Modeling of wave propagation in drill strings using acoustic transfer matrix method

In order to understand critical vibrations of a drill bit such as stick-slip and bit-bounce and their wave propagation characteristics through a drillstring system, it is critical to model the torsional, longitudinal, and flexural waves. The objective is to model these waves propagating through the drillstring in a computationally efficient way. Here, a modeling method based on an acoustic transfer matrix between two sets of wave variables at the ends of a cylindrical pipe is proposed. For a drillstring system with multiple pipe sections, the total acoustic transfer matrix is calculated by multiplying all individual matrices of which each is obtained for an individual pipe section. Since drillstring systems are typically extremely long, conventional numerical analysis methods such as FEM require a large number of meshes, which makes it difficult to analyze these drillstring systems. On the contrary, the analytical acoustic transfer matrix method requires significantly low computational costs. For the validation, experimental and numerical data are obtained from a laboratory measurement and by using a commercial FEM package, ANSYS, respectively. They are compared to the modeling results obtained by using the proposed method. It is shown that the modeling results are well matched with the experimental and numerical results.

In order to understand critical vibration of a drill bit such as stick-slip and bit-bounce and their wave propagation characteristics through a drill string system, it is critical to model the torsional, longitudinal, and flexural waves generated by the drill bit vibration. Here, a modeling method based on a vibration transfer matrix between two sets of structural wave variables at the ends of a constant cross-sectional, hollow, circular pipe is proposed. For a drill string system with multiple pipe sections, the total vibration transfer matrix is calculated by multiplying all individual matrices, each is obtained for an individual pipe section. Since drill string systems are typically extremely long, conventional numerical analysis methods such as a finite element method (FEM) require a large number of meshes, which makes it computationally inefficient to analyze these drill string systems numerically. The proposed "analytical" vibration transfer matrix method requires significantly low computational resources. For the validation of the proposed method, experimental and numerical data are obtained from laboratory experiments and FEM analyses conducted by using a commercial FEM package, ANSYS. It is shown that the modeling results obtained by using the proposed method are well matched with the experimental and numerical results.

To clarify the motion characteristic of the drill string in deviated well, the nonlinear dynamic model of lateral-torsional coupling for drill string system is established by the Lagrange equation. This model incorporates the contact between the drill string and borehole wall, torque dissipation, and borehole trajectory effects. Additionally, the contact behavior using linear elastic contact model is simulated. Meanwhile, the torque transfer law in the drill string system is described by a discrete torque-drag model. Finally, numerical simulations are employed to determine the dynamic properties of the drill string system. The results reveal that friction losses in drill string systems are increased with higher well inclination angles. The motion of BHA along the x direction is predominantly concentrated near the wellhole center at inclination angle of 65°, while in the y direction it primarily focuses on the low side of the wellhole. An increase in inclination angle leads to a more prominent occurrence of stick-slip motion in the drill string. When inclination angle more than 25°, there is a slightly higher collision frequency observed between the BHA and the low side of the borehole wall compared to that with the upper side. When increasing the WOB (weight on bit) to 160 kN, stick-slip motion becomes more pronounced within the drill string. Through parametric dynamics analysis of the drill string system, the rotary speed can be controlled in range from 40 to 70 r/min, and the WOB should be restricted in range from 20 to 40 kN in well depth 5000 m.

Heave compensated response of long multi-segment drill strings

Drill string models are of two major types- Conventional and Periodic. Conventional drill string models are widely used due to their simplicity in manufacturing and dynamics analysis. Drill strings are affected mainly by torsional, lateral and axial vibrations. The dispersive or propagative nature of these vibrations can only be analyzed by using periodic drill string models. Drill pipe makes up the majority of the drill string. In reality, at each end of the drill pipe, tubular, larger-diameter portions called the tool joints are located. Since the dimensions of the tool joint are negligible when compared to the drill pipe, conventional drill string models assume drill strings to be uniform structures. The tool joints in drill strings introduce a geometrical periodicity in the structure.A periodic structural component is comprised of a repeating array of cells, which are themselves an assembly of elements. The elements may have differing material properties as well as geometric variations. The periodic structures act as mechanical filters for the wave propagation. A material or geometrical change in the structure causes a disruption to the continuous propagation of vibration waves.There are three types of waves propagating in rotating structures: torsional, flexural (bending) and longitudinal. Of these waves, torsional and longitudinal waves are dispersive while flexural waves are non- dispersive. The proportions of the waves which are dispersed vary according to the Wavenumber. The wavenumber is a property of the wave and depends on the structural, material and geometrical properties of the wave guide. Waveguide is the medium through which a wave travels. The wave number, and hence the dispersion and propagation characteristics of waves can be tuned by varying the material and geometrical periodicity in the drill strings.This paper presents the vibration propagation and attenuation characteristics in conventional and periodic drill string models. The periodic drill string model is developed such that it can be easily scaled to a real drilling rig model. The research also features a laboratory setting which comprises a mini drilling rig and actual drilling samples. These features ensure robustness of the dynamics analyzed for the periodic drill string model.The research findings are analyzed under zero and non- zero borehole drill string interactions. Vibration information is collected from upper and lower parts of the drill string models to compare the propagation and attenuation characteristics. Proximity sensors are used for the data acquisition which is then analyzed using frequency and power spectrum graphs. The time and frequency domain vibration propagation characteristics are investigated for both the conventional and periodic drill string models. Laboratory testing analyzes (1) introduction of stop and pass band regions in frequency spectra by periodic drill string models, and (2) vibration attenuation in torsional and lateral vibration modes. The tests confirm the introduction of stop bands in frequency spectra for the periodic drill strings, while they were absent and had an all pass-band for conventional drill string models.The research opens up a new method of passive control of drilling vibrations- by introducing tool joint designs which could be tuned to efficiently dampen out the harmful vibrations affecting the drilling rigs.

The TDS changed the drive mode and established a simple, flexible multi-body drill string system. The system consists of a derrick, a hoisting system, TDS, and a drill string system, and is inserted into a long, narrow borehole. The drill string then interacts with mud, the borehole wall, and the bottom hole, which generates resonance and increases the risk of drilling accidents. Natural frequency, which is related to the structure of the drill string, determines critical speed. In a vertical well, the transverse, torsional, and longitudinal fluid–structure interaction vibrations of the flexible multi-body drill string system within 1,700 m was analysed using the ANSYS. The natural frequency and the associated critical speed for different bottomhole assemblies (BHAs) were obtained. Results show that reasonably selecting the TDS rotation speed and optimizing BHA offer practical engineering applications for increasing drilling speed, reducing drilling accidents, and improving economic returns.

This paper establishes a torsional model of a two-degree-of-freedom drill string system composed of a rotary table and bottom-hole assembly, constructs a friction model between the drill bit and rocks, and considers the influence of five different rock types on the stick-slip vibration of the drill string system. The stick-slip vibration of the drill string system is analyzed under changes in top drive torque, top drive rotational speed, and weight on bit. The results show that different rocks cause varying degrees of stick-slip vibration due to their distinct friction coefficients: rocks with higher friction coefficients are more prone to induce stick-slip vibration. Meanwhile, increasing rotational speed and torque, as well as reducing weight on bit, can mitigate the impact of stick-slip vibration. This study provides assistance for systematic research on the influence of different rocks on drill string stick-slip vibration.

Deep wells are commonly drilled while steering the drill bit. The steering process is completely controlled by the drilling-rig operator. A key element of this procedure is the measurement and communication of navigation information from the bottom of the well to the operator. Pressure pulses modulated onto the flow of the drill fluid are now employed in some cases to communicate this information. However, data rates are only a few binary bits per second with this method. This drastically limits the quantity of data available to the operator. As an alternative method, elastic waves generated within the steel drill string can be used as a carrier signal to transmit data. The drill string is commonly assembled from 10-m segments of threaded pipe and forms a periodic structure. The elastic wavelengths of interest are shorter than this periodic length. Consequently, these waves undergo significant dispersion. This paper presents new data for the propagation of elastic waves in a 2-km drill string. The influence of aperiodicity in the drill string, rotation of the drill string, and noise levels are studied in detail. The data verify a method for reducing the attenuation of a carrier signal by a factor of 2.

Parameter optimization based on deepwater drilling system simulation: A pre-salt exploration well in Brazil

During the drilling process, horizontal drill strings are often subject to stick-slip and back-pressure phenomena, which undermine drilling safety and affect drilling costs. However, most of the models proposed in the existing literature apply only to the analysis of the drill string motion state and are irrelevant to the rotary drilling process in coal mines. This paper presents a lumped-mass model of a drill string in a horizontal coal mine well. First, based on reasonable assumptions, the drill-string system was considered as four lumped-mass units. The lateral-torsional dynamics model was established based on the Lagrange dynamics theory. Further, combined with lateral movement, the intermittent contact between the drill string and borehole wall is described, and the friction torque due to this intermittent contact is calculated. Combined with the Karnopp bit-rock interaction, a drill-string dynamics model of horizontal wells that considers intermittent contact friction was developed. The proposed horizontal well drill-string model is more suitable for rotary drilling in a coal mine, and the nonlinear influencing factors are considered more comprehensive.

Axial harmonic excitation is an emerging method for enhancing drilling speed, yet its influence on the torsional dynamics of a drill string remains unclear. To investigate these effects, this study establishes a single-degree-of-freedom (SDOF) nonlinear torsional dynamic model capable of coupling axial harmonic excitation. The model, based on Stribeck friction theory, describes the interaction by coupling the axial harmonic load with the torsional dynamic equation. After non-dimensionalizing the model, the influence patterns of static load amplitude, dynamic load amplitude, and excitation frequency on the system’s dynamics are systematically investigated. The results show that increasing the static load amplitude aggravates stick-slip vibrations, whereas increasing the dynamic load amplitude is largely ineffective for suppression and may even induce complex motions. In contrast, adjusting the excitation frequency can suppress and even eliminate stick-slip vibrations, allowing the system to achieve stable, continuous rotation. Furthermore, an interaction effect exists between the static load amplitude and the excitation frequency; at any given frequency, the Percentage of Sticking Time (PST) increases as the static load amplitude grows. This study also reveals the non-monotonic nature of the frequency’s suppression effect on vibration. These findings demonstrate that frequency optimization is the fundamental strategy for vibration suppression, requiring the dynamic load frequency to be adjusted to a specific range based on the actual weight on bit (WOB) in drilling operations. This research provides not only a deep mechanistic understanding of the drill string’s nonlinear dynamics under complex excitation but also a key theoretical basis for designing vibration suppression strategies in advanced drilling technologies.

In this paper, a second order sliding mode control law for regulation of rotational speed in a non-minimum phase drill string system is proposed. In this regard, first, the nonlinear dynamic model of a drill string which is in contact with non-Newtonian mud is conducted. Next, a super twisting sliding mode control is designed that ensures the asymptotic regulation of output during sliding motion in a finite time and stable zero dynamics. It is shown that the proposed super twisting controller is capable of adjusting the output on a desired value by generating a proper sliding surface in a finite time. The convergence of the proposed controller for the dynamic model with a higher number of mode shapes is also investigated, and it is found that by increasing the number of obtained modes, the desired output needs less computation time with more accuracy.

Hysteretic bit/rock interaction model to analyze the torsional dynamics of a drill string

Drilling oil wells is a costly, complex and high risk operation, especially for many wells whose depths can be at least several thousand feet. To minimize the cost and risk involved in drilling, typically there are several sensors mounted near the drill bit, to measure important parameters such as temperature and pressure around the drill bit. The collected information needs to be sent to the surface, to assist the driller with controlling and steering the drill bit. Compared to the use of highly expensive and vulnerable cables for wired communication in deep oil wells, or very low rate communication using pulses of mud in wells, transmission of information using acoustic signals thru the drill string is a feasible and promising method. In this paper, we use a drill string acoustic communication testbed, where the receiver is a strain sensor. This sensor measures local fractional displacements due to received vibrations. Using experimental data, we study key characteristics of a drill string channel impulse response, sensed by a strain sensor. We also demonstrate how the strain channel response structure can control the communication system performance. [This work was supported in part by the National Science Foundation (NSF), Grant IIP-1340415.]

Wave propagation and thermal conduction properties can indicate structural damage to hot dry rock (HDR) caused by thermal shocks. Granite from the central paleo-uplift belt in the Daqing area in the northern Songliao Basin is the focus of this research. Wave propagation tests and thermal conduction tests were conducted on high-temperature specimens after natural cooling and water cooling. The influence of the cooling process with water on the apparent temperature and thermal shock velocity of rock masses is discussed. Changes in the P- and S-wave velocities, specific heat capacity, thermal diffusion coefficient, and thermal conductivity coefficient of specimens under different heat treatment conditions are analyzed and compared. The relationships between the wave propagation characteristics and the thermal conductivity values are established. The results indicate the following: (1) The apparent temperature and thermal shock velocity values of high-temperature rock masses show nonconstant rates of change from fast to slow. Rock masses with higher initial temperatures exhibit a continuous and strong thermal shock effect, and water temperature differences have only a limited effect on the thermal shock velocity over 20 s of cooling with water. (2) As the initial temperature increases or water temperature decreases, the P-wave velocity, S-wave velocity, thermal diffusion coefficient, and thermal conductivity coefficient values of high-temperature rock masses decrease overall, while the specific heat capacity values increase. The amplitude of change after water cooling is higher than that after natural cooling. When the initial temperature is below 100° C, the free water content is the main factor influencing the wave propagation characteristics and changes in the thermal conduction characteristics. When the initial temperature is greater than 300° C, the changes in both properties depend on the amount of thermal damage done to the rock mass. (3) The fitting results suggest that the wave propagation and thermal characteristics are closely related, and the damage factors are strongly consistent. The deviation of fitting coefficients is mainly due to the limited development of fractures in the small-sized specimens. The research results provide a reference for studies on thermal damage in HDR in the geothermal development process, and a method to determine the in situ thermal conductivity of reservoirs is proposed.