A finite difference approximation for dynamic calculation of vertical free hanging slender risers in re-entry application

The dynamic calculations of slender marine risers, such as Finite Element Method (FEM) or Modal Expansion Solution Method (MESM), are mainly for the slender structures with their both ends hinged to the surface and bottom. However, for the re-entry operation, risers held by vessels are in vertical free hanging state, so the displacement and velocity of lower joint would not be zero. For the model of free hanging flexible marine risers, the paper proposed a Finite Difference Approximation (FDA) method for its dynamic calculation. The riser is divided into a reasonable number of rigid discrete segments. And the dynamic model is established based on simple Euler-Bernoulli Beam Theory concerning tension, shear forces and bending moments at each node along the cylindrical structures, which is extendible for different boundary conditions. The governing equations with specific boundary conditions for riser’s free hanging state are simplified by Keller-box method and solved with Newton iteration algorithm for a stable dynamic solution. The calculation starts when the riser is vertical and still in calm water, and its behavior is obtained along time responding to the lateral forward motion at the top. The dynamic behavior in response to the lateral parametric excitation at the top is also proposed and discussed in this paper.     

钢悬链线立管与海床相互作用小尺寸三维试验研究

围绕钢悬链线立管(SCR)与海床的相互作用,在水箱内开展三维试验研究,研究在不同模拟运动激励下SCR触地点的应力状态。针对当前模拟试验中,全尺寸试验耗资巨大,且试验环境难以控制,缩尺试验大多模拟立管二维运动等现状,提出一套简单易行的三维管土作用试验装置,通过横向、纵向、垂向三个方向轨道位置的合理布置,使得立管可在单向、二维耦合和三个方向同时运动,对模型立管的顶端、底端的边界条件进行处理,通过驱动器在顶端施加位移,模拟在周期运动作用下,立管触地区与土的相互作用,在三维空间内研究立管的力学特性。由此指导立管的整体设计与分析,对保证SCR在深水油气开采中的安全可靠性,具有非常重要的意义。     

A variational formulation for three-dimensional analysis of extensible marine riser transporting fluid

This paper presents a model formulation for static and dynamic analysis of three-dimensional extensible marine riser transporting fluid. A variational model formulation is developed based on the principle of virtual work-energy and the extensible elastica theory. The virtual work-energy functional is composed of the virtual strain energy due to axial stretching, bending, and torsion and the virtual work done by the external and internal fluid. The governing dynamic equilibrium equations are derived in the Cartesian coordinate. The finite element method is used to obtain the numerical solutions. The numerical examples are provided to demonstrate interesting effects of fluid transportation and axial deformation on large displacements and dynamic properties of the three-dimensional extensible marine riser.     

Nonlinear Behaviour of Coflexip Risers

A modified Newton-Raphson iterative technique is formulated for obtaining the static configuration of the Lazy "S" flexible marine riser between the floater and mid-arch buoy under its submerged self weight and the applied top tension. The geometrically non-linear problem is solved by finite difference with the above technique. The problem is formulated as a regular boundary value problem with specified moments and deflections at both ends. Usually the bending stiffness of the flexible riser made of Coflexip pipe is very low. By use of the above analysis, several flexible riser configurations are analyzed and their characteristic behaviors are investigated. Also, changes in the riser characteristics due to quasi-static motion of the floater end are estimated for the safety of the riser layout.     

An inverse problem methodology for multiple parameter estimation in bend stiffeners

The flexible riser top connection is a critical region for lifetime assessment due to large tension/curvature variations and modeling uncertainties. The bend stiffener polyurethane mechanical response not only presents a nonlinear loading rate and temperature dependency but is also subjected to weather ageing during operation, which may affect its mechanical behavior over time. The top tension, employed for riser local cross-section stress calculation, is usually obtained from global dynamic analyses performed under selected environmental conditions, if direct measurement is not available. As a consequence, both the bend stiffener effect on the curvature distribution and the top tension time series present inherent uncertainties for riser lifetime (re)assessment. In the present work, a proposed monitoring approach composed by gyrometers installed along flexible riser/bend stiffener top connection system length combined with an inverse problem methodology is numerically investigated to estimate the following parameters: (i) polyurethane hyperelastic response and (ii) effective top tension. The top connection system is modeled using a large deflection beam bending model and the parameters are estimated using a damped least-square minimization approach with the Levenberg–Marquardt algorithm. For the preliminary feasibility investigation, the gyrometer experimental data is numerically estimated through Monte Carlo simulations. A case study is carried out to investigate the influence that the number of sensors, sensors arrangement, loading conditions and top connection model have on the inverse parameters estimation. The results indicate that the proposed monitoring approach and inverse parameter estimation methodology may effectively reduce flexible riser lifetime calculation uncertainties.     

A nonlinear viscoelastic bend stiffener steady-state formulation

Bend stiffeners are essential components of a flexible riser system, employed to ensure a smooth transition at the upper connection and to protect the riser against over bending and from accumulation of fatigue damage. The highly nonlinear rate dependent behavior of these structures directly affects the integrity assessment of the riser in one of its most critical regions, the top connection. A steady-state formulation (disregarding inertial forces) and numerical solution procedure is developed in this work employing the perturbation method for a nonlinear viscoelastic bend stiffener large deflection beam model subjected to harmonic loading conditions. For stochastic loading conditions, the response is calculated employing the superposition principle by summing up the steady-state result of a number of individual frequency components. A time domain formulation is also derived employing the state-variable approach for the numerical solution of the resulting hereditary integral in the governing equations. A case study is presented for the top connection system of a 4″ ID flexible riser using relaxation and tensile experimental data obtained from a typical class of bend stiffener polyurethane. Harmonic and stochastic input loading conditions are employed for time and frequency domain model comparison/validation and to assess loading history and frequency influence in the curvature response.     

Numerical Simulation of the Vortex-Induced Vibration of A Curved Flexible Riser in Shear Flow

A series of fully three-dimensional(3 D) numerical simulations of flow past a free-to-oscillate curved flexible riser in shear flow were conducted at Reynolds number of 185–1015. The numerical results obtained by the two-way fluid–structure interaction(FSI) simulations are in good agreement with the experimental results reported in the earlier study. It is further found that the frequency transition is out of phase not only in the inline(IL) and crossflow(CF) directions but also along the span direction. The mode competition leads to the non-zero nodes of the rootmean-square(RMS) amplitude and the relatively chaotic trajectories. The fluid–structure interaction is to some extent reflected by the transverse velocity of the ambient fluid, which reaches the maximum value when the riser reaches the equilibrium position. Moreover, the local maximum transverse velocities occur at the peak CF amplitudes, and the values are relatively large when the vibration is in the resonance regions. The 3 D vortex columns are shed nearly parallel to the axis of the curved flexible riser. As the local Reynolds number increases from 0 at the bottom of the riser to the maximum value at the top, the wake undergoes a transition from a two-dimensional structure to a 3 D one. More irregular small-scale vortices appeared at the wake region of the riser, undergoing large amplitude responses.     

The effect of nonlinear multi-contact coupling with gap between risers and guide frames on global spar motion analysis

Nonlinear multi-contact coupling between vertical risers and guide frames inside the spar moon-pool is studied. The existing numerical model for hull/mooring/riser coupled dynamics analysis treats riser as an elastic rod truncated at the keel (truncated riser model), and the risers are free to slide in vertical direction with constant tension, while restricted in horizontal direction. The truncated riser model neglects the portion of the riser inside the moon-pool and tends to overestimate the spar pitch motion. In the newly developed model, the risers are extended through the moon-pool with realistic boundary conditions at multiple guide frames, and thus additional contact forces and moments on the spar hull are considered. The gap effects between the riser buoyancy-cans and riser guide frames are also modeled using three different types of gap springs. Their different dynamic characteristics are extensively studied. The new riser model also considers the Coulomb damping between buoyancy-cans and riser guide frames and also allows the impact-like contact force calculation on risers for ensuring fatigue analysis.     

Large deformation three-dimensional static analysis of deep water marine risers

The problem of static three-dimensional, nonlinear, large deformation response of a marine riser is formulated within small strain theory and solved numerically. This type of analysis is necessary, for the new generation of drilling and production risers. The mathematical model takes properly into account the effects of internal and external pressure and the complete nonlinear boundary conditions, without linearizing the follower forces. The extensibility or inextensibility condition is used as the constitutive relation in the tangential direction. Torsion and bending are coupled. The external load and the boundary conditions are deformation dependent. A solution method is developed based on an incremental finite element algorithm, which involves a prediction-correction scheme. In the correction phase deformation dependent quantities are updated. The extensibility or inextensibility condition is used to reduce the degrees of freedom of the system. The numerical results of the developed computer code compare very well with available semi-analytical and numerical solutions. Three numerical applications are used to demonstrate the importance of large deformation, nonlinear and three-dimensional analyses.     

深海悬垂取水管振动特性研究

深海悬垂取水管的设计趋向于大直径、高内流流速,内流对取水管振动特性的影响不可忽略,分析内部流动引起的管道动态失稳行为以及评估失稳临界流速具有重要工程意义。基于小尺度模型试验,研究内流对深海悬垂取水管道振动特性的影响规律,结果表明：随着内流流速增加,取水管模型会发生动态失稳行为,表现为一种间歇性的近周期运动,该运动主要由管道一阶弯曲模态引起的不稳定性诱导。管道材料、顶端连接方式及底部配重块均影响其动态稳定性,顶端固定连接时质量比小的管道更易发生动态失稳;顶端变为铰接时,质量比大的管道失稳临界流速变小,质量比小的管道失稳临界流速变大。相比顶端边界条件,底部配重块对管道失稳临界流速影响不显著但可以减小其振动幅值。     

Simplified Prediction Model for Vortex-Induced Vibrations of Top Tensioned Risers

According to the characteristics of deepwater top tensioned risers, a simplified model is presented to predict the multi-modal response of vortex-induced vibration （VIV） in non-uniform flow based on energy equilibrium theory and the exporimental data from VIV self-excited and forced oscillations of rigid cylinders. The response amplitude of each mode is determined by a balance between the energy fed into the riser over the lock-in regions and the energy dissipated by the fluid damping over the remainders. Compared with the previous prediction models, this method can take fully account of the intrinsic nature of VIV for low mass ratio structures on lock-in regions, added mass and nonlinear fluid damping effect, etc. Moreover, it is the first time to propose the accurate calculating procedure for VIV amplitude correction factor by solving energy equilibrium equation and a closed form solution is presented for the case of a riser of uniform mass and cross-section oscillating in a uniform flow. The predicted values show a reasonable agreement with VIV experiments of riser models in stepped and sheared currents.     

驳船横荡运动下海洋立管的动力响应

海洋浮式生产系统下立管的受力情况复杂,国内的研究大多集中于两端固支或简支的情况。本文则以水面驳船的横荡运动作为立管上端的动力边界条件,将Matteo Luca Facchinetti的尾流振子模型与考虑外流涡激振动作用下海洋立管运动微分方程相结合,得到管道与流体的耦合振动方程,用Hermit插值函数将方程进行有限元离散,并用Newmark时程分析法及迭代法求解,得到管道各点的位移时程曲线。结果表明:立管的振动频率主要由上端驳船的运动频率所确定,随着驳船运动频率的增加,立管中点的位移幅值先增加后减小;在有动边界存在的条件下,改变外流流速对立管中点的位移幅值影响不大。     

超深水钻井作业隔水管顶张力确定方法

对于深水和超深水钻井作业,确定钻井隔水管系统顶张力是钻前设计非常重要的工作。研究三种隔水管系统顶张力确定方法,分别是理论方法、基于隔水管系统底部残余张力方法和基于下放隔水管系统的最大钩载方法。算例计算与超深水钻井实践对比表明,在相同的隔水管系统配置下,三种方法计算结果都接近于实际钻井作业时的顶张力设定值。但研究认为,基于下放最大钩载的顶张力计算方法简单实用,推荐作为优选方法。     

Coupled dynamic analysis for wave interaction with a truss spar and its mooring line/riser system in time domain

A full time-domain analysis program is developed for the coupled dynamic analysis of offshore structures. For the hydrodynamic loads, a time domain second order method is developed. In this approach, Taylor series expansions are applied to the body surface and free-surface boundary conditions, and the Stokes perturbation procedure is then used to establish the corresponding boundary value problems with time-independent boundaries. A higher-order boundary element method (HOBEM) is developed to calculate the velocity potential of the resulting flow field at each time step. The free-surface boundary condition is satisfied to the second order by fourth order Adams–Bashforth–Moultn method. An artificial damping layer is adopted on the free surface to avoid the wave reflection. The mooring-line/tendon/riser dynamics are based on the rod theory and the finite element method (FEM), with the governing equations described in a global coordinate system. In the coupled dynamic analysis, the motion equation for the hull and dynamic equations for mooring-lines/tendons/risers are solved simultaneously using the Newmark method. The coupled analysis program is applied for a truss Spar motion response simulation. Numerical results including motions and tensions at the top of mooring-lines/risers are presented, and some significant conclusions are derived.     

Coupling Effects of A Deep-Water Drilling Riser and the Platform and the Discharging Fluid Column in An Emergency Disconnect Scenario

As drilling operations move into remote locations and extreme water depths, recoil analysis requires more careful considerations and the incidence of emergency disconnect is increased inevitably. To accurately capture the recoil dynamics of a deep-water riser in an emergency disconnect scenario, researchers typically focus on modelling the influential subsystems (e.g., the tensioner, the mud discharge and seawater refilling process) which can be solved in the preprocessing, and then the determined parameters are transmitted into an existing global riser analysis software. Distinctively, the current study devotes efforts into the coupling effects resulting from that the suspended riser reacts the platform heave motion via the tensioner system in the course of recoil and the discharging fluid column follows the oscillation of the riser in the mud discharge process. Four simulation models are established based on lumped mass method employing different formulas for the top boundary condition of the riser and the discharging flow acceleration. It demonstrates that the coupling effects discussed above can significantly affect the recoil behavior during the transition phase from initial disconnect to the final hang-off state. It is recommended to develop a fully- coupled integrated model for recoil analysis and anti-recoil control system design before extreme deep-water applications.     

Dynamic Characteristics of Marine Risers Conveying Fluid

The lateral vibration differential equation for a marine riser conveying fluid is derived by useof the small deflection theory.and the effect of internal flow velocity and top tension on the natural fre-quency of the riser is studied by use of FEM.At the same time,the preliminary relationship between thenatural frequency and riser span under different internal flow velocities is obtained,the effect of riser sup-ports on the vibration frequency is computed.It is found that the natural frequency of the marine riser in-creases with the increase of top tension.however decreases with the increase of internal flow velocity.In ad-dition,the frequency decreases drastically with the increase of riser span.     

深海采矿立管在波流载荷下的弯矩响应分析

采矿立管是深海采矿系统的重要组成部分，立管的弯矩分析是确保立管正常使用的重要指标。立管所处海洋环境复杂，且立管底部的自由边界条件使得立管弯矩特性难以分析。本文基于波浪理论，使用Abaqus 有限元软件建立海洋采矿立管的模型，运用Abaqus中的AQUA海洋工程模块，考虑立管在轴向力、自重、浮力、波浪载荷、海流载荷及模拟海上平台水平和升沉运动共同作用下，对采矿立管进行弯矩分析，计算了提升泵不同安装位置、不同中继仓重量变化对弯矩的影响，结果表明：提升泵会增大安装位置的弯矩幅度，且安装在不同位置对立管弯矩会产生叠加影响；中继仓重量的增加提高了立管整体稳定性，但会使提升泵处弯矩波动产生向中部延伸的不利影响。     

Multiaxial fatigue analyses of stress joints for deepwater steel catenary risers

In the present study, the dynamic and fatigue characteristics of two types of stress joints are investigated under ocean environmental condition. Connected with the riser and the platform, stress joint at the vessel hang-off position should be one of the main critical design challenges for a steel catenary riser (SCR) in deepwater. When the riser is under a high pressure and deepwater working condition, the stress state for the joint is more complex, and the fatigue damage is easy to occur at this position. Stress joint discussed in this paper includes two types: Tapered Stress Joint (TSJ) and Sleeved Stress Joint (SSJ), and multiaxial fatigue analysis results are given for comparison. Global dynamic analysis for an SCR is performed first, and then the local boundary conditions obtained from the previous analysis are applied to the stress joint FE model for the later dynamic and multiaxial fatigue analysis. Results indicate that the stress level is far lower than the yield limit of material and the damage induced by fatigue needs more attention. Besides, the damage character of the two types of stress joints differs: for TSJ, the place where the stress joint connects with the riser is easy to occur fatigue damage; for SSJ, the most probable position is at the place where the end of the inner sleeve pipe contacts with the riser body. Compared with SSJ, TSJ shows a higher stress level but better fatigue performance, and it will have a higher material cost. In consideration of various factors, designers should choose the most suitable type and also geometric parameters.     

海沟影响下深水海洋管线成环行为研究

在深水海洋管线的安装过程中,制造工艺的偏差和外部环境的影响易导致管线上不均匀的扭矩分布,在张力的共同作用下,管线在其触地区可能出现“成环”现象,受到严重损伤,而海洋管线的触地区也是海沟集中形成的区域。为了研究海沟对海洋管线成环行为的影响,基于OrcaFlex软件和构建海沟模型的经验公式,建立了深水悬链线立管和海沟的三维数值模型。就海沟轮廓、位置和土壤属性对立管成环行为的影响展开参数分析,并研究了不同工况下成环的临界载荷。研究表明：海沟的产生和扩展、立管相对海沟的合理位置以及土壤参数中海床表面不排水抗剪强度和吸力因子的增加,可有效降低立管成环过程中的最大压缩力和最大弯矩,从而减少成环引起的损伤;临界载荷的分析则有助于对成环的临界条件进行预测,避免成环现象的发生。     

海洋环境荷载下输液立管的静、动力特性研究

考虑管内流动流体和管外海洋环境荷载共同作用 ,建立海洋立管侧向运动微分方程。用Hermite插值函数离散 ,在微机上编写海洋立管静、动力分析程序 ,通过计算分析研究管内流体对立管侧向变形和应力的作用 ;另外 ,探讨管内流体的流动速度和立管顶端的预张力对立管动力特性的影响。结果表明 ,立管变形和应力均随管内流体流动速度增加而增大 ,同时内流速度的增大会降低立管的固有频率 ,但适当增大立管顶端预张力会抵消内流流速增加引起的固有频率下降。