1   Introduction

With the fast-paced growth of the global economy and advances in technology, the demand for mineral resources is constantly increasing. Mineral resources, being nonrenewable and finite, constitute the essential material foundation for human survival and sustainable development. As land-based resources dwindle, it is imperative to redirect focus to alternative resources (Dai and Liu, 2013). Scientific ocean surveys have revealed that the international seabed area beyond national jurisdiction spans approximately 251.7 million square kilometers. This immense area, representing 49% of the earth's surface area, is rich in mineral resources (Yu et al., 2023). Polymetallic nodules, cobaltrich crusts, polymetallic sulfides, rare earth-rich sediments, and other rare minerals are widely distributed on the surfaces of underwater highland bedrock. Marine mineral resources, as a shared heritage of mankind, hold significant potential for development and utilization (Yang and Chen, 2010), adhering to the principle of "whoever has the ability to develop first" (Sterk and Stein, 2015; Chen, 2006).

China, notably reliant on external metal resources, has successfully secured five mining areas from the International Seabed Authority over the past decades. These areas include the Clarion Clipperton (C–C) polymetallic nodule mining area in the Pacific Ocean, the hydrothermal sulfide mining area in the southwest Indian Ocean, and the cobalt-rich crust mining area in the Western Pacific (Du et al., 2016; Xiao et al., 2019). As the mining exploration deadlines approach, China should gradually transition from the exploration stage to the mining stage. However, there is currently no mature and reliable system scheme that can achieve commercial exploitation (Li et al., 2022). Over the past decades, various countries worldwide have proposed different system schemes based on the characteristics of different minerals. In 1960, the University of California developed the tow-type mining system, consisting of a surface mining vessel, tow line, and buckets (Chen, 2006). South Korea's Bukyung University further developed this concept by developing the trawl lifting system based on previous studies (Yoon et al., 2005). Japan introduced the continuous rope bucket mining system (CLB mining method) (Masuda et al., 1971). In 1972, France proposed the shuttle vehicle mining system. In 2006, Shanghai Jiao Tong University developed a decentralized deepsea local test mining system based on previous theories (Ge et al., 2010; Liu et al., 2014). In the 1970 s, the mining method combining underwater mining vehicles and riser transportation gradually became the mainstream direction of research worldwide. This system mainly consists of underwater mining vehicles, rigid and flexible risers, surface mining vessels, and power control systems. The French AFERNOD Association first initiated systematic research on this combination in 1972. By 1978, a structural and mechanical assembly of mining vehicles was created for testing (Heine and Suh, 1978). In 1979, the German Preussag company completed the sea trial production of polymetallic oozers in the Red Sea (Bath, 1989). The technical designs for hydraulic lifting and airlifting systems were both proposed in the same year (Burns and Suh, 1979; Saito et al., 1989). In 1981, the feasibility of a deepsea mining system operating at a depth of 5 000 m of water was verified through simple experiments and calculations (Welling, 1981). The first large surface mining vessel was designed in 1985 (Kaufman et al., 1985). In 1987 and 1990, the former Soviet Union completed system tests in the Black Sea at water depths of 79 m (Kotlinski et al., 2008). In 1996 and 2003, the Indian Institute of Marine Technology (NIO) and the University of Siegen in Germany successfully completed sea trials of a mining system at a depth of 500 m (Wang et al., 2011; Yang and Xia, 2000). South Korea's KRISO successfully completed sea trials of mining vehicles at a depth of 1 370 m and hydraulic lifting tests at 1 200 m in 2013 and 2015, respectively (Sup et al., 2008). In 2021, the Belgian GSR company successfully completed the sea test of a pilot mining vehicle with a production capacity of 100 t/h at a depth of 4 500 m, marking the start of large-scale production testing for deep-sea mineral resources development (Bruyne et al., 2022).

China began deep-sea mining technology in 1991 (Yang and Chen, 2010; Chen, 2006; Tang et al., 2013). After more than 30 years of research and exploration, a mainstream deep-sea mining system scheme consisting of a large surface mining vessel, a lifting system combining rigid and flexible risers, and mining vehicles has been gradually established (Liu et al., 2014; Handschuh et al., 2001). However, stability in harsh weather conditions remains a significant challenge. The entire system needs to be recovered to avoid damage during harsh weather conditions, leading to substantial economic losses and environmental impacts. Consequently, further research and technological innovation are needed to improve the stability and efficiency of deep-sea mining systems. In addition, high construction and maintenance costs pose a major obstacle to the commercialization of these systems (Zou et al., 2023). This paper aims to design, analyze the dynamic response, and conduct experimental research on a new structural form of a deep-sea mining system based on a flexible riser. The goal is to propose a commercial deep-sea mining system that offers stable dynamic performance, low investment costs, better safety, and stronger adaptability to harsh weather conditions.

As an integrated linkage system spanning depths greater than 5 000 m depth span, the dynamic stability and control strategy of the deep-sea mining system are critical research areas. Researchers worldwide have conducted extensive studies on the simulation of risers and deep-sea mining systems. Simulation models and methods are essential for understanding the complex dynamics and behavior of these systems. In 1979, the frequency domain solution of risers under wave action was analyzed (Kirk and Etok, 1979). In 1980, a widely used wave linearization method was proposed for ocean engineering (Krolikowski and Gay, 1980). In 1989, the time-step numerical integration method was adopted to solve the riser motion equation, obtaining the dynamic response of the riser under the action of regular and random waves (Ahmad and Datta, 1989). In 2006, the dynamic response of top tension risers under different wave forces and marine environmental conditions was analyzed (Morkookaza et al., 2006). The dynamic characteristics of risers under different top tension conditions were studied in 2009 (Huera-Huarte and Bearman, 2009). In 2001, the lateral movement characteristics of risers in deep-sea mining systems were examined using the nonlinear finite element method, revealing that higher ship speeds lead to larger horizontal displacement of the riser (Liu et al., 2001). A method to calculate the nonlinear dynamic response of risers under random waves and large amplitude floating structure motions was proposed in 2008, concluding that the dynamic load caused by floating structures is far greater than that caused by waves (Chang et al., 2008). In 2011, a rigid riser model for a 1 000 m water deep mining system in the South China Sea was established by using Abaqus (Liu and Yang, 2012). The dynamic analysis of China's deep-sea mining pilot system scheme was completed in 2012 (Dai and Liu, 2012). In 2014, a modeling method for the flexible multibody in a deep-sea mining system was proposed using Abaqus and Adams (Chen et al., 2014). From the above research, it can be concluded that the geometric nonlinearity and dynamic response nonlinearity of risers are strong under ocean waves and currents (He et al., 2011; Guo et al., 2018). The dynamic stability of the deep-sea mining system presented in this paper faces great challenges owing to the movement of the shuttle tanker and the seabed mining subsystem. This paper focuses on a deep-sea mining system based on flexible risers as the engineering background. The motion characterization of flexible risers with large length-to-diameter ratios in ocean current conditions is researched. A dynamic response analysis prediction model for flexible risers is proposed, providing a scientific basis for enhancing deepsea mining technology. This research identifies key challenges and opportunities for improving the efficiency and sustainability of deep-sea mining operations. The feasibility of the control strategy will be verified by experimental research. In this paper, the deep-sea mining system based on a flexible riser is used as the model. Specifically, a collaborative movement experimental test between two tethered underwater devices in a 20-m-deep water tank was conducted. The results of this research can inform decision-making processes and guide future research in this field, leading to more effective and environmentally responsible practices in deep-sea mining.

2   System composition

This section introduces the composition of the deep-sea mining system based on flexible risers. According to the requirements of each subsystem, the deep-sea mining system is divided into several main parts as shown in Figure 1.

Figure  1  Deep-sea mining system based on a flexible riser

Download: Full-Size Img

• Surface support system: This consists of shuttle tankers.

• Transportation pipeline subsystem: This includes airlifting and hydraulic lifting methods, utilizing rubber pipes and flexible risers according to their respective characteristics.

• Underwater automatic navigation device.

• Seabed mining subsystem: This consists of one seabed mobile station and two mining vehicles.

2.1   Surface support system

The deep-sea mining system based on flexible risers eliminates the need for large surface mining vessels. Instead, multiple shuttle tankers are used as the surface support system as shown in Figure 2. Depending on the actual transportation requirements of the mining area, 2 ‒ 4 shuttle tankers will transport between the mining area and the shore base. The concept of using shuttle tankers for commercial transportation was first proposed by Bath in 1989. As surface support vessels, shuttle tankers need to be capable of transportation, ore storage, ore rough treatment, dehydration, and seawater discharge. Although shuttle tankers do not possess the comprehensive functions of large surface mining vessels, their simpler functionality meets the requirements of this system. To facilitate ore airlifting from a depth of 200 m, each shuttle tanker must be equipped with an air compressor. The main benefits of using shuttle tankers instead of large surface mining vessels include:

Figure  2  Surface support system: shuttle tankers

Download: Full-Size Img

• Cost savings: Shuttle tankers can save on construction and maintenance costs associated with large surface mining vessels and can shorten the construction cycle. These tankers are already used in the deep-sea oil and gas industry and can be leased or retrofitted accordingly.

• Enhanced stability: During deep-sea mining operations, the surface support system and underwater production system are decoupled. This decoupling means that the dynamic response of the surface support system has little influence on the underwater production system, leading to better adaptability to harsh weather conditions.

• Convenient adaptation to weather: In harsh weather conditions, the rubber pipe near the surface can be temporarily disconnected, and the operation of the underwater production system can be paused. The shuttle tankers can then sail away and return to the mining area once the weather improves. This approach reduces the cost of repeated launching and recovery of the underwater production system in harsh weather conditions.

In this system, each shuttle tanker needs to have a minimum ore storage and transportation capacity of at least 100 000 t. The typical operation mode involves the shuttle tanker arriving at the mining area, docking with the rubber pipe, and starting production. After 10 days of loading, the fully loaded shuttle tanker, carrying 100 000 t of ore, will leave the mining area and sail to shore for unloading. Meanwhile, a second shuttle tanker will dock and begin loading at the same time. The number of shuttle tankers required is determined by the distance between the mining area and the shore base.

2.2   Transportation pipeline subsystem

Currently, there is still a high reliance on marine risers made of lighter and sustainable materials for deep-sea resource production (Amaechi et al., 2022a). The transportation pipeline subsystem is the core of the entire deep-sea mining system. This paper will focus on the riser lifting approach. It comprises rubber pipes, flexible risers, multistage hydraulic lifting pumps, surface air compressors, seawater overflow discharge pipes, and control/power equipment. Its main function is to lift ore from the sea floor to the surface.

The transportation pipeline subsystem is mainly divided into two parts. Rubber pipes connecting the underwater automatic navigation device to the shuttle tankers will be used for depths of less than 200 m. A combination of rubber pipes and an airlifting system will be adopted to lift minerals from depths of 200 m to the surface. Rubber pipes, known for their higher flexibility and buoyancy, are widely used in shallow water areas of the deep-sea oil transportation industry. They enable dynamic decoupling of the shuttle tanker and underwater automatic navigation device, reducing the impact of ocean waves and currents on underwater production systems. The airlifting system will be the primary method for lifting minerals from 200 m depth to the shuttle tanker. Each shuttle tanker will be equipped with an air compressor as the main power source for airlifting, facilitating maintenance and repair in case of power equipment failure. This setup reduces the cost of underwater power source maintenance and the risk of damage. Furthermore, replacing large water pumps reduces the volume and weight of the underwater automatic navigation device.

The second part of the underwater transportation pipelines consists of non-metallic flexible risers. These risers connect the underwater automatic navigation device and the seabed mining subsystem, enabling two-phase mineral two-phase flow lifting from the seabed to a depth of 200 m. Typically composed of polymer materials, electrical power lines, and optical fiber lines, flexible risers exhibit good corrosion resistance and can withstand high internal and external pressures. The integration of electrical power lines and optical fiber lines within flexible risers is widely used in the deep-sea oil and gas industry (Reda et al., 2017; Reda et al., 2021; Amaechi et al., 2022b). Therefore, the flexible riser serves not only as a transportation pipeline but also as a major route for power and fiber signal transmission. Non-metallic flexible risers have low bending stiffness and small bending radii, allowing them to be produced in lengths ranging from hundreds to thousands of meters without interfaces (Amaechi et al., 2022c). This facilitates easy storage and installation operations for long risers. A multistage hydraulic lifting pump, installed in the seabed mobile station, will be used to lift minerals through the flexible riser. The main advantages of using hydraulic lifting for the 5 800-m-long flexible riser include:

• The pump is installed on the seabed mobile station, meaning its own weight does not affect the crawler-moving mining vehicle.

• The 5 800-m-long flexible riser remains in a tensioned state, preventing blockage caused by bending under normal conditions.

• Hydraulic lifting improves efficiency and reduces energy consumption (Xiao et al., 2014).

The flexible riser will keep a certain axial pretension for a long time during system operation. This axial tension, generated by the buoyancy of the underwater automatic navigation device, improves the structural dynamic stability of the several-thousand-meter-long flexible riser. It also reduces fatigue in the flexible riser, preventing buckling and other failure problems. Axial tension on the flexible riser is beneficial for the long-distance transportation of sparse coarse mineral two-phase fluids.

During the lifting process, the deep-sea mining system will lift a large amount of seawater to the surface. To address environmental protection concerns, the system will employ in situ seawater reinjection, discharging the lifted seawater back to the seabed.

In conclusion, the combined lifting method of airlifting and hydraulic lifting, tailored to the shape and water depth of the transportation pipeline, significantly improves the safety and reliability of the entire deep-sea mining system.

2.3   Underwater automatic navigation device

The underwater automatic navigation device as shown in Figure 3 is located at a depth of around 200 m. It acts as a relay station connecting the shuttle tankers with the seabed mining subsystem. The following functions highlight its role in the deep-sea mining system:

Figure  3  Underwater automatic navigation device

Download: Full-Size Img

As the connection link between the shuttle tanker and the seabed mining subsystem, the device allows for dynamic decoupling during both production and launching recovery stages.

As an underwater power station, it provides the necessary power for navigation/movement, ore collection, and lifting required by the underwater production system. Underwater floating power plants offer significant safety and cost competitive advantages.

The underwater automatic navigation device includes a temporary mineral storage tank, acting as a transition relay station between hydraulic and airlifting. The hydraulic lifting is powered by the seabed mobile station's hydraulic lifting pump, while the airlifting is powered by the shuttle tanker's air compressor. Once the airlifting system is stable, the air compressor starts working, continuously lifting the seawater to the surface and ensuring that minerals are promptly transferred to the shuttle tankers via airlifting once hydraulically lifted to the underwater automatic navigation device.

The underwater automatic navigation device features AUV automatic navigation motion control. It is equipped with a navigation propulsion system and a dynamic positioning system. During mining operations, the underwater automatic navigation device follows the movement of the seabed mining subsystem, ensuring coordinated motion across the entire deep-sea mining system. In harsh weather conditions, when the shuttle tanker needs to disconnect from the underwater production system, the rubber pipe is supported by a surface buoyancy system. During this stage, the navigation propulsion system and dynamic positioning system play a crucial role in maintaining the underwater fixed position of the production system, thereby increasing system reliability.

During the deep-sea mining operation, the flexible riser connecting the underwater automatic navigation device to the seabed mining subsystem needs to withstand a certain axial pretension over an extended period. This axial tension improves the structural dynamic stability of the thousand-meter-long flexible riser and reduces fatigue. The underwater automatic navigation device requires buoyancy adjustment capabilities to maintain positive buoyancy. By adjusting its buoynancy, it can provide a constant tension to the flexible riser under different operating depths and sea conditions.

2.4   Seabed mining subsystem

The seabed mining subsystem is mainly composed of a seabed mobile station and two mining vehicles. A rubber pipe connects the seabed mobile station to the mining vehicles, significantly increasing their operational range. The seabed mobile station acts as a mineral relay module, equipped with a mineral storage tank, hydraulic lifting pump, ore crusher, and other necessary equipment. It can receive and temporarily store the minerals collected by the mining vehicles and supply the crushed ore at a reasonable concentration into the flexible riser. The mineral storage tank cushions the impact on the flexible riser when ore collection volume fluctuates owing to changes in mineral abundance, enhancing the stability of the ore lifting process parameters and improving the ore lifting efficiency. The hydraulic lifting pump, installed inside the seabed mobile station, lifts ore from the seabed to a depth of 200 m. Its internal ore crusher ensures that the mineral size meets lifting particle size requirements before entering the flexible riser. As crawler-moving robots, the seabed mobile station and mining vessels mainly rely on the grip of track teeth to move on the soft seabed, generating grip through friction with seabed sediments. They require a certain negative buoyancy to generate a ground specific pressure of 5–9 kPa, depending on seabed sediment characteristics, for effectively moving on the soft seabed. GSR company successfully completed a sea trial of a 100 t/h production mining vehicle in 2022 (Bruyne et al., 2022), with a weight in water of around 15 t and a seabed contact area of about 20 m². For commercial volume purposes, the seabed mobile station's weight in water should reach at least 30 t, with a seabed contact area of 40 m². Thus, when the negative buoyancy of the seabed mobile station in water ranges from 20 to 36 t, it can achieve a specific ground pressure between 5 and 9 kPa. Therefore, the influence of flexible riser deformation on the seabed mobile station is acceptable. It is worth noting that the seabed mobile station does not maintain constant negative buoyancy in water.

In 2014, a study verified that an S-shaped pathway could achieve higher coverage of the mining area through numerical simulations and calculations (Han and Liu, 2013). Based on this study, the proposed movement pathway for the seabed mobile station and the entire seabed mining subsystem is outlined below:

As a commercial endeavor in deep-sea mineral resource exploitation, determining production capacity is crucial in designing and operating a deep-sea mining system. Bernard et al.(1987) and Herrouin et al.(1989) estimated the annual production capacity of deep-sea mining systems, establishing a standard of 1.5 million tons of dry weight per year to measure the system's economic viability. This translates to collecting 2.2 million tons of wet nodules annually, or 9 000 t per day, over 240–270 operating days each year (Bernard et al., 1987).

For a deep-sea mining system utilizing flexible risers, each shuttle tanker's mineral storage capacity is about 100 000 t. To ensure that the shuttle tanker can be filled within 10 days, the system production should reach at least 10 000 t per day, equating to 2.5 million tons per year with an expected 250 operating days. Each mining vehicle has a maximum speed of 2 m/s and an average speed of 1 m/s, allowing for a daily moving distance of 86 400 m at average speed. The width of the mining vehicle's collection head is 12 m, composed of 4 groups of hydraulic collection heads, each 3 m wide. Thus, the daily collection area for each mining vehicle is 1 036 800 m². Given an average nodule abundance of 7 kg/m² in the mining area, the theoretical daily production for each mining vehicle can reach 7 257.6 t. With an 80% collection rate, the actual daily production is 5 806.08 t per mining vehicle, allowing the system to achieve a daily production of more than 10 000 t when two mining vehicles operate at the same time.

The seabed mobile station will move along the pathway shown in Figure 4, serving as a temporary storage and transfer station. It needs to coordinate its movement with the mining vehicles' speed. Given a maximum mining vehicle speed of 2 m/s, and based on the pathway shown in Figure 5, the seabed mobile station needs to move 12 m for every 250 m the mining vehicle travels. Therefore, the maximum speed of the seabed mobile station is about 0.1 m/s when the mining vehicle moves at 2 m/s. The seabed mobile station is connected to the underwater automatic navigation device through the flexible riser. The underwater automatic navigation device moves at the same speed as the seabed mobile station. This slower speed reduces water resistance and minimizes flexible riser deformation, enhancing the system's structural stability.

Figure  4  Seabed mobile station movement pathway

Download: Full-Size Img

Figure  5  Seabed mining subsystem movement pathway

Download: Full-Size Img

3   System dynamics analysis

This section will describe the surface wave and current flow field characteristics impacting the flexible riser between the underwater automatic navigation device and the seabed mining subsystem. A model for the flexible riser's loading and motion response model has been developed, yielding the following results: 1) During deep-sea mining operations, the stress, displacement, and spatial morphology of the flexible riser under the influence of ocean waves and currents were determined. 2) The hydrodynamic response

and strength of the flexible riser were analyzed for different ocean current incident angles. In this section, the finite element method is used to calculate the dynamic response of the flexible riser in the deep-sea mining system. The theoretical model and solution method adopted are introduced below.

3.1   Finite element model of the hydrodynamic response of flexible riser

In this section, the finite element method is used to calculate the dynamic response of the flexible riser in a deepsea mining system. The following three basic equations of elasticity are employed to describe the compatibility conditions between the stress, strain, displacement, and external force of the elastomer: dynamic equilibrium equations, geometric equations, and constitute equations.

Stress, strain, and displacement are interconnected through these three basic equations as shown in Figure 6. By solving for one of these quantities using the basic unknowns, the other two can be determined. The Abaqus finite element software was used, with the displacement component selected as the basic unknown.

Figure  6  Compatibility conditions of elastic stress, strain, and displacement variables

Download: Full-Size Img

The core of the finite element method involves dividing the solution domain into a finite number of small units, each connected by unit nodes. The node displacement is taken as the basic unknown, and the displacement function within each unit is approximated using the node values and interpolation functions. When discretizing the flexible riser subjected to ocean waves and currents using Abaqus, the ele‐ment matrix equation is obtained, similar to Equation (1):

where

m_e is the element mass matrix

k_e is the element stiffness matrix

f_e is the element load matrix

Considering the energy dissipation of the structure, the damping matrix C is introduced into the global matrix Equation (2). The matrix Equation (3) is finally solved as follows:

The implicit Newmark method is used to solve Equation (3). This method calculates the displacement X_t+Δt, velocity ̇X_t+Δt, and acceleration Ẍ_t+Δt at time t+Δt based on the known values of displacement X_t, velocity X_t, and acceleration Ẍ _t at time t. The Newmark method assumes that the acceleration varies linearly during the time interval [t, t+Δt] and uses the following displacement and velocity equations:

Substituting Equations (4) and (5) into Equation (3) yields:

The effective stiffness matrix and payload vector are shown in Equations (7) and (8). The displacement of the structure can be obtained through an iterative solution of the external load over a given time interval. The stress and strain of the structure can be obtained by combining the geometric equation and the physical equation.

When $\chi \geqslant 0.5 \text { and } \lambda \geqslant \frac{(2 \chi+1)^2}{16}$ are satisfied, the numerical scheme is unconditionally stable. Its time step can be much larger than the central difference scheme. In this section, the Newmark implicit format is used for the numerical calculation of dynamic response.

3.2   Geometric model and finite element mesh division

Determining the geometry and material of the flexible riser is fundamental to the calculation and analysis process. The geometry selected refers to a nonmetal flexible riser used in the deep-sea oil industry. The key strength indices for the flexible riser include a tensile stiffness of 0.5×10⁶ N and a bending stiffness of 0.45×108 N/m². The flexible riser is assumed to be composed of isotropic materials with uniformly distributed density, having a density of 4 700 kg/m³. The specific parameters for the flexible riser material, as well as the values of hydrodynamic coefficients, are listed in Table 1.

Finite element meshing is a crucial step in finite element numerical simulation analysis as it directly affects the accuracy of the subsequent results. In this paper, the geometric model is established, as shown in Figure 7. For the solid model in the simulation, the PIPE32H element is applied in the Abaqus, which is a three-dimensional second-order hybridization element type. The mesh sizes are uniformly distributed in the circumferential and vertical directions. To verify the sensitivity analysis of the element, simulations were performed with 4 different spatial resolutions for working condition 1, as listed in Table 2. The calculated maximum displacements in the X-direction are listed in Table 3. The results indicate that the maximum displacements remain unchanged when the number of elements exceeds 7 000. Therefore, the total number of elements is selected as 7 000.

Figure  7  Simulated geometric model

Download: Full-Size Img

3.3   Wave and current load conditions

The problem of hydrodynamic load in marine engineering is complicated. The varying shapes of marine structures and different environmental factors can lead to different results. To address this, engineering structures are usually classified according to their characteristics, and targeted calculation methods are adopted.

The diameter of the flexible riser used in this section is 0.332 2 m, classifying it as a small-scale structure. The force problem of small-scale structures under wave action is relatively complicated, making it challenging to obtain practical engineering results by theoretical analysis alone. Therefore, Morison's equation is used to calculate fluid loads, as shown in Equation (9).

where F_D is the viscous resistance caused by the horizontal velocity u of the wave field, F_I is the inertial force caused by the horizontal acceleration $\frac{\partial u}{\partial t}$ of the wave field, ρ_w is the fluid density, C_D is the drag force coefficient, and C_M is the inertia force coefficient.

The values of C_D and C_M are related to the Re, KC, and structural surface roughness. Numerous experiments are usually needed to determine these values for specific structures. In practical marine engineering applications, the values of C_D and C_M are suggested by classification societies and specifications from various countries, as shown in Table 4. In this section, the values are taken in accordance with Chinese specifications.

3.4   Boundary conditions and working conditions

The rubber pipe connecting the shuttle tanker and the underwater automatic navigation device includes a certain length of margin to avoid impact from the shuttle tanker's undulating movements caused by ocean waves and currents. Therefore, the heave of the shuttle tanker will not be considered in this study. The seabed mining subsystem dictates the movement trajectory of the entire mining system. During operation, the seabed mobile station moves along the planned route, with the underwater automatic navigation device above it following the same trajectory. In this research model, the top side is the underwater automatic navigation device, and the bottom side is the seabed mobile station. The flexible riser maintains a certain axial tension force by adjusting the buoyancy of the underwater automatic navigation device. To apply the top pretension, the bottom of the flexible riser is set as a simply supported boundary condition, while an upward displacement is given to the top node. The size of the top pretension can be controlled by adjusting the displacement of the top node. In this research, the top pretension was set to 1.0 G, where G is the value of gravity.

The gravity effects on the flexible riser are simulated by adding acceleration along the vertical direction in Abaqus. The currents and waves are applied to the computational model as line loads as shown in Figure 8. The dynamic response and strength of the deep-sea mining system under steady shear flow are analyzed using different flow field velocities, as shown below: the surface (y = 2 000 m) flow rate is 1.7 m/s, the bottom (y = -4 000 m) flow rate is 0.15 m/s, and the flow rate decreases linearly with increasing water depth. The current incident angle is located in the XOZ plane, with 0° angle being the OX direction; clockwise rotation is considered positive. The effect of ocean waves and currents on the dynamic characteristics of the deep-sea mining system is studied using multiple numerical calculations. These calculations include 5 groups of working conditions designed to explore the influence of ocean current incident angles on the system. The specific working conditions are listed in Table 2.

Figure  8  Current speed and incident angle acting on the system

Download: Full-Size Img

4   Dynamics analysis results

The displacement and stress of the flexible riser under the influence of ocean waves and currents are critical to the safety and stability of the entire deep-sea mining system. The maximum displacement and stress values serve as important references for structural values. The positions where these maximum values occur provide important guidance for the strength design of the system. To validate the model, a comparative analysis was performed on the kinematic response of a single-top tension riser under constant shear flow in the Gulf of Mexico. The dynamics analysis results in this article align with the calculation results by William et al. (2018).

4.1   Spatial morphology and strength analysis of flexible riser

Under working condition 1, the initial spatial morphology of the flexible riser and its spatial morphology after deformation are shown in Figure 9 (t = 50–250 s). The top end of the flexible riser is connected to the underwater automatic navigation device, while the bottom end is connected to the seabed mobile station. Both ends move along the Z-direction and remain relatively static so that the flexible riser generates Z-direction displacement. In this research, the movement speed of the seabed mobile station and underwater automatic navigation device is 0.1 m/s, and only a straight track is considered. The flexible riser is affected by ocean waves and currents in the X-direction, causing the displacement in the X-direction to gradually increase over time. The maximum displacement is 63.29 m.

Figure  9  Comparison between the initial and postdeformation spatial morphology of the flexible riser

Download: Full-Size Img

Figure 10 shows the distribution of flexible riser displacement in the X-direction along its length at different times under working condition 1. As observed from Figure 10, the two ends of the flexible riser are hinged and move along the Z-direction, resulting in zero displacement in the X-direction at both ends. Under this working condition, with the ocean wave and current acting along the X-direction, the flexible riser deformation occurs in the X-direction. The maximum displacement occurs at the lower middle of the flexible riser.

Figure  10  Horizontal displacement of the flexible riser at different times distributed along the riser length

Download: Full-Size Img

Figure 11 illustrates the change in maximum horizontal displacement of the flexible riser over time under working condition 1. The figure indicates that the maximum displacement gradually increases with time, with the growth rate gradually decreasing until it finally stabilizes.

Figure  11  Maximum horizontal displacement of the flexible riser varying over time

Download: Full-Size Img

Figure 12 depicts the distribution of the equivalent stress of the flexible riser along the axial direction caused by the ocean wave and current. The results show that the equivalent stress of the flexible riser caused by ocean waves and currents increases gradually with time, reaching a maximum value near the lower end of the flexible riser before continuously decreasing.

Figure  12  Equivalent stress of the flexible riser distributed along the axial direction

Download: Full-Size Img

4.2   Force analysis at key position (flexible riser connection point)

The connection points of the flexible riser with the underwater automatic navigation device and the seabed mining subsystem are critical stress locations in the deep-sea mining system. The force changes at these points over time, as shown in Figures 13 and 14. Figure 13 illustrates that the force at the joint between the flexible riser and the underwater automatic navigation device gradually increases over time. This is attributed to the movement of underwater automatic navigation devices, which results in a gradual increase in the distance between the two ends. Additionally, the force initially decreases and then increases with the incident angle of the ocean wave and current. When the incident angle of the current is α = 90°, the force at the connection point between the flexible riser and the underwater automatic navigation device reaches its minimum value. The force change characteristics at the connection of the flexible riser and the seabed mining subsystem are similar, as shown in Figure 14.

Figure  13  Force at the connection between the flexible riser and underwater automatic navigation device changing over time

Download: Full-Size Img

Figure  14  Force at the connection between the flexible riser and seabed mining subsystem changing over time

Download: Full-Size Img

4.3   Effect of ocean current incident angle on hydrodynamic response and strength of flexible riser

The following figures illustrate the distribution characteristics of the flexible riser along the axial direction under the influence of different ocean current incident angles. Figure 15 represents the displacement components in the X and Zdirections. The displacement distribution curve in the X-direction changes similarly along the axial direction of the flexible riser under different ocean current incident angles. There is minimal change at both ends and significant change in the middle. When α = 0° and 180°, the current incident angle is either positive or negative along the X-axis, resulting in larger displacement of the flexible riser in the X-direction, with equal magnitude but opposite directions. When α= 90°, the current incident angle aligns with the Z-axis, and the X-direction displacement of the flexible riser is 0, the same as the initial time.

Figure  15  Displacement distribution in the X and Z direction

Download: Full-Size Img

The displacement in the Z-direction changes significantly along the axial direction of the flexible riser, with large displacement in the middle and small displacement at both ends. When α = 0° and 180°, the ocean current incident angle is along the X-axis, so the flexible riser is not affected by the ocean current from the Z-direction. As the underwater automatic navigation device and the seabed mobile station move along the Z-direction, the flexible riser generates the Z-direction displacement. When α= 45° and 135°, the current has a component in the Z-axis, resulting in a larger Z-axis displacement of the flexible riser compared to when α= 0° and 180°. When α= 90°, the current incident angle is aligned in the Z-direction, causing the Z-direction displacement of the flexible riser to be the largest.

Figure 16 shows the distribution of the equivalent stress along the length of the flexible riser caused by different ocean current incident angles at t= 250 s. The results show that when α = 90°, the equivalent stress is minimum, whereas when α = 0° and 180°, the equivalent stress is maximum.

Figure  16  Equivalent stress distribution on the flexible riser caused by different ocean current incident angles

Download: Full-Size Img

5   Collaborative movement test in a water tank

The underwater automatic navigation device and seabed mobile station are the two primary underwater components of the deep-sea mining system that utilizes a flexible riser. Collaborative movement between these two components is a critical characteristic of the system. Therefore, conducting feasibility experimental research and assessing the safety and stability of the entire system are crucial steps. A collaborative movement experimental test system has been designed and constructed within a 20-m-deep water tank. The objective of this test is to verify the feasi‐bility of collaborative movement between the two tethered underwater devices and propose an effective control strategy.

5.1   Water tank test system composition

In practical operating conditions, the underwater automatic navigation device typically follows the movements of the seabed mobile station. However, there are instances where the underwater automatic navigation device takes the lead in guiding the seabed mobile station. Regardless of the operating mode, the control principles of the collaborative movement remain the same. In this section, the operating mode where the seabed mobile station follows the movement of the underwater automatic navigation device is chosen as the water tank test model.

The experimental test system mainly comprises a surface structure, BlueROV, attitude sensor, track system, and cables, as shown in Figure 17. The surface structure can move along the OX direction to simulate the surface support system. BlueROV is used as the underwater automatic navigation device, and the track system replaces the seabed mobile station. BlueROV and the track system are connected via an 18 m optical cable, with an attitude sensor installed on the cable. The attitude sensor simulates the combined navigation and positioning system in the deepsea mining system.

Figure  17  Composition of the water tank test system

Download: Full-Size Img

In the deep-sea mining system, the combined navigation system plays a crucial role in locating and navigating the underwater automatic navigation device and seabed mobile station. Owing to limitations in test conditions, the attitude sensor and depth sensor are used as alternative methods for positioning and navigation. Specifically, three MPU6050 attitude sensors from InvenSense, as shown in Figure 18(a), are installed on BlueROV, the track system, and the connecting cable. These sensors integrate a 3-axis MEMS accelerometer and a 3-axis MEMS gyroscope, allowing measurement of the cable attitude and the relative positions of the two tethered underwater devices. Additionally, a Bar30 depth sensor, as shown in Figure 18(b), is mounted on BlueROV to monitor changes in water depth.

Figure  18  Attitude sensor and depth sensor

Download: Full-Size Img

5.2   Test procedure

After launching BlueROV, the track system, and the cable in the water, the cable remains tensioned owing to the positive buoyancy of BlueROV. The parameters of BlueROV and track system in side view and 3D view are shown in Figure 19. In a stationary state, BlueROV is positioned directly above the track system. Before moving, this yaw angle will be used as the input value for adjusting the yaw angle of the track system. BlueROV is given a motion command to move along the OX axis, with the expected pitch angle of the cable set to 80°. The pitch angle of the cable is continuously adjusted to maintain 80°, and the yaw angle of the track system is continuously corrected to match the input value during collaborative movement. The specific water tank test system parameters are listed below:

Figure  19  Parameters in side view and 3D view

Download: Full-Size Img

5.3   Test result

During this testing phase, direct visual observation of the collaborative movement between BlueROV and the track system is not feasible. Instead, the relative position of these two components is determined by the pitch angle of the cable attitude sensor θ_pitch. The moving direction in the XOY plane is obtained from the yaw angles of BlueROV θ_yaw1 and track system θ_yaw2. The picth and yaw angles are crucial metrics for evaluating the collaborative movement performance of the system underwater. The process of launching BlueROV and track system in water is shown in Figure 20.

Figure  20  BlueROV and track system launching in water

Download: Full-Size Img

The initial pitch angle of the attitude sensor is 88°. The initial yaw angles of BlueROV and track system are 12° and 22°, respectively. When BlueROV starts to move forward, its depth gradually increases under the tension of the cable, and the depth sensor value D_Rstarts to increase. Simultaneously, the track system also starts to move. Fifteen seconds later, the BlueROV depth sensor value stabilizes at around 1.44 m, and the cable maintains a consistent angle. After moving 10 m, BlueROV stops. Subsequently, BlueROV starts to rise and move backward. After moving backward about 3 m, the cable remains upright.

Processing the original data collected by three attitude sensors through MATLAB software generates curves shown in Figure 21 and Figure 22.

Figure  21  Pitch angle curve of the cable's attitude sensor

Download: Full-Size Img

Figure  22  Yaw angle curve of BlueROV and the track system

Download: Full-Size Img

Figure 21 shows the pitch angle of the attitude sensor on the cable θ_pitch slowly decreasing from the initial value of 88° and gradually converging toward the expected value of 80°. It fluctuates within a range of ±2° around 80°.

The distance from the water surface to the BlueROV bottom plate L₁ can be calculated through two methods using Equations (10) and (11).

The values of D_W, h_I, h₃, and L_C can be obtained from Table 5. L₁ can be calculated as 1.67 m using Equation (10).

The BlueROV depth sensor value D_RS is around 1.44 m. The value of h₂ can be obtained from Table 5. L₁ can be calculated as 1.64 m using Equation (11).

The distance from the water surface to the BlueROV bottom plate L₁ calculated by the two different methods shows a very small deviation. This deviation can be attributed to factors such as unknown water density and potential sensor inaccuracies. The results demonstrate the feasibility of BlueROV to move at a consistent depth.

Figure 22 shows the yaw angle of the track system has a large deviation during the first 60 s, with a maximum fluctuation range of about ±10°. Subsequently, from 60 s to 120 s, the fluctuation range decreases to ±5° and gradually converges toward the expected value. In this test, the yaw angle of BlueROV is set as the expected value. The results demonstrate that the track system can adjust its moving direction and follow the yaw angle of BlueROV. Specifically, the maximum deviation during the first 60 s can be attributed to the 10° deviation between the initial yaw angles of BlueROV and the track system.

As concluded from the above test, the track system exhibits the capability to continuously adjust the moving speed and moving angle through sensor data feedback. This adjustment ensures a stable relative position and synchronized moving direction between BlueROV and the track system. The tests successfully demonstrate the feasibility of collaborative movement between the two tethered underwater devices.

6   Discussion

To meet the requirements for commercial exploitation of deep-sea mineral resources, this paper proposes a deep-sea mining system utilizing a flexible riser. In the second section, the system's working mode, composition, and operation characteristics of each subsystem are introduced in detail. The system offers advantages such as stable dynamic performance, low investment cost, enhanced safety, and better adaptability to harsh weather conditions.

To verify the system stability under the linkage motion of the underwater automatic navigation device and the seabed mobile station, the hydrodynamic response and strength of the flexible riser are examined in the third and fourth sections. The results show that the flexible riser will experience displacement during system linkage operation, with the maximum displacement occurring in the middle and lower sections owing the the riser's own weight. The maximum displacement increases gradually over time, with the growth rate decreasing and eventually stabilizing. The spatial morphology of the flexible riser does not change significantly once the maximum displacement becomes stable, indicating that the system undergoes notable morphological changes initially, but these stabilize over time.

The force at the connection joint between the flexible riser and the equipment gradually increases as the equipment starts to move, with the increase rate decreasing over time. Once the system's spatial morphology stabilizes, the force also becomes stable.

The research considers the influence of ocean currents from different incident angles. The results show that the incident angle of the ocean current affects the system's morphology and equivalent stress. When α = 90°, the equivalent stress is minimized, whereas at α = 0° and 180°, the equivalent stress is maximized.

To study the feasibility of collaborative movement between two tethered underwater devices, an experimental test is conducted in a 20-m-deep water tank in the fifth section. The test results demonstrate the feasibility of collaborative motion by collecting the attitude sensor data and analyzing the relative position and yaw angle of the two tethered underwater devices during collaborative movement. The successful implementation of collaborative movement further validates the reliability and efficacy of the control strategy proposed in this paper.

After analyzing the system composition, working mode, operating characteristics, dynamic performance, and experimental research of the deep-sea mining system based on a flexible riser, the system's feasibility and stability have been preliminarily verified. However, factors such as system construction, assembly, and integration will also affect system feasibility. Therefore, the feasibility discussed in this paper is preliminary and has certain limitations. As a new structural form of a deep-sea mining system, many problems still need to be solved and further researched. In future studies, the rubber pipe at the surface and near the seabed will be considered for dynamic simulations. The pathway planning of the seabed mobile station will be researched to explore the stability of the overall system when the seabed mobile station moves with acceleration, deceleration, and turning. These future studies will be significant for the detailed design and development of the deep-sea mining system based on a flexible riser.

In the dynamic response analyses of this article, the boundary conditions and current loading conditions are simplified to intuitively reflect the morphological changes of the flexible riser. In future research, detailed and more accurate ocean current conditions and boundary condi‐tions, based on actual ocean conditions of the mining area, will be considered to make the simulation results increasingly closer to actual operations. The structural characteristics of the flexible riser will also be considered in future detailed research and analysis.

In the experimental research, an attitude sensor was used as a simple navigation and positioning method. However, it will not be used further in commercial systems. Instead, USBL/LBL beacons, inertial navigation, and DVL systems with higher positioning accuracy will be employed. The experimental test aims to propose and research a collaborative movement control strategy suitable for commercial systems using a simple navigation and positioning method, thus verifying the feasibility of collaborative movement between two tethered underwater devices.

7   Conclusions

This paper proposes the composition of a deep-sea mining system based on a flexible riser, along with its subsystems. It studies the strength and hydrodynamic response of the flexible riser in the deep-sea mining system under system linkage operation through numerical simulations. The feasibility of collaborative movement between the two tethered underwater devices is verified by experimental research.

1) The overall system scheme of the deep-sea mining system based on a flexible riser is proposed.

2) The composition and operational characteristics of the deep-sea mining system and its subsystems are comprehensively proposed.

3) A strength and hydrodynamic response analysis model of the flexible riser in the deep-sea mining system is established. Numerical simulations and analysis of the strength and hydrodynamic response of the flexible riser are conducted under system linkage operation in ocean current conditions.

4) The spatial morphology of the flexible riser and the stress characterization at key positions under the system linkage operation in ocean current conditions are determined.

5) The displacement and equivalent stress of the flexible riser caused by different ocean current incident angles are analyzed. The hydrodynamic response characteristics of the flexible riser caused by different ocean current incident angles are obtained.

6) A collaborative movement test was conducted in a 20-m-deep water tank, leading to the development of a control strategy for collaborative movement. The experiment successfully validated the feasibility of collaborative movement between two tethered underwater devices.