U.S. patent application number 11/759127 was filed with the patent office on 2007-12-20 for method of fracturing an earth formation, earth formation borehole system, method of producing a mineral hydrocarbon substance.
Invention is credited to Frederick Henry Kreisler RAMBOW.
Application Number | 20070289741 11/759127 |
Document ID | / |
Family ID | 39705343 |
Filed Date | 2007-12-20 |
United States Patent
Application |
20070289741 |
Kind Code |
A1 |
RAMBOW; Frederick Henry
Kreisler |
December 20, 2007 |
Method of Fracturing an Earth Formation, Earth Formation Borehole
System, Method of Producing a Mineral Hydrocarbon Substance
Abstract
Method of fracturing an earth formation by pumping a pressurized
fracturing fluid into a borehole in an earth formation thereby
fracturing the earth formation. At least during the pumping, a
strain distribution is monitored in an object that is located in
the earth formation and that is mechanically interacting with the
earth formation. The borehole system has a plurality of strain
sensors for monitoring the strain distribution in the object during
fracturing. After terminating the pumping of the pressurized
fracturing fluid, mineral hydrocarbon fluids may be allowed to flow
from the reservoir into the wellbore or another wellbore, and
produced via that wellbore.
Inventors: |
RAMBOW; Frederick Henry
Kreisler; (Houston, TX) |
Correspondence
Address: |
SHELL OIL COMPANY
P O BOX 2463
HOUSTON
TX
772522463
US
|
Family ID: |
39705343 |
Appl. No.: |
11/759127 |
Filed: |
June 6, 2007 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11107270 |
Apr 15, 2005 |
7245791 |
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11759127 |
Jun 6, 2007 |
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PCT/US06/13823 |
Apr 13, 2006 |
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11759127 |
Jun 6, 2007 |
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11107270 |
Apr 15, 2005 |
7245791 |
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PCT/US06/13823 |
Apr 13, 2006 |
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60939467 |
May 22, 2007 |
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Current U.S.
Class: |
166/250.01 ;
166/308.1; 166/369 |
Current CPC
Class: |
E21B 47/01 20130101;
E21B 47/007 20200501 |
Class at
Publication: |
166/250.01 ;
166/308.1; 166/369 |
International
Class: |
E21B 47/00 20060101
E21B047/00; E21B 43/00 20060101 E21B043/00; E21B 43/26 20060101
E21B043/26 |
Claims
1. A method of fracturing an earth formation, comprising: pumping a
pressurized fracturing fluid into a borehole in an earth formation
thereby fracturing the earth formation; and at least during the
pumping, monitoring a strain distribution in an object located in
the earth formation and mechanically interacting with the earth
formation.
2. The method of claim 1, wherein the object is located in the
borehole and is mechanically interacting with the earth formation
via the borehole wall.
3. The method of claim 1, wherein the object is located in an
offset borehole and is mechanically interacting with the earth
formation via the borehole wall of the offset borehole.
4. The method of claim 1, wherein the strain distribution is
analyzed to determine a deformation parameter of the object.
5. The method of claim 4, wherein the deformation parameter is one
of axial strain, bending curvature, and ovalization parameter.
6. The method of claim 1, further comprising controlling the
pumping of the pressurized fracturing fluid in response to the
monitoring.
7. A borehole system in an earth formation, the borehole system
comprising: a borehole reaching into an earth formation; a
fracturing fluid pump comprising a low-pressure input opening and a
high-pressure output opening, the high-pressure output opening
being in fluid communication with the wellbore; a fracturing fluid
supply in fluid communication with the low-pressure input opening;
an object located in the earth formation mechanically interacting
with the earth formation; and a plurality of strain sensors applied
to the object for monitoring a strain distribution in the
object.
8. The borehole system of claim 7, wherein the object is located in
the borehole and is mechanically interacting with the earth
formation via the borehole wall.
9. The borehole system of claim 7, further comprising an offset
borehole reaching into the earth formation at a location different
from the location of the borehole, wherein the object is located in
the offset borehole and is mechanically interacting with the earth
formation via the borehole wall of the offset borehole.
10. A method of producing a mineral hydrocarbon fluid from a
reservoir in an earth formation, comprising pumping a pressurized
fracturing fluid into a wellbore in an earth formation thereby
fracturing the earth formation in or in the vicinity of a mineral
hydrocarbon fluid containing reservoir; at least during the
pumping, monitoring a strain distribution in an object that is
located in the earth formation and that is mechanically interacting
with the earth formation; controlling the pumping of the
pressurized fracturing fluid in response to the monitoring;
terminating the pumping of the pressurized fracturing fluid, and
releasing the pressure; allowing mineral hydrocarbon fluid to flow
from the reservoir into the wellbore; and producing the mineral
hydrocarbon fluid via the wellbore or via another wellbore that
penetrates into the mineral hydrocarbon fluid containing
reservoir.
11. The method of claim 10, wherein the object is located in the
wellbore and is mechanically interacting with the earth formation
via the wellbore wall.
12. The method of claim 10, wherein the object is located in an
offset borehole and is mechanically interacting with the earth
formation via the borehole wall of the offset borehole.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This is a continuation-in-part of PCT/US2006/013823, filed
13 Apr. 2006, which is a continuation-in-part of U.S. Ser. No.
11/107,270, filed 15 Apr. 2005. The present application is also a
continuation-in-part of U.S. Ser. No. 11/107,270, filed 15 Apr.
2005. In addition, the present application also claims priority
benefits of U.S. provisional application 60/939,467, filed 22 May
2007, the content of which is incorporated herein by reference.
FIELD OF THE INVENTION
[0002] In one aspect, the present invention relates to a method of
fracturing an earth formation.
[0003] In another aspect, the present invention relates to an earth
formation borehole system.
[0004] In still another aspect, the present invention relates to a
method of producing a mineral hydrocarbon substance.
BACKGROUND OF THE INVENTION
[0005] A stimulation treatment that is routinely performed on oil
and gas wells in low-permeability reservoirs is so-called formation
fracturing. The aim is to stimulate the production of hydrocarbon
substances from the reservoir by opening new flow channels in the
rock surrounding a production well. Typically, a fracturing fluid
is pumped downward through a well bore tubular at relatively high
pressure, and forced out below a packer or between two packers that
seal off the annulus formed between the well bore wall and the well
bore tubular. The pressure is intended to cause fractures in the
form of cracks to open in the formation. The fluid typically
penetrates the formation through these cracks, causing the cracks
to grow.
[0006] The well bore tubular may be a production tubing or drill
pipe or any other suitable tubing or pipe.
[0007] Often, a proppant (typically also referred to as propping
agent) may be carried in the fracturing fluid into the cracks. Such
a proppant typically is a granular substance that is carried in
suspension by the fracturing fluid, that serves to keep the cracks
open when fracturing fluid dissipates or is withdrawn after a
fracturing treatment.
[0008] Fracturing also often occurs around injection wells, during
deep-well injection of liquids. The formation around an injection
well is often fractured due to an imbalance between the injection
pressure and the minimum horizontal rock stress opposing
fracturing. The resulting fractures can grow during injection,
which may span over several months to years. Flow and transport
around an injection well with a vertical fracture exhibits
important differences from radial transport that neglects the
presence of the fracture, and also from transport from a fracture
of constant length. Moreover, operators of injection wells want to
avoid the fractures to grow vertically out of the injection
interval.
[0009] U.S. Pat. No. 7,028,772 discloses a treatment well tilt
meter system, wherein one or more tilt meters are located at
different depths within a treatment well. Interconnection cable
lines interconnect each of the tilt meters, and a main wireline
extends from the tilt meter system to the surface. The tilt meters
are placed such that one or more tilt meters are located above,
below, and/or within an estimated pay zone region, in which a
perforation zone is formed.
[0010] A fracturing pump supply line is connected to the well head
for a fracturing operation. The tilt meter system is used to map
hydraulic fracture growth from collected down hole tilt data versus
time.
[0011] However, tilt meters do not provide a great wealth of
information. They essentially operate on the same principle as a
carpenter's level, in that they resolve tilt based on gravity. In
effect, tilt meters can merely provide feedback on fracture growth
or other subsurface processes in so far as they cause tilting or
bending of the well bore.
SUMMARY OF THE INVENTION
[0012] The present invention provides a method of fracturing an
earth formation, comprising: [0013] pumping a pressurized
fracturing fluid into a borehole in an earth formation thereby
fracturing the earth formation; and [0014] at least during the
pumping, monitoring a strain distribution in an object located in
the earth formation and mechanically interacting with the earth
formation.
[0015] The present invention further provides a borehole system in
an earth formation, the borehole system comprising: [0016] a
borehole reaching into an earth formation; [0017] a fracturing
fluid pump comprising a low-pressure input opening and a
high-pressure output opening, the high-pressure output opening
being in fluid communication with the wellbore; [0018] a fracturing
fluid supply in fluid communication with the low-pressure input
opening; [0019] an object located in the earth formation
mechanically interacting with the earth formation; and [0020] a
plurality of strain sensors applied to the object for monitoring a
strain distribution in the object.
[0021] The present invention still further provides a method of
producing a mineral hydrocarbon fluid from a reservoir in an earth
formation, comprising [0022] pumping a pressurized fracturing fluid
into a wellbore in an earth formation thereby fracturing the earth
formation in or in the vicinity of a mineral hydrocarbon fluid
containing reservoir; [0023] at least during the pumping,
monitoring a strain distribution in an object that is located in
the earth formation and that is mechanically interacting with the
earth formation; [0024] controlling the pumping of the pressurized
fracturing fluid in response to the monitoring; [0025] terminating
the pumping of the pressurized fracturing fluid, and releasing the
pressure; [0026] allowing mineral hydrocarbon fluid to flow from
the reservoir into the wellbore; and [0027] producing the mineral
hydrocarbon fluid via the wellbore or via another wellbore that
penetrates into the mineral hydrocarbon fluid containing
reservoir.
[0028] Monitoring the strain distribution enables detection of
bending as well as other types of deformation of the object. Thus,
fracturing can be monitored in cases where it leads to bending of
the object in the earth formation, as well as in cases where it
does not cause bending of the object in the earth formation.
[0029] The object in the earth formation may suitably be located in
the borehole or in the wellbore itself, and be mechanically
interacting with the borehole wall or the wellbore wall.
[0030] The invention will hereinafter be illustrated by way of
examples and preferred embodiments, with reference to the attached
drawing figures. Objects, features and advantages of the present
invention will be apparent to those skilled in the art from the
following description of the various embodiments and related
drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0031] In the attached drawing figures:
[0032] FIG. 1 shows a schematic cross sectional view of an earth
formation borehole system;
[0033] FIG. 2 shows wavelength response of FBG sensors wrapped
around part of a tube with a wrap angle of 20.degree. and
wavelength response of FBG sensors wrapped around another part of
the same tube with a wrap angle of 60.degree. relative to the axial
direction on the tube;
[0034] FIG. 3A shows a graph of wavelength shift (.DELTA..lamda.)
versus grating number (D.sub.N) measured in a 60.degree.-wrapped
fiber, superimposed on a graph showing derived curvature of a
bending tube;
[0035] FIG. 3B shows a similar graph as FIG. 3A for smaller
curvature;
[0036] FIG. 3C shows a graph of wavelength shift (.DELTA..lamda.)
versus grating number (D.sub.N) measured in a 20.degree.-wrapped
fiber, measured on a tube bent to a similar curvature as in graph
as FIG. 3B.
[0037] FIG. 4 shows a schematic top view of ovalization during a
fracturing operation in a borehole;
[0038] FIG. 5 shows a graph with a calculated combined ovalization
and bending wavelength response;
[0039] FIG. 6 shows the components of ovalization and bending to
the combined signal;
[0040] FIG. 7 is an elevational view of a cylindrical object
illustrating a plurality of sensors or transducers applied to the
object along three different sections (A, B, C) of the object;
[0041] FIG. 7A is a linear perspective of section A in FIG. 7;
[0042] FIG. 8 is a graph of illustrating the determination of
preferred number of strain sensors (N) and preferred number of
wraps needed to cover a predetermined length;
[0043] FIG. 9 is a graph illustrating the relationship between the
strain factor (m) and various wrap angles (.theta.);
[0044] FIG. 9A is a graph illustrating the relationship between
strain factor (m) and wrap angle (.theta.) according to a
predetermined Poisson ratio (.nu.);
[0045] FIG. 10 is a graph illustrating the relationship between
strain (.epsilon.) applied to steel and corresponding Poission's
ratio (.nu.);
[0046] FIG. 11 is a graph illustrating the relationship between the
length of sensing fiber and the length of the tubular object versus
the wrap angle (.theta.);
[0047] FIG. 12 is a graphical illustration of the resulting
wavelength response, relative to D.sub.N numbered strain sensor,
from a cylindrical object undergoing offset shear in a controlled
test;
[0048] FIG. 13 is an elevational view of a cylindrical object
illustrating shear forces on the object;
[0049] FIG. 13A is an image of a wavelength response illustrating
the corresponding strain measured by the strain sensors in FIG.
13;
[0050] FIG. 14 is a graph illustrating the wavelength response
resulting from the lateral force applied by the weight of a pipe,
plotted as wavelength shift (.DELTA..lamda.) versus grating number
(D.sub.N);
[0051] FIG. 15 is a graph showing the wavelength response resulting
from the forces from a weight suspended from the center of the pipe
horizontally suspended at each end, plotted as wavelength shift
(.DELTA..lamda.) versus grating number (D.sub.N);
[0052] FIG. 16 is an elevational view of a cylindrical object
illustrating bending forces on the object;
[0053] FIG. 16A is an image of a wavelength response illustrating
the corresponding strain measured by the strain sensors in FIG.
16;
[0054] FIG. 17 is a graph illustrating the wavelength response
resulting from the application of a crushing force applied near the
center of the pipe of FIG. 14, plotted as wavelength shift
(.DELTA..lamda.) versus grating number (D.sub.N);
[0055] FIG. 18 is a graph illustrating the wavelength response for
the pipe of FIG. 17, plotted as wavelength shift (.DELTA..lamda.)
versus grating number (D.sub.N), wherein the clamps near the center
of the pipe have been rotated 90 degrees;
[0056] FIG. 19 is an elevational view of a cylindrical object
illustrating crushing or ovalization forces on the object;
[0057] FIG. 19A is an image of a wavelength response illustrating
the corresponding strain measured by the strain sensors in FIG.
19;
[0058] FIG. 19B is a top view of FIG. 19;
[0059] FIG. 20 is a plot illustrating the relative strain amplitude
(W.sub.A) as a function of the azimuth angle (.phi.) in degrees
around a tubular object;
[0060] FIG. 21 is a graph illustrating the strain factor (m), and
nm shift, versus wrap angle (.theta.) for a structural material
undergoing plastic deformation.
[0061] FIG. 22 is a graph illustrating the wavelength shift
(.DELTA..lamda.) plotted versus grating number (D.sub.N) for
various levels of applied axial strain;
[0062] FIG. 23 is a graph comparing the average, peak and
root-mean-square (rms) wavelength response with calculated or
expected wavelength response, plotted as wavelength shift
.DELTA..lamda. (nm) versus the axial strain applied .epsilon..sub.a
(%);
[0063] FIG. 24 is a graph illustrating the average wavelength shift
.DELTA..lamda. (actual) over the applied strain sensors at each
level of applied axial strain .epsilon..sub.a (%), compared to the
calculated wavelength shift;
[0064] FIG. 25 is a graph of wavelength shift .DELTA..lamda. (nm)
versus grating number (D.sub.N), illustrating an axial strain of
about zero;
[0065] FIG. 26 is a graph of wavelength shift .DELTA..lamda. (nm)
versus grating number (D.sub.N), illustrating an applied axial
strain of 0.25 percent;
[0066] FIG. 27 is a graph of wavelength shift .DELTA..lamda. (nm)
versus grating number (D.sub.N), illustrating an applied axial
strain of 0.75 percent;
[0067] FIG. 28 is an elevational view of a cylindrical object
illustrating compressional forces on the object;
[0068] FIG. 28A is an image of a wavelength response illustrating
the corresponding strain measured by the strain sensors in FIG.
28;
[0069] FIG. 29 is a theoretical plot of delta strain
.DELTA..epsilon. versus distance (d) along a line above a
reservoir;
[0070] FIG. 30 is an elevational view of a cylindrical object
illustrating a plurality of sensors or transducers applied to the
object in a zig-zag pattern;
[0071] FIG. 30A is a cylindrical projection view the cylindrical
object of FIG. 30;
[0072] FIG. 31 schematically shows a view of a pliable support
structure;
[0073] FIG. 32 shows a perspective view of a cylindrical object
having the pliable support structure of FIG. 31 draped around
it;
[0074] FIG. 33 shows an elevated view of a series of pliable
support structures on a spool;
[0075] FIG. 34 schematically shows an elevated view of applying the
series of pliable support structures to a string of tubular
objects;
[0076] FIG. 35A schematically shows a perspective view of a pliable
support structure in the form of a clamshell structure;
[0077] FIG. 35B schematically shows another perspective view of the
same clamshell structure as depicted in FIG. 35A;
[0078] FIG. 36 schematically shows a perspective view of how a
plurality of clam shell parts can be stacked together;
[0079] FIG. 37 is a variation on FIG. 36 where couples of pivotably
connected claim shell parts are stacked;
[0080] FIG. 38 shows a schematic perspective view of clam shell
parts provided with a latching mechanism;
[0081] FIG. 39 shows a schematic detailed view of a specific
embodiment of the brackets of the latching mechanism provided with
a cavity for accommodating a free loop; and
[0082] FIG. 40 compares sinusoidal patterns of a set of strain
sensors wrapped around a tubular object with patterns of a set of
strain sensors draped on the tubular object in a zig-zag
pattern.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0083] The subject matter of the present invention is described
with specificity however, the description itself is not intended to
limit the scope of the invention. The claimed subject matter thus,
might also be embodied in other ways to include different steps or
combinations of steps similar to the ones described herein, in
conjunction with other present or future technologies. Moreover,
although the term "step" may be used herein to connote different
methods employed, the term should not be interpreted as implying
any particular order among or between various steps herein
disclosed except when the order of individual steps is explicitly
described.
[0084] FIG. 1 schematically shows a cross sectional view of a an
earth formation 6 borehole system, during a fracturing operation.
An object 10, in this embodiment a cylindrical object in the form
of a casing tubing, is provided in a borehole 13 that may have
previously been drilled into the earth formation 6. The borehole
may be a wellbore. The cylindrical object 10 is mechanically
interacting with the borehole wall 14 such that any displacement of
parts of the formation in a vicinity of the cylindrical object 10
results in a deformation of the object 10 that result in a strain
distribution in the object 10. Typical deformations could include
bending, axial or radial strains, hoop strain, ovalization.
[0085] A plurality of strain sensors 30 and 30A is applied to the
object 10, for monitoring a strain distribution in the object 10.
The plurality of strain sensors may comprise Fiber Bragg Gratings,
which may be interconnected with a single optical fiber. However,
in the embodiment as depicted in FIG. 1, the plurality of strain
sensors is divided into two sets, of which the first set 30 is
interconnected with a first optical fiber 20, and of which the
second set 30A is interconnected with a second optical fiber 20A.
All strain sensors are strain-coupled to the object 10, at a
predetermined preferred angle, to measure strain along the surface
of the object 10 in the predetermined preferred angle.
[0086] As will be explained herein below, the sensors may, for
instance, be wrapped around and/or draped around the object 10 or
be spiraling along the inside surface of the object 10, or be
incorporated in the wall material of the object 10. For the purpose
of the present specification, the term "draping around" is
understood to include draping "around" the interior of the object
or cylindrical object, for instance when the object concerns a tube
or a pipe.
[0087] The borehole system of FIG. 1 further includes a fracturing
fluid pump, schematically depicted at 17, and comprising a
low-pressure input opening 18 and a high-pressure output opening
19.
[0088] The low-pressure input opening 18 is in fluid communication
with a fracturing fluid supply 22. Fracturing fluid supplies are
known in the art, and may typically comprise a liquid fluid source
22a; an optional proppant source 22b; and an optional mixing
device, which is here schematically depicted at branch connection
22c, wherein a mixture of the liquid and the proppant is produced.
The present invention is not limited to a specific type of
fracturing fluid supply, and it also works when a proppant-free
fracturing fluid is employed.
[0089] Various liquids are known to be used for fracturing,
including distillate, diesel fuel, crude oil, dilute hydrochloric
acid, water, and kerosene. The fracturing liquid may optionally
comprise a proppant. Typical known proppants are often granular of
nature and may include materials such as sand grains, gravel,
aluminum pellets, walnut shells, or similar materials.
[0090] The high-pressure output opening is in fluid communication
with the borehole 13, via line 23. Fluid communication may be
established directly into the cased borehole, or via an inner
tubing 7 such as is the case in FIG. 1, or in any other suitable
way.
[0091] The casing 10 is provided with one or more perforations 12.
A bridge plug, here depicted in the form of packer 8, seals against
a lower portion of casing 10, to isolate a zone below the
perforations 12 from the pressure of the fracturing fluid 24 in the
borehole 13. It may also seal against the borehole wall of an open
hole section. An annular plug, here in the form of annular packer 9
sealing against an upper portion of casing 10 and a lower portion
of the inner tubing 7, is provided to isolate a zone above the
perforations 12 from the pressure of the fracturing fluid 24 in the
borehole 13.
[0092] During operation, the fracturing fluid is pumped in
pressurized condition into the borehole 13, for instance via inner
tubing 7, against the formation 6. The fluid is allowed to directly
contact the formation 6 via perforations 12. The pressure may be so
high as to break or separate the earth formation to initiate a
fracture 11a. Continued pumping results in growth of the fracture,
successively depicted at 11b through 11h. Such fracturing induces
displacements of the earth formation which in turn may exercise a
detectable deformation force on the casing 10 resulting in a
fracturing-induced strain distribution in the casing 10. This
strain distribution may be monitored during the pumping, e.g. by
imaging the deformation of the casing 10. Such imaging will be
further elucidated below. Monitoring may optionally continue after
terminating pump 17, for instance during the phase of dissipating
of the pressure.
[0093] The monitored strain distribution may be outputted, e.g.
displayed, stored, or transmitted. Alternatively, the strain
distribution is first analyzed to determine a deformation parameter
or a distribution of this deformation parameter along the object,
which then in turn may be outputted. Useful deformation parameters
include bending curvature of the object, ovalization parameter
(e.g. an aspect ratio given by the quotient of the largest diameter
and smallest diameter of an oval object), radial strain, axial
strain along a longitudinal axis of the object. The tilt angle of
the object at various positions along the object, e.g. relative to
the vertical or an original axial direction of the object, may be
derived from the bending curvature of the object as a function of
position along the object. This may involve integrating the
curvature.
[0094] The pumping of the pressurized fracturing fluid may be
controlled in response to the monitoring. Herewith it can be
avoided that too much or too little fracturing has been induced,
such that optional subsequent hydrocarbon fluid production via the
wellbore may be optimized.
[0095] The invention may also be advantageously applied on
wellbores that are not intended to produce hydrocarbon fluids, such
as injection wells in reservoir floods for recovery of hydrocarbons
via other wells in the field. Some wells are intended for injection
only, for instance for the purpose of disposing of a fluid such as
waste water, carbon diode or chemicals.
[0096] The continuing description refers to the use of strain
sensors in the form of a plurality of transducers that may comprise
one or more conventional Fiber Bragg Grating (hereinafter "FBG")
sensors such as, for example, the transducers described in U.S.
Pat. Nos. 5,798,521, 6,426,496, or 6,854,327. Optionally, FBG
sensors may be
[0097] i) specially treated (short-term blazed) as described in
"Characteristics of short-period blazed FBG sensors for use as
macro-bending sensors", APPLIED OPTICS, 41, 631-636 (2002), Baek,
S., et al.; and/or
[0098] ii) bent as described in "Long-Period Fiber Grating Bending
Sensors in Laminated Composite Structures", SPIE Conference on
Sensory Phenomena and Measurement Instrumentation for Smart
Structures and Materials, March 1998, San Diego, Calif., SPIE Vol.
3330, 284-292, Du, W., et al.; and/or
[0099] iii) coated as described in "Ultrastrong Fiber Gratings and
Their Applications", SPIE Conference Phototonics East "Optical
Fiber Reliability and Testing", 3848-26, Sep. 20, 1999, Starodubov,
D. S., et al.
[0100] Optical fiber that is treated to comprise Fiber Bragg
Gratings may be suitable for use in monitoring compaction-induced
strain on a tubular object. Fiber Bragg Gratings may be made by
laterally exposing the core of a single-mode fiber to a periodic
pattern of intense UV light. This creates areas of increased
refractive index within the fiber. The fixed index modulation is
referred to as a Fiber Bragg Grating. All reflected light signals
combine coherently to one large reflection at one wavelength when
the grating period is equal to half the input wavelength. Other
wavelengths of light are, for all intents and purposes,
transparent. Light therefore, moves through the grating with
negligible attenuation or signal variation with only the Bragg
wavelength being affected, i.e., strongly back-reflected at each
FBG sensor. In other words, the center frequency of the grating is
directly related to the grating period, which is affected by
thermal or mechanical changes in the environment. Thus,
temperature, strain and other engineering parameters may be
calculated by measuring the normalized change in reflected
wavelength. Being able to preset and maintain the grating
wavelength is, thus, what makes FBG sensors so useful. See "Fiber
Bragg Grating" 3M US Online, 27 Nov. 2000.
[0101] The present invention, however, is not limited to the use of
FBG-type sensors and may be implemented with conventional sensors
or transducers capable of detecting axial and/or radial strain such
as, for example, strain gauges as described in "Strain Gauge
Technology," A. L. Window (Editor), Elsevier Science Pub. Co.,
2.sup.nd edition, November 1992. Thus, the novel techniques and
methods described herein may be implemented and applied through the
use of any type of strain sensor or transducer capable of detecting
signals and transmitting signals, regardless of whether it is a FBG
sensor, strain gauge or other conventional type sensor or
transducer. Furthermore, the use of an optical fiber as a
transmission means to illustrate various applications of the
invention described herein is not exclusive of other well-known
transmission means that may be used to connect the transducers such
as, for example, electrical wires, which are capable of
transmitting power and a signal. Furthermore, conventional wireless
transducers may be used provided that they include a power
source.
[0102] Various tests have been made to study the feasibility of
employing FBG sensors wrapped around a tubular for making visible
fracturing-induced deformation of the earth formation.
[0103] For instance, FIG. 2 shows wavelength response (.lamda.) of
a large number of FBG gratings wrapped helically around a tubular.
The wavelength is shown for each successive FBG (D.sub.N), and it
this thus correlates to a local strain in the tubular along a
helical path on the tubular. Approximately two thirds of the fiber
was wrapped at a wrap angle of 20.degree. relative to the
longitudinal axis of the tubular, the wavelength shifts of which
are shown at 26. The remaining approximately one third of same
fiber was wrapped at a wrap angle of 60.degree. relative to the
longitudinal axis of the tubular. The wavelength response of the
FBG sensors applied along an application line of 60.degree. are
shown at 29. The tubular was bent approximately uniformly, and it
can clearly be seen that the sensitivity to bending is much larger
in the FBG sensors that were applied along the application line of
60.degree. than in those that were applied along the application
line of 20.degree..
[0104] FIGS. 3A and 3B shows wavelength shift (.DELTA..lamda.)
versus grating number (D.sub.N) of the 60.degree.-wrapped FBG
sensor fiber around a tubular that is clamped on one end and bent
under a load. In each of the FIGS. 3A and 3B, line 41 depicts the
measured wavelength shifts (plotted against the left axis, as
indicated by arrow), line 42 depicts a curvature model (plotted
against the right axis, as indicated by arrow), and line 43 depicts
calculated wavelength shifts based on the curvature model as shown
in line 42. The amount of bending in FIG. 3B was less than in FIG.
3A, and it is concluded that a bend with a radius of curvature of
approximately up to 25.times.10.sup.3 feet (7.5 km) is
detectable.
[0105] FIG. 3C has been added for comparison, showing approximately
the same bending as in FIG. 3B but monitored using the 20.degree.
wrap angle. No readable signal is obtained for these small radii of
curvature.
[0106] Since the expected fracture-induced bending of a tubular
object is expected to be low, 50.degree. or higher, e.g. 60.degree.
or higher, is expected to be a preferred wrap angle for this
application.
[0107] In the embodiment shown in FIG. 1, there are two sets of
sensors, set 30 and set 30A, set 30 being applied to the object
along a first preferred angle and set 30A being applied to the
object along a second preferred angle. As will be further explained
below, this enables differentiation between axial and radial
components of strain. However, this may not always be needed since
the radial strain would generally be expected to tend to relax,
once the pumping of the fracturing fluid has been terminated.
[0108] A cylindrical tube in a bore hole may undergo several types
of deformation under the influence of fracturing. For instance,
ovalization of the casing could occur in addition to bending and
axial straining. Ovalization could typically provide the highest
strain distribution signal, in particular when the monitoring is
performed from the same well or borehole as the fracturing. FIG. 4
shows a top-down schematical view (dimensions have been exaggerated
for clarity) of a horizontal section through the earth formation 6
and casing 10 in the bore hole system at a fracture 11. An
originally circular casing has ovalized due to the lateral
displacement of rock material on both sides of the fracture 11.
FIG. 5 shows a calculated wavelength shift signal as a function of
grating number of the combined effects of bending and ovalization.
As will be further explained herein below, the ovalization signal
has twice the frequency of the bending signal. FIG. 6 shows the two
signals separated as may be done utilizing Fourier analysis. Line
44 represents the bending signal and line 46 the ovalization
signal.
[0109] In the embodiment as depicted in FIG. 1, the casing 10 has
been selected as the object in which the strain distribution is
monitored. However, strain sensors could be applied to the inner
tubing 7 in essentially the same was as described above. Mechanical
interaction between the inner tubing 7 and the borehole wall 14
could be achieved e.g. providing centralizers (not shown) at
various axial positions to establish a mechanical coupling between
the inner tubing 7 and borehole wall 14, either directly or e.g.
via other objects such as the casing 10. Such coupling may be
capable of inducing detectable deformation in the inner tubing 7 in
response to displacements in the earth formation.
[0110] In the embodiment as depicted in FIG. 1, the plurality of
strain sensors is provided above packer 9, which corresponds to
essentially above the perforations 12 from which the fracturing is
initiated. This enables monitoring of the top of the fracture
(which is schematically indicated at dashed line 15), or fracture
height, and how it progresses over time. Clearly, strain sensors
may also be provided in, or extend to, the zone between packers 8
and 9, corresponding to the zone in direct vicinity of the
perforations 12, and/or be provided in, or extend to, a zone below
packer 8.
[0111] The object of which the deformation is monitored does not
have to be in the bore hole through which the fracturing fluid is
pumped into the earth formation: it may be anywhere in the earth
formation and mechanically interacting with the earth formation
anywhere.
[0112] For instance, in alternative embodiments, fracturing fluid
may be pumped into the formation via a so-called treatment well,
while the object and the plurality of strain sensors may be
provided in an offset well (not shown), so that the strain
distribution in the object can be monitored during fracturing at a
distance from the treatment well. The typical deformation in such
an offset well may be predominantly bending, such as e.g. shown in
U.S. Pat. No. 7,028,772. In case of a of strain sensors applied
along an application path that helically winds along the surface of
a cylindrical object, such bending results in a sinusoidal strain
around the object with a period corresponding to the wrap pitch, as
will be further set forth herein below.
[0113] Of course, both the treatment well and an offset well may be
provided with an object and strain sensors for monitoring the
fracturing in multiple wells at the same time.
[0114] The provision of the strain sensors, of course, does not
exclude embodiments wherein the strain sensors are combined with
other types of sensors, including tilt meters, flow sensors,
pressure sensors, micro-seismic sensors. In addition, a tagged
proppant may be employed, e.g. a proppant tagged with a
radio-active tracer to be able to measure where and how much
proppant has been put in the formation fracture.
[0115] A full disclosure will now be provided showing detailed
considerations for determination of preferred wrap angles and
showing various methods of applying the strain sensors to the
object, all of which may be useful for fracturing monitoring as
described above. A large part of the following disclosure has been
published in co-pending US Patent application published under
number US 2006/0233482, incorporated herein by reference in its
entirety.
[0116] Referring now to FIG. 7, an elevational view of a
cylindrical object 10 such as, for example, a tubular object (e.g.,
drill pipe) or casing, is illustrated with a plurality of FBG type
sensors 20 applied to the object 10 on a fiber 30 at different
preferred wrap angles in sections A, B and C. FIG. 7A is a linear
perspective of section A in FIG. 7, illustrating the fiber 30
wrapped around the tubular 10 at a preferred wrap angle represented
by .theta..sub.1 or .theta..sub.2. The preferred wrap angle may be
measured relative to a first imaginary reference line 40 extending
longitudinally along a surface of the object 10. Alternatively, the
preferred wrap angle may be measured relative to a second imaginary
reference line 50 circumferencing the object 10, which also
represents the circumference (C) in FIG. 7A. For purposes of the
following description, however, wrap angle .theta. and preferred
wrap angle .theta..sub.1 are defined relative to the second
imaginary reference line 50 and is represented by .theta..sub.1.
Nevertheless, .theta..sub.2 could be used, instead, by simply
substituting .pi./2-.theta..sub.2 for .theta..sub.1 or calculating
.theta..sub.1 based on .theta..sub.2 as
.theta..sub.1=90.degree.-.theta..sub.2.
[0117] In FIG. 7A, the length of one wrap of fiber 30 around the
object 10 is represented as S. The distance along the first
imaginary line 40, which may be the vertical distance between each
wrap of fiber 30, is represented as L. Relationships between
.theta..sub.1, L, X, S, and C are illustrated by:
L=S*sin(.theta..sub.1) and C=S*cos(.theta..sub.1). In this
transformed geometry, S represents the hypotenuse of a right
triangle formed by L, C, and S.
[0118] Axial strain along the axis of the object 10 caused by
compaction can be represented as .epsilon.=.DELTA.L/L. Axial strain
along the axis of the object 10 caused by compaction can be
translated to strain in the strain sensor 20 and represented as
.epsilon..sub.f=.DELTA.S/S, which may manifest itself in the strain
sensor 20 as axial, hoop and/or sheer stress. The relationship
between strain (.epsilon..sub.f) in the strain sensor 20 and its
wavelength response is therefore, represented by:
.DELTA..lamda.=.lamda.(1-Pe)K.epsilon..sub.f where .DELTA..lamda.
represents a strain sensor wavelength shift due to strain
(.epsilon..sub.f) imposed on the strain sensor 20 and .lamda.
represents the average wavelength of the strain sensor 20. The
bonding coefficient of the strain sensor 20 to a substrate or
system on which the strain is to be measured is represented by
K.
[0119] A "combined" response for bending (also buckling, shearing)
and axial strain may be represented by: .DELTA..lamda. = .lamda.
.function. ( 1 - P e ) K ( - 1 + sin 2 .times. .theta. ( 1 - ( - r
.times. .times. cos .times. .times. .PHI. R ) ) 2 + cos 2 .times.
.theta. ( 1 + v .function. ( - r .times. .times. cos .times.
.times. .PHI. R ) ) 2 ) ##EQU1## wherein .DELTA..lamda. is the
wavelength shift measured on a given grating and .lamda. is the
original wavelength of the grating which may nominally be 1560
nanometers. The term (1-P.sub.e) is a fiber response which is
nominally 0.8. Bonding coefficient K typically may be 0.9 or
greater. The wrap angle (or orientation angle of the sensor) with
respect to first imaginary axis of the tubular is represented by
.theta.. The axial strain .epsilon. on the tubular that may be from
compaction or other external source. The radius of the tubular or
cylindrical object is represented by r, and .phi. is an arbitrary
azimuth angle with respect to some reference along the axis of the
tubular that allows one to orient the direction of the buckle or
bend with respect to this. Capital R represents the bend radius of
the buckle or bend in the pipe. As the bend radius gets very large
(straight unbent pipe), this portion of the signal vanishes. The
Poisson ratio .nu. of the object may change with strain. An
independent measurement may be employed to extract the value of
.nu.. One can, by using two wrap angles simultaneously, solve for
this.
[0120] For simplicity in the examples that follow, the bonding
coefficient (K) is assumed to be constant. P.sub.e represents the
strain and temperature effect on the index of refraction of the
strain sensor 20. P.sub.e may be a function of strain and
temperature, including torque on the strain sensor 20, but is
neglected in the following examples. Since it is well known that
temperature variations may impart additional strain to the fiber
30, the strain sensors 20 and object 10, which affect the index of
refraction in the fiber 30, temperature variations may be
considered independently for calibrating the strain measurements.
This can easily be done either by a separate temperature
measurement that could be performed by mechanically decoupling
short lengths of the fiber 30 from the object 10, using a separate
but similar fiber that is entirely decoupled mechanically from the
object 10 or by any other means of measuring the temperature in the
vicinity of the object 10 undergoing the strain measurement.
[0121] The foregoing properties may be used to relate the strain
(.epsilon..sub.f) in the strain sensor 20 to the axial compaction
strain (.epsilon.) in the object 10. The strain (.epsilon..sub.f)
in the strain sensor 20 can be related to the preferred wrap angle
(.theta..sub.1) and the strain (.epsilon.) along the axis of the
object 10 by: .DELTA. .times. .times. S S = - 1 + sin .function. (
.theta. 1 ) 2 * ( 1 - ) 2 + cos .function. ( .theta. 1 ) 2 * ( 1 +
v .times. .times. ) 2 ##EQU2##
[0122] The Poisson ratio (.nu.) is an important property of the
object 10, which is relevant to the strain (.epsilon.) the object
10 may encounter as illustrated in the examples to follow.
[0123] The strain factor relating axial strain (.epsilon.) in the
object 10 to strain (.epsilon..sub.f) transmitted to the strain
sensor 20 is represented by: m = - 1 + sin .function. ( .theta. 1 )
2 * ( 1 - ) 2 + cos .function. ( .theta. 1 ) 2 * ( 1 + v .times.
.times. ) 2 ##EQU3## which may also be translated to:
.DELTA.S/S=m*.DELTA.L/L=m*.epsilon.. Comparison of the strain
factor (m) to other variables reveals that it is highly sensitive
to the preferred wrap angle (.theta..sub.1), somewhat sensitive to
the Poisson ratio (.nu.), and quite insensitive to applied axial
strain (.epsilon.) Application of the Sensors
[0124] The primary requirements for sensitivity and resolution are
a sufficient number of sensors 20 positioned around the
circumference (C) of the object 10 and adequate vertical spacing
between the sensors 20 so that a sinusoidal pattern associated with
a bend, buckle, shear or crushing (ovalization) force can be
clearly detected and imaged. As demonstrated by the relationships
below, sensitivity to axial strain and radial strain, and hence
bending strain, is also a function of the preferred wrap angle
(.theta..sub.1).
[0125] A desired sensitivity to axial strain in the cylindrical
structure may be selected based on considerations as set forth
below. Also set forth below, at least one strain factor
corresponding to the desired sensitivity may be calculated. Such a
strain factor represents a ratio between strain transmitted to the
strain sensor as caused by axial strain in the cylindrical
structure and the axial strain in the cylindrical structure. A
preferred wrap angle relative to an imaginary reference line
extending along a surface of the cylindrical structure may then be
determined, in dependence of the at least one determined strain
factor. The strain sensor may then be applied to the cylindrical
structure in alignment with the preferred wrap angle to measure
strain in the direction of the preferred wrap angle.
[0126] Preferably, at least ten strain sensors 20 per wrap of the
fiber 30 may be used to adequately capture one cycle of the
sinusoidal signal produced by a deformation of the object 10. It is
also desirable to have at least eight to ten turns or wraps of the
fiber 30 covering the vertical distance of the object 10 over which
the deformation is expected to occur. Fewer strain sensors 20 will
reduce the resolution and ability to unambiguously distinguish
between a bend, buckle, shear or crushing type deformation. In
terms of the preferred wrap angle (.theta..sub.1) and the diameter
(D) (in inches) of the object 10 the length of object 10 (in feet)
covered by each wrap is represented as: L 1 = .pi. * D * tan
.function. ( .theta. 1 ) 12 ##EQU4##
[0127] To obtain the length in feet, the length in meters must be
divided by 0.30. To obtain the diameter in inches, the diameter in
centimeters must be divided by 2.54.
[0128] In terms of the preferred wrap angle (.theta..sub.1) and the
diameter (D) (in inches) of the object 10, the length of one wrap
around the object 10 (in feet) is represented as: S 1 = .pi. * D *
cos .function. ( .theta. 1 ) 12 ##EQU5##
[0129] The total length of the fiber 30 (in feet) based on a
preferred number of wraps (N.sub.w) around the object 10 and the
length of one wrap (S.sub.1) around the object 10 (in feet) is
represented as: S=S.sub.1*N.sub.w
[0130] The axial length of the fiber 30 (in feet) along the object
10 is based on a preferred number of wraps (N.sub.w) around the
object 10 and the length of object 10 (in feet) covered between
each wrap is represented as: Z=L.sub.1*N.sub.w
[0131] Thus, the preferred number of wraps (N.sub.w) around the
object 10 may be determined by the axial length (Z) of the object
10 wrapped in the fiber 30 divided by the length (L.sub.1) of
object 10 covered between each wrap of the fiber 30. In addition to
the preferred wrap angle (.theta..sub.1), the preferred number of
wraps (N.sub.w) may be used to determine a preferred application of
the fiber 30 and strain sensors 20 to the object 10.
[0132] The strain sensor spacing may be as short as 1 centimeter or
as long as necessary to accommodate a judicious number of strain
sensors 20 per wrap of the fiber 30 on a object 10 having a large
diameter. The total number of strain sensors 20 per wrap of the
fiber 30 as a function of strain sensor spacing (S.sub.g) (in
centimeters) and wrap length (S.sub.1) is represented as: n = 2.54
* S 1 * 12 S g = 2.54 * .pi. * D * cos .function. ( .theta. 1 ) S g
##EQU6##
[0133] Assuming that all of the strain sensors 20 on the fiber 30
are within the wrapped portion of the fiber 30, then the total
number of strain sensors 20 on the fiber 30 is represented as: N =
2.54 * S * 12 S g = 2.54 * N w * .pi. * D * cos .function. (
.theta. 1 ) S g ##EQU7## Similarly, the preferred strain sensor
spacing (S.sub.g) may be easily determined with a known preferred
number of strain sensors (N) and a predetermined total length (S)
of fiber 30.
[0134] Roughly, the maximum number of strain sensors 20 that can be
used on one fiber 30 with this technique may be about 1000. Thus,
the preferred wrap angle (.theta..sub.1), the preferred number of
wraps (N.sub.w) and the preferred number of strain sensors (N) may
be used to determine a preferred application of the fiber 30 and
strain sensors 20 to the object 10.
[0135] Using the previous equations, plots such as the one in FIG.
8 may be compiled and used to determine the preferred number of
strain sensors (N) and the preferred number of wraps (N.sub.w)
needed to cover a predetermined length and diameter for the object
10 and the preferred strain sensor spacing (S.sub.g). Plotted on
the left axis are the length of the fiber (S, in units of 0.30
meter--corresponding to feet), the axial length (Z, in units of
0.30 meter--corresponding to feet) of the object 10 wrapped in the
fiber 30 and the total number (N) of strain sensors in the form of
gratings that may be compared to a wrap angle range for a
predetermined number of wraps (N.sub.w) and a predetermined strain
sensor spacing (S.sub.g). Plotted on the right axis are the total
number of gratings per wrap (n) and the axial length (L.sub.1 in
units of 0.30 meter--corresponding to feet) of the object 10
covered between each wrap that may be compared to a wrap angle
(.theta.) range for a predetermined strain sensor spacing (S.sub.g)
and a preferred number of wraps (N.sub.w). In FIG. 8, line 1 plots
the length of the object Z against wrap angle (.theta.) for a case
whereby D=15 cm (6.0 inches); line 2 plots the length of the fiber
(S) for a case where the number of wraps (N.sub.w)=100; line 3
plots the number of gratings having a spacing (S) of 5.0 mm; line 4
plots the number of gratings per wrap; and, line 5 plots the length
of the object Z against wrap angle (.theta..sub.1) per wrap.
[0136] In FIG. 8, D=152 mm (6 inches), N.sub.w=100 and S.sub.g=5
mm. This figure shows that wrap angles between 20 and 40 degrees
tend to optimize resolution considering the length of fiber (S) and
the length of the object (Z) being monitored. This information may
be used with the strain factor (m) to design a preferred
application of the fiber 30 to the object 10.
[0137] FIG. 9, illustrates the relationship between the strain
factor (m) and wrap angle .theta.. A predetermined Poisson ratio
(.nu.) of 0.5 was chosen based on the observation of steel tubular
performance after yielding at high compaction strains. A
predetermined strain (.epsilon.) of 5.0 percent was selected based
upon the maximum anticipated strain the object may encounter.
[0138] Based on these structural parameters (P(.nu.), (.epsilon.)),
the strain factor (m) may be determined for each wrap angle
illustrated in FIG. 9. The results in FIG. 9 reveal that the strain
each strain sensor experiences can be decreased or even reversed
(compression to tension) by carefully choosing the preferred wrap
angle (.theta.=.theta..sub.1).
[0139] The ability to easily regulate the amount of strain the
fiber and each strain sensor will be exposed to, and even the sign
of the strain (tension vs compression) is very important. Most
conventional fiber sensors manufactured from glass can be exposed
to no more than one or two percent strain (in tension) before
damage or failure occurs. Compressional strain in fiber sensors
manufactured from glass is even more problematic. Thus, high axial
compressional strain exerted on tubular objects in compacting
environments can be converted to mild extensional strain in the
fiber sensor by simply adjusting the wrap angle. The same principle
may be applied to recalculate the amount of strain on other
conventional sensor systems that may be used.
[0140] In FIG. 9A, the strain factor (m) is illustrated for each
wrap angle .theta. according to a predetermined Poisson ratio
(.nu.) of 0.3 and a predetermined strain (.epsilon.) of 0.10
percent for the object analyzed. These conditions could correspond
to applications where mild compaction may be anticipated. For good
sensitivity to mild compaction strains (compressional) and
excellent sensitivity to lateral deformations, it may be
advantageous based on FIG. 9A to select a preferred wrap angle of
on the order of 20 degrees.
[0141] FIGS. 9 and 9A illustrate that, at a zero-degree wrap angle,
the strain factor (m) is equal to the Poisson ratio (.nu.). In
other words, the compressional strain (.epsilon.) on the object is
translated to an axial expansion defined by Poisson's ratio (.nu.).
Likewise, in the limit of no wrap (vertical application along
casing or a 90-degree wrap angle) the extension or compression of
the object can be measured directly. The latter has the
disadvantage that, in high compressional strains, the fiber and/or
strain sensors are likely to be damaged and/or undergo buckling and
mechanically disconnect from the object. But for mild extensional
strains as often seen in an overburden layer, it may be best to
choose 90 degrees or near 90 degrees, such as between 80 and 90
degrees) (corresponding to axial application or near-axial
application).
[0142] FIG. 10 illustrates Poisson's ratio (.nu.) for steel versus
strain applied. For steel behaving elastically, the nominal Poisson
ratio is near 0.3. It has been observed that the Poisson ratio
(.nu.) of tubular objects undergoing high compaction strains
(beyond the elastic limit) is better approximated at 0.5. This is a
theoretical limit for the conservation of volume. The Poisson ratio
(.nu.) may therefore, be predetermined according to the anticipated
or maximum strain the object may encounter, however, may be between
about 0.3 and about 0.5 for tubular steel objects. As a general
rule, the Poisson ratio (.nu.) may be approximated at 0.5 if the
predetermined strain is at least 0.3 percent or greater in a
tubular steel object.
[0143] The principles illustrated in FIG. 9 and FIG. 9A may be used
to determine a preferred application of the strain sensors 20 to
the substantially cylindrical object 10 in FIG. 7A for monitoring
deformation of the object in various formation environments.
According to one method, a preferred wrap angle range (e.g.,
between 0 and 90 degrees) may be selected for determining the
relative strain factor (m) associated with each wrap angle in the
preferred wrap angle range. A broad wrap angle range between 0
degrees and 90 degrees may be preferred, however, different,
narrower, ranges may be selected. The strain factor (m) should be
determined for at least one wrap angle within the preferred wrap
angle range. The preferred wrap angle (.theta..sub.1) within the
preferred wrap angle range may be determined based on at least one
determined strain factor (m), and used to determine the preferred
application of the strain sensors 20 to the object 10 in FIG. 7A.
As illustrated in FIG. 8, a number of other variables, including
the preferred number of strain sensors (N) and the preferred number
of wraps (N.sub.w), may also be considered in determining the
preferred application of the strain sensors 20 to the object 10
based on sensitivity and resolution requirements.
[0144] Determining the preferred wrap angle (.theta..sub.1) within
the preferred wrap angle range may, alternatively, be based on a
preferred strain factor range comprising a plurality of the strain
factors determined in the manner described above. The determined
strain factor or determined strain factor range may be selected to
determine the preferred wrap angle (.theta..sub.1) within the
preferred wrap angle range based on a maximum strain the strain
sensor 20 and/or fiber 30 can withstand. If a transmission means
other than the fiber 30 is used, or wireless transducers are used,
then the determined strain factor or determined strain factor range
used to determine the preferred wrap angle (.theta..sub.1) within
the preferred wrap angle range may be based on a maximum strain the
alternative transmission means and/or transducers, or wireless
transducers, can withstand.
[0145] In FIG. 9, for example, the predetermined Poisson ratio
(.nu.) and anticipated axial strain (.epsilon.) reveal a need for
sensitivity to high compaction strains. Assuming the strain sensors
and/or fiber are limited to about 2 percent strain before failure
occurs, then the wrap angle at which the strain sensors and/or
fiber may fail at 5 percent anticipated strain on the object is
determined by dividing the maximum strain the strain sensor and/or
fiber may withstand (0.02) by the anticipated strain (0.05), which
reveals a strain factor (0.4) that corresponds with a wrap angle of
about 15 degrees. Consequently, a wrap angle of greater than about
15 degrees is required to prevent damage to the strain sensors
and/or fiber and preferably may be about 30 degrees. A wrap angle
greater than about 35 degrees, where the strain factor is zero, may
produce undesirable compression and buckling in the fiber and/or
strain sensors.
[0146] Once a preferred application of the strain sensors has been
determined, the strain sensors may be applied to the object 10
along a preferred application line represented by the fiber 30 in
FIG. 7A. The preferred wrap angle may be formed between the
preferred application line and the first imaginary reference line
40 or the second imaginary reference line 50. Such an application
line may be generally straight except for any curvature imposed by
following the curvature of the object to which the strain sensors
are to be applied.
[0147] The strain sensors 20 and the fiber 30 may be applied to an
exterior surface of the object 10 (as illustrated in FIG. 7), an
interior surface of the object 10, a channel within the object 10
or be made an integral component of the object 10 when forming or
manufacturing the object 10. In the event that the tubular object
10 comprises a screen assembly having multiple screen components,
including a sand screen, the strain sensors 20 and the fiber 30 may
be applied to an interior surface and/or an exterior surface of one
of the multiple screen components or in a channel within any one of
the multiple screen components or between any two of the component
layers. Additionally, the strain sensors 20 and the fiber 30 may be
applied to an exterior surface of one of the multiple screen
components and the interior surface of another one of the multiple
screen components.
[0148] Furthermore, the strain sensors 20 and the fiber 30 may be
applied to the object 10 in a protective sheath and/or a protective
sheet coating the strain sensors 20 and the fiber 30, provided that
the protective coating is capable of transferring strain from the
object 10 to the strain sensors 20. Acceptable protective coatings
may comprise, for example, a metal, a polymer, an elastomer, a
composite material or a thin tube comprising one or more of these
materials that is flexible yet capable of being applied to the
object 10 in a way that couples the strain experienced by the
object 10 with the strain sensors 20. In the event the object 10
must be run in a well bore, the strain sensors 20 and fiber 30 may
be applied before the object 10 is run in the well bore.
[0149] Alternatively, the strain sensors 20 and the fiber 30 may be
applied to the object 10 after it is run in the well bore using a
conduit, or may be applied to the interior or exterior surface of
the object 10 after the object 10 is run in the well bore. Any
conventional conduit capable of being coupled to the object 10 is
acceptable. Acceptable materials for the conduit may comprise, for
example, a metal, a polymer, an elastomer, a composite material or
a thin tube comprising one or more of these materials that is
flexible yet capable of being applied to the object 10 in a way
that couples the strain experienced by the object 10 with the
strain sensors 20.
[0150] The strain sensors 20 and the fiber 30 may be introduced
into an opening in the conduit and positioned therein with a fluid
capable of securing the strain sensors 20 and the fiber 30 within
the conduit and transferring strain on the object 10 to each strain
sensor 20. In one example, the fluid may at least partially
solidify and secure the strain sensors within the conduit. The
fluid may, for example, comprise any conventional polymer, polymer
solution, polymer precursor, or epoxy. The fluid may also be used
to convey the strain sensors 20 and the fiber 30 through the
conduit. Additionally, the strain sensors 20 and the fiber 30 may
be positioned in the conduit with the fluid by applying force on
either, or both, ends of the fiber 30 to push and/or pull the same
through the conduit. For example, a weighted object may be attached
to the leading end of the fiber 30 to propel (pull) the fiber 30
and strain sensors 20 through the conduit. The conduit may be
positioned within the object 10 along the preferred application
line or on the object 10 along the preferred application line. In
either case, the preferred wrap angle may be formed between the
preferred application line (represented by the fiber 30 in FIG. 7A)
and the first imaginary reference line 40 or the second imaginary
reference line 50. If the object 10 comprises a screen assembly
having multiple screen components, the conduit may be positioned
within one of the multiple screen components along the preferred
application line or on one of the multiple screen components along
the preferred application line.
[0151] Application of the strain sensors 20 and fiber 30 to a
object 10 after it has been positioned in a well bore may be
preferred in that this technique does not require the tubular
object to be rotated or a fiber spool to be rotated about the
object during application of the strain sensors 20 and the fiber
30. Similar advantages may be preferred by application of the
strain sensors 20 and the fiber 30 to the object 10 in a protective
sheet, which may be positioned on the object 10 and fastened along
one side as described further in U.S. Pat. No. 6,854,327.
Multiple and Variable Wrap Angles
[0152] As reservoir depletion progresses, the
sensitivity/resolution requirements and strain factors are likely
to change. By combining multiple wrap angles over a single zone of
the formation, the sensitivity and dynamic range of the
measurements may be extended. For example, a fiber wrapped at 20
degrees may fail at one level of strain while the same fiber
wrapped at 30 degrees or more may not fail at the same level of
strain or at a slightly higher level of strain.
[0153] Another advantage multiple wrap angles provide is better
characterization of the change in the Poisson ratio (.nu.) as the
structural material yields under higher strains. Common steel used
in tubulars may have a Poisson ratio of near 0.3 while it is
elastic but trends toward 0.5 after the material yields. Applying
the fiber 30 and strain sensors 20 at two or more wrap angles, as
illustrated in FIG. 7, will allow the characterization of this
change. This is particularly important for fibers that are wrapped
near the angle that would null the fiber strain. This null point
changes primarily as a function of the Poisson ratio (.nu.) for the
object 10. With multiple wrap angles, this behavior can be measured
directly on the object 10 in the well while it is undergoing
compaction strain. Thus, if different wrap angles may be preferred
due to different forces acting on the tubular object, the methods
described above in reference to FIGS. 9 and 9A may be used to
determine another preferred wrap angle within the preferred wrap
angle range. The preferred application of the strain sensors 20 may
be based on the preferred wrap angle and another preferred wrap
angle and applied to the object 10 over the same section or over
different sections as illustrated by section B and sections A, C in
FIG. 7, respectively. In either case, the preferred wrap angle and
another preferred wrap angle may each be determined according to a
respective determined strain factor (m). Each respective determined
strain factor (m) may be selected according to a predetermined
force and another predetermined force to be applied to the object
10, over the same section or over different sections, which impacts
the same by variations in the Poisson ratio (.nu.) and axial strain
(.epsilon.).
[0154] Restrictions on the number of strain sensors, the wrap
length and the strain sensor spacing may also be overcome using
multiple wrap angles. Therefore, multiple wrap angles may be used
to extend the measuring length of a single region along the object
or span multiple zones along the object as illustrated in sections
A, B and C of FIG. 7. The addition of multiple wrap angles may also
be used to branch into multiple objects such as multi-lateral
wells.
[0155] Although the wavelength response is more complicated, the
application of the fiber 30 and the strain sensors 20 at variable
wrap angles may also be desirable. Configurations utilizing
multiple and variable wrap angles over a single section of the
object 10, like section B in FIG. 7, may be preferred. Other
configurations, such as those suggested in U.S. Pat. No. 6,854,327,
may be used, however.
[0156] The present invention will now be described further with
reference to its application in different formation environments
such as, for example, formation shear and formation compaction. In
each of the examples to follow, a cylindrical object was tested
using a Distributed Sensing System (DSS) manufactured by Luna
Innovations Incorporated under license from NASA. The LUNA
INNOVATIONS.RTM. Distributed Sensing System (DSS) utilizes
technology covering an optical fiber containing multiple FBG
sensors, and a projection device or monitor capable of imaging a
wavelength response produced by the FBG sensors as a result of
structural strain detected by the FBG sensors. The present
invention, however, is not limited to such technology by the
following examples, and other transmission means and transducers
and/or strain sensors may be used as described hereinabove.
[0157] Strain sensors may be pre-positioned on the tubular object
and/or casing without having to run conventional logging tools into
the well. Accordingly, in-situ measurements can be taken of shear
forces at any time without disturbing the well and with essentially
no additional cost. The onset of damage can be observed
substantially in real time so that remedial action can be taken as
soon as possible.
[0158] In FIG. 11, line 1 plots the length of the object Z (in
units of 0.30 meter) against wrap angle (.theta.) for a case
whereby D=7.6 cm (3.0 inches); line 2 plots the length of the fiber
(S) for a case where the number of wraps (N.sub.w)=80; line 3 plots
the number of gratings having a spacing (S) of 2.0 mm; line 4 plots
the number of gratings per wrap; and, line 5 plots the length of
the object Z against wrap angle (.theta.) per wrap.
[0159] Assuming a 76-millimeter (3-inch) diameter tubular object to
be monitored across a slip or shear zone, the location of which is
known to be within ten feet, requires at least 6.1 meters (20 feet)
of coverage along the tubular. Applying the principles taught by
the present invention to the known variables illustrated in FIG. 11
reveals that about 20.4 meters (67 feet) of sensing fiber is needed
to cover about 7.3 meters (24 feet) of the tubular object assuming
a preferred wrap angle of about 21 degrees. Given a preferred
strain sensor spacing of about 2 centimeters, about 12 strain
sensors per wrap are recommended, which is greater than the minimum
recommendation of 10 strain sensors per wrap. The total number of
strain sensors is about 1000.
[0160] A need exists for imaging deformation of an object, in order
to image the shape and magnitude of the deformation. The same wrap
technique may be used to image, detect and measure bending and
buckling of the cylindrical object as will be explained in the
forthcoming examples.
EXAMPLE 1
Offset Shear
[0161] FIG. 12, illustrates the resulting wavelength response,
relative to each numbered strain sensor, from a cylindrical object
undergoing offset shear in a controlled test. Such shear may occur
in formations under influence of fracture growth The cylindrical
object is seventy-six (76) millimeters (three (3) inches) in
diameter and six hundred ten (610) millimeters (twenty-four (24)
inches) long. Although the strain sensor spacing along the optical
fiber in this test is about 1 centimeter, a spacing of 2
centimeters may be adequate to measure the same shear response in a
cylindrical object with the same diameter. A preferred wrap angle
of about 20 degrees was used. The detectable variation in
wavelength response, representing lateral offset, was between 0.025
mm (0.001 inches) up to about 15.24 mm (0.600 inches).
[0162] In this example, a 0.025 mm (0.001-inch) lateral offset
translates into a dogleg in the object of about less than one-half
degree for each one hundred-foot section of the object, which is
inconsequential. However, a lateral offset of about 2.54 mm (0.1
inch) over the same length of object translates into a dogleg of
approximately 48 degrees for each 30.5 meter (one hundred-foot)
section of the object, which could prevent entry with production
logging tools. Knowing the magnitude of the lateral offset (dogleg)
before attempting entry could therefore, prevent lost and stuck
logging tools and lost wells.
[0163] The wavelength response illustrated in FIG. 12 may be
imaged, in real time, on a projection device such as the monitors
manufactured by Luna Innovations. The detection of variations in
the wavelength response at each strain sensor as the object is
being monitored will reveal changes in the deformation of the
object and what type of force is causing the object to deform.
Variations in the wavelength response are therefore, revealed by
variations in the amplitude of the wavelength response at each
strain sensor. The ability to detect strain on the object and image
the same in the form of a wavelength response on a projection
device, however, is not limited to a cylindrical object and may be
applied to most any object capable of transferring strain from the
object to the strain sensor.
[0164] FIG. 13 represents a simple illustration of a shear force
applied to the object 10. Here, the object 10 is subjected to a
shearing force 210 on one side of the object 10 and another
shearing force 220 on another side of the object 10. The wavelength
response, representing strain on the object 10 measured by the
strain sensors 20, associated with the shearing forces 210, 220 is
periodic and approximately sinusoidal as illustrated in FIG. 13A.
The period of wavelength response or signal is equal to about one
cycle per wrap of the fiber 30 around the object 10. The amplitude
of the periodic signal is determined by the magnitude of shear
forces 210, 220. The wavelength response in FIG. 13A is positioned
adjacent the object 10 in FIG. 13 to illustrate points of strain on
the object 10 and the corresponding wavelength response produced as
a result of such strain. For example, the strain on the object 10
between the shear forces 210, 220 is minimal compared to the strain
on the object 10 near each shear force 210, 220 as illustrated by
the maximum wavelength response 230 and minimal wavelength
responses 240A, 240B. The minimal wavelength responses 240A, 240B
also illustrate how the shear forces 210, 220 cause the object 10
to compress and stretch (in tension), respectively. The application
of pre-positioned strain sensors 20 on the object 10 thus, enables
in-situ detection of strain on the object 10, which can be
translated through well-known conventional means and imaged in real
time.
[0165] Another effect of fracturing is local compaction. Axial
compaction is commonly measured with radioactive tags and special
logging tools, which typically requires shutting in the well.
Measurement of strain on the tubular object or casing below one
percent is difficult to achieve, however, with these conventional
techniques. At higher strains, a bend or a buckle in the casing or
tubular object is also difficult to detect without pulling the
production tubing and running acoustic or mechanical multi-finger
calipers or gyroscopes into the well.
[0166] The disadvantages associated with conventional means of
detecting and measuring strain induced by axial compaction may be
avoided with pre-positioned strain sensors. In other words, the
application of pre-positioned strain sensors on the object may be
used for in-situ detection and measurement of axial compaction
forces in the manner described above.
EXAMPLE 2
Axial Compaction
[0167] In this example, accurate measurements of low strain and
high sensitivity to bending or buckling induced by axial compaction
are important objectives. A thin-walled PVC pipe was tested using
the weight of the pipe, horizontally suspended by its ends, as the
applied force. A preferred wrap angle of about 20 degrees was used
to apply the strain sensors and optical fiber to a 3-meter
(10-foot) long section of the pipe with a 16.5-centimeter
(6.5-inch) diameter. A 5-centimeter strain sensor spacing was used
to resolve the wavelength response from a buckle or a bend.
[0168] In FIG. 14, the wavelength response resulting from the
lateral force applied by the weight of the pipe is illustrated. A
maximum lateral offset of about 1.78 mm (0.07 inches) was detected.
The wavelength response in FIG. 14 clearly reveals a bend or a
buckle because one period or cycle of the wavelength response
corresponds to one wrap of the fiber. A 1.78 mm (0.07-inch) lateral
offset represents less than a 7-degree bend or buckle for each one
hundred-foot section of the pipe, which is significant and can be
detected by conventional caliper and acoustic imaging tools. In
order to run such tools into the well, the well must be shut in and
the production tubing must be pulled.
EXAMPLE 3
Bending
[0169] In this example, the same pipe was tested using a weight
hung from the center of the pipe, which was horizontally suspended
at each end. The lateral offset due to a bend is about 5.791
millimeters (0.228 inches). As illustrated in FIG. 15, a relatively
clean periodic signal is apparent everywhere except at the ends and
at the center of the wavelength response where the weight is
hanging and distorting the signal. The distorted signals are a
special case related to pipe crushing caused by local loading on
the pipe.
[0170] FIG. 16 represents a simple illustration of a lateral force
on the object 10 induced by axial compaction. Here the object 10 is
subjected to a lateral force 310 on one side of the object 10. The
wavelength response, representing strain on the object 10 measured
by strain sensors 20, associated with the lateral force 310 is
periodic and approximately sinusoidal as illustrated in FIG. 16A.
The period of the wavelength response or signal is equal to about
one cycle per wrap of the fiber 30 around the object 10. The
amplitude of the periodic signal is determined by the magnitude of
the lateral force 310. The wavelength response in FIG. 16A is
positioned adjacent the object 10 in FIG. 16 to illustrate points
of strain on the object 10 and the corresponding wavelength
response produced as a result of such strain. For example, the
strain on the object 10 near the lateral force 310 is greater
compared to the strain on the object 10 at each end as illustrated
by the maximum wavelength responses 330A, 330B and the minimal
wavelength response 320. The maximum wavelength responses 330A,
330B also illustrate how the lateral force 310 causes the object 10
to compress and stretch (in tension), respectively.
EXAMPLE 4
Ovalization
[0171] In addition to detecting a bend or a buckle, the onset of
ovalization or crushing forces may also be detected and
distinguished from a bend or a buckle. A pure ovalization or
crushing force should produce a pure ovalization wavelength
response. In this example, the same pipe was tested with clamps
that were applied as a crushing force near the center of the pipe
and slightly tightened with the orientation of the applied force
aligned across the diameter of the pipe so as to slightly decrease
its cross-sectional diameter. The resulting wavelength response is
illustrated in FIG. 17, and reveals a period of about two cycles
per wrap as opposed to one cycle. In this example, the minimum
diameter is decreased by 1.27 millimeters (0.05 inches) due to the
applied crushing force.
EXAMPLE 5
[0172] In this example, the same pipe was tested by rotating the
clamps near the center of the pipe 90 degrees. The resulting
wavelength response is illustrated in FIG. 18, and also reveals a
period of about two cycles per wrap. In this example, the minimum
diameter is decreased by 1.78 millimeters (0.07 inches).
[0173] The increased strain (and therefore deformation) is obvious
when comparing FIG. 17 and FIG. 18. It is a simple matter to scale
the resulting shift in wavelength to a strain and the resulting
strain to a relative crushing.
[0174] FIG. 19 represents a simple illustration of a crushing force
on the object 10 induced by axial compaction. Here, the object 10
is subjected to a crushing force 410 on all sides of the object 10.
The wavelength response, representing strain on the object 10
measured by strain sensors 20, associated with the crushing force
410 is a substantially constant periodic signal as illustrated in
FIG. 19A. The period of the wavelength response or signal is equal
to about two cycles per wrap of the fiber 30 around the object 10,
which is easily distinguished from the wavelength response
exhibited by a bend or a buckle discussed in the examples above.
The amplitude of the periodic signal is determined by the magnitude
of the crushing force 410. The wavelength response in FIG. 19A is
positioned adjacent the object 10 in FIG. 19 to illustrate points
of strain on the object 10 and the corresponding wavelength
response produced as a result of such strain. For example, the
strain on the object 10 is substantially constant around the object
10 as illustrated by the substantially constant wavelength
responses 420A, 420B.
[0175] In FIG. 19B, an end view of FIG. 19 illustrates the crushing
force 410 and the resulting deformation of the object 10
illustrated by the dashed line 430.
[0176] FIG. 20 further illustrates the relative strain amplitude
(W.sub.A), as measured by a wavelength response in the FBG sensor
or other stain sensor or transducer, as a function of azimuth
around a tubular object subjected to a crushing force. The maximum
compressive strain (negative signal) occurs at 0 (or 360) and 180
degrees. The maximum tensile strain (positive signal) occurs at 90
and 270 degrees. The neutral stain occurs at 45, 135, 225, and 315
degrees.
EXAMPLE 6
Decreased Sensitivity
[0177] In this example, the sensitivity is decreased to allow for
measurements of higher axial strains (.epsilon..apprxeq.2 percent)
on a tubular object. As the structural material begins to undergo
plastic deformation, the Poisson ratio (.nu.) will tend towards 0.5
in the limit of plastic deformation. In FIG. 21, the solid line
plots the strain factor m as a function of wrap angle .theta.,
assuming .nu.=0.50 and .epsilon..apprxeq.2.0 percent. Therefore,
according to FIG. 21, a wrap angle of approximately
.theta..sub.1=30 degrees or greater is preferred. For example, a
wrap angle of 30 degrees will yield a strain factor (m) of 0.15,
which translates to a strain of 1.5 percent in the fiber for a 10
percent strain on the object. A wrap angle of 20 degrees would
yield a strain factor of 0.33, which would translate to a strain of
3.3 percent and would break or damage the fiber. The preferred wrap
angle could be slightly higher (about 35 degrees) to more nearly
null out the applied strain on the fiber (m=0) when very high axial
strains on the tubular object (on the order of 10 percent) are
expected and when the intent is to measure buckling rather than
axial strain. The dashed line in FIG. 21 shows the nm shift on the
right hand axis.
[0178] FIG. 22, illustrates the wavelength shift (.DELTA..lamda.,
in nm) for various levels of pure applied axial strain
(compression) on the same tubular object, plotted versus the
grating number (D.sub.N). In FIG. 22, the lines and their
associated axial strains are identified as follows: 16a=0.1% axial
strain; 16b=0.2% axial strain; 16c=0.3% axial strain; 16d=0.4%
axial strain; 16e=0.5% axial strain; 16f=0.75% axial strain;
16g=1.0% axial strain; 16h=1.25% axial strain; and 161=1.5% axial
strain. The signal at a 30-degree wrap angle is reduced from that
of a 20-degree wrap angle, as described in reference to FIG. 21.
The reduction in signal as a function of wrap angle thus, follows
the form shown in FIG. 21 and the strain factor (m) equation
described above.
[0179] A 30-degree wrap angle should easily accommodate and measure
up to five percent axial strain while imparting only a fraction of
that strain to the fiber. As the axial strain increases, the onset
of buckling and other higher modes of deformation are revealed by
the periodic nature of the wavelength response.
[0180] Even though FIG. 22 reveals the onset of tubular buckling,
the overall wavelength response remains substantially linear as
axial strain increases. This concept is further illustrated in FIG.
23, which compares the average (.quadrature.), the peak
(.diamond-solid.) and the root-mean-square (rms) (.times.)
wavelength response .DELTA..lamda. with the calculated (-) or
expected wavelength response at various levels of applied axial
strain .epsilon..sub.a. At about 1.5 percent axial strain, the peak
reading begins to diverge slightly from a linear response as the
structural material begins to slightly buckle.
[0181] One of the most sensitive areas in a well to compaction and
deformation is the completion zone. This is particularly true in
highly compacting unconsolidated formations in which sand control
is required.
[0182] In order to control formation areas comprising sand, the
base pipe is usually fitted with a filter, commonly referred to as
a sand screen. A gravel pack (carefully sized sand) may also be
used between the sand screen and the outer casing or formation. The
sand screen may comprise a conventional sand screen wire wrap and
multiple other conventional screen components (hereinafter referred
to as a screen assembly). The wire wrap in the screen assembly is
designed to allow fluid to flow through openings that are small
enough to exclude large particles.
[0183] High axial strain imposed on the base pipe can close the
wire wrap openings and impair fluid flow. Bends or buckles in the
base pipe may also compromise the structural integrity of the
screen assembly, thereby causing a loss of sand control. In this
event, the well must be shut in until repairs can be made. Such
failures require, at a minimum, a work over of the well and in
extreme cases, a complete redrill. Consequently, monitoring the
object for bends, buckles and axial strain in the completion zone
is preferred-particularly where sand control is required.
Accordingly, the strain sensors may be applied to the base pipe
and/or screen assembly at about a 20-degree wrap angle.
EXAMPLE 7
[0184] In this example, a 914-millimeter (36-inch) tubular object
having about a 76-millimeter (3-inch) diameter and a Poisson ratio
(.nu.) of about 0.5, was tested in a controlled environment using a
21-degree wrap angle for the application of the strain sensors and
fiber. Various amounts of axial strain .epsilon..sub.a were applied
at each end of the object, which was otherwise unsupported. The
average wavelength response (actual, .diamond-solid.) over the
applied strain sensors at each level of applied axial strain is
compared to the calculated wavelength (.quadrature.) response in
FIG. 24. At about 0.05 percent strain, there is a departure from
the linear calculated wavelength response suggesting a bend or a
buckle is beginning to form in the object tested.
[0185] The following Figures (FIGS. 25, 26 and 27) progressively
illustrate why a departure from the calculated wavelength response
occurs and how it can be used with a periodic signal to detect and
determine the magnitude of the bend or buckle in the same object
tested. For convenience, a vertical representation of the tubular
object, as it reacts to the applied axial strain, is illustrated
(in black) in the middle of FIGS. 25, 26 and 27. In FIGS. 25, 26
and 27, wavelength shift .DELTA..lamda. (nm) is plotted against
grating number (D.sub.N). In FIG. 25, the applied axial strain is
nominal or about zero.
[0186] In FIG. 26, applied axial strain is 0.25 percent. In FIG.
27, the applied axial strain is increased to 0.75 percent. In FIG.
26, the wavelength response illustrates the applied strain,
however, there is no apparent deformation in the object.
[0187] In FIG. 27, the wavelength response is noticeably greater
than the wavelength response in FIG. 26, and there appears to be a
bend or a buckle in the object. As the axial strain applied to each
end of the object increases, the object is compressed, which causes
deformation in the form of a bend or a buckle.
[0188] FIG. 28 represents a simple illustration of pure axial
strain (force) applied to the object 10. Here, the object 10 is
subjected to an axial force 520. The wavelength response 530,
representing strain on the object 10 measured by the strain sensors
20, associated with the axial force 520 is substantially constant
as illustrated in FIG. 28A. Thus, the axial force 520 causes the
object 10 to shorten or compress and expand in the direction
indicated by the arrows 510. As a result, the wavelength response
530 is substantially constant until the object 10 begins to deform
in the shape of a bend or a buckle as demonstrated by the
progressive illustration in FIGS. 25, 26 and 27, above.
[0189] One of the areas in the well where the least amount of
strain is likely to occur in compacting reservoirs is in the
overburden. The highest tensile strains are usually observed very
near the compacting zone and the magnitude of the strain reduces as
the distance from the compacting zone increases. This is reflected
in the theoretical plot in FIG. 29, plotting delta strain
(.DELTA..epsilon.) versus the distance (d) along the line (in feet)
as Delta S.sub.ext ZZ (*), wherein the reservoir is undergoing 8.0
percent compaction strain and the maximum extensional strain in the
overburden is 1.0 percent.
[0190] The actual magnitude of the extensional strain in the
overburden just above the reservoir is highly dependent upon the
reservoir geometry and the material properties of the reservoir and
overburden. The ratio of the extensional strain just above the
reservoir to the compressional strain in the reservoir can be used
as one diagnostic for reservoir performance. Likewise, the amount
of a tensional strain in the overburden affects such things as
seismic signals used for 4D seismic measurements. Thus, the fiber
and strain sensors are preferably applied at about 90 degrees
longitudinally along the object to increase sensitivity to tensile
strains. When the fiber and strain sensors are positioned on a
tubular object specifically designed for monitoring such strain, a
very accurate measurement can be made.
[0191] Furthermore, three or more fibers containing strain sensors
may be longitudinally and equidistantly positioned around the
tubular object in order to detect not only axial strain on the
object but also bending strain. The strain on the outside of the
radius of curvature of the bend or buckle will be higher (in
tension) than the strain on the inside radius. Thus, when 3 or more
fibers containing strain sensors are positioned in this manner, the
detection and measurement of a long radius bend is possible through
the uneven wavelength response.
[0192] Applying the string of sensors to the cylindrical object at
the preferred wrap angle is not limited to actually spiraling the
string around the object such as is exemplified in FIG. 7. As
illustrated in FIGS. 30 and 30A, the string, in the form of an
optical fiber 30, of strain sensors, preferably of the FBG-type,
has been applied on the cylindrical object 10 in a selected zig-zag
pattern 25. Here, FIG. 30 shows a perspective view of the object 10
with the optical fiber 30, while FIG. 30A shows a cylindrical
projection thereof. It is remarked that for reasons of clarity, the
strain sensors have not been explicitly indicated in FIG. 30A, nor
in the remaining FIGS. 31 to 35.
[0193] The zig-zag pattern comprises first and second application
lines, schematically represented in FIG. 30 by dashed lines 21 and
21', respectively. A first portion 20 of the strain sensors is
applied along the first application line 21 and a second portion
20' of the strain sensors is applied along the second application
line 21'. As best viewed in FIG. 30A, the first application line 21
extends on the exterior surface of the cylindrical object 10 at a
first preferred wrap angle .theta..sub.1 within a preferred first
wrap angle range that lies between 0 and 90.degree. from an
imaginary line perpendicular to the longitudinal axis. The second
application line 21' extends at a second preferred wrap angle
.theta..sub.1' within a preferred second wrap angle range that lies
between 90 and 180.degree.. The angles 0.degree., 90.degree., and
180.degree. are excluded from the first and second wrap angle
ranges.
[0194] As explained above, the preferred first wrap angle may also
be represented by .theta..sub.2=90.degree.-.theta..sub.1 to
represent the angle with the longitudinal axis. Likewise, the
preferred second wrap angle be represented relative to the
longitudinal axis as .theta..sub.2'=90.degree.-.theta..sub.1'.
[0195] The preferred first and second wrap angles may be determined
as described above, and may be based on first and/or second strain
factors.
[0196] The preferred second wrap angle may be chosen equal to
180.degree. minus the first preferred wrap angle, resulting in a
zig-zag pattern of two constant helicities of opposite parity.
However, the zig-zag pattern allows for two distinct wrap angles
corresponding to different strain factors.
[0197] The zig-zag pattern moreover allows for easy application of
the string of strain sensors without the need of continuously
wrapping.
[0198] As depicted in FIGS. 30 and 30A, the optical fiber, between
the first portion 20 of the strain sensors and the second portion
21' of the strain sensors, makes a loop 27 over a loop angle of
more than 180.degree.. This allows for an effectively sharp zig-zag
pattern without having to bend the optical fiber too much. A
minimum bend radius, specified for the fiber, may be
maintained.
[0199] When the loop angle equals 180.degree. plus the included
angle between the first application line and the second application
line, the string of strain sensors can enter and exit the loop in
directions along the respective application lines.
[0200] This loop is preferably mechanically decoupled, or at least
strain-isolated from the object, such that the fiber in the loop is
not significantly strained due to deformation of the object. When
the loop moreover comprises a third portion 20'' of the strain
sensors, the signal from such free loops 27 provides a calibration
point in the signal image because the signal originating from the
third portion 20'' of strain sensors is not significantly subject
to deformation strain caused by the object 10. In fact, the free
loops 27 allow for an integral temperature measurement because the
signal originating from the third portion 20'' of the strain
sensors is predominantly governed by temperature changes. Such
temperature measurement may be used to separate a contribution in
the signal from the first and second portions of the strain sensors
of deformation of the object from a temperature effect the
signal.
[0201] As explained above, the string of strain sensors may be
applied to the object in at least one of a protective sheath and a
protective sheet.
[0202] The string of strain sensors may be mechanically coupled, in
the selected zig-zag pattern, to a pliable support structure 60, as
schematically depicted in FIGS. 31 and 26.
[0203] The term "pliable support structure" includes not only
support structures formed from a pliable or compliant material but
also support structures comprising two or more relatively rigid
parts that are movable relative to each other to convey pliability,
such as pivotably inter-hinged shell parts or separate shell parts
that may be interconnected after bringing them together.
[0204] FIG. 31 shows an elevated view of the pliable support
structure 60 with the string of strain sensors in the form of an
optical fiber 30 with FBG type sensors (not shown). In the
embodiment as depicted, the free loops 27 reach beyond the
longitudinal edges 62L and 62R of the pliable support structure 60.
These loops may be protected by protective covers 65, which may be
provided in the form of protective sheets, bands, layers, tabs,
etc.
[0205] The pliable support structure 60 is capable of being draped
around the cylindrical object 10. FIG. 32 shows the cylindrical
object 10 with the pliable support structure 60 draped around it.
The longitudinal edges 62L and 62R are shown abutted against each
other in longitudinal direction relative to the cylindrical object.
Of course, the seam line formed by the edges may be straight or
corrugated, and may abut, overlap or leave a gap between them when
draped around the object 10. The seam may run in a generally
longitudinal direction such that the pliable support structure is
easily draped around the cylindrical object without the need of
wrapping it around the object.
[0206] The selected zig-zag pattern of the string of strain sensors
on the pliable support structure may comprise first and second
application lines extending in mutually differing directions
defining an included angle between the first and second application
lines of less than 180.degree.. The application lines each extend
in an essentially straight fashion within the plane of the support
structure. When draped around the object, the application lines
then follow the curvature of the object in an otherwise straight
line. A first portion of the strain sensors is mechanically coupled
to the pliable support structure along the first application line
and a second portion of the strain sensors is mechanically coupled
to the pliable support structure along the second application
line.
[0207] The fiber 30 has been visibly depicted in FIG. 32 to enhance
the understanding. However, the fiber 30 is not necessarily on the
exterior surface of the pliable support structure when draped
around the object 10. The fiber 30 may be sandwiched between the
pliable support structure and the object, or it may for instance be
sandwiched inside exterior layers of the pliable support structure,
or it may for instance be buried within a single layer of the
pliable support structure. The fiber may be located in a conduit
such as is described in embodiments above. The fiber may also be
integral to the pliable support structure.
[0208] Once draped around the cylindrical object, the pliable
support structure may be held in place in any suitable way,
including one or more of a zipper, straps, clamps, adhesive,
Velcro.RTM., or combinations of such means.
[0209] In a first group of embodiments, the pliable support
structure may be made of a generally compliant material, such as a
cloth, a blanket, a sheet, a fabric. A fabric may be woven from
strands, including strands comprising metal wires and/or epoxy
fiber glass combined with an elastomer such as comprising a butyl
rubber. A cloth may be formed of a metallic cloth. A sheet may
comprise a rubber sheet.
[0210] The pliable support structure may be more compliant than the
material of the cylindrical object around which it is to be
draped.
[0211] This group of embodiments may be stored on a spool 70, such
as is depicted in FIG. 33. In this figure, a number of pliable
support structures (60A, 60B, 60C, etc.) have been combined on a
continuous protective cover 66 to facilitate the application of the
pliable support structures to one or more cylindrical objects as
well as to protect the connecting optical fiber 30 between
neighboring pliable support structures and/or the free loops
27.
[0212] The spool 70 may be transported to a rig site, and used to
facilitate the act of draping of the pliable support structures
around a tubular object, such as for instance a casing 10, while it
is suspended in the rig. One of the pliable support structures may
paid out from the spool 70, separated from the protective cover 66,
and positioned against the tubular object 10 between two joints.
Subsequently, it may be draped around the tubular object 10 and
fastened to it. Protective rings, such as centralizers or clamps
shown in FIG. 34 at 80, may be provided over the joints and/or
collars to protect the fiber cable passing from one support
structure (e.g. 60B) to a next support structure (e.g. 60C).
[0213] The fiber 30 may be a continuous fiber, or it may be
provided with fiber connectors, preferably "dry-mate" type fiber
optic connectors, between subsequent pliable support structures on
the spool. In the case of the latter, the fiber connectors may
suitably be connected before applying the protective rings 80 so
that the connectors may also be protected underneath the protective
rings.
[0214] It will be appreciated that the application of a string of
strain sensors employing the pliable support structure, as
described here, in particular in a rig site environment, is
beneficial not only to strings of strain sensors arranged in a
zig-zag pattern but to strings laid out in any pattern, including
longitudinal strings of sensors and/or axially aligned strings of
sensors or generally meandering strings of sensors.
[0215] In a second group of embodiments, the pliable support
structure is provided in the form of a clamshell structure. An
example is shown in FIGS. 35A and 35B, where FIG. 35A shows on
perspective view and FIG. 35B shows another perspective view. Such
a clamshell structure may comprise at least first and second shell
parts comprising cylindrical sections 90, 90A each having a concave
interior and a convex exterior surface, each having left (91
respectively 91A) and right longitudinal edges (92, 92A). The shell
parts are hinged one to another along two longitudinal edges, for
instance the right edge 91A of the cylindrical section 90A with the
left edge 92 of the cylindrical section 90. The hinges 94 allow for
a pivotable rotation of one cylindrical section 90 relative to the
other cylindrical section 90A about the longitudinal axis.
[0216] The first and second shell parts may be relatively rigid,
whereby the pivotable rotatability provides pliability to the
clamshell structure. "Pliability" may also be achieved by providing
two or more separate clam shell parts that are connected to one
another after draping them around the cylindrical object, for
instance by means of a latching mechanism or by means of bands
binding the clam shell parts in place. The zig-zag pattern of the
string of sensors in one of the shell parts could match or
complement that of the pattern in the other of the shell parts.
[0217] The fiber 30 has been depicted as mechanically coupled to
the concave surface of the shell parts, with free loops 27
extending beyond the edges 91 and 92A which mark the extrema or
turning points of the zig-zag pattern.
[0218] Free loops 28 are also provided at the hinged edges 91A and
92 to allow flexibility facilitating the rotational movement of the
shell parts. Similar to the first group of embodiments, each or any
of the free loops 28 may be protected from impacts from the
outside, by a protective cover.
[0219] The clamshell structures may be draped around the tubular
object depicted in FIG. 34. The clamshell structure is contemplated
to be of particular relevance for draping around a screen assembly
but it can also be of relevance of draping around several pipe
elements joined in a pipe string. In any case, the shell parts may
have an open structure such as to allow passage of fluid there
through. Open structure may be provided by forming the clam shell
parts from a perforated sheet or expanded metal sheet rather than a
metal sheet. Similarly shaped polymeric or composite materials may
also be employed.
[0220] FIG. 36 shows how a plurality of clam shell parts (90, 95,
100) may be stacked together prior to their draping around the pipe
elements. In these embodiments, the strings of sensors are
connected between the clam shell parts by means of a flexibly
protected connective cable 96.
[0221] When draping these shell parts around the cylindrical
object, a first shell part would be attached and subsequent
adjoining shell parts would be fed off of the stack as they are
draped around the cylindrical object. At a rigsite, the cylindrical
object could gradually be lowered into the well as the next shell
parts are being draped around. The draping may also occur
simultaneously with making up the tubular joints in the slips.
[0222] The plurality of clam shell parts may be stacked in a
holding box or rack that could be moved laterally and/or
vertically, and/or rotated so as to feed the adjoining joints
without damaging the interconnecting flexible cables 96.
[0223] FIG. 37 shows a variation of FIG. 36, wherein couples of
pivotably hinged shell parts (90+90A; 95+95A) are stacked and
connected via the flexibly protected connective cable 96.
[0224] FIG. 38 shows a schematic perspective view of clam shell
parts 95 and 95A provided with a latching mechanism comprising
brackets 97 and 97A mounted to the clam shell parts in close
vicinity of the respective longitudinal edges 98 and 98A. The
brackets 97 and 97A are provided with longitudinally aligned
cylindrical bores 99 and 99A, through which a locking pin 101 may
be inserted after the set of brackets of one of the clam shells
have been longitudinally aligned with the set of brackets of the
other.
[0225] It will be appreciated that the string of strain sensors may
be mechanically coupled to the exterior convex surface of the
clamshell structure, and it may also be sandwiched between an inner
and an outer shell of each shell part. Such an inner and/or outer
shell part may be formed by, for instance, a relatively thin and
compliable protective sheet adhered to the other outer and/or inner
shell part.
[0226] At least one of the clam shell parts may cover more than
half a circle so that at least one free longitudinal edge of at
least one of the shell parts overlaps the mating longitudinal edge
of another adjacent shell part. Such overlap may be provided with a
protective housing space to accommodate free loops.
[0227] It will also be appreciated that the clamshell structure may
comprise three or more shell parts each hinged one to another to
form a chain. Free loops 28 may be provided at each hinging
edge.
[0228] In both groups of embodiments, the protective cover 65 may
be part of a closure mechanism. For instance, the latching brackets
97 and 97A shown in FIG. 38 may be sized and positioned to
accommodate the free loops 27 so as to be loose buffered, or strain
free decoupled from the cylindrical object.
[0229] In one example schematically shown in FIG. 39, the brackets
97 are provided with a cavity 102 to form a housing for
accommodating at least the free loops 27 of the string of sensors.
The cavity 102 may be less deep than the thickness t of the
brackets but deep enough for accommodating the string of sensors
30. The cavity may be of any suitable shape, including square,
rectangular, polygon, oval, ellipsoid, circular or it may be shaped
as a groove that accommodates the string of sensors 30. Such a
cavity 102 may be formed in the brackets in any suitable manor,
including by machining or molding.
[0230] Similarly, the free loops 27 may be accommodated in tabs or
sheets as for instance shown at 65 in FIG. 31.
[0231] Such protective covers also protects the string of sensors
against the cement if the cylindrical object concerns, for
instance, a casing that is cemented into a well. Otherwise, the
loops that are intended to be free loops may become mechanically
coupled to the cement.
[0232] The above described application of the plurality of
transducers in a zig-zag pattern may be employed in a method of
imaging deformation of an object, as will now be illustrated with
reference to FIG. 40. This Figure shows expected wavelength shift
(.DELTA..lamda.) on a given strain sensor grating plotted, on the
left vertical axis, against axial position (Z) of that strain
sensor grating along a tubular object.
[0233] The tubular object had a diameter of 17.78 cm (7 inch) and a
Poisson's ratio of 0.3, and the response of each sensor has been
calculated from expected local bend radii at the sensor locations
along the application lines of the sets of sensors, resulting from
subjecting the tubular object to an S-bend. The local bend radii
together form the S-bend as shown in line 33 in FIG. 40 against the
right-hand axis which plots the center of the tubular object
relative to the original axial position of the object. The object
is offset by 24 cm (9.5 inches) over an axial length of 3.6 m (12
feet). Such an offset may in realistic circumstances occur across a
boundary in the earth that is shearing, for instance across a fault
or a horizontal slip layer.
[0234] The calculations were made in respect of a first set of
optical strain sensor gratings spiral wrapped around the tubular
object at a wrap angle of 20.degree., and in respect of a second
set of optical strain sensor gratings draped around the tubular
object under a zig-zag pattern employing first and second wrap
angles of 20.degree. and 160.degree..
[0235] Line 31 in FIG. 40, with x-shaped data symbols, shows the
expected wavelength shift response for each sensor in the first
set. It shows a similar sinusoidal behavior as schematically
illustrated in FIG. 7A. Line 32, in diamond marks, shows the
expected wavelength response of each sensor in the second set. The
first and second sets give identical responses when they have the
same wrap angle on the structure. However, when the orientation of
the zig-zag drape changes the sign of the wavelength shift signal
reverses.
[0236] The signal from the square-marked strain sensors 34
originate from strain sensors in the loop parts of the second set,
that are not mechanically coupled to the tubular object. They show
zero wavelength shift, as they are not strained due to object
deformation. Any wavelength shift associated in these strain
sensors would be due to temperature and pressure effects and
therefore can be used to adjust for such effects on the object. The
loops also provide an orientation key that allow the direction of
any bending in the object to be ascertained.
[0237] The present invention may be utilized to detect and monitor
deformation of any substantially cylindrical object in an earth
formation, for example in a well bore, caused by structural strain.
As described herein, the present invention may be uniquely tailored
to detect and measure axial compaction, shear, bending, buckling,
and crushing (ovalization) induced strain on the well bore object
due to fracturing the formation.
[0238] Accordingly, the cylindrical object may be provided in the
form of a wellbore tubular, such as for instance a drill pipe, a
production tube, a casing tube, a tubular screen, a sand
screen.
[0239] In particular when employed on a casing tube or a production
tube, the methods described above may be used in a method of
producing a mineral hydrocarbon fluid from an earth formation,
comprising:
[0240] applying the string of interconnected strain sensors to the
cylindrical object in the form of a casing tube, a production tube,
or a screen;
[0241] inserting the cylindrical object into a wellbore in the
earth formation;
[0242] producing the mineral hydrocarbon fluid through the
cylindrical object.
[0243] The strain and bending condition of the cylindrical object
can thus be monitored during production and completion, such that
preventive and/or remedial action may be taken to maximize the
production efficiency in under the given circumstances.
[0244] It is therefore, contemplated that various situations,
alterations and/or modifications may be made to the disclosed
embodiments without departing from the spirit and scope of the
invention as defined by the appended claims and equivalents
thereof.
* * * * *