EP4486976A1 - System and method for determining a transfer of torque from the surface to a drill bit - Google Patents

Abstract

A method for determining a total torque output at a drill bit includes receiving an on-bottom pressure and an off-bottom pressure. The method also includes determining a differential pressure based upon the on-bottom pressure and the off-bottom pressure. The method also includes receiving a surface torque. The method also includes determining a torque transmission coefficient based at least partially upon the differential pressure and the surface torque. The method also includes determining the total torque output at the drill bit based at least partially upon the differential pressure, the surface torque, and the torque transmission coefficient.

Description

SYSTEM AND METHOD EOR DETERMINING A TRANSFER OF TORQUE FROM THE SURFACE TO A DRILL BIT

Cross-Reference to Related Applications

[0001] This application claims priority to U.S. Provisional Patent Application No.63/268, 879, filed on March 4, 2022, the entirety of which is incorporated by reference herein.

Background

[0002] Mud motors are part of a downhole assembly (also referred to as a bottom hole assembly or BHA) and are widely used for directional drilling and performance drilling. A mud motor is used to transform hydraulic energy of the drilling fluid (e.g., mud) into mechanical energy on a rotating shaft. More particularly, the mud motor transforms the hydraulic power, which is essentially the flow rate Q and the active differential pressure ΔP_a, into an output torque for the drill bit T and additional bit rotation from the motor that may be called RPM_m.

Summary

[0003] This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter.

[0004] A method for determining a total torque output at a drill bit is disclosed. The method includes receiving an on-bottom pressure and an off-bottom pressure. The method also includes determining a differential pressure based upon the on-bottom pressure and the off-bottom pressure. The method also includes receiving a surface torque. The method also includes determining a torque transmission coefficient based at least partially upon the differential pressure and the surface torque. The method also includes determining the total torque output at the drill bit based at least partially upon the differential pressure, the surface torque, and the torque transmission coefficient.

[0005] A computing system is also disclosed. The computing system includes at least one processor and a storage medium connected to the at least one processor. The storage medium includes instructions for configuring the computing system to perform operations. The operations include receiving an on-bottom pressure and an off-bottom pressure that are measured by a pressure sensor. The, wherein the pressure sensor is at a surface above a wellbore. The on-bottom pressure includes a pressure when a bottom hole assembly (BHA) is on a bottom of the wellbore. The off-bottom pressure includes the pressure when the BHA is off of the bottom of the wellbore. The operations also include determining a differential pressure that represents a difference between the on-bottom pressure and the off-bottom pressure. The operations also include receiving a surface torque measured by a torque sensor. The surface torque is a torque introduced to a drill string by a top drive. The torque sensor is coupled to the top drive. The drill string extends into the wellbore. The BHA is coupled to a lower end of the drill string. The BHA includes a mud motor and a drill bit. The operations also include determining a torque transmission coefficient based at least partially upon the differential pressure and the surface torque. The torque transmission coefficient is a positive unitless coefficient that is less than 1 and represents a torque between a rotor and stator rubber in the mud motor. The operations also include determining a total torque output at the drill bit based at least partially upon the differential pressure, the surface torque, and the torque transmission coefficient.

[0006] A non-transitory machine-readable storage medium is also disclosed. The storage medium has instructions stored thereon to configure a processor of a computing system to perform operations. The operations include receiving an on-bottom pressure and an off-bottom pressure that are measured by a pressure sensor. The pressure sensor is at a surface above a wellbore. The on-bottom pressure is a pressure when a bottom hole assembly (BHA) is on a bottom of the wellbore. The off-bottom pressure is the pressure when the BHA is off of the bottom of the wellbore. The operations also include determining a differential pressure that represents a difference between the on-bottom pressure and the off-bottom pressure. The operations also include receiving a surface torque measured by a torque sensor. The surface torque is a torque introduced to a drill string by a top drive. The torque sensor is coupled to the top drive. The drill string extends into the wellbore. The BHA is coupled to a lower end of the drill string. The BHA includes a mud motor and a drill bit. The operations also include determining a torque transmission coefficient based at least partially upon the differential pressure and the surface torque. The torque transmission coefficient is a positive unitless coefficient that is less than 1 and represents a torque between a rotor and stator rubber in the mud motor. The operations also include determining a total torque output at the drill bit based at least partially upon the differential pressure, the surface torque, and the torque transmission coefficient. The total torque output is determined by a model. Determining the total torque output includes multiplying a torque slope of the mud motor and the differential pressure to produce a first value, multiplying the surface torque and the torque transmission coefficient to produce a second value, and adding the first value and the second value to produce the total torque output. The operations also include generating a signal in response to the total torque output. The signal causes one or more parameters to vary. The one or more parameters include the on-bottom pressure, the off-bottom pressure, an amount of the torque introduced into the drill string by the top drive, a weight on the drill bit, a rate of rotation of the drill string, the BHA, or both, a toolface setting of the BHA, a flow rate of a fluid being pumped into the wellbore, or a combination thereof.

Brief Description of the Drawings

[0007] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the present teachings and together with the description, serve to explain the principles of the present teachings. In the figures:

[0008] Figure 1 illustrates an example of a system that includes various management components to manage various aspects of a geologic environment, according to an embodiment. [0009] Figure 2 illustrates a schematic view of a wellsite, according to an embodiment.

[0010] Figure 3A illustrates a perspective view of a mud motor showing external components thereof, according to an embodiment.

[0011] Figure 3B illustrates a cross-sectional side view of the mud motor showing internal components therein, according to an embodiment.

[0012] Figure 3C illustrates a cross-sectional view of a power section of the mud motor showing a rotor therein, according to an embodiment.

[0013] Figure 3D illustrates a cross-sectional view of the power section showing a stator therein, according to an embodiment.

[0014] Figure 4 illustrates a perspective view of the power section with a portion of the stator tube removed to show the rotor therein, according to an embodiment.

[0015] Figure 5A illustrates motion of a single cavity of a 6/7 lobe configuration power section, and Figure 5B illustrates a cross-sectional view of a portion of Figure 5A, according to an embodiment. [0016] Figure 6 illustrates a side view of a snapshot in time of different cavities inside the power section, according to an embodiment.

[0017] Figure 7 illustrates a graph showing a torque output curve for the power section, according to an embodiment.

[0018] Figure 8 illustrates a graph showing RPM output curves for the power section, according to an embodiment.

[0019] Figure 9 illustrates a graph showing the pressure along the length of the power section during a performance test, according to an embodiment.

[0020] Figure 10 illustrates a perspective view of the power section showing additional force on the rotor at the top of the mud motor due to the pumping of the drilling fluid, according to an embodiment.

[0021] Figures 11A-11C illustrate graphs showing real-time drilling parameters during well construction, according to an embodiment.

[0022] Figures 12A-12C illustrates graphs showing real-time drilling parameters during stall conditions for the mud motor, according to an embodiment.

[0023] Figure 13 illustrates a graph showing acoustic impedance for the mud motor, according to an embodiment.

[0024] Figure 14 illustrates a graph showing a comparison between the torque output according to the power section specifications and the measured surface torque, according to an embodiment. [0025] Figures 15A-15J illustrate graphs showing real-time mud motor automatic slide detection, according to an embodiment.

[0026] Figures 16A and 16B illustrate graphs showing real-time motor degradation indicators comparing the expected RPM output and measured RPM output, according to an embodiment.

[0027] Figure 17 illustrates a flowchart of a method for deriving the downhole torque measurement below the mud motor, according to an embodiment.

[0028] Figure 18 illustrates a flowchart of another method for deriving the downhole torque measurement below the mud motor, according to an embodiment.

[0029] Figure 19 illustrates a flowchart of another method for deriving the downhole torque measurement below the mud motor, according to an embodiment.

[0030] Figure 20 illustrates an example of a computing system for performing at least a portion of one or more of the methods disclosed herein, in accordance with some embodiments. Detailed Description

[0031] Reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying drawings and figures. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to one of ordinary skill in the art that the invention may be practiced without these specific details. In other instances, well-known methods, procedures, components, circuits, and networks have not been described in detail so as not to unnecessarily obscure aspects of the embodiments.

[0032] It will also be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first object or step could be termed a second object or step, and, similarly, a second object or step could be termed a first object or step, without departing from the scope of the present disclosure. The first object or step, and the second object or step, are both, objects or steps, respectively, but they are not to be considered the same object or step.

[0033] The terminology used in the description herein is for the purpose of describing particular embodiments and is not intended to be limiting. As used in this description and the appended claims, the singular forms “a,” “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that the term “and/or” as used herein refers to and encompasses any possible combinations of one or more of the associated listed items. It will be further understood that the terms “includes,” “including,” “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. Further, as used herein, the term “if’ may be construed to mean “when” or “upon” or “in response to determining” or “in response to detecting,” depending on the context.

[0034] Attention is now directed to processing procedures, methods, techniques, and workflows that are in accordance with some embodiments. Some operations in the processing procedures, methods, techniques, and workflows disclosed herein may be combined and/or the order of some operations may be changed. [0035] Figure 1 illustrates an example of a system 100 that includes various management components 110 to manage various aspects of a geologic environment 150 (e.g., an environment that includes a sedimentary basin, a reservoir 151, one or more faults 153-1, one or more geobodies 153-2, etc.). For example, the management components 110 may allow for direct or indirect management of sensing, drilling, injecting, extracting, etc., with respect to the geologic environment 150. In turn, further information about the geologic environment 150 may become available as feedback 160 (e.g., optionally as input to one or more of the management components 110).

[0036] In the example of Figure 1, the management components 110 include a seismic data component 112, an additional information component 114 (e.g., well/logging data), a processing component 116, a simulation component 120, an attribute component 130, an analysis/visualization component 142 and a workflow component 144. In operation, seismic data and other information provided per the components 112 and 114 may be input to the simulation component 120.

[0037] In an example embodiment, the simulation component 120 may rely on entities 122. Entities 122 may include earth entities or geological objects such as wells, surfaces, bodies, reservoirs, etc. In the system 100, the entities 122 can include virtual representations of actual physical entities that are reconstructed for purposes of simulation. The entities 122 may include entities based on data acquired via sensing, observation, etc. (e.g., the seismic data 112 and other information 114). An entity may be characterized by one or more properties (e.g., a geometrical pillar grid entity of an earth model may be characterized by a porosity property). Such properties may represent one or more measurements (e.g., acquired data), calculations, etc.

[0038] In an example embodiment, the simulation component 120 may operate in conjunction with a software framework such as an object-based framework. In such a framework, entities may include entities based on pre-defined classes to facilitate modeling and simulation. A commercially available example of an object-based framework is the MICROSOFT® .NET® framework (Redmond, Washington), which provides a set of extensible object classes. In the .NET® framework, an object class encapsulates a module of reusable code and associated data structures. Object classes can be used to instantiate object instances for use in by a program, script, etc. For example, borehole classes may define objects for representing boreholes based on well data. [0039] In the example of Figure 1 , the simulation component 120 may process information to conform to one or more attributes specified by the attribute component 130, which may include a library of attributes. Such processing may occur prior to input to the simulation component 120 (e.g., consider the processing component 116). As an example, the simulation component 120 may perform operations on input information based on one or more attributes specified by the attribute component 130. In an example embodiment, the simulation component 120 may construct one or more models of the geologic environment 150, which may be relied on to simulate behavior of the geologic environment 150 (e.g., responsive to one or more acts, whether natural or artificial). In the example of Figure 1, the analysis/visualization component 142 may allow for interaction with a model or model-based results (e.g., simulation results, etc.). As an example, output from the simulation component 120 may be input to one or more other workflows, as indicated by a workflow component 144.

[0040] As an example, the simulation component 120 may include one or more features of a simulator such as the ECLIPSE™ reservoir simulator (Schlumberger Limited, Houston Texas), the INTERSECT™ reservoir simulator (Schlumberger Limited, Houston Texas), etc. As an example, a simulation component, a simulator, etc. may include features to implement one or more meshless techniques (e.g., to solve one or more equations, etc.). As an example, a reservoir or reservoirs may be simulated with respect to one or more enhanced recovery techniques (e.g., consider a thermal process such as SAGD, etc.).

[0041] In an example embodiment, the management components 110 may include features of a commercially available framework such as the PETREL® seismic to simulation software framework (Schlumberger Limited, Houston, Texas). The PETREL® framework provides components that allow for optimization of exploration and development operations. The PETREL® framework includes seismic to simulation software components that can output information for use in increasing reservoir performance, for example, by improving asset team productivity. Through use of such a framework, various professionals (e.g., geophysicists, geologists, and reservoir engineers) can develop collaborative workflows and integrate operations to streamline processes. Such a framework may be considered an application and may be considered a data- driven application (e.g., where data is input for purposes of modeling, simulating, etc.).

[0042] In an example embodiment, various aspects of the management components 110 may include add-ons or plug-ins that operate according to specifications of a framework environment. For example, a commercially available framework environment marketed as the OCEAN® framework environment (Schlumberger Limited, Houston, Texas) allows for integration of addons (or plug-ins) into a PETREL® framework workflow. The OCEAN® framework environment leverages .NET® tools (Microsoft Corporation, Redmond, Washington) and offers stable, user- friendly interfaces for efficient development. In an example embodiment, various components may be implemented as add-ons (or plug-ins) that conform to and operate according to specifications of a framework environment (e.g., according to application programming interface (API) specifications, etc.).

[0043] Figure 1 also shows an example of a framework 170 that includes a model simulation layer 180 along with a framework services layer 190, a framework core layer 195 and a modules layer 175. The framework 170 may include the commercially available OCEAN® framework where the model simulation layer 180 is the commercially available PETREL® model-centric software package that hosts OCEAN® framework applications. In an example embodiment, the PETREL® software may be considered a data-driven application. The PETREL® software can include a framework for model building and visualization.

[0044] As an example, a framework may include features for implementing one or more mesh generation techniques. For example, a framework may include an input component for receipt of information from interpretation of seismic data, one or more attributes based at least in part on seismic data, log data, image data, etc. Such a framework may include a mesh generation component that processes input information, optionally in conjunction with other information, to generate a mesh.

[0045] In the example of Figure 1, the model simulation layer 180 may provide domain objects 182, act as a data source 184, provide for rendering 186 and provide for various user interfaces 188. Rendering 186 may provide a graphical environment in which applications can display their data while the user interfaces 188 may provide a common look and feel for application user interface components.

[0046] As an example, the domain objects 182 can include entity objects, property objects and optionally other objects. Entity objects may be used to geometrically represent wells, surfaces, bodies, reservoirs, etc., while property objects may be used to provide property values as well as data versions and display parameters. For example, an entity object may represent a well where a property object provides log information as well as version information and display information (e.g., to display the well as part of a model).

[0047] In the example of Figure 1, data may be stored in one or more data sources (or data stores, generally physical data storage devices), which may be at the same or different physical sites and accessible via one or more networks. The model simulation layer 180 may be configured to model projects. As such, a particular project may be stored where stored project information may include inputs, models, results, and cases. Thus, upon completion of a modeling session, a user may store a project. At a later time, the project can be accessed and restored using the model simulation layer 180, which can recreate instances of the relevant domain objects.

[0048] In the example of Figure 1, the geologic environment 150 may include layers (e.g., stratification) that include a reservoir 151 and one or more other features such as the fault 153-1, the geobody 153-2, etc. As an example, the geologic environment 150 may be outfitted with any of a variety of sensors, detectors, actuators, etc. For example, equipment 152 may include communication circuitry to receive and to transmit information with respect to one or more networks 155. Such information may include information associated with downhole equipment 154, which may be equipment to acquire information, to assist with resource recovery, etc. Other equipment 156 may be located remote from a well site and include sensing, detecting, emitting or other circuitry. Such equipment may include storage and communication circuitry to store and to communicate data, instructions, etc. As an example, one or more satellites may be provided for purposes of communications, data acquisition, etc. For example, Figure 1 shows a satellite in communication with the network 155 that may be configured for communications, noting that the satellite may additionally or instead include circuitry for imagery (e.g., spatial, spectral, temporal, radiometric, etc.).

[0049] Figure 1 also shows the geologic environment 150 as optionally including equipment 157 and 158 associated with a well that includes a substantially horizontal portion that may intersect with one or more fractures 159. For example, consider a well in a shale formation that may include natural fractures, artificial fractures (e.g., hydraulic fractures), or a combination of natural and artificial fractures. As an example, a well may be drilled for a reservoir that is laterally extensive. In such an example, lateral variations in properties, stresses, etc. may exist where an assessment of such variations may assist with planning, operations, etc. to develop a laterally extensive reservoir (e.g., via fracturing, injecting, extracting, etc.) As an example, the equipment 157 and/or 158 may include components, a system, systems, etc. for fracturing, seismic sensing, analysis of seismic data, assessment of one or more fractures, etc.

[0050] As mentioned, the system 100 may be used to perform one or more workflows. A workflow may be a process that includes a number of worksteps. A workstep may operate on data, for example, to create new data, to update existing data, etc. As an example, a may operate on one or more inputs and create one or more results, for example, based on one or more algorithms. As an example, a system may include a workflow editor for creation, editing, executing, etc. of a workflow. In such an example, the workflow editor may provide for selection of one or more predefined worksteps, one or more customized worksteps, etc. As an example, a workflow may be a workflow implementable in the PETREL® software, for example, that operates on seismic data, seismic attribute(s), etc. As an example, a workflow may be a process implementable in the OCEAN® framework. As an example, a workflow may include one or more worksteps that access a module such as a plug-in (e.g., external executable code, etc.).

[0051] System and Method for Determining a Transfer of Torque from the Surface to a Drill Bit when Drilling with a Mud Motor

[0052] Figure 2 illustrates a schematic view of a wellsite 200, according to an embodiment. The wellsite 200 may include a drilling rig 210 positioned at the surface 220. The drilling rig 210 may be positioned over a wellbore 230 that extends into a subterranean formation 240. A drill string 250 may extend from the drilling rig 210 into the wellbore 230. The drilling rig 210 may include surface torque equipment (e.g., a top drive) 212 that may be configured to cause the drill string 250 to rotate. This generates surface rotations per minute (RPM) and surface torque. A bottom hole assembly (BHA) 260 may be coupled to a lower end of the drill string 250. As described in greater detail below, the BHA 260 may include a motor (e.g., a mud motor) and a drill bit. There may be a torque below the motor, which may be the same as or different from the surface torque (e.g., when the BHA 260 is on-bottom in the wellbore 230).

[0053] Figure 3A illustrates a perspective view of a mud motor 300 showing external components thereof, and Figure 3B illustrates a cross-sectional side view of the mud motor 300 showing internal components therein, according to an embodiment. As shown in Figure 3A, the external components may include a top sub 310, a power section 320, a surface adjustable bent housing 330, a near-bit stabilizer 340, a drive shaft 350, or a combination thereof. The near-bit stabilizer 340 and/or the drive shaft 350 may be coupled to a drill bit 360. As shown in Figure 3B, the internal components may include the power section 320, a transmission section 370, a bearing section 380, and the drive shaft 350. The power section 320 transforms hydraulic power into mechanical power.

[0054] Figure 3C illustrates a cross-sectional view of the power section 320 showing a rotor 322 therein, and Figure 3D illustrates a cross-sectional view of the power section 320 showing a stator 324 therein, according to an embodiment. The power section 320 may include the rotor (e.g., moving part) 322 and the stator (e.g., stationary part) 324. The rotor 322 may be made of steel. The stator 324 may be or include a metal tube with rubber 326 bonded inside. The stator tube 324 may have a circular cross-section with the rubber 326 taking the form of one or more lobes. A thin wall stator 324 has the metal tube in the form of the lobe providing extra stiffness to add additional sealing capability to the stator 324.

[0055] Figure 4 illustrates a perspective view of the power section 320 with a portion of the stator tube 324 removed to show the rotor 322 therein, according to an embodiment. A portion of the fluid may be trapped between the rotor 322 and the rubber lining 326. The space fdled by this trapped fluid between the rotor 322 and rubber lining 326 is called a cavity 328, and the boundaries between these cavities 328 are called sealing lines and sealing surfaces.

[0056] Figure 5A illustrates motion of a single cavity of a 6/7 lobe configuration power section 320, and Figure 5B illustrates a cross-sectional view of a portion of Figure 5A, according to an embodiment. Each cavity 328 may move from up to down with both axial progression and orbital movement in a spiral-like motion when the fluid is travelling from up to down the power section 320. During this motion, the pressure inside the cavity 328 may change as the cavity 328 is moving along the power section 320. Figure 6 illustrates a side view of a snapshot in time of different cavities 328 inside the power section 320, according to an embodiment.

[0057] If the sealing lines and sealing surfaces are working, there may be no exchange of fluid between cavities 328 as the cavities 328 may be isolated from each other. However, sometimes there may be leakage between these cavities 328. The pressure may decrease almost linearly between the first cavities 328 that are open to the inlet of the power section 320 and the last cavities 328 that open to the outlet of the cavities 328. The pressure difference between two adjacent cavities 328 in the axial position (AP) yields the following equation: Inlet Pressure — Outlet Pressure P = -

Number of closed cavities

(1) [0058] There are two types of sealing lines: (1) low pressure sealing lines: separating cavities 328 with pressure difference equal to 1 AP; and (2) high pressure sealing lines: separating cavities 328 with a pressure difference equal to n_s P, where n_s is the number of lobes on the stator 324. These sealing lines may define the pressure separation between the cavities 328. There is a (e.g., direct) link between the output torque that the motor 300 is providing to the drill bit 360 and the pressure differential capability of the mud motor 300. More particularly, the torque output by the motor power section 320 follows the curve shown in the graph in Figure 7, which represents a torque output curve for the power section 320, according to an embodiment.

[0059] The other component of the mechanical power output by the motor 300 is the rotational speed RPM_m. This RPM_m also depends on the overall active differential pressure across the motor power section AP_a. Figure 8 illustrates a graph showing RPM output curves for the power section 320, according to an embodiment. This RPM_m may follow one or more of the curves.

[0060] Figure 9 illustrates a graph showing the pressure along the length of the power section 320 during a performance test, according to an embodiment. Executing a performance test of a motor power section 320 (e.g., using a dynamometer to monitor the pressure profile along the length of power section) may yield the curves shown in Figure 9. The performance test may include gradually increasing the torque output of the motor 300 with time until the motor 300 stalls. One area of the motor 300, which may take up the pressure, is the inlet portion as the torque and the differential pressure increases, whereas the output side of the motor 300 is almost constant during the test, regardless of the increase in torque.

[0061] Mud Motor Effects on Surface Measurements

[0062] Surface measurements during well construction may include the block position to estimate the rate of penetration (ROP), the hookload to obtain the weight on bit (WOB), the surface rotation per minute (RPM) to derive the bit RPM, the standpipe pressure (SPP) to help assess the pressure balance, the flow rate that provides the pumping regime, and/or the surface torque to attempt to obtain the current torque output at the bit and comprehend the efficiency of the well construction. These measurements may be used to monitor, advise, and/or autonomously control the well construction. The interpretation of one or more (e.g., four) of these measurements may be (e g., directly) affected by the presence of (or lack of) the mud motor 300 inside the BHA 260, whether it be in the steering mode or in power mode when combined with a rotary steerable system (RSS).

[0063] Block Position and ROP

[0064] In terms of the block position and ROP, the addition of the mud motor 300 inside of the BHA 260 may produce extra power at the drill bit 360, which in most cases may result in a higher ROP compared with the same BHA without the mud motor 300. This condition is particularly true when operating the mud motor 300 in a power situation.

[0065] Hookload. Surface WOB (WOBc and Downhole WOB (VKOB_n)

[0066] The hookload may be used to derive the downhole WOB applied to the drill bit 360. The presence of or lack of the mud motor 300 may alter the interpretation. When the mud motor 300 is present, there is additional weight with the fluid pushing the top portion of the rotor 322 which is open as shown in Figure 10. This extra force contributes marginally to the downhole WOB. When the mud motor 300 is close to stalling, this force may cause a positive feedback loop that may accelerate the stalling process. In essence, when stalling, the mud motor torque may be high. This high torque may result in increased pressure on the inlet portion of the mud motor 300. This inlet pressure increase may increase F_Fluid described in Figure 10, which may lead to increased WOB, and the increased WOB may increase the torque, and so on.

[0067] Surface RPM and downhole RPM

[0068] Using the surface RPM (RPM_S) to determine the overall RPM of the drill bit 360 may be calculated using following equation:

RPM_Bit = RPM_M + RPM_S (2)

[0069] Equation (2) means that when there is a mud motor 300 in the BHA 260, the bit RPM may be the sum of the surface RPM and the motor RPM shown previously in Figure 7.

[0070] Standpipe Pressure (SPP)

[0071] The standpipe pressure is a measurement to identify and/or prevent pressure imbalance inside the wellbore 230 currently being drilled. As such, the standpipe pressure is a decisive measurement that is monitored closely to avoid effects of a kick and/or blowout. The mud motor effect on this measurement may be seen in Figure 9. There is often a difference in pressure above the mud motor 300 when the drill bit 360 is on-bottom vs. when it is off-bottom. Figures 11A- 11C illustrate drilling parameters (e.g., surface WOB, ROP, surface torque, standpipe pressure, etc.) when operating the mud motor 300 with the standpipe pressure increasing with increased WOB and resulting drill bit torque demand. This added pressure above the mud motor 300 may directly translate to the standpipe pressure. The difference in pressure while raising the WOB may be more than 2,000 psi in some cases.

[0072] The standpipe pressure may be used to infer imbalance wellbore pressure. The presence of the mud motor 300 may change the pressure regime because additional torque at the bit 360 is used to construct the wellbore 230.

[0073] Flow rate

[0074] Under normal steady-state drilling conditions, even if the mud motor 300 is present in the BHA 260, the flow rate in the entire drill string 250 and BHA 260 is more or less the same as the surface flow rate measured directly at the pumps’ output. When operating with an RSS tool, the turbine RPM, which is inside the RSS tool, can be used to derive the actual downhole flow rate. This information may be useful because it allows the comparison of the surface flow rate from the pumps and the downhole flow rate at the BHA 260. With steady-state drilling conditions, both the surface flow rate and the downhole flow rate may be equal.

[0075] When the mud motor 300 is stalling, the operation becomes very different. As shown in Figures 12A-12C, when the WOB is increased to the stall point, the mud motor stall may be detected at the surface by the sudden jump in standpipe pressure. During this time, although the surface flow rate remains very steady, the downhole flow rate below the mud motor 300 experiences a sudden decrease related to the acoustic impedance of the mud motor 300. When increase in pressure happens at a time frame slower than the two-way travel time of the drilling fluid, it may result in a sharp decrease of flow rate below the mud motor 300. The decrease of flow rate may be determined with the equation:

AQ = - ^-, (3) where Z = the acoustic impedance of the assembly, AQ = the diminution of flow rate, and AP_a = the sudden increase of pressure.

[0076] This condition may affect the drilling. Figure 13 illustrates a scenario where drilling is taking place with a steady surface flow rate of 600 gal/min (gpm). A stringer is encountered downhole, and the pressure immediately increases by 1,200 psi. Assuming an impedance of 3 psi/gpm, it would result in a decrease of flow of about 400 gpm. In terms of how the mud motor 300 operates, this implies that instead of stalling along the 600 gpm curve, the stall may take place along the 200 gpm curve, meaning that the stall would take place much faster than anticipated.

[0077] Surface Torque and Downhole Torque

[0078] Referring again to Figure 7, it may be seen that below a certain pressure differential P limi , the torque output from the mud motor 300 is linear with respect to the differential pressure. This is because the torque generated by the rotor 322 comes almost exclusively from the imbalance in pressure between the cavities 328. The torque slope for the linear regime part may be defined as the dependency between the torque and the differential pressure: [0079] This torque slope may be geometry-driven and (e.g., directly) linked to the kinematics of the power section 320. It may not (or may partially) depend on the flow rate, the rubber type, the type of fluid, the interference fit, the power section length, or a combination thereof. When operating the power section 320 under normal regime, a user may use Equation 2 to model the torque output.

[0080] Figure 14 illustrates a graph showing a comparison between the torque output according to the power section specifications and the measured surface torque, according to an embodiment. The surface torque refers to the torque introduced to the drill string 230 at the surface (e.g., by the top drive 212). The surface torque does not reflect the behavior of the mud motor 300 downhole. The reason is that, when the power section 320 is operating, the top part of the rotor 322 may be free. As the lower part of the rotor 322 is (e g., directly) connected torsionally to the drill bit 360, this means that when the mud motor 300 is present, the torque generated at the bit 360 is from the rotor 322. The contribution of the surface top drive torque is coming from the contact pressure between the stator elastomer 326 and the rotor 322. This contribution may be less than (e.g., minimal compared to) the output torque coming from the pressure differential between cavities 322. This means that there is a torque discontinuity between the upper part of the bottom hole assembly (BHA) 260 (e.g., above the motor 300) and the lower part of the BHA 260 (e.g., below the motor 300). In one example, if there is perfect lubrication between the stator rubber 326 and the rotor 322, the contribution from the surface top drive 212 to the torque output may be nearly zero. [0081] The total torque output (T_Totai) in the lower part of the motor 300, in terms of the torque that is coming from the surface top drive (T_s,) and the torque being generated by the rotor (T_M), is shown in Equation 3:

Trotai - T_M + a T_s

(5) In this equation, the variable a is a positive unitless coefficient that is less than 1 and represents the transmission of torque between the stator rubber 326 and the rotor 322 via frictional contact pressure. The value of a may depend on a number of factors such as:

• The rubber type and rubber manufacturing process: the bigger the frictional capability of the rubber, the bigger a may be.

• The interference fit which is how tight the rotor 322 is fitting inside the stator 324: the tighter the interference fit, the bigger a may be.

• The rotor type and polishing process: the smaller frictional capability of the rotor 322, the smaller a may be.

• The lobe configuration: a higher lobe count results in a higher a value.

• The profile of the power section 322: frictional contact is playing a role here.

• The drilling fluid and its sand and solid content: this is the lubrication capability of the drilling fluid.

• The downhole temperature: due to the rubber thermal expansion, the higher the temperature, the higher the value of a.

• The downhole pressure: This depends on the difference between the internal pressure and the external pressure and also on the lobe deformation of the rubber 326.

• The compatibility between the mud and the rubber 326: the more the swelling of the rubber 326 due to the mud, the higher a may be.

• The surface RPM and the rotor RPM: This depends on both the relative RPM between the surface RPM and the rotor RPM and also the absolute value of both RPMs

• The flow rate: this effect is still uncharacterized.

[0082] The derivation of this positive unitless coefficient a reflects the transmission of torque between the stator rubber 326 and the rotor 322 via frictional contact pressure. [0083] Digital Well Construction Workflows

[0084] With greater understanding of how to interpret the surface measurements when a mud motor is present inside the BHA 260, examples are presented below showing how to use this information for monitoring, advising, and/or controlling the drilling process when constructing the wellbore 230 with the mud motor 300. This understanding of the motor physics can be used both in the planning phase (e.g., while preparing for a drilling operation) and/or in the execution phase. The path towards an autonomous well construction may be explored through analyzing the mechanical specific energy (MSE), an automatic slide detection for steering with the mud motor 300, an abnormal pressure detection, and a real-time mud motor efficiency and degradation.

[0085] MSE Calculation

[0086] The MSE may be used to monitor the drilling efficiency. Nonetheless, when the mud motor 300 is present inside the BHA 260, its estimation of the energy consumed at the drill bit 360 often suffers from a lack of understanding of the mud motor physics. When there is no mud motor, a formula for calculating MSE is: where A_bjt is the bit area, WOB_S, RPM_S, and T_s are the surface weight-on-bit, the surface RPM, and the surface torque, respectively. This equation may be useful as long as the focus is on the surface energy input when there is no motor 300 inside of the BHA 260.

[0087] However, most BHAs 260 include a mud motor 300 either on steering mode or on power mode to gain extra efficiency while constructing the wellbore 230. The formula may evolve when the motor 300 is being used. In addition, the MSE may be used to determine how efficiently the drill bit 360 is cutting the rock and making the wellbore 230 from the initially given energy. The new MSE formula will look like:

WOB_D , 120 ir RPM_Bit T_Total

MSE = MSE_Axiai + MSE_Tor = — — Abit A_bit ROP

WOB_D 120 TT (RPM_S + RPM_M) (T_M + a T_s)

MSE = — - 1 - - - — — -

Abit Abit ROP

(7) where W0B_D is downhole weight-on-bit, and a is the positive unitless torque transmission coefficient. This formula may be used to evaluate the efficiency of the drill bit 360. In many scenarios, the MSE may be used relatively by observing the trends in particular formations 240 and then a decrease or increase in the trends may be used to detect particular formations 240 or efficiency issues. However, when the mud motor 300 is present, not taking account of the motor kinematics could lead to wrong conclusions being made.

[0088] Automatic Slide Detection

[0089] Using downhole mud motors 300, directional drillers may be able to kick off the wellbore 230, build angle, and drill tangent sections. The surface adjustable bend housing may be used to steer the bit 360 to a desired direction. After orienting the bend to a specific direction (i.e., tool face angle), and by not allowing drill string rotation while drilling, a slide mode drilling operation may be triggered. A precise tool face orientation during the slide drilling may be used to achieve desired targets. However, many downhole drilling conditions may affect the slide performance such as the reactive torque, stalling of the mud motor 300, drilling through different formations, difficulties transferring weight to the bit 360, etc.

[0090] Directional drillers aim to maintain a predetermined ROP, toolface (TF), and transfer weight to the drill bit (WOB) without stalling the mud motor 300 to maintain high drilling efficiency. On the other hand, by increasing the hole depth, drillstring friction and drag may increase. Hence, transferring WOB and controlling TF performance may be more difficult as the depth increases. As a result, maintaining sufficient ROP and providing the desired trajectory to the target may be more problematic. Often, to increase the efficiency of the transfer of weight, drillers may rock the pipe while sliding using different types of systems.

[0091] Using mud motor behavior and its kinematics with surface measured data (i.e., surface torque), a user can automatically perform the pipe rocking similar to the method described above. This may increase the ability to maintain sufficient ROP and still deliver a desired toolface orientation. In addition, this understanding of the mud motor behavior allows the conception of an automated slide detection which is critical to any steering advisor workflow.

[0092] The method may be used to detect in real-time the slides performed by the mud motor 300 based (e.g., solely) on analyzing the surface data. This method is developed based on understanding the mud motor physical behavior in addition to the changes in torque, RPM, WOB, ROP, differential pressure, etc. Figures 15A-15J illustrate graphs showing real-time mud motor automatic slide detection, according to an embodiment.

[0093] Abnormal pressure detection [0094] Abnormal standpipe pressure is one of the indicators of a disfunction in the drilling fluid hydraulic system. This condition is defined as an observation of any change in standpipe pressure due to undesired events occurring during the well construction process. A greater perception of the mud motor physics allows for deriving an automated abnormal pressure detection based on a probabilistic approach. The model may have different physics-based priors depending on whether the mud motor 300 is present or not. In the case when the mud motor 300 is present, the model may separate the slide drilling from the rotary drilling and use the motor pressure knowledge to obtain a prior approximation. The physics-based prior will look like:

[0095] Real-Time Mud Motor Efficiency and Degradation

[0096] In spite of mud motors 300 being one of the most commonly used tools inside the BHA 260 as mentioned previously, there is still a lack of reliable procedures for monitoring and maintaining the well-being of the mud motors 300 during well construction. This problem results in maintenance and fleet management costs as well as unpredictable and costly failures. In addition, there may be, in some cases, efficiency losses due to the degradation of the mud motor 300 over time. The method presented here aims to estimate, in real time, the energy output and the efficiency of the mud motor 300 based on analyzing both surface and downhole data combined with the knowledge of the mud motor physics.

[0097] The method may rely on defining a motor wear indicator by comparing the expected RPM based on the motor power section specifications and the downhole output RPM measured with downhole tools below the motor 300. Figures 16A and 16B illustrate an example of the real time motor efficiency analysis from a drilling operation with a degradation rate of about 3.7%/100 ft. Figure 16A shows a near-constant flow rate and a slight variation in standpipe pressure. Yet, the RPM reduction can be seen clearly in Figure 16B suggesting that this RPM reduction is indeed the result of a mud motor degradation. This degradation rate may be used to assess the expected ROP reduction and also the expected durability of the mud motor 300 to avoid costly failures.

[0098] Workflows for determining a [0099] The workflows for determining a may be divided into two categories: (1) real-time execution workflows, and (2) planning workflows.

[0100] Real-time execution workflows:

[0101] The real-time execution workflows for deriving and using a for understanding the torque transmission from surface to the lower part of the BHA below the motor 300 may be based at least partially on updating the value of a with available measurement of torque downhole and/or using a model of a variations with respect to drilling parameters including temperature and pressure and mud motor conditions.

[0102] Figure 17 illustrates a flowchart of a method for deriving the downhole torque measurement below the mud motor 300, according to an embodiment. More particularly, Figure 17 may be used to determine (e.g., estimate) the torque transmission coefficient a during execution using downhole torque measurements.

[0103] Figure 18 illustrates a flowchart of another method for deriving the downhole torque measurement below the mud motor 300, according to an embodiment. The method in Figure 18 may be based at least partially upon artificial intelligence (Al) and/or machine learning (ML) in real-time. The model may be trained on available offset data prior to the well construction execution.

[0104] Planning Workflows

[0105] For the planning, a similar AI/ML method may be used. In addition, one or more finite element analysis (FEA) models and/or analytical models may also or instead be used.

[0106] How to Use the Derived Value of a

[0107] In one embodiment, the a values may be used during execution for:

• displaying the value of the torque transmission coefficient to better select the operating parameters by the user.

• to automatically determine or detect a mud motor degradation coefficient.

• to automatically determine or detect a sliding mode from a rotating mode.

• to automatically determine or derive alarms for abnormal pressure detection.

• to select appropriate: o mud motors o interference fit between the rotor and the stator o rotors and their type of polishing o rubbers for the stator o drilling fluids o BHAs o derive optimized planned trajectory o derive appropriate drilling parameters ranges

[0108] Thus, the present disclosure provides a method of calculating the torque transmission coefficient a from the top drive to below the motor 300 using downhole torque measurement below the motor 300. The method may also be used to derive, in real-time, the value of the torque transmission coefficient a via a ML/ Al model f using the function a = f (Temp, Pressure, RPM, W0B, P_a, flow). The method may also be used to derive, in realtime, the value of the torque transmission coefficient a via physical model based on analytical model g using the function a — g(Temp, Pressure, RPM, WOB, P_a, flow). The method may also be used to derive, in real-time, the value of the torque transmission coefficient a via Finite element model FE using the function a = FE(Temp, Pressure, RPM, WOB, EP_a, flow) . The method may also be used to display the variation of torque transmission coefficient a in either a log view or a direct parameter view. The method may also be used to determine the mud motor degradation coefficient using the derived value of the torque transmission coefficient a. The method may also be used to detect (e.g., automatically) the sliding mode and the rotating mode while performing directional drilling with the mud motor 300 using the derived value of the torque transmission coefficient a. The method may also be used to derive alarms regarding abnormal pressure detection using the derived value of the torque transmission coefficient a. The method may also be used to derive the torque transmission coefficient a by analyzing offset data fed inside a ML/ Al model. The method may also be used to derive the torque transmission coefficient a by analyzing offset data fed inside an analytical model depending on the drilling parameters and the drilling conditions. The method may also be used to derive the torque transmission coefficient a by analyzing offset data fed inside a finite element analysis (FEA) model depending on the drilling parameters and the drilling conditions. The method may also be used to select one or more of the following using the computed value of torque transmission coefficient a :

• type of mud motor power section;

• value of the power section interference fit to be used;

• type of rubber to be used; • type of rotor and the polishing scheme;

• type of drilling fluids; and/or

• the range of drilling parameters to be used including RPM, WOB, differential pressure, flow rate.

[0109] The method may also be used to derive a planned trajectory of a wellbore using the computed torque transmission coefficient a. The method may also be used to derive a BHA to drill the wellbore using the computed torque transmission coefficient a. The method may also be used to derive one or more pipe rocking parameters based on the computed torque transmission coefficient a.

[0110] Figure 19 illustrates a flowchart of another method 1900 for deriving the downhole torque measurement below the mud motor 300 (e.g., at the drill bit 360), according to an embodiment. An illustrative order of the method 1900 is provided below; however, one or more portions of the method 1900 may be performed in a different order, performed simultaneously, combined, repeated, or omitted.

[OHl] The method 1900 may include receiving an on-bottom pressure, as at 1905. The method 1900 may also include receiving an off-bottom pressure, as at 1910. The on-bottom pressure may include a pressure when the BHA 260 is on the bottom of the wellbore 230 (e.g., during drilling). The off-bottom pressure may include the pressure when the BHA 260 is off of the bottom of the wellbore 230 (e.g., when not drilling). The on-bottom pressure and/or the off-bottom pressure may be measured by a pressure sensor. The pressure sensor may be at the surface 220 above the wellbore 230 (e.g., on the drilling rig 210).

[0112] The method 1900 may also include determining a differential pressure, as at 1915. The differential pressure may be based upon the on-bottom pressure and the off-bottom pressure. The differential pressure may be a difference between the on-bottom pressure and the off-bottom pressure.

[0113] The method 1900 may also include receiving a surface torque, as at 1920. The surface torque may include a torque introduced to the drill string 250 by the top drive 212 (or other rotation device). The surface torque may be measured by a torque sensor. The torque sensor may be on the drilling rig 210 (e.g., coupled to the top drive 212).

[0114] The method 1900 may also include determining a torque transmission coefficient, as at 1925. The torque transmission coefficient may be based at least partially upon the differential pressure measurement and the surface torque measurement. The torque transmission coefficient may be a positive unitless coefficient that is less than 1 and represents the torque between the rotor 322 and the stator rubber 326 in the mud motor 300.

[0115] In one embodiment, determining the torque transmission coefficient may include multiplying a torque slope of the mud motor 330 and the differential pressure measurement to produce a first value. Determining the torque transmission coefficient may also include subtracting the first value from a torque below the mud motor 230 to produce a second value. Determining the torque transmission coefficient may also include dividing the second value by the surface torque to produce the torque transmission coefficient.

[0116] The torque transmission coefficient may also be determined based at least partially upon a temperature in the wellbore 230 (e.g., measured by the BHA 260), a pressure in the wellbore 230 (e.g., measured by the BHA 260), a rate of rotation of the drill string 250 and/or BHA 260 in the wellbore 230, a weight on the drill bit 360 in the wellbore 230, the differential pressure measurement, a flow rate of a fluid into the wellbore 230, or a combination thereof. The torque transmission coefficient may be determined using a machine learning (ML) artificial intelligence (Al) model, a physical model, a finite element (FE) model, or a combination thereof.

[0117] The method 1900 may also include determining a total torque output, as at 1930. The total torque output may be determined at the BHA 260 (e.g., at the drill bit 360). The total torque output may be determined based at least partially upon the differential pressure measurement, the surface torque measurement, the torque transmission coefficient, or a combination thereof. The total torque output may be determined by a model.

[0118] Determining the total torque output may include multiplying a torque slope of the mud motor 330 and the differential pressure measurement to produce a first value. Determining the total torque output may also include multiplying the surface torque measurement and the torque transmission coefficient to produce a second value. Determining the total torque output may also include adding the first value and the second value to produce the total torque output.

[0119] The method 1900 may also include determining that a performance of the mud motor is degrading, as at 1940. The determination may be in response to the total torque output deviating from an expected torque output by more than a predetermined torque threshold.

[0120] The method 1900 may also include determining that the drill string 250 is sliding in the wellbore 230, as at 1945. The determination may be in response to the total torque output being less than a predetermined torque threshold. The method 1900 may also or instead include determining that the drill string 250 is rotating in the wellbore 230, as at 1950. The determination may be in response to the total torque output being greater than the predetermined torque threshold. [0121] The method 1900 may also include determining that the BHA 260 has encountered an abnormal pressure event in the subterranean formation 240, as at 1955. The determination may be in response to the torque transmission coefficient, the total torque output, or both. The abnormal pressure event may be or include a region of the subterranean formation 240 that has a pressure that is greater than a predetermined upper pressure threshold or less than a predetermined lower pressure threshold. The abnormal pressure event may alter the behavior of the BHA 260 (e.g., the mud motor 300). As described below, the abnormal pressure event may be an indication of an influx, a blockage, a bit-balling event, the mud motor 300 stalling, downhole losses, or a combination thereof.

[0122] Determining that the BHA 260 has encountered an abnormal pressure event may include measuring a first standpipe pressure (SPP) at the surface 220. Determining that the BHA 260 has encountered an abnormal pressure event may also include determining a second SPP at the surface 220. Determining that the BHA 260 has encountered an abnormal pressure event may also include determining that first SPP differs from the second SPP by more than a predetermined pressure.

[0123] Determining the second SPP may include multiplying a first constant and a flow rate squared to produce a first value. The flow rate is of a fluid being pumped into the wellbore 230. Determining the second SPP may also include multiplying a second constant, the flow rate squared, and a depth of the drill bit 360 to produce a second value. Determining the second SPP may include multiplying a third constant and the total torque output to produce a third value. Determining the second SPP may include multiplying a fourth constant and a weight on the drill bit 360 to produce a fourth value. Determining the second SPP may include adding the first value, the second value, the third value, the fourth value, and a fifth constant to produce the second SPP. The first, second, third, fourth, and fifth constants are different.

[0124] The method 1900 may also include determining a torque transmission issue, as at 1960. The torque transmission issue may be an issue or problem that prevents the at least a portion of the torque from being transmitted from the surface (e.g., the top drive 212) to the drill bit 360. The torque transmission issue may be determined based at least partially upon the abnormal pressure event, a mechanical specific energy (MSE), or both. [0125] The method 1900 may also include generating a display, as at 1965. The display may show the torque transmission coefficient, the total torque output, the performance of the mud motor 300, the location(s) where the drill string 250 is slipping and/or rotating in the wellbore 230, the location(s) of abnormal pressure events in the wellbore 230, the location(s) of torque transmission issues, or a combination thereof.

[0126] The method 1900 may also include determining or performing a (e.g., wellsite) action, as at 1970. The wellsite action may be determined or performed based at least partially upon the torque transmission coefficient, the total torque output, the performance of the mud motor 300, the slipping and/or rotating of the drill string 250, the abnormal pressure events, the torque transmission issues, or a combination thereof. In one embodiment, performing the wellsite action may include generating and/or transmitting a signal (e.g., using the computing system 1400) which instructs or causes a physical action to take place. In another embodiment, performing the wellsite action may include physically performing the action (e.g., either manually or automatically).

[0127] Illustrative physical actions may include, but are not limited to, varying the off-bottom pressure, varying the on-bottom pressure, varying the weight on the drill bit 360, varying a rate of rotation of the drill string 250 at the surface 220 (e.g., using the top drive 212), varying an amount of torque introduced into the drill string 250 at the surface 220 (e.g., using the top drive 212), varying a toolface setting of the BHA 260 (e.g., while sliding), varying the flow rate of the fluid being pumped into the wellbore 230, checking for pack-off, checking for plugged nozzles in the drill bit 360, checking for blockages in the drill string 250 and/or BHA 260, determining location(s) of washouts in the wellbore 230, varying the drilling mud, circulating one or more pills to vary the pressure in the wellbore 230, stopping drilling, changing the BHA 260, checking the pumps for leaks or damage, or a combination thereof.

[0128] In some embodiments, the methods of the present disclosure may be executed by a computing system. Figure 20 illustrates an example of such a computing system 2000, in accordance with some embodiments. The computing system 2000 may include a computer or computer system 2001A, which may be an individual computer system 2001A or an arrangement of distributed computer systems. The computer system 2001A includes one or more analysis modules 2002 that are configured to perform various tasks according to some embodiments, such as one or more methods disclosed herein. To perform these various tasks, the analysis module 2002 executes independently, or in coordination with, one or more processors 2004, which is (or

15 are) connected to one or more storage media 2006. The processor(s) 2004 is (or are) also connected to a network interface 2007 to allow the computer system 2001 A to communicate over a data network 2009 with one or more additional computer systems and/or computing systems, such as 200 IB, 2001C, and/or 200 ID (note that computer systems 200 IB, 2001C and/or 200 ID may or may not share the same architecture as computer system 2001 A, and may be located in different physical locations, e.g., computer systems 2001A and 2001B may be located in a processing facility, while in communication with one or more computer systems such as 2001C and/or 200 ID that are located in one or more data centers, and/or located in varying countries on different continents).

[0129] A processor may include a microprocessor, microcontroller, processor module or subsystem, programmable integrated circuit, programmable gate array, or another control or computing device.

[0130] The storage media 2006 may be implemented as one or more computer-readable or machine-readable storage media. Note that, while in the example embodiment of Figure 20 storage media 2006 is depicted as within computer system 2001A, in some embodiments, storage media 2006 may be distributed within and/or across multiple internal and/or external enclosures of computing system 2001A and/or additional computing systems. Storage media 2006 may include one or more different forms of memory including semiconductor memory devices such as dynamic or static random access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), electrically erasable and programmable read-only memories (EEPROMs) and flash memories, magnetic disks such as fixed, floppy and removable disks, other magnetic media including tape, optical media such as compact disks (CDs) or digital video disks (DVDs), BLURAY® disks, or other types of optical storage, or other types of storage devices. Note that the instructions discussed above may be provided on one computer-readable or machine-readable storage medium, or may be provided on multiple computer-readable or machine-readable storage media distributed in a large system having possibly plural nodes. Such computer-readable or machine-readable storage medium or media is (are) considered to be part of an article (or article of manufacture). An article or article of manufacture may refer to any manufactured single component or multiple components. The storage medium or media may be located either in the machine running the machine-readable instructions, or located at a remote site from which machine-readable instructions may be downloaded over a network for execution. [0131] In some embodiments, computing system 2000 contains one or more torque module(s) 2008. It should be appreciated that computing system 2000 is merely one example of a computing system, and that computing system 2000 may have more or fewer components than shown, may combine additional components not depicted in the example embodiment of Figure 20, and/or computing system 2000 may have a different configuration or arrangement of the components depicted in Figure 20. The various components shown in Figure 20 may be implemented in hardware, software, or a combination of both hardware and software, including one or more signal processing and/or application specific integrated circuits.

[0132] Further, the steps in the processing methods described herein may be implemented by running one or more functional modules in information processing apparatus such as general purpose processors or application specific chips, such as ASICs, FPGAs, PLDs, or other appropriate devices. These modules, combinations of these modules, and/or their combination with general hardware are included within the scope of the present disclosure.

[0133] Computational interpretations, models, and/or other interpretation aids may be refined in an iterative fashion; this concept is applicable to the methods discussed herein. This may include use of feedback loops executed on an algorithmic basis, such as at a computing device (e.g., computing system 2000, Figure 20), and/or through manual control by a user who may make determinations regarding whether a given step, action, template, model, or set of curves has become sufficiently accurate for the evaluation of the subsurface three-dimensional geologic formation under consideration.

[0134] The foregoing description, for purpose of explanation, has been described with reference to specific embodiments. However, the illustrative discussions above are not intended to be exhaustive or limiting to the precise forms disclosed. Many modifications and variations are possible in view of the above teachings. Moreover, the order in which the elements of the methods described herein are illustrated and described may be re-arranged, and/or two or more elements may occur simultaneously. The embodiments were chosen and described in order to best explain the principles of the disclosure and its practical applications, to thereby enable others skilled in the art to best utilize the disclosed embodiments and various embodiments with various modifications as are suited to the particular use contemplated.

Claims

CLAIMS What is claimed is:

1. A method for determining a total torque output at a drill bit, the method comprising: receiving an on-bottom pressure and an off-bottom pressure; determining a differential pressure based upon the on-bottom pressure and the off-bottom pressure; receiving a surface torque; determining a torque transmission coefficient based at least partially upon the differential pressure and the surface torque; and determining the total torque output at the drill bit based at least partially upon the differential pressure, the surface torque, and the torque transmission coefficient.

2. The method of claim 1, wherein the on-bottom pressure and the off-bottom pressure are measured by a pressure sensor at a surface above a wellbore, wherein the on-bottom pressure comprises a pressure when a bottom hole assembly (BHA) is on a bottom of the wellbore, and wherein the off-bottom pressure comprises the pressure when the BHA is off of the bottom of the wellbore.

3. The method of claim 1 , wherein the surface torque is measured by a torque sensor, wherein the torque sensor is coupled to a top drive, wherein the surface torque comprises a torque introduced to a drill string by the top drive, wherein the drill string extends into a wellbore, wherein a bottom hole assembly (BHA) is coupled to a lower end of the drill string, and wherein the BHA comprises a mud motor and the drill bit.

4. The method of claim 1, wherein the torque transmission coefficient is a positive unitless coefficient that is less than 1 and represents a torque transmission between stator rubber and a rotor in a mud motor.

5. The method of claim 1, wherein determining the torque transmission coefficient comprises: receiving a torque below a mud motor; multiplying a torque slope of the mud motor and the differential pressure to produce a first value; subtracting the first value from the torque below the mud motor to produce a second value; and dividing the second value by the surface torque to produce the torque transmission coefficient.

6. The method of claim 1, wherein the torque transmission coefficient is also determined based at least partially upon a temperature in a wellbore, a pressure in the wellbore, a rate of rotation of a drill string in the wellbore, a weight on the drill bit in the wellbore, and a flow rate of a fluid pumped into the wellbore.

7. The method of claim 1, wherein determining the total torque output comprises: multiplying a torque slope of a mud motor and the differential pressure to produce a first value; multiplying the surface torque and the torque transmission coefficient to produce a second value; and adding the first value and the second value to produce the total torque output.

8. The method of claim 1, further comprising displaying the total torque output.

9. The method of claim 1, further comprising performing a wellsite action in response to the total torque output.

10. The method of claim 9, wherein the wellsite action comprises varying the on-bottom pressure, varying the off-bottom pressure, varying an amount of torque introduced into a drill string, varying a rate of rotation of the drill string, varying a weight on the drill bit, varying a toolface setting of a bottom hole assembly (BHA), varying a flow rate of a fluid being pumped into a wellbore, or a combination thereof.

1 1. A computing system, comprising: at least one processor; and a storage medium connected to the at least one processor, the storage medium including instructions for configuring the computing system to perform operations comprising: receiving an on-bottom pressure and an off-bottom pressure that are measured by a pressure sensor, wherein the pressure sensor is at a surface above a wellbore, wherein the on-bottom pressure comprises a pressure when a bottom hole assembly (BHA) is on a bottom of the wellbore, and wherein the off-bottom pressure comprises the pressure when the BHA is off of the bottom of the wellbore; determining a differential pressure comprising a difference between the on-bottom pressure and the off-bottom pressure; receiving a surface torque measured by a torque sensor, wherein the surface torque comprises a torque introduced to a drill string by a top drive, wherein the torque sensor is coupled to the top drive, wherein the drill string extends into the wellbore, wherein the BHA is coupled to a lower end of the drill string, and wherein the BHA comprises a mud motor and a drill bit; determining a torque transmission coefficient based at least partially upon the differential pressure and the surface torque, wherein the torque transmission coefficient is a positive unitless coefficient that is less than 1 and represents a torque between a rotor and stator rubber in the mud motor; and determining a total torque output at the drill bit based at least partially upon the differential pressure, the surface torque, and the torque transmission coefficient.

12. The computing system of claim 11, wherein the operations further comprise determining that performance of the mud motor is degrading in response to the total torque output deviating from an expected torque output by more than a predetermined torque threshold.

13. The computing system of claim 11, wherein the operations further comprise determining that the drill string is sliding in the wellbore in response to the total torque output being less than a predetermined torque threshold.

14. The computing system of claim 1 1 , wherein the operations further comprise determining that the drill string is rotating in the wellbore in response to the total torque output being greater than a predetermined torque threshold.

15. The computing system of claim 11, wherein determining the total torque output comprises: multiplying a torque slope of the mud motor and the differential pressure to produce a first value; multiplying the surface torque and the torque transmission coefficient to produce a second value; and adding the first value and the second value to produce the total torque output.

16. A non-transitory machine-readable storage medium having instructions stored thereon to configure a processor of a computing system to perform operations, the operations comprise: receiving an on-bottom pressure and an off-bottom pressure that are measured by a pressure sensor, wherein the pressure sensor is at a surface above a wellbore, wherein the on-bottom pressure comprises a pressure when a bottom hole assembly (BHA) is on a bottom of the wellbore, and wherein the off-bottom pressure comprises the pressure when the BHA is off of the bottom of the wellbore; determining a differential pressure comprising a difference between the on-bottom pressure and the off-bottom pressure; receiving a surface torque measured by a torque sensor, wherein the surface torque comprises a torque introduced to a drill string by a top drive, wherein the torque sensor is coupled to the top drive, wherein the drill string extends into the wellbore, wherein the BHA is coupled to a lower end of the drill string, and wherein the BHA comprises a mud motor and a drill bit; determining a torque transmission coefficient based at least partially upon the differential pressure and the surface torque, wherein the torque transmission coefficient is a positive unitless coefficient that is less than 1 and represents a torque between a rotor and stator rubber in the mud motor; determining a total torque output at the drill bit based at least partially upon the differential pressure, the surface torque, and the torque transmission coefficient, wherein the total torque output is determined by a model, and wherein determining the total torque output comprises: multiplying a torque slope of the mud motor and the differential pressure to produce a first value; multiplying the surface torque and the torque transmission coefficient to produce a second value; and adding the first value and the second value to produce the total torque output; and generating a signal in response to the total torque output, wherein the signal causes one or more parameters to vary, and wherein the one or more parameters comprise the on -bottom pressure, the off-bottom pressure, an amount of the torque introduced into the drill string by the top drive, a weight on the drill bit, a rate of rotation of the drill string, the BHA, or both, a toolface setting of the BHA, a flow rate of a fluid being pumped into the wellbore, or a combination thereof.

17. The non-transitory machine-readable storage medium of claim 16, wherein determining the torque transmission coefficient comprises: receiving a torque below the mud motor; multiplying the torque slope of the mud motor and the differential pressure to produce a third value; subtracting the third value from the torque below the mud motor to produce a fourth value; and dividing the fourth value by the surface torque to produce the torque transmission coefficient.

18. The non-transitory machine-readable storage medium of claim 16, wherein the torque transmission coefficient is determined also based at least partially upon a temperature in the wellbore, a pressure in the wellbore, a rate of rotation of the drill string or the BHA in the wellbore, a weight on the drill bit in the wellbore, and the flow rate of the fluid pumped into the wellbore, and wherein the torque transmission coefficient is determined using artificial intelligence (Al), machine-learning (ML), or both.

19. The non-transitory machine-readable storage medium of claim 16, wherein the operations further comprise determining that the BHA has encountered an abnormal pressure event at least partially in response to the torque transmission coefficient, the total torque output, or both, and wherein determining that the BHA has encountered the abnormal pressure event comprises: measuring a first standpipe pressure (SPP) at the surface; determining a second SPP at the surface; and determining that the first SPP differs from the second SPP by more than a predetermined pressure.

20. The non-transitory machine-readable storage medium of claim 19, wherein determining the second SPP comprises: multiplying a first constant and the flow rate squared to produce a first SPP value; multiplying a second constant, the flow rate squared, and a depth of the drill bit to produce a second SPP value; multiplying a third constant and the total torque output to produce a third SPP value; multiplying a fourth constant and the weight on the drill bit to produce a fourth SPP value; and adding the first SPP value, the second SPP value, the third SPP value, the fourth SPP value, and a fifth constant to produce the second SPP, wherein the first, second, third, fourth, and fifth constants are different.