
29. A structure as defined in claim 28 in which the ratio h.sub.max
/H is between about 0.65 and about 1.00.
30. A structure as defined in claim 29 in which the ratio h.sub.max
/H is about 0.8.
31. A structure as defined in claim 25 in which the value of r is
between about r.sub.1 and r.sub.2.
32. A floating structure as defined in claim 25 in which the ratio
h.sub.max /H is between about 0.75 and about 0.85.
33. A structure as defined in claim 32 in which the ratio h.sub.max
/H is about 0.8.
34. A floating structure for use in a body of water having an
expected maximum wave height h.sub.max which comprises:
a deck;
buoyancy means rigidly supporting said deck, said buoyancy means
providing a total still water displacement B and including at least
one slender vertical float member having a still water draft H,
each said vertical float member comprising two parts, the first
part resulting from a straight prismatic shape which runs the
entire vertical length of the vertical float member and an
auxiliary portion exterior to said prismatic portion having an
overall vertical length L, said auxiliary portion being placed
below the trough of the expected maximum design wave, for which the
shape of the slender, vertical float member is defined by a value
of r, said parameter r being the ratio of the maximum radius of the
auxiliary portion of the radius of the prismatic portion, which
value r is between about [r.sub.bt -(0.3441 kips/ft..sup.2
)(H.sup.2 /B)] and about [r.sub.bt +(34.41 kips/ft.)(H/B)] where
r.sub.bt is determined from Equations (10), (16) and (17);
anchor means at the bottom of said body of water;
an elongated member connecting each said vertical float member and
said anchor means, said elongated members associated therewith
being parallel;
said structure being free of any anchoring connection with the
water bottom other that said parallel elongated members.
35. An apparatus as defined in claim 34 including pivotal means
connecting the lower ends of said elongated members with said
anchor means and additional pivotal means connecting the upper ends
of said elongated members with said buoyancy means.
36. A structure as defined in claim 34 in which there are at least
three slender vertical float members and an elongated member
connecting each said slender vertical float members and said anchor
means, the said elongated members associated therewith being
parallel;
said structure being free of any anchoring connection to the water
bottom other than said elongated members.
37. An apparatus as defined in claim 34 in which said elongated
members are tubular members.
38. A structure as defined in claim 34 in which the value of r is
equal to r.sub.bt.
39. A structure as defined in claim 34 wherein said ratio h.sub.max
/H is about 0.8.
40. A structure as defined in claim 36 in which the ratio h.sub.max
H is about 0.8.
41. A floating structure for use in a body of water which
comprises:
a deck;
buoyancy means rigidly supporting said deck, said buoyancy means
providing a total still water displacement between about 15,000,000
pounds and about 60,000,000 pounds and including at least three
slender, vertical float members, each such vertical float member
having a still water draft between about 75 and about 150 feet and
comprising two parts, the first part resulting from a straight,
vertical prismatic shape which runs the entire vertical length of
the vertical float member and an auxiliary portion exterior to said
prismatic portion, said auxiliary portion being placed below the
trough of the maximum design wave, for which the shape of the
slender, vertical float member is defined by either (a) values of p
and r which when plotted as a point falls into the shaded regions
of either FIGS. 15B through 23B or falls into shaded regions
obtained by a linear interpolation between the shaded regions of
these figures, said interpolation being made on the basis of still
water displacement and still water draft, or (b) values of (L/H)
and r which when plotted as a point falls into the shaded regions
of either FIGS. 15A through 23A, or falls into shaded regions
obtained by a linear interpolation between the shaded regions of
these figures, said interpolation being made on the basis of still
waster displaceent and still water draft; anchor means at the
bottom of said body of water;
an elongated member interconnecting each said buoyancy means and
said anchor means, said elongated members associated therewith
being parallel;
said structure being free of any anchoring connection with the
water bottom other than said parallel elongated members.
42. An apparatus as defined in claim 41 in which said elongated
members are tubular members. .Iadd.
43. A structure as defined in claim 9 including means for
conducting drilling operations through said tubular members to
underground formations. .Iaddend. .Iadd.
44. A structure as defined in claim 9 wherein said anchor means
includes piles extending into the floor of said body of water
whereby holes can be drilled in said floor through said tubular
members. .Iaddend. .Iadd.
45. A structure as defined in claim 9 including wellhead equipment
located at the surface of the body of water. .Iaddend. .Iadd.
46. A structure as defined in claim 9 wherein said structure is
used as a production gathering facility. .Iaddend. .Iadd.
47. A structure as defined in claim 14 including means for
conducting drilling operations through said tubular members to
underground formations. .Iaddend. .Iadd.
48. A structure as defined in claim 14 wherein said anchor means
includes piles extending into the floor or said body of water
whereby holes can be drilled in said floor through said tubular
members. .Iaddend. .Iadd.
49. A structure as defined in claim 14 including wellhead equipment
located at the surface of the body of water. .Iaddend. .Iadd.
50. A structure as defined in claim 14 wherein said structure is
used as a production gathering facility. .Iaddend. .Iadd.
51. A structure as defined in claim 20 including means for
conducting drilling operations through said tubular members to
underground formations. .Iaddend. .Iadd.
52. A structure as defined in claim 20 including wellhead equipment
located at the surface of the body of water. .Iaddend. .Iadd.
53. A structure as defined in claim 20 wherein said structure is
used as a production gathering facility. .Iaddend. .Iadd.
54. A structure as defined in claim 27 including means for
conducting drilling operations through said tubular members to
underground formations. .Iaddend. .Iadd.
55. A structure as defined in claim 27 including wellhead equipment
located at the surface of the body of water. .Iaddend. .Iadd.
56. A structure as defined in claim 27 wherein said structure is
used as a production gathering facility. .Iaddend. .Iadd.
57. A structure as defined in claim 37 including means for
conducting drilling operations through said tubular members to
underground formations. .Iaddend. .Iadd.
58. A structure as defined in claim 37 including wellhead equipment
at the surface of the body of water. .Iaddend. .Iadd.
59. A structure as defined in claim 37 wherein said structure is
used as a production gathering facility. .Iaddend. .Iadd.
60. A structure as defined in claim 42 including means for
conducting drilling operations through said tubular members to
underground formations. .Iaddend. .Iadd.
61. A structure as defined in claim 42 including wellhead equipment
located at the surface of the body of water. .Iaddend. .Iadd.
62. A structure as defined in claim 42 wherein said structure is
used as a production gathering facility. .Iaddend.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to a structure floating on a body of water.
More particularly, the invention relates to a floating structure
from which drilling or production operations are carried out. In
its more specific aspects, the invention concerns a floating
structure having buoyancy means placed especially with respect to
the trough of a design wave so as to minimize mooring forces
imposed on the vertical elongated members which anchor the
structure, such as those forces which may be caused by passing
waves.
2. Setting of the Invention
In recent years there has been considerable attention attracted to
the drilling and production of wells located in water. Wells may be
drilled in the ocean floor from either fixed platforms in
relatively shallow water or from floating structures or vessels in
deeper water. The most common means of anchoring fixed platforms
include the driving or otherwise anchoring of long piles in the
ocean floor. Such piles extend above the surface of the water with
a support or platform attached to the top of the piles. This works
fairly well in shallower water, but as the water gets deeper, the
problems of design and accompanying costs become prohibitive. In
deeper water it is common practice to drill from a floating
structure.
In recent years there has been some attention directed toward many
different kinds of floating structures, for the most part
maintained on station by conventional spread catenary mooring
lines, or by propulsion thruster units. One scheme recently
receiving attention for mooring is employed in the so-called
vertically moored platform. One such platform is described in U.S.
Pat. No. 3,154,039, issued Oct. 27, 1964. A key feature of the
disclosure in the patent is that the floating platform is connected
to an anchor base only by elongated parallel members. The members
there are held in tension by excess buoyancy of the platform. This
feature offers a remedy for one of the major problems arising in
the conduct of drilling, or like operations from a floating
structure. This major problem is that ordinary hull-type barges or
vessels, in response to ocean waves, may exhibit substantial
amounts of vertical heave and angular roll motion. Such motions
significantly hinder drilling operations. Motion difficulties are
alleviated to a degree by use of the so-called semisubmersible
vessels or structures in which flotation buoyancy is provided by
long, slender vertical bottles or tanks. This design suffers the
inconvenience that, if carried to the logical extreme of having
very little waterplane area, the unit would become statically
unstable, requiring careful reballasting to offset changes in
vertical loads, such as drilling hook load (e.g., when pulling
drill pipe, etc.) or changes in weight of supplies. Some of those
problems are eliminated or at least reduced in the vertically
moored platform. Being subjected to tension, the elongated parallel
members of the vertically moored platform are substantially
inextensible and therefore restrain the platform to move primarily
in the horizontal direction. This virtually eliminates heave and
roll motions. In vertically moored structures heretofore
considered, exceptionally strong mooring would be required to
resist the vertical forces which might be imposed upon a structure
by the orbital motion of passing waves. The present invention
describes a means to minimize the mooring forces imposed by the
structure on the elongated members, such as those caused by passing
waves.
BRIEF DESCRIPTION OF THE INVENTION
Briefly, a preferred embodiment of this invention concerns a
floating structure having limited lateral movement for use in a
body of water. It is especially designed for an expected maximum
wave. This expected wave is usually called the "maximum design
wave." The structure includes a working platform supported by a
buoyancy means comprising a plurality of slender vertical float
members. The float members are rigidly anchored to the ocean floor
by a plurality of horizontally spaced-apart, parallel, elongated
members. The volume of the buoyancy means can be defined as
comprising two parts, the first part resulting from a straight,
vertical, prismatic shape which runs the entire vertical length of
each vertical float member. The volume of the prismatic portion
comprises from about 40 percent to about 80 percent of the total
displacement of the buoyancy means below the "still water" line.
The ratio of the displacement of the prismatic portion to the total
displacement is called the prismatic ratio p. A second volume of
displacement surrounds the prismatic portion and comprises the
remainder of the total displacement. This second volume is placed
below the trough of the design wave. This critical placement of the
second or auxiliary volume and the critical size minimizes the
critical mooring forces imposed on the vertical elongated members
by the structure due to the orbital motion of the passing
waves.
Various objects and a better understanding of the invention can be
had from the following description taken in conjunction with the
drawings.
DESCRIPTION OF THE DRAWINGS
FIG. 1 is a view of a floating structure of this invention;
FIG. 2 illustrates a perspective view of a part of one of the
vertical floats of FIG. 1;
FIG. 3 is a section taken along the line 3--3 of FIG. 1;
FIG. 4A illustrates relative vertical forces for ratios of the
radii and the lengths of the prismatic portion and the auxiliary
portion of the vertical buoyancy means for a still water draft of
100 feet;
FIG. 4B is similar to FIG. 4A and illustrates selection of limits
of the prismatic ratios for the same still water draft of 100
feet;
FIG. 5A is similar to FIG. 4A except it is for a still water draft
of 125 feet;
FIG. 5B is similar to FIG. 4B except it is for a still water draft
of 125 feet;
FIGS. 6A, 6B and 6C illustrate the variation in mooring force for
three fundamental types of vertically moored platforms which
consist respectively of only one slender, vertical float member; a
float member completely submerged; and a buoyancy member according
to this invention;
FIG. 7A shows the shape of a typical vertical buoyancy means of my
invention;
FIG. 7B shows the forces acting on a typical vertically moored
platform comprising only one vertical float member of my
invention;
FIG. 8 shows an example of overturning moment on a floating
structure such as shown in FIG. 1;
FIG. 9 shows an example of variation in mooring force for a given
leg due to the overturning moments shown in FIG. 8;
FIG. 10 demonstrates the typical influence on a floating structure
according to my invention due to coupling between net vertical
forces on individual legs;
FIGS. 11A and 11B illustrate the net variation in mooring force at
one leg of a vertically moored platform which comprises vertical
float members of a typical configuration according to my
invention;
FIGS. 12A and 12B illustrate the net variation in mooring force at
one leg of a vertically moored platform which comprises vertical
float members made up of prismatic cylinders;
FIGS. 13A and 13B illustrate the net variation in mooring force at
one leg of a vertically moored platform in which the float members
are made up of deep spheroidal floats only;
FIG. 14 shows the maximum variation in mooring force at a given
leg, expressed as a percent of the displacement per leg, for
various values of the shape parameters r and (L/H) (the term r, L
and H are defined hereinafter) and for particular platform size and
design condition, as noted;
FIGS. 15A through 23A illustrate (a) the best combinations of shape
parameters r and (L/H) and (b) the range of practical combinations
of these parameters for various platform sizes and design
conditions, as noted;
FIGS. 15B through 23B illustrate (a) the best combinations of shape
parameters p and r and (b) the range of practical combinations of
these parameters for various platform sizes and design conditions,
as noted.
Referring to the drawings in which identical numbers are employed
to identify identical parts, numeral 10 designates, generally, the
floating structure or platform. The floating structure 10 includes
a deck portion 12 which may have a derrick 14 mounted thereon. The
deck 12 is preferably an enclosed space where quarters, workshop
area, etc., are located. This is to aid in streamlining the system.
Various auxiliary means, including a port for helicopter, etc., may
be provided.
The deck 12 is supported by at least three vertical float means,
generally designated by the numeral 16. This includes an upper
"skinny" portion 18 and a lower "fat" portion 20. There are enough
of these vertical support means 16 to provide stability. This would
ordinarily be three or more. There are four shown as indicated in
FIG. 3. The size and placement of the lower portion 20 of the float
will be discussed later.
The platform is anchored by suitable means to the ocean floor.
Shown in the drawing is a baseplate 22. Anchor piles 24 extend into
the bottom of the ocean for whatever depth is needed to secure the
proper anchorage, e.g., 500 feet. These anchor members are secured
in place, for example, by cement 26. Connecting anchor members 24
to the working structure or platform are a plurality of elongated
member 28 alternately called risers. These elongated members 28 are
preferably large-diameter steel pipe, e.g., 20 to 30 inches in
diameter. These elongated members 28 could be cables of wire,
chain, and the like. However, it is preferred that they be pipe so
that operations can be conducted from the floating structure down
through them to underground formations. Preferably, it is desired
to drill down through these pipes.
The structure shown in FIG. 1 is essentially rigid in the vertical
direction, but is relatively free to move in the horizontal
direction. Restraint against horizontal movement is only the
horizontal component of riser tension, that component being
proportional to the angular departure of the riser from true
vertical. Under the action of wind, current and other steady
forces, the platform will be shifted horizontally until the
resultant horizontal restraint equals such applied loads. In
response to wave action the platform will oscillate back and forth
about the shifted or average position. The platform will, for storm
wave situations, generally oscillate horizontally so as to move
with the surrounding fluid. The horizontal motion of the platform
will basically satisfy the following relation. ##EQU1## in
which
X=the single amplitude horizontal motion of the platform.
A'=the horizontal, single amplitude wave motion of water at the
elevation of the platform center of buoyancy. See Equation (2).
B=the buoyancy or displacement of the platform.
H'=the "hydrodynamic mass" of water associated with acceleration of
the platform. For most configurations H' is essentially equal to
buoyancy.
M=the actual weight of the platform.
T=the wave period.
T.sub.n =the natural sway period, calculated from Equation (3).
Water motion A' is calculated, for simple wave theories, according
to the following equation. ##EQU2## in which
h=wave height, crest to trough.
S=the submergence of the platform center of buoyancy below still
water level.
.lambda.=wave length (=5.12T.sup.2, by Airy Theory).
Natural sway period of the platform is expressed as (3)
T.sub.n.sup.2 =L' (H'+M)/B-M
in which
L'=the length of vertical mooring lines or risers, and other
symbols are as previously defined.
For most platform configurations of interest, a design wave 100
feet high would cause the platform to move 50 feet either side of
the average shifted position. It is generally to be preferred that
steady storm shift of the platform be approximately equal to the
single amplitude of the wave induced motion. For the case just
described, an appropriate design shift would be 50 feet. For water
depth requiring vertical risers 1,000 feet long, such a horizontal
shift would correspond to a horizontal restraint equal to 1/20 of
the tension in the vertical mooring lines or risers. Thus, tension
in the risers should generally be between 15 and 25 times the
steady horizontal storm loads. Typically required total tensions in
the order of 10,000,000 pounds are to be expected. Typically such a
tension could be carried by 16 or 20 pipe risers which have 20
inches outside diameter with a wall thickness of 0.625 inches.
It has been found that when pipes such as risers 28 are under
tension and subject to angular rotation, the influence of tension
is to concentrate the angular rotation at the ends of the pipe.
Accordingly, means are provided in risers 28 to permit this angular
rotation with the two terminals of the riser pipe 28. This is
provided in the form of a ball joint 30 at the upper end and a ball
joint 32 at the lower end.
Another means of providing for the excess stresses which would be
built up near the ends of pipe 28 if they were not hinged, is to
provide a section of special size and wall thicknesses at the end
of the pipe to make them sufficiently strong to withstand the
imposed stresses. Other suitable means for limiting this
concentration of stress are described in the copending patent
application of Blenkarn and Dixon, Ser. No. 748,867 filed July 30,
1968.Iadd., now U.S. Pat. No. 3,559,410.Iaddend.. The vertical
members 16 are connected by cross bracing 34. This cross bracing is
preferably all located below the still waterline indicated by line
36. As mentioned earlier, this structure will be subjected to
various wave forces. In Naval engineering, when designing floating
structures, or other marine structures for that matter, it is quite
common to select what is known as a maximum design wave. The
maximum design wave will have a crest 38 and a trough 40.
There are concepts disclosed herein which teach the means by which
the mooring forces are minimized when using the invention as
exemplified by the embodiment of FIG. 1. A particularly desirable
shape for the vertically positioned elongated floats is illustrated
in FIG. 1. With reference to such a shape, the following applies.
The volume of buoyancy or displacement can be conceived as being
made up of two parts. The first part results from a straight,
vertical, prismatic shape which has the diameter of upper portion
13 and runs the entire vertical length of the structure. The volume
of this prismatic portion of the structure comprises between about
40 percent and about 80 percent of the total displacement. The
second or auxiliary volume of displacement is that part which is
the annulus volume between the prismatic volume and the inner wall
of enlarged portion 20. This auxiliary volume is placed below
trough 40 of the maximum design wave.
The auxiliary volume should be placed in a smooth and streamlined
fashion, as indicated above, as an annular space around the basic
prismatic volume. The size of the auxiliary volume in the annulus
portion of the "bottles" should be reduced to the extent of
displacement provided by the bracing 34 within the structure which
is below the trough of the design wave. The auxiliary volume in the
annular space should be streamlined and flared into the basic
prismatic volume to the extent practical. While I have discussed a
prismatic volume and an auxiliary volume, it is to be understood
that these two volumes can be continuous and that it is not
necessary that they be separated into physical compartments.
If a vertically moored platform is to be used, it is usually
necessary that variations of vertical mooring forces, which arise
in reaction to forces imposed on the structure by wave action, be
minimized within the range of wavelengths of importance.
Wavelengths of importance vary from one wave area to another but
many are typically in the range of from about 500 ft. to 2,000 ft.
Wave action on the structure results in (a) a net vertical force on
the structure, (b) a net couple on the structure due to vertical
forces on individual bottles, and (c) a net overturning moment on
the structure due to horizontal wave forces. All of these forces
contribute to the variation in mooring force.
The structures of my invention minimize the variation in mooring
force, for the range of wave lengths of importance, by permitting
offsetting contribution from each of the contributing factors: net
vertical force, net couple of vertical forces and net overturning
moment. If I did not use the structure of my invention to obtain
proper distribution, one of these forces might be overpowering. For
example, if vertical forces on individual bottles are eliminated or
minimized, thereby eliminating or minimizing the net vertical
forces and the net couple due to vertical force on the structure,
the variation in mooring force is due entirely to overturning
moment and can be undesirably large, especially for the longer
wavelengths. On the other hand, if the buoyancy arrangement is such
that a small amount of net vertical force is admissible for all
wavelengths, there is a phenomenon associated with this force, the
net coupling of vertical forces, which causes a net reduction in
overturning moments at the larger wavelengths. Therefore, a careful
selection of buoyancy distribution can result in a minimization of
mooring force variations over the entire range of important
wavelengths. This I teach.
The vertical forces on the structure are dominated by forces which
fall into two categories: namely, (a) variable buoyancy and (b)
vertical water acceleration forces. While there are other
contributions to the net vertical forces, they are of lesser
importance. All of these forces on the structure were calculated by
elementary, commonly understood means. However, the dominant two
forces were combined for the calculations into one net force,
heave, which is discussed below. The two categories of dominant
vertical forces act in opposite direction to one another and one of
the concepts of this invention is to carefully adjust the
magnitudes of these forces to obtain the desired net vertical
force. This is possible with my design for certain ratios (L/H) of
the length (L) of the enlarged portion to the total design draft
(H) and for certain ratios (r) of the radius R.sub.1 of the
enlarged portion to the radius R.sub.0 of the prismatic portion for
a selected draft where L, H, R.sub.0 and R.sub.1 are defined in
FIG. 1. As shown above, the prismatic ratio "p" is defined as the
ratio of the displacement of the prismatic portion to the total
displacement.
I shall first consider the net vertical forces on the structure. (I
shall consider the net overturning moment later and how my
structure minimizes such moment.) These various net vertical forces
can be calculated by using the following equation. ##EQU3##
where:
F=net change in vertical force, positive upwards
.DELTA.(.eta.)=total displacement below the instantaneous water
level
.DELTA.(O)=design displacement, or total displacement below design
still water level
k=wave decay factor, i.e., =2.pi./.lambda. where .lambda.=wave
length (Airy Theory)
.rho.=water mass density
g=gravitational acceleration
A(y)=cross section area (varies with depth or y)
.phi.(y)=hydrodynamic mass coefficient and varies with depth,
i.e., .phi.(y)=mass of cylinder + added fluid mass/mass of
cylinder
H=design draft
y=a vertical coordinate measured position upwards from the base of
the buoyancy means
.eta.=a vertical coordinate measured position upwards from the
design still water level to the instantaneous water surface (=Y-H).
In Equation (4) terms [.DELTA.(.eta.)-.DELTA.(O)] give the force
due to variable buoyancy, and the remaining term gives the force
due to vertical water acceleration.
Consider first two very elementary types of vertically moored
structures as shown in FIGS. 6A and 6B. In FIG. 6A is a buoy
consisting only of one cylinder. This buoy is moored by one or more
vertical tethers such that it is not free to move vertically, but
it can move horizontally or rotate. The buoy does not have an
annular, or auxiliary portion; all displacement is from the
prismatic portion. Therefore, the prismatic ratio p which is
defined as the ratio of the displacement of the prismatic portion
to the total displacement, equals one (p=1). The three curves in
FIG. 6A show the variation of net vertical force on the cylinder
due to passage of a single wave from three different wave trains.
The three wave trains have periods of 10, 14 and 20 seconds; the
corresponding wave lengths are 512, 1,004 and 2,048 ft.,
respectively. In this example and all subsequent examples it is
assumed that the wave height corresponding to each wavelength
equals either one-tenth of the wavelength or the maximum design
wave height, whichever is smaller. In this and most of the
subsequent examples, except where noted, the maximum design wave
height is 100 ft. Therefore, the corresponding wave heights for the
curves in FIG. 6A are 51.2, 100 and 100 ft., respectively. The
variation of net vertical forces is expressed as a percent of total
displacement. For example, a 20-second wave causes a reduction in
net vertical force of about 32 percent of the displacement when the
wave trough is aligned at the axis of the cylindrical buoy. When
the crest is aligned with the axis of the cylindrical buoy there is
an increase in net vertical force of about 22 percent of the
displacement. By virtue of the decrease in net vertical force at
the trough and the increase at the crest, this example demonstrates
that forces due to variable buoyancy are dominating for the high
prismatic ratio. As an explanation of terminology, the term
"leading crest" is that part of the wave halfway between the trough
and the next crest. The term "following crest" is that part of the
wave train at a point one-half way between the crest and the next
trough.
FIG. 6B shows similar curves for another fundamental configuration
of a vertically moored structure. In this case the entire
displacement is contributed by a spherical cavity at the bottom of
the buoy and the portion of the structure projecting upwards from
the sphere has an extremely small cross section. Consequently, the
prismatic portion contributes essentially nothing to the total
displacement, and the annular, or auxiliary, portion contributes
the entire displacement. The prismatic ratio equals zero (p=0). The
curves of FIG. 6B show that the maximum variation in net vertical
force is about 30 percent of the displacement in the long-period,
20-second wave. However, in this example, the vertically moored
structure experiences an increase in net vertical force when the
wave trough is aligned with the buoy, rather than a decrease as
with the cylindrical buoy in FIG. 6A. This example demonstrates
that for a low prismatic ratio the forces due to vertical water
acceleration are dominating.
My invention teaches that for a low prismatic ratio, forces due to
vertical water acceleration are dominating while for a high
prismatic ratio, forces due to variation in buoyancy are
dominating. Moreover, my invention teaches that for an intermediate
value of the prismatic ratio, p, there exists a balance between
variable buoyancy forces and vertical water acceleration forces
such that the variation in net vertical force for the wavelengths
of interest are substantially smaller than in the two fundamental
cases examined above.
Consider for example a vertically moored structure of my invention
as shown in FIG. 6C. In this case the parameters describing the
physical properties of the bottle are r=1.853, (L/H)=0.5 and
p=0.545. In addition, the maximum design wave height, h.sub.max, is
100 ft. and the draft, H, is 125 ft., which is the same as in the
two preceding examples. The curves of FIG. 6C show the variation of
net vertical force when the bottle is subjected to the same three
waves. In this case the maximum variation in force is about 7
percent and it occurs under the influence of both the 10 and 20
second waves, although it is an increase for the 10-second wave and
a decrease for the 20-second wave. FIG. 6C shows that for a bottle
with this specific distribution of displacement, vertical water
acceleration forces dominate for short-period waves while variable
buoyancy forces dominate for longer-period waves. Furthermore,
there is a wave (about a 16-second wave) for which there is
virtually no variation in net vertical force because there is a
perfect balance between the variable buoyancy and vertical water
acceleration forces.
If the prismatic ratio had been slightly greater, buoyancy forces
would have dominated as in FIG. 6A, consequently the maximum
variation due to the 20-second wave (a decrease in net vertical
force) would have been greater than 7 percent. If the prismatic
ratio had been smaller, as in FIG. 6B, vertical water acceleration
forces would have dominated and consequently the maximum variation
due to the 10-second wave (an increase in net vertical force) would
have been greater than 7 percent. Therefore, my invention teaches
that for the range of waves of interest, 10- to 20-second waves,
that a best balance between the two influencing vertical forces is
obtained for the combination of parameters in FIG. 6C, r=1.853,
L/H=0.5 and p=0.545.
There are other combinations of the parameters r, L/H and p for
which a best balance between the two vertical forces is obtained.
These are found by studying a wide range of practical combinations
of the parameters in the same manner as described for FIG. 6C. For
each set of parameters the maximum variation in net vertical force
due to any wave in the range of interest is noted. The maximum
variation is then plotted for each set of parameters on a type of
"contour" plot such as in FIGS. 4A, 4B, 5A and 5B. Such a plot
indicates the combination of parameters giving the lowest value for
the maximum variation, the "valleys," and also shows which sets of
parameters give slightly higher, but practically acceptable values
of the variation. FIGS. 4A and 4B give values for a 100-ft. draft
and FIGS. 5A and 5B for a 125-ft. draft.
The basic configuration of the bottle is described by any two of
the three parameters. The most fundamental set is r and L/H where p
is a function of these two parameters. On the other hand, it is
convenient to express the design of the buoyancy members in terms
of p and r. Therefore, both combinations of parameters are used in
FIGS. 4A through 5B to illustrate the preferred design
configurations. In FIG. 4A, solid line 80 represents the relation
between r and L/H for which the magnitude of the net vertical force
has been minimized over the selected range of wavelengths. The same
relationship is illustrated by solid line 80A of FIG. 5A. These
forces were evaluated using Equation (4).
It is recognized that the most practical selection of r and L/H may
not always be for the minimum net vertical force and therefore some
knowledge is needed of the influence of variations from the
minimum. Area 82 on either side of line 80, FIG. 4A, (or area 82A
of FIG. 5A) represents variations in r and L/H which might occur or
be possible if a net vertical force equal to 10 percent of the
total displacement would be tolerated. If a net vertical force
equivalent to 121/2% of the total displacement can be tolerated, r
and L/H can vary so long as their corresponding ordinate and
coordinate intersect within shaded area 84 in FIG. 4A.
In FIG. 4B, the solid line 90 represents the best selection of p
and r for a design draft of 100 feet, i.e., the magnitude of the
net vertical force has been minimized over the selected range of
wavelengths for the value of p and r falling on solid line 90, (in
FIG. 5B, solid line 90A represents the best selection of p and r
for a design draft of 125 feet.) In FIG. 4B, shaded area 92 and
shaded area 94, respectively represent regions for which changes
are less than 10 percent and 121/2 percent of the total
displacement. In FIG. 5B, shaded area 92A represents regions for
which changes are less than 10 percent of the total displacement
for 125 feet draft.
Citing FIGS. 4A and 4B, my invention teaches that for the design of
a vertically moored structure consisting of a single bottle having
a draft of 100 ft. that the maximum variation of net vertical force
on the structure could be minimized by keeping the displacement due
to the prismatic portion between 40 and 60 percent of the total
displacement (0.4.ltoreq.p.gtoreq.0.6). More specifically my
invention teaches the designer that a more practical design, one
for which the maximum variation of net vertical force is within
12.5 percent of the total displacement, can be obtained by
selecting combinations of design parameters which fall within the
shaded region 84 of FIG. 4A or 94 of FIG. 4B; or one for which the
maximum variation of net vertical force is within 10 percent of the
displacement can be obtained by a selected combination of design
parameters which lie within the shaded region, 82 of FIG. 4A or 92
of FIG. 4B. Furthermore, my invention teaches that if the
combination of design parameters lies on the heavy line, 80 in FIG.
4A or 90 in FIG. 4B, then the maximum variation of net vertical
force is reduced to the smallest amount possible.
Citing FIGS. 5A and 5B, my invention teaches that for the design of
a vertically moored structure of this nature having a draft of 125
feet, that the maximum variation of net vertical force on the
structure could be minimized by keeping the displacement due to the
prismatic portion between 45 and 65 percent of the total
displacement (0.45.ltoreq.p.ltoreq.0.65). More specifically my
invention teaches that a more practical design for a vertically
moored structure for which the maximum variation of net vertical
force is within 10 percent of the total displacement can be
obtained by selecting combinations of the design parameters which
fall within the shaded region of FIGS. 5A and 5B. Furthermore, my
invention teaches that if the combination of design parameters lies
on the heavy line in FIGS. 5A or 5B, then the maximum variation of
net vertical force is reduced to the smallest amount possible.
The configuration of a typical bottle is illustrated in FIG. 7A, in
which the basic design parameters L, H, R.sub.0 and R.sub.1 are
defined. My invention teaches that it is best to maintain the
annular or auxiliary displacement as low on the bottle
configuration as is possible; in this way the annular or auxiliary
displacement is maintained below the wave trough 40. The variation
in net vertical force rises sharply if the annular portion of the
displacement enters into the wave trough. Therefore, the height of
the annular or auxiliary displacement is measured from the lower
most point CK on the bottle. Consequently, my invention also
teaches that a most advantageous design is one for which
or
FIG. 7A also shows the approximate location of the center of
gravity CG and the center of buoyancy CB of a typical bottle
configuration. The center of gravity of a vertically moored
platform is generally higher than the center of buoyancy due to the
large mass of structure, such as bottle extension or deck, and
equipment located well above the design wave crest. Such a
structure would normally be unstable if not for the vertical
tethering force T which is usually applied near the base of the
structure, for example, CK.
This simple type of vertically moored structure consisting of a
single bottle is restrained from vertical motion, but is free to
move horizontally, and moreover, is subject to roll or pitch
motions. When subject to the horizontal component of oscillatory
wave forces, the platform moves back and forth through the water.
FIG. 7B shows the bottle at its furthermost excursion towards the
right; at this instant the structure is motionless and its
acceleration is a maximum towards the left. At this instant the
horizontal forces shown are in equilibrium. The governing
horizontal forces are (a) the fictitious force due to platform
acceleration F.sub.p which has a point of application at the center
of gravity, (b) the horizontal water particle acceleration (or
inertia) force F.sub..omega., which has a point of application in
the vicinity of the center of buoyancy CB, and (c) finally the
horizontal component of the tethering force T.sub.H which acts at
the point CK. The above mentioned forces can be calculated by
fundamental textbook dynamics and hydrodynamics. While these forces
are in equilibrium in terms of horizontal force, they produce
moments which are not by themselves in equilibrium. These moments
will hereinafter be called "overturning moments." Water particle
drag also produces components of horizontal force and overturning
moment which are small due to the shape of the bottle, and
therefore, will be negligible.
In the case of the simple vertically moored platform, consisting of
a single bottle, overturning moments cause the bottle to pitch
through an angle .theta., which is the single amplitude degree of
pitch motion. The degree of pitch is large enough for the couple
between the static vertical forces to be sufficient to counter
balance the overturning moments. The static vertical forces consist
of (a) the vertical component of the tethering force T.sub.V, (b)
the buoyancy force B and (c) the weight of the platform M.
I will now consider a more complex type of vertically moored
platform made up of three or more bottles, such as the structure
depicted in FIGS. 1, 2 and 3 which consists of four bottles, or
legs. The individual bottles, or legs, are interconnected by a deck
structure above water and structural bracing below water. The
overall structure is extremely rigid. Vertical mooring lines,
either cables or elongated tubular members, are attached to the
base of each bottle, or leg. Therefore, the platform is free to
move in a horizontal direction only and pitch or roll motions as
well as vertical motions are restrained. The platform is subjected
to the same forces and overturning moments as were the individual
bottles discussed previously; the vertical and horizontal water
particle acceleration forces, variable buoyancy force, and platform
inertia force.
The dynamic vertical forces are primarily the variable buoyancy and
vertical water acceleration forces as before. There is also a
vertical drag force, but this is insignificant compared to the
first two. The net resultant of these vertical forces is reacted by
variations in the tethering forces, which is the same as with the
single vertically moored bottle. Also as with the single bottle,
horizontal forces such as the platform inertia force and the
horizontal water inertia forces are reacted by the horizontal
component of the tethering force. However, because this more
complex vertically moored platform is not free to undergo pitch or
roll motion, the overturning moments must be reacted by an
additional variation in the tethering force. Overturning moment for
a multilegged vertically moored platform is still dominated by
coupling between the horizontal forces such as due to (a) platform
inertia, (b) horizontal water particle acceleration forces, and (c)
the horizontal component of the tethering force. There are other,
less significant sources of overturning moment such as shown in
FIG. 8 for a 100-ft., 20-second wave. As noted previously
horizontal drag produces a small but insignificant contribution to
overturning moment. Vertical water particle drag forces, due to the
phase difference of the wave cycle at different legs, also
contributes a small amount of overturning moment. Wind lift on the
deck may produce a small amount of moment. If elongated members,
such as risers, are used to tether the platform instead of cables
and if the ends of these members are rigidly attached to the
platform rather than attached by a hinged connection such as a
gimbal joint, then there is a significant amount of riser end
moment which adds to the overturning moment on a platform. The
dashed line in FIG. 8 shows the net overturning moment on a typical
four-legged, vertically moored platform due to a 100-foot-high,
20-second-period wave. The net overturning moment is not radically
different from the overturning moment due only to coupling of
horizontal forces.
Using simple textbook statics, the variation in net tethering force
due to overturning moment is calculated by making the most
reasonable assumption that the platform is very rigid compared to
the vertical tethers which act like elastic springs. For a
four-legged platform, overturning moment is most demanding on the
tethers at any given leg if the storm, or waves, approach the
platform along a diagonal rather than a direction normal to a side.
In this case the tethers at the two diagonally opposite legs which
are in line with the storm direction provide the entire reaction to
overturning moment. If the center-to-center leg spacing along a
side is "A," then the reaction to overturning moment in each
resisting leg is the value of the overturning moment divided by
A.sqroot.2. The tethering forces in the other two legs are not
affected by overturning moment.
Considering the influence of static horizontal forces such as wind
and current on variation of vertical tethering forces, one of the
two legs resisting overturning moment will be more heavily loaded
than the other. This leg, which will hereinafter be called Leg No.
4 as indicated in FIG. 11A, is that leg, or bottle, which is
oriented toward the oncoming waves. While the influence of static
horizontal forces will not be considered here, it is convenient to
distinguish this leg from the others. For a positive overturning
moment as shown in FIG. 8, the variation in tethering force at Leg
No. 4 is positive as shown in FIG. 9, for each of three different
waves. FIG. 9 shows the variation in tethering force in Leg No. 4
due to overturning moment only. The variation is expressed as a
percent of the displacement per bottle, or leg; in this case it is
a percent of one-fourth of the total displacement.
In a floating structure as described here, the legs may be spaced
200 feet apart, more or less. Because of the wide leg spacing, each
of the legs may experience different net vertical forces at any
given instant. Consequently, it is impossible for all of the legs
to simultaneously experience the maximum net vertical force for
long-period waves. Therefore, the net vertical force on the entire
four-legged structure will never be as great as four times the net
vertical force on a single vertically moored bottle, and in turn,
the reaction in the tethers at each leg due to net vertical force
only will never be as great as the reaction in the mooring lines of
a single bottle.
Furthermore, because of the wide leg spacing the differences in net
vertical forces on individual legs at any instant give rise to
couples which must also be reacted by variations in the tethering
forces. Consider the example depicted in FIG. 10, where the four
legs are spaced 200 feet apart in the outline of a square and a
wave with a 400-foot wavelength is passing the platform. There is
an instant when the crest of the wave is aligned with two legs and
the trough is aligned with the other two. If the variable buoyancy
forces are governing for this wave, then the net vertical forces on
the bottles at the crest are upwards and at the trough are
downwards, as illustrated by the arrows in FIG. 10. While the net
vertical force on the entire structure may be nearly balanced,
there is a relatively large couple, or moment, acting on the
structure due to the differences in net vertical force. In
accordance with my invention, this couple must be reacted by
variations in the tethering forces in the same manner as were
overturning moments.
It can be shown that if the variable buoyancy contribution to net
vertical force is greater than that due to vertical water particle
acceleration, such as with long period waves, then this coupling of
net vertical forces acts in the opposite sense to the dominant
source of overturning moment mentioned previously. Consequently,
the coupling between net vertical force on each leg tends to reduce
the influence of overturning moment, especially for long period
waves. However, as the net vertical force on individual legs is
increased in order to reduce the effect of overturning moment, the
net vertical force on the entire structure is increased. In other
words, as the variation in mooring force is decreased through a
reduction of the effect of overturning moment, it is at the same
time increased due to the increase of net vertical force on the
platform. There exists a proper amount of net vertical force on
individual bottles for which the net effect of these influences is
minimized. It is a concept of this invention to minimize the
variation in mooring force on the most heavily loaded leg, and
therefore the maximum mooring force over the range of important
wavelengths, through a proper selection of the ratios of variable
buoyancy force and vertical water acceleration force as was done
previously to minimize net vertical force for the single vertically
moored bottle.
There are three contributions to the variation in mooring force in
the most heavily loaded leg. These are (a) the reaction to net
vertical force on the entire structure, (b) the reaction to
overturning moments and (c) the reaction to coupling of vertical
forces on individual, widely spaced legs. FIG. 11A shows the
variations in mooring force in Leg No. 4 due to each of these
influences for a 100-ft., 20-sec. wave. The net variation is also
shown by the heavy line. For this example the platforms consist of
four bottles where each bottle has the same physical properties as
in FIG. 6C: r=1.853, L/H=0.5, p=0.545. The variation in mooring
force is expressed as a percent of the displacement per bottle. The
maximum variation for the 20-second wave is about 13.5 percent and
occurs shortly after the wave trough has passed the center of the
platform. In FIG. 11A it is worth pointing out that for the long
period wave, the variation due to coupling of net vertical forces
on individual legs while small in magnitude acts opposite in sense
to the variation due to overturning moments.
FIG. 11B shows the net variation in mooring force for three
different waves. It is evident from these curves that the maximum
variation in mooring force due to any of the waves in the range of
interest is 14.1 percent. For the platform examined in FIG. 11, the
draft is 125 feet, leg spacing is 160 feet, total displacement is
28,675 kips (1 kip=1,000 lb.), weight of structure and equipment is
about 18,675 kips and the total, still water mooring force is
10,000 kips. While the maximum net variation in mooring force is
14.1 percent of the displacement per leg, it is about 40 percent
(14.1.times.28,675/10,000=40.4) of the still water mooring force
per leg.
FIGS. 12 and 13 show the influence of other bottle configurations
on maximum net variation in mooring force. In each of these
examples the platform size including displacement is the same as in
FIG. 11 and only the proportions of prismatic and annular
displacements are altered by varying the shape of individual
bottles. The variation in mooring force due to overturning moment
is essentially the same in each case for similar waves. Therefore,
the net variation in mooring force is altered only by the variation
of net vertical forces on individual bottles.
In FIGS. 12A and 12B the displacement is due entirely to the
cylindrical prismatic portion (p=1). It is interesting that the
variation due to coupling of net vertical forces on individual
bottles almost completely counterbalances the variation due to
overturning moment. Consequently, the net variation in mooring
force is almost entirely due to total net vertical force on the
platform. As a result, the maximum variation in mooring force is 32
percent of the displacement per bottle and occurs when the trough
of the wave is at the center of the platform. This is very similar
to the response of the vertically moored, single cylindrical
bottle.
In FIGS. 13A and 13B the displacement is due entirely to the
annular portion at the base of the leg (p=0). In this case the net
variation of mooring force is a complex combination of the three
influences as shown in FIG. 13A for the 20-second wave. Because
vertical water acceleration forces are dominating instead of
variable buoyancy forces, the influences due to net vertical force
on individual legs act in the opposite sense as for FIG. 12A.
Consequently, the variation in mooring force due to coupling of net
vertical force on individual legs adds to the variation in mooring
force due to overturning moment. Furthermore, the maximum net
variation in mooring force, 45 percent, is much greater than the
net vertical force on a single bottle of this configuration.
It is apparent by comparing FIG. 11B with FIGS. 12B and 13B that
the maximum variation in mooring forces, for the range of waves of
interest, can vary significantly depending on the configuration of
the individual legs. I have discovered that there are certain
combinations of the design parameters r, L/H and p for which a
minimum value can be achieved for the maximum variation in mooring
force. A type of "contour" plot, similar to those prepared for net
vertical force on individual bottles in FIGS. 4 and 5, can be
prepared giving the percentage variation in mooring force as a
function of the shape parameters r, L/H and p.
In order to prepare such a plot we need to examine a large number
of examples such as in FIGS. 11, 12 and 13 for the range of waves
of interest and for a wide range of the shape parameters. For each
set of shape parameters the maximum variation of mooring force is
noted. Next, the values of maximum variation can be plotted as a
function of the shape parameters such as in FIGS. 14 or 15.
Actually, FIG. 14 assists in preparing FIG. 15. In FIG. 14 the
maximum variation (designated .vertline..DELTA.T.vertline.), as a
percent of displacement per leg (designated b), is plotted versus r
for fixed values of L/H. This simplifies the procedure for
determining the values of r and L/H at which the maximum variation
is an even value, such as 0.14, 0.16, 0.18, 0.20, etc. Finally, the
contours for fixed values of maximum variation are plotted versus
L/H and r as in FIG. 15A, or versus p r as in FIG. 15B. FIGS. 14,
15A and 15B have been prepared from calculations for a specific
platform and design criteria. The pertinent data are
1. Maximum Design Wave Height=100 feet,
2. Draft=125 feet,
3. Leg Spacing=160 feet,
4. Total Displacement=28,675 kips,
5. Platform Weight=18,675 kips,
6. Total Still Water Mooring Force=10,000 kips.
From FIG. 14 it is apparent that the minimum attainable value of
maximum variation is about 13.5 percent of displacement per leg
(28,675/4=7,170 kips). This would account for about a 39 percent
variation of the still water mooring force per leg
(13.5.times.28,675/10,000=38.7). It may not always be practical to
select a configuration for which the shape parameters indicate the
lowest value of maximum variation. However, my invention teaches
that a practical range of maximum variation, e.g., less than 1.2
times the lowest value, is attainable if the set of shape
parameters lie within the 16 percent contours
(1.2.times.13.5=16.2), the shaded regions of FIGS. 15A or 15B.
My invention teaches, when designing a platform for the size and
maximum design wave height listed above, that maximum variation of
mooring force for the range of wave lengths of practical interest
can be minimized to a range of practically acceptable values (e.g.,
less than about 16 percent) if the shape parameters which govern
the shape of the individual bottles lie within or near the shaded
regions of FIGS. 15A or 15B. Moreover, the best selection of shape
parameters in order to minimize variation in mooring forces are
those falling on the heavy dashed line in either FIGS. 15A or
15B.
FIG. 15 illustrates the best selection of shape parameters for a
limited case, namely one designed for a maximum wave, draft,
displacement, etc., equal to the values itemized above. I will now
demonstrate the best selection of shape parameters for other values
of leg spacing, draft, maximum design wave height, displacement and
platform weight.
Comparison of FIGS. 16, 15 and 17, in that order, demonstrates the
influence of varying leg spacing. In these examples all other
parameters remain constant, while the leg spacing takes values of
140 feet, 160 feet and 200 feet, respectively. Changing the leg
spacing has not significantly altered the position of the heavy
dashed line which describes the best selection of shape parameters.
Neither has it significantly altered the region for selection of
most pactical combinations of shape parameters, the shaded region
in each figure. (In these examples and all subsequent examples, the
shaded region bounds those sets of parameters for which the maximum
variation is less than or equal to 1.2 times the lowest attainable
value of maximum variation). However, for the range of values of
leg spacing examined, the minimum attainable value of maximum
variation is approximately proportional to the inverse of leg
spacing.
My invention teaches the best combination of shape parameters
defined by the heavy, dashed line in FIG. 15 and the most practical
combination of design parameters as defined by the shaded region in
FIG. 15 are independent of leg spacing. However, my invention also
teaches that the lowest attainable value of maximum variation is
inversely proportional to leg spacing.
Comparison of FIGS. 18, 15 and 19 in that order demonstrate the
effect of altering draft. In these three examples all parameters
are the same as listed above except the still water draft of the
bottles, which are 100 feet, 125 feet, and 150 feet, respectively.
Changing the draft does alter slightly the position of the heavy
dashed line and the shaded region, which denote the best
combination of shape parameters and the range of practical
combinations of the shape parameters, respectively.
As one example, my invention teaches for a platform with the
following properties:
1. Maximum Design Wave Height=100 feet
2. Total Displacement=28,675 kips
3. Platform Weight=18,675 kips
4. Total Still Water Mooring Force=10,000 kips and for a 100-foot
draft that the most practical combination of shape parameters are
those falling in the shaded region of FIGS. 18A and 18B and that
the best selection of shape parameters are those lying on or near
the heavy dashed line in FIGS. 18A and 18B. Also for a platform
with the above list of properties, but a draft of 150 feet, my
invention teaches that the most practical combination of shape
parameters are those lying in the shaded region of FIG. 19 and that
the best selection of shape parameters are those sets lying on or
near the heavy, dashed line of FIG. 19. Furthermore, for a platform
with the properties listed above and designed for a maximum design
wave height listed above but having a draft between 100 feet and
150 feet, the range of most practical sets of the shape parameters
are found approximately by interpolating between the shaded regions
of FIGS. 18, 15 and 19; and the best combination of shape
parameters are determined approximately by interpolating between
the heavy dashed lines in FIGS. 18, 15 and 19. For these figures
the maximum value of the prismatic ratio p is about 0.8 and the
minimum value is about 0.5. However, in FIG. 4 the minimum value of
p is about 0.4. I have found that for a wide range of design in
vertically moored platforms (covering the generally acceptable
sizes) that the prismatic ratio should be between about 0.4 and
0.8.
Furthermore, the lowest attainable value of maximum variation is
influenced significantly by changes in draft, especially for
shallower draft. The lowest value is about 15 percent for a
100-foot draft as compared to 13.5 percent for a 125-foot draft and
about 13.2 percent for a 150-foot draft. For a decrease in draft
less than 100 feet, the lowest value of the maximum variation rises
rapidly, while for an increase in draft about 150 feet there is
little additional reduction in the lowest value of maximum
variation. Therefore, my invention teaches that, at least for a
maximum design wave height h.sub.max of 100 feet, the penalty in
terms of variation of tethering force becomes very severe for a
draft H less than 100 feet (h.sub.max /H>1.00). Furthermore, my
invention teaches that, for the same maximum design wave height,
h.sub.max, the penalty in terms of unnecessary structure becomes
costly with a design draft H greater than 150 feet (h.sub.max
/H<0.67). Therefore, my invention teaches that for a platform of
the displacement being discussed here, 28.675 kips, the most
attractive ratio (h.sub.max /H) of maximum design wave height to
draft is about 0.8 and that the practical range for this ratio is
between 0.67 and 1.00 (0.67.ltoreq.h.sub.max /H.ltoreq.1.0).
In FIG. 18, the sharp convergence of the "contours" for values of
L/H greater than 0.5 demonstrates the effect of the annular portion
of the displacement projecting above the wave trough. The result is
that the values of maximum variation in mooring force rise sharply
as more of the annular displacement projects into the trough of the
wave. Therefore, my invention teaches that a best selection of
shape parameters is one which maintains the top of the annular, or
auxiliary, portion of displacement near or below the trough of the
maximum design wave. Mathematically, this teaching is formulated by
the bounds established by Inequalities (5) or (6).
Whereas I have taught that the best selection of draft for a given
maximum design wave should be determined from the ratio (h.sub.max
/H).congruent.0.8, it is also instructive to look at the influence
of varying draft for constant values of this ratio. FIGS. 20 and 21
demonstrate the values of maximum variation of mooring force for
other maximum design waves, 60 feet and 80 feet, and corresponding
draft, 75 feet and 100 feet, respectively. In each case the leg
spacing displacement and platform mass is the same as in FIG. 15.
Also, the ratio of maximum design wave height to draft is the same
in every case (h.sub.max /H0.8).
Comparison of FIGS. 20, 21, and 15 shows the influence of varying
draft for fixed ratios of (h.sub.max /H). The effect of smaller
draft is to alter the position of the heavy, dashed line and the
shaded region, which correspond to the best combination of shape
parameters and the most practical range of shape parameters,
respectively. More importantly such a comparison shows that the
lowest attainable value of maximum variation in mooring force is
not altered significantly by so large a variation in draft; in the
three examples the value is about 12.1 to 13.5 percent. This
observation strengthens my earlier teaching that the best ratio of
maximum design wave height to draft is about 0.8 (h.sub.max
/H.congruent.0.8), independently of the value of either draft or
maximum design wave height. However, the density of the lines in
FIG. 20 indicates for so small a draft (or more exactly, for so
large a displacement for the given draft) that the values of
maximum variation in mooring force are very sensitive to the
selection of the shape parameters.
As an example, my invention teaches for a platform with the
following properties:
1. Ratio: h.sub.max /H=0.8
2. Total Displacement=28,675 kips
3. Platform Mass=18,675 kips
4. Total Still Water Mooring Force=10,000 kips
and for a 75-foot draft that the most practical combination of
shape parameters are those falling in the shaded region of FIG. 20
and that the best selection of shape parameters are those lying on
or near the heavy, dashed line in FIG. 20. Also, for a platform
with the above list of properties, but a draft of 100 feet, my
invention teaches that the most practical combination of shape
parameters are those falling into the shaded region of FIG. 21 and
that the best selection of shape parameters are those sets lying on
or near the heavy, dashed line of FIG. 21. Furthermore, for a
platform with the dimensions listed above and for drafts lying
between 75 feet and 125 feet, the range of most practical
combinations of the shape parameters are found approximately by
interpolating between the shaded regions of FIGS. 20, 21 and 15;
and the best combination of shape parameters are determined
approximately by interpolating between the heavy, dashed lines in
FIGS. 20, 21 and 15.
Comparison of FIGS. 22, 15 and 23, in that order, demonstrate the
effect of total displacement on maximum variation of mooring force.
For each case shown the maximum design wave height is 100 feet,
draft is 125 feet and leg spacing is 160 feet. Total displacements
are 14,700 kips, 28,675 kips and 57,350 kips, respectively. The
ratio (M/B) of platform mass to total displacement is the same in
each case. Consequently, two parameters have been varied
simultaneously; however, as will be discussed shortly, variation of
the platform mass within practical limitations has no significant
influence on the values of maximum variation of mooring force.
Since the total still water mooring force T is simply the
difference between total displacement and platform mass, the ratio
(T/B) is also the same in each example. Therefore, in order to
express the variation of mooring force as a percent of the still
water mooring force, the value of the variation found in the
"contour" plots, which is expressed as a percent of displacement
per leg, is multiplied by 2.87 (=28,675/10,000) in each of these
examples.
As seen by the comparison, changing displacement has a significant
influence on selection of the proper shape parameters. Moreover,
the lowest attainable value of maximum variation rises with a
decrease in displacement, whereas this value does not decrease
significantly for an increase in displacement. From examination of
several other examples not shown here, it was found that the values
of maximum variation rise sharply for displacements less than about
20,000 kips in the case of the specific design properties listed
above.
Therefore, my invention teaches for a platform with the following
design parameters and dimensions:
1. Ratio: h.sub.max /H=0.8
2. Draft=125 feet
3. Ratio: M/B=18,675/28,675
4. Ratio: T/B=10,000/28,675
and for a 14,700-kip displacement that the most practical
combination of shape parameters are those falling in the shaded
region of FIG. 22 and that the best selection of shape parameters
are those lying on or near the heavy, dashed line in FIG. 22. Also,
for a platform with the above listed properties, but a 57,300-kips
displacement, my invention teaches that the most practical
combination of shape parameters are those falling into the shaded
region of FIG. 23 and that the best selection of shape parameters
are those sets lying on or near the heavy, dashed line of FIG. 23.
Furthermore, for a platform with the design properties listed above
and for displacements lying between 14,700 kips and 57,300 kips,
the range of most practical combinations of the shape parameters
are found approximately by interpolating between the shaded regions
of FIGS. 22, 15 and 23; and the best combinations of shape
parameters are determined approximately by interpolating between
the heavy, dashed lines in FIGS. 22, 15 and 23.
Several cases, not included herein, have been examined in which
platform mass was varied independently of all other parameters. It
was observed that such variation of platform mass, within practical
limitations, did not significantly alter the range of the most
practical combinations of shape parameters in each case, the shaded
regions, or the values of the best combination of shape parameters
in each case, the heavy, dashed line.
The practical range of platform mass was determined as follows. The
platform mass comprises (a) equipment of weight Q such as for
drilling or producing, and (b) the structural mass of the platform.
From design experience I have observed that the mass of the deck
required to provide the necessary support for the equipment of
weight Q is approximately Q/4. Also, the mass of the jacket
necessary to obtain the required displacement B is approximately
B/4. These two observations are sufficiently accurate for a
practical range of platform dimensions. Therefore, the total
platform mass is the sum of the above three contributions or
For the purposes of offshore petroleum drilling and production,
equipment weights might vary between 4,500 kips and 18,000 kips.
Therefore, the bounds on platform mass are a function of the design
displacement as follows:
Therefore, for the range of values for displacement which were
discussed previously (14,700 kips.ltoreq.B.ltoreq.57,300 kips), the
practical values of platform mass are bounded by the above
inequality.
In view of the above description of practical range for platform
mass, my invention teaches that the maximum net variation of
mooring force, where expressed as a function of displacement per
leg, is not significantly influenced by an alteration of the
platform mass. However, my invention teaches that the maximum
variation of mooring force expressed as a percent of the total
mooring force can be decreased by decreasing the platform mass, and
consequently, increasing the total mooring force, for a fixed
displacement, as demonstrated by the following derivation:
While I have heretofore taught the best selection of shape
parameters for only a few of the many examples studied, I now
propose to teach a means for determining the best selection of
shape parameters for the entire range of each of the parameters
which I have discussed. Many examples, not all of which have been
included herein, have been studied. These examples were selected
from the large range of cases bounded by the limits on the
following parameters:
1. Maximum design wave height, 60 ft..ltoreq.h.sub.max .ltoreq.100
ft.
2. Draft, 75 ft. .ltoreq.H .ltoreq.150 ft.
3. Leg Spacing, 140 ft..ltoreq.A.ltoreq.200 ft.
4. Displacement, 14,700 kips.ltoreq.B.ltoreq.57,300 kips
5. Platform Mass, see (8) for limits on M
6. Total mooring force, T=B-M Obviously, not all of the possible
combinations of these parameters could be examined. However, a
sufficient number of examples were studied so that an empirical
formulation could be derived, using curve fitting techniques, which
will give with suitable approximation the best selection of the
shape parameters.
Best Combination of Shape Parameters
Those combinations of shape parameters which give the lowest value
of maximum variation of mooring force (those combinations which
were defined by the heavy, dashed lines in FIGS. 15 through 23) are
defined by the formula
where ##EQU4##
In accordance with my earlier teaching Formula (10) is valid
for
Formula (10) gives the best value of r for each value of L as a
function of draft H, displacement B and the ratio (h.sub.max /H) of
maximum design wave height to draft. The best value of r for each L
is independent of leg spacing A and platform mass M as was taught
earlier.
Range of Practical Values
As was noted previously the range of most practical combinations of
the shape parameters is arbitrarily defined as containing all sets
for which maximum variation in mooring force is within 20 percent
of the lowest attainable value of maximum variation for the given
draft, displacement, etc. In FIGS. 15 through 23 this range was
defined by the shaded regions. Through the use of curve fitting
techniques, the range of practical values of r for each value L,
may be suitably approximated by ##EQU5## where r.sub.bt is defined
by Formula (10).
The empirical Formulas (10) through (14) which define the best or
most practical combinations of shape parameters are in terms of r
and L, only. The prismatic ratio p corresponding to each
combination of r and L, is determined directly from the values of r
and L, but depends on the overall bottle configuration. For the
general bottle shape associated with my invention (FIG. 7), p is
given approximately by ##EQU6## For other practical configurations,
the values of p will not be significantly different as long as
R.sub.1 is always the maximum radius of the bottle, R.sub.0 is the
bottle radius at still water level and L is the height of the
annular, or auxiliary, portion measured from the lowest point on
the bottle.
Previously, I taught that the best design draft for a given maximum
design wave height is determined by the the ratio (h.sub.max
/H=0.8). If this specific value is chosen for the ratio, the best
selection of the shape parameters is given by (10) and the most
practical range of shape parameters is given by (14), where C and n
are determined specifically by ##EQU7##
The selection of an exact maximum design wave height is somewhat
ambiguous. The simple wave theory employed in this study is
approximate, but suitable. There are other wave theories which
would render slightly different results for a specific maximum
design wave height and platform size. Therefore, it is more
practical to speak of a range of shape parameters in which the best
selection of shape parameters are contained; but, by this
definition, the best combination of parameters is not specified
exactly.
Suppose for example that it is impossible to say the ratio
(h.sub.max /H) is exactly 0.8, but the designer is reasonably
confident that this ratio is bounded by
My invention then teaches that the designer is reasonably certain
of designing the best configuration if for a given value of L,
r.sub.bt is bounded by
where ##EQU8##
Moreover, the range of "most practical" combinations of shape
parameters, the shaded regions, becomes the "union" of all regions
defined by (14) for all values of (h.sub.max /H) which are bounded
by (18). More specifically, the range of "most practical" values of
r for each L is bounded by ##EQU9## I taught previously that the
acceptable or practical range for the ratio h.sub.max /H is
approximately
For a ratio smaller than 0.65 there would be too much structure for
the maximum design wave height, and consequently, the structure
becomes unnecessarily expensive. If the ratio is greater than 1.00,
there is too small a structure for the maximum design wave height,
and consequently, the maximum variation in mooring force becomes
untractable. Therefore, my invention teaches the designer that the
best selection of draft is such that the ratio (h.sub.max /H) is
bounded as in (27). Under this condition, the best selection of
shape parameters is bounded by
where ##EQU10## My invention teaches the designer that the maximum
variation in mooring force is reasonably acceptable if the shape
parameters fall within the bounds set forth by (28) through (34)
above. However, he must also recognize that the very best design
may not have been defined.
The range of "most practical" values of r for each L is bounded by
##EQU11## This range comprises the union of all combinations of
shape parameters which are defined as the most practical
combinations by Formulas (10) through (14) for values of (h.sub.max
/H) satisfying (27).
Attention is directed to FIG. 3 which is taken along the line 3--3
of FIG. 1. This shows four vertical float members arranged in a
square and connected by cross bracing 34. As can be seen, there is
a plurality, in this case four, of riser pipes 28A which extend
upwardly through these vertical float members to the deck 12.
Derrick 14 supports drilling equipment which is used to drill holes
in the bottom of the body of water through these riser pipes 28A.
In this system the well head equipment, including blowout
preventers, etc., can be located at the surface. From the
arrangement of FIG. 3, it is seen that as many as 16 wells can be
conveniently drilled from this one structure. After the wells are
drilled, the structure can, if desired, remain on location and be
used as a production gathering facility.
FIG. 2 illustrates how the upper portion 28A of the riser pipes
extends through the lower end member 42 of section 20 of the float.
These pipes are rigidly attached, as by welding, to such floats or
portions of the structure so that the structure is rigidly
connected to the ocean floor by pipes 28A.
The predominating vertical forces acting on a properly designed,
vertically moored platform are associated with inertia and
acceleration phenomena. In viewing this invention it is
illustrative to separate these vertical forces into two categories:
namely, variable buoyancy and vertical water acceleration forces.
The two categories of forces act in opposite direction, and it is
the basic concept of the invention to balance the forces to give as
small a variation in mooring force as possible. In achieving the
desired balance, it may for some designs be desirable to increase
or adjust the acceleration force acting on the platform.
Acceleration force can be increased by addition of fins 50.
.Iadd.As indicated in FIG. 1, means 52 is provided to move said
horizontal fins 50 about a horizontal axis. .Iaddend.Recognize that
acceleration forces are associated with volumes of displaced and
therefore accelerated water. The action of the fins is to trap a
surrounding "hydrodynamic mass" or volume of water. In this way
acceleration forces are increased by opening the fins out to entrap
more hydrodynamic mass. On the other hand, when the fins are folded
into a vertical position, they do not influence acceleration
forces.
Installation of the vertically moored platform might typically be
done according to the following steps:
1. Launch, or otherwise remove the baseplate 22 from a
transportation barge.
2. Lower the baseplate 22 to the ocean floor by means of
guidelines.
3. Using a semisubmersible drilling unit (preferably dynamically
positioned) drive marine conductors 24 (e.g. 30 inches in diameter)
through the baseplate following subsea drilling practice.
4. Drill out through the marine conductor 24 for 20-inch surface
casing.
5. Run 20-inch surface casing string with the lower portion of ball
joint 32 at the top of this 20-inch casing string.
6. Cement casing string in the well.
7. Repeat the operation for other conductors and casings installed
in the baseplate.
8. Bring platform 10 to the location.
9. Ballast the platform to float at the designed draft.
10. Using, for example, derrick 14, run elongated members 28 in the
manner normally employed for installing marine risers, passing the
elongated members through vertical conductor pipes down through the
platform.
11. Make up ball joint 32 at the bottom of each elongated member
28.
12. Weld off, or otherwise fix, the top of elongated members 28 at
the platform deck.
13. Deballast the platform 10 in order to apply the proper tension
to the elongated members 28.
While a limited number of embodiments of the present invention have
been shown, various modifications can be made thereto without
departing from spirit or scope of the invention.
* * * * *