基于多元回归的超短半径水平井累积产油预测方法

随着油田的持续开发和老油区作业频繁等原因使井况日趋恶化,加上油藏的非均质性,严重影响油田采收率的提高.如在开发区内补打更新井、加密井,其建井周期长、成本高.在套管内侧钻中短半径水平井,不但可以节约钻井成本,而且还可以增大油层裸露面积,提高采收率和经济效益.但若准确选择有利的侧钻井位,需要首先建立累积产油量与侧钻井相关参数的关系.根据建立的数值模拟概念模型和确定的水平井开采方案,用正交设计对有效厚度、无因次距顶高度、油水井距、平均渗透率、平均剩余油饱和度、水平井开采阶段完善程度等6项因素进行了组合,并计算了25个数值模拟方案.利用多元回归,从模拟计算结果得到计算注水正韵律油层10年累积产油量的多元回归公式,可作为下步优选侧钻井位的依据.     

A contribution to efficient calculation of complex drill string dynamics for deep hole drilling

This paper presents a hybrid model to describe drill string dynamics for deep hole drilling. Generally, a typical rotary drill string has a length of several kilometers, but the diameter is less than half a meter. Due to the large ratio of length to diameter, a drill string is a very flexible system. Consequently, an operating drill string is always affected by axial, torsional and lateral vibrations, which potentially induce serious failures. In order to avoid fatal defects, simulations to forecast vibrations are necessary. The simulation should be capable to exhibit the complex dynamical phenomena, e.g. sick-slip, forward whirl and backward whirl, and interactions between drill string and borehole. Usually, these simulations are very time-consuming. In this work, a hybrid model consisting of lumped masses connected with weightless beam elements representing the drill string is developed. The interaction between the drill string and the borehole is implemented by unilateral constraints to describe the nonlinear contact behavior. It was shown that accuracy and simulating time were improved by this model with respect to classical finite-element models. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of the Dynamics of Slender Continua Using Karhunen-Loève-Transformation

The dynamics of continua with very small diameter–to–length ratio, like bridges or drill–strings, has been object of mechanical analysis for a long time. While it is often possible to create a well–suited mechanical model, it is difficult to determine the exact current loads and the exact operational state. For drill–strings, the load of the drill–bit depends on the material of the rock, but also on other unknown disturbances like differential sticking which can occur along the drill–string without being noticed directly. Karhunen–Loève–Transformation (KLT) provides a possibility to describe the dynamics of a continuous system with few Characteristic Functions (CF), as long as the motion of the system is stationary. On the other hand, the resulting CFs of the KLT are sensitive to changes in the dynamic system behavior. These changes can result e. g. from the occurrence of stick–slip of the bit or differential sticking of the string. On the basis of a simple model, we show that this sensitivity can be used to detect and characterize such changes. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of the dynamic phenomena “stick-slip” and “whirl” of a drill string demonstrator

Vibrations of drill strings in oil and gas well bores can reduce drilling performance or lead to damage of drill string components. These vibrations are neither optically observable nor measurable because of the geological formation. Hence usually simulations are used to understand the dynamic behavior. The test stand “OSTrator” adds more insight to this problem. The demonstrator represents a scaled drill rig granting direct access to the complex dynamic behavior of the real drill string. Two phenomena are of special interest: the stick-slip effect, a torsional oscillation, and the whirl effect, a periodic torsional-lateral movement with permanent wall contact. Since the OSTrator was built for showcase purposes, it has to be piloted in and out Stick-Slip and Whirl domains by a control algorithm. Therefore efficient multi-body-systems able to represent these two effects in faster than real time are demanded. In this presentation, the modeling of the stick-slip and the whirl effect are discussed. The models should be able to predict these effects and supply data to avoid or confront them. Key questions are the modeling of the wall contact and the resistance at the drill bit. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

气体钻井钻柱气固耦合横向振动数学模型的建立与控制

根据钻柱力学和动量守恒基本理论,建立了考虑气体钻井液对钻柱内外耦合影响时的钻柱横向振动模型,此模型与一般的梁式结构的振动模型不同,它包含了钻柱轴力、钻柱内注入压力、环空压力和钻柱内气体对钻柱振动的影响.同时给出边界条件和初始条件.通过把系统外激励函数当作控制变量,利用Banach空间几何性质证明了此系统存在唯一最优控制元.     

Model Order Reduction of a Drill-String-Model with Self-Excited Stick-Slip Vibrations

The dynamical behavior of a drill-string is defined by its small diameter-to-length ratio, which makes the string vulnerable to torsional vibrations. In combination with the nonlinear friction characteristic at the drill bit, this can lead to self-excited stick-slip vibrations which are detrimental to the drilling process. The string can be modeled by the Finite Element Method or as a Multi-Body system to represent the distributed character of the system. The analysis of the resulting high-dimensional model is, however, elaborate and time-consuming. We show that through Galerkin Projection onto the first two Characteristic Functions gained from Karhunen-Loève-Transformation, a reduced system can be obtained which reproduces the essential dynamical properties of the original system, e.g. the stick-slip motion. With the reduced system, the linear stability of the drill-string can be analyzed. We show that by reducing the inertia of the rotary table the system can be stabilized. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

大挠度钻柱强度分析的平衡微分方程法

对小井眼、大曲率井中钻柱强度问题,以井轴为基准轴,在对井轴弯挠描述和钻柱微段三维受力变形分析的基础上,建立大位移钻柱平衡微分方程,采用Longe-Kutta法解之求内力,并依此求应力和建立强度条件.对H767侧钻水平井施工中钻柱应力计算分析,结果说明与有限元模型和弹性化软绳模型比较相吻合,该模型比有限元模型计算简捷方便;比弹性化软绳模型更完善可信;该井钻柱破坏事故愿因在于井眼曲率过大,兼有应力集中.     

On the Wellbore Contact of Drill Strings in a Finite Element Model

In drill string dynamics the Finite Element Method is usually applied to models of very long drill strings in a wellbore with arbitrary curvature. Taking account of geometrical constraint between the drill string and the wellbore, a high density of nodes is necessary. This density is much higher than the one needed to describe the natural vibrations properly, so this firstly leads to an extension of the computing time. A penalty function is frequently utilized to describe the contact problem between the drill string and the wellbore where the contact normal force acts only on the nodal points of the drill string. It was recognized that only node-to-surface contact models cannot fulfill this geometrical constraint, because the segment between two nodal points deeply penetrates the wellbore wall in some cases. A process with Gaussian points along the segment in time domain will be introduced, so that the drill string will be described according to this geometrical constraint with good accuracy but with a smaller density of nodes and less computing time. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

井下钻柱纵向横向耦合振动模型建立与数值分析

针对井下钻柱运动的复杂性,基于动力学理论,建立了井下钻柱纵向和横向耦合振动的数学模型,并进行数值求解及分析.根据井下钻柱的实际工况,以整个井下钻柱为研究对象,提出了钻柱纵向和横向耦合振动的动力方程,并利用解析法和无量纲法分别求解出其动刚度和动阻尼的表达式,以及钻柱前两阶振动的固有频率.分析结果表明:当井下钻柱振动频率增大时,其动刚度呈幅值衰减的周期性变化,而其动阻尼呈幅值增强的周期性变化;井下钻柱长度和横截面面积越大,其动刚度和动阻尼的幅值越小;井下钻柱的Poisson(泊松)比对其振动的动刚度、动阻尼和前两阶固有频率没有影响;同时,井下钻柱的第二阶固有频率始终大于第一阶固有频率.该文的研究方法和模型为井下钻柱钻具分析和结果优化提供了理论参考和实际意义.     

Generalized Lorenz models and their routes to chaos. II. Energy-conserving horizontal mode truncations

All attempts to generalize the three-dimensional Lorenz model by selecting higher-order Fourier modes can be divided into three categories, namely: vertical, horizontal and vertical–horizontal mode truncations. The previous study showed that the first method allowed only construction of a nine-dimensional system when the selected modes were energy-conserving. The results presented in this paper demonstrate that a five-dimensional model is the lowest-order generalized Lorenz model that can be constructed by the second method and that its route to chaos is the same as that observed in the original Lorenz model. It is shown that the onset of chaos in both systems is determined by a number of modes that describe the vertical temperature difference in a convection roll. In addition, a simple rule that allows selecting modes that conserve energy for each method is derived.     

The rolling motion of a truncated ball without slipping and spinning on a plane

This paper is concerned with the dynamics of a top in the form of a truncated ball as it moves without slipping and spinning on a horizontal plane about a vertical. Such a system is described by differential equations with a discontinuous right-hand side. Equations describing the system dynamics are obtained and a reduction to quadratures is performed. A bifurcation analysis of the system is made and all possible types of the top’s motion depending on the system parameters and initial conditions are defined. The system dynamics in absolute space is examined. It is shown that, except for some special cases, the trajectories of motion are bounded.     

一种新的大位移井钻柱几何非线性分析方法

提出了基于实测的井深及相应的井斜角和方位角来获得确保井内钻柱参考构形长度不变的井眼轴线插值方法．当以空间大位移井的井眼轴线为钻柱的参考构形时,钻柱内的初始内力可以由井眼轴线的曲率和挠率确定．利用基于在空间自然坐标系下的包含所有单元刚体位移和常应变模式的位移函数,严格地按虚功原理推出了具有初始曲率和挠率的钻柱单元内由初始内力所引起的等效节点力计算公式,为大位移井钻柱的几何非线性处理提供了理论依据．澄清了钻柱有限元分析中的若干基本概念．为随后进行的以井眼轴线为参考构形的小变形分析,计算钻柱的自重和基于自然坐标系下的线性刚度矩阵及一致载荷列阵提供了保证．     

Bifurcation to Mean Flows in Convection

Convection with a strip plate in the middle is studied in this paper. Simultaneous instability of two convection modes of different vertical structures with a same horizontal wave number is possible in this system. It is found that the interaction of these two modes generates mean flows similar to those observed by Krishnamurti and Howard [9] in a turbulent convection experiment. Coupled nonlinear equations are derived for the amplitudes of the two modes. Traveling wave solutions and more complicated time-dependent solutions are also found near the onset of convection.     

TPL介入的产运销供应链联盟决策及运作效率评价

在生产商批发价格为内生变量且TPL物流服务水平影响零售商市场需求的情形下,研究了整体联盟、分散决策、产运联盟和运销联盟四种模式下产运销供应链系统内各决策主体的决策行为以及系统的运作效率。分别构建了各决策模式下的数学模型,并证明了系统最优解或博弈均衡解的存在性和唯一性。通过对上述四种模式下的运算结果进行两两比较,发现:较之整体联盟,其他三种决策模式下系统利润均出现损失;其他三种模式下的最优订购量、物流服务水平和二者的比值大小均取决于某些特定的条件,这导致TPL介入的供应链内部联盟并非一定能使系统整体运作效率获得提高。进一步通过数值算例对零售价格和可变物流服务成本进行了灵敏度分析,发现在大多数情形下,运销联盟模式下的系统运作效率是上述三种决策模式中最高的。     

环空钻柱结构三维非线性分析

应用有限元理论和牛顿－拉裴逊法对弯曲井眼中环空钻柱结构进行非线性分析．根据变形特点，提出了对不同参量采用不同形式的单元的描述计算分析方法。采用罚函数法处理待定边界问题。计算表明了井眼曲率对钻头侧向力的非线性效应。     

Analysis of a stochastic recovery-relapse epidemic model with periodic parameters and media coverage

This paper addresses, motivated by mathematical work on infectious disease models, the impacts of environmental noise and media coverage on the dynamics of recovery-relapse infectious diseases. A susceptible-infectious-recovered-infectious model is formulated with both vertical transmission and horizontal transmission. The existence and uniqueness of the positive global solution is studied by constructing suitable Lyapunov-type function. Then, the existence of positive periodic solutions is verified by applying Khasminskii"s theory. The existence of positive periodic solutions indicates the continued survival of the diseases. Besides, sufficient conditions for the extinction of the diseases are obtained. Numerical simulations then demonstrate the dynamics of the solutions. The paper extends the results of the corresponding deterministic system.     

Nonlinear dynamic analysis of a hybrid squeeze-film damper-mounted rigid rotor lubricated with couple stress fluid and active control

The hybrid squeeze-film damper bearing with active control is proposed in this paper and the lubricating with couple stress fluid is also taken into consideration. The pressure distribution and the dynamics of a rigid rotor supported by such bearing are studied. A PD (proportional-plus-derivative) controller is used to stabilize the rotor-bearing system. Numerical results show that, due to the nonlinear factors of oil film force, the trajectory of the rotor demonstrates a complex dynamics with rotational speed ratio s. Poincaré maps, bifurcation diagrams, and power spectra are used to analyze the behavior of the rotor trajectory in the horizontal and vertical directions under different operating conditions. The maximum Lyapunov exponent and fractal dimension concepts are used to determine if the system is in a state of chaotic motion. Numerical results show that the maximum Lyapunov exponent of this system is positive and the dimension of the rotor trajectory is fractal at the non-dimensional speed ratio s = 3.0, which indicate that the rotor trajectory is chaotic under such operation condition. In order to avoid the nonsynchronous chaotic vibrations, an increased proportional gain is applied to control this system. It is shown that the rotor trajectory will leave chaotic motion to periodic motion in the steady state under control action. Besides, the rotor dynamic responses of the system will be more stable by using couple stress fluid.     

气体钻井钻柱轴扭耦合动态屈曲数学建模与求解

针对钻柱轴扭耦合动态屈曲的基本问题构造哈密顿体系,在辛几何空间中将临界屈曲载荷和动态屈曲模态归结为辛本征值和本征解问题,从而形成一种辛几何算法.方法较好的解决了钻柱轴扭耦合动态屈曲的复杂边界条件问题.在解决气体钻井钻柱动态屈曲问题的研究中具有良好的应用前景.     

Transient amplification of maximum vibration amplitudes

Many low damped structures as turbine blades or drill strings are exposed to high dynamical loads causing high vibration amplitudes. These applications comprise sub-critical eigenfrequencies. Hereby, the lower eigenfrequencies have to be passed before reaching the operating point. Most investigations of vibration amplitudes caused by a resonance passage deal with the computation of single degree of freedom systems. Thereby, it has been shown that the stationary vibration response provides the highest possible amplitude. Further it can be stated that the maximum vibration response of the resonance passage decreases with an increasing sweep velocity [3]. Isolated modes of linear systems can be represented by single degree of freedom systems. Subsequently a mode shape can be described by the multiplication of the amplification function of the mode and the belonging eigenvector. There are only some recent works that deal with resonance passages of vicinal modes, e. g. [1]. In this paper the resonance passage of a three dimensional system with nearby modes is studied. To calculate the transient vibration response an analytical approach is used. It is shown that the maximum amplitude of the stationary vibration response is not the upper limit for the maximum amplitude of the resonance passage. Thus, the maximum amplitude may rise while the sweep velocity increases. Hence, regarding a multi degree of freedom system the maximum amplitude of the resonance passage can exceed the maximum amplitude of the stationary vibration response. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)