Simulation Study on the Sediment Dispersion during Deep-Sea Nodule Harvesting

Abstract

During the harvesting of polymetallic nodules on the seabed, the sediment plume due to disturbance on the seabed impacts the benthic ecosystem. A numerical simulation based on the SPH (smooth particle hydrodynamics) method is used to estimate the time and length scale of the plume impact near the seabed during a small-scale harvesting process. The simulation result considerably agrees with the one from the lab-scale water-channel experiment. It is found that, in the sediment plume, the traced sub-plume with iso-surface of lower sediment concentration travels a longer distance, and spends a longer time to achieve the stable state. Moreover, with the increase of the releasing rate of the disturbed sediment, the sub-plume spreads over greater distance, which also needs more time to achieve the stable state.

1. Introduction

With the increasing demand on the various resources in the ocean, the harvesting of the deep-sea polymetallic nodules, which is widely distributed on the surface of seabed, has attracted great interest in recent years [1]. Many countries, including China, have been given the access to explore the deep-sea nodules in Clarion-Clipperton Fracture Zone (CCZ), east Pacific Ocean. However, the harvesting process considerably disturbs the surface sediment all over the mining area as shown in Figure 1, which would produce a large-scale sediment plume [2], and may considerably impact the deep-sea ecosystem [3]. Therefore, it is essential to estimate the suspending time as well as the spreading area of the sediment particles before re-settling, in order to assess the environmental impact before the formal harvesting process is applied. Up to date, a number of works has been carried out to investigate the evolution of the sediment plume by field observation as well as numerical simulation [4,5,6,7,8,9,10]. However, more work needs to be done before an accurate and robust way to access the sediment plume impact is developed.

The particle-based simulation method, smoothed particle hydrodynamics (SPH) is a Lagrangian formulation of the generalized Navier–Stokes equations, which has been successfully used to model the behavior of particle suspensions [11,12], and near-field sediment transport simulation [13,14,15,16]. Tran-Duc et al. used a 3D SPH simulation to study the sediment dispersion, where the harvester is modeled as a source point producing sediments at a certain releasing rate [17]. In this study, we start from the SPH simulation proposed by Tran-Duc et al. [17]. The dispersion behavior of the sediment plume achieving a stable sate is analyzed at different sediment releasing rate in order to assess the size of the impact area during the mining process. Moreover, a lab-scale dispersion experiment is carried out, which shows good agreement with the numerical calculation.

2. Methods

2.1. Numercial Simulation

2.1.1. Govern Equation

The momentum equation controlling the sediment transportation is written as

$$\frac{Du}{dt}=-\frac{1}{\rho }\nabla P+\frac{1}{\rho }\nabla ·\left(\mu \nabla \mathit{u}\right)+\frac{\rho -{\rho }_f}{\rho }\mathit{g},$$

(1)

where $\mu$ and $\rho$ are the mean viscosity and density of the sediment plume, and ${\rho }_f$ is the density of the sea water. $\rho$ can be calculated as

$$\rho ={\rho }_f+\left(1-\frac{{\rho }_f}{{\rho }_s}\right)c,$$

(2)

where ${\rho }_s$ is the density of a sediment particle, and $c$ is the local sediment concentration in the plume. In addition,

$$\mu ={\mu }_m+{\mu }_T,$$

(3)

where ${\mu }_m$ and ${\mu }_T$ are the dynamic viscosity and turbulent viscosity, respectively. ${\mu }_m$ is a function of the sediment concentration. Here, it is estimated as

$${\mu }_m={\mu }_f{\left(1-\frac{\varnothing }{{\varnothing }_{max}}\right)}^{-2.5{\varnothing }_{max}},$$

(4)

according to the Krieger–Dougherty model [18], where $\varnothing =c/{\rho }_s$ is the volume fraction of the sediment, ${\varnothing }_{max}\approx 0.64$ [19] is the maximum packing volume fraction, and ${\mu }_f$ is the viscosity of sea water.

It is assumed that the sediment plume contains particles with $N_p$ sizes. The concentration distribution of particles of each size satisfies the following diffusion equation

$$\frac{D{c}_k}{dt}=-c_k\nabla ·\mathit{u}-\nabla ·\left({\mathit{w}}_{s,k}{c}_k\right)+\nabla ·\left(v_T\nabla c_k\right)+f_k{s}_c,$$

(5)

where $k=1,\dots ,N_P$, and $c_k$ is the particle concentration, $w_{s,k}$ is the settling velocity of the particles, and $f_k$ is the mass fraction of the particles of a certain size. $s_c$ is the source term production the sediment. $v_T$ is the turbulent diffusion rate, which is expressed in matrix form due to its anisotropic nature. For the anisotropic diffusion rate [20], it can be expressed as

$$v_T=\left(\begin{array}{ccc}{v}_{\mathrm{H}}& 0& 0\\ 0& v_{\mathrm{H}}& 0\\ 0& 0& v_v\end{array}\right),$$

(6)

where $v_{\mathrm{H}}$ and $v_v$ are the horizontal and vertical turbulent diffusivity coefficients, respectively. $v_{\mathrm{H}}=0.01 m^2/s$ is considered to be constant near the bottom boundary [17]. And according to the basic mixing length of the theory, $v_v=l_m{}^2{\gamma }_z$, where ${\gamma }_z$ is the shear rate normal to the current direction. We adopt the standard model, $l_m=\kappa$z when $z<\frac{\lambda \mathsf{\delta }}{\kappa }$ and $l_m=\lambda \delta$ elsewhere. $\kappa$ is the von Karman constant, and $\lambda$ = 0.08 is a model parameter. $\delta$ is the thickness of the boundary layer.

The items on the right end in Equation (5) respectively represent the weak compressibility of the fluid (caused by the SPH numerical calculation method), particle settling, turbulent diffusion, and the release of sediment in the harvesting area (source term). In addition, the total concentration of sediment can be expressed as

$$c={{\displaystyle \sum }}_{k=1}^{N_p}{c}_k,$$

(7)

For the items on the right end of the diffusion equation, considering the interaction between the particles, the settling velocity of the particles can be expressed as [21]

$$w_{s,k}=w_{s,k}^0{\left(1-\mathsf{\Phi }\right)}^a,$$

(8)

where $w_{s,k}^0$ is the single particle settling velocity without considering the particle interaction. According to Stokes theorem, it can be expressed as

$$w_{s,k}^0=\left(\rho -{\rho }_f\right)g{d}^2/18{\mu }_f,$$

(9)

where $g$ is the acceleration due to gravity and $d$ is the particle diameter.

For the source term, we assume that the initially released sediment has a Gauss distribution in the horizontal direction and a natural exponential distribution in the vertical direction. Therefore, the local mass flow of released sediment can be expressed as

$$s_c=s_{c,0}\exp \left[-\frac{{\left(x-x_0\right)}^2+{\left(y-y_0\right)}^2}{2{\sigma }^2}-\gamma z\right],$$

(10)

in which $x_0$ and $y_0$ are the location coordinates of the mining vehicle, and $\sigma$ and $\gamma$ represent the horizontal (x and $y$) and vertical ($z$) disturbance parameters, respectively. Therefore, the total mass flow rate ($M_{\mathrm{s}}$) of the sediment can be related to the local mass flow rate by

$$M_s=\int s_{c}dV\mathrm{or}{s}_{c,0}=\frac{M_s\gamma }{2\pi {\sigma }^2},$$

(11)

Due to the limited computing power to assess the dispersion area of the sediment plume achieving a stable state. We set $M_S$ as $0.69\mathrm{k}$ g/s and $1.38\mathrm{kg}/\mathrm{s}$, respectively, in the simulation to model the sediment disturbed during a small-scale mining process. The releasing rate of $1.38\mathrm{kg}/\mathrm{s}$ is $1/10$ of the releasing rate proposed during a full-scale harvesting process [17].

2.1.2. Simulation Model and Boundary Condition

The computation domain is shown in Figure 2, with a dimension of $\left(L_x,L_y,L_z\right)=\left(600 \mathrm{m},210 \mathrm{m},22 \mathrm{m}\right)$. The current is along the x-axis and follows the power law distribution along the z-axis, written as [17]

$$u_c\left(z\right)=\frac{{\overline{u}}_c}{\frac{z_0}{H}-1+\ln \left(\frac{H}{z_0}\right)}\ln (\frac{z}{z_0}),$$

(12)

in which $H$ is the height of the domain, ${\overline{u}}_c$ is the average velocity of the current, and $z_0$ is the roughness of the bottom. In the simulation, the bottom boundary (seabed) is set to be non-slip boundary, and the upper boundary is considered to be a uniform flow condition (natural free boundary conditions), i.e.,

$$\frac{\partial u_x}{\partial z}=\frac{\partial u_y}{\partial z}=\frac{\partial P}{\partial z}=0,$$

(13)

The periodic boundary condition is applied to the side faces normal to y-axis, and the outflow boundary normal to the x-axis satisfies (natural free boundary conditions)

$$\mathbf{n}·\nabla \mathbf{u}=\mathbf{n}·\nabla P=0,$$

(14)

where $n$ is the unit vector normal to the outflow boundary. In order to include the effect of deposition and erosion/resuspension process of the sediment at the bottom during the transportation, two factors, namely deposition factor, $f_d$, and erosion factor, $f_e$, are identified in the calculations. The boundary condition at the bottom can be expressed as

$${\left(\frac{dc}{dt}\right)}_{bottom}=\frac{\partial }{\partial z}\left(f_d{w}_{s}c+f_e{R}_e\right),$$

(15)

where $f_d$ is the deposition factor, which is a function of the current-induced bottom shear stress [22]

$$f_d=\left\{\begin{array}{c}1-{\tau }_b/{\tau }_d \mathrm{if} {\tau }_b<{\tau }_d \\ 0 \mathrm{if} {\tau }_b\ge {\tau }_d\end{array}\right.,$$

in which ${\tau }_d$ is critical bottom shear stress for deposition, beyond which the deposition phenomenon hardly occurs.

A strong bottom shear stress could also break the weakly bonded sediment flocs at the bottom into smaller fragments and resuspend them into the ambient water, which is known as bottom erosion. It is an extra source of sediment resuspension. An erosion factor is then defined as [22]

$$f_e=\left\{\begin{array}{c} 0 \mathrm{if} {\tau }_b<{\tau }_d\\ {\tau }_b/{\tau }_e-1\mathrm{if} {\tau }_b\ge {\tau }_d\end{array}\right.,$$

where the parameters are adopted according to van Rijin [22], and listed in

Table 1. Parameters used in the simulations.

Parameters	Value	Unit
Ocean water density ${\rho }_f$	1045	${\mathrm{kg}/\mathrm{m}}^3$
Dry sediment density ${\rho }_s$	2650	${\mathrm{kg}/\mathrm{m}}^3$
Initial wetted sediment density	1350	${\mathrm{kg}/\mathrm{m}}^3$
Critical stress for erosion ${\tau }_e$	0.18	${\mathrm{N}/\mathrm{m}}^2$
Critical stress for deposition ${\tau }_d$	0.1	${\mathrm{N}/\mathrm{m}}^2$
Bottom erosion rate $R_e$	${10}^{-4}$	${\mathrm{kg}/\mathrm{m}}^2\mathrm{s}$
Vertical distribution $\gamma$	2.0	$1/\mathrm{m}$
Horizontal distribution $\sigma$	10	$\mathrm{m}$
Horizontal diffusivity $v_H$	0.01	${\mathrm{m}}^2/\mathrm{s}$
Current velocity $u_c^f$	0.04	$\mathrm{m}/\mathrm{s}$
Lateral shift $\Delta S$	5	$\mathrm{m}$

.

2.1.3. Smoothed Particle Hydrodynamics (SPH)

In the SPH simulation, each SPH particle represents a fluid particle, which has physical properties of volume, mass, density, sediment concentration. For SPH particles, the pressure gradient and the viscosity term are rewritten as

$$-{\left(\frac{1}{\rho }\nabla P\right)}_i=-{{\displaystyle \sum }}_j{m}_j(\frac{P_i}{{\rho }_i^2}+\frac{P_j}{{\rho }_j^2}){\nabla }_i{W}_{ij},$$

(16)

and

$${\left(\frac{1}{\rho }\nabla ·\left(\mathsf{\mu }\nabla \mathit{u}\right)\right)}_i=\frac{2}{{\rho }_i}{{\displaystyle \sum }}_j\frac{V_j{\overline{\mu }}_{ij}}{r_{ij}}{\mathit{u}}_{ij}\frac{\partial W_{ij}}{\partial r_{ij}} ,$$

(17)

where $i$ and $j$ are the particle indices,${\nabla }_i{W}_{ij}=\partial W_{ij}/\partial {\mathit{r}}_{ij}=\partial W_{ij}/\partial r_{ij}{\widehat{\mathit{r}}}_{ij}$ is the gradient of the weight function $W_{ij}$ along x-axis, $r_{ij}=\left|{\mathit{r}}_{ij}\right|=\left|{\mathit{x}}_i-{\mathit{x}}_j\right|$, ${\widehat{\mathit{r}}}_{ij}={\mathit{r}}_{ij}/r_{ij}$. ${\mathit{u}}_{ij}={\mathit{u}}_i-{\mathit{u}}_j$, ${\overline{\mu }}_{ij}=\left({\mu }_i+{\mu }_j\right)/2$ are the difference of the velocity and the average viscosity, respectively. The continuity equation is discretized as

$$-{\left(c_k\nabla ·\mathit{u}\right)}_i={\left(c_k\right)}_i{{\displaystyle \sum }}_j{V}_j{\mathit{u}}_{ij}·{\nabla }_i{W}_{ij},$$

$${(\nabla ·\left({\mathit{w}}_{s,k}{c}_k\right))}_i={\displaystyle \sum }_j{V}_j\left[{\left({\mathit{w}}_{s,k{c}_k}\right)}_i+{\left(w_{s,k{c}_k}\right)}_j\right]·{\nabla }_i{W}_{ij},$$

(18)

$${(\nabla ·\left(v_T\nabla c_k\right))}_i=2{\displaystyle \sum }_j{V}_j\frac{{\left(c_k\right)}_{ij}}{r_{ij}}{\left({\displaystyle \sum }_{l=1}^3\frac{e_{ij,l}^2}{v_l}\right)}^{-1}\frac{\partial W_{ij}}{\partial r_{ij}},$$

where ${\left(C_k\right)}_{ij}=\left[{\left(C_k\right)}_i-{\left(C_k\right)}_j\right]/2$ [23]. The antisymmetric nature of the SPH settlement term and diffusion term formula ensures the conservation of sediment mass. In other words, the sediment received by an SPH particle is exactly equal to the sediment loss of its neighboring particles and thus the method is conservative. The sediment transport process (sedimentation and turbulent diffusion) of SPH particles plus additional sediment from sediment sources allows a changing in the sand content with time. The quality of SPH particles changes with the change of sand content according to

$$\Delta m_i=\left(1-\frac{{\rho }_f}{{\rho }_s}\right)·c_i{V}_i$$

(19)

where $V_i$ is the particle volume.

The weight function used in the simulation is a harmonic function [24]

$$W_5\left(r,h\right)={\alpha }_d\left\{\begin{array}{c}1 \eta =0\\ {\left(\frac{\sin \left(\pi \eta /2\right)}{\left(\pi \eta /2\right)}\right)}^5 0<\eta \le 2 \\ 0 \eta >2\end{array}\right.$$

(20)

where $\eta =\frac{r}{h}$ is the particle distance normalized by the smooth length $h$. Through numerical experiments [25], for the harmonic weight function, choosing h to be $1.2$ times the spatial resolution ($∆x$) can reduce the numerical errors in the SPH calculation, so this value is adopted here. In addition, the effective domain radius $R_w$ of the weight function is twice the smooth length of the selected weight function.

Due to the large amount of storage space and the large number of SPH particles required, three-dimensional SPH simulations for the sediment dispersion on the ocean scale are extremely challenging. For this reason, a parallel algorithm based on the memory distributed message passing interface (MPI) platform is proposed. Accordingly, the simulation domain is divided into $N_{CPU}$ domain components along the longest side in the x direction. The length of each component is $L_i=\frac{l_x}{N_{CPU}}$, which is processed by a $CP{U}_i$, as shown in Figure 3. The detailed parallel method is introduced by Tran-Duc et al. [17].

2.1.4. Simulation Parameters

In the simulation, the source point releasing the sediment is set at $\left(L_x,L_y,L_z\right)=\left(25 \mathrm{m},100 \mathrm{m},0 \mathrm{m}\right)$, as shown in Figure 2. The average flow rate is set to be $4\mathrm{cm}/\mathrm{s}$, which approaches the average flow rate near the seabed in CCZ from the survey [25]. The size of particles in the sediment, as well as the mass fraction and sedimentation velocity adopt in the simulation, according to the particles size distribution from the Peru Basin, Pacific Ocean [26], are shown in the

Table 2. Particle sizes, settling velocities, and mass fraction of the sediment adopt in the simulation.

Sizes	$\mathbf{Diameter}{\mathit{d}}_{\mathit{k}}$ $\left(\mathsf{\mu }\mathbf{m}\right)$	Settling Velocity ${\mathit{w}}_{\mathit{s},\mathit{k}}^0$ (m/s)	Mass Fraction ${\mathit{f}}_{\mathit{k}}$
1	>100	5.367$\times {10}^{-4}$	0.14
2	60–100	2$\times {10}^{-4}$	0.10
3	20–60	8.15$\times {10}^{-5}$	0.36
4	<20	2$\times {10}^{-5}$	0.40

. Other values of parameters used in the simulations are shown in the Table 1, in which initial wetted sediment density is the density of the sediment-water mixture at the releasing source (with the sediment concentration of 20%).

2.2. Laboratory Experiments

In order to verify the rationality of the SPH simulation, a lab-scale water-channel experiment was carried out, as shown in Figure 4. We adopted a water channel with the dimension, $\left(L_x,L_y,L_z\right)=\left(16 \mathrm{m},0.5 \mathrm{m},0.6 \mathrm{m}\right)$. A bentonite–water mixture with the concentration of $15\mathrm{wt}\%$ ($150,000\mathrm{ppm}$) was prepared to simulate the natural sediment. The bentonite particle has a similar density ($2.65\mathrm{g}/{\mathrm{cm}}^3$) and the particle size distribution to the natural sediment particles. A peristaltic pump was used to discharge the bentonite-water mixture placed in the beaker into the water channel through a tube, and the discharging port was located in the middle between side walls of the tank, and is $0.1\mathrm{m}$ from the bottom of the channel with adjustable discharging rate by controlling the rotational speed of the pump. Four turbidimeters (RBRmaestro3, RBR, Canada, measuring range from $0$ to $325\mathrm{ppm}$ with the error less than $2\%$) were deployed in the downstream area as shown in Figure 4 to evaluate the concentration of sediment particles in the plume at different distances from the source. The flowing velocity in the channel was set to $0.1\mathrm{m}/\mathrm{s}$. Since the experiment was limited by length of the channel, the turbidity can only be measured at the maximum dispersion distance of $11\mathrm{m}$.

3. Results and Discussion

The reliability of this numerical simulation was first checked by the laboratory experiment introduced above. As shown in Figure 5, in the experiment that with increasing releasing rate from $0.4\mathrm{g}/\mathrm{s}$ to $1.2\mathrm{g}/\mathrm{s}$, the concentration in the sediment plume increases within the discharging distance investigated. For comparison, the numerical simulation adopting the same working condition was applied. The calculation domain in this case, $\left(L_x,L_y,L_z\right)=\left(120 \mathrm{m},20 \mathrm{m},3 \mathrm{m}\right)$. As shown in Figure 6, change of the solid concentration with the dispersion distance was calculated at the height of $0.1\mathrm{m}$ above the bottom boundary in the center of the channel. Comparing Figure 6 with Figure 5 it can be observed that evolution of the turbidity with the dispersion distance is different at the distance smaller than $10\mathrm{m}$, which is due to different manners of sediment discharging method applied in the experiment (releasing at the height of $0.1\mathrm{m}$) and in the numerical simulation (releasing at the bottom boundary), and therefore, the peak turbidity was not captured at the height of $0.1\mathrm{m}$ in the simulation. In order to validate roughly the simulation result at larger dispersion distance, evolution of the turbidity measured from the experiment was fitted by an empirical model $c=a_1{e}^{b_{1}x}+a_2{e}^{b_{2}x}$, where $x$ is the dispersion distance from the source along the stream direction. $a_1$, $a_2$, $b_1$, and $b_2$ are parameters to be fitted by the experimental data and listed in

Table 3. Parameters adopt for fitting of the experimental data in Figure 5.

Parameters	${\mathit{a}}_1$	${\mathit{b}}_1$	${\mathit{a}}_2$	${\mathit{b}}_2$
0.4 g/s	1.779	−0.4451	0.29	−0.004554
0.8 g/s	4.606	−0.4534	0.7353	−0.008562
1.2 g/s	6.449	−0.3878	1.077	−0.008167

. Consequently, the sediment concentration at larger distance can be estimated, as shown in Figure 5. Comparing Figure 6 with Figure 5, it can be found that the concentration in the sediment plume calculated numerically is close to the lab-scale experimental result at the discharging distance larger than $10\mathrm{m}$, showing that our numerical simulation captures reasonably the behavior of the sediment plume.

Based on our simulation method, the large-scale evolution of the sediment plume during the mining process was investigated. As shown in Figure 7 and Figure 8, with the sediment releasing rate, $M_s=0.63\mathrm{kg}/\mathrm{s}$, after sediment particles being released to the environment, it diffuses with the current near the bottom, producing a sediment plume mainly at the downstream area, and the sediment concentration in the plume decreases from the source center to the edge of the plume. Iso-surfaces of sediment concentration with typical concentrations were traced to investigate the affection area due to suspending of sediment particles with different concentration.

We traced the sub-plume in the sediment plume with the concentration $c\ge 180\mathrm{mg}$/L, i.e., the surface of the sub-plume is an iso-surface with the sediment concentration, $c=180\mathrm{mg}/\mathrm{L}$. It can be found that the sediment is dispersed mainly along the stream direction (x-direction), and the sub-plume becomes stable at $\mathrm{t}\approx 0.5\mathrm{h}$, meaning that the sub-plume with $c\ge 180\mathrm{mg}$ quickly settles with the duration of $\mathrm{t}\approx 0.5\mathrm{h}$, and the dispersion distance from the source, X, is about $50\mathrm{m}$. When we focus on the sub-plume with $c\ge 63\mathrm{mg}/\mathrm{L}$, as shown in Figure 8, it can be found that the settling becomes much slower. The sub-plume becomes stable at $\mathrm{t}\approx 3.5\mathrm{h}$, with $\mathrm{X}\approx 470 \mathrm{m}$. Obviously, the sediment plume with a lower concentration travels a longer distance downstream from the releasing source before the stable state is achieved.

With $M_s$ increased to $1.38\mathrm{kg}/\mathrm{s}$, as illustrated in Figure 9, for the sub-plume with $c\ge 63\mathrm{mg}/\mathrm{L}$, the behavior is similar, while the sub-plume becomes stable with the duration, $\mathrm{t}\approx 5\mathrm{h}$, which is obviously longer than the condition when $M_s=0.69\mathrm{kg}/\mathrm{s}$. Furthermore, the dispersion distance, X, increases considerably to $720\mathrm{m}$, for the iso-surface of $63\mathrm{mg}/\mathrm{L}$. From Figure 7, Figure 8 and Figure 9, it can be found that the behavior of the dispersion distance along y-axis, Y, follows the same trend as X, while Y is much less than X, and it becomes stable with a much shorter period of time.

The temporal evolution of the advancing distance of the iso-surface is shown in Figure 10 and Figure 11. Clearly, iso-surfaces with different sediment concentrations, $\mathrm{c}$, all evolve in the same manner. A constant dispersion distance can be approached indicating that the sub-plume finally becomes stable. And the constant distance increases significantly with increasing of the releasing rate of the sediment at the source.

From the SPH simulation, it was found that the duration and the distance of the spreading of the sub-plume in the sediment plume depends on the concentration of the iso-surface traced. Therefore, it is important to determine a critical concentration above which the impact on the seabed environment should be a real concern. This critical concentration can then be adopted in order to estimate the impact area based on the simulation data. However, research on the benthic habitats in the CCZ is still insufficient [27]. According to a survey from the GSR company in Clarion-Clipperton Fracture Zone in 2017, the mean background sediment concentration at the height of 3.5 m from the seabed is 0.57 FTU (0.074 ppm). And it has been pointed out that benthic communities can survive in the sea water if the sediment concentration does not exceed the background level by more than $25\mathrm{mg}$/L [28]. Although this is not specific for the CCZ, it provides us a rough criterion for assessment of the magnitude of environmental impact due to dispersion of the sediment plume. Therefore, in the future work, the temporal evolution of the sub-plume with concentration larger than $25\mathrm{mg}$/L is suggested to be traced for the purpose of environmental assessment during the polymetallic nodules mining process. Moreover, the releasing rate of the sediment needs to be adjusted according to the real working condition. These, however, require a much larger computation domain as well as the time cost. Furthermore, particles in the bentonite sediment are cohesive, which results in particle aggregation and promotes settling of the sediment [29,30]. This property has not been considered in the present numerical simulation. These need to be further investigated in the near future.

4. Conclusions

A numerical simulation based on the SPH method was used to estimate the time and length scale of the impact near the seabed due to dispersion of the sediment plume during a small-scale harvesting process, and the result was found to agree with the one measured from the lab-scale water-channel experiment. It is indicated in the simulation that when achieving a stable state, the sub-plume with an iso-surface of a lower sediment concentration disperses a longer distance from the releasing source, and spending a longer time to achieve the stable state. Moreover, with the increase of the releasing rate of the sediment, the sediment plume spends more time to achieve a stable state, with a significant longer dispersion distance from the releasing source. It is suggested that the numerical method proposed could reasonably evaluate the area of impact on the benthic communities during the harvesting process by tracing the sub-plume with the iso-surface at the sediment concentration of $25\mathrm{mg}$/L.