U.S. patent application number 12/547464 was filed with the patent office on 2011-03-03 for methods and apparatus to calculate a distance from a borehole to a boundary of an anisotropic subterranean rock layer.
This patent application is currently assigned to SCHLUMBERGER TECHNOLOGY CORPORATION. Invention is credited to JAKOB BRANDT UTNE HALDORSEN, VIVIAN PISTRE.
Application Number | 20110051552 12/547464 |
Document ID | / |
Family ID | 43624730 |
Filed Date | 2011-03-03 |
United States Patent
Application |
20110051552 |
Kind Code |
A1 |
PISTRE; VIVIAN ; et
al. |
March 3, 2011 |
METHODS AND APPARATUS TO CALCULATE A DISTANCE FROM A BOREHOLE TO A
BOUNDARY OF AN ANISOTROPIC SUBTERRANEAN ROCK LAYER
Abstract
Methods and apparatus to calculate a distance from a borehole to
a boundary of an anisotropic subterranean rock layer are disclosed.
A disclosed example method includes transmitting a first signal
from a first transmitter at a first location in a borehole
traversing a subterranean formation, receiving the first signal at
a first receiver after a first time period at a second location in
the borehole, receiving the first signal at a second receiver after
a second time period at a third location in the borehole, and
calculating a first distance from the first transmitter to a first
portion of a boundary of a subterranean rock layer adjacent to the
borehole by compensating for an anisotropy of the subterranean rock
layer based on the first time period and the second time
period.
Inventors: |
PISTRE; VIVIAN; (BEIJING,
CN) ; HALDORSEN; JAKOB BRANDT UTNE; (SOMERVILLE,
MA) |
Assignee: |
SCHLUMBERGER TECHNOLOGY
CORPORATION
Sugar Land
TX
|
Family ID: |
43624730 |
Appl. No.: |
12/547464 |
Filed: |
August 25, 2009 |
Current U.S.
Class: |
367/33 ;
367/52 |
Current CPC
Class: |
G01V 1/50 20130101 |
Class at
Publication: |
367/33 ;
367/52 |
International
Class: |
G01V 1/48 20060101
G01V001/48; G01V 1/28 20060101 G01V001/28 |
Claims
1. A method to calculate a distance from a borehole to a boundary
of an anisotropic subterranean rock layer, the method comprising:
transmitting a first signal from a first transmitter at a first
location in a borehole traversing a subterranean formation;
receiving the first signal at a first receiver after a first time
period at a second location in the borehole; receiving the first
signal at a second receiver after a second time period at a third
location in the borehole; and calculating a first distance from the
first transmitter to a first portion of a boundary of a
subterranean rock layer adjacent to the borehole by compensating
for an anisotropy of the subterranean rock layer based on the first
time period and the second time period.
2. A method as defined in claim 1, wherein the first time period
starts when the first signal is transmitted by the first
transmitter and stops when the first signal is received by the
first receiver and the second time period starts when the first
signal is transmitted by the first transmitter and stops when the
first signal is received by the second receiver.
3. A method as defined in claim 1, further comprising: transmitting
a second signal from a second transmitter at a fourth location in
the borehole; receiving the second signal at the first receiver
after a third time period; receiving the second signal at the
second receiver after a fourth time period; calculating a second
distance from the second transmitter to a second portion of the
boundary of the subterranean rock layer adjacent to the borehole by
compensating for the anisotropy of the subterranean rock layer
based on the third time period and the fourth time period; and
determining a distance from the first transmitter to between the
first portion and the second portion of the boundary of the
subterranean rock layer.
4. A method as defined in claim 1, wherein: a first velocity of the
first signal from the first transmitter to the first receiver is a
value between an orthogonal velocity perpendicular to the borehole
and an inline velocity based on a first angle of propagation of the
first signal relative to the first portion of the boundary; and a
second velocity of the first signal from the first transmitter to
the second receiver is a value between the orthogonal velocity and
the inline velocity based on a second angle of propagation of the
first signal relative to the first portion of the boundary.
5. A method as defined in claim 4, wherein compensating for the
anisotropy of the subterranean rock layer includes calculating the
first distance from the first transmitter to the first portion of
the boundary based on at least one of the first velocity, the
second velocity, first time period, the second time period, the
first location of the first transmitter, the second location of the
first receiver, the first distance, the second distance, or an
inline velocity of the first signal along the borehole.
6. A method as defined in claim 5, wherein the first portion of the
boundary reflects the first signal based on at least one of a
change in rock type from the subterranean rock layer to a second
subterranean rock layer, a change in a lithology of the
subterranean rock layer, a change in a fault of the subterranean
rock layer, or a change in an unconformity within the subterranean
rock layer.
7. A method as defined in claim 3, wherein the first and second
signals are at least one or more acoustic signals, seismic signals,
sonic signals or ultrasonic signals.
8. A method as defined in claim 3, further comprising: moving at
least one of the first transmitter, the first receiver or the
second receiver a third distance; transmitting a third signal from
the first transmitter; receiving the third signal at the first
receiver after a fifth time period; receiving the third signal at
the second receiver after a sixth time period; calculating a fourth
distance from the first transmitter to a third portion of the
boundary of the subterranean rock layer by compensating for the
anisotropy of the subterranean rock layer based on the fifth time
period and the sixth time period; and determining the boundary of
the subterranean rock layer based on at least one of the first
distance to the first portion of the boundary, the second distance
to the second portion of the boundary, or the third distance to the
third portion of the boundary.
9. An apparatus to calculate a distance from a borehole to a
boundary of an anisotropic subterranean rock layer, the apparatus
comprising: a first transmitter at a first location to transmit a
first signal within a borehole of a subterranean rock layer; a
first receiver at a second location in the borehole to receive the
first signal after a first time period; a second receiver at a
third location in the borehole to receive the first signal after a
second time period; and a formation processor to calculate a first
distance from the first transmitter to a first portion of the
boundary of the subterranean rock layer by compensating for an
anisotropy of the subterranean rock layer based on the first time
period and the second time period.
10. An apparatus as defined in claim 9, further comprising a second
transmitter at a fourth location in the borehole to transmit a
second signal within the borehole of the subterranean rock
layer.
11. An apparatus as defined in claim 10, wherein: the first
receiver receives the second signal after a third time period; the
second receiver receives the second signal after a fourth time
period; and the formation processor calculates a second distance
from the second transmitter to a second portion of the boundary of
the subterranean rock layer adjacent to the borehole by
compensating for the anisotropy of the subterranean rock layer
based on the third time period and the fourth time period.
12. An apparatus as defined in claim 11, further comprising a
boundary migrator to determine a distance from the first
transmitter to between the first portion and the second portion of
the boundary of the subterranean rock layer.
13. An apparatus as defined in claim 11, wherein at least one of
the first transmitter, the second transmitter, the formation
processor, or the boundary migrator is located at a surface.
14. An apparatus as defined in claim 9, wherein the formation
processor is to: determine a first velocity of the first signal
from the first transmitter to the first receiver based on at least
one of a value between an orthogonal velocity perpendicular to the
borehole and an inline velocity or a first angle of propagation of
the first signal relative to the first portion of the boundary; and
determine a second velocity of the first signal from the first
transmitter to the second receiver based on at least one of the
value between the orthogonal velocity and the inline velocity or a
second angle of propagation of the first signal relative to the
first portion of the boundary.
15. An apparatus as defined in claim 14, wherein the formation
processor compensates for the anisotropy of the subterranean rock
layer by calculating the first distance from the first transmitter
to the first portion of the boundary based on at least one of the
first velocity, the second velocity, first time period, the second
time period, the first location of the first transmitter, the
second location of the first receiver, the first distance, the
second distance, or an inline velocity of the first signal along
the borehole.
16. An apparatus as defined in claim 9, wherein the first receiver
and the second receiver include one or more sensors positioned to
receive signals from different directions.
17. An apparatus as defined in claim 16, wherein the one or more
sensors associated with the first receiver are circumferentially
positioned around the first receiver and the one or more sensors
associated with the second receiver are circumferentially
positioned around the second receiver.
18. An apparatus as defined in claim 16, wherein at least one of
the first receiver, the second receiver, or the first transmitter
is coupled to a tool located in the borehole.
19. An apparatus as defined in claim 11, wherein: at least one of
the first transmitter, the first receiver or the second receiver is
moved a third distance; the first transmitter transmits a third
signal; the first receiver receives the third signal after a fifth
time period; the second receiver receives the third signal after a
sixth time period; the formation processor calculates a fourth
distance from the first transmitter to a third portion of the
boundary of the subterranean rock layer by compensating for the
anisotropy of the subterranean rock layer based on the fifth time
period and the sixth time period; and the boundary migrator
determines the boundary of the subterranean rock layer based on at
least one of the first distance to the first portion of the
boundary, the second distance to the second portion of the
boundary, or the third distance to the third portion of the
boundary.
20. An apparatus as defined in claim 9, farther comprising: a third
receiver at a fifth location in the borehole to receive the first
signal after a third time period; and a fourth receiver at a sixth
location in the borehole to receive the first signal after a fourth
time period.
21. An apparatus as defined in claim 20, wherein the formation
processor calculates the first distance from the first transmitter
to the first portion of the boundary of the subterranean rock layer
by compensating for the anisotropy of the subterranean rock layer
based on the first time period, the second time period, the third
time period, and the fourth time period.
22. An apparatus to calculate a distance from a borehole to a
boundary of an anisotropic subterranean rock layer, the apparatus
comprising a formation processor to calculate a first distance from
a first transmitter to a first portion of the boundary of a
subterranean rock layer by compensating for an anisotropy of the
subterranean rock layer based on a first time period and a second
time period corresponding to a first signal.
23. An apparatus as defined in claim 22, wherein the formation
processor is to: determine a first velocity of the first signal
from the first transmitter to a first receiver based on at least
one of a value between an orthogonal velocity perpendicular to the
borehole and an inline velocity or a first angle of propagation of
the first signal relative to the first portion of the boundary; and
determine a second velocity of the first signal from the first
transmitter to a second receiver based on at least one of the value
between the orthogonal velocity and the inline velocity or a second
angle of propagation of the first signal relative to the first
portion of the boundary.
24. An apparatus as defined in claim 23, wherein the formation
processor compensates for the anisotropy of the subterranean rock
layer by calculating the first distance from the first transmitter
to the first portion of the boundary based on at least one of the
first velocity, the second velocity, the first time period, the
second time period, a first location of the first transmitter, a
second location of the first receiver, the first distance, or an
inline velocity of the first signal along the borehole.
Description
FIELD OF THE DISCLOSURE
[0001] This disclosure relates generally to oil production and,
more particularly, to methods and apparatus to calculate a distance
from a borehole to a boundary of an anisotropic subterranean rock
layer.
BACKGROUND
[0002] Oil and gas producers typically image subterranean rock
layers to determine the location and shape of the subterranean rock
layers. Such imaging may also be used to identify a boundary
between the subterranean rock layer and an adjacent subterranean
rock layer. The imaging is often performed using an imaging tool
disposed within a borehole drilled into the subterranean rock layer
to be imaged.
[0003] Identifying a boundary of a subterranean rock layer is an
important aspect of oil or gas well production. For example,
identifying such a boundary of a rock layer enables oil or gas
producers to plan well locations to efficiently and optimally
extract oil or gas. Additionally, knowing the boundary of a rock
layer may prevent oil and gas producers from drilling into
undesired rock layers.
[0004] Currently, subterranean rock layer boundaries are imaged
and/or measured by time-indexed waveforms or signals that are
emitted by a transmitter and received by sensors or receivers.
These receivers are located a distance away from the transmitter in
a borehole. Typically, the transmitter(s) may be located on the
surface while the receivers are located in a borehole. The signal
emitted from the transmitter(s) propagates through the rock layer
being logged, reflects and/or refracts off of a boundary of the
rock layer, and is received by the receivers. The waveforms or
signals received by the receivers may be processed using signal
migration to determine the distance between the receivers in the
borehole and the rock layer boundary. However, the velocity of the
waveforms or signals may be affected by anisotropic properties in
the logged rock layer or boundary such as faults in the rock layer,
cracks in the rock layer, a change in lithology in the rock layer
or a change in an unconformity within the rock layer.
SUMMARY
[0005] Example methods and apparatus to calculate a distance from a
borehole to a boundary of an anisotropic subterranean rock layer
are described. An example method includes transmitting a first
signal from a first transmitter at a first location in a borehole
traversing a subterranean formation, receiving the first signal at
a first receiver after a first time period at a second location in
the borehole, and receiving the first signal at a second receiver
after a second time period at a third location in the borehole.
Additionally, the example method includes calculating a first
distance from the first transmitter to a first portion of a
boundary of a subterranean rock layer adjacent to the borehole by
compensating for an anisotropy of the subterranean rock layer based
on the first time period and the second time period.
[0006] An example apparatus includes a transmitter at a first
location to transmit a first signal within a borehole of a
subterranean rock layer, a first receiver at a second location in
the borehole to receive the first signal after a first time period,
and a second receiver at a third location in the borehole to
receive the first signal after a second time period. The example
apparatus further includes a formation processor to calculate a
first distance from the first transmitter to a first portion of the
boundary of the subterranean rock layer by compensating for an
anisotropy of the subterranean rock layer based on the first time
period and the second time period.
[0007] Alternatively, the example apparatus includes a formation
processor to calculate a first distance from a first transmitter to
a first portion of the boundary of a subterranean rock layer by
compensating for an anisotropy of the subterranean rock layer based
on a first time period and a second time period corresponding to a
first signal.
BRIEF DESCRIPTION OF THE DRAWINGS
[0008] FIGS. 1A-1D show typical seismic-while-drilling tools with
one or more transmitters located at the surface.
[0009] FIG. 2 shows a graph representing the effect of anisotropy
within a subterranean rock layer.
[0010] FIG. 3 shows an example wellsite system including a
transmitter and receivers to implement the example methods and
apparatus described herein.
[0011] FIG. 4 shows an example sonic logging-while-drilling
tool.
[0012] FIG. 5 shows an example seismic imaging tool within a
subterranean rock layer.
[0013] FIG. 6 shows the seismic imaging tool transmitting and
receiving signals affected by anisotropy within the subterranean
rock layer of FIG. 5.
[0014] FIG. 7 shows an example functional block diagram of the
logging and control processor of FIG. 3.
[0015] FIGS. 8, 9 and 10 are flowcharts of example processes that
may be used to implement the example logging and control processor,
the transmitters, the receivers, the example formation processor,
the example boundary migrator, command processor, and/or the
transmission manager of FIGS. 3, 5, 6, and 7.
[0016] FIG. 11 is a block diagram of an example processor system
that may be used to implement the example methods and apparatus
described herein.
DETAILED DESCRIPTION
[0017] Certain examples are shown in the above-identified figures
and described in detail below. In describing these examples, like
or identical reference numbers are used to identify common or
similar elements. The figures are not necessarily to scale and
certain features and certain views of the figures may be shown
exaggerated in scale or in schematic for clarity and/or
conciseness. Although the following discloses example systems
including, among other components, software or firmware executed on
hardware, it should be noted that such systems are merely
illustrative and should not be considered as limiting. For example;
it is contemplated that any form of logic may be used to implement
the systems or subsystems disclosed herein. Logic may include, for
example, implementations that are made exclusively in dedicated
hardware (e.g., circuits, transistors, logic gates, hard-coded
processors, programmable array logic (PAL), application-specific
integrated circuits (ASICs), etc.) exclusively in software,
exclusively in firmware, or some combination of hardware, firmware,
and/or software. Accordingly, while the following describes example
systems, persons of ordinary skill in the art will readily
appreciate that the examples are not the only way to implement such
systems. Further, the examples may be implemented by acoustic
signals that may include seismic signals, sonic signals, ultrasonic
signals and/or any other shear and/or compression signals.
[0018] Currently, oil and/or gas producers use time-indexed
waveforms of a signal to image a boundary of a subterranean rock
layer adjacent to a wellbore or a borehole. The frequency,
amplitude, and/or energy of the signal are specified so that the
signal can propagate through the rock layer being logged but
reflect off a boundary of the rock layer. For example, a signal
having a frequency of 8000 Hertz (Hz) may be specified to enable
the signal to propagate through a first rock layer. However, a
signal at this frequency may reflect off a boundary of the rock
layer. The boundary may include a change in rock type from the
subterranean rock layer being logged to a second type of rock in a
second subterranean rock layer, a change in a lithology of the
subterranean rock layer, a change in a fault of the subterranean
rock layer, or a change in an unconformity within the subterranean
rock layer.
[0019] The boundary is imaged by transmitting one or more acoustic
signals from a transmitter and recording when the signals are
received by one or more receivers. Each receiver may include one or
more sensors circumferentially located around the receiver so that
each sensor may detect the transmitted signal from a specified
direction. The sensors may include any type of transducer to
convert a detected acoustic (e.g., seismic, sonic, ultrasonic,
etc.) signal into an electrical signal and/or impulse decipherable
by a microcontroller, a transistor, and/or a processor. By aligning
the sensors in specified directions, oil and/or gas producers can
determine the direction from which a signal was reflected.
Typically, one or more transmitters) are located at the surface in
proximity of a well site while receivers are included within a tool
that is placed within a wellbore or borehole of a rock layer bring
logged.
[0020] In examples where one or more receivers are included within
a tool located in a borehole, the location of the receivers within
the tool may be fixed. In the case where the receiver locations are
fixed, the distance between each transmitter on the surface and
each receiver is known. In addition to knowing the distances
between transmitter(s) and receivers, oil and gas producers can
determine the time for a signal to propagate from a transmitter to
each receiver based on a logging and control processor that
measures the time period between the signal being transmitted and
the time at which each receiver receives the signal.
[0021] FIGS. 1A-1D show typical seismic-while-drilling tools that
include one or more transmitters 1 at the surface and one or more
receivers 2 in a borehole 3. FIGS. 1A and 1B show that the downhole
tool may include a single receiver 2 in the borehole 3.
Additionally, FIGS. 1A and 1C show that a single transmitter 1 may
be implemented as a single seismic (e.g., signal) source, while
FIGS. 1B and 1D show a plurality of the transmitters 1 providing
respective seismic sources. FIG. 1B shows the receiver 2 receiving
reflections and direct signals from the transmitters 1, while FIGS.
1C and 1D show multiple receivers 2 receiving signals directly from
the one or more transmitters 1.
[0022] Seismic images may be generated from the arrangements of the
transmitter(s) 1 and the receiver(s) 2 of FIGS. 1A-1D. FIG. 1A
shows a reflection of the signal off a rock layer boundary or bed
boundary 4. The seismic imaging of the bed boundary generates a
`zero-offset` vertical seismic profile arrangement. FIG. 1B shows a
reflection of the signals off the bed boundary 4. This seismic
imaging generates a `walkway` vertical seismic profile arrangement.
FIG. 1C shows a refraction through salt dome boundaries. This
seismic imaging generates a `salt proximity` vertical seismic
profile. FIG. 1D includes signal reflections off the rock layer
boundary 4 and/or some direct signals from the transmitter 1. This
seismic imaging generates a `walk above` vertical seismic profile.
The vertical profiles and/or arrangements referred to in FIGS.
1A-1D are labeled vertical because the receiver(s) 2 are oriented
vertically along the borehole 3.
[0023] Furthermore, each receiver(s) 2 may include sensors evenly
spaced around the circumference of the receiver. To determine the
distance from the tool in the borehole 3 to a first portion of the
boundary 4 of a rock layer, the transmitter(s) 1 transmits a first
signal. This first signal propagates in all directions through the
rock layer. When the signal reaches the boundary 4 of the rock
layer, the signal reflects back to the borehole 3. The receiver(s)
2 may then detect the reflected signal. Similarly, a second signal
may be transmitted by the transmitters) 1 and received by the
receiver(s) 2 after reflecting off the boundary 4. The distance to
the boundary 4 can be related to the time for the first signal to
reach each receiver 2, the distance from each of the receiver(s) 2
to the transmitter 1, and the velocity of the first signal. There
may be a separate time-distance relationship for each sensor within
the receiver 2 that receives the reflected first signal. Similarly,
the time for the second signal to reach each of the receivers 2,
the distance from the receivers 2 to the transmitters) 1, and the
velocity of the signal can be related to the distance to the
boundary 4. These relationships may then be combined into a
semblance model to calculate the distance to a portion of the
boundary 4.
[0024] In other typical examples, a sonic tool may be located
within the borehole 3. However, in these cases, the signal velocity
determined from the velocity of the signal in the direction (i.e.,
parallel to the longitudinal axis) of the borehole 3 (e.g., the
inline velocity) may differ from the velocity of the signal
propagating through the rock formation. The velocity of the signal
may differ in this manner due to anisotropy in the rock layer. For
example, an inline signal may have a velocity that differs by 20%
compared to a signal traveling in a direction perpendicular or
orthogonal to the borehole due to anisotropy in the rock layer.
More generally, the signal velocity may differ or vary based on an
angle of signal propagation, which may range from a direction along
(i.e., parallel to) the longitudinal axis of the borehole to a
direction perpendicular to the longitudinal axis of the borehole.
For example, if the anisotropy is uniform in the rock layer, a
signal traveling at an angle of 22 degrees from the longitudinal
axis of the borehole may have a velocity that is 5% slower than a
signal traveling in the inline direction (i.e., along the
longitudinal axis) of the borehole.
[0025] FIG. 2 shows a graph defining an example of anisotropy
within a subterranean rock layer. The x-axis shows a normalized
inline signal velocity (V.sub.INL) and the y-axis shows a
normalized orthogonal and/or perpendicular signal velocity
(V.sub.ORT). The inline signal velocity corresponds to a velocity
of the signal in the formation along an axis parallel to a
borehole, where the signal is sent from a transmitter directly to a
receiver. An anisotropy velocity line 5 shows a velocity of a
signal based on an angle of propagation (e.g., .theta.). The angle
of propagation is an angle at which a signal propagates through a
rock layer. If the signal is reflected back to the receivers by a
boundary of a rock layer that is parallel to the wellbore, Snell's
Law of Reflection indicates that the angle at which the signal
travels when transmitted by a transmitter, the angle at which the
signal is reflected off of the boundary of a rock layer, and the
angle at which the signal is received at a receiver are
substantially the same angle. Thus, a signal propagating through a
uniform rock layer should have a constant anisotropic velocity
based on the angle of transmission and reception, which is also
equal to the angle of propagation for a reflector parallel to the
wellbore.
[0026] As a result of anisotropy, a signal propagating in the
inline direction may have a normalized signal velocity of 0.8 while
a signal propagating in the orthogonal direction may have a
normalized signal velocity of 0.9. Thus, in this example, the
signal propagating in the orthogonal direction is 12.5% faster than
the signal propagating in the inline direction. The example in FIG.
2 shows a signal 6 having an angle of propagation .theta.. Based on
the anisotropy velocity line 5, the signal 6 propagating through a
rock formation at an angle of .theta. may have a normalized
anisotropic velocity of 0.86 (e.g., the length of the vector
representing the signal 6 from the origin to the velocity line
5).
[0027] FIG. 2 shows the anisotropy velocity line 5 as approximately
linearly dependent on the angle of propagation (e.g., 0.8 in the
V.sub.INL direction to 0.9 in the V.sub.ORT direction). However, in
other examples, anisotropy may be exponentially dependent,
logarithmically dependent, Gaussian dependent, inversely dependent,
and/or may exhibit any other types of functional dependence on the
angle of propagation. In yet other examples, the anisotropy may not
depend on the angle of propagation. However, the example methods
and apparatus described herein compensate for any type of
anisotropy that varies based on the angle of propagation.
[0028] As noted above, anisotropy may result from faults in a rock
layer, cracks in a rock layer, a change in lithology in a rock
layer, and/or a change in an unconformity within a rock layer. Not
compensating for anisotropy within a rock layer may create errors
in determining a distance of a rock layer boundary from a sonic
and/or seismic imaging tool. The error may result from assuming
that the signal velocity is uniform in all directions. In practice,
when a rock layer is affected by anisotropy, the signal velocity
may differ significantly from the inline signal velocity based on
the angle of propagation. Furthermore, because the angle of
propagation of the signal received by each receiver and/or sensor
is different for each receiver, the signal velocities may be
different based on these different angles. As a result of the
difference between the inline signal velocity and the anisotropic
signal velocity, the calculated distance to the boundary may be
significantly different from the actual distance.
[0029] The difference between the calculated distance and the
actual distance may result in oil or gas producers drilling
wellbores or boreholes in rock layers that may not contain the
desired natural resources, improperly routing boreholes through
rock layers with natural resources, and/or drilling into undesired
rock formations in a manner that weakens the subterranean rock
formations and/or diluting target formations with undesired rock
formations. Furthermore, oil and/or gas producers do not currently
account for anisotropy when imaging and/or determining rock layer
boundary locations due to complexities and uncertainties based on
the relationship between the signal velocity, the angle of
propagation, the distance to the boundary of the rock layer, and
the profile of anisotropy associated with the rock layer.
[0030] The example methods and apparatus described herein may be
used to calculate the shape and/or boundary of a rock layer or a
distance from a tool to a rock layer boundary by compensating for
the anisotropy in the rock layer. The example methods and apparatus
may be used to compensate for the anisotropy by analyzing
relationships between time periods and distances between
transmitter(s) and receivers and solving for the angle of each
signal received at a receiver to determine an effective anisotropic
signal velocity. In particular, the example methods and apparatus
described herein use the calculated anisotropic signal velocity for
the signal received by each receiver and/or sensor to determine the
distance to a portion of the rock layer boundary.
[0031] The example methods and apparatus also include one or more
transmitters within the tool that includes the receivers. Because
the transmitter(s) and receivers are included inline within the
same tool, the relationship between the tool and the distance to a
rock layer boundary can be determined using the signal propagation
time, the distance between the transmitter(s) and receivers, and
the signal velocities. Equation 1 below shows the relationship
between the time for a receiver to receive the reflected signal
(i.e., T), the distance from the receiver to a transmitter that
transmitted the signal (i.e., a), the anisotropic signal velocity
(i.e., V.sub.0), and the distance from the tool to the boundary
(i.e., X), for a boundary parallel to the wellbore.
T = ( 2 X ) 2 + a 2 V .theta. Equation 1 ##EQU00001##
[0032] Equation 1 indicates that the greater a time period, (T) for
a signal to reach a receiver, the greater the distance (X) between
the boundary and the tool based on a constant signal velocity
(V.sub..theta.) and distance of a receiver to the transmitter (2a).
The signal takes a longer time period to be received by receivers
farther from the transmitter. This longer time period indicates a
lower angle of propagation of the signal with the boundary and a
longer distance for the signal to travel to the receiver. In a
particular example corresponding to the signal 6 of FIG. 2 having
an angle of propagation .theta., the effective signal velocity
(i.e., V.sub..theta.) may be expressed as shown in Equation 2
below.
V .theta. = V INL ( 1 - 2 ) 1 + cos .theta. Equation 2
##EQU00002##
[0033] In Equation 2, .epsilon. is the difference between the
inline velocity (e.g., V.sub.INL) and a perpendicular velocity
(e.g., V.sub.ORT), divided by the inline velocity. In other
examples, Equation 2 may be expressed differently to reflect a
different relationship between the signal velocity (i.e.,
V.sub..theta.) and the propagation direction .theta.. FIG. 2
defines .theta. as an angle of transmission and/or reception of the
signal. Further, the inline signal velocity (e.g., V.sub.INL) is
the velocity of the signal measured in the direction of the
wellbore or borehole based on a time for the signal to travel
linearly from the transmitter to the receivers without reflecting
off the boundary.
[0034] The inline velocity is known by measuring the time for the
signal to propagate linearly from a transmitter to a receiver. By
knowing the distance between each transmitter and receiver, the
time for a signal to reach each receiver after reflecting off of a
rock layer boundary, and the effective velocity of the signal
related to the angle of propagation, the example methods and
apparatus may use semblance processing to combine the time-distance
anisotropic velocity (TDAV) relationship for each transmitter and
receiver to model the distance of the boundary as a best-fit model.
For example, three transmitters, thirteen receivers, and eight
sensors per receiver may yield 312 different transmitter and
receiver TDAV relationships. From these relationships, the
effective signal velocity dependent upon the angle of propagation
and the distance to the rock layer boundary are modeled using a
best-fit calculation. Because the distance to the boundary and the
angle of propagation within each TDAV relationship are unknown
dependent variables, the boundary distance can be expressed as a
function of the angle of propagation and the effective anisotropic
signal velocity. The best-fit calculation then uses the number of
relationships and the known inline signal velocity to solve for the
effective signal velocity resulting from the angle of propagation.
Upon knowing the effective anisotropic velocity for each
relationship, the distance to each reflection point of the rock
layer boundary can be calculated using Equation 1.
[0035] In examples where the reflecting formation boundary is not
substantially parallel to the wellbore, Equation 1 may be modified.
For example, if there is an angle between the reflecting boundary
of a rock layer and the wellbore axis (e.g., .phi.), the distance X
to the reflecting boundary in the Equation 1 may be replaced with a
different relation (e.g., X cos(.phi.)). In this example, the
distance X is a distance between a transmitter and a reflecting
boundary. Further, the distance between a transmitter and a
receiver in Equation 1 may be replaced by a different relation
(e.g., a+2X sin(.phi.)). With these different example relations,
the relationship between the distance to a rock layer boundary, the
distance from a transmitter to a receiver, and the propagation
angle remains the same. However, the transmission and/or the
reception angle (e.g., .theta.) may differ by twice the angle
between the reflecting boundary and the wellbore axis (e.g., by
2.phi.). Even in a homogeneous anisotropic formation the
transmitted and the received signal may propagate at two different
velocities. The effective velocity may be a weighted average of
these two different velocities. Nevertheless, the effective
velocity provides information about the propagation velocities
perpendicular to the wellbore, information that may not be
available by any other means. Additionally, the angle .phi. between
the formation boundary and wellbore axis may be included in
parameters determined by a best-fit procedure.
[0036] While the example methods and apparatus described herein
provide an imaging tool that may include one or more transmitters
and/or two or more receivers, the example methods and apparatus may
include an imaging tool having any number of transmitters and/or
receivers. For example, a sonic and/or seismic imaging tool may
include one transmitter and two receivers, with each receiver
including a sensor. Alternatively, a sonic and/or seismic imaging
tool may include three transmitters and thirteen receivers, with
each receiver including eight sensors
[0037] FIG. 3 shows a wellsite system 7 in which the example
methods and apparatus may be implemented. The wellsite system 7 may
be onshore or offshore. In the example wellsite system of FIG. 3, a
borehole 11 is formed in one or more subsurface formations by
rotary and/or directional drilling. A drillstring 12 is suspended
within the borehole 11 and has a bottomhole assembly 100 that
includes a drill bit 105 at its lower end. The wellsite system 7
includes a platform and derrick assembly 10 positioned over the
borehole 11 at the surface. The derrick assembly 10 includes a
rotary table 16, which may engage a kelly 17 at an upper end of the
drillstring 12 to impart rotation to the drillstring 12. The rotary
table 16 may be energized by a device or system not shown. The
example drillstring 12 is suspended from a hook 18 that is attached
to a traveling block (not shown). Additionally, the drillstring 12
is positioned through the kelly 17 and the rotary swivel 19, which
permits rotation of the drillstring 12 relative to the hook 18.
Additionally or alternatively, a top drive system (not shown) could
be used to impart rotation to the drillstring 12.
[0038] In the example depicted in FIG. 3, the wellsite system 7
further includes drilling fluid 26. For example, the drilling fluid
26 may comprise a water-based mud, an oil-based mud, a gaseous
drilling fluid, water, gas or other fluid for maintaining bore
pressure and/or removing cuttings from the area surrounding the
drill bit 105. The drilling fluid 26 may be stored in a pit 27
formed at the wellsite. A pump 29 delivers the drilling fluid 26 to
the interior of the drillstring 12 via a port in the rotary swivel
19, causing the drilling fluid 26 to flow downwardly through the
drillstring 12 as indicated by directional arrow 8. The drilling
fluid 26 exits the drillstring 12 via ports in the drill bit 105
and then circulates upwardly through the annulus region between the
outside of the drillstring 12 and the wall of the borehole 11 as
indicated by directional arrows 9. The drilling fluid 26 lubricates
the drill bit 105, carries cuttings from the formation up to the
surface as it is returned to the pit 27 for recirculation, and
creates a mudcake layer (not shown) (e.g., filter cake) on the
walls of the borehole 11.
[0039] Additionally, the wellsite system includes a communications
relay 45 and a logging and control processor 50. The example
communications relay 45 may receive information and/or data from
sensors, transmitters, and/or receivers located within the
bottomhole assembly 100. The information may be received by the
communications relay 45 via a wired communication path through the
drillstring 12 and/or via a wireless communication path. The
communications relay 45 transmits the received information and/or
data to the logging and control processor 50. Additionally, the
communications relay 45 may receive data and/or information from
the logging and control processor 50. Upon receiving the data
and/or information, the communications relay 45 may forward the
data and/or information to the appropriate sensor(s),
transmitter(s), and/or receiver(s) within the bottomhole assembly
100.
[0040] The example logging and control processor 50 may include a
user interface that enables parameters to be input and/or outputs
to be displayed. Additionally, the logging and control processor 50
may control imaging of a boundary of a rock layer. For example, the
logging and control processor 50 may position the bottomhole
assembly 100 and/or a sonic and/or seismic imaging tool within the
borehole 11, instruct transmitters to transmit a signal for
receivers and/or sensors to receive.
[0041] Additionally, the logging and control processor 50 may
calculate a distance from the borehole 11 to a portion of a rock
boundary based on the transmitted and received signal. Furthermore,
the logging and control processor 50 may compensate for anisotropy
within the rock layer while calculating the distance from the
borehole 11 to a boundary of the rock layer. While the logging and
control processor 50 is depicted uphole at the surface and within
the wellsite system 7, a portion or the entire logging and control
processor 50 may be positioned in the bottomhole assembly 100
and/or in a remote location. The logging and control processor 50
is described in greater detail in conjunction with FIG. 6.
[0042] In some examples, the tools of the bottomhole assembly 100
of FIG. 3 may include any number and/or type(s) of
logging-while-drilling (LWD) modules or tools (two of which are
designated by reference numerals 120 and 120A) that may be housed
in respective drill collars. The LWD modules 120 and/or 120A may be
part of an LWD tool suite of the type disclosed in P. Breton et
al., "Well Positioned Seismic Measurements," Oilfield Review, pp.
32-45, Spring 2002, incorporated herein by reference. The
bottomhole assembly 100 may also include measuring-while-drilling
(MWD) modules (one of which is designated by reference numeral
130), and a rotary-steerable system or mud motor 150. The MWD
module 130 may measure the azimuth and inclination of the drill bit
105 to, for example, monitor the borehole trajectory.
[0043] The bottomhole assembly 100 includes capabilities for
measuring, processing and/or storing information, as well as for
communicating information via, for example, a transmitter 122
and/or receivers 132A-B. The transmitter 122 is shown within the
LWD module 120. However, the transmitted 122 may be included within
the MWD module 130 and/or within a separate sonic and/or seismic
imaging tool. Additionally, the receivers 132A-B are shown within
the MWD module 130. However, the receivers 132A-B may be included
within the LWD module 120 and/or within a separate sonic and/or
seismic imaging tool. The transmitter 122 and/or the receivers
132A-B may be communicatively coupled to the communications relay
45 and/or the logging and control processor 50. Furthermore,
although the single transmitter 122 is shown, other examples may
include two or more transmitters. Additionally, although only the
two receivers 132A-B are shown, other examples may include more or
fewer receivers.
[0044] The transmitter 122 may be capable of transmitting any
signal including, but not limited to, acoustic signals, seismic
signals, sonic signals, ultrasonic signals, and/or any other
compression and/or shear signals. The receivers 132A-B may include
sensors that are capable of receiving the signal type generated by
the transmitter. For example, if the transmitter 122 generates a
seismic or acoustic signal with a center frequency of 8 kHz,
sensors within the receivers 132A-B may be configured to detect the
seismic signal with a 8 kHz center frequency while filtering other
signals types. The transmitter 122 may include any type of device
capable of generating a signal, while the receivers 132A-B include
sensors that are configured to detect and transduce a signal into
electrical data for processing by the logging and control processor
50.
[0045] Although the components of FIG. 3 are shown and described as
being implemented in a particular conveyance type, the example
methods and apparatus described herein are not limited to a
particular conveyance type but, instead, may be implemented in
connection with different conveyance types including, for example,
coiled tubing, wireline, wired drill pipe, and/or any other
conveyance types known in the industry. Additionally or
alternatively, the examples described herein may be implemented
with smart wells and/or intelligent completions.
[0046] FIG. 4 shows an example offshore rig 410 that includes a
logging-while-drilling (LWD) tool 430. The offshore rig 410
includes the transmitter 122 of FIG. 3 deployed near the surface of
the water. Alternatively, the transmitter 122 may be deployed
within the LWD tool 430. Additionally, the offshore rig 410 may
include a processor to control the transmission of signals from the
transmitter 122. The offshore rig 410 may also include acoustic
receivers and/or a recorder to capture reference signals near the
transmitter 122. Furthermore, the offshore rig 410 may include
telemetry equipment for receiving signals from the transmitter 122
and/or the receivers 132A-B within the LWD 430.
[0047] The telemetry equipment and/or the recorder may be coupled
to a processor so that transmitted and received signals may be
synchronized using uphole and downhole clocks. The example LWD tool
430 may be similar to the LWD modules 120 and/or 120A of FIG. 3
described in U.S. Pat. No. 6,308,137, incorporated herein by
reference. The LWD tool 430 includes at least the receivers 132A-B,
which may be communicatively coupled to a signal processor so that
recordings may be made of signals detected by the by the receivers
132A-B in synchronization with the transmitting of the signals by
the transmitter 122.
[0048] FIG. 5 shows an example seismic imaging tool 502 within a
subterranean formation 500 having a first rock layer 504 and a
second rock layer 506 forming a boundary 507 with the first rock
layer 504. The example seismic imaging tool 502 is located inline
within a borehole 508 and is positioned parallel to the boundary of
the first rock layer 504 to be imaged. The seismic imaging tool 502
may be used to image a shape and/or the boundary of the first rock
layer 504 such as where the first rock layer 504 meets the second
rock layer 506 at the boundary 507. Additionally, it should be
recognized that the seismic imaging tool 502 may not be shown to
scale in relation to the borehole 508 and/or the rock layers 504
and 506.
[0049] The example of FIG. 5 includes the two adjacent rock layers
504 and 506 that may include any types of subterranean rock.
Furthermore, the rock layers 504 and 506 may include the same
general rock type but the first rock layer 504 may include a rock
type with a first type of directionally aligned sediment while the
second rock layer 506 includes sediment aligned in a different
direction. Alternatively, the rock layers 504 and 506 may include
similar types of rocks with different directions of stress and/or
fracturing.
[0050] The seismic imaging tool 502 may be included within the
bottomhole assembly 100 of FIG. 3 or, alternatively, may be a
separate imaging tool. A control device (not shown) may be
structurally coupled to the seismic imaging tool 502 to position
and/or move the tool 502 within the borehole 508. Additionally, the
seismic imaging tool 502 may be communicatively coupled to the
logging and control processor 50 of FIG. 3.
[0051] The example seismic imaging tool 502 includes transmitters
122A-B, which are similar or identical to the transmitter 122 of
FIG. 3. Furthermore, the seismic imaging tool 502 includes
receivers 132A-D that are similar or identical to the receivers
132A-B of FIG. 3. The transmitters 122A-B are positioned some
distance away from the receivers 132A-D. Additionally, each of the
receivers 132A-D is spaced apart from the other receivers 132A-D.
Moreover, each of the receivers 132A-D may include one or more
sensors circumferentially positioned around the exterior of the
receiver. For example, if the seismic imaging tool 502 is
cylindrical in shape, a receiver with eight sensors may have
sensors positioned every 45 degrees around the circumference of the
receiver. Likewise, if the seismic imaging tool is rectangular in
shape, two sensors may be positioned on each side of the
receiver.
[0052] The example of FIG. 5 shows the transmitter 122A
transmitting a signal 510 through the first rock layer 504. The
signal 510 is depicted as three wavefronts. The signal 510 may
include any type of transmittable signal including an acoustic
signal, a seismic signal, a sonic signal, an ultrasonic signal,
and/or any other suitable signal. The frequency, amplitude, and/or
power may be specified such that the signal 510 propagates through
the first rock layer 504 and reflects off the boundary 507 between
the first rock layer 504 and the second rock layer 506.
[0053] The example signal 510 is transmitted by the transmitter
122A as a wave in all directions (i.e., omnidirectionally). Thus,
as each portion of the signal propagates through the rock layer 504
and reflects off the boundary 507 with the second rock layer 506,
the receivers 132A-D receive respective reflected portions of the
signal 510. In this manner, the receivers 132A-D may each receive a
reflected portion of the transmitted signal 510. FIG. 5 shows the
signal 510 affected by anisotropy within the first rock layer 504.
For example, the signal 510 is shown as propagating faster in the
inline direction (e.g., V.sub.INL) compared to the signal 510
propagating in the orthogonal direction (e.g., V.sub.ORT). In other
examples, the signal 510 may propagate through the first rock layer
504 faster in the orthogonal direction than the inline
direction.
[0054] FIG. 6 shows the seismic imaging tool 502 transmitting and
receiving signals affected by anisotropy within the first rock
layer 504 of FIG. 5. In FIG. 6, the first rock layer 504 is
transparent for clarity of explanation. The subterranean rock
formation 500 of FIG. 6 includes the seismic imaging tool 502 with
the transmitters 122A-B and the receivers 132A-D of FIG. 5.
Additionally, the example signal 510 of FIG. 5 is shown in FIG. 6
as signal paths 602-608.
[0055] The signal paths 602-608 originate at the transmitter 122A.
The first signal path 602 is received by the first receiver 132A
and is reflected by the boundary 507 at a first reflection point
612 at a reflection angle 610. The second signal path 604 is
received by the second receiver 132B and is reflected by the
boundary 507 of the first rock layer 504 at a second reflection
point 614. Similarly, the third signal path 606 is received by the
third receiver 132C and is reflected by the boundary 507 of the
first rock layer 504 at a third reflection point 616. Additionally,
the fourth signal path 608 is received by the fourth receiver 132D
and is reflected by the boundary 507 of the first rock layer 504 at
a fourth reflection point 618. Furthermore, the transmission angles
with respect to an axis orthogonal to the boundary 507 of each of
the signal paths 602-608 through the first rock layer 504 are the
same as the reflection angles (e.g., the reflection angle 610) at
the respective reflection points 612-618.
[0056] Because the distance from the reflection points 612-618 to
the respective receivers 132A-D is relatively short, the boundary
507 of the first rock layer 504 may be modeled as a flat or planar
surface at a constant distance from the tool 502 despite the fact
that rock layer boundaries are typically at least somewhat uneven.
The small signal reception area of the receivers 132A-D receives
only a small portion of the signal 510 that is reflected from a
small scale reflection point at the boundary 507. For example, the
small scale reflection point may only be a few decimeters (dm) from
the tool 502. At this small scale, a reflection point (e.g., each
of the reflection points 612-618) may be modeled as a substantially
flat or planar surface. In examples where the first rock layer
boundary 507 is slanted, curved, or otherwise defined as a surface
that is not at a substantially constant distance from the tool 502,
seismic image processing may still model the small scale nature of
the portion of the boundary as a flat or planar surface. Then,
signal migration of multiple seismic images from different portions
of the boundary 507 may be used to combine the calculated distances
from the tool 502 to the boundary into a smooth continuous boundary
to compensate for the localized flat surfaces provided by the
seismic imaging processing.
[0057] The reflection points 612-618 are generally mid-points of
the respective signal paths 602-608. Additionally, the distance
between the transmitters 122A-B and the receivers 132A-D is known
based on specifications of the seismic imaging tool 502. As a
result of the known distances, a distance 620 between the tool 502
and the boundary 507 of the first rock layer 504 can be calculated
based on the time required for each of the signal paths 602-608 to
propagate from the first transmitter 122A to the respective
receivers 132A-D. Additionally, an inline velocity can be
calculated when an inline portion of the signal 510 is received by
any one of the receivers 132A-D. This inline portion of the signal
510 propagates directly within the first rock layer 504 from the
transmitter 122A in a direction parallel to (.e., along the
longitudinal axis of) the seismic imagining tool 502 to the
receivers 132A-D.
[0058] The signal velocity associated with each of the signal paths
602-608 is affected by the anisotropy within the first rock layer
504. In the example of FIG. 6, signal portions traveling at an
angle that is closer to in the inline direction propagate faster
due to the anisotropy. For example, the portion of the signal 510
associated with the signal path 608 may have a greater velocity
than portions of the signal 510 associated with the signal paths
602-606. Similarly, the signal portion associated with the signal
path 606 may have a greater velocity than the signal portions
associated with the signal paths 602-604. As a result of the signal
portions having different velocities, the propagation time periods
for each of the signal portions along the respective signal paths
602-608 are based not only on the distance traveled by the signal
portions along the signal paths 602-608 but also on the anisotropic
velocity of each of the signal portions.
[0059] In calculating the distance 620, the effect of anisotropy in
the first rock layer 504 can be compensated by relating the
anisotropic signal velocity of each of the signal paths 602-608,
the angles of reflection for each signal paths 602-608, the known
distances between the transmitters 122A-B and the receivers 132A-D,
the inline signal velocity, and the time period or the transmission
time for each of the signal paths 602-608. In addition to the
signal paths 602-608 shown in FIG. 6, additional signal paths may
be associated with each of the sensors positioned around the
receivers 132A-D. Furthermore, the second transmitter 122B may
transmit a second signal to be received by each of the receivers
132A-D. Still further, the example in FIG. 6 may include additional
receivers and/or transmitters (not shown).
[0060] The logging and control processor 50 of FIG. 3 may compile
the collected transmission time periods for each of the signal
paths 602-608 as well as the transmission time periods for any
other signal paths not shown. The logging and control processor 50
may then model the combined data into a best-fit model (e.g., a
linear programming model) that determines the distance 620.
Additionally, the model may determine a distance from each of the
transmitters 122A-B and/or receivers 132A-D to the boundary 507 of
the first rock layer 504.
[0061] Furthermore, signal migration may be implemented to
determine the distance of the boundary of the first rock layer 504
from the tool 502 at the reflection points 612-618 and any other
reflection points not shown. These distances may then be modeled to
generate an image of a portion of the boundary 507 of the first
rock layer 504. Upon imaging this portion of the first rock layer
boundary 504, the seismic imaging tool 502 may be moved a distance
(e.g., 6 inches) to determine a distance to the next portion of the
first rock layer boundary 504.
[0062] FIG. 7 shows an example functional diagram of the logging
and control processor 50 of FIG. 3. The example logging and control
processor 50 sends transmission instructions to a tool (e.g., the
example tool 502, the LWD modules 120 and 120A, and/or the MWD
module 130) and processes received signals and/or messages from the
tool to calculate a distance from the tool to a portion of a rock
layer boundary using anisotropic compensation of the signal
velocity. Additionally, the logging and control processor 50 may
use signal migration and/or semblance processing of multiple
portions of calculated boundary positions to image and/or determine
a continuous rock layer boundary.
[0063] To receive signals and/or messages from sensors and/or
receivers within the tool, the example logging and control
processor 50 includes an input receiver 702. The example input
receiver 702 receives the signals and/or messages via a
communication path 720 that may be communicatively coupled to the
tool that includes the transmitters, receivers, and/or sensors. The
communication path 720 may include any wired communication path(s)
and/or any wireless communication path(s).
[0064] The input receiver 702 may receive the signals and/or
messages by polling each of the receivers and/or sensors for any
received signal data that may have been accumulated or collected by
the receivers and/or sensors. Alternatively, the input receiver 702
may receive the signals and/or messages or, generally, information
or data from the sensors and/or the receivers upon those sensors
and/or receivers detecting a signal portion (e.g., a portion of the
signal 510 of FIG. 5). Upon receiving the signals and/or messages,
the example input receiver 702 may queue the information or data
associated with the signals and/or messages until a formation
processor 704 is available to process the information.
Alternatively, the input receiver 702 may parse the received
messages for information included within the message including the
identity of the receiver and/or sensor that detected the signal
portion and transmitted the message, the time a signal was detected
and/or any other data included within the signal that was detected.
Upon parsing this information, the input receiver 702 may forward
the parsed information to the formation processor 704 for
processing. In yet another example, the input processor 702 may
buffer the received messages until the input processor 702 receives
a request for data from the formation processor 704. Upon receiving
the request, the input receiver 702 may forward the data or
information included within the received signals and/or messages
and/or the received messages to the formation processor 704.
[0065] To calculate a distance of a subterranean rock layer
boundary from a tool by compensating for anisotropy within the rock
layer, the example logging and control processor 50 of FIG. 7
includes the formation processor 704. The example formation
processor 704 receives messages and/or data included within the
received signals and/or messages from the input receiver 702. The
example formation processor 704 then matches those messages and/or
data with the data associated with the transmission of the
corresponding signal. The data associated with transmitting the
signal may include a time the signal was transmitted from a
transmitter (e.g., a timestamp), the signal type, and/or any other
data included within the signal.
[0066] By matching the received messages to the transmitted signals
and/or message data, the formation processor 704 can calculate the
inline velocity of the signal and determine the time period elapsed
for each signal portion to propagate from the transmitter to the
corresponding sensor and/or receiver. The formation processor 704
calculates the propagation time by subtracting the time at which a
portion of the signal was received by a sensor and/or receiver from
the time at which the signal was transmitted. Additionally, the
example formation processor 704 may calculate the inline signal
velocity by determining a first instance or occurrence for a
received signal and/or message from a receiver, calculating the
time period for the signal to propagate from the transmitter to the
receiver and/or sensor, and dividing the distance between the
transmitter and the receiver by the time period. Further, the
example formation processor 704 may calculate the inline signal
velocity by using semblance analysis of the signal traveling along
receivers within the seismic and/or sonic tool.
[0067] The first instance of the received signal and/or message is
generally a portion of the signal traveling in the direction along
the tool (i.e., inline) because this is the shortest distance for
the signal to travel. Subsequent instances or occurrences of the
receiver receiving portions of the signal are generally from
reflections off the rock layer boundary 507 because the distance to
the rock layer boundary 507 and back to the tool is greater than
the distance directly from the transmitter to the receiver.
[0068] The example formation processor 704 may determine distances
between each transmitter and receiver and/or sensor by accessing a
tool property database 706. For example, if the formation processor
704 processes a received signal or message that indicates the
signal portion was received by a sensor with an identification
value of DM01, the formation processor 704 may access the database
706 to determine that the sensor DM01 has a location that is two
meters from the transmitter.
[0069] Upon calculating the time periods, the example formation
processor 704 may generate an equation (e.g., using Equations 1
and/or 2 above), a mathematical relationship, and/or the
time-distance anisotropic velocity relationships for each receiver
and/or sensor that relates a distance to a portion of a rock layer
boundary to a propagation time of the signal, a distance of the
receiver from the transmitter, the inline velocity of the signal,
and/or the anisotropic velocity of the signal portion received.
[0070] Additionally, the formation processor 704 may determine an
orthogonal signal velocity based on a distance to a portion of a
rock layer boundary, a propagation time of the signal, a distance
of the receiver from the transmitter, and/or the inline velocity of
the signal. The formation processor 704 may then combine the
equations into an expression and/or data model (e.g., a system or
matrix of equations) to determine the anisotropic velocity of each
signal portion and/or a distance to a portion of the rock layer
boundary. The anisotropic velocity of each signal portion may be
expressed as a ratio of the inline velocity and an angle of
propagation and/or reflection of the signal portion through the
rock layer (e.g., using Equation 2 above).
[0071] The example formation processor 704 may determine that
additional data is needed to calculate a distance to a boundary. In
these cases, the formation processor 704 may send a message to a
command processor 706 to instruct a transmitter to transmit another
signal. Upon receiving this message, the command processor 706 may
instruct a transmission manager 708 to instruct a transmitter to
transmit a signal. The instructions may include a time to transmit
the signal and/or a signal type (e.g., signal frequency, signal
amplitude, signal duration, etc.).
[0072] The formation processor 704 may utilize a plurality of
equations to determine the angle of propagation for each signal
portion to determine the anisotropic velocity and the distance to a
portion of the rock layer boundary. Because the angle of
propagation is dependent on the distance to the boundary 507 (FIG.
5), the formation processor 704 may utilize any best fit model,
least squares best fit model, a variance minimization best fit
model, and/or any other best fit model. Alternatively, the
formation processor 704 may organize the equations into a matrix or
system of equations to model and/or determine the distance to the
rock layer boundary. Furthermore, because the points of reflection
of the signal portions are some distance apart, the formation
processor 704 may determine a distance from each point of
reflection at the boundary 507 to an orthogonal point in the
tool.
[0073] Upon calculating the distance(s) from the tool to the
portion of the rock layer boundary being imaged or measured, the
formation processor 704 forwards these distance(s) to a boundary
migrator 710. The example boundary migrator 710 determines
distances between the calculated distances between the tool and the
rock layer boundary 507 to generate a continuous rock layer
boundary for imaging. For example, if the boundary migrator 710
receives the distance to reflection points 612 and 614 of FIG. 6
from the formation processor 704, the boundary migrator 710
determines the distances from between the points 612 and 614 to the
tool 502. The example boundary migrator 710 determines these
distances using migration processing that estimates the distances
to the boundary 507 between the points 612 and 614 based on the
measured or calculated distances associated with the points
612-618.
[0074] Additionally, the example boundary migrator 710 of FIG. 7
may store the calculated distances to a database. Then, as the tool
moves within the borehole to determine distances to (i.e., to
image) other portions of the boundary, the boundary migrator 710
migrates (e.g., interpolates) the distances to the rock layer
boundary between the measurement locations of the tool. For
example, if there is a seven foot spacing between measurement
locations of the tool, the boundary migrator 710 may estimate the
rock layer boundary between these points based on the calculated
distances. As a result of the migration processing, the boundary
migrator 710 generates a continuous subterranean rock layer
boundary for portions of the rock layer that have been
measured.
[0075] The example boundary migrator 710 may also create images
from the calculated and/or estimated distances of the rock layer
boundary. These images may show the rock layer shape, depth,
boundary and/or any other information that may be determined from
the calculated distances. The example boundary migrator 710 may
transmit the images, the calculated distances and/or the estimated
distances to an operator via a communication path 728.
[0076] The example logging and control processor 50 includes the
command processor 706 to manage the activities and/or functions of
the formation processor 704, the boundary migrator 710, and/or the
transmission manager 708. The command processor 706 may receive
commands from an oil and/or gas producer operator via a
communication path 726. The operator may send instructions to the
command processor 706 to initiate imaging of a rock layer boundary,
to initiate image processing of a rock layer boundary, and/or to
determine an operating efficiency of the formation processor 704.
Additionally, an operator may transmit an image profile to the
example command processor 706 to specify locations within a
borehole that a tool is to image and/or measure. The command
processor 706 may then manage the timing of the transmission of
signals and the processing of the received data via the formation
processor 704 to ensure a rock layer is measured and/or imaged
according to the image profile. Additionally, the command processor
706 may instruct the movement of the tool.
[0077] To manage the generation and transmission of commands to
transmitters, sensors, and/or receivers included within the tool,
the example logging and control processor 50 of FIG. 7 includes the
transmission manager 708. Upon receiving an instruction to transmit
a signal, the transmission manager 708 determines which transmitter
is to transmit the signal, a time at which the signal is to be
transmitted, the type of signal to be transmitted, and/or any
signal properties of the signal to be transmitted. The example
transmission manager 708 then sends a transmission message to the
corresponding transmitter included within the tool via a
communication path 722. The communication path 722 may include any
wired and/or wireless communication path(s).
[0078] The transmission message may include the signal type the
transmitter is to transmit, a duration for the transmission of the
signal (e.g., 1 second), a time at which the signal is to be
transmitted, and/or signal properties (e.g., amplitude, frequency,
etc.). Alternatively, the transmission manager 708 may send a
transmission message to the appropriate transmitter at the time the
transmitter is to transmit a signal. Upon receiving the message,
the transmitter may then transmit the specified signal.
Additionally, the transmission manager 708 may send a transmission
message to the receivers and/or sensors to alert the receivers
and/or sensors that a signal will be transmitted. This alert may
activate the sensors and/or receivers and/or may provide to the
sensors and/or receivers the time at which the signal will be
transmitted.
[0079] The example tool property database 706 stores known
properties of the tool, including distances between transmitters,
receivers and/or sensors and/or locations of the sensors around a
circumference of the tool. The database 706 may also store the
angle of orientation for each of the sensors and/or the signal
type(s) that the transmitters are configured to output.
Furthermore, the database 706 may store identification information
for each of the transmitters, receivers, and/or sensors. The data
within the database 706 may be updated, added to, deleted, and/or
modified by an operator via a communication path 724. For example,
an operator may modify distances between receives and transmitters
after a redesign of the tool. The tool property database 706 may be
implemented by random access memory (RAM), read-only memory (ROM),
a programmable ROM (PROM), an electronically-programmable ROM
(EPROM), an electronically-erasable PROM (EEPROM), and/or any other
type of memory.
[0080] While an example manner of implementing the logging and
control processor 50 is depicted in FIG. 7, one or more of the
interfaces, data structures, elements, processes and/or devices
illustrated in FIG. 7 may be combined, divided, rearranged,
omitted, eliminated and/or implemented in any other way. For
example, the example input receiver 702, the example formation
processor 704, the example command processor 706, the example
transmission manager 708, and/or the example boundary migrator 710
illustrated in FIG. 7 may be implemented separately and/or in any
combination using, for example, machine-accessible or readable
instructions executed by one or more computing devices and/or
computing platforms (e.g., the example computing system 1100 of
FIG. 11).
[0081] Further, the example input receiver 702, the example
formation processor 704, the example command processor 706, the
example transmission manager 708, the example boundary migrator 710
and/or, more generally, the example logging and control processor
50 may be implemented by hardware, software, firmware and/or any
combination of hardware, software and/or firmware. Thus, for
example, any of the example input receiver 702, the example
formation processor 704, the example command processor 706, the
example transmission manager 708, the example boundary migrator 710
and/or, more generally, the example logging and control processor
50 can be implemented by one or more circuit(s), programmable
processor(s), application specific integrated circuit(s) (ASIC(s)),
programmable logic device(s) (PLD(s)) and/or field programmable
logic device(s) (FPLD(s)), etc.
[0082] FIGS. 8, 9, and 10 are flowcharts depicting example
processes that may be carried out to implement the example logging
and control processor 50, the example seismic imaging tool 502, the
example transmitters 122A-B, the example receivers 132A-D, the
example formation processor 704, the example boundary migrator 710,
the example command processor 706, and/or the transmission manager
708 of FIGS. 3, 5, 6, and/or 7. The example processes of FIGS. 8,
9, and/or 10 may be carried out by a processor, a controller and/or
any other suitable processing device. For example, the example
processes of FIGS. 8, 9, and/or 10 may be embodied in coded
instructions stored on any tangible computer-readable medium such
as a flash memory, a CD, a DVD, a floppy disk, a ROM, a RAM, a
programmable ROM (PROM), an electronically-programmable ROM
(EPROM), an electronically-erasable PROM (EEPROM), an optical
storage disk, an optical storage device, magnetic storage disk, a
magnetic storage device, and/or any other medium that can be used
to carry or store program code and/or instructions in the form of
methods, processes or data structures, and which can be accessed by
a processor, a general-purpose or special-purpose computer, or
other machine with a processor (e.g., the example computing system
1100 discussed below in connection with FIG. 11). Combinations of
the above are also included within the scope of computer-readable
media.
[0083] Processes comprise, for example, instructions and/or data
that cause a processor, a general-purpose computer, special-purpose
computer, or a special-purpose processing machine to implement one
or more particular processes. Alternatively, some or all of the
example operations of FIGS. 8, 9, and/or 10 may be implemented
using any combination(s) of ASIC(s), PLD(s), FPLD(s), discrete
logic, hardware, firmware, etc.
[0084] Also, one or more of the example operations of FIGS. 8, 9,
and/or 10 may be implemented using manual operations or as any
combination of any of the foregoing techniques, for example, any
combination of firmware, software, discrete logic and/or hardware.
Further, other processes implementing the example operations of
FIGS. 8, 9, and/or 10 may be employed. For example, the order of
execution of the blocks may be changed, and/or one or more of the
blocks described may be changed, eliminated, sub-divided, or
combined. Additionally, any or all of the example operations of
FIGS. 8, 9, and/or 10 may be carried out sequentially and/or
carried out in parallel by, for example, separate processing
threads, processors, devices, discrete logic, circuits, etc.
[0085] The example process 800 of FIG. 8 determines known
parameters associated with transmitters and/or receivers included
within a seismic imaging tool (e.g., the seismic imaging tool 502),
a LWD module, a MWD module, and/or any other type of measuring
device that includes transmitters and/or receivers. By determining
the known parameters including the number of transmitters,
receivers, and/or sensors, these known parameters associated with a
tool may be accessed by the example formation processor 704 of FIG.
7 to calculate and/or model a distance of the tool from a rock
layer boundary using anisotropy compensation. The example process
800 may be executed upon the setup and/or prior to lowering the
seismic imaging tool, LWD module, and/or MWD module into a
borehole. Additionally, the example process 800 may be carried out
upon the specification and/or design of the seismic imaging tool,
LWD module, and/or MWD module.
[0086] The example process 800 begins by identifying and storing
the number of transmitters included within the seismic imaging
tool, LWD module, and/or MWD module (block 802). Next, the example
process 800 identifies and stores the number of receivers within
the seismic imaging tool, LWD module, and/or MWD module (block
804). The example process 800 then identifies and stores the number
of sensors per receiver and the position of each sensor on the
respective receivers (blocks 806 and 808). The position of a sensor
may be identified by indicating on which side of a tool the sensor
is located and/or whether the sensor is directionally positioned to
receive signals from downhole, uphole, orthogonal to the tool, or
at an angle to the tool.
[0087] The example process 800 continues by identifying and storing
a distance between each transmitter and each receiver (block 810).
The distances may be calculated from the closet point of the
transmitter to a closest point on the receiver or a midpoint of the
transmitter to a midpoint of the receiver. Alternatively, the
example process 800 may include calculating a distance from each
transmitter to each sensor within each receiver. The example
process 800 then identifies and stores the signal type to be
emitted by the transmitter(s) (block 812). The signal type may
include a frequency of the signal, an amplitude of the signal,
and/or any other signal properties. Alternatively, the command
processor 706 of FIG. 7 may select a signal type to transmit if the
transmitters are capable of transmitting more than one type of
signal. Upon selecting a signal type to transmit, the command
processor 706 may transmit the signal type to the formation
processor 704 to calculate and model a distance to a rock layer
boundary. The number of transmitters, receivers, sensors per
receiver, distance and/or signal type identified by the example
process 800 may be stored to the tool property database 706 of FIG.
7. Additionally, identifying the sensors, transmitters and/or
receivers may include storing a unique identification value
associated with each device. An identification value may be
included within any message transmitted by the transmitters, the
receivers, and/or the sensors. Upon identifying the signal type,
the example process 800 ends.
[0088] The example process 900 of FIG. 9 determines a distance
between a tool and a rock layer boundary by compensating for
anisotropy within the rock layer. Multiple example processes 900
may be executed in parallel or series as multiple signals are
transmitted by transmitter(s) within a tool. Additionally, multiple
example processes 900 may be executed in parallel or series as
multiple signals are transmitted by transmitter(s) within other
tools communicatively coupled to a common processor (e.g., the
example logging and control processor 50 of FIG. 7).
[0089] The example process 900 begins by transmitting a first
signal from a first transmitter within a seismic imaging tool, LWD
module, and/or MWD module (block 902). The first signal is
transmitted through a subterranean rock layer. A portion of the
first signal may reflect off a boundary of the subterranean rock
layer back to one or more receivers. Additionally, another portion
of the first signal may travel inline with the tool and be received
by one or more receivers to determine an inline velocity of the
first signal. After a time period, the first signal is received by
a receiver (block 904). The first signal may be received by one or
more sensors within the receiver. Next, the receiver identifies the
sensor(s) that received a portion of the first signal (block 906).
The receiver may identify the sensors by a unique identification
message transmitted from each sensor that received the first
signal. Upon identifying the sensors, the receiver transmits a
received signal message to the example formation processor 704
within the logging and control processor 50 of FIG. 7 (block 908).
The received signal message may include a time the signal was
received, an identification value of the sensor, an identification
value of a receiver that received the signal, and/or any other data
that may have been included within the signal (e.g., an
identification value of the transmitter, a time the signal was
transmitted, etc.). Alternatively, each of the sensors may transmit
a received signal message including a unique identifier of the
sensor to the logging and control processor 50.
[0090] The example process 900 continues by determining if any
additional sensors within other receivers have also received the
first signal (block 910). If one or more of the other sensors have
received the first signal (blocks 910 and 904), those corresponding
receivers identify the sensor(s) that received the signal (block
908). The example process 900 may determine if there are no other
receivers to receive a signal if the logging and control processor
50 has received signal messages from all the receivers and/or if
after a specified time period, the example process 900 determines
that the signal did not reach a receiver and/or a receiver did not
detect a portion of the first signal. This time period may be an
estimation of the time for the first signal to propagate through
the first rock layer to reach all of the receivers included within
the tool. If no other receiver has received the signal, the example
process 900 determines if another signal is to be transmitted from
a transmitter (block 912).
[0091] If the example process 900 of FIG. 9 determines that another
signal is to be transmitted (block 912), the example process 900
instructs a transmitter to transmit another signal (block 914). The
transmitter that transmits the additional signal may include the
transmitter that transmitted the first signal and/or a different
transmitter. Upon transmitting another signal, the example process
executes blocks 906-910 again. However, if the example process 900
of FIG. 9 determines that another signal is not to be transmitted
(block 912), the example process 900 calculates a distance from the
tool, the receiver(s), and/or the transmitter(s) to a portion of a
boundary of the rock layer (block 916). The example process 916 in
conjunction with FIG. 10 details the calculation of the distance
including compensation for anisotropy within the rock layer.
[0092] Upon determining and/or modeling the distance to the
boundary, the example process 900 stores the distance (block 918).
This distance may be stored to the example boundary migrator 710
and/or any other database. Next, the example process 900 determines
if the tool is to be moved to another location within the borehole
(block 920). If the tool is to be moved to image another portion of
the boundary of the rock layer, the tool is moved a specified
distance and a signal is transmitted from a transmitter (block
914). The specified distance for the tool to be moved may range
from a few centimeters to a few kilometers depending on the process
type to image the complete boundary.
[0093] If the tool is not to be moved to another location (block
920), the example process 900 migrates the calculated distances to
determine and/or model the boundary of the subterranean anisotropic
rock layer (block 922). Migrating the calculated distances may
include interpolating the unmeasured portions of the boundary
between measured portions of the boundary to some average of the
portions of the boundary with known calculated distances. Upon
determining the boundary of the subterranean rock layer, the
example process 900 ends.
[0094] FIG. 10 depicts an example manner of implementing the
process 916 of FIG. 9. The example process 916 of FIG. 10
calculates and/or models a distance between a tool and a rock layer
boundary by compensating for anisotropy within the rock layer.
Multiple example processes 916 may be executed in parallel or
series as multiple signals are transmitted by transmitter(s) within
a tool. Additionally, multiple example processes 916 may be
executed in parallel or series as multiple signals are transmitted
by transmitter(s) within other tools communicatively coupled to a
common processor (e.g., the example logging and control processor
50 of FIG. 7).
[0095] The example process 916 begins by compiling received signals
and/or messages from each receiver and/or sensor for a single
location of a tool within a borehole (block 1002). Each received
signal and/or message may include a time the signal or message was
received by a receiver and/or sensor, an identification value of
the sensor and/or received that received the signal or message,
and/or any other data that may have been included within the signal
or message (e.g., identification value of the transmitter, time the
signal was transmitted, etc.). Additionally, the example process
916 may match the received signal data to data associated with the
corresponding transmitted signal.
[0096] Next, the example process 916 accesses the tool property
database 706 of FIG. 7 to determine the stored distances between
each of the transmitters, receivers and/or sensors (block 1004).
The example process 916 then determines the inline signal velocity
of the transmitted signal (block 1006). The inline signal velocity
may be determined by identifying a time period corresponding to
when one or more receivers and/or sensors detected a first instance
of the transmitted signal. When a signal is transmitted, the first
instance of the signal received by a sensor should be a portion of
the signal propagating in the direction of the tool. Portions of
the signal that are received at a later time period arrive later
because those portions of the signal have a greater distance to
travel by reflecting off a boundary and returning to the tool.
Thus, the example process 916 may identify the first instance of
the received signal, determine the time period from when the signal
was transmitted to when the signal was received, and divide a
distance between the transmitter and the receiver and/or sensor
that received the signal by that time period to determine the
inline signal velocity.
[0097] The example process 916 of FIG. 10 continues by calculating
a time period for each portion of the received signal to propagate
from the transmitters to each sensor and/or receiver (block 1008).
Then, for each transmitter and each sensor and/or receiver, the
example process 916 generates an equation relating a distance to a
portion of a rock layer boundary to the calculated time period, the
distance between the receiver and/or sensor with the transmitter,
and/or an anisotropic velocity of the signal (block 1010). The
anisotropic velocity of the portion of the signal received may be
expressed as a ratio of the inline velocity similar to Equation 2
above.
[0098] The example process 916 then compiles the equations for each
transmitter and receiver and/or sensor (block 1012). Next, the
example process 916 combines the compiled equations to solve for
the anisotropic signal velocity for each equation (block 1014). The
example process 916 may combine the equations (e.g., equations
similar to Equation 1) into a matrix where the anisotropic velocity
of each signal portion is the unknown variable. Alternatively, the
anisotropic velocity of each signal portion may be determined by
modeling the combined equations to determine a best fit solution.
The example process 916 may then or concurrently determine the
distance to the portion of the subterranean anisotropic rock layer
boundary (block 1016). Upon determining the anisotropic velocity
for each signal portion, the example process may determine the
distance using an equation similar to Equation 1. Alternatively,
the example process 916 may determine the distance to the boundary
by solving for the distance in the same model that also determines
the anisotropic signal velocity. In this manner, the best fit model
solves for the distance while solving for the anisotropic velocity
for each signal. Generally, the larger the number of equations, the
more accurate the model may be to determine the anisotropic signal
velocity and/or a distance to the boundary. For example, a tool
with three transmitters, thirteen receivers, and eight sensors per
receiver may yield 312 equations while one transmitter, two
receivers, and two sensors per receiver may yield four equations.
Upon determining the distance to a portion of the rock later
boundary, the example process 916 ends.
[0099] FIG. 11 is a block diagram of an example computing system
1100 that may be used to implement the example methods and
apparatus described herein. For example, the computing system 1100
may be used to implement the example logging and control processor
50, the example formation processor 704, and/or the example
boundary migrator 710. The example computing system 1100 may be,
for example, a conventional desktop personal computer, a notebook
computer, a workstation or any other computing device. A processor
1102 may be any type of processing unit, such as a microprocessor
from the Intel.RTM. Pentium.RTM. family of microprocessors, the
Intel.RTM. Itanium.RTM. family of microprocessors, the Intel.RTM.
Core.TM. family of microprocesors, and/or the Intel XScale.RTM.
family of processors. Memories 1106, 1108 and 1110 that are coupled
to the processor 1102 may be any suitable memory devices and may be
sized to fit the storage demands of the system 1100. In particular,
the flash memory 1110 may be a non-volatile memory that is accessed
and erased on a block-by-block basis.
[0100] An input device 1112 may be implemented using a keyboard, a
mouse, a touch screen, a track pad or any other device that enables
a user to provide information to the processor 1102.
[0101] A display device 1114 may be, for example, a liquid crystal
display (LCD) monitor, a cathode ray tube (CRT) monitor or any
other suitable device that acts as an interface between the
processor 1102 and a user. The display device 1114 as pictured in
FIG. 11 includes any additional hardware required to interface a
display screen to the processor 1102.
[0102] A mass storage device 1116 may be, for example, a
conventional hard drive or any other magnetic or optical media that
is readable by the processor 1102.
[0103] A removable storage device drive 1118 may, for example, be
an optical drive, such as a compact disk-recordable (CD-R) drive, a
compact disk-rewritable (CD-RW) drive, a digital versatile disk
(DVD) drive or any other optical drive. It may alternatively be,
for example, a magnetic media drive. A removable storage media 1120
is complimentary to the removable storage device drive 1118, in as
much as the media 1120 is selected to operate with the drive 1118.
For example, if the removable storage device drive 1118 is an
optical drive, the removable storage media 1120 may be a CD-R disk,
a CD-RW disk, a DVD disk or any other suitable optical disk. On the
other hand, if the removable storage device drive 1118 is a
magnetic media device, the removable storage media 1120 may be, for
example, a diskette or any other suitable magnetic storage
media.
[0104] At least some of the above described example methods and/or
apparatus are implemented by one or more software and/or firmware
programs running on a computer processor. However, dedicated
hardware implementations including, but not limited to, application
specific integrated circuits, programmable logic arrays and other
hardware devices can likewise be constructed to implement some or
all of the example methods and/or apparatus described herein,
either in whole or in part. Furthermore, alternative software
implementations including, but not limited to, distributed
processing or component/object distributed processing, parallel
processing, or virtual machine processing can also be constructed
to implement the example methods and/or systems described
herein.
[0105] It should also be noted that the example software and/or
firmware implementations described herein are stored on a tangible
storage medium, such as: a magnetic medium (e.g., a magnetic disk
or tape); a magneto-optical or optical medium such as an optical
disk; or a solid state medium such as a memory card or other
package that houses one or more read-only (non-volatile) memories,
random access memories, or other re-writable (volatile) memories.
Accordingly, the example software and/or firmware described herein
can be stored on a tangible storage medium such as those described
above or successor storage media.
[0106] Although certain example methods, apparatus, and
machine-accessible medium have been described herein, the scope of
coverage of this patent is not limited thereto. On the contrary,
this patent covers all methods, apparatus, and machine-accessible
medium fairly falling within the scope of the appended claims
either literally or under the doctrine of equivalents.
* * * * *