Dynamic Behavior of the Deepwater Flexible Pipeline During Pipe Laying Process

Journal of Marine Science and Engineering

Article Dynamic Behavior of the Deepwater Flexible Pipeline during Pipe Laying Process

Liquan Wang, Ming Ju, Xiaodong Xing * , Feihong Yun and Xiangyu Wang College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China; [email protected] (L.W.); [email protected] (M.J.); [email protected] (F.Y.); [email protected] (X.W.) * Correspondence: [email protected]

Received: 17 March 2020; Accepted: 13 April 2020; Published: 16 April 2020

Abstract: The dynamic behavior of the flexible pipeline during deepwater Flex-lay directly determines the structures of laying facilities and the actual installation process. A coupled dynamic model considering the effects of different factors was established in this paper. Based on the model, the initial attitude of the flexible pipeline during the laying process was determined by using the natural catenary theory and Morison equation. The hydrodynamic analysis of the HYSY201 pipelaying vessel was carried out by using the finite element software AQWA. Under the specific sea condition, a flexible pipeline with outer-diameter of 352.42 mm being laid onto the 3000 m deep seabed was simulated by using the software OrcaFlex to study the pipeline dynamic behaviors including axial tension, bending moment and stress-strain in the laying process, and the factors affecting the dynamic behavior of the pipeline were analyzed. The results show a significant correlation between the marine loads, vessel motion and the dynamic response of the pipeline. Compared with the static state case, the maximum axial tension, bending moment and stress-strain of the pipeline under the interaction of the marine loads and the vessel motion increased by 42.7%, 220%, 52% and 18.7%, separately. Among the marine loads, the surface wave had the most significant effect on the dynamic performance of the pipeline. When the wave direction acts on the width of the ship, the wave height is greater than 2 m and the spectrum period is eight seconds, the wave has the greatest influence on the dynamic response of the pipeline.

Keywords: ﬂexible pipeline; ﬂex-lay; pipelaying vessel; sea state; dynamic behavior

1. Introduction With the gradual development of oil and natural gas exploration in various countries, the proportion of offshore oil and natural gas resources is increasing. Submarine pipeline transportation is the main mode of marine oil and gas transportation, which has obvious advantages in terms of efficiency, economy and reliability [1,2]. Compared with rigid pipeline, flexible pipeline has significant advantages, so it is also widely used in drilling risers, production risers, export risers and workover risers [3]. As the exploration of the oil field is entering deepwater or ultra-deepwater areas, the main application of the Flex-lay system will confront greater challenges [4]. Due to the wide application of flexible pipes, a Flex-lay method for laying flexible pipes has appeared, its laying principle is similar to that of the Reel-lay method. Flexible pipes are reeled in the drum and unreeled into the sea through the laying system in the construction area [5,6]. Compared with other pipe laying methods, the Flex-lay method has a wider range of water depth and higher laying efficiency. Meanwhile, the curvature of the flexible pipe is smaller, which reduces the size and weight of the whole laying system and makes it easier to carry on the vessel. The dynamic behavior of the pipeline has direct influence on the working load of the pipeline laying system, which is an

J. Mar. Sci. Eng. 2020, 8, 286; doi:10.3390/jmse8040286 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2020, 8, 286 2 of 18 important design index of the laying tower system. In the actual process of pipeline laying, the dynamic behavior of the pipeline will be affected by factors such as ocean load and vessel motion. Therefore, it is of great significance for the design of flexible pipe and laying system to study the pipeline dynamic behavior and its influencing factors under the action of ocean loads. The analysis methods of pipeline laying process mainly include static and dynamic analysis [7]. Static analysis is used to analyze the discontinuous laying mode to analyze the attitude and stress of the laid flexible pipeline. Based on the elastic rod theory, the static equilibrium formula of submarine pipeline was derived by using perturbation method, and the nonlinear problem of submarine pipeline was solved by Konuk [8]. Lenci, S. simplified the J-lay laying problem, and compared it with the classical catenary theory to prove its applicability in deepwater and ultra-deepwater installation [9]. In order to solve the attitude and stress of S-lay pipeline in deep water, Brownnr put forward a solution method which ignores the pipeline stiffness bases of catenary theory, and the calculation results had high accuracy and efficiency [10]. Based on the static analysis, the dynamic analysis incorporates the interaction of environmental loads and the vessel motion to analyze the dynamic response of the flexible pipeline. In order to achieve constant tension in the laying of the pipeline laying system, Brewer analyzed the sensitivity of the pipeline tension in the deepwater [11]. Jasnapo et al. established the dynamic control equation of the submarine flexible-cable laying system based on the principle of d’Alembert, and analyzed the dynamic problems caused by the interaction between the flexible cable and the laying vessel [12]. Santillan et al. established a balance equation, considering the influence of platform motion and the vibration sensitivity on the flexible pipeline, and the results showed that increasing the riser buoyancy can reduce the axial force of the pipeline, which was verified by the simulation experiment [13]. Based on the principle of mass flow, Hong proposed a method to build a slender offshore equipment model. The absolute node formula is used to analyze the large displacement and angle structure of submarine pipeline, then the system control equation based on the principle of d’Alembert is established [14]. Gong and Zan et al. established the coupling model of the laying process of the deepwater S-lay system by using software OrcaFlex, and studied the ship motion and the dynamic behavior of the pipeline in the coupling model [15,16]. Wang established the theoretical model of subsea manifold installation based on the small deformation theory, and studied the dynamic characteristics of drill pipe in different installation stages of subsea manifold installation [17]. Past studies on the laying of submarine pipelines mostly focused on the S-lay and J-lay method for laying rigid pipelines, while few studied the dynamic behavior of flexible pipelines. Therefore, this paper uses flexible pipelines as the research object to study the dynamic behavior of the pipeline during the process of Flex-lay. A coupling model for Flex-lay is established, which mainly includes vessel motion, marine loads and pipeline dynamic model. The marine loads of the fourth-level sea condition is analyzed. The static tension and attitude of the pipeline are determined by using the catenary theory combined with the Morison hydrodynamic equation. The ANSYS-AQWA software is used to determine the relevant parameters of the pipelaying vessel HYSY201 as the analysis object. Finally, a comprehensive finite element model for Flex-lay was established by using Orcaflex software and used to carry out an illustrative example analysis of a 10-inch flexible pipeline being laid onto the seabed with a water depth of 3000 m. Finally, the influence of various factors of the marine environment on the dynamic behavior of the flexible pipeline was discussed.

2. Mechanical Model

2.1. Basic Assumptions In actual engineering, the dynamic behavior of the pipeline will change due to different flexible pipelines, marine environments and installation conditions. The laying process of placing the pipeline safely on the seabed is very complicated. The pipeline is affected by various factors, such as water J. Mar. Sci. Eng. 2020, 8, 286 3 of 18 depth, current, waves and the irregular moment of vessel in the marine environment. In order to simplify the model of flexible pipeline laying analysis, the following assumptions are proposed: J.(1) Mar. The Sci. marineEng. 2020, loads 8, x FOR in PEER the REVIEW model are assumed to be the ideal loads, and the seabed is simplified3 of 18 to a horizontal seabed with a constant stiffness; (2) The(1) The direction marine of loads ocean in the currents model and are assumed the deformation to be the ideal of the loads, flexible and pipelinethe seabed are is simplified assumed to lie to a horizontal seabed with a constant stiffness; in the same plane, and the speed of currents in the seabed is zero and the speed is the maximum in the (2) The direction of ocean currents and the deformation of the flexible pipeline are assumed to sea surface;lie in the same plane, and the speed of currents in the seabed is zero and the speed is the maximum in(3) the Under sea surface; the random marine loads, the torsional deformation of the flexible pipe is very small, so the torsional(3) Under deformation the random of marine the flexible loads, the pipe torsional is ignored deformation in the dynamic of the flexible analysis, pipe andis very the small, impact of the Flex-layso the torsional system deformation contact with of thethe flexible flexible pipe pipe is onignored the bending in the dynamic stiffness analysis, is ignored; and the impact of the(4) InFlex the‐lay mechanical system contact analysis, with the the flexible flexible pipe pipe on the with bending a multi-layer stiffness is structure ignored; is assumed to be a continuous(4) pipeIn the with mechanical uniform analysis, material the and flexible isotropy; pipe with a multi‐layer structure is assumed to be a continuous(5) The effects pipe of with laying uniform systems material in contact and isotropy; with flexible pipes on pipe bending stiffness is ignored. (5) The effects of laying systems in contact with flexible pipes on pipe bending stiffness is 2.2. Equationsignored. for Coupled Model

2.2.As theEquations depth for of Coupled the laying Model water increases, the impact of wind, current and waves on the flexible pipeline willAs the become depth of more the laying obvious, water and increases, the dynamic the impact behavior of wind, of current the flexible and waves pipeline on the will flexible become non-negligiblepipeline will [18 become]. During more the obvious, laying and process the dynamic of Flex-lay, behavior flexible of the pipelines,flexible pipeline the laying will become vessel, the layingnon structure‐negligible and [18]. the During ocean the constitute laying process a general of Flex Flex-lay‐lay, flexible system. pipelines, The dynamicthe laying behavior vessel, the of the flexiblelaying pipeline structure is a andffected the byocean many constitute factors a in general the system. Flex‐lay It system. can be The observed dynamic from behavior Figure of1 thatthe the flexibleflexible pipe pipeline is released is affected from theby many reel throughfactors in the the Flex-laysystem. It system can be observed to adjust from the directionFigure 1 that of thethe pipe, and isflexible clamped pipe intois released the water from by the the reel tensioner. through the Under Flex‐lay the system combined to adjust action the direction of marine of loadsthe pipe, and the layingand vessel is clamped motion, into the the pipeline water by will the tensioner. gradually Under form the the combined attitude shown action of in marine the figure. loads Theand pipelinethe can belaying divided vessel into motion, a suspended the pipeline part, will a sag gradually bend region form the and attitude a laid shown part, and in the the figure. attitude The of pipeline the pipeline can be divided into a suspended part, a sag bend region and a laid part, and the attitude of the is determined by the tension force, the linear density of the pipeline and the laying angle. pipeline is determined by the tension force, the linear density of the pipeline and the laying angle.

FigureFigure 1. 1.Schematic Schematic diagram diagram of of Flex Flex-lay‐lay pipeline pipeline installation. installation.

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Based on the coordinate system of the Flex-lay system, then applying Newton’s second law, the dynamic equation of the system can be obtained as:

.. MX(t) + CX(t) = frad(t) + fwave(t) + fc(t) + fw(t) + fp(t) (1) where M denotes the inertia matrix, C is the hydrostatic restoring matrix, X(t) represents the displacement matrix of the vessel motion, t represents time, f rad(t) represents the radiation forces due to changes in ﬂuid momentum caused by vessel motion, f wave(t) represents the wave load, f w(t) and f c(t) represent wind load and current load in the marine environment respectively, f p(t) indicates the tension of the pipeline at the tensioner position.

2.3. Pipelay Vessel Motion Due to the superposition of forced swaying caused by the marine environment and the inherent swaying of the vessel, vessels perform complex compound movements at sea. Under the combined action of wave and the damping of sea, the period and amplitude of the swaying will tend to stabilize. The sailing vessel has six degrees of freedom, including Surge, Sway, Heave, Roll, Pitch and Yaw, as shown in Figure1. The displacement matrix X(t) can be represented by above six parameters. In general, the motion of the vessel can be determined by the amplitude response operators (RAOs) corresponding to the above 6 degrees of freedom [19]. Each displacement RAO consists of a pair of numbers that define the vessel’s response to a specific degree of freedom in a specific wave direction and period. Therefore, the displacement matrix X(t) of the vessel under the action of different waves can be obtained with the RAOs of the laying vessel. At the same time, the radiating force of the fluid is generated by the change of the surrounding fluid due to the motion of the vessel. When calculating the radiative force, assuming that the fluid surrounding the vessel is an ideal fluid, the wave can be approximated as a linear wave. Using potential theory, the following representation can be obtained [20]:

.. Z t . frad(t) = A( )X(t) K(t τ)X(τ)dτ (2) − ∞ − 0 − where A( ) represents the additional mass of the vessel at infinite frequency. The second term ∞ represents fluid memory, which captures the transfer of fluid energy generated by the motion of the vessel in the form of free surface radiation waves. The convolution term K(t) is a matrix of retardation or memory functions. It contains the energy dissipation caused by the radiation waves generated by the vessel’s motion. When the other loads applied to the vessel are neglected in the frequency domain, its form of motion can be defined as:

n 2 o ω [M + A(ω)] + jωB(ω) + C X(jω) = Fwave(jω) (3) − where A(ω) and B(ω) represents the frequency and additional mass of the damping matrices, respectively. X(jω) represents the amplitude and phase of the vessel motion, Fwave(jω) represents linear forces caused by waves. Ogilvie determined A(ω) and B(ω) directly by applying a Fourier transform in a sinusoidal regime: Z 1 ∞ A(ω) = A( ) K(t) sin(ωt)dt (4) ∞ − ω 0 Z ∞ B(ω) = K(t) cos(ωt)dt (5) 0 J. Mar. Sci. Eng. 2020, 8, 286 5 of 18

By Fourier transform, K(t) and K(jω) can be represented by A(ω) and B(ω): Z 2 ∞ K(t) = B(ω) cos(ωt)dω (6) π 0 Z ∞ jωt K(jω) = K(t)e− dt = B(ω) + jω[A(ω) A( )] (7) 0 − ∞ Therefore, the vessel’s radiating force under diﬀerent environmental forces can be obtained by calculating the vessel’s damping matrix and additional mass matrix.

2.4. Metocean Conditions

2.4.1. Wind Conditions Wind loads on vessels are calculated according to the formula given by the Oil Companies International Marine Forum (OCIMF) on the Prediction of Wind and Current Loads on Very Large Crude Carriers. A varying or constant wind direction and velocity can be simulated by a model with diﬀerent kinds of spectra. The calculation formula for wind load is:

 2  Xwind = 0.5ρaA f UR Cwx   Y = 0.5ρ A U 2C (8)  wind a s R wy  2 Nwind = 0.5ρaAsLBPUR Cwn where Xwind and Ywind represent wind load in X and Y directions, respectively, Nwind represent wind load moment along OZ axis, ρa is the air density, Af and As are the side projected area of vessel and the front projected area, respectively. UR is the average wind speed, LBP is the vessel vertical length, Cwx, Cwy, Cwn are the wind force and wind moment coeﬃcients. They are derived from a hull model wind tunnel test conducted at the University of Michigan in 1960 [21].

h iT fw(t) = Xwind Ywind 0 0 0 Nwind (9)

2.4.2. Current Field The calculation of ship ﬂow loads is also calculated according to the formula given in Section 2.4.1. The calculation formula for current load is:

 2  Xc = 0.5ρcLBPDUc Ccx   Y = 0.5ρ L DU 2C (10)  c c BP c cy  2 2  Nc = 0.5ρcLBP DUc Ccn where Xc and Yc represent current load in X and Y directions, respectively, Nc represents wind load moment along OZ axis, ρc is the water density, D is the vessel draught, Uc is average velocity, Ccx, Ccy, Ccn are the current force and current moment coeﬃcients. They can also be obtained by the spectrum in the data given by OCIMF. Therefore, the current load on the laying vessel can be expressed as

h iT fc(t) = Xc Yc 0 0 0 Nc (11)

2.4.3. Wave Conditions In general, waves are characterized by statistics, including wave height, period and power spectrum. The spectral characterization of the wave conditions is very important in the determine the dynamic behavior of the ﬂexible pipeline during the laying process. JONSWAP wave spectrum is usually used in engineering to calculate wave load [22], which was proposed by the United States, the Netherlands, the United Kingdom, and Germany in the “North Sea Joint Wave Project” between J. Mar. Sci. Eng. 2020, 8, 286 6 of 18

1965 and 1970 [23]. The wave spectrum formula is expressed by the wave’s sense height and wave peak period:   2 2 (0.159ωTp 1) ς W/3  1948  exp [ − ] J. Mar. Sci. Eng. 2020, 8, x FOR SPEER(ω) REVIEW = 319.34  3.3 − 2σ2 6 of(12) 18 ς 4 5  4  Tp ω − (Tpω)  where Tp is the peak period of the spectrum, that is, the period corresponding to the largest spectral where Tp is the peak period of the spectrum, that is, the period corresponding to the largest spectral value in the wavewave spectrum.spectrum. σ σ representsrepresents the the peak peak attitude attitude parameter. parameter.ω ωrepresents represents the the peak peak period period of ofthe the spectrum. spectrum.

2.5. Pipeline Pipeline Model Model Compared withwith traditional traditional rigid rigid pipes, pipes, the the structure structure of flexible of flexible pipes pipes is more is complex.more complex. The flexible The flexiblepipe is manufactured pipe is manufactured in a layered in a structure, layered structure, composed composed of layers ofof materialslayers of withmaterials different with structures different structuresand functions and [functions24]. This layered[24]. This structure layered makesstructure the makes flexible the pipe flexible have pipe a better have compressive a better compressive strength, strength,corrosion corrosion resistance resistance and other and properties, other properties, but it greatly but increases it greatly the increases computational the computational cost during cost the duringdynamic the analysis. dynamic Therefore, analysis. Therefore, the flexible the pipe flexible is assumed pipe is toassumed be a uniform, to be a continuous,uniform, continuous, isotropic isotropicsingle-layer single pipe,‐layer as shown pipe, as in shown Figure 2in. Figure 2.

Figure 2. Simpliﬁed pipeline model. Figure 2. Simplified pipeline model.

During the process of the Flex-lay, the tension fp(t) of the pipeline at the point A is mainly composed During the process of the Flex‐lay, the tension fp(t) of the pipeline at the point A is mainly of two parts. One part is the axial tension caused by the wet weight of the underwater pipeline, which composed of two parts. One part is the axial tension caused by the wet weight of the underwater can be obtained by the static natural catenary algorithm. The other part is the hydrodynamic load on pipeline, which can be obtained by the static natural catenary algorithm. The other part is the the pipeline, which can be obtained through the semi-empirical Morison equation. hydrodynamic load on the pipeline, which can be obtained through the semi‐empirical Morison Therefore, f (t) can be expressed as: equation. p Therefore, fp(t) can be expressed as: f p(t) = FT + FMorison (13) fp(t)=FT+FMorison (13) Because the catenary method ignores the effects of pipe bending and torsional stiffness, the catenaryBecause algorithm the catenary calculation method results ignores are verythe effects close toof thepipe true bending equilibrium and torsional [25]. Because stiffness, of the catenarycharacteristics algorithm of flexible calculation pipes, the results results are of very the catenary close to model the true are equilibrium more accurate. [25]. The Because attitude of of the characteristicspipeline located of in flexible the ocean pipes, can the be expressed results of asthe the catenary catenary model state shownare more in Figureaccurate.3a. The coordinateattitude of theorigin pipeline of the located model isin the the touch ocean down can be point expressed of the pipe,as the x-axis catenary represents state shown the horizontal in Figure direction, 3a. The coordinate origin of the model is the touch down point of the pipe, x‐axis represents the horizontal z-axis represents a vertical direction, α represents the angle of pipe laying, FT(x) represents the tension direction,of unit pipe. z‐axis The represents basic governing a vertical equation direction, of catenary α represents theory the is: angle of pipe laying, FT(x) represents the tension of unit pipe. The basic governing equation of catenary theory is: q ” 2 z (x) = δ 1 + [z0 (x)]2 (14) zx"' 1  zx (14)   where δ = w/H, w indicates the wet weight of the pipe, H represents the constant horizontal component whereof the tension.δ = w/H The, w tension indicates of thethe unit wet pipeline weight atof any the position pipe, H can represents be obtained: the constant horizontal component of the tension. The tension of the unit pipeline at any position can be obtained: w FT(x) = wch(δx) (15) F xchx δ  (15) T 

Hydrodynamic in‐line forces from the current, acting on the pipeline, apply to an accelerated fluid environment in which the pipeline is kept vertical and stationary [26]. The hydrodynamic force on the pipeline can be expressed as Morison’s equation as:

Fmorison0.5 wCD duu w CA w u w A u (16)

In the equation, ρw represents the density of water, D is the outer diameter of the pipeline, A represents the cross‐sectional area of the pipe, u represents the velocity of the fluid, Cd and Cw

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Hydrodynamic in-line forces from the current, acting on the pipeline, apply to an accelerated ﬂuid environment in which the pipeline is kept vertical and stationary [26]. The hydrodynamic force on the pipeline can be expressed as Morison’s equation as:

. . F = 0.5ρwC Du u + ρwCwAu + ρwAu (16) morison d | | J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 7 of 18 In the equation, ρw represents the density of water, D is the outer diameter of the pipeline, representsA represents the the drag cross-sectional coefficient and area the of hydrodynamic the pipe, u represents mass, respectively. the velocity When of the the fluid, oceanC dloadand actsCw onrepresents the unit thepipeline, drag coe theffi abovecient and formula the hydrodynamic can be decomposed mass, respectively.into the drag When force of the the ocean unit load pipeline acts onin thethe ocean unit pipeline, in the normal the above and formula tangential can directions be decomposed Fn and intoFτ: the drag force of the unit pipeline in the ocean in the normal and tangential directions F and F : n τ 2 FCDv 0.5  sin (17) nwn1 2 Fn = 0.5ρwCnD1(v sin θ) (17) 2 FCDv 0.5 cos 2 (18) Fτ =0.5ρwwCτD1(v cos θ) (18) where Cn andand CCττ representsrepresents the the normal normal and and tangential tangential drag drag coefficients, coefficients, vv representsrepresents the the current velocity at at the position of the pipeline unit, unit, θ isis the angle between the the unit pipe and the horizontal direction.direction. Therefore, the forceforce onon anyany position position of of the the pipeline pipeline can can be be expressed expressed as as shown shown in Figurein Figure3b. 3b.Under Under the the load load of theof the current, current, the the tension tension of of the the pipeline pipeline at at point point A A can can bebe obtainedobtained by using the iterativeiterative method.

(a) (b)

FigureFigure 3. UnderwaterUnderwater pipeline pipeline model: model: ( (aa)) Attitude Attitude of of underwater underwater pipeline; pipeline; ( (bb)) Force Force of of pipeline pipeline unit. unit.

3.3. Numerical Numerical Implementation Implementation and and Dynamic Dynamic Characteristic Characteristic Analysis Analysis 3.1. Operating Parameters 3.1. Operating Parameters In general, the environment of Flex-lay operations can be expressed by sea state, and sea state In general, the environment of Flex‐lay operations can be expressed by sea state, and sea state can be divided into nine levels according to international standards. The Flex-lay operation should can be divided into nine levels according to international standards. The Flex‐lay operation should be capable of performing under the conditions of fourth-level sea state, so the marine environment be capable of performing under the conditions of fourth‐level sea state, so the marine environment of pipeline dynamic analysis is set to the fourth-level sea state. In addition, the ﬂexible pipeline will of pipeline dynamic analysis is set to the fourth‐level sea state. In addition, the flexible pipeline will be subject to the reaction force from the seabed, which is linearly related to the depth of the pipeline be subject to the reaction force from the seabed, which is linearly related to the depth of the pipeline sinking into the sea ﬂoor [27]. Therefore, the parameters of the marine environment are set as shown sinking into the sea floor [27]. Therefore, the parameters of the marine environment are set as shown in Table1. in Table 1.

Table 1. Marine environmental parameters.

Parameter Value Parameter Value Depth 3000 m Seabed stiffness 100 kN/m/m2 Sea density 1025 kg/m3 Seabed damping 1.0250 Surface current Sea temperature 15 °C 1.028 m/s velocity Seabed current 1.35 × 10−6 0 m/s Kinematic viscosity velocity m2/s Air kinematic 15 × 10−6 Spectral peak period 6.1~16.2 s viscosity m2/s

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Table 1. Marine environmental parameters.

Parameter Value Parameter Value Depth 3000 m Seabed stiﬀness 100 kN/m/m2 Sea density 1025 kg/m3 Seabed damping 1.0250 Sea temperature 15 ◦C Surface current velocity 1.028 m/s Seabed current velocity 0 m/s Kinematic viscosity 1.35 10 6 m2/s × − Air kinematic viscosity 15 10 6 m2/s Spectral peak period 6.1~16.2 s × − Wave height 1.25–2.5 m Air density 1.29 kg/m3 Wave type JONSWAP Wind speed 8.0–10.8 m/s

HYSY201 is the ﬁrst S-lay vessel for deep water in China, and mainly used for S-lay operations. It can also be used to do Flex-lay tasks after modiﬁcation [28]. HYSY201 is used as the mother vessel for analysis, and the vessel parameters are shown in Table2. The speed of the vessel is not considered in this analysis, and the default speed is 0.

Table 2. Vessel parameters.

Parameter Value Parameter Value overall length 204.65 m Vertical spacing 185.00 m molded breadth 39.20 m molded depth 14.00 m structure draft 11.00 m operation draft 7~9.5 m Ship displacement 59,101 T deadweight 34,850 T metacenter height 8.20 m Height center 13.60 m

At present, the main pipe manufacturers in the world are Technip, Wellstream and Flexibles. Therefore, the 10-inch ﬂexible pipe from Technip company is selected as the preset object. The performance parameters of the 10-inch ﬂexible pipe produced by Technip company are showed in Table3.

Table 3. Pipe parameters.

Parameter Value Parameter Value inner diameter 254 mm Tensile stiﬀness 3.09 108 N/m × outer diameter 352.42 mm Bending stiﬀness 3.21 105 N m × · Line density 4437 Kg/m3 Young modulus 6.04 106 MPa × allowable stressed 31 MPa Poisson’s ratio 0.3 Yield strength 549 MPa Yield strength 414 MPa

3.2. Vessel Response Parameter The hydrodynamic model of HYSY201 is established by the software AQWA, and the values of the vessel damping coefficient and additional mass are obtained by calculating the hydrodynamic model file, as shown in Figures4 and5. Figure4 shows that the damping coe fficient of the vessel increases first with the increase of the period, then gradually decreases after reaching the peak. Figure5 shows that the additional mass of the vessel decreases first and increases with the increase of the period, and then decreases continuously after reaching the peak. The maximum value of the damping coefficient and the additional mass moment of the vessel in the pitch and sway is much larger than the value in the roll direction. J. Mar. Sci. Eng. 2020, 8, 286 9 of 18 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 9 of 18 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 9 of 18

Figure 4. Vessel damping coefficient. FigureFigure 4.4. VesselVessel dampingdamping coecoefficientﬃcient..

Figure 5. Vessel additionaladditional mass.mass. Figure 5. Vessel additional mass.

FigureFigure6 6 shows shows the the response response spectrum spectrum ofof vessel vessel motion motion based based on on the the displacement displacement responseresponse Figure 6 shows the response spectrum of vessel motion based on the displacement response amplitudeamplitude operatorsoperators (RAOs).(RAOs). It can be observed from the ﬁgure,figure, under wave conditions,conditions, thatthat almostalmost amplitude operators (RAOs). It can be observed from the figure, under wave conditions, that almost allall the the responses responses of of the the vessel vessel are are very very signiﬁcant, significant, especially especially the Roll the motion,Roll motion which, which is the mostis the drastic. most all the responses of the vessel are very significant, especially the Roll motion, which is the most Thedrastic. vessel The motion vessel response motion response curves coincide curves withcoincide 0◦ and with 180 0°◦ ,and 45◦ 180°,and 13545°◦ inand the 135° wave in direction,the wave drastic. The vessel motion response curves coincide with 0° and 180°, 45° and 135° in the wave indicatingdirection, indicating that the symmetry that the ofsymmetry the mother of the vessel mother along vessel the section along isthe better. section The is response better. The of Pitchresponse and direction, indicating that the symmetry of the mother vessel along the section is better. The response Surgeof Pitch motion and Surge is larger motion at the is wave larger direction at the wave of 0◦ directionand 180◦, of and 0° theand response 180°, and of the Heave response Roll and of SwageHeave of Pitch and Surge motion is larger at the wave direction of 0° and 180°, and the response of Heave motionRoll and is Swage larger atmotion the wave is larger direction at the of wave 90◦. direction of 90°. Roll and Swage motion is larger at the wave direction of 90°.

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Figure 6. Vessel amplitude response operator (RAO) response. Figure 6. Vessel amplitude response operatoroperator (RAO)(RAO) response.response. 3.3. Dynamic Simulation 3.3. Dynamic Simulation The dynamic analysis analysis begins begins at at the the static static equilibrium equilibrium position, position, which which can can be determined be determined by the by The dynamic analysis begins at the static equilibrium position, which can be determined by the thepipeline pipeline model model described described above. above. The The initial initial equilibrium equilibrium position position of of the the Flex Flex-lay‐lay system system was pipeline model described above. The initial equilibrium position of the Flex‐lay system was determined throughthrough calculation, calculation, and and the startingthe starting configuration configuration was provided was provided for dynamic for simulation. dynamic determined through calculation, and the starting configuration was provided for dynamic Subsequently,simulation. Subsequently, by considering by considering the effects of the marine effects loads of marine and vessel loads motion, and vessel a model motion, of the a model Flex-lay of simulation. Subsequently, by considering the effects of marine loads and vessel motion, a model of systemthe Flex that‐lay fully system considers that fully various considers complex various non-linear complex problems non is‐linear established. problems The is model established. is composed The the Flex‐lay system that fully considers various complex non‐linear problems is established. The ofmodel three is parts: composed marine of environment, three parts: marine flexible environment, pipeline and flexible laying vessel. pipeline Finally, and laying the appropriate vessel. Finally, time model is composed of three parts: marine environment, flexible pipeline and laying vessel. Finally, stepthe appropriate was selected time through step was a large selected number through of experimental a large number analyses, of experimental and the axial analyses, tension, bendingand the the appropriate time step was selected through a large number of experimental analyses, and the moment,axial tension, stress bending and strain moment, of the stress pipeline and strain were calculatedof the pipeline at each were time calculated step to at study each the time dynamic step to axial tension, bending moment, stress and strain of the pipeline were calculated at each time step to behaviorstudy the of dynamic the pipeline behavior during of the the pipeline process ofduring Flex-lay. the process of Flex‐lay. study the dynamic behavior of the pipeline during the process of Flex‐lay. Under the above conditions, a numerical simulation is performed on the laying process of the Under the above conditions, a numerical simulation is performed on the laying process of the Flex-lay.Flex‐lay. The time history of the pipelinepipeline top tensiontension isis shownshown inin FigureFigure7 7.. The The maximum maximum dynamic dynamic Flex‐lay. The time history of the pipeline top tension is shown in Figure 7. The maximum dynamic tension of pipeline pipeline is is 4627 4627 kN kN at at 145 145 s, s,which which is 42.7% is 42.7% higher higher than than the thestatic static tension tension of 3242 of 3242 kN, and kN, tension of pipeline is 4627 kN at 145 s, which is 42.7% higher than the static tension of 3242 kN, and andthe minimum the minimum dynamic dynamic tension tension of the of pipeline the pipeline is 1823 is kN, 1823 which kN, is which 43.7% is lower 43.7% than lower the than static the tension. static the minimum dynamic tension of the pipeline is 1823 kN, which is 43.7% lower than the static tension. tension.It can be It seen can be that seen during that during the laying the laying of flexible of flexible pipelines, pipelines, the the impact impact on on the the pipeline pipeline under under the It can be seen that during the laying of flexible pipelines, the impact on the pipeline under the interaction ofof marinemarine loads loads and and vessel vessel motion motion is is very very significant. significant. Therefore, Therefore, the the design design of theof the Flex-lay Flex‐ interaction of marine loads and vessel motion is very significant. Therefore, the design of the Flex‐ systemlay system needs needs to consider to consider the pipelinethe pipeline dynamic dynamic tension. tension. lay system needs to consider the pipeline dynamic tension.

Figure 7. Time histories for the flexible pipeline top tension. Figure 7. Time histories for the flexible pipeline top tension. Figure 7. Time histories for the flexible pipeline top tension. Figure8 shows the maximum and minimum values of axial tension, bending moment and stress Figure 8 shows the maximum and minimum values of axial tension, bending moment and stress and strainFigure of 8 the shows pipeline the maximum during the and period minimum of 0–200 values s. As of shown axial tension, from Figure bending8a, there moment is a significant and stress and strain of the pipeline during the period of 0–200 s. As shown from Figure 8a, there is a significant diandfference strain between of the pipeline the static during axial the tension period and of the 0–200 maximum s. As shown and minimum from Figure axial 8a, tension there ofis a the significant pipeline. difference between the static axial tension and the maximum and minimum axial tension of the Thedifference largest between gap between the thestatic maximum axial tension and minimum and the tensionmaximum of the and pipeline minimum appears axial at tension the separation of the pipeline. The largest gap between the maximum and minimum tension of the pipeline appears at the pipeline. The largest gap between the maximum and minimum tension of the pipeline appears at the separation position between the pipeline and the tensioner, as the length of the pipeline increases, separation position between the pipeline and the tensioner, as the length of the pipeline increases,

J. Mar. Sci. Eng. 2020, 8, 286 11 of 18

J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 11 of 18 position between the pipeline and the tensioner, as the length of the pipeline increases, the difference betweenthe difference the maximum between and the minimum maximum axial and tension minimum gradually axial decreases tension gradually until the maximum, decreases minimum until the andmaximum, equivalent minimum values and coincide equivalent at the touchdownvalues coincide point. at the touchdown point. From FigureFigure8 8b,b, it it can can be be seen seen that that the the bending bending moment moment of of the the pipe, pipe, the the static static and and the the maximum maximum and minimumminimum bending bending moments moments of theof pipethe pipe show show a small a fluctuation, small fluctuation, which occurs which near occurs the separation near the pointseparation between point the between pipeline the and pipeline the tensioner. and the tensioner. After this, After it approaches this, it approaches zero and nozero obvious and no changesobvious arechanges observed are observed in the suspended in the suspended part. However, part. However, as the pipeline as the enterspipeline the enters sag bend the sag region, bend the region, bending the momentbending moment of pipe shows of pipe obvious shows obvious differences, differences, and reaches and reaches a maximum a maximum value ofvalue 314 of kN.m 314 kN.m near TDPnear (TouchTDP (Touch Down Down Point), Point), which which is 220% is higher220% higher than the than static the maximumstatic maximum bending bending moment moment of 93.41 of kN.m. 93.41 InkN.m. addition, In addition, it can be it observedcan be observed that there that are there obvious are obvious fluctuations fluctuations in the curve, in the which curve, indicate which indicate that the submarinethat the submarine pipeline pipeline will produce will produce a large disturbance a large disturbance during the during laying the process. laying process. ItIt can be seen from Figure8 8c,dc,d that that the the stress stress and and strain strain of of thethe pipelinepipeline havehave aa goodgood correlation.correlation. Similar to thethe bendingbending momentmoment ofof thethe pipeline,pipeline, thethe maximummaximum stress–strainstress–strain value of thethe pipelinepipeline appears near TDP. However,However, thethe didifferencefference isis thatthat thethe dynamicdynamic changechange ofof thethe stressstress andand strainstrain ofof thethe pipepipe has a a very very obvious obvious change change at at the the maximum maximum and and minimum minimum values values at the at point the point of separation of separation from fromthe tensioner, the tensioner, and then and gradually then gradually decreases decreases until untila significant a significant change change appeared appeared near nearthe point the point of TDP of TDPagain. again. The maximum The maximum strain strain value value is 2.354% is 2.354% and andthe maximum the maximum stress stress value value is 130.7 is 130.7 Mpa, Mpa, which which are are52% 52% and and 18.7% 18.7% larger larger than thanthe static the static value, value, respectively. respectively. In summary, In summary, the results the results show that show the that marine the marineenvironment environment and the and motion the motion of vessel of vesselhave a have significant a significant impact impact on the on dynamic the dynamic behavior behavior of the of thepipeline. pipeline.

(a) (b)

Figure 8. DynamicsDynamics behavior behavior of of the the pipeline: pipeline: (a) ( aAxial) Axial tension; tension; (b) ( bBending) Bending moment; moment; (c) Strain; (c) Strain; (d) (Stress.d) Stress.

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4.4. InﬂuencingInfluencing FactorsFactors ofof DynamicDynamic BehaviorBehavior

4.1.4.1. InfluenceInfluence of DiDifferentfferent FactorsFactors AccordingAccording toto thethe aboveabove results,results, itit cancan bebe deduceddeduced thatthat thethe dynamicdynamic behaviorbehavior ofof thethe pipelinepipeline willwill changechange duedue toto thethe eeffectsffects ofof marinemarine loadsloads andand vesselvessel motions.motions. InIn orderorder toto determinedetermine thethe influenceinfluence ofof marinemarine loadsloads and vesselvessel motion on the dynamicdynamic behavior of the pipeline during the Flex-lay,Flex‐lay, threethree casescases werewere studied:studied: wind load, current load and wavewave loadload actingacting independently;independently; wave loadload andand vesselvessel interactioninteraction andand allall factorsfactors actingacting together.together. TheThe valuevalue ofof thethe maximummaximum axialaxial tension,tension, bendingbending momentmoment and stress–strainstress–strain of thethe pipelinepipeline along thethe lengthlength isis shownshown inin FigureFigure9 9.. It It can can be be seen seen from from thethe figurefigure thatthat comparedcompared withwith thethe resultsresults ofof staticstatic analysisanalysis thatthat inin thethe absenceabsence of vessel interaction,interaction, thethe eeffectsffects ofof windwind loadload andand currentcurrent onon thethe pipelinepipeline areare notnot obvious,obvious, andand wavewave loadsloads havehave aa slightslight impactimpact onon the the dynamic dynamic behavior behavior of of the the pipeline. pipeline. When When the the vessel vessel interaction interaction is taken is taken into into account, account, the dynamicthe dynamic response response of the of pipeline the pipeline becomes becomes very obvious, very obvious, which shows which the shows importance the importance of the interaction of the betweeninteraction the between marine loads the marine and the loads vessel’s and motion the vessel’s on the dynamic motion behavioron the dynamic of the pipeline. behavior However, of the thepipeline. dynamic However, response the of dynamic the vessel response is fixed of when the thevessel laying is fixed vessel when is selected, the laying since vessel the influence is selected, of wavessince the on theinfluence dynamic of behaviorwaves on of the the dynamic flexible pipeline behavior during of the the flexible Flex-lay pipeline operation during is studied the Flex in‐ thelay followingoperation analysis.is studied in the following analysis.

(a) (b)

FigureFigure 9.9. EEffectffect of didifferentfferent factorsfactors onon pipelinepipeline dynamicdynamic responses:responses: ((a)) AxialAxial tension;tension; ((bb)) BendingBending moment;moment; ((cc)) Strain;Strain; ((dd)) Stress.Stress. 4.2. Influence of Wave Direction

In order to illustrate the impact of wave direction on the pipeline dynamic behavior during the Flex-lay operation, the wave state is specified with a significant wave height of 2.5 m and a peak period of eight seconds, and the wave direction is 0◦, 45◦, 90◦, 135◦ and 180◦, respectively. Under the above conditions, the dynamic behavior of the flexible pipeline was analyzed by using OrcaFlex software,

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4.2. Influence of Wave Direction In order to illustrate the impact of wave direction on the pipeline dynamic behavior during the Flex‐lay operation, the wave state is specified with a significant wave height of 2.5 m and a peak

J.period Mar. Sci. of Eng. eight2020 seconds,, 8, 286 and the wave direction is 0°, 45°, 90°, 135° and 180°, respectively. Under13 of the 18 above conditions, the dynamic behavior of the flexible pipeline was analyzed by using OrcaFlex software, and the axial tension, bending moment and stress and strain of the pipeline were obtained. andThe theresults axial are tension, shown bending in Figure moment 10, which and stress shows and that strain under of the different pipeline wave were obtained.directions, The there results are areobvious shown differences in Figure 10in, axial which tension, shows thatbending under moment different and wave stress–strain directions, of there the areflexible obvious pipeline. differences in axialFigure tension, 10a shows bending clearly moment that and the stress–strainaxial tension ofof thethe flexiblepipeline pipeline. dramatically varies with different waveFigure direction. 10a shows Under clearly 90° wave that conditions, the axial tension the maximum of the pipeline axial tension dramatically at the varies position with where different the wavepipe leaves direction. the tensioner Under 90◦ iswave 4826 conditions, kN, but the the maximum maximum axial axial tension tension at at the the same position position where is 3594 the pipe kN leavesunder 180° the tensioner wave conditions, is 4826 kN, and but the the difference maximum between axial tension the two at conditions the same positionis 34.3%. isSimilarly, 3594 kN Figure under 18010b◦ showswave conditions, the maximum and thebending difference moments between near the the two TDP conditions were 465.6 is 34.3%. kN.m Similarly, and 130.1 Figure kN.m, 10b showsrespectively, the maximum the difference bending reached moments 257%. near It thecan TDP be seen were from 465.6 the kN.m figure and that 130.1 the kN.m, response respectively, curve is thevery di smoothfference under reached the 257%. 180° Itwave can becondition, seen from but the the figure curve that will the fluctuate response under curve the is very other smooth wave underdirections, the 180 especially◦ wave condition, under the but 90° the wave curve direction. will fluctuate Figure under 10c,d theshow other that wave the maximum directions, von especially‐Mises understress theof pipelines 90◦ wave under direction. the 90° Figure wave 10c,d and show 180° that wave the is maximum 157 MPa von-Misesand 113 MPa, stress respectively, of pipelines with under a thedifference 90◦ wave of and38.9%, 180 and◦ wave the iscorresponding 157 MPa and maximum 113 MPa, respectively, strain is 3.05% with and a di 1.87%,fference respectively, of 38.9%, and with the a correspondingdifference of 63.1%. maximum In addition, strain is 3.05% it can and be 1.87%, seen from respectively, the Figure with 10b–d a difference that ofunder 63.1%. the In 90° addition, wave itconditions, can be seen the from maximum the Figure values 10b–d of the that bending under the moment, 90◦ wave stress, conditions, and strain the of maximum the pipeline values will of shift the bendingto the right, moment, and the stress, pipelines and strain of laid of part the will pipeline generate will a shift response. to the right,In summary, and the the pipelines simulation of laid results part willfully generate show that a response. the wave Indirection summary, has thea very simulation significant results effect fully on the show pipeline that the dynamic wave direction response, has of awhich very significantthe 90° wave eff directionect on the has pipeline the greatest dynamic impact response, on the of pipeline, which the and 90 the◦ wave 180° directionwave direction has the is greatestthe most impact favorable on thefor pipeline,pipeline laying. and the 180◦ wave direction is the most favorable for pipeline laying.

(a) (b)

Figure 10.10. EffectEﬀect of wavewave headingheading onon pipelinepipeline dynamicdynamic responses:responses: (a) Axial tension;tension; ((b)) BendingBending moment; ((cc)) Strain;Strain; ((dd)) Stress.Stress.

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4.3. Influence of Wave Height 4.3. Influence of Wave Height Wave height is considered to be another important factor in the dynamic behavior of the pipeline.Wave In height order is consideredto investigate to be the another effect important of wave factorheight in on the the dynamic pipeline behavior during of the pipeline.Flex‐lay Inoperation, order to investigatethe wave conditions the effect of with wave a heightwave direction on the pipeline of 0° duringand a peak the Flex-lay period operation,of eight seconds the wave is conditionsselected to withsimulate a wave the directiondynamic behavior of 0◦ and of a peakpipeline period under of eightdifferent seconds wave is heights selected of to 1.25 simulate m, 1.50 the m, dynamic1.75 m, 2.00 behavior m, 2.25 of m pipeline and 2.50 under m respectively. different wave Figure heights 11 shows of 1.25 the m, axial 1.50 tension, m, 1.75 bending m, 2.00 m, moment, 2.25 m andstress 2.50 and m strain respectively. of the pipeline Figure 11 under shows the the above axial conditions, tension, bending and the moment, results show stress that and the strain dynamic of the pipelineresponse under of the the pipeline above is conditions, significantly and different the results at showvaried that wave the heights. dynamic Figure response 11a,b of shows the pipeline that the is significantlymaximum axial diff erenttension at variedand bending wave heights. moment Figure of the 11 pipelinea,b shows are that4624 the kN maximum and 314.2 axial kN.m tension for Hs=2.5 and bendingm, and the moment maximum of the axial pipeline tension are and 4624 bending kN and 314.2moment kN.m of the for Hspipeline= 2.5 m,are and 3883 the kN maximum and 145 kN.m axial tensionfor Hs=1.25 and bendingm. The differences moment of under the pipeline the two are wave 3883 kNstates and are 145 19.1% kN.m and for Hs116.7%,= 1.25 respectively. m. The differences Figure under11c,d show the two the wave maximum states arestress 19.1% of the and pipeline 116.7%, under respectively. the 2.5 m Figure and 1.2511c,d m show waves the conditions maximum is stress 130.7 ofMPa the and pipeline 113.5 underMPa, respectively, the 2.5 m and with 1.25 a m difference waves conditions of 15.2%, isand 130.7 the MPa corresponding and 113.5 MPa, maximum respectively, strains withare 2.35% a diff erenceand 1.88%, of 15.2%, the difference and the corresponding is 25%. It can maximum be observed strains from are the 2.35% Figure and 11 1.88%, that the the response difference of isthe 25%. pipeline It can increases be observed as the from wave the height Figure increases, 11 that the and response the trend of of the the pipeline response increases curve of asthe the pipeline wave heightis almost increases, identical. and When the trendthe wave of the height response is less curve than of 2 m, the the pipeline dynamic is almost response identical. of pipeline When is thenot waveobvious. height However, is less thanwhen 2 m,the the wave dynamic height responseis more than of pipeline 2 m, the is notresponse obvious. of the However, pipeline when becomes the wavesignificant. height Therefore, is more than it 2should m, the be response avoided of during the pipeline the Flex becomes‐lay operation significant. when Therefore, the wave it should height be is avoidedhigher than during 2 m. the Flex-lay operation when the wave height is higher than 2 m.

(a) (b)

FigureFigure 11.11.E Effectﬀect of of wave wave height height on pipelineon pipeline dynamic dynamic responses: responses: (a) Axial (a) tension; Axial tension; (b) Bending (b) moment;Bending (moment;c) Strain; ( (cd)) Strain; Stress. (d) Stress.

4.4. Influence of Spectral Peak Period As a very important parameter of wave load, the spectral peak period has a significant impact on the dynamic response of the pipeline during the Flex‐lay operation. Under the sea conditions described above, six periods are selected in the range of 6 s to 16 s for analysis. The dynamic response

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4.4. Influence of Spectral Peak Period As a very important parameter of wave load, the spectral peak period has a significant impact onJ. Mar. the Sci. dynamic Eng. 2020, response 8, x FOR PEER of theREVIEW pipeline during the Flex-lay operation. Under the sea conditions15 of 18 described above, six periods are selected in the range of 6 s to 16 s for analysis. The dynamic response of the pipeline is obtained,obtained, shown in Figure 1212.. Figure 1212aa shows the maximum axial tension of the pipeline underunder di differentfferent spectral spectral peak peak periods. periods. At At the the disengagement disengagement position position of theof the pipeline pipeline from from the tensioner,the tensioner, the maximumthe maximum value value is 4627 is 4627 kN kN in the in the 8.0 8.0 s spectral s spectral peak peak period period and and the the minimum minimum value value is 3502is 3502 kN kN in in the the 14 14 s spectrals spectral peak peak period. period. The The di differencefference between between thethe twotwo wavewave conditions is 32.1%. Similarly, itit cancan bebe seen from Figure 1212b,b, under the two spectral peak periods, the maximum bending moments nearnear thethe bottomingbottoming point point were were 314.2 314.2 kN.m kN.m and and 114.7 114.7 kN.m, kN.m, respectively, respectively, with with a dia ffdifferenceerence of 173.9%.of 173.9%. Figure Figure 12 12c,dc,d reflects reflects the the maximum maximum stress stress and and strain strain values values of of the the pipeline pipeline underunder thethe above two wave conditions,conditions, respectively 130.7 MPa and 111.7 MPa, 2.35% and 1.85%,1.85%, thethe correspondingcorresponding didifferencesfferences are 17%17% andand 27%.27%. The simulation results show the impact of the wave spectrum peak period on the dynamic response of the pipeline, it has the greatest impact on the pipeline under the spectrum peakpeak periodperiod of of eight eight seconds. seconds. In In addition, addition, for for the the 10 10 second second and and 16 16 second second case, case, the the eff ecteffect of theof the waves waves of theof the spectral spectral peak peak period period on on the the dynamic dynamic response response of theof the pipeline pipeline is almost is almost the the same. same.

(a) (b)

Figure 12. EffectEﬀect of peak spectral period on pipeline dynamic responses: (a) Axial tension; (b) Bending moment; (c)) Strain; ((d)) Stress.

5. Conclusions In thisthis paper, aa dynamicdynamic couplingcoupling modelmodel forfor deepwaterdeepwater Flex-lay,Flex‐lay, consideringconsidering thethe layinglaying vesselvessel motion, marinemarine statestate and and pipeline pipeline dynamics dynamics model, model, was was established established to to study study the the dynamic dynamic behavior behavior of ﬂexibleof flexible pipelines pipelines during during the pipe the laying pipe process.laying process. Based on Based the above on model,the above the marinemodel, environment the marine ofenvironment the four-level of the sea four condition‐level sea was condition analyzed. was The analyzed. natural The catenary natural theory catenary and theory Morison’s and Morison’s equation equation were both used to determine the initial attitude of the flexible pipeline during the laying process. The hydrodynamic analysis of the pipelaying vessel HYSY201 was carried out by using the finite element software AQWA. The comprehensive finite element model of deepwater flex‐lay system was established by using OrcaFlex, and used to carry out an illustrative example analysis of a 10‐inch flexible pipeline being laid onto the seabed with a water depth of 3000 m. The flexible pipeline dynamic behavior including axial tension, bending moment and stress–strain in the laying

J. Mar. Sci. Eng. 2020, 8, 286 16 of 18 were both used to determine the initial attitude of the flexible pipeline during the laying process. The hydrodynamic analysis of the pipelaying vessel HYSY201 was carried out by using the finite element software AQWA. The comprehensive finite element model of deepwater flex-lay system was established by using OrcaFlex, and used to carry out an illustrative example analysis of a 10-inch flexible pipeline being laid onto the seabed with a water depth of 3000 m. The flexible pipeline dynamic behavior including axial tension, bending moment and stress–strain in the laying process were studied. The results show a significant correlation between the marine loads and the dynamic response of the pipeline. The following conclusions were obtained: (1) The dynamic response of the axial tension is the largest at the position where the pipeline is released from the tensioner and gradually decreases with the increase of the water depth, the maximum tension of the pipeline increases by 42.7% compared with the static tension. The bending moment of the pipeline is almost zero at suspended part and changes drastically enters the sag bend region. The maximum bending moment of the pipeline is increased by 220% compared with the static bending moment. There is a good correlation between the stress and strain of the pipeline. The maximum stress and strain values of the pipeline appear near TDP. The maximum value of the strain and the maximum stress value are 52% and 18.7% larger than the static values, respectively. It is proven that the marine loads and vessel motion have a significant effect on the dynamic response of the pipeline. (2) In the absence of vessel interaction, the effect of the wind and the current on the dynamic behavior of the pipeline is not obvious, and the wave load has a slight impact on the dynamic behavior of the pipeline. However, adding to the interaction of the vessel, the dynamic behavior of the pipeline becomes very obvious, which indicates that the interaction between the marine loads and the vessel motion has the most significant effect on the dynamic behavior of the pipeline. (3) The wave direction has a great influence on the dynamic response of the pipeline. The most adverse wave direction appears at 90◦, which has the greatest impact on the pipeline response. The most favorable wave direction is 180◦, which has the least impact on the pipeline. The differences in axial tension, bending moment and stress–strain under the two conditions are 34.3%, 257%, 38.9%, and 63.1%, respectively. Therefore, reasonable selection of the vessel’s forward direction during the Flex-lay can effectively reduce the pipeline’s dynamic response. (4) Wave height and spectral peak period are also important factors affecting the dynamic response of the pipeline. The dynamic response of the pipeline is positively related to the wave height. When the wave height is less than 2 m, the influence of the sense wave height on the dynamic response of the pipeline is small, but the influence becomes more obvious when the wave height exceeds 2 m. When the peak period of the spectrum is eight seconds, it has the greatest impact on the dynamic response of the pipeline. Therefore, the operation of the Flex-lay should be performed under the height of less than 2 m and avoid operating under the eight-second peak wave period.

Author Contributions: Conceptualization, L.W. and M.J.; Data curation, M.J. and X.X.; Formal analysis, M.J.; Methodology, M.J.; Project administration, L.W.; Supervision, L.W. and X.X.; Validation, M.J. and X.X.; Visualization, X.X.; Writing—original draft, M.J.; Writing—review & editing, M.J., X.X., X.W. and F.Y. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by National Science and Technology Major Project of China (Grant No. 2016ZX05057003), Heilongjiang Provincial Funding of National Science and Technology Major Project of China (Grant No. GX18A004), The School Land Integration Development Project of Yantai-development and test platform of subsea production system (Grant No. 2019XDRHXMPT29), Sealing Performance and Multi-Objective Structural Optimization of Deep-Sea Connector under High Gradient Temperature Fluctuation (Grant No. 51779064). Acknowledgments: The authors gratefully acknowledge the financial support from National Science and Technology Major Project of China (Grant No. 2016ZX05057003), Heilongjiang Provincial Funding of National Science and Technology Major Project of China (Grant No. GX18A004), The School Land Integration Development Project of Yantai-development and test platform of subsea production system(Grant No. 2019XDRHXMPT29) Sealing Performance and Multi-Objective Structural Optimization of Deep-Sea Connector Under High Gradient Temperature Fluctuation (Grant No. 51779064). Conflicts of Interest: The authors declare no conflict of interest. J. Mar. Sci. Eng. 2020, 8, 286 17 of 18

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