System and method to optimize damping performance by selectively generating frequency dependent stop and passbands

Abstract

A method and system for damping high frequency torsional oscillations (HFTO) of a downhole system including a motorized or non-motorized BHA, the damping system including a drilling system disposed at an end of the downhole system in operative connection with a drill bit, and a damping system installed on the drilling system, the damping system comprising a plurality of drill string subs distributed periodically along the drill string, the subs of the plurality designed and configured to put HFTO frequencies in passbands of torsional wave at a damper section, each sub comprising at least one damper element configured to dampen at least one HFTO mode, and stopband features directly adjacent at least some of the damper elements. A model of a drill string within a simulation may be used to determine design aspects of the damper sub that provides passband features and a stopband sub.

Description

[0001] SYSTEM AND METHOD TO OPTIMIZE DAMPING PERFORMANCE BY SELECTIVELY GENERATING FREQUENCY DEPENDENT STOP AND PASSBANDS

[0002] PRIORITY CLAIM

[0003] This application claims the benefit of the filing date of United States Provisional Patent Application Serial No. 63 / 733,168, filed December 12, 2024, the disclosure of which is hereby incorporated herein in its entirety by this reference.

[0004] TECHNICAL FIELD

[0005] The present disclosure generally relates to downhole operations and systems for damping vibrations of the downhole systems during operation.

[0006] BACKGROUND

[0007] Boreholes are drilled deep into the earth for many applications such as carbon dioxide sequestration, geothermal production, and hydrocarbon exploration and production. In all of the applications, the boreholes are drilled such that they pass through or allow access to a material (e.g., a gas or fluid) contained in a formation (e g., a compartment) located below the earth's surface. Different types of tools and instruments may be disposed in the boreholes to perform various tasks and measurements. In general, boreholes are drilled by rotating a drill bit disposed at an end of a drill string. An assembly of tools, including the drill bit, at the end of a drill string may be referred to as a bottom hole assembly (BHA). Drilling a borehole may result in vibratory behavior of the drill string and the BHA.

[0008] In operation, the vibratory behavior of downhole components can impact operational efficiencies. For example, severe vibrations in drill strings and bottomhole assemblies can be caused by cutting forces at the drill bit or by mass imbalances in downhole tools such as mud motors. Impacts from such vibrations can include, but are not limited to, reduced rate of penetration, reduced quality of measurements, and excess fatigue and wear on downhole components, tools, and / or devices. The vibratory behavior of the downhole components may include axial vibrations, lateral vibrations, and torsional vibrations including high-frequency torsional oscillations (HFTO). The drill string and / or BHA may include a damping system including at least one damping element configured to dampen HFTO frequencies. The amplitude of oscillations of some HFTO frequencies for a drill string and BHA may be too low to provide for adequate dampening by the damping system. In other words, the amplitude may be too low to cause the damping element(s) to sufficiently dampen the HFTO frequencies.

[0009] DISCLOSURE

[0010] Embodiments of the present disclosure address the issue of insufficient damping efficiency of torsional vibration dampers against high frequency torsional oscillations (HFTO) in both motorized and non-motorized applications of deep drilling. A type of drill string subs with periodic mechanical properties is proposed to generate stop / passbands in the frequency domain for torsional wave propagation along the drill string. By strategically adjusting the geometry or material properties of the periodic structure according to the associated design guidelines, the amplitudes of HFTO modes at the damper positions can be systematically increased, thereby significantly improving efficiency and performance of damper devices.

[0011] Modifying mode shapes and maximizing the amplitude at the position of a damper element is a new technology used to increase HFTO damping effect. This concept was first described in U. S. Patent No. 11,021,945 B2, issued June 1, 2021, and titled " Method To Mitigate Bit Induced Vibrations By Intentionally Modify ing Mode Shapes Of Drill Strings By Mass Or Stiffness Changes,” and in U. S. 11,692,404 B2, issued July 4, 2023, and titled “Optimized Placement of Vibration Damper Tools through Mode Shape Tuning,” the disclosures of each of which are hereby incorporated herein in their entireties by this reference. However, the mode shape tuning was only targeted in the damper tool section. A systematic and robust drill string design method for adjusting torsional wave propagation behavior along drill strings in different frequency ranges is not disclosed therein. In accordance with embodiments of the present disclosure, to improve damper performance, periodic drill string subs are designed to put HFTO frequencies in passbands of torsional wave at the damper section in both motorized and non-motorized BHA applications. In addition, a further section of periodic subs covering HFTO frequencies in its stopbands is inserted directly after the damper tool in non-motorized BHAs. In this way, the amplitudes of the HFTO mode shapes at the damper elements are increased and the damping effect is significantly amplified in both motorized and non-motorized BHA applications.

[0012] In some embodiments, a damping system for damping HFTO of a downhole system, the downhole system includes a bottom hole assembly. The system includes a drilling system disposed at an end of the downhole system in operative connection with a drill bit. The damping system installed on the drilling system includes a plurality of drill string subs distributed along the drill string, the subs of the plurality designed and configured to put HFTO frequencies in passbands of torsional wave at a damper section, each sub comprising at least one damper element configured to dampen at least one HFTO mode, and one or more of stopband features and passband features directly adjacent at least some of the damper elements.

[0013] In other embodiments, a method of forming a drill string includes determining a range of interest of HFTO frequency bands for analysis of at least a portion of a digital model of a drill string in a simulation, the drill string including a damping system of a plurality of subs distributed periodically along the drill string, each sub comprising at least one damper section. The method includes calculating, in the simulation, HFTO frequency band features for the range of interest for a respective sub along the drill string. The method includes determining, in the simulation, based on the calculating HFTO frequency band features, that a mode shape of at least one HFTO frequency band of the range of interest passes through at least one damper section of the drill string without decaying. The method includes providing, in the simulation, at least one stopband for each of the at least one HFTO stopbands to be positioned above and adjacent to the at least one damper section on the respective sub of the damping system, the stopband reducing a coupling of the drill string at the stopband and reducing a propagation of the mode shape of the at least one HFTO frequency band along the drill string above the stopband. The method includes manufacturing a physical sub including a stopband according to the stopband provided in the simulation. The method includes assembling the manufactured physical sub on a physical drill string.

[0014] In yet other embodiments, a method of forming a drill string includes determining a range of interest of HFTO frequency bands for analysis of at least a portion of a digital model of a drill string in a simulation, the drill string including a damping system of a plurality of subs distributed periodically along the drill string, each sub comprising at least one damper section. The method includes calculating, in the simulation, HFTO frequency band features for the range of interest for a respective sub along the drill string. The method includes determining in the simulation, based on calculating HFTO frequency band features, that a mode shape of at least one HFTO frequency band of the range of interest passes through the at least one damper section of the respective sub of the drill string in the simulation, the mode shape decaying prematurely before traveling an entire length, or at least a significant portion (e.g.. 80%) of the at least one damper section. The method includes providing, in the simulation, a passband to be positioned within the damper section of the respective sub on the drill string, the passband enables the mode shape of the at least one HFTO frequency band to travel the entire length of the damper section of the respective sub along the drill string in the simulation without prematurely decaying. The method includes manufacturing a physical sub including a passband according to the passband provided in the simulation. The method includes assembling the manufactured physical sub on a physical drill string.

[0015] BRIEF DESCRIPTION OF THE DRAWINGS

[0016] For a detailed understanding of the disclosure, reference should be made to the following detailed description, taken in conjunction with the accompanying drawings, in which like elements have generally been designated with like numerals, and wherein:

[0017] FIG. 1 is a schematic diagram of an example drilling system including one or more earth-boring tools.

[0018] FIG. 2A is a schematic diagram of a portion of a drilling string having a damping system in a simulation.

[0019] FIG. 2B is a schematic diagram indicating insufficient damping of HFTO modes with the portion of the drilling string of FIG. 2A.

[0020] FIG. 3A is a schematic diagram of a portion of a drilling string having a modified damping system in the simulation.

[0021] FIG. 3B is a schematic diagram indicating improved damping of HFTO modes with the modified portion of the drilling string of FIG. 3A.

[0022] FIG. 4 is a schematic diagram of a digital model of a drill string including periodic subs in a simulation.

[0023] FIG. 5 is a diagram of calculated passbands and stopbands for a simulation of periodically connected drill pipes of a drill string for various wave frequencies.

[0024] FIG. 6 is a flow chart of a method of forming a drill string according to embodiments of the present disclosure.

[0025] FIG. 7 is a flow chart of a method of forming a drill string according to embodiments of the present disclosure.

[0026] FIG. 8A is a flow chart of a method of varying one or more mechanical properties of a respective sub of a drill string in a simulation according to embodiments of the present disclosure. FIG. 8B is a flow chart of a method of varying one or more mechanical properties of a respective sub of a drill string in a simulation according to embodiments of the present disclosure.

[0027] FIG. 9 is a graphical representation of stopbands and passbands for varying mechanical properties of the representative sub according to embodiments of the present disclosure.

[0028] FIG. 10 is a graphical representation of stopbands and passbands for varying mechanical properties of the representative sub according to embodiments of the present disclosure.

[0029] FIG. 11 is a graphical representation of stopbands and passbands for varying mechanical properties of the representative sub according to embodiments of the present disclosure.

[0030] FIGS. 12A and 12B are graphical representations of stopbands and passbands for varying mechanical properties of the representative sub according to embodiments of the present disclosure.

[0031] MODE(S) FOR CARRYING OUT THE INVENTION FIG. l is a schematic diagram of an example of a drilling system 10 that may utilize one or more embodiments of an earth-boring tool and methods for drilling wellbores in a subterranean formation. The drilling system 10 may include an earth-boring tool, such as earth-boring tool 100, which is advanced through a subterranean formation by being rotated from an assembly on the surface. The drilling system 10 includes a drilling rig 11, which may include a derrick 12, a derrick floor 14, a draw works 16, a hook 18, a swivel 20, a Kelly joint 22, and a rotary table 24. A drill string 30, which may include drill pipe sections 32 and drill collar sections 34, extends downward from the drilling rig 11 into a wellbore 40. Various components of the distal end of the drill string 30, including the earth-boring tool 100, are collectively referred to in the industry as a “bottom hole assembly” (BHA) 50. The BHA 50 may include a number of measurement and analysis systems, such as a measurement-while-drilling (MWD) system or a logging-while-drilling (LWD) system. These systems may include various sensors for taking measurements.

[0032] During drilling operations, drilling fluid or “mud” may be circulated from a source 60 of drilling fluid through a fluid pump 62, through a desurger 64, and through a fluid supply line 66 into the swivel 20. The drilling fluid flows through the Kelly joint 22 into an axial central bore in the drill string 30. The fluid exits the drill string 30 via the earth-boring tool 100. More specifically, the fluid exits the earth-boring tool 100 through fluid ports or nozzles on a distal end of the earth-boring tool 100 near the point of contact with the subterranean formation. Upon exiting the earth-boring tool 100, the drilling fluid flows toward the surface of the formation through an annular space 42 between the outer surface of the drill string 30 and the inner surface of the wellbore 40. Upon reaching the surface, the fluid is returned to the fluid source 60 through a fluid return line 68. As discussed above, drilling operations may experience HFTO vibration frequencies, which may be harmful to the BHA and / or drill string.

[0033] To mitigate harmful HFTO frequency modes during deep drilling, different torsional vibration dampers such as fluid dampers, friction dampers, eddy current dampers, torque-based dampers, and the like may be used in damper sections of a drill string. For example, the torsional vibration dampers may include the dampers described in U. S. Patent App. Pub. No. 20200018377 entitled “Bit support assembly incorporating damper for high frequency torsional oscillation,” which is incorporated by reference herein in its entirety’. The dampers are often deployed in the BHA. However, the vibration amplitudes of HFTO modes at the damper position are sometimes undesirably low because the mode shape does not quickly decay above the BHA section due to absence of the decoupling effect by a motor in applications with a non-motorized BHA, or decays too quickly ahead of the damper section in both motorized and non-motorized BHAs. Both cases lead to insufficient damping effects against HFTO.

[0034] FIG. 2A is a schematic of a typical example of a non-motorized BHA 200 for a downhole simulation. The BHA 200 includes a damping section 220 along the drill string 210. The damping section 220 includes damper elements 222 and spacers elements 224. The BHA 200 exhibits both problem cases (e.g., the mode shape does not quickly decay above the BHA section due to absence of the decoupling effect and the mode shape decays too quickly ahead of the damper section) for HFTO modes as illustrated in the graph 260 of FIG. 2B of the simulation. The alternating arrangement of four damper elements 222 and four spacer elements 224 creates an unfavorable periodic structure in the damping section 220. The 252 Hz HFTO mode 262 is then located in a passband of the periodic structure, and the vibration wave at this frequency can pass through the damping section 220. The amplitude of the 252 Hz HFTO mode 262 is inadequate to be effectively damped by the damper elements 222 of the damping section 220 resulting in the ineffective damping (e.g., be less than 0.25% damping) of the 252 Hz HFTO mode 262. Further, due to the lack of motor decoupling, or a stopband design above the damping section 220 as discussed herein, the wave of the 252 Hz HFTO mode 262 continues to travel and has a non-decaying mode shape until it reaches the heavy weight drill pipes (not shown) of the simulation drill string 210.

[0035] In contrast, the 306 Hz HFTO mode 264 falls in a stopband of the simulation drill string 210. exhibiting a rapid amplitude decay within the damping section 220. In other words, the 306 Hz HFTO mode 264 decays prematurely resulting in the amplitude of the 306 Hz HFTO mode 264 being too low (e.g., inadequate) for the damper elements 222 to effectively dampen the 306 Hz HFTO mode 264 as the mode travels the length of the damping section 220. As indicated in FIG. 2B, the damping section 220 does not adequately dampen (e.g., damping less than 0.5%) the 306 Hz HFTO mode 264. This problem can be solved by modifying the torsional wave propagation behavior using the design methods disclosed herein.

[0036] Embodiments of the present disclosure are proposed to address these problems. FIG. 3A is a schematic of an example of a non-motorized BHA 300 in a simulation that includes a damping section 220 along the drill string 210 that has been modified to address the premature decay of the amplitude of the 306 Hz HFTO mode 264. The spacing of the four spacer elements 224 between the four damper element 222 has been modified, with respect to the damping section 220 of FIG. 2A, based on the methodology disclosed herein. As a result, the amplitude of the 306 Hz HFTO mode 264 does not prematurely decay as it travels the length of the damping section 220 of the simulated drill string 210 and the damping section 220 provides sufficient damping (e.g., greater than 1.8% damping) as shown in the graph 360 of the simulation in FIG. 3B.

[0037] The simulated non-motorized BHA 300 also includes a stopband 230 located adjacent and up hole of the damping section 220 along the drill string 210 of the simulation. The stopband 230 reduces the coupling of the drill string 210 with the damping section 220. The reduction of coupling may effectively decouple the damping section 220 from the simulated drill string 210 to reduce, or even prevent, the 252 Hz HFTO mode 262 from propagating along the drill string 210 above the stopband 230. The addition of the stopband creating structure 230 results in the effective (e.g., above 4%) damping of the 252 Hz HFTO mode 262 as shown in FIG. 3B. FIG. 4 shows a schematic of a digital model 400 of a drill string 210 in a simulation. The digital model 400 of the drill string 210 includes drill string subs, referred to herein as a respective sub 215, that are designed with a periodic arrangement along the drill string 210. The respective sub 215 (e.g., periodic sub) includes two alternating segments, namely a first portion 240 and second portion 250 that includes a field thread connection (not shown), that have different mechanical properties (e.g., length, diameter, material, density, and modulus of elasticity). The first portion 240 of the respective sub 215 having a first length 242 and a first diameter 244 and the second portion 250 of the respective sub 215 having a second length 252 and a second diameter 254. The second length 252 of the second portion 250 includes one-half the length of each joint 256 connected to the opposite ends of the first portion 240. Further, the first portion 240 having a first impedance and the second portion having a second impedance. The impedance of each portion 240, 250 of the respective sub 215 may be varied due to varying the material, the density, the modulus of elasticity, or the like as would be appreciated by one of ordinary skill in the art having the benefit of this disclosure.

[0038] In practice, the mechanical properties can also be adjusted by adding more inertia elements or by machining longitudinal slots on the existing subs in a more convenient way instead of manufacturing the entire section. The torsional wave propagation behavior through this periodic structure with repeating mechanical impedance jumps depends on the wave frequency, resulting in alternating passbands and stopbands in the frequency domain. If the wave frequency falls within a passband, the vibrational energy can be transmitted through the periodic structure sufficiently without significant energy loss. Otherwise, the wave frequency is in a stopband and the vibrational amplitude along the periodic structure will decay quickly after several repetitions of segments, generating a decoupling effect.

[0039] The stopbands / passbands of a periodic structure (e.g., respective sub) with an ideally identical circular cross-section in each of the two segments can be determined analytically by the dispersion equation of band gap theory. For other cross-sectional shapes or more complex periodic structures, numerical models using such as the finite element method can be built to perform the band gap analysis. The following text focuses on the band gap analysis using the analytical dispersion equation, which describes the relationship between wave number and wave frequency. The well-established dispersion equation for acoustic / longitudinal wave propagation is found for example in: Wave impedances of drill strings and other periodic media, The Journal of the Acoustical Society of America 112.6 (2002): 2527-2539 by D. S. Drumheller. Due to the equivalence between longitudinal and torsional waves, this equation can be transferred to the torsional direction considered in this disclosure and formulated as:

[0040] cost / cC,t,q +, t2)t ) = cos ( -^A cos ( -)lA -1( -zi.1 -ZA si ■n ( -<,)lA si ■n ( -^AV 7\ / \ c2 / 2 \z2z- \ ) \ c2J where k is wave number, a> is wave frequency, I is length, c is speed of torsional wave and z is impedance. The impedance is further determined by:

[0041] z = pc]

[0042] with the polar moment of inertia J = ~(Do ~ D f°rthe sub cross section with outer diameter Do. inner diameter D.. and density p.

[0043] The speed of torsional wave c depends on the material parameters (shear modulus G and density p) and is calculated by:

[0044] c =! —G

[0045] The stopband / passband calculation using the dispersion equation gives an analytic solution for an infinite repetition of a periodic structure. With a given wave frequency to, the wave number value k is complex in stopbands and real in passbands. The stopband / passband calculation may be used to determine HFTO frequency band features for the HFTO frequencies of interest. FIG. 5 shows an example schematic 500 of calculated bandgap features of periodically connected drill pipes in a simulation, where wave number solutions with real values are presented, formulating passbands 220' (provided by the damping section 220) in the frequency domain and stopbands 230 as gaps in between.

[0046] Calculations of HFTO mode shapes with a drill string model including stopband / passband subs have shown that a significant decoupling effect can also be created with a finite number of periodic elements. The simulation results shown above in FIGS. 3A and 3B illustrate that three elements for the stopband sub 230 after the damping section 220 may be sufficient to generate the decoupling for the HFTO mode shapes. As the number of periodic elements increases, the decoupling provided by the stopband subs becomes more effective. To meet the requirements of decoupling while minimizing the length of the additional periodic structure, the optimum number of periodic elements for a given BHA 300 can be quickly checked by mode shape calculation. In the event that the length is restricted, two elements for the stopband sub 230 after the damping section 220 may be sufficient to generate the decoupling for the HFTO mode shapes. Embodiments of the workflow of the design guidelines for possible parameters of stopband / passband subs are reflected in the flowcharts of FIGS. 6-8B discussed herein.

[0047] FIG. 6 is a flowchart for an embodiment of a method 600 of forming a drill string. At step 610, a range of interest of HFTO frequency bands is determined for an analysis of at least a portion of a digital model of a drill string in a simulation, the drill string including a damping system of a plurality of subs distributed periodically along the drill string, each sub comprising at least one damper section. For example, the drill string 210 includes periodically distributed subs (e g., respective sub 215) with each respective sub including a damper element 222. A range of interest of HFTO frequency bands is determined for the drill string 210 in the simulation.

[0048] At step 620, HFTO frequency bands for the range of interest are calculated in the simulation for a respective sub along the drill string. For example, it is determined whether the HFTO frequency bands within the range of interest are sufficiently dampened by the damping section within the simulation.

[0049] At step 630, based on the calculating HFTO frequency bands features, it is determined in the simulation that a mode shape of at least one HFTO frequency band of the range of interest passes through at least one damper section of the drill string without decaying. Depending on the application, the terms “decaying” or “premature decay” may mean having an amplitude of 95%. 90%, 80%, or 70% of the maximum amplitude. The terms “decaying” or “premature decay” as used herein means having an amplitude between 98% and 70% of the maximum amplitude. For example, it may be determined that a mode of an HFTO frequency band within the range of interest propagates along the drill string 210 in the simulation past the damping section 220.

[0050] At step 640, a stopband is provided in the simulation, the stopband to be positioned above and adjacent to the at least one damper section of the respective sub of the damping system, the stopband reducing the coupling of the drill string at the stopband and reducing propagation of the mode shape of the at least one HFTO frequency band along the drill string about the stopband. The term “reducing a propagation” as using herein means approximately 10% or more of the maximum amplitude. For example, for a non-motorized BHA, a stopband sub 230 is provided in the simulation to reduce the coupling of the drill string 210 to reduce propagation of the mode shape of the HFTO frequency band along the drill string 210. At step 650, a physical sub that includes a stopband according to the stopband provided in the simulation is manufactured and at step 660. the manufactured sub including the stopband is assembled on a physical drill string. For example, the manufactured sub, including the stopband as designed in the simulation, is installed on a physical drill string 30.

[0051] At optional step 670, it is determined in the simulation whether the stopband reduces propagation of mode shapes of a selection of predetermined HFTO frequencies, within the range of interest, along the drill string above the stopband in the simulation. The selection of predetermined HFTO frequencies may depend on the application. If other mode shapes of the selection of predetermined HFTO frequencies propagate past the stopband other design revisions may be necessary. For example, a sensitivity analysis may be performed as discussed herein. Additionally, a measurement above and below the stopband may be used to determine whether the stopband reduced propagation of mode shapes of a selection of frequencies.

[0052] FIG. 7 is a flowchart for an embodiment of a method 700 of forming a drill string. At step 710. a range of interest of HFTO frequency bands is determined for an analysis of at least a portion of a digital model of a drill string in a simulation, the drill string including a damping system of a plurality of subs distributed periodically along the drill string, each sub comprising at least one damper section. For example, the drill string 210 includes periodically distributed subs (e.g., respective sub 215) with each respective sub including a damper element 222. A range of interest of HFTO frequency bands is determined for the drill string 210 in the simulation.

[0053] At step 720, HFTO frequency bands for the range of interest are calculated in the simulation for a respective sub along the drill string. For example, it is determined whether the HFTO frequency bands within the range of interest are sufficiently dampened by the damping section within the simulation.

[0054] At step 730, based on the calculating HFTO frequency bands features, it is determined in the simulation that a mode shape of at least one HFTO frequency band of the range of interest passes through at least one damper section of the drill string, the mode shape decaying prematurely before traveling an entire length of the at least one damper section. For example, it may be determined that a mode of an HFTO frequency band within the range of interest decays prematurely before the mode shape travels the entire length of the damping section 220. At step 740, a passband is provided in the simulation, the passband to be positioned within the damper section of the respective sub on the drill string, the passband is configured to enable the mode shape of the at least one HFTO frequency band to travel the entire length of the damper section of the respective sub along the drill string in the simulation without prematurely decaying. For example, a passband sub (e.g., damping section) 220 is provided in the simulation configured to enable the mode shape of the HFTO frequency band to travel the length of the passband sub without prematurely decaying. In other words, the amplitude of the mode shape is sufficient to enable adequate damping.

[0055] At step 750, a physical sub that includes a passband, according to the passband provided in the simulation, is manufactured and at step 760, the manufactured sub, including the passband, is assembled on a physical drill string. For example, the manufactured sub including the passband, as designed in the simulation, is installed on a physical drill string 30.

[0056] At optional step 770, it is determined in the simulation whether the passband enables mode shapes of all HFTO frequencies, within the range of interest, to travel the entire length of the damper section without prematurely decaying. If other mode shapes prematurely decay, other design revisions to the passband may be necessary. For example, a sensitivity analysis may need to be performed as discussed herein.

[0057] FIG. 8A is a flow chart of an embodiment of a method 800A of a sensitivity analysis that may be used to determine potential design changes to a stopband or passband to reduce and / or prevent the propagation or premature decaying of mode shapes for all HFTO frequencies within the range of interest.

[0058] At step 810, a sensitivity analysis is conducted in the simulation by varying one or more mechanical properties of the respective sub of the drill string in the simulation. For example, the mechanical properties (e.g., length, diameter, material, density, and modulus of elasticity) may be modified to revise the passband 220' and stopband 230 of a respective sub 215.

[0059] At step 815, a first length of a first portion of the respective sub of the drill string in the simulation is varied between a first maximum value and a first minimum value. For example, the first length 242 of the first portion 240 of the respective sub 215 is varied between a first maximum value and a first minimum value. The first maximum value and first minimum value will be determined based on the application as would be appreciated by one of ordinary' skill in the art having the benefit of this disclosure. At step 820, a second length of a second portion of the respective sub of the drill string in the simulation is varied between a value of zero and a second maximum value. For example, the second length 252 of the second portion 250 of the respective sub 215 is varied between the value of zero and second maximum value. The second maximum value will be determined based on the application as would be appreciated by one of ordinary skill in the art having the benefit of this disclosure.

[0060] At optional step 825. a ratio of the second length to the first length in the simulation is varied between a value of zero and a third maximum value. For example, the ratio of the second length 252 to the first length 242 may be varied between a value of zero and the third maximum value. The third maximum value will be determined based on the application as would be appreciated by one of ordinary skill in the art having the benefit of this disclosure.

[0061] At step 850, the stopbands and passbands are represented graphically in the simulation for the HFTO frequencies within the range of interest. For example, a graph may be displayed in the simulation that indicates the passbands 220' and stopband 230 for the respective sub 215 as the mechanical properties are varied. As discussed above, a complex wave number may indicate stopband 230 regions, and a real number may indicate passband regions 220' for the respective sub 215.

[0062] At step 860, the stopband is revised in the simulation for reducing coupling and reducing propagation for the HFTO frequencies within the range of interest or the passband is revised in the simulation to enable the mode shape for the HFTO frequencies within the range of interest to travel the entire length of the damper section without prematurely decaying. For example, the stopband 230 is revised (e.g., redesigned) in the simulation to reduce coupling for all HFTO frequencies of interest to reduce propagation of the mode shape past the stopband sub 230. Likewise, the damping section 220 that provides the passband is revised (e.g., redesign) in the simulation to enable all HFTO frequencies of interest to travel the entire length of the damping section 220 without prematurely decaying. In other words, the amplitudes of the mode shapes will be maintained to ensure proper damping by the damper elements of the damping section 220.

[0063] At step 870. the passband sub according to the revised passband provided in the simulation is manufactured. At step 880, the stopband sub according to the revised stopband provided in the simulation is manufactured. The method 800A of FIG. 8A provides one embodiment of a method of conducting a sensitivity analysis by varying mechanical properties of the respective sub 215 of the digital model 400 of the drill string 210. Other embodiments to vary the mechanical properties exist as would be appreciated by one of ordinary skill in the art having the benefit of this disclosure. For example, FIG. 8B provides an additional embodiment of a sensitivity analysis.

[0064] FIG. 8B is a flow chart of an embodiment of a method 800B of a sensitivity analysis that may be used to determine potential design changes to a stopband or passband to reduce and / or prevent the propagation or premature decaying of mode shape for all HFTO frequencies within the range of interest.

[0065] At step 810, a sensitivity analysis is conducted in the simulation by varying one or more mechanical properties of the respective sub of the drill string in the simulation. For example, or more mechanical properties (e.g., length, diameter, material, density, and modulus of elasticity) may be modified to revise the passband 220' and stopband 230 of a respective sub 215.

[0066] At step 830, a first impedance of a first portion of the respective sub of the drill string in the simulation is varied between a first average value and a first minimum value. The impedance of the first portion 240 of the drill string 210 in the simulation may be varied in several ways. For example, at optional step 835 one or more of a first diameter, a first density, and a first shear modulus of the first portion of the respective sub is varied. For example, the first diameter 244, the density, and / or the shear modulus of the first portion 240 of the respective sub 215 may be varied. As one example, changing the material of the first portion 240 of the respective sub 215 in the simulation may vary the density and / or shear modulus.

[0067] At step 840, a second impedance of a second portion of the respective sub of the drill string in the simulation is varied between a second average value and a first maximum value. The impedance of the second portion 250 of the drill string 210 in the simulation may be varied in several ways. For example, at optional step 845 one or more of a second diameter, a second density, and a second shear modulus of the second portion of the respective sub is varied. For example, the second diameter 254, the density, and / or the shear modulus of the second portion 250 of the respective sub 215 may be varied. As one example, changing the material of the second portion 250 of the respective sub 215 in the simulation may vary the density and / or shear modulus.

[0068] At step 850, the stopbands and passbands are represented graphically in the simulation for the HFTO frequencies within the range of interest. For example, a graph may be displayed in the simulation that indicates the passbands 220' and stopband 230 for the respective sub 215 as the mechanical properties are varied. As discussed above, a complex wave number may indicate stopband 230 regions, and a real number may indicate passband regions 220' for the respective sub 215.

[0069] At step 860, the stopband is revised in the simulation for reducing coupling and reducing propagation for the HFTO frequencies within the range of interest or the passband is revised in the simulation to enable the mode shape for the HFTO frequencies within the range of interest to travel the entire length of the damper section without prematurely decaying. For example, the stopband 230 is revised (e.g., redesigned) in the simulation to reduce coupling for all HFTO frequencies of interest to reduce propagation of the mode shape past the stopband sub 230. Likewise, the damping section 220 that provides the passband is revised (e.g., redesign) in the simulation to enable all HFTO frequencies of interest to travel the entire length of the damping section 220 without prematurely decaying. In other words, the amplitudes of the mode shapes will be maintained to ensure proper damping by the damper elements of the damping section 220.

[0070] At step 870, the passband sub according to the revised passband provided in the simulation is manufactured. At step 880, the stopband sub according to the revised stopband provided in the simulation is manufactured.

[0071] FIG. 9 is a graphical representation 900 of stopbands 230 and passbands 220' for varying mechanical properties of a representative sub in a simulation. Specifically, varying a first length of a first portion of a representative sub, varying a second length of a second portion of a representative sub, and varying the ratio of the second length to the first length. The first length is varied from a maximum value of the first portion to a minimum value of the first portion. The second length is varied from a length of zero (0) to a maximum length for the second portion. The ratio is varied from a value of zero (0) to a maximum length ratio. Calculations of the passband regions 220' and stopband regions 230 are determined as the variations are made in levels (e.g., equal steps). As discussed above, for a given wave frequency ω, a complex number value may indicate a stopband region 230 and a real number value may indicate a passband region 220'.

[0072] Level 0 shown on the y-axis of the graphical representation 900 represents when the first length of the first portion of the representative sub is set at the maximum value and the second length of the second portion of the representative sub and the length ratio are both set at zero (0). Level 100 shown on the y-axis of the graphical representation 900 represents when the first length of the first portion of the representative sub is set at the minimum value and the second length of the second portion of the representative sub and the length ratio are both set at their respective maximum values. Each level on the y-axis is an equal step between level 0 and level 100. The number of levels (e.g., steps) is shown for illustrative purposes and may be varied. For example, the number of levels may be more or less than 100 and in some applications the levels may be 10 equal steps, 20 equal steps, 25 equal steps, 50 equal steps, or a different number of equal steps as would be appreciated by one of ordinary skill in the art having the benefit of this disclosure. The x-axis includes the HFTO frequencies 0 to 400 Hz and are the HFTO frequencies of interest for a particular application. The HFTO frequencies 0 Hz to 400 Hz are shown for illustrative purposes and may be varied as would be appreciated by one of ordinary skill in the art having the benefit of this disclosure. The lowest HFTO frequency may be greater than 0 and the highest HFTO frequency may be lower or higher than 400 Hz.

[0073] FIG. 10 is a graphical representation 1000 of stopbands 230 and passbands 220' for varying mechanical properties of a representative sub in a simulation. Specifically, varying a first length of a first portion of a representative sub and varying a second length of a second portion of a representative sub while the ratio of the second length to the first length remains constant. The first length is varied from a minimum value of the first portion to a maximum value of the first portion. The second length is varied from a minimum value for the second portion to a maximum length for the second portion. Calculations of the passband regions 220' and stopband regions 230 are determined as the variations are made in levels (e.g., equal steps). As discussed above, for a given wave frequency ω, a complex number value may indicate a stopband region 230 and a real number value may indicate a passband region 220’. As discussed above, the number of equal steps (e.g., levels) between the lower and upper bands of variation may be used. Likewise, the HFTO frequencies of interest may vary depending on the application.

[0074] FIG. 11 is a graphical representation 1100 of stopbands 230 and passbands 220' for varying mechanical properties of a representative sub in a simulation. Specifically, varying a first impedance of a first portion of a representative sub and varying a second impedance of a second portion of a representative sub. The impedances may be varied by varying diameter, density, and / or shear modulus of the first and second portions. The first impedance is varied from an average impedance value to a minimum impedance value for the first portion. The second impedance is varied from an average impedance value to a maximum impedance value for the second portion. Calculations of the passband regions 220' and stopband regions 230 are determined as the variations are made in levels (e.g., equal steps). As discussed above, for a given wave frequency co, a complex number value may indicate a stopband region 230 and a real number value may indicate a passband region 220'. As discussed above, the number of equal steps (e.g., levels) between the lower and upper bands of variation may be used. Likewise, the HFTO frequencies of interest may vary depending on the application.

[0075] FIGS. 12A and 12B are graphical representations 1200A, 1200B of stopbands 230 and passbands 220' for varying mechanical properties of a representative sub in a simulation. Specifically, the graphical representations 1200A, 1200B illustrate that that variation of different mechanical properties result in different stopbands regions 230 and passband regions 220'. The graphical presentation 1200A illustrates varying geometric aspects of the representative sub. Depending on the geographic variation, the HFTO frequency 306 Hz may be within the passband region 220' or may be within the stopband region 230. However, also modifying the material (e.g., density or modulus of elasticity ) of the representative sub moves the HFTO frequency 306 Hz entirely within the passband region 220'.

[0076] As disclosed herein, two sections of periodic structures (e.g., a respective sub) may be varied and analyzed in a simulation to improve damper performance. A damping section may be configured, which has a passband feature for HFTO frequencies, may be created by combining damper elements with spacer elements in the damper tool section. Immediately after the damper tool or at a finite distance (e.g., 5 meters, 10 meters, etc.) from the damper tool section, a periodic section may be inserted with a stopband feature for HFTO frequencies. This approach prevents both unfavorable cases, namely premature decay of HFTO frequency modes that may prevent adequate damping and the propagation of HFTO modes with inadequate amplitudes that may not be adequately dampened due to the inadequate amplitudes as described above. In motorized application, the decoupling effect may be provided by the motor itself instead of a stopband sub. The first period structure that includes a passband feature (e.g., the damping section 220) in combination with the motor may be used to dampen HFTO frequencies. The stopband / passband subs disclosed herein may be designed to drastically enhance the damping performance of actual damper devices in both motorized and non-motorized drilling applications by adding simple (dumb iron) drill string elements to create periodic structures in different sections of drill string. The passband design in the damper section is compatible with the existing BHA damper / spacer solution. The stopband sub 230 following the damping section 220 acts as a decoupler regardless of BHA set ups and may be more robust and reliable than the prior art torsional vibration isolators with highly flexible components. For example, the torsional vibration isolator as disclosed in U. S. Patent No. 11,208,853 entitles '‘Dampers for Mitigation of Dow nhole Tool Vibrations and Vibration Isolation Device for Downhole Bottom Hole Assembly." which issued on December 28, 2021, the disclosure which is hereby incorporated herein in its entirety by this reference.

[0077] In addition to the proposed solution, an adaptive design principle can be introduced, for example, several cover sleeve variants with different sizes can be produced and quickly added into the drill string to realize the periodic structure with different frequency ranges of pass / stopbands. Active control of the pass / stopband characteristics is also contemplated.

[0078] Additional non-limiting embodiments of the present disclosure are set forth below. Embodiment 1: A system for damping high frequency torsional oscillations (HFTO) of a downhole system, the downhole system comprising a bottom hole assembly (BHA), the system comprising: a drilling system disposed at an end of the downhole system in operative connection with a drill bit; and a damping system installed on the drilling system, the damping system comprising a plurality of drill string subs distributed along the drill string, the subs of the plurality designed and configured to put HFTO frequencies in passbands of torsional waves at a damper section, each sub comprising at least one damper element configured to dampen at least one HFTO mode, and one or more of stopband features and passband features.

[0079] Embodiment 2: The damping system of Embodiment 1, wherein the one or more stopband features and passband features are directly adjacent to at least some of the damper elements.

[0080] Embodiment 3: The damping system of Embodiment 1 or Embodiment 2, further comprising at least one mode-shape tuning element arranged on the drilling system, wherein the at least one mode-shape tuning element is configured and positioned on the drilling system to modify at least one of a shape of the at least one HFTO mode, a frequency of the at least one HFTO mode, an excitability of the at least one HFTO mode, and a damping efficiency of the at least one damper element. Embodiment 4: A method of forming a drill string, the method comprising: determining a range of interest of high frequency torsional oscillations (HFTO) frequency bands for analysis of at least a portion of a digital model of a drill string in a simulation, the drill string including a damping system of a plurality of subs distributed along the drill string, each sub comprising at least one damper section; calculating, in the simulation, HFTO frequency band features for the range of interest for a respective sub along the drill string; determining, in the simulation, based on the calculating HFTO frequency band features, that a mode shape of at least one HFTO frequency band of the range of interest passes through at least one damper section of the drill string without decaying; providing, in the simulation, a stopband to be positioned above and adjacent to the at least one damper section on the respective sub of the damping system, the stopband reducing a coupling of the drill string at the stopband and reducing a propagation of the mode shape of the at least one HFTO frequency band along the drill string above the stopband; manufacturing a physical sub that includes a stopband according to the stopband provided in the simulation; and assembling the manufactured physical sub on a physical drill string.

[0081] Embodiment 5: The method of Embodiment 4, further comprising determining, in the simulation, whether the stopband reduces propagation of mode shapes for a selection of predetermined HFTO frequencies, within the range of interest, along the drill string above the stopband.

[0082] Embodiment 6: The method of Embodiment 5, further comprising conducting, in the simulation, a sensitivity analysis, based on the determination the stopband does not reduce propagation of at least one mode shape of one HFTO frequency within the range of interest, by varying one or more mechanical properties of the respective sub of the drill string in the simulation. Embodiment 7: The method of Embodiment 6, wherein the varying, in the simulation, one or more mechanical properties of the respective sub of the drill string further comprises one or more of: varying a first length of a first portion of the respective sub of the drill string in the simulation between a first maximum value and a first minimum value, the first length being varied by a designated number of steps between the first maximum value and the first minimum value; varying a second length of a second portion of the respective sub of the drill string in the simulation between a value of zero and a second maximum value, the second length being varied by the designated number of steps between zero and the second maximum value; and varying a ratio of the second length to the first length in the simulation between a value of zero and a third maximum value, the ratio being varied by the designated number of steps between zero and the third maximum value.

[0083] Embodiment 8: The method of Embodiment 7, further comprising: graphically, in the simulation, representing stopbands and passbands for the HFTO frequencies within the range of interest based on varying one or more of the first length, the second length, and the ratio of the second length to the first length; revising, in the simulation, the stopband for reducing coupling and reducing propagation for the HFTO frequencies within the range of interest; and wherein manufacturing the physical sub that includes the stopband according to the revised stopband provided in the simulation.

[0084] Embodiment 9: The method of Embodiment 6, wherein the varying, in the simulation, one or more mechanical properties of the respective sub of the drill string further comprises: varying a first length of a first portion of the respective sub of the drill string in the simulation between a first minimum value and a first maximum value, the first length being varied by a designated number of steps between the first minimum value and the first maximum value; and varying a second length of a second portion of the respective sub of the drill string in the simulation between a second minimum value and a second maximum value, the second length being varied by the designated number of steps between the second minimum value and the second maximum value, wherein a ratio of the second length to the first length remains constant. Embodiment 10: The method of Embodiment 9, further comprising: graphically, in the simulation, representing stopbands and passbands for the HFTO frequencies within the range of interest based on varying the first length and varying the second length; revising, in the simulation, the stopband for reducing coupling and reducing propagation for the HFTO frequencies within the range of interest; and wherein manufacturing the physical sub that includes the stopband according to the revised stopband provided in the simulation.

[0085] Embodiment 11: The method of Embodiment 6, wherein the varying, in the simulation, one or more mechanical properties of the respective sub of the drill string further comprises: varying a first impedance of a first portion of the respective sub of the drill string in the simulation between a first average value and a first minimum value, the first impedance being varied by a designated number of steps between the first average value and the first minimum value; and varying a second impedance of a second portion of the respective sub of the drill string in the simulation between a second average value and a first maximum value, the second impedance being varied by the designated number of steps between the second average value and the first maximum value.

[0086] Embodiment 12: The method of Embodiment 11, wherein: varying the first impedance of the first portion of the respective sub of the drill string of the simulation between the first average value and the first minimum value comprises varying one or more of a first diameter of the first portion of the respective sub, varying a first density of a first material of the first portion of the respective sub, or varying a first shear modulus of the first material of the first portion of the respective sub; and varying the second impedance of the second portion of the respective sub of the drill string of the simulation betw een the second average value and the first maximum value comprises varying one or more of a second diameter of the second portion of the respective sub, varying a second density’ of a second material of the second portion of the respective sub, or varying a second shear modulus of the second material of the second portion of the respective sub.

[0087] Embodiment 13: The method of Embodiment 12, further comprising: graphically, in the simulation, representing stopbands and passbands for the HFTO frequencies within the range of interest based on varying the first impedance and varying the second impedance; revising, in the simulation, the stopband for reducing coupling and reducing propagation for the HFTO frequencies within the range of interest; and wherein manufacturing the physical sub that includes the stopband according to the revised stopband provided in the simulation. Embodiment 14: A method of forming a drill string, the method comprising: determining a range of interest of high frequency torsional oscillations (HFTO) frequency bands for analysis of at least a portion of a digital model of a drill string in a simulation, the drill string including a damping system of a plurality of subs distributed periodically along the drill string, each sub comprising at least one damper section; calculating, in the simulation, HFTO frequency band features for the range of interest for a respective sub along the drill string; determining in the simulation, based on calculating HFTO frequency band features, that a mode shape of at least one HFTO frequency band of the range of interest passes through the at least one damper section of the respective sub of the drill string in the simulation, the mode shape decaying prematurely before traveling an entire length of the at least one damper section; providing, in the simulation, a passband to be positioned within the damper section of the respective sub on the drill string, the passband enables the mode shape of the at least one HFTO frequency band to travel the entire length of the damper section of the respective sub along the drill string in the simulation without prematurely decaying; manufacturing a physical sub that includes a passband according to the passband provided in the simulation; and assembling the manufactured physical sub on a physical drill string.

[0088] Embodiment 15: The method of Embodiment 14, further comprising determining, in the simulation, whether the passband enables mode shapes for a selection of predetermined HFTO frequencies, within the range of interest, to travel the entire length of the damper section of the respective sub without prematurely decaying.

[0089] Embodiment 16: The method of Embodiment 15, further comprising conducting, in the simulation, a sensitivity analysis, based on the determination the passband does not enable the mode shape of at least one HFTO frequency within the range of interest to travel the entire length of the damper section of the respective sub in the simulation, by varying one or more mechanical properties of the respective sub of the drill string in the simulation. Embodiment 17: The method of Embodiment 16, wherein the varying one or more mechanical properties of the respective sub of the drill string in the simulation further comprises one or more of: varying a first length of a first portion of the respective sub of the drill string in the simulation between a first maximum value and a first minimum value, the first length being varied by a designated number of steps between the first maximum value and the first minimum value; varying a second length of a second portion of the respective sub of the drill string in the simulation between a value of zero and a second maximum value, the second length being varied by the designated number of steps between zero and the second maximum value; and varying a ratio of the second length to the first length in the simulation between a value of zero and a third maximum value, the ratio being varied by the designated number of steps between zero and the third maximum value.

[0090] Embodiment 18: The method of Embodiment 17, further comprising: graphically, in the simulation, representing stopbands and passbands for the HFTO frequencies within the range of interest based on varying the first length, varying the second length, and varying the ratio of the second length to the first length; revising, in the simulation, the passband, to enable the mode shape for the HFTO frequencies within the range of interest to travel the entire length of the damper section without prematurely decaying; and wherein manufacturing the physical sub that includes the passband according to the revised passband provided in the simulation.

[0091] Embodiment 19: The method of Embodiment 16, wherein the varying one or more mechanical properties of the respective sub of the drill string in the simulation further comprises: varying a first length of a first portion of the respective sub of the drill string in the simulation between a first minimum value and a first maximum value, the first length being varied by a designated number of steps between the first minimum value and the first maximum value; and varying a second length of a second portion of the respective sub of the drill string in the simulation between a second minimum value and a second maximum value, the second length being varied by the designated number of steps between the second minimum value and the second maximum value, wherein a ratio of the second length to the first length remains constant. Embodiment 20: The method of Embodiment 19, further comprising: graphically representing stopbands and passbands for the HFTO frequencies within the range of interest based on varying the first length and varying the second length; revising, in the simulation, the passband, to enable the mode shape for the HFTO frequencies within the range of interest to travel the entire length of the damper section without prematurely decaying; and wherein manufacturing the physical sub that includes the passband according to the revised passband provided in the simulation.

[0092] Embodiment 21: The method of Embodiment 16, wherein the varying one or more mechanical properties of the respective sub of the drill string in the simulation further comprises: varying a first impedance of a first portion of the respective sub of the drill string in the simulation between a first average value and a first minimum value, the first impedance being varied by a designated number of steps between the first average value and the first minimum value; and varying a second impedance of a second portion of the respective sub of the drill string in the simulation between a second average value and a first maximum value, the second impedance being varied by the designated number of steps between the second average value and the first maximum value.

[0093] Embodiment 22: The method of Embodiment 21, wherein: varying the first impedance of the first portion of the respective sub of the drill string in the simulation between the first average value and the first minimum value comprises varying one or more of a first diameter of the first portion of the respective sub. varying a first density of a first material of the first portion of the respective sub, or varying a first shear modulus of the first material of the first portion of the respective sub; and varying the second impedance of the second portion of the respective sub of the drill string in the simulation between the second average value and the first maximum value comprises varying one or more of a second diameter of the second portion of the respective sub, varying a second density of a second material of the second portion of the respective sub, or varying a second shear modulus of the second material of the second portion of the respective sub. Embodiment 23: The method of Embodiment 22, further comprising: graphically, in the simulation, representing stopbands and passbands for the HFTO frequencies within the range of interest based on varying the first impedance and varying the second impedance; and revising, in the simulation, the passband, to enable the mode shape for the HFTO frequencies within the range of interest to travel the entire length of the damper section without prematurely decaying; and wherein manufacturing the physical sub that includes the passband according to the revised passband provided in the simulation.

[0094] The embodiments of the disclosure described above and illustrated in the accompanying drawings do not limit the scope of the disclosure. Any equivalent embodiments are within the scope of this disclosure. Indeed, various modifications of the disclosure, in addition to those shown and described herein, such as alternate useful combinations of the elements described, will become apparent to those skilled in the art from the description.

Claims

1. CLAIMS2.What is claimed is:

1. A system for damping high frequency torsional oscillations (HFTO) of a downhole system, the downhole system comprising a bottom hole assembly (BHA), the system comprising:4.a drilling system disposed at an end of the downhole system in operative connection with a drill bit; and5.a damping system installed on the drilling system, the damping system comprising a plurality of drill string subs distributed along the drill string, the subs of the plurality designed and configured to put HFTO frequencies in passbands of torsional waves at a damper section, each sub comprising at least one damper element configured to dampen at least one HFTO mode, and one or more of stopband features and passband features.

2. The damping system of claim 1, wherein the one or more stopband features and passband features are directly adjacent to at least some of the damper elements.

3. The damping system of claim 1, further comprising at least one mode-shape tuning element arranged on the drilling system, wherein the at least one mode-shape tuning element is configured and positioned on the drilling system to modify at least one of a shape of the at least one HFTO mode, a frequency of the at least one HFTO mode, an excitability of the at least one HFTO mode, and a damping efficiency of the at least one damper element.

4. A method of forming a drill string, the method comprising: determining a range of interest of high frequency torsional oscillations (HFTO) frequency bands for analysis of at least a portion of a digital model of a drill string in a simulation, the drill string including a damping system of a plurality of subs distributed along the drill string, each sub comprising at least one damper section; calculating, in the simulation, HFTO frequency band features for the range of interest for a respective sub along the drill string;determining, in the simulation, based on the calculating HFTO frequency band features, that a mode shape of at least one HFTO frequency band of the range of interest passes through at least one damper section of the drill string without decaying; providing, in the simulation, a stopband to be positioned above and adjacent to the at least one damper section on the respective sub of the damping system, the stopband reducing a coupling of the drill string at the stopband and reducing a propagation of the mode shape of the at least one HFTO frequency band along the drill string above the stopband;9.manufacturing a physical sub that includes a stopband according to the stopband provided in the simulation; and10.assembling the manufactured physical sub on a physical drill string.

5. The method of claim 4, further comprising determining, in the simulation, whether the stopband reduces propagation of mode shapes for a selection of predetermined HFTO frequencies, within the range of interest, along the drill string above the stopband.

6. The method of claim 5, further comprising conducting, in the simulation, a sensitivity analysis, based on the determination the stopband does not reduce propagation of at least one mode shape of one HFTO frequency within the range of interest, by varying one or more mechanical properties of the respective sub of the drill string in the simulation.

7. The method of claim 6, wherein the varying, in the simulation, one or more mechanical properties of the respective sub of the drill string further comprises one or more of:14.varying a first length of a first portion of the respective sub of the drill string in the simulation between a first maximum value and a first minimum value, the first length being varied by a designated number of steps between the first maximum value and the first minimum value;15.varying a second length of a second portion of the respective sub of the drill string in the simulation between a value of zero and a second maximum value, the second length being varied by the designated number of steps between zero and the second maximum value; and varying a ratio of the second length to the first length in the simulation between a value of zero and a third maximum value, the ratio being varied by the designated number of steps between zero and the third maximum value.

8. The method of claim 7, further comprising:17.graphically, in the simulation, representing stopbands and passbands for the HFTO frequencies within the range of interest based on varying one or more of the first length, the second length, and the ratio of the second length to the first length; revising, in the simulation, the stopband for reducing coupling and reducing propagation for the HFTO frequencies within the range of interest; and18.wherein manufacturing the physical sub that includes the stopband according to the revised stopband provided in the simulation.

9. The method of claim 6, wherein the varying, in the simulation, one or more mechanical properties of the respective sub of the drill string further comprises: varying a first length of a first portion of the respective sub of the drill string in the simulation between a first minimum value and a first maximum value, the first length being varied by a designated number of steps between the first minimum value and the first maximum value; and20.varying a second length of a second portion of the respective sub of the drill string in the simulation between a second minimum value and a second maximum value, the second length being varied by the designated number of steps between the second minimum value and the second maximum value, wherein a ratio of the second length to the first length remains constant.

10. The method of claim 9, further comprising:22.graphically, in the simulation, representing stopbands and passbands for the HFTO frequencies within the range of interest based on varying the first length and varying the second length;23.revising, in the simulation, the stopband for reducing coupling and reducing propagation for the HFTO frequencies within the range of interest; and24.wherein manufacturing the physical sub that includes the stopband according to the revised stopband provided in the simulation.

11. The method of claim 6, wherein the varying, in the simulation, one or more mechanical properties of the respective sub of the drill string further comprises: varying a first impedance of a first portion of the respective sub of the drill string in the simulation between a first average value and a first minimum value, the first impedance being varied by a designated number of steps between the first average value and the first minimum value; and25.varying a second impedance of a second portion of the respective sub of the drill string in the simulation between a second average value and a first maximum value, the second impedance being varied by the designated number of steps between the second average value and the first maximum value.

12. The method of claim 11, wherein:27.varying the first impedance of the first portion of the respective sub of the drill string of the simulation between the first average value and the first minimum value comprises varying one or more of a first diameter of the first portion of the respective sub, varying a first density of a first material of the first portion of the respective sub, or varying a first shear modulus of the first material of the first portion of the respective sub; and28.varying the second impedance of the second portion of the respective sub of the drill string of the simulation between the second average value and the first maximum value comprises varying one or more of a second diameter of the second portion of the respective sub, varying a second density of a second material of the second portion of the respective sub, or varying a second shear modulus of the second material of the second portion of the respective sub.

13. The method of claim 12, further comprising:30.graphically, in the simulation, representing stopbands and passbands for the HFTO frequencies within the range of interest based on varying the first impedance and varying the second impedance;31.revising, in the simulation, the stopband for reducing coupling and reducing propagation for the HFTO frequencies within the range of interest; and wherein manufacturing the physical sub that includes the stopband according to the revised stopband provided in the simulation.

Images