Application of analytical model in the prediction of dynamic responses and fatigue damage of flexible risers: Part II – Dynamic analysis of flexible risers in large-scale domain using a direct moment correction method

In recent years, the dynamic responses of flexible risers have been the focus of many researchers. Most flexible risers undergo a substantial level of irregular motion from environmental loadings, which involves a continuous slip of helical wires. The slip of helical wires especially leads to a hysteretic effect by reducing the bending stiffness, making it hard to predict the dynamic responses of flexible risers. The current study, as an extension to Part I, presents a new large-scale dynamic analysis method for flexible risers. The suggested method creates a large-scale model for the dynamic analysis that considers a geometric and bending nonlinearity of flexible risers. The kinematics of each beam element is formulated based on a Green-Lagrangian strain and the interaction with the seabed, providing a realistic analysis of flexible risers. In particular, the current study introduces a direct moment correction method that modifies the internal force vector using an improved analytical model. The improved analytical model is assigned at each node of the large-scale model and estimates an accurate bending hysteresis curve considering the effect of shear deformation and varying tension. The suggested method corrects the bending moment and shear force of all beam elements based on the bending hysteresis curves obtained from the improved analytical model, by which a complex bending behavior of flexible risers is reflected in a large-scale domain. As a result, this study achieves a more accurate prediction of the dynamic responses and fatigue damage of flexible risers. A new dynamic analysis program, called OPFLEX, is developed herein based on the suggested analysis method. Using the developed program, the current study conducts several numerical investigations to identify the effect of the shear deformation and varying tension. Consequently, it is confirmed that the shear deformation of internal layers reduces the fatigue damage of helical wires by delaying the increase of internal stress. It is also identified that the effect of varying tension deteriorates the fatigue life of flexible risers through a continuous change of contact pressure during bending.     

桁架式Spar平台与系泊/立管系统的全时域非线性耦合动态分析

开发了对浮式平台系统进行耦合动态分析的全时域程序。采用二阶时域方法计算水动力荷载,在此方法中,对物面边界条件和自由水面边界条件进行泰勒级数展开,利用Stokes摄动展开分别建立相应的一阶、二阶边值问题,而且此边值问题的计算域不随时间变化。采用高阶边界元方法计算每一时刻流场中的速度势,利用四阶预报校正法对二阶自由水面边界条件进行数值积分。在自由表面加入一个人工阻尼层来避免波浪的反射。对于系泊缆索/立管/张力腿的动力分析,在一个总体坐标系中对控制方程进行描述,采用基于细长杆理论的有限元方法进行求解。在耦合动态分析中,采用Newmark方法对平台和系泊缆索/立管/张力腿的运动方程同时进行求解。利用开发的耦合分析程序对一个桁架式Spar平台的运动响应进行了数值模拟,给出了平台的位移和系泊缆索/立管上端点的张力,并得到了一些重要结论。     

Application of analytical model in the prediction of dynamic responses and fatigue damage of flexible risers: Part I – Improvement of analytical model considering shear deformation and varying tension effects

Flexible risers have been widely utilized for the transfer of oil and gas products from a well to production units. The components of flexible risers, unlike steel risers, experience complex contact phenomena during bending. The contact between helical wires and adjacent layers especially causes a significant level of bending nonlinearity, making it hard to estimate the structural responses. Accordingly, a large-scale dynamic analysis of flexible risers usually involves an analytical model that predicts the bending moment and axial stress of helical wires based on theoretical approaches. The analytical model consists of an axis-symmetrical model and a bending model. Among them, the bending model plays a critical role in the prediction of the bending responses of flexible risers. The conventional bending models usually neglect the shear deformation of internal layers and continuity of sliding force, which leads to a significant error of analysis. Furthermore, the previous bending models assume that the contact pressure on helical wires is constant during bending. In real operating conditions, however, most flexible risers experience a considerable change of tension that governs the slip of helical wires. Hence, the current study presents a new dynamic analysis method for flexible risers. The suggested analytical model improves the bending model based on an accurate estimation of the internal strain field considering the shear deformation and continuous sliding force. Also, this study proposes a stiffness update method to reflect the effect of varying tension in the dynamic analysis. The presented method updates the bending property of flexible risers considering the continuous change of the contact pressure from varying tension. For the validation of suggested method, the current study carries out numerical simulations with a pure bending and varying tension for the internal diameter 7 inches flexible risers. It is identified that the suggested analytical model provides accurate analysis results. Moreover, it is found that the effect of varying tension gives a significant impact on the bending behavior of flexible risers by changing the slip condition of helical wires. Part I of this series of papers describes the detailed formulation method for the analytical model and with some verification examples. The suggested analytical model is expanded to the large-scale dynamic analysis in Part II for the investigation of the effect of shear deformation and varying tension.     

An expeditious algebraic formulation to the buckling critical load of risers under dynamic compression

Dynamic compression of risers can play an important role in the structural stability of submerged pipes in catenary-like configuration. In this paper, the analytical formulation for the buckling critical load, developed in the early 2000's, is revisited and extended to cover a wider range of practical cases. A purely algebraic expression for the critical load is provided, eliminating the original formulation requirement related to solving transcendental equations, for both free and anchored risers. The analytic formulations and respective algebraic approximations are compared with numerical simulations, presenting a fairly good agreement. A discussion on the differences and similarities of each formulation ends this paper, highlighting their range of validity. Also, from the comparison, the analytical formulation developed in this work was more suitable for precise and fast determination of the critical buckling load for both riser types, rigid and flexible, and for most typical operating conditions. The proposed algebraic expressions were highly accurate and may substitute the previous analytical formulations for critical load prediction.     

非粘结柔性立管静态分析

海洋柔性立管因材料和结构上的复杂性在设计分析中存在许多技术难题。本文在变形能原理和能量守恒的基础上,推导出了柔性立管各层的刚度矩阵。将各层刚度矩阵进行叠加,得到柔性立管总体刚度矩阵,并用总体刚度矩阵求解静载荷作用下立管变形响应。同时基于ABAQUS软件建立八层非粘结柔性立管有限元模型,并将有限元计算结果和刚度矩阵计算结果进行比较。结果分析表明：运用推导得到的刚度矩阵求解静态载荷下立管的变形是一种简便且准确的方法。     

Theoretical and numerical analysis of bending behavior of unbonded flexible risers

This paper presents theoretical and numerical study on bending properties of unbonded flexible risers. To capture nonlinearities in layer's sliding, the stress component due to slip-stick behavior is considered and energy conservation principle considering sliding-caused heat consumption is employed in the analytical model. Besides, a finite element model estimating mechanics of unbonded flexible risers' bending is proposed. In the finite element model, couplings between bending moment–curvature and axial stress as well as contact interaction among layers and tendons have been considered. The theoretical and numerical results were validated against the corresponding experimental data in literature and mutually compared in analyzing nonlinear bending behavior of flexible risers. Moreover, the impacts of axisymmetric loads on riser's bending behavior have been further investigated.     

A numerical study on the installation configuration design of compliant vertical access riser (CVAR) in deepwater

In oil and gas transportation, the compliant vertical access riser (CVAR) system conducts economic and operational advantages due to its special configuration. In this paper, the static performance of the CVAR is studied by an efficient numerical method. According to the unique configuration of the CVAR, the mathematical model is established based on minimum total potential energy principle. The equilibrium equations are discretized by finite difference method and then solved by Newton-Raphson technique. The accuracy of the numerical method is verified by OrcaFlex software. Detailed parametric analysis is carried out based on practical engineering requirements. The effects of buoyancy section's configuration including buoyancy factor, buoyancy section's length and buoyancy section's location, and external environmental factors including wellhead offset distance, water depth and current velocity on installation shape and mechanical properties of the CVAR are analyzed. The research shows that the presented numerical method has good applicability and flexibility for the early installation configuration design of marine risers which have no touchdown section but only one touchdown point and are equipped with multiple buoyancy blocks subjected to forces of different directions and magnitudes, such as CVARs.     

An integrated methodology for the design of mooring systems and risers

Traditionally, the design of mooring lines and risers of floating production systems (FPS) has been performed separately, by different teams, employing uncoupled analysis tools that do not consider the nonlinear interaction between the platform hull and the mooring lines and risers. Design processes have been focused on fulfilling the design criteria of the respective component (mooring/riser) alone, with few or no consideration to the other component, and little interaction between the design teams. Nowadays the importance of employing analysis tools based on coupled formulations is widely recognized, and analysis strategies have been proposed to consider feedback between mooring lines and risers within their respective design processes.In this context, this work details a proposal of one single and fully integrated design methodology for mooring systems and risers for deep-water FPS. In this methodology, the design stages of both risers and mooring lines are incorporated in a single spiral, allowing the full interaction of different teams; mooring design implicitly considers the riser integrity, and vice-versa, leading to gains in efficiency and cost reduction.Different analysis strategies are employed, taking advantage of uncoupled and coupled numerical models. The models generated at the initial/intermediate design stages can be reused in subsequent stages: simpler models are used in the initial stages, and more refined models are gradually introduced, to reach an ideal balance between computational cost and accuracy of results. In the advanced stages, the exchange of information between mooring/riser also allows the definition of criteria for the selection of governing/critical loading cases to be revised and verified in detail. This leads to the reduction of the original loading case matrix, allowing a feasible use of time-consuming fully coupled analysis.Results of a case study illustrating the application of some of the main processes of the methodology are included.     

深水管中管钢悬链线立管的非线性动力分析

立管技术是深水资源开发的关键技术之一。管中管钢悬链线立管具有同心的外管与内管，其外管提供机械保护，内管提供油气通道，内、外管之间按照一定的距离安装扶正器以保护绝热材料，在深水油气开发中具有较大的应用价值。充分考虑在位立管承受的复杂载荷条件泡括动边界、波浪与海流载荷、立管自重、海水浮力、管内外静压力），以及整体和局部非线性因素（包括摩擦、滑移、接触、间隙等），采用时域有限元软件ABAQUS实现管中管钢悬链线立管的建模与非线性动力分析。     

超深水钻井隔水管动力分析理论研究与数值模拟

随着钻井作业向深水(500～1 500m)和超深水(1 500m以上)发展,在交变海洋环境载荷波浪力、海流力和浮式钻井平台运动的共同作用下,隔水管的动态响应更加显著.文中探讨了隔水管侧向振动的数学模型、动态特性分析中的结构与环境载荷建模技术及其非线性动力分析方法,研究并对比了不同分析方法在计算效率、计算精度和工程适用性等方面的差异.介绍了时域内应用ABAQUS软件进行超深水钻井隔水管非确定性动力分析的算法与详细流程,算例比较了不同边界条件对深水钻井隔水管动态特性的影响.研究表明,时域非确定性分析最为精确但需要时间最长,且只能采用线性AIRY波浪理论;理论上,海流主要引起隔水管动态响应的时不变部分,但该时不变部分不等同于海流引起的隔水管静态响应,一种简化方法只将海浪与钻井船运动作为动载荷而不考虑海流对动态响应的贡献;钻井船运动和波浪载荷是隔水管动态响应分析主要的动载荷,对于超深水隔水管来说,钻井船运动是首要的动载荷,其慢漂运动对隔水管性能有重要影响,而波浪仅对隔水管局部产生作用.     

Dynamic coupled analysis of the floating platform using the asynchronous coupling algorithm

This paper discusses the numerical modeling of the dynamic coupled analysis of the floating platform and mooring/risers using the asynchronous coupling algorithm with the purpose to improve the computational efficiency when multiple lines are connected to the platform. The numerical model of the platform motion simulation in wave is presented. Additionally, how the asynchronous coupling algorithm is implemented during the dynamic coupling analysis is introduced. Through a comparison of the numerical results of our developed model with commercial software for a SPAR platform, the developed numerical model is checked and validated.     

Fatigue predictions for flexible marine propellers using FSI analysis considering Euler force in the rotating frame

Analysis of flexible marine propellers in terms of their structural response and stress is the key to accurate fatigue prediction. At present, finite element method (FEM) analyses of flexible propellers have been performed as a part of the fluid–structure interaction (FSI) analysis using a numerical method for the flexible structures, which is identical to that used for their rigid counterparts. In this study, the Euler force in a rotating frame is employed as an additional external force on the blades of the marine propeller during the FSI analysis. The Euler force is an inertial force component in the rotating frame due to angular acceleration. Acceleration of the rotating frame arises from large deformations of the propeller due to its flexible characteristics. The angular acceleration of the propeller is obtained for each time step, and the resulting Euler force is accounted for as a body force. The FSI analysis results are compared to experimental results in terms of the structural response, stress, and fatigue. It is clear that the Euler force has a major effect on the fatigue characteristics of the propeller because it amplifies the main response components. In conclusion, incorporating the Euler force in FSI analyses of flexible marine propellers is necessary for adequate prediction of the propeller fatigue.     

串列双立管涡激振动抑制研究

实际工程中深海立管常以管群的方式出现,当立管彼此相互靠近时,会发生流场干涉效应。为研究立管间相互干涉作用及螺旋侧板抑制双立管涡激振动的效果,本文基于Ansys Workbench平台,采用双向流固耦合技术对Re=7800均匀来流下长径比为482的串列双立管进行三维数值模拟。结果表明,立管轴间距为5D时立管间有完整的涡旋脱落,下游立管在上游立管的尾流诱导下产生振动,双立管横向振动锁定在二阶模态,且振动方向相反。附加螺旋侧板能有效削弱双立管振动频率,降低上游立管横向振动幅值,但下游立管两向位移响应变化不大。     

Towards a model of hydrodynamic damping for a circular cylinder with helical strakes at low KC

This paper investigates the hydrodynamic damping of a circular cylinder with helical strakes at Keulegan-Carpenter (KC) number from 0.07 to 3 in the presence of steady currents. Experiments were performed with a straked cylinder oscillating in either in-line or cross currents over Reynolds number (based on the oscillating velocity amplitude) varying from 1260 to 54,000. With in-line current being present, the measured drag coefficients of the straked cylinder are found to depend on the ratio between the oscillating velocity amplitude and the steady current velocity. This phenomenon is further confirmed by computational fluid dynamics using large-eddy simulations. The drag coefficients obtained from the numerical simulations agree well with the experimentally determined values. Similar phenomenon is observed for the cases with cross background current. Based on the experimental data, empirical formulae are proposed to evaluate drag coefficients. These results are of importance in estimating the resonant motion and the fatigue life of risers, e.g. water intake risers, in the flow regime of low KC. Finally, recommendations are provided for fatigue analysis of risers with helical strakes from the perspective of engineering practice.     

Extreme response based reliability analysis of composite risers for applications in deepwater

As current oil reserves start to deplete, companies are looking to exploit deeper deposits. At these greater depths composite risers, with their high strength-to-weight ratio, reduce the effective tensions and bending moments compared to steel risers. However, there is still limited research into their behaviour, with one key missing element being a comparison with traditional riser designs which accounts for variances in material properties and wave loads. This paper therefore conducts a strength-based reliability analysis of composite catenary risers operating between 1,500 m and 4,000 m. A static global catenary model is combined with Classical Laminate Theory to determine the extreme response and its performance is verified against FEA. This response is evaluated with the Tsai-Wu failure criterion to determine first-ply failure. The effect of laminate moisture absorption on the long-term reliability of submerged composite-based risers is also investigated as it can cause a significant reduction in the strength of composite risers. The reliability analysis is conducted using the Monte Carlo Method, revealing that the composite risers perform well at 4000 m. The degradation in performance from moisture absorption becomes increasingly important at greater depths and needs further investigation for these applications.     

Predicting the wet collapse pressure for flexible risers with initial ovalization and gap: An analytical solution

As offshore hydrocarbon production moves towards ultra-deep water, flexible risers have to withstand the huge hydro-static pressure without collapse. They are designed with strong collapse capacities, allowing them to operate under the condition where their annuli are flooded by the seawater. However, initial imperfections can weaken the collapse capacity under such a flooded condition, triggering the so-called “wet collapse”. Two common initial imperfections, the carcass ovality and the radial gap between the carcass and pressure armor, would reduce the collapse strength of flexible risers significantly. Mostly, collapse analyses are performed through numerical simulations, which are less feasible for the design stage of flexible risers comparing with analytical models. To date, there are few analytical models available in public literature to predict the wet collapse pressure of flexible risers accounting for initial ovality and gap. To meet this demand, an analytical model is established in this paper to address these issues. This model is developed as a spring-supported arch, solving the collapse pressure with stability theories of ring and arched structures. This analytical model is verified by numerical simulations, which gives prediction results that correlate well with the numerical ones.     

深水钻井立管建模与角度安全控制

从水面钻井平台与水下立管联合作业的安全角度出发，提出一种将钻井立管的力学响应限制特性引入水面平台动力定位闭环控制中的位置保持方法，实现水面钻井平台（或船舶）基于立管角度响应的动态定位。利用有限元方法建立包括立管系统质量、系统刚度、结构阻尼和水动力载荷在内的立管运动控制模型。联合水面浮体和水下立管的低频运动特性建立水面浮体运动偏移与水下立管顶端角度及末端角度的相对运动关系模型。在此基础上，设计基于立管运行响应的动力定位控位方法，实现对立管顶端角度及末端角度的安全控制。仿真结果表明，所提出的方法可行，在外界突变的环境载荷瞬时作用于水面浮体时，能更快地跟踪新的期望最优位置，保证钻井立管运行在安全界限内。     

钢悬链线立管整体干涉分析研究

深水海洋立管具有柔性,特别是极端海况条件下,相邻立管之间可能发生互相干涉而增大立管的应力,从而影响其疲劳寿命.钢悬链线立管相比顶张力立管,有效张力较小,对环境载荷作用更加敏感,更容易发生碰撞.基于动力学分析软件OrcaFlex建立有限元模型,从允许碰撞的角度出发,对串列布置于张力腿平台上的两根钢悬链线立管进行整体碰撞分析,研究立管间距、尾流模型、拖曳力系数、海流流速和柔性接头刚度对立管碰撞的影响,阐述对碰撞范围、上下游立管相对运动速度、最大碰撞速度和最大碰撞能量的影响规律,为实际工程中立管的空间布置和结构优化设计提供参考.     

火箭弹发射时连接螺纹处强度的数值分析和研究

基于非线性有限元数值分析,研究了某型号火箭弹内连接螺纹在发射中的强度问题。计算中考虑了材料的非线性问题和螺纹间的接触问题。计算结果表明,接触部位存在着明显的应力集中现象,但螺纹部位总体的应力水平较低,能够保证火箭弹的发射安全。     

Influence of residual stresses and geometric imperfections on the elastoplastic collapse of cylindrical tubes under external pressure

The buckling problem of a circular cylindrical shell has long been widely investigated due to its great importance in the design of aerospace and marine structures. Geometric imperfections and residual stresses are inevitable in practice and have been so far frequently considered in analytical and numerical predictions. But little attention has been paid until now on the combined influence of such initial defects on the critical and often unstable response of such elastoplastic structures. In this paper, a shell finite element is designed within the total Lagrangian formulation framework to deal with the elastoplastic buckling and post-buckling of thin cylindrical tubes under external pressure and axial compression. A specific experimental process will be introduced in order to measure residual stresses in the shell very accurately, so as to include them in the numerical calculations. The present formulation will enable us to describe the complete non-linear solutions, namely the critical pressures (bifurcation and limit (collapse) loads), the bifurcation modes and the bifurcated equilibrium branches up to advanced post-critical states. Comparisons will be made between numerical results and the experimental critical value and deformation patterns of a new generation profiler. Furthermore, the combined effects of geometric imperfections, residual stresses and plasticity will be analyzed.