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

Description

BACKGROUND

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.

BRIEF DESCRIPTION OF THE DRAWINGS

These drawings illustrate certain aspects of some of the embodiments of the present disclosure, and should not be used to limit or define the disclosure:

FIG. 1 is a schematic view of a drilling system, according to one or more embodiments of the present disclosure;

FIG. 2 is a schematic of an information handling system;

FIG. 3 is a schematic of a chipset that may be utilized by the information handling system;

FIG. 4 is a schematic of an arrangement of resources on a computer network;

FIGS. 5A-5C are graphical representation of models that may predict the accumulation of drilling cuttings as a function of their precision and calculation time;

FIG. 6A is the first step of the workflow to model the formation of cuttings bed according to example embodiments of the present disclosure;

FIG. 6B is a graphical illustration of the workflow shown in FIG. 6A;

FIG. 7 is a schematic representing the moments of forces acting on a drilling cutting at the surface of the cuttings bed according to example embodiments of the present disclosure;

FIG. 8 illustrates the narrow slot approximation according to embodiments of the present disclosure;

FIGS. 9A-9E are graphical illustrations of the calculations of the mechanical stress and fluid shear stress as a function of the distance between the drill pipe and the cuttings bed surface according to embodiments of the present disclosure;

FIG. 10A-10B illustrate the work of the second step of the workflow to model the formation of cuttings bed according to embodiments of the present disclosure; and

FIG. 11 is an example of a workflow to optimize hole cleaning according to embodiments of the present disclosure.

DETAILED DESCRIPTION

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.

FIG. 1 is a schematic view of a drilling system 100, according to one or more embodiments. The drilling system 100 includes drilling platform 102 that supports a derrick 104 having a traveling block 106 for raising and lowering a drill string 108. The drill string 108 may include, but is not limited to, drill pipe and coiled tubing, as generally known to those skilled in the art. A kelly 110 supports drill string 108 as it is lowered through a rotary table 112. A drill bit 114 is attached to the distal end of the drill string 108 and is driven either by a downhole motor and/or via rotation of the drill string 108 from the well surface. As drill bit 114 rotates, it creates a borehole 116 that penetrates various subterranean formations 118. It should be noted that while FIG. 1 generally depicts a land-based drilling system 100, 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 120 (e.g., a mud pump) circulates a fluid 122 through a feed pipe 124 and into the interior of drill string 108. In some embodiments, fluid 122 may be a drilling fluid used in the presently described drilling system 100. 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 122” 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 102, or sampled downhole and subsequently provided to the fluid analysis system 142. For instance, “the fluid 122” may equally apply to reservoir fluids, gases, oils, water, and any other fluid that may be produced from a borehole. Moreover, drilling system 100 may 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 100, fluid 122 may be conveyed via drill string 108 to drill bit 114 and out at least one orifice in drill bit 114. The fluid 122 is then circulated back to the surface via an annulus 126 defined between drill string 108 and the walls of borehole 116. At the surface, the recirculated or spent fluid 122 exits the annulus 126 and may be conveyed to one or more fluid processing unit(s) 128 via a fluid return line 130. After passing through the fluid processing unit(s) 128, a “cleaned” fluid 122 is deposited into a nearby retention pit 132 (i.e., a mud pit). One or more chemicals, fluids, or additives may be added to the fluid 122 via a mixing hopper 134 communicably coupled to or otherwise in fluid communication with the retention pit 132.

The drilling system 100 may further include a bottom hole assembly (BHA) 136 arranged in the drill string 108 at or near the drill bit 114. The BHA 136 may include any of a number of sensor modules 138 (one shown) which may include formation evaluation sensors and directional sensors, such as measuring-while-drilling and/or logging-while-drilling tools. BHA 136 may also contain a telemetry system 140 that induces pressure fluctuations in the fluid flow. Data from the downhole sensor modules 138 are encoded and transmitted to the surface via the telemetry system 140 whose pressure fluctuations, or “pulses,” propagate to the surface through the column of fluid flow in drill string 108. 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 fluid 122 returning to the surface (i.e., the fluid returns) may be obtained and conveyed to a fluid analysis system 142 arranged at or near drilling platform 102. The sample may be conveyed to fluid analysis system 142 via a suction tube 144 fluidly coupled to a source of fluid 122 returning to the surface. In some embodiments, for instance, suction tube 144 may be fluidly coupled to fluid return line 130. In other embodiments, however, suction tube 144 may be directly coupled to the annulus 126 such that a sample of fluid 122 may be obtained directly from the well at or near the surface of the well. For example, fluid analysis system 142 may alternatively be arranged within fluid return line 130 prior to fluid processing unit(s) 128 and suction tube 144 may be omitted. Alternatively, suction tube 144 may be coupled to the possum belly at the mud tanks or a header box associated with fluid processing unit(s) 128, without departing from the scope of the disclosure.

Any suitable technique may be used for transmitting phase signals from the sensor modules 138 to the surface. As illustrated, a communication link 150 (which may be wired or wireless, for example) may be provided that may transmit data from sensor modules 138 to an information handling system 160 at surface. Information handling system 160 may include a processing unit 162, a monitor 164, an input device 166 (e.g., keyboard, mouse, etc.), and/or computer media 168 (e.g., optical disks, magnetic disks) that can store code representative of the methods described herein. The information handling system 160 may act as a data acquisition system and possibly a data processing system that analyzes information from sensor modules 138. For example, information handling system 160 may process the information from sensor modules 138 for 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.

FIG. 2 illustrates information handling system 160 which may be employed to perform various blocks, methods, and techniques disclosed herein. As illustrated, information handling system 160 includes a processing unit (CPU or processor) 202 and a system bus 204 that couples various system components including system memory 206 such as read only memory (ROM) 208 and random-access memory (RAM) 210 to processor 202. Processors disclosed herein may all be forms of this processor 202. Information handling system 160 may include a cache 212 of high-speed memory connected directly with, in close proximity to, or integrated as part of processor 202. Information handling system 160 copies data from system memory 206 and/or storage device 214 to cache 212 for quick access by processor 202. In this way, cache 212 provides a performance boost that avoids processor 202 delays while waiting for data. These and other modules may control or be configured to control processor 202 to perform various operations or actions. Another system memory 206 may be available for use as well. System memory 206 may include multiple different types of memory with different performance characteristics. It may be appreciated that the disclosure may operate on information handling system 160 with more than one processor 202 or on a group or cluster of computing devices networked together to provide greater processing capability. Processor 202 may include any general-purpose processor and a hardware module or software module, such as first module 216, second module 218, and third module 220 stored in storage device 214, configured to control processor 202 as well as a special-purpose processor where software instructions are incorporated into processor 202. Processor 202 may 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. Processor 202 may 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, processor 202 may 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 memory 206 or cache 212 or may operate using independent resources. Processor 202 may 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 204, which may connect each and every individual component to each other. System bus 204 may 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 ROM 208 or the like, may provide the basic routine that helps to transfer information between elements within information handling system 160, such as during start-up. Information handling system 160 further includes storage devices 214 or 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 device 214 may include software modules 216, 218, and 220 for controlling processor 202. Information handling system 160 may include other hardware or software modules. Storage device 214 is connected to the system bus 204 by 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 160. 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 202, system bus 204, 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 system 160 is a small, handheld computing device, a desktop computer, or a computer server. When processor 202 executes instructions to perform “operations”, processor 202 may perform the operations directly and/or facilitate, direct, or cooperate with another device or component to perform the operations.

As illustrated, information handling system 160 employs storage device 214, 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) 210, read only memory (ROM) 208, 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 160, an input device 222 represents 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 device 224 may 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 160. Communications interface 226 generally 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 202, 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) 208 for storing software performing the operations described below, and random-access memory (RAM) 210 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.

FIG. 3 illustrates an example information handling system 160 having a chipset architecture for information handling system 160 that may be used in executing the described method and generating and displaying a graphical user interface (GUI). Information handling system 160 is an example of computer hardware, software, and firmware that may be used to implement the disclosed technology. Information handling system 160 may include a processor 202, representative of any number of physically and/or logically distinct resources capable of executing software, firmware, and hardware configured to perform identified computations. Processor 202 may communicate with a chipset 300, discussed below, that may control input to and output from processor 202. In this example, chipset 300 outputs information to output device 224, such as a display, and may read and write information to storage device 214, which may include, for example, magnetic media, and solid-state media. Chipset 300 may also read data from and write data to RAM 210. Bridge 302 for interfacing with a variety of user interface components 304 may be provided for interfacing with chipset 300. User interface components 304 may 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 system 160 may come from any of a variety of sources, machine generated and/or human generated.

Chipset 300 may also interface with one or more communication interfaces 226 that 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 processor 202 analyzing data stored in storage device 214 or RAM 210. Further, information handling system 160 receives inputs from a user via user interface components 304 and executes appropriate functions, such as browsing functions by interpreting these inputs using processor 202.

In examples, information handling system 160 may 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.

FIG. 4 illustrates an example of one arrangement of resources on a computing network 400 that may employ the processes and techniques described herein, although many others are of course possible. As noted above, an information handling system 160, 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 system 160 is typically a primary copy (e.g., a production copy). During a copy, backup, archive or other storage operation, information handling system 160 may send a copy of some data objects (or some components thereof) to a secondary storage computing device 404 by utilizing one or more data agents 402.

A data agent 402 may be a desktop application, website application, or any software-based application that is run on information handling system 160. As illustrated, information handling system 160 may be disposed at any rig site (e.g., referring to FIG. 1), off site location, core laboratory, repair and manufacturing center, and/or the like. In examples, data agent 402 may communicate with a secondary storage computing device 404 using communication protocol 408 in a wired or wireless system. Communication protocol 408 may 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 system 160 may utilize communication protocol 408 to access processed measurements, operations with similar DTCs, troubleshooting findings, historical run data, and/or the like. This information is accessed from secondary storage computing device 404 by data agent 402, which is loaded on information handling system 160.

Secondary storage computing device 404 may operate and function to create secondary copies of primary data objects (or some components thereof) in various cloud storage sites 406A-N. Additionally, secondary storage computing device 404 may run determinative algorithms on data uploaded from one or more information handling systems 160, discussed further below.

Communications between the secondary storage computing devices 404 and cloud storage sites 406A-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 sites 406A-N, the secondary storage computing device 404 may 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 sites 406A-N. Cloud storage sites 406A-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 sites 406A-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 160 (e.g., referring to FIG. 1) as well as any implementation of information handling system 160 described in FIG. 4.

FIGS. 5A-5C summarize models that may be used to predict and alter the characteristics of drilling cuttings bed, discussed below, in borehole 116 in 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 160 (e.g., referring to FIG. 1). 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 FIG. 5A. 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 114 (e.g., referring to FIG. 1), eccentricity of drill string 108 (e.g., referring to FIG. 1), for example, on the cuttings bed properties.

The second group of models called 1D continuous transport models, as illustrated in FIG. 5B, 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 FIG. 5A, models illustrated in FIG. 5B may not be able to simulate real tool string position and effects related to rotation of drill string 108 (e.g., referring to FIG. 1). On the other hand, if one includes these factors, the assumption about the planar surface of the cuttings bed may become incorrect.

FIGS. 5C-1 to 5C-3 illustrate a third type of models called 3D CFD-DEM models. FIG. 5C-2 is an enlargement of the forces acting on the drilling cuttings on FIG. 5C-1 at position 5C-2. FIG. 5C-3 is an enlargement of the forces acting on the drilling cuttings on FIG. 5C-1 at position 5C-3. 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.

FIGS. 6A and 6B are discussed below. FIG. 6A illustrates a workflow 600 and FIG. 6B illustrates a graph of a modeled section of interest 650. Modeled section of interest 650 may 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. FIG. 6A illustrates a workflow 600 which is the first step of the two-step workflow to predict the shape and size of cuttings bed 652 (e.g., referring to FIG. 6B) according to example embodiments of the present disclosure. In examples, workflow 600 may be at least partially performed on information handling system 160 (e.g., referring to FIG. 1). Workflow 600 may begin in block 602 in which a plurality of cells 654 may be disposed evenly over a modeled section of interest 650, as illustrated in FIG. 6B. 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 cell 654 is defined as a modeled cell. Calculations in modeled cell 654 are 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. Cell 654 can contain drilling fluid, drilling cuttings moving in the drilling fluid, or non-moving drilling cuttings. Cells 654 that contain non-moving drilling cuttings form the cuttings bed 652. Generally, the number of cells 654 disposed across modeled section of interest 650 depends upon the required level of precision of the calculation and the available computational resources. The size (length of the side) of cell 654 is calculated as a ratio of the diameter of the wellbore and the number of cells 654. The number of cells 654 is an input parameter. Cells 654 may create a grid layer 656, which is a horizontal line of a plurality of cells 654 that may be adjacent to each other. After population of cells 654 across modeled section of interest 650, a first layer 658 is selected, working from bottom of modeled section of interest 650.

In block 604 of workflow 600, a first cell 660 of first grid layer 658 may be selected. In block 606 of workflow 600, it is determined if first cell 660 of block 604 is a cell 654 that is last in grid layer 656. If it is not, then workflow 600 moves to block 608 of workflow 600, which shifts workflow 600 to a cell adjacent in grid layer 656 to cell 654 identified in block 604 of workflow 600. It should be noted, that in this progression, cells 654 may be identified going left to right or right to left across grid layer 656. However, once a direction is chosen, workflow 600 may not go in the direction opposite of the chosen direction across grid layer 656.

In block 610 of workflow 600, cell 654 is viewed to determine if cell 654 is inside or intersected by borehole 116 or modeled section of interest 650. If not, workflow 600 reverts back to block 604 and workflow 600 shifts to an adjacent cell 654 according to the methods described above. However, referring back to block 610 in workflow 600, if cell 654 is inside borehole 116 or intersected by borehole 116, workflow 600 moves to block 612. In block 612 of workflow 600, a deposition criterion may be calculated utilizing information handling system 160. Deposition criterion may be based at least in part on the balance of the forces acting on cell 654 (or cuttings).

FIG. 7 is a schematic 700 representing the moments of forces acting on a cell 654 (e.g., referring to FIG. 6B), drilling cuttings, at the surface of cuttings bed 652 (e.g., referring to FIG. 6B). 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:

F G ⁢ r G > F D ⁢ r D , ( 1 ) where F G = m ⁢ ( 1 - ρ f ρ ) ⁢ g ⁢ sin ⁢ α ( 2 ) F D = τ ⁢ A , r G = d ⁢ sin ⁢ ϕ , r D = d ⁢ cos ⁢ ϕ ,

wherein F_G is the difference between gravitational and buoyancy forces, F_D is the drag force, r_G and r_D are the arms of F_G and F_D respectively; 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; ρ_f is the density of the fluid; and τ is the shear stress at the surface of cuttings bed 652. The shear stress consists of two components τ_z and τ_φ. τ_z is created by the axial flow of the fluid trough the annulus, and τ_φ is caused by rotation of the drill string 108:

τ z = τ 0 + K ⁢ γ z n , ( 3 ) τ φ = ( 1 - e r - R p d ) ⁢ τ φ ⁢ f + e r - R p d ⁢ τ φ ⁢ p , ( 4 ) τ φ ⁢ f = τ 0 + K ⁢ γ φ n , ( 5 ) τ φ ⁢ p = t 2 ⁢ π ⁢ R p 2 , ( 6 )

where τ_φf is the shear stress created by the angular motion of the fluid caused by pipe rotation; τ_φp is the mechanical stress at the surface of drill string 108 (e.g., referring to FIG. 6B); K and n are the consistency and flow indices of the fluid; R_p, r, t are the radius, the distance from the center, and the torque per unit length of drill string 108, respectively; γ_z and γ_φ are the shear rates along z and φ axes:

γ z = ∂ v z ∂ r , ( 7 ) γ φ = r ⁢ ∂ ∂ r ( v φ r ) ( 8 )

The drag force acting on cell 654, drilling cuttings, at the surface of drilling bed 652 is a vector sum of the shear forces acting along z and φ axes as illustrated below:

F D = A ⁢ τ z 2 + τ φ 2 ( 9 )

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 108, 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.

FIG. 8 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 654. Line 818 connecting center 816 of a grid cell 654 and center 800 of drill string 108 may be used to find the effective boundaries of slot 814. The object closest to the center of grid cell 654 intersected by lines 818, moving toward center 800 of drill string 108 may be considered as a first slot boundary 804. The closest object intersected by lines 818, moving in the opposite direction, is considered as a second slot boundary 808. The three examples with the different effective slot boundaries are shown in FIG. 8. For cell i₁, j₁, or 802, first boundary 804 at R_1,i1j1, is a cell of cuttings bed 652 and second boundary 808 is borehole wall 810 at R_2,i1,j1, for cell i₂, j₂, or 812, first boundary 804 at R_1,i2i2, is the surface of drill string 108 and second boundary 808 is a cell 654 of cuttings bed 652 at R_2,i2j2, and for cell i₃, j₃, or 812, first boundary 804 at R_1,i3j3, is the surface of drill string 108 and second boundary 808 is borehole wall 810 R_2,i3j3. The effective size of slot 814 is calculated as the difference between R_2ij−R_1ij.

As cuttings bed 652 grows, the effect of the decrease of the wellbore cross section is considered by multiplying v_z by the normalization coefficient which provides conservation of the total amount of fluid flowing through the section annulus:

v z ( r ij ) = C n ⁢ f z ( r ij , R 1 , ij , R 2 , ij ) , ( 10 )

where f_z(r_ij, R_1,ij, R_2,ij) is the function known from the narrow slot solution, r_ij is the distance between the center of the cell i, j and the center of drill string 108; R_1,ij, R_2,ij, are the effective slot boundaries for this cell; and C_n is the normalization coefficient which is calculated as follows:

C n = Q ∑ i , j ∉ Bed ⁢ f z ( r ij , R 1 , ij , R 2 , ij ) ⁢ Δ ⁢ S ij , ( 11 )

where Q is the flow rate through the section annulus, and ΔS_ij is the area of the cell i, j. As summation in the formula for C_n occurs over the cells that are not in cuttings bed 652, v_z(r_ij) increases and the shear rate at the surface of cuttings bed 652 increases as cuttings bed 652 grows. The value of the normalization coefficient is recalculated after one or more layers 656 are analyzed.

Referring back to FIGS. 6A and 6B, if the gravity force exerted on a cell 654 in FIG. 6B, as discussed above, is stronger than the buoyancy force and the shear forces created by the fluid flow and drill string rotation, the deposition criterion is met, and cell 654 is added to cuttings bed 652 in block 614 of workflow 600 in FIG. 6A. If in block 612 the gravity force exerted on cell 654 is not stronger than the buoyancy force and the shear forces created by the fluid flow and drill string rotation, then the deposition criterion is not met, and workflow 600 moves back to block 606. Likewise, if cell 654 is added to cuttings bed 652, workflow 600 also moves back to block 606. In block 606, it is again determined if cell 654 that is being analyzed is the last cell 654 in grid layer 656. If cell 654 is last in grid layer 656, then workflow 600 moves to block 616, which is one of three conditions that may be met to exit workflow 600.

In block 616, workflow 600 determines if drill string 108 is stuck in borehole 116, a first condition to determine if workflow 600 should end (referred to Exit in FIG. 6A). The first condition for a pipe stuck in borehole 116 is met if the distance between the center of any cell 654 at the surface of the cuttings bed 652 and center 800 of drill string 108 is less than pipe radius 626. If drill string 108 is stuck, then workflow 600 is ended (referred to Exit in FIG. 6A). If drill string 108 is not stuck, then workflow 600 shifts to block 618. In block 618, it is determined if at least one cell 654 of grid layer 656 is added to cutting bed 652 using the methods and systems described in block 612. In block 612, cuttings bed 652 may continue to grow and cross section area of borehole 116 available for the fluid flow continues to shrink and the shear forces acting on the surface of cuttings bed 652 become stronger. This may have several outcomes. For example, in one outcome, at some size of cuttings bed 652, the shear forces may overcome the gravity force. In this case, the deposition criterion, as described in block 612, will not be met for any cell 654 of the corresponding grid layer 656 and workflow 600 may end. However, if the deposition criterion is met then workflow 600 shifts to block 614. In block 614 cuttings bed 652 continues to grow, and at some point, cuttings bed 652 reaches the last grid layer 656 at the top of modeled section of interest 650 and workflow 600 is ended (referred to Exit in FIG. 6A). However, block 620 of workflow 600 determines if this is the last grid layer 656, then workflow shifts to block 622 if we do not or shift to exit if we do. In block 622, the velocity normalization coefficient is updated. The velocity normalization coefficient is updated in accordance with Equation (11). Its update considers reduction of the wellbore cross section free for fluid flow and corresponding increase of the z-component of the fluid velocity as the cuttings bed grows. After updating the velocity normalization coefficient in block 622, workflow 600 shifts to block 624.

In block 624, workflow 600 shifts up, or down, to the next grid layer 656 that has not been analyzed. From block 624, workflow shifts back to block 608 and the method described above may be repeated until workflow 600 is stopped for at least one of the reasons described above.

FIGS. 9A-9E are graphical illustrations of the calculations of the mechanical stress and fluid shear stress that enter Equations (3)-(9) as a function of the distance R between drill string 108 and cuttings bed 652 surface according to embodiments of the present disclosure. FIG. 9A is a graphical illustration of the mechanical shear stress and the fluid shear stress as a function of the distance R between drill string 108 and the surface of cuttings bed 652. The impact of the shear forces due to pipe rotation is mostly fluid shear (τ_φf) dominated for the cells of the cuttings bed 652 that are far from the surface of the pipe 108 and becomes mostly mechanical shear (τ_φp) dominated for the cells that are close to the surface of the pipe. The graph in FIG. 9B is a graphical illustration that represents the profile of the angular velocity of fluid v_φ as a function of the distance R between drill string 108 and the surface of cuttings bed 652. FIG. 9C is a graphical illustration that represents the profile of the axial velocity of fluid v_z as a function of the distance R between drill string 108 and the surface of cuttings bed 652. FIG. 9D is a graphical illustration that represents the corresponding shear rates γ_φ along the φ axe as a function of the distance R between drill string 108 and the surface of cuttings bed 652. FIG. 9E is a graphical illustration that represents the corresponding shear rates γ_z along the z axe as a function of the distance R between drill string 108 and the surface of cuttings bed 652.

FIGS. 10A and 10B are discussed below. FIGS. 10A-10B illustrate a workflow 1000 for modeling the destruction of inclined surfaces of the cuttings bed due to mechanical instability, which is the second step of the two-step workflow to predict the shape and size of cuttings bed 652. In examples, workflow 1000 may be at least partially performed on information handling system 160. A bed column 1050 may be identified as a part of a column of the grid 1049 which starts at the bottom of the grid and upper cells of which belong to the cuttings bed 652, as illustrated in FIG. 10B. The height 1051 of a cuttings bed column 1050 is identified as the number of the cells in this column. Workflow 1000 may begin with block 1002 in which a subset 1052 of the bed columns 1050 is identified. The subset 1052 is identified as cuttings bed columns 1050 the heights 1051 of which are less than a certain percent of the heights 1051 of all cuttings bed columns 1050. Workflow 1000 may iterate over all columns 1050 in cuttings bed 652 and all cells 654 in each column 1050.

After the subset of the bed columns 1052 with columns 1050 with cuttings bed 652 have been identified, workflow 1000 may shift to block 1004. The first column can be either the leftmost (in this case workflow 1000 moves left to right, and the last column is the rightmost column of the cuttings bed) or the rightmost (in this case workflow 1000 moves right to left and the last column is the leftmost column of the cuttings bed) column of the cuttings bed 652. The last cell of the column 1053 is its topmost cell and the first cell of the column 1054 is its lowest cell (as shown in FIG. 10B). In block 1004, workflow 1000 may begin with last cell 1053 of first column 1050, as illustrated in FIG. 10B. Once last cell 1053 of the first column has been identified, workflow 1000 may shift to block 1006. In block 1006, cell 654 is analyzed to determine if it is first cell of the column 1054 or a cell outside of the wellbore 1055 in column 1050, as illustrated in FIG. 10 B. If it is first cell 1054 or a cell outside of the wellbore 1055, then workflow 1000 moves to block 1008 in which an adjacent column 1050 is selected for analyses. It should be noted that workflow 1000 may move in one direction (i.e., left to right or right to left) for changing columns 1050 in block 1008. However, workflow 1000 may not move in one direction and then move in the opposite direction during analysis. After moving to column 1050 in block 1008, workflow 1000 shifts to block 1010 to determine if column 1050 in block 1010 is the last column in cuttings bed 652. If column 1050 in block 1010 is the last column, then workflow 1000 is stopped, if not, then workflow 1000 moves to block 1012.

Referring back to block 1006, if cell 654 is not first in column 1050 or is not outside the wellbore. Once a new cell is chosen, workflow 1000 may shift to block 1014. In block 1014, a cell 1056 closest to the current cell 654 is chosen from the cells of the subset of columns 1052. After cell 1056 is chosen in block 1014, workflow 1000 may move to block 1016. In block 1016, slope 1057 (e.g., referring to FIG. 10B) is calculated as the angle formed by line 1058 connecting current cell 654 and cell 1056 and horizontal line 1059 intersecting cell 1056. Slope 1057 is then analyzed to determine if the slope 1057 is greater than the repose angle 1060. A comparison of slope 1057 with the angle of repose 1060 is used as a criterion of stability of the corresponding part of the cuttings bed surface. If slope 1057 is greater than repose angle 1060, the current cell 654 is removed from cuttings bed 652 in block 1018. If not, then workflow 1000 may shift to block 1008 and analysis may continue as described above.

FIG. 11 is an example of a workflow 1100 to optimize hole cleaning according to embodiments of the present disclosure. Workflow 1100 may be at least in part performed on information handling system 160 (e.g., referring to FIG. 1). Workflow 1100 may allow for properties of cuttings directly measured at the rig site, such as size, shape, and density, to predict the characteristics of the cuttings bed in the inclined sections of the well. These characteristics of cuttings bed 652 (e.g., referring to FIG. 6B) may then be altered by changing available operational parameters in real time including the flow rate of the drilling fluid, the drilling fluid chemistry, the drilling fluid rheology, the force applied on drill bit 114 (e.g., referring to FIG. 1), the number of rotations per minute of drill bit 114, the eccentricity of the drill string, for example. Workflow 1100 may begin in block 1102 in which cuttings characteristics including size, shape, and density, for example are analyzed. Analysis of cuttings characteristics 1102 may be performed either manually or with the use of automatic methods. The automatic methods may include video registration of the cuttings with subsequent analysis of the cuttings' images. Analysis of the cuttings' images can be done with help of image processing algorithms that can be partially or fully based on artificial intelligence and/or machine learning (AI/ML) techniques. These characteristics may then be used in workflows 600 and 1000 to predict presence and properties of the cuttings bed. After the cutting characteristics are inserted into workflow 1100 in block 1104, the workflows may be run in block 1106 for each modeled section of interest 650 to predict cutting bed properties. The properties of the cuttings bed and their effect on the hole cleaning process are then analyzed in block 1108. If workflows 600, 1000, and/or 1100 predict that the cuttings bed is not formed or characteristics of the cuttings bed are acceptable for the required quality of the hole cleaning at the current operational parameters, workflow stops 1110. It can be run again (or each time) after the change of the operational parameters which may result in the change of properties of the cuttings bed 652. The change of the operational parameters may include drilling a new well section, changes of the flow rate, rate of penetration (ROP), rotations per minute (RPM), drilling fluid formulation, position of the tool string, etc. If workflows 600, 1000, and/or 1100 predict formation of the cuttings bed and its characteristics are not acceptable for the required quality of the hole cleaning, one or more changes to the operational parameters to alter the properties of cuttings bed 652 may then be proposed in block 1112. The changes to the operational parameters may then be inserted into the workflows 600, 1000, and/or 1100 in block 1112. From there, workflows 600, 1000, and/or 1100 in block 1106 may be run again to predict the cuttings bed properties in block 1106 according to the methods and systems described above.

The preceding description provides various examples of the systems and methods of use disclosed herein which may contain different method steps and alternative combinations of components. It should be understood that, although individual examples may be discussed herein, the present disclosure covers all combinations of the disclosed examples, including, the different component combinations, method step combinations, and properties of the system. It should be understood that the compositions and methods are described in terms of “comprising,” “containing,” or “including” various components or steps, the compositions and methods can also “consist essentially of” or “consist of” the various components and steps. Moreover, the indefinite articles “a” or “an,” as used in the claims, are defined herein to mean one or more than one of the elements that it introduces. The systems and methods may comprise any of the various features disclosed herein, comprising one or more of the following statements.

Statement 1. A method comprising: 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.

Statement 2. The method of Statement 1, wherein analyzing the drilling cuttings comprises measuring at least one of drilling cuttings characteristics selected from the group consisting of size, shape, density, and any combination thereof.

Statement 3. The method of Statement 1 or Statement 2, wherein analyzing of the drilling cuttings is performed at the rig site.

Statement 4. The method of any one of Statements 1-3, wherein analyzing of the drilling cuttings is performed while drilling an inclined well section.

Statement 5. The method of any one of Statements 1-4, wherein the at least one parameter controlling drilling operation comprises at least one parameter controlling drilling operation selected from the group of parameters controlling drilling operation consisting of drilling fluid flow rate, drilling fluid chemistry, drilling fluid rheology, a force applied on a drill bit, a number of rotations per minute of the drill bit, an eccentricity of a drill string, and any combination thereof.

Statement 6. The method of any one of Statements 1-5, wherein analyzing the drilling cuttings is performed by an operator.

Statement 7. The method of any one of Statements 1-6, wherein analyzing the drilling cuttings is performed automatically.

Statement 8. The method of any one of Statements 1-7, wherein analyzing the drilling cuttings is performed automatically with video registration of the drilling cuttings and analysis of drilling cuttings images is performed with an image processing algorithm.

Statement 9. The method of any one of Statements 1-8, wherein the change of the at least one parameter is performed by an operator.

Statement 10. The method of any one of Statements 1-9, wherein the change of the at least one parameter is performed automatically.

Statement 11. A method comprising: representing a modeled section of a wellbore by splitting the modeled section of the wellbore into a grid comprising a representation of a borehole when a change of inclination angle of a drilling string is above a threshold, wherein the grid is divided into grid layers and columns, each grid layers and columns divided into cells, wherein each cell represents drilling fluid, drilling cuttings moving in the drilling fluid, or non-moving drilling cuttings; populating the grid with a first cell in one of the two bottom corners of the grid; populating a grid layer with cells in a constant direction; calculating deposition criterion of a drilling cuttings when a cell is inside the representation of the borehole in the grid; adding the cell to a cuttings bed when the deposition criterion is met; updating velocity normalization coefficient when the cell is the last cell in the grid layer; adding a cell to a first end of a grid layer above a populated grid layer; populating the grid layer above the populated grid layer with cells in a constant direction; calculating deposition criterion of a drilling cuttings when a cell is inside the representation of the borehole in the grid; and stopping populating the grid layer when the grid layer is a final grid layer of the grid or when drill bit is stuck.

Statement 12. The method of Statement 11, further analyzing the drilling cuttings recovered from drilling the wellbore.

Statement 13. The method of Statement 11 or Statement 12, further predicting characteristics of the cuttings bed.

Statement 14. The method of any one of Statements 11-13, further predicting the effects of the characteristics of the cuttings bed on hole cleaning.

Statement 15. The method of any one of Statements 11-14, further changing at least one parameter controlling drilling operation when the hole cleaning is impaired by the effects of the characteristics of the cuttings bed.

Statement 16. The method of any one of Statements 11-15, further predicting an impact of the change of the at least one parameter controlling drilling operation on the characteristics of the cuttings bed.

Statement 17. The system of any one of Statements 11-16, predicting an impact of the change of the at least one parameter controlling drilling operation on the characteristics of the cuttings bed, wherein the at least one parameter controlling drilling operation comprises at least one parameter controlling drilling operation selected from the group of parameters controlling drilling operation consisting of drilling fluid flow rate, drilling fluid chemistry, drilling fluid rheology, a force applied on a drill bit, a number of rotations per minute of the drill bit, an eccentricity of a drill string, and any combination thereof.

Statement 18. A system comprising: a collector of drilling cuttings produced by drilling of a well in a subterranean formation; a sensor to measure the drilling cuttings; and an information handling system to analyze data collected by the sensor, predict characteristics of cuttings bed, predict the effects of the characteristics of the cuttings bed on hole cleaning, change at least one control parameter when the hole cleaning is impaired by the effects of the characteristics of the cuttings bed, and predicting an impact of the change of at least one control parameter on the characteristics of the cuttings bed.

Statement 19. The system of Statement 18, wherein the at least one control parameter comprises at least one control parameter selected from the group of control parameters consisting of drilling fluid flow rate, drilling fluid chemistry, drilling fluid rheology, a force applied on a drill bit, a number of rotations per minute of the drill bit, an eccentricity of a drill string, and any combination thereof.

Statement 20. The system of Statement 18 or Statement 19, wherein the sensor measures at least one of drilling cuttings characteristics selected from the group consisting of size, shape, density, and any combination thereof.

For the sake of brevity, only certain ranges are explicitly disclosed herein. However, ranges from any lower limit may be combined with any upper limit to recite a range not explicitly recited, as well as ranges from any lower limit may be combined with any other lower limit to recite a range not explicitly recited, in the same way, ranges from any upper limit may be combined with any other upper limit to recite a range not explicitly recited. Additionally, whenever a numerical range with a lower limit and an upper limit is disclosed, any number and any included range falling within the range are specifically disclosed. In particular, every range of values (of the form, “from about a to about b,” or, equivalently, “from approximately a to b,” or, equivalently, “from approximately a-b”) disclosed herein is to be understood to set forth every number and range encompassed within the broader range of values even if not explicitly recited. Thus, every point or individual value may serve as its own lower or upper limit combined with any other point or individual value or any other lower or upper limit, to recite a range not explicitly recited.

Therefore, the present examples are well adapted to attain the ends and advantages mentioned as well as those that are inherent therein. The particular examples disclosed above are illustrative only and may be modified and practiced in different but equivalent manners apparent to those skilled in the art having the benefit of the teachings herein. Although individual examples are discussed, the disclosure covers all combinations of all of the examples. Furthermore, no limitations are intended to the details of construction or design herein shown, other than as described in the claims below. Also, the terms in the claims have their plain, ordinary meaning unless otherwise explicitly and clearly defined by the patentee. It is therefore evident that the particular illustrative examples disclosed above may be altered or modified and all such variations are considered within the scope and spirit of those examples. If there is any conflict in the usages of a word or term in this specification and one or more patent(s) or other documents that may be incorporated herein by reference, the definitions that are consistent with this specification should be adopted.