Stability of drill strings in controlled directional wells

We formulate the problem of theoretical simulation of the bifurcation buckling of drill strings in deep directional and horizontal oil and gas wells, and propose the procedure for its solution. The analysis is made of the critical states in drill strings for various values of the well inclination, axial velocities of drill string motion and rotation. The buckling modes of the bifurcation drilling are constructed. Translated from Problemy Prochnosti, No. 6, pp. 71–81, November–December, 2008.     

Stress-strain state of a drill string and marine riser under their interaction in the open SEA

We consider the problem of interaction of a marine riser with a drill string inside it under the conditions of their joint bending in a strong sea current. We derive three-dimensional equations for the statics of the string and the riser which take into account the contact interaction and friction occurring under the displacements of the drill string inside the marine riser. A method is proposed for the numerical calculation of the stress-strain state of the drill string and marine riser. As an example, for the data of well drilling in the Straits of Gibraltar, we have calculated the regions of safe displacement of the offshore drilling rig that correspond to given safety factors. ^aCentral Research Institute for Prospecting for Nonferrous and Noble Metals, Moscow.^b“Energokosmos” Scientific Technical Center, Moscow, Russia. Translated from Problemy Prochnosti, No. 1, pp. 128 – 135, January – February, 1998.     

Self-excitation of deep-well drill string torsional vibrations

We address a problem of self-excitation of elastic torsional vibrations of a rotating drill string due to frictional interaction between the drill bit and rock at the deep well bottom. Using the d’Alembert solution to a wave equation, a mathematical model is constructed for a wave torsional pendulum in the form of a nonlinear ordinary differential equation with delayed argument. Special features of generation of self-excited vibrations of drill strings have been determined through computer simulation.     

大位移井钻柱纵向振动理论分析与ANSYS计算

钻柱振动是导致钻柱失效、疲劳损坏的主要原因,结合钻柱动力学理论以及运动微分方程,并通过ANSYS软件对大位移井钻柱的纵向振动模型的建立和分析做了合理的假设,经过ANSYS分析计算得出大位移井全井段钻柱的振动规律。     

《大位移井钻柱纵向振动理论计算与ANSYS分析》

钻柱振动是导致钻柱失效、疲劳损坏的主要原因,结合钻柱动力学理论以及运动微分方程,并通过ANSYS软件对大位移井钻柱的纵向振动模型的建立和分析做了合理的假设,经过ANSYS分析计算得出大位移井全井段钻柱的振动规律。     

Molecular dynamics simulation of the forces between colloidal nanoparticles in Lennard–Jones and <Emphasis Type="Italic">n</Emphasis>-decane solvent

Molecular-dynamics is utilized to simulate solvation forces between two nanoparticles immersed in two different solvents: Lennard–Jones spheres and and n-decane. Three different sizes and shapes of solvophilic nanoparticles are investigated. Nanoparticles in the Lennard–Jones liquid exhibit solvation forces that oscillate between attraction and repulsion as the nanoparticle separation increases. The magnitude of these solvation forces increases with particle size and depends on particle shape, consistent with the Derjaguin approximation. When n-decane is the solvent, the solvation forces are negligible for small nanoparticles, with sizes comparable to the end-to-end distance of all-trans decane. The solvation forces oscillate between attraction and repulsion for sufficiently large nanoparticles in decane—however the Derjaguin approximation does not appear to be effective at describing the dependence of nanoparticles forces on nanoparticle size and shape when decane is the solvent. For both the Lennard–Jones and n-decane solvents, it is apparent that the force profiles are influenced by the surface roughness of the nanoparticles. These factors should be taken into account in efforts to engineer colloidal suspensions.     

基于格林函数的多跨钻柱系统的振动特性分析

随着油气勘探开发向着深层、深水及非常规等复杂领域的不断扩展,钻井面临的井况与约束条件更加苛刻,钻柱的动力学特性更加复杂,失效问题频发。该文应用格林函数理论对多跨旋转钻柱双向耦合动力学特性进行了定量分析和研究。考虑多稳定器及不同约束条件,以钻柱整体为研究对象,基于Euler-Bernoulli梁模型和Hamilton原理建立了具有广义边界约束条件及多稳定器的旋转钻柱双向耦合动力学方程。采用分离变量法、Laplace变换及Laplace逆变换求解所获得的振动微分方程,得到了旋转钻柱系统横向振动的格林函数解以及以格林函数为基础的多跨旋转钻柱系统的闭合形式的模态函数及隐式的频率方程。定量地分析了稳定器位置、弹簧刚度系数与稳定器个数对钻柱系统振动特性的影响。数值结果表明:稳定器位置与固有频率的关系曲线中有相应阶次数目的峰值;随着等效弹簧的刚度系数的增大,系统的固有频率随之增大,但当刚度增加到一定值时,系统的一阶和二阶频率将趋于稳定。研究结果有助于深化对多跨旋转钻柱的动力学特性规律的认识,为提高钻速、减少钻柱失效及钻柱钻井技术的应用提供了新的研究方法和理论依据。     

On equations of a one-velocity heterogeneous medium

An analysis is made of equations of the one-velocity model of a heterogeneous mixture; in them, the internal interfractional-interaction forces and heat- and mass-exchange processes are allowed for. The characteristic equations and relations along the characteristic directions are found. It is shown that equations of the medium’s model, in which the interfractional-interaction forces are allowed for, belong to a hyperbolic type. A number of finite-difference and finite-volume schemes meant for integration of the model’s equations are considered. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 1, pp. 75–84, January–February, 2009.     

Riemann problem for the one-velocity model of a heterogeneous medium

The internal interfractional-interaction forces have been allowed for in the one-velocity model of a heterogeneous medium, and a complete solution of the Riemann problem has been obtained. The shock adiabat of the mixture, consistent with the model’s equations, has been used in constructing the solution with shock waves. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 6, pp. 1133–1141, November–December, 2008. Original article submitted February 27, 2006; revision submitted March 30, 2008.     

Numerical analysis of a three-dimensional branched pipeline using special software designed for estimation of the strength of the equipment of nuclear power plants

We describe the structure of an informational model of a branched three-dimensional pipeline, which is important for analysis of the stressed state of its elements, and formulate the basic principles of, its application. For rectilinear and (this is especially important) curvilinear segments of pipeline, we obtain relationships between the generalized displacements and generalized forces at every point of the considered segment. On the basis of these relationships, we formulate a procedure for application of the method of initial parameters to the analysis of the elastic state of the pipeline. This procedure is based on a simple single-stage sequence of passing through the entire pipeline to obtain a closed system of equations for the unknown generalized forces. In agreement with contemporary standards and documents, we develop an algorithm and realize an iteration procedure to take into account the effect of friction in the supports. Scientific and Engineering Center of Materials-Science Support of the Production and Certification of Equipment of Nuclear Power Plants at the Institute for Problems of Strength of the National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 87 – 100, March – April, 1998.     

Research on Buckling Behavior and Analysis of Sensitive Factors in Horizontal Well Drilling

Buckling behavior of the drill string in the wellbore is one of the key issues in the oil and gas well engineering, which has been investigated by many theoretical and experimental studies in recent years. In order to study the buckling characteristics of drill string in the horizontal well, the factors of gravity, friction, and boundary conditions were taken into account, and a numerical simulation model of horizontal drill string was built up. The buckling critical load of numerical simulation was proven to be in good agreement with the experimental results; that is to say the simulation result is reliable. The key factors of friction coefficient, length of horizontal well section, and radial clearance between drill string and wellbore annular which affect buckling critical load of drill string were discussed. The results show that the angular displacement of horizontal drill string changes in the form of sine when sinusoidal buckling occurs. The pipe string buckling critical load increases with the increasing of friction coefficient. Under the same condition, the buckling critical load of horizontal drill string decreases approximately linear with the raise of horizontal well length, and declines in exponential trend with the increasing of the annular clearance. The research can provide theoretical reference for the optimal design of horizontal well string and practical drilling operation.     

Motion of a curvilinear net on normal localized impact

Within the framework of a continuous computational model, the authors obtained equations of motion for a curvilinear netted structure that in the initial state has the shape of a spherical netted dome. The motion of the net in the case of loading of one node by a normal localized impact is considered. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 4, pp. 773–777, July–August, 2000.     

An anisotropic elastic formulation for configurational forces in stress space

A new variational principle for an anisotropic elastic formulation in stress space is constructed, the Euler–Lagrange equations of which are the equations of compatibility (in terms of stress), the equilibrium equations and the traction boundary condition. Such a principle can be used to extend recently obtained configurational balance laws in stress space to the case of anisotropy.     

Stress intensity near a crack in the composition of a half space and a layer under harmonic loading

We consider a three-dimensional problem for an elastic bimaterial body formed by a half space and a layer and containing a circular crack. The surface of the crack is subjected to the action of stationary torsional forces. The problem is reduced to the solution of a system of boundary integral equations of Helmholtz-potential type for the unknown jumps of displacements on the crack surfaces. The dynamic stress concentration in the vicinity of the crack contour is investigated. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 2, pp. 27–32, March–April, 2008.     

Effect of a riveted wide patch on stresses in a cracked plate

We study the stress-strain state and limiting equilibrium of a thin plate with curvilinear cracks reinforced by a wide patch. The patch is arbitrarily located relative to the cracks and attached to the plate with elastic rivets. The boundary-value problem is reduced to a system of singular integral and integro-algebraic equations and this system is solved by the method of mechanical quadratures. Numerical analysis is performed for the case of a plate with one curvilinear or rectilinear crack reinforced by an elliptic patch. The stress intensity factors formed in this reinforced cracked plate and ultimate loads are determined for various geometric and physical parameters of the plate, crack, patch, and rivets. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 1, pp. 37–46, January–February, 1998.     

Numerical analysis of composite shells of revolution with frames of complex shape

We consider the problem of application of the method of superelements to the numerical analysis of complex composite shells of revolution. The construction of the matrices of stiffness and forces for the superelements and the entire shell is carried out by the method of Godunov for the solution of systems of differential equations and operations over banded matrices. We also perform a comparative analysis of the effect of frames of different shapes on the stressed state of the shells. Zaporozh’e State University, Zaporozh’e, Ukraine. Translated from Problemy Prochnosti, No. 6, pp. 63–68, November–December, 1998.     

Calculation of natural and forced vibrations of a piping system. Part 1. Analysis of vibrations of a 3D beam system

Dynamic behavior of piping as a beam system has been analyzed with the use of the dynamic stiffness method. According to this method, the equations describing the relation between unknown parameters are written by the method of initial parameters, therefore, the solution procedure is similar to that for a static problem. It is shown that for curvilinear beams it is simpler and more efficient to apply a model that consists of straight segments and inertia-free rotation elements. To determine natural frequencies of 3D beam systems, it is proposed to use a method of disconnection of displacements, which makes it possible to discern the frequencies corresponding to different vibration modes (transverse, longitudinal, etc.). The approach allows a correct simulation of the system behavior under forced vibrations induced by a harmonic exciting force. __________ Translated from Problemy Prochnosti, No. 1, pp. 79–93, January–February, 2007.     

Problem of large displacements of buried pipelines. Part 1. Working out a numerical procedure

An effective numerical iteration procedure has been worked out for the analysis of the stress-strain state of a flat pipeline in a medium with allowance for possible presence of supports and branches. The governing equilibrium equations and geometrical equations used have been written in geometrically nonlinear formulation and supplemented with boundary conditions, obtained analytically for a semi-infinite pipeline under transverse-longitudinal elastic bending. The article considers an elastoplastic law of interaction between pipeline and the ground with the possibility of additional limitation of absolute pipeline displacements. The computational algorithm is based on the concepts of corrective and basic solution. Basic solution is refined in each iteration step using corrective solution. Corrective solution is direct solution of a system of linearized equations, in which, e.g., basic displacements of pipeline are used to determine forces of interaction between the pipe and the ground. The algorithm uses an efficient method of run in each iteration step, which minimizes the number of unknowns. The results of the calculations are compared with numerical and theoretical solutions presented in publications: cantilever curling by the action of end bending moment; laying of an underwater pipeline; stability loss in air, etc. __________ Translated from Problemy Prochnosti, No. 3, pp. 51–74, May–June, 2007.     

Solution of stationary heat-conduction problems for curvilinear regions using eigenfunction expansions (fundamental solutions)

Formulas for solution of stationary problems of heat conduction in bodies of a curvilinear shape have been obtained in explicit form using eigenfunction expansions; an analogous solution has been constructed for temperature fluctuations. An algorithm of computation of the boundary functions for classical regions has been proposed; these functions make it possible to reduce the boundary conditions of the problem to a homogeneous form. The exact fundamental solutions in the region of a rectangle with arbitrary smooth boundary conditions of the 1st kind have been constructed using them. These solutions are fundamental, since they can be used when boundary-value problems and inverse problems with unknown boundary conditions are considered for a wide range of curvilinear regions. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 1, pp. 163–169, January–February, 2009.