U.S. patent application number 12/758556 was filed with the patent office on 2010-12-09 for determining correction factors representing effects of different portions of a lining structure.
Invention is credited to Brian Clark, Frank Morrison, Edward Nichols, Richard A. Rosthal, Hong Zhang.
Application Number | 20100308832 12/758556 |
Document ID | / |
Family ID | 40522716 |
Filed Date | 2010-12-09 |
United States Patent
Application |
20100308832 |
Kind Code |
A1 |
Clark; Brian ; et
al. |
December 9, 2010 |
Determining Correction Factors Representing Effects of Different
Portions of a Lining Structure
Abstract
To determine effect on a magnetic field caused by a lining
structure in a wellbore, an array may be deployed into the wellbore
lined with the lining structure. The array comprises a plurality of
sensors including sensor A configured to operate as a transmitter,
sensor B configured to operate as either a transmitter or a
receiver, and sensor C configured to operate as a receiver. The
array measures magnetic fields using sensor B as a receiver and
sensor C in response to activation of sensor B as a transmitter and
sensor A. A plurality of lining structure correction factors can be
calculated based on the measured magnetic fields, based on the
reciprocity of the sensors.
Inventors: |
Clark; Brian; (Sugar Land,
TX) ; Morrison; Frank; (Berkeley, CA) ;
Nichols; Edward; (Berkeley, CA) ; Zhang; Hong;
(El Sobrante, CA) ; Rosthal; Richard A.;
(Richmond, CA) |
Correspondence
Address: |
SCHLUMBERGER OILFIELD SERVICES
200 GILLINGHAM LANE, MD 200-9
SUGAR LAND
TX
77478
US
|
Family ID: |
40522716 |
Appl. No.: |
12/758556 |
Filed: |
April 12, 2010 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
11868379 |
Oct 5, 2007 |
7795872 |
|
|
12758556 |
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Current U.S.
Class: |
324/338 |
Current CPC
Class: |
G01V 3/28 20130101 |
Class at
Publication: |
324/338 |
International
Class: |
G01V 3/18 20060101
G01V003/18 |
Claims
1.-22. (canceled)
23. A method, comprising: deploying an array comprising a plurality
of sensors, at least one of which is configured to operate as
either a transmitter or a receiver into a wellbore comprising an
electrically conductive tubular structure; activating a plurality
of the sensors as transmitters; operating a plurality of the
sensors as receivers to measure magnetic fields between couplings
of the plurality of sensors; and calculating a plurality of
correction factors for the electrically conductive tubular
structure based on the measurements.
24. The method of claim 23, further comprising applying the
plurality of correction factors to eliminate the effect of one or
more tubular structures for at least one of: 1) improved crosswell
evaluation of a reservoir, 2) improved surface-to-borehole
evaluation of a reservoir, 3) improved single well evaluation of a
reservoir, 4) improved steam assisted gravity drainage drilling, 5)
improved casing evaluation applications, 6) improved well avoidance
for plural wells in close proximities, 7) improved well
intersection techniques, and 8) improved reservoir monitoring
through casing.
25. The method of claim 23, wherein the sensors are physically
separated in the array by a minimum separation defined by at least
one of 1) frequency and 2) one or more casing characteristics, and
3) sensor characteristics (core size and core properties, or sensor
type); said minimum separation being sufficiently far enough that
the correction factor for each sensor is separable from the
correction factor for each adjacent sensor.
Description
CROSS-REFERENCE TO OTHER APPLICATIONS
[0001] This application is a continuation of U.S. patent
application Ser. No. 11/868,379, filed on Oct. 5, 2007.
TECHNICAL FIELD
[0002] The invention relates generally to determining correction
factors representing effects of different portions of a lining
structure using measurements from an array having at least one
transmitter and plural receivers.
BACKGROUND
[0003] Geological formations form reservoirs for the accumulation
of hydrocarbons in the subsurface of the earth. Such formations
contain networks of interconnected paths in which fluids are
disposed that ingress or egress from the reservoir. Knowledge of
both the porosity and permeability of the geological formations are
useful to determine the behavior of the fluids in this network.
From information about porosity and permeability, efficient
development and management of hydrocarbon reservoirs may be
achieved. Considering that hydrocarbons are electrically insulating
and most water contains highly conductive salts, resistivity
measurements are a valuable tool in predicting the presence of a
hydrocarbon reservoir in the formations.
[0004] One technique to measure formation resistivity involves the
use of electromagnetic induction using transmitters of low
frequency magnetic fields that induce electrical currents in the
formation. The induced currents in turn produce secondary magnetic
fields that are measured in an adjacent wellbore (or at some
distance away in the same wellbore) by a magnetic field
receiver.
[0005] The performance of a magnetic field receiver or a magnetic
field transmitter positioned within a wellbore casing may be
compromised by the casing's effect on the magnetic field to be
measured. Specifically, the measurable magnetic field induces a
current that flows concentrically about the receiver coil and tends
to reduce the magnetic field within the casing. The magnetic
permeability of the casing also acts to distort the magnetic field
and influences the behavior of the currents. The measurable
magnetic field may be highly attenuated as a result and the
measurements made by the receiver may be influenced by variations
in attenuation caused by variations in the casing's conductivity,
permeability, thickness and diameter. Often, a cased wellbore
reduces the magnetic field signal to a level that is undetectable
by standard receivers. Moreover, the variance in conductivity,
permeability, thickness and diameter along a longitudinal axis of a
length of casing makes it difficult to determine an attenuation
factor (which represents attenuation of the measurable magnetic
field caused by the casing) at any selected point. The inability to
determine an attenuation factor at a selected point along the
casing may cause errors in field measurements that are not easily
corrected.
BRIEF DESCRIPTION OF THE DRAWINGS
[0006] FIGS. 1 and 2 depict conventional prior art
transmitter/receiver arrangements for conducting electromagnetic
(EM) inductive surveys of a subterranean formation.
[0007] FIG. 3 illustrates a transmitter/receiver arrangement
according to embodiments of the present disclosure to enable
determination of lining structure correction factors using an array
of EM transmitters and receivers.
[0008] FIGS. 4 and 5 illustrate various cross-well surveying
techniques according to embodiments of the present disclosure
employing the array of FIG. 3.
[0009] FIG. 6 illustrates an alternative transmitter/receiver
arrangement according to embodiments of the present disclosure to
enable determination of lining structure correction factors.
[0010] FIGS. 7 and 8 illustrate yet another transmitter/receiver
arrangement according to embodiments of the present disclosure to
determine lining structure correction factors.
[0011] FIG. 9 illustrates a tool having a transmitter and receivers
in accordance with embodiments of the present disclosure.
[0012] FIG. 10 illustrates an inductive coupler used in the tool of
FIG. 9 to reduce coupling between the transmitter and receivers in
accordance with embodiments of the present disclosure.
DETAILED DESCRIPTION
[0013] In the following description, numerous details are set forth
to provide an understanding of the present invention. However, it
will be understood by those skilled in the art that the present
invention may be practiced without these details and that numerous
variations or modifications from the described embodiments are
possible.
[0014] As used here, the terms "above" and "below"; "up" and
"down"; "upper" and "lower"; "upwardly" and "downwardly"; and other
like terms indicating relative positions above or below a given
point or element are used in this description to more clearly
describe some embodiments of the invention. However, when applied
to equipment and methods for use in wells that are deviated or
horizontal, such terms may refer to a left to right orientation, a
right to left orientation, or a diagonal orientation as
appropriate. Further, while the most common situation is one where
the axis of symmetry of the magnetic field produced by the
transmitter or measured by the receiver is aligned with the
borehole, this method applies to arbitrary orientations of
transmitter or receiver.
[0015] An electromagnetic (EM) induction survey technique is
provided for surveying a subterranean formation. In one
transmitter/receiver arrangement, the survey is performed using
cross-well logging, in which EM transmitters are placed in one
wellbore and EM receivers are placed in a second wellbore. In
alternative transmitter/receiver arrangements, the surveying can be
performed with surface-to-wellbore (or wellbore-to-surface)
logging. In surface-to-wellbore logging, EM transmitters are placed
at or near the surface (e.g., land surface, sea floor) or towed in
a body of water, and EM receivers are placed in a wellbore. In
wellbore-to-surface logging, EM transmitters are placed in a
wellbore, while EM receivers are placed at or near a surface (e.g.,
land surface, sea floor) or towed in a body of water. In single
well logging, the transmitters are place in the same wellbore as
the receivers. The EM induction survey technique disclosed with the
present application corrects for the effect of an electrically
conductive lining structure (e.g., a casing or liner used to line
an inner surface of a wellbore) on measurements taken during
logging. The correction is accomplished by adding auxiliary sensors
(e.g., EM transmitters and/or EM receivers) to a logging tool
string that is deployed into a wellbore. The auxiliary sensors
(transmitters and/or receivers) produce measurements from which
lining structure correction factors can be computed to represent
effects of portions of the lining structure. These auxiliary
transmitters and/or receivers may include any sensor that can
measure a dc or ac magnetic field, including for example a loop
(coil) assembly disposed around a magnetic core, or fluxgate
magnetometers.
[0016] The EM induction survey technique according to various
embodiments is beneficial in that the technique accounts for lining
structure inhomogeneity. Often, a lining structure does not have
constant properties along its length. Rather, a lining structure
(which can be formed of a material such as steel or other metal) is
inhomogeneous in that the conductivity, permeability, thickness and
diameters of the lining structure can vary along its length. The
presence of coupling devices (such as collars) and of centralizers
adds to the inhomogeneity. Due to the inhomogeneous nature of a
typical lining structure, conventional EM induction survey
techniques have not properly or adequately corrected for
attenuation effects of the lining structure.
[0017] Although computation of lining structure correction factors
is discussed in the context of surveying a subterranean structure,
techniques according to some embodiments can be used in other
applications, such as to remove double indications of defects
("ghosting" effect) of a lining structure (or pipe or other
electrically conductive tubular structure) in a tool that uses eddy
current methods to inspect such an electrically conductive tubular
structure.
[0018] FIG. 1 shows conventional equipment used in the measurement
of geological (subterranean) formation 10 resistivity between two
wellbores 12a and 12b using EM induction. A transmitter T (20) is
located in one wellbore 12a, while a receiver R (24) is placed in
another wellbore 12b. The transmitter T 20 and receiver R 24 are
coupled to a controller 28 that controls activation of the
transmitter T 20 and to receive measurement data from the receiver
R 24. Alternatively, there may be two independent controllers that
are synchronized with each other. The transmitter T 20 typically
includes a coil (not shown) having a multi-turn loop (having
N.sub.T turns of wire) wrapped around a magnetically permeable core
(mu-metal or ferrite) with a cross-sectional A.sub.T. The
transmitter T 20 may further include a capacitor (not shown) for
tuning the frequency of the coil. When an alternating current,
I.sub.T, at frequency f.sub.0 passes through the multi-turn loop, a
time varying magnetic moment, M.sub.T, is produced in the
transmitter T 20. The magnetic moment is defined as follows:
M.sub.T=N.sub.TI.sub.TA.sub.T. (Eq. 1)
[0019] The magnetic moment M.sub.T produces a magnetic field
B.sub.R that can be detected by the receiver R 24. In a short form,
the response may be governed by the following:
B.sub.R=k.sub.fM.sub.T. (Eq. 2)
[0020] The geological factor, k.sub.f, is a function of the
electrical conductivity distribution of the geological formation 10
between the transmitter 20 and the receiver 24. In a practical
survey, M.sub.T is known (through the measurement of I.sub.T). The
receiver R 24 typically includes one or more antennas (not shown).
Each antenna includes a multi-turn loop of wire wound around a core
of magnetically permeable metal or ferrite. The changing magnetic
field sensed by the receiver R 24 creates an induced voltage in the
receiver coil (not shown). The induced voltage (V.sub.R) is a
function of the detected magnetic field (B.sub.R), the frequency
(f.sub.0), the number of turns (N.sub.R) of wire in the receiver
coil, the effective cross-sectional area of the coil (A.sub.R), and
the effective permeability (.mu..sub.R) of the coil. Thus, V.sub.R
is proportional to:
f.sub.0B.sub.RN.sub.RA.sub.R.mu..sub.R. (Eq. 3)
[0021] While f.sub.0 and N.sub.R are known, the product,
A.sub.R.mu..sub.R, is difficult to calculate. In practice, these
constants may be grouped together as k.sub.R, and Eq. 3 may be
simplified as:
V.sub.R=k.sub.RB.sub.R, (Eq. 4)
where k.sub.R=f.sub.0N.sub.RA.sub.R.mu..sub.R.
[0022] Thus, instead of determining the product A.sub.R.mu..sub.R,
it is more convenient to determine k.sub.R according to the
following procedures. First, the receiver coil is calibrated in a
known field, at a known frequency. Then, the exact value for
k.sub.R is derived from the magnetic field (B.sub.R) and the
measured voltage (V.sub.R) according to the following equation:
k.sub.R=B.sub.R/V.sub.R (Eq. 5)
[0023] When the system is placed in a conducting geological
formation 10, the time-varying magnetic field, B.sub.R, which is
produced by the transmitter magnetic moment M.sub.T, produces a
voltage in the geological formation 10, which in turn drives a
current, I.sub.1, in the formation. The current, I.sub.1, is
proportional to the conductivity of the geological formation and is
concentric about the longitudinal axis of the wellbore if the
formation is azimuthally symmetric about the axis of the
transmitter. The magnetic field proximate to the wellbore results
from a free space field called the primary magnetic field, while
the field resulting from current I.sub.1 is called the secondary
magnetic field. In more complex geological formations or when the
wells are far apart compared to a skin depth in the formation,
there are higher order terms and the relationship between voltage
and formation conductivity is more complicated. In addition, for an
arbitrary orientation of a transmitter, the fields are more
complicated. The process of determining the spacial distribution of
formation conductivity from the measurements is known as inversion.
A discussion of inversion is beyond the scope of this patent.
[0024] The current I.sub.1 is typically out of phase with respect
to the transmitter current, I.sub.T. At very low frequencies, where
the inductive reactance is small, the current I.sub.1 is
proportional to dB/dt and is 90.degree. out of phase with respect
to I.sub.T. As the frequency increases, the inductive reactance of
the formation 10 increases, and the phase of the induced current
I.sub.1 increases to greater than 90.degree.. The secondary
magnetic field induced by current I.sub.1 also has a phase shift
relative to the induced current I.sub.1, and the total magnetic
field as detected by receiver R 24 is complex.
[0025] The complex magnetic field detected by receiver R 24 may
thus be separated into two components: a real component, B.sub.R,
which is in-phase with the transmitter current, I.sub.T, and an
imaginary (or quadrature) component, B.sub.1, which is
phase-shifted by 90.degree.. The values of the real component,
B.sub.R, and the quadrature component, B.sub.1, of the magnetic
field at a given frequency and geometrical configuration uniquely
specify the electrical resistivity of a homogeneous formation
pierced by the wellbores 12a and 12b. In an inhomogeneous
geological formation, however, the complex field is measured at a
succession of points along the longitudinal axis of the receiver
wellbore for each of a succession of transmitter locations. The
multiplicity of measurements thus obtained can be used to determine
the inhomogeneous resistivity distribution between the wellbores
12a and 12b. The method described above with regard to ac
measurements (equations 3 and 4) will also work equally well for dc
measurements (such as could be used for well positioning). The same
approach can be applied to dc magnetic fields.
[0026] The discussion above assumes that the wellbores 12a and 12b
are not lined with an electrically conductive or magnetically
permeable lining structure, such as a metallic casing. FIG. 1
depicts casing 16a and 16b lining wellbores 12a and 12b
respectively. The electrically conductive or magnetically permeable
casings 16a and 16b interfere with resistivity measurements.
Additionally, it may occur that only one of the wells is lined with
an electrically conductive or magnetically permeable casing and
that the other is either unlined (open hole) or lined with a
plastic or fiberglass casing which does not interfere with the
electric or magnetic fields.
[0027] Inside of a conductive and magnetic lining structure, the
net effective moment of the transmitter (M.sub.eff) is reduced by
the eddy currents that are induced in the lining structure, and
magnetic shielding due to the magnetic property of the lining
structure. These effects act to reduce the moment of the
transmitter as seen from outside. The degree of this reduction
depends upon the properties of the casing, the design of the
transmitter and the frequency of operation. At high frequencies the
shielding is nearly perfect and very little field is observed
outside of casing. For this reason, the technique described above
is limited to low frequencies in metal-cased wells. The effective
moment, the moment seen by a receiver outside the conductive lining
structure, is conveniently expressed by:
M.sub.eff=k.sub.cM.sub.T, (Eq. 6)
where k.sub.c is the lining structure attenuation factor. While we
have spoken of the attenuation, note that the constant k.sub.c is
complex. Not only is the moment attenuated, but the phase is
changed.
[0028] An analogous situation is present with respect to a receiver
if it is surrounded by a conductive lining structure, and the
situation is exacerbated if both the transmitter and the receiver
are surrounded by conductive lining structures.
[0029] As depicted in FIG. 2, a conventional surveying technique
that attempts to correct for the casing effect utilizes an
auxiliary receiver 54 and an auxiliary transmitter 72 in
conjunction with the principal transmitter 20 and principal
receiver 24 depicted in FIG. 1. The principal transmitter 20 and
auxiliary receiver 54 are disposed in the wellbore 12a, and the
principal receiver 24 and auxiliary transmitter 72 are disposed in
the wellbore 12b.
[0030] The wellbores 12a and 12b are lined with casings 16a and
16b. In addition to general attenuation, the conductive casings
16a, 16b are typically non-homogenous and they include couplers
(collars) and centralizers which add to the inhomogeneities. For
example, the properties of a casing may vary from one depth to
another. To mitigate effects of such casing inhomogeneity, the
correction technique according to FIG. 2 includes the auxiliary
receiver 54 in the proximity of the principal transmitter 20. The
auxiliary receiver 54 is also referred to as an "offset monitor,"
since it is a sensor to measure magnetic field in the casing some
distance away from the transmitter. The auxiliary receiver 54
permits detection of a magnetic field, B.sub.a, close to the
transmitter, where characteristics are dependent primarily on the
casing properties (not on the formation properties). The magnetic
field, B.sub.a, at auxiliary receiver 54 can then be used to
correct for casing attenuation effects in the magnetic field that
is induced in the principal receiver 24. Specifically, a magnetic
field B.sub.a is induced in the auxiliary receiver 54. The magnetic
field B.sub.a is related to the magnetic moment, M.sub.T, of
transmitter 20, a casing attenuation factor k.sub.TR, and a
geometric factor a. This relation is expressed as follows:
B.sub.a=ak.sub.TRM.sub.T (Eq. 7)
[0031] The casing attenuation factor (also referred to as a casing
corrector factor), k.sub.TR is a function of the properties of
conductive liner 16a. Because auxiliary receiver 54 is inside liner
16a and in close proximity (e.g., .ltoreq.5-10 m) to transmitter
20, the magnetic field B.sub.a sensed by auxiliary receiver 54 is
dominated by the properties of the conductive liner 16a. Note that
the casing factor k.sub.TR is not equal to the casing k.sub.c
factor from equation 6. The casing factor k.sub.TR does not
represent the magnetic moment as seen by a sensor at some distance
outside of the well, due to the fact that this casing factor
includes the influence of the casing on the transmitter and also
includes the effect of the casing on the monitor receiver. If the
transmitter and receiver had the same design and if they were far
enough apart but not seeing the formation and if the transmitter
were operated in the linear regime and if the casing properties
were the same at the transmitter and at the receiver, then we might
write:
k.sub.T= {square root over (k.sub.TR)} (Eq. 8)
[0032] Unfortunately, it is seldom the case that the transmitter
and receiver are the same design, far apart, and operated in linear
regime or that the casing is homogeneous. Typically, the auxiliary
receiver has a different construction than the transmitter and the
transmitter is not operated in a linear regime. Thus, this
measurement provides only an approximate means to partially correct
the transmitter moment for casing effect.
[0033] In a similar manner, an auxiliary transmitter 72 in the
second wellbore 12b can be used to correct the effects of the
casing 16b on the far receiver 24. As with the auxiliary receiver
54, the auxiliary transmitter 72 is placed in close proximity with
the receiver 24 so that the magnetic field at the receiver 24
depends only on the casing and not on the formation. Similar
procedures for performing corrections are followed for
transmitter/receiver pair 72, 24 as with the transmitter-receiver
pair 20, 54.
[0034] The technique of FIG. 2 and equation 8 may not produce
accurate results for a number of reasons. The transmitter 20 and
auxiliary receiver 54 (or the receiver 24 and auxiliary transmitter
72) may be of different designs, or the transmitter 20 may be
operated in a non-linear manner, or the casing may be different at
the transmitter 20 and auxiliary receiver 54 (or the receiver 24
and auxiliary transmitter 72) or the auxiliary sensor may not be
the correct distance from the main sensor. Specifically, operation
of a transmitter in non-linear fashion refers generally to the
magnetic field output from the transmitter as a function of drive
current, while, non-linearity operation is mainly caused by
magnetic hysterises loss inside transmitter core. By comparison,
linear operation versus non-linear operation for the receiver is
based on the pickup voltage of receiver as a function of the
strength of external magnetic field. Any of these common situations
will cause errors in the casing correction method used for
arrangements as shown in FIG. 2.
[0035] In the ensuing discussion, reference is made to casings and
casing effects; however, the techniques discussed can also be
applied to other lining structures (or other conductive or magnetic
tubular structures).
[0036] In general, to perform casing effect correction for a casing
of arbitrary inhomogeneity, an array of transmitters and receivers
can be used, such as the array 110 of transmitters and receivers
depicted in the arrangement of FIG. 3. The array 110 depicted in
FIG. 3, deployed in a wellbore 100, includes a primary transmitter
20, an auxiliary transmitter 21, a first auxiliary receiver 54, and
a second auxiliary receiver 55. The first auxiliary receiver 54 and
auxiliary transmitter 21 are provided at the same location in the
wellbore 100 (within the same box as depicted in FIG. 3).
[0037] Since transmitters and receivers both include multi-turn
solenoids on mu-metal cores, the transmitters and receivers can
serve a dual role so that in fact 21 and 54 can be implemented with
the same physical device but selectively connected either to a
current source (as a transmitter) or to an amplifier (as a
receiver). Alternatively, instead of using a single multi-turn coil
for both receiving and transmitting, two coils wound on a common
core can be used.
[0038] To simplify the ensuing description, the array 110 of
transmitters 20, 21 and receivers 54, 55 are equivalently
represented as transmitters T.sub.1, T.sub.2 (respectively) and
receivers R.sub.1, R.sub.2 (respectively), as shown in FIG. 3. The
array 110 of transmitters T.sub.1, T.sub.2 and receivers R.sub.1,
R.sub.2 are deployed in a wellbore 100, which is lined with casing
101.
[0039] Modeling has shown that for typical casing and frequency of
operation, if the axial spacing between a transmitter and receiver
located in the same wellbore is greater than about a particular
distance (such as, for some embodiments, five meters), the casing
attenuation factors at the transmitters and receivers are
independent of each other. For example, the magnetic field at
receiver R.sub.2 due to transmitter T.sub.1, B.sub.2.sup.1 (the
superscript indicates the transmitter involved, the subscript the
receiver in question) is given simply by:
B.sub.2.sup.1=B.sub.02.sup.1k.sub.1k.sub.2, (Eq. 10)
where B.sub.02.sup.1 is the free space (no casing) magnetic field
at R.sub.2 which can be calculated since the separation between
T.sub.1 and R.sub.2 is known and the moment, M.sub.T, is known from
measurement of the current in the transmitter T.sub.1. A free space
magnetic field B for a transmitter whose moment is oriented in the
z-direction can be calculated according to:
, B = .mu. o .mu. M T 4 .pi. r 3 ( 2 x 2 r 2 u _ x + 3 xy r 2 u _ y
+ 3 xz r 2 u _ z ) ( Eq . 11 ) ##EQU00001##
where r is the distance between the transmitter and receiver,
.sub.x, .sub.y, .sub.z are unit vectors in the x, y, and z
directions, respectively, .mu..sub.o is the permeability of vacuum,
and .mu. is the relative permeability of the formation.
[0040] In Eq. 10, the attenuation factor k.sub.1 represents the
casing attenuation at the transmitter T.sub.1, and the attenuation
factor k.sub.2 represents the casing attenuation at the first
auxiliary receiver R.sub.2.
[0041] Similarly, the magnetic field at the second auxiliary
receiver R.sub.3 due to the transmitter T.sub.1 is given by:
B.sub.3.sup.1=B.sub.03.sup.1k.sub.1k.sub.3, (Eq. 12)
where k.sub.3 represents the casing attenuation at the second
auxiliary receiver R.sub.3.
[0042] If the auxiliary transmitter T.sub.2 (instead of T.sub.1) is
activated, then the measured field at the second auxiliary receiver
R.sub.3 is given by:
B.sub.3.sup.2=B.sub.03.sup.2k.sub.2k.sub.3. (Eq. 13)
[0043] These equations can be solved as follows:
k 1 = B 3 1 B 03 1 B 2 1 B 02 1 B 3 2 B 03 2 k 2 = B 3 2 B 03 2 B 2
1 B 02 1 B 3 1 B 03 1 k 3 = B 3 1 B 03 1 B 3 2 B 03 2 B 2 1 B 02 1
( Eq 14 ) ##EQU00002##
[0044] From the above, the three unknowns, k.sub.1, k.sub.2, and
k.sub.3 can be readily derived based on measured and calculated
magnetic fields. The casing attenuation factor k.sub.1 for the
principal transmitter, T.sub.1 (20 in FIG. 3), can be obtained from
measurements using the array 110 that includes the principal
transmitter, an auxiliary transmitter, and two auxiliary receivers.
The transmitter attenuation factor, previously denoted by k.sub.c
(in Eq. 6), and here denoted by k.sub.1, is the casing attenuation
factor seen by a distant receiver, for example cross-well receiver
24 in FIG. 4 (located in wellbore 102). Effectively, based on a
number of measurements made by plural receivers of the array 110 in
the casing 101, the casing effect of the principal transmitter 20
(represented by k.sub.1 or k.sub.c) can be derived. Note that the
measurements made by the plural receivers include the strength of
the transmitter moment. One virtue of this method is that it
applies even if the transmitter is operated in a nonlinear regime.
This method gives a means to accurately correct for the effect of
an electrically conductive and/or permeable lining structure on an
external measurement using only local measurements internal to the
well.
[0045] The above is based on a number of observations. When a
receiver is inside a casing, then the receiver's coupling with a
distant receiver (such as a receiver located in another wellbore or
a receiver in the same wellbore located a large distance away) is
equal to the coupling that would have existed in the absence of a
casing times a casing attenuation factor. This casing attenuation
factor is a function of the casing properties in the vicinity of
the receiver and is independent of the location or characteristics
of the distant receiver or of the formation. Another observation is
that when two receivers are located a sufficient distance apart,
then the coupling between two receivers inside a casing is equal to
the coupling that would exist in the absence of casing times a
product of casing attenuation factors, one for each of the
sensors.
[0046] The magnetic field B.sub.R measured at receiver 24 due to EM
fields induced by the principal transmitter 20 is:
B.sub.R=k.sub.ck.sub.fM.sub.T. (Eq. 15)
[0047] Since M.sub.T is known, simply dividing both sides by
bk.sub.cM.sub.T yields the desired formation attenuation factor
k.sub.f.
[0048] The computations discussed above can be performed by a
controller 104 (FIG. 4) that is electrically connected to the array
of transmitters and receivers 20, 21, 54, 55 (in wellbore 100) and
remote receiver 24 (in wellbore 102). The controller 104, which can
include a computer, transceiver circuitry, and other circuitry,
controls operation of transmitters and receives measured signals
from the receivers in wellbores 100 and 102. The computer can
include one or more processors and software executable on the
processors to discuss the various computations discussed herein.
Alternatively, the controller can be programmed to simply collect
all the necessary data and the calculations can be performed
later.
[0049] Note that while the array of transmitters and receivers in
wellbore 100 can be used to perform a casing effect correction for
casing 101 in the first the wellbore 100, a similar array of
transmitters and receivers can be provided in the second wellbore
102 to perform casing effect correction for casing 103 in the
second wellbore 102 if both wells are cased. As depicted in FIG. 5,
in addition to the principal receiver 24 (R.sub.4) located in the
wellbore 102 inside casing 103, an auxiliary receiver 59 (R.sub.5)
is also provided, as well as auxiliary transmitters 57 and 61
(T.sub.3, T.sub.4). The transmitters T.sub.3, T.sub.4 and receivers
R.sub.4, R.sub.5 make up a second array 111 located in the second
wellbore 102. The auxiliary transmitters T.sub.3 and T.sub.4 are
placed in close proximity to receivers R.sub.4 and R.sub.5 (similar
to placement of transmitters and receivers in the array 110) such
that activation of the transmitters T.sub.3 and T.sub.4 will
generate three sets of magnetic fields as measured by receivers
R.sub.4 and R.sub.5. The technique discussed above in connection
with FIG. 4 is applied to derive casing attenuation factors for the
casing in the second wellbore 102.
[0050] Note that a logging tool that has a receiver string often
includes multiple receivers. Thus, the provision of auxiliary
receivers may not be necessary, since a receiver string already
includes multiple receivers.
[0051] In another example, FIG. 6 shows a receiver string that
includes four receivers R.sub.1, R.sub.2, R.sub.3, and R.sub.4. The
string of receivers is deployed in the wellbore 102 that is lined
with casing 103. In addition to the receivers, the array depicted
in FIG. 6 also includes transmitters T.sub.1, T.sub.2, T.sub.3, and
T.sub.4.
[0052] The array of FIG. 6 thus includes multiple elements, where
each element of the array is composed of a transmitter T.sub.i,
with moment M.sub.i, and a receiver R.sub.i (i=1, 2, 3, 4 in the
four-element array of FIG. 6). Each element can include a
co-located transmitter and receiver, where the transmitter and
receiver are implemented with coils located on a common core, as
indicated by 200 in FIG. 6. Alternatively, the sense coil of the
receiver can be driven as a transmitter.
[0053] The geometric factor, a, varies for each combination so, for
example, a.sub.ij is the geometric factor for receiver i and
transmitter j. There is a unique casing attenuation factor for each
T.sub.i-R.sub.i element denoted by k.sub.i (shown schematically as
k.sub.1, k.sub.2, k.sub.3 and k.sub.4 in FIG. 6). The field
measured by a specific receiver, R.sub.i, from a specific
transmitter, T.sub.j, is denoted by B.sub.i.sup.j. Thus
B.sub.1.sup.2=a.sub.12k.sub.1k.sub.2M.sub.2 is the field measured
at position 1 from a transmitter located at position 2 and it has
been attenuated by a factor k.sub.2 (at the transmitter) and
k.sub.1 (at the receiver). Further, to simplify the following
equations, it should be noted that a.sub.12M.sub.2 is the free
space field that would be measured at receiver 1 from transmitter
2, denoted here as B.sub.01.sup.2, and can be calculated from a
knowledge of M.sub.2 and the geometry of the array.
[0054] Proceeding in the manner for the array depicted in FIGS. 3
and 4, multiple measurements are made between various
transmitter-receiver pairs to determine k.sub.1, k.sub.2, k.sub.3
and k.sub.4. For example:
B.sub.2.sup.1=B.sub.02.sup.1k.sub.1k.sub.2, (Eq. 16)
B.sub.3.sup.1=B.sub.03.sup.1k.sub.1k.sub.3, (Eq. 17)
B.sub.2.sup.3=B.sub.03.sup.1k.sub.2k.sub.3. (Eq. 18)
As before,
k 2 k 3 = B 3 2 B 03 2 . ( Eq . 19 ) ##EQU00003##
Taking the ratio of B.sub.2.sup.1 to B.sub.3.sup.1 yields
B 2 1 B 3 1 = B 02 1 B 03 1 k 2 k 3 , ( Eq . 20 ) ##EQU00004##
and solving for k.sub.3,
k 3 = B 3 2 B 03 2 B 3 1 B 03 1 B 02 1 B 2 1 ( Eq . 21 )
##EQU00005##
Other pairs of T and R yield similar equations to solve for each of
the attenuation factors, k.sub.i.
[0055] The above equations express the determination of the casing
attenuation factor of the transmitter based on measured and
computed magnetic fields. The following describes how the casing
attenuation factors of transmitters and receivers can be expressed
in terms of impedances. The impedances are defined as the ratio of
V/I where V is the voltage measured by a receiver divided by the
current at a transmitter.
[0056] Reciprocity exists between a transmitter and a receiver in
straight mode so long as the transmitter is operated in the linear
region. In straight mode, the voltage measured by a receiver is the
open-circuit voltage in the main coil of the receiver. In other
words, the main coil of the receiver is connected to a measurement
circuit to measure the voltage with the measurement circuit having
a high input impedance such that little current flows. Ideally, the
measurement circuit has infinite input impedance such that no
current flows in the coil so that the voltage measured is a true
open-circuit voltage.
[0057] A transmitter mimics a receiver in straight mode. That is,
if there are two receivers each including coils wound about
magnetic cores, then if receiver 1 is excited with current I.sub.1
and the voltage V.sub.2.sup.1 on receiver 2 is measured, or if
receiver 2 is excited with current I.sub.2 and the voltage
V.sub.1.sup.2 on receiver 1 is measured, then
Z 12 = V 2 1 I 1 = Z 21 = V 1 2 I 2 . ( Eq . 22 ) ##EQU00006##
[0058] In Eq. 22, Z.sub.12 is the impedance representing the
coupling from receiver 1 to 2, and Z.sub.21 represents the coupling
from receiver 2 to receiver 1. Note that according to Eq. 22, in
straight mode, the impedances Z.sub.12 and Z.sub.21 have the same
values.
[0059] FIG. 7 illustrates a transmitter/receiver arrangement that
includes three receivers 302, 304, and 306, where at least two of
the receivers can also be operated as a transmitter. More
generally, 302, 304, and 306 are referred to as elements 302, 304,
and 306, which are disposed in a casing 310. With the elements
positioned in the casing 310 and subjected to an external field (a
magnetic field that is propagated from a remote transmitter, either
from crosswell, or surface, or the same well), the impedances
Z.sub.1, Z.sub.2, and Z.sub.3 of the elements 302, 304, and 306,
respectively, are expressed as follows:
Z.sub.1=k.sub.1Z.sub.1,0,
Z.sub.2=k.sub.2Z.sub.2,0, (Eq. 23)
Z.sub.3=k.sub.3Z.sub.3,0,
where the notation Z.sub.N,0 (N=1, 2, or 3) indicates the voltage
that would have been read by receiver N in the absence of the
casing 310.
[0060] If all the couplings between these three receivers are
measured:
Z.sub.12=k.sub.12Z.sub.12,0,
Z.sub.13=k.sub.13Z.sub.13,0, (Eq. 24)
Z.sub.23=k.sub.23Z.sub.23,0.
[0061] Based on the assumption that a coupling between receivers
inside a casing is equal to the coupling that would have existed in
the absence of casing multiplied by a product of a casing
attenuation factor, and the reciprocity assumption in straight
mode, both discussed above,
k.sub.12=k.sub.1k.sub.2,
k.sub.13=K.sub.1k.sub.3, (Eq. 25)
k.sub.23=k.sub.2k.sub.3.
[0062] Each of the individual coefficients can be derived:
k 1 = k 12 k 13 k 23 , k 2 = k 12 k 23 k 13 , k 3 = k 13 k 23 k 12
. ( Eq . 26 ) ##EQU00007##
[0063] Note that k.sub.12, k.sub.13, k.sub.23, are readily derived
based on measured voltages at receivers in response to excitations
of transmitters in the same casing, according to the arrangement of
FIG. 2. Note that k.sub.12, k.sub.13, k.sub.23 are derived from
Z.sub.12, Z.sub.13, and Z.sub.23, according to Eq. 24, where
Z.sub.12, Z.sub.13, and Z.sub.23 are derived based on measured
voltages V.sub.12, V.sub.13, and V.sub.23 at receivers 302, 304,
306, respectively, in response to the excitation of appropriate
transmitters in the same casing 310. The voltage V.sub.12 is the
measured voltage at receiver 304 in response to the excitation of
transmitter 302. V.sub.13 is the voltage measured at receiver 306
in response to the excitation of transmitter 302. V.sub.23 is the
measured voltage at receiver 306 in response to the excitation of
transmitter 304.
[0064] The techniques discussed above assume that the receivers are
operated in straight mode. There is, however, also another mode in
which a receiver can be operated: feedback mode. In feedback mode,
the main coil voltage of the receiver is used to generate a current
in the feedback coil that partially cancels the main coil voltage.
The degree of cancellation is frequency dependent and depends upon
the details of the electronics that generate the current. The
casing effect in straight mode is different from the casing effect
in feedback mode. Moreover, the casing effect in feedback mode
changes if the feedback circuit is changed.
[0065] In feedback mode, the reciprocity assumption discussed
above, where Z.sub.12=Z.sub.21, is no longer true. In other words,
there is no reciprocity between a straight mode transmitter and a
feedback mode receiver. Thus, to measure the casing effect for a
receiver in feedback mode, the procedure is to first measure the
casing effect for the receiver in straight mode, and then to
compute the casing effect for the feedback mode using a ratio of
the signal in feedback mode to the signal in straight mode, by
measuring the ratios
V Feedback_Casing V Straight_Casing and V Feedback_Air V
Straight_Air , ##EQU00008##
thereby obtaining the feedback sensor casing correction factor
as
k Feedback = k Straight V Feedback_Casing V Straight_Air V
Straight_Casing V Veedback_Air ( Eq . 27 ) ##EQU00009##
[0066] In the discussion above, reference has been made to using a
single multi-turn coil for implementing both a receiver and a
transmitter. In other words, the single multi-turn coil can be
operated to selectively receive a signal or transmit a signal.
[0067] However, in practice it may be difficult to optimize a
single multi-turn coil for both receiving and transmitting. In
general, receiver coils have a large number of turns to produce a
large voltage, while transmitter coils have a smaller number of
turns to minimize inductance. It may be desirable to have two coils
wound on the same core and use one for the transmitter and the
other for the receiver. The casing effect of a receiver is
dependent upon the particular design of the receiver, including the
arrangement of coil and core and how feedback is used. If a second
coil is used as a transmitter, then its geometrical layout should
be as similar to the receiver coil, as much as possible, in order
to result in a similar casing effect.
[0068] Calibration of the transmitter (where "calibration" refers
to deriving the casing attenuation factor for the transmitter)
presents some additional issues, particularly when the transmitter
is run in a highly nonlinear mode while in casing. In other words,
the effective transmitter moment, as seen by a receiver far away,
outside of the casing, is a very nonlinear function of the current.
In terms of casing correction factors, this means that the casing
correction factor for the transmitter is a function of transmitter
current and field strength. Thus, it may not be possible to use the
transmitter as a receiver since the sensor's behavior as a receiver
will result in a substantially different field strength than when
the same is operated as a transmitter. It is still possible to
generalize the result from above to calibrate the transmitter.
[0069] Referring again to FIG. 3, we see that at least one of the
sensors is operated as either a transmitter or a receiver. This is
equally true when calibrating the transmitter, except that the
primary transmitter may be operated only as a transmitter.
[0070] FIG. 8 is similar to FIG. 7, but FIG. 8 shows a transmitter
402 and two receivers 404, 406. Calibration can proceed as above,
except that in the arrangement of FIG. 8, the transmitter 402 is
used as a transmitter only. From the first expression (for k.sub.1)
of Eq. 26, the casing correction factor k.sub.1 for the transmitter
402 can be obtained. Since this is a direct measure of the
effective moment of the transmitter 402, the measurement
automatically includes all of the details of the transmitter 402
that are either unknown or extremely difficult to model. These
effects include: transmitter current, transmitter core, drive
waveform, spatial dependence of .sigma. and .mu., spatial
dependence of core and casing dimensions, collars, eccentering,
nonlinear effects in core and casing, remnant magnetization in core
and casing, polarization of core and casing, interaction between
different harmonics, changes in electrical or magnetic properties
due to temperature, pressure or aging.
[0071] Since the technique above is a direct measurement of the
field produced by the transmitter, it is sensitive only to the
effective moment of the transmitter. The moment is the same whether
the field is measured inside of the casing sufficiently far away
from the transmitter or at a distance outside the casing.
[0072] Another issue in performing measurements according to the
example techniques above is eliminating any parasitic coupling
among antennas (e.g., the coils in transmitters and receivers). A
transmitter that is driven with significant current and voltage can
be located in the same tool string as a receiver that is attempting
to measure small magnetic fields. There are various ways to
minimize or reduce coupling between such transmitter and receiver,
minimizing direct electrical contact between the antenna sections
caused by through-wires. In one example, as depicted in FIG. 9,
inductive couplers 500, 502 separate the three antennas 504, 506,
and 508. The antenna 504 can be for a transmitter, while antennas
506 and 508 can be for auxiliary receivers. The inductive couplers
500 and 502 may each include an air gap between the primary and
secondary inductive coupler portions to keep the capacitive
coupling small. The air gaps may be omitted in other
implementations. In some embodiments, capacitive shields cover the
antennas. Power and telemetry can be passed at a high frequency
between the antenna sections. The inductive coupler 500, 502 is
efficient at high frequency to pass power and telemetry, but is
inefficient at the transmitter frequency.
[0073] As depicted in FIG. 9, cartridges 510, 512, and 514 are
associated with respective antennas 504, 506, and 508. The
cartridges 510, 512, and 514 include electronic circuitry to
perform related tasks, such as to cause transmission by a
transmitter or to enable detection by a receiver.
[0074] FIG. 10 shows an example inductive coupler that has an air
gap 600 between inductive coupler portions. The left inductive
coupler portion is connected by wires 602 to a bulkhead 604 for
connection to the next section of the tool, while the right
inductive coupler portion is connected over wires 606 to a bulkhead
608 for connection to another section of the tool. The components
of FIG. 10 can be provided in a fiberglass housing 610 (or in
another type of housing).
[0075] In various embodiments, the above may be achieved with a
number of sensors exceeding the minimum of three described above
for embodiments having no constraints. In considering the number of
sensors that are needed in order to determine all the effective
areas by measuring the cross-couplings, there are concerns about
some of the constraints on separability and signal strength.
Assuming no constraints, only 3 sensors are needed.
[0076] If, however, minimum and maximum spacing constraints are
assumed, additional sensors may be necessary to accomplish the
methods of the present disclosure. The constraint most often
measured is that the spacing between two receivers must be at least
twice the inter-receiver spacing. With 4 sensors, we have only to
following:
A.sub.13=A.sub.1A.sub.3
A.sub.14=A.sub.1A.sub.4 (Eq. 28)
A.sub.24=A.sub.2A.sub.4
which is inadequate to determine 4 coefficients. Under such
constraints, it results that at least 5 sensor are sufficient for
determining all the coefficients, even if we assume that the
minimum spacing is 2 and the maximum is 3.
A 13 = A 1 A 3 A 14 = A 1 A 4 A 24 = A 2 A 4 A 25 = A 2 A 5 A 35 =
A 3 A 5 A 1 = A 13 A 14 A 25 A 24 A 35 A 2 = A 13 A 24 A 25 A 14 A
35 A 3 = A 13 A 24 A 35 A 14 A 25 A 4 = A 14 A 24 A 35 A 13 A 25 A
5 = A 14 A 25 A 35 A 13 A 24 ( Eq . 29 ) ##EQU00010##
[0077] The casing correction factors determined according to
methods disclosed above may be applied to eliminate the effect of
one or more casings in various applications. For example, improved
evaluation of a reservoir including crosswell techniques,
surface-to-borehole techniques, and single well evaluation
techniques is achieved by applying the casing correction factors in
each scenario to take into account the effect of the casing in a
single well (for surface-to-borehole or single well techniques) or
in a plurality of wells. Additionally, the casing correction
factors may be used to improved drilling techniques for parallel
wells, such as with steam assisted gravity drainage drilling, well
avoidance in scenarios having a plurality of wells in close
proximity to one another, and well intersection techniques (as
generally described in U.S. patent application Ser. No. 11/833,032,
entitled "Magnetic Ranging While Drilling Parallel Wells," filed
Aug. 2, 2007 (Atty. Docket 19.0442). Further applications may also
include improved casing evaluation for examining the status of
casing already in place, for instance to evaluate the state of
corrosion of the casing, and improved reservoir monitoring (e.g.,
resistivity, conductivity, and fluid invasion generally) through
casing.
[0078] While the invention has been disclosed with respect to a
limited number of embodiments, those skilled in the art, having the
benefit of this disclosure, will appreciate numerous modifications
and variations therefrom. It is intended that the appended claims
cover such modifications and variations as fall within the true
spirit and scope of the invention.
* * * * *