Method to Alter the Process of Cuttings Bed Formation in a Wellbore

Once a prospective reservoir of oil or natural gas in a subterranean formation has been located, a drilling rig is set up to drill a wellbore penetrating the subterranean formation. The drilling rig includes power systems, mechanical motors, a rotary turntable drill, and a circulation system that circulates drilling fluid, sometimes called “mud,” throughout the borehole. The fluid serves to remove materials, sometimes called “drilling cuttings,” as the drill bit loosens them from the surrounding rock during drilling and to maintain adequate wellbore pressure.

At least some drilling operations involve rotating a drill bit at the distal end of the pipe, sometimes called “drill string,” and transmitting rotary motion to the drill bit using a multi-sided pipe known as a “kelly” with a turntable. In other drilling operations, the drill bit is rotated with a motor near the drill bit such that the drill string does not rotate. In both cases, as drilling progresses, drilling fluid circulates through the pipe and out of the drill bit into the wellbore. The drilling cuttings are removed from the wellbore by the circulating drilling fluid. New sections are added to the pipe progressively as the drilling continues to extend the drill bit further into the subterranean formation.

Drilling oil and gas wells requires efficient transport of drilling cuttings to maintain a high rate of penetration and smooth drilling. However, the transport of drilling cuttings in an inclined well section with a small borehole is a major challenge in drilling operations. Drilling cuttings are easily accumulated in the inclined well section due to gravity and form a cuttings bed ultimately. It significantly affects the process of cuttings transport and can places the drill pipe under increased torque, and increased drag/pick up weights, reduced slack off weights, overpull, stuck pipe, broken drill tools, slow rates of penetration, high or uncontrollable equivalent circulating density (ECD), pack-off, downhole losses and contribute to borehole instability all of which result in lost time incidents and nonproductive time. For this reason, the development of methods that would allow the operator to alter the process of cuttings bed formation to avoid the related negative consequences is required.

Disclosed herein are methods and systems to predict and alter the characteristics of cuttings bed in a wellbore in real time or ahead of time during planning to avoid the consequences of poor hole cleaning, i.e., high torque and drag, stuck drills, broken drill tools, lost circulation, low rates of penetration, and any related delays in the drilling schedule. In some embodiments, the methods may include collecting drilling cuttings from drilling a wellbore penetrating a subterranean formation, analyzing the drilling cuttings, predicting characteristics of cuttings bed based at least in part on the drilling cuttings, predicting the effects of the characteristics of the cuttings bed on hole cleaning, changing at least one parameter controlling drilling operation when the hole cleaning is impaired by the effects of the characteristics of the cuttings bed, and predicting an impact of the change of the at least one parameter on the characteristics of the cuttings bed.

is a schematic view of a drilling system, according to one or more embodiments. The drilling systemincludes drilling platformthat supports a derrickhaving a traveling blockfor raising and lowering a drill string. The drill stringmay include, but is not limited to, drill pipe and coiled tubing, as generally known to those skilled in the art. A kellysupports drill stringas it is lowered through a rotary table. A drill bitis attached to the distal end of the drill stringand is driven either by a downhole motor and/or via rotation of the drill stringfrom the well surface. As drill bitrotates, it creates a boreholethat penetrates various subterranean formations. It should be noted that whilegenerally depicts a land-based drilling system, those skilled in the art will readily recognize that the principles described herein are equally applicable to subsea drilling operations that employ floating or sea-based platforms and rigs, without departing from the scope of the disclosure. The principles may also be applicable to other forms of drilling including, but not limited to, dual gradient drilling, managed pressure drilling, and underbalanced drilling.

A drilling fluid pump(e.g., a mud pump) circulates a fluidthrough a feed pipeand into the interior of drill string. In some embodiments, fluidmay be a drilling fluid used in the presently described drilling system. However, it should be noted that the principles of the present disclosure are equally applicable to any type of fluid return or sampled fluid derived from a borehole. Accordingly, usage of “the fluid” is meant to encompass, without limitation, any other type of fluid that may be circulated through a borehole, produced at the surface at or near the platform, or sampled downhole and subsequently provided to the fluid analysis system. For instance, “the fluid” may equally apply to reservoir fluids, gases, oils, water, and any other fluid that may be produced from a borehole. Moreover, drilling systemmay equally be replaced or otherwise equated with any borehole fluid analysis system, such as a wellhead installation used to produce fluids to the surface.

In drilling system, fluidmay be conveyed via drill stringto drill bitand out at least one orifice in drill bit. The fluidis then circulated back to the surface via an annulusdefined between drill stringand the walls of borehole. At the surface, the recirculated or spent fluidexits the annulusand may be conveyed to one or more fluid processing unit(s)via a fluid return line. After passing through the fluid processing unit(s), a “cleaned” fluidis deposited into a nearby retention pit(i.e., a mud pit). One or more chemicals, fluids, or additives may be added to the fluidvia a mixing hoppercommunicably coupled to or otherwise in fluid communication with the retention pit.

The drilling systemmay further include a bottom hole assembly (BHA)arranged in the drill stringat or near the drill bit. The BHAmay include any of a number of sensor modules(one shown) which may include formation evaluation sensors and directional sensors, such as measuring-while-drilling and/or logging-while-drilling tools. BHAmay also contain a telemetry systemthat induces pressure fluctuations in the fluid flow. Data from the downhole sensor modulesare encoded and transmitted to the surface via the telemetry systemwhose pressure fluctuations, or “pulses,” propagate to the surface through the column of fluid flow in drill string. At the surface the pulses are detected by one or more surface sensors (not shown), such as a pressure transducer, a flow transducer, or a combination of a pressure transducer and a flow transducer.

During the drilling operation, a discrete or continuous sample of fluidreturning to the surface (i.e., the fluid returns) may be obtained and conveyed to a fluid analysis systemarranged at or near drilling platform. The sample may be conveyed to fluid analysis systemvia a suction tubefluidly coupled to a source of fluidreturning to the surface. In some embodiments, for instance, suction tubemay be fluidly coupled to fluid return line. In other embodiments, however, suction tubemay be directly coupled to the annulussuch that a sample of fluidmay be obtained directly from the well at or near the surface of the well. For example, fluid analysis systemmay alternatively be arranged within fluid return lineprior to fluid processing unit(s)and suction tubemay be omitted. Alternatively, suction tubemay be coupled to the possum belly at the mud tanks or a header box associated with fluid processing unit(s), without departing from the scope of the disclosure.

Any suitable technique may be used for transmitting phase signals from the sensor modulesto the surface. As illustrated, a communication link(which may be wired or wireless, for example) may be provided that may transmit data from sensor modulesto an information handling systemat surface. Information handling systemmay include a processing unit, a monitor, an input device(e.g., keyboard, mouse, etc.), and/or computer media(e.g., optical disks, magnetic disks) that can store code representative of the methods described herein. The information handling systemmay act as a data acquisition system and possibly a data processing system that analyzes information from sensor modules. For example, information handling systemmay process the information from sensor modulesfor determination of drilling fluid quality. This processing may occur at surface in real-time. Alternatively, the processing may occur downhole or at another location after recovery of the drilling fluid at surface.

illustrates information handling systemwhich may be employed to perform various blocks, methods, and techniques disclosed herein. As illustrated, information handling systemincludes a processing unit (CPU or processor)and a system busthat couples various system components including system memorysuch as read only memory (ROM)and random-access memory (RAM)to processor. Processors disclosed herein may all be forms of this processor. Information handling systemmay include a cacheof high-speed memory connected directly with, in close proximity to, or integrated as part of processor. Information handling systemcopies data from system memoryand/or storage deviceto cachefor quick access by processor. In this way, cacheprovides a performance boost that avoids processordelays while waiting for data. These and other modules may control or be configured to control processorto perform various operations or actions. Another system memorymay be available for use as well. System memorymay include multiple different types of memory with different performance characteristics. It may be appreciated that the disclosure may operate on information handling systemwith more than one processoror on a group or cluster of computing devices networked together to provide greater processing capability. Processormay include any general-purpose processor and a hardware module or software module, such as first module, second module, and third modulestored in storage device, configured to control processoras well as a special-purpose processor where software instructions are incorporated into processor. Processormay be a self-contained computing system, containing multiple cores or processors, a bus, memory controller, cache, etc. A multi-core processor may be symmetric or asymmetric. Processormay include multiple processors, such as a system having multiple and physically separated processors in different sockets, or a system having multiple processor cores on a single physical chip. Similarly, processormay include multiple distributed processors located in multiple separate computing devices but working together such as via a communications network. Multiple processors or processor cores may share resources such as system memoryor cacheor may operate using independent resources. Processormay include one or more state machines, an application specific integrated circuit (ASIC), or a programmable gate array (PGA) including a field PGA (FPGA).

Each individual component discussed above may be coupled to system bus, which may connect each and every individual component to each other. System busmay be any of several types of bus structures including a memory bus or memory controller, a peripheral bus, and a local bus using any of a variety of bus architectures. A basic input/output (BIOS) stored in ROMor the like, may provide the basic routine that helps to transfer information between elements within information handling system, such as during start-up. Information handling systemfurther includes storage devicesor computer-readable storage media such as a hard disk drive, a magnetic disk drive, an optical disk drive, tape drive, solid-state drive, RAM drive, removable storage devices, a redundant array of inexpensive disks (RAID), hybrid storage device, or the like. Storage devicemay include software modules,, andfor controlling processor. Information handling systemmay include other hardware or software modules. Storage deviceis connected to the system busby a drive interface. The drives and the associated computer-readable storage devices provide nonvolatile storage of computer-readable instructions, data structures, program modules and other data for information handling system. In one aspect, a hardware module that performs a particular function includes the software component stored in a tangible computer-readable storage device in connection with the necessary hardware components, such as processor, system bus, and so forth, to carry out a particular function. In another aspect, the system may use a processor and computer-readable storage device to store instructions which, when executed by the processor, cause the processor to perform operations, a method or other specific actions. The basic components and appropriate variations may be modified depending on the type of device, such as whether information handling systemis a small, handheld computing device, a desktop computer, or a computer server. When processorexecutes instructions to perform “operations”, processormay perform the operations directly and/or facilitate, direct, or cooperate with another device or component to perform the operations.

As illustrated, information handling systememploys storage device, which may be a hard disk or other types of computer-readable storage devices which may store data that are accessible by a computer, such as magnetic cassettes, flash memory cards, digital versatile disks (DVDs), cartridges, random access memories (RAMs), read only memory (ROM), a cable containing a bit stream and the like, may also be used in the exemplary operating environment. Tangible computer-readable storage media, computer-readable storage devices, or computer-readable memory devices, expressly exclude media such as transitory waves, energy, carrier signals, EM waves, and signals per se.

To enable user interaction with information handling system, an input devicerepresents any number of input mechanisms, such as a microphone for speech, a touch-sensitive screen for gesture or graphical input, keyboard, mouse, motion input, speech and so forth. An output devicemay also be one or more of a number of output mechanisms known to those of skill in the art. In some instances, multimodal systems enable a user to provide multiple types of input to communicate with information handling system. Communications interfacegenerally governs and manages the user input and system output. There is no restriction on operating on any particular hardware arrangement and therefore the basic hardware depicted may easily be substituted for improved hardware or firmware arrangements as they are developed.

As illustrated, each individual component described above is depicted and disclosed as individual functional blocks. The functions these blocks represent may be provided through the use of either shared or dedicated hardware, including, but not limited to, hardware capable of executing software and hardware, such as a processor, that is purpose-built to operate as an equivalent to software executing on a general-purpose processor. Illustrative embodiments may include microprocessor and/or digital signal processor (DSP) hardware, read-only memory (ROM)for storing software performing the operations described below, and random-access memory (RAM)for storing results. Very large-scale integration (VLSI) hardware embodiments, as well as custom VLSI circuitry in combination with a general-purpose DSP circuit, may also be provided.

illustrates an example information handling systemhaving a chipset architecture for information handling systemthat may be used in executing the described method and generating and displaying a graphical user interface (GUI). Information handling systemis an example of computer hardware, software, and firmware that may be used to implement the disclosed technology. Information handling systemmay include a processor, representative of any number of physically and/or logically distinct resources capable of executing software, firmware, and hardware configured to perform identified computations. Processormay communicate with a chipset, discussed below, that may control input to and output from processor. In this example, chipsetoutputs information to output device, such as a display, and may read and write information to storage device, which may include, for example, magnetic media, and solid-state media. Chipsetmay also read data from and write data to RAM. Bridgefor interfacing with a variety of user interface componentsmay be provided for interfacing with chipset. User interface componentsmay include a keyboard, a microphone, touch detection and processing circuitry, a pointing device, such as a mouse, and so on. In general, inputs to information handling systemmay come from any of a variety of sources, machine generated and/or human generated.

Chipsetmay also interface with one or more communication interfacesthat may have different physical interfaces. Such communication interfaces may include interfaces for wired and wireless local area networks, for broadband wireless networks, as well as personal area networks. Some applications of the methods for generating, displaying, and using the GUI disclosed herein may include receiving ordered datasets over the physical interface or be generated by the machine itself by processoranalyzing data stored in storage deviceor RAM. Further, information handling systemreceives inputs from a user via user interface componentsand executes appropriate functions, such as browsing functions by interpreting these inputs using processor.

In examples, information handling systemmay also include tangible and/or non-transitory computer-readable storage devices for carrying or having computer-executable instructions or data structures stored thereon. Such tangible computer-readable storage devices may be any available device that may be accessed by a general purpose or special purpose computer, including the functional design of any special purpose processor as described above. By way of example, and not limitation, such tangible computer-readable devices may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other device which may be used to carry or store program code in the form of computer-executable instructions, data structures, or processor chip design. When information or instructions are provided via a network, or another communications connection (either hardwired, wireless, or combination thereof), to a computer, the computer properly views the connection as a computer-readable medium. Thus, any such connection is properly termed a computer-readable medium. Combinations of the above should also be included within the scope of the computer-readable storage devices.

Computer-executable instructions include, for example, instructions and data which cause a general-purpose computer, special purpose computer, or special purpose processing device to perform a certain function or group of functions. Computer-executable instructions also include program modules that are executed by computers in stand-alone or network environments. Generally, program modules include routines, programs, components, data structures, objects, and the functions inherent in the design of special-purpose processors, etc. that perform particular tasks or implement particular abstract data types. Computer-executable instructions, associated data structures, and program modules represent examples of the program code means for executing blocks of the methods disclosed herein. The particular sequence of such executable instructions or associated data structures represents examples of corresponding acts for implementing the functions described in such blocks.

In additional examples, methods may be practiced in network computing environments with many types of computer system configurations, including personal computers, hand-held devices, multi-processor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, and the like. Examples may also be practiced in distributed computing environments where tasks are performed by local and remote processing devices that are linked (either by hardwired links, wireless links, or by a combination thereof) through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

illustrates an example of one arrangement of resources on a computing networkthat may employ the processes and techniques described herein, although many others are of course possible. As noted above, an information handling system, as part of their function, may utilize data, which includes files, databases, directories, metadata (e.g., access control list (ACLS) creation/edit dates associated with the data, etc.), and other data objects. The data on the information handling systemis typically a primary copy (e.g., a production copy). During a copy, backup, archive or other storage operation, information handling systemmay send a copy of some data objects (or some components thereof) to a secondary storage computing deviceby utilizing one or more data agents.

A data agentmay be a desktop application, website application, or any software-based application that is run on information handling system. As illustrated, information handling systemmay be disposed at any rig site (e.g., referring to), off site location, core laboratory, repair and manufacturing center, and/or the like. In examples, data agentmay communicate with a secondary storage computing deviceusing communication protocolin a wired or wireless system. Communication protocolmay function and operate as an input to a website application. In the website application, field data related to pre- and post-operations, generated DTCs, notes, and/or the like may be uploaded. Additionally, information handling systemmay utilize communication protocolto access processed measurements, operations with similar DTCs, troubleshooting findings, historical run data, and/or the like. This information is accessed from secondary storage computing deviceby data agent, which is loaded on information handling system.

Secondary storage computing devicemay operate and function to create secondary copies of primary data objects (or some components thereof) in various cloud storage sitesA-N. Additionally, secondary storage computing devicemay run determinative algorithms on data uploaded from one or more information handling systems, discussed further below.

Communications between the secondary storage computing devicesand cloud storage sitesA-N may utilize REST protocols (Representational state transfer interfaces) that satisfy basic C/R/U/D semantics (Create/Read/Update/Delete semantics), or other hypertext transfer protocol (“HTTP”)-based or file-transfer protocol (“FTP”)-based protocols (e.g., Simple Object Access Protocol).

In conjunction with creating secondary copies in cloud storage sitesA-N, the secondary storage computing devicemay also perform local content indexing and/or local object-level, sub-object-level or block-level deduplication when performing storage operations involving various cloud storage sitesA-N. Cloud storage sitesA-N may further record and maintain, EM logs, map DTC codes, store repair and maintenance data, store operational data, and/or provide outputs from determinative algorithms that are located in cloud storage sitesA-N. In a non-limiting example, this type of network may be utilized as a platform to store, backup, analyze, import, perform extract, transform and load (“ETL”) processes, mathematically process, apply machine learning models, and augment data sets.

Transport of drilling cuttings in an inclined well section with a small borehole is a major challenge in drilling operations. Drilling cuttings or cavings are easily accumulated in the inclined well section due to gravity forming a drilling cuttings bed. Inefficient transport of drilling cuttings produced by the drill bit, reamer, under reamer or from formation cavings, during drilling may result torque, and, increased drag/pick up weights, reduced slack off weights, overpull, stuck pipe, broken drill tools, slow rates of penetration, high or uncontrollable ECD, pack-off, downhole losses and contribute to borehole instability all of which which result in lost time incidents and nonproductive time. For this reason, the development of methods that would allow one to alter the process of cuttings bed formation to avoid the related negative consequences is required. Since direct measurements of the cuttings bed characteristics are limited, modeling is needed to predict these characteristics and find the values of operational parameters such as drill string RPM, flow rates, circulation timings, fluid rheology and densities to alter them to provide optimal regime of cuttings transport and efficient hole cleaning. However, direct measurements of the cuttings bed characteristics are limited. As direct measurements of drilling cuttings deposition are limited, methods and systems are presented to understand the connection between properties of the drilling cuttings bed and the parameters that control the drilling process including cuttings density and size, rate of penetration, the rotation per minute of the drill bit, the flow rate of the drilling fluid, the drilling fluid rheology, the geometry of the borehole and the geometry of the tool string, for example. Disclosed herein are methods and systems to alter the process of drilling cuttings bed utilizing, at least in part, information handling system(e.g., referring to) as well as any implementation of information handling systemdescribed in.

summarize models that may be used to predict and alter the characteristics of drilling cuttings bed, discussed below, in boreholein real time as a function of their precision and calculation time. Each of the models discussed may be at least partially run and/or performed on information handling system(e.g., referring to). Models that require the fewest amount of calculation time are based on the concept of the so-called critical cuttings transport velocity called 1D equilibrium velocity models which are represented in. Models of this type predict the minimal velocity of the drilling fluid required to overcome forces resulting in the formation of the cuttings bed. These models, however, may not be able to predict the cuttings bed properties and influence of these properties on the transport of drilling cuttings, as well as influence of a set of important operational parameters including the rate of penetration, the number of rotations per minute of drill bit(e.g., referring to), eccentricity of drill string(e.g., referring to), for example, on the cuttings bed properties.

The second group of models called 1D continuous transport models, as illustrated in, assume that drilling cuttings may be considered as a continuous phase and that the surface of the cuttings bed is planar. The transport of drilling cuttings is simulated in these models by solving a set of 1D mass and momentum conservation equations. Although models of this type may be more precise than those based on the critical transport velocity calculation of the first group, they have a set of major disadvantages. In particular, the larger the size of drilling cuttings, the lower the precision of the assumption that may be considered as a continuous phase. Also, similarly to models based on the calculation of the critical transport velocity of the first group of, models illustrated inmay not be able to simulate real tool string position and effects related to rotation of drill string(e.g., referring to). On the other hand, if one includes these factors, the assumption about the planar surface of the cuttings bed may become incorrect.

illustrate a third type of models called 3D CFD-DEM models.is an enlargement of the forces acting on the drilling cuttings onat positionC-.is an enlargement of the forces acting on the drilling cuttings onat positionC-. The third type of models, 3D CFD-DEM models, are on the opposite side of the precision/speed spectrum. They are based on the full physics simulations that combine 3D Computational Fluid Dynamics calculations for the fluid flow and detailed particle-particle interaction to describe the dynamics of drilling cuttings. Models of this type, in principle, may allow for the simulation of the available operational parameters on the characteristics of the cuttings bed with the required level of precision. However, the large calculation times required for those models make them unpractical for real-time applications where calculation times are restricted.

Disclosed herein are methods to model the process of formation of cuttings bed allowing the proper trade-off between precision and calculation time. In some embodiments, the methods allow one to model the influence of the available operational parameters on the properties of the cuttings bed and doesn't require significant calculation time. That makes it suitable for real-time hole cleaning optimization. In embodiments, the expected hydraulic response in the wellbore may be modelled based on the received real-time drilling parameters and compare the modelled hydraulic responses to the actual pressure responses at the rig site for optimization, leading to a more accurate detection of drilling disfunction. The drilling disfunction includes pack off, stuck pipe, mud losses, influx (the flow of formation fluids or gases held in the pore spaces or fractures of a formation into the wellbore), wellbore breathing, excessive surge and swab, wellbore washout, drill string washout, for example.

The drilling fluid may be analysed measuring its viscosity, electrical stability, chemical properties such as pH, particle-size distribution, dimensions of the drilling cuttings, mineralogy of the drilling cuttings, for example. Any sensor capable of measuring the drilling fluid and drilling cuttings properties may be used including thermometer, viscometer, conductivity sensor, densitometer, gas detector, ultrasonic sensor, Raman spectrometer, mass spectrometer, laser sensor, cameras such as charge-coupled device cameras, flame ionization detector gas chromatograph, for example. Drill-monitor sensors to monitor surface revolutions-per-minute (rpm), rotary torque, and hook load, for example, may be used as well.

In some embodiments, the impact of the drilling fluid pumped downhole on the efficiency of solids removal from various formations during the planning phase is modelled to adjust the fluid rheological properties for optimal hole cleaning under expected wellbore conditions. The expected wellbore conditions include rotary or slide drilling with expected flow rate ranges, cuttings size, cuttings density, the rotations per minute of the drill string, the expected wellbore temperature and inclination, for example. In embodiments, the effect of the design of different tools on the efficiency of these tools to remove drilling cuttings and optimal operation conditions for such tools may also be modelled.

are discussed below.illustrates a workflowandillustrates a graph of a modeled section of interest. Modeled section of interestmay be defined as any section of the well in which characteristics of the cuttings bed are assumed to be the same in any plane perpendicular to the axis of the section.illustrates a workflowwhich is the first step of the two-step workflow to predict the shape and size of cuttings bed(e.g., referring to) according to example embodiments of the present disclosure. In examples, workflowmay be at least partially performed on information handling system(e.g., referring to). Workflowmay begin in blockin which a plurality of cellsmay be disposed evenly over a modeled section of interest, as illustrated in. The minimal requirement for the modeled section is that the change of the inclination angle in it doesn't exceed a threshold. This threshold is an input parameter which controls splitting a wellbore into modeled sections. This threshold may be 2°, 5°, 10°, 15°, 20°, 25°, 30°, 35°, 40°, 45°, 50°, 55°, 60°, 65°, 70°, 75°, 80°, 85°, 90° from the vertical axis or any number in between.

A cellis defined as a modeled cell. Calculations in modeled cellare performed on the grid. The grid consists of square cells of equal size. A cell represents a (small enough) part of the space inside the annulus of the well. Cellcan contain drilling fluid, drilling cuttings moving in the drilling fluid, or non-moving drilling cuttings. Cellsthat contain non-moving drilling cuttings form the cuttings bed. Generally, the number of cellsdisposed across modeled section of interestdepends upon the required level of precision of the calculation and the available computational resources. The size (length of the side) of cellis calculated as a ratio of the diameter of the wellbore and the number of cells. The number of cellsis an input parameter. Cellsmay create a grid layer, which is a horizontal line of a plurality of cellsthat may be adjacent to each other. After population of cellsacross modeled section of interest, a first layeris selected, working from bottom of modeled section of interest.

In blockof workflow, a first cellof first grid layermay be selected. In blockof workflow, it is determined if first cellof blockis a cellthat is last in grid layer. If it is not, then workflowmoves to blockof workflow, which shifts workflowto a cell adjacent in grid layerto cellidentified in blockof workflow. It should be noted, that in this progression, cellsmay be identified going left to right or right to left across grid layer. However, once a direction is chosen, workflowmay not go in the direction opposite of the chosen direction across grid layer.

In blockof workflow, cellis viewed to determine if cellis inside or intersected by boreholeor modeled section of interest. If not, workflowreverts back to blockand workflowshifts to an adjacent cellaccording to the methods described above. However, referring back to blockin workflow, if cellis inside boreholeor intersected by borehole, workflowmoves to block. In blockof workflow, a deposition criterion may be calculated utilizing information handling system. Deposition criterion may be based at least in part on the balance of the forces acting on cell(or cuttings).

is a schematicrepresenting the moments of forces acting on a cell(e.g., referring to), drilling cuttings, at the surface of cuttings bed(e.g., referring to). The deposition criterion is met if the moment of the difference between gravitational and buoyancy forces is greater than the moment of the drag force as follows:

wherein Fis the difference between gravitational and buoyancy forces, Fis the drag force, rand rare the arms of Fand Frespectively; d, A, ρ, m, ϕ are the size, effective cross section, density, mass, and angle of repose of drilling cuttings respectively; g is the gravitational acceleration; α is the inclination angle; ρis the density of the fluid; and τ is the shear stress at the surface of cuttings bed. The shear stress consists of two components τand τ. τis created by the axial flow of the fluid trough the annulus, and τis caused by rotation of the drill string:

where τis the shear stress created by the angular motion of the fluid caused by pipe rotation; τis the mechanical stress at the surface of drill string(e.g., referring to); K and n are the consistency and flow indices of the fluid; R, r, t are the radius, the distance from the center, and the torque per unit length of drill string, respectively; γand γare the shear rates along z and φ axes:

The drag force acting on cell, drilling cuttings, at the surface of drilling bedis a vector sum of the shear forces acting along z and φ axes as illustrated below:

A narrow slot approximation is used to calculate the fluid velocity profiles. This approximation allows one to consider 3D effects related to the eccentricity and rotation of drill string, and, at the same time, the approximation doesn't require significant calculation times as compared to a full-physics Computational Fluid Dynamics simulations. According to the narrow slot approximation, fluid velocities in each point of the annulus may be calculated by analytical formula derived for 1D flow in a narrow slot, if the effective size of the slot is known for this point.

is a graphical illustration of a narrow slot approximation according to embodiments of the present disclosure. The narrow slot approximation is used to find the effective narrow slot size for the center of a given grid cell. Lineconnecting centerof a grid celland centerof drill stringmay be used to find the effective boundaries of slot. The object closest to the center of grid cellintersected by lines, moving toward centerof drill stringmay be considered as a first slot boundary. The closest object intersected by lines, moving in the opposite direction, is considered as a second slot boundary. The three examples with the different effective slot boundaries are shown in. For cell i, j, or, first boundaryat R, is a cell of cuttings bedand second boundaryis borehole wallat R, for cell i, j, or, first boundaryat R, is the surface of drill stringand second boundaryis a cellof cuttings bedat R, and for cell i, j, or, first boundaryat R, is the surface of drill stringand second boundaryis borehole wallR. The effective size of slotis calculated as the difference between R−R.

As cuttings bedgrows, the effect of the decrease of the wellbore cross section is considered by multiplying vby the normalization coefficient which provides conservation of the total amount of fluid flowing through the section annulus:

where f(r, R, R) is the function known from the narrow slot solution, ris the distance between the center of the cell i, j and the center of drill string; R, R, are the effective slot boundaries for this cell; and Cis the normalization coefficient which is calculated as follows: