CN109661502B

CN109661502B - Method for controlling drill bit trajectory by predicting drill bit walk and wellbore spiral

Info

Publication number: CN109661502B
Application number: CN201780054409.3A
Authority: CN
Inventors: R·W·斯宾塞; T·P·乌诺; J·M·汉森
Original assignee: Baker Hughes Inc
Current assignee: Baker Hughes Holdings LLC
Priority date: 2016-07-20
Filing date: 2017-07-19
Publication date: 2022-09-23
Anticipated expiration: 2037-07-19
Also published as: CA3031465A1; CN109661502A; BR112019001148A8; NO20190197A1; BR112019001148A2; GB2567376B; WO2018017724A1; GB2567376A; GB201901944D0; BR112019001148B1; CA3031465C; SA519400930B1

Abstract

A method of controlling a trajectory of a drill bit in a subterranean formation, comprising: receiving drilling parameters for operating a particular Bottom Hole Assembly (BHA); constructing, using a computer processor, a directional drilling simulator comprising computer models of the BHA and the subterranean formation; calculating axial and lateral movement of a drill bit connected to a bottom end of the BHA using formation parameters and drilling parameters; predicting a bit walk of the drill bit by considering and calculating contact forces and frictional forces between the BHA and a wall of a borehole in the subterranean formation using the computer model of the BHA; and determining an adjusted drill bit trajectory that takes into account the predicted drill bit walk. The method comprises the following steps: determining adjusted drilling parameters for operating the BHA to substantially follow the adjusted drill bit trajectory, and operating the BHA in accordance with the adjusted drilling parameters.

Description

Method for controlling drill bit trajectory by predicting drill bit walk and wellbore spiraling

Priority claim

The present application claims benefit OF filing date entitled "METHODS OF CONTROLLING driving BIT BY preliminary wall AND rolling spring" to U.S. provisional patent application serial No. 62/364,833 filed on 20.7.2016. This application also claims benefit of the filing date of U.S. patent application Ser. No. 15/348,003 filed on 10.11.2016, a continuation-in-part application entitled "DIRECTIONAL DRILL AHEAD SIMULATOR: DIRECTIONAL WELL PREDICTION USE BHA AND BIT MODELS" filed on 17.10.2014, claim the benefit of U.S. provisional patent application Ser. No. 61/892,959 filed on 18.10.2013, AND claim the benefit of U.S. provisional patent application Ser. No. 62/364,833 filed on 20.7.20.2016, each of which disclosure is incorporated herein by reference in its entirety.

The subject matter of the present application also relates to the subject matter of U.S. patent application serial No. 14/517,445 entitled "AXIAL MOTION drive BIT MODEL" filed on day 10, month 17 2014, which application claims the benefit of U.S. provisional patent application serial No. 61/892,992 filed on day 10, month 18, 2013, and to the subject matter of U.S. patent application serial No. 14/517,454 entitled "LATERAL MOTION drive BIT MODEL" filed on day 10, month 17, 2014, which application claims the benefit of U.S. provisional patent application serial No. 61/893,011 filed on day 10, month 18, 2013, each of which disclosure is also incorporated by reference in its entirety.

Technical Field

Embodiments of the present disclosure relate to methods of controlling a drill bit trajectory in a subterranean formation to improve drilling operations and drilling planning by accounting for and predicting drill bit walk and wellbore spiraling.

Background

Geological formations are used in many applications such as hydrocarbon recovery, geothermal recovery, and carbon dioxide sequestration. Typically, a borehole is drilled into the formation to provide access to the formation. A drilling rig, whether disposed on land or at the surface, operates a drill string connected to a drill bit to drill a borehole. Since operating a drilling machine is very expensive, the desired geometry and end position can be achieved by precisely drilling the drill hole, thereby achieving efficiency. When drilling a borehole in an earth formation, a predetermined drilling path extending into the earth formation may be provided for an operator to follow. The drilling path may bend, turn, or otherwise be non-linear, thereby requiring an operator to control the direction in which the earth-boring tool enters the formation. Components contained in the drill string, such as a Bottom Hole Assembly (BHA) and one or more earth-boring tools (e.g., an earth-boring drill bit, a reamer, or another tool configured to remove earth material when forming or enlarging a borehole), may be selected according to their ability to perform and create a nonlinear borehole within a nonlinear borehole.

The process of directional drilling is complicated by the complex interaction of the drill bit with the walls of the lined well bore of the subterranean formation. In drilling with rotary drill bits, particularly fixed-cutter rotary drill bits, it is known that if a lateral force (commonly referred to as a side force or a radial force) is applied to the drill bit, the drill bit may "walk" or "drift" from a straight path parallel to the intended longitudinal axis of the well bore. When the drill is stroked with an increase in the directional angle, it can be said that the drill is stroked rightward or exhibits "right stroking". Similarly, when the drill bit is stroking in a decreasing azimuth, it can be said that the drill bit is stroking left or exhibits "left stroking". When the drill bit is not traveling or drifting from a straight path parallel to the longitudinal axis of the well bore at the bottom of the well bore, the drill bit may be referred to as an "anti-travel" drill bit and may be said to exhibit "neutral travel". In a similar manner, a drill bit may be said to exhibit a tendency to "build" when the drill bit drifts in a direction that causes an increase in the inclination angle, and a drill bit may be said to exhibit a tendency to "drop" when the drill bit drifts in a direction that causes a decrease in the inclination angle.

Many factors or variables may at least partially contribute to the reaction forces and torques applied to the drill bit and BHA by the surrounding subterranean formation. Such factors and variables may include, for example, "weight on bit" (WOB), rotational speed of the drill bit and BHA, the physical properties and characteristics of the subterranean formation being drilled, the fluid dynamics of the drilling fluid, the length and configuration of the BHA into which the drill bit is mounted, and various design factors for the drill bit and BHA, including cutting element size, radial layout, back (or front) skew angle, side skew angle, and the like. Various sophisticated modeling and calculation methods known in the art may be used to calculate the forces and torques acting on the drill bit and BHA under predetermined conditions and parameters. For example, a wellbore design may be created by: the trajectory of the drill bit and BHA through the subterranean formation is estimated using three-dimensional modeling software by inputting design variables associated with drilling parameters and lithology data and using calculation software to estimate the reaction forces and torques applied to the drill bit and BHA by the surrounding subterranean formation during drilling by mathematical calculations.

Disclosure of Invention

A method for predicting a path of a borehole to be drilled in a rock formation by a Bottom Hole Assembly (BHA) comprising a drill bit coupled to a drill pipe, the BHA being operated by a drilling rig is disclosed. The method comprises the following steps: constructing a model of the BHA having (a) dimensions, geometry, mass distribution, material density, and material stiffness of the BHA, and (b) dimensions and geometry of the borehole predicted to be drilled, the BHA model configured to calculate (c) one or more contact points between the BHA and a wall of the borehole, and (d) forces exerted on the BHA at the one or more contact points, the forces including side force vectors exerted on the drill bit, and (e) bit inclination; calculating a confined compressive strength of the rock formation using an axially moving bit model that receives drilling parameters of the drilling rig, bit design information, and lithology information including formation rock strength; calculating lateral motion of the drill bit using a lateral motion drill bit model that receives (i) the calculated confined compressive strength, (ii) the lithology information, (iii) the drill bit design information, and (iv) the bit side force vector and bit inclination angle from the BHA model; calculating a ratio of lateral motion to axial motion using the lateral motion drill bit model; calculating an inclination angle and an azimuth direction of the BHA using a BHA steering model that receives the ratio; and iterating the steps by: updating the BHA model to include extending the borehole by an incremental distance in the inclination direction and the azimuth direction; and shifting the BHA by the incremental distance in the extended borehole; wherein the method is implemented by a processor.

Further disclosed is a non-transitory computer-readable medium having computer-executable instructions for predicting a path of a borehole to be drilled in a formation by a Bottom Hole Assembly (BHA) having a drill bit coupled to a drill pipe, the BHA operated by a drilling rig by implementing the following steps. The steps include: constructing a model of the BHA having (a) dimensions, geometry, mass distribution, material density, and material stiffness of the BHA, and (b) dimensions and geometry of the borehole predicted to be drilled, the BHA model configured to calculate (c) one or more contact points between the BHA and a wall of the borehole, and (d) forces exerted on the BHA at the one or more contact points, the forces including side force vectors exerted on the drill bit, and (e) bit inclination; calculating a confined compressive strength of the rock formation using an axially moving bit model that receives drilling parameters of the drilling rig, bit design information, and lithology information including formation rock strength; calculating lateral motion of the drill bit using a lateral motion drill bit model that receives (i) the calculated confined compressive strength, (ii) the lithology information, (iii) the drill bit design information, and (iv) the bit side force vector and bit inclination angle from the BHA model; calculating a ratio of lateral movement to axial movement; calculating a tilt angle and an azimuth direction of the BHA using a BHA steering model that receives the ratio; and iterating the steps by: updating the BHA model to include extending the borehole by incremental distances in the inclination and azimuth directions; and shifting the BHA by the incremental distance in the extended borehole.

In some embodiments, a method of controlling a trajectory of a drill bit in a subterranean formation may include: receiving drilling parameters for operating a particular Bottom Hole Assembly (BHA); constructing, with a computer processor, a directional drilling simulator that may include a computer model of the BHA and the subterranean formation; calculating, with the computer processor, axial and lateral movement of a drill bit connected to a bottom end of the BHA using at least one formation parameter and at least one drilling parameter; predicting, with the computer processor, a bit walk of the drill bit by considering and calculating contact forces and frictional forces between the BHA and a wall of a borehole in the subterranean formation using the computer model of the BHA; determining, with the computer processor, an adjusted drill bit trajectory that is to account for the predicted drill bit walk. The method may comprise: determining adjusted drilling parameters for operating the BHA to substantially follow the adjusted drill bit trajectory, and operating the BHA in accordance with the adjusted drilling parameters.

In further embodiments, a method of planning and drilling a wellbore in a subterranean formation may include defining a target in a designated subterranean formation. The method may comprise: predicting a wellbore spiral and a bit walk of a drill bit connected to a particular Bottom Hole Assembly (BHA), the predicting may include: using a computer processor programmed to execute a directional drilling simulator, which may include a computer model of the BHA and the specified subsurface formation; receiving, with the computer processor, lithology data and drilling parameters for operating the BHA in the specified subsurface formation; calculating, with the computer processor, a ratio of lateral motion to axial motion using a lateral motion bit computer model and an axial motion bit computer model; predicting, with the computer processor, a bit trajectory by considering and calculating a lateral contact force, an angular displacement, and a friction force using the computer model of the BHA; and adjusting, with the computer processor, the drill bit trajectory based at least in part on the prediction from the computer model of the BHA. The method may comprise: adjusting the drilling parameters for operating the BHA to substantially follow the adjusted drill bit trajectory, and drilling the wellbore in the specified subterranean formation based at least in part on the adjusted drill bit trajectory.

In a further embodiment, a method of controlling a trajectory of a drill bit in a subterranean formation may comprise: receiving lithology data for a particular subsurface formation; and receiving one or more drilling parameters for operating a Bottom Hole Assembly (BHA), which may include weight-on-bit, torque, rotational speed, rate of penetration, drilling fluid flow rate, or lateral aggressiveness of the drill bit. The method may include predicting a drill bit walk of a drill bit of a wellbore helix and the BHA, which may include: constructing, using a computer processor, a directional drilling simulator that may include dynamic computer models of the BHA and the subterranean formation; considering, using the computer processor, the wellbore spiral and the bit walk of the drill bit by rotating a direction of normal contact force on the drill bit by a constant angle; calculating, using the computer processor, a combined force on the BHA by adding torsional friction force to a normal contact force in the dynamic computer model in each iteration of finite element analysis; predicting, with the computer processor, the drill bit trajectory based at least in part on calculating the combined forces on the BHA; and adjusting, with the computer processor, the drill bit trajectory based at least in part on the prediction of the drill bit trajectory. The method may include adjusting the one or more drilling parameters based at least in part on a prediction of the wellbore spiral and the bit walk of the drill bit.

Drawings

This patent or application document contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the office upon request and payment of the necessary fee.

While the specification concludes with claims particularly pointing out and distinctly claiming what are regarded as embodiments of the present invention, various features and advantages of the disclosed embodiments may be more readily ascertained from the following description when read with reference to the accompanying drawings in which:

FIG. 1 shows a cross-sectional view of an exemplary embodiment of a drill string and drill bit disposed in a borehole penetrating the earth;

FIG. 2 depicts aspects of output from a Bottom Hole Assembly (BHA) model;

FIG. 3 illustrates a tilt angle measurement convention;

FIG. 4 illustrates a process flow diagram of a method for predicting a tilt angle of a borehole being drilled;

FIGS. 5A and 5B, collectively referred to as FIG. 5, show a more detailed process flow diagram of a method for predicting the inclination angle of a borehole being drilled;

FIG. 6 depicts aspects of a front steering angle model;

FIG. 7 depicts aspects of a front steering angle model applied to a BHA;

FIG. 8 depicts aspects of a rear steering angle model applied to a BHA;

FIG. 9 is a flow chart of a method for predicting a path of a borehole to be drilled in an earth formation by a BHA having a drill bit coupled to a drill pipe, wherein the BHA is operated by a drilling rig;

FIG. 10 depicts aspects of a frame of reference of a drill bit;

FIG. 11 depicts aspects of a first cutting edge cutting formation rock;

FIG. 12 depicts aspects of a second cutting edge cutting formation rock;

FIG. 13 depicts aspects of a third cutting edge cutting formation rock;

FIG. 14 depicts aspects of the formation rock after being cut by three cutting edges;

FIG. 15 depicts aspects of a cast-in-place pile used as a virtual representation of a drill bit and formation rock;

FIG. 16 depicts aspects of cutting facets and cutting edge chamfer represented by a cast-in-place pile;

FIG. 17 depicts aspects of rock cut by cutting facets and cutting edge chamfer;

FIG. 18 depicts aspects of the projected area of rock cut by a series of cutting edges on one cutting edge blade on a drill bit on the R-Z plane;

FIG. 19 depicts aspects of a chamfered cutting edge out of the page with two stacked bored piles;

FIG. 20 depicts aspects of a cutting edge represented by a cast-in-place pile at a rock interface;

FIG. 21 depicts aspects of three orthogonal forces exerted on the cutting edge by the local rock surface interfacing with the cutting edge;

FIG. 22 depicts aspects of Circumferential (CIR) and Side (SID) forces exerted on a cutting edge by local rock surfaces interfacing with the cutting edge;

FIG. 23 depicts aspects of the relationship between a cutting edge and a local rock surface interfacing with the cutting edge;

FIG. 24 depicts aspects of the inherent specific energy required to cut rock as a function of cutting edge back bevel angle;

FIG. 25 depicts aspects of forces acting on a cutting edge;

fig. 26A-26C, collectively referred to as fig. 26, depict aspects of various back bevel angles of the cutting edge;

FIG. 27 depicts aspects of the force model parameter Ψ as a function of the back bevel angle parameter θ for Furi mountain sandstone;

FIG. 28 depicts aspects of a comparison of predicted weight-on-bit to measured weight-on-bit in a first laboratory drilling simulator test;

FIG. 29 depicts aspects of a comparison of predicted weight-on-bit to measured weight-on-bit in a second laboratory drilling simulator test;

FIG. 30 depicts aspects of a comparison of predicted weight-on-bit to measured weight-on-bit in a third laboratory drilling simulator test;

FIG. 31 depicts aspects of a comparison of predicted penetration rates versus measured penetration rates at actual field locations;

FIG. 32 is a flow chart of a method for predicting the amount of axial movement of a drill bit having one or more cutting edges for drilling a borehole into formation rock;

FIG. 33 is a flow diagram depicting aspects of a lateral motion drill bit model;

FIG. 34 depicts aspects of a drill bit having gage pads configured to wear or crush formation rock and gage trimmers configured to cut formation rock;

FIG. 35 depicts aspects of a gage pad in relation to a gage dresser;

FIG. 36 depicts aspects of a simulation utilizing gage pads and gage trimmers to remove formation rock laterally;

FIG. 37 depicts aspects of lateral displacement as a function of simulated axial displacement;

FIG. 38 depicts aspects of a comparison of predicted results using a lateral motion drill bit model with a measured lab side load drilling experiment of bedford limestone;

FIG. 39 is a flow chart of a method for predicting a change in lateral displacement using a change in axial displacement of a drill bit drilled in a formation;

FIG. 40 is a process flow diagram of a directional drilling simulator;

FIG. 41 is a simplified diagram of a downhole view of the borehole shown in FIG. 1;

42A-42K are a series of graphs of drilling simulation results that take into account bit walk at build time;

FIGS. 43A-43K are a series of graphs of drilling simulation results considering the walk of a right-hand drill bit as it falls;

FIG. 44A is a simplified diagram of a top view of a wellbore spiral;

FIG. 44B is a simplified diagram of a side view of a wellbore spiral;

FIG. 45 is a simplified lateral cross-sectional view of a BHA in a wellbore and showing force vectors acting on the BHA; and is provided with

FIG. 46 is a series of graphs of drilling simulation results considering left hand drill bit walk in the build direction while turning.

Detailed Description

In some instances, the illustrations presented herein are not intended to be actual views of any particular material, component, or system, but are merely idealized representations which are employed to describe embodiments of the present disclosure. Additionally, common elements between the drawings may retain the same numerical designation.

The following description provides specific details such as procedures, acts, and structures in order to provide a thorough description of embodiments of the present disclosure. However, it will be understood by those of ordinary skill in the art that embodiments of the present disclosure may be practiced without these specific details. Indeed, embodiments of the disclosure may be practiced in conjunction with conventional techniques employed in the industry. Only those acts and structures necessary for an understanding of the embodiments of the present disclosure are described in detail below. Additional actions or structures for controlling the trajectory of a drill bit in a subterranean formation may be performed by conventional techniques.

The article "a" or "an" has been used to introduce elements of an embodiment. The article is intended to mean that there are one or more of the elements. The terms "comprising" and "having" are intended to be inclusive such that there may be additional elements other than the listed elements. The conjunction "or" when used with a list of at least two terms is intended to mean any term or combination of terms. The terms "first," "second," and the like, do not denote a particular order, but rather are used to distinguish one element from another.

The flow diagrams depicted herein are just examples. There may be many variations to these diagrams or the steps (or operations) described therein without departing from the spirit of the invention. For example, the steps may be performed in a differing order, or steps may be added, deleted or modified. All of these variations are considered a part of the claimed invention.

A drilling method is disclosed for predicting or simulating the geometry of a borehole that is to be or is being drilled based on operating parameters applicable to a drill string by a drilling rig. In this way, the operating parameters may be selected such that the actual borehole has a desired geometry, such as trajectory or path, bend radius, and final ending location. It is known in the art to employ software to simulate the drilling trajectory of the BHA and associated drill string in directional drilling applications. For example, the computer processing system 12 may be programmed with a software program commercially developed and deployed by beckhause corporation of houston, texas, referred to as a "directional drilling simulator (DDAS)". DDAS is also published on 21.5.2015 and U.S. patent application publication No. 2015/0142406 entitled "direct drill ahead simulator," the disclosure of which is incorporated by reference in its entirety. The drilling method uses a drill string steering model (i.e., a steering algorithm) to predict the inclination angle of the drill bit and thus the borehole being drilled. The DDAS may include additional models for predicting axial and lateral motion, and may also include models for predicting drilling performance of a particular drill bit design in a real drilling environment. In particular, the dynamics of the DRILL BIT were modeled using an AXIAL MOTION DRILL BIT MODEL (referred to as DRILLBIT) and a LATERAL MOTION DRILL BIT MODEL (referred to as SIDECUT) disclosed in U.S. patent application publication No. 2015/0142403, published 5-month-21 2015 and entitled "AXIAL MOTION DRILL BIT MODEL," and U.S. patent application publication No. 015/0142404, published 5-month-21 2015 and entitled "LATERAL MOTION DRILL BIT MODEL," the entire contents of each of which are also incorporated herein by reference in their entirety. Formation lithology of a particular subterranean formation, as well as drilling rig operating parameters such as weight on bit, rotational speed, rate of penetration, drilling fluid flow rate, lateral aggressiveness of the drill bit, or drill string torque, are input into the DRILLBIT and/or SIDCUT to accurately estimate the motion of the drill bit based on the calculated interaction of the drill bit, BHA, and formation rock. For example, drilling parameters specific to the BHA and specific to a defined target in a specified subsurface formation may be received.

Next, the apparatus for drilling a borehole is discussed. FIG. 1 shows a cross-sectional view of an exemplary embodiment of a drill pipe 5 disposed in a borehole 2 penetrating the earth 3, which earth 3 may include a formation 4. The formation 4 represents any subsurface material of interest that may be drilled by a drill pipe 5. In the embodiment of fig. 1, the drill pipe 5 is a drill string made up of drill rods 6 coupled together in series. A drill bit 7 is provided at the distal end of the drill pipe 5. The drill string together with the drill bit 7 may be referred to as a Bottom Hole Assembly (BHA). The drilling rig 8 is configured to perform drilling operations, such as rotating the drill pipe 5 and thus the drill bit 7 to drill the borehole 2. Further, the drilling rig 8 is configured to pump drilling fluid (sometimes referred to as drilling mud) through the drill pipe 5 in order to lubricate the drill bit 7 and flush cuttings from the borehole 2. A mud motor (not shown) may be included in the BHA. The mud motor is configured to convert energy from the drilling fluid into additional rotational energy for rotating the drill bit 7. The steering device 9 is coupled to the drill pipe 5 and is configured to steer the drilling of the borehole 2 in a desired or intended direction using, for example, the extendable pad 13. Other steering configurations, such as a configuration that bends the BHA, may also be used. The desired direction may include an oblique direction (i.e., up or down with respect to the surface of the earth) and/or an azimuthal direction (i.e., with respect to a reference azimuth such as true north or grid north). It will be appreciated that in one or more embodiments, the steering device 9 is disposed proximate the drill bit 7 (e.g., within three feet (0.914 meters)), such that a force or a portion of a force applied by the steering device 9 to the drill pipe 5 may also be applied to the drill bit 7. In one or more embodiments, the steering device 9 may be considered part of the BHA. In some embodiments, a rotary steerable drilling system (RSS) may be used to steer the BHA in the borehole 2. For example, the RSS may include the AutoTrak eXact high build Rotary Steerable System (RSS) ("AutoTrak eXact RSS") commercially available from Beckhous, Houston, Tex. The controller 11 is configured to control the steering device 9 to steer the drilling of the borehole 2 in a desired direction. The controller 11, which may include downhole electronics, may also serve as an interface for telemetry to transfer data or commands between downhole components and a computer processing system 12 disposed at the surface of the earth 3. Non-limiting embodiments of telemetry include pulsed mud and wired drill pipe. The system operations, control and/or data processing operations may be performed by the controller 11, the computer processing system 12 or a combination thereof. The BHA may include sensors 10 configured to sense various downhole parameters that may be transmitted uphole according to programmed instructions to a computer processing system 12 to be used by an operator or analyst to control drilling operations for data recording, processing, or display. The computer processing system 12 may be configured to accept inputs including simulated drilling operations (e.g., via the sensors 10 or via user input devices) to improve aspects of active drilling operations by including corrective measures to change operating parameters to provide recommendations for equipment selection and operation or both for subsequently planning drilling operations. The sensor signals may be provided at selected time intervals, at depth intervals along the drill path, at reduced intervals during drilling of the non-linear portion of the borehole, or a combination thereof.

The controller 11 may receive signals from the downhole sensors 10, as well as any other sensors used in the drilling assembly, and process the signals according to programmed instructions. Controller 11 may send the results of the processed signals (e.g., current downhole conditions, current location, location relative to a predetermined drill path, current operating parameters, recommended operating parameters, current equipment deployed, and recommended equipment for deployment) to an electronic display of computer processing system 12 that may be used by an operator to control drilling operations. In some embodiments, the measured property of the formation 4 may be utilized by the computer processing system 12. In other embodiments, the measured characteristics may be extrapolated using the computer processing system 12 by accessing a database of characteristics of the geographically closest formations and accepting the estimated characteristics of the formation 4 at the computer processing system 12 (e.g., using linear, polynomial, or other known extrapolation techniques). Examples of downhole parameters include BHA inclination angle, BHA acceleration, and recordable formation parameters such as mineralogy. The teachings disclosed herein may be implemented in real time by a computer processing system that receives sensor data, or the teachings may be implemented by another computer processing system that does not receive sensor data in real time.

In support of the teachings herein, various analysis components, including digital and/or analog systems, may be used. For example, the steering device 9, downhole sensors 10, controller 11, or computer processing system 12 may include digital and/or analog systems. The computer processing system 12 may have components such as processors, storage media, memory, inputs, outputs, communication links (wired, wireless, pulsed mud, optical, etc.), user interfaces, software programs, signal processors (digital or analog), and other such components (such as resistors, capacitors, inductors, etc.) to provide for the operation and analysis of the devices and methods disclosed herein in any of several ways that are well known in the art. It is believed that these teachings may be, but are not necessarily, implemented in conjunction with a set of non-transitory computer-executable instructions stored on a non-transitory computer-readable medium comprising memory (e.g., Read Only Memory (ROM), Random Access Memory (RAM), optical (compact disc read only memory (CD-ROM)), or magnetic (disk, hard drive)) or any other type that, when executed, cause a computer to implement the methods of the present invention. In addition to the functions described in this disclosure, these instructions may provide equipment operation, control, data collection and analysis, and other functions deemed relevant by a system designer, owner, user, or other such person. The processed data, such as the results of implementing the method, may be transmitted as a signal through the processor output interface to the signal receiving device. The signal receiving means may be a display monitor or a printer for presenting the results to the user. Alternatively or additionally, the signal receiving means may be a memory or a storage medium. It will be appreciated that storing the results in a memory or storage medium will cause the memory or storage medium to transition from a previous state (containing no results) to a new state (containing results). Further, if the result exceeds a threshold, an alarm signal may be transmitted from the processor to the user interface.

In the following, certain definitions are given for convenience. The process of drilling subterranean formations is typically a three-dimensional process in that the drill bit not only penetrates the formation linearly along the longitudinal axis, but also purposefully or unintentionally drills along a curved path or at an angle relative to the theoretical longitudinal axis that extends into the subterranean formation in a direction substantially parallel to the earth's gravitational field. As used in this disclosure, the term "drilling operation" means and includes any operation performed during the formation or enlargement of a borehole in a subterranean formation. For example, drilling operations include drilling, reaming, and other formation removal processes.

Accordingly, the term "earth-boring tool" as used in this disclosure means and includes any type of tool used for earth removal during formation or enlargement of a borehole in a subterranean formation, and includes, for example, fixed-cutter (i.e., "drag") bits, roller cone bits, percussion bits, core bits, eccentric bits, bi-center bits, reamers, mills, hybrid bits, and other bits and tools known in the art.

As used in this disclosure, the term "BHA model" refers to a finite element model or beam model that models the dynamics of the BHA (i.e., drill string and drill bit) in the borehole. In the BHA model, the user may create the hole geometry by specifying the length of the hole section and the inclination angle of the two ends of the hole section. Each section may be represented by a series of circles, where each circle represents a cross-section of the borehole. The model automatically represents the cross-section of the BHA between the two ends of the hole section that the user has specified. Once a hole is formed, a drill string or BHA may be created and placed into the hole. The finite element model or beam model calculates the manner in which the drill string is placed in the borehole, the location where the drill string is in contact with the borehole, the manner in which the drill string bends or flexes, and the magnitude and direction of the contact force at which the drill string contacts the borehole wall, based on the operating parameters applied to the BHA by the drilling rig. The BHA model may also calculate the bit inclination of the drill bit, which is the angle between the longitudinal axis of the drill bit and the longitudinal axis of the borehole, or the difference between the inclination angle of the drill bit and the inclination angle of the borehole. One example of a BHA model that is commercially developed and employed by Beckhous corporation of Houston, Tex is known as BHASYS PRO. FIG. 2 shows an example of the output provided by the BHA model, showing the direction and magnitude of the contact force and the geometry of the BHA. Since BHA models are known to those skilled in the art, further details of these models are not discussed in further detail.

The basic convention and coordinate system used in this disclosure are the definition of inclination angle, build rate (BUR) and Dog Leg Severity (DLS). The tilt angle θ is measured from the depth axis, as shown in FIG. 3. BUR is measured as the change in tilt angle with respect to the measurement depth. In other words, the build rate is the "hole curvature" projected onto the vertical plane. Dog Leg Severity (DLS) is the change in hole angle relative to the measurement depth. Regardless of the orientation of the hole, the dog leg severity is simply the "curvature of the hole". It may be bent sideways, or bent upwards, etc.

The tilt angle will be indicated by the symbol theta. The subscript "new" used with thetaxnew refers to the inclination angle at the very end of the survey section (bottom of the hole) created by the predictive BUR algorithm. Thetaard refers to the survey cross-section at the top of the newly created survey section. It is referred to as "old" because in BHASYS PRO the inclination angles at which the survey sections join are always equal to each other. Thus, the inclination angle at the bottom of the hole of the survey segment N will be equal to the inclination angle at the top of the survey segment N + 1.

Next, a directional drilling simulation method 40 for adding a new borehole section to the BHA model is discussed. Aspects of method 40 are depicted in fig. 4. First, the BHA model was run. The BHA model gives force, bit inclination, moment, and curvature information to the axial and lateral motion bit models. The model also gives the hole curvature and BHA alignment within the hole to the steering model. Next, an axial motion drill bit model is run using inputs from formation lithology recordings and rig operating parameters. The model calculates rock strength (e.g., confined compressive strength) and rate of penetration (ROP). The ROP and rock strength are then given to the side-moving drill bit model. The lateral motion bit model uses this data, along with data supplied by the BHA model such as bit side force and bit inclination angle, to calculate the ratio of lateral ROP to axial ROP, or lateral displacement to axial displacement, of the drill bit over a specified period of time. This is called dL/dZ. The front steering angle δ _ front for the BHA is derived from dL/dZ and is defined as:

using a small angle approximation, the alternative definition is:

the steering model is invoked next (explained in detail below). The steering model uses a delta-front calculation to calculate the inclination and azimuth of the end of a new hole section that will be created by the simulated borehole. A new bore section is created based on the calculated inclination angle and azimuth angle. The BHA and bit are moved down to the bottom of the new bore section and three models (BHA, axial motion bit model, and lateral motion bit model) are invoked again. Thus, the loop continues until the simulation stops. The drilling simulation method 40 first runs the BHA model and then feeds its results to the axial and lateral drill bit models that are incorporated into the drilling simulation method 40. The drilling simulation method 40 then predicts the location and geometry of the next hole section.

There are alternatives or sequences of running models, but the emphasis is that the steering model is fed with information by other models, and that the new simulated bore section is placed in the direction that the drill bit/BHA system wants to drill as calculated by the steering model.

Fig. 5A and 5B are flow charts depicting further details of the drilling simulation method 40. In an actual drilling scenario, the general directional behavior of the drill bit will be determined or influenced by the following factors: WOB/ROP relationships; lateral bit force/lateral ROP relationship; bit inclination, bit rotational speed (e.g., RPM); confined Compressive Strength (CCS) of formation rock; drilling fluid flow rate (in case of excess in weak lithology); and dynamic stability of the borehole while drilling. These and other factors are therefore included in the model that feeds information to the steering model.

Next, the drill string steer model is discussed. The drill string steering model includes a front steering angle model. Steering accuracy can be improved by adding a rear steering angle model to the front steering angle model. The front steering angle model is based on kinematic motion of a two-wheeled vehicle such as a bicycle. Fig. 6 shows a simplified diagram of such a vehicle in a top view and illustrates aspects related to front steering angles.

The following equation describes the rate of angular change with respect to vehicle time as a function of the vehicle's speed V, the length L of the wheelbase, and the front steering angle δ.

The steering angle is the angle between the longitudinal axis of the vehicle and the direction in which the front wheels are pointing. The front steering angle model analogizes this two-wheeled vehicle to the portion of the BHA from the drill bit to the first contact point with the borehole wall. One difference between the bicycle path and directional drilling is that the rear wheels of the bicycle do not follow the path of the front wheels in turns. In directional drilling, the second contact point of the BHA does follow the path of the drill bit, which brings the first contact point into contact with the formation. For simplicity, this difference is ignored at this time.

FIG. 7 depicts aspects of a front steering angle applied to a BHA. The BHA of the drilled borehole is described using the following parameters:

time of orientation angle of carrier reference system

V：

s: measuring the depth;

ds: measuring a change in depth; and

δ: the steering angle of the drill bit. Steering angle delta can be conceptually viewed as the angle between the axis of the tool (the first point of contact behind the bit from the bit) and the instantaneous trajectory of the bit

As discussed above, the steering angle of the BHA is affected by certain drilling and lithology parameters. All of these parameters change during normal drilling operations. Now δ (t) will be denoted δ, assuming it can change throughout the run as time or depth changes, since the parameters mentioned above will change with time or depthAnd (6) changing. Using L to represent the distance from the bit to the first contact point of the BHA behind the bit, equation directly addressed above

The rewritables are:

the dt term in the denominator may be cancelled, resulting in the following equation:

these formulae can be rewritten as:

where d θ/ds is the variation of the bit axis inclination angle (and hole inclination angle) with respect to depth.

The curvature of a circular section (i.e., a borehole cross-section) is mathematically defined as:

where R is the radius of the circular survey cross-section and k is the curvature of the circular survey cross-section (i.e., the radius of curvature of the borehole at the survey cross-section). Thus, the instantaneous curvature (or curvature of one iteration) can be described mathematically as:

this equation can be rewritten to provide the change in tilt angle per change in depth as:

this equation may be manipulated to find a new inclination angle θ for a new survey cross-section predicted by the drilling simulation method in an iteration _New 。θ _{Old age} Is the inclination angle at the bottom of the well before a new survey is made. As is the distance into the borehole through the simulation during each iteration in the drilling simulation method. Theta.theta. _New The hook steering model can then be written as:

as mentioned above, the steering model may be improved by combining the rear steering model with the front steering model. FIG. 8 depicts aspects of a rear steering angle model. In FIG. 8, the BHA has a front pseudo-steered wheel and a rear pseudo-steered wheel. The rear wheels must follow the path of the drilled borehole as they guide the BHA on the steering axis of the rear wheels. The rear steering angle model is very similar to the front steering angle model. The only two differences are that the rear steering angle now appears in the equation directly above, and the cosine of the front steering angle also modifies the prediction in the following equation:

rear steering angle delta _{Rear end} Is the angle between the drill inclination angle theta and the cutting edge axis at the first point of contact of the BHA after the drill tip, or it may be defined as the angle between the drill inclination angle theta at the first point of contact after the drill tip and the drill inclination angle theta at the location where the drill contacts the wall. Using the latter definition, the rear steering angle can be written as:

δ _{rear end} ＝θ _{(first contact point after the drill)} –θ _{(contact point at drill)} 。

FIG. 9 is a flow chart of one example of a method 90 for predicting the path of a borehole to be drilled in a formation by a Bottom Hole Assembly (BHA) having a drill bit coupled to a drill pipe, the BHA being operated by a drilling rig. Block 91 calls for constructing a BHA model of the BHA. The model of BHA includes: (a) size, geometry, mass distribution, material density, and material stiffness of the BHA; and (b) predicting the size and geometry of the drilled borehole. The BHA model is configured to calculate: (c) one or more contact points between the BHA and the borehole wall; and (d) a force exerted on the BHA at the one or more contact points, the force comprising a lateral force vector exerted on the drill bit; and (e) bit inclination. Block 92 calls for calculating the confined compressive strength of the formation using an axial motion drill bit model that receives drilling parameters of the drilling rig, drill bit design information, and lithology information including formation rock strength. Block 93 calls for calculating the lateral motion of the drill bit using a lateral motion drill bit model that receives: (i) an axial ROP from an axial motion drill bit model; (ii) lithology information; and (iii) bit design information; and (iv) bit side force vectors and bit inclination angles from the BHA model. Block 94 calls for calculating a ratio of lateral to axial motion. Block 95 calls for calculating the inclination angle and azimuth direction of the BHA using the BHA steering model that receives the ratio. The tilt angle together with the azimuthal direction (e.g., direction or angle relative to true north) provides a three-dimensional direction. Block 96 calls for iterating the above steps by: updating the BHA model to include extending the borehole by incremental distances in the dip angle direction and the azimuth direction and shifting the BHA by the incremental distances in the extended borehole.

Each block in method 90 may be implemented by a processor, such as in a computer processing system. Further, the data used by the method 90 as input to the various models discussed above may be updated in real-time as the actual borehole is drilled according to the drilling parameters used to obtain the predicted borehole path. The updated data may be obtained from one or more sensors disposed on the BHA drilling the actual borehole. In this way, the accuracy of the predicted path may be improved by using the updated data. The sensors may include borehole caliper sensors and/or formation sensors configured to sense data from which formation lithology may be derived. Examples of formation sensors include natural gamma ray sensors and neutron tools that emit neutrons and sense neutrons or gamma rays resulting from the interaction of the neutrons with the formation.

Next, the axial motion drill bit model (i.e., DRILLBIT) is discussed. The axial bit model is part of a directional drilling simulator. It allows prediction of drilling performance of a particular drill bit design in a real drilling environment, and in particular, the forces on the drill bit are calculated using a PDC cutting edge force model. Given the operating parameters, formation properties, and a particular bit design, the axial model predicts the rate of penetration (ROP) with a specified weight-on-bit (WOB) or predicts the WOB with a specified ROP. The overall method is as follows: (a) calculating the cutting area (projected onto a vertical plane) of the land and chamfer for each of the cutting edges representing the drill bit according to the drill bit design and operating parameters; (b) estimating the confined compressive strength of the rock stratum according to the details of the rock stratum, the drilling depth and the mud weight; (c) given these estimated cutting areas, the detailed geometry of the manner of engagement of the edge of the cutting edge with the rock, and the CCS of the formation, the forces on the face and chamfer of the cutting edge are calculated using a "force model" (discussed below); (d) and summing the forces on all cutting edges to yield a net force on the drill bit. These forces are easily converted to WOB (weight on bit) and TOB (torque on bit) if ROP is specified. If a WOB is specified, an iterative procedure is used by which ROP is adjusted until the predicted WOB matches the specified WOB.

If a directional drilling simulator (DDAS) is drilling with a specified ROP, the only thing returned from the axial motion bit model used by the DDAS is the CCS and some information about the bit design. However, if the DDAS is drilling with the specified WOB, then the CCS, ROP, and information about the bit design will be transmitted back to and used by the DDAS. In particular, SIDECUT (side-motion bit model) requires CCS values and information about bit design in order to predict the lateral migration of a bit with applied side loads.

Axial motion drill model assumptions: the drill bit is drilling "in the center" and the drill bit rotation axis always coincides with the fixed Z axis in the rock reference frame, as shown in fig. 10. The axial model calculates the cutting area and force as each cutting edge passes through a vertical plane defined as [ Y ═ 0, X >0 ]. In this frame of reference, the Z axis lies on the bit rotational axis, and positive Z is in the tip-to-shank direction. The rock face is defined in this plane as a single line of communication defined in this vertical plane. Fig. 10 shows this frame of reference superimposed with a vertical plane. The drill bit in fig. 10 is a Polycrystalline Diamond Compact (PDC) drill bit.

As part of the axial model discussion, drill bit rotation and rock surface updating are now discussed. In one or more embodiments, the drill bit and rock surface are modeled using nodes, and node locations are updated based on drill bit-rock interactions. The cutting edges on the drill are first sorted according to the increasing angle (angular position on the drill). Consider a drill bit having 3 cutting edges and the parameters listed in table 1.

TABLE 1

During one rotation of this drill bit the rock surface is updated as follows: (1) calculating the intersection of the cutting edge 1 and the rock and updating the rock surface accordingly; (2) rotating the drill bit by an angle (45-0) and modifying the drill bit vertical position accordingly based on the RPM and ROP; (3) calculating the intersection of the cutting edge 2 with the rock and updating the rock surface accordingly; (4) rotating the drill bit through an angle (270-45) and modifying the drill bit vertical position accordingly based on the RPM and ROP; (5) calculating the intersection of the cutting edge 3 with the rock and updating the rock surface accordingly; (6) the drill bit is rotated through an angle (360-. This sequence is repeated until a run termination criterion (e.g., number of iterations) is met. Fig. 11 to 14 show the progression of rock surface updates.

The axial model is computationally fast, since in one or more embodiments it is only necessary to track the rock surface in one 2D plane and calculate the cutting edge interaction with the rock surface in this plane. This is possible for the case of a drill bit drilling in the center. When the cutting edge passes the X-Z plane, it cuts away the top of the cast-in-place pile to renew the rock surface as shown in fig. 15.

Further, as part of the axial model discussion, the calculation of the cutting area is now discussed. In one rotation of the drill bit, the amount of drill bit movement down DZ is ROP/(5X RPM) for a given ROP and RPM. ROP is in feet per hour (ft/hr), while DZ is in inches in this equation. If the cutting edges are sorted by increasing angle (see previous discussion), the amount of vertical movement DZ' associated between one cutting edge passing through a vertical plane and the next cutting edge passing through the same vertical plane is simply scaled by the difference DAA in the angle values, as shown in the equation below.

DZ′＝DZ X DAA/360

Thus, when each cutting edge (sorted by increasing angle) passes through a vertical plane, all cutting edges are moved downwards relative to the rock pile by an amount DZ'. The comparison of the overlap between the cutting edge and the rock surface allows the cutting area of the cutting edge to be calculated and then used in the cutting edge force model.

The edges and chamfer of a PDC cutting edge are initially represented as an ellipse (a circle with a non-zero back bevel angle projected onto a vertical plane) as the cutting edge passes through the rock "plane". These ellipses are exact (analytical) representations for unworn cutting edges with designed back bevel and side bevel angles. The ellipse is broken down into vertical cast-in-place piles having a user-specified width (e.g., default width of 0.003 inches). The rock surface is also broken down into an identical set of cast-in-place piles matching the position of the cutting edge cast-in-place piles (along the X-axis), as shown in fig. 15. Fig. 16 shows this configuration. Figure 16 shows the cutting edge face (and chamfer) with a non-zero back bevel angle outward from the page at the viewer. If the cutting edge is allowed to wear, the edge of the cutting edge in contact with the rock will deviate from the ideal ellipse. This bias, applied on a cast-in-place pile basis, is determined by a wear model discussed further below in this disclosure. The cutting area is depicted in fig. 16. The upper patch is the (projected) cutting area on the cutting edge face and the lower patch is the (projected) cutting area on the chamfer. It should be noted that these areas depend on the position of the rock surface relative to the cutting edge at a particular cast-in-place pile. The rock surface may intersect only a portion of the chamfer and not the face at the location of the cast-in-place pile. The cutting zones on the chamfer and face remain independently tracked because the cutting force performance is different for each cutting zone. This is also discussed later. It is also possible that the cutting edge cast-in-place pile is completely worn and no longer present.

It should be noted that the vertical cast-in-place pile is used because it is a natural choice in predicting cutting edge wear. One cutting edge pile is uniquely associated with one rock pile. By this option, a certain error can be introduced at the side of the cutting edge. The force model discussed below has extensive bookkeeping to account for cast-in-place piles that intersect only the chamfer and those that intersect the chamfer and face of the cutting edge.

Further, as part of the axial model discussion, the updated rock surface is now discussed. A new rock face (after cutting) is created by cutting away the rock cast-in-place pile at the bottom-most position of the cutting edge cast-in-place pile. This is illustrated by the dashed line in fig. 17. Fig. 17 shows the renewed rock surface of the new cutting edge. If the cutting edge wears, the renewed rock surface will only be the lowermost end of the cast-in-place pile when the cast-in-place pile is cutting. If the cast-in-place pile is not cut, the rock surface at said location will not change.

Further, as part of the axial model discussion, the cutting edge interaction is now discussed. There is typically an overlap in the radial extent of adjacent (in radial coordinate) cutting edges. The shape and magnitude of the cutting zone depend on the radial overlap of the cutting edges and their respective angles. Fig. 18 shows an example. This example represents the cutting area of all cutting edges on a single blade of a PDC bit. The cutting zones on the cutting edge and the forces associated with these cutting zones depend on the cutting edge layout and operating parameters (e.g., RPM, ROP) on the drill bit. After several revolutions of the bit, the magnitude and shape of the cutting zone stabilizes to a constant value of fixed ROP and RPM. It should be noted that the image in FIG. 18 is a general "bit profile" image generated by the axial model. For drawing purposes only, the cutting edges and corresponding cutting zones have been rotated back into the X-Z plane, taking into account the helix angle. The reason is twofold: (1) such that the image will conform to a typical engineered "side view" of the drill bit; and (2) the geometry of the cutting zone is mapped within its associated cutting edge.

Further, as part of the axial model discussion, the effective back bevel angle of the cutting edge is now discussed. The effective back bevel angle is the angle that plays a role in the cutting force. The effective back rake angle is not the design back rake angle found in the drill bit design file. Both are related, but only. The effective back rake angle is the angle between (normal to) the local cutting surface and the local rock surface. Fig. 19 shows the chamfer cutting edge out of the page. Two cast-in-place piles are superimposed on the image. The two large arrows indicate the surface normal of the cutting edge chamfer at the location of the cast-in-place pile. The small arrow is the surface normal of the cutting face at one of the cast-in-place pile locations. The dots represent vectors outward from the page and parallel to the local rock surface that the cutting edge will see when passing through the rock. The effective back bevel angle (EBR) is the angle between this vector and the arrow. It is clear that the EBR may depend on the position on the cutting edge along the edge of the cutting edge, whether the notch is on the chamfer or on the face.

Fig. 20 is a close-up of the bottom of the edge of the cast-in-place pile (at the edge of the cutting edge). The edge of the cutting edge is delineated by the contact between the cast-in-place pile and the triangle. The vector arrow into the cutting edge is the normal to the local cutting edge surface (on the chamfer or on the face). It should be noted that this orientation vector is three-dimensional and has three components, each associated with an axis in a right-hand coordinate system. There is a component in the normal vector that is outward from the page. Angle of rotation

Referred to as the "cut" angle.

A simple two-dimensional (2D) rotation operator is constructed that rotates the bottom edge of the bored concrete pile into the horizontal plane. This operator is applied to the three-dimensional (3D) normal (red vector depicted in fig. 20) perpendicular to the local cutting edge surface. If the resulting rotated normal vector (normalized) has components (Nx, Ny, Nz) where X and Z have previously defined the reference frame ") and Y is from" out of the picture ", the effective back bevel angle (EBR) and the effective side bevel angle (ESR) are given by:

and is provided with

ESR＝SIN ^-1 (N _x )。

These expressions for EBR and ESR are calculated on a cast-in-place pile basis for all cast-in-place piles intersecting the cutting edge.

Further, as part of the axial model discussion, the forces on the cutting edge are now discussed. The force on the cutting edge is calculated by summing the forces on the individual cast-in-place piles across the cutting edge. The force on the cast-in-place pile alone will depend on the cutting area on the chamfer, the cutting area on the face, the effective back rake angle, the formation, the Confined Compressive Strength (CCS), the drilling depth, and the mud weight. The details of the force model are given in different cross sections. Once the normal (Fn) and circumferential (Ft) forces on the cast-in-place pile are calculated, they are transformed back into the drill bit reference frame. The net force on the drill bit is the sum of the individual cutting edge forces, which are themselves the sum of the individual cast-in-place pile forces. Consider fig. 21 showing a local (bored pile) rock surface with normal (Fn), tangential (Ft), and radial (Fr) forces generated by a force model. The force model is applied on a cast-in-place pile basis. Fn is always normal to the local rock surface (regardless of its orientation with respect to the earth). Ft is in a direction normal to the X-Z plane, and Fr is perpendicular to the plane containing Fn and Ft.

By this nomenclature, the following force components may be defined.

F _N Component in XYZ coordinate System

F _NY ＝0

F _R Component in XYZ coordinate System

F _RY ＝0

Component of Ft in XYZ coordinate System

F _TZ ＝0

F _TY ＝F _T

F _TX ＝0

At this point, all Z components may simply be added to get weight on the cutting edge, all Y components to get circumferential force, and all X components to get radial force. However, this does not take into account the helix angle. Please remember that the force model is located in the reference frame of the local rock surface. Therefore, the correction of the helix angle α must be performed. The final equation for the force on a particular cast-in-place pile is given by the following equation.

WGT (vertical force) ═ F _NZ +F _RZ )COS(α)+F _TY SIN(α)

SID (side force) ═ F _NX +F _RX

CIR (circumferential force) ═ F _NZ +F _RZ )SIN(α)+F _TY COS(α)

TRQ (torque on bored concrete pile) ═ R _pic CIR (see below for R _pic Definition of (1)

It should be noted that the helix angle is calculated for each cast-in-place pile and is given by the following equation:

where ROP is the rate of penetration (ft/hr), RPM is the bit rotational speed, and R _pic Is the radial position of the bored-in pile (in the horizontal plane from the drill)Distance of head axis to cast-in-place pile).

These force components on the cast-in-place pile are graphically illustrated in fig. 22. In fig. 22, AA is the angle of the cutting edge, and CIR and SID are defined as above. It should be noted that the view is from a perspective looking down to a horizontal plane from the handle end to the tip end. In the XYZ reference system, and with reference to fig. 22, the force on the cast-in-place pile is given by the following equation.

dF _X ＝CIR SIN(AA)+SID COS(AA)

dF _Y ＝SID SIN(AA)-CIR COS(AA)

dF _Z ＝WGT

The total force on the cutting edge is simply the sum of these forces for all (N) cast-in-place piles associated with said cutting edge, given as:

where N is the number of cast-in-place piles associated with a particular cutting edge. Thus, the net force and moment on the drill is the sum of the forces and moments on all the cutting edges on the drill.

Next, the cutting force model is discussed. The force on the PDC cutting edge is given by two orthogonal components: a "tangential" component parallel to the local rock surface and a "normal" component perpendicular to the local rock surface. It should be noted that in estimating such things as weight-on-bit and bit torque, Fn and Ft must be converted to the bit reference frame. The model is defined by the following equation:

F _t ＝εA

wherein:

F _t cutting force parallel to the local rock surface

F _n Cutting force perpendicular to the local rock surface

Epsilon ═ intrinsic specific energy "

A is the projected cutting area; and is

Ratio to Ft (correlation to be defined)

Fig. 23 and 18 define PDC cutting edges in relation to rock. Fig. 23 is a side view of a cutting edge moving through a rock, where Fn and Ft are indicated. FIG. 18 shows one blade of a PDC bit with the cutting edge facing out of the page. Fig. 18 shows the significance of the projected cutting area (blackened area) associated with the removed rock (hereinafter).

The cutting force model is extended to practical form by identifying the nature of the "intrinsic specific energy" and developing a means to characterize its value from log, drilling depth and mud weight on a site-specific basis.

Next, epsilon discusses the inherent specific energy aspect of the cutting edge force model. The "intrinsic specific energy" term ε is the effective cutting strength (or cutting resistance) of the rock. This effective strength will depend on the following: wellbore pressure; a hole depth; the weight of the slurry; lithology; the orientation of the cutting edge of the drill; cutting edge geometry (face/chamfer); and the cutting edge interface coefficient of friction. The orientation of the cutting edges on the drill bit and the orientation of the formation rock relative to the drill bit provide the orientation of the cutting edges relative to the formation rock to be cut, which is taken into account in the inherent specific energy disclosed herein. Assuming that the "intrinsic specific energy" is equal to the confined compressive strength of the rock, the modification is that this limit also includes the limits due to cutting edge, mud column and pore pressure effects. Confined Compressive Strength (CCS) is considered to be the Unconfined Compressive Strength (UCS) modified by a term associated with confining pressure and is defined as follows:

wherein CCS is the confined compressive strength (calculated); UCS is unconfined compressive strength (from logging); FA is internal friction angle (from logging); and CP is the confining pressure (calculated from log, mud weight and drilling depth). It should be noted that when there is no confining pressure (CP ═ 0), the Confined Compressive Strength (CCS) is equal to the Unconfined Compressive Strength (UCS). The confining pressure CP in the expression will depend on the hole depth, mud weight and lithology, and is discussed further below.

The intrinsic specific energy cannot be equated to CCS because for fugi mountain sandstone at atmospheric conditions, epsilon can exit as a function of the cutting edge back bevel angle theta, as shown in figure 24. As shown in fig. 24, it is apparent that the strength of the rock increases as the cutting edge back angle increases. This is associated with the additional margin of the cutting edge to the rock. When theta is 0, the internal specific energy epsilon is close to the uniaxial compressive strength of the Furi mountain sandstone. Thus, it was concluded that: by algebraic form, the intrinsic specific energy can be represented by a first order approximation: epsilon (θ) CCS, where a reasonable functional form of γ (see fig. 24) is considered: gamma (theta) ═ 1+ A ₂ TAN(θ)。A ₂ Are multiplication parameters that are included to allow adjustment during model fitting of laboratory or field data.

Next, the cutting force inclination angle aspect of the cutting edge force model is discussed. The ratio of Fn to Ft is also not simple. Fig. 25 illustrates the forces acting on the cutting edge. The cutting edge back bevel is given by θ, while ψ is the bevel angle due to friction from the net cutting force normal to the cutting face. According to fig. 25, the ratio can be expressed as:

wherein the angle of inclination of the net cutting edge force with respect to the rock surface is given by a ═ θ + Ψ. Thus, the following associations may be made:

the effective back tilt angle θ is a well-defined parameter. On the other hand, Ψ is less direct. Depending on the degree of anticline, the rock may "flow" up the cutting edge or "down" under the cutting edge, as shown in fig. 26A-26C. Based on laboratory experiments on fugi mountain sandstone, the relationship of ψ and back-bevel angle θ is shown in fig. 27.

Note that in fig. 27 the data is more or less symmetric about θ -45 degrees, and the following form of ψ can be inferred:

ψ＝TAN ^-1 [Cμ(90-2θ)/90]

where θ is in degrees and C μ is a constant that may be related to the interfacial friction coefficient between the cutting edge and the rock. It should be noted that C μ can be considered a free parameter and can be determined by fitting laboratory drilling data to a model, so it is not required to be related to some physical mechanism. It should be noted that in the discussion that follows, the force model coefficients A ₃ ＝Cμ。

Next, the confining pressure aspect of the cutting force model is discussed. The Confining Pressure (CP) model is one of the key elements of a successful "drilling" simulation. The confining pressure model used in drilbit is based on distinguishing permeable formations from impermeable formations according to the following lithology logs.

Σ _{Impermeable to water} Shale +% coal +% polyhalite +% sand shale mixture +% anhydrite

Σ _{Permeable to water} Sandstone (Bingzhi)

The percentage is the fraction of the indicated rock type, and at each depth the sum of these fractions is one. If the formation is considered to be impermeable, the CP at that depth is simply the Bottom Hole Pressure (BHP) calculated from the hole depth and mud weight as follows: cp (psi) ═ BHP ═ 0.052x depth (ft) x mud weight (ppg). If the formation is considered to be permeable, the confining pressure is the above minus the pore pressure: cp (psi) ═ Δ P, where Δ P ═ 0.052x depth (ft) x [ mud weight (ppg) -Pp ], and Pp ═ max [8.5, mud weight (ppg) -0.5 ]. The effective porosity and confining pressure CP (used in the confined compressive strength calculation) of the formation are calculated according to the following:

CP＝ΔP，Φ _eff >0.2

CP＝BHP，Φ _eff <0.05

CP＝ΔP[(Φ _eff -0.05)/0.15]+BHP[(0.2-Φ _eff )/0.15]。

is the measured porosity of the formation or the porosity inferred from the well log data. Note that the last entry above is an interpolation between the maximum allowed CP (i.e., BHP) and the minimum allowed CP (i.e., Δ P), and this interpolation is based on effective porosity.

Next, the mud weight correction factor aspect of the cutting force model is discussed. The mud weight correction factor is implemented in the drilbit. The correct interpretation of this effect is by the "chip suppression effect" which is related to the displacement of the chip produced during cutting. If the fluid cannot migrate between the chip being produced and the formation from which the chip is being produced, the chip is affected by the entire load of the fluid column and the formation is more difficult to drill. However, swarf can be easily removed if the fluid can migrate into the fracture and balance the stress on the swarf. Since fluids migrate through the created fractures in this mechanism, the migration will depend on the mud viscosity (related to mud weight) and will be independent of whether the formation is initially permeable or impermeable. The mud correction factors are:

eta-2.998-0.8876 log (mud weight)

Where mud weight is given in pounds per gallon (ppg).

Next, aspects of implementing the cutting edge force model are discussed. The force model is applied to the cutting edge chamfer and the cutting edge facet independently. Depending on the operating parameters, all or a portion or none of the chamfered and faced cast-in-place piles will engage the rock. The associated "bookkeeping" for this is an integral part of the axial bit model. Many logs do not give specific lithology (sandstone, limestone, etc.) at a specific depth, but rather give mixed lithology in terms of fractional content. In general, the sum of the scores at a given depth is one. The axial model satisfies this by: (i) assigning (by laboratory or field calibration for a particular lithology) values to the force model coefficients a1, a2, A3, and (ii) weighting these force model coefficients at a particular depth according to the scores of the associated lithology. For example, if at a certain depth, the log indicates 25% shale and 75% limestone. Then, at this depth: a1 ═ 0.25X A1 shale +0.75x A1 limestone; a2 ═ 0.25 xa 2 shale +0.75 xa 2 limestone; and a3 ═ 0.25X A3 shale +0.75x A3 limestone.

Next, the example is presented using DRILLBIT. Figures 28 to 30 show a comparison of predicted and measured weights at several laboratory drilling simulator tests. During each drilling test, the specified WOB is changed and the measured ROP is recorded. The upper and lower limits in these plots are calculated by propagating the uncertainty of porosity, friction angle, and UCS in the drilbit. In fig. 28, the drilling fluid is water and the rock is galaxite limestone. In fig. 29, the drilling fluid is 11 pounds (lb.) (4.990Kg) of water-based drilling mud, and the rock is galaxicon limestone. In fig. 30, the drilling fluid is 16lb. (7.257Kg) oil-based drilling mud and the rock is mankstone shale. Another example is a comparison of the predicted ROP and the measured ROP as shown in fig. 31. ROP is predicted using lithology logs from this location and the actual drill bit design used in the field and the actual WOB applied to the drill bit. The legend for this chart is: SHA: the fraction of shale; SSA: a fraction of sandstone; LSO: the fraction of limestone; and D, DOL: the fraction of dolomite; and (3) POR: porosity of the formation; and (3) CP: the predicted confining pressure; and a UCS: unconfined compressive strength.

FIG. 32 is a flow chart of a method 320 for predicting the amount of axial movement of a drill bit having one or more cutting edges for drilling a borehole into formation rock. Block 321 entails receiving lithology data of the formation rock. Block 322 calls for receiving drilling parameters including mud weight and bit depth for a drilling rig that is to operate drill pipe coupled to a drill bit and drill bit design information. Block 323 calls for calculating a confined compressive strength of the formation rock using the received lithology data, drilling parameters, and drill bit design information. Block 324 calls for calculating a cutting area of each of the one or more cutting edges into the formation rock. Block 325 calls for calculating an effective back bevel angle for each of the one or more cutting edges. Block 326 calls for using the calculated confined compressive strength of the formation rock, the cutting area, and the effective back bevel angle of the one or more cutting edges, and calculating the force applied to each of the one or more cutting edges by considering the orientation of each of the one or more cutting edges relative to the surface of the rock to be cut. Block 327 calls for summing the calculated forces applied to each of the one or more cutting edges to calculate WOB and TOB (bit torque). The above method may be implemented by a processor. If a ROP is specified, method 320 may be used to calculate a WOB and a TOB that provide the specified ROP. Alternatively, if a WOB is specified, a ROP and TOB may be calculated to provide the specified ROP. If a WOB is specified, the values of ROP and TOB may be changed to calculate a resulting WOB and this value compared to the specified WOB until an acceptable or zero difference is reached. Method 320 may entail representing the drill bit with a first set of virtual cast-in piles and representing the formation rock with a second set of virtual cast-in piles. In one or more embodiments, the first set of bored piles is aligned with the second set of virtual bored piles at the interface of the drill bit and the formation rock. That is, if the first set of cast-in-place piles extends downwards and the second set of cast-in-place piles extends downwards, the two sets of cast-in-place piles will overlap. When using cast-in-place piles, the cutting area, the effective back bevel angle, and the force applied to each cutting edge are calculated on a cast-in-place pile-by-cast-in-place pile basis, while WOB and TOB are calculated by summing the forces on each cast-in-place pile.

Next, a side-moving bit model (i.e., SIDECUT) is discussed. SIDECUT is a procedure for calculating the lateral migration dL (relative to the borehole) of a drill bit drilling a formation as a function of the drilling depth (dZ) along the borehole. Fig. 33 is a flow diagram depicting aspects of the SIDECUT procedure. The drill bit may have a rake angle (relative to the borehole) and an applied side load that forces the drill bit against the borehole wall. SIDECUT may be used in PDC bits, roller cone bits, and hybrid bits combining aspects of PDC bits and roller cone bits. FIG. 34 depicts aspects of a PDC bit in a three-dimensional view.

The procedure allows any of the following values: a rate of penetration of the drill bit (ROP) through the formation; bit rotational speed (RPM); a drill bit inclination angle relative to a borehole side load applied to the drill bit; bit geometry (gage pad length, gage pad depression, fraction of bit circumference occupied by gage pad); and Confined Compressive Strength (CCS) of the formation. In one or more embodiments, CCS is calculated in drilbit, which provides CCS to SIDECUT.

Gage pad recession, defined as the radial distance that the gage pad is recessed inward from the location of the outermost edge of a polishing gage (PDC) dresser, may vary relative to the vertical position on the gage pad. This allows for tapered, stepped, and other gage pad geometries. FIG. 35 illustrates these aspects in a two-dimensional representation.

SIDECUT uses a two-dimensional (2D) description of the drill bit and formation. The reason is the calculation speed. However, more computation time may be used to implement a complete three-dimensional (3D) model. There is excellent agreement between the simplified 2D model and the more complex 3D model.

In fig. 34, a 3D representation of a PDC bit shows PDC cutting edges (small cylinders) and gage pads (rectangular structures). The collection of PDC cutting edges and associated gage pads are referred to as "blades". In fig. 35, the 2D representation shows a single insert and shows the gage pad and the PDC cutting edge below the gage pad ("abrasive gage dresser"). Under an applied side load, the blade is forced to the right against the rock. The dotted line in fig. 35 is the initial rock face in SIDECUT. The rock is simply "shrink wrapped" to the drill bit to initialize the rock face and indicated by the filled region to the right. It should be noted that the outer surface of the gage pad in fig. 35 is recessed from the outer edge of the abrasive gage dresser in a radial (R) position. This is known as "gage pad recession" and is of great significance in controlling the directional drilling characteristics of PDC bits. The vertical (Z) extent of the gage pads is referred to as the "gage pad length" and the fraction of the bit circumference occupied by the gage pads is referred to simply as the "fraction" in the following discussion.

SIDECUT takes into account bit geometry and rock wear when calculating lateral migration of the drill bit in the borehole. The sliding wear model is used to estimate rock wear. The amount of rock worn at a particular location on the borehole wall is proportional to the total sliding distance of the gage pad across that location and the contact stresses applied to that location and the confined compressive strength of the formation. The sliding distance is determined by the bit RPM, ROP, gage pad length, and "fraction". The contact stress is determined by the applied side load and the instantaneous rock-pad contact area.

The SIDECUT procedure is now discussed in more detail.

1. And (5) initializing. The drill bit structure: a 2D drill bit is constructed by constructing a series of equally spaced (vertical) points or nodes from the top of the gage pad to the bit tip. Distinguishing those points associated with the gage pad from those points associated with the PDC cutting edge. The vertical spacing is set to a prescribed value DZ. The totality of the PDC cutting edges below the gage pads is represented by a single vertical configuration with a prescribed back bevel angle. The series of equally spaced nodes may have an arbitrary shape in R-Z space (see FIG. 35). Thus, this generality may encompass tapered and stepped gage pads. The method may also allow for 2D bit profiles, but the implementations described herein only assume continuous vertical blades as representative of PDC cutting structures.

Rock formation: the initial rock surface is a series of equally spaced (vertical) points or nodes that are clones of the initial drill bit representation. The rock nodal position is initially identical to the bit nodal position. The stiffness (spring constant) K is assigned to the rock. When the gage pad is pushed into the rock, the restoring force of the rock against the gage pad is determined by the penetration depth of the pad into the rock, and the depth is determined by the rock stiffness. For example, the rock stiffness may depend on rock properties or other parameters provided by lithology logging. The associated equation for pad-rock contact stress is:

σ＝KΔ

where Δ is pad penetration depth (in), and K is "stiffness" (psi/inch).

2. And (6) circulating the treatment. The treatment cycle includes three procedures discussed below: force balancing, rock removal, and hole growth. At each vertical position of the drill bit relative to the rock, all three procedures apply to this example in the order given below. The drill bit is then moved by an amount DZ (see fig. 15) and the process is repeated until a certain specified drilling distance is reached. This distance is typically a multiple of the gage pad length.

A. The restoring force of the rock to the drill bit is balanced to equal the side load applied on the drill bit.

Referring to FIG. 35: (a) moving the drill bit laterally; (b) calculating the penetration depth of the pad into the rock and the penetration depth of the PDC cutting edge into the rock by comparing the lateral (R) position of the drill bit node to the rock node; (c) calculating forces on the gage pad and PDC cutters on a node-by-node basis according to the method discussed in the force model below; (d) summing all nodal forces (pad and cutting edge) to obtain a net rock restoring force to the bit and comparing to the specified side load; (e) calculating a difference between the net restoring force and the specified side load; and (f) using this difference in the root lookup procedure until the net restorative force equals the specified side load (go to "a").

The force of a single pad node against the gage pad is now provided. The contact force on a single pad node is:

F＝σdA

where σ is the pad-rock contact stress as presented above, and dA 2 pi R FR DZ/N, where R is the drill bit radius, FR is the fraction of the drill bit circumference occupied by the pad, DZ is the vertical pitch point spacing, N is the number of blades on the drill bit, and dA is the total pad area of a single pad over the vertical distance DZ.

The force of a single rock node against the PDC cutting edge is now provided. The restoring force of the rock against the cutting edge depends on the cutting depth of the cutting edge into the rock. For this example, assume that this force is perpendicular to the rock surface. The PDC cutting edge force model (other cutting edge force models may also be used) discussed further in the section on drilbit is given by:

F _N ＝ζF _T

F _T ＝MSE AOC

MSE＝γCCS

γ＝1+A ₂ tan(EBR)

ζ＝tan(EBR+χ)

AOC＝ΔdZ

where MSE is the mechanical specific energy, CCS is the confined compressive strength, AOC is the cutting area, EBR is the effective back bevel angle, Δ is the depth of cut (penetration depth), and a2 and A3 are the force model calibration coefficients.

B. Rock removal by gage pads and PDC cutters.

At this stage, the restoring force of the rock to the drill bit has been balanced by the specified side load applied to the drill bit. The drill bit removes rock by wearing it, crushing it or cutting it (PDC cutters). Rock removal is performed on a node-by-node basis for all nodes representing the drill bit (pads and cutting edges).

Rock removal by the pad. On a node-by-node basis, at a set of rock nodes adjacent to the mat, it is checked whether the contact stress exceeds CCS. If so (which is user-optional), the rock node may be adjusted to simply reflect the displacement. That is, the new R position of the rock node is at the R position of the corresponding pad node. If the contact stress is less than CCS, the new rock node R location is determined by the sliding wear model. The amount δ by which the rock node moves in the + R direction due to wear is given by:

δ＝dx cos(TILT)

dL＝FR 2πR RPMΔt

wherein: TILT (drill bit inclination angle relative to the hole axis, radians), dL, sliding distance of pads on a given rock node in one depth step dZ, FR, fraction of the drill bit circumference occupied by the pads, RPM, ROP, penetration rate (ft/hr), R, drill bit radius (in), CCS, confined compressive strength (psi), σ, contact stress at the rock node location (see above) (psi), Δ t, length of time the drill bit takes to drill distance dZ (min), dZ, depth step (specified vertical node spacing) (in), and XK, XN, XB are wear model coefficients (calibrated by the laboratory). The Z coordinate of the rock node is unchanged. It should also be noted that if a pad node does not contact its neighboring rock node, the rock node position remains unchanged.

Rock removal by means of a cutting edge. The Z coordinate of the rock node does not change, but the "new" R position of the rock node is simply the outer position of the cutting edge. That is, the lateral position of the "cutting edge" node on the drill bit must be greater (greater R coordinate) than the adjacent rock node. If not, nothing is cut and the rock node remains unchanged.

C. The borehole is lengthened.

The last part of the calculation is to increase the borehole by the amount dZ. This is only done at the end of traversing all rock nodes and removing rock according to the previous segment. Recall that dZ is the specified vertical nodal spacing of both the drill bit and the rock. Thus, once rock is removed from the previous segment, a single rock node is added. If there are N rock nodes at this time:

R(N+1)＝R(N)+dZ tan(TILT)

Z(N+1)＝Z(N)-dZ

it should be noted that r (n) above has considered the rock removal described in the previous section. It should also be noted that the Z coordinate is positive. This is why "-dZ" in the new rock node is in the vertical position.

Instead of actually moving the drill bit down for the next time step, the index of the rock is simply adjusted. As an example, the penetration depth Δ of the pad at rock node k is:

Δ(k)＝PAD _R (j)-ROCK _R (k)，k＝j+ISHIFT

wherein the depth of a rock node is Z ═ j + ISHIFT-1). times.dZ. When ISHIFT is 0, the top of the pad is aligned with the top of the rock. J is an initially set index that simply spans the padding nodes. This technique, and the fact that this is a static 2D model, rather than a dynamic 3D model, is why SIDECUT runs quickly on computer processing systems.

3. And (5) post-analysis. At this point, the lateral displacement L of the drill bit is obtained as a function of the drilling depth Z. A straight line is fit to this data to obtain a slope dL/dZ, which is a measure of the lateral aggressiveness of the drill bit for the conditions specified for the simulation. This straight line fitting procedure is automated in SIDECUT.

Fig. 35 shows the rock and bit geometry halfway through the SIDECUT simulation of drilling a borehole. Fig. 36 shows a graph of simulated axial depth versus lateral side cutting as shown in fig. 35. Fig. 37 shows the results of the force balance at each depth step during the SIDECUT simulation with a specified side load of 800lb (362.9 Kg). Figure 37 shows the sensitivity of gage pad contact area to bit RPM and gage pad length. Fig. 38 illustrates aspects of SIDECUT predictions compared to a measured lab side load drilling experiment of bedford limestone.

FIG. 39 is a flow chart of a method 390 for predicting changes in lateral displacement using changes in axial displacement of a drill bit drilled in formation rock. Block 391 calls for constructing a virtual representation of a drill bit and formation rock, the drill bit including a gage pad configured to remove rock by abrading or crushing the rock during the moving contact, and a cutting edge configured to cut into the rock during the moving contact. Block 392 calls for adjusting the lateral penetration depth until the rock reaction force is equal to the side force applied to the drill bit to provide a lateral displacement of the drill bit to provide an adjusted lateral penetration depth. Block 393 entails removing the formation rock to a location where the pad and cutting edge contact the formation rock at the adjusted lateral penetration depth and a selected axial displacement of the drill bit. Block 394 calls for moving the drill bit in the drilling direction to the end of the currently drilled borehole. Block 395 calls for iterating the adjusting, the removing, and the moving to predict a change in lateral displacement with a change in axial displacement of the drill bit. The method 390 may also include using a first set of nodes as a representation of the drill bit and a second set of nodes as a representation of the formation. The method 390 may also include setting the selected axial displacement to be an axial distance between two nodes in the axial direction. The method 390 may also include initializing nodes such that nodes at the boundary of the drill bit overlap the formation.

Next, improvements to DDAS are discussed that include additional models for considering and predicting bit walk and/or wellbore spiraling of the drill bit and BHA system during directional drilling applications. One embodiment, referred to herein as a "constant bit walk model," supplements the drill string steering model of DDAS by varying the contact force (i.e., applied side load) by rotating it by a constant angle. Another embodiment, referred to herein as a "torsional friction bit walk model," supplements the drill string steering model of the DDAS by considering the torsional frictional forces between the components of the drill string and the walls of the wellbore when calculating the net contact force (i.e., applied side load) in each calculation of a processing cycle.

In the constant bit walk model, historical laboratory drilling data is used to determine the actual walk behavior of a particular bottom hole assembly. For example, historical data may indicate that a particular BHA will move 12 ° to the left. Using this historical information, the contact forces (i.e., applied side loads) in the drill string steering model of the DDAS may be rotated the same or substantially the same number of degrees (e.g., 12 °) to account for bit walk in the simulation calculations. In other words, the direction of the contact force on the bit may be rotated in a counter-clockwise direction, for example from a top-down drilling view, to account for left-hand bit play. The constant angle may be based on a specified characteristic of the subterranean formation and/or based on testing of bit walk characteristics in a particular drill bit. In some embodiments, the constant angle may be obtained by calculating the constant angle using an empirical formula. In other embodiments, the constant angle may be obtained from a table having known values, such as formation drilling and/or bit walk characteristics. Alternatively, the constant angle may be obtained by using a value equal to the angle between the contact force at the drill bit and the friction force.

In a torsional friction drill bit walk model, Finite Element Analysis (FEA) calculations used in the "force balance" components of the BHA finite element program/protocol may include calculating the torsional friction force between components of the drill string (e.g., gage pads) and the walls of the wellbore, which modifies the direction and magnitude of the net contact force (i.e., applied side load) in each calculation of the processing cycle. The torsional friction force can be calculated using the following formula:

F _f ＝F _n *FricCoefficient,

wherein F _f Denotes torsional friction force, F _n Represents the normal contact force and FricCoefficient represents the coefficient of friction.

In some embodiments, a single coefficient of friction may be assigned to one or more individual components of the BHA. In addition, consideration of torsional friction in the calculations may also affect displacement, such as angular displacement (i.e., inclination angle) of the drill bit, which may further affect drill bit walk, as described in further detail below with respect to fig. 45.

Figure 40 is a process flow diagram of a DDAS method 400 that includes additional models (i.e., a constant bit walk model and a torsional friction bit walk model) for accounting for and predicting bit walk and/or wellbore spiraling. As described above with respect to FIG. 4, the BHA model may provide force, bit inclination, moment, and curvature information to the axial and lateral moving bit models at 402. The BHA model may also provide the steering computer model (i.e., the drill string steering model or steering algorithm) with the hole curvature and BHA alignment within the hole. Further, the BHA model may operate in the drilling depth domain within the DDAS. At 404, the BHA model may calculate the BHA contact force (F) _n ) And/or bit angular displacement, including inclination. Both the inclination of the drill bit (relative to the borehole) and the applied side load that forces the drill bit against the borehole wall are considered in the SIDECUT procedure. At 406, the friction values may be applied individually or collectively by applying the friction values toOne or more components of the BHA (e.g., gage pads, ribs, steering devices, etc.) to calculate BHA friction (F) _f ). At 408, the BHA model may then apply the calculated friction to the BHA at each iteration of the DDAS using FEA with error reduction iterations, and may calculate final values for the angular displacement, contact force, and/or friction. In this way, torsional friction between the borehole wall and the drill bit and/or BHA may be calculated and applied to predict BUR and walk rate.

At 414, the axial motion drill bit model may use inputs from formation lithology data (shown at 412) and drilling rig operating parameters (shown at 410). As mentioned above, the axial motion drill bit model may calculate rock strength and ROP, and these calculations may then be given to the lateral motion drill bit model. At 416, the lateral motion drill bit model may use the rock strength and ROP data from the axial motion drill bit model and the data supplied by the BHA model, such as bit side force and bit inclination, for example, to calculate a ratio of lateral ROP to axial ROP, or alternatively, a ratio of lateral displacement to axial displacement of the drill bit for a particular depth or a particular time period, as described in more detail above with reference to fig. 4.

At 418, the steering computer model may include a front steering angle model, or optionally, a rear steering angle model, as explained in more detail above with reference to fig. 5A-8. To account for and predict drill bit walk and/or wellbore spiraling, in some embodiments, the steering computer model may rotate the contact force at the drill bit by a constant walk angle. Alternatively or additionally, the steering computer model may account for frictional forces by applying a side-motion bit model side-cut result in the direction of the rotational contact force at the bit. At 420, the steering computer model may then use the updated model to calculate the inclination angle and azimuth angle of the end of the new bore section to be created. At 422, a new bore section may be created based on the calculated inclination angle and azimuth angle. The drill string (i.e., BHA and drill bit) may then be moved down to the bottom of the new borehole section at 424, and at the beginning of the next iteration (shown at 426), the three models (BHA model, axial motion drill bit model, and lateral motion drill bit model) may be recalled. Thus, the loop continues until the simulation stops. In other words, the drilling simulation method first runs the model of the BHA, and then feeds its results to the axial-motion and lateral-motion drill bit models, which may be incorporated into the DDAS method. The DDAS method then predicts the location and geometry of the next hole segment. As mentioned above, it should be understood that alternative ways or sequences of running the model may be used. However, regardless of the process or sequence, the steering computer model may be supplied with information by other models, including a constant bit walk model and a torsional friction bit walk model, and new simulated bore sections may be placed in the direction that the drill bit/BHA system wants to drill as calculated by the steering computer model. It will be appreciated that the initial conditions and past behavior, as well as forces on the drill bit and/or BHA, may affect the future behavior of the drill bit trajectory.

Further, the steering computer model may use any combination of models or models for accounting for and predicting drill bit walk and/or wellbore spiraling. For example, a constant bit walk model and a torsional friction bit walk model may be applied separately or in combination. In some embodiments, the original DDAS method (i.e., without regard to bit walk and/or wellbore spiral) may be a contact force (F) at the bit(s) _n ) The direction of motion applies the side-cut results of the side-moving bit model while taking into account angular displacement. Alternatively, torsional friction force (F) _f ) May be applied to the BHA model to complement the original DDAS method. In other embodiments, the user may input a constant angle to rotate the contact force at the drill bit by a predicted walk angle. In still other embodiments, the computer program may calculate the walk angle using, for example, an empirical formula or a table of formation properties and/or known values with the bit configuration. Alternatively, the walk angle may be automatically updated within the computer program according to a defined function of certain parameters of the BHA. For example, gage pad length, lateral force on the bit, coefficient of friction, ROP, RMP, etc. may be decomposed into equations, alone or in combination, for calculating bit walk angle. In other embodiments, the walk angle may be calculated by assuming the walk angle is equal to the angle between the contact force and the friction force at the drill bit. It should be understood that any type of user input may be usedOr a calculated value to adjust the angle of the contact force.

Fig. 41 is a simplified diagram of a downhole view 500 of the borehole 2 shown in fig. 1. An end view of the drill pipe 5, seen downhole, followed by the drill bit 7 is depicted. As shown, the drill bit 7 is tilted in any direction due to the side contact force 504 in any direction. In a constant bit walk model, the lateral contact force 504 calculated and employed in the BHA finite element program/protocol of DDAS may be rotated to the rotational contact force 506 at a constant angle θ in each iteration of the processing cycle. The value of the constant angle θ may be empirically selected based on laboratory or field data of the actual bit walk angle such that the results of the simulation are consistent with historical data for the same or substantially similar BHA design. In the embodiment of fig. 41, the rotational contact force 506 is shown as rotating in a counterclockwise direction of the lateral contact force 504. In a constant bit walk model, the rotational variation of the lateral contact force 504 may be the only programmed variation to the DDAS. By way of example and not limitation, the constant angle θ may be between about 10 ° and about 20 °, and more specifically, between about 12 ° and about 15 °. As one non-limiting exemplary embodiment, the constant angle θ may be about 12 °.

42A-42K contain a series of graphs showing the results of system walk for the entire BHA system using a constant bit walk model in DDAS. Showing A, commercially available from Beckhols, Houston, Tex _UTO T _RAK ^TM Left hand drill walk (negative turn rate) results when the eXact Rotary Steerable System (RSS) was constructed. In some embodiments, the DDAS may be programmed with a constant 12 ° drill walk angle. Various results are shown versus Measured Depth (MD). Fig. 42A shows inclination angle versus MD, fig. 42B shows azimuth angle versus MD, fig. 42C shows build-up rate (BUR) versus MD, fig. 42D shows turn rate versus MD, fig. 42E shows Dog Leg Severity (DLS) versus MD, and fig. 42F shows first contact force versus MD. Various parameter pairs MD are shown. Fig. 42G shows rate of penetration (ROP) versus MD, fig. 42H shows bit rotational speed (RPM) versus MD, fig. 42I shows Weight On Bit (WOB) versus MD, fig. 42J shows rib force versus MD, and fig. 42K shows rib orientation versus MD. The examination and the results show that the drill bit comprises a constant drill bit swimming modelThe behavior predicted by the DDAS method of (a) is consistent with that observed in laboratory testing.

43A-43K contain a series of graphs showing the results of system walk rate for the entire BHA system using a constant bit walk model in DDAS. Shown in using A _UTO T _RAK ^TM As a result of the right-hand drill walk (positive turn rate) as the eXact RSS drops. In some embodiments, the DDAS may also be programmed with a constant 12 ° drill run. Various results are shown for MD. Fig. 43A shows the bank angle versus MD, fig. 43B shows the azimuth angle versus MD, fig. 43C shows the BUR versus MD, fig. 43D shows the turning rate versus MD, fig. 43E shows the DLS versus MD, and fig. 43F shows the first contact force versus MD. Various parameter pairs MD are shown. Fig. 43G shows ROP versus MD, fig. 43H shows RPM versus MD, fig. 43I shows WOB versus MD, fig. 43J shows rib force versus MD, and fig. 43K shows rib orientation versus MD. The results show, by examination, that the behavior predicted by the DDAS method, including the constant bit walk model, is consistent with that observed in laboratory testing.

Fig. 44A is a simplified diagram of a top view of the wellbore spiral 600, and fig. 44B is a simplified diagram of a side view of the wellbore spiral 600 of fig. 44A. Helical (i.e., spiral) holes are a well known phenomenon in the industry and can be measured by the lateral distance 602 (side shift) of each measurement depth 604, as shown in fig. 44B. A right-handed spiral 606 is shown in fig. 44B. While the drill bit appears primarily to walk to the left as the drill pipe is rotated in a clockwise direction, it has been observed that the wellbore spiral exhibits both left-handed and right-handed threads. Detailed information about wellbore spiraling can be found in "BoreholeQuality Design and Practices to Maximize Drill Rate Performance", published in 2010 by dupriest et al, f.e., the society of petroleum engineers, the disclosure of which is incorporated herein by reference in its entirety.

Although wellbore spiraling is present in many boreholes, wellbore spiraling is typically avoided due to negative effects and complexity, such as improper casing placement. The wellbore spiral is typically detected from a wellbore log. In the past, attempts have been made to predict and correct wellbore spiraling, which is more evident in horizontal leg and lateral erosion systems. In addition to predicting drill bit walkThe borehole helicity is predicted using a constant bit walk model. In one embodiment, a 12 ° correction factor may be implemented in a constant bit walk model. In this embodiment, modeling may be used to predict wellbore spiraling behavior in addition to drill bit travel. In the laboratory, when the rib force is set to 0%, at A _UTO T _RAK ^TM Spiral behavior was observed in lateral simulations in the case of eXact RSS. Right-handed threaded helical wellbores are primarily observed. Once the spiral behavior is predicted by modeling, the results can be used to take into account the predicted behavior and take corrective action. For example, a longer gauge drill bit that is less aggressive in the lateral direction may tend to help reduce wellbore spiraling.

As previously mentioned, in a torsional friction drill bit walk model, the calculations used in the "force balancing" components of the BHA model may include calculations of torsional friction forces between components of the drill string and the walls of the wellbore, which modify the direction and magnitude of the net contact force (i.e., applied side load) in each calculation of the processing cycle. For example, dynamic modeling software including BHASYS, BHASYS PRO, and BHASYS Td software from Beckhous, Houston, Tex, may be used to calculate the torsional friction between components of the BHA and the wellbore. Further, a torsional friction drill walk model may also be used to predict wellbore helicity, the results of which may be used to take corrective action based on consideration of the predicted helical behavior.

FIG. 45 is a simplified lateral cross-sectional view 700 of a BHA in a wellbore and illustrating force vectors acting on the BHA. In fig. 45, the drill pipe 5 and the drill bit 7 are arranged in the horizontal leg of the borehole 2. The longitudinal axis 702 represents the vertical leg of the borehole 2 prior to being built into the horizontal leg. Normal force vector 704 represents the direction and magnitude of normal contact force on drill bit 7 as calculated in previous DDAS software. In the torsional friction bit walk model, a torsional friction force vector 706 is calculated and summed with the normal force vector 704 to yield a resultant vector 708 having a different direction and magnitude than the normal force vector 704. The torsional friction force vector 706 represents the direction and magnitude of the friction force tangent to the borehole 2 and perpendicular to the normal contact force, and represents the friction force existing between components of the BHA and the wall of the borehole 2. In a build scenario representing left-hand drill play, the drill bit 7 may be rolled to the left, which is shown as the normal force vector 704 being displaced from vertical in fig. 45. Torsional friction due to bit rotation, represented by torsional friction vector 706, may also cause bit 7 to be displaced further out of alignment with longitudinal axis 702. In one embodiment, normal force vectors 704 and torsional friction force vectors 706 may be added as is common in vector addition. The resultant vector 708 represents the combined forces and may be used in a torsional friction bit walk model of the DDAS software, which has been found to accurately predict and account for bit walk and/or wellbore spiraling. In some embodiments, the coefficient of friction is used to calculate the tangential friction. Finally, the drill bit 7 may also exhibit a tilt due to the force, which in turn may increase the additional displacement force. In drilling, and more particularly in directional drilling, it is well known in the art that the drill bit 7 drills laterally faster as the force applied to the lateral side of the drill bit 7 is greater.

FIG. 46 contains a series of graphs illustrating the results of bit walk using the torsional friction bit walk model in DDAS. The results of the left hand drill walk in the build direction when a 90 ° turn is performed in the lateral direction with RSS are shown. Various results are shown in fig. 46 for MD, including hole inclination angle versus MD, azimuth angle versus MD, BUR versus MD, and cornering rate versus MD. Modeling may be provided to compare the coefficient of friction with the walk rate in the build and descent scenarios. For example, the model may include the results of the swimming rate at 90 ° and 270 ° rib orientations of the turn. Alternatively, the model may include the results of the swimming speed as the ribs are constructed and lowered at 0 ° and 180 ° orientations. For example, the results may indicate that a slight build is natural for a particular BHA when turning left or right. In particular, the result of this scenario may show a 1.5 ° build of a left or right turn, possibly due to gravity hitting the lateral side of the drill bit 7 and/or due to a tilt in the build direction. Once friction is introduced into the system, for example, a 90 ° right turn BHA may swim to the left as it is pushed, thereby creating a larger build. Alternatively, a 270 ° left turn BHA may "walk slightly" to the right, resulting in less build up, and may ultimately exhibit "true" left-hand play at a coefficient of friction of, for example, about 0.25.

In the simulations used to generate the data in the graph shown in FIG. 46, calculations were performed using coefficients of friction of 0, 0.1, 0.25, and 0.4, which resulted in calculated walk rates of 1.6 °/100ft. (1.6 °/30.48m), 1.9 °/100ft. (1.9 °/30.48m), 2.2 °/100ft. (2.2 °/30.48m), and 2.6 °/100ft. (2.6 °/30.48m), respectively. In one example, a coefficient of friction of about 0.3 results in AUTOT _RAK ^TM The bit force walk angle on the eXact RSS was about 15 degrees, which is consistent with laboratory testing.

Once the predictions of bit walk and wellbore spiraling are made using the modeling and simulation techniques disclosed herein, adjustments and/or modifications can be made to the wellbore plan, BHA configuration, tool components, etc. in order to ensure that the results of the drilling process match the wellbore plan. For example, a drilling services company may employ DDAS as disclosed herein to suggest to a drilling operator to modify the design of the BHA, drill bit, drilling parameters, or wellbore plan to improve the directional drilling process. For example, selecting or adjusting a parameter may include adjusting weight on bit, torque applied to the drill string in the BHA, rotational speed of the drill string, rate of penetration, or drilling fluid flow rate. Further, as non-limiting examples, adjusting the lateral aggressiveness of the drill bit may include adjusting the gauge of the drill bit, the blade configuration, the gage pad length, the gage pad position, or the cutting element layout on the drill bit. The drill bit trajectory may be adjusted during drilling with a rotary steering drilling system connected to the BHA, which may be configured to adjust the drill bit trajectory, for example, based at least in part on calculations from a model of the BHA. It should be understood that receiving parameters for operating the BHA may include receiving drilling parameters specific to the BHA, and receiving lithology data may include receiving lithology data specific to a defined target in the subterranean formation. The drilling parameters and lithology data may be received in real time prior to drilling and/or during a drilling operation. Further, adjustments and/or modifications to the wellbore plan and BHA system may be made in real time prior to drilling and/or during drilling operations.

Additional non-limiting exemplary embodiments of the disclosure are described below.

Embodiment 1: a method of controlling a trajectory of a drill bit in a subterranean formation, the method comprising: receiving drilling parameters for operating a particular Bottom Hole Assembly (BHA); constructing, with a computer processor, a directional drilling simulator comprising a computer model of the BHA and the subterranean formation; calculating, with the computer processor, axial and lateral movement of a drill bit connected to a bottom end of the BHA using at least one formation parameter and at least one drilling parameter; predicting, with the computer processor, a bit walk of the drill bit by considering and calculating contact forces and frictional forces between the BHA and a wall of a borehole in the subterranean formation using the computer model of the BHA; determining, with the computer processor, an adjusted drill bit trajectory that is to account for the predicted drill bit walk; determining adjusted drilling parameters for operating the BHA to substantially follow the adjusted drill bit trajectory; and operating the BHA in accordance with the adjusted drilling parameter.

Embodiment 2: the method of embodiment 1, further comprising: predicting a wellbore spiral by considering and calculating the contact force and the friction force using the computer model of the BHA.

Embodiment 3: the method of embodiment 1, wherein constructing the directional drilling simulator comprising the BHA computer model comprises: constructing a three-dimensional model of the BHA and the subsurface formation; configuring the BHA computer model as a dynamic model in a depth domain; configuring the BHA computer model to predict a build rate based at least in part on a predicted drill bit walk of the drill bit using an error reduction iteration at each step of a finite element analysis; and configuring the BHA computer model to operate in real-time during a drilling operation.

Embodiment 4: the method of embodiment 1, wherein: calculating the axial and lateral motions of the drill bit comprises calculating the axial motion of the drill bit using a lateral motion drill bit model based at least in part on using an axial motion drill bit model separate from the lateral motion drill bit model and the computer model of the BHA; and determining the adjusted bit trajectory comprises using a steering computer model separate from the laterally moving bit model and the axially moving bit model, wherein the steering computer model is configured to apply results from the laterally moving bit model adjusted by predicting the computer model of the BHA.

Embodiment 5: the method of embodiment 1, wherein determining the adjusted drill bit trajectory further comprises: calculating a new inclination angle and a new azimuth angle of the drill bit; increasing the borehole in the subterranean formation by a distance; moving the drill bit in a drilling direction to an end of the borehole; and iterating the calculating, the increasing, and the moving to update the computer model of the BHA.

Embodiment 6: the method of embodiment 1, wherein predicting the bit walk of the drill bit by considering and calculating the contact force and the friction force between the BHA and the wall of the borehole further comprises considering an angular displacement of the drill bit.

Embodiment 7: the method of embodiment 1, wherein predicting the bit walk of the drill bit by considering and calculating the contact force and the friction force between the BHA and the wall of the borehole further comprises calculating a torsional friction force between at least one component of the BHA and the wall of the borehole.

Embodiment 8: the method of embodiment 1, wherein determining the adjusted drill bit trajectory comprises applying a calculation of the lateral motion of the drill bit in the direction of the contact force and rotating the direction of the contact force on the drill bit by a constant angle.

Embodiment 9: the method of embodiment 8, wherein rotating the direction of the contact force on the drill bit by a constant angle further comprises obtaining the constant angle by at least one of: calculating the constant angle using empirical formulas, obtaining the constant angle from a table with known values, or using a value equal to the angle between the contact force at the drill bit and the friction force.

Embodiment 10: the method of embodiment 8, wherein rotating the direction of the contact force on the drill bit by a constant angle comprises rotating the direction of the contact force on the drill bit by about 12 ° in a counterclockwise direction from a top down view of the borehole.

Embodiment 11: the method of embodiment 1, wherein determining the adjusted drilling parameters for operating the BHA comprises: adjusting lateral aggressiveness of the drill bit by adjusting at least one of gauge, blade configuration, gage pad length, gage pad position, or cutting element placement on the drill bit; adjusting at least one of a weight-on-bit, a torque of a drill string applied to the BHA, a rotational speed of the drill string, a rate of penetration, or a drilling fluid flow rate; and adjusting the drill bit trajectory during drilling with a rotary steerable drilling system operably connected to the BHA.

Embodiment 12: a method of planning and drilling a wellbore in a subterranean formation, comprising: defining a target in a specified subsurface formation; predicting drill bit walk of a wellbore spiral and a drill bit connected to a particular Bottom Hole Assembly (BHA), comprising: using a computer processor programmed to execute a directional drilling simulator comprising a computer model of the BHA and the specified subsurface formation; receiving, with the computer processor, lithology data and drilling parameters for operating the BHA in the specified subsurface formation; calculating, with the computer processor, a ratio of lateral motion to axial motion using a lateral motion bit computer model and an axial motion bit computer model; predicting, with the computer processor, a bit trajectory by considering and calculating a lateral contact force, an angular displacement, and a friction force using the computer model of the BHA; and adjusting, with the computer processor, the drill bit trajectory based at least in part on the prediction from the computer model of the BHA; adjusting the drilling parameters for operating the BHA to substantially follow the adjusted drill bit trajectory; and drilling the wellbore in the designated subterranean formation based, at least in part, on the adjusted drill bit trajectory.

Embodiment 13: the method of embodiment 12, further comprising: updating the drilling parameters during drilling using information received from at least one sensor connected to the BHA.

Embodiment 14: the method of embodiment 12, wherein predicting the drill bit trajectory comprises calculating a friction force between at least one component of the BHA and a borehole wall and adding the friction force to the contact force.

Embodiment 15: the method of embodiment 12, wherein adjusting the drill bit trajectory comprises rotating a direction of lateral contact force on the drill bit by a constant angle, wherein the constant angle is based on a characteristic of the subterranean formation and on testing of drill bit walk characteristics in a particular drill bit.

Embodiment 16: the method of embodiment 12, wherein adjusting the drilling parameters for operating the BHA further comprises: selecting components of the BHA based at least in part on a prediction of the wellbore helix and the bit walk of the drill bit; adjusting at least one of a weight-on-bit, a torque of a drill string applied to the BHA, a rotational speed of the drill string, a rate of penetration, or a drilling fluid flow rate; and adjusting the lateral aggressiveness of the drill bit by adjusting at least one of a gauge, a blade configuration, a gage pad length, a gage pad position, or a cutting element layout on the drill bit.

Embodiment 17: the method of embodiment 12, wherein adjusting the drilling parameters for operating the BHA comprises adjusting the drilling parameters using a rotary steering drilling system.

Embodiment 18: a method of controlling a trajectory of a drill bit in a subterranean formation, the method comprising: receiving lithology data for a particular subsurface formation; receiving one or more drilling parameters for operating a Bottom Hole Assembly (BHA), the one or more drilling parameters comprising at least one of weight-on-bit, torque, rotational speed, rate of penetration, drilling fluid flow rate, or lateral aggressiveness of a drill bit; predicting a bit walk of a wellbore spiral and a drill bit of the BHA, comprising: constructing, with a computer processor, a directional drilling simulator comprising a dynamic computer model of the BHA and the subterranean formation; considering, using the computer processor, the wellbore spiral and the bit walk of the drill bit by rotating a direction of normal contact force on the drill bit by a constant angle; calculating, using the computer processor, a combined force on the BHA by adding a torsional friction force and the normal contact force in the dynamic computer model of the BHA at each iteration of a finite element analysis; predicting, with the computer processor, the drill bit trajectory based at least in part on calculating the combined forces on the BHA; and adjusting, with the computer processor, the drill bit trajectory based at least in part on the prediction of the drill bit trajectory; and adjusting the one or more drilling parameters based at least in part on the prediction of the wellbore spiral and the bit walk of the drill bit.

Embodiment 19: the method of embodiment 18, wherein calculating the combined force on the BHA comprises calculating the torsional friction force using the formula: f _f ＝F _n FricCoefficient, wherein F _f Representing said torsional friction force, F _n Represents the normal contact force and FricCoefficient represents the coefficient of friction; and wherein an individual coefficient of friction may be assigned to one or more individual components of the BHA.

Embodiment 20: the method of embodiment 18, wherein adjusting the drill bit trajectory comprises: adjusting the drill bit trajectory with a rotary steering drilling system operatively connected to the BHA, the rotary steering drilling system configured to adjust the drill bit trajectory based at least in part on calculations from the dynamic computer model of the BHA.

While the foregoing description contains many specifics, these should not be construed as limiting the scope of the invention, but merely as providing certain exemplary embodiments. Similarly, other embodiments of the invention may be devised which do not depart from the spirit or scope of the present disclosure. For example, features described herein with reference to one embodiment may also be provided in other embodiments described herein. The scope of the invention is, therefore, indicated and limited only by the appended claims and their legal equivalents, rather than by the foregoing description. All additions, deletions, and modifications to the disclosed embodiments that fall within the meaning and scope of the claims are encompassed by the present disclosure.

Claims

1. A method of controlling a trajectory of a drill bit in a subterranean formation, the method comprising:

receiving drilling parameters for operating a particular bottom hole assembly;

constructing, with a computer processor, a directional drilling simulator comprising a computer model of the bottom hole assembly and the subterranean formation;

calculating, with the computer processor, axial and lateral movement of a drill bit connected to a bottom end of the bottom hole assembly using at least one formation parameter and at least one drilling parameter;

predicting, with the computer processor, a bit walk of the drill bit by considering and calculating contact forces and frictional forces between the bottom hole assembly and a wall of a borehole in the subterranean formation using the computer model of the bottom hole assembly, wherein predicting the bit walk of the drill bit comprises updating a steering computer model based at least in part on the considered and calculated frictional forces;

determining, with the computer processor, an adjusted drill bit trajectory for accounting for predicted drill bit walk, the determining the adjusted drill bit trajectory comprising applying a calculation of the lateral motion of the drill bit in a direction of the contact force and rotating a direction of the contact force on the drill bit by a constant angle, wherein the constant angle is obtained by at least one of: calculating the constant angle using an empirical formula, obtaining the constant angle from a table with known values, or using a value equal to the angle between the contact force at the drill bit and the friction force;

determining adjusted drilling parameters for operating the bottom hole assembly to substantially follow the adjusted drill bit trajectory; and

operating the bottom hole assembly according to the adjusted drilling parameters.

2. The method of claim 1, further comprising: predicting a wellbore spiral by considering and calculating the contact force and the friction force using the computer model of the bottom hole assembly.

3. The method of claim 1 or 2, wherein receiving drilling parameters further comprises receiving lithology data for operating the particular bottom hole assembly in a specified subsurface formation.

4. The method of claim 3, wherein operating the bottom hole assembly in accordance with the adjusted drilling parameters comprises drilling a wellbore in the designated subterranean formation based, at least in part, on the adjusted drill bit trajectory.

5. The method of claim 1 or 2, wherein constructing a directional drilling simulator comprising a computer model of the bottom hole assembly comprises:

constructing a three-dimensional model of the bottom hole assembly and the subterranean formation;

configuring a computer model of the bottom hole assembly into a dynamic model in a depth domain;

configuring a computer model of the bottom hole assembly to predict a build rate based at least in part on predicted drill bit walk of the drill bit using an error reduction iteration in each step of a finite element analysis; and

configuring a computer model of the bottom hole assembly to operate in real time during a drilling operation.

6. The method of claim 1 or 2, wherein:

calculating the axial and lateral motions of the drill bit includes using a lateral motion drill bit model based at least in part on the axial motion of the drill bit, the axial motion of the drill bit calculated using an axial motion drill bit model separate from the lateral motion drill bit model and the computer model of the bottom hole assembly; and is

Determining the adjusted bit trajectory includes using the steering computer model separate from the laterally moving bit model and the axially moving bit model, wherein the steering computer model is configured to apply results from the laterally moving bit model adjusted by predictions of the computer model of the bottom hole assembly.

7. The method of claim 6, wherein calculating the axial and lateral motions of the drill bit comprises calculating a ratio of the lateral motion to the axial motion using the lateral motion drill bit computer model and the axial motion drill bit computer model.

8. The method of claim 1 or 2, wherein predicting the bit walk of the drill bit by considering and calculating the contact force and the frictional force between the bottom hole assembly and the wall of the borehole further comprises considering an angular displacement of the drill bit.

9. The method of claim 1 or 2, wherein predicting the bit walk of the drill bit comprises calculating the friction between at least one component of the bottom hole assembly and a borehole wall and adding the friction to the contact force.

10. The method of claim 1 or 2, wherein predicting the bit walk of the drill bit by considering and calculating the contact force and the friction force between the bottom hole assembly and the wall of the borehole further comprises calculating a torsional friction force between at least one component of the bottom hole assembly and the wall of the borehole.

11. The method of claim 10, wherein predicting the bit walk of the drill bit by considering and calculating the contact force and the friction force further comprises calculating the torsional friction force using the equation:

F _f ＝F _n *FricCoefficient,

wherein: f _f Representing said torsional friction force, F _n Represents the normal contact force and FricCoefficient represents the coefficient of friction; and is provided with

Wherein: individual coefficients of friction can be assigned to one or more individual components of the bottom hole assembly.

12. The method of claim 1 or 2, wherein determining the adjusted drill bit trajectory further comprises:

calculating a new inclination angle and a new azimuth angle of the drill bit;

an adding step of adding the borehole in the subterranean formation by a distance;

a moving step of moving the drill bit to an end of the drill hole in a drilling direction; and

iterating the calculating, adding, and moving steps to update the computer model of the bottom hole assembly.

13. The method of claim 1 or 2, wherein rotating the direction of the contact force on the drill bit by a constant angle comprises rotating the direction of the contact force on the drill bit by about 12 ° in a counter-clockwise direction from a top-down view of the borehole.

14. The method of claim 1 or 2, wherein determining the adjusted drilling parameters for operating the bottom hole assembly comprises:

adjusting lateral aggressiveness of the drill bit by adjusting at least one of a gauge, a blade configuration, a gage pad length, a gage pad position, or a cutting element layout on the drill bit;

adjusting at least one of a weight on bit, a torque applied to a drill string of the bottom hole assembly, a rotational speed of the drill string, a rate of penetration, or a drilling fluid flow rate; and

adjusting the drill bit trajectory during drilling with a rotary steering drilling system operatively connected to the bottom hole assembly.

15. The method of claim 14, wherein adjusting the bit trajectory with the rotary steering drilling system during drilling comprises adjusting the bit trajectory based at least in part on calculations from the computer model of the bottom hole assembly.

16. The method of claim 1 or 2, further comprising: updating the drilling parameters during drilling using information received from at least one sensor connected to the bottom hole assembly.

17. The method of claim 2, wherein operating the bottom hole assembly according to the adjusted drilling parameters further comprises:

selecting a component of the bottom hole assembly based at least in part on a prediction of the wellbore spiral and the bit walk of the drill bit;

adjusting the lateral aggressiveness of the drill bit by adjusting at least one of a gauge of the drill bit, a blade configuration, a gage pad length, a gage pad position, or a cutting element layout on the drill bit.

18. The method of claim 1 or 2, wherein operating the bottomhole assembly according to the adjusted drilling parameter comprises adjusting at least one of weight-on-bit, torque, rotational speed, rate of penetration, drilling fluid flow rate, or lateral aggressiveness of a drill bit.