U.S. patent application number 10/412915 was filed with the patent office on 2003-11-27 for method of detecting signals in acoustic drill string telemetry.
This patent application is currently assigned to Baker Hughes Incorporated. Invention is credited to Jogi, Pushkar, Kingman, John.
Application Number | 20030218940 10/412915 |
Document ID | / |
Family ID | 29401383 |
Filed Date | 2003-11-27 |
United States Patent
Application |
20030218940 |
Kind Code |
A1 |
Jogi, Pushkar ; et
al. |
November 27, 2003 |
Method of detecting signals in acoustic drill string telemetry
Abstract
A method of acoustic telemetry in a drill string in a wellbore,
comprises transmitting an acoustic signal related to a parameter of
interest from a transmitting location into the drill string. The
signals propagated through the drill string are detected at a
receiving location, where the detected signals include noise. A
drill string transfer matrix is determined defining the propagation
of signals through a transfer interval between the receiving
location and the transmitting location. The detected signals and
the drill string transfer matrix are used for obtaining an estimate
of the acoustic signal.
Inventors: |
Jogi, Pushkar; (Houston,
TX) ; Kingman, John; (Grand Junction, CO) |
Correspondence
Address: |
PAUL S MADAN
MADAN, MOSSMAN & SRIRAM, PC
2603 AUGUSTA, SUITE 700
HOUSTON
TX
77057-1130
US
|
Assignee: |
Baker Hughes Incorporated
Houston
TX
|
Family ID: |
29401383 |
Appl. No.: |
10/412915 |
Filed: |
April 14, 2003 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60376637 |
Apr 30, 2002 |
|
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|
Current U.S.
Class: |
367/82 |
Current CPC
Class: |
G01V 11/002 20130101;
E21B 47/16 20130101 |
Class at
Publication: |
367/82 |
International
Class: |
H04H 009/00 |
Claims
What is claimed is:
1. A method of acoustic telemetry in a drill string in a wellbore,
comprising: a. transmitting an acoustic signal related to a
parameter of interest from a transmitting location into the drill
string; b. detecting signals propagated through the drill string at
a receiving location, said detected signals including noise; c.
determining a drill string transfer matrix defining the propagation
of signals through a transfer interval between the receiving
location and the transmitting location; and d. using said detected
signals and the drill string transfer matrix for obtaining an
estimate of the acoustic signal.
2. The method of claim 1 wherein detecting signals at a receiving
location comprises detecting a first time-series of measurements
related to a force on said drill string and a second time-series of
measurements related to a motion of said drill string.
3. The method of claim 2 wherein using said detected signals and
the drill string transfer matrix for obtaining an estimate of the
acoustic signal comprises: a. transforming said first time-series
of measurements and said second time-series of measurements to a
frequency domain; b. combining said transformed first time-series
of measurements and said transformed second time-series
measurements with said transfer matrix to generate an inferred
force related signal at said second location and an inferred motion
related signal at said second location; c. transforming said
inferred force related signal and said inferred motion related
signal to the time domain generating an inferred time-series force
at said second location and an inferred time-series motion at said
second location; and d. decoding said inferred force signal and
said inferred motion signal to determine said transmitted parameter
of interest.
4. The method of claim 1 wherein determining the drill string
transfer matrix comprises: i. inputting data related to mechanical
properties and material properties for each of a plurality of
sections of the drill string; ii. calculating for each of the
plurality of sections of the drill string, a transfer matrix
related to each section of the drill string; and iii. combining
each of the plurality of section transfer matrices with each
succeeding section transfer matrix.
5. The method of claim 1 wherein the transmitting location is a
downhole location proximate a bottom end of the drill string and
said receiving location is proximate a top end of the drill
string.
6. The method of claim 1 wherein the transmitting location is
proximate a top end of the drill string and the receiving location
is downhole proximate a bottom end of the drill string.
7. The method of claim 2, wherein the measurement related to drill
string motion is one of (i) an acceleration, (ii) a velocity, and
(iii) a displacement.
8. The method of claim 2 wherein using said detected signals and
the drill string transfer matrix for obtaining an estimate of the
acoustic signal comprises: i. transforming said transfer matrix to
a time domain; ii. combining said first time-series of measurements
and said second time-series of measurements with said transformed
transfer matrix to generate an inferred force related signal at
said second location and an inferred motion related signal at said
second location; and iii. decoding said inferred force signal and
said inferred motion signal to determine said transmitted parameter
of interest.
9. The method of claim 3, wherein the step of transforming said
first time-series of measurements and said second time-series of
measurements includes windowing said first time-series of
measurements and said second time-series of measurements.
10. The method of claim 3, wherein the step of transforming said
inferred force related signal and said inferred motion related
signal to the time domain includes band-limiting said inferred
force related signal and said inferred motion related signal in the
frequency domain before transformation to the time domain.
11. A method of reducing noise in an acoustic signal transmitted at
a second location and received at a first location in a drill
string, comprising: a. calculating a transfer matrix related to a
transmission interval of the drill string; b. detecting time series
data sets of vibrations at said first location comprising a first
time-series data set of measurements related to a force on said
drill string and a second time-series data set of measurements
related to an acceleration of said drill string; c. transforming
said first time-series data set and said second time-series data
set to a frequency domain; d. combining said transformed first
time-series data set and said transformed second time-series data
set with said transfer function to generate an inferred force
related signal at said second location and an inferred acceleration
related signal at said second location; and e. transforming said
inferred force related signal and said inferred acceleration
related signal to the time domain generating an inferred
time-series of force at said second location and an inferred
time-series of acceleration at said second location.
12. The method of claim 11 wherein calculating the drill string
transfer matrix comprises: i. calculating for each of a plurality
of drill string sections, a transfer matrix related to each section
of the drill string; and ii. combining each of the plurality of
section transfer matrices with each succeeding section transfer
matrix.
13. The method of claim 11 wherein the second transmitting location
is a downhole location proximate a bottom end of the drill string
and said first receiving location is proximate a top end of the
drill string.
14. The method of claim 11 wherein the second transmitting location
is proximate a top end of the drill string and the first receiving
location is downhole proximate a bottom end of the drill string.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] This invention is in the field of signal processing, and is
more specifically directed to acoustic drill string telemetry.
[0003] 2. Description of the Related Art
[0004] The petroleum industry relies heavily on the operation of
drilling into the earth, both on land and offshore, in the
exploration for and production of petroleum products. Over the
years, the more readily found and accessible petroleum reservoirs
have of course been discovered and depleted first. As a result, the
exploration and production operations must necessarily concentrate
to a greater degree on less accessible and less readily
discoverable reserves. In order to reach these locations, the
depths of drilling have increased, the locations at which drilling
takes place have become increasingly difficult and less accessible,
and the drilling operations have necessarily become more complex.
Accordingly, drilling operations in the search for and production
of petroleum products have become more expensive, with this trend
likely to continue in the future. Because of this increasing cost,
the accuracy and efficiency of the drilling operation is becoming
even more important.
[0005] The success and efficiency of the drilling operation depends
to a large degree on the quantity and quality of information that
the drilling operator has about the sub-surface structure into
which the drilling is taking place, and also about parameters
concerning the operation of the drill bit as it proceeds into the
earth. Many techniques for acquisition and communication of such
information have been tried and used in the industry.
[0006] A system which utilizes the drill string as a medium for the
transmission of data is referred to as acoustic telemetry or stress
wave telemetry. Acoustic telemetry systems are known in the art.
For example U.S. Pat. No. 5,477,505 to Drumheller and U.S. Pat. No.
5,303,203 to Kingman describe such systems. The typical system
includes transmitters, such as solenoids, eccentric motors, and
piezoelectric transducers, which intentionally vibrate the drill
string in a manner corresponding to the desired data. These data
may include information concerning drilling parameters and
formation parameters. In the case of stress wave telemetry the
desired information is obscured by undesirable bit and drilling
noise that is also transmitted through the drill string.
[0007] It has been discovered that vibrations, whether from the
drill bit itself or intentionally generated by transmitters, are
not communicated through the drill string in an ideal manner, due
to the non-ideal response of the drill string to such vibrations.
Conventional drill strings, which consist of a number of lengths of
drill pipe joined by pipe joints, inherently have frequency domain
stopbands that attenuate acoustical signals at the stopband
frequencies. This frequency-dependent attenuation can severely
distort some signals. Other factors also distort the vibrations
communicated along a drill string from downhole to the surface.
Such factors include noise generated by the drilling fluid, or mud,
which is conventionally pumped through the drill string at
relatively high pressures. This high pressure flow of fluid causes
significant vibrations in the drill string. Other devices in the
drilling operation, such as bearings in the swivels at the top of
the drill string, the rattling of chains which turn the kelly
bushing, or the motor in a top drive drilling arrangement, and the
slap of the casing against the drill string or well bore, also
generate significant acoustical vibrations which are received by
and transmitted along the drill string. These vibrations are
superimposed upon the desired data signal, and will accordingly be
detected at the top of the drill string by such detectors as are
attempting to detect the data signal transmitted from the downhole
location.
[0008] Considering the vibrations generated by a transmitter as
"signal" and the vibrations generated by the drill bit and the
other vibrations caused by drilling mud flow and the mechanical
sources discussed in the prior paragraph as "noise", it has been
found that the amplitude of the noise can be substantially greater
than the signal amplitude. Noise at this level not only clouds the
analysis of the information, but indeed drowns out the information
itself.
[0009] Vibration-state inference techniques have been described to
determine downhole force and displacement at a position close to
the bit from similar measurements at a second location in the
drillstring, (see SPE 74718, Macpherson, et al., "Application and
Analysis of Simultaneous Near Bit and Surface Dynamics
Measurements", SPE Drilling and Completions, Society of Petroleum
Engineers, December 2001). However, there is no suggestion therein
of using such a technique for purposes of acoustic telemetry in a
drillstring.
[0010] The methods of the present invention overcome the foregoing
disadvantages of the prior art by providing a technique for
removing a portion of the surface generated noise thereby improving
the signal to noise ratio of acoustic signals transmitted along a
drill string.
SUMMARY OF THE INVENTION
[0011] In one aspect, a method of acoustic telemetry in a drill
string in a wellbore, comprises transmitting an acoustic signal
related to a parameter of interest from a transmitting location
into the drill string. The signals propagated through the drill
string are detected at a receiving location, where the detected
signals include noise. A drill string transfer matrix is determined
defining the propagation of signals through a transfer interval
between the receiving location and the transmitting location. The
detected signals and the drill string transfer matrix are used for
obtaining an estimate of the acoustic signal.
[0012] In another aspect, a method of reducing noise in an acoustic
signal transmitted at a second location and received at a first
location in a drill string, comprises calculating a transfer matrix
related to a transmission interval of the drill string. Time series
data sets of vibrations are detected at the first location
comprising a first time-series data set of measurements related to
a force on the drill string and a second time-series data set of
measurements related to an acceleration of the drill string. The
first time-series data set and the second time-series data set are
transformed to a frequency domain. The transformed first
time-series data set and the transformed second time-series data
set are combined with the transfer function to generate an inferred
force related signal at the second location and an inferred
acceleration related signal at the second location. The inferred
force related signal and the inferred acceleration related signal
are transformed to the time domain generating an inferred
time-series of force at the second location and an inferred
time-series of acceleration at the second location.
[0013] Examples of the more important features of the invention
thus have been summarized rather broadly in order that the detailed
description thereof that follows may be better understood, and in
order that the contributions to the art may be appreciated. There
are, of course, additional features of the invention that will be
described hereinafter and which will form the subject of the claims
appended hereto.
BRIEF DESCRIPTION OF THE DRAWINGS
[0014] For detailed understanding of the present invention,
references should be made to the following detailed description of
the preferred embodiment, taken in conjunction with the
accompanying drawings, in which like elements have been given like
numerals, wherein:
[0015] FIG. 1 is a schematic of a drilling system for use with a
method according to one embodiment of the present invention;
[0016] FIG. 2 is a block diagram of a frequency-domain method
according to one embodiment of the present invention; and
[0017] FIG. 3 is a block diagram of a time-domain method according
to one embodiment of the present invention.
DESCRIPTION OF PREFERRED EMBODIMENTS
[0018] Referring now to FIG. 1, a conventional drilling rig 2 is
shown powering drill string 4, which conventionally consists of
multiple sections of drill pipe 6 and a bottomhole assembly 11.
Sections 6 are connected to one another by tool joints 8 in the
conventional manner. Drill bit 10 is connected at the bottom end of
drill string 4, and can be a rotary bit, jet or spud bit, or other
type of drill bit conventional in the art. As shown in FIG. 1 drill
bit 10 is connected to bottomhole assembly 11, which in turn is
connected to sections 6 of drill string 4. The bottomhole assembly
11 is typically made up of multiple sections (not shown) of drill
collars having a substantially larger diameter than that of the
drill pipe 6. Provision of such a bottomhole assembly 11 is
conventional in the drilling art, and is useful for housing such
equipment as detectors for sensing parameters of interest of the
drilling operation and the surrounding formation, as well as for
other conventional functions. While such a bottomhole assembly 11
is shown in FIG. 1, it should be noted that the presence of
bottomhole assembly 11 is not required for purposes of the instant
invention, such presence depending upon the particular drilling
operation being performed. However, for purposes of acoustic
telemetry as will be described hereinbelow, an acoustic transmitter
13 for vibrating drill string 4, according to information to be
transmitted from downhole to the surface, is preferably located in
such a bottomhole assembly 11. Alternatively, the acoustic
transmitter 13 may be located at other locations in the drill
string 4.
[0019] In one preferred embodiment, the acoustic transmitter 13
excites axial vibration modes. Alternatively, the acoustic
transmitter may excite torsional vibration modes and a combination
of torsional and axial vibration modes. Such transmitter devices
are known in the art and will not be described here further.
[0020] Detector sub 12 is connected within drill string 4 near the
surface of the earth. Sub 12 contains detectors, such as force
transducers, accelerometers, strain gages, piezoelectric
transducers, optical transducers, and the like, for detecting
stress and motion related to vibrations in drill string 4 and
generating electrical signals corresponding to the detected
vibration-induced parameters. The electrical signals generated from
the detectors within sub 12 are communicated to computer system 19.
Computer system 19 analyzes the signals corresponding to the
vibrations of drill string 4 to remove a portion of the unwanted
noise signals to enable enhanced decoding of the downhole
transmitted information relating to the downhole measured data,
according to one preferred embodiment of the invention described
hereinbelow.
[0021] The drill bit 10 generates vibrational noise as the bit 10
disintegrates the formation. This noise propagates up the drill
string 4 and mixes with the vibrationally encoded data signal
generated by transmitter 13. In addition, drilling rig noise is
generated and transferred to the drill string 4 at the surface.
Both the surface generated noise and the downhole generated noise
are received along with the data signal at sub 12. The method
described below is useful in removing a portion of the surface
generated noise for enhancing detection of the data signal
transmitted downhole. Other techniques known in the art may be used
for minimizing the downhole generated noise.
[0022] The present invention uses vibration-state inference to
estimate the vibration state at one location in the drill string
from vibration measurements made at another location in the same
drill string. The objective is to remove the influence of unwanted
vibration sources (noise) on the measurements while correcting for
changes made to the signal by the transmission path (the drill
string). In a typical preferred embodiment, the measurement
location is at the surface and the inference position is at the
downhole transmitter. Alternatively, in another preferred
embodiment, for transmission of command signals to a downhole tool,
the surface may be the inferred position and the measurements may
be made at a downhole location.
[0023] Vibration-state inference requires determining both stress
(either axial or torsional), and motion in the drill string 4. The
determination of stress (axial and torsional) is commonly
accomplished by determining a related strain with strain gages (not
shown) or force measuring devices known in the art. For purposes of
the following discussion and theoretical analysis, strain and
stress are to be considered interchangeable indications for stress
in the drill string 4. The motion measurement typically detects
displacement, velocity, or acceleration of the drill string 4. Both
axial and torsional (or rotational) motions may be detected. One
skilled in the art will recognize that accelerometer and velocity
measurements can be related to displacement using common
techniques. For purposes of the following discussion and
theoretical analysis, acceleration, displacement, and velocity are
to be considered interchangeable indications for motion of the
drill string 4.
[0024] Vibration-state inference relies on the knowledge of the
mechanical system between the position of measurement and the
position of inference, called the transmission interval, and the
assumption that there is no externally applied excitation within
the transmission interval. Of major utility is that the
vibration-state inference technique does not depend on knowledge
outside the transmission interval. Therefore, knowledge (or
measurement) of the top and bottom boundary conditions (noise of
the drill bit and surface equipment) of the drill string are not
needed.
[0025] Theory:
[0026] The equation of motion for longitudinal vibrations of a
uniform drill string is 1 A 2 u ( x , t ) t 2 + u ( x , t ) t - E A
2 u ( x , t ) x 2 = 0 ( 1 )
[0027] Therefore, 2 2 u ( x , t ) t 2 + A u ( x , t ) t - c 0 2 2 u
( x , t ) x 2 = 0 ( 2 )
[0028] Where 3 c 0 2 = E ( 3 )
[0029] In the above equations, function u(x,t) represents the
displacement, A the cross sectional area, .rho. the mass density of
the material of the drill string, .mu. the damping coefficient,
c.sub.0 the velocity of longitudinal waves and E is the Young's
modulus.
[0030] Consider solutions of the form
u(x,t)=u.sub.0(x)e.sup.j.omega.t (4)
[0031] On substituting equation 4 in equation 3 4 [ - 2 + j A ] u 0
- c 0 2 2 u 0 x 2 = 0 5 2 u 0 x 2 + 2 c 0 2 ( 1 - j A ) u 0 = 0 ( 5
)
[0032] The unknown complex function u.sub.0(x) therefore satisfies
the equation of the form 6 2 u 0 x 2 + k 2 u 0 = 0 ( 6 )
[0033] where, 7 k 2 = 2 c 0 2 ( 1 - j A ) ( 7 )
[0034] The solution of equation 6 is
u.sub.0=A.sub.1 sin(kx)+B.sub.1 cos(kx) (8)
[0035] The force f.sub.0 is given by 8 f 0 = E A u 0 x ( 9 ) = E A
k [ A 1 cos ( kx ) - B 1 sin ( kx ) ] ( 10 )
[0036] Consider the following boundary conditions:
[0037] At the top (x=0), using equation 8, the displacement u.sub.s
is
u.sub.s=u.sub.0.vertline..sub.x=0=B.sub.1 (11)
[0038] and using equation 10, the force f.sub.0 at x=0 is
f.sub.s=f.sub.0.vertline..sub.x=0=E Ak A.sub.1 (12)
[0039] Similarly, at a downhole location l feet away (x=l), the
displacement u.sub.d is
u.sub.d=u.sub.0.vertline..sub..sub.x=l=A.sub.1 sin(kl)+B.sub.1
cos(kl) (13)
[0040] and the force f.sub.d at x=l is
f.sub.d=f.sub.0.vertline..sub.x=l=E Ak[A.sub.1 cos(kl)-B.sub.1
sin(kl)] (14)
[0041] The four equations 11-14 can be used to obtain the
displacement and force (u.sub.d & f.sub.d) at downhole location
in terms of the measured displacement and force (u.sub.s &
f.sub.s) at the surface location as follows:
[0042] Substitute A.sub.1 & B.sub.1 from equations 11 & 12
into equation 13 9 u d = 1 E A k sin ( kl ) f s + cos ( kl ) u s (
15 ) f.sub.d=cos(kl)f.sub.s-E Ak sin(kl)u.sub.s (16)
[0043] From equation 4 it can be easily seen that the velocity (v)
and acceleration (a) are given by 10 v = u t = j u 0 ( x ) j t a =
2 u t 2 = - 2 u 0 ( x ) j t ( 17 )
[0044] Equation 15 and 16 can therefore, be expressed in terms of
velocity v.sub.d & v.sub.s as 11 v d = j E A k sin ( kl ) f s +
cos ( kl ) v s ( 18 ) 12 f d = cos ( kl ) f s - E A k j sin ( kl )
v s ( 19 )
[0045] and, in terms of acceleration a.sub.d & a.sub.s as 13 a
d = - 2 E A k sin ( kl ) f s + cos ( kl ) a s ( 20 ) f d = cos ( kl
) f s + E A k 2 sin ( kl ) a s ( 21 )
[0046] The above equations can be expressed in the matrix form as
follows 14 [ u d f d ] = [ cos ( kl ) sin ( kl ) E A k - E A k sin
( kl ) cos ( kl ) ] [ u s f s ] ( 22 ) [ v d f d ] = [ cos ( kl ) j
E A k sin ( kl ) - E A k j sin ( kl ) cos ( kl ) ] [ v s f s ] ( 23
) [ a d f d ] = [ cos ( kl ) - 2 E A k sin ( kl ) E A k 2 sin ( kl
) cos ( kl ) ] [ a s f s ] ( 24 )
[0047] Equations 24 can be written in the following general form:
15 [ a d f d ] = [ T 11 T 12 T 21 T 22 ] [ a s f s ] ( 28 )
[0048] where 16 T 11 = T 22 = cos ( kl ) , T 12 = - 2 E A k sin (
kl ) and T 21 = E A k 2 sin ( kl ) ( 28 a )
[0049] In equation 24, the vector 17 [ a d f d ] ,
[0050] which is a column matrix of acceleration (displacement or
velocity) and internal force, is known as the state vector.
Equation 24 shows that the state vector at a surface location s is
transferred to the state vector at the downhole location d at
distance l, through the square matrix, which is known as the
transfer matrix. It is a function of the elastic and dynamic
properties of the drill string system and frequency. Therefore, for
known values of the state vector at the surface and a chosen value
of frequency, .omega., it is possible to infer (or compute) the
state vector at the downhole location, for known properties of the
drill string.
[0051] As is commonly known, a typical drill string comprises drill
collars and drill pipe sections with varying lengths and diameters.
For a series of varying tubulars, each characterized by its own
transfer matrix, T.sub.1, T.sub.2, T.sub.3, . . . Tn, the transfer
matrix representing the effect of all the tubulars connected
end-to-end is:
[T.sub.n].multidot.[T.sub.n-1].multidot.[T.sub.n-2].multidot. . . .
.multidot.[T.sub.1]. For the extreme ends of the transmission
interval, for example end a and end b with a system of n connected
tubulars; 18 [ ub Fb ] = [ [ Tn ] [ T3 ] [ T2 ] [ T1 ] ] [ ua Fa ]
( 29 )
[0052] Note that in matrix algebra [A][B].noteq.[B][A], therefore
order is important in calculating the system transfer matrix. The
calculation starts multiplying transfer matrices from the inference
end, not from the measurement end.
[0053] Sign convention:
[0054] Using a right handed coordinate system, with x axis
coinciding with the axis of the tubular, the face with outward
normal pointing in the positive direction of the x-axis, represents
the positive face of the section. In this arrangement, the
displacements are positive if they coincide with the positive
direction of the coordinate system and forces are positive when
acting on the positive face with vector direction pointing in the
positive direction.
[0055] The results in equation 28 represent the transfer matrix for
the case where the direction is from upper (or surface) to lower
end (downhole), i.e. for estimating force and displacement at the
lower end (downhole) using known (measured) forces and acceleration
at the surface (or upper end). In essence, the signal transmitted
from a downhole transmitter can be inferred from surface force and
displacement measurements.
[0056] Evaluation of k:
[0057] From equation 7, k can be expressed as 19 k = c 0 ( 1 - A j
) ( 30 )
[0058] It can be shown that (for example, see Kolsky, H., Stress
Waves in Solids, Ch. 5, Dover Publications, Inc, 1963) 20 A = 2 c 0
( 31 )
[0059] Where .alpha. is the attenuation coefficient. Also, 21 = 2 Q
c 0 ( 32 )
[0060] On substituting equations 31 and 32 into equation 30
therefore 22 k = c 0 ( 1 - 1 Q j ) ( 33 )
[0061] where Q is a quality factor representing the sharpness of a
resonance peak of the vibrational system.
[0062] The solution to Equations 22-24 and equations 28 and 29 can
be easily obtained using a computer using techniques known in the
art.
[0063] The above inference-state analysis is directed to
longitudinal (axial) vibrations, but is also valid for torsional
vibrations by making the following substitutions into the above
equations;
[0064] replace
[0065] E by G, the shear modulus;
[0066] u by .theta., the angular displacement;
[0067] f by T, torque;
[0068] A by I.sub.p, the polar moment of inertia; and
[0069] c.sub.t.sup.2=G/.rho., the shear wave velocity.
[0070] Also note that the above analysis concerns steady-state
conditions or frequency domain operations only. However,
steady-state conditions are not required. Time-domain
(arbitrary/non-periodic) signals may be analyzed as well if the
initial (time zero) vibration state at the inference point is
known. Many time-frequency domain transformation algorithms, for
example discrete Fourier transforms an Fast-Fourier transforms
implicitly assume that the time data signal, or record, is periodic
(i.e. that it repeats itself indefinitely). Real world signals,
however, are commonly finite in length. Techniques are known in the
art to deal with data that are not truly periodic while still
enjoying the utility of digital transform methods. One method
involves "windowing" the finite length record. This technique
essentially tapers the beginning and ending segments of the record
such that it may be considered to be periodic. Various window
functions are known in the art and include, but are not limited to,
(i) Hanning, (ii) Hamming, and (iii) Blackman. The use of such
techniques yield results for the finite length signal record that
approximate the spectral characteristics of a periodic signal with
similar characteristics.
[0071] In a frequency domain operational example, shown in block
diagram form in FIG. 2, in 201, downhole transmitter 13 imparts
encoded data signals into the drill string 4 that travel through
the drill string 4 toward the surface. In 202, the drill string
acceleration a.sub.s and drill string force f.sub.s are measured at
surface receiver 12 and input as time-series data to computer
system 19 for analysis. In 203, mechanical data, such as lengths
and diameters, and mechanical properties, such as density and
elastic modulus, are input for each drill string section between
the measuring location and the downhole inference location at
transmitter 13. The mechanical data and mechanical properties are
used to compute a transfer matrix using the techniques described
herein, see 204. In 205, the acceleration and force time-series
data are transformed to the frequency domain using techniques known
in the art, such as the Fourier transform. In 206, the transformed
acceleration and force measurements are multiplied, in the
frequency domain, by the transfer matrix as described previously to
calculate an inferred acceleration and inferred force, in the
frequency domain, at the downhole inference location at transmitter
13. In 207, the frequency domain inferred downhole acceleration and
inferred downhole force are transformed back to the time domain
using Fourier transform, or equivalent techniques, thereby
generating inferred acceleration and force time-series data that
can be decoded in step 208 to yield the downhole encoded and
transmitted data. The sequence described above relates to data sent
from a downhole location to a surface location but could also be
used for transmitting data from a surface location to a downhole
location.
[0072] Alternatively, in a time domain operational example, shown
in block diagram form in FIG. 3, in 301, downhole transmitter 13
imparts encoded data signals into the drill string 4 that travel
through the drill string 4 toward the surface. In 302, the drill
string acceleration a.sub.s and drill string force f.sub.s are
measured at surface receiver 12 and input as time-series data to
computer system 19 for analysis. In 303, mechanical data, such as
lengths and diameters, and mechanical properties, such as density
and elastic modulus, are input for each drill string section
between the measuring location and the downhole inference location
at transmitter 13. The mechanical data and mechanical properties
are used to compute a transfer matrix using the techniques
described herein, see 304. In 305, the frequency dependent transfer
matrix is transformed to the time domain using techniques known in
the art, such as the Fourier transform. One skilled in the art will
appreciate that just as the time domain signal must be shaped or
windowed to provide acceptable results, so to the frequency signal
must be shaped, for example, by band-limiting the Fourier
coefficients. This ensures that the resultant operator is
sufficiently tapered to accurately approximate a periodic signal,
when transformed. In 306, the acceleration and force measurements
are combined with the transfer matrix using standard convolution
methods to calculate an inferred acceleration and inferred force,
in the time domain, at the downhole inference location at
transmitter 13, thereby generating inferred acceleration and force
time-series data that can be decoded in step 207 to yield the
downhole encoded and transmitted data. The sequence described above
relates to data sent from a downhole location to a surface location
but could also be used for transmitting data from a surface
location to a downhole location.
[0073] A major advantage in using the transfer matrix method is
that a large, complex system can be broken down into its components
which have simple elastic and dynamic properties. Calculations can
be then made, by proceeding from one component to the other,
starting from one end of the first component to the next and so on.
In a drill string, the components can be drill pipes, drill
collars, etc. with different dimensions and material properties.
This technique is computationally more efficient than solving such
a system using other common techniques such as finite element
methods.
[0074] In the method discussed above, it has been shown (using
equation 24) that it is possible to infer or estimate the motion
(i.e. displacement, velocity or acceleration) and force (or stress)
at one location from known (measured) motion and stress at another
location thereby enabling improved acoustic drill string telemetry.
The knowledge of boundary conditions or noise sources outside the
interval between the measurement point and the inference point is
not needed.
[0075] The foregoing description is directed to particular
embodiments of the present invention for the purpose of
illustration and explanation. It will be apparent, however, to one
skilled in the art that many modifications and changes to the
embodiment set forth above are possible without departing from the
scope and the spirit of the invention. It is intended that the
following claims be interpreted to embrace all such modifications
and changes.
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