MAGNETIC MONOPOLE RANGING SYSTEM AND METHODOLOGY
BACKGROUND
The present disclosure relates generally to oil field exploration and, more
particularly, to a magnetic monopole positioning and ranging system and methodology.
In the traditional induction tools used in oil field exploration, coil type antennas
are used to transmit and receive electromagnetic signals. Typically, these coil type antennas have
included magnetic dipoles. Each of the antenna types may radiate an electromagnetic field with a
different radiation pattern. The radiation patterns may limit the effectiveness of the tools to
certain downhole applications in certain formation types.
FIGURES
Some specific exemplary embodiments of the disclosure may be understood by
referring, in part, to the following description and the accompanying drawings.
FIG. 1 is a diagram that illustrates an example drilling system, according to
aspects of the present disclosure.
FIG. 3 is a diagram that illustrates an example magnetic monopole logging
system, according to aspects of the present disclosure.
FIGS. 3A-B are diagrams illustrating the difference between a magnetic
monopole element and a magnetic dipole element, according to aspects of the present disclosure.
FIGS. 4A-C are charts that illustrate the magnetic field direction and field
strength contour lines for an infinitesimal magnetic dipole oriented in z-direction.
FIGS. 5A-C are charts that illustrate the magnetic field direction and field
strength contour lines for a finite length magnetic dipole.
FIGS. 6A-C are charts that illustrate the magnetic field direction and field
strength contour lines for a magnetic monopole, according to aspects of the present disclosure.
FIG. 7 is a diagram that illustrates two isolated magnetic poles, according to
aspects of the present disclosure.
FIGS. 8A-B are charts that illustrate the voltage and frequency responses caused
by a magnetic monopole antenna compared to a magnetic dipole antenna, according to aspects of
the present disclosure.
FIG. 9 is a diagram that illustrates a monopole magnetic field measured by a
biaxial receiver, according to aspects of the present disclosure.
FIG. 10 is a diagram illustrating an example positioning system, according to
aspects of the present disclosure.
FIGS. 11A-F are charts that illustrate the results of an example positioning
simulation with synthetic data, according to aspects of the present disclosure.
FIG. 1 is a diagram that illustrates example receivers and R2 for the derivative
operation, according to aspects of the present disclosure.
FIGS. 13A-F are charts that illustrate the results of an example ranging simulation
with synthetic data, according to aspects of the present disclosure.
FIG. 14 is a diagram of an example drilling system utilizing magnetic monopoles,
according to aspects of the present disclosure.
FIG. 15 is a diagram of an example drilling system utilizing magnetic monopoles,
according to aspects of the present disclosure.
While embodiments of this disclosure have been depicted and described and are
defined by reference to exemplary embodiments of the disclosure, such references do not imply a
limitation on the disclosure, and no such limitation is to be inferred. The subject matter disclosed
is capable of considerable modification, alteration, and equivalents in form and function, as will
occur to those skilled in the pertinent art and having the benefit of this disclosure. The depicted
and described embodiments of this disclosure are examples only, and not exhaustive of the scope
of the disclosure.
DETAILED DESCRIPTION
For purposes of this disclosure, an information handling system may include any
instrumentality or aggregate of instrumentalities operable to compute, classify, process, transmit,
receive, retrieve, originate, switch, store, display, manifest, detect, record, reproduce, handle, or
utilize any form of information, intelligence, or data for business, scientific, control, or other
purposes. For example, an information handling system may be a personal computer, a network
storage device, or any other suitable device and may vary in size, shape, performance,
functionality, and price. The information handling system may include random access
memory (RAM), one or more processing resources such as a central processing unit (CPU) or
hardware or software control logic, ROM, and/or other types of nonvolatile memory. Additional
components of the information handling system may include one or more disk drives, one or
more network ports for communication with external devices as well as various input and
output (I/O) devices, such as a keyboard, a mouse, and a video display. The information handling
system may also include one or more buses operable to transmit communications between the
various hardware components. It may also include one or more interface units capable of
transmitting one or more signals to a controller, actuator, or like device.
For the purposes of this disclosure, computer-readable media may include any
instrumentality or aggregation of instrumentalities that may retain data and/or instructions for a
period of time. Computer-readable media may include, for example, without limitation, storage
media such as a direct access storage device (e.g., a hard disk drive or floppy disk drive), a
sequential access storage device (e.g., a tape disk drive), compact disk, CD-ROM, DVD, RAM,
ROM, electrically erasable programmable read-only memory (EEPROM), and/or flash memory;
as well as communications media such wires, optical fibers, microwaves, radio waves, and other
electromagnetic and/or optical carriers; and/or any combination of the foregoing.
Illustrative embodiments of the present disclosure are described in detail herein.
In the interest of clarity, not all features of an actual implementation may be 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 specific
implementation goals, which will vary from one implementation to 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 benefit of
the present disclosure.
To facilitate a better understanding of the present disclosure, the following
examples of certain embodiments are given. In no way should the following examples be read to
limit, or define, the scope of the disclosure. Embodiments of the present disclosure may be
applicable to target (such as to an adjacent well) following, target intersecting, target locating,
well twining such as in SAGD (steam assist gravity drainage) well structures, relief wells for
blowout wells, river crossing, construction tunneling, horizontal, vertical, deviated, multilateral,
u-tube connection, intersection, bypass (drill around a mid-depth stuck fish and back into the
well below), or otherwise nonlinear wellbores in any type of subterranean formation.
Embodiments may be applicable to injection wells, and production wells, including natural
resource production wells such as hydrogen sulfide, hydrocarbons or geothermal wells; as well
as borehole construction for river crossing tunneling and other such tunneling boreholes for near
surface construction purposes or borehole u-tube pipelines used for the transportation of fluids
such as hydrocarbons. Embodiments described below with respect to one implementation are
not intended to be limiting.
The terms "couple" or "couples" as used herein are intended to mean either an
indirect or a direct connection. Thus, if a first device couples to a second device, that connection
may be through a direct connection or through an indirect mechanical or electrical connection
via other devices and connections. Similarly, the term "communicatively coupled" as used herein
is intended to mean either a direct or an indirect communication connection. Such connection
may be a wired or wireless connection such as, for example, Ethernet or LAN. Such wired and
wireless connections are well known to those of ordinary skill in the art and will therefore not be
discussed in detail herein. Thus, if a first device communicatively couples to a second device,
that connection may be through a direct connection, or through an indirect communication
connection via other devices and connections.
Modern petroleum drilling and production operations demand information
relating to parameters and conditions downhole. Several methods exist for downhole
information collection, including logging while drilling ("LWD") and measurement-while
drilling ("MWD"). In LWD, data is typically collected during the drilling process, thereby
avoiding any need to remove the drilling assembly to insert a wireline logging tool. LWD
consequently allows the driller to make accurate real-time modifications or corrections to
optimize performance while minimizing down time. MWD is the term for measuring conditions
downhole concerning the movement and location of the drilling assembly while the drilling
continues. LWD concentrates more on formation parameter measurement. While distinctions
between MWD and LWD may exist, the terms MWD and LWD often are used interchangeably.
For the purposes of this disclosure, the term LWD will be used with the understanding that this
term encompasses both the collection of formation parameters and the collection of information
relating to the movement and position of the drilling assembly.
FIG. 1 is a diagram illustrating an example drilling system 100, according to
aspects of the present disclosure. The drilling system 100 includes rig 101 at the surface 11 and
positioned above borehole 103 within a subterranean formation 102 that comprises a plurality of
formation strata 102a-c. The formation strata 102a-c may comprise different types of rock with
different characteristics (e.g. porosity, resistivity, permeability, etc.), separated by boundaries.
Certain of the formation strata 102a-c may contain hydrocarbons, and the drilling system 100
may extend the borehole 103 until that formation strata is contacted.
The drilling system 100 may comprise a drilling assembly 104 coupled to the rig
101. The drilling assembly 104 may comprise a drill string 105 and bottom hole assembly
(BHA) 106. The drill string 105 may comprise a plurality of pipe segments that are threadedly
connected. In the embodiment shown, the drill string 105 is positioned within a well casing or
liner 112. The casing 12 may comprise a metal tubular secured within the borehole 103 using
cement, for example, and may function to prevent the borehole 103 from collapsing during the
drilling process.
The BHA 106 may comprise a drill bit 109, a steering assembly 108, a
LWD/MWD apparatus 107, and telemetry system 114. The steering assembly 108 may control
the direction in which the drill bit 109 is pointed and, therefore, the direction in which the
borehole 103 will be extended by the drill bit 109. The telemetry system 14 may provide
communications between the BHA 106 and a control unit 110 positioned at the surface 11. The
control unit 110 may comprise an information handling system with a processor and memory
device, and may generate commands to and receive information from the elements of the BHA
106. Additionally, at least one processor may be located within the bottom hole assembly 106 to
receive commands from the surface unit 110, to generate communications to the surface unit
110, or to otherwise control the operation of the elements of the BHA 106.
The LWD/MWD apparatus 107 may comprise one or more transmitters 116 and
receivers 118, which may be used to take measurements of the surrounding formation 102 and
strata 102a-c to characterize the formation. The transmitters 116 and receivers 118 may
comprise numerous types of transmitters and receives, including coil antenna, electrodes, Hall
effect sensors, etc. In certain embodiments, the transmitters 116 and receivers 118 may be
combined into transducers incorporated within the LWD/MWD apparatus 107. The transmitters
16 and receivers 118 may generate signals when commanded by the control unit 110 or by a
processor within the BHA 106 or the LWD/MWD apparatus 107. Measurements taken using the
transmitters 116 and receivers 116 may either be stored within the LWD/MWD apparatus 107
for later retrieval at the surface, or transmitted to the control unit 1 0 through the telemetry
system 114.
According to aspects of the present disclosure, at least one of the transmitters 116
and the receivers 118 may comprise a magnetic monopole. As used herein and will be described
below, a magnetic monopole transmitter or receiver may comprise a type of magnetic dipole
transmitter or receiver in which the poles are separated such that the effects of the magnetic
coupling between the poles on the magnetic fields proximate to the poles are substantially
reduced or eliminated. When the magnetic coupling effects are substantially reduced or
eliminated, the radiation pattern of the magnetic fields from/to each pole may be substantially
radial, thereby pointing to or from the corresponding pole. The radial direction may
advantageously be maintained even in the presence of layered formations, such as formation 102.
Additionally, as will be described below, because the electromagnetic field radiated by a
magnetic monopole are in a radial direction from the monopole, they may be useful for
positioning and ranging type of systems, using computationally simpler calculations that are used
in other positioning and ranging applications.
In Fig. 1, transmitter 6 comprises a magnetic monopole, and the arrows
extending from the transmitter 1 6 illustrates part of the electromagnetic field radiating from the
transmitter 116. As can be seen, the electromagnetic field extends radially outward from the
transmitter 16 into the surrounding formation. To the extent there are magnetic elements within
the suiTounding formation, the electromagnetic field generated by the transmitter 116 may
generate a magnetic field within the magnetic elements, which may be measured by the receiver
118. The measurements may then be processed and used in the drilling operations. For
example, measurements taken using the magnetic monopole may be used in conjunction with the
steering assembly 108 to identify the location of a target borehole (not shown) and cause the
borehole 103 to avoid, intersect, or follow the target borehole. Other applications are possible,
as will be described below.
FIG. 2 is a diagram of an example measurement/logging system 200, according to
aspects of the present disclosure. The system 200 may be used in conjunction with magnetic
monopole transmitters and/or receives and may be incorporated, for example, into a LWD/MWD
apparatus or a wireline logging tool. The system 200 may comprise a system control center 220
communicable coupled to a communications unit 230. In certain embodiments, the system
control center may comprise an information handling system positioned at the surface of a
drilling operation and the communications unit 230 may be positioned downhole. The
communications unit 230 may also comprise an information handling system, and may comprise
parts of a downhole telemetry system and LWD/MWD apparatus or control apparatus within a
downhole wireline tool.
In certain embodiments, at least one transmitter 210 and at least one receiver 240
may be communicably coupled to the communications unit 203. At least one of the transmitter
210 and the receiver 240 may comprise a magnetic monopole. The other one of the transmitter
210 and the receiver 240 that is not a magnetic monopole may comprise a galvanic source or a
dipole, including a magnetic dipole or an electric dipole. As used herein a galvanic source may
comprise a source of direct current electrical energy. In certain embodiments, different
quantities and types of transmitters and receivers may be used within the system 200, with some
or all operating at different frequencies. For example, in certain embodiments, a magnetic dipole
receiver 240 may be used to collect the signal transmitted by a magnetic monopole transmitter
210. Additionally, although system 200 includes both a receiver 240 and a transmitter 210, other
systems may include only receivers or only transmitters.
The system control center 220 may issue commands to the transmitter 210 and/or
receiver 240 through the communications unit 230 that cause the transmitter 210 and/or receiver
240 to perform certain actions. For example, transmitter 210 may transmit an electromagnetic
signal when a "transmit" command is received from the system control center 220 via a
communications unit 230. The electromagnetic signal may travels through surrounding
formations, as well as through the borehole and the downhole tool, and a part of it may be
measured or collected at the receiver 240. Because the transmitted electromagnetic signal
interacts with the formation and the borehole as it travels through them, it contains information
about the properties of the formation and the borehole.
The received electromagnetic signal may be sent from the receiver 240 to the
system control center 220 via the communications unit 230. Once at the system control center
220, the received electromagnetic signal may be transmitted to or processed by a data acquisition
unit 250 and a data processing unit 260 communicably coupled to the system control unit 220.
For example, the data processing unit 260 may invert the electromagnetic signal collected at the
receiver 240 to calculate characteristics of the formation and borehole. In certain embodiments, a
visualization unit (not shown) may be connected to the communications unit 230 or the system
control center 220 to monitor and intervene in the drilling operations, for example, to stop the
drilling process, modify the drilling speed, modify the drilling direction, etc.
In certain embodiments, some or all of the system control center 220,
communications unit 230, receiver 240 and transmitter 210 may be located at different physical
locations. For example, in certain applications, one or more magnetic monopole transmitters 210
may be positioned at a surface level, at least one receiver 240 may be positioned downhole in a
MWD/LWD apparatus, and the communications unit 230 may be located somewhere between
the transmitters 210 and receivers 240, such as at the surface above the borehole, near the
transmitters 210, or near the receivers 240. As used herein, the surface level may comprise areas
that are at, above, or otherwise proximate to the upper surface of a formation. In another
embodiments, one or more transmitters 210 may be positioned in a first borehole or well, one or
more receivers 240 may be located in another borehole or well, and the communications unit 230
may be positioned at surface level, somewhere between to the two boreholes or wells.
Additionally, in certain embodiments, measurement or logging systems may only comprise
transmitters or receivers.
FIGS. 3A and 3B are diagrams illustrating the difference between a magnetic
monopole element 350 according to aspects of the present disclosure and an existing magnetic
dipole element 300. The magnetic dipole element 300 comprises a coil antenna 310 that
conducts current in a counter-clockwise direction, producing an equivalent magnetic dipole
direction shown as arrow 340. The magnetic dipole element 300 may be thought of as a negative
(or south) pole 320 and a positive (or north) pole 330 positioned proximate to each other. As can
be seen, the magnetic monopole element 350 comprises an elongated coil antenna 360 with a
large number of windings that also conducts a time-varying current to produce negative and
positive poles 370 and 380. Unlike poles 320 and 330, however, the poles 370 and 380 of the
elongated antenna 360 may be separated by a distance such that the effects of the magnetic
coupling between the poles 370 and 380 on the magnetic fields in the regions of space near the
poles 370 or 380 can be substantially reduced or eliminated. As will be discussed below with
reference to FIGS. 4-6, the separation between the poles must be at least a few times larger than
the range of use of the magnetic monopole.
The magnetic monopole element 350 may be considered a varying current
monopole due to the use of a time-varying current to generate the poles 370 and 380 in the coil
antenna 360. Varying current monopoles may also be generated using coil antennas with
different shaped windings, such as square loop windings, provided the shape does not close onto
itself. Direct-current monopoles are also possible, and may be constructed using an elongated
magnet or by magnetizing an elongated elements, such as a casing.
As describe above, magnetic monopoles may generate or receive electromagnetic
signals in a substantially radial pattern that is generally free from the effects of a magnetic
coupling with the corresponding, opposite pole. Although the magnetic coupling between the
poles of a magnetic monopole may still exist, the distance between the poles may make the
curvature negligible with respect to a target in the formation near the magnetic monopole.
Magnetic dipoles, in contrast, generate or receive electromagnetic signals in a pattern that is
curved with respect to the corresponding, opposite pole due to the proximity of the poles. To
illustrate the differences, FIGS. 4-5 are diagrams showing the radiation patterns of magnetic
dipole configurations, while FIG. 6 includes diagrams illustrating the radiation patterns of an
example magnetic monopole antenna configuration.
In particular, FIGS. 4A-C illustrate the magnetic field direction and field strength
contour lines for an infinitesimal magnetic dipole oriented in z-direction. In FIG. 4A, a field
direction for the imaginary part of the magnetic field is shown on a grid in the x-z plane in a
homogeneous formation of conductivity s = 0.05 S/m for a magnetic dipole. The magnetic
dipole is oriented in the z-direction in the Cartesian coordinate system, and the frequency is 10
kHz. The relative permeability and permittivity of the formation is selected to be equal to unity.
As can be seen, the magnetic field forms a closed loop starting from the positive pole and ending
at the negative pole (the poles are illustrated as circles in the center of the diagram), with the
lines of radiation having a curvature corresponding to the distance between the poles.
Notably, FIG. 4A is not a true vector representation of the field because it
contains the direction information but no information about the field's strength. This was done to
better illustrate the field direction in places where the field strength is low. Further, because the
real part of the magnetic field has a very low amplitude at low frequencies, the imaginary part
was plotted in these figures to demonstrate the field direction. FIGS. 4B and 4C show the
contour plots of normalized strength of the x - and z- components of the H-field with respect to
position, respectively. As can be seen, the strength of the magnetics field decays with respect to
the distance from the transmitter.
FIGS. 5A-C illustrate the magnetic field direction and field strength contour lines
for a finite length magnetic dipole, corresponding to a coil with a finite wire thickness and
multiple windings of the turns. For the purposes of this depiction, separation between the two
ends of the coil (and thus the two poles of the dipole) is assumed to be equal to L = 5 cm. The
frequency of operation is still 10 kHz, and the formation properties are the same as in FIGS 4AC.
This configuration may be modeled by integrating the fields produced by magnetic dipoles
over the tool's length.
FIG. 5A shows the magnetic field direction for this case. Notably, although in
these plots some separation between the fields of the poles can be seen, and the fields become
more radial in close proximity to the poles, the poles are still not isolated and the magnetic fields
show the coupling effects from the poles in the form of curvature. FIGS. 5B and 5C show the
corresponding contour plots of the normalized field components in the x - and z- direction,
respectively. As can be seen, although the strength of the magnetics field still decays with
respect to the distance from the transmitter, the magnetic field extends farther when the poles are
separated.
FIGS. 6A-C illustrate the magnetic field direction and field strength contour lines
for a magnetic monopole, according to aspects of the present disclosure. In the embodiment
shown, the transmitter and receiver are separated by a distance of L = 10 m. The field direction
close to the positive pole is shown in FIG. 6A, and it can be seen to be almost completely radial
in direction from the pole with very little coupling between the two poles. Thus, magnetic fields
in this region are effectively that of a magnetic monopole. FIGS. 6B and 6C illustrate contour
lines for the normalized strength of the magnetic dipole in x- and z- directions, and also illustrate
that the coupling between the positive and negative poles has been almost completely eliminated.
FIGS. 6A-C illustrate that fields radiated by a monopole tool are in a radial
direction by applying an empirical approach where one of the poles of a magnetic dipole is
isolated using an integration of infinitesimal magnetic dipoles over a long distance.
Alternatively, using the duality of the magnetic monopole with an electric charge, fields due to
an isolated magnetic pole can be written directly as:
H(f)
4pm r
EQUATION1
where r is the position vector with the hypothetical magnetic charge qm assumed to be at the
origin; H is the magnetic field vector; and m is the permeability of the medium. Magnetostatic
conditions are assumed in writing Equation 1. In electrodynamic construction of the magnetic
monopole, the term in Equation 1 can be considered as the amplitude of the magnetic field
phasor, except that the distance calculations will be valid only so long as the frequency is low
enough for near field approximation.
Based on the known fields of a single magnetic monopole (e.g., the fields
described using equation 1), the fields due to an arbitrary distribution of magnetic monopoles
may be determined, for example, using the superposition principle. In an example case, FIG. 7
illustrates a magnetic dipole modeled as a system of two isolated magnetic poles. Using
derivations performed for an electric dipole in combination with the duality principle, the
magnetic fields of the magnetic dipole shown in FIG. 7 may be written as:
EQUATION2
Equation 2 may be rewritten as Equation 3, below, when the observation point is much further
than the spacing between the poles.
pm 3 2r 2
EQUATION3
As illustrated in Equation 3, the strength of the fields increases in proportion to the spacing
between the poles. Thus, the distance between the poles of the magnetic dipole with respect to
the creation of a magnetic monopole not only determine how closely it resembles a real magnetic
monopole, but also affect the strength of the radiated fields as well. For downhole applications,
where directionality and field strength are important due to the size of the areas to be measured,
a magnetic monopole with high field strength and directionality may be created by locating one
end of a coil winding at surface level and another end downhole.
FIGS. 8A-B illustrate the voltage and frequency responses caused by a magnetic
monopole antenna compared to a magnetic dipole antenna, according to aspects of the present
disclosure. In particular, FIG. 8A shows the absolute value of the induced voltage on a coil
receiver 10 ft away from a magnetic monopole comprising two z-oriented poles separated by a
distance of L = 10m, and from a magnetic dipole with a finite physical length of 5 cm and a
radius of 2.375 inches. The induced voltage from the monopole is shown as a dashed line, and
the induced voltage from the magnetic dipole is shown as a solid line. FIG. 8B shows the phase
angles of the induced voltages on the coils using the same dashed and solid line indicators. As
can be seen, the monopole may induce a larger voltage onto the coil receiver due to the higher
field strength of the monopole, but the frequency responses of the receiver to the magnetic
monopole and magnetic dipole antennas are similar.
According to aspects of the present disclosure, magnetic monopole transmitters
and receivers may be positioned and used in various types of tools and configurations to perform
many different types of measurements and operations related to a hydrocarbon recovery
operations. One example operation is the determination of the position of a downhole object
using the radial magnetic field of the magnetic monopole to determine a relative position vector
between a transmitter and a receiver. In certain embodiments, the position may comprise the
absolute position of a downhole object, such as a BHA or drill bit, or the position with respect to
the surface. In certain embodiments, the position may comprise the relative position of the
downhole object, such as a BHA, drill bit, casings, etc., with respect to another downhole
element.
In one embodiment, one or more monopole transmitters may be placed at a
surface level of a drilling site at known locations. As used herein, a monopole transmitter
positioned at the surface level may include monopole transmitters mounted on stands above
surface, laid on the surface, or buried proximate to the surface. In addition to the one or more
monopole transmitters placed at the surface, at least one receiver may be located downhole to
measure and calculate the relative position vector between the one or more surface monopole
transmitters and the downhole receiver. In certain embodiments, the receiver may be coupled to
a downhole element, such as a LWD/MWD apparatus or a wireline tool. Because the position of
the surface level transmitters is known, the position of the receiver may be determined using the
measured relative vectors between the transmitters and the receivers. In this way, accurate
positioning calculations may be made even in environments containing formation layers with
magnetic properties. In certain embodiments, the position can be tracked over time, allowing an
operator to determine, for example, if a well is being drilled in the correct location and along the
planned path of the well.
In certain embodiments, the vector relationship between a monopole transmitter
and a receiver may be written as:
r - n a = r
EQUATION4
where, r is the position vector of the receiver, ' is the location vector of z'th transmitter, n is
the unit vector in the direction of the magnetic field due to il transmitter at the receiver and d ' is
the distance between th transmitter and the receiver. In the case where there are T such
transmitters (i.e. i = 0, . . . , T-l) used, the vectors may be separated into components of
Cartesian coordinates to obtain the following a matrix equation:
x
1 0 0 - 0 ··· 0 x
y
0 1 0 - 0 ··· 0 y
0 0 1 - 0 · 0
0 0 1 0 _r-i
d r-i
EQUATION5
In matrix Equation 5, it is assumed that the transmitter locations and the field direction at the
receivers are exactly known, as is the receiver's relative orientation with respect to the global
reference coordinate system, which can be obtained a gravitometer and an inclinometer tool.
nx ' , ny ' , n'_) represents the x , y , and z components of the unit vector n . The receiver position can
be solved by, for example, multiplying both sides of the expression with the pseudo-inverse of
the matrix containing the unit vectors.
The equations above assume that the receiver is able to resolve the exact direction
of the field vectors, which may be accomplished by use of a tri-axial receiver that may detect
field information in three directions, such as for example in the directions of the x-, y-, and zaxis.
Positioning may still be accomplished if the receiver is biaxial—i.e., if the receiver may
detect field information in two directions, such as for example an x-axis and y-axis. FIG. 9
illustrates a magnetic field measured by a biaxial receiver, where the field direction due to a
monopole transmitter V at a receiver R is shown. For a biaxial receiver, the projection of a field
vector in the plane of the receivers may be found, which is shown as vector u . An arbitrary
vector that is orthogonal to the plane formed by the receivers (shown as v ) can also be defined.
Then, vectors u and v and transmitter location (c', y z') may be used to define a plane on which
receiver location (x, y , z) also lies. In a parametrical equation form, this plane may be defined as:
r - a u - b v - r
EQUATION6
Variables d and b' in Equation 6 may be real numbers with a different value for
each point on the plane. If position vector r is not an arbitrary point on the plane but instead
denotes the receiver position specifically, d and b' become constant unknowns whose values
may be solved to determine r . In certain embodiments, if there are at least three transmitters
and the planes defined by the transmitter and the receiver locations are independent, the receiver
position can be inverted. An example matrix equation that can be solved to obtain the receiver
location (x, y , z) comprises:
EQUATION7
Fig. 10 is a diagram illustrating an example positioning system, according to
aspects of the present disclosure. The positioning system comprises three monopole transmitters
To, Ti, and T2 respectively located on a surface at (2000, -1000, 0), (1000, 0, 0) and (3000, 0, 0)
meters, where (x, y , z) is a vector whose components represents the position in the corresponding
axis of the Cartesian coordinates. A downhole receiver R traces a path—such as a well bore—
that can be parameterized as (x, y , z ) = (2000 · cos(6') - 17600,-700,-20000 · sin ( )) meters where
Qis varied between 0° and 30° in 1° steps. Receiver R may comprise a tri-axial receiver capable
of measuring all components of the magnetic field, whose relative orientation with respect to the
reference coordinate system is known.
FIGS. 1 A-F illustrate the results of an example positioning simulation using the
positioning system shown in FIG. 10 and synthetic data, where the inverted position is obtained
using a Monte Carlo simulation. Notably, because the receiver R is a tri-axial receiver, Equation
5 has been used to determine the position of the receiver R. The basic field model for the
monopole transmitters described in Equation 1 was used for the simulation, with the monopole
strength, assumed to be unity and properties of the formation not taken into account (i.e.,
4pm
the formation is assumed to be a homogeneous, isotropic medium with no loss). When fields at
the receiver position were calculated, a combination of multiplicative and additive noises was
added to take into account all the irregularities and errors in the measurement, written as:
H =H d , (l + u (- 0.5,0.5)/SNR)+ 2 ·10 10 · «(-0.5,0.5)
EQUATION8
where SNR is a definition of signal to noise ratio (or, in this case, signal to multiplicative noise
ratio since additive noise distribution is assumed to be independent of the measured field) and is
taken to be equal to 30 in the simulations. The function «(-0.5,0.5) represents a random number
taken from a uniform distribution between -0.5 and 0.5.
In FIGS. 11A-F, the position of the receiver is calculated as the parameter Qis
changed between 0° and 30° in 1° steps. At each step, the inversion was repeated 100 times (with
different random noise added to the ideal noiseless data), and the mean value and the standard
deviations of the receiver position was found. The values are plotted in FIGS. 11A-C as a
function of true vertical depth (TVD), while the corresponding errors with respect to the true
receiver position are shown in FIGS. 11D-F. In these figures, the darker line represents the mean
value and the lighter line on either side represents the mean plus and minus one standard
deviation of the inverted results. The real receiver location is also shown as a solid line on FIGS.
11A-C, demonstrating that fairly accurate determination of position is possible using a very
simple inversion process.
Based on the simulation results in FIGS. 11A-F, the positioning system described
above may produce an accurate determination of the position of the receiver R relative to the
transmitters. Notably, the results may become less accurate as the receiver moves downward
because the field amplitude gets smaller and the effect of additive noise becomes stronger. In the
embodiment shown, error in the z-position is larger than the other components because the
transmitters are all assumed to be on the surface (z = 0 plane), reducing the resolution in the zdirection.
Other transmitter orientations can be used, however, to increase the range and
accuracy in the z-direction and in other directions.
In addition to determining the position of a downhole element using a magnetic
monopole, magnetic monopoles also may be used to determine the range between a transmitter
and a receiver. Notably, if the position of a receiver relative to a transmitter is known, then its
range may be easily calculated. However, the range to a downhole element may also be
determined using magnetic monopoles if the relative position of the downhole element is not
known. It may be useful to determine the distance between downhole elements even if their
exact positions are not known. For example, in certain instances, pressure containment may be
lost in a downhole well (the target well) and a secondary well (the relief well) may be drilled to
intersect the target well to contain the pressure. Distance measurements may be used to
determine the distance between the relief well and the target well to ensure that the relief well
accurately intersects the target well.
In certain embodiments, a distance or range calculation between a transmitter and
a receiver may be calculated using a field equation similar to Equation (1), with a component (or
projection) of the field H r ) in an arbitrary direction c written as:
4pm r
EQUATION9
The range between a transmitter and a receiver may be determined using Equation 10 by taking a
derivative of f in Equation 9 with respect to a Cartesian direction, in this casej
EQUATION10
In practice, the derivative operation of Equation 10 may correspond to a gradient measurement
of the magnetic field that may be performed using two receivers in close proximity to each other,
separated in the derivative direction, . Specifically, the two receivers may take first and second
measurements of the magnetic field, and the first and second measurements may be subtracted to
perform the derivative operation or calculate the gradient measurement of the magnetic field.
FIG. 12 illustrates example receivers Ri and R for the derivative operation,
arranged in close proximity in the direction. The result of the derivative operation in Equation
10 can be written as:
EQUATION11
Assuming c and j are orthogonal to each other, such that c j = 0 , then the ratio of to its
derivative at r becomes:
EQUATION12
Accordingly, if f j is known, the distance from the transmitter to the receiver may be obtained
by calculating the ratio of the field to its derivative or gradient at that position. If two receivers in
close proximity (such as Ri and R2 in FIG. 12) are used to find the derivative or gradient, the
average value of the field at these two receivers may be used to find the field itself.
In certain embodiments, the positioning system shown in FIG. 10 may be adapted
to a ranging positioning sensor by adding additional downhole receivers to calculate the field
derivatives downhole. FIGS. 13A-F illustrate example ranging simulation results using the
system described above and synthetic data. The ranges were calculated using two receivers
located at (x, y , z ± 50m) applying Equation 12, with the simulated range shown as a dashed line,
the true range shown as a solid line, the derivative direction (j) taken as the z-direction, and (x, y ,
å) is the point whose range is found. Notably, the range with respect to all three transmitters
was calculated separately for x- and y - components (components orthogonal to the derivative
direction).
FIGS. 13A-F demonstrate that accurate ranges may be calculated at various
receiver positions relative to the transmitters, with the range being accurate up to a distance of
approximately 3000 m using the disclosed method and the chosen parameter set. In most cases,
a single derivative using two receivers may be enough to calculate the range, but additional
receivers may improve the accuracy. However, if the two receivers lie at the same radial
distance from a magnetic monopole transmitter, field amplitude at these two receivers may be
the same, preventing calculation of a derivative value. To prevent such blind spots, a derivative
may be found in all three orthogonal directions in a practical implementation.
In certain embodiments, the general position and/or range calculations
magnetic monopoles described above may be used is specific downhole applications, such as
position marking on a target well. As described above, in certain instances, such as in a blowout,
it may be necessary to intersect a first well, called a target well, with a second well, called a
relief well. The second well may be drilled for the purpose of intersecting the target well, for
example, to relieve pressure from the blowout well. Contacting the target well with the relief
well typically requires multiple downhole measurements to identify the precise location of the
target well and the point on the target well where the relief well should intersect the target well.
Quickly and accurately intersecting the target well may be important to the success of the
operation.
FIG. 14 is a diagram of an example drilling system utilizing magnetic monopoles,
according to aspects of the present disclosure. In the embodiment shown, a target well 1410 is
disposed within a formation and a relief well 1430 is being drilled to intersect the target well
1410. In the embodiment shown, one or more magnetic monopole transmitters 1420 may be
within the target well 1410 proximate to a casing 1415 at a position in which the relief well 1430
is to intersect the target well 1410. A drilling assembly (not shown) within the target well 1430
may include at least one receiver to measure the radial magnetic fields generated by the
monopole transmitters 1420.
One or more control systems (not shown) may be coupled to the transmitters 1420
and the receivers to cause the transmitters 1420 to generate the radial magnetic fields and the
receivers to measurement the magnetic fields. At least one the distance from the transmitters
1420 to the receivers or the relative position of the transmitters 1420 to the receivers may be
calculated at the control systems. Using the range or position calculations, the trajectory of the
relief well 1430 may be recalculated and adjusted to ensure that the relief well 1430 intersects
the target well 1410 at the position indicated by the transmitters 1430. Without the magnetic
monopole transmitters 1420, the relief well 1430 may detect the casing 1415 of the well 1410
that needs to be intersected but will not be able to estimate the exact point on the well 1410
where the intersection should occur.
Another example drilling application using magnetic monopoles and the
corresponding range and position calculations described above comprises a SAGD application.
In SAGD systems, a second well is drilled parallel to an existing horizontal well in a desired
region of space, and high pressure steam may be injected into the upper wellbore to heat the oil
and reduce its viscosity, causing the heated oil to drain into the lower wellbore, where it may be
pumped out. FIG. 15 illustrates one embodiment of a SAGD system utilizing magnetic
monopoles. As shown in the embodiment of FIG. 15, magnetic monopole transmitters 1520 may
be installed on an existing first horizontal well 1510 proximate to well casing 1515. A second
well 1530 may be drilled to follow or mirror the first well 1510 at a pre-determined distance. A
drilling assembly (not shown) within the second well 1530 may comprise at least one receiver
which measures the radial magnetic fields generated by the transmitters 1520. The
measurements may be used to determine the range and or relative position of the receivers with
respect to the transmitters 1520, which can in turn be used to adjust the trajectory of the second
well 1530.
Magnetic monopoles may be used for other applications as well. For example,
magnetic monopoles may be used to ensure that multiple wells within the same formation do not
intersect, using the radial magnetic fields generated by the magnetic monopoles to calculate the
range between the wells to ensure that they maintain a given certain distance from each other.
Additionally, magnetic monopoles may be used with typical wireline or LWD/MWD tools to
increase the range of the resulting measurements due to the stronger magnetic fields generated
by the magnetic monopole. Likewise, in all the applications described above, the positions and
relative operations of the receivers and the transmitters may be switched.
According to aspects of the present disclosure, an example method for downhole
operations using a magnetic monopole may include positioning at least one of a transmitter and a
receiver within a first borehole. At least one of the transmitter and the receiver may be a
magnetic monopole. The transmitter may generate a first magnetic field, and the receiver may
measure a signal corresponding to the first magnetic field. A control unit communicably coupled
to the receiver may determine at least one characteristic using the received signal.
In certain embodiments, the transmitter and receiver may be located on the same
tool, such as a wireline tool or a LWD/MWD apparatus, that may be positioned within the first
borehole. The receiver may measure secondary magnetic fields generated by the primary
magnetic field, and the control unit may determine formation characteristics, such as
permittivity, resistivity, etc., based on the secondary magnetic field.
In certain embodiments, either the transmitter or the receiver may be positioned at
surface level above the first borehole or within a second borehole, and a relative position and/or
distance between the two may be determined. For example, the receiver may be positioned
within the first borehole on a logging-while-drilling or measurement-while drilling tool and the
transmitter may be one of a plurality of transmitters located within the second borehole. In
certain embodiments, the second borehole may comprise a target well and the plurality of
transmitters may be positioned at an intersection point on the target well. In certain
embodiments, the second borehole may be a horizontal well, such as in a SAGD application, and
the plurality of transmitters may be positioned along the length of the horizontal wellbore.
Distance and/or position calculations may be made with respect to the plurality of transmitters
and receiver, and the calculations may be used to determine a drilling trajectory of the first
borehole.
Therefore, the present disclosure is well adapted to attain the ends and advantages
mentioned as well as those that are inherent therein. The particular embodiments disclosed above
are illustrative only, as the present disclosure may be modified and practiced in different but
equivalent manners apparent to those skilled in the art having the benefit of the teachings herein.
Furthermore, no limitations are intended to the details of construction or design herein shown,
other than as described in the claims below. It is therefore evident that the particular illustrative
embodiments disclosed above may be altered or modified and all such variations are considered
within the scope and spirit of the present disclosure. Also, the terms in the claims have their
plain, ordinary meaning unless otherwise explicitly and clearly defined by the patentee. The
indefinite articles "a" or "an," as used in the claims, are defined herein to mean one or more than
one of the element that it introduces. Additionally, the terms "couple", "coupled", or "coupling"
include direct or indirect coupling through intermediary structures or devices.

What is claimed is:
1. A method for downhole measurements, comprising:
positioning at least one of a transmitter and a receiver within a first borehole,
wherein at least one of the transmitter and the receiver comprises a magnetic monopole;
generating a first magnetic field at the transmitter;
measuring at the receiver a signal corresponding to the first magnetic field; and
determining at least one downhole characteristic using the received signal at a
control unit communicably coupled to the receiver.
2. The method of claim 1, wherein positioning at least one of the transmitter and the
receiver within the first borehole comprises one of
positioning the transmitter and the receiver within the first borehole on a wireline
tool; and
positioning the transmitter and the receiver within the first borehole on a loggingwhile-
drilling or measurement-while drilling tool.
3. The method of claim 1, wherein positioning at least one of the transmitter and the
receiver within the first borehole comprises permanently positioning the transmitter and the
receiver on a casing.
4. The method of claim 11, further comprising positioning the other of the
transmitter and the receiver either at a surface level or within a second borehole.
5. The method of claim 4, wherein
positioning at least one of the transmitter and the receiver within the first borehole
comprises positioning the receiver within the first borehole on a logging-while-drilling or
measurement-while drilling tool; and
positioning the other of the transmitter and the receiver either at the surface level
or within a second borehole comprises positioning a plurality of transmitters within the second
borehole.
6. The method of claim 5, wherein positioning the plurality of transmitters within
the second borehole comprises positioning the plurality of transmitters proximate to an
intersection point in a target borehole.
7. The method of claim 5, wherein positioning the plurality of transmitters within
the second borehole comprises positioning the plurality of transmitters along the length of a
horizontal borehole.
8. The method of any one of claims 5-7, wherein determining at least one downhole
characteristic using the received signal comprises determining at least one of a distance between
the plurality of transmitters and the receiver, and a position of the receiver relative to the
plurality of transmitters.
9. The method of claim 8, further comprising altering a drilling trajectory based, at
least in part, on the downhole characteristic.
10. The method of claim 1, wherein the transmitter is permanently positioned in the
first borehole.
1 . The method of claim 1, wherein determining at least one downhole characteristic
using the received signal comprises determining at least one of a distance between the
transmitter and the receiver, and a position of the receiver relative to the transmitter.
2. The method of claim 1 , further comprising performing a first measurement and a
second measurement of the first magnetic field, wherein determining the distance between the
transmitter and the receiver comprises calculating a gradient measurement of the magnetic field
using the first measurement and the second measurement
13. The method of claim 12, wherein calculating the gradient measurement comprises
calculating a difference between the first measurement and the second measurement.
14. The method of claim 12, wherein the second measurement is a gradient
measurement.
15. The method of any one of claims 12, 13 or 14, wherein determining the distance
between the transmitter and the receiver comprises determining a ratio of the first measurement
to the gradient measurement.
16. The method of claim 11, wherein the position is calculated at least in part from a
direction of the first magnetic field.
17. The method of claim 11, wherein the position is calculated only by using a
direction of the first magnetic field.
18. An apparatus for downhole measurements, comprising:
a transmitter that generates a magnetic field; and
a receiver that detects the magnetic field generated by the transmitter, wherein at
least one of the transmitter and the receiver comprises a magnetic monopole.
19. The apparatus of claim 18, further comprising:
a control unit communicably coupled to the transmitter and the receiver, the
control unit comprising a set of instructions that, when executed by a processor of the control
unit, cause the processor to
generate a first command to the transmitter to generate a first magnetic
field; and
generate a second command to the receiver to measure a signal
corresponding to the first magnetic field; and
determine at least one downhole characteristic using the received signal.
20. The apparatus of claim 18, wherein the magnetic monopole is one of a varyingcurrent
monopole and a direct-current monopole.
21. The apparatus of claim 20, wherein the varying-current monopole comprises an
elongated coil.
22. The apparatus of claim 20, wherein the varying-current monopole comprises an
elongated magnet.
23. The apparatus of claim 2 1 or 22, wherein the other one of the receiver or
transmitter is a galvanic source or dipole.
24. The apparatus of claim 23, wherein the other one of the receiver or the transmitter
is an electric dipole.
25. The apparatus of claim 18, wherein the transmitter and the receiver are coupled to
one of a wireline tool and a logging-while-drilling or measurement-while drilling tool.
26. The apparatus of claim 19, wherein
the signal corresponding to the first magnetic field comprises a secondary
magnetic field generated by the first magnetic field; and
the at least one downhole characteristic comprises at least one characteristic of a
formation surrounding a borehole.
27. The apparatus of claim 18, wherein
one of the transmitter and the receiver is located within a first borehole; and
the other of the transmitter and the receiver is located either at a surface level or
within a second borehole.
28. The apparatus of claim 19, wherein the at least one downhole characteristic
comprises at least one of a distance between the transmitter and the receiver, and a position of
the receiver relative to the transmitter.
29. The apparatus of claim 27, wherein
the receiver is positioned within the first borehole on a logging-while-drilling or
measurement-while drilling tool; and
the transmitter comprises a plurality of transmitters positioned within the second
borehole.
30. The apparatus of claim 29, wherein
the second borehole comprises a target borehole; and
the plurality of transmitters are positioned proximate to an intersection point in
the target borehole.
31. The apparatus of claim 29, wherein
the second borehole comprises a horizontal borehole; and
the plurality of transmitters are positioned along the length of the horizontal
borehole.
32. The apparatus of any one of claims 29 to 31, wherein the at least one downhole
characteristic comprises at least one of a distance between the plurality of transmitters and the
receiver, and a position of the receiver relative to the plurality of transmitters.