Stability Analysis and Environmental Influence Evaluation on a Hybrid Mooring System for a Floating Offshore Wind Turbine

Abstract

Floating offshore wind turbines (FOWTs) are one of the innovative solutions to achieve net-zero emissions. Given that Taiwan has abundant wind power resources in its western waters and wind farms are evaluated as potential sites, a strategic emphasis on the extensive expansion of wind power is imperative. This paper chooses four different designs of hybrid mooring systems, comparing them with the conventional pure chain mooring arrangement in shallow water regions in Taiwan through integrated numerical simulations, ANSYS AQWA, and Orcina OrcaFlex. The use of synthetic fiber ropes in hybrid moorings provides substantial economic and operational advantages, making them the preferred alternative to traditional chains in deepwater offshore renewable energy (ORE) mooring configurations. Hybrid mooring enables the FOWT to survive in extreme sea conditions and is presented as the ultimate limit state (ULS) and fatigue limit state (FLS). In addition, hybrid mooring not only reduces mooring line costs but also minimizes the footprint area on the seabed, enhancing economic competitiveness and optimizing marine space utilization. However, it increases the entanglement risk that may pose a potential threat to marine mammals. Building on prior research, this paper proposes a unique approach to calculate the mooring line swept volume, which is essential for entanglement assessment and marine spatial planning.

1. Introduction

According to the research on global offshore wind speed rankings conducted by 4C Offshore in 2013 [1], Taiwan has abundant wind power resources in its western offshore waters. These wind farms are considered potential global sites for wind energy. While global cumulative floating offshore wind capacity is expected to experience significant growth, projecting an increase from 12.4 GW in 2030 to 39 GW in 2035 [2], this paper aims to develop a mooring system design for FOWTs. To enhance economic competitiveness, the costs of mooring lines can be reduced through the use of hybrid mooring technology [3]. Synthetic fiber ropes present great potential as a material for permanent mooring systems due to their cost-effectiveness and superior tension performance, attributed to their lighter weight and lower axial stiffness [4]. Given the widespread use and excellent characteristics of fibers in the oil and gas industry, synthetic fiber ropes are considered promising candidates for mooring lines in floating offshore wind applications [5]. However, shallower water depth conditions in Taiwan limit the feasibility of taut-type mooring systems, making them unsuitable for relatively shallow waters. Therefore, this study emphasizes the integration of taut-type and catenary-type mooring systems to create a hybrid mooring system.

Utsunomiya et al. (2019) conducted an at-sea experiment on a hybrid polyester mooring system [6], which revealed no serious deterioration or apparent damage. Although strength reduction could be more significant over long-term operation, the safety factor designed for synthetic fiber ropes still encompasses the required range. Through experimental investigation and decay analysis, Xu et al. (2021) found that polyester effectively restricts the heave motion of Wave Energy Converts (WECs) more than nylon due to its higher stiffness and greater damping [7]. Consequently, they highlighted nylon as a more favorable material for WECs compared to polyester. However, in contrast to WECs, floating offshore wind turbines (FOWTs) require mooring systems with restraint capability and moderate platform motion. Xue et al. (2018) conducted fatigue analyses on chain–fiber–chain mooring for semi-submersible platforms [8]. Using the T-N curve method, Wu et al. (2015) performed analytical numerical analysis to calculate the fatigue damage for low frequency and wave frequency tension [9]. Additionally, Xu et al. (2021) provided experimental data to investigate the dynamic tension response in hybrid moorings, proposing seven different mooring concepts considering the ultimate limit state (ULS) [10].

The arrangement of turbine arrays and the deployment of station-keeping systems play crucial roles in floating offshore wind farms. Further investigation is needed to address the adverse impacts on the marine environment and conservation issues caused by FOWTs. With an increasing number of these devices set to be deployed, there is a growing global concern for sustainability. One potential impact is entanglement hazard for whales, dolphins, or other large marine mammals (commonly referred to as marine megafauna), as their movement may be restricted by the high density of mooring lines in floating wind farms. On 29 June 2022, a whale was found entangled in the ropes of a data buoy in the Norwegian part of the Barents Sea, Norway (as shown in Figure 1). It can be inferred that mooring systems contribute to entanglement risk for marine mammals to some extent.

1.1. Marine Data

Since the offshore area of Hsinchu has the highest wind power density in the Taiwan Strait, as depicted in Figure 2, it makes Hsinchu’s offshore waters an ideal research site for FOWTs. The water depth of Hsinchu is approximately 100 m.

The top priority of FOWT technology is to ensure platform stability and the feasibility of mooring systems under the extreme sea state, and this study chooses the ultimate limit state (ULS). According to the requirements outlined in DNVGL-ST-0119 [11], the wind turbine system must withstand a 50-year typhoon return period for each design case. Moreover, during extreme sea states, turbine blades cease rotating (parking). Given the unique location of the Taiwan Strait, consideration is given to the special monsoon sea state to approach a realistic scenario. Environmental conditions including wind, wave, current, and turbine state are listed in

Table 1. Environmental conditions in Hsinchu, Taiwan (Hsinchu data buoy of the Central Weather Bureau, Taiwan; HYCOM database; Environmental Impact Assessment Act of Offshore Wind Power Project (W1N), Taiwan).

Sea State Case	Normal	Monsoon	50-Year Return Period
$H_s \left(\mathrm{m}\right)$	1.67	3.58	9.1
$T_p \left(\mathrm{s}\right)$	5.17	8.79	12.7
$U_{10 }(\mathrm{m}/\mathrm{s})$	7.32	7.3	28.9
$U_{150} (\mathrm{m}/\mathrm{s})$ *	10.77	10.77	42.55
$v_0 (\mathrm{m}/\mathrm{s})$	0.65	0.65	1
$v_{100} (\mathrm{m}/\mathrm{s})$ *	0	0	0
Wind turbine state	Operating	Operating	Parking

* Vertical wind and current load profiles follow the power law method (Justad, 2017) [13]; the power law exponent is defined as 1/7.

. This study uses the JONSWAP spectrum to simulate irregular waves. The peak enhancement factor, $\gamma$, is determined to be 2.08 in the western waters of Taiwan (Ou, 1977) [12]. In Table 1, $U_{10}$ represents the wind speed at 10 m above sea level, $U_{150}$ is the wind speed at 150 m above sea level, which shares the same elevation as the wind turbine nacelle, where the turbine experiences the largest thrust, $v_0$ denotes the current velocity at the sea surface, and $v_{100}$ represents the current velocity at the seabed.

Table 2. Annual probability of different sea state distribution in Hsinchu.

Hsinchu	Probability (%)	Annual During Time (h)
Normal sea state	66.66621	5839.96
Monsoon sea state	33.33311	2919.98
50-year return period	0.00068	0.06
Sum	100	8760

presents the annual probability of different sea state distributions in Hsinchu. The annual probability distribution is used in fatigue analysis.

1.2. Floating Platform and Wind Turbine

This study uses a 15 MW wind turbine proposed by IEA [14] and VolturnUS-S Reference semi-submersible platform (as shown in Figure 3), which is designed to support the IEA-15 MW-240 R-wind turbine by UMaine (The University of Maine) [15]. The draft of the floater is 20 m, and the mass of the platform and inertia properties with the loading of the tower, RNA, and blades are shown in

Table 3. Semi-submersible platform general system properties (with turbine) [15].

Parameter	Value (Unit)
Platform type	Semi-submersible
Platform mass (with turbine)	20,131 (t)
Draft (with turbine)	20 (m)
Vertical center of gravity from SWL	−2.234 (m)
Actual volumetric displacement	19,634 (m3)
Mass moments of inertia ($I_{xx}$)	$4.457 \times {10}^7$ (t × m2)
Mass moments of inertia ($I_{xz}=I_{zx}$)	$1.152\times {10}^6$ (t × m2)
Mass moments of inertia ($I_{yy}$)	$4.449 \times {10}^7$ (t × m2)
Mass moments of inertia ($I_{zz}$)	$2.394 \times {10}^7$ (t × m2)

.

Meanwhile, this paper adopts the thrust curve and power curve of the IEA-15 MW-240 R-wind turbine [14]. The operational state of the wind turbine depends on the wind speed at the hub. The wind turbine starts to operate at a cut-in wind speed, 3 m/s, while the thrust of the turbine reaches the maximum value, 2100 kN, at a rated wind speed of 10.77 m/s. Beyond the cut-out wind speed of 25 m/s, the turbine enters an idling state. The key features and parameters of the IEA-15-MW wind turbine are outlined in

Table 4. IEA-15 MW-240 R-wind turbine properties [14].

Parameter	Value (Unit)
Blade mass	65.7 (t)
RNA mass	1446 (t)
Tower mass	1211 (t)
Tower diameter at base	10 (m)
Rotor diameter	240 (m)
Hub height	150 (m)
Hub diameter	6 (m)
Cut-in wind speed	3 (m/s)
Cut-out wind speed	25 (m/s)
Rated wind speed	10.77 (m/s)

.

1.3. Synthetic Fiber Ropes

Synthetic fiber ropes exhibit diverse material properties. Characteristics such as displacement, minimum breaking load (MBL), and axil stiffness mass per unit may affect the mooring system performance. Castillo et al. (2020) have confirmed that synthetic fiber ropes serve as optimization tools for achieving a cost-effective and reliable mooring system design [1]. Synthetic fiber ropes are advantageous in terms of reduced corrosion problems, with wet polyester experiencing lower abrasion rates compared to dry polyester ropes, as proposed by Herduin et al. (2016) [16]. However, it is crucial to note several adverse effects associated with synthetic fiber ropes. According to Weller et al. (2015), synthetic fiber ropes demonstrate high stress–strain performance, with larger diameters leading to a greater strain range [4]. Hong-Duc et al. (2019) found that synthetic fiber ropes could result in an increase in lineic mass and drag diameter [17]. Currently, modeling research and experiments focused on synthetic fiber ropes have made significant progress. The pros and cons of using these ropes as mooring lines are summarized in

Table 5. Properties of synthetic fiber ropes (summarized by this paper).

Advantages	Disadvantages
Cost-effective	Tension–elongation relations
Good tension performance	Dynamic stiffness
Lighter weight	Lower stiffness/strength
Less corrosion	Increase drag diameter in marine growth

.

Synthetic fiber ropes, such as nylon and polyester, are among the most common materials used in mooring systems due to their requirement for high strength and ductility. Polyethylene and polypropylene also serve as suitable candidates for marine applications, exhibiting stiffness characteristics similar to nylon and polyester. However, it is important to note that polyethylene and polypropylene are sensitive to temperature and may become vulnerable when directly exposed to ultraviolet (UV) light. In contrast, aramid and HMPE (High Modulus Polyethylene) are mostly tested for taut mooring, with only a few commercial examples available [4]. Given the varied mechanical properties of synthetic fiber ropes, this study focuses on nylon and polyester as research targets due to their superior performance.

1.4. Hybrid Mooring System

1.4.1. Theory and Properties

A hybrid mooring system is a combination of chains, steel wire ropes, and synthetic fiber ropes such as nylon ropes, polyester ropes, and other materials. This concept was proposed by Garza-Rios et al. (2000) and was mainly designed to achieve the desired tension for Floating Production Storage and Offloading (FPSO) [18]. Each mooring line consists of a number of segments (more than two) that decrease the tension of lines and increase the flexibility of the system. Figure 4 shows the geometry of three segments of hybrid mooring. Segment $S1$ is the chain segment, which starts from an anchor $A$, along the touchdown part $d$ and suspends line $l1$ to connection point $B$; Segment $S2$ is the wire or fiber rope (line $\overline{BC}$); Segment $S3$ is the chain segment, which starts from connection point $C$ and attaches to the fairlead $D$ on the platform, providing the main weight for tension and restoring force. For two segment lines, the whole hybrid mooring line is divided into two components, suspended fiber ropes and a bottom chain, and line $\overline{CD}$ in Figure 4 does not exist.

It is assumed that no hydrodynamic loads are exerted at the endpoints of each segment. The weight of the suspended chain segment serves as the major source of tension. While the applied horizontal load at fairlead is $T_H$ and $\omega$ is the weight of the chain per unit length, the length of the suspended line, $L_s$, can be written by Equation (1) [19].

$$L_s=\mathrm{h}\sqrt{(2\frac{T_H}{\omega h}+1)}$$

(1)

The tension along the mooring line, $T$, is given by Equation (2) [19].

$$T=\sqrt{{T_H}^2+{T_V}^2}=\frac{T_H}{\cos \theta }$$

(2)

The horizontal distance between the fairlead point (D) and the anchor point (A) can be expressed as follows:

$$\mathrm{X}=l-h{\left(1+2\frac{T_H}{\omega h}\right)}^{\frac{1}{2}}+\frac{T_H}{\omega }{\cosh }^{-1}(1+\frac{\omega h}{T_H})$$

(3)

Meanwhile, the weight of synthetic fiber rope is negligible. The static catenary shape of the hybrid mooring lines can be given as:

$$T_{chain}=T_H\cosh \left(\frac{\omega l_1}{T_H}\right)$$

(4)

$$T_{syn}=S_{b}p{\left(\frac{{l_2}_T-{l_w}_2}{{l_w}_2}\right)}^q$$

(5)

where ${ S}_b$ is the average breaking strength of synthetic fiber rope and $p$ and $q$ are constants determined empirically [20].

The axial stiffnesses of all materials are assumed to be linear for simplicity. The combination of chain and synthetic fiber ropes can be found in the following relations (Johanning et al., 2008) [21]:

$${EA}_{Hybrid}=(L_{Chain}+L_{Syn}){\left[{\left(\frac{{EA}_{Chain}}{L_{Chain}}\right)}^{-1}+{\left(\frac{{EA}_{Syn}}{L_{Syn}}\right)}^{-1}\right]}^{-1}$$

(6)

$$w=\frac{w_{Chain}{L}_{Chain}+w_{Syn}{L}_{Syn}}{L_{Chain}+L_{Syn}}$$

(7)

where $w$ is the submerged weight of the mooring line.

A comparison of different mooring system types, assuming a similar water depth, is listed in

Table 6. Comparison of different mooring system types (summarized by this paper).

Mooring System	Catenary	Taut Type	Hybrid Type
Suitable water depth (Qiao et al., 2013 [22])	70–500 m	More than 250 m	More than 70 m
Station-keeping mechanism	Weight of suspended segment of lines	Elastic elongation of rope characteristics	Restoring force from the weight and elasticity of ropes
Mooring line materials	Chain	Fiber and steel wire	Chain, fiber, and steel wire
Force on anchor	Horizontal only	30–45 degrees (90 degrees for TLP)	Horizontal only
Touchdown to the seabed	Mooring and anchor	Anchor only	Mooring and anchor
Mooring System	Catenary	Taut Type	Hybrid Type
Footprint range	Large	Small	Medium
Platform response by wave force	Medium	Small	Medium
Pretension on fairlead point	Low	High	Medium
Cost of mooring	Expensive	Cheap	Medium
Cost of anchor	Cheap	Expensive	Cheap
Cost of O&M	Cheap	Expensive	Medium
Installation complexity	Easy	Complicated	Medium

. In a hybrid mooring system, which is a combination of catenary and taut types, the restoring force of the station-keeping mechanism includes the weight of the chain and the elastic elongation properties of the fibers. Additionally, the hybrid type is less restrictive in water depth conditions and shares the advantages of both catenary and taut moorings, making it a potential candidate for FOWTs.

1.4.2. Applications and Design Symbols

This study uses the same chain size and level, an R3 studless chain, with a nominal diameter of 0.185 m (m) as selected in the UMaine VolturnUS-S technical report [15]. In addition, synthetic fiber ropes and their line types used in the research include nylon (eight-strand Multiplait) and polyester (eight-strand Multiplait). The properties of these ropes generally depend on the nominal diameter, which can be computed through empirical formulas provided by OrcaFlex [23]. Mooring system configurations are shown in Figure 5a,b. Green lines represent the synthetic fiber ropes, and the bottom chain is dark orange. In Figure 5a, the origin, (x,y) = (0,0), is assumed to be located at the center of mass of the platform horizontally. Three anchors are represented by white points, (x,y) = (−650,0) and (x,y) = (325,±563) in meters, and the anchor depth is equal to the water depth in the Hsinchu offshore region, 100 m. Mooring system parameters are summarized in

Table 7. Mooring system parameters.

Parameter	Value (Unit)
Water depth	100 (m)
Anchor depth	100 (m)
Anchor radial spacing	650 (m)
Fairlead depth	14 (m)
Fairlead radial spacing	58 (m)
Total unstretched length 1	610 (m)

¹ The sum of the synthetic fiber ropes and bottom chain.

.

In addition, this paper puts emphasis on the comparison between different ratios of synthetic fiber ropes to bottom chain length. Section 3.1 Preliminary Screening presents a detailed basis and explanations of how final cases are determined.

Table 8. Four designs of hybrid mooring systems.

Case Symbol	Length of Fiber Rope in the Middle (m)	Length of Bottom Chain (m)	Color of Case
Pure chain	-	610	Blue
N10-C600	10 m of Nylon	600	Orange
N70-C540	70 m of Nylon	540	Yellow
P10-C600	10 m of Polyester	600	Purple
P100-C510	100 m of Polyester	510	Green

lists the symbols of the simulated cases. As shown in Figure 5b, the design with two segments (a total unstretched length of 610 m) is used. The tests in the following results analysis are presented as the corresponding colors in Table 8.

1.5. Entanglement Assessment

According to Benjamins et al. (2014), moorings are likely to pose a relatively modest risk of entanglement for most marine megafauna, particularly when compared to those posed by fisheries [24]. It was reported that Indo-Pacific humpbacked dolphins (Sousa chinensis, also known as Chinese white dolphin) in Hong Kong SAR waters were found to be entangled in wire ropes used for anchoring boats.

Since the mentioned examples in Norway and Hong Kong are not isolated cases internationally, the entanglement hazard should be minimized and mitigated in a floating offshore wind farm given the high density of mooring lines underwater. Harnois et al. (2015) [25] highlight three crucial parameters related to the assessment of entanglement to marine megafauna: tension characteristics, the swept volume ratio, and mooring line curvature, which are used to quantify and evaluate the entanglement risk.

• Tension characteristics;
• Mooring becomes slack and tensioned due to the floater motion. Slack mooring has a higher entanglement risk. The tension characteristics are described in terms of the relation between restoring force and platform surge motion;
• Mooring line swept volume ratio;
• The swept volume estimates the volume of water occupied by the mooring line. A higher mooring line swept volume means more significant movement of the mooring, and this leads to a higher risk of contact between marine mammals and mooring lines;
• Mooring line curvature;
• The curvature of the mooring line is the angle change at a specific point on the mooring line, which is expressed in degrees per meter. The higher curvature of the mooring causes a greater entanglement risk because the bending line could loop around the body of marine mammals.

Following the assessment methods proposed by Harnois et al. (2015) [25], this study takes a different approach to calculating mooring line swept volume for entanglement risk assessment. Parra et al. (2006) indicated that Indo-Pacific humpbacked dolphins, inhabiting the coastal waters of the eastern Indian and Western Pacific Oceans, mostly occur in waters where water depth is shallower than 15 m [26].

2. Methodology

This paper follows the design procedure proposed by Kim et al. (2013) [27]. The overall design flowchart of this study is shown in Figure 6. This study uses hydrodynamic analysis software, ANSYS AQWA (2021 R1), to complete the hydrodynamic diffraction and radiation of the FOWT platform response in the frequency domain. These results are then imported into Orcina OrcaFlex to simulate the coupled interaction of the FOWT system in different environmental forces, which include wave, wind, and current. Moreover, the mooring line swept volume is calculated through programming.

2.1. ANSYS AQWA

ANSYS AQWA is a professional hydrodynamic analysis software based on the boundary element method and finite element boundary method for potential flow solutions. AQWA assumes that the fluid is homogeneous, incompressible, inviscid, and irrotational, and it follows the governing equation as shown in Equation (8). It follows the three-dimensional Green’s function source distribution method, three-dimensional radiation, and three-dimensional diffraction theory to calculate the first- or second-order wave force, added mass, inviscid damping, and hydrostatic stiffness of the floating structure. This introduction refers to the theory of ANSYS AQWA in the Aqwa Theory Manual (2021 R1) [28].

$$F\left(\omega \right)=M_s{X}^{″}F\left(\omega \right)+M_a\left(\omega \right)·X^{″}+B\left(\omega \right)·X^{\prime }+C·X$$

(8)

where $F\left(\omega \right)$ is the sum of the Froude–Krylov excitation force and wave diffraction force, $M_s$ is structure mass (includes the floater itself and ballast), $M_a\left(\omega \right)$ is added mass in the frequency domain, $B\left(\omega \right)$ is radiation damping in the frequency domain, $C$ is the damping coefficient in hydrostatics, and $X^{″}$, $X^{\prime }$, and $X$ are the displacement, velocity, and acceleration of the structure, respectively.

2.2. Orcina OrcaFlex

This study uses OrcaFlex to analyze floating platforms, mooring system designs, stability assessment, and marine space utilization. However, OrcaFlex does not include the calculations of three-dimensional diffraction and radiation in hydrodynamics. Therefore, the hydrodynamic computations are accomplished in ANSYS AQWA in the first place, and the results are imported into OrcaFlex afterward. A time domain calculation of floating structure performance in OrcaFlex is based on the following motion equation:

$$M\left(p,a\right)+C\left(p,v\right)+K\left(p\right)=F(p,v,t)$$

(9)

where $M\left(p,a\right)$ is the inertia force of the floater, $C\left(p,v\right)$ is damping force, $K\left(p\right)$ is stiffness load, $F(p,v,t)$ is the external force acting on the floater, $p,v,a$ are the vectors of displacement, velocity, and acceleration, respectively, and $t$ is simulation time [29].

OrcaFlex provides an implicit time domain integration method to solve motion equations using the generalized-α integration scheme proposed by Chung and Hulbert (1993) [28]. The iterative method is introduced to solve $p,v,a$, the vectors of displacement, velocity, and acceleration, in Equation (9). The lumped mass method is a finite element model used for mooring lines. This approach divides one mooring line into several segments, and the junction points of the segments are called nodes. The segments only model the axial and torsional properties of the line. The other properties (such as mass, weight, and buoyancy) are all lumped into the nodes. The length of each segment can be decided when it is required.

2.3. Convex Hull Algorithm

This study includes the calculations of the mooring line swept volume to quantify the required marine space that an FOWT needs in an offshore wind farm. Analysis of the mooring line swept volume in the water column not only provides an approach to assess the marine spatial planning but also to evaluate the risk of entanglement of marine mammals. The concept of the mooring line swept volume is highlighted in the grey area in Figure 7, simulated using OrcaFlex.

This study uses a convex hull algorithm [30] to calculate mooring line swept volume. A convex hull (illustrated in Figure 8a,b) is defined either as the intersection of all sets containing a given subset in a space, or, equivalently, as the sets of all combinations of points in the subset. It takes a series of points and outputs the indices of the points lying on the boundary of the convex hull. The boundary of the convex hull is the simple closed curve with a minimum perimeter containing all points. This study utilizes the convex hull method based on Jarvis’ March Algorithm, also known as the Gift Wrapping Algorithm). As depicted in Figure 9, this algorithm begins with $i=0,$ and point $p_0$ is the leftmost point in the set. The first point $p_{i+1}$ is selected under the regulation that all points lie to the right of the line $\overline{p_i{p}_{i+1}}$. After wrapping the convex set of points, we can compute the area (volume in 3D) of the selected boundary.

2.4. Fatigue Analysis

Mooring systems experience continuous exposure to cyclic loading from ocean conditions. According to the mooring system failure risk assessment outlined in API RP 2SK [31], this study uses Palmgren–Miner’s rule, combining it with the rainflow counting method. The hypothesis is based on the use of a uniaxial cycle counting method for each load, and the fatigue damages are calculated as follows:

$$D_i=\frac{n_i}{N_i}$$

(10)

where $n_i$ is the number of cycles of operation and $N_i$ is the total number of cycles that produce failure at that stress level. After that, the total damage per year can be defined as the sum of all damages. The event of failure is defined as $D\ge 1.0$.

The American Petroleum Institute (API) (API RP 2SK, 2005) [32] proposed a standard that provides a definition of the tension range related to the fatigue lifetime for each mooring component. In 2008, the API provided the T-N curve corresponding to mooring lines. The number of cycles to failure and the corresponding tension range can be expressed as below:

$$N=K{\left(\frac{T}{RBS}\right)}^{-m}$$

(11)

which can also be given as:

$$\log N=\log K-m\log \left(\frac{T}{RBS}\right)$$

(12)

where $N$ is defined as the fatigue mechanism that occurs when a number of cycles is reached, $T$ is the tension range, $K$ is the intercept parameter of the curve, and $m$ is the slope of the T-N curve.

3. Results and Discussions

This chapter presents the results of the hybrid mooring system supporting the FOWT in various environmental conditions. The analysis encompasses the motion of FOWTs and dynamic tension performance. In addition, the results include an assessment of fatigue and ecology, and the economic aspects of the hybrid mooring system are shown as well, which include mooring cost estimation, fatigue analysis, and entanglement risk assessment.

3.1. Preliminary Screening

According to the standard requirements proposed in DNVGL-RP-0286 [33], DNVGL-OS-E301 [34], DNVGL-OS-E302 [35], DNVGL-OS-E303 [36], and COREWIND D2.1 [37], the following restrictions regarding platform excursion, angular motion, the tension of the mooring lines, and synthetic fiber ropes need to be ensured.

Firstly, the nominal diameters of fibers are determined by checking if the maximum tension exceeds 70% of the MBL. Since the shorter length of fibers in the same total upstretched mooring results in a larger tension of the line (discussed in Section 3.3), cases N10-C600 and P10-C600 are examined. In

Table 9. Tension tests of N10-C600 and P10-C600.

Diameter of Nylon (m)	MBL (kN)	Tension Level ≤ 70% MBL (kN)	Maximum Tension in Simulation (kN)	Pass (O) or Not Pass (X)
0.2	5574	3902	5600	X
0.3	12,540	8778	6126	O
0.4	22,300	15,610	6895	O
Diameter of Polyester (m)	MBL (kN)	Tension Level ≤ 70% MBL (kN)	Maximum Tension in Simulation (kN)	Pass (O) or Not Pass (X)
0.2	6819	4773	8554	X
0.3	15,340	10,738	9367	O
0.4	27,270	19,089	9710	O

, the cases where the maximum tension is larger than 70% of the MBL do not meet the safety requirements recommended by DNVGL and are discarded for safety concerns. Meanwhile, candidates where the maximum tension is smaller than 70% of the MBL are selected. As a result, it is determined that the diameter of nylon and polyester is 0.3 m, and the properties of the chosen materials are organized in

Table 10. Mooring material properties and parameters (provided by OrcaFlex).

Materials	Chain	Nylon	Polyester
Line type/grade	R3 studless	Eight-strand Multiplait	Eight-strand Multiplait
Mass per unit length	685 (kg/m)	58.3 (kg/m)	71.8 (kg/m)
Axial stiffness	3270 (MN)	10,620 (kN)	98,100 (kN)
Minimum breaking load, MBL	22,286 (kN)	12,540 (kN)	15,340 (kN)
Nominal diameter	0.185 (m)	0.3 (m)	0.3 (m)
Drag coefficient ($D_x$)	2.4	1.2	1.2
Drag coefficient ($D_z$)	1.15	0.008	0.008

.

Based on the standard requirements, the maximum surge motion in N80-C530 exceeds 30 m, which results in the maximum allowable length of hybrid nylon being N70-C540. Similarly, the seabed clearance in P110-C500 is less than 0 m, which means that the polyester segment touches the seabed. Therefore, the maximum allowable length of hybrid polyester is P100-C510. In summary, Table 8 presents the final cases simulated and compared in this paper.

3.2. Free Decay

In free decay tests, fluid around the structure causes energy loss in the platform, and the movement of the floater decays under damping effects. Figure 10 is an example of a free decay test presented in the time domain. $x_n$ and $t_n$ are extremum amplitude of motion and corresponding time at $n^{th}$ amplitude. Logarithmic decrement, δ, is used to estimate the damping ratio in the time domain in oscillation movement, and the damping ratio, ζ, is used to describe how oscillation decays after a displacement.

Lamarque et al. (2000) [38] and Wang et al. (2021) [39] indicated that the logarithmic decrement formula, and a dimensionless measure, the damping ratio ζ, can be derived by the following equations subsequently.

$${\Delta }_n=\frac{1}{k}\sum _{n=1}^k\ln \left|\frac{x_n}{x_{n+1}}\right|$$

(13)

$${\mathsf{\zeta }}_n=\frac{{\mathsf{\delta }}_n}{\sqrt{{\left(2\pi \right)}^2+{{\mathsf{\delta }}_n}^2}} where \mathsf{\delta }\triangleq \ln \frac{x_n}{x_{n+1}}$$

(14)

Figure 11 shows the damping ratio results in heave motion. The x-axis is the number of amplitudes that is mentioned above and the y-axis is the damping ratio (%). Generally, the damping ratio decreases when the number of amplitudes increases. N70-C540 has the lowest damping ratio compared to other cases. Since nylon is the lightest in weight and has the lowest stiffness, the total weight of the hybrid nylon mooring system becomes lower. Therefore, the damping capability of the hybrid nylon is lower than the others. This result can also be verified by comparing it with the experimental research conducted by Xu et al. (2021) [7]. Polyester is more effective in restricting the heave motion of Wave Energy Converts (WECs) than nylon due to its higher stiffness and greater damping.

Free decay tests are simulated to obtain natural period results. By Fast Fourier Transform (FFT), free decay results in the time domain being transformed into power spectrum density distributions, which indicates the natural period results of the platform. Figure 12 depicts the surge-free decay tests in the time domain. It is observed that the amplitudes of the pure chain are lower than N70-C540, which means that the damping is more effective in the pure chain than in the hybrid case. It also indicates that the hybrid case leads to a more severe motion of the platform, while the pure chain design has better damping performance.

Natural periods of the FOWT can be obtained by analyzing the power spectrum density results. In Figure 13, the time that the peak value of PSD takes place is the natural period of the motion. The results of the natural period in six DOFs for all cases are summarized in

Table 11. The natural period in six DOFs for all cases.

Natural Period (s)	Pure Chain	N10-C600	N70-C540	P10-C600	P100-C510
Surge	59.8	74.2	121.4	61.6	74.1
Sway	59.3	73.2	119.6	61.1	74.1
Heave	20.4	20.4	20.4	20.4	20.4
Roll	27.2	27.3	27.8	27.2	27.5
Pitch	27.2	27.3	27.8	27.1	27.5
Yaw	64.9	71.5	98.9	65.4	81.1

. It is found that natural periods in heave, roll, and pitch motion are almost the same, which indicates that they are not influenced by different mooring types. The reason for this phenomenon is that these three DOFs are dominated by the hydrodynamic characteristics of the platform itself rather than the mooring system. However, the natural period in surge, sway, and yaw becomes greater as the length of nylon and polyester increases. Since fiber ropes are lighter and more flexible than chains, they need more time to achieve platform stability, and the time period of each oscillation is larger. This explains why the increments in hybrid nylon cases are larger than hybrid polyester cases: nylon is relatively lighter in mass and possesses lower stiffness.

According to Xu et al. (2021) [7], both natural heave and pitch periods of different hybrid moorings are identical. Therefore, this reveals that the results shown in this paper and experimental data are in good agreement.

3.3. Irregular Waves

Figure 14a,b present the statistical results of platform surge and pitch under ULS using a boxplot. Figure 14a shows that N70-C540 has the largest median and maximum surge. Similarly, P100-C510 has a larger surge motion than P10-C600. Longer fiber causes larger surge motion, which indicates that hybrid mooring is less effective in constraining platform excursion. However, in Figure 14b, the pitch value of all cases approximates each other. This means that hybrid mooring does not affect platform pitch motion, and pitch motion is mainly dominated by platform characteristics. Therefore, the efficiency of converting wind power into energy remains the same in hybrid mooring.

Figure 15a,b present the statistical results of tension on Line 1 and Line 2 under ULS using a boxplot. First of all, it can be seen that Line 1 tension is larger because Line 1 is heading toward the environment, where the maximum force is applied. Moreover, it is observed that longer fiber results in smaller maximum, median, and minimum tension, and smaller tension variation. This indicates that hybrid mooring improves tension performance significantly. The fact that hybrid mooring has lower tension variation also causes lower fatigue damage on the mooring line.

Both platform motion and tension results are similar to the experimental data proposed by Xu et al. (2021) [7]. It is verified that hybrid nylon cases have lower overall tension but larger surge motion than hybrid polyester. Moreover, it can be inferred that longer synthetic fiber ropes will increase the surge motion and reduce the tension of the mooring, while the heave motion is not affected noticeably.

3.4. Mooring Costs Estimation

In addition to ensuring the stability of the station-keeping system, it is important to calculate if the levelized cost of energy (LCOE) is sufficiently cost-effective. The overall economics of FOWTs is also a crucial factor in maintaining their viability.

3.4.1. Footprint Area

One of the advantages of hybrid mooring is that it requires less footprint area. This benefit also enhances array arrangement efficiency and improves marine spatial planning. Figure 16 depicts the footprint area of different mooring cases. The platform location is in light blue, and three black points represent three anchors. This study defines the footprint area of FOWTs as follows. First, all mooring touchdown points in the simulation period are tracked and recorded. To present the maximum anchor footprint difference, the farthest touchdown points from the platform, which are the vertices in the triangle under ULS, are chosen. After locating the three farthest touchdown points of the three mooring lines, these points are connected, forming a triangle area that serves as the footprint range.

After that, the footprint area can be quantified for comparison by calculating the area of triangles in Figure 16. Meanwhile,

Table 12. Footprint area comparison.

Case	$\mathbf{Footprint} \mathbf{Area} ({\mathbf{m}}^2$)	Area Reduction
Pure chain	193,182	-
N10-C600	148,878	23%
N70-C540	87,009	55%
P10-C600	183,681	5%
P100-C510	145,050	25%

presents the estimated footprint area. The area reduction in the tables is calculated using the following formula, Equation (15), for comparison between the hybrid mooring and the pure chain case.

$$Footprint area reduction=\frac{{Area}_{Hybrid case}}{{Area}_{Pure chain}}\times 100\%$$

(15)

In Table 12, it is observed that longer fiber cases require less footprint area. The area reduction in the longer nylon case, N70-C540, is up to 55%, while the longer polyester case also reduces the footprint area by 25%. In addition, the area reduction is more noticeable in hybrid nylon than in hybrid polyester. The results indicate that the hybrid mooring system optimizes seabed space utilization, making it a better option for marine spatial planning.

3.4.2. Mooring Costs

This subsection provides an estimation of the mooring costs for all cases, with the minimum breaking load serving as a key factor in the costs of chain and fiber ropes [1]. Klingan et al. (2016) summarize mooring material price per mass, as presented in

Table 13. Properties of various mooring materials related to price.

Property	Chain R3	Nylon	Polyester	Steel Wire
Unit mass of price (EUR/kg) (Klingan, 2016) [40]	2.45	4.116	6.86	4.9
Mass per length (kg/m) [19]	$\mathrm{19,900}\times d^2$	$647.6\times d^2$	$797.8\times d^2$	$3989.7\times d^2$
MBL (kN) [23]	$\mathrm{19,600}\times d^2\times (44-80d)$	$\mathrm{139,357}\times d^2$	$\mathrm{170,466}\times d^2$	$\mathrm{633,358}\times d^2$

. By combining the minimum breaking load (MBL) and price-related properties of the mooring line, the mooring cost dependent on the mooring diameter can be finalized [40]. The mass per length and MBL properties are based on empirical data provided by OrcaFlex [23].

Based on the formula shown in Table 13, the price curve, which includes the minimum breaking load and the price of mooring per length, is presented in Figure 17, where different grades of chains are in black, noted with different types of lines. As seen in the figure, the slopes of the chain curve climb dramatically as the MBL increases, indicating that the price of the chain could be significantly high when a larger MBL is needed. On the other hand, price curves of nylon, polyester, and steel wire are diagonal lines with smaller slopes. This suggests that with the same value of the MBL, nylon is the most cost-effective material and polyester and steel wire have slightly higher costs, while the costs of the chain are the most expensive.

After computing the price per length for selected materials, the mooring costs of all cases in this paper can be calculated by the following formula:

$${Mooring price}_{material}={Price}_{material} \left(\frac{\mathrm{€}}{\mathrm{m}}\right)\ast {Mooring length}_{material}$$

(16)

Since each case has three mooring lines, the total cost of each case in

Table 14. Initial mooring costs of different cases.

Case	Chain	Nylon	Polyester	Sum (EUR)	Cost Reduction
Price (EUR/m)	1669	240	493	-	-
Pure chain	3,053,611	-	-	3,053,611	-
N10-C600	3,003,552	7197	-	3,010,749	1%
N70-C540	2,703,197	50,378	-	2,753,575	10%
P10-C600	3,003,552	-	14,777	3,018,329	1%
P100-C510	2,553,019	-	147,769	2,700,788	12%

is the product of the mooring price per length and three. Furthermore, the cost reduction in the hybrid case is calculated for comparison with pure chain design to quantify the value of the cost-effective characteristics of synthetic fiber ropes. The equation is expressed as follows:

$$Cost reduction=\left(\frac{{Cost}_{Hybrid case}}{{Cost}_{Pure chain}}\right)\times 100\%$$

(17)

It is observed that longer fiber cases have a larger cost reduction. Additionally, it is noticeable that chain material serves as a major cost of the mooring system in all cases. The results show that the hybrid mooring design can effectively reduce the cost of the mooring system for the FOWT, and the cost reduction in P100-C510 in this study is up to 12%.

The bottom chain segment is used to provide the mooring tension when it is suspended in waters, where the weight of the chain is applied to the mooring and the tension gives the restoring force to the platform to restrain its excursion. If a specific section of the bottom chain segment remains on the seabed during the whole simulation period, it means that this section does not suspend in the waters and does not provide the restoring force to the platform. Therefore, theoretically, if this section is removed, the platform and mooring system will not be affected by this adjustment because the restoring force remains the same. This section of the bottom chain segment is named redundant length in this paper (as shown in Figure 18), and it is defined as the length between the farthest touchdown point and the designed anchor point. After removing the redundant bottom chain segments, the overall platform and mooring performance remain the same.

The length of the redundant bottom chain segment can be calculated as follows:

$$Redundant Length=D_{Anchor}-D_{The farthest touchdown}$$

(18)

where $D_{Anchor}$ represents the distance between the specific point and the origin point

After removing the redundant length, the optimal mooring costs can be modified. The optimal mooring cost is calculated by subtracting the cost of the redundant length of the bottom chain. The results are shown in

Table 15. Optimal mooring costs of different cases.

Case	Chain	Nylon	Polyester	Sum (EUR)	Cost Reduction
Price (EUR/m)	1669	240	493	-	-
Pure chain	1,764,448	-	-	1,764,448	-
N10-C600	1,472,612	7197	-	1,479,809	16%
N70-C540	775,643	50,378	-	826,021	53%
P10-C600	1,662,769	-	14,777	1,677,546	5%
P100-C510	1,002,212	-	147,769	1,149,980	35%

. It can be found that the cost reduction increases, indicating that the cost of the mooring system is reduced by removing this redundant length. Meanwhile, Figure 19 presents verification that removing the redundant length of the bottom chain does not affect the platform motion and mooring tension.

3.5. Fatigue Analysis

According to Ridge et al. (2010), nylon is considered a preferable alternative because of its low modulus and cost, but it has poor wet fatigue performance [41]. They propose the operational parameters of different mooring materials in T-N curves. In this paper, a logarithmic scale on the y-axis is used to depict T-N curves for fatigue analysis, as shown in Figure 20. The T-N curve defines the number of cycles to failure.

The fatigue damage under three sea states (shown in Table 1) is cumulated using the rainflow counting method. The weight distribution follows the annual probability, as shown in Table 2. Figure 21 shows the results of the annual fatigue damage at each segment. The blue bars represent the fatigue damage on chain segments in each case, while the other colors represent fiber ropes, with two bars present in hybrid cases. However, the fatigue of the polyester segment is too small to be visible. As observed in the bar chart, nylon exhibits the largest fatigue damage. This observation is consistent with the T-N curve, where nylon can withstand the lowest tension range under the same cycles to failure. However, in comparison between the two hybrid nylon cases, fatigue damage in case N70-C540 is smaller than in N10-C600 because the tension variation in the longer nylon case is smaller than in the shorter nylon case. This fact is also evident in Figure 15a, indicating that longer nylon can reduce fatigue damage in hybrid mooring. On the contrary, fatigue damage in polyester and chain segments is negligible compared to nylon.

3.6. Entanglement Assessment

3.6.1. Mooring Line Swept Volume

This paper utilizes a convex hull algorithm to calculate the mooring line swept volume. All the convex sets, representing the locations of each node in the mooring line in a time series, are tracked and recorded. By wrapping all the scatter points, the maximum swept volume can be obtained. Figure 22 illustrates the convex hull diagrams of the swept volume of mooring lines as an example. The cases are the results of N70-C540 cases under ULS.

In addition, a dimensionless factor called the ‘’swept volume ratio’’ is introduced for comparison. The ratio is based on the concept of the probability of mooring lines coming into contact with marine mammals. A reference water column of mooring line movement, defined in this paper, is depicted in white in Figure 23. It takes the form of a triangular prism, resulting from the product of the seabed’s base area and the perpendicular water depth, representing the limited range of mooring movement. The swept volume ratio, the probability of contact, is calculated as the percentage of the mooring line swept volume divided by the reference water column, as shown in Equation (19).

$$Swept Volume Ratio \left(Probability of contact\right)\left(\%\right)=\frac{Mooring Line Swept Volume \left(m^3\right)}{Reference Water Column \left(m^3\right)}\ast 100(\%)$$

(19)

The results are shown in Figure 24. Line 2 and Line 3 have a greater swept volume than Line 1. Since the environmental conditions mainly apply forces in 0 degrees, the movements of mooring Line 1 generally occur in the x-z plane, inducing a much smaller swept volume. On the contrary, Line 2 and Line 3 have larger swept volumes because of their three-dimensional movements. In addition, it can be found that longer fiber ropes cause a larger mooring line swept volume. Since N70-C540 has the largest surge movement (as shown in Figure 14a), the mooring line swept volume becomes larger. Moreover, given that fiber ropes are lighter than chains, they are easier to push, which leads to a greater swept volume. To conclude, the higher swept volume ratio found in the hybrid mooring system could increase the entanglement risk. Therefore, hybrid mooring is relatively more threatening to marine mammals.

3.6.2. Curvature

Figure 25 presents the maximum curvature along mooring lines under ULS. In Figure 25a, the maximum curvature of the pure chain design occurs at the fairlead point, while the curvatures in the hybrid cases are much lower. Moreover, in Figure 25b,c, hybrid cases result in higher curvature than the pure chain. The surge of the platform leads to the deformation of the catenary mooring shape, causing higher curvature in Line 2 and Line 3. In addition, longer fiber cases exhibit higher curvature results because longer fibers lead to larger surge movement of the platform (as shown in Figure 14a). While the surge motion serves as the major factor influencing curvature, the property discontinuity between different materials might have a minor effect on curvature. Therefore, it can be inferred that hybrid mooring causes larger curvature, especially at joint points, indicating a higher risk of entanglement.

3.6.3. Tension Characteristics

Tension characteristics are computed through static offset tests to obtain the restoring force curve for different mooring configurations. These curves illustrate the relationship between horizontal displacement (surge) on the x-axis and mooring tension on the y-axis. Figure 26 depicts the restoring force curves of Line 1, Line 2, and Line 3, respectively. The tension of the pure chain increases significantly under a small horizontal displacement, indicating a dramatic tension variation in response to a small surge. In contrast, the curves of hybrid moorings are smoother, indicating a more gradual increment of tension when subjected to a small surge. According to the definition by Harnois et al. (2015), the flexibility of slack mooring is the key reason for the higher entanglement risk [25]. Although hybrid mooring provides better tension performance, the lower tension and increased flexibility could raise the entanglement risk.

According to Xu et al. (2021) [7], experimental data show that the lower pretension results in a slack configuration in waves. This finding verifies the high flexibility in the hybrid mooring system. Due to the shorter suspended chain segment length in hybrid mooring, the lower pretension leads to a slacker configuration, posing a higher risk of entanglement based on the definition from Harnois et al. (2015) [25].

In summary, the overall evaluation of entanglement risk, including swept volume, line curvature, and tension characteristics, suggests that hybrid mooring is a less attractive candidate as it leads to larger risk. It is important to note that this study aims to compare the relative risk of entanglement among different mooring configurations rather than determining the absolute risk. To conclude, longer fibers contribute to a higher risk of entanglement, and nylon has a higher risk than polyester due to its lighter weight and elasticity. Moreover, generally, Line 2 and Line 3 (tailing) pose more danger than Line 1 (heading) because of the positive surge motion.

4. Conclusions

This paper presents the feasibility of a hybrid mooring system through static and dynamic analysis under ULS and FLS tests. The discussion includes cost estimation, marine spatial planning, and sustainability assessment, with a focus on evaluating the relative entanglement risk to marine mammals.

Several advantages of hybrid mooring systems are highlighted in this paper. Firstly, hybrid mooring significantly reduces overall tension values and tension variations, ensuring that mooring lines do not experience extreme tension, as is the case with a pure chain configuration. Secondly, the pitch motion, which greatly influences the efficiency of converting wind power into energy, remains unaffected by different mooring designs. Additionally, polyester exhibits better fatigue resistance than nylon, making it a favorable material in hybrid mooring. Furthermore, hybrid mooring not only reduces mooring line costs but also minimizes the footprint area on the seabed, enhancing economic competitiveness and optimizing marine space utilization.

The superior tension performance makes hybrid mooring an excellent choice for floating offshore wind turbines (FOWTs). However, attention must be given to several disadvantages. Larger surge movements are observed in hybrid cases, indicating they are less effective in constraining platform excursions due to lower stiffness and lighter weight. Moreover, the elasticity and larger platform movement in hybrid mooring increase flexibility and result in a larger mooring line swept volume, leading to a higher entanglement risk. This suggests that a hybrid mooring system is a less attractive option for sustainability purposes.

Table 16. Overall comparisons among pure chain and hybrid cases in this paper.

Category		Pure Chain	Hybrid with Nylon	Hybrid with Polyester
Platform stability	Excursion (surge)	Small	Large	Medium
	Inclination (pitch) (related to efficiency)	Medium	Medium	Medium
Mooring system	Tension performance	Worse	Better	Medium
	Fatigue damage	Small	Large	Small
	Footprint area	Large	Small	Medium
	Mooring costs	Large	Small	Medium
Entanglement assessment	Mooring line swept volume	Small	Large	Small
	Mooring line curvature	Small	Large	Medium
	Tension characteristics	Small	Large	Medium

summarizes the advantages and disadvantages of the hybrid mooring system compared to the pure chain case. While hybrid moorings are more attractive in most stability analysis and mooring performance aspects, they could pose a higher entanglement risk when considering marine mammal protection. Achieving a balance between engineering requirements and biodiversity considerations is crucial for future research.