Note: Descriptions are shown in the official language in which they were submitted.
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EXPANSION CONE AND SYSTEM
BACKGROUND OF THE INVENTION
[0005] The present disclosure relates generally to wellbore casings and/or
pipelines,
and in particular to wellbore casings and/or pipelines that are formed using
expandable tubing.
BRIEF DESCRIPTION OF THE DRAWINGS
[0006] Figure 1 is an illustration of a conventional method for drilling a
borehoie in a
subterranean formation.
[0007] Figure 2 is an illustration of a device for coupling an expandable
tubular
member to an existing tubular member.
[0008] Figure 3 is an illustration of a hardenable fluidic sealing material
being pumped
down the device of Figure 2.
[0009] Figure 4 is an illustration of the expansion of an expandable tubular
member
using the expansion device of Figure 2.
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[0010] Figure 5 is an illustration of the completion of the radial expansion
and plastic
deformation of an expandable tubular member.
[0011] Figure 6 is a side view of an exemplary embodiment of an expansion
device of
Figure 2.
[0012] Figures 7 and 7a are cross sections of the exemplary embodiment of the
expansion device of Figure 6.
[0013] Figure 8 is a side view of another exemplary embodiment of an expansion
device of Figure 2.
[0014] Figures 9 and 9a are cross sections of the exemplary embodiment of the
expansion device of figure 8.
[0015] Figure 10 is a longitudinal cross section of a seamless expandable
tubular
member.
[0016] Figure 11 is a radial cross section of the seamless expandable tubular
member
of Figure 10.
[0017] Figure 12 is an illustration of the expansion of the seamless
expandable
tubular member of Figure 10 using the expansion device of Figure 6.
[0018] Figure 13 and 13a are top views of the expansion of the seamless
expandable
tubular member as shown in Figure 12.
[0019] Figures 14 and 14a are the top views of another embodiment of the
expansion
of the seamless expandable tubular member of Figure 10 using an expansion
device.
[0020] Figure 15a is a side view of another embodiment of an expansion device.
[0021] Figures 15b and 15c are cross sectional views of the expansion device
of
Figure 15a.
[0022] Figure 16a is a side view of another embodiment of an expansion device.
[0023] Figures 16b and 16c are cross sectional views of the expansion device
of
Figure 16a.
[0024] Figures 17a and 17b are illustrations of a computer model of a tapered
expansion device and an expandable tubular member.
[0025] Figure 17c is an illustration of experimental data for the length of
the tapered
expansion device surface versus the taper angle of the expansion device for
the computer
model of Figs. 17a and 17b.
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[0026] Figure 17d is an illustration of the true stress-strain curve for the
expandable
tubular member in the computer model of Figs. 17a and 17b.
[0027] Figure 18 is an illustration of the total axial expansion force versus
the friction
shear factor for the computer model of Figs. 17a and 17b.
[0028] Figure 19 is an illustration of the influence of the taper angle of an
expansion
device on the ideal work, frictional work, and redundant work, during the
expansion of the
expandable tubular member of the computer model of Figs. 17a and 17b.
[0029] Figure 20 is an illustration of the total axial expansion force versus
the taper
angle of an expansion device, during the expansion of the expandable tubular
member of the
computer model of Figs. 17a and 17b.
[0030] Figure 21 is an illustration of a free body diagram of various forces
acting on
the tapered expansion device of the computer model of Figs. 17a and 17b.
[00311 Figure 22 is an illustration of the influence of the taper angle on the
radial force
acting on the expansion device of the computer model of Figs. 17a and 17b.
[0032] Figure 23 is an illustration of the effective strain in the expandable
tubular
member versus the taper angle of an expansion device one of the computer model
of Figs. 17a
and 17b.
[0033] Figures 24a and 24b are illustrations of a computer model of a
polynomial
curvature expansion device and expandable tubular niember.
[0034] Figure 25 is an illustration of experimental data for the location of
an inflection
point in the expansion surface of the polynomial curvature expansion device of
the computer
model of Figs. 24a and 24b.
[0035] Figure 26 is an illustration of polynomial curvature expansion device
surface
shapes with different ratios of Lf/L of the computer model of Figs. 24a and
24b.
[0036] Figure 27 is an illustration of the axial expansion force required for
the
polynomial curvature expansion device with different Lf/L ratios and a
constant length of the
polynomial curvature expansion surface (L) and for a shear friction factor of
m=0.05 of the
computer model of Figs. 24a and 24b.
[0037] Figure 28 is a comparison of the axial expansion force for the
polynomial
curvature expansion device for different Lf/L ratios at various shear friction
factors for a given
length of the expansion surface of the computer model of Figs. 24a and 24b.
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_. .~.~...~._ ._ ~. . ~ ~.~:..
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[0038] Figure 29 is a comparison of the axial expansion force for the
polynomial
curvature expansion device for different lengths of the expansion surface at
various shear
friction factors for the optimum L~L ratio of 0.6 of the computer model of
Figs. 24a and 24b.
[0039] Figure 30 is a comparison of the axial expansion force between the
optimum
tapered angle expansion device of the computer model of Figs. 17a and 17b and
the optimum
polynomial curvature expansion device of the computer model of Figs. 24a and
24b for a friction
shear factor of m=0.10.
[0040] Figure 31 is a comparison of the axial expansion force between the
optimum
tapered angle expansion device of the computer model of Figs. 17a and 17b and
the optimum
polynomial curvature expansion device of the computer model of Figs. 24a and
24b for a friction
shear factor of m=0.05
[0041] Figure 32 is a comparison of the steady state radial force between the
optimum tapered angle expansion device of the computer model of Figs. 17a and
17b and the
optimum polynomial curvature expansion device of the computer model of Figs.
24a and 24b for
a friction shear factor of m=0.10.
[0042] Figure 33 is a comparison of the steady state radial force between the
optimum tapered angle expansion device of the computer model of Figs. 17a and
17b and the
optimum polynomial curvature expansion device of the computer model of Figs.
24a and 24b for
a friction shear factor of m=0.05.
[0043] Figure 34 is an illustration of the total axial expansion force versus
expansion
device displacement for the optimum tapered expansion device of the computer
model of Figs_
17a and 17b and a friction shear factor of m=0.10.
[0044] Figure 35 is an illustration of the total axial expansion force versus
expansion
device displacement for the optimum polynomial expansion device of the
computer model of
Figs. 24a and 24b and a friction shear factor of m=0.10.
[0045] Figure 36 is an illustration of the total axial expansion force versus
expansion
device displacement for the optimum tapered expansion device of the computer
model of Figs.
17a and 17b and a friction shear factor of m=0.05.
[0046] Figure 37 is an illustration of the total axial expansion force versus
expansion
device displacement for the optimum polynomial curvature expansion device of
the computer
model of Figs. 24a and 24b and a friction shear factor of m=0.05.
[0047] Figure 38 is a comparison of the maximum effective strain between the
optimum tapered angle expansion device of the computer model of Figs. 17a and
17b and the
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optimum polynomial curvature expansion device of the computer model of Figs.
24a and 24b for
a friction shear factor of m=0.10.
[0048] Figure 39 is a comparison of the maximum effective strain between the
optimum tapered angle expansion device of the computer model of Figs. 17a and
17b and the
optimum polynomial curvature expansion device of the computer model of Figs.
24a and 24b for
a friction shear factor of m=0.05.
DETAILED DESCRIPTION
[0049] Referring initially to Figure 1, a conventional device 100 for drilling
a borehole
102 in a subterranean formation 104 is shown. The borehole 102 may be lined
with a casing
106 at the top portion of its length. An annulus 108 formed between the casing
106 and the
formation 104 may be filled with a sealing material 110, such as, for example,
cement. In an
exemplary embodiment, the device 100 may be operated in a conventional manner
to extend
the length of the borehole 102 beyond the casing 106.
[0050] Referring now to Figure 2, a device 200 for coupling an expandable
tubular
member 202 to an existing tubular member, such as, for example, the existing
casing 106, is
shown. The device 200 includes a shoe 206 that defines a centrally positioned
valveable
passage 206a adapted to receive, for example, a ball, plug or other similar
device for closing the
passage. An end of the shoe 206b is coupled t6 a lower tubular end 208a of a
tubular launcher
assembly 208 that includes the lower tubular end, an upper tubular end 208b,
and a tapered
tubular transition member 208c. The lower tubular end 208a of the tubular
launcher assembly
208 has a greater inside diameter than the inside diameter of the upper
tubular end 208b. The
tapered tubular transition member 208c connects the lower tubular end 208a and
the upper
tubular end 208b. The upper tubular end 208b of the tubular launcher assembly
208 is coupled
to an end of the expandable tubular member 202. One or more seals 210 are
coupled to the
outside surface of the other end of the expandable tubular member 202.
[0051] An expansion device 212 is centrally positioned within and mates with
the
tubufar launcher assembly 208. The expansion device 212 defines a centrally
positioned fluid
pathway 212a, and includes a lower section 212b, a middle section 212c, and an
upper section
212d. The lower section 212b of the expansion device 212 includes an inclined
expansion
surface 212ba that supports the tubular launcher assembly 208 by mating with
the tapered
tubular transition member 208c of the tubular launcher assembly. The upper
section 212d of
the expansion device 212 is coupled to an end of a tubular member 218 that
defines a fluid
pathway 218a. The fluid pathway 218a of the tubular member 218 is fluidicly
coupled to the
fluid pathway 212a defined by the expansion device 212. One or more spaced
apart cup seals
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220 and 222 are coupled to the outside surface of the tubular member 218 for
sealing against
the interior surface of the expandable tubular member 202. In an exemplary
embodiment, cup
seal 222 is positioned near a top end of the expandable tubular member 202. A
top fluid valve
224 is coupled to the tubular member 218 above the cup seal 222 and defines a
fluid pathway
226 that is fluidicly coupled to the fluid pathway 218a.
[0052] During operation of the device 200, as illustrated in Figure 2, the
device 200 is
initially lowered into the borehole 102. In an exemplary embodiment, during
the lowering of the
device 200 into the borehole 102, a fluid 228 within the borehole 102 passes
upwardly through
the device 200 through the valveable passage 206a into the fluid pathway 212a
and 218a and
out of the device 200 through the fluid pathway 226 defined by the top fluid
valve 224.
[0053] Referring nowto Figure 3, in an exemplary embodiment, a hardenable
fluidic
sealing material 300, such as, for example, cement, is then pumped down the
fluid pathway
218a and 212a and out through the valveable passage 206a into the borehole 102
with the top
fluid valve 224 in a closed position. The hardenable fluidic sealing material
300 thereby fills an
annular space 302 between the borehole 102 and the outside diameter of the
expandable
tubular member 202.
[0054] Referring now to Figure 4, a plug 402 is then injected with a fluidic
material
404. The plug thereby fits into and closes the valveable passage 206a to
further fluidic flow.
Continued injection of the fluidic material 404 then presturizes a chamber 406
defined by the
shoe 206, the bottom of the expansion device 212, and the walls of the
launcher assembly 208
and the expandable tubular member 202. Continued pressurization of the chamber
406 then
displaces the expansion device 212 in an upward direction 408 relative to the
expandable
tubular member 202 thereby causing radial expansion and plastic deformation of
the launcher
assembly 208 and the expandable tubular member.
[0055] Referring now to Figure 5, the radial expansion and plastic deformation
of the
expandabie tubular member 202 is then completed and the expandable tubular
member is
coupled to the existing casing 106. The hardenable fluidic sealing material
300, such as, for
example, cement fills the annulus 302 between the expandable tubular member
202 and the
borehole 102. The device 200 has been withdrawn from the borehole and a
conventional
device 100 for drilling the borehole 102 may then be utilized to drill out the
shoe 206 and
continue drilling the borehole 102, if desired.
[0056] Referring now to Figures 6, 7 and 7a, an expansion cone 600 includes an
upper cone 602, a middle cone 604, and a lower tubular end 606. The upper cone
602 has a
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~..,e..~.,...~ . ,.. . . i
CA 02584492 2009-03-24
leading surface 608 and an outer inclined surface 610 that defines an angle
a,. The middle
cone 604 has an outer inclined surface 612 that defines an angle aZ. In an
exemplary
embodiment, the angle a, is greater than the angle a2. The outer inclined
surfaces 610 and 612
together form the expansion surfaces 614 that upon displacement of the
expansion cone 600
relative to the expandable tubular member 202 radially expand and plastically
deform the
expandable tubular member. In an exemplary embodiment, the expansion cone 600
defines
one or more outer inclined expansion faceted surfaces 616. In an exemplary
embodiment, one
or more contact points 618 are formed at the intersection of the one or more
outer inclined
expansion faceted surfaces 616.
[0057] Referring now to Figures 8, 9 and 9a, an exemplary embodiment of an
expansion cone 800 with an outside expansion surface 802 defining a parabolic
equation, is
shown. The expansion cone 800 has an upper expansion section 804 and a lower
tubular end
806. The upper expansion section 804 has a leading surface 808 and the outside
expansion
surface 802 is defined by a parabolic equation. In an exemplary embodiment,
the expansion
cone 800 defines one or more outer inclined expansion faceted surfaces 810. In
an exemplary
embodiment, one or more contact points 812 are formed at the intersection of
the outer inclined
expansion faceted surfaces 810.
[0058] In an exemplary embodiment, the expansion device 212 consists of one or
more of the expansion devices 600 and 800.
[0059] Referring nowto Figures 10 and 11, an exemplary embodiment of a
seamless
expandable tubular member 1000 is shown. The seamless expandable tubular
member 1000
includes a wall thickness ti and t2 where ti is not equal to t2. In an
exemplary embodiment, the
seamless expandable tubular member 1000 has a non-uniform wall thickness.
[0060] In an exemplary embodiment, the expandable tubular member 202 consists
of
one or more of the seamless expandable tubular members 1000.
[0061] Referring now to Figures 12, 13 and 13a, in an exemplary embodiment the
expansion cone 600 is displaced by a conventional expansion device, such as,
for example, the
expansion devices commercially available from Baker Hughes Inc., Enventure
Global
Technology, or Weatherford International, in an upward direction 1200 relative
to the seamless
expandable tubular member 1000 thereby causing radial expansion and plastic
deformation of
the seamless expandable tubular member. In an exemplary embodiment, stress
concentrations
1300 are formed within the seamless expandable tubular member 1000 where the
contact point
618 of the expansion cone 600 is displaced into the seamless expandable
tubular member.
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[0062] The use of seamless expandable tubular members, such as, for example
the
seamless expandable tubular member 100, with a variable wall thickness may
require higher
expansion forces when the expansion device encounters areas of increased wall
thickness. An
expansion device may take the path of least resistance when the expansion
device encounters
an area of increased wall thickness t, and over-expand the corresponding area
of thin wall
thickness t2 of the seamless expandable tubular member in comparison to the
thicker wall
section tl- The use of a faceted expansion cone, such as, for example, the
expansion cone 600
creates areas of stress concentrations in the seamless expandable tubular
member, which may
assist in maintaining a proportional wall thickness during the radial
expansion and plastic
deformation process. In addition, the use of a faceted expansion cone, such
as, for example,
the expansion cone 600 creates areas of stress concentrations in the seamless
expandable
tubular member, which may result in reduced expansion and initiation forces.
[0063] Referring to Figures 14 and 14a, in an exemplary embodiment, an
expansion
cone 1400 includes a plurality of outer inclined expansion faceted surfaces
1402, having
corresponding widths (VVj, that intersect to form contact points 1404. Several
factors may be
considered when determining the appropriate number of outer inclined expansion
faceted
sUrfaces 1402, such as, for example, the coefficient of friction between the
expansion cone and
the expandable tubular member 1000, pipe quality, and data from lubrication
tests. In an
exemplary embodiment, for an expandable tubular member with uniform thickness,
the number
of circumferential spaced apart contact points may be infinity. In an
exemplary experiniental
embodiment, the dimensions of the final design of an expansion cone may
ultimately be refined
by performing an empirical study.
[0064] In an exemplary embodiment, the following equations may be used to make
a
preliminary calculation of the optimum number of outer inclined expansion
faceted surfaces
1402 on an expansion cone 1400 for expanding an expandable tubular member
1000:
R=(Dt+Dexa)/2; (1)
Sin (aJ2) = 1-(H/R); and (2)
N = 360 1a; (3)
where,
D1= Original tubular member inside diameter;
D,P= Expanded tubular member inside diameter;
H= Gap between gap surface and tubular member inside diameter;
R= Radius of polygon at midpoint of expansion cone;
a= Angle between circumferential spaced apart contact points of polygon; and
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N= Number of polygon flat surfaces.
In an exemplary embodiment, expandable tubular member 1000 has an original
inside diameter
of 4.77" that is expanded to an inside diameter of 5.68" utilizing an
expansion cone 1400_ In an
exemplary embodiment, there is a lubricant gap depth of .06". The optimum
number of outer
inclined expansion faceted surfaces 1402 is determined as follows:
R=(D,+Dexp)/2= (4.77-5.68)/2= .42;
Sin (al2) = 1-(H/R) = 1-(.06/.42);
a/2= 12.3 ;
a= 24.6 ;
N = 360 / a= 360 /24.6 = 15;
Accordingly, the theoretical number (N) of outer inclined expansion faceted
surfaces 1402, on
an expansion cone 1400 having a tapered faceted polygonal outer expansion
surface is 15, but
the actual number that may result from an empirical analysis may depend on
tubular member
quality, coefficient of friction, and data from lubrication tests. In an
exemplary embodiment, a
range for the actual number (N) of outer inclined expansion faceted surfaces
1402 necessary to
expand an expandable tubular member having an original inside diameter of
4.77" to an inside
diameter of 5.68" may range from 12 to15.
[0065] Referring to Figures 15a, 15b and 15c, in an exemplary embodiment,
expansion cone 1500 includes tapered faceted polygonal outer expansion
surfaces 1510, a
front end 1500a, a rear end 1500b, recesses 1512, internal passage 1530 for
drilling fluid,
internal passages 1514 for lubricating fluids, and radial passageways 1516.
The width 1520 of
tapered faceted polygonal outer expansion surfaces 1510 of expansion cone 1500
may be
constant for the length of the cone, resulting in trapezoidal shaped lubricant
gap 1522 between
each contact surface 1510. The follo+niing equations may be used for
calculating the width (VV)
1520 of the contact surface:
W = [2R sin(a/2)] / K; (4)
R = (D1+D2)/4; (5)
a= 360 degrees/ N; (6)
where:
W Width of contact point;
D1 = initial tubular member diameter;
D2 = expanded diameter;
N= Number of polygon flat surfaces; and
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K= System friction coefficient that must be determined.
In an exemplary embodiment, K is between 3 to 5 for an expandable tubular
member having an
original inside diameter of 4.77" and an expanded inside diameter of 5.68". N
may range from
12 to15. In an exemplary embodiment, K is 4.2.
[0066] Referring nowto Figures 16a, 16b and 16c, in an exemplary embodiment,
expansion cone 1600 has a tapered faceted polygonal outer expansion surface
1610, a front
end 1600a, a rear end 1600b, recesses 1612, internal passage 1630 for drilling
fluid, internal
passages 1614 for lubricating fluids, and radial passageways 1616. The width
1620 of tapered
faceted polygonal outer expansion surfaces 1610 of expansion cone 1600 may
vary the length
of the cone. In an exemplary embodiment, width 1620 of tapered faceted
polygonal outer
expansion surfaces 1610 may be larger at the front end W1 and become smaller
toward the
rear end W2.
[0067] In several exemplary embodiments, the tapered faceted polygonal outer
expansion surface of an expansion cone may be implemented in any expansion
cone, including
one or more of expansion cones 600, 800, 1404, 1500, and 1600. Furthermore, it
may be
implemented in any expansion device including one or more expansion surfaces.
[0068] The optimum taper angle 0 of the tapered portion of each expansion
cone,
including the tapered portions in expansion cones 600, 800, 1400, 1500, and
1600, may be
dependant on the amount of friction between the tapered portion of the
expansion cone and the
inside diameter of the tubular member. In an exemplary experimental
embodiment, a cone
angle of 8.5 to 12.5 was shown to be sufficient to expand an expandable
tubular member
having an original inside diameter of 4.77" to an inside diameter of 5.68".
The optimum taper
angle 0 may be determined after testing the lubricant system to determine the
exact coefficient
of friction. A cone angle greater than 10 may be required to minimize the
effect of thinning the
tubular member wall during expansion and may potentially reduce failures
related to collapsing.
[0069] Referring to Figures 17a and 17b, in an exemplary experimental
embodiment
1700, using finite element analysis ("FEA"), the radial expansion and plastic
deformation of an
expandable tubular member 1702 by a tapered expansion device 1704 displaced in
direction
1706 relative to the expandable tubular member, was modeled using commercially
available
FEA software DEFORM-2D in order to predict the actual performance of a
corresponding actual
tapered expansion device during the radial expansion and plastic deformation
of an actual
expandable tubular member_ The FEA optimized the taper angle 6 of the tapered
expansion
device 1704 for minimum expansion forces. The tapered expansion device surface
1708 of the
tapered expansion device 1704 has a length L. The tapered expansion device
1704 has an
,..~.m.,:,v . . . - . i ,,,,-.~... .:... ..... . ........
.,~....:.~.....,..,..W._..,.... .. .., , . .. ,.. ... ... . ....
CA 02584492 2009-03-24
initial diameter po and a final diameter D, . Since the initial diameter po
and the final diameter
D, are fixed in the tapered expansion device 1704, any increase in the taper
angle 8 vvnuld
result in an increase in the length L of the expansion surface 1708. .
[0070] Referring to Figure 17c, in the exemplary experimental embodiment 1700
using FEA, the length L of the expansion surface 1708 versus the taper an.gle
9 is shovan. The
length L of the expansion surface 1708 increases as the taper angle 0
decreases.
[00711 Referring to Figure 17d, in the exemplary experimental embodiment 1700
using FEA, a true stress-strain cur,/e 1710 for the expandable tubular member
1702 yvith a
modulus of elasticity of E=30x10P psi and a Poisson's ratio of 0.3, is
provided. In the FEA, the
expansion device 1704 was modeled as rigid bodywhile the expandable tubular
member 1702
was modeled as an elastic-plastic object.
[0072] In an exemplary embodiment, friction conditions at the interface 1712
k+etween
the expansion device 1704 and the expandable tubular member 1702 influence
metal flow and
stresses acting on the expansion device. Interface friction conditions may be
expressed
quantitativel;r in terms of a factor or coefficient. The fhction shear stress,
fs, maybe expresseci
usiiig Coulomb or shear friction If Coulomb friction is assumed, the friction
shear stress takes
thefollovvir?g form
f5=up (7)
p being a compressive normal stress at tfie interface and ubelng the
coefficient of
frictio.ri_ However, if shear friction is assunaed; thefiietiqn shear stress
takes tfre fonri
of
f C
T, ($)
k bEing. the in stantaneous shear strength of the rihaterial and m being. the
friction
shear factor, 0<rr<1. The instantaneous shear strength can be expressed as a
fUnction of ifrstantaneous yield strength, a, assuming the material obeys a
von
Mises yield criterion.
[0073] V4fien contact pressures at the interface 1712 become large, the shear
stress
predicted by Coulorrib friction can exceed the shear strength of the material.
TherEfore; shear
friction should be used to model the interface friction conriitions for
operations that produce high
contact stresses Since there is potential for large contact stress in the
radial expansion and
plastic deformatioti of the expandable tubular memkier 1702 by the expansion
device 1704, the
shear friction model was used in all experimental embodiments.
11
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[0074] Referring to Figure 18, in the exemplary experimental embodiment 1700
using
FEA, a total axial expansion force curve 1800 shows axial expansion force as a
function of the
friction shear factor (m) for a given tapered expansion device surface 1708
angle of 10 . The
total axial expansion force curve 1800 increases with increasing friction
shear factor (m). In an
exemplary embodiment, in cold forming of steels with lubrication, the friction
shear factor (m)
falls in the range 0.05 < m < 0.15.
[0075] In an exemplary embodiment, the actual work wa required to cause radial
expansion and plastic deformation of the expandable tubular member 1702 is
comprised of
three components, a) ideal work w;, b) frictional work wf and c) redundant
work %. The actual
work wa required to cause deformation is the sum of the three components, wa =
wi + wf + wr .
Ideal work w;, is the work required for homogeneous deformation, which exists
only when plane
sections remain plane during the deformation. Frictional work wf, is consumed
at the interface
between the deforming metal and the tool faces that constrain the metal.
Redundant work wr, is
due to internal shearing and bending that causes distortion of plane sections
as they pass
through the deformation zone, which increases the strain in the deforming
metal.
[00761 Referring to Figure 19, in the exemplary experimental embodiment 1700
using
FEA, the influence of the taper angle 8 of the tapered expansion device
surface 1708 on the
actual work wa, ideal work w;, frictional work wf, and redundant work w, is
shown. The actual
work wa is the sum of the frictional work wf, the redundant work wf, and the
ideal work w, The
ideal work w; remains constant and does not depend on the taper angle 8 of the
tapered
expansion device surface 1708. However, the frictional work wf and redundant
work w, largely
depend on the taper angle 8 of the tapered expansion device surface 1708. The
frictional work
wf increases with decreasing taper angle 8 of the tapered expansion device
surface 1708, while
the redundant work wr increases with increasing taper angle 8 of the tapered
expansion device
surface. The actual work wa is minimized, thereby minimizing the required
total axial expansion
force, at the low point 8-1 on the actual work wa curve. The low point 8-1 on
the actual work wa
curve thereby determines the optimum taper angle 6 of the tapered expansion
device surface
1708.
[0077] Referring to Figure 20, in the exemplary experimental embodiment 1700
using
FEA, total axial expansion force curves 2002, 2004, and 2006 are shown as a
function of taper
angle 8 for three different friction shear factors (m), is shown. Axial
expansion force curve 2002
has a friction shear factor of m=0.10 and a minimum axial expansion force at a
taper angle of
8 . Axial expansion force curve 2004 has a friction shear factor of m=0.05 and
a minimum axial
12
__ ~ ...i . .. ..._ ... _ ..
CA 02584492 2009-03-24
a
expansion force at a taper angle of 7 . Axial expansion force curve 2006 has a
friction shear
factor of m=0.0 and a minimum axial expansion force at a taper angle of 5 .
[0078] Referring to Figure 21, in the exemplary experimental embodiment 1700
using
FEA, a free-body diagram 2100 illustrates the forces acting on the tapered
expansion device
1704 including the force required to deform the expandable tubular member 1702
FN, the axial
force component Fz, the radial force component Fr, and the friction force Ff.
The following
equations explain the forces acting on the tapered expansion device 1704:
F,=FN cos(8) - Ff sin(8) and (9)
F2= FN sin(6) + Ff cos(6); (10)
where
FN = Normal force during deformation
Ff = Frictional Force
Fr = Radial force acting on the tapered expansion device 1704
FZ = Axial force acting on the tapered expansion device 1704
The axial force component FZ increases with increase in the taper angle 6 of
the tapered
expansion device surface 1708, while the contribution from friction force Ff
to the axial force
component decreases with increase in the taper angle 6 of the tapered
expansion device
surface 1708. This is because, with increase in taper angle 6, the cos(6) term
decreases while
the sin(6) term increase. In an exemplary embodiment, however, the initial
increase in the axial
force for small taper angles in the presence of friction is due to the
contribution from the friction
force because for smaller angles the cos(8) is approximately one, while the
sin(8) term is
negligibie.
[0079] Referring to Figure 22, in the exemplary experimental embodiment 1700
using
FEA, radial reaction force curve 2202 shows the radial reaction force F, on
the expansion device
1704 as a function of taper angle A and friction shear factor (m)_ In an
exemplary embodiment,
the radial reaction force Fr decreases with increase in the taper angle 6, and
the radial reaction
force Fr was independent of the friction shear factor (m). The radial reaction
force curve 2202
was approximately linear for taper angles of 15 degrees or greater, and non-
linear for taper
angles less than 15 degrees.
[0080] Referring to Figure 23, in the exemplary experimental embodiment 1700
using
FEA, effective strain curve 2302 in the expandable tubular member 1702 as a
function of taper
angle 6 for three different friction shear factors (m), is shown. In an
exemplary embodiment, the
maximum effective strain in the expandable tubular member 1702 increased with
increasing
taper angle 0, and was independent of friction shear factor (m). In an
exemplary embodiment,
13
-4. .
CA 02584492 2009-03-24
the increase in the maximum effective strain with increasing taper angle 8 is
due to increased
redundant deformation wr in the expandable tubular member 1702 for large taper
angles. In an
exemplary embodiment, taper angles of approximately 15 degrees or greater were
more
effective at straining the expandable tubular member 1702.
[0081] Referring to Figures 24a and 24b, in an exemplary experimental
embodiment
2400 using finite element analysis ("FEA"); the radial expansion and plastic
deformation of an
expandable tubular member 1702 by a polynomial curvature expansion device 2402
displaced
in direction 1706 relative to the expandable tubular member, was modeled using
commercially
available FEA software DEFORM-2D in order to predict the actual performance of
a
corresponding actual polynomial curvature expansion device during the radial
expansion and
plastic deformation of an actual expandable tubular member. In an exemplary
embodiment, the
FEA optimized the shape and length L of the polynomial curvature expansion
device 2402 for
minimum expansion forces. Polynomial curvature expansion device surface 2404
has a length
L. In an exemplary embodiment, the polynomial curvature expansion device 2402
has an initial
diameter po at one end and a final diameter D, at another end_
[0082] Referring to Figure 25, in the exemplary experimental embodiment 2400
using
FEA, the shape of a polynomial curvature expansion device surface 2502 is
illustrated. The
polynomial curvature expansion surface 2502 has a length L and an inflection
point Lf. In an
exemplary embodiment, the ratio of L~L determines the shape of the polynomial
curvature
expansion surface 2502.
[0083] In the exemplary experimental embodiment 2400 using FEA, the polynomial
curvature is expressed as:
r(z) = ao + alz + a2z2 + a3z' + adz4 (11)
ao = R, (12)
a, = 0 (13)
az = input (14)
a, ~ [a2 + Z(RLZ R ) (15)
_ ~ 1a2 3(Rl~ (16)
aa Z + Z where
r(z) = radial distance from the centerline of the expansion cone; and
z={ongitudinal distance along the polynomial curvature expansion surface
14
CA 02584492 2009-03-24
In an exemplary embodiment, the optimum polynomial curvature expansion surface
for
minimum axial expansion forces for a friction shear factor m=0.10 was r(z) =
2.020 - 0.150z2 -
0.043z3 + 0.055z4. In an exemplary embodiment, the optimum polynomial
curvature expansion
surface for minimum axial expansion forces for a friction shear factor m=0.05
was r(z) = 2.020 -
0.0952- 0.023z3 + 0.0232 .
[0084] Referring to Figure 26, in the exemplary experimental embodiment 2400
using
FEA, five different polynomial curvature expansion device surfaces 2602, 2604,
2606, 2608,
and 2610, are shown. Polynomial curvature expansion device surface 2602 has a
Lr/L = 0.67.
Polynomial curvature expansion device surface 2604 has a Lf/L = 0.60.
Polynomial curvature
expansion device surface 2606 has a Lf/L = 0.50. Polynomial curvature
expansion device
surface 2608 has a LVL = 0.40. Polynomial curvature expansion device surface
2610 has a LVL
= 0.32.
[0085] Referring to Figure 27, in the exemplary experimental embodiment 2400
using
FEA, axial expansion force curves 2702, 2704, 2706, and 2708 are shown for
increasing ratios
of Lf/L for four different polynomial curvature expansion device surface
lengths at a constant
friction shear factor of m=0.05. In an exemplary embodiment, the axial
expansion force curve
2702 has a polynomial curvature expansion device surface length of 0.75 inches
and the
minimum axial expansion force was found at a L~L ratio of 0.6. In an exemplary
embodiment,
the axial expansion force curve 2704 has a polynomial curvature expansion
device surface
length of 1_1626 inches and the minimum axial expansion force was found at a
L~L ratio of 0.6.
In an exemplary embodiment, the axial expansion force curve 2706 has a
polynomial curvature
expansion device surface length of 2.0 inches and the minimum axial expansion
force was
found at a LpL ratio of 0.6. In an exemplary embodiment, the axial expansion
force curve 2708
has a polynomial curvature expansion device surface length of 2.25 inches and
the minimum
axial expansion force was found at a LrlL ratio of 0.6. In an exemplary
embodiment, the
minimum axial expansion force for the four axial expansion force curves 2702,
2704, 2706, and
2708, was found to be at the LVL ratio of about 0.6, thus, the ratio L~L at
which the minimum
axial expansion force occurs was found to be independent of the length of the
polynomial
curvature expansion surface for a given shear friction factor (m).
[0086] Referring to Figure 28, in the exemplary experimental embodiment 2400
using
FEA, axial expansion force curves 2802, 2804, and 2806 are shown for
increasing LdL ratios at
three different friction shear factors (m) and a constant polynomial curvature
expansion surface
length of 1.1626 inches. Axial expansion force curve 2802 has a friction shear
factor of m=0.1
and a minimum axial expansion force at a L~L ratio of 0_6. Axial expansion
force curve 2804
CA 02584492 2009-03-24
has a friction shear factor of m=0.05 and a minimum axial expansion force at a
LWL ratio of 0.6.
Axial expansion force curve 2806 has a friction shear factor of m=0.0 and a
minimum axial
expansion force at a Lr/L ratio of 0_6_ For the three axial expansion force
curves 2802, 2804,
and 2806, the minimum axial expansion force was found to be at the Lf/L ratio
of 0.6, thus, the
ratio LdL at which the minimum axial expansion force occurs was found to be
independent of the
shear friction factor (m) for a given length of the polynomial curvature
expansion surface.
[0087] Referring to Figure 29, in the exemplary experimental embodiment 2400
using
FEA, axial expansion force curves 2902, 2904, and 2906 are shown for
increasing lengths of
the polynomial curvature expansion device surface 2404 with the optimum Lf/L
ratio of 0.6 for
three different shear friction factors (m). Axial expansion force curve 2902
has a friction shear
factor of m=0.1, the optimum length of the polynomial curvature expansion
device surface 2404
was found to be 1.625 inches for a expansion cone that is to achieve a 0.25"
increase in
diameter. Axial expansion force curve 2904 has a friction shear factor of
m=0.05, the optimum
length of the polynomial curvature expansion device surface 2404 was found to
be 1.875 inches
for a expansion cone that is to achieve a 0.25" increase in diameter. Axial
expansion force
curve 2906 has a friction shear factor of m=0.0, the optimum length of the
polynomial curvature
expansion device surface 2404 was found to be 2.5 inches for a expansion cone
that is to
achieve a 0.25" increase in diameter.
[0088] Referring to Figure 30, in the exemplary experimental embodiments 1700
and
2400 using FEA, axial expansion force 3002 corresponding to an optimum taper
angle of 8
degrees for the tapered expansion device surface 1708 is compared to the axial
expansion
force 3004 corresponding to an optimum polynomial curvature expansion device
surface 2404
with an optimum LJL ratio of 0.6 and a length of 1_625 inches, for a friction
shear factor of
m=0.10. The optimum tapered expansion device surface 1708 and the optimum
polynomial
curvature expansion device surface 2404 required approximately the same axial
expansion
force, for a friction shear factor of m=0.10.
[0089] Referring to Figure 31, in the exemplary experimental embodiments 1700
and
2400 using FEA, axial expansion force 3102 corresponding to an optimum taper
angle of 7
degrees for the tapered expansion device surface 1708 is compared to the axial
expansion
force 3104 corresponding to an optimum polynomial curvature expansion device
surface 2404
with an optimum L~L ratio of 0.6 and a length of 1.875 inches, for a friction
shear factor of
m=0.05. The optimum tapered expansion surface 1708 and the optimum polynomial
curvature
expansion surface 2404 required approximately the same axial expansion force,
for a friction
shear factor of m=0.05.
16
CA 02584492 2009-03-24
[0090] Referring to Figure 32, in the exemplary experimental embodiments 1700
and
2400 using FEA, radial expansion force 3202 required for the optimum taper
angle of 8 degrees
for the tapered expansion surface 1708 is compared to the axial expansion
force 3204 required
for the optimum polynomial curvature expansion surface 2404 with the optimum
Lr/L ratio of 0_6
and a length of 1.625 inches, for a friction shear factor of m=0.10. The
radial reaction force
produced by the polynomial curvature expansion surface 2404 was 16.4% lower
than that of the
tapered expansion surface 1708, for a friction shear factor of m=0.10.
[0091] Referring to Figure 33, in the exemplary experimental embodiments 1700
and
2400 using FEA, radial expansion force 3302 required for the optimum taper
angle of 7 degrees
for the tapered expansion surface 1708 is compared to the axial expansion
force 3304 required
for the optimum polynomial curvature expansion surface 2404 with the optimum
LfIL ratio of 0.6
and a length of 1.875 inches, for a friction shear factor of m=0.05. The
radial reaction force
produced by the polynomial curvature expansion surface 2404 was 5% lower than
that of the
tapered expansion surface 1708, for a friction shear factor of m=0.05.
[0092] Referring to Figure 34, in an exemplary experimental embodiment 1700
using
FEA, total axial expansion force curve 3402 shows the total axial expansion
force versus the
displacement of the tapered expansion device 1704 with an optimum taper angle
of 8 degrees
for a friction shear factor of m=0.10. The total axial expansion force curve
3402 has transient
force spike 3404 at the beginning of the displacement of the tapered expansion
device 1704
and transient force spike 3406 at the end of the displacement of the tapered
expansion device.
[0093] Referring to Figure 35, in an exemplary experimental embodiment 2400
using
FEA, total axial expansion force curve 3502 shows the total axial expansion
force versus the
displacement of the polynomial curvature expansion device 2402 with the
optimum polynomial
curvature expansion surface 2404 with the optimum LVL ratio of 0.6 and a
length of 1.625
inches for a friction shear factor of m=0.10. There are no transient force
spikes at the beginning
or at the end of the displacement of the polynomial curvature expansion device
2402 for a
friction shear factor of m=0.10. The lack of transient force spikes may result
in longer
equipment life in comparison to the corresponding tapered expansion device
1704.
[0094] Referring to Figure 36, in an exemplary experimental embodiment 1700
using
FEA, total axial expansion force curve 3602 shows the total axial expansion
force versus the
displacement of the tapered expansion device 1704 with an optimum taper angle
of 7 degrees
for a friction shear factor of m=0.05. The total axial expansion force curve
3602 has transient
17 -
CA 02584492 2009-03-24
force spike 3604 at the beginning of the displacement of the tapered expansion
device 1704
and transient force spike 3606 at the end of the displacement of the tapered
expansion device.
[0095] Referring to Figure 37, in an exemplary experimental embodiment 2400
using
FEA, total axial expansion force curve 3702 shows the total axial expansion
force versus the
displacement of the polynomial curvature expansion device 2402 with the
optimum polynomial
curvature expansion surface 2404 with the optimum L~L ratio of 0.6 and a
length of 1.875
inches for a friction shear factor of m=0.05. There are no transient force
spikes at the beginning
or at the end of the displacement of the expansion device 2402 for a friction
shear factor of
m=0.05. The lack of transient force spikes may result in longer equipment life
in comparison to
the corresponding tapered expansion device 1704.
[0096] Referring to Figure 38, in an exemplary experimental embodiment using
FEA,
the maximum effective strain 3802 corresponding to an optimum taper angle of 7
degrees for
the tapered expansion surface 1708 is compared to the maximum effective strain
3804
corresponding to an optimum polynomial curvature expansion surface 2404 with
an optimum
WL ratio of 0.6 and a length of 1.625 inches, for a friction shear factor of
m=0.10. The
maximum effective strain 3802 produced by the optimum tapered expansion
surface 1708 was
approximately the same as the maximum effective strain 3804 produced by the
optimum
polynomial curvature expansion surface 2404, for a friction shear factor of
m=0.10.
[0097] Referring to Figure 39, in an exemplary experimental embodiment using
FEA,
the maximum effective strain 3902 corresponding to an optimum taper angle of 7
degrees for
the tapered expansion surface 1708 is compared to the maximum effective strain
3904
corresponding to an optimum polynomial curvature expansion surface 2404 with
an optimum
Lf/L ratio of 0.6 and a length of 1.875 inches, for a friction shear factor of
m=0.05. The
maximum effective strain 3902 produced by the optimum tapered expansion
surface 1708 was
approximately the same as the maximum effective strain 3904 produced by the
optimum
polynomial curvature expansion surface 2404, for a friction shear factor of
m=0.05.
[0098] An expansion device for radially expanding a tubular member has been
described that includes a first tapered outer surface.
[0099] An expansion device for radially expanding a tubular member has been
described that includes: a first tapered outer surface defined by a polynomial
equation.
[00100] An expansion device for radially expanding a tubular member has been
described that includes: a first tapered outer surface defined by a polynomial
equation; wherein
the polynomial equation has a LrlL ratio ranging from about 0.32 to 0.67.
18
.~. .~.. _, .. _ . .
_ ~.
CA 02584492 2009-03-24
[00101] An expansion device for radially expanding a tubular member has been
described that includes: a first tapered outer surface defined by a polynomial
equation; wherein
the polynomial equation has a Lf/L ratio ranging from about 0.32 to 0.67;
wherein the length of
the first tapered outer surface ranges from 0.5 inches to 2.5 inches.
[00102] An expansion device for radially expanding a tubular member has been
described that includes: a first tapered outer surface defined by a polynomial
equation; wherein
the polynomial equation has a Lf/L ratio ranging from about 0.32 to 0.67;
wherein the length of
the first tapered outer surface ranges from 1.6 inches to 1.9 inches.
[00103] An expansion device for radially expanding a tubular member has been
described that includes: a first tapered outer surface defined by a polynomial
equation; wherein
the polynomial equation has a Lr/L ratio ranging from about 0.32 to 0.67; and
wherein the first
tapered outer surface comprises one or more facets in cross section.
[00104] An expansion device for radially expanding a tubular member has been
described that includes: a first tapered outer surface defined by a polynomial
equation; wherein
the polynomial equation has a Lr/L ratio ranging from about 0.32 to 0.67;
wherein the first
tapered outer surface comprises one or more facets in cross section; wherein
the number of
facets ranges from about 12 to 16.
[00105] An expansion device for radially expanding a tubular member has been
described that includes: a first tapered outer surface defined by a polynomial
equation; wherein
the polynomial equation has a Lr/L ratio ranging from about 0.32 to 0.67;
wherein the first
tapered outer surface comprises one or more facets in cross section; wherein
the number of
facets ranges from about 12 to 16; wherein the faceted surfaces are wider near
the front of the
expansion device and become narrower toward the rear end of the expansion
device.
[00106] An expansion device for radially expanding a tubular member has been
described that includes a first tapered outer surface; wherein the first
tapered outer surface
comprises an angle of attack ranging from about 6 to 10 degrees.
[00107] An expansion device for radially expanding a tubular member has been
described that includes a first tapered outer surface; wherein the first
tapered outer surface
comprises an angle of attack ranging from about 6 to 10 degrees; a second
tapered outer
surface comprising a second angle of attack coupled to the first tapered outer
surface; and
wherein the first angle of attack is greater than the second angle of attack.
[00108] An expansion device for radially expanding a tubular member has been
described that includes a first tapered outer surface; wherein the first
tapered outer surface
19
CA 02584492 2009-03-24
comprises an angle of attack ranging from about 6 to 10 degrees; a second
tapered outer
surface comprising a second angle of attack coupled to the first tapered outer
surface; wherein
the first angle of attack is greater than the second angie of attack; wherein
the first angle of
attack ranges from about 6 to 20 degrees; and wherein the second angle of
attack ranges from
about 4 to 15 degrees.
[00109] An expansion device for radially expanding a tubular member has been
described that includes a first tapered outer surface; wherein the first
tapered outer surface
comprises an angle of attack ranging from about 6 to 10 degrees; a second
tapered outer
surface comprising a second angle of attack coupled to the first tapered outer
surface; wherein
the first angle of attack is greater than the second angie of attack; and one
or more intermediate
tapered outer surfaces coupled between the first and second tapered outer
surfaces.
[00110] An expansion device for radially expanding a tubular member has been
described that includes a first tapered outer surface; wherein the first
tapered outer surface
comprises an angle of attack ranging from about 6 to 10 degrees; a second
tapered outer
surface comprising a second angle of attack coupled to the first tapered outer
surface; wherein
the first angle of attack is greater than the second angle of attack; and one
or more intermediate
tapered outer surfaces coupled between the first and second tapered outer
surfaces; wherein
the angle of attack of the intermediate tapered outer surfaces continually
decreases from the
first tapered outer surface to the second tapered outer surface.
[00111] An expansion device for radially expanding a tubular member has been
described that includes a first tapered outer surface; wherein the first
tapered outer surface
comprises an angle of attack ranging from about 6 to 10 degrees; a second
tapered outer
surface comprising a second angle of attack coupled to the first tapered outer
surface; wherein
the first angle of attack is greater than the second angle of attack; and one
or more intermediate
tapered outer surfaces coupled between the first and second tapered outer
surfaces; wherein
the angle of attack of the intermediate tapered outer surfaces decreases in
steps from the first
tapered outer surface to the second tapered outer surface.
[00112] An expansion device for radially expanding a tubular member has been
described that includes a first tapered outer surface; wherein the first
tapered outer surface
comprises an angle of attack ranging from about 6 to 10 degrees; wherein the
first tapered outer
surface comprises one or more facets in cross section.
[00113] An expansion device for radially expanding a tubular member has been
described that includes a first tapered outer surface; wherein the first
tapered outer surface
CA 02584492 2009-03-24
comprises an angle of attack ranging from about 6 to 10 degrees; wherein the
first tapered outer
surface comprises one or more facets in cross section; wherein the number of
facets ranges
from about 12 to 16.
[00114] An expansion device for radially expanding a tubular member has been
described that includes a first tapered outer surface; wherein the first
tapered outer surface
comprises an angle of attack ranging from about 6 to 10 degrees; wherein the
first tapered outer
surface comprises one or more facets in cross section; wherein the faceted
surfaces are wider
near the front of the expansion device and become narrower toward the rear end
of the
expansion device.
[00115] An expansion device for radially expanding a tubular member has been
described that includes a first tapered outer surface; wherein the first
tapered outer surface
comprises an angle of attack ranging from about 6 to 10 degrees; a second
tapered outer
surface comprising a second angle of attack coupled to the first tapered outer
surface; and
wherein the first angle of attack is greater than the second angle of attack;
wherein the first
tapered outer surface and the second tapered outer surface comprise one or
more facets in
cross section.
[00116] An expansion device for radially expanding a tubular member has been
described that includes a first tapered outer surface; wherein the first
tapered outer surface
comprises an angle of attack ranging from about 6 to 10 degrees; a second
tapered outer
surface comprising a second angle of attack coupled to the first tapered outer
surface; and
wherein the first angle of attack is greater than the second angle of attack;
wherein the first
tapered outer surface and the second tapered outer surface comprise one or
more facets in
cross section; wherein the number of facets ranges from about 12 to 16.
[00117] An expansion device for radially expanding a tubular member has been
described that includes a first tapered outer surface; wherein the first
tapered outer surface
comprises an angle of attack ranging from about 6 to 10 degrees; a second
tapered outer
surface comprising a second angle of attack coupled to the first tapered outer
surface; and
wherein the first angle of attack is greater than the second angle of attack;
wherein the first
tapered outer surface and the second tapered outer surface comprise one or
more facets in
cross section; wherein the faceted surfaces are wider near the front of the
expansion device and
become narrower toward the rear end of the expansion device.
[00118] An expansion device for radially expanding a tubular member has been
described that includes: a first tapered outer surface defined by a polynomial
equation; wherein
21
CA 02584492 2009-03-24
the polynomial equation has a Lf/L ratio ranging from about 0.32 to 0.67;
wherein the length of
the tapered outer surface ranges from about 1.6 inches to 1.9 inches; wherein
the tapered outer
surface comprises one or more facets in cross section; wherein the number of
facets ranges
from about 12 to 16; wherein the faceted surfaces are wider near the front of
the expansion
device and become narrower toward the rear end of the expansion device.
[00119] An expansion system for radially expanding a tubular member has been
described that includes a first tapered outer surface; and means for
displacing the expansion
device relative to the expandable tubufar member.
[00120] An expansion system for radially expanding a tubular member has been
described that includes: an expansion device that includes a first tapered
outer surface defined
by a polynomial equation; and means for displacing the expansion device
relative to the
expandable tubular member.
[00121] An expansion system for radially expanding a tubular member has been
described that includes: an expansion device that includes a first tapered
outer surface defined
by a polynomial equation; wherein the polynomial equation has a LJL ratio
ranging from about
0.32 to 0.67; and means for displacing the expansion device relative to the
expandable tubular
member; and means for displacing the expansion device relative to the
expandable tubular
member_
[00122] An expansion system for radially expanding a tubular member has been
described that includes: an expansion device that includes a first tapered
outer surface defined
by a polynomial equation; wherein the polynomial equation has a LJL ratio
ranging from about
0.32 to 0.67; wherein the length of the first tapered outer surface ranges
from 0.5 inches to 2.5
inches; and means for displacing the expansion device relative to the
expandable tubular
member.
[00123] An expansion system for radially expanding a tubular member has been
described that includes: an expansion device that includes a first tapered
outer surface defined
by a polynomial equation; wherein the polynomial equation has a LJL ratio
ranging from about
0.32 to 0.67; wherein the length of the first tapered outer surface ranges
from 1.6 inches to 1.9
inches; and means for displacing the expansion device relative to the
expandable tubular
member.
[00124] An expansion system for radially expanding a tubular member has been
described that includes: an expansion device that includes a first tapered
outer surface defined
by a polynomial equation; wherein the polynomial equation has a LeL ratio
ranging from about
22
~ .. ._ ._. _ _
_ ..~-~.~.,.~._.~r.....,~ :
CA 02584492 2009-03-24
0.32 to 0.67; and wherein the first tapered outer surface comprises one or
more facets in cross
section; and means for displacing the expansion device relative to the
expandable tubular
member.
[00125] An expansion system for radially expanding a tubular member has been
described that includes: an expansion device that includes a first tapered
outer surface defined
by a polynomial equation; wherein the polynomial equation has a L~L ratio
ranging from about
0.32 to 0.67; wherein the first tapered outer surface comprises one or more
facets in cross
section; wherein the number of facets ranges from about 12 to 16; and means
for displacing the
expansion device relative to the expandable tubular member.
[00126] An expansion system for radially expanding a tubular member has been
described that includes: an expansion device that includes a first tapered
outer surface defined
by a polynomial equation; wherein the polynomial equation has a LJL ratio
ranging from about
0.32 to 0.67; wherein the first tapered outer surface comprises one or more
facets in cross
section; wherein the number of facets ranges from about 12 to 16; wherein the
faceted surfaces
are wider near the front of the expansion device and become narrower toward
the rear end of
the expansion device; and means for displacing the expansion device relative
to the expandable
tubular member.
[00127] An expansion system for radially expanding a tubular member has been
described that includes an expansion device that includes a first tapered
outer surface; wherein
the first tapered outer surface comprises an angle of attack ranging from
about 6 to 10 degrees;
and means for displacing the expansion device relative to the expandable
tubular member.
[00128] An expansion system for radially expanding a tubular member has been
described that includes: an expansion device that includes a first tapered
outer surface; wherein
the first tapered outer surface comprises an angle of attack ranging from
about 6 to 10 degrees;
a second tapered outer surface comprising a second angle of attack coupled to
the first tapered
outer surface; and wherein the first angle of attack is greater than the
second angle of attack;
and means for displacing the expansion device relative to the expandable
tubular member_
[00129] An expansion system for radially expanding a tubular member has been
described that includes an expansion device that includes a first tapered
outer surface; wherein
the first tapered outer surface comprises an angle of attack ranging from
about 6 to 10 degrees;
a second tapered outer surface comprising a second angle of attack coupled to
the first tapered
outer surface; wherein the first angle of attack is greater than the second
angle of attack;
wherein the first angle of attack ranges from about 6 to 20 degrees; and
wherein the second
23
CA 02584492 2009-03-24
angle of attack ranges from about 4 to 15 degrees; and means for displacing
the expansion
device relative to the expandable tubular member.
[00130] An expansion system for radially expanding a tubular member has been
described that includes an expansion device that includes a first tapered
outer surface; wherein
the first tapered outer surface comprises an angle of attack ranging from
about 6 to 10 degrees;
a seoond tapered outer surface comprising a second angle of attack coupled to
the first tapered
outer surface; wherein the first angle of attack is greater than the second
angle of attack; and
one or more intermediate tapered outer surfaces coupled between the first and
second tapered
outer surfaces; and means for displacing the expansion device relative to the
expandable
tubular member.
[00131] An expansion system for radially expanding a tubuiar member has been
described that includes an expansion device that includes a first tapered
outer surface; wherein
the first tapered outer surface comprises an angle of attack ranging from
about 6 to 10 degrees;
a second tapered outer surface comprising a second angle of attack coupled to
the first tapered
outer surface; wherein the first angle of attack is greater than the second
angle of attack; and
one or more intermediate tapered outer surfaces coupled between the first and
second tapered
outer surfaces; wherein the angle of attack of the intermediate tapered outer
surfaces
continually decreases from the first tapered outer surface to the second
tapered outer surface;
and means for displacing the expansion device relative to the expandable
tubular member.
[00132] An expansion system for radially expanding a tubular member has been
described that includes an expansion device that includes a first tapered
outer surface; wherein
the first tapered outer surface comprises an angle of attack ranging from
about 6 to 10 degrees;
a second tapered outer surface comprising a second angle of attack coupled to
the first tapered
outer surface; wherein the first angle of attack is greater than the second
angle of attack; and
one or more intermediate tapered outer surfaces coupled between the first and
second tapered
outer surfaces; wherein the angle of attack of the intermediate tapered outer
surfaces
decreases in steps from the first tapered outer surface to the second tapered
outer surface; and
means for displacing the expansion device relative to the expandable tubular
member.
[00133] An expansion system for radially expanding a tubular member has been
described that includes an expansion device that includes a first tapered
outer surface; wherein
the first tapered outer surface comprises an angle of attack ranging from
about 6 to 10 degrees;
wherein the first tapered outer surface comprises one or more facets in cross
section; and
means for displacing the expansion device relative to the expandable tubular
member.
24
CA 02584492 2009-03-24
[00134] An expansion system for radially expanding a tubular member has been
described that includes an expansion device that includes a first tapered
outer surface; wherein
the first tapered outer surface comprises an angle of attack ranging from
about 6 to 10 degrees;
wherein the first tapered outer surface comprises one or more facets in cross
section; wherein
the number of facets ranges from about 12 to 16; and means for displacing the
expansion
device relative to the expandable tubular member.
[00135] An expansion system for radially expanding a tubular member has been
described that includes an expansion device that includes a first tapered
outer surface; wherein
the first tapered outer surface comprises an angle of attack ranging from
about 6 to 10 degrees;
wherein the first tapered outer surface comprises one or more facets in cross
section; wherein
the faceted surfaces are wider near the front of the expansion device and
become narrower
toward the rear end of the expansion device; and means for displacing the
expansion device
relative to the expandable tubular member.
[00136] An expansion system for radially expanding a tubular member has been
described that includes an expansion device that includes a first tapered
outer surface; wherein
the first tapered outer surface comprises an angle of attack ranging from
about 6 to 10 degrees;
a second tapered outer surface comprising a second angle of attack coupled to
the first tapered
outer surface; and wherein the first angle of attack is greater than the
second angle of attack;
wherein the first tapered outer surface and the second tapered outer surface
comprise one or
more facets in cross section; and means for displacing the expansion device
relative to the
expandable tubular member.
[00137] An expansion system for radially expanding a tubular member has been
described that includes an expansion device that includes a first tapered
outer surface; wherein
the first tapered outer surface comprises an angle of attack ranging from
about 6 to 10 degrees;
a second tapered outer surface comprising a second angle of attack coupled to
the first tapered
outer surface; and wherein the first angle of attack is greater than the
second angle of attack;
wherein the first tapered outer surface and the second tapered outer surface
comprise one or
more facets in cross section; wherein the number of facets ranges from about
12 to 16; and
means for displacing the expansion device relative to the expandable tubular
member.
[00138] An expansion system for radially expanding a tubular member has been
described that includes an expansion device that includes a first tapered
outer surface; wherein
the first tapered outer surface comprises an angle of attack ranging from
about 6 to 10 degrees;
a second tapered outer surface comprising a second angle of attack coupled to
the first tapered
CA 02584492 2009-03-24
outer surface; and wherein the first angle of attack is greater than the
second angle of attack;
wherein the first tapered outer surface and the second tapered outer surface
comprise one or
more facets in cross section; wherein the faceted surfaces are wider near the
front of the
expansion device and become narrower toward the rear end of the expansion
device; and
means for displacing the expansion device relative to the expandable tubular
member.
[00139] An expansion system for radially expanding a tubular member has been
described that includes: an expansion device that includes a first tapered
outer surface defined
by a polynomial equation; wherein the polynomial equation has a L~L ratio
ranging from about
0.32 to 0.67; wherein the length of the tapered outer surface ranges from
about 1.6 inches to
1.9 inches; wherein the tapered outer surface comprises one or more facets in
cross section;
wherein the number of facets ranges from about 12 to 16; wherein the faceted
surfaces are
wider near the front of the expansion device and become narrower toward the
rear end of the
expansion device; and means for displacing the expansion device relative to
the expandable
tubular member.
[00140] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface.
[00141] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface defined by a polynomial equation.
[00142] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface defined by a polynomial equation;
wherein the
polynomial equation has a LdL ratio ranging from about 0.32 to 0.67.
[00143] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface defined by a poiynomiaf equation;
wherein the
polynomial equation has a LVL ratio ranging from about 0.32 to 0_67; wherein
the length of the
first tapered outer surface ranges from 0.5 inches to 2.5 inches.
26
CA 02584492 2009-03-24
[00144] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface defined by a polynomial equation;
wherein the
polynomial equation has a L~L ratio ranging from about 0.32 to 0.67; wherein
the length of the
first tapered outer surface ranges from 1.6 inches to 1.9 inches.
[00145] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface defined by a polynomial equation;
wherein the
polynomial equation has a LJL ratio ranging from about 0.32 to 0.67; and
wherein the first
tapered outer surface comprises one or more facets in cross section.
[00146] A method of radially expanding a tubular member has been described
that
inciudes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface defined by a polynomial equation;
wherein the
polynomial equation has a LWL ratio ranging from about 0.32 to 0.67; wherein
the first tapered
outer surface comprises one or more facets in cross section; wherein the
number of facets
ranges from about 12 to 16.
[00147] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface defined by a polynomial equation;
wherein the
polynomial equation has a LVL ratio ranging from about 0.32 to 0.67; wherein
the first tapered
outer surface comprises one or more facets in cross section; wherein the
number of facets
ranges from about 12 to 16; wherein the faceted surfaces are wider near the
front of the
expansion device and become narrower toward the rear end of the expansion
device.
[00148] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface; wherein the first tapered outer
surface comprises an
angle of attack ranging from about 6 to 10 degrees.
27
a .. . _. . _- .__
CA 02584492 2009-03-24
[00149] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface; wherein the first tapered outer
surface comprises an
angle of attack ranging from about 6 to 10 degrees; a second tapered outer
surface comprising
a second angle of attack coupled to the first tapered outer surface; and
wherein the first angle of
attack is greater than the second angle of attack.
[00150] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface; wherein the first tapered outer
surface comprises an
angle of attack ranging from about 6 to 10 degrees; a second tapered outer
surface comprising
a second angle of attack coupled to the first tapered outer surface; wherein
the first angle of
attack is greater than the second angle of attack; wherein the first angle of
attack ranges from
about 6 to 20 degrees; and wherein the second angle of attack ranges from
about 4 to 15
degrees.
[00151] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface; wherein the first tapered outer
surface comprises an
angle of attack ranging from about 6 to 10 degrees; a second tapered outer
surface comprising
a second angle of attack coupled to the first tapered outer surface; wherein
the first angle of
attack is greater than the second angle of attack; and one or more
intermediate tapered outer
surfaces coupled between the first and second tapered outer surfaces.
[00152] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface; wherein the first tapered outer
surface comprises an
angle of attack ranging from about 6 to 10 degrees; a second tapered outer
surface comprising
a second angle of attack coupled to the first tapered outer surface; wherein
the first angle of
attack is greater than the second angle of attack; and one or more
intermediate tapered outer
surfaces coupled between the first and second tapered outer surfaces; wherein
the angle of
attack of the intermediate tapered outer surfaces continually decreases from
the first tapered
outer surface to the second tapered outer surface.
28
i -~..~..~..,....~N..T.~____,~,..._.W~.. _-....___.. ... _
CA 02584492 2009-03-24
[00153] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface; wherein the first tapered outer
surface comprises an
angle of attack ranging from about 6 to 10 degrees; a second tapered outer
surface comprising
a second angle of attack coupled to the first tapered outer surface; wherein
the first angle of
attack is greater than the second angle of attack; and one or more
intermediate tapered outer
surfaces coupled between the first and second tapered outer surfaces; wherein
the angle of
attack of the intermediate tapered outer surfaces decreases in steps from the
first tapered outer
surface to the second tapered outer surface.
[00154] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface; wherein the first tapered outer
surface comprises an
angle of attack ranging from about 6 to 10 degrees; wherein the first tapered
outer surface
comprises one or more facets in cross section.
[00155] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface; wherein the first tapered outer
surface comprises an
angle of attack ranging from about 6 to 10 degrees; wherein the first tapered
outer surface
comprises one or more facets in cross section; wherein the number of facets
ranges from about
12 to 16.
[00156] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface; wherein the first tapered outer
surface comprises an
angle of attack ranging from about 6 to 10 degrees; wherein the first tapered
outer surface
comprises one or more facets in cross section; wherein the faceted surfaces
are wider near the
front of the expansion device and become narrower toward the rear end of the
expansion
device.
[00157] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
29
.... . .,
CA 02584492 2009-03-24
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface; wherein the first tapered outer
surface comprises an
angle of attack ranging from about 6 to 10 degrees; a second tapered outer
surface comprising
a second angle of attack coupled to the first tapered outer surface; and
wherein the first angle of
attack is greater than the second angle of attack; wherein the first tapered
outer surface and the
second tapered outer surface comprise one or more facets in cross section.
[00158] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface; wherein the first tapered outer
surface comprises an
angle of attack ranging from about 6 to 10 degrees; a second tapered outer
surface comprising
a second angle of attack coupled to the first tapered outer surface; and
wherein the first angle of
attack is greater than the second angle of attack; wherein the first tapered
outer surface and the
second tapered outer surface comprise one or more facets in cross section;
wherein the number
of facets ranges from about 12 to 16.
[00159] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubuiar member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface; wherein the first tapered outer
surface comprises an
angle of attack ranging from about 6 to 10 degrees; a second tapered outer
surface comprising
a second angle of attack coupled to the first tapered outer surface; and
wherein the first angle of
attack is greater than the second angle of attack; wherein the first tapered
outer surface and the
second tapered outer surface comprise one or more facets in cross section;
wherein the faceted
surfaces are wider near the front of the expansion device and become narrower
toward the rear
end of the expansion device.
[00160] A method of radially expanding a tubular member has been described
that
includes radially expanding at least a portion of the tubular member by
extruding at least a
portion of the tubular member off of an expansion device; wherein the
expansion device
comprises a first tapered outer surface defined by a polynomial equation;
wherein the
polynomial equation has a LWL ratio ranging from about 0.32 to 0.67; wherein
the length of the
tapered outer surface ranges from about 1.6 inches to 1.9 inches; wherein the
tapered outer
surface comprises one or more facets in cross section; wherein the number of
facets ranges
from about 12 to 16; wherein the faceted surfaces are wider near the front of
the expansion
device and become narrower toward the rear end of the expansion device.
CA 02584492 2009-03-24
[00161] The teaching of the present disclosure may be applied to the
construction
and/or repair of wellbore casings, pipelines, and/or structural supports.
[00162] Although illustrative embodiments of the invention have been shown and
described, a wide range of modification, changes and substitution is
contemplated in the
foregoing disclosure. In some instances, some features of the present
invention may be
employed without a corresponding use of the other features, and some steps of
the present
invention may be executed without a corresponding execution of other steps.
Accordingly, all
such modifications, changes and substitutions are intended to be included
within the scope of
this invention as defined in the following claims, and it is appropriate that
the claims be
construed broadly and in a manner consistent with the scope of the invention.
In the claims,
means-plus-function clauses are intended to cover the structures described
herein as
performing the recited function and not only structural equivalents, but also
equivalent
structures.
31
