1. Introduction
A subsea production system is an essential component in offshore platform installation. Subsea production systems are mainly composed of subsea trees, subsea manifolds, subsea well control systems, and subsea processing systems [
1,
2]. Forming the core of the subsea production system is the subsea tree, the primary function of which is to control the flow of produced oil and gas, monitor oil and gas parameters, as well as form an isolation barrier between the underground reservoir and the environment containing the subsea wellhead system [
3]. The submarine environment is relatively safe compared to the sea surface, but the installation of the subsea trees is more complicated.
According to the China Classification Society (CCS) fixed platform specifications, the splash zone refers to the area where the seawater rises and falls periodically due to the action of waves, that is, the wave height in this area [
4]. As shown in
Figure 1, the installation of a subsea tree generally goes through three stages, where the subsea tree passes through the splash zone, continues to be decentralized, and is lowered to the designated position. The subsea tree passing through the splash zone denotes the process of entering the water from the air, which is the most dangerous stage of the installation procedure and is generally an exceedingly slow operation. When the subsea tree is lowered, the waves of the ocean rise and fall, generating relative speed between the seawater and the subsea tree, generating an interaction force when the two make contact with each other. When the subsea tree enters the water, it generates an additional impact force, affecting the stability of the subsea tree. Improper operation may cause the subsea tree to overturn or be damaged by the assault of the water at the bottom, potentially causing engineering accidents.
It is technically challenging for the subsea tree to pass through the splash zone [
5]. Therefore, to ensure that the installation process is completed safely and efficiently, it is necessary to carry out appropriate simulations and careful calculations before installation to determine the installation safety window, evaluate possible accident risk factors, and formulate corresponding emergency rescue plans. Rhee et al. [
6] and Howison et al. [
7] stated that when the structure entered the water, the water surface became a free liquid surface. The effect of air had little effect on the final result, but they noticed that the structure was subjected to uneven forces during the water ingress. In terms of test methods, Cui et al. [
8] and Hao et al. [
9] studied the influence of different rods and different conditions on the process of entering the water. Since the 21st century, scholars have focused their research on wedges entering the water. Carcaterra et al. [
10], Yettou et al. [
11], Tveitnes et al. [
12], and Tian et al. [
13] assessed water ingress at different angles and speeds to obtain wedges, and their results regarding surface pressure and angle when entering the water corresponded with each other. Regarding numerical calculation, Fraenkel et al. [
14] and Oger et al. [
15] summarized the previous theory and derived a numerical solution for the problem involving a two-dimensional axisymmetric structure entering the water, while Moore et al. [
16], Facci et al. [
17], and Takagi [
18] extended the two-dimensional structure to one that was three-dimensional. Furthermore, it was believed that the above method for calculating the maximum impact hydrodynamic pressure of the wedge into the water was higher than the actual pressure. Shi et al. [
19], Jiang et al. [
20], and Shen [
21] used numerical algorithms to simulate and analyze the change law of impact load under different shapes, speed of entry, and angle of entry.
In the past, research involving structural installation and decentralization has mainly focused on the force of different object shapes at different water inflow speeds and angles. However, few studies exist involving the marine environment, such as current speed, wave height, and the stability of the subsea tree installation. Guan [
22] studied wave impacts on structures in the splash zone by using a simplified one-dimensional numerical model. Jia and Agrawal [
23] proposed a coupled fluid-structure interaction (FSI) approach to predict wave induced motions, wave loads, dynamic stresses, and deformation of subsea structure and equipment in the splash zone during installation. Du et al. [
24] used the explicit formulation dynamic analysis finite element to predict the wave slamming forces on the subsea equipment bottom panels in the splash zone during installation. Nam et al. [
25] presented an experimental study of the deepwater lifting and lowering operations of a subsea manifold, and regular wave tests were carried out to investigate the vessel motion and wire tension responses during the deepwater lifting operation. El Mouhandiz et al. [
26] studied the hoist wire dynamics and lowering speeds of the subsea structure installation while passing through the splash zone. Previous studies mostly focused on the influence of a single factor on the subsea tree passing through the splash zone, and no safety window for engineering applications was developed for engineering applications. In this paper, taking Lingshui 17-2 actual engineering project as an example, the engineering ship, subsea tree, and its installation tools are modeled, the influence of multiple marine environments is considered, and the multi-body movement relationship between the engineering ship and the lowered structure is established. The effects of velocity, wave height, period, and lowering speed on the installation of the subsea tree is analyzed, the safety window is established to guide the installation of the subsea tree.
2. Installation Theory of the Subsea Tree Passed Through the Splash Zone
When the subsea tree passes through the splash zone, the deformation of the free water surface is considered. Air is a compressible gas, which satisfies the ideal gas state equation. The water is not viscous and incompressible. It was assumed here that the length of the subsea tree is
l, and the install speed is
V(t). The theoretical model of the subsea tree into water is shown in
Figure 2.
In the process of entering the water, since the two are in surface contact, the phenomenon of compressed air will occur. The air is squeezed by both solid and liquid, and the middle air will escape to both sides. When the solid-liquid contact is close enough, the relative flat-bottom width is sufficiently small, that is, when
h/
l ≤ 1 is satisfied, the movement of the air sandwiched between the two can be regarded as flowing along the
x-axis direction, regardless of the air viscosity. The equations of motion and continuity are obtained as follows:
In Equations (1) and (2), u is the moving speed of the air layer in the horizontal direction, p is the pressure of air, ρa is the density of air, and h is the thickness of the air layer.
In the process of entering the water, the air is continuously squeezed by both solid and liquid states, and the intermediate air will continue to escape to both sides. When the solid and liquid come into contact, some air will still be exhausted in the future, which forms an air cushion, and the process of compressing air can be expressed by the following equation of state:
In Equation (3), γ represents the specific heat ratio of air, and p0 and ρ0 correspond to the air pressure and density in the initial state, respectively.
Assuming the initial time
t = 0,
h (x, t) = h
0,
V (t) =
V0, and
η (x, t) represent the height of the free water surface, then the distance between the subsea tree and the water surface can be expressed as:
Further analyzing Equation (4), the relationship between the thickness of the air cushion and the height of the water surface can be expressed as:
By analyzing the movement process and combining the momentum theorem, we can obtain the speed change equation of the subsea tree under the action of gravity and the reaction of compressed air:
In Equation (5), Ms represents the quality of the subsea tree.
When passing through the splash zone, the ship, cable, and the subsea tree form a multi-body motion system that interact with each other. After the subsea tree enters the water, it has six degrees of freedom in the water, which is simplified to a two-dimensional plane motion. The force diagram of the subsea tree is shown in
Figure 3.
According to Newton’s second law:
where
is the cable tension,
is the buoyancy of the subsea tree,
is the fluid resistance experienced by the subsea tree,
is the additional mass force of the subsea tree, and
is the gravity of the subsea tree.
Perpendicular to the cable:
The bottom end of the cable is connected to the subsea tree. In the horizontal direction:
In the vertical direction:
In the above Equations, v is the vertical speed of the ship crane, φ is the speed of the lowering rope, l is the length of the lowering rope, and θ is the angle between the rope and the horizontal direction.
The theoretical calculations shown above are the basic theory of the subsea tree entering the water. It mainly analyzes the movement and force of the subsea tree when it passes through the splash zone. However, due to the complexity of the problem of the subsea tree passing through the splash zone, the current theory cannot accurately give the calculation. To solve the problem, simulation software is needed to calculate the entering conditions of the subsea tree.
4. Conclusions
This article was based on the theory of lowering the subsea tree through the splash zone. The OrcaFlex software was used to analyze the installation process of the Lingshui 17-2 subsea tree through the splash zone under different velocities, wave heights, periods, and lowering speeds.
Subsea trees are most significantly affected by sea conditions when they pass through the splash zone. As the depth of the tree increases after entering the water, the tree offset displacement and cable forces decrease. The wave height represents the main factor involved in the offset displacement of the subsea tree and the change in cable tension. An excessively high wave height causes vertical displacement of the subsea tree. During this process, overturning accidents, damage to cables, and lifting equipment may occur, therefore demanding careful attention to the plan. Velocity mainly affects the horizontal migration of the tree during the lowering process, and there is almost no risk of the tree overturning or sudden changes in cable stress. Changes in velocity cause horizontal offset of the tree. The lower the installation speed, the higher the attack pressure may be, and it is necessary to select the safest and most economical installation speed, adhering to the marine environmental parameters. Combining the research methods above with safe operating standards allows for the determination of the safety window when the tree is installed, providing guidance for the installation.