U.S. patent application number 11/743508 was filed with the patent office on 2007-11-08 for method of analyzing a subterranean formation and method of producing a mineral hydrocarbon fluid from the formation.
Invention is credited to Erik Jan Banning-Geertsma, Teruhiko HAGIWARA, Richard Martin Ostermeier.
Application Number | 20070256832 11/743508 |
Document ID | / |
Family ID | 38617438 |
Filed Date | 2007-11-08 |
United States Patent
Application |
20070256832 |
Kind Code |
A1 |
HAGIWARA; Teruhiko ; et
al. |
November 8, 2007 |
METHOD OF ANALYZING A SUBTERRANEAN FORMATION AND METHOD OF
PRODUCING A MINERAL HYDROCARBON FLUID FROM THE FORMATION
Abstract
Method of analyzing a subterranean formation traversed by a
wellbore. The method uses a tool comprising a transmitter antenna
and a receiver antenna, the subterranean formation comprising one
or more formation layers. The tool is suspended inside the
wellbore, and one or more electromagnetic fields are induced in the
formation. One or more time-dependent transient response signals
are detected and analyzed. Electromagnetic anisotropy of at least
one of the formation layers is detectable. Geosteering cues may be
derived from the time-dependent transient response signals, for
continued drilling of the well bore until a hydrocarbon reservoir
is reached. The hydrocarbon may then be produced.
Inventors: |
HAGIWARA; Teruhiko;
(Houston, TX) ; Banning-Geertsma; Erik Jan;
(Houston, TX) ; Ostermeier; Richard Martin;
(Houston, TX) |
Correspondence
Address: |
SHELL OIL COMPANY
P O BOX 2463
HOUSTON
TX
772522463
US
|
Family ID: |
38617438 |
Appl. No.: |
11/743508 |
Filed: |
May 2, 2007 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60797556 |
May 4, 2006 |
|
|
|
Current U.S.
Class: |
166/250.16 ;
166/254.1; 166/66; 175/50 |
Current CPC
Class: |
G01V 3/28 20130101 |
Class at
Publication: |
166/250.16 ;
166/254.1; 166/66; 175/50 |
International
Class: |
E21B 47/00 20060101
E21B047/00; E21B 49/00 20060101 E21B049/00 |
Claims
1. A method of analyzing a subterranean formation traversed by a
wellbore, using a tool comprising a transmitter antenna and a
receiver antenna, the subterranean formation comprising one or more
formation layers and the method comprising: suspending the tool
inside the wellbore; inducing one or more electromagnetic fields in
the formation; detecting one or more time-dependent transient
response signals; analyzing the one or more time-dependent
transient response signals taking into account electromagnetic
anisotropy of at least one of the formation layers.
2. The method of claim 1, wherein the at least one formation layer
comprises three or more sub-layers.
3. The method of claim 2, wherein one of the three or more
sub-layers has a first resistivity or conductivity that is
different from a second resistivity or conductivity of another one
of the three or more sub-layers.
4. The method of claim 2, wherein the sub-layers that are not
individually resolved in the transient response signals jointly are
approximated as one anisotropic formation layer.
5. The method of claim 1, wherein analyzing the one or more
time-dependent transient response signals taking into account
electromagnetic anisotropy includes deriving an anisotropy
parameter of the at least one formation layer from the detected one
or more time-dependent transient response signals.
6. The method of claim 5, wherein the anisotropy parameter
comprises at least one from a group of parameters comprising
anisotropy ratio, anisotropic factor, conductivity along a
principal anisotropy axis, resistivity along the principal
anisotropy axis, conductivity in a plane perpendicular to the
principal anisotropy axis, resistivity in a plane perpendicular to
the principal anisotropy axis; tool axis angle relative to the
principal anisotropy axis.
7. The method of claim 1, wherein analyzing the one or more
time-dependent transient response signals comprises combining
multi-axial transient measurements to derive an anisotropy
parameter.
8. The method of claim 1, wherein analyzing the one or more
time-dependent transient response signals taking into account
electromagnetic anisotropy comprises deriving at least one of
time-dependent apparent conductivity, time dependent apparent
resistivity, time-dependent dip angle, and time-dependent azimuth
angle from the time dependence of the transient response
signals.
9. The method of claim 1, wherein one of the formation layers
comprises an anomaly, and wherein analyzing the one or more
time-dependent transient response signals comprises determining at
least one of a distance and a direction between the tool and the
anomaly from the one or more time-dependent transient response
signals.
10. The method of claim 1, wherein inducing one or more
electromagnetic fields in the formation comprises generating a
transmission and terminating the transmission, and detecting one or
more time-dependent transient response signals comprises measuring
a receiver response as a function of time following the terminating
the transmission.
11. A method of producing a mineral hydrocarbon fluid from an earth
formation, the method comprising steps of: suspending a drill
string in the earth formation, the drill string comprising at least
a drill bit and measurement sub comprising a transmitter antenna
and a receiver antenna; drilling a well bore in the earth
formation; inducing an electromagnetic field in the earth formation
employing the transmitter antenna; detecting one or more
time-dependent transient electromagnetic response signals from the
electromagnetic field, employing the receiver antenna; deriving a
geosteering cue from the electromagnetic response; continue
drilling the well bore in accordance with the geosteering cue until
a reservoir containing the hydrocarbon fluid is reached; producing
the hydrocarbon fluid.
12. The method of claim 11, wherein drilling the well bore
comprises operating a steerable drilling system in the earth
formation.
13. The method of claim 11, wherein inducing the electromagnetic
field in the earth formation comprises generating a transmission
and terminating the transmission, and detecting one or more
time-dependent transient response signals comprises measuring a
receiver response as a function of time following the terminating
the transmission.
14. The method of claim 11, wherein deriving the geosteering cue
comprises analyzing the one or more transient response signals
taking into account electromagnetic anisotropy of at least one of
the formation layers.
15. The method of claim 11, wherein deriving the geosteering cue
comprises locating an electromagnetic anomaly in the earth
formation based on the one or more time-dependent transient
response signals.
16. The method of claim 15, wherein locating the electromagnetic
anomaly comprises determining at least one of a distance from the
measurement sub to the anomaly and a direction from the measurement
sub to the anomaly.
17. The method of claim 16, wherein determining the distance
comprises determining a time in which one of apparent conductivity
and apparent resistivity begins to deviate from the corresponding
one of conductivity and resistivity of formation in which the
device is located.
18. The method of claim 16, wherein determining the distance
comprises determining a time in which one of apparent dip and
apparent azimuth reaches an asymptotic value.
19. The method of claim 16, wherein determining the distance
comprises determining a time in which one of apparent dip and
apparent azimuth and cross-component response, reaches a non-zero
value.
20. The method of claim 15, wherein locating the electromagnetic
anomaly comprises deriving at least one of time-dependent apparent
conductivity, time dependent apparent resistivity, time-dependent
dip angle, and time-dependent azimuth angle from the time
dependence of the transient response.
21. The method of claim 11, wherein deriving the geosteering cue
comprises deriving at least one of time-dependent apparent
conductivity, time dependent apparent resistivity, time-dependent
dip angle, and time-dependent azimuth angle from the time
dependence of the transient response.
22. A computer readable medium storing computer readable
instructions that analyze one or more detected time-dependent
transient electromagnetic response signals that have been detected
by a tool suspended inside a wellbore traversing a subterranean
formation after inducing one or more electromagnetic fields in the
formation, wherein the computer readable instructions take into
account electromagnetic anisotropy of at least one formation layer
in the subterranean formation.
Description
CROSS REFERENCE TO EARLIER APPLICATION
[0001] The present application claims benefit under 35 USC .sctn.
119(e) of U.S. Provisional application No. 60/797,556 filed 4 May
2006.
FIELD OF THE INVENTION
[0002] In one aspect, the present invention relates to a method of
analyzing a subterranean formation traversed by a wellbore. In
another aspect the invention relates to a method of producing a
mineral hydrocarbon fluid from an earth formation. In still another
aspect, the invention relates to a computer readable medium storing
computer readable instructions that analyze one or more
electromagnetic response signals.
BACKGROUND OF THE INVENTION
[0003] In logging while drilling (LWD) geo-steering applications,
it is advantageous to detect the presence of a formation anomaly
ahead of or around a bit or bottom hole assembly. There are many
instances where "Look-Ahead" capability is desired in LWD logging
environments. Look-ahead logging comprises detecting an anomaly at
a distance ahead of a drill bit. Some look-ahead examples include
predicting an over-pressured zone in advance, or detecting a fault
in front of the drill bit in horizontal wells, or profiling a
massive salt structure ahead of the drill bit.
[0004] In U.S. Pat. No. 5,955,884 to Payton, et al, a tool and
method are disclosed for transient electromagnetic logging, wherein
electric and electromagnetic transmitters are utilized to apply
electromagnetic energy to a formation at selected frequencies and
waveforms that maximize radial depth of penetration into the target
formation. In this transient EM method, the current applied at a
transmitter antenna is generally terminated and a temporal change
of voltage induced in a receiver antenna is monitored over
time.
[0005] When logging measurements are used for well placement,
detection or identification of anomalies can be critical. Such
anomalies may include for example, a fault, a bypassed reservoir, a
salt dome, or an adjacent bed or oil-water contact.
[0006] U.S. patent applications published under Nos. 2005/0092487,
2005/0093546, 2006/0038571, each incorporated herein by reference,
describe methods for localizing such anomalies in a subterranean
earth formation employing transient electromagnetic (EM) reading.
The methods particularly enable finding the direction and distance
to a resistive or conductive anomaly in a formation surrounding a
borehole, or ahead of the borehole, in drilling applications.
[0007] Of the referenced U.S. patent application publications, US
2006/0038571 shows that transient electromagnetic responses can be
analyzed to determine conductivity values of a homogeneous earth
formation (single layer), and of two or three or more earth layers,
as well as distances from the tool to the interfaces between the
earth layers.
[0008] In principle, the methodology as set forth in US
2006/0038571 would work for any number of layers. However, the
larger the number of layers, and particularly when the layers are
thin, the more complicated the analysis is. For instance, a thinly
laminated sand/shale sequence would be difficult to analyze
employing the methodology as set forth in US 2006/0038571.
SUMMARY OF THE INVENTION
[0009] In accordance with the invention there is provided a method
of analyzing a subterranean formation traversed by a wellbore,
using a tool comprising a transmitter antenna and a receiver
antenna, the subterranean formation comprising one or more
formation layers and the method comprising:
[0010] suspending the tool inside the wellbore;
[0011] inducing one or more electromagnetic fields in the
formation;
[0012] detecting one or more time-dependent transient response
signals;
analyzing the one or more time-dependent transient response signals
taking into account electromagnetic anisotropy of at least one of
the formation layers.
[0013] The electromagnetic properties of a formation layer
comprising a number of thin layers may be approximated by one
formation layer comprising an electromagnetic anisotropy. It is
thereby avoided to have to take into account each thin layer
individually when inverting the responses.
[0014] Amongst other advantages of taking into account
electromagnetic anisotropy, is that anisotropy information may be
useful in precisely locating mineral hydrocarbon fluid containing
reservoirs, as such reservoirs are often associated with
electromagnetic anisotropy of formation layers.
[0015] The result of the analyzing step mentioned above may be
outputted, including displayed or stored or transmitted or
otherwise made conveyed and made available to an operator or a
geosteering system. Such a geosteering system may use the result of
the analysis to generate a geosteering cue in response. The
geosteering cue may in itself be outputted, including displayed or
stored or transmitted or otherwise made conveyed and made available
to an operator and/or used to continue drilling in response to the
geosteering cue.
[0016] Said method of analyzing a subterranean formation may be
used in a geosteering application, wherein a geosteering cue may be
derived from the one or more time-dependent transient response
signals, taking into account electromagnetic anisotropy, and
wherein a drilling operation may be continued in accordance with
the derived geosteering cue in order to accurately place a
well.
[0017] Thus, in another aspect there is provided a method of
producing a mineral hydrocarbon fluid from an earth formation, the
method comprising steps of:
[0018] suspending a drill string in the earth formation, the drill
string comprising at least a drill bit and measurement sub
comprising a transmitter antenna and a receiver antenna;
[0019] drilling a well bore in the earth formation;
[0020] inducing an electromagnetic field in the earth formation
employing the transmitter antenna;
[0021] detecting a transient electromagnetic response signal from
the electromagnetic field, employing the receiver antenna;
[0022] deriving a geosteering cue from the electromagnetic
response;
[0023] continue drilling the well bore in accordance with the
geosteering cue until a reservoir containing the hydrocarbon fluid
is reached;
[0024] producing the hydrocarbon fluid.
[0025] In still another aspect, the invention provides a computer
readable medium storing computer readable instructions that analyze
one or more detected time-dependent transient electromagnetic
response signals that have been detected by a tool suspended inside
a wellbore traversing a subterranean formation after inducing one
or more electromagnetic fields in the formation, wherein the
computer readable instructions take into account electromagnetic
anisotropy of at least one formation layer in the subterranean
formation.
BRIEF DESCRIPTION OF THE DRAWINGS
[0026] The present invention is described in more detail below by
way of examples and with reference to the attached drawing figures,
wherein:
[0027] FIG. 1A is a block diagram showing a system implementing
embodiments of the invention;
[0028] FIG. 1B schematically illustrates an alternative system
implementing embodiments of the invention;
[0029] FIG. 2 is a flow chart illustrating a method in accordance
with an embodiment of the invention;
[0030] FIG. 3 is a graph illustrating directional angles between
tool coordinates and anomaly coordinates;
[0031] FIG. 4A is a graph showing a resistivity anomaly in a tool
coordinate system;
[0032] FIG. 4B is a graph showing a resistivity anomaly in an
anomaly coordinate system;
[0033] FIG. 5 is a graph illustrating tool rotation within a
borehole;
[0034] FIG. 6 schematically shows directional components involving
electromagnetic induction tools relative to an electromagnetic
induction anomaly;
[0035] FIG. 7 is a graph showing the voltage response from coaxial
V.sub.zz(t), coplanar V.sub.xx(t), and the cross-component
V.sub.zx(t) measurements for L=1 m, for .theta.=30.degree., and a
distance D=10 m from a salt layer;
[0036] FIG. 8 is a graph showing the voltage response from coaxial
V.sub.zz(t), coplanar V.sub.xx(t), and the cross-component
V.sub.zx(t) measurements for L=1 m, for .theta.=30.degree., and a
distance D=100 m from a salt layer;
[0037] FIG. 9 is a graph showing apparent dip (.theta..sub.app(t))
for an arrangement as in FIG. 7;
[0038] FIG. 10 is a graph showing apparent conductivity
(.sigma..sub.app(t)) calculated from both the coaxial (V.sub.zz(t))
and the coplanar (V.sub.xx(t)) responses for the same conditions as
in FIG. 9;
[0039] FIG. 11 is a graph showing apparent dip .theta..sub.app(t)
for the L=1 m tool assembly when the salt face is D=10 m away, for
various angles between the tool axis and the target;
[0040] FIG. 12 is a graph similar to FIG. 11 whereby the salt face
is D=50 m away from the tool;
[0041] FIG. 13 is a graph similar to FIG. 11 whereby the salt face
is D=100 m away from the tool;
[0042] FIG. 14 is a schematic illustration showing a coaxial tool
with its tool axis parallel to a layer interface;
[0043] FIG. 15 is a graph showing transient voltage response as a
function of t as given by the coaxial tool of FIG. 14 in a
two-layer formation at different distances from the bed;
[0044] FIG. 16 is a graph showing the voltage response data of FIG.
15 in terms of the apparent conductivity (.sigma..sub.app(t));
[0045] FIG. 17 is similar to FIG. 16 except that the resistivities
of layers 1 and 2 have been interchanged;
[0046] FIG. 18 shows a graph of the .sigma..sub.app(t) for the case
D=1 m and L=1 m, for various resistivity ratios while the target
resistivity is fixed at R.sub.2=1 .OMEGA.m;
[0047] FIG. 19 shows a comparison of apparent conductivity at large
values of t, .sigma..sub.app(t.fwdarw..infin.), for coaxial
responses where D=1 m and L=1 m as a function of conductivity
.sigma..sub.2 of the target layer while the local conductivity
.sigma..sub.1 is fixed at 1 S/m;
[0048] FIG. 20 graphically shows the same data as FIG. 19 plotted
as the ratio of target conductivity over local layer conductivity
.sigma..sub.1 versus ratio of the late time apparent conductivity
.sigma..sub.app(t.fwdarw..infin.) over local layer conductivity
.sigma..sub.1;
[0049] FIG. 21 shows a graph containing apparent conductivity
(.sigma..sub.app(t)) versus time for various combinations of D and
L;
[0050] FIG. 22 graphically shows the relationship between ray-path
RP and transition time t.sub.c;
[0051] FIG. 23 is a schematic illustration showing a coaxial tool
approaching or just beyond a bed boundary;
[0052] FIG. 24 is a graph showing transient voltage response as a
function of t as given by the coaxial tool of FIG. 23 at different
distances D from the bed;
[0053] FIG. 25 is a graph showing the voltage response data of FIG.
24 in terms of the apparent conductivity (.sigma..sub.app(t));
[0054] FIG. 26 is similar to FIG. 25 except that the resistivities
of layers 1 and 2 have been interchanged;
[0055] FIG. 27 presents a graph comparing .sigma..sub.app(t) of
FIG. 25 and FIG. 26 relating to D=1 m;
[0056] FIG. 28 shows a graph of .sigma..sub.app(t) on a linear
scale for various transmitter/receiver spacings L in case D=50
m;
[0057] FIG. 29 graphically shows distance to anomaly ahead of the
tool verses transition time (t.sub.c) as determined from the data
of FIG. 25;
[0058] FIG. 30 schematically shows a coplanar tool approaching or
just beyond a bed boundary;
[0059] FIG. 31 is a graph showing transient voltage response data
in terms of the apparent conductivity (.sigma..sub.app(t)) as a
function of t as provided by the coplanar tool of FIG. 30 at
different distances D from the bed;
[0060] FIG. 32 shows a comparison of the late time apparent
conductivity (.sigma..sub.app(t.fwdarw..infin.)) for coplanar
responses where D=50 m and L=1 m as a function of conductivity
.sigma..sub.1 of the local layer while the target conductivity
.sigma..sub.2 is fixed at 1 S/m;
[0061] FIG. 33 graphically shows the same data as FIG. 32 plotted
as the ratio of target conductivity .sigma..sub.2 over local layer
conductivity .sigma..sub.1 versus ratio of the late time apparent
conductivity .sigma..sub.app(t.fwdarw..infin.) over local layer
conductivity .sigma..sub.1;
[0062] FIG. 34 graphically shows distance to anomaly ahead of the
tool verses transition time (t.sub.c) as determined from the data
of FIG. 31;
[0063] FIG. 35 schematically shows a model of a coaxial tool in a
conductive local layer (1 .OMEGA.m), a very resistive layer (100
.OMEGA.m), and a further conductive layer (1 .OMEGA.m);
[0064] FIG. 36 is a graph showing apparent resistivity response
versus time, R.sub.app(t), for a geometry as given in FIG. 35 for
various thicknesses .DELTA. of the very resistive layer;
[0065] FIG. 37 schematically shows a model of a coaxial tool in a
resistive local layer (10 .OMEGA.m), a conductive layer (1
.OMEGA.m), and a further resistive layer (10 .OMEGA.m);
[0066] FIG. 38 is a graph similar to FIG. 36, showing apparent
resistivity response R.sub.app(t) versus time for a geometry as
given in FIG. 37 for various thicknesses .DELTA. of the conductive
layer;
[0067] FIG. 39 schematically shows a model of a coaxial tool in a
conductive local layer (1 .OMEGA.m) in the vicinity of a highly
resistive layer (100 .OMEGA.m) with a separating layer having an
intermediate resistance (10 .OMEGA.m) of varying thickness in
between;
[0068] FIG. 40 is a graph similar to FIG. 36, showing apparent
resistivity response versus time, R.sub.app(t), for a geometry as
given in FIG. 39 for various thicknesses .DELTA. of the separating
layer;
[0069] FIG. 41 shows calculated coaxial transient voltage responses
for an L=1 m tool in an anisotropic formation wherein
.sigma..sub.H=1 S/m (R.sub.H=1 .OMEGA.m) for various values of
.beta..sup.2;
[0070] FIG. 42 shows apparent conductivity based on the responses
of FIG. 41;
[0071] FIG. 43 shows apparent conductivity based on coaxial
responses for an L=1 m tool in a formation wherein
.sigma..sub.H=0.1 S/m for various values of .beta..sup.2;
[0072] FIG. 44 shows apparent conductivity based on coaxial
responses for an L=1 m tool in a formation wherein
.sigma..sub.H=0.01 S/m for various values of .beta..sup.2;
[0073] FIG. 45 shows a graph plotting late time asymptotic value of
coaxial apparent conductivity .sigma..sub.Zz(t.fwdarw..infin.) from
FIGS. 44 to 44, normalized by .sigma..sub.H, against a variable
representing .beta..sup.2;
[0074] FIG. 46 shows apparent dip angle .theta..sub.app(t) as a
function of time based on calculated coaxial, coplanar and
cross-component transient responses from a L=1 m tool in a
formation of R.sub.H=10 .OMEGA.m and R.sub.V/R.sub.H=9;
[0075] FIG. 47 shows an electromagnetic induction tool in a
formation layer comprising a package of alternating sets of
sub-layers;
[0076] FIG. 48 shows a graph of apparent resistivity in co-axial
measurement and co-planar measurement of the geometry as in FIG.
47;
[0077] FIG. 49 schematically shows directional components of an
electromagnetic induction tool relative to an anisotropic
anomaly;
[0078] FIG. 50 shows a plot of the apparent conductivity
(.sigma..sub.app(z; t)) in both z- and t-coordinates for various
distances D;
[0079] FIG. 51 shows a plot of the apparent conductivity
(.sigma..sub.app(z; t)) in both z- and t-coordinates;
[0080] FIG. 52 schematically shows a model of a structure involving
a highly resistive layer (100 .OMEGA.m) covered by a conductive
local layer (1 .OMEGA.m) which is covered by a resistive layer (10
.OMEGA.m), whereby a coaxial tool is depicted in the resistive
layer;
[0081] FIG. 53A shows apparent resistivity in both z and t
coordinates whereby inflection points are joined using curve fitted
lines;
[0082] FIG. 53B shows an image log derived from FIG. 53A;
[0083] FIG. 54A schematically shows a coaxial tool seen as
approaching a highly resistive formation at a dip angle of
approximately 30 degrees;
[0084] FIG. 54B shows apparent dip response in both t and z
coordinates for z-locations corresponding to those depicted in FIG.
54A.
DETAILED DESCRIPTION OF THE INVENTION
[0085] The present invention will now be described in relation to
particular embodiments, which are intended in all respects to be
illustrative rather than restrictive. Alternative embodiments will
become apparent to those skilled in the art to which the present
invention pertains without departing from its scope.
[0086] It will be understood that certain features and
sub-combinations are of utility and may be employed without
reference to other features and sub-combinations specifically set
forth. This is contemplated and within the scope of the claims.
[0087] Embodiments of the invention relate to analysis of
electromagnetic (EM) induction signals and to a system and method
for determining distance and/or direction to an anomaly in a
formation from a location within a wellbore. The analysis is
sensitive to electromagnetic anomalies, in particular
electromagnetic induction anomalies.
[0088] Both frequency domain excitation and time domain excitation
have been used to excite electromagnetic fields for use in anomaly
detection. In frequency domain excitation, a device transmits a
continuous wave of a fixed or mixed frequency and measures
responses at the same band of frequencies. In time domain
excitation, a device transmits a square wave signal, triangular
wave signal, pulsed signal or pseudo-random binary sequence as a
source and measures the broadband earth response. Sudden changes in
transmitter current cause transient signals to appear at a receiver
caused by induction currents in the formation. The signals that
appear at the receiver are called transient responses because the
receiver signals start at a first value after a sudden change in
transmitter current, and then they decay (or increase) with time to
a new constant level at a second value. The technique disclosed
herein implements the time domain excitation technique.
[0089] As set forth below, embodiments of the invention propose a
general method to determine a direction from a measurement sub to a
resistive or conductive anomaly using transient EM responses. As
will be explained in detail, the direction to the anomaly is
specified by a dip angle and an azimuth angle. Embodiments of the
invention propose to define an apparent dip (.theta..sub.app(t))
and an apparent azimuth (.phi..sub.app(t)) by combinations of
multi-axial, e.g. bi-axial or tri-axial, transient measurements.
The true direction, in terms of dip and azimuth angles ({.theta.,
.phi.}), may be determined from the analysis of the apparent
direction ({.theta..sub.app(t), .phi..sub.app(t)}). For instance,
the apparent direction ({.theta..sub.app(t), .phi..sub.app(t)})
approaches the true direction ({.theta., .phi.}) as a time (t)
increases, if the anomaly has a high thickness as seen from the
tool.
[0090] Time-dependent values for apparent conductivity may be
obtained from coaxial and coplanar electromagnetic induction
measurements, and can respectively be denoted as
.sigma..sub.coaxial(t) and .sigma..sub.coplanar(t). Both read the
conductivity in the total present formation around the tool. The
.theta..sub.app(t) and .phi..sub.app(t) both initially read zero
when an apparent conductivity .sigma..sub.coaxial(t) and
.sigma..sub.coplanar(t) from coaxial and coplanar measurements both
read the conductivity of the formation surrounding the tool nearby.
The apparent conductivity will be further explained below and can
also be used to determine the location of an anomaly in a
wellbore.
[0091] Whenever in the present specification the term
"conductivity" is employed, it is intended to cover also its
inverse equivalent "resistivity", and vice versa. The same holds
for the terms "apparent conductivity" and "apparent
resistivity".
[0092] FIGS. 1A and 1B illustrate systems that may be used to
implement the embodiments of the method of the invention. A surface
computing unit 10 may be connected with an electromagnetic
measurement tool 2 disposed in a wellbore 4.
[0093] In FIG. 1A, the tool 2 is suspended on a cable 12. The cable
12 may be constructed of any known type of cable for transmitting
electrical signals between the tool 2 and the surface computing
unit 10.
[0094] In FIG. 1B, the tool is comprised in a measurement sub 11
and suspended in the wellbore 4 by a drill string 15. The drill
string 15 further supports a drill bit 17, and may support a
steering system 19. The steering system may be of a known type,
including a rotatable steering system or a sliding steering system.
The wellbore 4 traverses the earth formation 5 and it is an
objective to precisely direct the drill bit 17 into a hydrocarbon
fluid containing reservoir 6 to enable producing the hydrocarbon
fluid via the wellbore. Such a reservoir 6 may manifest itself as
an electromagnetic anomaly in the formation 5.
[0095] Referring again to both FIGS. 1A and 1B, one or more
transmitters 16 and one are more receivers 18 may be provided for
transmitting and receiving electromagnetic signals into and from
the formation around the wellbore 4. A data acquisition unit 14 may
be provided to transmit data to and from the transmitters 16 and
receivers 18 to the surface computing unit 10.
[0096] Each transmitter 16 and/or receiver 18 may comprise a coil,
wound around a support structure such as a mandrel. The support
structure may comprise a non-conductive section to suppress
generation of eddy currents. The non-conductive section may
comprise one or more slots, optionally filled with a non-conductive
material, or it may be formed out of a non-conductive material such
as a composite plastic. Alternatively, the support structure is
coated with a layer of a high-magnetic permeable material to form a
magnetic shield between the antenna and the support structure.
[0097] Each transmitter 16 and each receiver 18 may be bi-axial or
even tri-axial, and thereby contain components for sending and
receiving signals along each of three axes. Accordingly, each
transmitter module may contain at least one single or multi-axis
antenna and may be a 3-orthogonal component transmitter. Each
receiver may include at least one single or multi-axis
electromagnetic receiving component and may be a 3-orthogonal
component receiver.
[0098] A tool/borehole coordinate system is defined as having x, y,
and z axes. The z-axis defines the direction from the transmitter T
to the receiver R. It will be assumed hereinafter that the axial
direction of the wellbore 4 coincides with the z-axis, whereby the
x- and y-axes correspond to two orthogonal directions in a plane
normal to the direction from the transmitter T to the receiver R
and to the wellbore 4.
[0099] The data acquisition unit 14 may include a controller for
controlling the operation of the tool 2. The data acquisition unit
14 preferably collects data from each transmitter 16 and receiver
18 and provides the data to the surface computing unit 10. The data
acquisition unit 14 may comprise an amplifier and/or a digital to
analogue converter, as described in co-pending U.S. application
Ser. No. 11/689,980 filed on 22 Mar. 2007, incorporated herein by
reference, to amplify the responses and/or convert to a digital
representation of the responses before transmitting to the surface
computing unit 10 via cable 12 and/or an optional telemetry unit
13.
[0100] The surface computing unit 10 may include computer
components including a processing unit 30, an operator interface
32, and a tool interface 34. The surface computing unit 10 may also
include a memory 40 including relevant coordinate system
transformation data and assumptions 42, an optional direction
calculation module 44, an optional apparent direction calculation
module 46, and an optional distance calculation module 48. The
optional direction and apparent direction calculation modules are
described in more detail in already incorporated US patent
application publication 2005/0092487 and need not be further
described here, other than specifying that these optional modules
may take into account formation anisotropy.
[0101] The surface computing unit 10 may include computer
components including a processing unit 30, an operator interface
32, and a tool interface 34. The surface computing unit 10 may also
include a memory 40 including relevant coordinate system
transformation data and assumptions 42, a direction calculation
module 44, an apparent direction calculation module 46, and a
distance calculation module 48. The surface computing unit 10 may
further include a bus 50 that couples various system components
including the system memory 40 to the processing unit 30. The
computing system environment 10 is only one example of a suitable
computing environment and is not intended to suggest any limitation
as to the scope of use or functionality of the invention.
Furthermore, although the computing system 10 is described as a
computing unit located on a surface, it may optionally be located
below the surface, incorporated in the tool, positioned at a remote
location, or positioned at any other convenient location.
[0102] The memory 40 preferably stores one or more of modules 48,
44 and 46, which may be described as program modules containing
computer-executable instructions, executable by the surface
computing unit 10. Each module may comprise or make use of a
computer readable medium that stores computer readable instructions
for analyzing one or more detected time-dependent transient
electromagnetic response signals that have been detected by a tool
suspended inside a wellbore traversing a subterranean formation
after inducing one or more electromagnetic fields in the formation.
The instructions may implement any part of the disclosure that
follows herein below.
[0103] For example, the program module 44 may contain computer
executable instructions to calculate a direction to an anomaly
within a wellbore. The program module 48 may contain computer
executable instructions to calculate a distance to an anomaly or a
thickness of the anomaly. The stored data 42 may include data
pertaining to the tool coordinate system and the anomaly coordinate
system and other data for use by the program modules 44, 46, and
48. Preferably, the computer readable instructions take into
account electromagnetic anisotropy of at least one formation layer
in the subterranean formation. For further details on the computing
system 10, including storage media and input/output devices,
reference is made to US patent application publication
2005/0092487, incorporated herein by reference. Accordingly,
additional details concerning the internal construction of the
computer 10 need not be disclosed in connection with the present
invention.
[0104] FIG. 2 is a flow chart illustrating the procedures involved
in a method embodying the invention. Generally, in procedure A, the
transmitters 16 transmit electromagnetic signals. In procedure B,
the receivers 18 receive transient responses. In procedure C, the
system processes the transient responses. The procedures may then
end or start again.
[0105] Procedure C may comprise determining a distance and/or a
direction to the anomaly may be determined. Procedure C may
comprise creating an image of formation features based on the
transient electromagnetic responses. Electromagnetic anisotropy of
at least one of the formation layers may be taken into account.
[0106] FIGS. 3-6 illustrate the technique for implementing
procedure C for determining distance and/or direction to the
anomaly. FIGS. 6 and 41 to 49 illustrate how electromagnetic
anisotropy may be taken into account, e.g. in determining distance
and/or direction to the anomaly.
Tri-Axial Transient EM Responses
[0107] FIG. 3 illustrates directional angles between tool
coordinates and anomaly coordinates. A transmitter coil T is
located at an origin that serves as the origin for each coordinate
system. A receiver R is placed at a distance L from the
transmitter. An earth coordinate system, includes a Z-axis in a
vertical direction and an X-axis and a Y-axis in the East and the
North directions, respectively. The deviated borehole is specified
in the earth coordinates by a deviation angle .theta..sub.b and its
azimuth angle .phi..sub.b. A resistivity anomaly A is located at a
distance D from the transmitter in the direction specified by a dip
angle (.theta..sub.a) and its azimuth (.phi..sub.a).
[0108] In order to practice embodiments of the method, FIG. 4A
shows the definition of a tool/borehole coordinate system having x,
y, and z axes. The z-axis defines the direction from the
transmitter T to the receiver R. The tool coordinates in FIG. 4A
are specified by rotating the earth coordinates (X, Y, Z) in FIG. 3
by the azimuth angle (.phi..sub.b) around the Z-axis and then
rotating by .theta..sub.b around the y-axis to arrive at the tool
coordinates (x, y, z). The direction of the anomaly is specified by
the dip angle (.nu.) and the azimuth angle (.phi.) where:
cos = ( b ^ z a ^ ) = cos .theta. a cos .theta. b + sin .theta. a
sin .theta. b cos ( .PHI. a - .PHI. b ) ( 1 ) tan .phi. = sin
.theta. b sin ( .PHI. a - .PHI. b ) cos .theta. a sin .theta. b cos
( .PHI. a - .PHI. b ) - sin .theta. a cos .theta. b ( 2 )
##EQU00001##
[0109] Similarly, FIG. 4B shows the definition of an anomaly
coordinate system having a, b, and c axes. The c-axis defines the
direction from the transmitter T to the center of the anomaly A.
The anomaly coordinates in FIG. 4B are specified by rotating the
earth coordinates (X, Y, Z) in FIG. 3 by the azimuth angle
(.phi..sub.a) around the Z-axis and subsequently rotating by
.theta..sub.a around the b-axis to arrive at the anomaly
coordinates (a, b, c). In this coordinate system, the direction of
the borehole is specified in a reverse order by the azimuth angle
(.phi.) and the dip angle (.nu.).
Transient Responses in Two Coordinate Systems
[0110] The method is additionally based on the relationship between
the transient responses in two coordinate systems. The magnetic
field transient responses at the receivers [R.sub.x, R.sub.y,
R.sub.z,] which are oriented in the [x, y, z] axis direction of the
tool coordinates, respectively, are noted as
[ V xx V xy V xz V yx V yy V yz V zx V zy V zz ] = [ R x R y R z ]
[ T x T y T z ] , ( 3 ) ##EQU00002##
wherein the right-hand side of the equation represents all
combinations of receiver axis and transmitter axis, whereby
V.sub.ij=R.sub.iT.sub.j denotes voltage response sensed by receiver
R.sub.i (i=x, y, z) from signal transmitted by transmitter T.sub.j
(j=x, y, z). Each transmitter may comprise a magnetic dipole
source, [M.sub.x, M.sub.y, M.sub.z], in any direction.
[0111] When the resistivity anomaly is distant from the tool, the
formation near the tool is seen as a homogeneous formation. For
simplicity, the method may assume that the formation is isotropic.
Only three non-zero transient responses exist in a homogeneous
isotropic formation. These include the coaxial response and two
coplanar responses. Coaxial response V.sub.zz(t) is the response
when both the transmitter and the receiver are oriented in the
common tool axis direction. Coplanar responses, V.sub.xx(t) and
V.sub.yy(t), are the responses when both the transmitter T and the
receiver R are aligned parallel to each other but their orientation
is perpendicular to the tool axis. All of the cross-component
responses are identically zero in a homogeneous isotropic
formation. Cross-component responses are either from a
longitudinally oriented receiver with a transverse transmitter, or
vise versa. Another cross-component response is also zero between a
mutually orthogonal transverse receiver and transverse
transmitter.
[0112] The effect of the resistivity anomaly is seen in the
transient responses as time increases. In addition to the coaxial
and the coplanar responses, the cross-component responses
V.sub.ij(t) (i.noteq.j; i, j=x, y, z) become non-zero.
[0113] The magnetic field transient responses may also be examined
in the anomaly coordinate system. The magnetic field transient
responses at the receivers [R.sub.a, R.sub.b, R.sub.c,] that are
oriented in the [a, b, c] axis direction of the anomaly
coordinates, respectively, may be noted as
[ V aa V ab V ac V ba V bb V bc V ca V cb V cc ] = [ R a R b R c ]
[ T a T b T c ] ( 4 ) ##EQU00003##
wherein the right-hand side of the equation represents all
combinations of receiver orientation and transmitter orientation,
whereby V.sub.ij=R.sub.iT.sub.j denotes voltage response sensed by
receiver R.sub.i (in orientation i=a, b, c) from signal transmitted
by transmitter T.sub.j (in orientation j=a, b, c). Each transmitter
may comprise a magnetic dipole source, [M.sub.a, M.sub.b, M.sub.c],
along the orientation a, b, or c.
[0114] When the anomaly is large and distant compared to the
transmitter-receiver spacing, the effect of spacing can be ignored
and the transient responses can be approximated with those of the
receivers near the transmitter. Then, the method assumes that axial
symmetry exists with respect to the c-axis that is the direction
from the transmitter to the center of the anomaly. In such an
axially symmetric configuration, the cross-component responses in
the anomaly coordinates are identically zero in time-domain
measurements.
[ V aa V ab V ac V ba V bb V bc V ca V cb V cc ] = [ V aa 0 0 0 V
aa 0 0 0 V cc ] ( 5 ) ##EQU00004##
The magnetic field transient responses in the tool coordinates are
related to those in the anomaly coordinates by a simple coordinate
transformation P(.nu., .phi.) specified by the dip angle (.nu.) and
azimuth angle (.phi.).
[0115] [ V xx V xy V xz V yx V yy V yz V zx V zy V zz ] = P ( ,
.phi. ) tr [ V aa V ab V a c V ba V bb V bc V ca V cb V cc ] P ( ,
.phi. ) ( 6 ) P ( , .phi. ) = [ cos cos .phi. cos sin .phi. - sin -
sin .phi. cos .phi. 0 sin cos .phi. sin sin .phi. cos ] ( 7 )
##EQU00005##
Determination of Direction
[0116] The assumptions set forth above contribute to determination
of target direction, which is defined as the direction of the
anomaly from the origin. The tool is in the origin. When axial
symmetry in the anomaly coordinates is assumed, the transient
response measurements in the tool coordinates are constrained and
the two directional angles may be determined by combinations of
tri-axial responses.
[ V xx V xy V xz V yx V yy V yz V zx V zy V zz ] = P ( , .phi. ) tr
[ V aa 0 0 0 V aa 0 0 0 V CC ] P ( , .phi. ) ( 8 ) ##EQU00006##
In terms of each tri-axial response
[0117] V.sub.xx=(V.sub.aa cos.sup.2.nu.+V.sub.cc
sin.sup.2.nu.)cos.sup.2.phi.+V.sub.aa sin.sup.2.phi.
V.sub.yy=(V.sub.aa cos.sup.2.nu.+V.sub.cc
sin.sup.2.nu.)sin.sup.2.phi.+V.sub.aa cos.sup.2.phi.
V.sub.zz=V.sub.aa sin.sup.2.nu.+V.sub.cc cos.sup.2.nu. (9)
V.sub.xy=V.sub.yx=-(V.sub.aa-V.sub.cc)sin.sup.2.nu. cos .phi. sin
.phi.
V.sub.zx=V.sub.xz=-(V.sub.aa-V.sub.cc)cos .nu. sin .nu. cos
.phi.
V.sub.yz=V.sub.zy=-(V.sub.aa-V.sub.cc)cos .nu. sin .nu. sin .phi.
(10)
The following relations can be noted:
V.sub.xx+V.sub.yy+V.sub.zz=2V.sub.zz+V.sub.cc
V.sub.xx-V.sub.yy=(V.sub.cc-V.sub.aa)sin.sup.2.nu.(cos.sup.2.phi.-sin.su-
p.2.phi.)
V.sub.yy-V.sub.zz=-(V.sub.cc-V.sub.aa)(cos.sup.2.nu.-sin.sup.2.nu.
sin.sup.2.phi.)
V.sub.zz-V.sub.xx=(V.sub.cc-V.sub.aa)(cos.sup.2.nu.-sin.sup.2.nu.
cos.sup.2.phi.) (11)
[0118] Several distinct cases can be noted. In the first of these
cases, when none of the cross-components is zero, V.sub.xy.noteq.0
nor V.sub.yz.noteq.0 nor V.sub.zx.noteq.0, then the azimuth angle
.phi. is not zero nor .pi./2 (90.degree.), and can be determined
by,
.phi. = 1 2 tan - 1 V xy + V yx V xx - V yy ( 12 ) ##EQU00007##
By noting the relation,
[0119] V xy V xz = tan sin .phi. and V xy V yz = tan cos .phi. ( 13
) ##EQU00008##
the dip (deviation) angle .nu. is determined by,
tan = ( V xy V xz ) 2 + ( V xy V yz ) 2 ( 14 ) ##EQU00009##
In the second case, when V.sub.xy=0 and V.sub.yz=0, then .nu.=0 or
.phi.=0 or .pi. (180.degree.) or .phi.=.+-..pi./2 (90.degree.) and
.nu.=.+-..pi./2 (90.degree.), as the coaxial and the coplanar
responses should differ from each other
(V.sub.aa.noteq.V.sub.cc).
If .phi.=0, then the dip angle .nu. is determined by,
[0120] = - 1 2 tan - 1 V xz + V zx V xx - V zz ( 15 )
##EQU00010##
If .phi.=.pi. (180.degree.), then the dip angle .nu. is determined
by,
[0121] = + 1 2 tan - 1 V xz + V zx V xx - V zz ( 16 )
##EQU00011##
[0122] Also, with regard to the second case, If .nu.=0, then
V.sub.xx=V.sub.yy and V.sub.zx=0. If .phi.=.+-..pi./2 (90.degree.)
and .nu.=.+-..pi./2 (90.degree.), then V.sub.zz=V.sub.xx and
V.sub.zx=0. These instances are further discussed below with
relation to the fifth case.
[0123] In the third case, when V.sub.xy=0 and V.sub.xz=0, then
.phi.=.+-..pi./2 (90.degree.) or .nu.=0 or .phi.=0 and
.nu.=.+-..pi./2 (90.degree.).
[0124] If .phi.=.pi./2, then the dip angle .nu. is determined
by,
= - 1 2 tan - 1 V yz + V zy V yy - V zz ( 17 ) ##EQU00012##
[0125] If .phi.=-.pi./2, then the dip angle .nu. is determined
by,
= + 1 2 tan - 1 V yz + V zy V yy - V zz ( 18 ) ##EQU00013##
[0126] Also with regard to the third case, If .nu.=0, then
V.sub.xx=V.sub.yy and V.sub.yz=0. If .phi.=0 and .nu.=.+-..pi./2
(90.degree.), V.sub.yy=V.sub.zz and V.sub.yz=0. These situations
are further discussed below with relation to the fifth case.
[0127] In the fourth case, V.sub.xz=0 and V.sub.yz=0, then .nu.=0
or .pi.(180.degree.) or .+-..pi./2 (90.degree.).
[0128] If .nu.=.+-..pi./2, then the azimuth angle .phi. is
determined by,
.phi. = - 1 2 tan - 1 V xy + V yx V xx - V yy ( 19 )
##EQU00014##
[0129] Also with regard to the fourth case, if .nu.=0 or
.pi.(180.degree.), then V.sub.xx=V.sub.yy and V.sub.yz=0. This
situation is also shown below with relation to the fifth case.
[0130] In the fifth case, all cross components vanish,
V.sub.xz=V.sub.yz=V.sub.xy=0, then .nu.=0, or .nu.=.+-..pi./2
(90.degree.) and .phi.=0 or .+-..pi./2 (90.degree.).
[0131] If V.sub.xx=V.sub.yy then .nu.=0 or .pi.(180.degree.).
[0132] If V.sub.yy=V.sub.zz then .nu.=.+-..pi./2 (90.degree.) and
.phi.=0.
[0133] If V.sub.zz=V.sub.xx then .nu.=.+-..pi./2 (90.degree.) and
.phi.=.+-..pi./2 (90.degree.).
Tool Rotation Around the Tool/Borehole Axis
[0134] In the above analysis, all the transient responses
V.sub.ij(t) (i, j=x, y, z) are specified by the x-, y-, and z-axis
directions of the tool coordinates. However, the tool rotates
inside the borehole and the azimuth orientation of the transmitter
and the receiver no longer coincides with the x- or y-axis
direction as shown in FIG. 5. If the measured responses are {tilde
over (V)}.sub. {tilde over (j)}( ,{tilde over (j)}={tilde over
(x)},{tilde over (y)},{tilde over (z)}), where {tilde over (x)} and
{tilde over (y)} axis are the direction of antennas fixed to the
rotating tool, and .psi. is the tool's rotation angle, then
[ V x ~ x ~ V x ~ y ~ V x ~ z V y ~ x ~ V y ~ y ~ V y ~ z V z x ~ V
z y ~ V zz ] = R ( .psi. ) tr [ V xx V xy V xz V yx V yy V yz V zx
V zy V zz ] R ( .psi. ) ( 20 ) R ( .psi. ) = [ cos .psi. - sin
.psi. 0 sin .psi. cos .psi. 0 0 0 1 ] Then , ( 21 ) V x ~ x ~ = ( V
aa cos 2 + V cc sin 2 ) cos 2 ( .phi. - .psi. ) + V aa sin 2 (
.phi. - .psi. ) V y ~ y ~ = ( V aa cos 2 + V cc sin 2 ) sin 2 (
.phi. - .psi. ) + V aa cos 2 ( .phi. - .psi. ) V zz = V aa sin 2 +
V cc cos 2 ( 22 ) V x ~ y ~ = V y ~ x ~ = - ( V aa + V cc ) sin 2
cos ( .phi. - .psi. ) sin ( .phi. - .psi. ) V z x ~ = V x ~ z = - (
V aa + V cc ) cos sin cos ( .phi. - .psi. ) V y ~ z = V z y ~ = - (
V aa - V cc ) cos sin sin ( .phi. - .psi. ) The following relations
apply : ( 23 ) V x ~ x ~ + V y ~ y ~ + V zz = 2 V aa + V cc V x ~ x
~ - V y ~ y ~ = ( V cc - V aa ) sin 2 { cos 2 ( .phi. - .psi. ) -
sin 2 ( .phi. - .psi. ) } V y ~ y ~ - V zz = - ( V cc - V aa ) {
cos 2 - sin 2 sin 2 ( .phi. - .psi. ) } V zz - V x ~ x ~ = ( V cc -
V aa ) { cos 2 - sin 2 cos 2 ( .phi. - .psi. ) } Consequently , (
24 ) .phi. - .psi. = 1 2 tan - 1 V x ~ y ~ + V y ~ x ~ V x ~ x ~ +
V y ~ y ~ .phi. - .psi. = tan - 1 V y ~ z V x ~ z = tan - 1 V z y ~
V z x ~ ( 25 ) ##EQU00015##
[0135] The azimuth angle .phi. is measured from the tri-axial
responses if the tool rotation angle .psi.is known. To the
contrary, the dip (deviation) angle .nu. is determined by
tan = ( V x ~ y ~ V x ~ z ) 2 + ( V x ~ y ~ V y ~ z ) 2 ( 26 )
##EQU00016##
without knowing the tool orientation .psi..
Apparent Dip Angle and Azimuth Angle and the Distance to the
Anomaly
[0136] The dip and the azimuth angle described above indicate the
direction of a resistivity anomaly determined by a combination of
tri-axial transient responses at a time (t) when the angles have
deviated from a zero value. When t is small or close to zero, the
effect of such anomaly is not apparent in the transient responses
as all the cross-component responses are vanishing. To identify the
anomaly and estimate not only its direction but also the distance,
it is useful to define the apparent azimuth angle .phi..sub.app(t)
by,
.phi. app ( t ) = 1 2 tan - 1 V xy ( t ) + V yx ( t ) V xx ( t ) -
V yy ( t ) .phi. app ( t ) = tan - 1 V yz ( t ) V xz ( t ) = tan -
1 V zy ( t ) V zx ( t ) ( 27 ) ##EQU00017##
and the effective dip angle .nu..sub.app(t) by
tan app ( t ) = ( V xy ( t ) V xz ( t ) ) 2 + ( V xy ( t ) V yz ( t
) ) 2 ( 28 ) ##EQU00018##
for the time interval when .phi..sub.app(t).noteq.0 nor .pi./2
(90.degree.). For simplicity, the case examined below is one in
which none of the cross-component measurements is identically zero:
V.sub.xy(t).noteq.0, V.sub.yz(t).noteq.0, and
V.sub.zx(t).noteq.0.
For the time interval when .phi..sub.app(t)=0, .nu..sub.app(t) is
defined by,
[0137] app ( t ) = - 1 2 tan - 1 V xz ( t ) + V zx ( t ) V xx ( t )
- V zz ( t ) ( 29 ) ##EQU00019##
For the time interval when .phi..sub.app(t)=.pi./2 (90.degree.),
.nu..sub.app(t) is defined by,
[0138] app ( t ) = - 1 2 tan - 1 V yz ( t ) + V zy ( t ) V yy ( t )
- V zz ( t ) ( 30 ) ##EQU00020##
[0139] When t is small and the transient responses do not see the
effect of a resistivity anomaly at distance, the effective angles
are identically zero, .phi..sub.app(t)=.nu..sub.app(t)=0. As t
increases, when the transient responses see the effect of the
anomaly, .phi..sub.app(t) and .nu..sub.app(t) begin to show the
true azimuth and the true dip angles. The distance to the anomaly
may be indicated at the time when .phi..sub.app(t) and
.nu..sub.app(t) start deviating from the initial zero values. As
shown below in a modeling example, the presence of an anomaly is
detected much earlier in time in the effective angles than in the
apparent conductivity (.sigma..sub.app(t)). Even if the resistivity
of the anomaly may not be known until .sigma..sub.app(t) is
affected by the anomaly, its presence and the direction can be
measured by the apparent angles. With limitation in time
measurement, the distant anomaly may not be seen in the change of
.sigma..sub.app(t) but is visible in .phi..sub.app(t) and
.nu..sub.app(t).
FIRST MODELING EXAMPLE
[0140] FIG. 6 depicts a simplified modeling example wherein a
resistivity anomaly A is depicted in the form of, for example, a
massive salt dome in a formation 5. The salt interface 55 may be
regarded as a plane interface. FIG. 6 also indicates coaxial 60,
coplanar 62, and cross-component (64) measurement arrangements,
wherein a transmitter coil and a receiver coil are spaced a
distance L apart from each other. It will be understood that in a
practical application, separate tools may be employed for each of
these arrangements, or a multiple orthogonal tool. For further
simplification, it can be assumed that the azimuth direction of the
salt face as seen from the tool is known. Accordingly, the
remaining unknowns are the first distance D.sub.1 to the salt face
55 from the tool, the second distance D.sub.2 of the other side of
the salt from the tool, the isotropic or anisotropic formation
resistivity, and the approach angle (or dip angle) .theta. as shown
in FIG. 6. The thickness .DELTA. of the salt dome is defined as
.DELTA.=D.sub.2-D.sub.1. In case the resistivity in the anomaly A
is anisotropic, the electromagnetic properties of the anomaly may
be characterized by normal resistivity R.sub..perp. in the
direction of the principal axis of the anisotropy (or normal
conductivity .sigma..sub..perp.), and in-plane resistivity R.sub.//
(or in-plane conductivity .sigma..sub.//) in any direction within a
plane perpendicular to the principal axis. In case of anisotropy,
R.sub.//.noteq.R.sub..perp..
[0141] Before discussing anisotropy in more detail, isotropic
formations will first be illustrated with resistivity
R(=R.sub.//=R.sub..perp.) (or its inverse
.sigma.=.sigma..sub.//=.sigma..sub..perp.).
[0142] FIG. 7 and FIG. 8 show the calculated transient voltage
response (V) from coaxial V.sub.zz(t) (line 65), coplanar
V.sub.xx(t) (line 66), and cross-component V.sub.zx(t) (line 67)
measurements for a tool having L=1 m, for .theta.=30.degree., and
located at a distance of D.sub.1=10 m respectively D.sub.1=100 m
away from a salt face 55. In the calculations, D.sub.2 has been
assumed much larger than 100 m, such that within the timescale of
the calculation (up to 1 sec) any influence from the other side of
the salt A is not detectable in the transient response. Moreover,
when the anomaly is large and distant compared to the
transmitter-receiver spacing L, the effect of the spacing L can be
ignored and the transient responses can be approximated with those
of the receivers near the transmitter.
[0143] The effect of the resistivity anomaly A (as depicted in FIG.
6) is seen in the calculated transient responses as time increases.
In addition to the coaxial and coplanar responses (65, 66), the
cross-component responses Vij(t) (i.noteq.j; I, j=x, y, z) become
non-zero. In order to facilitate analysis of the responses, they
may be converted to apparent dip and/or apparent conductivity.
The apparent dip angle .theta..sub.app(t), as calculated by
[0144] .theta. app ( t ) = - 1 2 tan - 1 V zx ( t ) + V xz ( t ) V
zz ( t ) - V xx ( t ) , ( 31 ) ##EQU00021##
is shown in FIG. 9 for a L=1 m tool assembly when the salt face 55
is D.sub.1=10 m away and at the approach angle of
.theta.=30.degree..
[0145] The apparent conductivity (.sigma..sub.app(t)) from both the
coaxial (V.sub.zz(t) of FIG. 7) and the coplanar (V.sub.xx(t) of
FIG. 7) responses are shown in FIG. 10 (lines 68, respectively line
69), wherein the approach angle (.theta.=30.degree.) and salt face
distance (D.sub.1=10 m) are the same as in FIG. 9. Details of how
the apparent conductivities are calculated will be provided
below.
[0146] Note that the true direction from the tool to the salt face
(i.c. 30.degree.) is reflected in the apparent dip
.theta..sub.app(t) plot of FIG. 9 as early as 10.sup.-4 second,
when the presence of the resistivity anomaly is barely detected in
the apparent conductivity (.sigma..sub.app(t)) plot of FIG. 10. It
takes almost 10.sup.-3 second for the apparent conductivity to
approach an asymptotic .sigma..sub.app(late t) value.
[0147] FIG. 11 shows the apparent dip .theta..sub.app(t) for the
L=1 m tool assembly when the salt face is D=10 m away, but at
different angles between the tool axis and the target varying from
0 to 90.degree. in 15.degree. increments. The approach angle
(.theta.) may be reflected at any angle in about 10.sup.-4 sec.
[0148] FIG. 11 and FIGS. 12 and 13 compare the apparent dip
.theta..sub.app(t) for different salt face distances (D=10 m; 50 m;
and 100 m) and different angles between the tool axis and the
target.
[0149] The distance to the salt face can be also determined by the
transition time at which .theta..sub.app(t) takes an asymptotic
value. Even if the salt face distance (D) is 100 m, it can be
identified and its direction can be measured by the apparent dip
.theta..sub.app(t).
[0150] In summary, the method considers the coordinate
transformation of transient EM responses between tool-fixed
coordinates and anomaly-fixed coordinates. When the anomaly is
large and far away compared to the transmitter-receiver spacing,
one may ignore the effect of spacing and approximate the transient
EM responses with those of the receivers near the transmitter.
Then, one may assume axial symmetry exists with respect to the
c-axis that defines the direction from the transmitter to the
anomaly. In such an axially symmetric configuration, the
cross-component responses in the anomaly-fixed coordinates are
identically zero. With this assumption, a general method is
provided for determining the direction to the resistivity anomaly
using tri-axial transient EM responses.
[0151] The method defines the apparent dip .theta..sub.app(t) and
the apparent azimuth .phi..sub.app(t) by combinations of tri-axial
transient measurements. The apparent direction {.theta..sub.app(t),
.phi..sub.app(t)} reads the true direction {.theta., .phi.} at
later time. The .theta..sub.app(t) and .phi..sub.app(t) both read
zero when t is small and the effect of the anomaly is not sensed in
the transient responses or the apparent conductivity. The
conductivities (.sigma..sub.coaxial(t) and .sigma..sub.coplanar(t))
from the coaxial and coplanar measurements both indicate the
conductivity of the near formation around the tool.
[0152] Deviation of the apparent direction ({.theta..sub.app(t),
.phi..sub.app(t)}) from zero identifies the anomaly. The distance
to the anomaly is measured by the time when the apparent direction
({.theta..sub.app(t), .phi..sub.app(t)}) starts to deviate from
zero or by the time when the apparent direction
({.theta..sub.app(t), .phi..sub.app(t)}) starts approaches the true
direction ({.theta., .phi.}). The distance can be also measured
from the change in the apparent conductivity. However, the anomaly
is identified and measured much earlier in time in the apparent
direction than in the apparent conductivity.
Apparent Conductivity
[0153] As set forth above, apparent conductivity can be used as an
alternative technique to apparent angles in order to determine the
location of an anomaly in a wellbore. The time-dependent apparent
conductivity can be defined at each point of a time series at each
logging depth. The apparent conductivity at a logging depth z is
defined as the conductivity of a homogeneous formation that would
generate the same tool response measured at the selected
position.
[0154] In transient EM logging, transient data are collected at a
logging depth or tool location z as a time series of induced
voltages in a receiver loop. Accordingly, time dependent apparent
conductivity (.sigma.(z; t)) may be defined at each point of the
time series at each logging depth, for a proper range of time
intervals depending on the formation conductivity and the tool
specifications.
[0155] The induced voltage of a coaxial tool with
transmitter-receiver spacing L in the homogeneous formation of
conductivity (.sigma.) is given by,
V zZ ( t ) = C ( .mu. o .sigma. ) 3 / 2 8 t 5 / 2 - u 2 where u 2 =
.mu. o .sigma. 4 L 2 t ( 32 ) ##EQU00022##
and C is a constant.
[0156] The time-changing apparent conductivity depends on the
voltage response in a coaxial tool (V.sub.zZ(t)) at each time of
measurement as:
C ( .mu. o .sigma. app ( t ) ) 3 / 2 8 t 5 / 2 - u app ( t ) 2 = V
zZ ( t ) where u app ( t ) 2 = .mu. o .sigma. app ( t ) 4 L 2 t (
33 ) ##EQU00023##
and V.sub.zZ(t) on the right hand side is the measured voltage
response of the coaxial tool. From a single type of measurement
(coaxial, single spacing), the greater the spacing L, the larger
the measurement time (t) should be to apply the apparent
conductivity concept. The .sigma..sub.app(t) should be constant and
equal to the formation conductivity in a homogeneous formation:
.sigma..sub.app(t)=.sigma.. The deviation from a constant (.sigma.)
at time (t) suggests a conductivity anomaly in the region specified
by time (t).
[0157] The induced voltage of the coplanar tool with
transmitter-receiver spacing L in the homogeneous formation of
conductivity (.sigma.) is given by,
V xX ( t ) = C ( .mu. 0 .sigma. ) 3 / 2 8 t 5 / 2 ( 1 - u 2 ) - u 2
where u 2 = .mu. o .sigma. 4 t L 2 ( 34 ) ##EQU00024##
and C is a constant. At small values of t, the coplanar voltage
changes polarity depending on the spacing L and the formation
conductivity.
[0158] Similarly to the coaxial tool response, the time-changing
apparent conductivity is defined from the coplanar tool response
V.sub.xX(t) at each time of measurement as,
C ( .mu. o .sigma. app ( t ) ) 3 / 2 8 t 5 / 2 ( 1 - u app ( t ) 2
) - u app ( t ) 2 = V xX ( t ) where u app ( t ) 2 = .mu. o .sigma.
app ( t ) 4 L 2 t ( 35 ) ##EQU00025##
and V.sub.xX(t) on the right hand side is the measured voltage
response of the coplanar tool. The longer the spacing, the larger
the value t should be to apply the apparent conductivity concept
from a single type of measurement (coplanar, single spacing). The
.sigma..sub.app(t) should be constant and equal to the formation
conductivity in a homogeneous formation:
.sigma..sub.app(t)=.sigma..
[0159] When there are two coaxial receivers, the ratio between the
pair of voltage measurements is given by,
V zZ ( L 1 ; t ) V zZ ( L 2 ; t ) = - .mu. o .sigma. 4 t ( L 1 2 -
L 2 2 ) ( 36 ) ##EQU00026##
where L.sub.1 and L.sub.2 are transmitter-receiver spacing of two
coaxial tools.
[0160] Conversely, the time-changing apparent conductivity is
defined for a pair of coaxial tools by,
.sigma. app ( t ) = - ln ( V zZ ( L 1 ; t ) V zZ ( L 2 ; t ) ) ( L
1 2 - L 2 2 ) 4 t .mu. o ( 37 ) ##EQU00027##
at each time of measurement. The .sigma..sub.app(t) should be
constant and equal to the formation conductivity in a homogeneous
formation: .sigma..sub.app(t)=.sigma..
[0161] The apparent conductivity is similarly defined for a pair of
coplanar tools or for a pair of coaxial and coplanar tools. The
.sigma..sub.app(t) should be constant and equal to the formation
conductivity in a homogeneous formation:
.sigma..sub.app(t)=.sigma.. The deviation from a constant (.sigma.)
at time (t) suggests a conductivity anomaly in the region specified
by time (t).
[0162] As will be illustrated below, apparent conductivity
(.sigma..sub.app(t)), whether coaxial or coplanar, may reveal three
parameters in relation to a two-layer formation, including:
(1) the conductivity of a local first layer in which the tool is
located; (2) the conductivity of one or more adjacent layers or
beds; and (3) the distance of the tool to the layer boundaries.
Analysis of Coaxial Transient Response in Two-Layer Models
[0163] To illustrate usefulness of the concept of apparent
conductivity, the transient response of a tool in a two-layer earth
model, as in FIG. 14 for example, can be examined.
[0164] FIG. 14 illustrates a coaxial tool 80 in which both a
transmitter coil (T) and a receiver coil (R) are wound around the
common tool axis z and spaced a distance L apart. The symbols
.sigma..sub.1 and .sigma..sub.2 may represent the conductivities of
two formation layers. The coaxial tool 80 be placed in a horizontal
well 88 traversing formation layer 5 and extending parallel to the
layer interface 55.
[0165] In the present example, a horizontal well is depicted such
that the distance from the tool to the layer boundary corresponds
to the distance of the horizontal borehole to the layer boundary.
Under a more general circumstance, the relative direction of a
borehole and tool to the bed interface is not known.
[0166] The calculated transient voltage response V(t) for the L=1 m
transmitter-receiver offset coaxial tool at various distances D
between the tool 80 and the layer boundary 55 is shown in FIG. 15
for D=1, 5, 10, 25, and 50 m. The formation can be analyzed using
these responses, employing apparent conductivity as further
explained with regard to FIGS. 16 and 17.
[0167] FIG. 16 shows the voltage data of FIG. 15 plotted in terms
of apparent conductivity, for a geometry wherein .sigma..sub.1=0.1
S/m (R.sub.1=10 .OMEGA.m) and .sigma..sub.2=1 S/m (R.sub.2=1
.OMEGA.m). Similarly, FIG. 17 illustrates the apparent conductivity
in a two-layer model where .sigma..sub.1=1 S/m (R.sub.1=1 .OMEGA.m)
and .sigma..sub.2=0.1 S/m (R.sub.2=10 .OMEGA.m).
[0168] The apparent conductivity plots reveal a "constant"
conductivity at small t, and at large t but having a different
value, and a transition time t.sub.c that marks the transition
between the two "constant" conductivity values and depends on the
distance D.
[0169] As will be further explained below, in a two-layer
resistivity profile, the apparent conductivity as t approaches zero
can identify the layer conductivity .sigma..sub.1 around the tool,
while the apparent conductivity as t approaches infinity can be
used to determine the conductivity .sigma..sub.2 of the adjacent
layer at a distance. The distance to the bed boundary 55 from the
tool 80 can also be measured from the transition time t.sub.c
observed in the apparent conductivity plots.
[0170] At small values of t, the tool reads the apparent
conductivity .sigma..sub.1 of the first layer 5 around the tool 80.
Conductivity at small values of t is thought to correspond to the
conductivity of the local layer 5 where the tool is located in. At
small values of t, the signal reaches the receiver directly from
the transmitter without interfering with the bed boundary. Namely,
the signal is affected only by the conductivity .sigma..sub.1
around the tool.
[0171] At large values of t, the tool reads 0.4 S/m for a two-layer
model where either .sigma..sub.1=1 S/m (R.sub.1=1 .OMEGA.m) and
.sigma..sub.2=0.1 S/m (R.sub.2=10 .OMEGA.m), or .sigma..sub.1=0.1
S/m (R.sub.1=10 .OMEGA.m) and .sigma..sub.2=1 S/m (R.sub.2=1
.OMEGA.m). The value of 0.4 is believed to correspond to some
average between the conductivities of the two layers, because at
large values of t, nearly half of the signals come from the
formation below the tool and the remaining signals come from above,
if the time for the signal to travel the distance between the tool
and the bed boundary is small.
[0172] This is further investigated in FIG. 18, which shows
examples of the .sigma..sub.app(t) plots for D=1 m and L=1 m, but
for different resistivity ratios of the target layer 2 while the
local conductivity (.sigma..sub.1) is fixed at 1 S/m (R.sub.1=1
.OMEGA.m). The apparent conductivity at large values of t is
determined by the target layer 2 conductivity, as shown in line 71
in FIG. 19 when .sigma..sub.1 is fixed at 1 S/m.
[0173] Numerically, the late time conductivity may be approximated
by the square root average of two-layer conductivities as:
.sigma. app ( t -> .infin. ; .sigma. 1 , .sigma. 2 ) = .sigma. 1
+ .sigma. 2 2 . ( 39 ) ##EQU00028##
This is depicted as line 72 in FIG. 19.
[0174] Thus, the conductivity at large values of t (as t approaches
infinity) can be used to estimate the conductivity (.sigma..sub.2)
of the adjacent layer when the local conductivity (.sigma..sub.1)
near the tool is known, for instance from the conductivity as t
approaches zero as illustrated in FIG. 20.
Estimation of D, The Distance to the Electromagnetic Anomaly
[0175] The distance D from the tool to the bed is reflected in the
transition time t.sub.c. The transition time at which the apparent
conductivity (.sigma..sub.app(t)) starts deviating from the local
conductivity (.sigma..sub.1) towards the conductivity at large
values of t depends on D and L, as shown in FIG. 21.
[0176] For convenience, the transition time (t.sub.c) can be
defined as the time at which the .sigma..sub.app(t.sub.c) takes a
cutoff conductivity (.sigma..sub.c). In this case, the cutoff
conductivity is represented by the arithmetic average between the
conductivity as t approaches zero and the conductivity as t
approaches infinity. The transition time (t.sub.c) is dictated by
the ray path RP:
RP = ( L 2 ) 2 + D 2 , ( 40 ) ##EQU00029##
that is the shortest distance for the electromagnetic signal
traveling from the transmitter to the bed boundary, to the
receiver, independently of the resistivity of the two layers.
Conversely, the distance (D) to the anomaly can be estimated from
the transition time (t.sub.c), as shown in FIG. 22.
Look-Ahead Capabilities of EM Transient Method
[0177] By analyzing apparent conductivity or its inherent inverse
equivalent (apparent resistivity), the present invention can
identify the location of a resistivity anomaly (e.g., a conductive
anomaly and a resistive anomaly). Further, resistivity or
conductivity can be determined from the coaxial and/or coplanar
transient responses. As explained above, the direction to the
anomaly can be determined if the cross-component data are also
available. To further illustrate the usefulness of these concepts,
the foregoing analysis may also be used to detect an anomaly at a
distance ahead of the drill bit.
[0178] FIG. 23 shows a coaxial tool 80 with transmitter-receiver
spacing L placed in, for example, a vertical well 88 approaching or
just beyond an adjacent bed that is a resistivity anomaly. The tool
80 includes both a transmitter coil T and a receiver coil R, which
are wound around a common tool axis and are oriented in the tool
axis direction. The symbols .sigma..sub.1 and .sigma..sub.2 may
represent the conductivities of two formation layers, and D the
distance between the tool 80 (e.g. the transition antenna T) and
the layer boundary 55.
[0179] The calculated transient voltage response of the L=1 m
(transmitter-receiver offset) coaxial tool at different distances
(D=1, 5, 10, 25, and 50 m) as a function of t is shown in FIG. 24,
in a case wherein .sigma..sub.1=0.1 S/m (corresponding to
R.sub.1=10 .OMEGA.m), and .sigma..sub.2=1 S/m (corresponding to
R.sub.2=1 .OMEGA.m). Though difference is observed among responses
at different distances, it is not straightforward to identify the
resistivity anomaly directly from these responses.
[0180] The same voltage data of FIG. 24 is plotted in terms of the
apparent conductivity (.sigma..sub.app(t)) in FIG. 25. From this
Figure, it is clear that the coaxial response can identify an
adjacent bed of higher conductivity at a distance. Even a L=1 m
tool can detect the bed at 10, 25, and 50 m away, if low voltage
response can be measured for 0.1-1 seconds long.
[0181] The .sigma..sub.app(t) plot exhibits at least three
parameters very distinctly in the figure: the early time
conductivity; the later time conductivity; and the transition time
that moves as the distance (D) changes. In FIG. 25, it should be
noted that, at early time whereby t is close to zero, the tool
reads the apparent conductivity of 0.1 S/m, which is representative
of the layer just around the tool. The signal that reaches the
receiver R not yet contains information about the boundary 55. At
later time, the tool reads close to 0.55 S/m, representing an
arithmetic average between the conductivities of the two layers. At
later time, t.fwdarw..infin., nearly half of the signals come from
the formation below the tool and the other half from above the
tool, if the time to travel the distance (D) of the tool to the bed
boundary is small. The distance D is reflected in the transition
time t.sub.c.
[0182] FIG. 26 illustrates the .sigma..sub.app(t) plot of the
coaxial transient response in the two-layer model of FIG. 23 for an
L=1 m tool at different distances (D), except that the conductivity
of the local layer (.sigma..sub.1) is 1 S/m (R.sub.1=1 .OMEGA.m)
and the conductivity of the target layer (.sigma..sub.2) is 0.1 S/m
(R.sub.2=10 .OMEGA.m). Again, the tool reads at early time the
apparent conductivity of 1.0 S/m that is of the layer just around
the tool. At a later time, the tool reads about 0.55 S/m, the same
average conductivity value as in FIG. 25. The distance (D) is
reflected in the transition time t.sub.c.
[0183] Hence, the transient electromagnetic response method can be
used as a look-ahead resistivity logging method.
[0184] FIG. 27 compares the .sigma..sub.app(t) plot of FIG. 25 and
FIG. 26 for L=1 m and D=50 m. The late time conductivity is
determined solely by the conductivities of the two layers
(.sigma..sub.1 and .sigma..sub.2) alone. It is not affected by
where the tool is located in the two layers. However, because of
the deep depth of investigation, the late time conductivity is not
readily reached even at t=1 second, as shown in FIG. 25. In
practice, the late time conductivity may have to be approximated by
.sigma..sub.app(t=1 second) which slightly depends on D as
illustrated in FIG. 25.
[0185] Numerically, the late time apparent conductivity may be
approximated by the arithmetic average of two-layer conductivities
as:
.sigma. app ( t -> .infin. ; .sigma. 1 , .sigma. 2 ) = .sigma. 1
+ .sigma. 2 2 . ##EQU00030##
This is reasonable considering that, with the coaxial tool, the
axial transmitter induces the eddy current parallel to the bed
boundary. At later time, the axial receiver receives horizontal
current nearly equally from both layers. As a result, the late time
conductivity must see conductivity of both formations with nearly
equal weight.
[0186] FIG. 28 compares the .sigma..sub.app(t) plots for D=50 m but
with different spacing L. The .sigma..sub.app(t) reaches a nearly
constant late time apparent conductivity at later times as L
increases. The late time apparent conductivity
(.sigma..sub.app(t.fwdarw..infin.) is nearly independent of L.
However, the late time conductivity defined at t=1 second, depends
on slightly the distance (D).
[0187] Thus, the late time apparent conductivity
(.sigma..sub.app(t.fwdarw..infin.)) at t=1 second can be used to
estimate the conductivity of the adjacent layer (.sigma..sub.2)
when the local conductivity near the tool (.sigma..sub.1) is known,
for instance, from the early time apparent conductivity
(.sigma..sub.app(t.fwdarw.0)=.sigma..sub.1).
Estimation of the Distance (D) to the Electromagnetic Anomaly
[0188] The transition time (t.sub.c) at which the apparent
conductivity starts deviating from the local conductivity
(.sigma..sub.1) toward the late time conductivity clearly depends
on D, the distance of the tool to the bed boundary, as shown in
FIG. 25 for a L=1 m tool.
[0189] For convenience, the transition time (t.sub.c) is defined by
the time at which the .sigma..sub.app(t.sub.c) takes the cutoff
conductivity (.sigma..sub.c), that is, in this example, the
arithmetic average between the early time and the late time
conductivities:
.sigma..sub.c={.sigma..sub.app(t.fwdarw.0)+.sigma..sub.app(t.fwdarw..infi-
n.)}/2. The transition time (t.sub.c) is dictated by the ray-path
RP, D minus L/2 that is, half the distance for the EM signal to
travel from the transmitter to the bed boundary to the receiver,
independently on the resistivity of the two layers. Conversely, the
distance (D) can be estimated from the transition time (t.sub.c),
as shown in FIG. 29 when L=1 m.
Analysis of Coplanar Transient Responses in Two-Layer Models
[0190] While the coaxial transient data were examined above, the
coplanar transient data are equally useful as a look-ahead
resistivity logging method.
[0191] FIG. 30 shows a coplanar tool 80 with transmitter-receiver
spacing L placed in a well 88 and approaching (or just beyond)
layer boundary 55 of an adjacent bed that is the resistivity
anomaly. On the coplanar tool, both a transmitter T and a receiver
R are oriented perpendicularly to the tool axis z and parallel to
each other. The symbols .sigma..sub.1, and .sigma..sub.2 may
represent the conductivities of two formation layers.
[0192] Corresponding to FIG. 25 for coaxial tool responses where
L=1 m, the apparent conductivity (.sigma..sub.app(t)) for
calculated coplanar responses is plotted in FIG. 31 for different
tool distances from the bed boundary 55. It is clear that the
coplanar response can also identify an adjacent bed of higher
conductivity at a distance. Even a L=1 m tool can detect the bed at
10 m, 25 m, and 50 m away if low voltage responses can be measured
for 0.1-1 seconds long. The .sigma..sub.app(t) plot for the
coplanar responses exhibits three parameters equally as well as for
the coaxial responses.
[0193] Like it was the case in the co-axial geometry, it is also
true for the coplanar responses that the early time apparent
conductivity (.sigma..sub.app(t.fwdarw.0)) is the conductivity of
the local layer (.sigma..sub.1) where the tool is located.
Conversely, the layer conductivity can be measured easily by the
apparent conductivity at earlier times.
[0194] The late time apparent conductivity
(.sigma..sub.app(t.fwdarw..infin.)) is some average of
conductivities of both layers. The conclusions derived for the
coaxial responses apply equally well to the coplanar responses.
However, the value of the late time conductivity for the coplanar
responses is not the same as for the coaxial responses. For coaxial
responses, the late time conductivity is close to the arithmetic
average of two-layer conductivities in two-layer models.
[0195] FIG. 32 shows the late time conductivity
(.sigma..sub.app(t.fwdarw..infin.)) for coplanar responses as
obtained from the model calculations (line 77) whereby D=50 m and
L=1 m, but for different conductivities of the local layer while
the target conductivity is fixed at 1 S/m. Late time conductivity
is determined by the local layer conductivity, and is numerically
close to the square root average as,
.sigma. app ( t -> .infin. ; .sigma. 1 , .sigma. 2 ) = .sigma. 1
+ .sigma. 2 2 , ##EQU00031##
as is shown by line 78 in FIG. 32.
[0196] To summarize, the late time conductivity
(.sigma..sub.app(t.fwdarw..infin.)) can be used to estimate the
conductivity of the adjacent layer (.sigma..sub.2) when the local
conductivity near the tool (.sigma..sub.1) is known, for instance,
from the early time conductivity
(.sigma..sub.app(t.fwdarw.0)=.sigma..sub.1). This is illustrated in
FIG. 33 wherein line 79 has been obtained from model calculations
and line 79a displays the average approximation.
Estimation of the Distance (D) to the Electromagnetic Anomaly
[0197] The transition time t.sub.c at which the apparent
conductivity starts deviating from the local conductivity
(.sigma..sub.1) toward the late time conductivity clearly depends
on the distance (D) of the tool 80 (e.g. the transmitter T) to the
bed boundary 55, as shown in FIG. 30.
[0198] The transition time (t.sub.c) may be defined by the time at
which the .sigma..sub.app(t.sub.c) takes the cutoff conductivity
(.sigma..sub.c) that is, in this example, the arithmetic average
between the early time and the late time conductivities:
.sigma..sub.c={.sigma..sub.app(t.fwdarw.0)+.sigma..sub.app(t.fwdarw..infi-
n.)}/2. The transition time (t.sub.c) is dictated by the ray-path,
D minus L/2 that is, half the distance for the EM signal to travel
from the transmitter to the bed boundary to the receiver,
independently of the resistivity of the two layers.
[0199] Conversely, the distance (D) can be estimated from the
transition time (t.sub.c), as shown in FIG. 34, where L=1 m.
Analysis of Transient Electromagnetic Response Data for Three or
More Formation Layers
[0200] The next model shows a conductive near layer, a very
resistive layer, and a further conductive layer. The geological
configuration is depicted in FIG. 35, together with a coaxial tool
80 in a relatively conductive formation 82 wherein an anomaly is
located in the form of a relatively resistive layer 83. As shown,
the formation on the other side of layer 83, as seen from tool 80
and identified in FIG. 35 by reference numeral 84, is identical to
the formation 82 on the tool side of the layer 83. However, the
method will also work if the formation 84 on the other side of
layer 83 would constitute a layer that has different properties
from those of the near formation 82.
[0201] In either case, the tool "sees" the anomaly 83 as a first
layer at a first distance D1 away and having a thickness .DELTA.,
and it "sees" the formation on the other side of the anomaly 83 as
a second layer 84 at a second distance D.sub.2=D.sub.1+.DELTA. away
and having infinite thickness. FIG. 36 is a graph showing
calculated apparent resistivity response R.sub.app versus time t
for a geometry as given in FIG. 35. For the calculation of FIG. 36,
it has been assumed that the anomaly is formed of a resistive salt
bed, having a resistivity of 100 .OMEGA.m, and that the formation
is formed of for instance a brine-saturated formation having a
resistivity of 1 .OMEGA.m. The tool has been modeled as being
oriented with its main axis parallel to the first interface 81
between the brine-saturated formation 82, and the distance between
the main axis and the first layer 83, D.sub.1, has been taken 10 m.
The resistive bed thickness .DELTA. has been varied from a fraction
of a to 100 meters in thickness.
[0202] The first climb of R.sub.app(t) is the response to the salt
and takes place at 10.sup.-4 s with an L=1 m tool when the salt is
at D.sub.1=10 m away. If the salt is fully resolved (by infinitely
thick salt beyond D.sub.1=10 m), the apparent resistivity should
read 3 .OMEGA.m asymptotically. The subsequent decline of
R.sub.app(t) is the response to a conductive formation behind the
salt (resistive bed). R.sub.app(late t) is a function of conductive
bed resistivity and salt thickness. If the time measurement is
limited to 10.sup.-2 s, the decline of R.sub.app(t) may not be
detected for the salt thicker than 500 m.
[0203] With respect to the resistive bed resolution, the coaxial
responds to a thin (1-2 m thick) bed. The time at which
R.sub.app(t) peaks or begins declining depends on the distance to
the conductive bed behind the salt. As noted previously, when
plotted in terms of apparent conductivity .sigma..sub.app(t), the
transition time may be used to determine the distance to the
boundary beds.
[0204] Another three-layer formation was also modeled, as shown in
FIG. 37. In this instance, the intermediate layer 83 was a more
conductive layer than the surrounding formation 82. This conductive
bed 83 may be considered representative of, for instance, a shale
layer. The coaxial tool 80, having an L=1 m spacing, is located in
a borehole in a formation 82 having a resistivity of 10 .OMEGA.m
and is located D.sub.1=10 m from the less resistive (more
conductive) layer 83, which has a resistivity of 1 .OMEGA.m. The
third layer 84 is beyond the conductive bed 83 and has a
resistivity of 10 .OMEGA.m as does layer 82. The conductive bed 83
was modeled for a range of thicknesses A varying from fractions of
a meter up to an infinite thickness. The apparent resistivity, as
calculated, is set forth in FIG. 38.
[0205] The decrease in R.sub.app(t), which can be seen in FIG. 38,
is attributed to the presence of the shale (conductive) layer and
appears as t.fwdarw.10.sup.-5 s. The shale response is fully
resolved by an infinitely thick conductive layer that approaches 3
.OMEGA.m. The subsequent rise in R.sub.app(t) is in response to the
resistive formation 84 beyond the shale layer 83. The transition
time is utilized to determine the distance D.sub.2 from the tool 80
to the interface 85 between the second and third layers (83
respectively 84). R.sub.app(late t) is a function of conductive bed
resistivity. As the conductive bed thickness .DELTA. increases, the
time measurement must likewise be increased (>10.sup.-2 s) in
order to measure the rise of R.sub.app(t) for conductive layers
thicker than 100 m.
[0206] Still another three-layer model is set forth in FIG. 39,
wherein the coaxial tool 80 is in a conductive formation 82 (1
.OMEGA.m), and a highly resistive second layer 84 (100 .OMEGA.m) as
might be found in, for instance, a salt dome. Formation 82 and the
second layer 84 are separated by a first layer 83 that has an
intermediate resistance (10 .OMEGA.m). The thickness A has been
varied in the calculations of the apparent resistivity response, as
depicted in FIG. 40.
[0207] The response to the intermediate resistive layer is seen at
10.sup.-4 s, where R.sub.app(t) increases. If the first layer 83 is
fully resolved by an infinitely thick bed, the apparent resistivity
approaches a 2.6 .OMEGA.m asymptote. As noted in FIG. 40, the
R.sub.app(t) undergoes a second stage increase in response to the
100 .OMEGA.m highly resistive second layer 84. Based on the
transition time, the distance to the interface is determined to be
110 m.
[0208] Though complex, the apparent resistivity or apparent
conductivity in the above examples delineates the presence of
multiple layers. The observed changes of apparent conductivity (or
apparent resistivity) allow determination of the distances D.sub.1
and D.sub.2.
Transient Electromagnetic Responses Involving Formation
Anisotropy
[0209] As stated above, an electromagnetic anomaly may display
anisotropic electromagnetic properties. An example is shown in FIG.
6, if R.sub.//.noteq.R.sub..perp..
[0210] Various mechanisms may give rise to a macroscopic
electromagnetic induction effect. For instance, oriented fractions
may generate an anisotropic response. Electromagnetic anisotropy
may also arise intrinsically in certain types of formations, such
as shales, of may arise as a result of sequences of relatively thin
layers.
[0211] In the way as depicted in FIG. 6, the principal anisotropy
direction corresponds to the approach angle .theta.. This
correspondence is mainly for reasons of simplicity in setting forth
the embodiments, and need not necessarily be the case in every
situation within the scope of the invention.
[0212] In the following it will be explained how electromagnetic
anisotropy of at least one of the formation layers may be taken
into account when analyzing time-dependent transient response
signals. This may comprise determining one or more anisotropy
parameters that characterize the anisotropic electromagnetic
properties. Amongst anisotropy parameters are anisotropy ratio
.alpha..sup.2, anisotropic factor .beta., conductivity along a
principal anisotropy axis .sigma..sub..perp. (or resistivity along
the principal anisotropy axis R.sub..perp.), conductivity in a
plane perpendicular to the principal anisotropy axis .sigma..sub.//
(or resistivity in a plane perpendicular to the principal
anisotropy axis R.sub.//); tool axis angle relative to the
principal anisotropy axis.
[0213] Using the concepts of apparent conductivity or apparent
resistivity and/or apparent dip or azimuth, the distance and/or
direction to an anomaly may be determined from the time-dependent
transient response signals even when the anomaly, and/or a distant
formation layer, comprise(s) an electromagnetic anisotropy or when
the transmitter and/or receiver antennae are embedded in an
anisotropic formation layer.
[0214] Using the principles set forth above, the analysis taking
into account anisotropy may be extended to multiple bedded
formations, including those where only a distant formation layer or
target anomaly gives anisotropic electromagnetic induction
responses (such as for instance in FIG. 6) or where a local
formation layer wherein the transmitter and receiver antennae are
located, displays anisotropic behavior and one or more other,
isotropic or anisotropic layers are present at a distance. The
distance and direction from the tool to the more distant layers
and/or the target anomaly may then be determined, provided that
anisotropy is taken into account.
[0215] In the forthcoming explanation, for reasons of simplicity,
it will be assumed that the anisotropy has a vertically aligned
principal axis, such that the angle between the tool axis z and the
principal anisotropy axis corresponds to the dip angle or deviation
angle .theta.. The term horizontal resistivity R.sub.H may be
employed, which generally corresponds to the resistivity in the
anisotropy plane perpendicular to the principal anisotropy
direction. The term vertical resistivity R.sub.V generally refers
to resistivity in the principal anisotropy direction or normal
direction.
Transient EM Responses in a Homogeneous Anisotropic Formation
[0216] Considered is an anisotropic formation, in which a vertical
resistivity R.sub.V (or its inverse vertical conductivity
.sigma..sub.V) is different from the horizontal resistivity R.sub.H
(or horizontal conductivity .sigma..sub.H). Assumed is that the
formation is azimuth-symmetric, in the horizontal direction. The
tool axis z is deviated from the vertical direction by the dip
(deviation) angle .theta. in the zx-plane. The transmitter antenna
is placed at origin. The receiver antenna is placed at (x=Lsin
.theta., y=0, z=Lcos .theta.). There may be four independent
combinations of transmitter and receiver orientations that render
non-zero responses.
[0217] In addition to a coaxial response, V.sub.Zz, there are two
coplanar responses, V.sub.Xx and V.sub.Yy, and one cross-component
response V.sub.Xz=V.sub.Zx. One coplanar response, V.sub.Xx, is
from a transverse transmitter antenna and receiver antenna that are
oriented within the zx-plane. Another coplanar response, V.sub.Yy,
is from a transverse transmitter and receiver both of which are
oriented in the y-axis direction. The cross-component response is
from a transverse receiver antenna with the longitudinally oriented
transmitter antenna, or vise versa. The transverse receiver antenna
is directed within the zx-plane. Any cross-component involving
either a transmitter or a receiver oriented in the y-axis
direction, i.e. V.sub.Yx and V.sub.xy and V.sub.Yz and V.sub.Zy are
all vanishing.
[0218] The above has been set forth in tool-coordinates. It is
further remarked that any antenna that is sensitive to a transverse
component of an electromagnetic induction field suffices as a
transverse antenna.
[0219] Applicants have derived the transient response in time
domain, expressed in terms of horizontal conductivity .sigma..sub.H
and anisotropic factor .beta., are given by:
V Zz ( t ) = C ( .mu. 0 .sigma. H ) 3 / 2 8 t 5 / 2 - u 2 { 1 + 1 2
( .beta. 2 - u 2 ( .beta. 2 - 1 ) - 1 ) - 1 4 u 2 ( - u 2 ( .beta.
2 - 1 ) - 1 ) } ; ( 41 ) V Xx ( t ) = C ( .mu. 0 .sigma. H ) 3 / 2
8 t 5 / 2 - u 2 { [ 1 - u 2 ] + cos 2 .theta. sin 2 .theta. [ 1 2 (
.beta. 2 - u 2 ( .beta. 2 - 1 ) - 1 ) - 1 4 u 2 ( - u 2 ( .beta. 2
- 1 ) - 1 ) ] } ; ( 42 ) V Zx ( t ) = V Xz ( t ) = C ( .mu. 0
.sigma. H ) 3 / 2 8 t 5 / 2 - u 2 { cos .theta. sin .theta. [ 1 2 (
.beta. 2 - u 2 ( .beta. 2 - 1 ) - 1 ) - 1 4 u 2 ( - u 2 ( .beta. 2
- 1 ) - 1 ) ] } ; and ( 43 ) V Yy ( t ) = C ( .mu. 0 .sigma. H ) 3
/ 2 8 t 5 / 2 - u 2 { [ 1 - u 2 ] - 1 sin 2 .theta. [ 1 2 ( .beta.
2 - u 2 ( .beta. 2 - 1 ) - 1 ) - 1 4 u 2 ( - u 2 ( .beta. 2 - 1 ) -
1 ) ] + 1 2 [ .alpha. 2 ( 3 - 2 u 2 .beta. 2 ) - u 2 ( .beta. 2 - 1
) - ( 3 - 2 u 2 ) ] } . ( 44 ) ##EQU00032##
In these equations,
[0220] u 2 = .mu. o .sigma. H 4 L 2 t ##EQU00033##
and C is a constant. The anisotropic factor .beta. is defined
as:
.beta. = 1 + ( .alpha. 2 - 1 ) sin 2 .theta. ; .alpha. 2 = .sigma.
V .sigma. H . ( 45 ) ##EQU00034##
[0221] The following remarks may be made based on these
equations:
1. The coaxial response depends only on the horizontal resistivity
R.sub.H(=1/.sigma..sub.H) and the anisotropic factor .beta. that is
determined by the anisotropy ratio
.alpha..sup.2=.sigma..sub.V/.sigma..sub.H=R.sub.H/R.sub.V, and the
dip angle .theta.. Conversely, neither the anisotropy nor the dip
angle can be determined from coaxial measurements alone.
2. Both coplanar responses depend on the horizontal resistivity,
the anisotropic factor, and the dip angle.
3. In vertical boreholes with .theta.=0, the coaxial response
depends only on the horizontal resistivity, while the coplanar
response is determined by both the horizontal resistivity and the
vertical resistivity.
4. In horizontal logging with .theta.=.pi./2, the coaxial response
depends on both the horizontal resistivity and the vertical
resistivity, but the coplanar response is determined solely by the
horizontal resistivity.
[0222] 5. Because u.sup.2.fwdarw.0 as t.fwdarw.large, the dip angle
is determined by:
2 V Xz ( t ) V Xx ( t ) - V Zz ( t ) = tan 2 .theta. + O ( u 2 ) ,
( 46 ) ##EQU00035##
whereby O(u.sup.2) denotes a remainder on the order of u.sup.2.
Late Time Responses in a Homogeneous Anisotropic Formation
[0223] Similar to the investigation set forth above with regard to
layer models, the late time limits may be derived. As
t.fwdarw..infin., u.sup.2.fwdarw.0, and therefore these limits
converge. Taking into account anisotropy, the late time limits of
equations (41) to (44) are:
V Zz ( t ) = C ( .mu. 0 .sigma. H ) 3 / 2 8 t 5 / 2 { 1 + 3 4 (
.alpha. 2 - 1 ) sin 2 .theta. } ; ( 47 ) V Xx ( t ) = C ( .mu. 0
.sigma. H ) 3 / 2 8 t 5 / 2 { 1 + 3 4 ( .alpha. 2 - 1 ) cos 2
.theta. } ; ( 48 ) V Xz ( t ) = C ( .mu. 0 .sigma. H ) 3 / 2 8 t 5
/ 2 { 3 4 ( .alpha. 2 - 1 ) cos .theta.sin .theta. } ; and ( 49 ) V
Yy ( t ) = C ( .mu. 0 .sigma. H ) 3 / 2 8 t 5 / 2 { 1 + 3 4 (
.alpha. 2 - 1 ) } . ( 50 ) ##EQU00036##
[0224] The dip (deviation) angle is determined by:
.theta. = 1 2 tan - 1 2 V Xz ( t ) V Xx ( t ) - V Zz ( t ) . ( 51 )
##EQU00037##
[0225] The anisotropy ratio .alpha..sup.2 may be determined
from:
V Zz ( t -> .infin. ) + V Xx ( t -> .infin. ) 2 V Yy ( t
-> .infin. ) = 1 + 3 8 ( .alpha. 2 - 1 ) 1 + 3 4 ( .alpha. 2 - 1
) . ( 52 ) ##EQU00038##
[0226] When the dip angle .theta. is known or estimated, the
anisotropy ratio may alternatively be determined from:
V Xx ( t -> .infin. ) - V Zz ( t -> .infin. ) V Xx ( t ->
.infin. ) + V Zz ( t -> .infin. ) = 3 4 ( .alpha. 2 - 1 ) 2 + 3
4 ( .alpha. 2 - 1 ) cos 2 .theta. . ( 53 ) ##EQU00039##
[0227] It is further remarked that the sum of the co-axial response
with the Xx coplanar response is independent from the approach
angle.
Apparent Conductivity For Co-Axial and Co-Planar Responses in a
Homogeneous Anisotropic Formation
[0228] Similar to the investigation set forth above with regard to
layer models, apparent conductivity is also a useful derived
formation quantity in case of an anisotropic formation layer.
[0229] The apparent conductivity is defined for both coaxial
(.sigma..sub.Zz(t)) and coplanar (.sigma..sub.Xx(t),
.sigma..sub.Yy(t)) responses. The apparent conductivity is the
time-varying conductivity that would give the measured coaxial or
coplanar response at time t if the formation would be homogeneous
and isotropic.
[0230] As before, the time-changing apparent conductivities depend
on the voltage response in a coaxial tool (V.sub.zZ(t)) or in a
coplanar tool (V.sub.Xx(t) at each time of measurement as:
V Zz ( t ) = C ( .mu. 0 .sigma. Zz ( t ) ) 3 / 2 8 t 5 / 2 - u 2 ;
( 54 ) V Xx ( t ) = C ( .mu. 0 .sigma. Xx ( t ) ) 3 2 8 t 5 2 ( 1 -
u 2 ) - u 2 wherein ( 55 ) u 2 = .mu. 0 .sigma. Zz ( t ) 4 t L 2 ,
or ( 56 a ) u 2 = .mu. 0 .sigma. Xx ( t ) 4 t L 2 , ( 56 b )
##EQU00040##
Then, at large t, the apparent conductivity approaches the value
determined by the anisotropic conductivity and the dip angle as
follows:
.sigma. Zz ( t .fwdarw. large ) = .sigma. H { 1 + 3 4 ( .alpha. 2 -
1 ) sin 2 .theta. } 2 3 for coaxial response ; ( 57 ) .sigma. Xx (
t .fwdarw. large ) = .sigma. H { 1 + 3 4 ( .alpha. 2 - 1 ) cos 2
.theta. } 2 3 for Xx - coplanar response ; ( 58 ) .sigma. Yy ( t
.fwdarw. large ) = .sigma. H { 1 + 3 4 ( .alpha. 2 - 1 ) } 2 3 for
Yy - coplanar response . ( 59 ) ##EQU00041##
In terms of the apparent conductivity,
[0231] .sigma. Xx ( t ) 3 2 + .sigma. Zz ( t ) 3 2 | t .fwdarw.
large = .sigma. H 3 2 { 2 + 3 4 ( .alpha. 2 - 1 ) } ; and ( 60 )
.sigma. Xx ( t ) 3 2 - .sigma. Zz ( t ) 3 2 | t .fwdarw. large =
.sigma. H 3 2 { 3 4 ( .alpha. 2 - 1 ) cos 2 .theta. } . ( 61 )
##EQU00042##
[0232] The anisotropy ratio .alpha..sup.2 may be estimated from the
ratio of equations (61) and (60), and the estimated .theta. as:
.sigma. Xx ( t ) 3 / 2 - .sigma. Zz ( t ) 3 / 2 .sigma. Xx ( t ) 3
/ 2 + .sigma. Zz ( t ) 3 / 2 | t -> large = 3 4 ( .alpha. 2 - 1
) 2 + 3 4 ( .alpha. 2 - 1 ) cos 2 .theta. . ( 62 ) ##EQU00043##
MODELING EXAMPLES
[0233] FIGS. 41 to 45 relate to transient electromagnetic induction
measurements, and analysis thereof, in a homogeneous anisotropic
formation for various .beta..sup.2 (in order of increasing
anisotropy: 1.0; 0.8; 0.6; 0.4; 0.3) for a coaxial L=1 m tool.
[0234] Of these Figures, FIG. 41 shows the calculated coaxial
voltage responses for a formation wherein the conductivity in
horizontal direction .sigma..sub.H=1 S/m (R.sub.H=1 .OMEGA.m). The
lines show the voltage response as a function of time t (ranging
from 1E-08 sec to 1E+00 sec on a logarithmic scale) after a
step-wise sudden switching off of the transmitter. Line 101
corresponds to a homogeneous isotropic formation (.beta..sup.2=1.0)
and should ideally correspond to a dipole solution. Lines 102, 103,
104, and 105 represent increasing anisotropy and respectively
correspond to .beta..sup.2=0.8, .beta..sup.2=0.6, .beta..sup.2=0.4,
and .beta..sup.2=0.3.
[0235] FIG. 42 shows the apparent conductivity that has been
calculated from the responses as shown in FIG. 41. The same line
numbers have been used as in FIG. 41.
[0236] FIG. 43 is similar to FIG. 42 but it shows the apparent
conductivity that has been derived from responses calculated for
formations with .sigma..sub.H=0.1 S/m (R.sub.H=10 .OMEGA.m). The
same general behavior is found.
[0237] FIG. 44 is similar to FIGS. 42 and 43, but it shows the
apparent conductivity that has been derived from responses
calculated for formations with .sigma..sub.H=0.01 S/m (R.sub.H=100
.OMEGA.m). The same general behavior is again found.
[0238] In each of FIGS. 42, 43, and 44, the late time apparent
conductivity is constant for each of the anisotropic factors,
indicative of a macroscopically homogeneous formation. The late
time apparent conductivity decreases with anisotropic factor as is
expected because the vertical conductivity, along the principal
axis of the anisotropy, is lower than the horizontal
conductivity.
[0239] FIG. 45 plots the late time asymptotic value of coaxial
apparent conductivity .sigma..sub.Zz(t.fwdarw..infin.) over
.sigma..sub.H against
{ 1 + 3 4 ( .beta. 2 - 1 ) } 2 / 3 . ##EQU00044##
The resulting straight line demonstrates the linear relationship.
When taking into account the anisotropy, the correct value of the
horizontal formation resistivity (or conductivity) can thus be
extracted from the asymptotic coaxial apparent conductivity
values.
[0240] Even for highly anistropic formations, the apparent
conductivity is almost indistinguishable from apparent conductivity
of a homogeneous isotropic formation with a lower conductivity.
Interpretation mistakes may thus easily be made if anisotropy is
not taken into account when analyzing.
[0241] As follows from the above, anisotropy can be taken into
account, for instance by combining co-axial responses with coplanar
responses. The precise embodiment depends on which of the
parameters are known or estimated. The sum of the co-axial response
with the Xx coplanar response is independent from the approach
angle. If C and .sigma..sub.H are known or estimated then the
anisotropy ratio .alpha..sup.2 follows from the late time value of
sum V.sub.Zz+V.sub.Xx. If, on the other hand, the approach angle
.theta. is known, C and .sigma..sub.H don't need to be known
because the anisotropy ratio .alpha..sup.2 may be derived from Eq.
(53). If none of the other parameters is known, Eq. (52) may be
employed requiring combining co-axial response with two independent
co-planar responses.
Apparent Dip in a Homogeneous Anisotropic Formation
[0242] In FIG. 46, apparent dip angles .theta..sub.app(t) derived
using Eq. (51) from calculated coaxial, coplanar and
cross-component transient responses from a L=1 m tool in a
formation of R.sub.H=10 .OMEGA.m and R.sub.V/R.sub.H=9, for various
approach angles, or dip angles. Line 106 corresponds to
.theta.=30.degree.; line 107 to .theta.=45.degree.; line 108 to
.theta.=600; and line 109 to .theta.=75.degree.. The dip angle is
thus reflected accurately by the asymptotic value of the apparent
dip. The asymptotic value is reached in approximately 1E-06
sec.
Apparent Resistivity for Co-Axial and Co-Planar Responses in a
Formation Layer Comprising Multiple Sub-Layers
[0243] FIG. 47 shows an electromagnetic induction tool 80 in a
formation layer 110 comprising a sequence or package of alternating
sets of sub-layers 112 and 114, set 112 having electromagnetic
properties, notably conductivity, that is different from set 114.
The tool axis is depicted in the plane of the sub-layers.
[0244] While each sub-layer in the laminate of thin layers may have
isotropic properties such as isotropic conductivity, the combined
effect of the sub-layers may be that the formation layer that
consists of the sub-layers exhibits an anisotropic electromagnetic
induction. If each sub-layer 112, 114 in the formation layer 110
acts as an individual resistor, the macroscopic resistivity
(inverse of conductivity) of the formation layer in a planar
direction may be a resultant of all the layer-resistors in parallel
while the macroscopic resistivity in a normal direction (i.e.
perpendicular to the layers) may be a resultant of all the layer
resistors in series.
In equation form:
R V = 1 .DELTA. .intg. 0 .DELTA. R ( z ) z ( 63 ) ##EQU00045##
for the resistivity in the vertical, or principal direction,
and
.sigma. H = 1 .DELTA. .intg. 0 .DELTA. .sigma. ( x ) x ( 64 )
##EQU00046##
for the conductivity in the horizontal, or in-plane, direction
perpendicular to the principal direction. Of course, .sigma..sub.V
can be found using .sigma..sub.V=1/R.sub.V, and R.sub.H can be
found using R.sub.H=1/.sigma..sub.H. Hence the in-plane resistivity
is typically lower than the resistivity in the principal direction.
These equations also hold for more general cases whereby the
sub-layers are not of equal thickness and/or the sublayers are not
of equal conductivity.
[0245] FIG. 48 shows the calculated apparent resistivity for the
tool in the geometry of FIG. 47, whereby L=1 m; the resistivity of
sub-layers 112 is 10 .OMEGA.m; the resistivity of sub-layers 114 is
1 .OMEGA.m, and each sub-layer is 10 m of thickness. Line 115
corresponds to apparent resistivity for co-axial measurement
geometry while line 116 corresponds to apparent resistivity for
co-planar measurement geometry.
[0246] The apparent resistivity represented by lines 115 and 116
reflect the near-layer resistivity of 1 .OMEGA.m at short times
after the switching off of the transmitter. After a time span of
approximately 2E-5 sec, the apparent resistivity starts to increase
due to the higher resistivity of 10 .OMEGA.m in the first adjacent
sub-layers 112. So far, the apparent resistivity reflects what was
set forth above for formations comprising two or three isotropic
formation layers.
[0247] However, for later times the sub-layers are no longer
individually resolved in the responses, in which case apparent
resistivity is believed to reflect contributions from the sub-layer
where the tool 80 is located, the adjacent layers and next adjacent
layers, and so on. Effectively, the transient responses will show
the macroscopic anisotropic behavior. In the example of FIG. 48,
the collection of the isotropic sub-layers that are not
individually resolved in the transient responses are described by
assuming an anisotropic layer with an anisotropic ratio of
.alpha..sup.2=R.sub.H/R.sub.V=1/(.sigma..sub.HR.sub.V)=1/(0.555.5)=0.33,
which can be found out using the late time apparent resistivities
as set forth above for the homogeneous anisotropic formation. It
may be better to invert the responses assuming a homogenous
anisotropy than to try and determine the individual sub-layer
structure.
[0248] The dotted lines 117 and 118 in FIG. 48, which correspond to
the co-axial and co-planar apparent conductivities calculated for
R.sub.H=1.82 (i.e. 1/0.55) .OMEGA.m and R.sub.V=5.5 .OMEGA.m,
indeed match the drawn lines 115 and 116 well, at large t.
[0249] The combined, "macroscopic," anisotropic effect of a
sub-layered anomaly, such as is shown in FIG. 49, may also be
observed. Here, the anomaly A is formed of a formation layer having
a thickness .DELTA. comprising a thinly laminated sequence of a
first formation material A1 and a second formation material A2.
FIG. 49 also indicates coaxial 60, coplanar 62, and cross-component
64 measurement arrangements, wherein a transmitter coil T and a
receiver coil R are spaced a distance L apart from each other. The
distance between the transmitter coil T and the nearest interface
55 between the near formation layer and the anomaly A is indicated
by D.sub.1.
[0250] Using the principles set forth above, the analysis taking
into account anisotropy may be extended to multiple bedded
formations, including those where only a distant formation layer
displays macroscopic electromagnetic induction responses (such as
for instance in FIG. 49) or where a local formation layer wherein
the transmitter and receiver antennae are located, displays
anisotropic behavior but whereby one or more other, isotropic or
anisotropic layers are present at a distance.
Geosteering Applications
[0251] As stated before in this specification, electromagnetic
anisotropy may arise intrinsically in certain types of formations,
such as shales. A shale may cap a reservoir of mineral hydrocarbon
fluids. It would thus be beneficial to precisely locate a shale
during drilling of a well, and drill between for instance 10 m and
100 m below the shale to enable optimal production of the
hydrocarbon fluids from the reservoir. This can be done either by
traversing the shale or steering below the shale in a deviated well
such as a horizontal section.
[0252] In other cases, the hydrocarbon containing reservoir may
have materialized in the form of a stack of thin sands, which
itself may exhibit anisotropic electromagnetic properties. It would
be beneficial to identify the presence of such sands and steer the
drilling bit into these sands.
[0253] In each of these cases, geosteering may be accomplished by
performing the transient electromagnetic analysis while drilling
and taking into account formation anisotropy. This may be
implemented using the system as schematically depicted in FIG.
1A.
[0254] More generally, geosteering decisions may be taken based on
locating any type of electromagnetic anomaly using transient
electromagnetic responses. Such geosteering applications allow to
more accurately locate hydrocarbon fluid containing reservoirs and
to more accurately drill into such reservoirs allowing to produce
hydrocarbon fluids from the reservoirs with a minimum of water.
[0255] In order to produce the mineral hydrocarbon fluid from an
earth formation, a well bore may be drilled with a method
comprising the steps of:
[0256] suspending a drill string in the earth formation, the drill
string comprising at least a drill bit and measurement sub
comprising a transmitter antenna and a receiver antenna;
[0257] drilling a well bore in the earth formation;
[0258] inducing an electromagnetic field in the earth formation
employing the transmitter antenna;
[0259] detecting a transient electromagnetic response from the
electromagnetic field, employing the receiver antenna;
[0260] deriving a geosteering cue from the electromagnetic
response.
[0261] Drilling of the well bore may then be continued in
accordance with the geosteering cue until a reservoir containing
the hydrocarbon fluid is reached.
[0262] Once the well bore extends into the reservoir containing the
mineral hydrocarbon fluid, the well bore may be completed in any
conventional way and the mineral hydrocarbon fluid may be produced
via the well bore.
[0263] Geosteering may be based on locating an electromagnetic
anomaly in the earth formation by analysing the transient response
in accordance with the present specification, and taking a drilling
decision based on the location relative to the measurement sub. The
location of the anomaly may be expressed in terms of distance
and/or direction from the measurement sub to the anomaly.
[0264] To facilitate executing the drilling decision, the drill
string may comprise a steerable drilling system 19, as shown in
FIG. 1A. The drilling decision may comprise controlling the
direction of drilling, e.g. by utilizing the steering system 19 if
provided, and/or establishing the remaining distance to be
drilled.
[0265] Accordingly, the geosteering cue may comprise information
reflecting distance between the target ahead of the bit and the
bit, and/or direction from the bit to target. Distance and
direction from the bit to the target may be calculated from the
distance and direction from the tool to the bit, provided that the
bit has a known location relative to the electromagnetic
measurement tool.
[0266] Transient electromagnetic induction data may be correlated
with the presence of a mineral hydrocarbon fluid containing
reservoir, either directly by establishing conductivity values for
the reservoir or indirectly by establishing quantitative
information on formation layers that typically surround a mineral
hydrocarbon fluid containing reservoir.
[0267] In preferred embodiments, the transient electromagnetic
induction data, processed in accordance with the above, is used to
decide where to drill the well bore and/or what is its preferred
path or trajectory. For instance, one may want to stay clear from
faults. Instead of that, or in addition to that, it may be
desirable to deviate from true vertical drilling and/or to steer
into the reservoir at the correct depth.
[0268] The distance from the measurement sub to an anomaly in the
formation may be determined from the time in which one of apparent
conductivity and apparent resistivity begins to deviate from the
corresponding one of conductivity and resistivity of formation in
which the measurement sub is located and/or determining time in
which one of apparent dip and apparent azimuth and cross-component
response starts to deviate from zero. The distance may also be
determined from when one of apparent dip and apparent azimuth
reaches an asymptotic value.
[0269] The electromagnetic anomaly may be located using at least
one of time-dependent apparent conductivity, time dependent
apparent resistivity, time-dependent dip angle, and time-dependent
azimuth angle from the time dependence of the transient response,
in accordance with the disclosure elsewhere hereinabove.
[0270] Any of the above mentioned time-dependencies can provide a
useful geosteering cue.
Fast Imaging Utilizing Apparent Conductivity and Apparent Angle
[0271] Apparent conductivity and apparent dip may also be used to
create an "image" or representation of the formation features. This
is accomplished by collecting transient apparent conductivity data
at different positions within the borehole.
[0272] The apparent conductivity should be constant and equal to
the formation conductivity in a homogeneous formation. The
deviation from a constant conductivity value at time (t) suggests
the presence of a conductivity anomaly in the region specified by
time (t). The collected data may be used to create an image of the
formation relative to the tool.
[0273] When the apparent resistivity plots (R.sub.app(z; t)) or
apparent conductivity plots ((.sigma..sub.app(z; t)) at different
tool positions are arranged together to form a plot in both z- and
t-coordinates, the whole plot may be used as an image log to view
the formation geometry, even if the layer resistivity may not be
immediately accurately determined.
[0274] An example of such an image representation of the transient
data as shown in FIG. 50 for a L=1 coaxial tool. The z coordinate
references the tool depth along the borehole. The
.sigma..sub.app(z; t) plot shows the approaching bed boundary as
the tool moves along the borehole.
[0275] FIG. 51 shows another example. The z-coordinate represents
the tool depth along the borehole with the borehole intersecting
the layer boundary in this case. The .sigma..sub.app(z; t) plot
clearly helps to visualize the approaching and crossing the bed
boundary as the tool moves along the borehole, for instance during
drilling of the borehole.
[0276] Another example is shown in FIG. 52 wherein a 3-layer model
is used in conjunction with a coaxial tool having a 1 m spacing is
in two differing positions in the formation. The results are
plotted on FIG. 53A, where the apparent resistivity R.sub.app(t) is
plotted at various points as the coaxial tool 80 approaches the
resistive layer (see FIG. 53B).
[0277] FIG. 53A may be compared to FIG. 53B to discern the
formation features. Starting in the 10 .OMEGA.m layer 82, the drop
in R.sub.app(t) is attributable to the 1 .OMEGA.m layer 83 and the
subsequent increase in R.sub.app(t) is attributable to the 100
.OMEGA.m layer 84. Curves (91, 92, 93) may readily be fitted to the
inflection points to identify the responses to the various beds,
effectively imaging the formation. Line 91 corresponds to the
deflection points caused by the 1 .OMEGA.m bed 83, line 92 to the
salt 84, and line 93 to the deflection points caused by 10 .OMEGA.m
bed 82. Moreover, the 1 .OMEGA.m curve may be readily attributable
to direct signal pick up between the transmitter and receiver when
the tool is located in the 1 .OMEGA.m bed.
[0278] In still another example, the apparent dip
.theta..sub.app(t) may be used to generate an image log. In FIG.
54A a coaxial tool is seen as approaching a highly resistive
formation at a dip angle of approximately 30 degrees. The apparent
dip response is shown in FIG. 54B. As noted previously, the time at
which the apparent dip response occurs is indicative of the
distance to the formation. When the responses for different
distances are plotted together, a curve may be drawn indicative of
the response as the tool approaches the bed, as shown in FIG.
54B.
[0279] Summarising, the subterranean formation traversed by a
wellbore may be imaged using a tool comprising a transmitter for
transmitting electromagnetic signals through the formation and a
receiver for detecting response signals in a procedure comprising
steps wherein
[0280] the tool is brought to a first position inside the
wellbore;
[0281] the transmitter is energized to propagate an electromagnetic
signal into the formation;
[0282] a response signal that has propagated through the formation
is detected;
[0283] a derived quantity is calculated for the formation based on
the detected response signal for the formation;
[0284] the derived quantity for the formation is plotted against
time.
[0285] Then the tool is moved to at least one other position within
the wellbore, whereafter the steps set out above are repeated.
Optionally, this can be done again. Then an image of the formation
within the subterranean formation is created based on the plots of
the derived quantity.
[0286] Optionally tool is then again moved to at least one more
other position within the wellbore and the whole procedure can be
repeated again.
[0287] Creating the image of the formation features may include
identifying one or more inflection points on each plotted derived
quantity and fitting a curve to the one or more inflection
points.
[0288] Thus an image of the formation may be created using apparent
conductivity/resistivity and apparent dip angle without the
additional processing required for inversion and extraction of
information. This information is capable of providing geosteering
queues as well as the ability to profile subterranean
formations.
* * * * *