COMPENSATED CROSS-WELL TOMOGRAPHY METHODS AND SYSTEMS
BACKGROUND
Modern oil field operations demand a great quantity of information relating to the
parameters and conditions encountered downhole. Among the types of desired information is the
extent and distribution of fluids in the reservoir formations. While it is possible to glean a
general picture with surface surveys, such surveys are limited by the effects of the subsurface
layers overlying the region of interest. Such effects can be eliminated or reduced by the use of
boreholes in or near the region of interest. With a suitable arrangement of borehole transmitters
and receivers, crosswell tomography can be used to extract a comparatively detailed image of the
region of interest, suitable for planning and monitoring production from a reservoir.
Initially, crosswell tomography was performed using seismic transmitters and receivers,
but more recently the focus has been on the use of electromagnetic (EM) transmitters and
receivers. As with any geophysical survey, noise and inaccuracies in the survey system will
negatively impact image quality. One important cause of this degradation in crosswell
tomography is mismatches between assumed and actual values for sensor gains and phases.
These mismatches can result from a number of causes including differences in sensor types,
calibration errors, variation in borehole configurations (e.g., mud composition and borehole
radius), and environmental parameters such as temperature and pressure. Phase mismatches can
be caused or exacerbated by latencies in electronic systems and synchronization errors for the
widely-distributed components of a typical crosswell tomography system. Traditional methods
crosswell tomography do not appear to adequately address such inaccuracies.
BRIEF DESCRIPTION OF THE DRAWINGS
In the attached drawings:
Fig. 1 shows an illustrative drilling environment;
Fig. 2A shows an illustrative multilateral environment for crosswell tomography;
Fig. 2B shows an illustrative multiple borehole environment for crosswell tomography;
Fig. 3 is a function block diagram of an illustrative compensated crosswell tomography
system;
Figs. 4A and 4B shows illustrative configurations for electromagnetic (EM) transmit and
receive antennas;
Fig. 5 is a high-level flow diagram of an illustrative inversion process;
Fig. 6 is a detailed flow diagram of an illustrative inversion process;
Fig. 7 shows an illustrative reservoir model for simulation;
Fig. 8 shows traditional inversion results for the illustrative simulation;
Fig. 9 shows compensated inversion results for the illustrative simulation; and
Fig. 10 is a flow diagram of an illustrative compensated crosswell tomography method.
While the invention is susceptible to various alternative forms, equivalents, and
modifications, specific embodiments thereof are shown by way of example in the drawings and
will herein be described in detail. It should be understood, however, that the drawings and
detailed description thereto do not limit the disclosure, but on the contrary, they provide the
foundation for one of ordinary skill to discern the alternative forms, equivalents, and
modifications that are encompassed with the described embodiments by the scope of the
appended claims.
DETAILED DESCRIPTION
The issues identified in the background are at least in part addressed by the disclosed
compensated crosswell tomography methods and systems. In at least some method embodiments,
data is obtained from at least two receivers in response to each of at least two transmitters, the
transmitters and receivers being located in boreholes near the region of interest. The data is
combined to form at least one compensated value that compensates for any transmitter and
receiver gain or phase inaccuracies. An inversion is then performed to identify the subsurface
structure that best matches these compensated values. At least some system embodiments
implement this method using software that then outputs one or more images derived from the
subsurface structure.
The disclosed systems and methods employ at least one borehole in or near the subsurface
region of interest. Such boreholes may be drilled as illustrated in Fig. 1. A drilling platform 2 is
equipped with a derrick 4 that supports a hoist 6 for raising and lowering a drill string 8. The
hoist 6 suspends a top drive 10 that is used to rotate the drill string 8 and to lower the drill string
through the well head 12. Sections of the drill string 8 are connected by threaded connectors 7.
Connected to the lower end of the drill string 8 is a drill bit 14 that rotates to create and extend a
borehole 16 along a desired path 18. A pump 20 circulates drilling fluid through a supply pipe 20
to top drive 10, downhole through the interior of drill string 8, through orifices in drill bit 14,
back to the surface via the annulus around drill string 8, and into a retention pit 24. The drilling
fluid transports cuttings from the borehole into the pit 24 and aids in maintaining the integrity of
the borehole 20.
Logging instruments 26 may be positioned on the drill string 8. A telemetry module 28
may provide communication between the logging instruments 26 and a surface interface 34 using
any one of various available telemetry technologies. In one example, acoustic sensors 30 and 32
detect mud pulse telemetry carrying data from the logging instruments. A data processing system
38 is coupled to the surface interface 34 by a wired or wireless communications link 36 to
control and acquire measurements from the logging instruments 26. The illustrated data
processing system 38 is a general purpose computer with one or more input devices 42 and one
or more output devices 44 for interacting with a user. Software on information storage media 40
(or in the computer's internal memory) configures the computer's internal processor(s) to acquire
crosswell tomography measurements and derive a model of the subsurface structure for display
to the user.
Logging instruments 26 preferably include acoustic transducers for sending and/or
receiving acoustic signals, or electromagnetic antennas for sending and/or receiving
electromagnetic ("EM") signals. Though illustrated on a drill string, the logging instruments can
additionally be conveyed on a wire line or a coiled tubing string. Data processing system 38
acquires measurements using multiple transmitters and receivers in various positions in and
around the region of interest.
Fig. 2A shows an illustrative configuration in which various transmitters ("T") and
receivers ("R") are positioned in each of the branches of a multilateral well, including a
substantially vertical branch penetrating the region of interest and five substantially horizontal
branches extending outward in various directions along the top of the reservoir. Fig. 2B shows a
different illustrative configuration in which multiple transceiver (transmitter and receiver) nodes
are positioned throughout a region of interests using multiple vertical wells, some of which may
include lateral branches having additional transceiver nodes. Some or all of the boreholes may be
open (i.e., uncased). Similarly, some or all of the boreholes may be cased and the sensors
positioned inside the casing. Where the casing causes too much attenuation, the sensors may be
configured to send/receive low frequency magnetic waves. Some systems may employ additional
sensors positioned at the surface.
The number and position of the nodes depends on the region's volume, properties
(resistivity or acoustic impedance), and the desired resolution of the model. Generally, however,
a greater number of nodes offers better model accuracy, and a three dimensional arrangement of
nodes may be preferred to a two dimensional arrangement, which in turn may be preferred to a
one dimensional arrangement. Where some of the nodes are spaced too far from the region of
interest to be useful, they may be omitted to avoid introducing unnecessary noise into the
inversion process.
Fig. 3 is a function block diagram of a compensated crosswell tomography system. Each of
the nodes in Figs. 2A-2B includes at least one sensor 302 for transmitting and/or receiving
acoustic or EM signals. For an EM system the sensors are antennas or magnetometers. Suitable
antenna configurations include a coil antenna (see, e.g., Fig. 4A) with an optional bucking coil
(see, e.g., Fig. 4B), a toroidal antenna, an electrical gap antenna, a spaced-electrode antenna, and
a horn antenna. For an acoustic system, the suitable sensors include piezoelectric transducers,
magnetic coil speakers, bender bars, and conventional seismic sources.
Some of the sensors are coupled to a transmitter 304 to transmit signals into the formation,
some are coupled to a receiver 306 to receive signals from the formation, some are switchable
between transmit and receive mode. In the latter case, a switch 308 may be provided between the
sensor 302 and its associated transmitter 304 and receiver 306. Some embodiments may even
provide multiple transmitters and receivers for at given sensor, e.g., for different signal
frequencies. Conversely, the system may include multiple sensors 302 coupled to a given
transmitter 304 or receiver 306, e.g., to enable the transmitter or receiver to send or receive
signals in different directions or polarizations. Tilted antennas are contemplated for making
measurements of orthogonal or linearly independent EM signal components.
Each node includes a telemetry unit 310 that controls the associated transmitters 304 and
receivers 306 (and switches 308) in accordance with commands from a system control center
314. A network 312 couples the control center 314 to the various nodes via conventional wired
or wireless communication links to the well head of each well in the system, and an interface unit
at each well head completes the communications chain via an intrawell telemetry channel such as
a wireline, an electromagnetic telemetry link, an acoustic telemetry link, or a mud pulse
telemetry technique. Any suitable configuration can be used for network 312.
During normal operation, the control center 314 iterates through each of the available
transmitters 304, causing them to fire in turn while all of the other nodes are set to detect and
capture any resulting receive signal. The telemetry units 310 capture the receiver signals for each
transmitter firing and communicate them to the control center 314. Such measurements may be
repeated and combined to improve signal to noise ratio. The data processing unit 38 acquires the
set of receiver responses to each transmitter firing and processes them as outlined below to
produce a model of the subsurface structure. A user can view and interact with the model via a
visualization unit 44.
Fig. 5 shows a high-level block diagram of an inversion process. Raw data (the amplitude
and phase of each receiver's responses to each transmitter) is processed in block 502 to obtain
compensated data. In block 504, an iterative inversion process adapts a structural model of the
region of interest until the compensated data are matched by predicted data. A forward model
block 506 generates the predicted data based on the current structural model, and the inversion
block responsively adapts the structural model until the error between the predicted and
compensated data values falls below a threshold. The adapted structural model is then output by
block 504 for visualization and/or analysis to determine the amount and distribution of fluids in
the reservoir.
The compensated data is formed by constructing ratios of the raw data. These ratios are
designed to compensate for any systematic errors in the transmit/receive characteristics of the
various sensors. Because of this compensation, the results of the inversion process are much
improved relative to those of an inversion process performed directly on the raw data. Moreover,
this approach relaxes system design constraints, enabling the use of a variety of sensor types, and
operation in diverse borehole and environmental circumstances. The synchronization
requirements are relaxed, and the system can more easily accommodate miscalibration or
parameter drift of the sensors.
Let V be a complex value representing the amplitude and phase of a signal measurement
by receiver i in response to transmitter j . Let it be related to the "true" signal measurement V y
V = c c V
where c and are complex values representing the gain and phase errors between the actual and
assumed characteristics of receiver i and transmitter j . These errors can be eliminated by
combining this measurement with the measurement of receiver i in response to a second
transmitter m, and the measurements of a second receiver k to both transmitters j and m to form a
compensated value i¾ :
Piikjm
Note the cancellation of the gain and phase errors. If the system includes a total of T transmit
antennas and a total of R receive antennas, there are a total of !/(2( -2)!) transmitter pairs and a
total of R l R-2) ) receiver pairs, yielding up to T R l T-2) R-2) ) compensated values. For a
system with T=4 and R=16, there would be up to 64 measurements from which up to 720
compensated values could be calculated. In practice the measurements may be made at multiple
frequencies, further increasing the number of measurements to be matched in the inversion
process.
Fig. 6 is a more detailed block diagram of an inversion process. The raw data is denoted
as vt ,r,f where t , r and f in the subscript represent a particular transmitter, receiver and frequency,
respectively. Once raw data is obtained, it is passed through an initial processing stage to obtain
the compensated data pt i,t2,ri,r2,f- Note that prior to determining the compensated values, some
embodiments normalize the raw data with respect to measurements predicted by an assumed
(perhaps constant resistivity) background model. Such normalization may be useful for reducing
the dominance of strong signal channels in the inversion process.
A parallel track in Fig. 6 begins with an initial model of the subsurface structure in the
region of interest, represented in the figure by the conductivity values j , where the
superscript indicates an iteration number and i, j , k represent spatial indices in the x , y , and z
directions for cells in the conductivity grid. The conductivity grid needs to be chosen large
enough to cover the region of interest and other features that might affect the measurements. A
forward model 604 operates on the model to predict the signal measurements for every
transmitter-receiver combination and frequency using an initial guess for the formation
conductivity. The predicted data due to this conductivity profile (denoted as vF are processed
by a block 606 that performs the same operations as block 602. The output of block 606 is
denoted P t\,t2,r\,r2 ck 608 determines the difference between the outputs of blocks 602 and
608, producing p DIF
ti,t2,ri,r2j- Block 610 evaluates the magnitude of this difference to determine
whether the model has converged. In some embodiments, convergence is determined by
comparing the magnitude of the difference to the magnitude of compensated data pt i,t2,ri,r2,f , e.g.,
testing whether \ \ p DIF \ \ < c || || , where P D F andP are vectors whose elements are producing
p DIF ti,t2,ri,r2,f- and Pti,t2,ri,r2,f , respectively and c is a constant. If convergence is satisfied, the block
6 11 outputs the conductivity model. Otherwise, block 612 derives a set of changes for the
conductivity model based on p D F , and block 614 applies the changes to the conductivity model
to arrive at an updated model " for iteration step n.
Fig. 7 shows a top view of a simulation model for comparing the performance of the
disclosed method to a tomography method that fails to compensate the raw data. The simulation
model is a formation bed with nine vertical boreholes each having a transceiver positioned 70
meters above the bottom of the formation bed. The boreholes are evenly spaced apart by 500
meters in X and Y directions. The formation bed is assumed to have two resistive anomalies in
an otherwise homogeneous medium of 1 W-m resistivity. Both anomalies have a thickness of 65
m in z-direction. If the middle transceiver is taken as the origin, the first anomaly is the volume
defined between 155m and 285 m in x-direction, and -130 to 130 m. in y-direction. This anomaly
has a resistivity of 25 W-m. The second anomaly is defined between -290 and -150 m in xdirection
and 120 and 330 m in y-direction. Resistivity of this anomaly is taken as 20 W-m. A
multi-frequency system with z-directed coil transmitters was considered with operating
frequencies of 1, 2, 5 and 10 Hz. Synthetic data was created with a 3-D finite difference time
domain (FDTD) code according to the conductivity profile described above. A 5% multiplicative
gain noise was applied to the synthetic data.
The results from the traditional inversion of this data are shown in Fig. 8. The true
locations of the anomalies are indicated with dashed lines. The inverted image exhibits severe
artifacts due to noise. Although several peaks close to the targets are observed, results also show
many false positives and it is not possible to reliably determine the shape and boundaries of the
reservoir.
The results from inversion using compensated values in accordance with the method
disclosed above are shown in Fig. 9. The conductivity image is unaffected by the presence of
sensor gain and phase errors. It can be seen that higher intensity regions match very accurately
with reservoir boundaries and any false positives occurring due to sensor gain and phase noises
are eliminated.
Fig. 10 shows an illustrative flow diagram for compensated crosswell tomography. In
block 1002, data is obtained from at least two receivers in response to transmissions from at least
two transmitters. At least one of the receivers or transmitters are located inside a borehole. The
transmitters and receivers can also be distributed among two or more boreholes and on the
surface. In block 1004, data is obtained from additional pairs of receivers in response to
additional pairs of transmitters. In block 1006, at least one compensated value is derived based
on the responses of the receivers to the transmitters. The compensated value is expressible as:
where i and k are receiver indices andj and m are transmitter indices. An inversion is performed
based at least in part on the derived compensated value(s), as shown in block 1008. Finally, in
block 1010, a sub-surface image of a target area is produced based on the inversion. The image
can provide information about at least one formation property, such as acoustic velocity,
attenuation, seismic reflectivity, electromagnetic resistivity, or electrical permittivity.
The operations represented in Fig. 10 can be implemented as software on a general
purpose computer. The processor(s) in such a computer are configured to execute software stored
on disk or in memory, the software causing the processors to obtain the data, process it, and
display resulting images in accordance with user commands.
One of ordinary skill, upon reviewing the foregoing disclosure, will recognize various
alternative forms, equivalents, and modifications to disclosed elements and operations. For
example, the compensated measurement formula is not the only one that yields cancellation of
the gain and phase errors, as combinations of measurements by three receivers in response to
three transmitters, or four receivers in response to four transmitters, etc, will yield similar
cancellations. Where possible, the following claims embrace such alternative forms, equivalents,
and modifications.
CLAIMS
WHAT IS CLAIMED IS:
1. A method for improving image quality of crosswell tomography, comprising:
obtaining data from at least two receivers in response to transmissions from at least two
transmitters, wherein the transmitters and receivers are distributed among two or more boreholes;
deriving at least one compensated value that combines the data from the at least two
receivers' responses to the at least two transmitters; and
performing an inversion based at least in part on said compensated value to obtain a subsurface
image.
2. The method of claim 1, wherein said compensated value compensates for inaccuracies
including sensor gains and phase variations.
3. The method of claim 1, wherein said inversion employs a forward model that relates sub
surface formation properties to said at least one compensated value.
4. The method of claim 1, wherein said compensated value is expressible by the following
equation
v'
'vk
'
m , wherein i and k are receiver indices and j and m are transmitter indices.
5. The method of claim 1, wherein said obtaining data further includes obtaining data from
additional receivers in response to additional pairs of transmitters.
6. The method of claim 1, wherein said data is expressible as a complex value to represent gain
and phase.
7. The method of claim 1, wherein the receivers include at least one of: a magnetic dipole, an
electric dipole, spaced-apart electrodes.
8. The method of claim 1, wherein said image provides information about at least one formation
property selected from a set of consisting of: acoustic velocity, attenuation, seismic reflectivity,
and electromagnetic resistivity.
9. A system for improving image quality of crosswell tomography, comprising:
a memory unit that stores inversion software; and
a processor coupled to said memory to execute the software, wherein said software
configures said processor to:
obtain data from at least two receivers in response to transmissions from at least two
transmitters, wherein one of said receivers or transmitters are in a borehole;
derive at least one compensated value based on responses of said transmitters and
said receivers; and
perform an inversion based at least in part on said compensated value to obtain a sub
surface image.
10. The system of claim 9, further comprising a network electrically coupled to said processor, at
least two transmitters, and at least two receivers, wherein at least one of said transmitters or one
of said receivers is located inside said borehole.
11. The system of claim 9, wherein said network is electrically coupled to at least one sensor, at
least one transmitter, and at least one receiver.
12. The system of claim 9, wherein said compensated value compensates for inaccuracies
including sensor gains and phase variations.
13. The system of claim 9, wherein said compensated value is expressible by the following
equation
v'
'vk
'
m , wherein i and k are receiver indices and j and m are transmitter indices.
14. The system of claim 9, wherein said software further configures the processor to obtain data
from additional receivers in response to additional pairs of transmitters.
15. The system of claim 9, wherein said data is expressible as a complex value to represent gain
and phase.
16. The system of claim 9, wherein said transmitters and receivers are distributed among two or
more boreholes.
17. The system of claim 9, wherein said image provides information about at least one formation
property selected from a set of consisting of: acoustic velocity, attenuation, seismic reflectivity,
and electromagnetic resistivity.
18. The system of claim 9, wherein the transmitters and receivers are each coupled to an antenna,
the antenna being in the set consisting of coils, solenoids, wire antennas, electrodes, gap
antennas, and toroids.