U.S. patent application number 15/447629 was filed with the patent office on 2018-09-06 for gradually tapered coiled tubing in extended reach wellbores.
The applicant listed for this patent is SCHLUMBERGER TECHNOLOGY CORPORATION. Invention is credited to Jahir Pabon, Tianxiang Su.
Application Number | 20180252056 15/447629 |
Document ID | / |
Family ID | 63357241 |
Filed Date | 2018-09-06 |
United States Patent
Application |
20180252056 |
Kind Code |
A1 |
Pabon; Jahir ; et
al. |
September 6, 2018 |
GRADUALLY TAPERED COILED TUBING IN EXTENDED REACH WELLBORES
Abstract
Maximum penetration of coiled tubing in extended reach
horizontal wellbores is significantly increased by using a
continuously tapered portion of coiled tubing. In particular, the
tubing wall thickness is continuously tapered such that the well
thickness gradually decreases toward the far end of the coiled
tubing. The exterior dimension remains constant while the internal
diameter gradually increases. The non-linear thickness profile of
the tubing is optimized for extended reach in horizontal wellbores.
In some cases, the thickness profile is optimized for providing a
uniform axial strain on the tubing in the horizontal section of the
well.
Inventors: |
Pabon; Jahir; (Newton,
MA) ; Su; Tianxiang; (Somerville, MA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
SCHLUMBERGER TECHNOLOGY CORPORATION |
Sugar Land |
TX |
US |
|
|
Family ID: |
63357241 |
Appl. No.: |
15/447629 |
Filed: |
March 2, 2017 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
E21B 17/20 20130101;
E21B 19/22 20130101 |
International
Class: |
E21B 17/20 20060101
E21B017/20; E21B 19/22 20060101 E21B019/22 |
Claims
1. A coiled tubing configured for extended reach in a horizontal
portion of a well, the tubing comprising a tapered portion having a
near end and a far end, and configured for deployment from a
surface location into the horizontal portion of the well such that
the far end is further from the surface location, the tapered
portion having a tubing wall thickness that continuously and
non-linearly decreases from the near end to the far end, thereby
facilitating further reach into the horizontal portion of the well
by the far end without buckling of the tubing when compared to
non-tapered tubing, discontinuously tapered tubing and linearly
tapered tubing.
2. The coiled tubing according to claim 1, wherein the tubing wall
thickness of the tapered portion decreases at an exponential rate
from the near end to the far end.
3. The coiled tubing according to claim 1, wherein the tubing wall
thickness of the tapered portion has a thickness profile that is
optimized for reach.
4. The coiled tubing according to claim 1 wherein the tubing wall
thickness of the tapered portion has a thickness profile that is
optimized for uniform axial strain along the tapered portion.
5. The coiled tubing according to claim 1, wherein the far end of
the tapered portion is fitted to a bottom hole assembly.
6. The coiled tubing according to claim 1, further comprising a
non-tapered portion joined to the near end.
7. The coiled tubing according to claim 1, wherein the tapered
portion is free of welds that join tubing having different wall
thicknesses at a location of a joint.
8. A method of deploying coiled tubing into a horizontal portion of
a wellbore from a surface location comprising: lowering a tapered
portion of the coiled tubing into the wellbore from the surface
location, the tapered portion having near end and a far end, the
far end being lowered into the wellbore first, the tapered portion
having a tubing wall thickness that continuously and non-linearly
decreases from the near end to the far end; and pushing the tapered
portion into the horizontal portion of the wellbore such that the
far end reaches further into the horizontal portion without
buckling of the tubing when compared to non-tapered tubing,
discontinuously tapered tubing and linearly tapered tubing.
9. The method according to claim 8, wherein the tubing wall
thickness of the tapered portion decreases at an exponential rate
from the near end to the far end.
10. The method according to claim 8, wherein the wall thickness of
the tapered portion has a thickness profile that is optimized for
reach.
11. The method according to claim 8, wherein the wall thickness of
the tapered portion has a thickness profile that is optimized for
uniform axial strain along the tapered portion.
12. The method according to claim 8, wherein the wellbore includes
a vertical portion above the horizontal portion, and said pushing
is performed at least in part by lowering a non-tapered portion of
the coiled tubing into the vertical portion, the non-tapered
portion being joined to the near end of the tapered portion.
13. The method according to claim 8, wherein the horizontal portion
traverses a hydrocarbon bearing subterranean rock formation and the
method further comprises performing an intervention operation on
the wellbore at the location of the far end using said coiled
tubing.
Description
FIELD
[0001] The subject disclosure generally relates to the field of
coiled tubing in wellbores. More particularly, the subject
disclosure relates to techniques for deploying coiled tubing in
extended reach wellbores.
BACKGROUND
[0002] Coiled tubing has been used in many extended reach wells.
Due to its inherent characteristics, coiled tubing has rather
limited extended reach capability. Many wells that can be
successfully drilled by the drillers cannot be properly serviced by
conventional coiled tubing deployment techniques. Buckling and
lockup are problems for coiled tubing operations in horizontal
wells. The problems originate from the friction exerted by the
wellbore/casing on the coiled tubing during run-in-hole (RIH)
operations. The friction compresses the tubing, causing axial
strain to develop along its length. When enough tubing is injected
and the compressive strain reaches a critical level, the tubing
will buckle, undergo large deformation, and eventually lockup
inside the wellbore. When lockup happens, most of the pushing force
applied on the surface will not be transmitted to the downhole end,
and consequently the coiled tubing cannot be pushed further into
the hole.
[0003] Known techniques for extending the reach of coiled tubing
include pumping friction reducer into the tubing-wellbore/casing
annulus, using agitator and/or tractor to shake/pull the tubing at
the bottom end. Tapered coiled tubing has been designed, but it is
mainly used for reducing the hanging weight of tubing in vertical
wells. When tapered tubing is used for extended reach purpose,
people optimize the length of different sections of the tubing with
different diameters.
[0004] I. McCourt and J Kubie, "Limits on the penetration of coiled
tubing in horizontal oil wells: effect of the pipe geometry," Proc.
IMechE Vol. 219 Part C: J. Mechanical Engineering Science, pp
1191-1197 (2005) (hereinafter "McCourt et al.") discusses
increasing the penetration of coiled tubing in horizontal oil wells
using coiled tubing made by welding together several non-tapered
tubing sections. Each successive tubing section has a uniform, but
decreased wall thickness. The tubing is thus made up of several
"steps" where non-tapered tubing sections having different wall
thickness are welded together. This discontinuous tapering profile
is shown to have some increased penetration properties over
non-tapered coiled tubing.
[0005] K. Stanley et al, "Continuously Taped Coiled Tubing," Soc.
of Petroleum Engineers inc. Paper No. 68881 (2001) (hereinafter
"Stanley et al.") discusses designing and manufacturing coiled
tubing having a continuously linear profile over part of the tubing
length. That is, the tapered section of the tubing changes
thickness in a linear fashion.
SUMMARY
[0006] This summary is provided to introduce a selection of
concepts that are further described below in the detailed
description. This summary is not intended to identify key or
essential features of the claimed subject matter, nor is it
intended to be used as an aid in limiting the scope of the claimed
subject matter.
[0007] According to some embodiments, coiled tubing is configured
for extended reach in a horizontal portion of a well. The tubing
includes a tapered portion with a tubing wall thickness that
continuously and non-linearly decreases from the near end to the
far end of the tapered portion. The tapered portion of tubing
facilitates further reach into the horizontal portion of the well
without buckling of the tubing when compared to non-tapered tubing,
discontinuously tapered tubing and linearly tapered tubing.
[0008] According to some embodiments, the tubing wall thickness of
the tapered portion decreases at an exponential rate from the near
end to the far end. The thickness profile can be optimized for
reach, or in some cases for uniform axial strain. According to some
embodiments, the tapered portion is free of welds that join tubing
having different wall thicknesses at the location of the joint.
[0009] According to some embodiments, a method is described for
deploying coiled tubing into a horizontal portion of a wellbore.
The method includes lowering a tapered portion of the coiled tubing
into the wellbore from a surface location. The tapered portion of
the tubing has a tubing wall thickness that continuously and
non-linearly decreases from the near end to the far end. The method
also includes pushing the tapered portion of the tubing into the
horizontal portion of the wellbore, such that the far end reaches
further into the horizontal portion without buckling of the tubing
when compared to non-tapered tubing, discontinuously tapered tubing
and linearly tapered tubing.
[0010] As used herein the term "coiled tubing" refers to a type of
tubing that is typically supplied spooled on a large reel on the
surface. The term "coiled tubing" does not mean that the tubing is
in a coiled form when deployed in a wellbore.
[0011] Further features and advantages of the subject disclosure
will become more readily apparent from the following detailed
description when taken in conjunction with the accompanying
drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0012] The subject disclosure is further described in the detailed
description which follows, in reference to the noted plurality of
drawings by way of non-limiting examples of the subject disclosure,
in which like reference numerals represent similar parts throughout
the several views of the drawings, and wherein:
[0013] FIG. 1 is a diagram of continuously tapered coiled tubing
being deployed in an extended reach portion of a wellbore,
according to some embodiments;
[0014] FIG. 2 is a plot of tubing thickness profiles for coiled
tubing optimized for extended reach in horizontal wells, according
to some embodiments;
[0015] FIG. 3 is a plot of tubing thickness profiles for coiled
tubing optimized for uniform axial stress in horizontal wells,
according to some embodiments;
[0016] FIGS. 4A and 4B are diagrams showing results of two dynamic
simulations in which non-tapered tubing and tubing tapered to
optimize reach, according to some embodiments, are injected into a
horizontal channel;
[0017] FIG. 5 is a graph plotting simulated axial displacement
(movement) of the downhole end of the non-tapered and the tubing
tapered according to some embodiments;
[0018] FIGS. 6A and 6B are diagrams showing results of two further
dynamic simulations in which non-tapered tubing and tubing tapered
to optimize reach, according to some embodiments, are injected into
a horizontal channel;
[0019] FIG. 7 is a graph plotting axial displacement (movement) of
the downhole end of the non-tapered and the tapered tubing with
3000 meters of tubing placed initially in the well; and
[0020] FIG. 8 is a plot comparing a linearly tapered tubing profile
with an optimally tapered tubing profile, according to some
embodiments.
DETAILED DESCRIPTION
[0021] The particulars shown herein are by way of example and for
purposes of illustrative discussion of the examples of the subject
disclosure only, and are presented in the cause of providing what
is believed to be the most useful and readily understood
description of the principles and conceptual aspects of the subject
disclosure. In this regard, no attempt is made to show structural
details in more detail than is necessary, the description taken
with the drawings making apparent to those skilled in the art how
the several forms of the subject disclosure may be embodied in
practice. Furthermore, like reference numbers and designations in
the various drawings indicate like elements. As used herein, the
terms and phrases "deviated section or portion of the well",
"deviated section or portion", "horizontal section or portion of
the well", and "horizontal section or portion" are used
interchangeably to indicate the section of the well that departs
from the vertical wellbore.
[0022] As mentioned, buckling and lockup are problems for coiled
tubing operations in horizontal wells. Friction exerted by the
wellbore/casing on the coiled tubing during run-in-hole (RIH)
operations compresses the tubing, causing axial strain to develop
along its length. It has been found that typically the compressive
strain is small near the downhole end, but it increases gradually
towards the surface end. When enough tubing is injected and the
compressive strain reaches a critical level, the tubing will
buckle, undergo large deformation, and eventually lockup inside the
wellbore. When lockup happens, most of the pushing force applied on
the surface will not be transmitted to the downhole end, and
consequently the coiled tubing cannot be pushed further into the
hole. According to some embodiments, techniques are described that
(1) reduce the friction, and (2) increase the tubing's capability
to resist buckling. According to some embodiments, uniform axial
strain along the tubing can be achieved. According to some
embodiments, the tubing thickness profile along its length is
maximized to achieve maximum reach in a horizontal wellbore.
According to some embodiments, tubing thickness is optimized to
keep its deformation in the reversible elastic, instead of the
irreversible plastic, regime.
[0023] FIG. 1 is a diagram of continuously tapered coiled tubing
being deployed in an extended reach portion of a wellbore,
according to some embodiments. Wellbore 130 is shown penetrating
the earth from wellsite 120 at the surface through earth 100 and
into subterranean rock formation 110. The wellbore 130 includes an
extended horizontal portion 132 within formation 110, which
according to some embodiments is a hydrocarbon-bearing rock
formation. Coiled tubing 140 is being used to perform an
intervention on the well. In this case the intervention is
performed in the horizontal portion 132 of wellbore 130 at
locations that include the far end of the horizontal section, near
the well bottom 134, using bottom hole assembly (BHA) 152 that is
attached to the far end of coiled tubing 140. According to some
embodiments, a tapered portion of coiled tubing 150 is used within
the horizontal portion 132 of wellbore 130. The tapered portion 150
has a continuously tapered tubing wall profile such that the tubing
wall becomes gradually thinner and thinner near the far end (where
the BHA is located). In FIG. 1, the horizontal reach distance d is
shown.
[0024] According to some embodiments, the tapered portion 150 of
coiled tubing 140 is designed having a thickness profile along its
length that maximizes the reach of the tubing in horizontal
wellbores. Reducing the thickness of the tubing while keeping its
outer diameter fixed can reduce the tubing weight (per unit length)
and therefore reduce dry friction. At the same time, however, the
tubing's capability to resist buckling is compromised with small
wall thickness. Therefore, to achieve maximum reach, the tubing
thickness should be reduced to a level such that the tubing can
still resist buckling everywhere along its length: F(x)=F.sub.cr.
Here, F(x) is the internal compressive load along the tubing, which
has been parameterized by the arc length x, with x=0 denoting the
downhole end and x increases towards the surface end. Also, in the
above equation, the critical buckling force F.sub.cr is given by
F.sub.cr=2 {square root over (EI.rho.gA/r)}, where E, I, .rho., A,
g, r are respectively the Young's modulus, second area moment of
inertia, volumetric density, cross section area of the tubing,
gravity constant and clearance between the tubing and the
wellbore/casing. Moreover, noticing that the compression load F(x)
should balance the friction along the tubing, i.e.,
F(x)=.intg..sub.0.sup.x .mu..rho.gA(s)ds in a quasi-static
equilibrium situation, we obtain the following integral
equation:
2 EI ( x ) .rho. gA ( x ) r = .intg. 0 x .mu. .rho. gA ( s ) ds ( 1
) ##EQU00001##
[0025] If tubing thickness t is much smaller than the outer radius
r.sub.0, we can Taylor expand the above equation, keeping only the
terms that is on the linear order of tubing thickness, and obtain
the following solution for tubing thickness profile:
t ( x ) = t 0 exp ( x - x 0 .lamda. 1 ) ( 2 ) ##EQU00002##
[0026] In the above equation, t.sub.0 is the thickness of the
tubing at a reference location x=x.sub.0. The solution suggests
that, for a thin wall tubing (t<<r.sub.0), the optimal
thickness increases from the downhole end towards the surface end
in an exponential manner, with a characteristic length constant
.lamda..sub.1 given by .lamda..sub.1= {square root over
(2Er.sub.0.sup.2/.mu..sup.2.rho.g.DELTA.r)}. Plugging in the
typical values for coiled tubing operations, this length scale is
about 15,000 feet.
[0027] The above equation for optimal thickness profile holds under
the assumption that the tubing wall is thin. When the thickness
increases to a level that is not negligible with respect to the
tubing outer radius, this equation will be invalid. The exact
solution to Eq.(1), without assuming small thickness, is:
x - x 0 .lamda. 1 / 2 = 3 t _ 2 ? 2 t _ + 2 2 2 a tanh ( t _ 2 - 2
t _ + 2 2 ) 3 t _ 0 2 ? 2 t _ 0 + 2 + 2 2 a tanh ( t _ 0 2 - 2 t _
0 + 2 2 ) ? indicates text missing or illegible when filed ( 3 )
##EQU00003##
Here t=t/r.sub.0 is the dimensionless tubing thickness.
[0028] FIG. 2 is a plot of tubing thickness profiles for coiled
tubing optimized for extended reach in horizontal wells, according
to some embodiments. In particular, the two curves show thickness
profiles that have been optimized for extended reach. Curve 210 is
a sample approximation valid for small thicknesses (using Eq. 2),
while curve 212 is an exact solution for the optimized thickness
profile (using Eq. 3). On the vertical axis, thickness t is
normalized by the outer radius of the tubing r.sub.0. When this
normalized thickness value is 1, the tubing is solid. On the
horizontal axis, the tubing length x is normalized by the length
scale .lamda..sub.1=2Er.sub.0.sup.2/.mu..sup.2.rho.g.DELTA.r. The
typical value of this length scale is about 15,000 feet. As can be
seen, the approximate solution matches well with the exact solution
when the wall thickness is small.
[0029] In the discussion supra, the optimization of tubing
thickness was calculated for extended reach purposes. According to
to some embodiments, the tubing thickness can be optimized such
that the entire tubing is under a uniform axial stress. For
example, for a uniform stress .sigma..sub.y we can solve:
.sigma..sub.y A(x)=.intg..sub.0.sup.x .mu..rho.gA(s)ds (4)
The exact solution is an exponential relation:
2 t _ - t _ 2 2 t _ 0 - t _ 0 2 = exp ( x - x 0 .lamda. 2 ) ( 5 )
##EQU00004##
where .lamda..sub.2=.sigma..sub.y/.mu..rho.g is the characteristic
length scale. The typical value for .lamda..sub.2 is about 52,000
feet. For thin wall tubing with t<<r0, the above full
solution simplifies to:
t = t 0 = exp ( x - x 0 .lamda. 2 ) ( 6 ) ##EQU00005##
[0030] FIG. 3 is a plot of tubing thickness profiles for coiled
tubing optimized for uniform axial stress in horizontal wells,
according to some embodiments. Curve 310 is the exact solution
(using Eq. 5), while the curve 312 is the approximate solution for
thin wall tubing (using Eq. 6). On the vertical axis, thickness t
is normalized by the outer radius of the tubing r.sub.0. On the
horizontal axis, the tubing length x is normalized by the length
scale .lamda..sub.2=.sigma..sub.y/.mu..rho.g. The typical value of
this length scale is about 52,000 feet. As expected, the
approximate solution matches well with the exact solution when the
wall thickness is small.
[0031] According to some embodiments, thickness profiles are
calculated based on both extended reach and also on uniform stress
purposes using the yielding stress. The profile that calls for a
thicker wall can be selected. In general, the solution calling for
the thicker tubing wall will be the one optimizing the reach
because .lamda..sub.1<.lamda..sub.2 (the wall thickness
increases faster from the downhole end to surface end for the
extended reach profile).
[0032] Four dynamic simulations were performed to test if tapered
tubing has better buckling resistance than non-tapered tubing. In
these simulations, we inject coiled tubing into a horizontal
wellbore and solve Newton's motion law to obtain the configurations
of the tubing as a function of time. In particular, the tubing is
modeled as Kirchhoff rod with linear elasticity properties and the
channel is modeled as a frictional viscoelastic contact.
[0033] FIGS. 4A and 4B are diagrams showing results of two dynamic
simulations in which non-tapered tubing and tubing tapered to
optimize reach, according to some embodiments, are injected into a
horizontal channel. In the first simulation, we put coiled tubing
of uniform thickness (i.e. non-tapered) into the wellbore of inner
diameter 6.125 inches. The outer and inner diameter of the tubing
are respectively 2.375 and 1.995 inches. Therefore, thickness of
the tubing is uniformly t=0.19 inches (16% of the outer radius) and
clearance between the tubing and the wellbore is r=1.875 inches.
Young's modulus and density of the tubing are set as E=207 GPa and
.rho.=7900 kg/m.sup.3, respectively. Moreover, the friction
coefficient between the tubing and the wellbore is set as
.mu.=0.25. Using these parameters, we can estimate the length of
the tubing that can be injected into a horizontal wellbore before
the first sinusoidal buckling wave forms is L.sub.sin=2 {square
root over (EI/(.rho.gA.DELTA.r))}/.mu.=1180 m=3871 feet. Also, the
length of the tubing that can be injected before first buckled
helix forms is L.sub.hei=2 {square root over
(2EI/(.rho.gA.DELTA.r))}/.mu.=1669 m=5476 feet. In this simulation,
we initially (time=0 sec) put a length of 1800 m tubing inside the
wellbore and then begin to push and inject more tubing at time>0
sec. To minimize the transient effect, we perform injection by
controlling the force at the injection end to target an injection
speed of v.sub.target=40 feet/min. In particular, for the first 5
seconds, we linearly ramp up the pushing force from zero to exactly
balance the friction force correspondingly to 1800 m tubing. After
5 seconds (time>5 sec), the pushing force is set as:
F = mg { 1 + 1 2 ( 1 ? v v target ) [ 1 ? exp ( ? time ? 5 10 ) ] }
##EQU00006## ? indicates text missing or illegible when filed
##EQU00006.2##
Here mg is the weight of the tubing currently inside the wellbore
(it is increasing as more and more tubing is injected), v is the
current tubing velocity at the injection end in the wellbore axial
direction. The exponential function is set to avoid a sudden jump
in the pushing force at time=5 seconds. As expected (since
L.sub.hei<1800 m), in this simulation, the coiled tubing buckles
into helices. FIG. 4A illustrates the first 200 m of the un-tapered
tubing near the injection end where buckling occurs.
[0034] In a second simulation, we keep all parameters the same as
the one discussed above, except the thickness profile of the tubing
is set to be non-uniform. In particular, for a section of tubing
L=519 m near the downhole end, we design a uniform tubing thickness
of 0.06 inches (inner tubing diameter ID=2.2563 inch, outer
diameter OD=2.375 inch). We expect this length of the tubing near
the downhole end is short enough to withstand friction without
buckling during injection. Behind this section towards the surface
end, the thickness of the tubing gradually increases accordingly to
Equation (3), from 5% of the tubing outer radius to 16%. In this
simulation, we again initially put 1800 m of the tubing inside the
wellbore and then apply a linear ramp-up pushing force to target an
injection speed of V.sub.target=40 feet/min. Not like the first
simulation, in this case, the tubing remains straight and does not
buckle. FIG. 4B shows the 200 m of the tapered tubing near the
injection end. The simulation results demonstrate that tapered
tubing has a better resistance to buckling and can be injected
further without lockup.
[0035] FIG. 5 is a graph plotting simulated axial displacement
(movement) of the downhole end of the non-tapered and the tubing
tapered, according to some embodiments. Curve 510 shows the
movement of the downhole end of the uniform thickness tubing as a
function of time. Curve 512 shows the movement of the end of a
tapered tubing. As can be seen under the same pushing condition,
the uniform tubing moves slower than the non-uniform one due to
buckling. Note that in these first two simulations, the downhole
ends of both tubing's are moving at all times.
[0036] In the third and fourth simulations, we put tubing with
longer initial length inside the wellbore. In particular, the
initial length of the tubing inside the wellbore is 3000 m instead
of 1800 m. These two simulations again compare a tubing with
uniform thickness with a tubing tapered to optimize reach. The
thickness of the uniform tubing is the same as in the first
simulation, while the thickness of the tapered tubing gradually
increases from the downhole end accordingly to Equation (3), from
1% of the tubing outer radius to 16%. All other parameters are the
same as the first two simulations. FIGS. 6A and 6B are diagrams
showing results of third and fourth simulations. FIG. 6A shows
simulation results of a non-tapered coiled tubing injected into a
horizontal channel at a constant velocity of 40 feet/min with 3000
meters of tubing initially in the channel. As can be seen, the
tubing buckles into helices. FIG. 6B shows simulation results of a
tubing with the optimized thickness profile (using Eq. 3) injected
in the channel. The tapered tubing can be injected much further
than the first case without buckling. FIG. 7 is a graph plotting
axial displacement (movement) of the downhole end of the
non-tapered and the tubing tapered according to some embodiments in
the third and fourth simulations (i.e. with 3000 meters of tubing
placed initially). Curve 710 shows the movement of the downhole end
of a uniform thickness tubing as a function of time. Curve 712
shows the movement of the end of a tapered tubing. The two tubing's
are under the same pushing condition. As can be seen, the tapered
tubing moves into the wellbore, while the uniform thickness tubing
locks up and cannot be pushed forward. The simulation results
demonstrate that tapered tubing has a better resistance to buckling
and can be injected further without lockup.
[0037] Note that in the discussion and simulations, supra,
optimized tubing profiles have been compared to non-tapered tubing.
In the following discussion, optimized tubing profiles are compared
to linearly tapered tubing.
[0038] We estimate the reach of a linearly tapered tubing, whose
outer radius is r.sub.0 and inner radius increases from r.sub.i1 to
r.sub.i2 linearly. We equate the critical buckling load with the
friction-induced tubing compressive load:
2 EI .rho. gA r = .intg. 0 s .mu. .rho. gAds + F 0 .
##EQU00007##
Here F.sub.0 is the applied load at the downhole end of the tubing.
For example, due to a BHA attached to the bottom end of the tubing.
The above equation leads to the estimation of reach of the tubing
as:
L = 1 .mu. ( r o 2 ? r i 2 2 ) ( r o 2 + r i 2 2 ) E .rho. g r r o
2 ? ( r i 2 3 ? r i 1 3 ) 3 ( r i 2 ? r i 1 ) . ? indicates text
missing or illegible when filed ##EQU00008##
[0039] With this formula, we now compare the reach of a linear
tapered tubing and one with optimal thickness profile. For a value
of F.sub.0=6728.8N, the needed thickness of the coiled tubing at
the bottom is 5% of r.sub.0. If we limit the maximum thickness to
16% of r.sub.0 at the upper end of the tubing, then the reach with
the optimal thickness profile (optimized for extended reach, using
eq. e) is 1281 meters. The reach with a linear thickness profile is
1141 meters. For a value of F.sub.0=1401.1 N, the needed thickness
of the coiled tubing at the bottom is 1% of r.sub.0. If we again
limit the maximal thickness to 16% of r.sub.0 at the upper end of
the tubing, then the reach with the optimal thickness profile is
3261.7 meters. The reach with a linear thickness profile in this
case is 2001.8 meters. Note that in these calculations, we have
replaced the portion of constant thickness tube on the downhole end
and with the effective force F.sub.0. In practice the BHA size and
weight will determine the force F.sub.0 for any particular
application. For many applications, such as pumping acid, the BHA
can be quite minimal, and therefore even the smaller of force
F.sub.0 values that were simulated, 1401.1 N would be more than
adequate. As can be seen from the simulation, the lighter the BHA
load, the greater the advantage of exponential, optimally tapered
tubing profile has over a linearly tapered tubing profile. However,
the simulations demonstrate that even for relatively heavy BHAs
(e.g. coiled tubing drilling applications), the optimal tubing
still will have a longer reach than the linear tapered tubing.
[0040] FIG. 8 is a graph comparing a linearly tapered tubing
profile with an optimally tapered tubing profile, according to some
embodiments. The graph plots tubing wall thickness against tubing
length. The wellbore inner diameter was 6.125 inch. In both cases
the tubing outer diameter was 2.375 inch (outer radius is 1.1875
inch), the maximum tubing thickness was 16% of outer radium and the
minimum tubing thickness was 1% of outer thickness. The Young's
modulus was 207 GPa and density 7900 kg/m.sup.3, which reflect
values for steel tubing. As can be seen, the reach-optimized tubing
profile shown in curve 812 has a distinctive exponential shape
compared to the linear tubing profile shown in curve 810. As was
calculated in the simulations, discussed supra, the exponentially
shaped, reach-optimized tubing profile is capable of much further
horizontal reach without buckling than the linear profile
tubing.
[0041] The non-linear continuously tapered tubing profile
techniques as described herein according to many embodiments also
have advantages over a step-wise discontinuous taper profiles such
as discussed in McCourt et al. For example, the continuously
tapered tubing profile does not rely on welding together mismatched
thicknesses. The continuously tapered profile can potentially be
made with much fewer numbers of welds than the step-wise profile,
since each "step" relies on an additional weld. Furthermore, an
optimized continuously tapered portion of coiled tubing can offer
better performance than a step-wise profile due to being closer to
optimal thickness profile. Note that although the continuously
tapered tubing profile, according to some embodiments, does not
rely on welding together mismatched thicknesses, there may be times
when it is useful to nevertheless weld sections of the tapered
tubing together. In such cases, however, the thickness vs. length
relationship over the entire tapered portion should still be
satisfied and as a consequence the ends of tubing being welded will
have the same cross-section (rather than being of mismatched
thicknesses).
[0042] Although only a few examples have been described in detail
above, those skilled in the art will readily appreciate that many
modifications are possible in the examples without materially
departing from this subject disclosure. Accordingly, all such
modifications are intended to be included within the scope of this
disclosure as defined in the following claims. 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. Thus,
although a nail and a screw may not be structural equivalents in
that a nail employs a cylindrical surface to secure wooden parts
together, whereas a screw employs a helical surface, in the
environment of fastening wooden parts, a nail and a screw may be
equivalent structures. It is the express intention of the applicant
not to invoke 35 U.S.C. .sctn. 112, paragraph 6 for any limitations
of any of the claims herein, except for those in which the claim
expressly uses the words `means for` together with an associated
function.
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