Numerical Simulations and Experimental Study on the Reeling Process of Submarine Pipeline by R-Lay Method

Abstract

During the reeling process of the reel-lay method, the pipe will be subjected to combined loading of tension and bending. Excessive ovalization of the pipe will affect the structural performance and even lead to structural instability of the pipe. In this paper, a numerical simulation model of the pipe-reeling process is established by finite element tools. The Ramberg–Osgood material model is used to study the ovalization and bending moment of the pipe cross-section during the pipe-reeling process based on the Von Mises plasticity and nonlinear kinematic hardening rules. The results show that the ovalization and bending moment of the pipe section will change significantly during the pipe-reeling process. Subsequently, one set of 6-inch pipe-reeling experimental setups was designed to conduct a full-scale experiment. Compared with the experimental results, the feasibility of the finite element model is verified. Finally, the effects of diameter-to-thickness ratio, the material parameters of the pipe, and the pipe axial tension on the ovalization and bending moment changes are studied. Research shows that each parameter has a certain influence on the pipe of the reeling process, and the diameter-to-thickness ratio of the pipe has the most obvious effect. When the diameter-to-thickness ratio decreases, the bearing capacity for bending moments and the ability to resist ovalization of pipe are enhanced. At the same time, each parameter has a significant impact on the reeling process of the pipeline.

1. Introduction

As a new submarine pipeline-laying method, the reel-lay method is increasingly used in offshore oil and gas development projects. At the onshore base, a series of short pipes are welded into one pipeline through the welding station, and reeled onto the reel by the shipboard equipment. Then, the pipe-laying vessel sails to the target sea area, and the pipeline is laid into the water through the cooperation of straighteners and tensioners in the pipeline-laying system [1,2,3]. Compared with the traditional S-lay and J-lay, the reel-lay method is faster, safer, and more efficient. When the pipeline is reeled onto the reel, the degree of bending of the pipeline almost reaches the limit, and the cross-section of the pipe will be obviously ovalized [4]. This will affect the structural performance of the pipeline, and structural instability may even occur in severe cases [5]. Generally speaking, increasing the radius of the reel can effectively reduce the ovalization of the pipe, but the increase in the size of the reel will pose new challenges to the design of the ship. Therefore, it is necessary to analyze the behavior of the pipe during the reeling process to ensure the safety of the pipe while taking into account the design size of the reel.

After a welding inspection at the onshore base, the pipeline is reeled to the reel with the cooperation of the reel and the tensioner. As shown in Figure 1, the pipe is being reeled along the plane of the inner diameter of the reel. In this process, the pipe deformation will ngradually change from an elastic to elastic-plastic state. The pipe section will gradually deform due to being subjected to the bending moment of the reel and the tension of the tensioner.

As the deformation of the pipeline gradually changes from an elastic to plastic state, permanent deformation of the pipeline will cause the cross-section shape of the pipeline to gradually change from round to ellipse; this phenomenon is called ovalization [6]. For pipes used in the reel-lay method, at the 6 o’clock and 12 o’clock positions of the neutral axis, the deformation of the pipe cross-section in the circumferential direction will cause circumferential compression and stretching. The nonuniform strain distribution of the pipe section in the circumferential direction leads to the occurrence of ovalization. Although some extent of recovery occurs when the pipe is released from the bending, there is still some ovalization that is permanent, so it has a very important impact on the performance of the pipe. Det Norske Veritas standard DNV-OS-F101 stipulates the allowable range of ovalization of a pipeline:

$$\frac{\Delta D}{D}=\frac{D_{\max }-D_{\min }}{D}<3\%,$$

(1)

where D_max and D_min represent the maximum and minimum outer diameter of the pipe after deformation, respectively, and D represents the outer diameter of the pipe without deformation. The maximum and minimum pipe diameters are shown in Figure 2.

As an important feature of pipe-bending response, ovalization has been taken as a research object by many scholars. Braize [7] studied the relationship between ovalization and the bending moment of the pipe during the bending process, and named the phenomenon that occurs during the pipe-bending process “the Braizer effect”. Ovalization reduces the bending stiffness of the pipe and causes the ultimate load to be unstable. Reissner et al. [8] considered two independent variables, the rotation of the cross-section reference line and the stress function, and studied the ovalization instability of the initial straight pipe. The integral formula and iterative numerical solution method for the ovalization instability of the circular initial straight pipe were proposed. After the 1980s, more and more scholars have launched research on this issue. Bathe and Almeida [9] proposed a simple and effective hypothesis for linear analysis of curved pipeline components, assuming that the displacement, rotation, and ovalization parameters are cubic interpolation along the pipeline. Kyriakides [10,11,12,13], based on the second invariant plastic flow isotropic strengthening theory and virtual work principle, established a set of equations to solve the pipeline deformation. Pan and Lee [14,15,16,17,18] also established a set of mathematical methods to solve the deformation and buckling of the pipe section based on nonlinear loop theory and the intrinsic time function. However, due to the limitations of the intrinsic time function itself, this method is less widely used than the method proposed by Kyriakides. Kuznetsov and Levyakov [19] took into account the geometric nonlinear problem of pure bending annular shells with arbitrary cross-sections, and proposed a new element algorithm to solve this problem. Taking the open-section profile as the object, a method for solving the pure bending problem of thin plates is given by using the new algorithm, and the correctness of the method is verified by comparison with the results of other authors. Corona [20,21] conducted a new set of bending tests on aluminum alloy pipes to re-discuss the problem that the wrinkle wavelength is larger than the measured value when the pipe curvature is accurately predicted when the pipe is buckled. In order to solve this problem, taking the anisotropy into consideration, it was tested and characterized by Hill’s quadratic anisotropic yield function, and the calculated tube response agreed with the measured results.

The finite element method is applied to the study of pipe-bending problems by most researchers. Based on elastoplastic finite element analysis, Yoo et al. [22] studied the collapse pressure of a medium-thickness cylinder under external pressure, and proposed an analytical yield trajectory considering the interaction between local instability and plastic failure caused by initial ovalization. The results agree with the finite element calculation results. Shun feng Gong et al. [23] developed a two-dimensional theoretical model based on the model proposed by Kyriakides and his colleagues. The model could successfully explain the buckling behavior of the pipeline under the combined tension, bending, and external pressure, and was verified by the finite element model. Giannoula [24] used a two-dimensional axisymmetric model to study the influence of cyclic load on the mechanical properties of thick-walled seamless steel pipes, and he found that obvious anisotropy and ovalization of the pipe appear under the action of cyclic load. Yafei Liu [25] et al. used two models to establish a finite element model of pipe reeling and unreeling on a rigid reel, and studied the process of reeling and unreeling of steel pipes under external pressure. The measurement results of the tension and the collapse pressure were accurately reproduced. Jong Rae Cho et al. [26] used the finite element method to discuss different cyclic bend processes using the relationship of hysteretic loop deformation compatibility. However, most of their research focuses on the free bending of the pipe, while few studies consider the change of bending moment and ovalization of the pipe under the condition that the pipe is in contact with the rigid surface during bending.

The reeling process of the reel-lay method is investigated with finite elements and an experimental method in this paper, which establishes a finite element model of the 6-inch pipe-reeling process. The Ramberg–Osgood material model is used in the finite element model, and the Von Mises plasticity and nonlinear kinematic hardening rules are used to study the changes in the ovalization and bending moment of the pipe cross-section during the reeling process. Subsequently, the feasibility of the finite element model was verified by the designed full-scale reeled pipe experiment. Finally, the influence of the pipe diameter-to-thickness ratio D/t, yield stress, and hardening index on the change of ovalization and bending moment in the process of pipe reeling is studied.

2. Experiments

2.1. Experimental Equipment

For the pipe-reeling test, an experimental system as shown in Figure 3 was designed, which mainly included: gear wheel, pins, reel, hydraulic motor, experiment frames, and test pipe. Compared with the experiments of other scholars [27,28], the setup of the test system was closer to the real working conditions. The reel was placed horizontally on the experiment frame, and four hydraulic motors were arranged around the frame as the driving device of the reel. Pins were evenly distributed on the reel and mesh, with the gear wheels on the hydraulic motor. A reel with a diameter of 8 m was selected for the experiments.

A thin-walled steel pipe made of X65 was used in this test. The material of the pipeline was X65 steel, which is commonly used in marine engineering. The outer diameter of the pipe was 0.168 m, and the D/t value was 10. The material properties and geometric parameters of the pipeline are shown in

Table 1. Material properties and geometric parameters of pipeline.

Parameter	Value	Parameter	Value
Outside diameter	0.16 8m	Inner diameter	0.1344 m
Thickness	0.0168 m	Length (single)	12.0 m
Yield stress	448 MPa	Young modulus	207 GPa
Poisson’s ratio	0.3	Hardening index	10.3
Tensile strength	531 MPa	Density	7800 kg/m3

. The length of single pipe used in the test was 12 m, and several sections of pipe were welded into a longer pipe. After welding, both ends of the whole pipe were welded with connecting devices.

2.2. Experimental Procedure

During the experiment, one end of the pipeline is connected to the reel through the end socket, and the other end is drawn by a winch to provide continuous tension of 100 kN. The reel is driven by the hydraulic motors, and the pipe is reeled on the reel under the cooperation of the hydraulic motors and the winch. When a part of the pipe is reeled up, the pipe-reeling operation is stopped. The pipe cross-section where the pipe and the reel fit together and the position 2 m away from this section are recorded.

In order to correspond to the simulation case, the end displacement of the pipe in the simulation is converted into the reeling distance of the pipe, and different pipe-reeling lengths are selected, respectively. As shown in Figure 4, the deformation of the outer cross-section of the pipe is measured by vernier caliper, and the corresponding ovalization change is calculated. The overflow valve controls the working pressure of the hydraulic motor of the experimental device. Through the speed-regulating valve, the speed of the reel can be adjusted to control the reeling speed of the pipe. The pressure gauge can read the working pressure of the motor, and the output torque of the motor can be calculated through the working pressure and displacement of the motor. In order to ensure the accuracy of the results, the experiment was repeated three times with three different pipes of the same length.

3. Pipeline-Reeling Process Analysis

During the reeling process, the pipe will contact and bend along the rigid surface of the reel under the combined action of bending moment and tension, so the above model can be simplified as shown in Figure 5a. In the analysis and simulation, it is assumed that the length of the pipe is infinite and that the selected section of pipe is a standard circular shape. At the same time, the initial defects of the pipe are ignored, and taking the cross-section on the pipeline, a polar coordinate system with the origin at the center of the pipeline is established, as shown in Figure 5b. The average radius of the pipe is R and the thickness is t. W and V are the radial and circumferential directions at any point in the cross-section, respectively, and r represents the radius at any point in the section. When the pipe reels up, the pipe will deform as shown in Figure 5c. The dotted line and the solid line in Figure 5c indicate the undeformed and deformed pipe section, respectively; w and v are the deformation amount in the radial and the circumferential direction at any point in the cross-section.

3.1. Pipeline Stress Analysis

During the reeling process, it is assumed that the plane section is perpendicular to the middle surface of the tube section, as shown in Figure 5a,b. In addition, a small strain and limited rotation of the pipe section axes are assumed [29]. The strain of the pipe in the axial direction can be expressed as:

$${\epsilon }_x={\epsilon }_x^0+\zeta \kappa ,$$

(2)

where ${\epsilon }_x^0$ represents the strain of the pipe’s neutral axis in the x direction, κ represents the curvature of the pipe, and ζ is the distance from any point of the cross-section to the central axis. ζ is derived from the geometric relationship in Figure 5c.

$$\zeta =\left(\mathrm{r}+w\right)\cos \theta -v\sin \theta ,$$

(3)

Meanwhile, the strain of the pipe in the circumferential direction can be expressed as

$${\epsilon }_{\theta }={\epsilon }_{\theta }^0+\zeta {\kappa }_{\theta },$$

(4)

where,

$${\epsilon }_{\theta }^0=\left(\frac{v^{\prime }+w}{R}\right)+\frac{1}{2}{\left(\frac{v^{\prime }+w}{R}\right)}^2+\frac{1}{2}{\left(\frac{v-w^{\prime }}{R}\right)}^2,$$

(5)

$${\kappa }_{\theta }=\left(\frac{v^{\prime }-w^{″}}{R^2}\right)/\sqrt{1-{\left(\frac{v-w^{\prime }}{R}\right)}^2},$$

(6)

where κ is the bending curvature of the pipe, $v^{\prime }$ and $w^{\prime }$ represent the first derivatives of v and w with respect to θ, and $w^{″}$ represents the second derivative of w to θ.

Due to the large deformation of the pipe during the reeling process, the Bauschinger effect needs to be considered when analyzing the stress and strain response of marine engineering pipeline materials [30]. In order to accurately describe the mechanical properties of materials, many scholars mainly use the Ramberg–Osgood model [31,32,33], which is simple in form and can better describe the plastic deformation behavior of materials. The stress-strain curve equation is as follows:

$$\mathit{\epsilon }=\frac{\mathit{\sigma }}{E}\left(1+\frac{3}{7}{\left|\frac{\mathit{\sigma }}{{\sigma }_y}\right|}^{n-1}\right),$$

(7)

where σ is the stress tensor; E is the elastic modulus; σ_y is the yield stress; and n is the material’s hardening index.

Generally speaking, for the elastoplastic steel pipe material, the Von Mises model is used to describe the nonlinear hardening behavior of the material, and the model is simplified using the J₂ plasticity assumption. The plane stress of the above formula can be simplified as:

$$\frac{1}{E_s}=\frac{1}{E}\left[1+\frac{3}{7}{\left(\frac{{\sigma }_e}{{\sigma }_y}\right)}^{n-1}\right],$$

(8)

where E_s is the secant modulus of elasticity, and σ_e is the equivalent stress. It can be defined by

$${\sigma }_e^2=\left[{\sigma }_x^2-{\sigma }_x{\sigma }_{\theta }+{\sigma }_{\theta }^2\right],$$

(9)

The model is completed by combining the nonlinear kinematic hardening rule with the flow rule. The flow rule specifies the translation of the yield surface in the stress space during the process of loading. Therefore, the corresponding stress in the axial direction and the circumferential direction at any point in the cross-section can be obtained through the constitutive model. The equation is as follows:

$${\sigma }_x=\frac{E_s}{1-v^2}\left[{\epsilon }_x+v{\epsilon }_{\theta }\right],$$

(10)

$${\sigma }_{\theta }=\frac{E_s}{1-v^2}\left[{\epsilon }_{\theta }+v{\epsilon }_x\right],$$

(11)

According to the knowledge of material mechanics, the stress at any position of the cross section can be obtained approximately while ignoring the radial stress.

3.2. Pipeline Bending Moment Analysis

In the case of ignoring the geometric defects and residual stress of the pipeline, through the above calculation, the force of the pipeline section can be divided into the tensile stress and the compressive stress, as shown in Figure 6. The upper part of the pipe section is the tensile stress zone, and the lower part is the compressive stress zone. The corresponding stresses are σ_tens and σ_comp, respectively.

Figure 6 shows that the bending moment and tension on the cross-section of the pipeline can be calculated by the following Equations (12) and (13):

$$M=-{\mathrm{A}}_{\mathrm{comp}}{\overline{y}}_{\mathrm{comp}}{\sigma }_{\mathrm{comp}}+{\mathrm{A}}_{\mathrm{tens}}{\overline{y}}_{\mathrm{tens}}{\sigma }_{\mathrm{tens}},$$

(12)

$$T=2Rt\left[\psi {\sigma }_{\mathrm{comp}}+\left(\pi -\psi \right){\sigma }_{\mathrm{tens}}\right],$$

(13)

where A_comp and A_tens are the area of the tension zone and the compression zone of the cross-section, respectively; ${\overline{y}}_{\mathrm{comp}}$ and ${\overline{y}}_{\mathrm{tens}}$ are the distance from the center of the compression and tension area to the center of the cross-section, respectively; and ψ is the half of the angle between the two neutral plastic axes. From the geometric relationship in Figure 6, we can get

$${\mathrm{A}}_{\mathrm{tens}}=2\left(\pi -\psi \right)Rt,$$

(14)

$${\mathrm{A}}_{\mathrm{comp}}=2\psi Rt,$$

(15)

$${\overline{y}}_{\mathrm{tens}}=R\frac{\sin \psi }{\pi -\psi },$$

(16)

$${\overline{y}}_{\mathrm{comp}}=R\frac{\sin \psi }{\psi },$$

(17)

The mathematical relationship between angle ψ and R can be obtained by transforming the above formula into Equation (13):

$$\psi =\frac{T-2\pi Rt{\sigma }_{\mathrm{tens}}}{2Rt({\sigma }_{\mathrm{comp}}-{\sigma }_{\mathrm{tens}})},$$

(18)

After the mathematical transformation calculation, the expression of the bending moment of the pipe can be obtained as follows:

$$M=-2t{R}^2\sin \left[\frac{\pi \left({\sigma }_1-{\sigma }_{\mathrm{tens}}\right)}{{\sigma }_{\mathrm{comp}}-{\sigma }_{\mathrm{tens}}}\right]{\sigma }_{\mathrm{comp}}+2t{R}^2\sin \left[\frac{\pi \left({\sigma }_1-{\sigma }_{\mathrm{tens}}\right)}{{\sigma }_{\mathrm{comp}}-{\sigma }_{\mathrm{tens}}}\right]{\sigma }_{\mathrm{tens}},$$

(19)

where σ₁ represents the stress caused by the pipe tension.

4. FEM Simulation

4.1. FEM Model

A three-dimensional model as shown in Figure 7 was established in ABAQUS software to simulate the reeling operation of the pipeline under constant tension. A 6-inch pipeline with a D/t = 10 was selected, and the material properties and geometric parameters of the pipeline were set to the same parameters as the experiment. The three-dimensional node-incompatible solid element C3D8I was selected to mesh the pipeline, and the number of elements in the model was 144,000. This type of element enhances the bending behavior of the model through compatible modes, which is very suitable for large deformation nonlinear problems [34]. Meanwhile, a rigid analytical plane with a radius of 4 m was established to simulate the inner surface of the reel. The pipe and the rigid plane adopt frictionless constraints [25], and the constraint between the pipe and the reel is defined by the contact with limited slippage. The contact relationship adopts an exponential softening contact pressure relationship, where the pressure and contact gap are set to 3.4 MPa and 0.00254 mm, respectively.

4.2. Material Model

The pipe material models of the simulation are completely consistent with the experimental pipeline. The yield strength of the material is 448 MPa, the Young’s modulus is 207 GPa, and the hardening index is 10.3. Using the Ramberg–Osgood constitutive model to describe the material of the pipe, the stress-strain relationship shown in Figure 8 can be obtained. The Von Mises yield criterion is adopted, and the material is assumed to be isotropic and linearized in the finite element software.

4.3. Boundary Conditions

The full-pipe model was selected, and the symmetry of the y-z plane was considered. Symmetrical boundary conditions were applied on the X = 0 plane to avoid stress concentration by means of elastic constraints. The right end of the pipeline couples the end face of the pipe with the reference point through the kinematic coupling relationship, by coupling the displacement in the z-direction and the rotation around the x-axis and y-axis to ensure that the plane remains flat during the loading process and the cross-section can be freely deformed. Considering that the actual process of pipe reeling is completed by the reel and the tensioner together, the bending moment of the pipe is not directly applied to the pipe. Therefore, a y-direction displacement is applied to the reference point and the displacement in the z-direction of the reference point is restricted while maintaining the degrees of freedom in other directions. Meanwhile, a constant tension load of 10 kN is applied to the right end surface to simulate the pipe bending along a rigid curved surface. Fixed constraints are applied to the rigid analytical surface of the reel.

4.4. FEM Simulation

An FEM simulation of the reeling process of the pipeline was performed based on the above FEM model. Figure 9 and Figure 10 reflect the stress and strain nephogram when the pipe is bent along the reel. It can be seen from Figure 9 that the stress of the pipe almost reached the limit of material performance as the pipe was reeled up. However, Figure 10 shows that the obvious strain of the pipe is concentrated near or close to the rigid section, and the strain changes at other locations are relatively small.

The ovalization and bending moment change curves of the pipe cross-section during the pipe-reeling process are shown in Figure 11 and Figure 12. With the increase of the applied displacement, the ovalization of the pipeline gradually increases to a peak value of about 1.3%, then a slight decrease occurs, and it finally reaches a stationary value at 1.24%. Similar to the change in ovalization, the bending moment experienced by the pipeline exhibits an approximately linear increase in the early stage, and then gradually reaches a stable value of about 218 kN·m.

Due to the action of the bending moment and tension during the beginning of pipe reeling, the pipe cross-section will undergo short-term elastic deformation and then enter plastic deformation. The ovalization at this stage increases approximately linearly. Subsequently, the slope of the curve gradually decreases, and the curve finally reaches the peak, indicating that the pipeline has reached the limit of curvature. When the pipe continues to reel up, the tension on the pipe cross-section is gradually reduced, so the ovalization decreases until it reaches a plateau. The same explanation can also be applied to the bending moment change of the pipe cross-section. After reaching the plateau value, all the energy of the pipe reeling is converted into the bending moment of the pipe.

In summary, an obvious ovalization phenomenon occurs in the process of pipe reeling. Therefore, it is necessary to take into account the occurrence of pipeline ovalization when designing pipe-laying equipment and pipelines. The bending moment change of the pipeline will also have a very important reference value for the driving force design of the pipeline-coiling process.

At the same time, taking the touch point between the pipe and the rigid plane as the origin, as shown in Figure 5a, the stress distribution in different directions around the touch point between the pipe section and the rigid plane is obtained. Figure 13 and Figure 14, respectively, show the stress distribution of the outer surface and inner surface of the pipe at the specified cross-section, where S11, S22, and S33 represent the three directions of x, y, and z, respectively.

The maximum axial stress component of the pipeline shown in Figure 13 is 620 MPa, the stress component values of the stress tensor in the y and z directions are significantly lower than in the axial direction, and its absolute value is lower than 200 MPa. It means that the axial stress component of the pipe represents the main stress of the pipe bending along the reel, and the stress in the other two directions accounts for the ovalization of the pipe cross-section. Meanwhile, it can be seen from the figure that the axial stress component is tensile stress at the top of the pipe and compressive stress at the bottom of the pipe, which is consistent with the previous analysis. The axial stress distribution is a typical bending stress distribution, and there are extreme values around −90°, 0°, 90°, and 180°. These points are located at the places where the pipe maximum deformation occurs.

Figure 14 shows the stress component distribution at the same position on the inner surface. The axial stress distribution is generally similar to the outer surface, but the stress values in the other two directions are opposite. However, it can be seen from the distribution of the axial stress component of the inner surface of the pipe that there is a decrease of stress at the center position. The reason for this phenomenon is the extrusion of the pipe by the rigid section.

By comparing the simulation results with the experiment results as shown in

Table 2. Comparison of results.

	Reeling Distance (mm)	Simulation Value	Experiment 1	Experiment 2	Experiment 3	Average Relative Error
Ovalization	125	0.591%	0.553%	0.556%	0.562%	5.75%
	250	1.193%	1.125%	1.128%	1.134%	5.36%
	390	1.275%	1.197%	1.202%	1.207%	5.73%
	540	1.238%	1.166%	1.167%	1.174%	5.57%
	700	1.245%	1.166%	1.167%	1.171%	6.18%
Bending moment (kN·m)		218	243	225	221	5.35%

. It can be seen that the error between the experiment results and the simulation results is within the allowable range. The ovalization change of the pipeline measured in the experiment is smaller than the simulated value, but the bending moment value measured in the experiment is larger than the simulated value. There are two main reasons for this situation. On the one hand, the material mechanics model used in the simulation is different from the actual situation. The values of mechanical property parameters of the practical submarine pipelines, especially the yield strength and ultimate strength, are obviously greater than those specified by the API. On the other hand, the working conditions in the simulation are different from those in the actual situation. In the experiment, the value of the torque during the reeling process is calculated from the working pressure and delivery capacity of the hydraulic motor, and the experiment results will be larger due to efficiency and leakage. In summary, the simulation method in this paper can realize the prediction of the ovalization and the bending moment of the pipe cross-section during the pipe-reeling process.

5. Influencing Factors of the Reeling Process

From the above discussion, it can be seen that during the reeling process of the pipe, the ovalization and bending moment of the pipe will have corresponding effects due to different factors [35]. In order to determine the influence of different factors on the ovalization and bending moment of the pipeline, several important factors including D/t, yield strength, and hardening index were studied. Curvature can intuitively indicate the changes in pipeline ovalization and bending moment. In previous studies, the rotation angle φ of the reference point has usually been used to define the pipeline curvature. Generally, a position with a certain length of the section position can be used as a reference point, so L = 3D is considered to be suitable [36]. The average curvature of the section at this time can be given by

$$\kappa =\phi /L,$$

(20)

5.1. Effect of Diameter-to-Thickness Ratio

According to the requirements of marine engineering and related pipeline standards, pipelines with D/t values will be selected according to the actual situation in actual engineering applications. In order to study the influence of different D/t values on the ovalization and bending moment changes of the pipe cross-section, the D/t values 10, 15, and 20 were adopted. The change of the ovalization and the bending moment of the pipe cross-section with curvature are shown in Figure 15a,b.

Figure 15a shows the ovalization of the pipe section with a D/t value of 10 has the smallest change with curvature, while the pipe with a D/t of 20 has the largest change, and the corresponding maximum values are 1.27% and 4.47%, respectively. It shows that the change of pipe ovalization increases with the increase of D/t. When the D/t value of the pipeline reaches 20, the extent of ovalization of the pipe has exceeded that defined by DNV, indicating that the pipeline at this time is no longer suitable for pipe-laying operations. On the contrary, as shown in Figure 15b, the maximum value of the bending moment experienced by the pipe decreases with the increase of the D/t value. When curvature of pipe reaches 0.16 m⁻¹, the bending moments of the pipe with D/t values of 10 and 20 are 156 kN·m and 115 kN·m, respectively, indicating that the larger the D/t value of the pipe, the smaller the bending moment on the pipe section under the same curvature. The reason is that when the outer diameter of the pipeline is constant, and when the D/t value of the pipeline is increasing gradually, the section moment of inertia of the pipe will inevitably decrease, resulting in the bending stiffness of the pipe being reduced and the ovalization being significantly increased.

5.2. Effect of Yield Strength

As an important indicator of pipeline performance, the yield strength has a very important impact on the pipeline. Therefore, under the condition that the geometrical parameters and other material parameters of pipe remain unchanged, three common marine engineering steels, X60, X65, and X70, with yield strengths 414 MPa, 448 MPa, and 482 MPa, respectively, were selected for analysis. The ovalization and bending moment change with the curvature of the pipes with different yield strengths are shown in Figure 16a,b.

Figure 16a shows that the difference in yield strength has a certain impact on the ovalization of the pipeline. Under the same curvature, the ovalization of the pipeline becomes more obvious with the increase of the yield strength. When the pipe curvature reaches 0.16 m⁻¹, the ovalization change of the X70 pipe section is 1.32%, and the ovalization changes of the X65 and X60 pipes are 1.29% and 1.27%, respectively. Similar to the change of ovalization, it can be seen from Figure 16b that the change of yield strength has the same effect on the bending moment bearing capacity, but it is more obvious. When the curvature of the pipes reaches 0.16 m⁻¹, the bending moments are 200 kN·m, 214 kN·m, and 230 kN·m, respectively, indicating that the higher the material yield strength of the pipe, the more torque is required to drive the reel. The reason is that the increase in yield strength increases the pipe stress under the same bending curvature increment, which leads to the increase of ovalization and bending moment.

5.3. Effect of Hardening Index

In the Ramberg–Osgood constitutive model, the hardening index determines the plastic properties of the material, and has a very important influence on the pipe during the reeling process. A 6-inch pipe with a D/t value of 10 and a yield strength of 448 MPa was selected, and the hardening indexes of different pipes were set to 10.3, 15, and 20. The finite element simulation analysis was performed, and the results are shown in Figure 17a,b.

Similar to the yield strength, Figure 17a shows that when the hardening indexes are 10.3, 15, and 20, the maximum value of the calculation results of the ovalization changes are 1.27%, 1.29%, and 1.31%, respectively, indicating that the change of ovalization increases with the increase of the hardening index. On the contrary, it can be seen from Figure 17b that the maximum bending moment of the pipe decreases with the increase of the hardening index. The maximum values of the bending moment are, respectively, 214 kN·m, 200 kN·m, and 193 kN·m, and the pipeline will reach the limit state earlier because of the increase of the hardening index. The reason for the above phenomenon is that the enhancement of the hardening index makes the strain-hardening effect of the material increase, which leads to the strain of the pipe section being greater under the same curvature increment condition. Therefore, the pipe with a large hardening index will reach the limit of ovalization first, and the bending moment of the pipe will be reduced due to the increase of deformation.

5.4. Effect of Axial Tension

In most of reeling operations, the cooperation of the tensioner is required. Under the joint action of the reel and the tensioner, the reeled pipe will be subjected to the bending moment generated by the reel and the tension provided by the tensioner. Therefore, the axial tension provided by the tensioner will also have a very important effect on the ovalization and bending moment of the pipeline. In the finite element model, a 6-inch pipe with the same D/t value and material properties was selected as in the previous sections, and the tension on the right end of the pipe was set to 100 kN, 1000 kN, and 3000 kN, respectively. For the pipes subjected to different axial tensions, the variations of ovalization and the bending moment of the pipe cross-section with the curvature are shown in Figure 18a,b.

It can be seen from Figure 18a that as the axial tension increases, the ovalization of the pipeline gradually increases with the curvature. When the axial tension is 100 kN, 1000 kN, and 3000 kN, the maximum values of the calculated ovalization changes are 1.27%, 1.40%, and 1.66%, respectively. However, there are obvious differences with the above three factors. When the D/t value or the material parameters of the pipe are different, the influence of different parameters on the ovalization can maintain the same curve trend of each factor. Nevertheless, the influence of different tensions on the pipeline is almost the same at the front of the curve and begins to differ when the curvature reaches 0.05, then the difference among different tensions becomes larger with the curvature increases. Figure 18b shows that the bending moment decreases with the increase of the axial tension. The maximum bending moments corresponding to the three different tensions are 214 kN·m, 211 kN·m, and 195 kN·m, respectively. From the curve of T = 3000 kN in the figure, it can be clearly seen that after the bending moment of the pipeline reaches the maximum value, there is a significant decrease. There are two reasons for this phenomenon. On the one hand, due to the effect of the axial tension, the reduction of the pipe cross-section accelerates the process of pipe ovalization. On the other hand, the tension is always perpendicular to the cross-section of the pipeline, but the effect of the tension on the reeling of the pipeline is reduced, resulting in the above-mentioned difference. In summary, selecting an appropriate axial tension during the pipe-reeling process can effectively reduce the torque required, and control the ovalization of the pipe within a reasonable range at the same time.

6. Conclusions

In this paper, a numerical simulation model of the pipe-reeling process is established by the finite element method. Subsequently, a set of 6-inch pipe-reeling experimental set-ups was designed, and a full-scale coiling experiment was carried out. The accuracy of the finite element model was verified by comparing the finite element results with the experiment results. Finally, the established finite element model was used to study the influence of pipe diameter/thickness ratio, material parameters, and axial tension on the change of pipe cross-section ovalization and bending moment during pipe reeling. The results show that during the reeling process of the pipe, the ovalization and bending moment of the pipe cross-section will change significantly. In addition, the following conclusions are obtained:

(1) Obvious ovalization occurs in the pipe cross-section during the reeling of the pipe. The ovalization of the pipe cross-section increases approximately linearly in the early stage, and gradually increases to a peak. Then, it decreases slightly and finally reaches equilibrium. Similar to the change of the ovalization, the bending moment increases approximately linearly in the early stage, then gradually reaches a stable value. The stress component in the axial direction of the pipe is the main stress of the bending along the reel. The stress in the other two directions accounts mainly for the ovalization deformation of the pipe cross-section. The values are significantly lower than the axial stress component. It is proven that it is necessary to consider the occurrence of pipeline ovalization when designing reel-lay equipment and pipelines. At the same time, the design of driving equipment for reel-lay can be guided by the change of bending moment of the pipeline.

(2) The diameter-to-thickness ratio has a very obvious effect on the ovalization and bending moment changes of the pipe cross-section during the reeling process. Among the three selected pipes with different D/t values, the ovalization of the pipe with the D/t value of 20 has the largest change, and the pipe with the smallest change has a D/t value of 10. Contrary to the change of ovalization, the maximum bending moments corresponding to the two types of pipes are 115 kN·m and 156 kN·m, respectively. When D/t value reaches 20, the ovalization of the pipeline has exceeded the allowable range specified in the DNV standard, indicating that the pipeline does not have the ability to perform the reel-lay method.

(3) The material properties will also have a certain influence on the ovalization and bending moment of the pipe section during the reeling process. With the yield strength or hardening index increasing, the ovalization becomes more obvious. However, the above two factors of material properties have completely opposite effects on the bending moment of the pipe cross-section. The higher the material yield strength of the pipeline, the greater the bending moment that the pipeline bears. The bending moment of the pipes decreases with the increase of the hardening index. Therefore, in order to reach the requirements of relevant standards, the influence of pipeline material parameters needs to be considered in the design of the reel-lay equipment.

(4) The effect of axial tension during the pipe-reeling process has an important influence on the ovalization and bending moment of the pipe cross-section. The increase in axial tension will increase the ovalization change of the pipe cross-section and reduce the bending moment of the pipe cross-section. When the axial tension is large enough, as the curvature increases, the ovalization process of the pipe cross-section will be accelerated, and the bending moment of the pipe will decrease after reaching the peak value. Therefore, selecting an appropriate axial tension during the reeling process can effectively reduce the torque required for the pipe reeling, and at the same time, control the ovality change of the pipe within a reasonable range.

Future research is required to study the numerical solution of the R-lay reeling process on the basis of optimizing the simulation and experiment project. This research mainly includes the following parts: Firstly, a method to simplify the experiment is necessary. For example, using similar principles to test small-scale pipes or performing simplified full-scale tests on the reeling process. Secondly, comparing the other research on the simulation of pipe laying, optimizing the simulation model, and making the simulation result closer to the test result to minimize the error and reduce the calculation cost, to support the development of pipe laying and equipment.