System and method for damping vibrations in a drill string

Abstract

A viscous damper includes an inertia, element which includes an outer surface. The viscous damper further includes a chamber having an inner surface and a volume, the inertia element inside the chamber. The viscous damper further includes a damping fluid in a first portion of the volume, the fluid having a viscosity and a. temperature. The viscous damper further includes a gap between the outer surface of the inertia element and the inner surface of the chamber, the gap filled with the damping fluid. The viscous damper further includes a first material in a. second portion of the volume, wherein the second portion of the volume decreases or increases with a change of the temperature of the damping fluid.

Description

Attorney Docket No.: 65DDE-510066-WO-2 (000229) SYSTEM AND METHOD FOR DAMPING VIBRATIONS IN A DRILL STRING INVENTOR(S): Andreas Hohl (DE), Bastian Sauthoff (DE), Volker Peters (DE), and Sebastian Jung (DE) CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to and the benefit of co-pending U.S. Provisional Application Serial No.63 / 627,535, filed January 31, 2024, the entirety of which is incorporated by reference herein in its entirety and for all purposes. BACKGROUND OF THE INVENTION 1. Field of Invention

[0002] The present disclosure relates to damping drill string vibrations, and more specifically is directed to identifying an inertia ring assembly (“IRA”) that maximizes drill string dampening over a designated range of frequencies. 2. Description of Prior Art

[0003] Drilling systems are employed for excavating hydrocarbon-producing wellbores in a subterranean formation. These drilling systems typically include a drill string of a drill pipe string, a drill bit, and a collar connecting the drill bit to the drill pipe string. The drill pipe string is generally made up of joints of drill pipe connected in series by engaging threads on their opposing ends. Usually, the drill string is rotated by a top drive or rotary table provided in a drilling rig on the surface while drilling mud is circulated within the drill string to remove cuttings formed by rotating the drill bit in the formation. Often, devices such as mud motors, mud pulsers, turbines, and imaging devices are installed within a drill string for use during drilling. IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229)

[0004] Reactive forces from the bit rotating against the subterranean rock formations generate vibrations in the drill string, which are generally most pronounced in the drill pipe string. Depending on the forces and physical characteristics of the drill pipe string and the formation, the vibrations are in directions that are lateral, radial, torsional, and combinations. Recent advancements in drilling technology have increased both rates of penetration (“ROP”) through the formation and weight on bit (“WOB”), and in turn, increased magnitudes of vibrational displacement in drill pipe strings; and sometimes the vibrations reach a level referred to as high frequency torsional oscillations (“HFTO”). HFTO is referred to as an instability of a single torsional mode. It is unstable if the energy into the system which is through the bit rock interaction is higher compared to the energy output through any damping / dissipative forces. For example, when drilling a hard rock formation, resonance-induced HFTO is localized in a lower bottom-hole assembly (“BHA”) or a lower part of the drill string. In particular, a mode shape of HFTO is associated with distribution of mass, density of mass, structural or material stiffness, damping characteristic of the drill string or BHA, and combinations. Typically, there will be damping in the system which is called material damping or structural damping. For example, material damping is implemented to convert mechanical energy into thermal energy by deforming a material of structure. For example, when a drilling tabular is deformed, material damping is caused by the damping effects of the material, such as a damping fluid, of the structure. It is possible to modify material damping by replacing one material with another material having a different damping factor. As another example, structural damping is implemented to reduce a vibration of structure in thread connections by dissipating its energy. In some embodiments, if unstable, the amplitude of HFTO may increase until it is limited by a dissipative force which stabilizes the forces again. In the case of HFTO this stabilizing force is achieved when the amplitude of HFTO measured in rotary speed fluctuation at the bit is equal to the average rotary speed at the bit provided by top drive, mud motor, and alike. In this IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) case, the harmonic fluctuation of the bit rotary speed through HFTO leads to zero or very short negative values, this jump in the rotary speed leads to energy dissipation and therefore stabilizes HFTO at a high amplitude. This high amplitude is called a plateau, that is the amplitude is constant at a high level and only scaled if the average rotary speed is changed at the bit. The process of increasing vibrations from a value close to zero, e.g., because another HFTO-prone formation is drilled or because another operational parameter is chosen (for example, a higher weight on bit (“WOB”) or a lower bit rotary speed is summarized as HFTO along with the constant amplitude on the defined plateau). These vibrations, especially when reaching the HFTO level of vibrations, may dislodge devices that are coupled within drill strings separating a lower portion of the BHA below the vibrations from an upper portion of the BHA above the vibrations. Therefore, the reduction of vibrations associated with different undesirable HFTO modes is important to prevent tool damage and reduce non-production time (NPT) in drilling.

[0005] To reduce vibrations in a drill string, including HFTO, damping systems are mounted on drill strings above the BHA. Damping systems often include a weight circumscribing a portion of the string, which is sometimes immersed in a fluid. Typically, HFTO is controlled in two different ways. One way refers to the avoidance of the instability of the torsional modes leading to high vibrational amplitudes. That is, the WOB is decreased, the rotary speed is increased, or the coupling with stick / slip is avoided to prevent HFTO because the energy input is smaller than what is called material damping. The negative effect may be a lower rate of penetration caused by the limitations in operational parameters. Very often, HFTO may not be avoided in the operational parameter range at least with a reasonable rate of penetration. In this case, attempts are made to limit the amplitude of HFTO (the plateau amplitude described above), which is proportional to the average bit rotary speed. In this case, the amplitude is limited by a reduction of the rotary speed which again may compromise the rate of penetration. IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) Adding damping and increasing energy output and therefore stabilizing the system in a wider parameter range may therefore lead to avoidance or stability of all relevant HFTO-related and damaging modes and therefore enable a high rate of penetration without any compromise of reliability of the system which might lead to non-productive time due to tripping or excessive repair and maintenance costs. SUMMARY OF THE INVENTION

[0006] A drill string with one or more inertia ring assemblies (“IRAs”), which are designed by an iterative method to maximize damping in the drill string. Each IRA is made up of an annular housing that circumscribes a portion of the drill string, a cavity is inside the housing that has a ring and fluid. The design is optimized by an iterative process that changes fluid and ring properties and adjusts the spacing between the ring and inner walls of the housing. Also in this disclosure are new elements necessary to enable adjustment of fluid properties. The iterative process considers changes in fluid properties due to different downhole conditions. The final design may have multiple IRAs that have different damping characteristics. BRIEF DESCRIPTION OF DRAWINGS

[0007] Some of the features and benefits of the present invention having been stated, others will become apparent as the description proceeds when taken in conjunction with the accompanying drawings, in which:

[0008] FIG. 1 is a side partial sectional view of an example of a drilling system with a drill string experiencing high frequency torsional oscillations (“HFTO”).

[0009] FIG. 2 is a side sectional view of an example of a portion of the drill string of FIG. 1 having an inertia ring assembly (“IRA”).

[0010] FIGS.2a and 2b are side sectional views of alternate examples of the IRA of FIG.2. IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229)

[0011] FIG.2c is a side sectional view of an example of the IRA.

[0012] FIGS. 3a-3f are graphs having plots representing changing values of damping coefficients over a range of natural frequencies.

[0013] FIG. 4 is a side partial sectional view of an example of the drilling string fitted with IRAs designed to optimize damping.

[0014] FIG.5 is a perspective sectional view of an alternate example of the drill string of FIG. 2 having a compensation device.

[0015] FIGS. 6a and 6b are graphs with plots of pressure and viscosity of a damping fluid in the device of FIG.5.

[0016] FIGS. 7a and 7b are perspective sectional views of the drill string of FIG. 5 having an alternate compensation device.

[0017] FIGS.8a-8f and 9a-9f are graphs with plots of pressure and viscosity of a damping fluid in the device of FIGS.7a and 7b.

[0018] FIGS. 10a and 10b are perspective sectional views of the drill string of FIG. 5 having another alternate compensation device.

[0019] While subject matter is described in connection with embodiments disclosed herein, it will be understood that the scope of the present disclosure is not limited to any particular embodiment. On the contrary, it is intended to cover all alternatives, modifications, and equivalents thereof. IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) DETAILED DESCRIPTION OF INVENTION

[0020] The method and system of the present disclosure will now be described more fully hereinafter with reference to the accompanying drawings in which embodiments are shown. The method and system of the present disclosure may be in many different forms and should not be construed as limited to the illustrated embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey its scope to those skilled in the art. Like numbers refer to like elements throughout. In an embodiment, usage of the term “about” includes + / - 5% of a cited magnitude. In an embodiment, the term “substantially” includes + / - 5% of a cited magnitude, comparison, or description. In an embodiment, usage of the term “generally” includes + / - 10% of a cited magnitude.

[0021] It is to be further understood that the scope of the present disclosure is not limited to the exact details of construction, operation, exact materials, or embodiments shown and described, as modifications and equivalents will be apparent to one skilled in the art. In the drawings and specification, there have been disclosed illustrative embodiments and, although specific terms are employed, they are used in a generic and descriptive sense only and not for the purpose of limitation.

[0022] Shown in a partial side sectional view in FIG. 1 is an example of a drilling system 10 excavating into a formation 12 to form a wellbore 14. Drilling system 10 includes a drill string 16, which includes a pipe string 18 made up of lengths of drill pipe threaded together, and a bottom hole assembly (“BHA”) 20 mounted on a lower end of the pipe string 18. BHA 20 includes downhole tools 102. The lower end of the BHA is connected to a drill bit 22 with teeth or compacts (not shown) for contacting and crushing the rock in the formation 12. The downhole tools 102 include imaging devices (nuclear, electromagnetic, acoustic, etc.), mud IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) motors, mud pulsers, and other currently known or later-developed equipment. The pipe string 18 and the downhole tools 102 have an axial bore 108 (FIG. 2) that allow drilling fluid (mud) to pass through the drill string 16 and leaves the drill bit 22 through nozzles (not shown). The drilling fluid returns to the earth surface through an annulus 17 and carries drill cuttings outside of the wellbore. A derrick 26 on the surface provides a structure for inserting lengths of drill pipe into the wellbore 14 for lengthening the pipe string 18 and also for drive means (not shown) such as a top drive or rotary table for rotating the drill string 16 and bit 22. A controller 28 is optionally included that optionally receives and records signals from within the wellbore 14, and in alternatives provides command signals to devices coupled with the derrick 26 and / or within wellbore 14. In the example of FIG. 1, curved dashed lines adjacent to the drill string 16 are shown which represent oscillations or vibrations in the drill string 16, which as described above are high frequency torsional oscillations (HFTO). The high frequency oscillations are induced in the drill string 16 by the drilling process and the process of cutting the formation, respectively. HFTO are torsional oscillations typically above 50 Hz.

[0023] Shown in a side sectional view in FIG. 2 is an example of an inertia ring assembly (“IRA”) 30 mounted in the downhole tool 102 in a bottom hole assembly for damping the high frequency oscillations in the drill string 16. The downhole tool is also referred to herein as damping tool or viscous damper. The IRA 30 includes an outer housing 32 which has an annular configuration. A cavity 34 is formed within housing 32, which is also annular in the drill string or BHA. An inertia element 36 is within cavity 34 and spaced radially away from the inner and outer walls of the housing 34 by gaps and , respectively. Inertia element 36 is shown as an annular ring-like member. The upper and lower surfaces of inertia element 36 are spaced axially from the upper and lower surfaces of housing 34 respectfully by gaps and . Fluid 38 is within gaps , , and . In an embodiment, inertia element 36 includes multiple inertia elements 361-n arranged concentrically around a longitudinal axis AX IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) of the BHA, the drill string or the damping tool, stacked vertically or along the longitudinal axis AX, which in alternatives are ring-like members or made up of arc like segments.

[0024] For an example, fluid 38 in the IRA 30 includes a Newtonian fluid that is linear and has a damping factor but not a stiffness factor . Stiffness measures the extent to which an object resists deformation in response to an applied force. Non-Newtonian fluids are also included, that have both a damping factor and a stiffness factor . Fluid 38 optionally includes silicon oils with different defined viscosities. Fluid 38 is also referred to as damping fluid or viscous fluid. In embodiments, the material making up the inertia element 36 has adensity of at least about 7500 / or greater (e.g. steel, bronze, iron, copper or the like) sothat a mass moment of inertia of the inertia element 36 increases the damping. Modal damping of each mode is proportional to a corresponding mass moment of inertia . In alternatives, a less dense material provides the benefits of being tunable to a suitable frequency, e.g., the frequency of the IRA 30 coupled with the stiffness is calculated using the stiffness of the fluid and the mass moment of inertia of a mode based on equation 1. In particular, the frequency of the IRA 30 is similar to the natural frequency of the system based on equation 2 that shall be dampened.where is a stiffness factor of the fluid 38 of the IRA, is a mass moment of inertia,is an angular natural frequency of the BHA 20 without inertia elements, is a natural frequency of the BHA 20 without inertia elements, and is a frequency of the IRA with inertia elements. IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229)

[0025] may increase with smaller gaps and higher gap numbers. If the gap number may not be increased sufficiently (because of tolerances, changes of the gap downhole due to pressure, thermal expansion, etc.), the use of a lighter material is beneficial to keep the gap number tuned. The one or more inertia elements 361-n of the IRAs 30 are not physically attached to each other in the sense that they are rotatable with respect to each other. In alternatives, the one or more inertia elements 361-nin the IRA 30 are spaced close to each other and a one or more gap in the cavity to allow the fluid 38 to flow between the different one or more inertia elements 361-n in the IRA 30, to allow for filling the cavity 34. In embodiments there are multiple cavities 341-n, wherein each inertia element of the one and more inertia elements 361-nresides in one cavity.

[0026] An analytical equation is used to calculate the damping that is provided by each of the one or more inertia elements 361-n of the IRA 30 to the system (BHA 20 and drill string 16). For this purpose, the properties of an HFTO-related mode of the BHA 20 are calculated, which is typically done with a numerical model like a finite element model. For example, the finite element model is implemented to emulate the properties of the HFTO-related mode of the BHA 20, such as a plurality of HFTO transient dynamic responses and their corresponding HFTO severities. In the analytical approach the modal properties of the oscillation modes of the BHA 20 as an approximation are not changed if the BHA 20 interacts with the inertia elements. The modal properties for each critical HFTO-related torsional mode include the deflection of the mode shapeat the axial position of a specific inertia element of the one or more inertia elements 361-n, the natural frequencyof the mode, and if existent the modal damping associated with the mode. Using this approach, a semi-analytical or analytical model is used to calculate the damping that is provided by each inertia element that is placed in the BHA 20 at a certain position. Typically, the damping is proportional to the mass moment of inertia IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) indicating that a high-density material is beneficial, and increasing with the power of 2 withrespect to the amplitude of the mode shape ( ) at the position. Furthermore, the modaldamping is high close to the tuned frequency, that is, the stiffness provided by the fluid stiffness and the mass moment of inertia are used to calculate the tuned frequency based on equation 3.

[0027] By tendency a small damping factor leads to very high damping at and close to the tuned frequency but only in a narrow frequency range and vice versa. Therefore, dependent on the frequency range of HFTO where damping is efficient, a different is beneficial, which is largely influenced by the fluid selection (selection of the damping fluid 38). As per the workflow for each inertial element, the modal damping provided by the damping tool 102 is calculated for each relevant frequency and at the end, the modal damping is summed over all inertia elements 361-n. If the damping tool 102 is placed close to the bit or at the bit where the mode shape amplitude is typically very high and the damping is provided efficiently, an approximation of the modal properties may be used, thus, the modal properties may not be derived from a numerical model. For this purpose, a value is calculated based on equation 4 to describe the likelihood of the HFTO mode shape occurring. In particular, the value defines the smallest slope of the torque characteristic for which the system is marginally stable. It is assumed that the value for the relevance of a mode with respect to HFTO is constant for all critical HFTO modes. For a given angular natural frequency , the amplitude of the mode shape at the bit is calculated based on equation 5.IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229)where is the amplitude of a mode shape at the bit,amplitude of a mode shape at the inertia element or a specific inertia element of the one or more inertia elements 361-n, is a modal damping factor.

[0028] Using the approximation for a damping tool 102 with 0, the damping provided for a single inertia ring assembly at the bit could be approximated analytically or semi analytical if both and are not equal to zero. The analytical or semi analytical model that does assume that the modes are not changing leads to an already quite accurate solution. For example, damping estimated using a numerical solution is more accurate for a specific BHA 20, and provides advantages, especially if the optimization of the IRA 30 is done application specific and the BHA 20 is known. In an example of optimizing damping of a BHA 20, an IRA 30 is coupled onto the BHA 20, which has a natural frequency that is the same as or substantially equal to that of the BHA 20. Further in this example, a design of the IRA 30 is optimized, which results in the IRA 30 having a natural frequency that is closer to the natural frequency of the BHA 20 than that achieved by prior art methodologies.

[0029] In an example of a numerical solution, the numerical model of the BHA 20 is coupled with a dynamic model of the IRA 30, which includes a damping fluid 38 and one or more inertia elements 361-n. Each of the one or more inertia elements of the IRA 30 has a respective mass moment of inertia and a respective axial position in the IRA 30 along axis AX. The dynamic model is represented by , , and . and are derived at the frequency of the HFTO mode and for a specific mode shape amplitude at the point of the inertia ring assembly in the BHA 20 and for a specific temperature and pressure. The specific temperature and pressure change the properties of the inertia ring assembly as discussed. Examples of the IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) numerical model of the BHA 20 include a finite element model (for example using beam elements) or calculated or derived from a discrete element model or a transfer matrix model. The numerical model of the BHA 20 is then combined with a dynamic model of , , and of the one or more inertia elements 361-n of the IRA 30 by coupling them to the mass, damping, and stiffness matrix of the numerical model of the BHA 20. The modal damping is calculated from such a model using a modal analysis of the combined model, one of the results is the modal damping associated with the mode and the natural frequency of the mode. The implementation of the IRA with , , and into the numerical model of the BHA 20 changes the natural frequency, the mode shape amplitude, and the modal damping associated with the mode. Furthermore, the values for and are dependent on the natural frequency and the mode shape amplitude where the IRA 30 is placed on the BHA 20. Therefore, this approach needs to be done for every natural frequency of the BHA 20 that is critical, e.g., according to the criterion. Furthermore, an iterative method needs to be used because the values and and are natural frequency and mode shape amplitude dependent. The values for and are taken for example at specific temperatures, pressures, and mode shape amplitudes as derived from the lab tests at the natural frequency of the currently considered mode. If the gaps of the IRA are changed this could be used by scaling and with the gap number that accounts for the viscous shear in the gaps or by use of another appropriate model that considers the change of the size of the gap (width of the gap). Inserting the inertias coupled with and into the numerical model will change the natural frequency of the mode and its mode shape. The mode shape is used to scale the amplitude along the BHA 20, for example, a certain revolution per minute (RPM) fluctuation or angular acceleration is assumed at the bit and then the mode shape amplitudes at different positions in the BHA 20 are calculated by the ratio of the mode shape amplitude at the bit to the mode shape amplitude at the position of the one or more inertia elements of the IRA. If the natural frequency of the mode is changed by the IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) addition of the inertia ring assembly or the damping tool 102, the values of and will change because they are typically frequency dependent (value changes when the natural frequency of the BHA 20 changes) and amplitude dependent (value changes if the mode shape changes). An iterative method is to be employed where the properties of and are changed (e.g., with the Nelder Mead method) until the natural frequency and amplitude assumed to derive and match the natural frequency of the BHA 20, with the inertia ring assembly of the damping tool 102 mounted onto the BHA 20, and with and at exactly that natural frequency. From the converged solution of the iterative method, the modal damping is a very accurate solution without any approximations. Additionally, the change in the temperature of the viscous fluid (fluid 38 caused by the energy dissipation in the viscous fluid may also be added as an additional parameter. The temperature of the fluid is different from the operation temperature and will be dependent on the modal damping and the mode shape amplitudes along the BHA 20. The modal damping in this sense is derived for every mode (includes frequency) and every temperature, mode shape amplitude, and pressure if the parameters, such as and , are dependent on these. An alternative to the method described above which solves the problem in the frequency domain is a solution in the time domain, where the parameters are applied to the BHA 20 model and the IRA, and then with a defined excitation, the mode shape amplitude is captured over the frequency. The ratio of the mode shape amplitude in a certain frequency range (for example using the Half Power Method) is used to calculate or approximate the damping of the HFTO that is achieved.

[0030] Deriving an effective damping from a mode shape amplitude dependent damping curve from a specific mode: the modal damping for a mode will be typically mode shape amplitude dependent. Therefore, the energy output is mode shape amplitude dependent, that means for example for higher mode shape amplitudes the modal damping coefficient is lower or higher compared to a constant modal damping for each mode shape amplitude. A very high value of IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) 4% damping could, for example, be achieved for an angular acceleration at the bit of 2000 rad / sec2, however, the damping could be 3% for 2500 rad / sec2. A safety factor to the maximum modal damping of a mode or a natural frequency (analytical approach) could be used. One method could be to use the damping value that is provided for a specific bandwidth of a mode shape amplitude interval (e.g., for an interval of 1500 rad / sec2, which could for example be from 500 rad / sec2to 2000 rad / sec2). The mode shape amplitude interval could be specified with the lowest mode shape amplitude, e.g., at 500 rad / sec2, and the highest allowed mode shape amplitude, e.g., 8000 rad / sec2. In this range, the interval is defined as the maximum modal damping of the mode that is present for the specified mode shape amplitude interval. The mode shape amplitude interval is chosen to not allow the mode shape amplitude to “jump” over the effective mode shape amplitude damping range to a higher mode shape amplitude where the damping is lower. This kind of event could for example occur if an impact is leading the mode to higher mode shape amplitudes or if stick / slip, here defined as a low frequency movement of the whole BHA, is present and superimposed to HFTO. The allowed amplitude range that incorporates the interval needs to be larger compared to the interval and should be defined in a not-damaging mode shape amplitude range, e.g., using the mode shape to scale the mode shape amplitude components in the BHA 20 that are prone to the loads associated with HFTO which are acceleration and dynamic torsional torque.

[0031] Target function: The target function is used to define an optimal effect of the optimized inertia ring assembly or damping tool 102. The properties of the inertia ring assembly will be varied to achieve the best result regarding the target function. This optimization of the target function is due to the complexity of the problem done with numerical optimization. There are different mathematical methods that may be used for that purpose. For example, minimizing the target function using the Nelder Mead method, or using the same method to maximize a IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) target function. A target function could also be compared to a to-be-achieved damping. A simple example of a target function is:

[0032] Herein, the minimum effective modal damping for a specific natural frequency in a specific temperature, pressure, and mode shape amplitude range is calculated for all possible variations of those parameters. Regarding the mode shape amplitude, the effective damping could be calculated as pointed out above. Now the minimum damping in a defined frequencyrange … , could be maximized, that is max . The target function couldincorporate a weighting function that for example suggests that the damping at a certain frequency should be higher. The information of how much damping should be provided at a certain frequency or mode of the BHA 20 could for example be extracted from downhole data that is used to identify the modes that are excited incorporating the use of models to identify which modes are sensitive to HFTO. The target function could also demand that the sum of the damping in the frequency range should be as high as possible, or a combination of maximizing the minimum damping in a certain frequency range with this kind of criterion. Furthermore, the so-called Sc value is a stability index that directly relates the modal properties with the damping added by the damping tool 102 to the bit-to-formation interaction that excited HFTO assuming a velocity dependent characteristic of the drilling torque. Similar weighted values which are a combination of the achieved damping, the modal properties of the considered modes are derived to specify a target function. The target function may be maximized or minimized by changing the sign of the function using the 1 / target function or using a constant offset which does not qualitatively change the outcome of the approach. IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229)

[0033] In a non-limiting example of optimizing damping of a BHA 20, values of and are estimated from testing with a test rig (not shown) having a mechanical shaker. A chassis. Similar to outer housing 32 (FIG. 2), having an attached inertia element 36, is mounted onto the shaker. The shaker then shakes the chassis and inertia element with a force and frequency to create a harmonic movement of the chassis. The attached inertia element moves relative to the chassis due to the fluid transferring chassis movement to the inertia element; from the relative movement, the values for and are derived based on a value of the mass moment of inertia of the inertia element, which is derived from CAD models or measured. This may be done for multiple parameter variations (e.g., different temperatures, different frequencies, different amplitudes) resulting in a look-up table for and for one specific damping fluid 38 and configuration of the inertia element and the gap(s) between the inertia element and inner sidewalls of the enclosure (chassis) where the inertia element is housed. Temperature changes of the damping fluid 38 through the energy dissipation in the viscous fluid may be considered if found to be relevant. Optionally, and are derived from a model of the damping fluid; such as a force model; from a simulation of the force model and are derived. A force model could also be used to directly estimate the damping in a numerical model of the BHA 20, for example using time-domain simulations where the inertia element is coupled to a finite element model (or similar model) of the BHA 20 with the force model of the damping fluid. The effective modal damping or a similar value representing the effective modal damping , such as dissipated energy, may be derived from the results of the simulations. Thus, a plurality of fluid properties of the damping fluid exist for a plurality of operational parameters in a predetermined downhole design. For example, the force model of the damping fluid is determined by calculating inertia / gap cavity interaction for the plurality of operational parameters in the predetermined downhole design. As a result, the force model of the damping fluid is implemented to determine a plurality of values of the damping fluid by scaling the IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) measured value for the plurality of operational parameters in the predetermined downhole design. Likewise, the force model of the damping fluid is implemented to determine a plurality of values of the damping fluid by scaling the measured value for the plurality of operational parameters in the predetermined downhole design.

[0034] The relationships below illustrate variables affecting the values of and and how the values that are present in the application can be derived from the laboratory test results.fT, P, (9)where: T: temperature P: pressure S, : gap number in the laboratory: thermal expansion K, : rotational stiffness factor in the laboratoryC , : rotational damping factor in the laboratory: mass moment of inertia

[0035] The gap number Sp is a geometric factor and represents mathematically resulting shear stresses in the damping fluid 38 for a given movement (rotation) of the inertia element. The gap number is calculated based geometric dimensions of the inertial ring assembly.

[0036] In equation 10 , , and are the gaps (gap sizes) as shown in FIG. 2, ro is the outer radius of the inertia element 36 measured from the axis Ax, riis the inner radius of the inertia element 36 measured from the axis Ax. The gap number can be adjusted by adjusting the size of one or more of the gaps , , and or the inner radius ri or outer radius ro of the inertia element. Although, the gap number is determined by geometrical parameters, it IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) depends on the temperature and the pressure applied on the damping tool 102 and as present in the wellbore 14. The geometrical dimensions such as the inner and outer radius (ri, ro) of the inertia element 36 and the sizes of the gaps , , and depend on the temperature and pressure and cause variation of the inner and outer radius of the inertia element as well as the sizes of the gaps due to thermal expansion / contraction. The gap number is determined in the laboratory for a given configuration of the inertia ring assembly (test set-up) (inertia element geometry, housing, gaps sizes, material properties). In an inertia assembly there can be more than one inertia element. For each of the inertia elements the gap number is determined in the laboratory. The gap number is determined for each of the gaps in each of the inertia elements. Alternatively, one gap number is determined for each inertia element in the housing of the inertia ring assembly which represents all gaps that exist between the inertia element and the housing, such as , , and . The gap size from the lab can be used to determine the

[0037] In some embodiments, the plurality of fluid properties of the damping fluid are temperature and pressure dependent due to thermal expansion or deformation of the drilling system caused by pressure and alike. Thus, the force model is used to determine the plurality of fluid properties of the damping fluid for estimating downhole conditions based on equations 11 and 12. Herein, the gap number Sp is used to scale the measured values of and for different operational parameters. A combined model is determined by using the plurality of fluid properties of the damping fluid by combining the numerical model of the BHA 20 and the dynamic model of the inertia. Based on the combined model, modal analysis is used to determine a plurality of optimal parameters of the IRA 30 to damp vibrations associated with a plurality of HFTO related modes of the BHA 20 by iteratively performing a plurality ofIM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229)where: T: Temperature P: Pressure f: frequency A: amplitude Geometry test set-up (L: length, D: diameter of inertia element, etc.) Material properties test set up ( : thermal expansion, E: Young’s modulus, etc.)S , f L, D, … , , T, P : gap number in the laboratoryS , f L, D, … , , T, P : gap number of potential downhole implementation: downhole K, : the rotational stiffness factor of potential downhole implementationC , : the rotational damping factor of potential downhole implementation

[0038] In some embodiments, a plurality of HFTO frequencies are determined for the plurality of HFTO related modes of the BHA 20 based on a predetermined Sc criterion. In an example of the numerical approach, a first vector is derived by a first dynamic model of the BHA 20without inertia elements, in which the natural frequency is f , . A new mode shape isassumed with mode shape amplitude at inertia elements A , . In modal damping a seconddynamic model of the BHA 20 (e.g., FEM model) with inertia elements is performed. A second vector is derived by the second dynamic model of the BHA 20 with inertia elements. In an example, the modal damping is calculated for the second dynamic model of the BHA 20 with inertia elements to identify an optimal mode by solving an optimization problem using predetermined optimizer criteria based on a Modal Assurance Criterion (MAC) criterion, frequency, and Sc value. The relevant mode is alternatively identified using the mode that is closest to that of the previous iteration based on the MAC criteria, closest frequency, and Sc values. The MAC is calculated as a normalized scalar product of the first vector and the second vector. The MAC is optionally used in the modal analysis to indicate the similarity of two IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) mode shapes. In the optimal solution, the optimal mode for the second dynamic model of the BHA 20 with inertia elements is derived to match the natural frequency of the BHA 20.

[0039] In this modal analysis combined model, a first plurality of modal properties for the first dynamic model of the BHA 20 without inertia elements for the plurality of HFTO related modes of the BHA 20. For example, the first plurality of modal properties for the first dynamic model of the BHA 20 without inertias include a mode shape amplitude, a natural frequency, and a modal damping coefficient of the BHA 20 without inertias based on the plurality of operational parameters in the predetermined downhole design. Likewise, a second plurality of modal properties of the second dynamic model of the BHA 20 with inertia elements for the plurality of HFTO related modes of the BHA 20 are estimated. For example, the second plurality of modal properties for the second dynamic model of the BHA 20 with inertia elements include a respective mode shape amplitude, a respective natural frequency, and a respective modal damping coefficient for each of the one or more inertias based on the plurality of operational parameters in the predetermined downhole design. Natural frequency f ,New mode shape Amplitude at inertias A ,Dissipated energy, temperature difference to downhole temperature

[0040] Based on the plurality of HFTO frequencies, the first plurality of modal properties and the second plurality of modal properties, a target function is determined to achieve a maximum amount of drill string or BHA damping. In particular, the target function is evaluated for convergence based on equation 13. For example, the target function is evaluated for convergence by comparing a natural frequency of the combined model to a natural frequency at which the values of and are measured. Thus, an inertia element is identified from the one or more inertia elements of the IRA 30 by solving the target function based on predetermined optimizer criteria. In particular, the inertia is identified from the one or more IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) inertia elements of the IRA by selecting a mode shape of the inertia element which is closest to the mode shape from a previous iteration based on Modal Assurance Criterion (MAC), and closest frequency and value. _f , f , (13)where f , is the natural frequency of the BHA with the inertial number i+1 and f ,is the natural frequency of the BHA with the inertial element i.

[0041] The new frequency f , derived from the combined model by adding the inertiaelement i+1 matches the frequency f , that was taken to evaluate K , and C , . If thereis convergence according to target function and optimizer criteria, then an inertia element is identified, and which has the optimal parameters of the inertia element (e.g., ring dimensions, ring material, gap values , , and , fluid properties, a number of inertia element, etc.) used in this iteration. If convergence has not yet occurred, then another iteration is performed with different inertia element parameters that are selected by comparing the results of the target function of multiple instances i for the BHA 20 with inertia elements. Thus, a damping system of IRAs for the BHA is formed by using the plurality of optimal parameters of the optimized inertia elements. The damping system of IRAs is mounted to a drill string or BHA to excavate through a formation while reduce HFTO in the BHA 20.

[0042] In this numerical method, the combined model is formulated in an optimization problembased on equation 14 to estimate modal damping D , natural frequency f , , and mode shapevector associated with the second dynamic model of the BHA 20 with inertia elements using a modal analysis. Natural frequencies result from a modal analysis (standard method). It is possible to reduce the number of degrees of freedom to increase efficiency by reduction methods (for example the component mode synthesis) IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229)where: x: Vector of containing degrees of freedom of the BHA and the inertias M: Mass matrix C: Damping matrix, consisting of degrees of freedom that belong to the BHA and to the inertia element, both are coupled K: Stiffness matrix, consisting of degrees of freedom that belong to the BHA and to the inertia element, both are coupled

[0043] In some embodiments, the optimization problem is solved using an iterative process. In an initial step of the iterative process to identify an optimal IRA 30 design to maximize damping of a drill string and BHA 20 (“iterative process”), properties of IRAs are assigned (or assumed) to consider different HFTO frequencies that are to be dampened. Examples of properties being assigned include gap number, material properties, geometry of the cavity, coefficient of thermal expansion, number of IRAs, material properties, and geometry of each IRA. The different HFTO frequencies are identified by a modal analysis (numerical model), where the criticality of the modes would be sorted by the Sc value that they have without added damping of the damping tool. These HFTO frequencies could be alsoconstrained to a frequency range ( to ), such as a range of expected operation. In anexample, the HFTO frequencies are the natural frequencies that are critical to be excited, which is estimated by the Sc criterion (for example), and different from the analytical model. In a non-limiting example, it is assumed that there are frequencies in the HFTO frequency range from to and that these modes have a constant Sc value, or that the Sc value is IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) frequency dependent. With this assumption, the amplitude of the mode shape at the drill bit is calculated by using the equation for Sc; which is a variable missing from the analytical equation that derives the modal damping for each HFTO frequency. Embodiments exist in which one application has three critical frequencies, e.g., one at 50 Hz, one at 200 Hz, one at 310 Hz, and in another application has a different number of critical frequencies and that are at different magnitudes, such as, 150 Hz and 170 Hz. Commonly HFTO frequencies in a drill string are between 50 Hz and 500 Hz.

[0044] In another step of the iterative process, different HFTO frequencies are considered with inertia elements at different tuned frequencies . Graphically illustrated in each of FIGS. 3a-3f are graphs 40, 42, 44, 46, 48 . Fig 3F show a graph 50 representing a summation of the damping coefficient of the inertia elements as shown in FIGs 3a to 3e. Each graph 40, 42, 44, 46, 48, and 50 including a series of plots 52 a-h, 54 a-h, 56 a-h, 58 a-h, 60 a-h, and 62 a-h that represent changing values of damping coefficients (ordinate) over a range of natural frequencies. The graphs 40, 42, 44, 46, 48, and 50 each have an abscissa 64, 68, 72, 76, 80, and 84 representing frequency and ordinates 66, 70, 74, 78, 82, and 86 representing a damping coefficient. FIGS.3a-3e relate to one of five different inertia elements, and where each of the plots 52a-h, 54 a-h, 56 a-h, 58 a-h, and 60 a-h in each figure represent the variation of damping coefficient over the frequencies at a particular temperature, which in this example have different properties. Further in this example, the five different inertia elements have different characteristics. The temperature is increasing from the uppermost graph to the lowermost graph in the plots FIG.3a-3f. In each of FIGS.3a-3e, the uppermost graph(having the greatest values of damping coefficients) represents IRA 30 characteristics at 80 °C, and the lowermost graph (having the lowest values of damping coefficients) represents IRA 30 characteristics at 150 °C, and there is a 10 °C difference between adjacent plots. For the purposes of discussion herein, the damping coefficient of the HFTO mode is considered to be the target value. It is noted that IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) for a specific HFTO frequency, each frequency has a modal damping coefficient. In this example, the maximum model damping of the inertial element NO.1 represented in FIG.3a is at about 210 Hz, the maximum modal damping of the IRA 30 represented in FIG.3b is at 250 Hz, and is at 340 Hz for the IRA 30 represented in FIG.3c. If an IRA 30 has a tuned frequency close to an HFTO frequency, the damping coefficient will be high. Above and especially below the tuned frequency, the damping coefficient will be low. In an example, for all HFTO frequencies in the defined frequency range from to , the 5 inertial elements in the IRA 30 are each tuned to different frequencies in this range to cover the whole range. In this example, the is not assumed, as it is dependent on a particular fluid used in the IRA. In an example of the optimization process, the variables listed above are adjusted so that the damping of each of the inertia elements is above a certain level over the range of HFTO frequencies being considered for designing the IRA and BHA 20. Shown in FIG.3f is a summation of the plots shown in FIGS. 3a-3e, which illustrates a total damping of the combined 5 inertial elements in the IRA represented in FIGS 3a-3e.

[0045] In an alternative step of the iterative process, different HFTO frequencies areconsidered with different damping properties ( / J) of each inertial element. The frequency ofhas greater effects with lower values of ; in which the system behaves similar to a fluid damper with Newtonian fluid (where 0). In this alternative, an HFTO frequency istargeted by assigning fHFTO= / 2 .

[0046] In another step of the iterative process, an optimal number of inertial elements is selected so that the damping in the frequency range is optimized with respect to a target function. For example, the optimal number of inertia elements is determined by maximizing the minimum damping in a frequency range. In some embodiments, an optimal amount of damping is not necessarily that results in the highest magnitude at a particular frequency range; IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) but which maintains damping over the expected spectrum of operating frequencies. For example, an optimal number of inertia elements is reached when all frequencies are considered and damping would not increase if an inertia element is added, given for example a defined installation space. In an alternative, it is assumed that the design space is constant and the number of inertia elements is varied in this design space, i.e., additional inertia elements have smaller dimensions. In examples having multiple inertia elements, additional components are included that separate adjacent inertia elements, which would consume from the mass moment of inertia of the inertia elements (a lower mass moment of inertia means a lower damping coefficient, linear dependency). Example optimums consider the trade-off between that at which each HFTO frequency may be assigned, and without design space being consumed by elements that do not contribute to damping.

[0047] In another step of the iterative process, the properties of the IRA 30 and the included inertia elements are assigned based on the lab test properties of the damping fluids tested. In alternatives, the properties of the inertia elements are adjusted or scaled from properties corresponding to conditions of the fluid when tested, such as temperature and / or pressure, to conditions anticipated in use in a wellbore. The properties of the inertia elements are assigned in a way that a temperature range is considered with varying influence of the fluid properties based on expected downhole temperature, such as fluid viscosity, which is variable with temperature changes, influences and . Low viscosities often result in a correspondingly small HFTO frequency range and small gaps, which due to their dimensions and manufacturing tolerances, may close due to material responses to temperature and / or pressure.

[0048] Optionally, in the iterative process, the IRA 30 is positioned proximate to the bit, because of a mode shape amplitude at the downhole side of the bit . In an example, proximate to the bit is a distance from the bit where the mode shape amplitude is not IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) significantly below the mode shape amplitude at the bit, examples of the mode shape amplitude being not significantly below the mode shape amplitude is about 90% of the amplitude at the bit, about 95% of the amplitude at the bit, about 99% of the amplitude at the bit, and all values ranging between about 90% of the amplitude at the bit to about 99% of the amplitude at the bit.

[0049] Referring now to FIGS. 2a and 2b, shown are alternate examples of the IRA 30a, 30b configured to compensate for property changes of fluid 38 when exposed to conditions in the wellbore 14. In alternatives, the compensation affects changes in the gap number during operation, such as due to the thermal expansion of a inertia element and surrounding parts. Fluid properties and some damping properties are temperature dependent. Options also exist for compensating for changes in the fluid 38, such as active or passive cooling (through mud) to hold the temperature optimal for optimal damping. As the fluid 38 is also pressure dependent, the present disclosure considers pressure compensation of the fluid 38, which in examples allows for a smaller housing 32. In a non-limiting example, the temperature dependency of the fluid 38, including fluid properties and , is compensated by changinggaps ( , , and ) as a function of the temperature. The fluid properties , arealso affected by the gap size (through the changing shear stress distribution in the fluid 38). Higher temperature corresponds to lower viscosity in the fluid 38 and reduced values of and , which is not optimal over an anticipated range of operating temperatures. As disclosedherein, reducing one or more of gaps ( , , and ) increases values of , –thereby compensating for a reduction in viscosity of the fluid 38 due to increased temperaturesdownhole. In embodiments, gaps ( , , and ) remain present throughout a fullrange of anticipated operating temperatures to prevent wedging an inertia element inside itshousing. Examples of reducing a dimension of one or more of gaps ( , , and )includes an inertia element having designated dimensions and a particular coefficient of IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) thermal expansion, so that when the ambient temperature increases during operation and due to higher temperature in the wellbore 14A with increasing wellbore depth, the inertia elementexpands in volume by an amount, which reduces values of one or more of gaps ( , ,and ); so that the resulting values of , remain the same or substantially the same, even with reduced values of viscosity of the fluid 38 due to the increased temperature. In the embodiment of FIG. 2a, the inertia element in the IRA 30a includes an adjustment element made from a material that is expendable with temperature. Exemplary shown in FIG. 2A is a pair of adjustment elements 36Ai, 36Ao in the inertia element spaced radially apart from one another. The adjustment elements 36Ai, 36Ao are part of the inertia element 36 and are made from a different material than the rest of the inertia element. If the temperature is increasing in the IRA the adjustment elements 36Ai, 36Ao expand. With the expansion of the adjustment element the inertia element is increasing and consequently the gaps , , and are reduced, represented by Gxu36Ao, Gxu36Ai, Gro36Ao, GxL36Ao, GxL36Ai, and Gri36Ai. The adjustment element may be made from a material that expands with increasing temperature, such as for example SMA, bimetal, plastic, polyethylene, aluminum). An inertia coupling 90 is shown coupling the adjustment elements 36Ai and 36Ao together. For example, a thermal expansion coefficient of adjustment elements 36Ai and 36Ao is selected so that one or more of gaps Gro36Ao, Gri36Ao is reduced at increased temperature to compensate for any temperature induced changes in the properties of fluid 38. FIG.2A shows an embodiment for adjusting the gaps in the IRA including a single inertia element. In an alternative with more inertia elements the inertia elements 361-n each include coupling elements 361-nAi and 361-nAo, and coupling inertia elements 901-n.

[0050] In the alternative shown in FIG.2b, the IRA 30b includes an inertia element 36b inside its housing. A wall 92b of housing 32b includes more than one layer of material, where the layers have different coefficients of thermal expansion. The layer of material can include IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) rubber plastics, composite materials, or metals. As shown in FIG. 2b, when an ambient temperature is increased, such as when disposed in a wellbore, one or more of the layers expand by an amount to that an initial gap GAxu1is reduced by a differential GAxu to a reduced gap GAxu2. By reducing the initial gap GAxu1 to reduced gap GAxu2 adjusts values of , to compensate for any lowered viscosity in fluid 38 due to increased temperature. Optionally, wall 92b is made up of a single material having a coefficient of thermal expansion that compensates for the lowered viscosity of fluid 38 from increased temperature. The foregoing discussion of thermal expansion is not limited to the upper axial wall as shown in FIG.2b, and in alternatives further included are one or more of the inner radial wall, outer radial wall, and lower axial wall.

[0051] In another alternative, a switch (not shown) or switches are installed that graduallydecrease one or more of gaps ( , , and ) to compensate for any changes in theviscosity of the fluid 38. The switches are mechanical parts that are subject to forces through springs or fluids. The spring forces could increase over thermal expansion or the resistance against the force decreases with temperature, e.g., by use of a suitable material such as rubber. If the switch mechanism is activated, the gaps surrounding are decreased in steps suitable for compensation of the temperature effect on the fluid. Optional materials include materials with a strong temperature dependent shape, such as but not limited to a shape memory alloy (“SMA”) or bimetal. A device with SMA may activate a force which changes the gap geometry based on the temperature.

[0052] In an alternative shown in FIG. 2C the gap between the inertial element 36 and the housing 210 is adjusted by an adjustment mechanism 206. Wall 109 represents the barrier to the inner bore 108 of the drill string. The inertia element 36 defines gaps , , and , to the surrounding housing 210. At least one wall 200 of the housing 210 is movable and the IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) position of wall 200 is adjustable by the adjustment mechanism 206. The adjustment mechanism 206 includes an activator 204 which is controllable by a controller (not shown). The controller may control the activator 204 based on the temperature and pressure variations encountered within the wellbore 14. The activator 204 moves a lever 202 which is connected to the movable wall 200. With increasing temperature, the activator 204 controls the leaver 202 in a manner that reduces the gap to compensate adjust the gap number in a way that compensates for a reduced viscosity of the damping fluid 38 due to the temperature increase. When the temperature decreases, the controller controls the activator to increase the gap to adjust the gap number in a way that compensates for an increase viscosity of the damping fluid 38 due to the temperature decrease. Also shown in FIG. 2C are bearings 208 and 212 which are supporting the inertia element 36 within the housing 210 and allowing smooth rotation of the inertia element 36 relative to housing 210. The controller may either control the activator 204 automatically without the interference of a human being or may control the activator 204 based on control information sent from a surface location to the controller in the wellbore through a telemetry means, such as mud pulse telemetry, or wired pipe. The activator may be an electrically or hydraulically driven activator. In an alternative embodiment the activator may be controlled by a material (e.g., SMA, bimetal, plastic, polyethylene, aluminum) that expands with increasing temperature or contracts with decreasing temperature. In this embodiment the activator is not connected to a controller and does not receive control messages. A typical gap size in a damping tool is in the range of 0.1 mm to 0.6 mm this includes the clearance between the bearing surfaces in the bearings of the inertia element (208, 212). The gap size is subject to variation due to thermal expansion or contraction of the housing material and the inertial element material. The gap number Sp,lab as defined in equation 10 linearly scales the stiffness factor Kdand damping factor Cdof the damping fluid 38 in the gap of the inertial ring assembly (equation 11 and 12), which can be used to determine an optimized gap number Sp,dh under IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) downhole conditions (downhole temperature, downhole pressure, expected frequency of the HFTO). The downhole gap number Sp,dh in equation 11 and 12 is varied and the stiffness and damping factor are calculated using the gap number Sp,labdetermined in the laboratory. A damping coefficient is calculated using the determined stiffness factor and damping factor. The gap number Sp,dh is again varied and an updated stiffness factor and damping factor is determined. An updated damping coefficient is determined using the updated stiffness factor and damping factor. This process is repeated until an optimized damping coefficient for an expected frequency range of HFTO is determined. The gap number Sp,dhthat belongs to the optimized damping coefficient is used to adjust the gap or the gaps between the inertia element and the housing. This optimization process is performed for each inertia element in the inertia ring assembly. The gap number determined in the laboratory provides a means to scale the stiffness factor Kdand damping factor Cdfor different gap geometries at downhole conditions. That is, the gap number of the gap configuration in the lab allows to derive (or to scale) stiffness factor, damping factor and damping coefficient for a different gap configuration (such as the gap configuration downhole). The gap or the gaps of an inertia ring assembly can be optimized by using the gap number. The optimization of the gap can then be achieved by one of the embodiments described herein.

[0053] Referring now to FIG. 4, shown in a partial side sectional view is an example of a drilling system 10A with a drill string 16A made up of a pipe string 18A and BHA 20A on its lower end. Ancillary equipment (not shown) similar to that in FIG. 1 is optionally included. Mounted in BHA 20A are one or more down hole tools. One downhole tool is a damping tool 102 or viscous damper. Damping tool 102 includes one or more inertia elements 1201-n , which in examples are designed and fabricated in accordance with the present disclosure. Each of the one or more inertia elements 1201-n1. In alternatives, a single inertia element 120 is mounted in the BHA 20A. In this example drill string 16A is rotated, as described above with regard to IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) FIG.1, to form wellbore 14A. Illustrated in the example of FIG.4 is that the damping tool 102 provides an amount of damping to the drill string 16A, which counters or damps the formation of HFTO (FIG.1) in the drill string 16A due to the rock formation 12A; and thereby avoids the undesired effects created by HFTO in a drill string.

[0054] In the example of FIG.5 is a perspective sectional view of a drilling tool 102, which is part of the drilling string 16A in a wellbore 14A (FIG. 4) and the BHA 20A (FIG. 4) used for subterranean excavation. Drilling tool 102 is also referred to downhole damping tool. The downhole tool is also referred herein as a damping tool. Tool 102 has a body 106 and a bore 108A extending axially through the body 106. Drilling fluid or mud 110 flows through the axial bore 108A to a drill bit including the mounted BHA 20A (FIG.4) and is transferred back to the surface outside the string 16A and through an annulus 17A (FIG. 4) between the drill string 16A and the wall of the wellbore 14A (FIG. 4). The drilling tool 102 is affected by downhole pressure Pannulus 180 in the annulus 17A (FIG. 4) between the drilling tool and the wall of the wellbore, the pressure Pbore 188 in the axial bore 108A, and downhole temperature T. In the example shown, a damping fluid 112 is inside a chamber 114 formed within body 106. The chamber 114 has a volume Vchamber. The chamber 114 may be formed annular around the axial bore 108A. An inner sidewall 116 is defined between chamber 114 and axial bore 108A, and an outer sidewall 118 is defined between chamber 114 and the outer surface 119 of the drilling tool 102, and between the annulus 17A (FIG. 4) of the wellbore 14A (FIG.4) and the chamber 114. Inertia rings 120 are also disposed in chamber 114 and submerged in the fluid 112; in the example shown there are a pair of rings 120, alternative embodiments include a single inertia ring or three or more. The inertia rings 120 are spaced axially apart from one another, spaced radially from sidewalls 116, and 118, and submerged in the damping fluid 112. Gaps 124 are shown in axial spaces between the inertia ring(s) 120 and stators 122. Annular gaps 125 are shown in annular spaces between the inertia rings 120 and the outer sidewall 118 IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) and the inertia rings 120 and the inner sidewall 116. In the example shown, depending on the viscosity of the damping fluid 112, the inertia rings 120 are rotatable about axis AX, and moveable with respect to body 106. The annular stators 122 extend radially inward from the outer sidewall 118 into chamber 114 and between the inertia rings 120. The combination of the inertia rings 120, stators 122, axial gaps 124, annular gaps 125, and damping fluid 112 are optionally referred to herein as an inertia ring assembly 126. There exists an axial gap to both axial sides of a single inertia ring 120. One gap is located on an uphole side of the single inertia ring 120 and a second axial gap is located on a downhole side of the single inertia ring 120. Each inertia ring is supported by at least one axial bearing and one radial bearing (not shown). The radial bearing is preferred to be between the inertia ring 120 and the inner sidewall 116. The annular gap between the inertia ring 120 and the inner sidewall is provided by the clearance between of the bearing surfaces. In an embodiment the radial bearing may be between the inertia ring and the outer sidewall 118. An inertia ring is supported by two axial bearings. One axial bearing is between the inertia ring 120 and the stator 122 uphole of the inertia ring and another axial bearing is between the inertia ring 120 and the stator 122 downhole of the inertia ring.

[0055] Furthermore, an example of damping fluid 112 is silicon oil which has a defined density (density value) and viscosity (viscosity value) at surface conditions. Both properties are changed if temperature and pressure are applied to the damping fluid 112. A deviation from a target value for viscosity and density has a negative effect on the damping property of the inertia ring assembly 126, because the value of the shear rate of the fluid in the annular and axial gaps depends on the viscosity value of the silicon oil. When the viscosity of the damping fluid 112 surpasses a target value by an amount at which shear forces from the movement of the inertia rings 120 within the damping fluid 112 in the gaps 124 exceed an applied torque from the rotation of the drill string 16A, the inertia rings 120 become coupled with the body IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) 106. Conversely, when the viscosity is below the target value, the thickness of the damping fluid 112 in the gaps 124 lacks adequate cohesion or friction to transmit torque from the drilling tool body 106 to the inertia rings 120. During drilling operations, downhole temperature Tannulus182 and downhole pressure Pannulus180 applied to the drilling tool 102 typically increase with depth; and often affects pressure in chamber 114. The pressure level or value in the chamber 114 depends on the values for the downhole temperature Tannulus182, Tbore 190 and pressure Pannulus180, Pbore188 applied to the drilling tool 102, the stiffness of the material making up the inner and outer sidewalls 116, 118, and the difference of thermal volume expansion of the damping fluid 112 and the material of the inner and outer sidewalls 116, 118 of the drilling tool 102, as well as the compressibility of the damping fluid 112. As the viscosity value and the density value of the damping fluid 112 also depend on inner pressure Pchamber184 and temperature Tchamber186 in chamber 114, during drilling operations the viscosity value and density value of the fluid 112 deviate from the target values; which in turn affects damping of the inertia ring assembly 126 and the drilling tool 102. For example, damping fluid 112 has a large enough viscosity to guarantee proper damping, but without being too viscous so that the inertias 120 are still moveable relative to the drilling tool body 106. Generally, an increase in temperature causes a drop in the damping fluid viscosity value, whereas an increase in pressure causes an increase in the damping fluid viscosity value; although not to the same scale. A need therefore exists for maintaining the viscosity of a damping fluid within an operational range of the viscosity in which the damping tool 102 operates efficiently (dampens HFTO efficiently). For the purposes of discussion herein, the operation range of the viscosity value of the damping fluid 112 describes a range of viscosities of the damping fluid 112 in which the inertia ring assembly 126 damps high frequency torsional oscillations (HFTO) in a drill string during drilling. The operation range of the viscosity is determined by laboratory experiments and / or be mathematical simulations. IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229)

[0056] While the temperature-depended viscosity value change of the damping fluid 112 is independent of the inner pressure Pchamber in chamber 114, the inner pressure and with that the pressure related viscosity value change depends on several properties of the damping fluid 112 and the stiffness of inner and outer sidewalls 116, 118. The following effects have an impact to the inner pressure in chamber 114: compressibility of the damping fluid 112 (the effect of which is greater for a highly viscous oil), and with that the volume reduction of the chamber due to pressure depends on the applied pressure Pannulus178, Pbore188 itself. In examples in which thermal expansion coefficients of body 106 and damping fluid 112 are different, there is a difference in volume expansion due to an increased temperature; which affects pressure inside chamber 114. In alternatives where damping fluid 112 is viscous, such as a highly viscous oil, the thermal volume expansion of the body 106 made from steel is quite smaller, which results in an increase of pressure Pchamber184 inside chamber 114. Stresses on body 106 created from differences between pressure Pannulus 178, Pbore 188 in the wellbore 14A (FIG.4), the pressure Pbore 188 in the axial bore 108A, and pressure Pchamber 184 inside chamber 114 cause a corresponding deformation of sidewalls 116, and 118, and the direction of deformation depends on which of these pressures is greater. The change in pressure Pchamber184 in the chamber by the resulting volume reduction or expansion of chamber 114 depends on the stiffness of the material of sidewalls 116, 118. The pressure in the annulus Pannulus 178 is mainly defined by the depth of the wellbore and is referred herein as downhole pressure. The temperature in the annulus is mainly defined by the temperature of the rock formation 12A (FIG.4), depends on the depth and is referred herein as downhole temperature.

[0057] As described in more detail below, drilling tool 102 has fluid viscosity value maintaining features or fluid viscosity adjusting features that maintain or adjust the viscosity value of the damping fluid 112 within values so that operation of the inertia ring assembly 126 provides adequate damping over a range of pressures and temperatures anticipated inside the IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) wellbore. One example of such a feature includes the sidewalls 116, and 118 having adequate mechanical integrity so that deformation under expected downhole conditions does not increase the viscosity of fluid 112 outside of its operational range (i.e., a pressure increasing deformation). Examples of sidewalls 116 and 118 having adequate mechanical integrity include sidewalls 116, and 118 that resist a pressure increasing deformation due to their radial thicknesses and / or being made from a particular material. Another example of a fluid viscosity maintaining feature includes compensating for pressure increases within chamber 114 in response to exposure of tool 102 to downhole conditions (increased temperature and pressure compared to conditions at the earth surface). Examples of pressure compensation include a portion or portions of the volume Vchamber of chamber 114 having matter with compressibility different from the fluid 112, e.g., a gas, an elastic member, or a medium that is more compressible than the fluid 112. This may be used to adjust the level of inner pressure in a way, that the level of viscosity (viscosity value) of the oil (damping fluid) in chamber 114 is adjusted to a level in the range of a target value (operational range of viscosity of inertia ring assembly). In this example, cavity 128 is shown within chamber 112 which includes a gas 130 or other substance whose volume V128changes in response to changes in pressure. Further optionally included is a cavity 132 with substance 134 whose volume changes in response to changes in temperature. The cavity 132 has a volume V132. The cavity 128 occupies a first portion V128of the of the volume of the chamber Vchamber. The cavity 132 occupies a second portion V132of the volume of the chamber Vchamber. A third portion Vfluidof the volume of the chamber Vchamber is occupied by the damping fluid. The material 134 can be a solid material or a liquid material. Examples of substance 134 include paraffin wax with a large coefficient of thermal expansion compared to the coefficient of thermal expansion of the high viscous oil (damping fluid 112) in the chamber 114, a material having a highly non-linear thermal volume expansion so that a phase transition (e.g., from solid state to liquid state or vice versa) occurs IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) in an applicable temperature range. It is within the capabilities of one skilled in the art to identify substances and volumes suitable for anticipated operating conditions in the borehole. Optionally, inside chamber 114 is an accumulator (not shown) filled with air (or other gas) and initially preloaded by a specified pressure (e.g., multiples of 100 bar). In one embodiment the gas 130 in cavity 128 and the material 134 in cavity 132 are in contact with the damping fluid 112. This is, there is no barrier that confines the gas 130 in cavity 128 or confines the material 134 in cavity 132. The gas can freely move inside the chamber 114 or inside the damping fluid 112. The same is true for the material 14. The gas may solubilized in the damping fluid volume Vfluid. In an alternative embodiment there may exist a barrier between the damping fluid 112 and the gas 130 and / or the damping fluid 112 and the material 134. The barrier separates the gas 130 or the material 134 from the damping fluid 112. The barrier is a flexible barrier, such as a bellow. The bellow may be made from rubber, an elastomer or a metal. The barriers allow compression or expansion of the gas and the material. The volume of the gas, volume of the material and the volume of the fluid define the volume of the chamber.

[0058] Referring now to FIG. 6a, shown is graph 136 with an abscissa representing values of downhole temperature, an ordinate representing values of downhole pressure, and an origin O where abscissa and ordinate intersect. Lines 1381-8 on graph 136 represent contour lines at corresponding downhole pressures Pannulus and temperatures Tannulus at which fluid 112 in chamber 114 is at a constant pressure. Each of lines 1381-8 represents a prophetic operating scenario for different embodiments of tool 102 as described above. For brevity, lines 1381-8are only shown within a range of downhole temperatures and pressures, referred to as a field of operation, and illustrated by an ellipse 140 in a dashed outline. Lines (not shown) representing pressures greater than and less than the pressure corresponding to lines 1381-8 extend substantially parallel to lines 1381-8, with lines of greater pressure being farther from the origin O and lines of lower pressure being closer to the origin O. Similarly, in FIG. 6b IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) graph 142 includes contour lines 1441-8 representing a constant viscosity of fluid 112 in chamber 114 at different downhole pressures Pannulus and temperatures Tannulus. Also similar to FIG. 6a, lines 1441-8are within a field of operation inside ellipse 140. Lines 1441-8each represent a target viscosity for operation. Lines (not shown) of larger viscosities have generally the same contour as lines 1441-8, but with corresponding greater downhole pressures.

[0059] In FIGS. 6a and 6b, contour lines 1381 and 1441 were generated in dependency of wellbore pressure Pannulusand wellbore temperature Tannulusbased on damping fluid 112 in chamber 114 is a high viscous silicon oil, and inner and outer sidewalls 116, and 118 being stiff so that they experience little deformation when subjected to anticipated downhole pressures. Here internal pressure increases are mainly driven by temperature induced volume expansion of the damping fluid 112 inside chamber 114. The contour lines 1382and 1442illustrate a scenario in which sidewalls 116 and 118 are less stiff, which increases internal pressure and an increased deformation dependency on downhole pressure. The temperature dependence is decreased because volume expansion by temperature is partly compensated by the deformation of sidewalls 116, 118. Lines 1381 (high stiffness) , 1382 (medium stiffness) representing internal pressure are more horizontally oriented for a region with medium stiffness compared to one with a high stiffness. For the viscosity, as illustrated by 1441 (high stiffness) and 1442 (medium stiffness) a similar effect is observed. In a field of operation (temperature range and pressure range encountered inside the wellbore (operating conditions)) the level of viscosity for a medium stiffness of sidewalls 116, 118 is less depending on temperature (curve 1442). For a field of operation as shown, the range of viscosity (variation of viscosity) by temperature change is smaller for a medium stiffness than for a high stiffness. In general, the range of viscosity is adjusted to the shape of the field of operation by adaption of the stiffness of sidewalls 116, 118. Lines 1383and 1443represent a scenario in which compartment (cavity) 128 contains a gas (e.g., air), fluid 112 in chamber 114 is a highly viscous silicon oil for HFTO IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) damping, and sidewalls 116 and 118 have a medium stiffness. In alternatives, compartment 128 includes separate volume regions, and optionally, gas is solubilized within fluid 112 inside chamber 114. That is gas 130 is not only in cavity 128 but distributed over the volume Vchamberof chamber 114. Depending on the volume ratio of chamber 114 and the volume of compartment 128, the internal pressure level in chamber 114 (illustrated by lines 1383 and 1443 ) is adjusted by changes in the volume of the chamber Vchamber that is filled with damping fluid Vfluid, the volume of the chamber that is filled with the gas 130 (V128), volume of the chamber that is filled with the material 134 V132. Increasing the volume V128of the gas 130 (or compartment 128) the pressure level in the chamber 114 is shifted to a lower values for the field of operation. That is, the pressure change in the chamber is smaller with increasing pressure and increasing temperature in the wellbore. This results in a shift of viscosity level, too, which is shifted also to lower values in the field of operation. That is, the change in the viscosity is smaller with increasing pressure and increasing temperature in the wellbore. This method is used to adjust the level of viscosity, e.g., if it is too high due to the increased pressure level introduced by the medium stiffness of sidewalls 116, 118. Optionally, the range of viscosity deviation from the target level is adjusted and the target level of viscosity itself is shifted more into the center of the field of operation. However, the dependency of viscosity on temperature is still there which results in the fact the viscosity is too high for low temperature and high pressure and too low for high temperature and low temperature. Temperature increase in the chamber due to temperature increase in the borehole lead to temperature increase of the damping fluid 112. Consequently, the viscosity of the damping fluid is reduced, leading to improper operation of inertia ring assembly 126 (or damping tool 102). Using a material for the sidewalls of the chamber 114 with reduced stiffness compared to a standard downhole device material (steel) will lead to deformation of the sidewalls under increased pressure conditions in the wellbore and reduction of the volume in chamber 114. This IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) results in a pressure increase in chamber 114 which will lead to an increase in viscosity of damping fluid, at least partially compensating for the viscosity decrease due to the temperature increase. The material 134 showing a volume increase due to a temperature increase leads to a similar effect. The volume increase of the volume V132of material 134 will cause a pressure increase in chamber 114 and a viscosity increase, at least partially compensating for the viscosity decrease in response to the temperature increase. While a temperature increase inside the wellbore can lead to a too low viscosity of the damping fluid, a pressure increase in the chamber, due to an increase in pressure in the wellbore, can lead to a too high viscosity also shifting the inertia ring assembly outside its operational range. A gas volume V128 in cavity 128 or solubilized in damping fluid 112, which is compressible (such as air), can compensate for the pressure increase in camber 114, maintaining the viscosity value of the damping fluid within the target viscosity zone (operational range).

[0060] Still referring to FIGS. 6a and 6b, lines 1385 and 1445 represent a scenario in which compartment 128 includes gas, and lines 1386 and 1446 illustrate a scenario with gas in compartment 128 and material 134 in compartment 132, where material 134 has a coefficient (or coefficient function) of thermal expansion which is quite larger than the value of the damping fluid 112 in chamber 114. Further in this example, the compressibility of material 134 is in the range of the compressibility of damping fluid 112 in chamber 114. Material 134 of this example is optionally a paraffin wax. If the temperature is increased, the thermal volume expansion of compartment 132, filled with material 134, increases pressure in the chamber 114. By this, the temperature depending viscosity loss of fluid 112 in chamber 114 is compensated by an increase in pressure, depicted by 1446. In this example, the internal pressure for low temperatures and medium downhole pressures remains in an acceptable range, which means that the viscosity increase by pressure is in the same range as for higher temperatures. By this, the viscosity is adjusted to have a near-linear value or less varying value for the encountered IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) pressure and temperature changes in the field of operation. The less varying viscosity values within the field of operation, compared to the behavior without the viscosity adjusting feature(s) (volume of material 134, volume of gas 130) allow an efficient operation of inertia ring assembly 126.

[0061] For oil filled HFTO downhole drilling tools (damping tools) the damping property, which depends on the viscosity, becomes more equal (less variation) in the field of operation, if the above discussed options for tool 102 (such as but not limited to, sidewall 116, 118 stiffness, damping fluid 112 characteristics, gas 130 characteristics, volume of compartments 128, 132 (volume of gas V128 and volume V134 of material 134), and material 134 characteristics) are balanced and the viscosity is controlled as represented by line 1446. The characteristics of material 134 are determined by compressibility, thermal coefficient of expansion, existence of a phase transition at a temperature encountered in the wellbore (field of operation). The characteristics of gas 130 are determined by compressibility and thermal coefficient of expansion. In an example, the internal pressure in the chamber 114 and the viscosity are impacted by material 134 in compartment 132 or volume V132, which has a non- linear thermal volume expansion established a phase transition in a temperature range encountered by the downhole tool 102 in the wellbore and while drilling. In one example, damping fluid 112 is a silicon oil, and material 134 is a paraffin wax with a phase transition from solid to liquid, in one embodiment the phase transition temperature ranges up to around 100°C. Examples of paraffin wax undergo a large thermal volume expansion over a phase transition temperature (~100°C), which is optionally used to increase the internal pressure in chamber 114 at the phase transition temperature to maintain the viscosity value at a target value or to shift the viscosity towards the target value. An example of this response is illustrated by lines 1387and 1388. As depicted by lines 1447and 1448, the viscosity experiences an increase as well. In alternatives combining the material 134 being paraffin wax (or a substance or IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) substances with similar characteristics) with the damping fluid 112 being a gas, a further linearization of the viscosity level in the field of operation is realized. In general, the feature of rapid thermal volume expansion due to phase transition is used to increase or maintain a defined viscosity level at a defined temperature rapidly, too. This is especially in scope if the viscosity at higher temperatures is on an accepted level, but too low at lower temperatures (e.g., line 1442).

[0062] Typically, increasing internal pressure results in an increase of viscosity as well, and too much of an increase in viscosity may detrimentally affect the damping ability of a viscous damping tool. Shown in a perspective sectional view in FIGS. 7a and 7b, is an example of operation of an alternate embodiment of the damping tool 102A, which is equipped to limit internal pressure increases to in turn maintain the viscosity of the damping fluid 112 to a designated range. Included in tool 102A is a wall or barrier 146 in a rearward portion of tool 102A and distal from inertia ring(s) 120. Wall 146 is an annular member with an outer diameter that joins an inner surface of sidewall 118, and projects radially inward into chamber 114 so that its inner diameter is spaced radially outward from sidewall 116 to define a gap 148 between inner sidewall 116 and wall 146. In an alternative embodiment wall 146 projects radially outward from inner sidewall 116. Gap 148 is then defined between outer sidewall 118 and wall 146. A membrane 150 extends along a rearward radial surface of wall 146, across gap 148, and axially along inner sidewall 116. Opposing ends of membrane 150 sealingly attach to an inner surface 121 of sidewall 118 and a rearward wall 152 at an end of chamber 114 to define a space 154 in the rearward end of chamber 114. In the example shown, a gas 156 is trapped in space 154 (volume V154) by the membrane 150 and walls 118, 152. For example, gas 156 (e.g., air) is precompressed to a designated level, which as shown is equal to or greater than the pressure of fluid 112. The pressure of the gas may be at room temperature and atmospheric pressure between 1 bar and 200bar. A surface of membrane 150 opposite gas 156 is in direct IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) communication with damping fluid 112 in chamber 114 through gap 148. The combination of membrane 150 and trapped gas 156 defines an accumulator 158 that compensates for pressure changes inside chamber 114. Wall 146 is optionally sized to prevent the extrusion of membrane 150 into chamber 112 due to a pressure differential between space 154 and chamber 114, in particular at lower pressures of the damping fluid 112 as present at the surface of the earth and when damping tool 102A is assembled. In a non-limiting example of operation, illustrated in FIG.7b is that pressure in chamber 114 increases over that depicted in FIG.7a, such as due to exposure to conditions in a wellbore as described above (field of operation), and exceeds the pressure in space 154 to create a pressure differential across the membrane 150. The pressure differential creates a flow of damping fluid 112 through gap 148 to deform membrane 150 as shown in FIG.7b, which in turn compresses gas 156 and reduces the volume V154of space 154. It is within the capabilities of one skilled to design an accumulator 158 that compensates for increased pressure in the fluid 112 so that its viscosity remains in a target zone and allows for continued damping capabilities of the inertia ring assembly 126. In embodiments the accumulator or the volume V154can be at any location in the chamber 114 and the wall 146 can take any form as long as it supports the membrane 150.

[0063] The effect of the embodiment of FIGS. 7a and 7b combined with the embodiments represented by graphs 136 (FIG.6a) and graphs 142 (FIG.6b) (cavities 132 and 128 filled with material 134 and gas 130) are graphically illustrated in FIGS.8a-8f. In this example, levels p3 and p4 (FIG. 8a) are shifted to higher temperatures in FIG. 8b and without a change in p1 or p2. This results in a shift of viscosity levels v3 and v4 (FIG. 8d) to higher pressure levels, as shown in FIG. 8e. Increasing viscosity in the field of operation for values higher than v2 is limited and the viscosity stays close to a target viscosity in this range. Which is shown in FIG. 8f and provides an advantage during drilling operations having a large range of temperature and pressure. The initial pressure level in space 154 is optionally adjusted to adapt the level of IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) viscosity of fluid 112 to a defined field of operation. Plots are provided in FIGS. 9a – 9f illustrating the pressure and viscosity of fluid 112 in damping tool 102A at initial pressures of 200bar, 280bar, and 350bar in space 154. Shown in FIG. 9a the initial pressure of the accumulator 158 is at a pressure below p2 so pressures in chamber 114 above p2 activate accumulator 158 to compensate for fluid expansion in chamber 114 in the complete field of operation. Shown in FIG. 9b is that the target viscosity is not in the center of the field of operation. In an alternative, the initial pressure level in space 154 is increased to ~p3; which compensates for a reduction in viscosity of damping fluid 112 at higher temperatures. In this example, there is a wide range in the field of operation, which is covered by the target viscosity. In embodiments in which the field of operation is shifted to lower downhole pressures due to different operational conditions, the viscosity level is adjusted easily by an increase of initial pressure (space 154) to a level of ~p4, as shown in FIG.9e. In alternatives, the initial pressure is adjusted outside of a wellbore, such as in a service shop on the surface, or by an additional device located in the drilling tool 102A, e.g. a pressure pump (not shown) which pumps gas from a second pressure vessel into space 156 and an adjustable relief valve (not shown) to decrease the pressure in space 154. This device is piloted uphole and is set up by a downlink or is piloted by a control unit in the drilling tool 102 which is driven by sensors, e.g. a temperature sensor and / or a pressure sensor, which measures the pressure in space 154 or in the bore hole. The downlink is sent using downhole telemetry, such as mud pulse telemetry, electromagnetic telemetry, acoustic telemetry, or telemetry through a wired pipe.

[0064] Another alternative tool 102B is shown in the perspective sectional view in FIG. 10a, and which includes an accumulator 158B made up of a membrane 150B having an end attached to rearward wall 152B of chamber 112. In this example, an opposing end of membrane 150B attaches to a rearward-facing surface of wall 146B and a rupture disk 160B is disposed in gap 148B between wall 146B and side wall 116. A first space 1541B is defined between membrane IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) 150B and sidewall 116, and a second space 1542B is defined between membrane 150B, the rearward surface of wall 146B, sidewall 118, and rearward wall 152B. A gas 156B is in the first space 1541B, and in the second space 1542B is a substance, which may have the same or different properties and conditions of gas 156B. In a non-limiting example, rupture disk 160B fractures at a designated pressure differential between chamber 112 and first space 1541B, which allows a flow of fluid 112 through gap 148B into first space 1541B, which compensates for pressure increase inside chamber 112, such as those described above. The rupture disc fractures at a pressure significantly greater than 1 bar (e.g, between 50 and 100 bar), so that the rupture disc does not fracture during assembly of the damping tool 102B at the earth surface. When the rupture disc fractures the gas will move freely inside the volume of the chamber. The substance in the second space 1542B is a solid or a fluid. In one embodiment the substance 1542B comprises a phase transition in a temperature range encountered by the downhole tool 102B in the wellbore and while drilling. The substance 1542B may be paraffin.

[0065] An optional accumulator 162 is shown in the example of tool 102B in FIGS. 10a and 10b. Accumulator 162 includes a housing 164 with a cylinder 166 inside housing 164. As shown, inside cylinder 166 is a fluid 168 (such as a gas) and a spring 170. A piston 172 is in a portion of cylinder 166 and has an outer periphery in sealing contact with the inner surface of cylinder 166. A larger diameter end of piston 172 is in contact with an end of spring 170 opposite the bottom or closed end of cylinder 166. A smaller diameter end of piston 172 projects from the larger diameter end in a direction away from spring 170 and through an opening in housing 164. A membrane 174 (e.g. a rubber membrane) spans over the smaller diameter end of piston 172 and opening in the housing 164 and is a barrier to fluid communication between the fluid 168 in cylinder 166 and the damping fluid 112 in the space outside cylinder 166. Referring back to FIG. 10A, a pair of accumulators 162 are shown mounted inside chamber 114 and submerged in fluid 112. In an example, accumulator 162 IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) operates similarly to accumulator 158 (FIGS.7a and 7b), i.e., piston 172 is urged into cylinder 166 when the pressure of damping fluid 112 is at a level to compress gas 168 and overcome the force required to compress spring 170. Options available by using the accumulator 162 include placement one or more rubber element (e.g. of O-rings (not shown)) on either the larger or smaller diameter portions of piston 172 to adjust the force (due to pressure exerted on the respective surface areas of the larger or smaller diameter portions of piston 172 by fluid 112). Another option is the adjustment of a spring constant of spring 170.

[0066] The present invention described herein, therefore, is well adapted to carry out the objects and attain the ends and advantages mentioned, as well as others inherent therein. While a presently preferred embodiment of the invention has been given for purposes of disclosure, numerous changes exist in the details of procedures for accomplishing the desired results. For example, embodiments exist in which inertia ring assembly 30 and inertia ring assembly 126 are identical or substantially the same. Embodiments of a downhole tool 102 exist having an inertia ring assembly (or assemblies) 30, 126 that is optimized as described herein, and also having compensation means as illustrated in FIGS. 5, 7a, 7b, 10, and 10b. These and other similar modifications will readily suggest themselves to those skilled in the art, and are intended to be encompassed within the spirit of the present invention disclosed herein and the scope of the appended claims. IM-#10609132.1

Claims

Attorney Docket No.: 65DDE-510066-WO-2 (000229) CLAIMS What is claimed is:

1. A viscous damper comprising: an inertia element comprising an outer surface; a chamber comprising an inner surface and a volume, the inertia element inside the chamber; a damping fluid in a first portion of the volume, the fluid having a viscosity and a temperature; a gap between the outer surface of the inertia element and the inner surface of the chamber, the gap filled with the damping fluid; a first material in a second portion of the volume, wherein the second portion of the volume decreases or increases with a change of the temperature of the damping fluid.

2. The viscous damper of claim 1, wherein the second portion of the volume decreases with increasing temperature and leads to a pressure decrease in the chamber with the increasing temperature.

3. The viscous damper of claim 1, wherein the first material comprises gas.

4. The viscous damper of claim 3, wherein the gas comprises air.

5. The viscous damper of claim 1, wherein the first material is in contact with the damping fluid and is freely moveable inside the chamber.

6. The viscous damper of claim 1, wherein: the first material is a solid or a fluid, and the first material is different to the damping fluid.

7. The viscous damper of claim 1, further comprising a second material, the second material different to the damping fluid and different to the first material, the second material in a third portion of the volume of the chamber.

8. The viscous damper of claim 7, wherein the second material is one of a solid and a fluid.

9. The viscous damper of claim 8, wherein the second material comprises paraffin.

10. The viscous damper of claim 8, wherein the second material comprises a phase transition at an anticipated operating temperature of the viscous damper.

11. The viscous damper of claim 1, wherein the second portion of the volume is separated from the first portion of the volume by a flexible barrier. IM-#10609132.1Attorney Docket No.: 65DDE-510066-WO-2 (000229) 12. The viscous damper of claim 1, wherein the second portion of the volume is separated from the first portion of the volume by a rupture disc.

13. The viscous damper of claim 1, wherein the chamber includes a sidewall, and the sidewall is formed from a material that has a smaller value of stiffness than steel.

14. A method for making viscous damper comprising: receiving an inertia element, the inertial element having an outer surface; deposing the inertia element inside a chamber, the chamber comprising an inner surface and a volume; receiving a damping fluid in a first portion of the volume, the fluid having a viscosity and a temperature; filling, using the damping fluid, a gap between the outer surface of the inertia element and the inner surface of the chamber; filling a first material in a second portion of the volume, wherein the second portion of the volume decreases or increases with a change of the temperature of the damping fluid.

15. The method of claim 14, wherein the second portion of the volume decreases with increasing temperature and leads to a pressure decrease in the chamber with the increasing temperature.

16. The method of claim 14, wherein the first material comprises gas.

17. The method of claim 14, wherein the first material is in contact with the damping fluid and is freely moveable inside the chamber.

18. The method of claim 14, wherein: the first material is a solid or a fluid, and the first material is different from the damping fluid.

19. The method of claim 14, further comprising: filling a second material in a third portion of the volume of the chamber, the second material different to the damping fluid and different to the first material.

20. The method of claim 20, wherein the second material is one of a solid and a fluid. IM-#10609132.1

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