SYSTEMS AND METHODS FOR GUIDING THE DRILLING OF A HORIZONTAL WELL

Abstract

System and methods for guiding the drilling of a horizontal well are disclosed. A current is provided in at least one conductor positioned in a target vertical well. A magnetic field generated by the current is measured at a drilling assembly that is drilling the horizontal well. A direction from the drilling assembly to the target vertical well is determined based at least in part on the measured magnetic field. A distance from the drilling assembly to the target vertical well is determined based at least in part on the measured magnetic field. The determination of the distance includes determining at least one gradient.

Description

FIELD OF THE INVENTION

The invention relates generally to systems and methods for guiding the drilling of a horizontal well and, more specifically, to systems and methods for guiding the drilling of a horizontal well into an intersection with a vertical well.

BACKGROUND OF THE INVENTION

Directional drilling, or slant drilling, is typically utilized to drill non-vertical wells. Directional drilling is utilized in a wide variety of applications, including oil drilling, utility installation drilling, and in-seam drilling. In some applications, directional drilling is utilized to intersect an existing vertical well with a horizontal well. Various techniques and methods are typically utilized in an attempt to accurately intersect the vertical well with the horizontal well that is being drilled.

One conventional technique that is utilized is to rely on directional surveys in an attempt to place the horizontal well in close proximity to a vertical target well. However, this technique may often be ineffective due to errors in the surveying of the two wells and the land survey at the surface.

Other conventional techniques utilize various sensors that are intended to assist in the guiding of the intersection of the horizontal well with a vertical well. The sensors may be situated either in the drilling assembly of the horizontal well with a signal source in the existing vertical well or, alternatively, in the existing vertical well with a signal source in the drilling assembly of the horizontal well. However, many of these conventional techniques may also include small but inherent errors in determining the intersection of the vertical and horizontal wells. Errors in estimating the positions of both the vertical and horizontal wells can accumulate as drilling and surveying progresses. Eventually, the additive errors impacting the path or trajectory may be so large as to prevent a desired near intersection of the two wells.

Additionally, it can be difficult to accurately determine a range or distance between a horizontal well that is being drilled and a target vertical well utilizing the prior art techniques. A failure to accurately determine the range or distance often leads to failed intersections or poor intersections between the two wells. A poor determination of range or distance may prevent a driller that is guiding the drilling of the horizontal well from being able to plan and take corrective maneuvers in steering the drilling of the horizontal well. Thus, without an accurate determination of range or distance, a driller may not be able to correct the direction of the drilling of the horizontal well in order to intersect a vertical well.

Accordingly, there is a need for improved systems and methods for guiding the drilling of a horizontal well in order to intersect a vertical well.

BRIEF DESCRIPTION OF THE INVENTION

According to one aspect of the invention, a method is provided for guiding the drilling of a horizontal well. A current is provided in at least one conductor positioned in a target vertical well. A magnetic field generated by the current is measured at a drilling assembly that is drilling the horizontal well. A direction from the drilling assembly towards the target vertical well is determined based at least in part on the measured magnetic field. A distance from the drilling assembly to the target vertical well is determined based at least in part on the measured magnetic field. The determination of the distance also includes at least one gradient.

According to another aspect of the invention, a system is provided for guiding the drilling of a horizontal well. The system can include at least one conductor, one or more sensors, and a control unit. The at least one conductor is positioned in a target vertical well. The at least one conductor carries a current signal. The one or more sensors are associated with a drilling assembly that is drilling the horizontal well. The one or more sensors measure the intensity of a magnetic field generated by the current signal. The control unit receives the intensity measurements from the one or more sensors. The control unit determines a direction from the drilling assembly towards the target vertical well based at least in part on the received intensity measurements. The control unit determins a distance from the drilling assembly to the target vertical well based at least in part on the received intensity measurements. At least one gradient calculation is utilized to determine the distance from the drilling assembly to the target vertical well.

Other aspects of the invention will become apparent from the following description taken in conjunction with the following drawings.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

Having thus described the invention in general terms, reference will now be made to the accompanying drawings, which are not necessarily drawn to scale, and wherein:

FIG. 1 is a schematic diagram of an exemplary intersection of a vertical well by a horizontal well in accordance with an illustrative aspect of the invention.

FIG. 2 is a schematic diagram of a target vertical well, according to an illustrative aspect of the invention.

FIG. 3 is a schematic diagram of an exemplary drilling assembly that is utilized to detect a target vertical well, according to an illustrative aspect of the invention.

FIG. 4 is a schematic diagram that depicts the current direction of the drilling assembly and the target direction to the target vertical well, according to an illustrative aspect of the invention.

FIG. 5A is a top view schematic diagram of the drilling of a horizontal well to form an intersection or near-intersection with a vertical well, according to an illustrative aspect of the invention.

FIG. 5B is a cross sectional view taken along the line A to A′ of the drilling of a horizontal well to form an intersection or near-intersection with a vertical well, according to an illustrative aspect of the invention.

FIG. 6 is a top view schematic diagram of exemplary adjustments that are made during the drilling of a horizontal well to form an intersection or near-intersection with a target vertical well, according to an illustrative aspect of the invention.

FIG. 7 is a block diagram of an exemplary control unit that is utilized in accordance with certain aspects of the invention.

FIG. 8 is an exemplary flowchart of the general operation of the control unit of FIG. 7, according to an illustrative aspect of the invention.

FIG. 9 is a graphical representation of one example of falloff rates for two different alternating current magnetic fields having different intensities, in accordance with an illustrative aspect of the invention.

FIG. 10A is an exemplary flowchart depicting the operations that can be taken by the control unit of FIG. 7 to determine a distance or range to a target vertical well, in accordance with an illustrative aspect of the invention.

FIG. 10B is a graphical representation of the distances and values that can be measured and/or determined by utilizing the exemplary operations depicted in FIG. 10A, in accordance with an illustrative aspect of the invention.

FIG. 11 is an exemplary flowchart depicting the operations that can be taken by the control unit of FIG. 7 to determine a direction to a target vertical well, in accordance with an illustrative aspect of the invention.

DETAILED DESCRIPTION OF THE INVENTION

Illustrative aspects of the inventions now will be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all aspects of the inventions are shown. Indeed, the invention may be embodied in many different forms and should not be construed as limited to the aspects set forth herein; rather, these aspects are provided so that this disclosure will satisfy applicable legal requirements. Like numbers refer to like elements throughout the description and drawings.

The invention is described below with reference to block diagrams of systems, methods, apparatuses and computer program products according to an aspect of the invention. It will be understood that each block of the block diagrams, and combinations of blocks in the block diagrams, respectively, can be implemented by computer program instructions. These computer program instructions may be loaded onto a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions which execute on the computer or other programmable data processing apparatus create means for implementing the functionality of each block of the block diagrams, or combinations of blocks in the block diagrams discussed in detail in the descriptions below.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions that implement the function specified in the block or blocks. The computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions that execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the block or blocks.

Accordingly, blocks of the block diagrams support combinations of ways to perform the specified functions, combinations of steps for performing the specified functions and program instruction for performing the specified functions. It will also be understood that each block of the block diagrams, and combinations of blocks in the block diagrams, can be implemented by special purpose hardware-based computer systems that perform the specified functions or steps, or combinations of special purpose hardware and computer instructions.

The invention may be implemented through an application program running on an operating system of a computer. The invention also may be practiced with other computer system configurations, including hand-held devices, multiprocessor systems, microprocessor based or programmable consumer electronics, mini-computers, mainframe computers, etc.

Application programs that are components of the invention may include routines, programs, components, data structures, etc. that implement certain abstract data types, perform certain tasks, actions, or tasks. In a distributed computing environment, the application program (in whole or in part) may be located in local memory, or in other storage. In addition, or in the alternative, the application program (in whole or in part) may be located in remote memory or in storage to allow for the practice of the inventions where tasks are performed by remote processing devices linked through a communications network. Exemplary aspects of the invention will be described with reference to the figures, in which like numerals indicate like elements throughout the several drawings.

Disclosed are aspects of systems and methods for guiding or controlling the drilling of a horizontal well or hole so as to intersect or very nearly intersect an existing vertical well or a series of vertical wells. As used herein, the term “horizontal” means parallel to or approximately parallel to level ground or the plane of the horizon. As used herein, the term “vertical” means being in a position or direction that is perpendicular to or approximately perpendicular to the plane of the horizon. The vertical wells to be intersected may be disposed more or less in a straight line; however, it will be appreciated that the horizontal well may be utilized to intersect other vertical well arrangements.

A signal may be transmitted, injected, or otherwise communicated into an existing vertical well that is a target for the intersection or near intersection by a horizontal well that is to intersect the vertical well. The drilling assembly utilized in the drilling of the horizontal well may include or contain sensing components that are capable of identifying the signal in the vertical well. Once the signal in the vertical well has been identified, the location of the vertical well in relation to the drilling assembly may be accurately determined.

Both a direction from the drilling assembly to the vertical well and a range or distance between the drilling assembly and vertical well may be determined. Based at least in part on these determinations, the steered path, course, or trajectory of the horizontal well may he controlled so as to bring about an intersection or near-intersection of the horizontal well and the target vertical well. Other target vertical wells may then be located and intersected by the horizontal well by utilizing the same technique. Accordingly, a single horizontal well may intersect a second well or multiple vertical wells.

FIG. 1 is a schematic diagram of an exemplary application 100 in which a vertical well 105 is intersected by a horizontal well 110 in accordance with an illustrative aspect of the invention. It will be appreciated that the systems, methods, and techniques described in aspects of the invention may be utilized in a wide variety of applications. For example, aspects of the invention may be utilized in the drilling of horizontal wells in conjunction with collecting hydrocarbon products.

Certain hydrocarbon products such as gases, for example, methane often found captured in relatively shallow coal deposits (also referred to as coal bed methane, or CBM) are usually held in place by the hydrostatic pressure of water. In order to collect these gases or other hydrocarbon products, the partial pressure of the water can be reduced by a suitable “dewatering” process. The “dewatering” process removes a critical amount of water in order to release the gases and induce a flow of the gases toward the wellbore of a nearby well, such as, for example, the vertical well 105 of FIG. 1. The gases or other hydrocarbon products are then extracted from the well, compressed, and piped to market. In order to complete the “dewatering,” a vertical well 105 can be underreamed within a coal seam or coal seams.

The underreaming functions to enlarge a section 115 of the wellbore which is within a coal seam past its original drilled size. The wellbore can be enlarged to any size such as, for example, to a diameter of several feet. The enlarged wellbore section 115 acts as a reservoir or sump for collection of the water, thereby allowing a more efficient removal of water in order to collect the gases. A horizontal well 110 that is being drilled is steered into an intersection or near-intersection with the vertical well 110 near the enlarged section 115 of the wellbore in order to remove the water and later to produce the methane gas flowing into the enlarged section 115.

An extension of this method utilizes a steered horizontal well 110 to interconnect multiple vertical wells, thereby further increasing efficiency in collecting gases. A further extension of the method is to drill a complex pattern of horizontal wells and interconnected passages between strategically placed vertical wells. Such a configuration of horizontal and vertical wells reduces the number of surface locations needed to facilitate drilling and collection of gases. Accordingly, such a configuration may be more efficient and may reduce the environmental impact caused at the surface.

According to aspects of the invention, at least one vertical well 105 is intersected or nearly intersected by a horizontal well 110. The drilling of the horizontal well 110 can be precisely or accurately guided utilizing a measurement while drilling (MWD) system, technique, and/or method. Although aspects of the invention are described herein as utilizing a measurement while drilling (MWD) system or technique, it will be appreciated that other tools, systems, techniques and/or methods can be utilized in accordance with aspects of the invention. A directional driller (not shown) that is directing or guiding the drilling of the horizontal well 110 is supplied with data or information that will assist in completing the intersection or near-intersection. The directional driller can be an individual, entity and/or a system or system component that is guiding the drilling of the horizontal well 110. The directional driller can be located at or associated with a surface location 117 at which the drilling of the horizontal well 110 is commenced. The directional driller guides a steerable drilling assembly 120 that is utilized to drill the horizontal well. The data provided to the directional driller can include information associated with a direction from the drilling assembly 120 to the target vertical well 105 and information associated with a distance from the drilling assembly to the target vertical well 105. The data allows the directional driller to orient the drilling assembly 120 and control the placement and drilling of the horizontal well 110. Additionally, the data allows an accurate intersection or near-intersection between the horizontal well 110 and the enlarged section 115 of the vertical well 105. The accurate intersection or near-intersection achieved by utilizing the data allows a reduction of the size needed for the enlarged section 115 of the vertical well 105. By increasing the accuracy in guiding the drilling assembly 120 to the target vertical well 105, both the size of the enlarged section 115 and the time needed to underream and clean the vertical well 105 can be reduced.

With continued reference to FIG. 1, the drilling assembly 120 includes at least one motor 125 and at least one drill bit 130. The drilling assembly 120 also includes one or more sensors 135 that are utilized to locate the target vertical well 105. A wide variety of techniques, methods, or systems can be utilized to locate the target vertical well 105. According to an aspect of the invention, the one or more sensors 135 are sensors that are capable of detecting a magnetic field such as, for example, a magnetic field that is generated or created by an alternating current. One or more conductors 140 are positioned in the vertical well 105 or near the vertical well 105. The one or more conductors 140 are utilized to carry a current through at least a portion of the length of the vertical well 105. The current is supplied to the one or more conductors 140 by an appropriate current generation source such as, for example, a suitable alternating current generation source 145.

The alternating current generation source 145 is connected to one end of the one or more conductors 140. An alternating current is driven through the one or more conductors 140 in order to generate alternating current magnetic fields that can be detected by the one or more sensors 135 in the drilling assembly 120. The one or more conductors 140 are also connected to or terminated at a ground 150 such as, for example, to earth ground. The one or more conductors 140 are terminated at a ground 150, such as earth ground, at their distal ends. By connecting the one or more conductors 140 to a ground 150, the one or more conductors 140 create a discrete source for detection by the one or more sensors 135, as explained in greater detail below with reference to FIG. 2.

Additionally, at least a portion of the vertical well 105 may include an appropriate casing 155, as will be understood by those skilled in the art. The casing 155 can be any suitable well casing or combination of well casings. Similarly, at least a portion of the horizontal well 110 may include an appropriate casing 160. The casing 160 can be any suitable well casing or combination of well casings.

FIG. 2 is a schematic diagram of a target vertical well 105, according to an illustrative aspect of the invention. One or more conductors, similar to 140 in FIG. 1, are lowered into the target vertical well 105. The one or more conductors, such as 140, make up a wireline 205. The wireline 205 is lowered into the target vertical well 105 by a suitable wireline lowering device 207. The wireline 205 is extended from the surface through the target vertical well 105, and the wireline 205 is terminated to a ground, similar to 150 in FIG. 1, at its distal end. The wireline 205 includes a grounding electrode 210 that forms a suitable connection to earth ground.

The grounding electrode 210 is any suitable contact electrode that forms a connection to earth ground, as will be understood by those of skill in the art. At the surface, one side of an alternating current generation source, shown as 145 and similar to that shown in FIG. 1, is connected to the wireline 205, and the alternating current generation source, such as 145, drives an alternating current into the wireline 205. The opposite side of the alternating current generation source, such as 145, is connected to a ground, such as 150, for example, to earth ground. Accordingly, an alternating current is driven through the wireline 205 and allowed to return to the alternating current generation source, such as 145, through the earth. The alternating current that is communicated onto or present in the wireline 205 creates or generates one or more alternating current magnetic fields or lines of magnetic flux, such as 215. Given an elongated wireline 205, the alternating current magnetic fields propagate in perpendicular or substantially perpendicular manner from the wireline 205. At the end of the wireline 205, the grounding electrode 210 functions to diffuse the alternating current into the earth. The alternating current magnetic field may have many different intensities and/or frequencies. For example, the alternating current magnetic field may be a low-frequency field.

In the horizontal well, shown as 110 in FIG. 2, in progress, the drilling assembly, such as 120, includes one or more sensors, such as 135, that detect the alternating current magnetic fields that are produced as a result of the current in the wireline 205. The one or more sensors, such as 135, can include any number of sensors that are capable of detecting the alternating current magnetic fields such as, for example, an orthogonal triad of alternating current sensors. According to an aspect of the invention, the one or more sensors 135 have a sensitivity of approximately 0.3 nanoteslas; however, it will be appreciated that sensors with other sensitivities may be utilized as desired. For example, sensors with a sensitivity of approximately 0.1 nanoteslas can be utilized. Additionally, the one or more sensors 135 are capable of detecting very low intensities of low-frequency alternating current magnetic fields. It will be appreciated that the magnitude of the current signal within the wireline 205 can be controlled so that the alternating current magnetic fields propagated from the wireline 205 have intensities that fall within the sensitivity range of the one or more sensors 135.

FIG. 3 is a schematic diagram of an exemplary drilling assembly 120 that is be utilized to detect a target vertical well, such as 105, according to an illustrative aspect of the invention. The one or more sensors, such as 135, in the drilling assembly 120 detect the alternating current magnetic field that is produced by the wireline 205. The field vector at the one or more sensors 135 is at a right angle to a target direction to the target vertical well 105. Additionally, the field vector at the one or more sensors 135 is at a tangent to the concentric lines of magnetic flux that are propagating from the wireline 205.

The alternating current magnetic field is detected and measured by the one or more sensors 135. The one or more sensors 135 then communicate the measurements to one or more control units that process the measurements. The information can be communicated via any appropriate communication technique(s) or device(s) such as, for example, a mud pulse system, a steering toot probe, a wired connection, a wireless connection, a cellular connection, and/or a radio connection. A first control unit 305 can be included in or associated with the drilling assembly 120. The first control unit 305 can process the measurements and communicate or transmit to a directional driller information associated with a distance and/or a direction from the drilling assembly 120 to the target vertical well 105. The communicated information can be further processed by at least one control unit (not shown) associated with the directional driller.

Information associated with the direction and distance to the target vertical well 105 can be communicated or provided to the directional driller in an appropriate form that allows the directional driller to guide the drilling of the horizontal well 110 to achieve an intersection or near-intersection with the target vertical well 105. With the provided information, the directional driller can adjust the path of the drilling assembly 120 as needed to achieve the intersection or near-intersection within acceptable limits of curvature, or “dogleg” in the horizontal well 110. Small amounts of dogleg in the horizontal well 110 may be acceptable. The acceptable dogleg may vary depending on the application, and the acceptable dogleg can be expressed in any appropriate form such as, for example, in degrees per 100 feet or in degrees per 30 meters. Relatively larger amounts of dogleg or curvature of the hole may cause problems in the continuation of the drilling and/or in the later installation of pipe in the horizontal well 110.

FIGS. 4-6 are schematic diagrams depicting the guidance of the drilling of a horizontal well 110 to create an intersection or near-intersection with a target vertical well 105, according to an illustrative aspect of the invention. FIG. 4 is a schematic diagram that depicts the current direction 405 of the drilling assembly, shown in FIGS. 1-3 as 120, and the target direction 420 to the target vertical well 105. As shown in FIG. 4, the target direction 425 to the target vertical well 105 forms approximately a right angle with a line 410 that is approximately tangential to the are of the alternating current magnetic field 415 that is emitted from the wireline 205. An approximate angle θ 425 represents the difference between the current direction 405 and the target direction 420 if such a difference exists.

FIG. 5A is a top view schematic diagram of the drilling of a horizontal well, shown in FIG. 1 as 110, to form an intersection or near-intersection with a vertical well, shown in FIG. 1 as 105, according to an illustrative aspect of the invention. Similarly, FIG. 5B is a cross sectional view taken along the line A to A′ of FIG. 5A and depicting the drilling of a horizontal well 110 to form an intersection or near-intersection with a vertical well 105, according to an illustrative aspect of the invention. FIG. 5B is a view along the path taken by the horizontal well 110 in progress, and FIG. 5B depicts the formation of the intersection or near-intersection between the horizontal well 110 and the vertical well 105 at an enlarged section 115 of the vertical well 105.

FIG. 6 is a top or plan view schematic diagram of adjustments that may be made during the drilling of a horizontal well 110 to form an intersection or near-intersection with a target vertical well 105. In other words, FIG. 6 illustrates how a directional driller utilizes the capability for determining range and/or direction in order to guide the drilling of the horizontal well 110. With reference to FIG. 6, from a starting location 600 of the drilling assembly 120, the current direction 405 of the drilling assembly 120 is shown. The current direction 405 can be the direction from the drilling assembly 120 to a target position 610 of the vertical well 105 that is based on a survey taken at the surface or on some other estimated location of the vertical well 105. Also shown in FIG. 6 is the target direction 420 towards the target vertical well 105. A directional driller that is guiding the drilling assembly 120 can follow or approximately follow the current direction 405 until the drilling assembly 120 reaches a distance 605 from the vertical well 105 at which the one or more sensors 135 may detect the alternating current magnetic field.

The distance 605 may be referred to as the detection range of the one or more sensors 135. The detection range 605 of the one or more sensors is dependent upon the type or types of sensors that are utilized. The approximate detection range 605 is typically a known value that is associated with one or more of the sensors; however, the detection range 605 may be determined and/or verified by any suitable method or technique. Additionally, it will be appreciated that the detection range 605 may vary according to a variety of factors such as, for example, the density of the earth and/or other materials that are situated between the drilling assembly 120 and the target vertical well 105.

Once the drilling assembly 120 reaches or is within the detection range 605, the directional driller can adjust the path of the drilling assembly based on the measurements taken by the one or more sensors 135. The directional driller can adjust the path in order to form an intersection or near-intersection between the horizontal well 110 and the vertical well 105. An enlarged section 115 of the vertical well 105 may be situated at the intersection or near-intersection. As shown in FIG. 6, the drilling of the horizontal well 110 can be guided along an adjusted path 615 based at least in part on the measurements taken by the one or more sensors 135 in order to form the intersection or near-intersection.

According to an aspect of the invention, the measurements taken by the one or more sensors 135 are processed by one or more control units, similar to 305 in FIG. 7, in order to provide the directional driller with appropriate information associated with an accurate direction and an accurate distance or range from the drilling assembly 120 to the target vertical well 105. The processed measurements and/or data can be provided to the directional driller in an appropriate format that facilitates the guiding of the drilling assembly 120 by the directional driller.

FIG. 7 depicts a block diagram of an exemplary control unit 305 utilized in accordance with the invention in order to determine the direction and distance from the drilling assembly, such as 120, to a target vertical well, such as 105. The control unit 305 can be a control unit associated with the drilling assembly 120. A similar control unit can be associated with the directional driller at the surface. It will be appreciated that aspects of the invention may utilize any number of control units. For example, certain aspects may utilize a single control unit.

The control unit 305 of FIG. 7 includes a memory 705 and a processor 710. The memory 705 stores programmed logic 715 (e.g., software) in accordance with the invention. One example of software or a computer-readable medium is program code or a set of instructions operable to receive and process measurements data in order to determine a distance and/or direction from the drilling assembly, such as 120, to a target vertical well, such as 105. The memory 705 also includes data 720 utilized in the operation of the aspect of the invention, and also includes an operating system 725. The data 720 can include measurements data taken by the one or more sensors, such as 135, in the drilling assembly 120. The processor 710 utilizes the operating system 725 to execute the programmed logic 715, and in doing so, may also utilize the data 720. A data bus 730 provides communication between the memory 705 and the processor 710. Users can interface with the control unit 305 via one or more user interface device(s) 735 such as a keyboard, mouse, control panel, or any other devices capable of communicating digital data to or from the control unit 305.

The control unit 305 can communicate with external devices such as, for example, the one or more sensors 135, via one or more appropriate interface devices 740. The one or more interface devices 740 can also facilitate the output of data by the control unit 305 to one or more suitable output devices such as, for example, a display, and/or to one or more other system components or external devices. It will be appreciated that communication with external devices may be facilitated with any suitable data communication technique such as, for example, communication via a direct connection, communication via a wired network connection, communication via a wireless network connection and/or communication via a cellular network connection. Further the control unit 305 and the programmed logic 715 implemented thereby may comprise software, hardware, firmware or any combination thereof.

FIG. 8 is an exemplary flowchart of example general operations taken by a control unit, such as 305, in accordance with an illustrative aspect of the invention. It will be appreciated that some or all operations described herein can be achieved by a single control unit or by a combination of control units utilized in accordance with the invention. Once the control unit, such as 305, commences operations, the control unit 305 goes to block 805 and receive measurements from the one or more sensors, such as 135, in the drilling assembly, such as 120. The received measurements can be associated with the alternating current magnetic field that is generated by the wireline, such as 205, in the vertical well, such as 105. For example, the received measurements can be associated with a strength of the alternating current magnetic field.

At block 810, the control unit 305 determines a distance from the drilling assembly 120 to the target vertical well 105. At block 815, the control unit 305 determines a direction from the drilling assembly 120 to the target vertical well 105. The path of the drilling assembly can be adjusted based at least in part on the determined direction and distance or range in order to facilitate an intersection or near-intersection between the horizontal well 110 and the target vertical well 105.

At block 820, the distance and/or direction determinations can optionally be adjusted. The adjustments can place the determinations in a more appropriate form for subsequent processing or actions that may be taken based upon the determinations. For example, if the directional driller is an individual and the distance determinations are made using metric units (e.g., meters), then the distance determinations can be adjusted to standard units (e.g., feet) before they are communicated and/or displayed to the directional driller. As another example, if the directional driller is an individual, then the direction determination can be adjusted or corrected to magnetic north prior to being communicated and/or displayed to the directional driller.

For example, the direction determination includes an approximate angle θ 425 representing the difference between the current direction 405 of the drilling assembly 120 and the target direction 420 to the vertical well 105. The angle θ can be corrected to magnetic north in order to provide the directional driller with a desired heading for the drilling of the horizontal well 110 in order to achieve an intersection or near-intersection with the target vertical well 105. It will be understood that any adjustments made to the distance and/or direction determinations are optional and may not be necessary. For example, if the path of the drilling assembly 120 is automatically controlled by a suitable device or system such as, for example, a computerized guidance system, then adjustments to the distance and/or direction determinations may not be necessary.

At block 825, the direction and/or the distance determinations can optionally be communicated to the directional driller. The communication to the directional driller can include a communication to a control unit associated with the directional driller from another control unit such as, for example, a control unit associated with the drilling assembly 120. The communication can also include a communication to an appropriate output device associated with the directional driller such as, for example, a display associated with the directional driller.

The operations described in FIG. 8 can be performed continuously or periodically as the horizontal well 110 is drilled. With reference to FIG. 8, the operations of the control unit 305 continue at block 805 following the determination of a direction and a distance to a target vertical well 105, and the optional adjustment and communication of these determinations. At block 805, the control unit 305 receives new measurements from the one or more sensors 135, and the control unit 305 utilizes these new measurements to determine a new or updated direction and/or distance to a target vertical well 105. As shown in FIG. 8, the operations of the control unit 305 are performed continuously; however, it will be appreciated that the operations of the control unit 305 can be performed periodically.

For example, the control unit 305 can receive and process measurements at predetermined time intervals such as, for example, every ten seconds. Many different predetermined time intervals may be utilized in accordance with aspects of the invention, as will be understood by those of skill in the art. Additionally, it will be understood that the control unit 305 can direct the storage of any number of received measurements, determined values, and/or adjusted values. For example, the control unit 305 can store a measurement or a value in the memory 705 of the control unit 305. As another example, the control unit 305 can direct an associated memory device to store a measurement or a value.

It will be appreciated that the operations described above with reference to FIG. 8 do not necessarily have to be performed in the order set forth in FIG. 8, but instead can be performed in any suitable order. Additionally, it will be understood that, in certain aspects of the invention, the control unit 305 can perform more or less than all of the operations set forth in FIG. 8. It will also be appreciated that the operations set forth in FIG. 8 can be performed by any appropriate control unit or combination of control units such as, for example, a control unit associated with the drilling assembly and/or a control unit associated with the directional driller.

According to an aspect of the invention, a distance or range between the drilling assembly, such as 120 shown in FIG. 1, and the target vertical well, such as 105 shown in FIG. 1, is determined. The distance or range is determined utilizing one or more measurements that are taken by the one or more sensors, such as 135 shown in FIG. 1, of the drilling assembly, such as 120 shown in FIG. 1. In some aspects of the invention, the one or more sensors 135 include three sensors that measure the intensity of an alternating current magnetic field that is generated by a wireline 205 in the target vertical well 105; however, it will be understood that the drilling assembly 120 may include or be associated with any number of sensors that are configured to measure the intensity of the alternating current magnetic field.

The three sensors respectively measure the intensity of the alternating current magnetic field in three directions or dimensions. For example, a first sensor measures the intensity of the alternating current magnetic field in a direction that roughly corresponds to the current path of the drilling assembly 120, which can be referred to as the Z direction. As discussed earlier with reference to FIG. 4, the Z direction forms an approximate right angle with a line 410 that is approximately tangential to the arc of the alternating current magnetic field 415 that is emitted from the wireline 205. The second and third sensors measure the intensity of the alternating current magnetic field in respective directions that are perpendicular to the current path of the drilling assembly 120, which can be referred to respectively as the X direction and the Y direction. The X direction and the Y direction are additionally perpendicular to one another. The three sensors can take scalar and/or vector measurements of the alternating current magnetic field.

Once the intensity of the alternating current magnetic field has been determined by the three sensors, a single intensity measurement or value of the intensity is determined or calculated based on a combination of the thee intensity measurements, as will be understood by those of skill in the art. It will be appreciated that other suitable determinations of the intensity of the alternating current magnetic field can be utilized in accordance with aspects of the invention.

The distance or range is then determined or calculated based on one or more intensity measurements. Many different methods can be utilized in order to determine the distance or range, as will be appreciated by those of skill in the art. A few methods are discussed herein by way of example only. A first exemplary method assumes a relatively simple model of the alternating current magnetic field. The first exemplary method assumes a model in which there is no loss or very little loss of the current present on the wireline 205 into the surrounding vertical well 105 (i.e., the current producing the field is precisely known), and for which the grounding electrode 210 has a low termination resistance value, which creates a resistive path to ground with little or no current loss. In other words, the first exemplary model assumes a relatively ideal or ideal, straight current-carrying wire.

In the first exemplary method, the relationship between the value of the alternating current carried by the wireline 205, the generated field intensity, and the distance or range is given by the following equation:

$\begin{array}{cc}H=\frac{{\mu }_0·I}{2\pi ·r^n}& \left(1\right)\end{array}$

where “H” represents the generated field intensity, “I” represents the value of the alternating current carried by the wireline 205, “r” represents the distance or range, “n” represents the falloff rate of the magnetic field, and “μ₀” is a constant of 4π*10⁻⁷ T·m/A, or the permeability of free space. Equation (1) represents a special case of the Biot-Savart Law for the magnetic field intensity due to a current in a thin, infinitely long straight conductor. The value of “n” can be assumed to be equal to 1; however, it will be appreciated that other values for “n” may be utilized. For example, the value of “n” can change as the one or more sensors 135 approach the wireline 205 and the diffuse currents become more concentrated as the distance or range decreases. Simplifying equation (1) yields:

$\begin{array}{cc}H=\frac{2·I·{10}^{-7}}{r^n}\mathrm{or}H=\frac{K·I}{r^n}& \left(2\right)\end{array}$

where “K” is a constant of 2×10⁻⁷. Solving for distance or range yields:

$\begin{array}{cc}{r}^n=\frac{K·I}{H}\mathrm{or}r={\left(\frac{K·I}{H}\right)}^{-n}& \left(3\right)\end{array}$

This equation can be used to calculate range, and the current and the field intensity should be known (or closely estimated).

If a low loss wire model is assumed, then equation (3) can be utilized to determine or calculate the distance or range between the drilling assembly 120 and a target vertical well 105 if the current in the wireline 205 is known and the intensity of the alternating current magnetic field is known, accurately measured, and/or closely approximated. It will be appreciated that a value for the current can be assumed for the calculation based upon a current that is supplied to the wireline 205 by the alternating current generation source 145. Alternatively, the current can be measured in the wireline 205 by an appropriate current measuring device such as, for example, an ammeter or a current sensing transformer, and the current measurement can be communicated to a control unit such as, for example, the control unit 305 associated with the drilling assembly 120.

The second exemplary method for determining a distance between a drilling assembly 120 and a target vertical well 105 makes no or limited assumptions about the loss of current from the wireline 205 to the surrounding vertical well 105 and/or earth. Additionally, the second exemplary method does not assume that the amplitude of the alternating current in the wireline 205 is a known amplitude; however, the second exemplary method can assume that the alternating current in the wireline 205 has a constant or approximately constant amplitude. For certain applications, such as for example, the CBM application 100 depicted in FIG. 1, the wireline 205 may not have a current with an exactly known amplitude flowing through it. For example, as the wireline 205 approaches the grounding electrode 210, the amplitude of the current may not be exactly known at or near the terminal end of the wireline 205 connected to the grounding electrode 210. It will be appreciated that at least a portion of the current may be lost to the surrounding vertical well 105 and/or that at least a portion of the current may be diffused into the earth.

FIG. 9 is a graphical representation of one example of falloff rates for two different alternating current magnetic fields having different intensities. The falloff rates depicted in FIG. 9 represent the falloff rates of magnetic field intensity over distance as the magnetic fields propagate away from a source such as, for example, the wireline 205. With reference to FIG. 9, the field intensity versus distance is illustrated for the two magnetic fields 905, 910. The first magnetic field 905 represents a magnetic field that is generated by a lower amplitude of current in the wireline 205 relative to the current that generated the second magnetic field 910.

At a distance “r₁” from the source (e.g., the wireline 205), the intensity of the first magnetic field 905 is “H_a1” and the intensity of the second magnetic field 910 is “H_b1”. The slope or gradient of the first magnetic field 905 at “r₁” is Δ H_a1/Δ r₁, and the slope or gradient of the second magnetic field 910 at “r₁” is Δ H_b1/Δ r₁. The falloff rate is expressed as an exponential “n” in the denominator. The falloff rate of intensity over distance for each field is approximately the same and may be given by:

$\begin{array}{cc}\mathrm{FalloffOverDist}=\frac{1}{r^n}& \left(4\right)\end{array}$

Thus, the distance or range “r1” is independent of the strength of the source and of the attenuation effect.

According to an aspect of the invention, the second exemplary method for determining a distance or range can make use of one or more gradient calculations. For example, the second exemplary method can make use of the measurements of the intensity of the alternating current magnetic field to calculate one or more gradients. A method that utilizes one or more gradients to determine a distance or range can also be referred to as gradient ranging. Differentiating equation (2) above provides a rate of change of the alternating current magnetic field intensity as the distance changes given a value of the current in the wireline 205. Differentiating equation (2) leads to the derivative of the filed intensity with respect to distance, which can be referred to as the field gradient. The field gradient is given by:

$\begin{array}{cc}\frac{H}{r}=\frac{-n·K·I}{r^{n+1}}& \left(5\right)\end{array}$

where “K” is a constant of 2×10⁻⁷. The derivative can be utilized with the intensity value at a location to determine or calculate the distance or range to the target vertical well 105. Taking the ratio of the intensity to the gradient results in an expression for the distance or range “r” and the falloff rate “n”, given as:

$\begin{array}{cc}\frac{H}{\left(\frac{H}{r}\right)}=\frac{\left(K·I\right)}{-r^n}·\frac{\left(r^{n+1}\right)}{\left(-n·K·I\right)}=\frac{-r}{n}& \left(6\right)\end{array}$

From equation (6), “r” is determined as:

$\begin{array}{cc}-r=n·\left[\frac{H}{\left(\frac{H}{r}\right)}\right]& \left(7\right)\end{array}$

In equation (7), the constant “K” and the current “I” are no longer used. Further, a close approximation for dH/dr can be given by ΔH/Δr. Accordingly, the rate of change of the measured intensity over a change in distance can be utilized in a determination of a distance between the drilling assembly 120 and a target vertical well 105. In a situation in which a single set of sensors 135 is included in the drilling assembly 120, the gradient can be measured and/or approximated by utilizing the sensors 135 in at least two positions. At each position, the intensity of the alternating current magnetic field is measured, and a determination of the distance or range to the target vertical well 105 is made based at least in part on the intensity measurements at each position. Each measured intensity can be the total intensity of the alternating current magnetic field that is measured at each position. Additionally, at each position, a depth of the drilling assembly 120 from the surface can be inputted and/or measured. The value of “n” can also be inputted and/or entered. It will be appreciated that a predetermined value for “n” can be inputted such as, for example, a default value of one.

According to an aspect of the invention, the measurements can be made in many different modes of operation for the drilling assembly 120 such as, for example, a drilling mode, pushing on the bit, or in a pulling-back or off-bottom mode. One or more sets of data can be taken to improve the accuracy of the distance or range determination. One or more sets of data can be taken at one or more locations or positions of the drilling assembly 120. It will be appreciated that a plurality of determinations based on a plurality of data sets can be averaged together to improve the accuracy of the determinations.

FIG. 10A is an exemplary flowchart depicting exemplary operations taken by the control unit, such as 305 of FIG. 7, to determine a distance or range to a target vertical well 105, in accordance with an illustrative aspect of the invention. The operations depicted in FIG. 10A utilize a drilling assembly 120 that is operating in a pulling-back or off-bottom mode. At block 1005, the drilling assembly 120 is located or stopped at a first position “P_a”. Point “P_a” is a point that is situated at a desired depth. At point “P_a”, the drill bit 130 is pulled off the bottom by an appropriate distance such as, for example, by one or two foot. At point “P_a”, the distance or range to the target vertical well 105 is given as “r_a”. At block 1010, data is acquired from the one or more sensors 135 and the total magnetic field intensity “H_a” is determined by the control unit 305. The data and/or the field intensity “H_a” is stored for later use at block 1015.

At block 1020, the drilling assembly 120 is moved to a different position “P_b” in the horizontal well 110. For example, the drilling assembly 120 is moved forward in the horizontal well 110 by a predetermined distance “Δr₁”. The predetermined distance “Δr₁” can be any appropriate distance such as, for example, a distance that is much smaller than the distance or range from the drilling assembly 120 to the target vertical well 105. At position “P_b”, the distance or range to the target vertical well 105 is given as “r_b”. At block 1025, data is acquired from the one or more sensors 135 and the total magnetic field intensity “H_b” is determined by the control unit 305. The data and/or the field intensity “H_b” is stored for later use at block 1030.

At block 1035, the drilling assembly 120 is moved to a different position “P_c” in the horizontal well 110. For example, the drilling assembly 120 is moved forward in the horizontal well 110 by a predetermined distance “Δr₂”. The predetermined distance “Δr₂” can be any appropriate distance such as, for example, a distance that is much smaller than the distance or range from the drilling assembly 120 to the target vertical well 105. The predetermined distance “Δr₂” can be approximately equal to the distance “Δr₁”; however, it will be understood that “Δr₂” may be a different distance than “Δr₁”. At position “P_c”, the distance or range to the target vertical well 105 is given as “r_c”. At block 1040, data is acquired from the one or more sensors 135 and the total magnetic field intensity “H_c” is determined by the control unit 305. The data and/or the field intensity “H_c” is stored for later use at block 1045.

At block 1045, several data values are stored by the control unit 305 for later use. For example, values for “P_a”, “P_b”, and “P_c” are stored. The corresponding depths at “P_a”, “P_b”, and “P_c” can respectively be “r₁”, “r₂”, and “r₃”. Additionally, the values can be referenced to the same point such as, for example, to the drill bit 130 of the drilling assembly 120. Values for “n” and “K” can also be stored by the control unit 305. The value for “n” can be set to a default value such as, for example, to 1.0. The value of “K” can be 2×10⁻⁷. It will be appreciated that other values can be stored by the control unit 305. These other values may include values utilized in calculations other than those for gradient ranging. These other values may include for example, a value of the current “I” that is present in the wireline 205.

At block 1050, values for the average intensity between two positions and the difference in intensity for two positions is calculated by the control unit 305 according to the following equations:

$\begin{array}{cc}{H}_{\mathrm{avg}1}=\frac{\left(H_a+H_b\right)}{2}\Delta H_1=H_b-H_aH_{\mathrm{avg}2}=\frac{\left(H_b+H_C\right)}{2}\Delta H_2=H_c-H_b& \left(8\right)\end{array}$

At block 1055, one or more gradient ranging calculations are determined by the control unit 305 according to the following equations:

$\begin{array}{cc}{\mathrm{Range}}_{\mathrm{grad}1}=n·\frac{H_{\mathrm{avg}1}}{\left(\frac{\Delta H_1}{\Delta r_1}\right)}-\frac{\Delta r_1}{2}{\mathrm{Range}}_{\mathrm{grad}2}=n·\frac{H_{\mathrm{avg}2}}{\left(\frac{\Delta H_2}{\Delta r_2}\right)}-\frac{\Delta r_2}{2}& \left(9\right)\end{array}$

The determined gradient range values are referenced to position “P_a”. Additionally, the values can be corrected to the depth of the drilling assembly 120.

At block 1060, the two gradient range values are averaged by the control unit 305 according to the following equation:

$\begin{array}{cc}{\mathrm{Range}}_{\mathrm{avg}}=\frac{\left({\mathrm{Range}}_{\mathrm{grad}1}+{\mathrm{Range}}_{\mathrm{grad}2}\right)}{2}& \left(10\right)\end{array}$

The determined value for Range_avg represents the distance or range from the drilling assembly 120 to the target vertical well 105.

It will be appreciated that the operations described above with reference to FIG. 10A do not necessarily have to be performed in the order set forth in FIG. 10A, but instead may be performed in any suitable order. Additionally, it will be understood that, in certain aspects of the invention, the control unit 305 can perform more or less than all of the operations set forth in FIG. 10A. It will also be appreciated that the operations set forth in FIG. 10A can be performed by any appropriate control unit or combination of control units such as, for example, a control unit associated with the drilling assembly and/or a control unit associated with the directional driller.

FIG. 10B is a graphical representation of exemplary distances and values that can be measured and/or determined by utilizing the exemplary operations depicted in FIG. 10A.

According to another aspect of the invention, a direction from the drilling assembly 120 to the target vertical well 105 is determined. The one or more sensors 135 are utilized to measure the components of the alternating current magnetic field. The measured components of the alternating current magnetic field are utilized to determine or calculate a relative direction angle “θ” 425 between the current path of the drilling assembly 120 and the actual direction to the target vertical well 105.

According to an aspect of the invention, the components of the alternating current magnetic field are measured in three directions. A sensor “k” measures the component of the field in the Z direction, a sensor “i” measures the component of the field in the X direction, and a sensor “j” measures the component of the field in the Y direction. The values measured by the “i” and “j” sensors can be resolved into a “radial” value. The radial value is a vector that lies in a plane that is situated at a right angle to the direction of the borehole of the horizontal well 110. The radial value is given by:

radial=√{square root over ((i²+j²))}   (11)

The value measured by the “k” sensor can be referred to as an “axial” value. The value measured by the “k” sensor is a value that is aligned with the borehole or the current path of the drilling assembly 120. The direction to the target “θ” 425 is determined by the following equation:

$\begin{array}{cc}\theta ={\tan }^{-1}\left(\frac{\mathrm{axial}}{\mathrm{radial}}\right)& \left(12\right)\end{array}$

In the event that the current path of the drilling assembly 120 coincides or very nearly coincides with the direction “θ” 425 to the target vertical well 105, the tangent field will form a right angle with the axial sensor “k” and the output of the sensor “k” will be zero. Additionally, the phase of the axial sensors can change 180 degrees as the axial null orientation is passed in rotating the current path of the drilling assembly 120 from left side of “θ” 425 to the right side of “θ” 425, or vice versa.

The determined value of “θ” 425 can be a value that is relative to the current path of the drilling assembly 120. According to an aspect of the invention, the value of “θ” 425 can be adjusted. For example, the value of “θ” 425 can be corrected to magnetic north so that a directional driller may be presented with familiar terminology while steering the drilling of the horizontal well 110.

FIG. 11 is an exemplary flowchart depicting exemplary operations taken by a control unit, such as 305 in FIG. 7, at block 815 of FIG. 8 to determine a direction to a target vertical well 105, in accordance with an illustrative aspect of the invention. At block 1105, the components of the alternating current magnetic field are measured by one or more sensors 135 and communicated to the control unit 305. At block 1110, the measurements are stored by the control unit 305. At block 1115, the control unit 305 determines a radial value according to equation (11) above. At block 1120, the control unit 305 determines an axial value in the direction of the current path of the drilling assembly 120. At block 1125, the control unit 305 determines the direction to the target vertical well 105, or “θ” 425, based at least in part on the radial value and the axial value.

It will be appreciated that the operations described above with reference to FIG. 11 do not necessarily have to be performed in the order set forth in FIG. 11, but instead can be performed in any suitable order. Additionally, it will be understood that, in certain aspects of the invention, the control unit 305 can perform more or less than all of the operations set forth in FIG. 11. It will also be appreciated that the operations set forth in FIG. 11 can be performed by any appropriate control unit or combination of control units such as, for example, a control unit associated with the drilling assembly and/or a control unit associated with the directional driller.

Many modifications and other aspects of the invention set forth herein will come to mind to one skilled in the art to which the invention pertains having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. Therefore, it is to be understood that the invention is not to be limited to the specific aspects disclosed and that modifications and other aspects are intended to be included within the scope of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.

Claims

1. A method for guiding the drilling of a horizontal well, comprising:

providing a current in at least one conductor positioned in a target vertical well;

measuring, at a drilling assembly that is drilling the horizontal well, a magnetic field generated by the current;

determining, based at least in part on the measured magnetic field, a direction from the drilling assembly towards the target vertical well; and

determining, based at least in part on the measured magnetic field, a distance from the drilling assembly to the target vertical well, wherein determining the distance comprises determining at least one gradient.

2. The method of claim 1, wherein providing a current comprises providing a low frequency alternating current by a current generation source.

3. The method of claim 2, further comprising:

terminating the at least one conductor to earth ground at a distal end of the at least one conductor that is opposite to an end that is terminated to the current generation source.

4. The method claim 1, further comprising:

outputting at least one of the determined direction and the determined distance to a directional driller controlling the path of the drilling assembly.

5. The method of claim 4, wherein outputting at least one of the determined direction and the determined distance comprises displaying the determined direction, and further comprising:

correcting the determined direction to true north prior to displaying the determined direction.

6. The method of claim 1, further comprising:

adjusting the path of the drilling assembly based at least in part on one or more of the determined distance and the determined direction.

7. The method of claim 1, wherein determining the at least one gradient comprises:

determining a rate of change of the magnetic field as the distance from the drilling assembly to the target vertical well changes.

8. The method of claim 7, wherein determining the rate of change of the magnetic field as the distance from the drilling assembly to the target vertical well changes comprises:

measuring the intensity of the magnetic field at a first position of the drilling assembly in the horizontal well and at a second position of the drilling assembly in the horizontal well;

determining a difference in intensity between the measured intensity at the first position and the measured intensity at the second position;

determining a distance between the first position and the second position; and

determining the rate of change of the intensity of the magnetic field as the distance from the drilling assembly to the target vertical well changes based at least in part on the determined difference in intensity and the determined distance between the first position and the second position.

9. The method of claim 1, wherein determining the at least one gradient comprises:

determining a plurality of gradient calculations; and

averaging the plurality of determined gradient calculations.

10. The method of claim 1, wherein determining the direction from the drilling assembly to the target vertical well comprises:

determining a plurality of components of the measured magnetic field along respective axes;

determining a radial value of the direction based at least in part on at least one of the plurality of components;

determining an axial value of the direction based at least in part on at least one of the plurality of components; and

determining the direction based at least in part on the determined radial value and the determined axial value.

11. A system for guiding the drilling of a horizontal well, comprising:

at least one conductor positioned in a target vertical well and operable to carry a current signal;

one or more sensors associated with a drilling assembly that is drilling the horizontal well, wherein the one or more sensors are operable to measure the intensity of a magnetic field generated by the current signal; and

a processor operable (i) to receive the intensity measurements from the one or more sensors, (ii) to determine a direction from the drilling assembly towards the target vertical well based at least in part on the received intensity measurements, and (iii) to determine a distance from the drilling assembly to the target vertical well based at least in part on the received intensity measurements, wherein at least one gradient calculation is utilized to determine the distance.

12. The system of claim 11, wherein the current signal comprises a low frequency alternating current signal generated by a current generation source.

13. The system of claim 12, wherein the at least one conductor is terminated to earth ground at a distal end of the at least one conductor that is opposite to an end that is terminated to the current generation source.

14. The system claim 11, further comprising at least one output device operable to display at least one of the determined direction and the determined distance to a directional driller controlling the path of the drilling assembly.

15. The system of claim 14, wherein:

the at least one output device is operable to display the determined direction; and

the control unit is further operable to correct the determined direction to true north prior to the display of the determined direction.

16. The method of claim 11, wherein the path of the drilling assembly is adjusted based at least in part on one or more of the determined distance and the determined direction.

17. The system of claim 11, wherein the processor determines the at least one gradient calculation by determining a rate of change of the intensity of the magnetic field as the distance from the drilling assembly to the target vertical well changes.

18. The system of claim 17, wherein the one or more sensors are operable to measure the intensity of the magnetic field a first position of the drilling assembly in the horizontal well and at a second position of the drilling assembly in the horizontal well; and

the processor determines the rate of change of the intensity of the magnetic field as the distance from the drilling assembly to the target vertical well changes by: determining a difference in intensity between the measured intensity at the first position and the measured intensity at the second position; determining a distance between the first position and the second position; and determining the rate of change of the intensity of the magnetic field as the distance from the drilling assembly to the target vertical well changes based at least in part on the determined difference in intensity and the determined distance between the first position and the second position.

19. The system of claim 11, wherein the at least one gradient calculation comprises a plurality of gradient calculations that are averaged together.

20. The system of claim 11, wherein the processor determines the direction from the drilling assembly towards the target vertical well by:

identifying a plurality of components of the measured intensity along respective axes;

determining a radial value of the direction based at least in part on at least one of the identified plurality of components;

determining an axial value of the direction based at least in part on at least one of the identified plurality of components; and

determining the direction based at least in part on the determined radial value and the determined axial value.