Well trajectory planning using bounding box scan for anti-collision analysis

A method for evaluating a planned well trajectory for avoidance of collision with an existing wellbore includes constructing a bounding box about the planned well trajectory and a bounding box for a trajectory of at least one existing wellbore. If there is no intersection between the bounding boxes, the planned well trajectory is used for drilling a well.

BACKGROUND

This disclosure relates generally to the field of wellbore trajectory planning for multiple wells proximate each other drilled through subsurface formations. More specifically, the disclosure relates to techniques for more efficiently identifying well trajectories which do not present material risk of collision with other proximate wellbores.

Subsurface formations in a particular geographic area may have a one or more reservoirs containing economically useful materials such as oil and gas. In order to economically extract such materials wellbores may be drilled from selected positions on the Earth's surface or the bottom of a body of water such as a lake or ocean. Such wellbores may be drilled along preselected trajectories in order to reduce and/or minimize distances between surface or water bottom locations of the wellbores while intersecting one or more reservoirs or portions thereof by wellbores. Drilling along such preselected trajectories is known in the art as directional drilling. Directional drilling uses certain types of drilling tools, for example steerable drilling motors or rotary steerable directional drilling systems to cause a drill bit to drill the well along the preselected trajectory. It is also known in the art to measure the position of each well along its trajectory at selected positions in order to determine how closely the well is following the predetermined trajectory.

The measurements of position have inherent error because of limitations in the accuracy of the sensors used to make the measurements. Thus, the absolute position of any wellbore at any position along its trajectory is subject to a degree of uncertainty. A description of a standard technique for calculating positional uncertainty at any point along a particular wellbore is described in H. S. Williamson,Accuracy Prediction for Directional Measurement While Drilling, paper no. 67616, 15 (4), Society of Petroleum Engineers, Richardson, Tex. (December 2000). The positional uncertainty calculation according to methods such as described in the foregoing publication is computationally expensive and may be time consuming, including, in particular, the computation of separation distances between wells in detail over entire well trajectories.

SUMMARY

A method according to one aspect for evaluating a planned well trajectory for avoidance of collision with an existing wellbore includes constructing a bounding box about the planned well trajectory and a bounding box for a trajectory of at least one existing wellbore. If there is no intersection between the bounding boxes, the planned well trajectory is used to drill a well.

Other aspects and advantages will be apparent from the description and claims that follow,

DETAILED DESCRIPTION

InFIG. 1, a drilling unit or “drilling rig” is designated generally at11. The drilling rig11inFIG. 1is shown as a land-based drilling rig. However, as will be apparent to those skilled in the art, the examples described herein will find equal application on marine drilling rigs, such as jack-up rigs, semisubmersibles, drill ships, and the like.

The drilling rig11includes a derrick13that is supported on the ground above a rig floor15. The drilling rig11includes lifting gear, which includes a crown block17mounted to derrick13and a traveling block19. The crown block17and the traveling block19are interconnected by a cable21that is driven by draw works23to control the upward and downward movement of the traveling block19. The draw works23may be configured to be automatically operated to control rate of drop or release of the drill string into the wellbore during drilling. One non-limiting example of an automated draw works release control system is described in U.S. Pat. No. 7,059,427 issued to Power et al. and incorporated herein by reference.

The traveling block19carries a hook25from which is suspended a top drive27. The top drive27supports a drill string, designated generally by the numeral31, in a wellbore33. According to an example implementation, the drill string31may be in signal communication with and mechanically coupled to the top drive27through an instrumented sub29. As will be described in more detail, the instrumented top sub29may include sensors (not shown separately) that provide drill string torque information. Other types of torque sensors may be used in other examples, or proxy measurements for torque applied to the drill string31by the top drive27may be used, non-limiting examples of which may include electric current (or related measurement corresponding to power or energy) or hydraulic fluid flow drawn by a motor (not shown) in the top drive. A longitudinal end of the drill string31includes a drill bit2mounted thereon to drill the formations to extend (drill) the wellbore33.

The top drive27can be operated to rotate the drill string31in either direction, as will be further explained. A load sensor26may be coupled to the hook25in order to measure the weight load on the hook25. Such weight load may be related to the weight of the drill string31, friction between the drill string31and the wellbore33wall and an amount of the weight of the drill string31that is applied to the drill bit2to drill the formations to extend the wellbore33.

The drill string31may include a plurality of interconnected sections of drill pipe35a bottom hole assembly (BHA)37, which may include stabilizers, drill collars, and a suite of measurement while drilling (MWD) and or logging while drilling (LWD) instruments, shown generally at51.

A steerable drilling motor41may be connected proximate the bottom of BHA37. It will be appreciated by those skilled in the art that other directional drilling systems known in the art, a non-limiting example of which is a rotary steerable directional drilling system may be used in other directional drilling implementations. The steerable drilling motor41may be any type known in the art for rotating the drill bit2and/or selected portions of the drill string31and to enable change in trajectory of the wellbore during slide drilling or to perform rotary drilling. Example types of drilling motors include, without limitation, positive displacement fluid operated motors, turbine fluid operated motors, electric motors and hydraulic fluid operated motors. The present example motor41may be operated by drilling fluid flow. Drilling fluid may be delivered to the drill string31by mud pumps43through a mud hose45. In some examples, pressure of the drilling mud may be measured by a pressure sensor49. During drilling, the drill string31is rotated within the wellbore33by the top drive27, in a manner to be explained further below. As is known in the art, the top drive27is slidingly mounted on parallel vertically extending rails (not shown) to resist rotation as torque is applied to the drill string31. During drilling, the bit2may be rotated by the motor41, which in the present example may be operated by the flow of drilling fluid supplied by the mud pumps43. Although a top drive rig is illustrated, those skilled in the art will recognize that the present example may also be used in connection with systems in which a rotary table and kelly are used to apply torque to the drill string31. Drill cuttings produced as the bit2drills into the subsurface formations to extend the wellbore33are carried out of the wellbore33by the drilling mud as it passes through nozzles, jets or courses (none shown) in the drill bit2.

Signals from the pressure sensor49, the hookload sensor26, the instrumented top sub29and from an MWD/LWD system or steering tool51(which may be communicated using any known wellbore to surface communication system, such as mud pulse telemetry to provide just one example), may be received in a control unit48, which will be further explained with reference toFIG. 2. Signals from the MWD/LWD system51may be used to perform surveys of the well at selected positions along its trajectory both during drilling and thereafter during “washing”, “reaming” or drill string movement procedures.

FIG. 2shows a block diagram of the functional components of a non-limiting example of the control unit48. The control unit48may include a drill string rotation control system. Such system may include a torque related parameter sensor53. The torque related parameter sensor53may provide a measure of the torque (or related measurement as explained above) applied to the drill string (31inFIG. 1) at the surface by the top drive or kelly. The torque related parameter sensor53may be implemented, for example, as a strain gage in the instrumented top sub (29inFIG. 1) if it is configured to measure torque. The torque related parameter sensor53, as explained above may also be implemented, for example and without limitation, as a current measurement device for an electric rotary table or top drive motor, as a pressure sensor for an hydraulically operated top drive, or as an angle of rotation sensor for measuring drill string rotation. In principle, the torque related parameter sensor53may be any sensor that measures a parameter that can be directly or indirectly related to the amount of torque applied to the drill string.

The output of the torque related parameter sensor53may be received as input to a processor55. In some examples, output of the pressure sensor49and/or one or more sensors of the MWD/LWD system or steering tool51may also be provided as input to the processor55. A particular input from the MWD/LWD system or steering tool51may be the orientation angle with respect to geomagnetic or geodetic direction and Earth's gravity of a bend in the housing of the steerable drilling motor (41inFIG. 1). The foregoing may be referred to as “toolface angle”, or “toolface.” Toolface angle may be measured with reference to geomagnetic or geodetic direction when the wellbore is inclined from vertical below a selected threshold inclination angle, as a non-limiting example five degrees. Above the threshold wellbore inclination angle, the toolface may be measured with reference to the uppermost surface of the wellbore, known as “high side” toolface.

The processor55may be any programmable general purpose processor such as a programmable logic controller (PLC) or may be one or more general purpose programmable computers or may include one or more application-specific processors (e.g., ASICs). The processor55may receive user input from user input devices, such as a keyboard57. Other user input devices such as touch screens, keypads, and the like may also be used. The processor55may also provide visual output to a display59. The processor55may also provide output to a drill string rotation controller61that operates the top drive (27inFIG. 1) or rotary table (FIG. 3) to rotate the drill string as will be further explained below.

The drill string rotation controller61may be implemented, for example, as a servo panel (not shown separately) that attaches to a manual control panel for the top drive. One such servo panel is provided with a service sold under the service mark SLIDER, which is a service mark of Schlumberger Technology Corporation, Sugar Land, Tex. The drill string rotation controller61may also be implemented as direct control to the top drive motor power input (e.g., as electric current controls or variable orifice hydraulic valves). The top drive control can also be implemented as computer coded instructions in the control unit48that, when executed by a processor (e.g., processor55), enables operation of the top drive controller27. The type of drill string rotation controller is not a limit on the scope of the present disclosure.

The processor55may also accept as input signals from the hookload sensor26. The processor55may also provide output signals to the automated draw works23as explained with reference toFIG. 1.

Referring once again toFIG. 1, an example “directional” wellbore, that is, one that is drilled along a selected trajectory other than vertical, may be initially drilled as a vertical wellbore, shown at70. During this part of the drilling operation, the draw works23are released to enable some of the weight of the drill string35to be transferred to the drill bit2. During this part of the drilling operation, the drill string35may be rotated to maintain the trajectory of the wellbore substantially along a vertical path. Signals from the pressure sensor49may be conducted to the control unit48which in turn may operate the draw works23as explained with reference toFIG. 2so that the measured pressure does not exceed a value associated with “stalling” of the steerable drilling motor41.

Survey measurements made during directional drilling or at other times on any particular wellbore may be included in a database for processing according to example methods consistent with the present disclosure. An example computing system that may be used to perform such calculations is shown inFIG. 3. The computing system100may be an individual computer system101A or an arrangement of distributed computer systems. The computer system101A may include one or more analysis modules102that may be configured to perform various tasks according to some embodiments, such as the tasks described below. To perform these various tasks, analysis module102may execute independently, or in coordination with, one or more processors104, which may be connected to one or more storage media106. The processor(s)104may also be connected to a network interface108to allow the computer system101A to communicate over a data network110with one or more additional computer systems and/or computing systems, such as101B,101C, and/or101D (note that computer systems101B,101C and/or101D may or may not share the same architecture as computer system101A, and may be located in different physical locations, for example, computer systems101A and101B may be on a ship underway on the ocean or on a well drilling location, while in communication with one or more computer systems such as101C and/or101D that may be located in one or more data centers on shore, aboard ships, and/or located in varying countries on different continents).

A processor can include a microprocessor, microcontroller, processor module or subsystem, programmable integrated circuit, programmable gate array, application-specific integrated circuit, a system-on-a-chip (SoC) processor, or another suitable control or computing device.

The storage media106can be implemented as one or more computer-readable or machine-readable storage media. Note that while in the exemplary embodiment ofFIG. 3the storage media106are depicted as within computer system101A, in some embodiments, the storage media106may be distributed within and/or across multiple internal and/or external enclosures of computing system101A and/or additional computing systems. Storage media106may include one or more different forms of memory including semiconductor memory devices such as dynamic or static random access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), electrically erasable and programmable read-only memories (EEPROMs) and flash memories; magnetic disks such as fixed, floppy and removable disks; other magnetic media including tape; optical media such as compact disks (CDs) or digital video disks (DVDs); or other types of storage devices. Note that the instructions discussed above may be provided on one computer-readable or machine-readable storage medium, or alternatively, can be provided on multiple computer-readable or machine-readable storage media distributed in a large system having possibly plural nodes. Such computer-readable or machine-readable storage medium or media may be considered to be part of an article (or article of manufacture). An article or article of manufacture can refer to any manufactured single component or multiple components. The storage medium or media can be located either in the machine running the machine-readable instructions, or located at a remote site from which machine-readable instructions can be downloaded over a network for execution.

It should be appreciated that computing system100is only one example of a computing system, and that computing system100may have more or fewer components than shown, may combine additional components not depicted in the example embodiment ofFIG. 3, and/or computing system100may have a different configuration or arrangement of the components depicted inFIG. 3. The various components shown inFIG. 3may be implemented in hardware, software, or a combination of both hardware and software, including one or more signal processing and/or application specific integrated circuits.

An example method for determining whether a proposed well trajectory is within a prescribed safe distance from another well trajectory, or any other well trajectory where multiple wellbores may exist to produce fluids from various reservoirs within a field of geographically proximate reservoirs may be explained as follows.

First, the proposed trajectory may have an ellipse of uncertainty (“EOU”) calculated for each of a plurality of selected positions along the planned well trajectory. Calculating the EOU may be performed, for example, as described in H. S. Williamson,Accuracy Prediction for Directional Measurement While Drilling, paper no. 67616, 15 (4), Society of Petroleum Engineers, Richardson, Tex. (December 2000), incorporated herein by reference. One output of the calculation technique described in the foregoing reference is an error covariance matrix of uncertainty. Such covariance matrix is defined in Eq. A-16 in the appendix thereof.

In the present example, a “bounding box” may be generated to encompass the proposed well trajectory and to encompass well trajectory survey data from: (i) proximate wellbores; (ii) all wells drilled from one or more wellbore “slots” (or common wellhead locations) in the case of bottom supported platform or bottom positioned well position templates; (iii) all wells drilled from individual structures, such as bottom supported platforms or water bottom templates; and (iv) all wells drilled in an entire “field” which may include one or more structures and/or reservoirs therein. The bounding boxes represent large volume and simple shape boxes used to test whether there is any overlap between such bounding boxes.

In the present example, AABB (axis-aligned bounding boxes) may be constructed subject to the constraint that the edges of the box are parallel to the coordinate axes. In other examples, different alignment bounding boxes may be used. However, it should be understood that before storage or intersection detection, the coordinates of all the bounding boxes should ideally be referenced to a common origin and coordinate system. Further, various coordinate systems may be used in connection with the disclosed techniques, such as geodetic, spherical, or grid coordinates, which can be obtained by standard coordinate transformation methods.

As an example, Cartesian coordinates may be used in one embodiment, wherein the three main axes are North (N) displacement from the surface position (or water bottom position) of the well, East (E) displacement from the surface or water bottom position and Vertical (V), i.e., true vertical depth of the wellbore. Six coordinates are needed to define a bounding box, note Nmax (upper boundary in the North direction), Nmin (lower boundary in the North direction), Emax, Emin, (maximum and minimum in the East direction) and Vmax, Vmin (maximum and minimum true vertical depth).

Wellbore collisions (intersection of a well being drilled with an existing well) may occur if the actual position of a wellbore differs from its presumed position based on survey data. The presumed position of the well consists of a well path centerline and an associated EOU which is derived from a selected error model. An error model that may be used is the ISCWSA (Industry Steering Committee on Wellbore Survey Accuracy) model which considers the error as an EOU. An EOU is an ellipsoid with equal probability on the surface. The size of EOU may be determined by a confidence multiplier.

Thus, to build a reliable bounding box, the EOU may be taken into consideration and a bounding box may be defined which encloses not only individual survey points but the EOU at each survey point inside. The confidence multiplier may then be selected. The confidence multiplier may be set by the policy of the operator of a given field or structure to correspond to an acceptable probability of collision; such probability may be associated with a Gaussian error distribution.

The bounding box for a planned well trajectory may be hierarchically compared to bounding boxes for nearby wells, associated template slots (if used), associated drilling structures and an associated field, such as a geologic field or a geographically proximate set of drilling structures. In the present example therefore, one may build a bounding box for a well, for nearby wells, for slots, for a structures, and for a field. Only when a higher-hierarchical bounding box has been detected to have intersection with the planned well's bounding box, the lower-hierarchical bounding box will be used to do a further collision scan. The hierarchy will be explained below with reference toFIG. 4.

The bounding box may be defined based on the EOU. As previously explained, the bounding box should enclose the entire EOU at any well path position. In some examples, to align the bounding box with an anti-collision standard (especially some standard with the definition of a separation factor), the pedal surface of the EOU will also be needed to be enclosed by the bounding box. The reason for defining a bounding box to enclose the pedal surface of the EOU is that in practice, the pedal curve method is frequently used for separation factor calculations. Various methods of calculating separation factor are known in the art. The separation factor may be defined as the ratio of the distance between a point on a subject well and a point on another well divided by the combined uncertainty of the positions in each well. Various methods known in the art can be considered in how to combine the uncertainties. Examples may include simple addition of the uncertainties, or as is the case for the pedal curve, the addition of the associated covariance matrices, then by multiplication of the resulting matrix with the vector between the positions yields a single uncertainty distance.

Basically, the EOU maximum radius calculated is not the radius of ellipsoid used, but the radius of the pedal surface of the EOU is used. By taking the foregoing into consideration, the bounding box may be defined to enclose all the pedal surface of ellipsoids inside. Calculating the pedal surface of an ellipsoid may be performed, for example, using a method described in, Eva Baranová,Cyclical Elliptical Pedal Surfaces,Journal of Mathematics and System Science 1 (2011) 1-6, David Publishing.

Considering the complexity of the form of an ellipsoid and that of the pedal curve, in the present example, it is possible to simply consider a more conservative volume which can enclose the EOU inside: a bounding sphere of EOU. In this case, only the major axis length in 3D for the EOU is needed.

In such case,
Major axis in 3D=Max(Eigenvalues of Covariance Matrix)  (1)

The covariance matrix may be calculated as explained above. In the three above defined coordinate directions (N, E, V), this major axis length will be used for calculating extreme or maximum values for defining the bounding box. In an example implementation one may first calculate the extreme or maximum values at each survey position, whether along an existing well or along a planned well trajectory. In the following expressions, TempNmax stands for temporary Nmax, and correspondingly temporary maximum and minimum values may be defined for the remaining five positional variables: TempNmin, TempEmax, TempEmin, TempVmax, TempVmin.
TempNmax=N+0.5*Hole diameter+max{a,Major axis in 3Dat this station}  (2)
TempNmin=N−0.5*Hole diameter−max{a,Major axis in 3Dat this station}  (3)
TempEmax=E+0.5*Hole diameter+max{a,Major axis in 3Dat this station}  (4)
TempEmin=E−0.5*Hole diameter−max{a,Major axis in 3Dat this station}  (5)
TempVmax=V+Major axis in 3Dat this station  (6)
TempVmin=V−Major axis in 3Dat this station  (7)

wherein a represents a defined minimum extreme value in case the EOU radius is too small near the uppermost portion of the well.

Using the above calculations, one may obtain the extreme or maximum positional uncertainty values at each survey position or selected position along an existing or planned well trajectory. To find the extreme values for an entire well survey, similar calculations may be performed for each survey position, wherein
Nmax=max(TempNmax)  (8)
Nmin=min(TempNmin)  (9)
Emax=max(TempEmax)  (10)
Emin=min(TempNmin)  (11)
Vmax=max(TempVmax)  (12)
Vmin=min(TempVmin)  (13)

The slot, structure, and field bounding boxes are then constructed. The slot bounding boxes are defined by the greatest or smallest of the 6 min/max values of each well bounding box that belongs to its particular slot. This process may then be repeated for the structures using the bounding boxes of the slots. The process may then be repeated for the field(s) using the bounding boxes of the structures. Other hierarchical levels could be considered in other embodiments, and the foregoing examples of hierarchy is not intended to limit the scope of the disclosure.

After defining the geometry of the bounding boxes as explained above, well collision testing may be performed as follows, wherein A represents a well trajectory under consideration, and B represents bounding boxes evaluated hierarchically as will be further explained with reference toFIGS. 4 and 5.
IfA's data is invalid orBis invalid,treat as collision likely.  (14)
IfA·Nmax<B·Nmin,no collision likely  (15)
IfA·Nmin>B·Nmax,no collision likely  (16)
IfA·Emax<B·Emin,no collision likely  (17)
IfA·Emin>B·Emax,no collision likely  (18)
IfA·Vmax<B·Vmin,no collision likely  (19)
IfA·Vmin>B·Vmax,no collision likely  (20)

If any of the foregoing six geometric conditions fails, then collision should be considered likely and a more detailed anti-collision analysis should be performed on the subject well trajectory (A).

FIG. 4shows an example hierarchy for evaluation according to the geometric conditions for bounding boxes described above in equations (15) through (20). At86, an entire field may be evaluated, wherein the values of max and min for N, E and V will be for an entire field for element B to evaluate its bounding box with reference to a planned wellbore trajectory represented by A in equations (15) through (20). The drilling structure level evaluation is shown at84. Slot level (if templates are used) is shown at82, and individual wellbore level is shown at80.

FIG. 5shows a flow chart of an example bounding box scan method. The scan may begin at120for a planned well. At122, the bounding box of field i may be retrieved from a database, at124. A planned well trajectory may be checked for intersection with the bounding box of the i-th field at126. If there is no intersection of the bounding boxes, at150, the i-th field may be removed from further evaluation and the proposed well trajectory may be considered safe with respect to the i-th field. At166, if the i-th field is the only field under consideration, the process may end at170. If there are additional fields for evaluation, the process may return to124for the i+1-th field. The foregoing process may be repeated until all relevant fields have been evaluated.

At128, if the bounding boxes as described above have any intersection, the process may then evaluate the bounding box of structure m at130, wherein existence of any intersection between the bounding box of the planned well and the m-th structure may be determined at132. If there is no intersection, at136, the process may revert to162, where a next structure (m+1) may be evaluated. The foregoing may be repeated until all structures in a particular field are evaluated as explained above. In the event there is intersection between any structure's bounding box and the planned well trajectory bounding box, at134, the process may retrieve from the database the bounding box for a first slot (n=1) associated with the structure m for which there is intersection between the planned well trajectory bounding box and the first slot bounding box. At160, if there is no intersection between the planned trajectory bounding box and the first slot bounding box, the process may revert to156and the next slot n=n+1 may have its bounding box evaluated against the planned trajectory bounding box. The foregoing may be repeated until all slot bounding boxes have been evaluated If there is intersection between any slot's bounding box and the planned trajectory bounding box, at142, a first existing well trajectory bounding box p=1 may be retrieved at144evaluated against the planned well trajectory bounding box at146. If there is no bounding box intersection, at148, the next existing well path in the present slot, p=p+1, at154, may have its bounding box evaluated. The foregoing may be repeated until all existing well trajectories in the present slot have been evaluated. If the existing well trajectory bounding box intersects the bounding box of any well in the present slot, at146, a complete anti-collision scan over the entire well trajectory of each of the existing well and the planned well trajectories may be performed, for example using the EOU technique described above. Adjustments to the planned well trajectory may be made over intervals where the possible minimum distance (considering the EOU at the relevant positions along each well trajectory) between well trajectories falls below a minimum distance between wellbores prescribed by any applicable safety standard (e.g., governmental agency, well operator policy, drilling contractor policy, etc.).

When all fields, structures, slots and well trajectories have been evaluated, the process may end at170.

The present evaluation method may also be used during the drilling of a wellbore, using equipment as described with reference toFIG. 1or other above-described directional drilling systems. When performed during drilling, at selected wellbore length intervals, e.g., every 30 meters, the drilling may be stopped and a directional survey may be taken at such time. A well trajectory may be calculated based on the survey being made and previous surveys. The well trajectory may be calculated using any method known in the art, for example and without limitation, radius of curvature, minimum curvature, and tangential techniques. The calculated trajectory may be used as explained above to calculate a bounding box, and the bounding box may be evaluated as explained with reference toFIG. 5to determine if changes in the planned trajectory yet to be drilled should be made to reduce the chance of collision with an existing well.

A method for calculating likelihood of well collision according to the present disclosure may reduce the time and computational cost needed to determine whether a planned well trajectory or a while drilling well trajectory is safe by rapidly screening fields, drilling structures, and existing well trajectories for those that are unlikely to require detailed anti-collision evaluation. Additional details regarding the techniques described in this U.S. Provisional Patent Application may be further understood with reference to the attached Appendix A (incorporated herein by reference and also attached hereto) entitled “Well Trajectory Planning Using Bounding Box Scan for Anti-Collision Analysis.”

While only certain embodiments have been described in the present disclosure, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as disclosed herein. Accordingly, the scope of the invention should be limited only by the attached claims.