Dynamic analysis of deepwater steel lazy wave riser with internal flow and seabed interaction using a nonlinear finite element method
Introduction
Steel lazy wave risers (SLWRs) can be used as an effective deepwater oil and gas exploitation system production as their low cost and good reliability. The resultant top loads and fatigue life are also significantly improved in comparison with to free-hanging catenary configuration. This type of riser has been employed as a viable solution in deepwater and ultra-deepwater applications due to elimination of partial tension. Compared with traditional steel catenary risers (SCRs) as shown in Fig. 1 (a), there is a sag bend and an arc bend indicated in Fig. 1 (b) at the middle section of the SLWR by introducing additional buoyancy modules. In addition, the sag and arc parts can isolate the riser motions from vessel motions, which avoid the amplification of dynamic response induced by vessel motions. This means that the dynamic responses of a SLWR can be independently analyzed due to the decoupling between the riser top and the touchdown point.
Extensive researches have been performed using nonlinear numerical theory on the dynamic analysis of SCRs. For example, Walton and Polachek (1960), as one of the earliest researchers, applied the lumped mass model to investigate the dynamic responses of a two-dimensional (2-D) vertical tube. But in their model, the bending and torsional rigidity were ignored. Along the same lines, Buckham (2003), Low and Langley (2006), Zhu and Yoo (2014, 2015) and Fan et al. (2018) conducted a series of parametric studies on the three-dimensional (3-D) SCRs. Another common approach is finite difference method based on the principle of equilibrium for the microelements (Jason et al., 2000; Sophia, 2007; Chatjineorgiou, 2008). The finite difference method can provide solutions in a reasonable time on standard computers, but does not simulate accurately the boundary conditions, which may cause some numerical instability. On this regard, finite element method (FEM) is adopted to take with complex flexible pipe profile and boundary conditions. Cook (1974), Bathe (1996), Garrett (2005), Kim et al. (2010), Kim et al. (2013), Ji et al. (2016) and Qiao and Ou (2013) applied FEM together with minimum energy principle to formulate dynamic equation of motion for mooring/riser system. However, in their beam models, the transformation process of the physical parameters from local to global system requires long computation time and large computer CPU. Recently, a special FEM absolute coordinate based elastic rod theory has also been widely used (Ran, 2000; Berzeri and Shabana, 2000; Tahar and Kim, 2008; Yang et al., 2012) to simulate the dynamic performance of mooring or riser system. The corresponding model is formulated directly in a global coordinate system which can reduce significantly the number of effective elements for complex structures. Thus, this paper presents an alternative but more intimate SLWR formulation using the absolute coordinate approach. The application of the absolute coordinate approach for the solution of the rod equations is also found the previous study by the same authors (2018). The internal flow effect is identified and quantified by adding plug flow term to the effective tension equation. Meanwhile, the structure-seabed interaction is also simulated by using nonlinear quadratic spring combined with Coulomb friction model.
All above studies of the dynamic features of slender structures were still based on the traditional SCR tests, which will not represent SLWR events, i.e. the static configuration of the SLWR under the environment of currents and waves, the effects of internal flow and the seabed interaction on the dynamic responses of the SLWR. In addition, the dynamic responses of the SLWR are more complicated than those of the traditional SCR because the introduction of the suspended part would lead to large-angle deformations of the arch bend and the sage bend. Only a few studies of SLWR have been reported to date. Base on the natural catenary theory and linear beam theory, Wang et al. (2011) proposed an analytical model to investigate the static behavior of a SLWR on plastic seabed. Along the same lines, Jang (2013, 2014) investigated the nonlinearity of a SLWR configuration using infinite beam model. Later, Ruan et al. (2014) developed a new analytical model of a SLWR subjected to current loads and elastic seabed. Santillan and Virgin (2011) presented a parametric study on lazy-S and steep-S shaped risers by regarding the suspended part as a concentrated lift force applied at the arch bend top. They also conducted relevant model tests by using small-scale models to validate the numerical solutions. Wang et al. (2014, 2015) obtained the numerical solutions of the installation, abandonment, transfer and recovery process of the SLWR using finite difference method based on nonlinear large deflection beam theory. Wang and Duan (2015) further extended the theory to investigate the effect of the internal flow velocity on the mechanical performance of the SLWR. They found that the internal flow has significant influence on the axial tension, while does not contribute much to the configuration, bending moment and equivalent stress of the SLWR.
However, these mentioned studies are limited to the static analysis of a SLWR within 2-D plane, and they are not appropriate when the dynamic performance of a SLWR is considered. Based on the natural catenary, Li and Nquyen (2010) investigated preliminarily the dynamic behavior of a SLWR. In his model, each segment was regarded as a simple catenary and thus the effect of the bending stiffness was ignored. Kim and Kim (2015) used commercial analysis techniques to compare the dynamic performance of traditional SCRs and SLWRs. The numerical simulations suggested that the application of the SLWR can significantly reduce the stress level and fatigue damage near touch-down zone. But they did not provide the detail model of dynamic characteristics for the SLWR. The nonlinear dynamic analysis of the SLWR has not been exhaustive studied and it still needs to be better and comprehensively analyzed. In addition, it could be computationally more efficient, and physically realistic, to model dynamic problems of the SLWR with respect to some uncertainties, i.e. the internal flow and seabed effect.
The primary objective of this study is to investigate the nonlinear dynamic behavior of a SLWR subjected to the vessel offsets and wave-current loads. The nonlinear model of wave-current-SLWR interaction is based on the 3-D large deformation rod theory proposed by Ran (2000). An efficient FEM absolute coordinate approach is presented to discrete the motion equation and extensible condition, so that nodal variables can be expressed as global position displacements and their derivatives. This eliminates all transformation functions, which is typically required in commercial FEM softwares. In order to simulate the entire pipeline accurately, the formulas are also generalized to include the effect of internal flow and riser-seabed interaction, which are of particular importance for the 3-D dynamic performance of the suspended section. A classic Newton-Raphson approach is used to solve the static configuration of the SLWR, whereas an Adams-Moulton iteration scheme is applied to update the dynamic response at each time step. Calculations are made concerning the mechanical behaviors of the touchdown segment laid on the seabed, the decline segment, the buoyance segment and the hang-off segment suspended in the water. This paper is organized as follows. Section 2 briefly describes the developed numerical model. In Section 3, the present model is verified against the published numerical results. In Section 4, the effects of the harmonic motion parameters, the incident wave parameters and the geometric parameters on the dynamic tension of the SLWR are presented and discussed. Finally, the conclusions are summarized in Section 5.
Section snippets
Problem definition
When considering the effect of the top motion, wave-current loads, the riser-seabed interaction and the internal flow, the dynamic nonlinear analysis of the SLWR are complicated within 3-D space due to the particularity of introducing buoyancy segment. To facilitate this calculation, the following assumptions and simplifications are made for the SLWR in this work:
- (1)
The internal flow is assumed to be an elongated cylinder with infinite flexibility and the cross-section has the same velocity at
Static analysis of SLWR
To validate the present model, the developed nonlinear FEM was firstly used to investigate the configuration and static behavior of a SLWR described by Ruan et al. (2014). In the numerical simulation, the water depth is d=1500 m, the current velocity is v=0.2 m/s, the top inclined angle is θT=87o, the key geometric parameters of the SLWR are given in Table 1. Using a simple catenary analytical solution as an iterative algorithm for finite element analysis, only 4 iterations with 130 elements
Numerical results
So far, many papers have considered the static performance of the SLWR. However, the static analysis sometimes leads the incorrect frequency distribution of tension and may further bring about non-conservative results. In certain condition, the SLWR may be subjected to the top node motion or wave-current loads. In addition, the middle buoyance modules can induce more complex dynamic responses. Therefore, in this section, numerical simulations are conducted to investigate the time history of the
Conclusions
This study presents a time-domain numerical scheme to study the dynamic performance of the SLWR subjected to the vessel offsets and wave-current loads, by using a nonlinear 3D finite element method. The numerical model is based on a large deformation rod theory in terms of a global coordinate system, which prevents all transformations involving trigonometric functions. To accurately considering the additional lift force induced by the middle modules, the numerical model is divided into four
CRediT authorship contribution statement
Yong Cheng: Conceptualization, Methodology, Software, Writing - original draft. Lianyang Tang: Data curation, Software, Validation, Writing - review & editing. Tianhui Fan: Resources, Visualization, Supervision.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
The authors are grateful to the National Science Foundation of China (Grant No. 51861130358, 51579122, 51609109, 51709118), Natural Science Found of Jiangsu province (BK20160556), the Funds for Marine Economic Development of Guangdong Province (Grant No. GDME-2018B003), the Science and Technology Program of Guangzhou (Grant No. 201804010482), the State Key Laboratory of Ocean Engineering, China (Shanghai Jiao Tong University) (Grant No. 1905, 1708) and the State Key Laboratory of Coastal and
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