Nonlinear Dynamic Analysis of Deepwater Drilling Risers Subjected to Random Loads

Excited by ocean currents, random wave and vessel motion, deepwater drilling risers exhibit significant dynamic response. In time domain, a method is proposed to calculate the nonlinear dynamic response of deepwater drilling risers subjected to random wave and dynamic large displacement vessel motion boundary condition. Structural and functional loads, external and internal pressure, free surface effect of irregular wave, hydrodynamic forces induced by current and wave, as well as wave and low frequency (drift) motion of the drilling vessel are all accounted for. An example is presented which illustrates the application of the proposed method. The study shows that long term drift motion of the vessel has profound effect on the envelopes of bending stress and lateral displacement, as well as the range of lower flex joint angle of the deepwater riser. It can also be concluded that vessel motion is the principal dynamic loading of nonlinear dynamic response for the deepwater risers rather than wave force.     

Time and frequency domain coupled analysis of deepwater floating production systems

The dynamic analysis of a deepwater floating structure is complicated by the fact that there can be significant coupling between the dynamics of the floating vessel and the attached risers and mooring lines. Furthermore, there are significant nonlinear effects, such as geometric nonlinearities, drag forces, and second order (slow drift) forces on the vessel, and for this reason the governing equations of motion are normally solved in the time domain. This approach is computationally intensive, and the aim of the present work is to develop and validate a more efficient linearized frequency domain approach. To this end, both time and frequency domain models of a coupled vessel/riser/mooring system are developed, which each incorporate both first and second order motions. It is shown that the frequency domain approach yields very good predictions of the system response when benchmarked against the time domain analysis, and the reasons for this are discussed. It is found that the linearization scheme employed for the drag forces on the risers and mooring lines yields a very good estimate of the resulting contribution to slow drift damping.     

Random dynamic response of a tethered buoyant platform production riser

A new normal mode spectral analysis method is presented for calculating r.m.s. riser deflections, bending stresses and lower ball joint angles. Forces on the riser consist of: (a) non-linear fluid drag taking account of the relative velocity due to tethered buoyant platform (TBP) motion, riser elastic deflection and wave induced fluid velocity, (b) wave induced fluid acceleration, (c) inertia forces due to TBP acceleration, and (d) buoyancy. The non-linear fluid drag forces are linearized using Tung and Wu's approximation based on the r.m.s. relative fluid velocity and current. A wide range of results is presented for risers in water depths up to 1000 m and it is observed that 6 normal modes are sufficient for calculating bending stresses. A static analysis is also presented for bending stresses due to wave and current induced drag forces and riser offset.     

A hybrid time/frequency domain approach for efficient coupled analysis of vessel/mooring/riser dynamics

The dynamic analysis of a deepwater floating structure is complex due to dynamic coupling between the platform and the moorings/risers. Furthermore, the system response at the incident wave frequency and at the resonant low frequency is coupled due to geometric and hydrodynamic nonlinearities. As such, it is generally held that a fully coupled time-domain analysis should be used for an accurate prediction of the dynamic response. However, in a recent work, it is found that for an ultra-deepwater floating system, a fully coupled frequency-domain analysis can provide highly accurate response predictions. One reason is the accuracy of the drag linearization procedure over the motions at two time scales, another is the minimal geometric nonlinearity of the moorings/risers in deepwater. In this paper, the frequency-domain approach is investigated for intermediate water depths, and it is found that the accuracy reduces substantially as geometric nonlinearity becomes important. Therefore, a novel hybrid approach is developed, in which the low-frequency motion is simulated in the time domain while the wave frequency motion is solved in the frequency domain at regular intervals. Coupling between the two analyses is effected by the fact that (i) the low-frequency motion affects the line geometry for the wave frequency motion, and (ii) the wave frequency motion affects the modeling of the drag forces, which damp the low-frequency motion. The method is found to be nearly as accurate as fully coupled time domain analysis even for a system with a preponderance of nonlinear and coupling effects, but requiring only one-tenth of the computational effort.     

立管对深水半潜式生产平台定位性能影响研究

基于三维频域势流理论,计算船体的水动力参数;采用动态耦合方法分析了深海半潜式生产平台各系统之间的相互作用特征,研究了立管系统对锚泊系统定位能力的影响。计算结果表明,立管系统在一定程度上增加了整个系统的刚度,其所受的附加质量和阻尼可降低平台的低频响应,从而降低平台的偏移和系泊缆的张力;海流将增大立管上的拖曳力,使平台偏移更远,锚索上的张力更大;立管系统对锚泊系统定位性能的最终影响需综合考虑多种因素的叠加。对目标平台而言,由于服役海域的流速较大,对立管的拖曳作用较为明显。因此,为确保平台的安全性,当服役海域流速较大时,带有多立管的平台,其锚泊系统的设计应考虑立管的影响。     

Tension and Drag Forces of Flexible Risers Undergoing Vortex-Induced Vibration

This paper presents the results of an experimental investigation on the variation in the tension and the distribution of drag force coefficients along flexible risers under vortex-induced vibration (VIV) in a uniform flow for Reynolds numbers (Re) up to 2.2×10⁵. The results show that the mean tension is proportional to the square of the incoming current speed, and the tension coefficient of a flexible riser undergoing VIV can be up to 12. The mean drag force is uniformly and symmetrically distributed along the axes of the risers undergoing VIV. The corresponding drag coefficient can vary between 1.6 and 2.4 but is not a constant value of 1.2, as it is for a fixed cylinder in the absence of VIV. These experimental results are used to develop a new empirical prediction model to estimate the drag force coefficient for flexible risers undergoing VIV for Reynolds number on the order of 10⁵, which accounts for the effects of the incoming current speed, the VIV dominant modal number and the frequency.     

不规则波激励下磁力双稳态波浪能转换装置的能量捕获特性研究

该研究提出了一种新型磁力双稳态机构,主要由一对同向充磁的负刚度磁环,附加一对异向充磁的正刚度磁环组成,可通过调整磁环参数有效改变双稳态装置的势垒高度,从而克服传统型双稳态装置在小幅波浪激励下转换效率低的难题。基于Cummins方程建立了系统的时域非线性动力学模型,其中采用状态空间模型替代了辐射力的卷积积分项用于加快计算速度。采用四阶龙格库塔方法求解动力学方程,获得系统响应解。采用Jonswap波浪谱,研究了不规则波激励下波浪能转换装置的转换效率随双稳态结构参数以及波浪激励参数的变化规律。结果表明,新型磁力双稳态机构在合适参数下可以达到降低势垒高度和拓宽平衡点间距的效果,从而显著提高波能捕获效率,拓宽波能捕获频带,尤其是大幅提高了系统在小波高激励下的捕获宽度。     

Frequency domain analysis of dynamic response of drag dominated offshore structures

The paper describes a method for stochastic representation of the hydrodynamic drag forces on offshore structures subjected to irregular waves. It is shown that, for the case of zero current, it is possible to construct a genuinely quadratic representation of the drag force which reproduces the statistical properties of the standard formulation of the drag force very closely, and which at the same time has sufficient flexibility to ensure a spectral density that accurately approximates the desired force spectrum. The distinct advantage of the new representation is that it brings dynamic analysis of extensive linear structures back into the frequency domain.     

Forces on a smooth submarine pipeline in random waves — A comparative study

Forces on a smooth submarine pipeline, fixed horizontally near a plane boundary, have been investigated under random wave conditions. The submarine pipeline was subjected to Pierson-Moskowitz spectrum (P-M spectrum) at various energy levels. The water particle kinematics were computed based on the linear random wave model and the Morison equation was chosen as the wave force predictor model. The inline hydrodynamic coefficients of drag and inertia were evaluated using two different methods, one in the frequency domain and the other in the time domain. Five mathematical formulations were considered for the analysis of transverse wave forces and these were compared in terms of the correlation coefficient. The transverse force was also analyzed in terms of the transverse root mean square (rms) coefficient. The inline hydrodynamic coefficients of drag and inertia and the transverse rms coefficient were correlated with the Keulegan-Carpenter number or period parameter, the relative clearance of the pipeline from the bed and the depth parameter. Finally, the results of the random wave tests were compared with those of regular waves under similar pipeline conditions.     

The Optimal Design of TMD for Offshore Structures

This paper presents the optimal design procedure of Tuned Mass Damper(TMD)for re-ducing vibration of an actual steel jacket offshore platform excited by random wave loading.In this study,a frequency domain is taken.The force on the structure is determined by use of the linearized Morisonequation for an input Power Spectral Density(PSD)of wave elevation.The sensitivity of optimum valuesof TMD to characteristic parameters of random wave spectrum is analyzed.An optimized TMD designfor the modeled platform is given based on design conditions and the findings of the study.     

Dynamic Analysis of Semi-Submersible Production Platform Under the Failure of Mooring Lines

This paper quantitatively studies the transient dynamic response of a semi-submersible production platform with the loss of one or several positioning mooring lines.A semi-submersible platform,production risers,and positioning mooring lines are all included in the numerical simulation.Increased motion of the semi-submersible platform,tension variation of the remaining mooring lines/risers and the risk of mooring line or riser clashing are all investigated through fully coupled time-domain analysis.Combined environmental loads are selected from irregular waves and the steady current varying from very rough to extreme sea conditions.Three dimension radiation/diffraction theories and Morison’s equation are applied to calculate first-order wave force and second-order mean drift force of floating semi-submersible platform.Nonlinear time-domain finite element methods are employed to analyze the behavior of mooring lines and risers.Results show that the failure of mooring lines seriously reduce the platform’s stability performance.The tension of the rest lines is also increased accordingly.Remaining lines which are closer to the failed lines will have larger tension increase to compensate.Line-Line distance provides practical information for the risk of clashing investigation.     

Dynamic Response Study of Steel Catenary Riser Based on Slender Rod Model

A numerical model of the steel catenary riser(SCR) is built based on the slender rod model. The slender rod model,which describes the behavior of the slender riser in terms of the center line position, can solve the geometrical nonlinearity effectively. In a marine environment, the SCR is under the combined internal flow and external loads,such as wave and current. A general analysis considers only the inertial force and the drag force caused by the wave and current. However, the internal flow has an effect on the SCR; it is essential to explore the dynamic response of the SCR with the internal flow. The SCR also suffers the lift force and the fluctuating drag force because of the current. Finite element method is utilized to solve the motion equations. The effects of the internal flow, wave and current on the dynamic response of the SCR are considered. The results indicate that the increase of the internal flow density leads to the decrease of the displacement of the SCR, while the internal flow velocity has little effect on the SCR. The displacement of the SCR increases with the increase of the wave height and period. And the increasing wave period results in an increase in the vibration period of the SCR. The current velocity changes the displacements of the SCR in x-and z-directions. The vibration frequency of the SCR in y-direction increases with the increase of the current velocity.     

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.     

Hybrid Analysis Approach for Stochastic Response of Offshore Jacket Platforms

The dynamic response of offshore platforms is more serious in hostile sea environment than inshallow sea.In this paper,a hybrid solution combined with analytical and numerical method is proposedto compute the stochastic response of fixed offshore platforms to random waves,considering wave-struc-ture interaction and non-linear drag force.The simulation program includes two steps:the first step is theeigenanalysis aspects associated the structure and the second step is response estimation based on spectralequations.The eigenanalysis could be done through conventional finite element method conveniently andits natural frequency and mode shapes obtained.In the second part of the process,the solution of theoffshore structural response is obtained by iteration of a series of coupled spectral equations.Consideringthe third-order term in the drag force,the evaluation of the three-fold convolution should be demanded fornonlinear stochastic response analysis.To demonstrate this method,a numerical analysis is carrie     

Nonlinear dynamic analysis of deep water risers

The paper presents a theoretical and numerical approach to the dynamical behaviour of risers in deep water which takes into account two types of nonlinearity; that due to viscous drag forces and that due to the large displacements of the riser when submitted to strong axial loads. As the second nonlinearity may have a significant influence upon the behaviour of risers in deep water, a method for automatically updating the structural geometry during the dynamic analysis is given. A computer programme has been written for this purpose.     

Simulation of wave power devices

Classical frequency and time domain models of a single degree of freedom wave power device are presented. In the time domain, a convolution integral is conventionally used to represent the fluid dynamic radiation force, characterised by added mass and damping in the frequency domain. This integral is replaced by an approximate ordinary differential equation (ODE) model which is faster and more convenient in simulations. A time domain model of the fluid dynamics of an oscillating water column (OWC) device is derived to illustrate the technique. Digital simulations of the OWC are used to compare the accuracy of the classical and ODE models. The simulation of the ODE model runs about six times as fast as the classical model based on convolution, yet characterises the fluid dynamics accurately.     

Review of flexible risers and articulated storage systems

The anchorage system for mid-ocean loading or production consists of an articulated tower for mooring the tanker. Flexible risers are also essential components of the anchorage system. The present paper provides a state-of-the-art review on articulated storage systems and flexible risers, giving theoretical background for the development of computer software for the static analysis of flexible risers.In the state-of-the-art review for flexible risers, various analysis techniques for elastic lines and flexible risers under self-weight, current and wave forces are presented. The dynamic response of the flexible riser, including vortex-induced oscillations, is also outlined.The literature concerning the articulated tower and tanker is relatively scarce. Available works related only to dynamic responses of articulated towers. The combined response of tower and tanker is only studied by Chakrabarti and Cotter [(1978), Analysis of a tower-tanker system. In Proceedings of the 10th Offshore Technology Conference, OTC 3202, pp. 1301–1310] in a limited sense. The review of these works is summarised relevant to this paper.In the end, the static analysis of the flexible riser under its self-weight and current is presented using a finite difference approach. The problem essentially involves geometrical non-linearity, which is tackled with the help of an iterative solution based on modified Newton-Raphson technique. The theoretical formulation presented is being used to develop the computer software for the static analysis of the flexible risers.     

Hull/mooring/riser coupled dynamic analysis and sensitivity study of a tanker-based FPSO

A computer program is developed for hull/mooring/riser coupled dynamic analysis of a tanker-based turret-moored FPSO (Floating Production Storage and Offloading) in waves, winds, and currents. In this computer program, the floating body is modeled as a rigid body with six degrees of freedom. The first- and second-order wave forces, added mass, and radiation damping at various yaw angles are calculated from the second-order diffraction/radiation panel program WAMIT. The wind and current forces for various yaw angles of FPSO are modeled following the empirical method suggested by OCIMF (Oil Company International Marine Forum).

The mooring/riser dynamics are modeled using a rod theory and finite element method (FEM), with the governing equations described in a generalized coordinate system. The dynamics of hull, mooring lines, and risers are solved simultaneously at each time step in a combined matrix for the specified connection condition. For illustration, semi-taut chain-steel wire-chain mooring lines and steel catenary risers are employed and their effects on global FPSO hull motions are investigated. To better understand the physics related to the motion characteristics of a turret-moored FPSO, the role of various hydrodynamic contributions is analyzed and assessed including the effects of hull and mooring/riser viscous damping, second-order difference-frequency wave-force quadratic transfer functions, and yaw-angle dependent wave forces and hydrodynamic coefficients. To see the effects of hull and mooring/riser coupling and mooring/riser damping more clearly, the case with no drag forces on those slender members is also investigated. The numerical results are compared with MARIN's wave basin experiments.     

Practical stochastic fatigue analysis of offshore platforms

A method for stochastic fatigue analysis of offshore platforms is presented. The method accounts for the nonlinearity in the drag loading term, and for the systematic deviation from a Gaussian process for a platform response. The method is based on an assumed form of the stress response process at a hot spot. A number of full scale measurements for elements in fixed platforms and for marine risers show very good agreement with this assumed form. A conventional spectral fatigue approach with stochastic linearization of the drag term in the basis for the new method, which uses results from linearizations in two or more sea states. The method is easily implemented in standard computer programs presently used within the offshore oil industry for fatigue analysis.     

Extreme value prediction of inundation drag force with and without current

This paper deals with drag forces due to irregular waves on a vertical slender structure in the splash zone, i.e. in the vicinity of still-water free surface, by considering the inundation effect due to instantaneous wave elevation. The force turns out to be a third-order quantity with respect to wave elevation. The focus of this paper is however limited to extreme value prediction of this force in stochastic waves. Based upon a transformation of random variables and use of the Rice formula, the mean up-crossing rate of inundation drag force is obtained in the frequency domain both by direct numerical integration and asymptotic evaluation for high levels using the Laplace method. The extreme value distribution of this force is then established by the Poisson probability law assuming independent up-crossing events. The proposed method agrees very well with time-domain simulations both for the mean up-crossing rate and the extreme value prediction. The effect of correlation between wave elevation and horizontal water particle velocity and the presence of current have been studied.