# TWO COIL GUIDANCE SYSTEM FOR TRACKING BOREHOLES

A method and apparatus for tracking the drilling progress of a borehole such as a horizontal borehole that is drilled under an obstacle along a prescribed path is based upon triangulation from two laterally separated loops of wire lying on the ground, which generate corresponding alternating magnetic fields.

**Description**

**CROSS REFERENCE TO RELATED APPLICATIONS**

This application claims the benefit under 35 U.S.C. 119(e) of U.S. Provisional Application No. 61/166,443, filed Apr. 3, 2009 and entitled “Two Coil Guidance System for Tracking Boreholes,” the entire disclosure of which is hereby incorporated herein by reference.

**BACKGROUND OF THE INVENTION**

The present invention relates to a method and apparatus for tracking and guiding the drilling of a borehole, and more particularly to tracking a borehole being drilled generally horizontally under an obstacle such as a river, a highway, a railroad, an airport runway or the like, where access to the ground above the borehole is difficult or perhaps not possible. Various well-known drilling techniques have been used in the placement of underground transmission lines, communication lines, pipelines, or the like through or beneath obstacles of various types. In order to traverse the obstacle, the borehole must be tunneled along a planned path underneath the obstacle from an entry point on the Earth's surface to a desired exit point The borehole then may receive a casing which may be used, for example, as a pipeline or for receiving cables for use as power transmission lines, communication lines, or the like. In the drilling of such boreholes, it is important to maintain them on a carefully controlled track following a prescribed drilling proposal, for often the borehole must remain within a precisely defined right of way as it passes under the obstacle and its entry and exit points on opposite sides of the obstacle must often be at precisely defined locations. In order to do this, the driller must have an accurate determination of the lateral position of the borehole as it is being drilled, as well as the precise distance to the exit location so that appropriate adjustments to the inclination and direction of drilling can be made. Even if the radial distance to the exit location from the entry point of the borehole into the Earth is precisely known and the radial distance of the drill bit from its entry point into the Earth is precisely known, safety considerations alone give high priority to directly determining the relative location of the desired borehole exit point with respect to the drill bit location as the exit point is approached.

Conventional directional drilling techniques used to drill such boreholes commonly use a steering tool which measures the borehole inclination, azimuth and tool roll angle at each station along the path where measurements are made. The borehole coordinates are computed and tabulated from these steering tool data as a function of the measured distance along the borehole, which may be referred to as the measured depth of the steering tool, or the “away” distance from a reference point such as the borehole entry point. However, these borehole coordinates suffer from serious cumulative effects caused by small errors in the inclination and azimuth determinations made at regularly spaced stations along the borehole, and the lateral errors generated by such conventional borehole surveying are intolerable.

A number of prior electromagnetic systems present problems to the user since they require access to the land directly above the path to be followed by the borehole in order to permit placement of surface grids or other guidance systems. Often, however, access to this land is not available; furthermore, the placement of guidance systems of this kind can be extremely time consuming, and thus expensive. The Earth's magnetic field is usually utilized for determining azimuthal direction in such prior systems, but this creates additional problems because of the disturbances caused by nearby steel objects such as bridges, vehicular traffic and trains. Therefore, although steering tool inclinometers provide good inclination measurements, usually to a precision of 0.1 or 0.2 degrees, the standard steering tool azimuthal direction determination provided by the Earth Field magnetometers is inadequate.

To avoid the need for placing guide wire grids on the earth's surface above the proposed borehole path, systems have been provided for guiding a drill in which a solenoid generates magnetic field signals that are measured at field sensors at the drill stem. One such system is illustrated in U.S. Pat. No. 5,513,710 to Kuckes, which discloses a drilling guidance method for drilling boreholes under rivers and other obstacles using a direct current powered solenoid and an industry standard MWD system.

U.S. Pat. Nos. 6,626,252 and 6,814,163, to Kuckes, similarly describe a drill tool which includes a three-axis magnetometer for detecting vector components of target magnetic fields produced by a large solenoid which incorporates a coil surrounding a large ferromagnetic core. The solenoid is connected to a reversible source of direct current of sufficient magnitude to provide a target magnetic field in the region of the proposed path of the drilling.

In systems for guiding horizontal boreholes such as those described in the '710, the '252 and the '163 patents, the drilling equipment is placed at a location where a borehole is to be started, while the target solenoid is positioned at or near the area where the borehole is to exit the ground. The borehole entrance may be at or near one side of an obstacle, such as the bank of a river, with the borehole passing beneath the river to an exit beyond the opposite bank. Drilling the borehole is begun at the entrance site and conventional survey methods are used to guide the drill for a major part of the distance toward the exit location. As the borehole nears the desired exit site; for example, within about 100 meters, further guidance is by way of the target solenoid field. Whenever a survey is required, the drill is stopped and the sensor system in the drilling tool is activated to measure the x, y and z components of the total magnetic field in the region of the sensor. These measurements, together with downhole tool orientation measurements, are then used to determine the distance and direction from the drilling tool to the solenoid.

Still another prior system is illustrated in U.S. Pat. No. 6,466,020 to Kuckes et al, wherein a target magnetic field for borehole drilling guidance is generated by a loop/guide wire antenna system on the Earth's surface above the proposed path of the borehole. The loop is energized by a known current to generate a magnetic field that is measured by two single-axis electromagnetic field sensors that lie on an imaginary spherical surface at the known radial distance from a point such as the entry point of the borehole. These sensors are approximately perpendicular to the radius of this spherical segment and to each other. Measurement of the two perpendicular electromagnetic field components generated by the loop is made by the two sensors at a selected borehole site. The radial distance from the drill bit entry point to the selected measurement site is determined using standard integration techniques, as well as steering tool measurements of inclination from the Earth's gravity and azimuth from the Earth's magnetic field along the borehole together with the measured depth of the sensors. The electromagnetic field measurements by these two sensors together with this computed radial distance from the entry point are matched to theoretically computed values for field vectors on the imaginary spherical surface at the known radial distance of the measurement site to determine the location of the drill bit.

A second embodiment of the system described in the '020 patent includes two electromagnetic field source loops, both near the punch-out location. A guide wire leg of each loop is positioned on the Earth's surface along the proposed path of the borehole to produce corresponding electromagnetic fields on that path. The loop geometry is designed so that there is a rapid variation in the x and y components of the fields generated near the portion of the borehole beyond the edge of the loops. The rapid variations in the x and y field components in this region are used find the radial distance from the drill bit to the proposed punch out location. The radial distance to the punch out point is usually a critical parameter.

Although such prior systems are useful in various drilling guidance applications, it has been found that a continuing problem in horizontal drilling of boreholes is the accurate determination of the lateral position of the drill bit in a borehole and the direction of drilling when the drill bit is far from the point at which the borehole passes under an obstacle; for example when it is at a great distance from the shore of a river.

**SUMMARY OF THE INVENTION**

The present invention is directed to an improved method and apparatus for providing guidance in drilling boreholes. The invention disclosed herein uses two electromagnetic sources consisting of two laterally spaced-apart loops of wire carrying alternating current to provide target magnetic fields that are used to determine the location and direction of the drill head and to guide further drilling. At least one of the loops is significantly off to one side of the borehole being tracked, and preferably both loops are laterally spaced from the proposed path. In one preferred form of the invention, two laterally spaced loops are on opposite sides of the proposed path and of the exit point of the borehole. Vector components of the electromagnetic fields are measured near the drill bit in the borehole by an array of magnetic field sensors, and accelerometers are provided to determine the direction of the Earth's gravitational field at the location of the magnetic field sensors. These electromagnetic field and accelerometer measurements are analyzed by mathematical techniques using the known loop geometry and electric currents to determine the drill bit location and the azimuthal direction of drilling. The drilling inclination direction is determined using standard accelerometer data. Alternatively, the location vector to the drilling point can be determined from the measured electromagnetic field vectors without the use of an accelerometer. The detailed geometry, power levels and frequency of operation and signal averaging time are subject to design criteria constraints including factors such as the size and location of the spaces available for positioning the loops and the consequent diameters of the loops and the number of turns of wire in each loop.

The method, and the advantages, of the present system are illustrated by selecting an exemplary set of typical parameters for the wire loops used in the invention. In this example, two source wire loops are provided, one on each side of the borehole path, with each loop being approximately 50 meters in diameter and the loops being laterally separated by 150 meters. Each loop is powered by 5 kilowatts to generate corresponding magnetic fields, which may be referred to as target fields. Measurement of the target magnetic fields generated by this current at a selected point, such as a field detector on a drill head 500 meters distant from the loops, readily provides a lateral location precision of 5 meters with respect to the proposed path and a few degrees precision in the drilling direction after a short period of signal averaging. Measurements made at a drilling location closer to the source loops will yield more precise results.

**BRIEF DESCRIPTION OF THE DRAWINGS**

The foregoing and additional objects, features and advantages of the present invention will be apparent to those of skill in the art from a consideration of the following detailed description of a preferred embodiment thereof, taken in conjunction with the accompanying drawings, in which:

**DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT**

A unique and novel feature of the present application is the utilization of two independent, laterally separated source loops to generate electromagnetic fields for use in determining the location and direction of field sensors, and more particularly for guiding borehole drilling. Such laterally displaced source loops give a much greater useful range away from the electromagnetic field source for better distant location resolution and for more accurately guiding the drilling of a borehole, than has heretofore been possible.

One embodiment of the apparatus utilized in the method of the present invention is generally illustrated at **10** in **12** is drilled under an obstacle such as a river for use in the laying of pipeline, for example. The apparatus incorporates a drill head having a down-hole industry standard drilling motor **14** for driving a drilling bit under the control of equipment at a drill rig **16** at the Earth's surface. The crossing of the river **18** may entail drilling along a planned path **20** which may pass under the river at a depth of 30 meters, for example, to a planned “punch-out point”, or exit location **22**, which may be, for example, 1000 to 1500 meters away from a borehole entry point **24**. The progress of the borehole may be tracked for part of the distance to the exit point by conventional survey equipment, but as the drill bit moves further away from the entry point **24**, guidance of the drill bit is best carried out by the use of target magnetic fields generated by two wire loops **26** and **28**. In this case the loops are illustrated as being located beyond the far bank **32** of the river **18**, on the surface **34** of the Earth at the exit side of the river. It will be understood that the loops may be located on the near side of the river or other obstacle, or in some cases pairs of loops may be provided on both sides of the obstacle for precision guidance of the drill. The method is particularly important for drilling guidance while drilling under a river or other obstacle where it is impractical to deploy a guide wire system on the surface.

The loops **26** and **28** are energized, as will be explained below, to produce target magnetic fields that are detected at selected measurement stations along the proposed path by a measurement while drilling (MWD) package **36** located on the drill head at or near the drilling motor **14** to provide the information needed to guide the drilling at each measurement station under the river and subsequently under the earth's surface **34** as drilling progresses toward the proposed exit location **22**. As illustrated in the embodiment of **14** is mounted on a drill stem **38** to drive a drill bit **40**, in conventional manner. The MWD package **36** preferably includes a conventional three component accelerometer to measure the direction of gravity and a conventional three component magnetometer to measure alternating magnetic fields, and is mounted on the drill stem adjacent, and just above, the drilling motor.

In the preferred form of the invention, the loop sources **26** and **28** are laterally spaced from each other, and are positioned by land surveying techniques at selected, known locations with respect to the proposed path **20** of the borehole being drilled. At least one of the loop sources is laterally displaced a significant distance from the proposed path **20**. Preferably, both loops are displaced from the path. And advantageously the loops are on opposite sides of path **20**, as illustrated in **50** and **51** of loops **26** and **28**, respectively, are separated by approximately 150 meters, and in the illustrated embodiment are equally spaced by distances **52** and **53** on opposite sides of the path **20**, with a line between the center points **50** and **51** being perpendicular to the proposed path **20**.

The loops **26** and **28** are energized by a 5 kw motor/generator set **54** through suitable power control electronics **56** and power lines **58** and **60**, respectively, as diagrammatically illustrated in **26** may be energized by an alternating current having a frequency of 1 Hertz, while loop **28** is energized by alternating current at a frequency of 1.14 Hertz, to produce corresponding magnetic fields in the Earth in the region of the path **20**. Alternatively, the loops may be separately energized by AC currents at the same frequency, in which case two sets of measurements are made sequentially, first with one loop powered and then with the second being powered. The important point is that independent measurements are made of the electromagnetic field components generated by each loop.

In the illustrated embodiment of the invention, the magnetic field source loops **26** and **28** are positioned near the planned punch-out point **22** of the borehole, in this case on the far side of the obstacle under which the borehole is to be drilled, from the entry point of the borehole. It will be understood, however, that the source loops can be positioned at any location along, or even beyond, the path **20**, wherever precise lateral control of the drill bit and thus of the direction of drilling, is needed. It is to be noted that the larger the lateral separation of the loops and the fewer the number of turns for a fixed length of wire and excitation power, the better. The choice of parameters, in the example given above, is based on the limitations imposed by land accessibility and other such factors in the region of the path **20** of the borehole, and may vary in accordance with specific applications.

Data Acquisition and Processing

Typically, the direction of drilling a borehole, such as the illustrated borehole **24**, is initially controlled by standard borehole surveying techniques in which a steering tool measures the borehole inclination, azimuth and tool roll angle at successive stations along the path of the borehole. The borehole coordinates are computed and tabulated from the steering tool data as a function of the measured distance along the borehole and directional signals are generated and sent to the steering tool to control further drilling. However, as described above, these borehole coordinates suffer from serious cumulative effects caused by small errors in the inclination and azimuth determinations made at regularly spaced stations along the borehole, and the lateral errors generated by such conventional borehole surveying can cause serious problems. In accordance with the present invention, these lateral errors are overcome by utilizing the magnetic fields generated by laterally spaced loops **26** and **28** located where lateral drilling precision is needed.

To obtain the data needed for accurate location of the drill head, which may include the drilling motor **14** and the drill bit **40**, the loops **26** and **28** are electrically excited by alternating current after drilling has been stopped at a measurement station along the proposed borehole path. The resulting alternating electromagnetic fields are detected by the downhole MWD instrument package **36** on the drill string, and the resulting output data signals are transmitted uphole to the drilling apparatus **16**, a few minutes of data are recorded and the data file is generated.

As illustrated in **36** incorporates conventional magnetometers **60** for measuring the x, y and z vector components of the AC magnetic fields generated by the current flow in the loops **26** and **28** and the x, y and z components of the Earth's magnetic field. The AC magnetometer output signals are supplied through corresponding AC amplifiers **62**, and the Earth's magnetic field vector signals are supplied directly, to respective inputs of multiplexer and telemetry circuitry **64** which is driven by a suitable downhole clock circuit **66**. The MWD package also incorporates x, y and z accelerometers **68** for measuring the x, y and z components of the Earth's gravity and supplies corresponding output signals to inputs of multiplexer **64**. The multiplexer output is connected by way of a suitable communications link such as a cable **70** to uphole communication equipment **72** which includes an instrument power supply and telemetry circuits **74**. Equipment **72** also includes an uphole computer **76** which receives demultiplexed data signals from the telemetry circuitry **74** at Earth's field circuit **76**, gravity circuit **78**, and AC field circuit **80**. These signals are recorded at corresponding data files **82**, **84** and **86**, respectively, and the computer then determines the direction of further drilling in processor **90** and sends suitable drill control signals downhole by way of controller circuit **92** and telemetry **74** to a downhole controller **94** for the drill motor **14**.

As illustrated in **56** for the motor/generator set **54** includes an uphole clock **98** which generates a square wave clock signal **100**, illustrated in **102** which is connected by way of respective lines **58** and **60** to supply an alternating current **104**, illustrated in **26** and **28**. Electronics **56** also includes meters **106** for measuring the current in each loop.

The first step for processing the recorded magnetic field data at processor **90** is the generation of a reference wave form by a reference clock **110** (**98** for the loop switching circuitry **102**. Magnetic field data signals from the downhole magnetometers **60** that are stored in the AC field data files **86** are time averaged with respect to the reference wave form to produce two single-row data matrices of the three magnetic field components. This is done for magnetic field signals generated by the magnetometers in response to the magnetic fields H1 and H2 produced by the loops **26** and **28**, respectively, either simultaneously when the loops are energized by different frequencies, or sequentially when they are energized by a single frequency. The location of the magnetic field sensor **60** with respect to the two loops, and thus the location of the drill with respect to the proposed path of the borehole, and the direction of drilling, can be determined by mathematically optimizing the match between measured and computed field components using mathematically well known methods, e.g. by using a least squares fitting method.

Since the least squares method, using Taylor series expansions to linearize the fitting process, is so well suited to computerized analysis of these data a procedure based upon this method will be described. The first step is to precisely lay out the two electromagnetic source loops, or coils, **26** and **28** on the ground as shown in **26**. As illustrated, the loop is defined by n straight line segments **120**, which may be referred to generally as segments Ws(**1**) . . . Ws(n), with adjacent segments being joined at nodes **122** The loop, or coil, **26** has N turns, and when energized by the source **56** carries an electric current I. In the illustration, the positive current flows counterclockwise. A surveyor's wire file listing the three dimensional coordinates of the vectors Rw(i), Rw(i−1) . . . Rw(i−n) with respect to a reference origin point **124** for the wire element nodes **122** of the coils **26** and **28** is generated using standard land surveying techniques with customary away, elevation, right (aer) coordinate axes as illustrated in **124** by its away, elevation and right (aer) coordinates. The elevation unit vector e defining the aer system points vertically upwards, as illustrated by axis **130**. The away axis **132** is horizontal, usually chosen to be from the entry point toward the proposed borehole exit point, and the right unit vector axis **134** is also horizontal and points to the right of the away axis.

The electromagnetic Law of Biot Savart can be used to compute the H1aer and H2aer (away, elevation, right) vector components of the electromagnetic fields H1 and H2 specified in the away, elevation, right coordinate system for any location P at which the target electromagnetic field is to be evaluated. The location P is defined by the vector Raer as shown in

The field H(i) for a wire segment as shown in

*H*(*i*)=(*N*I*Huv*(*i*)/(4**pi*b*))*(cos *B*(*i*)−cos *A*(*i*))

*Huv*=cross(*Ws*(*i*),*r*(*i*))/*mag*(cross(*Ws*(*i*),*r*(*i*))

*b=mag*(cross(*Ws*(*i*),*r*(*i*))

cos *B*(*i*)=dot(*r*(*i*),*Ws*(*i*))/(*mag*(*r*(*i*))**mag*(*Ws*(*i*)))

cos *A*(*i*)=dot(*r*(*i−*1),*Ws*(*i*))/(*mag*(*r*(*i−*1))**mag*(*Ws*(*i*))) (Eq. 1)

The function mag denotes the conventional magnitude of a vector, e.g. mag(R) denotes sqrt(dot(R,R)). Thus the theoretical vectors H1aerth and H2aerth for the electromagnetic field vectors H1 and H2 generated by each loop, as represented by their aer vector components, is readily done.

To control the drilling of a borehole, the driller is given the proposed borehole path coordinates expressed in the aer coordinate system and the measured borehole coordinates found in the course of drilling are expressed in the same aer system. Usually, the coordinates of a borehole being drilled are obtained in the course of drilling using conventional borehole surveying techniques based upon integrating a large number of station measurements of gravity and of the Earth's magnetic field along the borehole. The difficulty is that, far away from the borehole entry point, a borehole survey generated in this way does not have sufficient precision due to the cumulative build up of error along the borehole length. In accordance with the present invention, the driller is provided with the approximate survey file of the borehole, and this is improved upon using the method and apparatus of this invention.

To make an electromagnetic determination of the location and drilling azimuth, measurements of three components of the electromagnetic fields generated by the loops **26** and **28**, and of gravity, are made by the borehole instrument **36** at a location P at a chosen depth, or away distance along the borehole. The instrument **36** sensing axes are defined by an xyz coordinate system **140** fixed to the downhole drilling tool. The z axis **142** of system **140**, illustrated in **144** and **146**, respectively, are perpendicular to z and to each other, the xyz system forms a right handed system of coordinate axes.

The analysis of the H1xyz and H2xyz data, i.e., the xyz vector components of the measurements of the down-hole electromagnetic fields produced by loops **26** and **28**, respectively, is best analyzed by transforming them to a bes coordinate system **150**, whose axes are shown in **140** in

*s*=cross(*g,z*)/*mag*(cross(*g,z*)) (Eq. 2)

The elevation unit vector “e” is a unit vector pointing in the opposite direction as g, i.e.

*e=−g/mag*(*g*) (Eq. 3)

Finally, the projection of the borehole direction z in the horizontal plane is in the direction of the unit vector b given by

*b*=cross(*e,s*) (Eq. 4)

The matrix to transform a vector represented by its xyz components to its representation using bes components is given by the 3 by 3 matrix:

xyztobes=[b′;e′;s′] (Eq. 5)

The measurements of the electromagnetic fields H1x, H1y, H1z generated by loop **1** are conveniently represented by the 3 by 1 matrix:

H1xyz=[H1x;H1y;H1z] (Eq. 6)

Similarly, the measurements H2x, H2y, H2z are represented by the 3 by 1 matrix:

H2xyz=[H2;H2y;H2z] (Eq. 7)

And the representation of the H1 and H2 measurements in the bes coordinate system is given by the matrix products:

*H*1*bes=xyztobes*H*1*xyz and H*2*bes=xyztobes*H*2*xyz* (Eq. 8)

These 3 by 1 matrix representations of the measurements of H1 and H2 are to be compared to theoretical values of the corresponding quantities H1th and H2th, which are conveniently calculated using the Law of Biot Savart with respect to the “aer” coordinate system used by the land surveyor. The matrix representation of H1th and H2th with respect to the aer coordinate axes will be written as:

H1aerth=[H1ath;H1eth;H1rth] and

H2aerth=[H2ath,H2eth,H2rth] (Eq. 9)

To compare the theoretical and measured field values, represent the H1th and H2th vectors in the bes coordinate system. The matrix to transform vectors from the aer system to the bes system is given by:

*aertobes*=[cos(*Aab*)0 sin(*Aab*);0 1 0;−sin(*Aab*)0 cos(*Aab*)] (Eq. 10)

The representation of the theoretical values H1th and H2th calculated with respect to a surface aer system can be converted to a down-hole bes system by the expressions:

*H*1*besth=aertobes*H*1*aerth H*2*besth=aertobes*H*2*aerth* (Eq. 11)

The mathematical problem is thus reduced to finding the value of the vector R from the reference origin to the drill bit represented by the 3 by 1 matrix Raer and of the azimuthal angle Aab (

RA0=[Ra0;Re0;Rr0;Aab0] (Eq. 11)

The values of the elements of RA0 can usually obtained from the driller's borehole survey, but if a survey is not available, an educated guess is usually sufficient. Then, together with RA0, define an associated 4 by 1 difference matrix:

dRA=[dRa;dRe;dRe,dAab] (Eq. 12)

The intent is to make the elements of

*RA=RA*0+*dRA* (Eq. 13)

such that the 6 values of H1besth and H2besth evaluated at the 4 element values of RA match the 6 electromagnetic field measurement values contained in H1bes and H2bes. Call the values of H1besth and H2besth, evaluated at RA0, H1besth0 and H2besth0 and form a 6 by 1 matrix H12besth0, i.e.:

H12besth0=[H1bth0;H1eth0;H1sth0;H2bth0;H2eth0;H2sth0] (Eq. 14)

The corresponding theoretically computed field values computed at RA, which at the moment is unknown, can be written as:

H12besth=[H1bth;H1eth;H1sth;H2bth;H2eth;H2sth] (Eq. 15)

Now Taylor expand H12besth0 about the region RA0, and call that value H12besth i.e. write the matrix equation which represents 6 linear equations with 4 unknowns, i.e.:

*H*12*besth=H*12*besth*0+*dH*12*besdRAb*dRA.* (Eq. 16)

The quantity dH12besdRAb is a 6 by 4 matrix with 24 “derivative” elements, i.e.,

Each of the derivatives in this relation are to be read as calculus partial derivatives evaluated at the element values contained in RA0; e.g., dH1bthdRa in the notation of calculus would be written as dH1bth/dRa. The derivative dH1bthdRa is the change in H1bth per unit change in the parameter Ra near the RA0 while holding Re0, Rr0 and Aab0 constant. In a computer program it can be computed, for example by evaluating H1bth at [Ra0; Re0; Rr0; Aab0] and at [Ra0+0.01; Re0; Rr0; Aab0] (where “0.01” is any appropriately small number). The first value H1bth is subtracted from the second and this difference is divided by 0.01, following the basic definition of differentiation.

To proceed, equate the Taylor series expansion (Eq.16) of H12besth about the 4 by 1 matrix RA0 to the measurement matrix H12besmeas:

*H*12*besmeas=H*12*besth=H*12*besth*0+*dH*12*besdRA*dRA *

H12besmeas=[H1bes;H2bes] (Eq. 18)

This over determined equation is readily solved for dRA in the least squares sense using the computer program “MATLAB” operation of left matrix division as

*dRA=dH*12*besdRA*\(*H*12*besmeas−H*12*besth*0) (Eq. 19)

The improved value for the 4 by 1 matrix RA, which contains the element values wanted is:

*RA=RA*0*+dRA* (Eq. 20)

This procedure is repeated iteratively using this value of RA for a new RA0. The procedure quickly minimizes the quantity Error2 given by the inner matrix product below of the last iteration; i.e.:

Error2=(*H*12*bes−H*12*besth*)′*(*H*12*bes−H*12*besth*) (Eq. 21)

Thus the value of the drill bit location Raer and the azimuthal drilling direction with respect to the a axis; i.e., the angle Aab, have been determined from electromagnetic and accelerometer measurements.

Alternatively, the location vector Raer to the drilling point can be determined from the measured vectors H1xyz and H2xyz without the use of an accelerometer. This can be done by comparing scalar vector invariants of the measured electromagnetic field vectors to corresponding computed values. To demonstrate this method, consider the magnitude of H1, the magnitude of H2 and the magnitude of the projection of (H1−H2) upon a plane perpendicular to (H1+H2). The approximate inverse cube decrease in the field magnitudes H1 and H2 with the distance away from each source loop makes these quantities good for determining the away component Ra and the right side component Rr. For two similar laterally separated loops lying on approximately the same plane the H1 and H2 vectors are vertical at the Earth's surface; however, the direction of these vectors diverge direction with depth into the Earth. Thus the projection of the difference vector H1−H2 onto the plane perpendicular to the direction of H1+H2; i.e., the near vertical direction, can give a good measure of the elevation component Re. These three parameters are not only good for this idealized configuration but also for most cases of practical interest.

Thus, the three quantities H1mag, H2mag and H12mag, defined below, can be computed from the H1 and H2 measurements and from theoretical computations; i.e.:

*H*1*mag=sqrt*(dot(*H*1,*H*1))

*H*2*mag=sqrt*(dot(*H*2,*H*2))

*H*12*mag=sqrt*(dot(*H*12*p,H*12*p*)

*H*12*p*=(*H*1*−H*2)−dot((*H*1*−H*2),*H*12plus*uv*)**H*12plus*uv *

*H*12plus*=H*1+*H*2

*H*12plus*uv=H*12plus/*sqrt*(dot(*H*12plus,*H*12plus)) (Eq. 22)

From the three quantities H1mag, H2mag and H12mag, form the 3 by 1 field measurement matrix H12perpmeas; i.e.:

H12perpmeas=[H1mag;H2mag;H12mag]; (Eq. 23)

A first guess for the aer representation of the sensor location vector Raer0 is written as a 3 by 1 matrix, as follows:

Raer0=[Ra0;Re0;Rr0]; (Eq. 24)

The vector Raer to the best fit sensor location is written asRaer0 plus a small correction 3 by 1 correction matrix dRaer; i.e.:

*Raer=Raer*0*+dRaer=Raer*0*+[dRa;dRe; dRr];* (Eq. 25)

Using the same procedure as defined by

*H*12*perpth=H*12*perpth*0+*dH*12*perpdRaerdRaer* (Eq. 26)

The derivative matrix dH12perpdRaer is similar to the derivative matrix of (Eq.17); i.e.

As in (Eq. 17), each of the elements of dH12perpdRaer is a partial derivative; e.g., dH1magdRa is the partial derivative of H1mag with respect to Ra, etc., and can be computed in the same manner as outlined for the elements of the matrix of (Eq. 17). The three linear equations implicit in (Eq. 26) are solved for the three unknowns in dRaer, after equating H12perpth to the corresponding 3 by 1 measurement matrix H12perpmeas The solution for dRaer is found using the MATLAB “\” operation, as:

*dRaer=dH*12*perpdRaer*\(*H*12*perpmeas−H*12*perpth*0) (Eq. 28)

The improved value for the 3 by 1 matrix Raer is:

*Raer=Raer*0+*dRaer* (Eq. 29)

This procedure is repeated iteratively using this value of Raer for a new Raer0 to minimize the error implicit with the linear nature of a Taylor expansion. The final Raer matrix has the three components of the drill bit location vector Raer required to locate the drill bit with respect to the proposed path. From this, the driller can determine the appropriate drill control signals needed to progress along the path to the desired exit point.

Although the present invention has been described in terms of a preferred embodiment, it will be understood that variations and modifications may be made in the above-described system without departing from the true spirit and scope thereof as defined in the following claims.

## Claims

1. A method for drill guidance, comprising:

- determining a proposed path for a borehole;

- positioning first and second current-conducting loops in known, laterally separated locations with respect to said proposed path;

- causing said first and second loops to generate corresponding first and second magnetic fields, each of said fields having an alternating polarity;

- positioning magnetic field sensors at a measurement location in said borehole;

- measuring, at said measurement location, the vector components of said first and second magnetic fields and

- determining, from said measured vector components of said first and second fields, the location of the sensors with respect to the locations of the magnetic loop sources.

2. The method of claim 1, further including:

- determining the direction of the gravity vector at said measurement location; and determining from said gravity vector and said measured magnetic field vectors the direction of the borehole at said sensors with respect to a surface direction.

3. The method of claim 1, wherein generating electromagnetic fields includes directing alternating currents of known amplitude and frequency through said loops.

4. The method of claim 1, wherein generating electromagnetic fields includes simultaneously directing alternating currents of known amplitudes and different frequencies through each of said loops.

5. The method of claim 1, wherein positioning said first and second loops includes placing said loops on opposite sides of said proposed path.

6. The method of claim 1, further including determining the lateral distance of said measuring location from the proposed path and the direction of said borehole with respect to the direction of the proposed path.

7. Apparatus for borehole surveys comprising:

- a downhole tool located in a borehole in the Earth, said tool having an axis and including a magnetometer for measuring x, y and z vector components of magnetic fields at the tool;

- an electromagnetic excitation system including two electrical loop conductors at known locations, laterally spaced from each other and from a proposed path of said borehole, and carrying known alternating electrical currents producing corresponding alternating electromagnetic fields in the region of said magnetometer;

- computer circuitry;

- a telemetry link for transmitting measurement data signals corresponding to the respective measured vectors of magnetic fields generated by each of said loops from said magnetometer to said computer circuitry; and

- circuits in said computer circuitry responsive to said measurement signals for determining the location of the borehole sensors.

8. The apparatus of claim 7, wherein said downhole tool further includes sensors for measuring the Earth's gravity vector and for determining the orientation of the downhole tool, said telemetry link transmitting measurement data signals corresponding to said gravity vector and orientation measurement to said computer for determination of the direction of the borehole with respect to said proposed path.

9. The apparatus of claim 8, wherein said downhole tool is a measurement while drilling instrument.

10. The apparatus of claim 8, wherein the electrical current supplied to each of said loops is an alternating current of a different frequency.

11. The apparatus of claim 8, wherein:

- said two electrical loop conductors carry first and second alternating currents, respectively, said currents producing corresponding first and second electromagnetic fields in the region of said downhole tool in said borehole; and

- said electrical loop conductors are spaced on opposite sides of said proposed path of said borehole.

12. The apparatus of claim 11, wherein each of said loop conductors comprises multiple turns of wire.

13. A method for location determination, comprising:

- positioning first and second current-conducting loops at known spaced locations;

- energizing said loops with known electrical currents to produce corresponding first and second electromagnetic fields;

- positioning a magnetic field vector sensor to detect x, y and z vector components of said first and second fields; and

- determining from said vector components the location of said sensor with respect to said loops.

14. The method of claim 13, wherein:

- positioning said loops includes positioning the loops on opposite sides of a proposed path to be followed by said sensor; and

- determining the location of said sensor includes locating said sensor with respect to said path.

15. The method of claim 13, wherein energizing said loops includes supplying alternating current of a known amplitude and frequency to one loop at a time.

16. The method of claim 13, wherein energizing said loops includes supplying alternating current of known amplitude and different known frequencies to each loop.

17. The method of claim 13, further including:

- detecting, at the location of said sensor, the Earth's gravity vectors and the orientation vectors of the sensor; and

- determining from said vectors the direction of the sensor with respect to the locations of said loops.

18. The method of claim 13, wherein determining the location of the sensor includes:

- time averaging magnetic field vector data obtained for each of said loops by the sensor;

- calculating theoretical location vectors for the sensor; and

- optimizing the match between theoretical location values and measured magnetic field vector data to determine the location of the sensor.

19. The method of claim 18, wherein;

- positioning said loops includes positioning the loops on opposite sides of a proposed path to be followed by said sensor; and

- determining the location of said sensor includes locating said sensor with respect to said path.

20. The method of claim 19, wherein energizing said loops includes supplying alternating current of a known amplitude and frequency to one loop at a time.

21. The method of claim 19, wherein energizing said loops includes supplying alternating current of known amplitude and different known frequencies to each loop.

**Patent History**

**Publication number**: 20100256913

**Type:**Application

**Filed**: Mar 31, 2010

**Publication Date**: Oct 7, 2010

**Inventor**: Arthur F. Kuckes (Ithaca, NY)

**Application Number**: 12/751,154

**Classifications**

**Current U.S. Class**:

**Well Logging Or Borehole Study (702/6);**Downhole Test (73/152.54)

**International Classification**: E21B 47/00 (20060101);