METHODS AND SYSTEMS FOR ANALYZING FORMATION PROPERTIES WHEN
PERFORMING SUBTERRANEAN OPERATIONS
Background
Hydrocarbons, such as oil and gas, are commonly obtained from subterranean formations.
The development of subterranean operations and the processes involved in removing
hydrocarbons from a subterranean formation are complex. Typically, subterranean operations
involve a number of different steps such as, for example, drilling the wellbore at a desired well
site, treating the wellbore to optimize production of hydrocarbons, and performing the necessary
steps to produce and process the hydrocarbons from the subterranean formation.
Modern oil field operations demand a great quantity of information relating to the
parameters and conditions encountered downhole. Such information may include characteristics
of the earth formations traversed by the borehole and data relating to the size and configuration
of the borehole itself. The collection of information relating to conditions downhole, which
commonly is referred to as "logging," can be performed by several methods including wireline
logging, measurement-while-drilling (MWD), logging-while-drilling (LWD), drillpipe conveyed
logging, and coil tubing conveyed logging. A variety of logging tools are available for use with
each of these methods.
The basic techniques for electromagnetic logging for earth formations are well known. For
instance, induction logging to determine resistivity (or its inverse, conductivity) of earth
formations adjacent a borehole is one of the techniques used in the search for and recovery of
hydrocarbons. Generally, a transmitter transmits an electromagnetic signal that passes through
formation materials around the borehole and induces a signal in one or more receivers. The
properties of the signal received, such as its amplitude and/or phase, are influenced by the
formation resistivity, enabling resistivity measurements to be made. The measured signal
characteristics and/or formation properties calculated therefrom may be recorded as a function of
the tool's depth or position in the borehole, yielding a formation log that can be used to analyze
the formation.
During drilling operations, it is important to be able to anticipate the properties of
formations ahead of the bit. For instance, it is undesirable to drill into a high pressure water zone
or other formation zones that can hinder the performance of subterranean operations. Seismic
models and other approaches currently utilized for looking ahead of the bit such as traditional
electromagnetic methods as proposed, for example, in U.S. Patent No. 6,856,909 or crosscomponent
induction methods as proposed, for example, in US2005/0098487 have a number of
disadvantages. For instance, the long wave length of a seismic wave limits its resolution. The
same is true for the electromagnetic method. Furthermore, the electromagnetic method requires
a prior knowledge of formation resistivity which may not be available during the drilling
process.
Brief Description of the Drawings
Figure 1 shows an illustrative logging while drilling environment;
Figure 2 shows an illustrative wireline logging environment;
Figure 3A and 3B depict schematic views of a formation bed configuration ahead of
the bit in accordance with exemplary embodiments of the present invention;
Figure 4 shows the coil configuration of a triaxial induction tool;
Figure 5 shows a triaxial induction tool located in a borehole in angled formation
beds;
Figure 6 demonstrates a rotational transformation definition;
Figure 7 shows a graph used to illustrate the shape of position derivatives of the
magnetic coupling between a transmitter and a receiver;
Figure 8 shows a minimum square error curve fit to the position derivative data
points;
Figure 9 shows a Hough transform of the data points using a parameterized cosine
function;
Figure 10 shows a flow diagram for the disclosed method of determining dip angles
in a dipping earth formation;
Figure 11 shows a resistivity log of a model bedded formation;
Figure 12 shows a dipmeter log calculated from the first derivative of the coupling;
Figure 13 shows a dipmeter log calculated from the second derivative of the
coupling;
Figure 14 shows a histogram of the dipmeter log of Figure 1 ;
Figure 15 shows a histogram of the dipmeter log of Figure 1 ;
Figure 16 depicts the procedure for time reversal for boundary detection ahead of a
bit in accordance with an exemplary embodiment of the present invention;
Figures 17A and 17B depict the calculated real and imaginary part, respectively, of
the second reflected signal in the frequency domain, as a function of frequency for several
transmitter-bed distances;
Figure 18 depicts the difference between the real part of the second reflected signal
(Z) at a distance of 3[m] to the bed and at a distance of 0.5 [m] to the bed in the frequency
domain; and
Figure 19 depicts a schematic view of a formation bed configuration ahead of the bit
where the transceiver array is positioned at an angle to a geological formation.
While embodiments of this disclosure have been depicted and described and are
defined by reference to exemplary embodiments of the disclosure, such references do not imply a
limitation on the disclosure, and no such limitation is to be inferred. The subject matter
disclosed is capable of considerable modification, alteration, and equivalents in form and
function, as will occur to those skilled in the pertinent art and having the benefit of this
disclosure. The depicted and described embodiments of this disclosure are examples only, and
are not exhaustive of the scope of the disclosure.
Detailed Description
For purposes of this disclosure, an information handling system may include any
instrumentality or aggregate of instrumentalities operable to compute, classify, process, transmit,
receive, retrieve, originate, switch, store, display, manifest, detect, record, reproduce, handle, or
utilize any form of information, intelligence, or data for business, scientific, control, or other
purposes. For example, an information handling system may be a personal computer, a network
storage device, or any other suitable device and may vary in size, shape, performance,
functionality, and price. The information handling system may include random access
memory (RAM), one or more processing resources such as a central processing unit (CPU) or
hardware or software control logic, ROM, and/or other types of nonvolatile memory. Additional
components of the information handling system may include one or more disk drives, one or
more network ports for communication with external devices as well as various input and
output (I/O) devices, such as a keyboard, a mouse, and a video display. The information
handling system may also include one or more buses operable to transmit communications
between the various hardware components.
For the purposes of this disclosure, computer-readable media may include any
instrumentality or aggregation of instrumentalities that may retain data and/or instructions for a
period of time. Computer-readable media may include, for example, without limitation, storage
media such as a direct access storage device (e.g., a hard disk drive or floppy disk drive), a
sequential access storage device (e.g., a tape disk drive), compact disk, CD-ROM, DVD, RAM,
ROM, electrically erasable programmable read-only memory (EEPROM), and/or flash memory;
as well as communications media such wires, optical fibers, microwaves, radio waves, and other
electromagnetic and/or optical carriers; and/or any combination of the foregoing.
Illustrative embodiments of the present invention are described in detail herein. In
the interest of clarity, not all features of an actual implementation may be described in this
specification. It will of course be appreciated that in the development of any such actual
embodiment, numerous implementation-specific decisions may be made to achieve the specific
implementation goals, which may vary from one implementation to another. Moreover, it will
be appreciated that such a development effort might be complex and time-consuming, but would
nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of
the present disclosure.
To facilitate a better understanding of the present invention, the following examples
of certain embodiments are given. In no way should the following examples be read to limit, or
define, the scope of the invention. Embodiments of the present disclosure may be applicable to
horizontal, vertical, deviated, or otherwise nonlinear wellbores in any type of subterranean
formation. Embodiments may be applicable to injection wells as well as production wells,
including hydrocarbon wells. Embodiments may be implemented using a tool that is made
suitable for testing, retrieval and sampling along sections of the formation. Embodiments may
be implemented with tools that, for example, may be conveyed through a flow passage in tubular
string or using a wireline, slickline, coiled tubing, downhole robot or the like. "Measurementwhile-
drilling" ("MWD") is the term generally used for measuring conditions downhole
concerning the movement and location of the drilling assembly while the drilling continues.
"Logging-while-drilling" ("LWD") is the term generally used for similar techniques that
concentrate more on formation parameter measurement. Devices and methods in accordance
with certain embodiments may be used in one or more of wireline, MWD and LWD operations.
The terms "couple" or "couples" as used herein are intended to mean either an indirect or
direct connection. Thus, if a first device couples to a second device, that connection may be
through a direct connection, or through an indirect mechanical or electrical connection via other
devices and connections. Similarly, the term "communicatively coupled" as used herein is
intended to mean either a direct or an indirect communication connection. Such connection may
be a wired or wireless connection such as, for example, Ethernet or LAN. Such wired and
wireless connections are well known to those of ordinary skill in the art and will therefore not be
discussed in detail herein. Thus, if a first device communicatively couples to a second device,
that connection may be through a direct connection, or through an indirect communication
connection via other devices and connections.
The present application is directed to improving efficiency of subterranean operations and
more specifically, to a method and system for looking ahead of a bit when performing drilling
operations.
Turning now to Figure 1, oil well drilling equipment used in an illustrative LWD
environment is shown. A drilling platform 2 supports a derrick 4 having a traveling block 6 for
raising and lowering a drill string 8. A kelly 10 supports the drill string 8 as it is lowered
through a rotary table 12. A drill bit 14 is driven by a downhole motor and/or rotation of the drill
string 8. As bit 14 rotates, it creates a borehole 16 that passes through various formations 18. A
pump 20 may circulate drilling fluid through a feed pipe 22 to kelly 10, downhole through the
interior of drill string 8, through orifices in drill bit 14, back to the surface via the annulus around
drill string 8, and into a retention pit 24. The drilling fluid transports cuttings from the borehole
into the pit 24 and aids in maintaining the borehole integrity.
A logging tool 26 may be integrated into the bottom-hole assembly near the bit 14. The
logging tool 26 may include receivers and transmitters. In one embodiments, the logging tool 26
may include a transceiver array that functions as both a transmitter and a receiver. As the bit
extends the borehole through the formations, logging tool 26 may collect measurements relating
to various formation properties as well as the tool orientation and position and various other
drilling conditions. The orientation measurements may be performed using an azimuthal orientation
indicator, which may include magnetometers, inclinometers, and/or accelerometers, though other
sensor types such as gyroscopes may be used in some embodiments. The logging tool 26 may take
the form of a drill collar, i.e., a thick-walled tubular that provides weight and rigidity to aid the
drilling process. A telemetry sub 28 may be included to transfer tool measurements to a surface
receiver 30 and to receive commands from the surface receiver 30.
At various times during the drilling process, the drill string 8 may be removed from the
borehole as shown in Figure 2. Once the drill string has been removed, logging operations can be
conducted using a wireline logging tool 34, i.e., a sensing instrument sonde suspended by a cable
having conductors for transporting power to the tool and telemetry from the tool to the surface. A
logging facility 44 may collect measurements from the logging tool 34, and may include computing
facilities for processing and storing the measurements gathered by the logging tool.
As would be appreciated by those of ordinary skill in the art, with the benefit of this
disclosure, an electromagnetic wave propagating in a medium with permittivity s(r) and
magnetic permeability m( ) may be expressed by the following wave equation:
V E(r,r) - r r ) E(r , = 0
This equation is invariant under time reversal operation. Specifically, if E(r, t) is a
solution, then E(r,-t) will also be a solution to this equation. The methods and systems disclosed
herein take advantage of the time reversal invariance of Eq. (1) as discussed in more detail
below.
Figures 3A and 3B depict a schematic view of a formation bed configuration 302 ahead of
the drill bit ("bit"). As would be appreciated by those of ordinary skill in the art, the logging tool
26 transceivers 304 may be replaced by separate transmitters and receivers for transmission and
detection of electromagnetic pulse signals. In the exemplary formation of Figure 3, the
formation comprises a first portion having resistivity p i and a second portion having resistivity
p2. However, as would be appreciated by those of ordinary skill in the art, with the benefit of
this disclosure, the methods and systems disclosed herein are not limited to any specific
formation configuration.
Figure 3A depicts horizontal transceivers 304. However, in another exemplary
embodiment, the transceivers 304 may be tilted as shown in Figure 3B. Accordingly, the
transceivers used in conjunction with the methods and systems disclosed herein may be coaxial,
tilted or horizontal transceivers.
In another exemplary embodiment, the transceiver array may be virtually steered into any
desired orientation by adjusting the relative phase between a coaxial and a horizontal transceiver
pair as disclosed in U.S. Patent No. 6,272,706 (hereinafter, "virtually steerable transceiver").
Operation of a virtually steerable transceiver is next discussed in conjunction with Figures 4-15.
Figure 4 shows a conceptual sketch of a coil arrangement for a downhole induction tool. A
triad of transmitter coils Tx, Ty and Tz, each oriented along a respective axis, is provided. A
triad of similarly oriented, balanced, receiver coil pairs (Rlx, R2x), (Rly, R2y) and (Rlz, R2z) is
also provided. The transmitter-receiver spacings LI and L2, together with the number of turns in
each receiver coil, are preferably chosen so as to set the direct coupling between each transmitter
and the corresponding combined receiver pairs equal to zero. Hereafter, each of the receiver coil
pairs will be treated as a single balanced receiver coil. For clarity, it is assumed that the three
coils in each triad represent actual coils oriented in mutually perpendicular directions, with the zaxis
corresponding to the long axis of the tool. However, it is noted that this coil arrangement
can be "synthesized" by performing a suitable transformation on differently oriented triads.
Figure 5 shows a formation having a series of layered beds 102 dipping at an angle. A
wellbore 104 passing through the beds 102 is shown containing an induction tool 106. A first
(x,y,z) coordinate system is associated with the beds 102, and a second coordinate system
(x",y",z") is associated with the induction tool 106. As shown in Figure 6, the two coordinate
systems are related by two rotations. Beginning with the induction tool's coordinate system
(x",y",z"), a first rotation of angle b is made about the z" axis. The resulting coordinate system is
denoted (x',y\ z'). Angle b is the strike angle, which indicates the direction of the formation dip.
A second rotation of angle a is then made about the y' axis. This aligns the coordinate system
with the beds. Angle a is the dip angle, which is the slope angle of the beds.
Any vector in one of the coordinate systems can be expressed in terms of the other
coordinate system by using rotational transform matrices. Thus, if v" is a vector expressed in the
(x",y",z") coordinate system, it can be expressed mathematically in the (x,y,z) coordinate system
as:
where:
cos a -sin a cos sin 0 cos a cos b cos a sin b -sin a
R = R R - 0 0 - hb cosP 0 -sina cos 0 (2)
sin a cos a 0 0 1 sin a cos b sin a sin b cos a
Consequently, given measurements in the coordinate system of the induction tool, the
corresponding measurements in the coordinate system of the beds can be determined if the dip
and strike angles are known.
Moran and Gianzero, in "Effects of Formation Anisotropy on Resistivity Logging
Measurements" Geophysics, Vol. 44, No. 7, p. 1266 (1979), noted that the magnetic field "h" in
the receiver coils can be represented in terms of the magnetic moments "m" at the transmitters
and a coupling matrix "C":
h=Cm (3)
In express form, equation (3) is:
zx c Mz
Of course, equation (3) is also valid in the induction tool coordinate system, so:
h"=C"m" (5)
The relationship between the coupling matrices C and C" can be determined from
equations (1), (3), and (5) to be:
C"=R 1CR=R - R 1CR R (6)
The induction tool can determine each of the elements of C" from magnetic field
measurements. Coupling matrix element C j"(i,j=x", y", z") is calculated from:
where RjTj is the magnetic field measured by the ith receiver in response to the jth transmitter,
and mj is the magnetic moment of the jth transmitter. If each of the transmitters has the same
magnetic moment m, the coupling matrix can be expressed:
Note that due to changes in the formation as a function of depth, the coupling constants are also
functions of depth. The strike angle can be determined directly from the measured signals. For
example, it can be calculated by:
TzRy
= tan (9)
TzRx
Knowing the strike angle, an inverse b rotation can be carried out. Based on equation (6),
the coupling matrix becomes:
C' R 'R - R CR l O
Accordingly, the signal measurements allow a straightforward determination of coupling
matrix C" and strike angle b. The remaining angle is the dip angle a .
If the dip angle a were known, an inverse a rotation could be done to determine the
coupling coefficients in the bed coordinate system. To determine the dip angle, we postulate a
correction angle g . When a rotation is performed about the y' axis, the coupling matrix becomes:
C(r) =R C"R _ =R R- CR R ( 11)
Equations (10) and ( 11) represent the virtual steering of the transmitters and receivers so that
after the rotation, the transmitter and receivers are oriented in a direction that has no strike (b=0)
and a dip angle of g .
In studying the behavior of the coupling matrix C(y) , it has been found that the
derivatives of certain elements can be used to identify the dip angle a . The first and second
derivatives of RxTx(y) as a function of depth z can usually be represented as
e 00 = - x = cos(2( -a)) + (12)
dz
(r =- R =c ¥ s 2 r - )) + (i 3)
dz
where A, B, C and D are not functions of g . The derivatives of RzTz(y) can also be represented
in the same form, albeit with different constants. This form does not apply when the sonde is
straddling an interface between formation beds.
Figure 7 shows a resistivity log of a model formation showing four beds of different
resistivities. Adjacent to the resistivity log are plots of derivatives of RxTx(y) confirming the
form of equations (12) and (13). These are calculated using the response of a generic 3-coil triad
sonde as it is logged in a dipping formation having a 30° dip and 40° strike. After all data has
been acquired, at each logging point the sonde is virtually steered to arrive at the derivatives as a
function of the rotation angle. The amplitudes of the derivatives at each logging position have
been normalized and resealed according to depth for plotting purposes.
Because the form of the derivatives as a function of correction angle g is known, the
unknowns A, B and a , or C, D and a , can be determined when the derivatives are plotted as a
function of the correction angle g . Accordingly, coupling coefficient measurements may be
taken, rotated to correct for the strike angle b, and rotated through a series of correction angles g
to obtain depth logs of RxTx(y). The set of correction angles may be predetermined, e.g., 0°, 10°,
20°, 30°, . . . , 180°. The depth logs may then be differentiated with respect to depth to obtain the
first and/or second derivatives.
The derivatives, if plotted as a function of correction angle g , would have the form of
equations (12), (13). The dip angle g may consequently be calculated from the derivatives in
several ways. For example, a simple least-squares curve fit to the data would work, as shown in
Figure 8. Another method with may be used involves a Hough transform. The use of the Hough
transform is discussed by D. Tores, R. Strickland and M. Gianzero, "A New Approach to
Determining Dip and Strike Using Borehole Images," SPWLA 31.sup.st Annual Logging
Symposium, Jun. 24-27, 1990.
First the bias is removed. In equations (12) and (13), the constants B and D represent the
bias. The bias can be largely eliminated by identifying the maximum and minimum values, and
subtracting the average of the maximum and minimum values. Thus, pure cosine functions y'(y)
and y"(y) may be found by:
00 = B (r) - ^[max (C' - in (y))] = A cos(2( - )) (14)
= (r) - i[max(C" 00) - min( 00)] = Ccos(2( - )) (15)
where max and min denotes the maximum and minimum values in the interval 0 < g < 180°.
Equations (14) and (15) can be parameterized, i.e. one of the unknowns can be written as a
function of the other unknown. For example:
A a ) = (16)
cos(2(/ - ))
C( ) = (17)
cos(2(^ - ))
In other words, given a known correction angle g and a known corresponding value y'(y) or
y"(y), the amplitude A or C is a function of the dip angle a . There may be multiple values of A or
C for a given dip angle. Each combination of correction angle g and corresponding value y'(y)
gives a different A(a) curve. Figure 9 shows a set of A(a) curves for nine different values of
correction angle g . This is the Hough transform of measurement data satisfying equation (14).
One concern with using the Hough transform is the size of transform space that must be
considered. As the range of the parameters is increased, the computational requirements are
increased. It is expected that the range of the amplitude parameter can be limited to between
twice the maximum value of y'(y) and twice the minimum value of y'(y), or between twice the
maximums and minimums of y"(y) when the second derivative is being used.
Of particular interest in Figure 9 are the intersection points of the various curves. The two
intersection points represent amplitude A and dip angle a values that are valid for each of the
data points. Accordingly, they specify a curve that passes through each of the points, and the dip
angle value has been determined for this depth. Although there are two solutions, they are
equivalent, i.e. an inversion in the amplitude is equivalent to a 180° phase shift. Accordingly, the
solution with a>90° may be ignored. The process is repeated for each logging depth to obtain a
log of dip angle versus depth.
The intersections may be found by quantizing the parameter space into bins, and counting
the number of curves that pass through each bin. The bins with the highest number of curves
contain the intersections. More detail on the use of Hough transforms may be found in many
standard reference texts.
Figure 10 shows a flowchart of this method. In block 1002, the transmitters are sequentially
fired, the receiver signals are measured, and the coupling matrix elements in equation (8) are
calculated. In block 1004, the inverse b-rotation is performed on the coupling matrix. A set of
dip-correction g -rotations is then applied to the matrix to determine a set of terms (either
RxTx(y) or RzTz(y)) as a function of logging tool position. In block 1006, the selected set of
terms is differentiated with respect to position to determine either the first or second derivative.
In block 1008 a curve parameter identification technique is performed on the set of differentiated
terms. This technique may be curve fitting, a Hough transform, or some other technique. In block
1010, the identified curve parameters are used to calculate the dip angle a . A dip angle is
determined for each tool position in the borehole.
A comparison of the results of using the first and second derivatives to calculate dip angle
is now made. Figure 1 shows a resistivity log of a model formation. The model formation has
beds that dip at 30° across the borehole. Figure 12 shows the dip angle calculated for the model
formation using the first derivative. In the neighborhood of bed interfaces between lowresistivity
beds, the calculated angle deviates downward from the true dip, but is generally
accurate for thicker beds. Figure 3 shows the dip angle calculated for the same formation using
the second derivative. While there is some scatter in the neighborhood of thin beds, the dip
calculation is generally quite accurate. Figure 14 shows a histogram of the dip angle results in
Figure 12, and Figure 15 shows a histogram of the dip angle results in Figure 13. The first
derivative method shows a false peak at 10° as well as a peak at the true dip of 30°. In the second
derivative, the false peak is absent.
The disclosed method can be utilized to determine regional dip and strike information in
wells where conditions are not favorable for the operation of traditional resistivity wireline
dipmeters or resistivity imaging tools. Such conditions include, but are not limited to, wells
drilled with oil based mud and wells with highly rugose wellbores. It is noted that the disclosed
method can be used for both wireline operations and LWD operations. In LWD operations, the
method, in addition to determining regional dip and strike, can be further used to facilitate
geosteering in highly deviated and/or horizontal wells.
Figure 16 depicts the procedure for time reversal for boundary detection ahead of a bit in
accordance with an exemplary embodiment of the present invention. The time reversal
procedure set forth in Figure 16 is equally applicable to electromagnetic waves and acoustic
waves.
First, at step 402 a short electromagnetic pulse (X) is emitted from the transceiver array
304. As discussed in detail below, the method steps disclosed herein are equally applicable to
instances where an acoustic wave is initially generated by the transceiver array instead of an
electromagnetic wave. This pulse is then reflected by the bed boundaries ahead of the bit as a
pulse s(t) in the time domain. The transceiver array 304 detects this first reflected signal s(t) at
step 404. However, due to the dispersion of the medium, the detected signal s(t) is typically
spread out in the time domain.
In accordance with an exemplary embodiment of the present disclosure, the detected signal
s(t) is time reversed as s(-t) at step 406. Additionally, because a portion of the initially generated
signal (X) is lost to the formation, at step 408, in one embodiment, the amplitude of the time
reversed signal s(-t) may be adjusted to compensated for that loss. This time reversed signal
with the adjusted amplitude is then retransmitted as a new pulse s(-t) at step 410. The signal s(-t)
is then reflected again by the medium as a new reflected pulse s (t) which is detected by the
transceiver array 304 as a second reflected signal at step 412. The second reflect signal sr(t) is
naturally focused to give a significant improved sharpness in the time domain. At step 414, the
change in sr(t) from a previously obtained value is monitored. The process then returns to step
402 and the same steps are repeated to monitor the changes in sr(t) over time, as the drill bit
progresses through the formation.
In order to monitor the change in the received time reversed signal sr(t) (hereinafter,
"measured signal" or "measured response"), one can compare the signal with known, precalculated
bed-transmitter separation and boundary property information. This can be carried
out by assuming a known distance to bed boundary and a known resistivity contrast between the
upcoming bed of interest and the formation surrounding the drill bit (i.e. current bed). The
expected time reversed response of the tool may then be calculated. Next, the calculated
response may be compared with the measured response. This comparison may be iteratively
carried out continually while performing drilling operations. In one exemplary embodiment, this
iterative process may continue until the difference between the measured response and the
calculated response is equal to or less than a preset, threshold, acceptable error value. Based on
this comparison of the calculated response with the measured response, the assumed values for
the distance to the bed boundary and the resistivity contrast between the current bed and an
upcoming bed may be modified. As the drilling operations continue and more measured data
goes into the iterative process, information of interest such as, for example, distance from an
upcoming bed and its properties (e.g., resistance for electromagnetic waves, acoustic impedance
for acoustic waves) are further refined.
In Figure 17, the response to an approaching bed with resistivity contrast is theoretically
calculated in the frequency domain. Specifically, figures 17A and 17B depict the calculated real
and imaginary part, respectively, of the second reflect signal sr(t) in the frequency domain, as a
function of frequency for several transmitter-bed distances. In the exemplary embodiment
depicted in Figures 17A and 17B, the formation 304 has a first resistivity (p of 100 ohm.m and
a second resistivity (p2) of 0.1 ohm.m. As would be appreciated by those of ordinary skill in the
art, with the benefit of this disclosure, a Fourier transformation of these signals may be used to
produce the time domain impulse response of the formation.
As would be appreciated by those of ordinary skill in the art, with the benefit of this
disclosure, there may be discernible differences in the detected signal at different transmitter-tobed
distances. For instance, Figure 18 depicts the difference between the real part of the second
reflected signal sr(t) at a distance of 3[m] to the bed and at a distance of 0.5 [m] to the bed in the
frequency domain.
As would be appreciated by those of ordinary skill in the art, with the benefit of this
disclosure, the methods and systems disclosed herein are not limited to transceiver arrays with an
orientation perpendicular to the tool string axis as shown in Figure 3. For instance, Figure 19
depicts an exemplary embodiment where the transceiver array 602 is positioned at an angle to a
geological feature 604. In this embodiment, the methods and systems disclosed herein may be
utilized to detect sideway boundaries. The ability to use the methods and systems disclosed
herein with sensitivity to detect sideway boundaries is of particular importance when guiding a
drill bit in a horizontal well bore.
Further, although the present methods are disclosed in conjunction with electromagnetic
waveforms, the principles disclosed herein are equally applicable to other wave forms such as,
for example, acoustic waves. For instance, the acoustic wave equation obeys the same time
reversal symmetry. Specifically, the acoustic wave equation may be used to describe the scalar
pressure field p(r, t) as:
where p is the acoustic pressure (the local deviation from the ambient pressure) and c is the
speed of sound. Accordingly, the transceiver may generate and receive acoustic waves instead
of electromagnetic waves in accordance with an embodiment of the present invention. As would
be appreciated by those of ordinary skill in the art, with the benefit of this disclosure, because the
earth formation is less dispersive to acoustic waves than electromagnetic waves, the use of
acoustic waves instead of electromagnetic waves may be desirable in certain applications. For
instance, the resistivity contrast may be small between a hydrocarbon bearing zone and a fresh
water bearing zone. In contrast, the difference in acoustic impedance between the two zones
may be higher and therefore, easier to detect.
As would be appreciated by those of ordinary skill in the art, with the benefit of this
disclosure, when signal loss in the medium is non-negligible, time reversal may break down.
However, there are established techniques that can be used to compensate for the attenuation in
both the received signal s(t) and the retransmitted time-reversed signal s(-t). One such technique
is disclosed in "Frequency dispersion compensation in time reversal techniques for UWB
electromagnetic waves" by Yavuz et al., published in IEEE Geosience and Remote Sensing
Letters, v2, no.2, pp. 233-237, 2005. Additionally, one may take advantage of the phase
information. Specifically, operation of an electromagnetic wave propagating LWD tool for
measuring resistivity of formation surrounding a wellbore is based on measuring the signal
attenuation and phase shift between a transmitter and receiver. Similarly, information contained
in the phase portion of the time reversed signal can be used in combination with its amplitude to
refine the measurement.
As would be appreciated by those of ordinary skill in the art, with the benefit of this
disclosure, in one exemplary embodiment, the methods and systems disclosed herein may be
implemented using an information handling system.- In one embodiment, the transceiver array
may be communicatively coupled to an information handling system through a wired or wireless
network. Operation of such systems are well known to those of ordinary skill in the art and will
therefore not be discussed in detail herein. The information handling system may control
generation of signals by the transceiver array and/or process the signals detected to analyze the
formation ahead of the bit. Specifically, software including instructions in accordance with the
methods disclosed herein may be stored in computer-readable media of an information handling
system. The information handling system may then use those instructions to carry out the
methods disclosed herein. In one exemplary embodiment, the information handling system may
store the values of the measured signal in each iteration as it carries out the methods disclosed
herein. In one embodiment, the information handling system may include a user interface that
may provide information relating to formation properties to a user in real time.
The present invention is therefore well-adapted to carry out the objects and attain the ends
mentioned, as well as those that are inherent therein. While the invention has been depicted,
described and is defined by references to examples of the invention, such a reference does not
imply a limitation on the invention, and no such limitation is to be inferred. The invention is
capable of considerable modification, alteration and equivalents in form and function, as will
occur to those ordinarily skilled in the art having the benefit of this disclosure. The depicted and
described examples are not exhaustive of the invention. Consequently, the invention is intended
to be limited only by the spirit and scope of the appended claims, giving full cognizance to
equivalents in all respects.
CLAIMS
What is claimed is:
1. A method of analyzing a subterranean formation comprising:
transmitting a first signal from a transmitter to the formation;
receiving a second signal from the formation;
wherein the second signal is a reflection of the first signal from the
formation;
generating a third signal,
wherein the third signal is the second signal reversed in time;
transmitting the third signal to the formation;
receiving a fourth signal;
wherein the fourth signal is a reflection of the third signal from the
formation;
monitoring the fourth signal.
2. The method of claim 1, wherein generating the third signal further comprises
compensating for loss in amplitude of the second signal.
3. The method of claim 1, wherein at least one of the first signal, the second signal,
the third signal and the fourth signal is selected from a group consisting of an
electromagnetic wave and an acoustic wave.
4. The method of claim 1, wherein the first signal is a pulse signal.
5. The method of claim 1, further comprising:
assuming a distance to a bed boundary;
assuming a resistivity contrast between an upcoming bed and a current bed; and
determining a calculated signal using the assumed distance to the bed boundary
and the assumed resistivity contrast.
6. The method of claim 5, further comprising:
comparing the fourth signal with the calculated signal;
adjusting at least one of the assumed distance to the bed boundary and the
assumed resistivity contrast between the upcoming bed and the current
bed based, at least in part, on the comparison of the fourth signal and the
calculated signal.
7. The method of claim 1, further comprising:
assuming a distance to a bed boundary;
assuming an acoustic impedance contrast between an upcoming bed and a current
bed; and
determining a calculated signal using the assumed distance to the bed boundary
and the assumed acoustic impedance contrast.
8. The method of claim 7, further comprising:
comparing the fourth signal with the calculated signal;
adjusting at least one of the assumed distance to the bed boundary and the
assumed acoustic impedance contrast between the upcoming bed and the
current bed based, at least in part, on the comparison of the fourth signal
and the calculated signal.
9. A system for analyzing formation properties comprising:
an information handling system;
a transmitter placed in a formation and communicatively coupled to the
information handling system;
a receiver placed in the formation and communicatively coupled to the
information handling system;
wherein the transmitter transmits a first signal in response to instructions
from the information handling system;
wherein the receiver receives a second signal, the second signal being a
reflection of the first signal;
wherein the receiver communicates the second signal to the information
handling system;
wherein the transmitter transmits a third signal in response to instructions
from the information handling system, the third signal being the second signal
reversed in time;
wherein the receiver receives a fourth signal, the fourth signal being a
reflection of the third signal;
wherein the information handling system uses the fourth signal to at least
one of determine a property of an upcoming bed and determine a distance to a bed
boundary.
10. The system of claim 9, wherein the transmitter and the receiver are part of a
transceiver.
11. The system of claim 10, wherein the transceiver is selected from a group
consisting of a coaxial transceiver, a tilted transceiver, a horizontal transceiver and a virtually
steerable transceiver.
12. The system of claim 9, wherein at least one of the first signal, the second signal,
the third signal and the fourth signal is selected from a group consisting of an
electromagnetic wave and an acoustic wave.
13. A method for anticipating an upcoming bed when performing subterranean
operations in a formation, comprising:
generating a first signal into the formation;
receiving a reflection of the first signal as a second signal;
generating a third signal into the formation, wherein the third signal is the second
signal reversed in time;
receiving a reflection of the third signal as a fourth signal;
determining a calculated signal using assumed formation properties;
comparing the fourth signal with the calculated signal;
modifying the assumed formation properties if the difference between the fourth
signal and the calculated signal exceeds a threshold value.
14. The method of claim 13, wherein at least one of the first signal, the second signal,
the third signal and the fourth signal is selected from a group consisting of an
electromagnetic wave and an acoustic wave.
15. The method of claim 13, wherein the assumed formation properties comprise at
least one of a distance to a boundary between a current bed and an upcoming bed, a
resistivity contrast between the upcoming bed and the current bed, and an acoustic
impedance contrast between the upcoming bed and the current bed.
16. The method of claim 13, wherein generating the third signal further comprises
compensating for loss in amplitude of the second signal.
17. The method of claim 13, wherein an information handling system at least one of
determines a calculated signal using assumed formation properties, compares the fourth
signal with the calculated signal, and modifies the assumed formation properties if the
difference between the fourth signal and the calculated signal exceeds a threshold value.
18. The method of claim 13, further comprising storing the fourth signal in a
computer readable media.
19. The method of claim 13, wherein a transceiver generates at least one of the first
signal and the third signal and receives at least one of the second signal and the fourth signal.
20. The method of claim 19, wherein the transceiver is selected from a group
consisting of a coaxial transceiver, a tilted transceiver, a horizontal transceiver and a virtually
steerable transceiver.