Wellbore Hole Profile Determination

The disclosure generally relates to drilling of wellbores and more particularly, to determining the wellbore diameter while drilling the wellbore.

The hole diameter of a wellbore may be a critical aspect in hydrocarbon recovery operations. The size of the hole may vary depending on several factors including drill bit size and other equipment on the drill string, type of formation the wellbore is formed in, future completion and production operations, etc. The hole profile may be planned to optimize drilling operations (e.g., mud weights, cementing operations, etc.) and knowledge of the current hole profile while drilling may assist in adjusting current drilling operations to account for differing wellbore conditions. Factors such as wellbore inclination, azimuth, formation type encountered, etc. may influence the hole profile, thus altering wellbore conditions.

The description that follows includes example systems, methods, techniques, and program flows that embody aspects of the disclosure. However, it is understood that this disclosure may be practiced without these specific details. For instance, this disclosure refers to inclination and azimuth as wellbore properties. Aspects of this disclosure can also be applied to any other types of wellbore properties. In other instances, well-known instruction instances, protocols, structures, and techniques have not been shown in detail in order not to obfuscate the description.

Example implementations relate to determining the hole profile of a wellbore while drilling the wellbore in a subsurface formation. The diameter of the wellbore may play a crucial role in hydrocarbon recovery operations, with implications in well design, production operations, etc. For example, the hole diameter may be crucial in determining calculations while drilling the wellbore such as drill string buckling (stable regions versus unstable regions), torque and drag calculations (such as limits, overpull, etc.), hydraulic calculations (pressure losses, flow regime, etc.), hole cleaning (packoff of the drill string, preparation for cementing operations), stuck pipe (due to mud cake), etc. While drilling a wellbore in a subsurface formation, it may be assumed that the diameter of the wellbore may be approximately uniform and approximately similar to the diameter of the drill bit (or other drilling component on the drill string, such as a reamer). However, the diameter of the wellbore may fluctuate from the assumed diameter depending on a number of factors such as wellbore inclination and/or azimuth, subsurface formation properties (i.e., lithology, principal stresses, etc.), etc. The fluctuation in wellbore diameter may result in a varying hole profile throughout the depth of the wellbore. For example, if there are no issues the hole profile may be a gauge hole (e.g., the hole diameter is approximately uniform and approximately similar to the drill bit diameter or within a tolerance of the expected hole diameter). Alternatively, a breakout, washout, key seat, or any other hole profile variation may occur, resulting in a hole profile that differs from a gauge hole profile.

When the hole profile differs from the assumed hole profile, drilling failures such as buckling of the drill string, pressure losses, packoff of the drill string, stuck pipe, etc. may occur. Conventional operations may assume the hole profile based on the drill bit size (as mentioned above) and in some instances may include a safety factor (such as 5% above drill bit diameter). However, this assumption may not capture the hole profile along the depth of the wellbore, resulting in misleading drilling calculations while drilling (as mentioned above) and thus potential drilling failures. In some implementations, the hole profile may be generated via logging while drilling (LWD) tools implemented on the drill string, such as a caliper log. However, in some instances the caliper log may not be available, or the data from a caliper log may not be able to be communicated to the surface while drilling the wellbore, but instead may only be available with the LWD tools are returned to surface when the drill string is tripped out of the wellbore. The addition of an LWD caliper log in a drill sting assembly may also increase drilling costs.

In some implementations, a hole profile generator may be configured to determine and/or update the hole profile of a wellbore, layer-by-layer, without a caliper log, while drilling a wellbore. The hole profile generator may be a “virtual three dimensional (3D) caliper log” in the absence of electronic LWD caliper logs on the drill string assembly. Prior to and/or during drilling operations, the properties of the subsurface formation including principal stresses, lithology of the subsurface formation layers (such as composition, grain size, etc.), etc. may be obtained. Additionally, the wellbore properties of a wellbore such as inclination, azimuth, etc. may be obtained while drilling the wellbore. For example, a drill string assembly may be configured to drill a wellbore in a subsurface formation. The drill string assembly may include a mud motor, MWD tools, LWD tools, etc. that may be utilized to assist in drilling the wellbore such as steer the drill bit, determine the drill bit location in the subsurface formation, etc. In some implementations, the drill string assembly may include one or more sensors. The one or more sensors may be configured to obtain and communicate the wellbore properties while drilling the wellbore with a drill bit in a subsurface formation. In some implementations, the hole profile generator may select a failure criteria for a depth interval of the wellbore. The failure criteria may be selected based on the subsurface formation properties corresponding to the depth interval. For example, failure criterion such as Mogi-Coulomb, Mohr-Coulomb, or other failure criteria may be selected based on the lithology of the subsurface formation for the corresponding depth interval. The mineral content, chemical composition, grain size, and other lithological properties may affect how the rock structure withstands stresses when the stresses are altered (such as when rock is removed to form a wellbore). Accordingly, the proper failure criteria may be selected to account for the lithology of the subsurface formation when determining the hole profile of the wellbore. In some implementations, the depth interval may include n number of axial layers. The hole profile generator may iteratively determine the layer failure volume of each radial layer within an axial layer (based on the wellbore properties and the failure criteria) until the breakout angle of the interval layer is approximately zero. The hole profile generator may then determine the layer failure volume of the axial layer based on the layer failure volumes of each radial layer before proceeding to the subsequent axial layer of the depth interval to determine the respective layer failure volume. Moreover, the radial distance of the wellbore at the depth interval may be determined based on the layer failure volumes of the n number of axial layers within the depth interval.

In some implementations, the hole profile generator may verify the radial distance of the depth interval. For example, the hole profile generator may determine hydraulic calculations (such as standpipe pressure (SPP), equivalent circulating density (ECD), etc.) and use the hydraulic calculations to verify the radial distance for the current depth interval. Once verified, the hole profile generator may generate a hole profile of the wellbore for the corresponding depth interval. In some implementations, the hole profile of the depth interval may be added to a hole profile log to update the hole profile log. The hole profile generator may continuously determine and update the hole profile log for subsequent depth intervals as the wellbore is drilled.

In some implementations, the hole profile across depths of the wellbore may be utilized to fingerprint the hole profile type at certain depths. For example, the hole profile may indicate the wellbore at a measured depth and/or over a measured depth interval is an in gauge hole (no issues), or may have experienced a breakout, washout, key seat, etc.

In some implementations, the hole profile generator may utilize caliper measurements (such as when an electronic LWD caliper log is a part of the drill string assembly). The caliper measurements may be utilized to adjust the radial distance, verify the radial distance, update the hole profile generator, etc. For example, the caliper measurements may be utilized to train and/or update the hole profile generator if the hole profile generator is configured with a learning machine, such as a neural network.

In some implementations, a drilling operation may be performed based on the hole profile. The drilling operations may prevent and/or address drilling failures such as lost circulation, stuck pipe, buckling of the drill pipe, etc. Examples of drilling operations include adjusting the mud weight, adjusting one or more drilling parameters (such as weight-on-bit (WOB), torque-on-bit (TOB), etc.), adjusting cementing operations, performing procedures to release stuck drill pipe, etc. For instance, the hole profile may indicate a washout across a depth interval. Accordingly, the mud weight (i.e., drilling fluid) and/or the pump speed may be adjusted to maintain returns to efficiently remove drill cuttings from the wellbore, manage ECD to prevent lost circulation and/or a kick, prevent packoff of the drilling string, etc.

is a schematic depicting an example well system, according to some implementations. In particular,is a schematic diagram of a well systemthat includes a drill stringhaving a drill bitdisposed in a wellborefor drilling the wellborein the subsurface formation. While depicted for a land-based well system, example embodiments can be used in subsea operations that employ floating or sea-based platforms and rigs. The drill bitforming the wellboreis an example for which wellbore properties may be obtained from and utilized by a hole profile generator to determine the hole profile at measured depths of the wellboreas described herein can be performed.

The well systemmay further include a drilling platformthat supports a derrickhaving a traveling blockfor raising and lowering the drill string. The drill stringmay include, but is not limited to, drill pipe, drill collars, and downhole tools(such as a drill string assembly). The downhole toolsmay comprise any of a number of different types of tools including measurement while drilling (MWD) tools, logging while drilling (LWD) tools, mud motors, and others. A kellymay support the drill stringas it may be lowered through a rotary table. Whileis described relative to a drill bit, aspects of the disclosure may be applied to any downhole cutting structure or multiple downhole cutting structures. For instance, the drill bitmay include roller cone bits, polycrystalline diamond compact (PDC) bits, natural diamond bits, any hole openers, reamers, coring bits, and the like. As the drill bitrotates, it may crush or cut rock to create and extend a wellborethat penetrates various subterranean formations. The drill bitmay be rotated by various methods including rotation by a downhole mud motor and/or via rotation of the drill stringfrom the surfaceby the rotary table. A pumpmay circulate drilling fluid through a feed pipeto the kelly, downhole through interior of the drill string, through orifices in the drill bit, back to the surfacevia an annulus surrounding the drill string, and into a retention pit. Parameters of drilling the wellboremay be adjusted to increase, decrease, and/or maintain the rate of penetration (ROP) of the drill bitthrough the subsurface formation. Drilling parameters may include parameters measured at the surfaceincluding weight-on-bit (WOB), torque-on-bit (TOB), rotations-per-minute (RPM) of the drill string, etc. In some implementations, the downhole toolsmay include sensors to obtain drilling parameters and/or wellbore properties as the drill bitdrills the subsurface formation. The drilling parameters obtained from the sensors may include downhole WOB, downhole TOB, downhole RPM, drill bit vibration, etc. The wellbore properties may include inclination, azimuth, etc. In some implementations, the sensors may obtain subsurface formation properties such as lithology, permeability, etc.

The well systemincludes a computerthat may be communicatively coupled to other parts of the well system. The computercan be local or remote to the drilling platform. A processor of the computermay perform simulations (as further described below). In some implementations, the processor of the computermay control drilling operations of the well systemor subsequent drilling operations of other wellbores. For instance, the processor of the computermay include a hole profile generator that may be configured to generate and/or update a hole profile of a wellbore, without the use of a caliper log, while the drill bitdrills the wellborein the subsurface formation. The a hole profile generator may utilize one or more wellbore properties (such as inclination, azimuth, etc.) obtained from one or more sensors on the downhole tools, such as LWD tools. In some implementations, the hole profile generator may be utilized for automation in the drilling process. For example, a drilling rig may be configured with automation to drill a wellbore. The hole profile generator may be utilized by the automated drilling rig to drill the wellbore, update and/or modify drilling operations, etc. An example of the computeris depicted in, which is further described below.

are illustrations depicting example hole profiles, according to some implementation. The hole profiles described inare example hole profiles, and the operations described herein may be applicable to any other suitable hole profile.includes a cross-sectional view of an in-gauge hole profileof a wellbore. When a wellboreis in-gauge, the radii of the wellboremay be approximately equidistant about the central axis. For example, the diametermay be approximately similar to the diameter. The diameters,may be approximately similar to the diameter of the drill bit, underreamer, etc. utilized to drill the wellbore.

includes a cross-sectional view of a breakout hole profileof a wellbore. A breakout may be an elongation and/or enlargement of a portion of the wellborecross section. A breakout, such as breakouts,may occur when the stress concentration of the subsurface formation surrounding the wellbore exceeds the strength of the rock. The breakouts,may occur in the direction of the minimum horizontal stress (σ) of the subsurface formation, perpendicular to the to the direction of the maximum horizontal stress (σ). For example, the wellboremay have an intended profile(e.g., the drill bit diameter). However, a breakout,may occur in the direction of the diameter(i.e., the direction of the minimum horizontal stress). Thus, the diametermay be greater than the diameterand the profile of the wellborediffers from the intended profile. This may result in drilling failures such as an increase in drill cuttings that may pack off the drill string, loss of pressure of the drilling fluid due to an increase in wellbore cross-sectional area (which may result in failure to clean the wellbore of drill cutting, thus packing off the drill string), increase in torque and drag on the drill string, etc.

includes a cross-sectional view of a washout hole profile. A washout of a wellboremay be when the diameter of the wellboremay become larger than the intended profile. For example, both the diameterand diameter(i.e., the diameter in both the minimum and maximum horizontal stress direction) may become larger than the diameter of the intended profile(e.g., the drill bit diameter). A washout may occur in various scenarios such as inadequate drilling fluid properties, high formation pressure, formation instability, mechanical factors (such as excessive RPM, WOB, etc.), chemical reactions (between drilling fluid and the subsurface formation), etc. The washout may result in an increased cross-sectional area of the wellbore, resulting in drilling failures such as pressure losses, packing off of the drill string, etc. For example, when drilling a horizontal well, drill cutting may accumulate on the low side of the wellbore (in the direction of gravity). One of the functions of drilling fluid is to transport the drill cuttings to the surface to maintain a clean wellbore and prevent the drill cuttings from packing in the drill string. When a washout occurs, there may be an excess of drill cuttings and the flow rate of the drilling fluid may decrease (due to the increased cross-sectional area of the wellbore). Thus, drill cuttings may accumulate in the wellbore, increasing the risk of packing in the drill string.

includes a cross-sectional view of a key seat profile. A key seat profileof a wellboremay occur when a drill string rubs against one side of the wellbore, resulting in a channel forming in the wellbore wall. A key seatmay occur when a wellbore is inclined and/or deviated (i.e., the inclination of a wellbore may be greater than 0 degrees). Thus, the drill string may be in contact with a side of the wellborewhen the drill string rotates and moves through the wellbore. This contact may result in the formation of a key seat. For example, a portion of the wellboremay include a key seat such that the diametermay be greater than the diameter, resulting in the portions of the wellborehaving a diameter greater than the diameter of the intended profile.

To help illustrate,are schematics depicting example wellbores, according to some implementations.includes a partial cross-sectional side viewof a wellbore. A drill stringis positioned in the wellboreand may be drilling the wellborethrough a subsurface formation. The wellboremay have an inclination, a, measured in degrees deviated from vertical. When drilling, forcesmay be applied along the central axis of the wellbore (z-axis) to the drill stringto drill the wellboresuch as forces applied by the traveling block, the weight of the drill string, etc. Forcesmay also be applied along the z-axisin the opposite direction, such as friction force. The inclinationof the wellbore and the forcesmay result in the drill string to contact the wall of the wellbore, resulting in the formation of a key seat profile. A partial cross-sectional viewincludes a hole profile view of the wellborewith a drill stringcontacting the wall of the wellborerelative to the x-axisand y-axisof the wellbore. The position of the contact on the wellborewall may be defined as the anglefrom the x-axisof the wellbore. A normal forcemay be applied to the drill stringwhen the drill stringcontacts the wellborewall, resulting in potential buckling of the drill string.

includes a partial cross-sectional side viewof an inclined section of a wellbore. The depths of the wellborelocation in the subsurface formation may be defined by the x-axis, y-axis,, and z-axis. The anglemay define the drilling direction relative to the maximum horizontal stress. The anglemay define the angle, measured clockwise, from the x-axis. Axis,, andmay define the axes of the wellbore, similar to the x-axis, y-axis, and z-axisof. When the wellboreis curved, the drill string, may contact the wall of the wellbore, resulting in a key seat hole profile and potential buckling of the drill stringor increased friction force on the drill string.

Example operations for generating and/or updating a hole profile are now described. This section describes operations associated with some implementations of the invention. In the discussion below, the flow diagrams may be described with reference to the example system presented above. In certain implementations, the operations are performed by executing instructions residing on machine-readable media (e.g., software), while in other implementations, the operations are performed by hardware and/or other logic (e.g., firmware). In some implementations, the operations are performed in series, while in other implementations, one or more of the operations can be performed in parallel. Moreover, some implementations perform less than all the operations shown in the flow diagrams.

The operations described inutilize the term “breakout” when describing when rock is removed from a wellbore wall, resulting in the radius of the wellbore in at least a portion of the wellbore being greater than the intended radius. The term “breakout” may also refer to the hole profile type, as described in.

are flowcharts depicting example operations to generate a hole profile at measured depth layers of a wellbore being drilled in a subsurface formation, according to some implementations. Flowcharts-of, respectively, are described in reference to the hole profile generator on the processor of the computerof. Additionally, the flowcharts-are described in reference toand. However, other systems and components can be used to perform the operations now described. The operations described in the flowchart-may be performed while drilling the wellbore and/or after the wellbore has been drilled. For example, the hole profile log may be updated in real time during the drilling of the wellbore. Operations of the flowcharts-continue between each other through transition points A and B. Operations of the flowchartstart at block.

At block, the processor of the computermay determine a depth interval for a wellbore being drilled in a subsurface formation. The depth interval may be 50 feet measured depth (MD), 200 feet MD, 1000 feet MD, etc. of the wellbore that has been drilled. In some implementations, the length of the depth interval may depend on the wellbore environment. For example, if the surrounding rock is stable (i.e., no breakouts may be occurring), then the length interval may be longer relative to a region where breakouts may be occurring and/or are known to occur and thus, finer depth intervals may be desired for increased accuracy of identifying hole profile types, as described below.

At block, the processor of the computermay obtain wellbore properties and subsurface formation properties for the depth interval. The wellbore properties may include the inclination, azimuth, etc. of the wellbore for the corresponding depth interval. The wellbore properties may be obtained from one or more sensors positioned on the drill string assembly proximate the drill bit, such as the LWD tool.

The subsurface formation properties may include lithology of the subsurface formation, in-situ stresses of the subsurface formation, etc. Lithology (and any other suitable rock properties) may be obtained from sources such as well logs of the subsurface formation (from the current wellbore, offset wellbore, etc.). For example, one or more logging tools may be positioned in an offset wellbore to obtain subsurface formation properties. Alternatively, or in addition to, one or more sensors may be positioned on the drill string assembly and configured to obtain subsurface formation properties while drilling the wellbore. The in-situ stresses (the stresses present in the subsurface formation prior to drilling) may include the maximum horizontal principal stress, the minimum horizontal principal stress, the vertical principal stress, etc. In some implementations, the principal stresses may be obtained prior to drilling the wellbore.

Operations of the flowchartnow proceed to blocksand. The operations of blocksandmay be performed in series or in parallel.

At block, the processor of the computermay transform the stresses based on the wellbore properties and the subsurface formation properties. When a wellbore is drilled, the in-situ stresses may be altered due to the removal of material, resulting in a redistribution of stresses around the wellbore. Transformation of the stresses may indicate the updated status of the stresses surrounding the wellbore at the corresponding depth interval, given the current orientation of the wellbore (e.g., inclination, azimuth, etc.). For example, the stresses for a depth interval may be transformed as follows (using Equations 1-6 below):

where σis the maximum horizontal principal stress, σis the minimum horizontal principal stress, σis the vertical principal stress, σis the normal stress along the x-axis, σis the normal stress along the y-axis, σis the normal stress along the z-axis, σis the shear stress on the x-plane along the y-direction, σis the shear stress on the y-plane along the z-direction, σis the shear stress on the x-plane along the z-direction, α is the drilling direction with respect to σ, and i is the well inclination angle.

In some implementations, the stresses in the subsurface formation extending past the wellbore wall may be determined. For example, stresses 2, 3, etc. times the radii away from the center point of the wellbore may be transformed. The in-situ stresses at various radial distances away from the center point of the wellbore for the depth interval may be transformed as follows (using Equations 7-12 as follows):

where σis the radial stress in the near field, σis the tangential stress in the near field, σis the axial stress in the near field along the well axis, τis the shear stress on the r-plane along the θ-direction, τis the shear stress on the r-plane along the z-direction, τis the shear stress on the θ-plane along the z-direction, σis the normal stress along the x-axis, θis the normal stress along the y-axis, σis the normal stress along the z-axis, σis the shear stress on the x-plane along the y-direction, σis the shear stress on the y-plane along the z-direction, σis the shear stress on the x-plane along the z-direction, R is the radius of the borehole, r is the radial distance in the near field from the well center, θ is the angle measured clockwise from the x-axis, Pis the pressure in the borehole, and ν is Poisson's ratio. To calculate the in-situ stresses from the borehole wall (1 radius from the center of the wellbore) to the specified radial distance into the subterranean formation (n times the radius of the wellbore, such as 3, 4, or 5), the iteration can change the radial distance analyzed into the subterranean formation by the distance increment, for example, 0.2 of the radius each iteration.

The transformation of stresses at the depth interval may be performed at each theta (θ) angle of the wellbore and/or up to a specified maximum radial distance from the center point of the wellbore. In some implementations, the stress transformation may be performed for theta angles 0 degrees to 180 degrees (i.e., half of the wellbore) and direct symmetry may be applied to the opposite side of the wellbore to transform the stresses for the remaining half of the wellbore.

At block, the processor of the computermay select a failure criteria based on the subsurface formation properties. In some implementations, failure criteria may be lithology specific. For example, lithological properties such as mineral content, grain size, chemical composition, etc. may influence how stress affects said rock when the stresses in the subsurface formation may be altered (such as when a wellbore is formed in the subsurface formation. Accordingly, failure criteria may be tailored for specific lithologies. Thus, the failure criteria may be selected based on the lithology of the subsurface formation for the corresponding depth interval. For example, a Mogi-Coulomb failure criteria may be selected for a carbonate lithology or a Mohr-Coulomb failure criteria may be selected for a sandstone and/or shale lithology. Other criteria such as Lade criteria, Drucker-Prager criteria, etc. may be selected. The utilization of the selected failure criteria for the depth interval is described below.

To help illustrate,are charts depicting example hole profiles of wellbores drilled in subsurface formations with different lithologies, according to some implementations.includes a chartof a hole profile of a wellbore drilled in a shale formation. In the example implementation the shale formation may have a uniaxial compressive strength (UCS) of 35 megapascals (MPa) and the wellbore is drilled at a 30 degree inclination. The chartincludes an x-axisand a y-axis. The x-axis is the caliper of the wellbore having units in inches (in). The y-axisis the depth of the wellbore having unites in feet (ft). At a depth, and depth, there is approximately no breakout, depicted by the respective hole profiles,. At the depths,, the respective hole profiles,indicate breakouts. Thus, the caving volume for the depths between approximately 1400 ft and 5400 ft for the wellbore depicted in the charttotal to be approximately 2569.66 cubic inches (in3).

includes a chartof a hole profile of a wellbore drilled in a carbonate formation. In the example implementation the shale formation may have an unconfined compressive strength (UCS) of 35 megapascals (MPa) and the wellbore is drilled at a 30 degree inclination (similar to the wellbore of, for comparative purposes). The chartincludes an x-axisand a y-axis. The x-axis is the caliper of the wellbore having units in inches (in). The y-axisis the depth of the wellbore having unites in feet (ft). At a depth, and depth, there is approximately no breakout, depicted by the respective hole profiles,. At the depths,, the respective hole profiles,indicate breakouts. Thus, the caving volume for the depths between approximately 1400 ft and 5400 ft for the wellbore depicted in the charttotal to be approximately 130.46 in3.

As shown, the wellbore drilled in the carbonate formation yields less caving volume than the wellbore drilled in the shale formation in similar drilling conditions. Thus, selection of the failure criteria based on the lithology of the formation may impact the determination of the radial distance of the depth intervals, as described below.

At block, the processor of the computermay determine the layer failure volume for a radial layer of an axial layer in the depth interval. A depth interval may be divided into one or more axial layers, where each axial layer may have one or more radial layers at and/or extending beyond the wellbore wall.

To help illustrate,is a schematic depicting a depth interval, according to some implementations. In particular,includes a depth intervalwith a wellbore. The depth intervalincludes two axial layers along the axisof the wellbore; the axial layerand the axial layer. Each axial layer,in the depth interval may have a length of 1 inch, 1 foot, 10 feet, etc. Moreover, each axial layer,may have uniform length or different lengths. Each axial layer,may include one or more radial layers that extend into the subsurface formation along the axisof the wellbore, such as radial layerand radial layerthat are at the wellbore wallor extend beyond the wellbore wall, respectively. Each radial layer may be n radii away from the center point of the wellbore. For example, radial layers,may be 0.1 times the radius into the subsurface formation. In some implementations, the depth intervalmay be configured with a maximum radial distancein which the layer failure volume may be calculated for (as described below).

Returning to the flowchart of, the layer failure volume may first be determined for the radial layer nearest the wellbore wall, such as the radial layerof. The failure criteria (selected in block) may first be applied to each theta (θ) angle of the wellbore (i.e., every degree, 10 degrees, 45 degrees, etc.) to determine if breakout has occurred and, if so, at what orientation in the wellbore. The failure criteria may be applied with respect to the transformed stresses at each theta (θ) angle of the wellbore determined in block. For example, if the depth interval was a carbonate formation and the Mogi-Coulomb failure criterion were selected, the stability analysis for each theta (θ) angle may be determined as follows (using Equations 13-18 below):

where τis the octahedral shear stress, σis the effective mean stress,

σis the maximum principal stress at theta (θ), σis the intermedia principal stress theta (θ), σis the minimum principal stress theta (θ), q is the slope of the line relating to σand σ, a is the Mogi parameter, and b is the Mogi parameter.

Alternatively, if the depth interval was a sandstone or shale formation and the Mohr-Coulomb failure criterion were selected, the stability analysis for each theta (θ) angle may be determined as follows (using Equations 13-17 above and 19-20 below):

where UCS is the Uniaxial compressive strength of the subsurface formation. For both Equations 18 and 20, if F is less than or equal to 0, then shear failure may occur at the respective theta (θ), indicating breakout of the subsurface formation at the respective theta (θ). In some implementations, the failure criteria may be applied for each theta (θ) between 0 degrees and 180 degrees. Accordingly, direct symmetry may be applied to the opposite side of the wellbore to determine if failure criteria is present around wellbore at the axial layer.

With the orientation of the breakouts in the wellbore wall for the radial layer, the breakout angle of the breakout (if present) may be determined. This may be determined by taking the difference in theta (θ) between the edges of the breakout. For example, if it is determined that there is a breakout between 35 degrees and 75 degrees in the radial layer, then the breakout angle may be 40 degrees. Moreover, given the breakout angle, the width of the radial layer, and the length of the axial layer, the layer failure volume for said radial layer may be determined. For example, the axial layer length multiplied by the radial layer width multiplied by the width of the breakout (derived from the breakout angle) may provide the layer failure volume.

In some implementations, the Carr classification may be utilized to determine the orientation of the breakout to account for the azimuthal direction of the wellbore. For example, the angle of repose, represented by gamma, may be determined as follows ((using Equation 20 below):

where α is the inclination and φ is the azimuthal direction. An angle of repose less than 30 degrees indicates very free flowing, between 30 degrees and 38 degrees indicates free flowing, 38 degrees to 45 degrees indicates fair to passable flow, 45 degrees to 55 degrees indicates cohesive, and greater than 55 degrees indicates very cohesive (non-flowing). By determined the angle of repose, factors may be implemented into the failure criteria to determine and/or adjust the orientation of the breakout.