Quantized attractors in wave models of torsion vibrations of deep-hole drill strings

We pose the problem of self-excitation of elastic wave torsional vibrations of a rotating drill string, which arise as a result of frictional interaction of the drill bit with the rock at the bottom of the deep hole. We use d’Alembert’s solution of the wave equation to construct a mathematical model of the wave torsion pendulum in the form of a nonlinear ordinary differential equation with retarded argument. We show that there exists a range of variation in the angular velocity of the drill string rotation, where, along with the unstable stationary solution characterized by the absence of vibrations, there are oscillatory solutions in the form of a stable limit cycle (attractor). The self-excitation of these vibrations is soft, and the self-oscillations themselves belong to the class of relaxation vibrations, because their period can be divided into several separated intervals corresponding to slow and fast variations in the state of the system. The velocities of the drill bit elastic motions on each of these time intervals remain constant, and the durations of all of them are the same and equal to the time interval (quantum) of the twist mode propagation from the drill bit to the drill string top and conversely.     

结构力学分析方法在南海水平井钻进预测中的应用

本文探讨了结构力学分析方法-非线性有限元性在预测水平井钻进中的工程应用,在钻探水平井尤其是大位移水平井中,事先较准确地预测出钻柱的钻进扭矩及钻头前进的方向,是取得水平井成功的关键条件之一。利用非线性有限元理论,着重分析了水平井实际钻进中的钻柱大变形非线性及钻柱与井壁的接触非线性问题,并导出了一套非线性有限元钻柱力学模式,在此基础上编制了一套非线性力学计算程序软件,并在海洋石油南海西部石油公司一个钻井平台水平井钻井进行了五口井的实际验证,获得了一些有启迪性的结论。     

复合材料结构力学分析CAE软件现状

复合材料结构分析软件是用以分析、设计复合材料结构的重要工具,常用的复合材料结构分析软件包括基于CAD软件发展而来的复合材料分析工具、通用有限元软件自带复合材料分析工具和以Digimat等为代表的专业化复合材料结构分析软件。本文对常用的复合材料分析软件进行了综述,介绍其主要功能,从学术、应用等多方面探讨相关产品的优点及不足;论述了专业化复合材料结构分析软件的特点及功能;分析了复合材料结构分析软件的现状和发展趋势;探讨了复合材料结构力学分析CAE软件在国产化方面所需进一步解决的问题。     

隔水管弯曲对钻柱振动影响的计算与分析

海洋油气资源钻探中隔水管的弯曲对钻柱振动以及钻进特性有特别的影响。为得到隔水管弯曲对钻柱振动的影响规律,对南海已钻深水井使用非线性有限元软件建立全井钻井数值计算模型,研究获得了不同垂深时隔水管弯曲对钻柱振动特性的影响规律。研究表明:隔水管弯曲会加剧钻柱的振动,钻柱振动加剧会导致钻井能耗上升、钻头切削能力下降并且会加快钻柱疲劳;当隔水管的弯曲达到某临界值,钻柱与隔水管间的接触力会陡增;井口的钩载越大,隔水管弯曲带来的井口钩载波动量越大;井越深,隔水管弯曲对全井钻柱最大弯矩和钻头切削能力的影响越小。     

Dynamics of rotating conveying mud drill string subjected to torque and longitudinal thrust

In the view of fluid-structure interactions and rotor dynamics, this paper models the lateral vibration of a vertical downward rotating elastic drill string conveying mud subjected to supporting stabilizers, bit torque and longitudinal thrust. The dynamic model involves the rotational inertia of the drill string tube cross section, the gyroscopic effect caused by rotation, the damping due to friction with the surrounding fluid, the gravity force and mud buoyancy. Damped natural frequency, stability and resonance of the drill string system are determined by quadratic eigenvalue problem and investigated at influences of the stabilizer, rotational angular speed, mud flowing velocity, bit torque and thrust. As a result, the drill string can lose stability both at simultaneous and separate influences of the mud conveying, bit torque and thrust, whereas the rotation, stabilizer and gravity of the drill string can improve system stability; the rotational angular speed causing system resonance decreases with the increase of the mud flowing velocity, bit torque and thrust.     

波动钻压下阶梯钻柱系统稳定性研究

处于狭长井筒中的钻柱,其动力响应受到钻具组合、内外钻井液流动以及钻井参数等因素的影响,钻柱动力失稳导致的剧烈振动是井壁坍塌和钻具失效的重要原因。考虑到钻杆和钻铤在刚度和线密度上存在很大的差别,论文将钻柱简化为单阶梯输液管柱,钻井液沿着钻柱内部向下泵入并从环空返回地面。耦合考虑钻柱自重、随时间简谐变化的波动钻压、稳定器以及钻井液的水动力和阻尼力,建立了直井中钻柱横向振动的解析模型。利用有限单元法离散为四阶常微分方程后,采用Bolotin法得到临界频率方程确定系统的不稳定区范围,研究了钻压、钻杆长度、稳定器安装位置、钻井液的流速和密度等参数对系统稳定性影响的机理。研究表明：钻压的平均值和波动幅值都是钻柱失稳的驱动因素,而系统的稳定性对处于受拉状态的钻杆的长度变化不敏感。在论文所研究的参数范围内,降低钻井液流速和密度、下移稳定器的安装位置均有助于增强系统的稳定性。     

Torsional vibration analysis of push-the-bit rotary steerable drilling system

Ordinary drillstring torsional vibration is a very common phenomenon that has been attracted great interesting. Through Measurement data, a series of studies and analysis of torsional vibration characteristics of the bottom hole assembly (BHA) have been developed. However, for rotary steerable system (RSS), especially push-the-bit mode, its drill torsional vibration phenomenon will demonstrate the new properties, because that the underground implementing agencies will generate cycle torque and drag to the BHA in the orientation process. This process is completely different to the previous. A set of “strap-down” measurement system was developed in this paper, and the triaxial accelerometer and triaxial fluxgate were installed near the bit. Proposed a method of solver drill bit rotation speed using real-time downhole measurement data (sampling frequency 100 Hz), and the torsional vibration mathematical model of push-the-bit RSS was established. We found that the torsional vibration phenomenon of push-the-bit RSS is more serious than the ordinary drilling system by downhole measurement data analysis, even in most cases manifested as stick-slip. The torsional vibration was divided into five different modes, which showing different statistical regularities. Corresponding analysis of the angular displacement and speed, we found that the drill bit always appears low-speed in the position of oriented. This is a strong proof of that the RSS implementing agencies pushing the BHA caused the drill bit torsional vibration more serious. This work is supplemented and development of the drill string torsional vibration studies. Contribute to the better understanding of the dynamics of the push-the-bit RSS. Put forward a new way of analysis the rotary steerable drillstring fatigue damage predicted, steering ability and the torsional vibration control.     

Measuring the efficiency of vertical drill-strings: A vibration perspective

A drill-string is a slender structure with nonlinear dynamics; it is an equipment used in the oil industry to drill the rock in the search of oil and gas. The aim of this paper is to investigate the efficiency of the drilling process in terms of input/output power. The continuum system is linearized about a prestressed configuration, the finite element method is applied to discretize the linear system, then a reduced-order model is constructed using the normal modes of the linear system; only torsional and axial vibrations are considered in the analysis. Uncertainties related to the speed imposed at the top are also included in the analysis. The rotational top speed is modeled using two different stochastic processes and the Monte Carlo Method is employed to approximate the statistics of the response of the resulting stochastic differential equations.     

气体钻井中接触非线性问题的数值算法研究

根据动量守恒和钻柱力学的基本理论,建立了气体钻井三维弯曲井眼钻柱动力学模型和钻柱与井壁接触碰撞模型;提出了一种求解钻柱与井壁接触非线性有限元方程的元胞自动机算法。该方法具有编程简单、收敛速度快等优点,以实际工况为例进行仿真模拟,选取有代表性节点的仿真计算结果并加以分析。仿真结果表明:该方法较好地解决了三维弯曲井眼中钻柱与井壁接触碰撞的复杂边界条件问题,在解决气体钻井钻柱与井壁接触非线性问题的研究中具有良好的应用前景。     

Understanding root cause of stick–slip vibrations in deep drilling with drag bits

In search for the root cause of stick–slip, a mode of torsional vibrations of a drilling assembly, a linear stability analysis of coupled axial–torsional vibrations has been carried out. It has been shown that in a rotary drilling system with axial and torsional degree of freedom two distinct modes of self-excited vibrations are present: axial and torsional. These axial (torsional) modes of vibrations are due to resonance between the cutting forces acting at the bit and the axial (torsional) natural modes of drillstring vibrations. It has been demonstrated that although axial and torsional modes of vibrations do affect each other the underlying mechanisms driving these modes of vibrations are completely different. In particular, the only driving mechanism of the axial vibrations is the regenerative effect, while there are two distinct mechanisms that drive the torsional vibrations: (i) the cutting action of the bit, and (ii) the wearflat/rock interaction. Moreover, in the case of the torsional vibrations the regenerative effect plays only a secondary role. The results of the present study indicate that the axial compliance can play a stabilizing role. In particular, the stabilizing role of the axial compliance increases as the ratio of the torsional to the axial natural frequency of the drillstring vibrations decreases.     

Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects

In this article, a discrete model of a drill-string system is developed taking into account stick-slip and time-delay aspects, and this model is used to study the nonlinear motions of this system. The model has eight degrees-of-freedom and allows for axial, torsional, and lateral dynamics of both the drill pipes and the bottom-hole assembly. Nonlinearities that arise due to dry friction, loss of contact, and collisions are considered in the development. State variable dependent time delays associated with axial and lateral cutting actions of the drill bit are introduced in the model. Based on this original model, numerical studies are carried out for different drilling operations. The results show that the motions can be self-exited through stick-slip friction and time-delay effects. Parametric studies are carried out for different ranges of friction and simulations reveal that when the drill pipe undergoes relative sticking motion phases, the drill-bit motion is suppressed by absolute sticking. Furthermore, the sticking phases observed in this work are longer than those reported in previous studies and the whirling state of the drill pipe periodically alternates between the sticking and slipping phases. When the drive speed is used as a control parameter, it is observed that the system exhibits aperiodic dynamics. The system response stability is seen to be largely dependent upon the driving speed. The discretized model presented here along with the related studies on nonlinear motions of the system can serve as a basis for choosing operational parameters in practical drilling operations.     

Equivalent boundary model of lunar soil drilling simulation by DEM

Aiming to solve the computational cost problem in the discrete element simulation for lunar soil drilling sampling, an equivalent boundary method was proposed. A high-accuracy DEM model of lunar soil was established firstly. As the novel alterable constitutive law, the accuracy of the model was verified to meet the performance of real lunar soil very much both in shear strength indices and elastic–plastic behavior. A common drill bit in the geological exploration field for sampling soil was chosen as the simulation object. In preanalysis, it was known that with the increase of drilling depth, the stress concentration area was always near the drill bit, while the affected area of the lunar soil was a cylindrical area around the drill pipe, which extended towards the drilling direction instead of extending around it. Then a big boundary drilling simulation scene was established to investigate the flow direction of lunar soil particles. The motion law of particles and the velocity field information were obtained, and a U-shape chain was described around the drill bit. Finally an equivalent boundary was set near the U-shaped chain, and the size was determined by comparing the soil stress in the fierce collision zone and around the reference boundary. This method could be a reference for other lunar soil drilling researches with other drills of different sizes.     

PROGRESS IN MEASUREMENT TECHNOLOGY FOR DRILL STRING VIBRATION

随着深井、超深井数量的快速增加, 钻柱振动导致的钻具失效问题更加突出. 针对钻柱振动的研究可分为理论与数值模拟、测量分析两种方法. 由于钻柱振动具有复杂的非线性特征, 使得理论与数值模拟研究受到了很大限制, 因此井下振动测量技术的研究显得尤为重要. 本文比较全面和系统地介绍了国内外钻柱振动测量技术研究现状和进展情况, 并对几个应用较为成熟的国外测量系统的工作原理、分析方法及应用技术进行了详细的综述. 所得结论可为我国井下振动测量技术的发展提供重要参考.     

钻进速度对钻屑温度影响的实验研究

利用钻屑温度预测冲击地压时,钻进速度是影响钻屑温度的一个重要因素。本文利用自行研制的钻头温度测试装置,对钻头温度变化进行监测,分析不同钻进速度对钻头温度变化的影响规律。实验结果表明:钻孔时,钻进速度减慢,钻头与孔壁之间的摩擦时间增长,摩擦产生的热量增多,使钻头温度升高。钻进速度对钻屑温度有较大影响,使用钻屑温度法预测冲击地压时,应制定统一的钻进速度指标,增加预测准确性。     

Shock and traveling wave phenomena on an externally damped, non-linear string

We examine the propagation of shocks and traveling wave phenomena on a one-dimensional string that is executing finite-amplitude, transverse vibrations in a resisting medium. As part of our study, we develop an approach that allows us to describe, albeit approximately, the evolution and propagation of a shock front using analytical methods. In addition, exact traveling wave solutions, one of which involves the Lambert W-function, of the string's equation of motion are determined and analyzed. Lastly, a possible new form of the solution to the linearized problem is presented and extensions and other applications of the present work are briefly discussed.     

Localized waves in a string of infinite length lying on a damaged elastic base under finitely many impacts

Asymptotic solutions of the problem of dynamics of an infinitely long string lying on an elastic base with prescribed damage under the action of finitely many periodic impacts are constructed in the two cases of small and large damage of the elastic base. The condition of resonance origination in the string is obtained in the case of small damage when the standing wave is localized in the region of damage. At the final stage of the damage growth in the elastic base, when its value is close to the critical one, the localized mode and the resonance are absent, and only a traveling wave exists in the string.     

A novel torque analysis method for drilling deep lunar soil by DEM

In order to solve the torque design problem of deep lunar soil sampling using drilling, a novel torque analysis method was presented based on discrete element model (DEM). This method includes three stages: drilling simulation of the bit and stem segment, resultant torque calculation, and predicted curve fitting. First, special drilling models were designed for a bit and stem separately. A high-density equivalent particle group, boundary vibration control, pre-drilling simulation and constant pressure surface control were designed for the bit and stem drilling modelling at different depths to ensure the rationality of the model. An example of the torque synthesis process was given, and the simulation time was analyzed. Finally, the simulation predicted torque curve was plotted and compared with the experimental curve. The experimental and simulation curves show that as the drilling depth increases, the torque increases approximately linearly first and then flattens out gradually after a depth of 1 m. The consistency between the two results indicated that the proposed method was validated. Using this method, engineers can take short time to analyze the torque and design basic parameters of the drill mechanism. The problem of high experimental cost and long simulation time in torque design is solved.     

Experimental study of the rock-bit interaction

A rock-drilling machine to facilitate full-scale drilling experiments has been built. The machine uses a sixinch tricone roller bit to study the dynamics of the rock-bit interaction. This process is not well understood, and there is a definite need to establish criteria for drill-bit wear and for the directional stability of the drill bit. The research undertaken here is one step towards this goal. Specifically, this paper presents the results of a time-series analysis of forces measured on a drill bit. It is found that there exist no simple relationships between the forces, but some qualitative relationships are found. A strong correlation exists between the vertical force and two of the tangential forces on the drill-bit legs. Some correlation is seen between the other forces, but to a lesser extent. Most of the forces show a dominant frequency at the rate of rotation of the drill bit. This may be due to a hard spot in the formation, hole eccentricity, uneven-bit-roller loading or simply hole deviational effects. Also a frequency which corresponded to three times the rotational rate was dominant. This is interpreted as a result of the three roller cones acting on, for example, a hard spot in the formation. Comparing the observed frequencies to the calculated expected frequencies due to roller-tooth impact, only the lower of the expected frequencies were seen. The higher expected frequencies were apparently attenuated. Some of the intermediate frequencies that were observed cannot be explained in terms of the simple relationships discussed above, and it is concluded that the drill-bit/rock interaction is a very complex process which is not yet fully understood.     

Helical traveling waves in elastic rods

We pose the problem on free harmonic bending vibrations of an infinite rotating tubular elastic rod with an internal fluid flow, prestressed by a torque and a longitudinal force. We show that these vibrations can only be realized as traveling circular helical waves. It is shown that, for any wavelength, there exist four waves, two having the form of a left-handed helix and the other two having the form of a right-handed helix. Each of these waves propagates in the positive and negative directions of the longitudinal rod axis at different velocities. These phenomena can manifest themselves in deep-hole drill columns.     

Andronov–Hopf bifurcations in wave models of torsional vibrations of drill strings

A wave model of torsional vibrations of rotating drill strings is set up. The ranges of rotational speed in which self-excited vibrations occur are found. Andronov–Hopf bifurcations occur at the limits of these ranges. The conditions for the occurrence and development of self-excited oscillatory processes are established