Pipelines are widely used for transporting oil resources in the context of offshore oil exploitation. The pipeline stress-strength analysis is an important stage in related design and ensuing construction techniques. In this study, assuming representative work environment parameters, pipeline lifting operations are investigated numerically. More specifically, a time-domain coupled dynamic analysis method is used to conduct a hydrodynamic analysis under different current velocities and wave heights. The results show that proper operation requires the lifting points are reasonably set in combination with the length of the pipeline and the position of the lifting device on the construction ship. The impact of waves on the pipeline is limited, however lifting operations under strong wind and waves should be avoided as far as possible.

With the further development of the offshore oil industry, offshore oil and gas transportation are becoming more and more prosperous as well [

The pipeline stress-strength analysis is an important stage in overall construction design [

Scholars have done a lot of research on the mechanical behavior of the pipeline already. For example, Preston et al. [

As can be seen from the brief review of the most advanced research, the current research on the mechanical behavior of the pipeline focuses on modeling and simulation analysis of the whole deep-sea system cooperative operation, the dynamic characteristics analysis of the lifting pipe, and the process of laying from water surface to seabed [

In this paper, the pipeline lifting operation is modeled in OrcaFlex, and the hydrodynamic response in the process of pipe lifting is calculated by the time-domain coupling dynamic analysis method. To ensure the authenticity of the simulation to the greatest extent, the simulation time step must be less than the period of the shortest natural node. It should not exceed 1/10 of the shortest natural period of the model. Combined with the calculation results of hydrodynamic performance then, some guiding suggestions are given.

When the lifting force is applied to a pipeline, the pipeline will deflect. In an actual engineering project, compared with the length of the pipe section to be lifted, the lifting height and angle change is minimal. Therefore, the small deflection linear theory can be used to calculate the deflection of the pipeline. The lifting process is a problem of moving boundaries in the pullback step, so a multipoint lifting model of the pipeline can be built using a polynomial interpolation function. To find the position of the moving boundary, the displacement correction methods, such as load concentration correction, horizontal spacing correction, and iterative calculation, are used to convert the large deformation geometric nonlinear problem of the pipeline to a piecewise linear problem [

_{i}_{i}

Based on the small deflection beam theory, the relationship among the physical parameters is as follows:

Corner:

Bending moment:

Uniform load:

Selecting the linear interpolation function as the calculation equation, the differential equation for bending deformation is as follows:

The solution of the

The interpolation function of section _{i}_{+10}, _{i}_{+11}, _{i}_{+12}, _{i}_{+13} represent the unknown coefficients, _{i}_{i}_{+1}(_{i}_{i}_{+1} represents the weight increment of segment

According to the mechanics of materials, the deflection angle is 0, corner is 0, and bending moment is 0 at the ending point of the pipeline. Then the following equation can be gotten,

The _{i}_{0}, _{i}_{1}, _{i}_{2} (

After the simplification, there are still some unknown coefficients which can be calculated according to the lifting height of each point and the pipeline ending point _{i}

The value of parameter _{i}

The interpolation function of each segment is as follows:

The angle and moment can be gotten by solving _{1} can be known according to the following equation:

After calculating the deflection curve of the pipeline, the equations of the rotation angle, bending moment and shear force of each pipeline segment can be obtained according to the linear beam theory:

After obtaining the interpolation function, the maximum stress can be calculated using the following equation:_{max}; ^{4} − ^{4})/64; _{max} represents the maximum deflection.

Using the deflection equation of the last segment _{n}

Due to the particularity of the marine environment, the load on the subsea pipeline system is relatively complex. For subsea pipelines, waves and currents are the most important external loads. Since the pipe lifting operation is rarely carried out under strong wind conditions, to save calculation time, the wind load is not considered in this paper.

When calculating and analyzing the pipeline, it is assumed that the pipeline is a flexible structure. The calculation and analysis mainly include the axial tension borne by the pipeline, the action of environmental load, and the coupling dynamic response of the whole system. The lump-mass method is used for modeling. The performance of the pipeline is equivalent to a nonlinear spring, which is discretized into the lump-mass model [

The wave and current forces on the submarine pipeline can be calculated by the Morrison equation:

Normal component of current force:

Tangential component of current force:

Normal component of wave force:

Tangential component of wave force:_{n}_{t}_{m}_{n }= v⋅sinθ_{t }= v⋅cosθ_{n }= u⋅sinθ_{t }= u⋅cosθ

As an important marine environment load, the submarine surface sediments will also affect the dynamic behavior of the pipeline lifting operation [

The hydrodynamic analysis includes static and dynamic analysis. Static analysis has two main functions: to analyze whether the system structure reaches static equilibrium under the action of gravity, buoyancy, and flow viscosity. The other is to provide an initial state for dynamic analysis.

The dynamic analysis starts from the steady-state provided by static analysis. It includes the self-construction stage and model maintenance analysis stage. The self-construction stage is where the wave and ship motion gradually increase from static to the given value. This stage generally requires a wavelength of time. After the self-construction stage, the model can enter the maintenance analysis stage. The dynamic simulation calculation adopts two sets of explicit and implicit calculation methods. Both calculate the system’s geometric shape at each time step and fully consider the nonlinear geometric factors, including the spatial variation of wave load and contact load. The equation of motion is solved by explicit forward Euler integration with a fixed step size. The initial model parameters are obtained through static analysis to calculate the forces and moments of each free body and node, including gravity, buoyancy, hydrodynamic and air resistance, hydrodynamic added mass, tension and shear force, bending moment, seabed friction, object contact force, the force exerted by hinge and winch, etc.

The numerical solution of the boundary problem for the pipeline is the discrete lumped mass method [

Among them,

_{i}_{dni}_{dti}_{ani}

The lumped mass model is shown in

In OrcaFlex, there are two temporal discretization schemes, explicit and implicit integrations. The explicit time integration takes a constant time step to integrate forward. At the beginning of the simulation, after a preliminary static analysis, the initial positions and orientations of all nodes in the model are known. The forces and moments of all free bodies and nodes are calculated, including gravity, buoyancy, hydrodynamic force, hydrodynamic added mass, tension and shear, bending and moment, seabed friction, etc.

The motion control equation for each free body and node in the model is as follows:

For implicit integration, the generalized-α method is used in OrcaFlex [

Although it is easy to achieve stability using implicit integration, the corresponding calculation results are often inaccurate. For rapidly changing physical phenomena, such as fast collisions, more attention should be paid to the accuracy of the calculation results. In this case, it is necessary to compare the calculation results of the implicit and explicit integration formats in order to study the sensitivity of the time step. Both methods recalculate the geometry of the system after each time step, so the numerical simulations are adequate for geometric nonlinearities, including spatial variations of wave loads and contact loads. The time domain simulation steps in this paper are shown in

The coordinate system can be divided into the global coordinate system and vessel coordinate system. Both use the right-hand coordinate system. The origin of the global coordinate system is set on the sea level, the

The upper boundary condition of the pipeline model mainly depends on the motion of the vessel to which it is connected. The motion of the vessel depends on RAOs. RAOs, known as response amplitude operators are a concept of engineering statistics in the field of ship or floating body designs, which can be used to calculate the behavior of ships working in sea conditions. Vessel RAOs can generally be obtained by model experiment or CFD (Computational Fluid Dynamics). It is usually necessary to calculate the motion of a floating body under various wave conditions. Its essence is a transfer function from wave excitation to vessel motion. In OrcaFlex, once the RAOs are determined, the vessel’s motion will be determined. The vessel length is 103 m, the width is 16 m, and the depth is 13.32 m. The design draft is 6.66 m, the transverse stability radius is 1.84 m, the longitudinal stability radius is 114 m, the displacement is 8800 T, the front projection on the water surface is 191 m^{2}, and the side projection on the water surface is 927 m^{2}. The square coefficient _{B}^{2}. The data of RAOs, wave drift force, added mass coefficient, and damping coefficient of the ship is from diffraction analysis of a 103 m long ship in a 400 m water depth pool.

The seabed has an important impact on the touchdown part of the pipeline. The seabed is non smooth. There is friction between the seabed and the pipeline touchdown area. The friction has a certain positive effect on the pipeline, which will hinder the low-frequency movement of the pipeline, that is, slow movement. However, how to accurately simulate the seabed friction is very difficult. We need the actual detection data of the seabed, which is generally unavailable. It is the seabed friction optimization model provided by OrcaFlex. The advantage of this model is straightforward. When the combined velocity

In OrcaFlex, the parameters related to the pipeline are as follows [^{3}; the unit length-weight is 0.187 t/m; the bending stiffness is 9.16 × 10^{4} kN.m^{2}; the axial stiffness 5.06 × 10^{6 }kN; the water depth is 100 m. The effects of current velocity and different wave heights are simulated, respectively. The range of current velocity is 0–4 m/s, and one current velocity is taken every 0.5 m/s. The wave height range is 0–3 m, and one wave height is taken every 0.5 m. The current direction and wave direction are taken as 0°.

The schematic model of the pipeline lifting operation is shown in

In order to verify the correctness of the lumped mass method, a towed cable based on the mathematical formulation above is taken and let it move under the specified boundary condition [

Parameter | Cable | Array | Drogue |
---|---|---|---|

Length (m) | 723 | 273.9 | 30.5 |

Mass per length (kg/m) | 1.5895 | 5.07 | 0.58 |

Wet weight per length (N/m) | 2.33 | 0 | 0.57 |

Diameter (m) | 0.041 | 0.079 | 0.025 |

Axial stiffness EA (N) | 1 × 10^{8} |
1 × 10^{8} |
5 × 10^{6} |

Bending stiffness EI (N.m) | 1000 | 1000 | 0.01 |

_{w} |
2 | 1.8 | 1.8 |

Point A which is located at 8.2 m of Array section is selected to make some comparisons between the lumped mass model and the previous research. The variations of depth of point A are compared to the results of Gobat et al. [

Through observation, the bending moment, curvature, and effective tension all have sudden changes at the positions where the pipeline length is 20, 40, and 70 m. The trend is to increase sharply at first, then decrease, and then increase sharply at these three coordinate positions. Three lifting cables cause this phenomenon to facilitate operation and prevent damage to the pipeline due to the large arc bow of the pipeline during pipeline lifting. The contact position between the lifting cable and the pipeline is analyzed. The left and right of the contact point are affected by gravity and hydraulic damping. The tension along the pipeline direction increases gradually on the left of the 20 m contact point, and the tension increases sharply at the contact point due to the stress on both sides. In the section from 20 m contact point to 40 m contact point and from 40 m contact point to 70 m contact point, there is a small concave arc bow due to gravity. This arc bow is affected by the gravity component of the pipelines on both sides along the axial centerline, resulting in a compression effect, offsetting part of the tension and reducing the tension value. At the 70 m contact point, while being acted by the lifting cable and the left end pipeline, it is also acted by the gravity of the longer pipeline at the right end. Therefore, the tension and bending moment at this position are very large, which is easy to cause pipeline damage or fracture, especially when the pipeline is lifted to the highest position. At the 100 m position, the pipeline is in the transition position between the upper convex arc bow of the lifted pipeline and the lower concave arc bow of the not lifted pipeline. At this time, the pipeline becomes basically a straight segment at the critical point, and the bending moment decreases sharply. However, the tension at this position is still large due to the lifting force and the gravity of the not lifted pipeline.

It is not difficult to explain this phenomenon by analyzing the action process of ocean currents on pipelines. The pipeline is divided into two parts, with the 70 m contact point as the boundary. There is an upward convex arc bow in part before the 70 m contact point. After facing the current, the current generates lifting force on this section of the pipeline, balancing the tension formed by a part of the lifting cable opposite gravity’s direction the greater the flow velocity, the greater the lift that can be provided, and the better the balance effect. Therefore, the tension in this section is negatively correlated with the flow velocity. Similarly, the arc bow of this section after the 70 m contact point is concave, so the current will have a downward component on the pipeline after facing the current, which increases the tensile effect of pipe lifting operation on this section. Therefore, the greater the flow velocity, the greater the tension. This is also verified on the bending moment diagram and curvature diagram. The bending moment before and after the convex and concave transition points also has a similar trend. Still, it is opposite to the trend of tension. Before the transition point, due to the action of lift, the degree of convexity on the arc bow is deepened, and the greater the flow velocity, the greater the bending moment. After the transition point, the flow direction of the current faces the concave arc bow, which makes the alignment of this section of the pipeline close to the seabed more straight, so the bending moment decreases with the increase of velocity.

In this paper, based on the basic parameters of a certain pipeline and the specific work environment parameters, combined with the specific operation, the model of the pipeline lifting operation has been implemented by OrcaFlex. The hydrodynamic analysis under different current velocities and wave heights has been researched. This study demonstrates the following:

The changes of tension and bending moment in the process of pipe lifting obviously show the difference in the front and rear sections from the position of the bow lifting cable (the position of the 70 m contact point in the example) to the bending transition point. Therefore, before construction, it is necessary to reasonably set the lifting point in combination with the pipeline’s length and the lifting device’s position on the construction vessel.

The effect on the pipeline before and after the contact point is always one favorable and one harmful. Therefore, during construction, it is necessary to pay attention not to let the tension or bending moment of a certain section break through the safety limit.

The effects of wave heights and current velocities on the dynamic characteristics of pipeline lifting operation is mainly reflected in the effective tension. The greater the wave height and current velocity, the greater the effective tension. Although the wave in these cases has limited impact on the pipeline, considering the complexity and difficulty of the pipe lifting operation procedure, the operation in case of strong wind and waves should be avoided as far as possible.