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.     

旋转导向系统底部钻具组合力学计算新方法

底部钻具组合(Bottom Hole Assembly, BHA)的力学计算是进行旋转导向系统钻具组合设计和井眼轨迹控制的基础．本文在纵横弯曲法、加权余量法和有限元法的基础上,提出了一种基于管柱单元组合的BHA力学求解方法．该方法以保持微分方程特解相同的条件作为管柱单元划分依据,对底部钻具组合进行单元划分;将管柱单元的挠曲线通解替代传统加权余量法的试函数,结合单元节点类型和组合关系,构建出包含边界条件和通解系数的线性方程组．对于边界条件未知问题,以支点反力符号条件为约束条件,以挠曲线越界程度、切点处弯矩平衡条件为目标函数,建立了以边界条件未知量为变量的多目标优化数学模型．应用多目标优化算法求解出边界变量,进而得出通解系数;最后,得出管柱单元内各点位移和载荷．以推靠式旋转导向系统BHA力学计算为案例,对比本文方法与加权余量法的计算结果,发现两者计算结果相差较小,表明本文方法可用于旋转导向系统底部钻具组合的力学计算．     

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。     

水平井钻柱接触问题的间隙元法

长中半径水平井钻柱与井壁的接触问题是大面积接触的几何非线性问题。本文通过构造“多向接触间隙元”把钻柱与井壁结合起来研究,能方便正确地反映这种接触状态的变化规律,也能解决一般有限元法会遇到的总刚奇异性问题。运用本文方法,可以对整体钻柱或下部钻柱进行接触有限元分析。采用欧拉-修正的牛顿迭代法进行运算,给出钻头受力变形值,为井眼轨道控制提供了重要依据。 现场实验证明,在井眼轨道跟踪预测和钻具组合性能评价方面,本文计算结果与实测结果符合很好,对提高钻进速度,保证钻井质量有较大的实用意义。     

Controlling torsional vibrations of drill strings via decomposition of traveling waves

Torsional vibrations in drill strings, especially stick-slip vibrations, are detrimental to the drilling process as they slow down the rate of penetration and may lead to failure of the drilling equipment. We present a method for controlling these vibrations by exactly decomposing the drill string dynamics into two traveling waves traveling in the direction of the top drive and in the direction of the drill bit. The decomposition is derived from the wave equation governing the string vibrations and is achieved with only two sensors that can be placed directly at the top drive and at a short distance below the top drive (e.g., 5 m). Therefore, downhole measurements along the string and at the bit are not necessary, which is a major advantage compared to other control concepts for drill string dynamics. The velocity of the top drive is then controlled in order to absorb the wave traveling in the direction of the top drive, thus achieving a reflection coefficient of zero for the frequency range of the undesired torsional vibrations. The proposed algorithm is implemented for both a numerical example and an experimental setup; results show that the control concept works very effectively.     

Self-excited stick–slip oscillations of drill bitsOscillations stick–slip auto-entretenues d'un outil de forage

This Note studies the self-excited stick–slip oscillations of a rotary drilling system with a drag bit, using a discrete model which takes into consideration the axial and torsional vibration modes of the bit. Coupling between these two vibration modes takes place through a bit-rock interaction law which accounts for both frictional contact and cutting processes at the bit-rock interface. The cutting process introduces a delay in the equations of motion which is ultimately responsible for the existence of self-excited vibrations, exhibiting stick–slip oscillations under certain conditions. To cite this article: T. Richard et al., C. R. Mecanique 332 (2004).     

井孔约束下水平井段钻柱的浑沌运动

考虑了钻柱即时构形中轴向力对钻柱弯曲的影响,计及由于弯曲变形而产生的轴向附加力,得到了水平井段钻柱在周期性波动钻压激励下的非线性参数激励振动系统,导出了根据钻柱的物理和几何性质以及井孔尺寸计算系统参数的公式,选通过Calerkin法对控制方程在空间域内加权消残,然后在时间时间域内用Melnikov-Holmes方法得到了钻柱可能发生浑沌振动的参数激励的阈值,文中结果可能对钻井轨迹的控制具有一定的指导意义。     

石油钻井旋转导向实验转台测试系统设计

设计了一种实验转台测试系统,主要用于在实验室环境下验证石油钻井旋转导向工具可行性并测试其性能参数。提出了总体方案,设计并完成了系统的关键组成部分：两轴手动转台、合力测试仪、惯性测量模块、信号处理系统,完成了计算参数和姿态误差角测试实验。实验结果表明,所设计的各部分工作正常,满足系统的总体要求。这为将来石油钻井导向工具的井下实验打下很好的基础。     

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.     

井下多股淹没射流水力清岩能力分析

研究石油钻井井下射流的水力清岩能力对钻井业有重要意义。本文借助于预处理方法和多块网格对接技术由计算机数值模拟了形状复杂的钻井PDC钻头井底下的多股淹没射流流场。为体现井底有岩屑时射流场对其的清洗作用。文中借助河流泥沙运动理论，分析了岩屑在井下的受力与运动以考虑固相的作用。因岩屑主要为推移运动。在井底除环空外的大部分地方可简化视为二维运动。提出了钻头井底水力清岩能力的体现参数-水力挟岩力。并通过数值模拟显示了井下流场，描述了转速，射流流量，喷嘴面积，射流雷诺数及井下过流空间等流场控制参数对井底水力清岩能力的不同影响，指出相关水力参数在射流时的优化方向。为复杂的井底流场控制和钻头的合理设计做探索基础。     

间隙元在钻柱瞬态动力学分析中的应用

为了描述钻柱与井壁的随机碰撞接触状态，本文构造了动力间隙元，并推导了动力间隙元的相对压缩量和迭代求解格式。把动力间隙元与梁单元相结合，采用Newmark直接积分法和冲量定理，进行了钻柱碰撞接触非线性瞬态动力学分析。经工程应用表明，构造的动力间隙元能够描述钻柱的碰撞接触状态，所设计的偏心防斜钻具已在大庆油田得到应用，取得了明显的经济和社会效益。     

Stochastic torsional stability of an oil drill-string

The aim of this paper is to investigate the influence of uncertainties on the torsional vibration of drill-strings, in order to find out which uncertainty affects most significantly the torsional stability. The unstable torsional behavior is commonly associated to polycrystalline diamond compact bits, and manifests itself in the form of stick-slip oscillations. The stick-slip is a severe type of self-excited vibration characterized by large fluctuations in the rotation of the bit. It not only increases the bit wear, but also can cause drill-string failures. The analysis were done using a mathematical model of the drill-string based on classical torsion theory discretized by means of the finite element method. The bit-rock torque was included in the model as a nonlinear boundary condition at the bottom end of the drill-string. The values of the model parameters are typical values of a real drilling situation, which are subject to a high degree of uncertainty, what justifies a stochastic analysis. We have built probability distributions for the uncertain parameters and used Monte Carlo method to obtain the stochastic stability maps.     

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.     

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.     

石油钻井底部钻具组合大挠度三维分析

精确描述了石油钻井底部钻具组合在三维弯曲井眼中的变形约束条件及边界条件，应用加权余量法，对底部钻具组合静力大挠度问题进行了三维分析研究，并编写了相应的计算机分析程序。该程序可以在普通微机上运行，能迅速模拟计算底部钻具组合任一点的挠度、转角和内力，同时求得钻头对地层的机械作用力和偏转角。通过算例分析，本文初步阐明了井眼曲率及方程中的非线性项对钻头力学特性的影响效果。     

Vibration localization in disordered periodically stiffened double-leaf panels

Vibration localization in periodically stiffened double-leaf multi-span panels is studied by employing the transfer matrix method. The localization factors of the ordered and disordered systems are calculated based on the Lyapunov exponent. The numerical results show that the propagation of vibration in rib-stiffened periodic double-leaf panels exhibits passbands and stopbands. The vibration localization phenomenon occurs and is enhanced with the increasing disorder of span-length. The torsional rigidities of the stiffeners have a significant effect on the pass bands and the localization factor. With the torsional rigidity of the stiffeners increasing, the vibration localization factor first decreases, then increases and finally tends to be the situation of the rib-stiffened single-leaf panels. It is also noted that for the double-leaf panels a passband appears among the lower dimensionless frequencies for some particular values of torsional rigidity of the stiffeners while a stopband always exists for the single-leaf panels.     

求解中短半径弯螺杆钻具的纵横弯曲法

介绍了一种求解中短半径($K=1^\circ$/m$ \sim 3^\circ$/m)弯螺杆 钻具的纵横弯曲法, 以指导弯螺杆钻具的设计和使用. 采用变刚度梁柱理论, 并应用等效载荷法对具有初始结构弯角的梁柱进行等效处理, 根据钻具组合支座连续条件及 边界条件建立了中短半径水平井造斜螺杆钻具组合的力学模型, 进而求得钻头侧向力, 依此 预测弯螺杆钻具的造斜能力. 这种分析方法得到了成功应用.     

Influence of Drilling Parameters on the Accuracy of Hole-drilling Residual Stress Measurements

Multiple measurements using the hole drilling method were made in samples with a “known” state of residual stress. Drilling parameters were independently varied (bit rotation speed, bit diameter, and hole depth) to determine the effect on accuracy and repeatability. The study showed that accurate results can be achieved without ultra-high drill rotation speeds and that, in aluminum and stainless steel, speeds over 5 krpm and 10 krpm (respectively) were sufficient. Inaccuracies were evident in the stainless steel at speeds below 10 krpm and were attributed to non-circular holes, which may have been the result of bit vibration. There were no significant trends associated with altering the hole depth and only a slight trend associated with bit diameter variation.