The present disclosure relates generally to downhole ranging and, more specifically,
to a ranging assembly utilizing triaxial electric and magnetic field measurements to
5 determine and track the relative location of multiple wellbores.
BACKGROUND
Determining the position and direction of a conductive pipe (metallic casing, for
example) accurately and efficiently is required in a variety of downhole applications.
Perhaps the most important of these applications is the case of a blown out well in which
lo the target well must be intersected very precisely by a relief well in order to stop the
blowout. Other important applications include drilling of a well parallel to an existing well
in Steam Assisted Gravity Drainage ("SAGD) systems, avoiding collisions with other
wells in a crowded oil field where wells are drilled in close proximity to each other and
tracking an underground drilling path using a current injected metallic pipe over the ground
15 as a reference. In SAGD applications, a common practice is to use wireline systems for
electromagnetic ranging between the wells. However, this requires access to both wells
which is both time-consuming, and expensive. An alternative practice is to use
electromagnetic logging-while-drilling systems, as these only require access to a single
well.
20 However, the aforementioned approaches may only measure and process magnetic
fields using inductive sensors. While this has served as a practical solution in the past, this
could limit thc operation to low frcqucncies and may not utilizc all available
electromagnetic information. Recently, other methods related to magnetic field gradient
measurements have been disclosed, but these latter methods require the emplacement of
25 multiple, proximal inductive sensors to approximate the magnetic field gradients, rather
than measure the magnetic field gradients directly.
Accordingly, there is a need in the art for improved andlor alternative downhole
ranging techniques.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1A illustrates a relative positioning system according to certain illustrative
en~bodimentso f the present disclosure;
FIG. 1B illustrates three collocated, orthogonal triaxial magnetic field sensors
5 positioned along a drilling assembly utilized in a relative positioning system, according to
certain illustrative embodiments of the present disclosure;
FIG. IC is a cross-sectional view of an electric field sensor orientation of the
drilling assembly, according to certain illustrative embodiments of the present disclosure;
FIG. ID illustrates axially separated electric field sensors positioned along the
lo drilling assembly, according to certain illustrative embodiments of the present disclosure;
FIG. 2 is a flow chart showing a generalized ranging method used to calculate the
distancc betwccn a first targct wcll and a sccond well, thc direction to thc first targct wcll,
or the orientation of the first target well, according to certain illustrative methods of the
present disclosure;
15 FIG. 3A is a flow chart of a method utilized to calculate direction, distance and
orientation of a target well using triaxial electric and magnetic field measurements,
according to certain illustrate methods of the present disclosure;
FIG. 3B is a flow chart showing how the direction from a bottom hole assembly to a
target well can be determined using the Poynting Vector, according to certain illustrative
20 methods of the present disclosure;
FIG. 3C is a flow chart showing how thc distance from a bottom hole asscmbly to a
target well can be determined using the ratio of the Poynting Vector to the gradient of the
Poynting Vector, according to certain illustrative methods of the present disclosure;
FIG. 3D is a flow chart showing how the distance from a bottom hole assembly to a
25 target well can be determined using the gradient of the measured electric field, according to
certain illustrative methods of the present disclosure;
FIG. 3E is a flow chart showing how the distance from a bottom hole assembly to a
target well can be determined using the impedance of the measured electric and magnetic
fields, according to certain illustrative methods of the present disclosure; and
30 FIG. 3F is a flow chart showing how the orientation of thc target well can be
determined using the measured electric field, according to certain illustrative methods of
the present disclosure.
DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS
Illustrative embodiments and related methodologies of the present disclosure are
described below as they might be employed in ranging systems and methods utilizing
triaxial electric and magnetic field measurements to drill and/or track the relative location
5 of wellbores. In the interest of clarity, not all features of an actual implementation or
n~ethodologya re described in this specification. It will of course be appreciated that in the
development of any such actual embodiment, numerous implementation-specific decisions
must be made to achieve the developers' specific goals, such as compliance with systemrelated
and business-related constraints, which will vary from one implementation to
10 another. Moreover, it will be appreciated that such a development effort might be complex
and time-consuming, but would nevertheless be a routine undertaking for those of ordinary
skill in the art having the bcncfit of this disclosure. Furthcr aspects and advantagcs of thc
various embodiments and related methodologies of the disclosure will become apparent
from consideration of the following description and drawings.
15 As described herein, illustrative embodiments and methods of the present disclosure
describe ranging systems that utilize triaxial electric and magnetic field measurements to
retrieve the Poynting vector, which is the measure of the directional energy flux density of
an electromagnetic field. In general, the target well is cased and excited by a time varying
current source. In one embodiment of the disclosure, the target well is excited by a time
20 varying current source at the target well head. In another embodiment of the disclosure, the
targct wcll is cxcited by a timc varying current sourcc on thc surface. In yct anothcr
embodiment, the target well is excited by a time varying current source disposed in the
monitoring well.
Once measured, utilizing various algorithms described herein, processing circuitry
25 located on the bottom hole assembly ("BHA") (andlor at least partially at a remote location
such as on the surface, further up the borehole, or at a facility remote from the well site)
analyzes the triaxial measurement data to determine the distance and direction to the target
casing. It is noted here that the teachings that are disclosed here are also valid for any
elongated conductive body other than a casing. In one embodiment, the direction of the
30 Poynting Vcctor will providc the dircction to the targct well. In anothcr cmbodiment, thc
gradient of the measured Poynting Vector will provide the distance of the target well. In
yet another embodiment, the imaginary component of the measured impedance will provide
the distance of the target well. In another, analysis of both the distance and direction of the
Poynting Vector will provide the orientation of the target well. In yet another embodiment,
analysis of the electric fields will provide the orientation of the target well.
Moreover, as will be described herein, the Poynting Vector, impedance, and electric
fields are rotationally invariant to the orientation of the triaxial electric and magnetic field
5 sensors in the measurement well. Accordingly, in certain embodiments, the sensors can be
rotating as part of the BHA or wireline device, and yet recover the same values of the
Poynting Vector, impedance, and electric fields.
Although the present disclosure may be utilized in a variety of applications, the
following description will focus on applications for accurately, and reliably positioning a
lo well being drilled, the monitoring or "injector" well (i.e., second well), with respect to a
nearby target first well, usually the producer well, so that the injector well can be
n~aintaincd approximatcly parallel to the producer well. The targct well must bc of a
higher conductivity than the surrounding formation, which may be realized through the use
of an elongated conductive body along the target well, such as, for example, casing which
15 is already present in most wells to preserve the integrity of the well. Also, the method and
system of the disclosure are particularly desirable for the drilling of SAGD wells because
the two wells can be drilled close to one another as is required in SAGD operations. These
and other applications andlor adaptations will be understood by those ordinarily skilled in
the art having the benefit of this disclosure.
20 FIG. IA illustrates a relative positioning system 100 according to an exemplary
cmbodimcnt of thc present disclosure. In this embodirncnt, a producer well 10 is drillcd
using any suitable drilling technique. Thereafter, producer well 10 is cased with casing 11.
An injector well 12 is then drilled using BHA 14 which may be, for example, a loggingwhile
drilling ("LWD) assembly, measurement-while drilling assembly ("MWD) or other
25 desired drilling assembly. Although injector well 12 is described as being subsequently
drilled, in other embodiments producer well 10 and injector well 12 may be drilled
simultaneously. Moreover, in yet another alternate embodiment, BHA 14 inay be
embodied as a wireline application (without a drilling assembly) performing logging
operations, as will be understood by those same ordinarily skilled persons mentioned
30 hcrcin.
In this exemplary embodiment, the BHAIdrilling assembly 14 includes one or more
electromagnetic field transmitters 16. Such a transmitter may be, for example, a coil, tilted
coil, or con~binations of electrodes, or other controlled electromagnetic field source.
Drilling assembly 14 also includes one or more triaxial electric and/or magnetic field
sensors 18 positioned above drill bit 20. As understood in the art, the sensors used to
measure electric and magnetic fields are different; however, such sensors may be described
herein separately as electric and magnetic field sensors or jointly as electromagnetic field
5 sensors. Such sensors may include, for example, combinations of electrodes, coils, tilted
coils, magnetometers, or magnetorestrictive sensors. The particular arrangement of sensors
18 along drilling assembly 14 may take a variety of forms. FIGS. IB-ID illustrate a variety
of alternative arrangements for sensors 18. In one illustrative embodiment, the electric and
magnetic fields are measured along the x,y,z axes (is., triaxial) using three collocated
10 electric and magnetic field sensors 18. Such an embodiment is illustrated in FIG. IB,
which illustrates three collocated, orthogonal triaxial magnetic field sensors (e.g., coils)
positioncd along drilling asscrnbly 14 which arc oriented at an anglc of 45 dcgrccs rclativc
to the axis A of drilling assembly 14.
In yet other illustrative embodiments, the radial electric fields can be measured
15 using at least four electrodes at unifonn angles about the mandrel circumference. For
example, four electrode may be used as sensors 18, and are radially positioned around the
mandrel circumference of drilling assembly 14 at angles of 90 degrees, as shown in FIG.
1 C which illustrates a cross-sectional view of drilling assembly 14 extending along second
wellbore 12. In yet another embodiment (not shown), eight electrodes are located at angles
20 of 45 degrees about the mandrel circumference. In yet another alternate embodiment as
shown in FIG. ID, the axial clcctric ficlds can be mcasurcd on drilling asscrnbly 14 using
at least two electrodes sensors 18 axially separated about axis A of the mandrel. In some
embodiments, the electrodes are directly exposed to the drilling fluids and formation, and
operate via galvanic coupling. In other embodiments, the electrodes are not directly
25 exposed to the drilling fluids and formation, and operate via capacitive coupling. In certain
other embodiments, regardless of the sensor design utilized, the centers of each sensor are
collocated. These and other sensor designs may be utilized with the present disclosure, as
will be understood by those ordinarily skilled in the art having the benefit of this
disclosure.
30 Rcfcrring back to FIG. IA, during an cxcmplary drilling opcration using rclativc
positioning system 100, drilling assembly 14 is deployed downhole to drill injector well 12
after, or contemporaneously with, the drilling of producer well 10. In order to maintain
injector well 12 at the desired distance and direction from producer well 10, relative
positioning system 100 activates transmitter 16 to propagate electromagnetic fields 22 to
thereby induce a current along target casing 11 of producer well 10. As a result,
electromagnetic fields 24 radiate from target casing 11, where the triaxial electric and
magnetic fields are measured by sensors 18. Local or remote processing circuitry then
5 utilizes the triaxial electromagnetic field measurements to determine the distance or
direction to producer well 10, in addition to the orientation of producer well 10. Once the
relative position is determined, the circuitry generates signals necessary to steer the drilling
assembly 14 in the direction needed to maintain the desired distance and direction from
producer well 10.
10 Although not shown, note that in alternate embodiments the current along casing 11
may be excited by a time varying current source at the target well head. In another
embodirncnt of the disclosurc, the target wcll is cxcited by a currcnt source on the surface.
Furthermore, although not shown as well, drilling assembly 14 includes processing
circuitry necessary (i.e., system control center) to achieve the relative positioning of the
15 present disclosure in real-time. Such circuitry includes a communicatio~~usn it to facilitate
interaction between drilling system 14 and a remote location (such as the surface). A
visualization unit may also be connected to communications unit to monitor the
measurement data being process; for example, an operator may intervene the system
operations based on this data. A data processing unit may convert the received data into
20 information giving the target's position, direction and orientation in real-time. Thereafter,
rcsults may be displaycd via the visualizing unit.
The system control center of drilling assembly 14 also includes the
storage/communication circuitry necessary to perform the calculations described herein. In
certain embodiments, that circuitry is con~inunicablyc oupled to trailsnlitters 16 utilized to
25 generate electromagnetic fields 22, and also likewise coupled to sensors 18 in order to
process the received electric and magnetic fields forming the electromagnetic field 24.
Additionally, the circuitry on-board drilling assembly 14 may be communicably coupled
via wired or wireless connections to the surface to thereby communicate data back uphole
and/or to other assembly components (to steer a drill bit forming part of assembly 14, for
30 cxamplc). In an altcrnatc cinbodiment, thc system control ccntcr or othcr circuitry
necessary to perform one or more aspects of the techniques described herein may be
located at a remote location away from drilling assembly 14, such as the surface or in a
different wellbore. For example, in certain embodiments, the transmitter may be located in
another well or at the surface. In other embodiments, the electromagnetic field
measurements may be communicated remotely to the system control center for processing.
These and other variations will be readily apparent to those ordinarily skilled in the art
having the benefit of this disclosure.
5 Moreover, the on-board circuitry includes at least one processor and a nontransitory
and computer-readable storage, all interconnected via a system bus. Software
instructions executable by the system control center for implementing the illustrative
relative positioning methodologies described herein in may be stored in local storage or
some other computer-readable medium. It will also be recognized that the positioning
lo software instructions may also be loaded into the storage from a CD-ROM or other
appropriate storage media via wired or wireless methods.
Moreover, those ordinarily skilled in thc art will appreciate that various aspects of
the disclosure may be practiced with a variety of computer-system configurations,
including hand-held devices, multiprocessor systems, microprocessor-based or
15 programmable-consu~ller electronics, minicon~puters, nlainfraille computers, and the like.
Any number of computer-systems and computer networks are acceptable for use with the
present disclosure. The disclosure may be practiced in distributed-computing
environments where tasks are performed by remote-processing devices that are linked
through a communications network. In a distributed-computing environment, program
20 modules may be located in both local and remote computer-storage media including
memory storage devices. The present disclosure may therefore, be implemented in
connection with various hardware, software or a combination thereof in a computer system
or other processing system.
Now that a generalized illustrative embodinlent of the present disclosure has been
25 described, the methodology by which relative positioning is determined will now be
described. As previously mentioned, embodiments of the present disclosure utilize both
electric and magnetic field measurements for electromagnetic ranging. Illustrative
embodiments may be exemplified in the following theoretical example, which is not
intended to limit the scope of disclosure. With reference to FIG. lA, target well 10 may be
30 defined by the triaxial coordinate system r = (x, y, z} and can be approximated by an
infinitely long current source oriented in the z direction in a homogeneous geological
formation of conductivity o such that the electric current along casing 11 can be
approximated as:
J(r)= I&-S)(z ) GZ, Eq.(l).
Here, J(r) is the current density, I is the current, 6(r) and 6(z) are delta functions, and G7. is
a unit vector directed along the axis of the current source. Given the radial symmetry about
targct wcll 10, clcctromagnetic fields 24 can be described in cylindrical coordinates r = (z,
5 p, 8) about the z-axis. Note that the cylindrical coordinates r = (z, p, 0) can be transformed
to Cartesian coordinates r = (x,y,z), and vice versa. Of particular interest to
electromagnetic ranging is the distance to target well 10, p = d(x2 + 9) (note that d denotes
the square root), and the direction (angle) to target well 10, 6. The orientation of target
well 10 relative to drilling assembly 14 can be also be retrieved.
LO As will be understood by those ordinarily skilled in the art having the benefit of this
disclosure, the electric field at an angular frequency w about target well 10 only has a zdirected
axial component:
E, (r,w ) = ((iwpo/(2n))Ko(ikp)Gz, Eq.(2),
Where k = d(iw,uo) is the wavenumber, p is the radial distance between the two wells in the
15 xyxy-plane, and KO is the modified Bessel hnction of the second kind of order zero. It is
also noted here that in a case where target well 10 is aligned with the axial direction of
drilling asseinbly 10, the z-directed axial component of the electric field can be measured
by placing two axially separated sensors/receivers 18 (e.g., electrodes) along drilling
asscmbly 14.
20 Therefore, it follows that the magnetic field at an angular frequency w about target
well 10 has a 0-directed tangential component:
Ho (r,w ) = ((ik4/(2n ) ) K~(ikpQ) a Eq-(3),
where K1 is the modified Bessel function of the second kind of order one, and fie is a unit
vector in thc azimuthal dircction about thc axis of the currcnt source. At low frequencies
25 used for and small distances typically encountered in electromagnetic ranging, the modified
Bessel functions in Equations (2) and (3) can be approximated by:
KO (ikp)- - ln (ikp) Eq.(4), and
K~(ikp)= -l/(ikp") %(5)
such that the electric field (Eq.2) and magnetic field (Eq.3) at an angular frequency w are
30 respectively expressed as:
Ez (r,w ) = - ((iwpo/ (2n )) ln (ikp)G z Eq.(6), and
Ho(r,w) =- I/(2np) GO Eq.(7).
Originating from conservation of energy considerations, the Poynting Theorem generally
states that for any electron~agnetic field, there must be electron~agnetic energy flowing in
the medium due to the electromagnetic fields. The Poynting Vector, S, which is the
measure of the directional energy flux density of an electromagnetic field, can be derived
s from the cross product of the electric E and magnetic H field vectors. For linear dispersive
media with losses, which is typical for earth materials, the Poynting Vector is defined in the
frequency domain as:
S = .5E x H* = .5(EyPz - EzPy)Qx+ .5(EzPx- ExPz)Qy + .5(ExPy - EYPx)&
Eq.(8)7
lo where * denotes the complex conjugate, and Qx, Qy, and Q are unit vectors in in x-, y-, and
z-directed unit vectors in Cartesian coordinates relative to the axis of the current source. In
cylindrical coordinates, the Poynting Vector (Eq.8) is express as:
S = .5E x H* = .5(EoP, - EzPe)Qr + .5 ( E x z - EzPr)Qe + .5(ErPe - E0Pr)fiz
Eq.(9)7
1s where Qr, Qe, and Q, are radial-, azimuthal-, and axial-directed unit vectors in cylindrical
coordinates relative to the axis of the current source. Fro111 Equations 6 and 7 above,
Equation 9 may be reduced to:
S=.5ExH*=(-.5EzH*e)Qr=-((iu~r/2)/(4n2p))ln(ikp)Qr W.(lO).
In the illustrative embodiments of the present disclosure, the system control center
20 utilizes the method described above to achieve the relative positioning calculations
described herein. FIG. 2 is a flow chart showing a generalized ranging method 200 used to
calculate the distancc bctwecn a first target wcll and a sccond wcll, thc dircction to the first
target well, or the orientation of the first target well, according to certain illustrative
methods of the present disclosure. Again, the specific application may be, for example, a
25 SAGD application. With reference to FIGS. 1 and 2, at block 202, a first wellbore 10 is
drilled using any suitable methodology. First wellbore 10 has a higher conductivity than
the surrounding formation which, for example, may be achieved using casing 11 of first
wellbore 10 or through utilization of some other elongated conductive body positioned
along first wellbore 10.
30 At block 204, one or more electric andlor magnetic sensors 18 are deployed into a
sccond wcllborc 12. In certain embodiments, thcrc may be two scnsors that arc radially
separated along the axis of second wellbore 12. Sensors 18 may be deployed in second
wellbore 12 in a variety of ways including, for example, along drilling assembly 14 utilized
in a SAGD operation or a subsea operation. Note that in alternative methodologies, the
first and second wellbores 10,12 may be drilled contemporaneously.
At block 206, a current is induced along first wellbore 10 which results in an
electromagnetic field 24 being emitted from first wellbore 10. In general, the current is
5 induced using a time varying current source that may be generated in a variety of ways. In
one embodiment of the disclosure, the current is induced along casing 1 1 by a time varying
current source at the well head of first wellbore 10. In another embodiment of the
disclosure, the current is induced along casing 11 by a time varying current source on the
surface. In yet another embodiment as shown in FIG. 1, the current is induced along casing
lo 11 by an electromagnetic transmitter 16 positioned along drilling assembly 14 in second
well 12.
At block 208, the clcctromagnctic field 24 is thcn rcccivcd by sensor(s) 18. As will
be described in more detail below, at block 210, via the system control center, the relative
positioning system 100 utilizes the measured triaxial electric or magnetic fields to
15 calculate, in real-time, the distance between the first and second wellbores, the direction to
the first wellbore relative to the second wellbore, or the orientation of the first wellbore.
After analyzing the measured triaxial electromagnetic fields, relative positioning system
100 determines what actions, if any, are necessary to maintain or correct the desired drilling
path at block 212. Such actions may be, for example, a change in direction, speed, weight
20 011 bit, etc., to thereby steer the BHA as desired. Simultaneously, the algorithm returns to
block 206 whcrc it continucs to cxcitc the transmitters to continuously monitor andlor
adjust the drill path as necessary.
FIG. 3A is a flow chart of a method 300 utilized to calculate direction, distance and
orientation of a target well using triaxial electric and magnetic field measurements,
25 according to certain illustrate methods of the present disclosure. After current has been
induced along the casing, the emitted electromagnetic field 24 (FIG. 1A) is sensed by
sensors 18 as previously described. At block 330, the transient triaxial electric and
magnetic fields are measured by sensors 18. At block 304, the system control center of the
relative positioning system then transforms (e.g., using Fourier transform) the measured
30 clcctric and rnagnctic fields into thcir rcspcctivc frequency-domain clcctric and rnagnctic
fields, as defined by Equations 6 and 7 described above. The system control center may
then utilize the frequency-domain electric and magnetic fields in a variety of algorithms to
conduct ranging, as described in the illustrate flow charts of FIGS. 3B-3F.
FIG. 3B is a flow chart showing how the direction from a BHA to a target well can
be determined using the Poynting Vector, according to certain illustrative methods of the
present disclosure. At block 306, the system control center first calculates the Poynting
Vector using Equations 8-10. It can be observed that S in Equation 10 is always directed
5 along fir towards the target well. Thus, by evaluating the Poynting Vector from triaxial
electric and magnetic field measurements, the system control center determines the
direction to the target well at block 308. The magnetic field is actually recovered from
magnetic induction measurements. It follows that the magnitude of Equation 10 is scaled
by the magnetic permeability, but the direction of the Poynting Vector remains unchanged.
lo While Equation 10 demonstrates it is possible to recover the direction to the target well
from the Poynting Vector, Equation 10 also demonstrates that it is not straightforward to
recover the distance to the target well from the Poynting Vector, as the magnitude of
Equation 10 is a nonlinear bction with respect to the range p, and is dependent upon the
current, wavenumber, and permeability of the medium; all of which may be unknown.
1s FIG. 3C is a flow chart showing how the distance from a BHA to a target well can
be determined using the ratio of the Poynting Vector to the gradient of the Poynting Vector,
according to certain illustrative methods of the present disclosure. Using the data from
blocks 304 and 306, the system control center calculates the Poynting Vector gradient at
block 3 10. Here, the system control center calculates the gradient of the Poynting Vector
20 dS/dp using:
dS/dp = ((iwp/Z)/(4n2~)()1 - In (ikp))t ir, Eq.(l 11,
where the variables were defined previously. The ratio of the Poynting Vector to the
gradient of the Poynting Vector can then be calculated using:
p(ll((1- In(iW)) - 1) = lSl/(IdS/dpO, Eq.(12),
25 which, for likpl< l ( - l l P >= IEzl/(laEJaPl), Eq.(17),
which simplifies as:
Is P= - I E ~ I I ( I ~ E . J ~ P I ) , Eq.(lZI).
As a result of Equation 18, at block 316, the distance can be calculated from the
absolute value and gradient of the electric field vector by utilizing the finite difference in
space for the gradient, the same way it is traditionally done for the magnetic fields.
Gradient measurements of the electric fields require multiple electric field measurements,
20 instead of the multiple magnetic field measurements that are traditionally used.
FIG. 3E is a flow chart showing how the distance from a BHA to a target well can
be determined using the impedance of the measured electric and magnetic fields, according
to certain illustrative methods of the present disclosure. To calculate the distance in this
illustrative method, the system control center calculates the impedance at block 318 using
2s the impedance transfer function Z(r,w):
Z(r, w) = (Ez(r,rn))/(ffe(r,o)) = - iwpIpln(ikp) Eq.(l9),
where the variables were defined previously. Using L'Hopital's rule as ikp -t 0, it follows
that:
((11~I)( - l l P ) ) = (Ez(r,rn))l(He(r,rn)), Eq.(20),
30 which reduces to:
P = (Il~~llm[(G(r,~))l(ffe(r,rn))l, Eq.(2 I),
where Im represents the imaginary component of the impedance at a radial frequency,
scalcd by a product of the angular frequency and magnetic pcrmcability. As a rcsult, at
block 320, the system control center calculates the distance from a combination of electric
and magnetic field measurements and also two parameters; frequency and magnetic
permeability. For most formations, the magnetic permeability can be assumed to be that of
free space (i.e., non-magnetic). In this illustrative method, the magnetic field is actually
5 recovered from magnetic induction measurements, and it follows that Equation 21 can be
expressed as:
P = (114 Im[(&(r,w))l(Be(r,w))I, Eq.(22),
which illustrates that the systcm control ccntcr may calculatc the distance using a
combination of the measured electric field and magnetic induction measurements, as well
lo as the angular frequency.
The orientation independent of the triaxial measurements described herein should
also be noted. As previously mentioned, the triaxial electric and magnetic fields are
measured by sensors attached to a BHA, and are defined by the Cartesian coordinate
system r ' = {x ', y ', z ') , which is related to the Cartesian coordinate system of the target
15 well r = {x, y, z) through the three (generally unknown) Euler angles u, ,4, 8:
r ' = R(u, p, (a)r Eq.(23),
where R(u, p, (a) is the Euler rotation matrix. The rotational invariance of the cross product
states that:
S(r',a) = R(a, ,4, q)S(r,o) = .5E(r',a) x H*(rJ,o) = .5R(u, ,4, q)E(r,o) x R(u, P,
20 q)H*(r,a),
Ecl.(24),
which preserves both the amplitude and the direction of the Poynting Vector, regardless of
the coordinate system r' = {x', y', z'). The Euler rotation matrix R(u, ,4, (a) can be
retrieved by Procrustes analysis:
25 lIS(r,a) - R-'(% pt (a)S(r ',a)ll~ -f min, Eq.(25),
subject to the constraint S,(r,w) = 0. In particular, Equation 25 enables the relative
direction and orientation between the BHA and the target well to be estimated when the
two are not parallel.
It also follows that the amplitudes of the total axial electric and total tangential
30 magnetic fields in the cylindrical coordinate system r = (z, y, 8):
IEZ(r,w)l= d ( ~ ~ '~,a,) (+r E ~(r~9,a,)+ EZz,( r ',a)), Eq.(26), and
I Hs(r,w)l = d(H2,.(r ',o+) H ~(r~ ',o), + H'~.( r ',a)), Eq.(27)
are equal to the amplitude of the total electric and magnetic field vectors measured in the
BHA's coordinate system r ' = {x ', y ', z ') . Accordingly, the measured electric and
magnetic fields described herein, as well as the Poynting Vector calculated using the
ranging method described by Equation 12, are rotationally invariant to the coordinate
5 system of the BHA.
FIG. 3F is a flow chart showing how the orientation of the target well can be
determined using the measured electric field, according to certain illustrative methods of
the prcscnt disclosurc. Here, at block 322, the system control ccntcr first calculates the
electric field vector using Equation 26. It is observed that the measured electric field in
lo Equation 26 is always directed along the z-axis, which is the target well's axial direction,
regardless of the orientation of the BHA. Thus, by evaluating the electric field vector from
triaxial electric field measurements, the system control center can determine the orientation
of the target well at block 324. This is especially useful in situations where the axis of the
target well is not parallel to the BHA axis.
15 Although triaxial electric and magnetic field measurements have been described
herein, the present disclosure may also be utilized to conduct ranging using one or two
mcasurcd componcnts of thc clcctric and magnetic ficlds rather than complctc triaxial
measurements of the electric and magnetic fields. Thus, in certain illustrative methods,
components of the electric field alone may be utilized to calculate the distance to the target
20 well or the direction of the target well, which may be accomplished by appropriately
choosing the electrode configuration such that Equation 26 is approximated with one or
two measured components of the electric field, rather than all three components of the
electric field.
In yet other illustrative methods, components of the magnetic field may also be used
2s along with the non-triaxial electric field measurement to calculate the distance and
dircction to the targct well. Again, this may be accomplishcd by appropriatcly choosing thc
magnetic field sensor orientations such that Equation 27 is approximated with one or two
measured components of the magnetic field, rather than all three components of the
magnetic field.
30 Although the present disclosure has focused on SAGD applications, systems and
methods of the present disclosure may also be utilized in well avoidance applications.
Here, a second well may be drilled, wherein the relative positioning system is used to avoid
a first well. Other applications include T-intersection applications, in which a relief well
must be drilled in order to relieve a blown out well. These and other applications will be
apparent to those ordinarily skilled in the art having the benefit of this disclosure.
Embodiments described herein further relate to any one or more of the following
paragraphs :
5 1. A method for downhole ranging, comprising drilling a first wellbore, the
first wellbore comprising an elongated conductive body; deploying an electric field
sensor in a second wellbore; inducing a current along the first wellbore that results in an
electromagnetic field being emitted from the first wellbore; receiving the electromagnetic
field utilizing the electric field sensor, wherein an electric field of the electromagnetic field
lo is measured; and utilizing the measured electric field to thereby calculate: a distance
between the first and second wellbores; or a direction of the first wellbore in relation to the
sccond wcllborc.
2. A method as defined in paragraph 1, wherein the direction of the first
wellbore is a direction of the measured electric field.
15 3. A method as defined in any of paragraphs 1-2, further comprising
determining an orientation of the first wellbore using the measured electric field.
4. A method as defined in any of paragraphs 1-3, hrther comprising
calculating a gradient of the measured electric field.
5. A method as defined in any of paragraphs 1-4, further comprising
20 calculating a ratio of the measured electric field to the gradient of the measured electric
ficld; and calculating thc distance bctwecn the first and second wcllbores using the ratio.
6. A method as defined in any of paragraphs 1-5, wherein a magnetic field
sensor is deployed in the second wellbore, the method further comprising measuring a
magnetic field of the electromagnetic field; and utilizing the measured electric field and
25 measured magnetic field to thereby calculate the distance between the first and second
wellbores or the direction of the first wellbore in relation to the second wellbore.
7. A method as defined in any of paragraphs 1-6, further comprising utilizing
the measured electric and magnetic fields to calculate a Poynting Vector; and utilizing the
Poynting Vector to calculate the distance between the first and second wellbores or the
30 dircction of thc first wcllbore in relation to thc sccond wcllborc.
8. A method as defined in any of paragraphs 1-7, wherein the direction of the
first wellbore is a direction of the Poynting Vector.
9. A method as defined in any of paragraphs 1-8, further conlprising
calculating a gradient of the Poynting Vector.
10. A method as defined in any of paragraphs 1-9, further comprising
calculating a ratio of the Poynting Vector to the gradient of the Poynting Vector; and
5 calculating the distance between the first and second wellbores using the ratio.
1 1. A nlethod as defined in any of paragraphs 1 - 10, further compi-ising
calculating an impedance of the measured electric and magnetic fields.
12. A method as defined in any of paragraphs 1-11, further comprising
calculating the distance between the fist and second wellbores using the impedance.
LO 13. A method as defined in any of paragraphs 1-12, wherein calculating the
distance comprises calculating a ratio of an imaginary component of the impedance at a
radial frequency to a product of the radial frequency and magnetic permeability; and
calculating the distance between the first and second wellbores using the ratio.
14. A method as defined in any of paragraphs 1-13, wherein the measured
15 electric field is a triaxial electric field ineasurenlent.
15. A method as defined in any of paragraphs 1-14, wherein the measured
magnetic field is a triaxial magnetic field measurement.
16. A method as defined in any of paragraphs 1-1 5, wherein the measured
electric and magnetic fields are total electric and magnetic fields; and the measured total
20 electric and magnetic fields are rotationally invariant.
17. A method as defined in any of paragraphs 1-16, wherein the calculated
Poynting Vectors are rotationally invariant.
18. A method as defined in any of paragraphs 1-17, wherein the distance or
direction calculatioils are conducted in real-time.
25 19. A method as defined in any of paragraphs 1-18, wherein the
electromagnetic sensor in the second wellbore in deployed on a bottom hole assembly.
20. A method as defined in any of parapdphs 1-19, wherein the bottom hole
assembly is a drilling assembly, logging assembly, or wireline assembly.
21. A method as defined in any of paragraphs 1-20, further comprising steering
30 the bottom hole assembly deployed along the second wellborc using thc distancc or
direction calculations.
22. A method as defined in any of paragraphs 1-20, wherein an axis of the
bottom hole assembly is not parallel with an axis of the first wellbore.
23. A method as defined in any of paragraphs 1-22, wherein the first wellbore is
a producer well; and the second wellbore is an injector well, wherein the method is utilized
in a Steam Assisted Gravity Drainage operation.
24. A method as defined in any of paragraphs 1-23, wherein the first wellbore is
5 a blow out well and the second wellbore is a relief well.
25. A method as defined in any of paragraphs 1-23, further coitlprises avoiding
the first wellbore using the distance calculation.
26. A method as defined in any of paragraphs 1-25, wherein inducing the
current along the first wellbore comprises inducing the current using a time-varying current
lo source at a wellhead of the first well; a time-varying current source at a surface location; or
a time-varying current source along the bottom hole assembly.
27. A relativc positioning systcm for downhole ranging, comprising a bottom
hole assembly to be positioned along a monitoring well; one or more triaxial electric and
magnetic field senqors positioned along the bottom hole assembly; and processing circuitry
15 coupled to the sensors and configured to ii~lplen~ena tn lethod cottlprising: measuring an
electric field emitted from a target well; and utilizing the measured electric field to thereby
calculate: a distance between the monitoring well and the target well; or a direction of
the target well in relation to the monitoring well.
28. A relative positioning system as defined in paragraph 27, further comprising
20 an electromagnetic transmitter positioned along the bottom hole assembly.
29. A relativc positioning system as defincd in any of paragraphs 27-28,
wherein the sensors are three collocated, orthogonal magnetic coils oriented at an angle of
45 degrees relative to an axis of the bottom hole assembly; at least four electrodes
positioned radially positioned around the bottom hole assembly; or at least two electrodes
25 axially separated along the bottom hole assembly.
30. A relative positioning system as defined in any of paragraphs 27-29,
wherein the bottom hole assembly is a drilling assembly, logging assembly or wireline
assembly.
31. A relative positioning system as defined in any of paragraphs 27-30,
30 whcrcin the processing circuitry is fk-ther configured to implcment any of the mcthods of
claims 3-17.
Moreover, the methodologies described herein may be embodied within a system
comprising processing circuitry to inlpleillent any of the methods, or a in a computerprogram
product comprising instructions which, when executed by at least one processor,
causes the processor to perform any of the methods described herein.
Accordingly, through use of the foregoing illustrative systems and methods, the
distance, direction and orientation of a target well can be retrieved through rotationally
s invariant analysis of triaxial electric and magnetic field measurements from a BHA having
electromagnetic sensors. The triaxial electric and magnetic field sensors can be deployed
in any downhole device without explicitly needing to process or retrieve rotational
information about the downhole BHA or wireline device. Moreover, the distance, direction
and orientation of the target well can be retrieved from a single measurement position.
LO The advantages of the present disclosure are numerous. For example, such
advantages include: direct measurement of the electric field andlor electric field gradients
gcncratcd by thc targct wcll using triaxial clcctric ficld scnsors; thc dircction of thc
measured electric field retrieves the orientation of the target well; the direction of the target
well is retrieved from the measured electric field and electric field gradient; direct
15 measurement of the Poynting Vector andlor Poynting Vector gradients of electromagnetic
fields generated by the target well using triaxial electric and magnetic field sensors; the
direction of the Poynting Vector retrieves the direction to and orientation of the target well;
direct measurement of the impedance transfer function of electromagnetic fields generated
by the target well using triaxial electric and magnetic field sensors; the impedance transfer
20 hnction retrieves the distance to the target well; rotational invariance of the electric fields,
clcctric ficld gradients, Poynting Vector, Poynting Vcctor gradient, and the impedancc
transfer function relative to sensor orientation; and real-time integration with drilling
systems.
Although various embodiments and methodologies have been shown and described,
2s the disclosure is not limited to such embodiments and methodologies and will be
understood to include all modifications and variations as would be apparent to one skilled
in the art. Therefore, it should be understood that the disclosure is not intended to be
limited to the particular forms disclosed. Rather, the intention is to cover all modifications,
equivalents and alternatives falling within the spirit and scope of the disclosure as defined
30 by the appcndcd claims.

CLAIMS
WHAT IS CLAIMED IS:
1. A method for downhole ranging, comprising:
5 drilling a first wellbore, the first wellbore comprising an elongated conductive
body; deploying an electric field sensor in a second wellbore;
inducing a current along the first wellbore that results in an electromagnetic field
being emitted from the first wellbore;
receiving the electromagnetic field utilizing the electric field sensor, wherein an
lo electric field of the electromagnetic field is measured; and
utilizing the measured electric field to thereby calculate:
a distance between thc first and sccond wellborcs; or
a direction of the first wellbore in relation to the second wellbore.
2. A method as defined in claim 1, wherein the direction of the first wellbore is a
15 direction of the measured electric field.
3. A method as defined in claim 1, further comprising determining an orientation of
the first wellbore using the measured electric field.
4. A method as defined in claim 1, fbrther comprising calculating a gradient of the
measured electric field.
20 5. A method as defined in claim 4, further comprising:
calculating a ratio of the measured electric field to the gradient of the measured
electric field; and
calculating the distance between the first and second wellbores using the ratio.
6. A method as defined in claim 1, wherein a magnetic field sensor is also deployed in
25 the second wellbore, the method further comprising:
measuring a magnetic field of the electromagnetic field; and
utilizing the measured electric field and measured magnetic field to thereby
calculate:
the distance between the first and second wellbores; or
30 thc dircction of the first wellborc in rclation to the sccond wellbore.
7. A method as defined in claim 6, further comprising:
utilizing the measured electric and magnetic fields to calculate a Poynting Vector;
and utilizing the Poynting Vector to calculate:
the distance between the first and second wellbores; or
5 the direction of the first wellbore in relation to the second wellbore.
8. A method as defined in claim 7, wherein the direction of the first wellbore is a
direction of the Poynting Vector.
9. A method as defined in claim 7, further comprising calculating a gradient of the
Poynting Vector.
lo 10. A method as defined in claim 9, further comprising:
calculating a ratio of the Poynting Vector to the gradient of the Poyntiilg Vector;
and calculating the distance between the first and second wellbores using the ratio.
1 I. A method as defined in claim 6, further comprising calculating an impedance of the
measured electric and magnetic fields.
1s 12. A method as defined in claim 11, fiu-ther comprising calculating the distance
between the first and second wellbores using the impedance.
1 3. A method as defined in claim 12, wherein calculating the distance comprises:
calculating a ratio of an imaginary component of the impedance at a radial
frequency to a product of the radial frequency and magnetic permeability; and
20 calculating the distance between the first and second wellbores using the ratio.
14. A method as defined in claim 1, wherein the measured electric field is a triaxial
electric field measurement.
15. A method as defined in claim 6, wherein the measured magnetic field is a triaxial
magnetic field measurement.
25 16. A method as defined in claim 6, wherein:
the measured electric and magnetic fields are total electric and magnetic fields; and
the measured total electric and magnetic fields are rotationally invariant.
17. A method as defined in claim 7, wherein the calculated Poynting Vectors are
rotationally invariant.
18. A method as defined in claim 1, wherein the distance or direction calculations are
conducted in real-time.
s 19. A method as defined in claim 1, wherein the electric field sensor in the second
wellbore in deployed on a bottom hole assembly.
20. A 111ethod as defined in claim 19, wherein the bottom hole assembly is a drilling
assembly, logging assembly, or wireline assembly.
21. A method as defined in claim 19, further comprising steering the bottom hole
10 assenlbly deployed along the second wellbore using the distance or direction calculations.
22. A method as defined in claim 19, wherein an axis of the bottom hole assembly is
not parallel with an axis of the first wellbore.
23. A method as defined in claim 1, wherein:
the first wellbore is a producer well; and
15 the second wellbore is an injector well, wherein the method is utilized in a Steam
Assisted Gravity Drainage operation.
24. A method as defined in claim 1, wherein:
the first wellbore is a blow out well; and
the second wellbore is a relief well.
20 25. A method as defined in claim 1, hrther conlprises avoiding the first wellbore using
the distance calculation.
26. A method as defined in claim 19, wherein inducing the current along the first
wellbore comprises inducing the current using:
a time-varying current source at a wellhead of the first well;
2s a time-varying current source at a surface location; or
a time-varying current source along the bottom hole assembly.
The present disclosure relates generally to downhole ranging and, more specifically,
to a ranging assembly utilizing triaxial electric and magnetic field measurements to
5 determine and track the relative location of multiple wellbores.
BACKGROUND
Determining the position and direction of a conductive pipe (metallic casing, for
example) accurately and efficiently is required in a variety of downhole applications.
Perhaps the most important of these applications is the case of a blown out well in which
lo the target well must be intersected very precisely by a relief well in order to stop the
blowout. Other important applications include drilling of a well parallel to an existing well
in Steam Assisted Gravity Drainage ("SAGD) systems, avoiding collisions with other
wells in a crowded oil field where wells are drilled in close proximity to each other and
tracking an underground drilling path using a current injected metallic pipe over the ground
15 as a reference. In SAGD applications, a common practice is to use wireline systems for
electromagnetic ranging between the wells. However, this requires access to both wells
which is both time-consuming, and expensive. An alternative practice is to use
electromagnetic logging-while-drilling systems, as these only require access to a single
well.
20 However, the aforementioned approaches may only measure and process magnetic
fields using inductive sensors. While this has served as a practical solution in the past, this
could limit thc operation to low frcqucncies and may not utilizc all available
electromagnetic information. Recently, other methods related to magnetic field gradient
measurements have been disclosed, but these latter methods require the emplacement of
25 multiple, proximal inductive sensors to approximate the magnetic field gradients, rather
than measure the magnetic field gradients directly.
Accordingly, there is a need in the art for improved andlor alternative downhole
ranging techniques.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1A illustrates a relative positioning system according to certain illustrative
en~bodimentso f the present disclosure;
FIG. 1B illustrates three collocated, orthogonal triaxial magnetic field sensors
5 positioned along a drilling assembly utilized in a relative positioning system, according to
certain illustrative embodiments of the present disclosure;
FIG. IC is a cross-sectional view of an electric field sensor orientation of the
drilling assembly, according to certain illustrative embodiments of the present disclosure;
FIG. ID illustrates axially separated electric field sensors positioned along the
lo drilling assembly, according to certain illustrative embodiments of the present disclosure;
FIG. 2 is a flow chart showing a generalized ranging method used to calculate the
distancc betwccn a first targct wcll and a sccond well, thc direction to thc first targct wcll,
or the orientation of the first target well, according to certain illustrative methods of the
present disclosure;
15 FIG. 3A is a flow chart of a method utilized to calculate direction, distance and
orientation of a target well using triaxial electric and magnetic field measurements,
according to certain illustrate methods of the present disclosure;
FIG. 3B is a flow chart showing how the direction from a bottom hole assembly to a
target well can be determined using the Poynting Vector, according to certain illustrative
20 methods of the present disclosure;
FIG. 3C is a flow chart showing how thc distance from a bottom hole asscmbly to a
target well can be determined using the ratio of the Poynting Vector to the gradient of the
Poynting Vector, according to certain illustrative methods of the present disclosure;
FIG. 3D is a flow chart showing how the distance from a bottom hole assembly to a
25 target well can be determined using the gradient of the measured electric field, according to
certain illustrative methods of the present disclosure;
FIG. 3E is a flow chart showing how the distance from a bottom hole assembly to a
target well can be determined using the impedance of the measured electric and magnetic
fields, according to certain illustrative methods of the present disclosure; and
30 FIG. 3F is a flow chart showing how the orientation of thc target well can be
determined using the measured electric field, according to certain illustrative methods of
the present disclosure.
DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS
Illustrative embodiments and related methodologies of the present disclosure are
described below as they might be employed in ranging systems and methods utilizing
triaxial electric and magnetic field measurements to drill and/or track the relative location
5 of wellbores. In the interest of clarity, not all features of an actual implementation or
n~ethodologya re described in this specification. It will of course be appreciated that in the
development of any such actual embodiment, numerous implementation-specific decisions
must be made to achieve the developers' specific goals, such as compliance with systemrelated
and business-related constraints, which will vary from one implementation to
10 another. Moreover, it will be appreciated that such a development effort might be complex
and time-consuming, but would nevertheless be a routine undertaking for those of ordinary
skill in the art having the bcncfit of this disclosure. Furthcr aspects and advantagcs of thc
various embodiments and related methodologies of the disclosure will become apparent
from consideration of the following description and drawings.
15 As described herein, illustrative embodiments and methods of the present disclosure
describe ranging systems that utilize triaxial electric and magnetic field measurements to
retrieve the Poynting vector, which is the measure of the directional energy flux density of
an electromagnetic field. In general, the target well is cased and excited by a time varying
current source. In one embodiment of the disclosure, the target well is excited by a time
20 varying current source at the target well head. In another embodiment of the disclosure, the
targct wcll is cxcited by a timc varying current sourcc on thc surface. In yct anothcr
embodiment, the target well is excited by a time varying current source disposed in the
monitoring well.
Once measured, utilizing various algorithms described herein, processing circuitry
25 located on the bottom hole assembly ("BHA") (andlor at least partially at a remote location
such as on the surface, further up the borehole, or at a facility remote from the well site)
analyzes the triaxial measurement data to determine the distance and direction to the target
casing. It is noted here that the teachings that are disclosed here are also valid for any
elongated conductive body other than a casing. In one embodiment, the direction of the
30 Poynting Vcctor will providc the dircction to the targct well. In anothcr cmbodiment, thc
gradient of the measured Poynting Vector will provide the distance of the target well. In
yet another embodiment, the imaginary component of the measured impedance will provide
the distance of the target well. In another, analysis of both the distance and direction of the
Poynting Vector will provide the orientation of the target well. In yet another embodiment,
analysis of the electric fields will provide the orientation of the target well.
Moreover, as will be described herein, the Poynting Vector, impedance, and electric
fields are rotationally invariant to the orientation of the triaxial electric and magnetic field
5 sensors in the measurement well. Accordingly, in certain embodiments, the sensors can be
rotating as part of the BHA or wireline device, and yet recover the same values of the
Poynting Vector, impedance, and electric fields.
Although the present disclosure may be utilized in a variety of applications, the
following description will focus on applications for accurately, and reliably positioning a
lo well being drilled, the monitoring or "injector" well (i.e., second well), with respect to a
nearby target first well, usually the producer well, so that the injector well can be
n~aintaincd approximatcly parallel to the producer well. The targct well must bc of a
higher conductivity than the surrounding formation, which may be realized through the use
of an elongated conductive body along the target well, such as, for example, casing which
15 is already present in most wells to preserve the integrity of the well. Also, the method and
system of the disclosure are particularly desirable for the drilling of SAGD wells because
the two wells can be drilled close to one another as is required in SAGD operations. These
and other applications andlor adaptations will be understood by those ordinarily skilled in
the art having the benefit of this disclosure.
20 FIG. IA illustrates a relative positioning system 100 according to an exemplary
cmbodimcnt of thc present disclosure. In this embodirncnt, a producer well 10 is drillcd
using any suitable drilling technique. Thereafter, producer well 10 is cased with casing 11.
An injector well 12 is then drilled using BHA 14 which may be, for example, a loggingwhile
drilling ("LWD) assembly, measurement-while drilling assembly ("MWD) or other
25 desired drilling assembly. Although injector well 12 is described as being subsequently
drilled, in other embodiments producer well 10 and injector well 12 may be drilled
simultaneously. Moreover, in yet another alternate embodiment, BHA 14 inay be
embodied as a wireline application (without a drilling assembly) performing logging
operations, as will be understood by those same ordinarily skilled persons mentioned
30 hcrcin.
In this exemplary embodiment, the BHAIdrilling assembly 14 includes one or more
electromagnetic field transmitters 16. Such a transmitter may be, for example, a coil, tilted
coil, or con~binations of electrodes, or other controlled electromagnetic field source.
Drilling assembly 14 also includes one or more triaxial electric and/or magnetic field
sensors 18 positioned above drill bit 20. As understood in the art, the sensors used to
measure electric and magnetic fields are different; however, such sensors may be described
herein separately as electric and magnetic field sensors or jointly as electromagnetic field
5 sensors. Such sensors may include, for example, combinations of electrodes, coils, tilted
coils, magnetometers, or magnetorestrictive sensors. The particular arrangement of sensors
18 along drilling assembly 14 may take a variety of forms. FIGS. IB-ID illustrate a variety
of alternative arrangements for sensors 18. In one illustrative embodiment, the electric and
magnetic fields are measured along the x,y,z axes (is., triaxial) using three collocated
10 electric and magnetic field sensors 18. Such an embodiment is illustrated in FIG. IB,
which illustrates three collocated, orthogonal triaxial magnetic field sensors (e.g., coils)
positioncd along drilling asscrnbly 14 which arc oriented at an anglc of 45 dcgrccs rclativc
to the axis A of drilling assembly 14.
In yet other illustrative embodiments, the radial electric fields can be measured
15 using at least four electrodes at unifonn angles about the mandrel circumference. For
example, four electrode may be used as sensors 18, and are radially positioned around the
mandrel circumference of drilling assembly 14 at angles of 90 degrees, as shown in FIG.
1 C which illustrates a cross-sectional view of drilling assembly 14 extending along second
wellbore 12. In yet another embodiment (not shown), eight electrodes are located at angles
20 of 45 degrees about the mandrel circumference. In yet another alternate embodiment as
shown in FIG. ID, the axial clcctric ficlds can be mcasurcd on drilling asscrnbly 14 using
at least two electrodes sensors 18 axially separated about axis A of the mandrel. In some
embodiments, the electrodes are directly exposed to the drilling fluids and formation, and
operate via galvanic coupling. In other embodiments, the electrodes are not directly
25 exposed to the drilling fluids and formation, and operate via capacitive coupling. In certain
other embodiments, regardless of the sensor design utilized, the centers of each sensor are
collocated. These and other sensor designs may be utilized with the present disclosure, as
will be understood by those ordinarily skilled in the art having the benefit of this
disclosure.
30 Rcfcrring back to FIG. IA, during an cxcmplary drilling opcration using rclativc
positioning system 100, drilling assembly 14 is deployed downhole to drill injector well 12
after, or contemporaneously with, the drilling of producer well 10. In order to maintain
injector well 12 at the desired distance and direction from producer well 10, relative
positioning system 100 activates transmitter 16 to propagate electromagnetic fields 22 to
thereby induce a current along target casing 11 of producer well 10. As a result,
electromagnetic fields 24 radiate from target casing 11, where the triaxial electric and
magnetic fields are measured by sensors 18. Local or remote processing circuitry then
5 utilizes the triaxial electromagnetic field measurements to determine the distance or
direction to producer well 10, in addition to the orientation of producer well 10. Once the
relative position is determined, the circuitry generates signals necessary to steer the drilling
assembly 14 in the direction needed to maintain the desired distance and direction from
producer well 10.
10 Although not shown, note that in alternate embodiments the current along casing 11
may be excited by a time varying current source at the target well head. In another
embodirncnt of the disclosurc, the target wcll is cxcited by a currcnt source on the surface.
Furthermore, although not shown as well, drilling assembly 14 includes processing
circuitry necessary (i.e., system control center) to achieve the relative positioning of the
15 present disclosure in real-time. Such circuitry includes a communicatio~~usn it to facilitate
interaction between drilling system 14 and a remote location (such as the surface). A
visualization unit may also be connected to communications unit to monitor the
measurement data being process; for example, an operator may intervene the system
operations based on this data. A data processing unit may convert the received data into
20 information giving the target's position, direction and orientation in real-time. Thereafter,
rcsults may be displaycd via the visualizing unit.
The system control center of drilling assembly 14 also includes the
storage/communication circuitry necessary to perform the calculations described herein. In
certain embodiments, that circuitry is con~inunicablyc oupled to trailsnlitters 16 utilized to
25 generate electromagnetic fields 22, and also likewise coupled to sensors 18 in order to
process the received electric and magnetic fields forming the electromagnetic field 24.
Additionally, the circuitry on-board drilling assembly 14 may be communicably coupled
via wired or wireless connections to the surface to thereby communicate data back uphole
and/or to other assembly components (to steer a drill bit forming part of assembly 14, for
30 cxamplc). In an altcrnatc cinbodiment, thc system control ccntcr or othcr circuitry
necessary to perform one or more aspects of the techniques described herein may be
located at a remote location away from drilling assembly 14, such as the surface or in a
different wellbore. For example, in certain embodiments, the transmitter may be located in
another well or at the surface. In other embodiments, the electromagnetic field
measurements may be communicated remotely to the system control center for processing.
These and other variations will be readily apparent to those ordinarily skilled in the art
having the benefit of this disclosure.
5 Moreover, the on-board circuitry includes at least one processor and a nontransitory
and computer-readable storage, all interconnected via a system bus. Software
instructions executable by the system control center for implementing the illustrative
relative positioning methodologies described herein in may be stored in local storage or
some other computer-readable medium. It will also be recognized that the positioning
lo software instructions may also be loaded into the storage from a CD-ROM or other
appropriate storage media via wired or wireless methods.
Moreover, those ordinarily skilled in thc art will appreciate that various aspects of
the disclosure may be practiced with a variety of computer-system configurations,
including hand-held devices, multiprocessor systems, microprocessor-based or
15 programmable-consu~ller electronics, minicon~puters, nlainfraille computers, and the like.
Any number of computer-systems and computer networks are acceptable for use with the
present disclosure. The disclosure may be practiced in distributed-computing
environments where tasks are performed by remote-processing devices that are linked
through a communications network. In a distributed-computing environment, program
20 modules may be located in both local and remote computer-storage media including
memory storage devices. The present disclosure may therefore, be implemented in
connection with various hardware, software or a combination thereof in a computer system
or other processing system.
Now that a generalized illustrative embodinlent of the present disclosure has been
25 described, the methodology by which relative positioning is determined will now be
described. As previously mentioned, embodiments of the present disclosure utilize both
electric and magnetic field measurements for electromagnetic ranging. Illustrative
embodiments may be exemplified in the following theoretical example, which is not
intended to limit the scope of disclosure. With reference to FIG. lA, target well 10 may be
30 defined by the triaxial coordinate system r = (x, y, z} and can be approximated by an
infinitely long current source oriented in the z direction in a homogeneous geological
formation of conductivity o such that the electric current along casing 11 can be
approximated as:
J(r)= I&-S)(z ) GZ, Eq.(l).
Here, J(r) is the current density, I is the current, 6(r) and 6(z) are delta functions, and G7. is
a unit vector directed along the axis of the current source. Given the radial symmetry about
targct wcll 10, clcctromagnetic fields 24 can be described in cylindrical coordinates r = (z,
5 p, 8) about the z-axis. Note that the cylindrical coordinates r = (z, p, 0) can be transformed
to Cartesian coordinates r = (x,y,z), and vice versa. Of particular interest to
electromagnetic ranging is the distance to target well 10, p = d(x2 + 9) (note that d denotes
the square root), and the direction (angle) to target well 10, 6. The orientation of target
well 10 relative to drilling assembly 14 can be also be retrieved.
LO As will be understood by those ordinarily skilled in the art having the benefit of this
disclosure, the electric field at an angular frequency w about target well 10 only has a zdirected
axial component:
E, (r,w ) = ((iwpo/(2n))Ko(ikp)Gz, Eq.(2),
Where k = d(iw,uo) is the wavenumber, p is the radial distance between the two wells in the
15 xyxy-plane, and KO is the modified Bessel hnction of the second kind of order zero. It is
also noted here that in a case where target well 10 is aligned with the axial direction of
drilling asseinbly 10, the z-directed axial component of the electric field can be measured
by placing two axially separated sensors/receivers 18 (e.g., electrodes) along drilling
asscmbly 14.
20 Therefore, it follows that the magnetic field at an angular frequency w about target
well 10 has a 0-directed tangential component:
Ho (r,w ) = ((ik4/(2n ) ) K~(ikpQ) a Eq-(3),
where K1 is the modified Bessel function of the second kind of order one, and fie is a unit
vector in thc azimuthal dircction about thc axis of the currcnt source. At low frequencies
25 used for and small distances typically encountered in electromagnetic ranging, the modified
Bessel functions in Equations (2) and (3) can be approximated by:
KO (ikp)- - ln (ikp) Eq.(4), and
K~(ikp)= -l/(ikp") %(5)
such that the electric field (Eq.2) and magnetic field (Eq.3) at an angular frequency w are
30 respectively expressed as:
Ez (r,w ) = - ((iwpo/ (2n )) ln (ikp)G z Eq.(6), and
Ho(r,w) =- I/(2np) GO Eq.(7).
Originating from conservation of energy considerations, the Poynting Theorem generally
states that for any electron~agnetic field, there must be electron~agnetic energy flowing in
the medium due to the electromagnetic fields. The Poynting Vector, S, which is the
measure of the directional energy flux density of an electromagnetic field, can be derived
s from the cross product of the electric E and magnetic H field vectors. For linear dispersive
media with losses, which is typical for earth materials, the Poynting Vector is defined in the
frequency domain as:
S = .5E x H* = .5(EyPz - EzPy)Qx+ .5(EzPx- ExPz)Qy + .5(ExPy - EYPx)&
Eq.(8)7
lo where * denotes the complex conjugate, and Qx, Qy, and Q are unit vectors in in x-, y-, and
z-directed unit vectors in Cartesian coordinates relative to the axis of the current source. In
cylindrical coordinates, the Poynting Vector (Eq.8) is express as:
S = .5E x H* = .5(EoP, - EzPe)Qr + .5 ( E x z - EzPr)Qe + .5(ErPe - E0Pr)fiz
Eq.(9)7
1s where Qr, Qe, and Q, are radial-, azimuthal-, and axial-directed unit vectors in cylindrical
coordinates relative to the axis of the current source. Fro111 Equations 6 and 7 above,
Equation 9 may be reduced to:
S=.5ExH*=(-.5EzH*e)Qr=-((iu~r/2)/(4n2p))ln(ikp)Qr W.(lO).
In the illustrative embodiments of the present disclosure, the system control center
20 utilizes the method described above to achieve the relative positioning calculations
described herein. FIG. 2 is a flow chart showing a generalized ranging method 200 used to
calculate the distancc bctwecn a first target wcll and a sccond wcll, thc dircction to the first
target well, or the orientation of the first target well, according to certain illustrative
methods of the present disclosure. Again, the specific application may be, for example, a
25 SAGD application. With reference to FIGS. 1 and 2, at block 202, a first wellbore 10 is
drilled using any suitable methodology. First wellbore 10 has a higher conductivity than
the surrounding formation which, for example, may be achieved using casing 11 of first
wellbore 10 or through utilization of some other elongated conductive body positioned
along first wellbore 10.
30 At block 204, one or more electric andlor magnetic sensors 18 are deployed into a
sccond wcllborc 12. In certain embodiments, thcrc may be two scnsors that arc radially
separated along the axis of second wellbore 12. Sensors 18 may be deployed in second
wellbore 12 in a variety of ways including, for example, along drilling assembly 14 utilized
in a SAGD operation or a subsea operation. Note that in alternative methodologies, the
first and second wellbores 10,12 may be drilled contemporaneously.
At block 206, a current is induced along first wellbore 10 which results in an
electromagnetic field 24 being emitted from first wellbore 10. In general, the current is
5 induced using a time varying current source that may be generated in a variety of ways. In
one embodiment of the disclosure, the current is induced along casing 1 1 by a time varying
current source at the well head of first wellbore 10. In another embodiment of the
disclosure, the current is induced along casing 11 by a time varying current source on the
surface. In yet another embodiment as shown in FIG. 1, the current is induced along casing
lo 11 by an electromagnetic transmitter 16 positioned along drilling assembly 14 in second
well 12.
At block 208, the clcctromagnctic field 24 is thcn rcccivcd by sensor(s) 18. As will
be described in more detail below, at block 210, via the system control center, the relative
positioning system 100 utilizes the measured triaxial electric or magnetic fields to
15 calculate, in real-time, the distance between the first and second wellbores, the direction to
the first wellbore relative to the second wellbore, or the orientation of the first wellbore.
After analyzing the measured triaxial electromagnetic fields, relative positioning system
100 determines what actions, if any, are necessary to maintain or correct the desired drilling
path at block 212. Such actions may be, for example, a change in direction, speed, weight
20 011 bit, etc., to thereby steer the BHA as desired. Simultaneously, the algorithm returns to
block 206 whcrc it continucs to cxcitc the transmitters to continuously monitor andlor
adjust the drill path as necessary.
FIG. 3A is a flow chart of a method 300 utilized to calculate direction, distance and
orientation of a target well using triaxial electric and magnetic field measurements,
25 according to certain illustrate methods of the present disclosure. After current has been
induced along the casing, the emitted electromagnetic field 24 (FIG. 1A) is sensed by
sensors 18 as previously described. At block 330, the transient triaxial electric and
magnetic fields are measured by sensors 18. At block 304, the system control center of the
relative positioning system then transforms (e.g., using Fourier transform) the measured
30 clcctric and rnagnctic fields into thcir rcspcctivc frequency-domain clcctric and rnagnctic
fields, as defined by Equations 6 and 7 described above. The system control center may
then utilize the frequency-domain electric and magnetic fields in a variety of algorithms to
conduct ranging, as described in the illustrate flow charts of FIGS. 3B-3F.
FIG. 3B is a flow chart showing how the direction from a BHA to a target well can
be determined using the Poynting Vector, according to certain illustrative methods of the
present disclosure. At block 306, the system control center first calculates the Poynting
Vector using Equations 8-10. It can be observed that S in Equation 10 is always directed
5 along fir towards the target well. Thus, by evaluating the Poynting Vector from triaxial
electric and magnetic field measurements, the system control center determines the
direction to the target well at block 308. The magnetic field is actually recovered from
magnetic induction measurements. It follows that the magnitude of Equation 10 is scaled
by the magnetic permeability, but the direction of the Poynting Vector remains unchanged.
lo While Equation 10 demonstrates it is possible to recover the direction to the target well
from the Poynting Vector, Equation 10 also demonstrates that it is not straightforward to
recover the distance to the target well from the Poynting Vector, as the magnitude of
Equation 10 is a nonlinear bction with respect to the range p, and is dependent upon the
current, wavenumber, and permeability of the medium; all of which may be unknown.
1s FIG. 3C is a flow chart showing how the distance from a BHA to a target well can
be determined using the ratio of the Poynting Vector to the gradient of the Poynting Vector,
according to certain illustrative methods of the present disclosure. Using the data from
blocks 304 and 306, the system control center calculates the Poynting Vector gradient at
block 3 10. Here, the system control center calculates the gradient of the Poynting Vector
20 dS/dp using:
dS/dp = ((iwp/Z)/(4n2~)()1 - In (ikp))t ir, Eq.(l 11,
where the variables were defined previously. The ratio of the Poynting Vector to the
gradient of the Poynting Vector can then be calculated using:
p(ll((1- In(iW)) - 1) = lSl/(IdS/dpO, Eq.(12),
25 which, for likpl< l ( - l l P >= IEzl/(laEJaPl), Eq.(17),
which simplifies as:
Is P= - I E ~ I I ( I ~ E . J ~ P I ) , Eq.(lZI).
As a result of Equation 18, at block 316, the distance can be calculated from the
absolute value and gradient of the electric field vector by utilizing the finite difference in
space for the gradient, the same way it is traditionally done for the magnetic fields.
Gradient measurements of the electric fields require multiple electric field measurements,
20 instead of the multiple magnetic field measurements that are traditionally used.
FIG. 3E is a flow chart showing how the distance from a BHA to a target well can
be determined using the impedance of the measured electric and magnetic fields, according
to certain illustrative methods of the present disclosure. To calculate the distance in this
illustrative method, the system control center calculates the impedance at block 318 using
2s the impedance transfer function Z(r,w):
Z(r, w) = (Ez(r,rn))/(ffe(r,o)) = - iwpIpln(ikp) Eq.(l9),
where the variables were defined previously. Using L'Hopital's rule as ikp -t 0, it follows
that:
((11~I)( - l l P ) ) = (Ez(r,rn))l(He(r,rn)), Eq.(20),
30 which reduces to:
P = (Il~~llm[(G(r,~))l(ffe(r,rn))l, Eq.(2 I),
where Im represents the imaginary component of the impedance at a radial frequency,
scalcd by a product of the angular frequency and magnetic pcrmcability. As a rcsult, at
block 320, the system control center calculates the distance from a combination of electric
and magnetic field measurements and also two parameters; frequency and magnetic
permeability. For most formations, the magnetic permeability can be assumed to be that of
free space (i.e., non-magnetic). In this illustrative method, the magnetic field is actually
5 recovered from magnetic induction measurements, and it follows that Equation 21 can be
expressed as:
P = (114 Im[(&(r,w))l(Be(r,w))I, Eq.(22),
which illustrates that the systcm control ccntcr may calculatc the distance using a
combination of the measured electric field and magnetic induction measurements, as well
lo as the angular frequency.
The orientation independent of the triaxial measurements described herein should
also be noted. As previously mentioned, the triaxial electric and magnetic fields are
measured by sensors attached to a BHA, and are defined by the Cartesian coordinate
system r ' = {x ', y ', z ') , which is related to the Cartesian coordinate system of the target
15 well r = {x, y, z) through the three (generally unknown) Euler angles u, ,4, 8:
r ' = R(u, p, (a)r Eq.(23),
where R(u, p, (a) is the Euler rotation matrix. The rotational invariance of the cross product
states that:
S(r',a) = R(a, ,4, q)S(r,o) = .5E(r',a) x H*(rJ,o) = .5R(u, ,4, q)E(r,o) x R(u, P,
20 q)H*(r,a),
Ecl.(24),
which preserves both the amplitude and the direction of the Poynting Vector, regardless of
the coordinate system r' = {x', y', z'). The Euler rotation matrix R(u, ,4, (a) can be
retrieved by Procrustes analysis:
25 lIS(r,a) - R-'(% pt (a)S(r ',a)ll~ -f min, Eq.(25),
subject to the constraint S,(r,w) = 0. In particular, Equation 25 enables the relative
direction and orientation between the BHA and the target well to be estimated when the
two are not parallel.
It also follows that the amplitudes of the total axial electric and total tangential
30 magnetic fields in the cylindrical coordinate system r = (z, y, 8):
IEZ(r,w)l= d ( ~ ~ '~,a,) (+r E ~(r~9,a,)+ EZz,( r ',a)), Eq.(26), and
I Hs(r,w)l = d(H2,.(r ',o+) H ~(r~ ',o), + H'~.( r ',a)), Eq.(27)
are equal to the amplitude of the total electric and magnetic field vectors measured in the
BHA's coordinate system r ' = {x ', y ', z ') . Accordingly, the measured electric and
magnetic fields described herein, as well as the Poynting Vector calculated using the
ranging method described by Equation 12, are rotationally invariant to the coordinate
5 system of the BHA.
FIG. 3F is a flow chart showing how the orientation of the target well can be
determined using the measured electric field, according to certain illustrative methods of
the prcscnt disclosurc. Here, at block 322, the system control ccntcr first calculates the
electric field vector using Equation 26. It is observed that the measured electric field in
lo Equation 26 is always directed along the z-axis, which is the target well's axial direction,
regardless of the orientation of the BHA. Thus, by evaluating the electric field vector from
triaxial electric field measurements, the system control center can determine the orientation
of the target well at block 324. This is especially useful in situations where the axis of the
target well is not parallel to the BHA axis.
15 Although triaxial electric and magnetic field measurements have been described
herein, the present disclosure may also be utilized to conduct ranging using one or two
mcasurcd componcnts of thc clcctric and magnetic ficlds rather than complctc triaxial
measurements of the electric and magnetic fields. Thus, in certain illustrative methods,
components of the electric field alone may be utilized to calculate the distance to the target
20 well or the direction of the target well, which may be accomplished by appropriately
choosing the electrode configuration such that Equation 26 is approximated with one or
two measured components of the electric field, rather than all three components of the
electric field.
In yet other illustrative methods, components of the magnetic field may also be used
2s along with the non-triaxial electric field measurement to calculate the distance and
dircction to the targct well. Again, this may be accomplishcd by appropriatcly choosing thc
magnetic field sensor orientations such that Equation 27 is approximated with one or two
measured components of the magnetic field, rather than all three components of the
magnetic field.
30 Although the present disclosure has focused on SAGD applications, systems and
methods of the present disclosure may also be utilized in well avoidance applications.
Here, a second well may be drilled, wherein the relative positioning system is used to avoid
a first well. Other applications include T-intersection applications, in which a relief well
must be drilled in order to relieve a blown out well. These and other applications will be
apparent to those ordinarily skilled in the art having the benefit of this disclosure.
Embodiments described herein further relate to any one or more of the following
paragraphs :
5 1. A method for downhole ranging, comprising drilling a first wellbore, the
first wellbore comprising an elongated conductive body; deploying an electric field
sensor in a second wellbore; inducing a current along the first wellbore that results in an
electromagnetic field being emitted from the first wellbore; receiving the electromagnetic
field utilizing the electric field sensor, wherein an electric field of the electromagnetic field
lo is measured; and utilizing the measured electric field to thereby calculate: a distance
between the first and second wellbores; or a direction of the first wellbore in relation to the
sccond wcllborc.
2. A method as defined in paragraph 1, wherein the direction of the first
wellbore is a direction of the measured electric field.
15 3. A method as defined in any of paragraphs 1-2, further comprising
determining an orientation of the first wellbore using the measured electric field.
4. A method as defined in any of paragraphs 1-3, hrther comprising
calculating a gradient of the measured electric field.
5. A method as defined in any of paragraphs 1-4, further comprising
20 calculating a ratio of the measured electric field to the gradient of the measured electric
ficld; and calculating thc distance bctwecn the first and second wcllbores using the ratio.
6. A method as defined in any of paragraphs 1-5, wherein a magnetic field
sensor is deployed in the second wellbore, the method further comprising measuring a
magnetic field of the electromagnetic field; and utilizing the measured electric field and
25 measured magnetic field to thereby calculate the distance between the first and second
wellbores or the direction of the first wellbore in relation to the second wellbore.
7. A method as defined in any of paragraphs 1-6, further comprising utilizing
the measured electric and magnetic fields to calculate a Poynting Vector; and utilizing the
Poynting Vector to calculate the distance between the first and second wellbores or the
30 dircction of thc first wcllbore in relation to thc sccond wcllborc.
8. A method as defined in any of paragraphs 1-7, wherein the direction of the
first wellbore is a direction of the Poynting Vector.
9. A method as defined in any of paragraphs 1-8, further conlprising
calculating a gradient of the Poynting Vector.
10. A method as defined in any of paragraphs 1-9, further comprising
calculating a ratio of the Poynting Vector to the gradient of the Poynting Vector; and
5 calculating the distance between the first and second wellbores using the ratio.
1 1. A nlethod as defined in any of paragraphs 1 - 10, further compi-ising
calculating an impedance of the measured electric and magnetic fields.
12. A method as defined in any of paragraphs 1-11, further comprising
calculating the distance between the fist and second wellbores using the impedance.
LO 13. A method as defined in any of paragraphs 1-12, wherein calculating the
distance comprises calculating a ratio of an imaginary component of the impedance at a
radial frequency to a product of the radial frequency and magnetic permeability; and
calculating the distance between the first and second wellbores using the ratio.
14. A method as defined in any of paragraphs 1-13, wherein the measured
15 electric field is a triaxial electric field ineasurenlent.
15. A method as defined in any of paragraphs 1-14, wherein the measured
magnetic field is a triaxial magnetic field measurement.
16. A method as defined in any of paragraphs 1-1 5, wherein the measured
electric and magnetic fields are total electric and magnetic fields; and the measured total
20 electric and magnetic fields are rotationally invariant.
17. A method as defined in any of paragraphs 1-16, wherein the calculated
Poynting Vectors are rotationally invariant.
18. A method as defined in any of paragraphs 1-17, wherein the distance or
direction calculatioils are conducted in real-time.
25 19. A method as defined in any of paragraphs 1-18, wherein the
electromagnetic sensor in the second wellbore in deployed on a bottom hole assembly.
20. A method as defined in any of parapdphs 1-19, wherein the bottom hole
assembly is a drilling assembly, logging assembly, or wireline assembly.
21. A method as defined in any of paragraphs 1-20, further comprising steering
30 the bottom hole assembly deployed along the second wellborc using thc distancc or
direction calculations.
22. A method as defined in any of paragraphs 1-20, wherein an axis of the
bottom hole assembly is not parallel with an axis of the first wellbore.
23. A method as defined in any of paragraphs 1-22, wherein the first wellbore is
a producer well; and the second wellbore is an injector well, wherein the method is utilized
in a Steam Assisted Gravity Drainage operation.
24. A method as defined in any of paragraphs 1-23, wherein the first wellbore is
5 a blow out well and the second wellbore is a relief well.
25. A method as defined in any of paragraphs 1-23, further coitlprises avoiding
the first wellbore using the distance calculation.
26. A method as defined in any of paragraphs 1-25, wherein inducing the
current along the first wellbore comprises inducing the current using a time-varying current
lo source at a wellhead of the first well; a time-varying current source at a surface location; or
a time-varying current source along the bottom hole assembly.
27. A relativc positioning systcm for downhole ranging, comprising a bottom
hole assembly to be positioned along a monitoring well; one or more triaxial electric and
magnetic field senqors positioned along the bottom hole assembly; and processing circuitry
15 coupled to the sensors and configured to ii~lplen~ena tn lethod cottlprising: measuring an
electric field emitted from a target well; and utilizing the measured electric field to thereby
calculate: a distance between the monitoring well and the target well; or a direction of
the target well in relation to the monitoring well.
28. A relative positioning system as defined in paragraph 27, further comprising
20 an electromagnetic transmitter positioned along the bottom hole assembly.
29. A relativc positioning system as defincd in any of paragraphs 27-28,
wherein the sensors are three collocated, orthogonal magnetic coils oriented at an angle of
45 degrees relative to an axis of the bottom hole assembly; at least four electrodes
positioned radially positioned around the bottom hole assembly; or at least two electrodes
25 axially separated along the bottom hole assembly.
30. A relative positioning system as defined in any of paragraphs 27-29,
wherein the bottom hole assembly is a drilling assembly, logging assembly or wireline
assembly.
31. A relative positioning system as defined in any of paragraphs 27-30,
30 whcrcin the processing circuitry is fk-ther configured to implcment any of the mcthods of
claims 3-17.
Moreover, the methodologies described herein may be embodied within a system
comprising processing circuitry to inlpleillent any of the methods, or a in a computerprogram
product comprising instructions which, when executed by at least one processor,
causes the processor to perform any of the methods described herein.
Accordingly, through use of the foregoing illustrative systems and methods, the
distance, direction and orientation of a target well can be retrieved through rotationally
s invariant analysis of triaxial electric and magnetic field measurements from a BHA having
electromagnetic sensors. The triaxial electric and magnetic field sensors can be deployed
in any downhole device without explicitly needing to process or retrieve rotational
information about the downhole BHA or wireline device. Moreover, the distance, direction
and orientation of the target well can be retrieved from a single measurement position.
LO The advantages of the present disclosure are numerous. For example, such
advantages include: direct measurement of the electric field andlor electric field gradients
gcncratcd by thc targct wcll using triaxial clcctric ficld scnsors; thc dircction of thc
measured electric field retrieves the orientation of the target well; the direction of the target
well is retrieved from the measured electric field and electric field gradient; direct
15 measurement of the Poynting Vector andlor Poynting Vector gradients of electromagnetic
fields generated by the target well using triaxial electric and magnetic field sensors; the
direction of the Poynting Vector retrieves the direction to and orientation of the target well;
direct measurement of the impedance transfer function of electromagnetic fields generated
by the target well using triaxial electric and magnetic field sensors; the impedance transfer
20 hnction retrieves the distance to the target well; rotational invariance of the electric fields,
clcctric ficld gradients, Poynting Vector, Poynting Vcctor gradient, and the impedancc
transfer function relative to sensor orientation; and real-time integration with drilling
systems.
Although various embodiments and methodologies have been shown and described,
2s the disclosure is not limited to such embodiments and methodologies and will be
understood to include all modifications and variations as would be apparent to one skilled
in the art. Therefore, it should be understood that the disclosure is not intended to be
limited to the particular forms disclosed. Rather, the intention is to cover all modifications,
equivalents and alternatives falling within the spirit and scope of the disclosure as defined
30 by the appcndcd claims.
CLAIMS
WHAT IS CLAIMED IS:
1. A method for downhole ranging, comprising:
5 drilling a first wellbore, the first wellbore comprising an elongated conductive
body; deploying an electric field sensor in a second wellbore;
inducing a current along the first wellbore that results in an electromagnetic field
being emitted from the first wellbore;
receiving the electromagnetic field utilizing the electric field sensor, wherein an
lo electric field of the electromagnetic field is measured; and
utilizing the measured electric field to thereby calculate:
a distance between thc first and sccond wellborcs; or
a direction of the first wellbore in relation to the second wellbore.
2. A method as defined in claim 1, wherein the direction of the first wellbore is a
15 direction of the measured electric field.
3. A method as defined in claim 1, further comprising determining an orientation of
the first wellbore using the measured electric field.
4. A method as defined in claim 1, fbrther comprising calculating a gradient of the
measured electric field.
20 5. A method as defined in claim 4, further comprising:
calculating a ratio of the measured electric field to the gradient of the measured
electric field; and
calculating the distance between the first and second wellbores using the ratio.
6. A method as defined in claim 1, wherein a magnetic field sensor is also deployed in
25 the second wellbore, the method further comprising:
measuring a magnetic field of the electromagnetic field; and
utilizing the measured electric field and measured magnetic field to thereby
calculate:
the distance between the first and second wellbores; or
30 thc dircction of the first wellborc in rclation to the sccond wellbore.
7. A method as defined in claim 6, further comprising:
utilizing the measured electric and magnetic fields to calculate a Poynting Vector;
and utilizing the Poynting Vector to calculate:
the distance between the first and second wellbores; or
5 the direction of the first wellbore in relation to the second wellbore.
8. A method as defined in claim 7, wherein the direction of the first wellbore is a
direction of the Poynting Vector.
9. A method as defined in claim 7, further comprising calculating a gradient of the
Poynting Vector.
lo 10. A method as defined in claim 9, further comprising:
calculating a ratio of the Poynting Vector to the gradient of the Poyntiilg Vector;
and calculating the distance between the first and second wellbores using the ratio.
1 I. A method as defined in claim 6, further comprising calculating an impedance of the
measured electric and magnetic fields.
1s 12. A method as defined in claim 11, fiu-ther comprising calculating the distance
between the first and second wellbores using the impedance.
1 3. A method as defined in claim 12, wherein calculating the distance comprises:
calculating a ratio of an imaginary component of the impedance at a radial
frequency to a product of the radial frequency and magnetic permeability; and
20 calculating the distance between the first and second wellbores using the ratio.
14. A method as defined in claim 1, wherein the measured electric field is a triaxial
electric field measurement.
15. A method as defined in claim 6, wherein the measured magnetic field is a triaxial
magnetic field measurement.
25 16. A method as defined in claim 6, wherein:
the measured electric and magnetic fields are total electric and magnetic fields; and
the measured total electric and magnetic fields are rotationally invariant.
17. A method as defined in claim 7, wherein the calculated Poynting Vectors are
rotationally invariant.
18. A method as defined in claim 1, wherein the distance or direction calculations are
conducted in real-time.
s 19. A method as defined in claim 1, wherein the electric field sensor in the second
wellbore in deployed on a bottom hole assembly.
20. A 111ethod as defined in claim 19, wherein the bottom hole assembly is a drilling
assembly, logging assembly, or wireline assembly.
21. A method as defined in claim 19, further comprising steering the bottom hole
10 assenlbly deployed along the second wellbore using the distance or direction calculations.
22. A method as defined in claim 19, wherein an axis of the bottom hole assembly is
not parallel with an axis of the first wellbore.
23. A method as defined in claim 1, wherein:
the first wellbore is a producer well; and
15 the second wellbore is an injector well, wherein the method is utilized in a Steam
Assisted Gravity Drainage operation.
24. A method as defined in claim 1, wherein:
the first wellbore is a blow out well; and
the second wellbore is a relief well.
20 25. A method as defined in claim 1, hrther conlprises avoiding the first wellbore using
the distance calculation.
26. A method as defined in claim 19, wherein inducing the current along the first
wellbore comprises inducing the current using:
a time-varying current source at a wellhead of the first well;
2s a time-varying current source at a surface location; or
a time-varying current source along the bottom hole assembly.