Air-Lift Pumping System for Hybrid Mining of Rare-Earth Elements-Rich Mud and Polymetallic Nodules around Minamitorishima Island

Abstract

REE-rich mud under the seabed at a 5500–5700 m water depth around Minamitorishima island and polymetallic nodules buried in the deep seabed are very promising and attractive to explore and develop. REEs are critical to develop due to the recent paradigm shift to renewable energies based on green technologies. Numerical analysis using a one-dimensional drift–flux model for gas–liquid–solid three-phase flow and gas–liquid two-phase flow was conducted to examine the characteristics of an air-lift pumping system for mining these mineral resources. Empirical equations of REE-rich mud and the physical properties of polymetallic nodules around Minamitorishima island were utilized in the analysis. As a result, the characteristics, i.e., the performance of the system, were clarified in three cases: REE-rich mud, polymetallic nodules, and both. The time transient, i.e., the unsteady characteristics of the system, was also shown, such as the start-up and feeding slurry with REE-rich mud and polymetallic nodules. The findings from the unsteady characteristics will be useful in considering the operation of a real project or a commercial system in the future.

1. Introduction

Rare-earth elements-rich mud (REE-rich mud hereafter), which also contains micro-sized polymetallic (manganese) nodules, was found under the seabed at a 5500–5700 m water depth around Minamitorishima island [1,2,3]. Also, polymetallic (manganese) nodules are buried in the surface of the deep seabed in this area [4]. REE-rich mud exists on the east side of Tahiti in the South Pacific and also around Hawaii in the Central Pacific [5]. It has attracted attention due to its volume and composition, comprising materials such as REEs, manganese, nickel, cobalt, etc. The exploration and development of these mineral resources is urgent because of the recent paradigm shift from fossil fuels to renewable energy sources through lower carbon technologies.

In this study, an air-lift pumping system, as shown on the left side of Figure 1, is applied for mining REE-rich mud and polymetallic nodules from the deep sea. The system is composed of a mining ship, in which an air compressor and a gas–liquid–solid separator are installed; a lifting pipe; an air pipe; and a mining unit, including an excavator, a collector, and a classifier on the seabed.

The system transports mud or ores from the seabed to the sea surface through a lifting pipe continuously by use of seawater flow driven by the hydrostatic pressure difference between the inside and outside of the lifting pipe when compressed air is input from the middle of the lifting pipe via the air injection point.

When lifting REE-rich mud, there is slurry flow, i.e., a mixture of REE-rich mud and seawater below the air injection point, and two-phase flow with air and slurry above the air injection point. In the case of lifting polymetallic nodules, there is two-phase flow with seawater and polymetallic nodules below the air injection point and three-phase flow with air, seawater, and polymetallic nodules above the air injection point. Further, in the case of lifting both REE-rich mud and polymetallic nodules, there is two-phase flow with slurry and polymetallic nodules below the air injection point and three-phase flow with air, slurry, and polymetallic nodules above the air injection point. Lifted slurry with REE-rich mud and polymetallic nodules is classified by the gas–liquid–solid separator on the mining ship.

The air-lift pumping system is one of the hydraulic dredging systems. The other is an ESP (electric submersible pump) system, as shown on the right side of Figure 1, which utilizes several electric submersible pumps installed in series on the lifting pipe. The advantage of the air-lift pumping system is that it is maintenance-free, as there are no specific devices underwater compared with the ESP system. Therefore, the air-lift pumping system is likely used for relatively deep seas (5000 to 6000 m water depth). Allseas Ltd. (Châtel-Saint-Denis, Switzerland) lifted polymetallic nodules amounting to about 3000 tons, 86.4 tons per hour, from the seabed around Hawaii in 2022 using an air-lift pumping system from the Deep Research Technology company [6,7]. On the other hand, the JOGMEC (Japan Organization for Metals and Energy Security) lifted clashed hydrothermal polymetallic ores continuously by use of an ESP system from 1600 m water depth in the Okinawa trough in 2017 [8].

The efficiency of an air-lift pumping system, however, is generally lower than that of an ESP system. Several schemes have been devised to increase efficiency. For example, back pressure is specified at the exit of the lifting pipe and introduces pressurized air to the inlet of the air compressor such that the required power is reduced. In addition, applying back pressure keeps the mixture velocity at the exit of the lifting pipe at a lower level such that erosion inside the lifting pipe and the gas–liquid–solid separator is reduced. Further, another option is to use a centrifugal classifier on the seabed to selectively classify highly REE-rich mud.

In Japan, the Technology Research Association of Manganese Nodule Mining System composed of a government agency and related private enterprises also cooperating with the National Research Institute was organized, and then the large-scale national project, the Manganese Nodule Mining System, was started in FY 1981 to explore and develop the polymetallic nodules from the deep seabed around Hawaii [9]. During the project, which ran until FY1997, the Air-Lift Pumping System Working Group conducted several laboratory tests and a pilot test to design and manufacture pieces of machinery for an air-lift pumping system [10].

Research and development activities have been also conducted to explore REE-rich mud around Minamitorishima island in the second stage of the Cross-ministerial Strategic Innovation Promotion Program. In 2022, a pilot test was conducted to excavate and convey mud continuously at the rate of 70 tons per day from the seabed of 2470 m water depth, offshore from Ibaragi prefecture [11].

The Consortium for Promotion of REE-Rich Mud and Manganese Nodule Development was organized at the University of Tokyo in 2014 to examine various kinds of technologies for mining REE-rich mud and polymetallic nodules under the deep seabed around Minamitorishima island, such as the exploration, environmental monitoring, dredging and lifting systems and mineral processing, and smelting [12]. In the consortium, an experimental study was conducted to explore the optimum conditions of a hydrocyclone; one of the centrifuge classifiers that selectively classifies highly REE-rich mud [13]. Shimizu et al. measured the viscosities of the slurries with REE-rich mud after classification to determine the flow characteristics when lifting highly REE-rich mud [14].

In this study, numerical simulations of the air-lift pumping system are conducted to examine the mechanical characteristics of transporting REE-rich mud and polymetallic nodules from the deep seabed around Minamitorishima island using a one-dimensional drift–flux model [15]. The drift–flux model was originally developed for gas–liquid two-phase flow. The model is an approximate formulation compared to more rigorous multi-phase formulations. The velocities are expressed in terms of the center-of-mass velocity of the mixture and the drift velocities as functions of flow regimes. The scheme does not account for the complexity of multiphase flow such as fluid turbulence and interactions between each phase on a microscopic scale. However, because of its simplicity and applicability to a wide range of multi-phase flow problems of practical engineering interest, the drift–flux model is of considerable importance. For the application of the air-lift pumping analysis as they apply to mining mineral resources, such as REE-rich mud and polymetallic nodules from the deep seabed, it is sufficient to consider the flow in the axial direction, i.e., one-dimensionally, because the ratio of the pipe diameter to the total pipe length of the lifting pipe is very small (on the order of 10⁻⁴–10⁻⁵). Hatakeyama [16] and Hatakeyama et al. [17,18] extended the scheme for gas–liquid–solid three-phase flow by considering the drift velocities of the solid phase and then applied the one-dimensional scheme for simulations of an air-lift pumping system, which transports polymetallic nodules from the deep seabed. In previous research, Shimizu et al. [19] conducted numerical simulations using a one-dimensional drift flux model to find out the optimum mining conditions for REE-rich mud. However, the cases of mining polymetallic nodules and of mining both REE-rich mud and polymetallic nodules at the same time (hybrid mining, hereafter) have not been examined. Also, the dimensions of scale in previous research were not large enough to yield a profitable production rate. Therefore, in this study, a one-dimensional drift–flux model is applied for the analysis of mining polymetallic nodules and REE-rich mud, considering gas–liquid–solid three-phase flow and gas–liquid two-phase flow. The dimensions of scale are larger than those used in previous research [19] to meet a profitable production rate. Slurry mixed with REE-rich mud and seawater is regarded as a pseudo-plastic fluid (a non-Newtonian fluid). Empirical equations, derived from experiments [14,20] representing the flow characteristics for both the original slurry mixed with REE-rich mud and seawater and slurry mixed with REE-rich mud after the classification process were utilized. The simulation results are shown for the cases of transporting REE-rich mud only, polymetallic nodules only, and hybrid mining, i.e., both. Also, parametric studies were conducted to examine the effect of parameters on the lifting characteristics. The lifting characteristics of REE-rich mud are compared between the cases using empirical equations of the original slurry with REE-rich mud and those of the underflow (UF) slurry after classification by the hydrocyclone. In the case of polymetallic nodules, different particle sizes and a drag coefficient were utilized. The lifting characteristics were also compared by changing the back pressure at the exit of the lifting pipe. The unsteady-state characteristics, i.e., the time transient of the system are also shown. These results should provide useful information for operating an air-lift pumping system on upcoming large-scale projects or in commercial production systems.

2. Numerical Scheme: One-Dimensional Drift–Flux Model for Two- and Three-Phase Flow

The numerical scheme used in the study is a one-dimensional drift–flux model based on previous studies by Hatakeyama [16] and Hatakeyama et al. [17] for mining polymetallic nodules. Gas–liquid–solid three-phase flow and gas–liquid two-phase flow analyses are applied for mining both REE-rich mud and polymetallic nodules.

The momentum equation of the mixture, i.e., the gas–liquid–solid three-phase flow is given by Equation (1).

$$\begin{array}{l}{\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }t}}\left({\rho }_M{V}_M\right)+{\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }z}}\left({\rho }_M{V_M}^2\right)\\ =-{\displaystyle \frac{\mathsf{\partial }{P}_M}{\mathsf{\partial }z}}-{\displaystyle \frac{4{\tau }_W}{D}}+{\rho }_{M}g-{\displaystyle \frac{\mathsf{\partial }\left({\rho }_G{F}_G{W_G}^2\right)}{\mathsf{\partial }z}}-{\displaystyle \frac{\mathsf{\partial }\left({\rho }_L{F}_L{W_L}^2\right)}{\mathsf{\partial }z}}-{\displaystyle \frac{\mathsf{\partial }\left({\rho }_S{F}_S{W_S}^2\right)}{\mathsf{\partial }z}}\end{array}$$

(1)

${\rho }_M$ in Equation (1) represents the density of the mixture, evaluated by Equation (2).

$${\rho }_M=F_G{\rho }_G+F_L{\rho }_L+F_S{\rho }_S$$

(2)

$V_M$, which represents the center-of-mass velocity of the mixture, is given by Equation (3).

$$V_M=\left(F_G{\rho }_G{V}_G+F_L{\rho }_L{V}_L+F_S{\rho }_S{V}_S\right)/{\rho }_M$$

(3)

where $P_M$: pressure of the mixture [Pa(G)], ${\tau }_W$: shear stress by pipe friction [Pa], $D$: pipe diameter [m], $g$: gravitational acceleration [m/s²], ${\rho }_k\left(k=G,L,S\right)$: density of the $k$-phase [kg/m³], $G$: Gas, $L$: Liquid, $S$: Solid, $F_k\left(k=G,L,S\right)$: volume fraction of the $k$-phase [-], $W_k=V_k-V_M\left(k=G,L,S\right)$: relative velocities of the $k$-phase to the center-of-mass velocity of the mixture, [m/s], $V_k\left(k=G,L,S\right)$: velocities of the $k$-phase [m/s], $t$: time [s], $z$: coordinate in the axial direction of the lifting pipe, from bottom to top [m].

The mass conservation equation of the mixture is given by Equation (4).

$${\displaystyle \frac{\mathsf{\partial }{\rho }_M}{\mathsf{\partial }t}}+{\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }z}}\left({\rho }_M{V}_M\right)={\mathrm{\Gamma }}_G+{\mathrm{\Gamma }}_L+{\mathrm{\Gamma }}_S$$

(4)

where ${\mathrm{\Gamma }}_k\left(k=G,L,S\right)$ is the generation term of the $k$-phase per unit volume [kg/(m³·s)].

The mass conservation equation of the gas-phase is given by Equation (5).

$${\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }t}}\left(F_G{\rho }_G\right)+{\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }z}}\left(F_G{\rho }_G{V}_G\right)={\mathrm{\Gamma }}_G$$

(5)

The mass conservation equation of the solid phase is given by Equation (6).

$${\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }t}}\left(F_S{\rho }_S\right)+{\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }z}}\left(F_S{\rho }_S{V}_S\right)={\mathrm{\Gamma }}_S$$

(6)

Also,

$$F_G+F_L+F_S=1$$

(7)

Using these equations, the time transient of the center-of-mass velocity of the mixture, pressure, and volume fraction of the gas, liquid, and solid in each phase is traced in each section along the lifting pipe.

The relative velocities of the $k\left(=G,S\right)$-phase to the center-of-mass velocity of the mixture are evaluated by the drift velocities of the $k\left(=G,S\right)$-phases to the flux of the mixture $J_M$, which is defined by Equation (8).

$$V_{k\_dfj}=\left(C_{k0}-1\right)J_M+V_{kj}\begin{array}{cc}\hspace{1em}& \left(k=G,S\right)\end{array}$$

(8)

Parameters used in the drift velocity of the gas-phase $V_{G\_dfj}$ are shown in

Table 1. Parameters used in the drift velocities of gas-phase [21].

Flow Regime	${\mathit{F}}_{\mathit{G}}$ Range	${\mathit{V}}_{\mathit{G}\mathit{j}}$	${\mathit{C}}_{\mathit{G}0}$
Bubble flow	$F_G\le 0.2$	$\sqrt{2}{\left({\displaystyle \frac{\sigma g\Delta \rho }{{{\rho }_L}^2}}\right)}^{1/4}{\left(1-F_G\right)}^{1.5}$	$1.2-0.2\sqrt{{\rho }_G/{\rho }_L}$
Slug flow	$0.3\le F_G\le 0.7$	$0.35{\left({\displaystyle \frac{g\Delta \rho D_P}{{\rho }_L}}\right)}^{1/2}$	$1.2-0.2\sqrt{{\rho }_G/{\rho }_L}$
Annular flow	$F_G\ge 0.8$	${\displaystyle \frac{1-F_G}{F_G+4\sqrt{{\rho }_G/{\rho }_L}}}{\left({\displaystyle \frac{\Delta \rho g{D}_P\left(1-F_G\right)}{0.015{\rho }_L}}\right)}^{1/2}$	$1+{\displaystyle \frac{1-F_G}{F_G+4\sqrt{{\rho }_G/{\rho }_L}}}$

Note that a linear approximation was adopted for evaluating $V_{Gj}$ in the range of 0.2 to 0.3, and 0.7 to 0.8.

and specified in each flow regime. The volume of the gas expands toward the exit in the lifting pipe, such that the flow regime changes depending on the volume fraction of the gas-phase. The flow regime is classified into three types, i.e., bubble flow, slug flow, and annular flow, depending on the volume fraction of the gas-phase [21]. A linear approximation is adopted in a range between the two flow regimes, $0.2\le F_G\le 0.3$ and $0.7\le F_G\le 0.8$, to evaluate the parameters. The scheme used in the previous research [19] is adjusted to fit the high-volume fraction of the gas-phase by adding the annular flow regime and the transition.

The drift velocity of the solid phase is derived using the hindered settling velocity of the particle system $V_{Sj}$, which is expressed using the voidage function $F_0(\epsilon )$. Equation (9) is employed in this study to determine $V_{Sj}$ [22,23].

$$V_{Sj}=-V_{SS}{F}_0(\epsilon )=-V_{SS}{\epsilon }^{1.35}$$

(9)

where

$V_{SS}$: terminal velocity [m/s],

$\epsilon$: porosity, defined in Equation (10).

$$\epsilon =1-{\displaystyle \frac{F_S}{F_L+F_S}}={\displaystyle \frac{F_L}{F_L+F_S}}$$

(10)

Also, the distribution parameter for the solid phase $C_{S0}$ is calculated by using Equation (11).

$$C_{S0}={\displaystyle \frac{1.2V_L}{J_M}}$$

(11)

Akagawa’s equation, shown by Equation (12) is used to evaluate the pressure drop of the mixture $\Delta P_M$ [24,25].

$$\Delta P_M=\Delta P_L{\left(1-F_G\right)}^{-Z_a}$$

(12)

where $Z_a$ is the parameter used in Akagawa’s equation.

$\Delta P_L$ in Equation (12), which represents the pressure drop of the liquid-phase, is given by Equation (13).

$$\Delta P_L=\lambda {\displaystyle \frac{{\rho }_L}{2}}{J_L}^2{\displaystyle \frac{L}{D}}$$

(13)

For mining REE-rich mud, slurry mixed with REE-rich mud and seawater is categorized as a pseudo-plastic fluid as defined by Equation (14).

$$\tau =K{\dot{\gamma }}^n$$

(14)

where $K$: the flow consistency index [Pa·sⁿ], $n$: the flow behavior index [-].

The parameters defined in the pseudo-plastic fluid, i.e., the flow consistency index $K$ and the flow behavior index $n$ depend on the volume concentration of mud in the liquid-phase $C_X$.

Hanamura et al. [20] tested the viscosities of slurry with REE-rich mud sampled from the deep seabed around Minamitorishima island and derived empirical equations as shown by Equations (15) and (16), which show relations between the flow consistency index $K$, and the flow behavior index $n$ versus the volume concentration $C_X$ in the range of 0 to 10%.

$$K={\mu }_0\left(8.91\times {10}^6{C_X}^{2.83}+1.0\right)$$

(15)

$$\begin{array}{l}n=-1.85{C_X}^{0.282}+1.0\begin{array}{rrr}\hfill & \hfill & \hfill \end{array}\left(0\le C_X\le 0.05\right)\\ n=-0.639C_X+0.237\begin{array}{rrr}\hfill & \hfill & \hfill \left(0.05\le C_X\le 0.10\right)\end{array}\end{array}$$

(16)

Also, Shimizu et al. measured the viscosities of slurry with REE-rich mud classified by a hydrocyclone [14]. The slurry is divided into the underflow (UF) slurry including coarser particles, and the overflow (OF) slurry with fine particles. The UF and OF slurries represent the flow characteristics of the pseudo-plastic fluid as well as the original slurry (ORG). The UF contains a high concentration of REEs because they are adsorbed in coarse-sized biogenic calcium phosphates (BCP), the host-phase of REE-rich mud [13].

Figure 2 shows the flow consistency index $K$ versus volume concentration $C_X$. In the figure, the solid line shows an approximation curve with power equations for the UF, Equation (17). The dashed line shows the empirical equation from Hanamura et al. [20]. The flow consistency index $K$ increases when the volume concentration $C_X$ increases. The characteristics of the ORG are similar to those of Hanamura’s equation. Under the same volume concentration $C_X$, the flow consistency index $K$ of the UF is small compared with the ORG.

Figure 3 demonstrates the flow behavior index $n$ versus volume concentration $C_X$. In the figure, the solid line shows an approximation curve with power equations, Equation (18) represents the case of the UF. The dashed line shows the empirical equations from Hanamura et al. [20]. The flow behavior index $n$ decreases when the volume concentration $C_X$ increases. Under the same volume concentration $C_X$, the flow behavior index $n$ of the UF is large compared with the ORG.

For the UF, the flow consistency index $K$ is small, and the flow behavior index $n$ is large compared with the ORG under the same volume concentration. In the latter simulation, Equations (15) and (16) are used for the original slurry without a hydrocyclone. Equations (17) and (18) are used for the underflow slurry classified by a hydrocyclone.

$$K={\mu }_0\left(6.76\times {10}^5{C_X}^{2.56}+1.0\right)$$

(17)

$$n=-1.09{C_X}^{0.175}+1.0$$

(18)

The pressure drop $\Delta P_L$ is evaluated using these empirical equations by previous studies [20,26,27,28]. Note that the pipe friction factor under turbulent flow, is calculated using formulas by Kemblowski and Kolodziejski [29] in the case of a smooth circular pipe, and the equations derived by Masuyama and Hatakeyama [27] in the case of a rough circular pipe.

For mining polymetallic nodules, $\Delta P_L$ is evaluated by Equation (19) under the assumption that the solid phase exists in the liquid-phase. Note that an additional frictional dissipation of energy should be considered in the case of the solid-liquid two-phase flow with coarse particles through the horizontal and inclined pipe.

$$\Delta P_L=\lambda {\displaystyle \frac{{\rho }_L}{2}}{\left(J_L+J_S\right)}^2{\displaystyle \frac{L}{D}}$$

(19)

Equations (1) and (4)–(6) are integrated over the control volume and discretized by using the finite volume method. The pressure and volume fraction of each phase are defined at the center of each control volume. The velocities are defined at the boundary between two control volumes. Figure 4 shows the overall flow chart of the program. The time in the analysis proceeds with the time-step $\Delta t$. At each time, the center-of-mass velocity of the mixture and the pressure are evaluated temporarily at first, and then the volume fractions of each phase are evaluated based on the center-of-mass velocity of the mixture and the pressure. The iteration procedure is repeated until the errors of these valuables decrease within the criteria. The SIMPLE scheme is adopted to solve the fluid properties. Also, the first-order upwind difference scheme is used for convective terms in momentum and mass conservation equations.

3. Verifications, Comparisons with Published Experimental Data

3.1. Lifting Characteristics of Water

Figure 5 shows the lifting characteristics of water, i.e., the lifted water versus the input air under normal conditions by plotting experimental data from previous studies [30,31,32,33,34] and the calculated results. The solid lines in the figure represent the related calculations.

Table 2. Model dimensions used for calculations (water).

Case	HW	L	LE	LO	LU	RS	D	Previous Studies
	[m]	[m]	[m]	[m]	[m]	[-]	[m]
1	440	448	100	8	340	0.926	0.3	Weber and Dedegil [30]
2	135	143	130	8	5	0.942	0.3	Weber and Dedegil [30]
3	2.08	2.74	1.988	0.663	0.09	0.75	0.0409	Heywood et al. [31]
4	9	12.5	8.15	3.5	0.85	0.7	0.0757	Usami and Yamakado [32]
5	200	212.6	184	12.6	16	0.936	0.151	Saito et al. [33]
6	200	212.6	130	12.6	70	0.912	0.151	Saito et al. [33]
7	200	212.6	100	12.6	100	0.888	0.151	Saito et al. [33]
8	200	212.6	71	12.6	129	0.849	0.151	Saito et al. [33]
9	193	196.5	184.3	3.5	8.7	0.981	0.1023	Shimizu and Takagi [34]

$H_W$: water depth of air-lift pump (length of lifting pipe from sea surface to bottom) [m], $L$: total length of lifting pipe [m], $L_E$: length of lifting pipe from sea surface to air injection point [m], $L_O$: length of lifting pipe over sea surface [m], $L_U$: length of lifting pipe under air injection point [m], $R_S\left(=L_E/\left(L_E+L_O\right)\right)$: submerged ratio [-].

shows the model dimensions used for the calculations based on the parameters of the related previous experiments. For all cases, as the input air increases, the lifted water increases, and the curves have a convex upward shape. The calculated results are in good agreement with the experimental ones across the various dimensions of experimental apparatuses.

3.2. Lifting Characteristics of Mud

Figure 6 shows the lifting characteristics of slurry, i.e., the lifted slurry versus the input air by plotting experimental data from previous studies [31,32,34] and the calculated results. The solid lines in the figure represent the related calculations.

Table 3. Model dimensions used for calculations (mud). Abbreviations are defined in Table 2 (see also Figure 6).

Case	HW	L	LE	LO	LU	RS	D	Previous Studies
	[m]	[m]	[m]	[m]	[m]	[-]	[m]
1	2.08	2.74	1.988	0.663	0.09	0.75	0.0409	Heywood et al. [31]
2	9	12.5	8.15	3.5	0.85	0.7	0.0757	Usami and Yamakado [32]
3, 4	193	196.5	184.3	3.5	8.7	0.981	0.1023	Shimizu and Takagi [34]

and

Table 4. Material properties used for calculations (mud).

Case	Water	Solid		Slurry			Previous Studies
	Density	Material	Density	CX	K	n
	[g/cm3]		[g/cm3]	[%]	[Pa·sn]	[-]
1	1.0	Kaolin	2.58	8.1	1.55	0.242	Heywood et al. [31]
2	1.0	Bentonite	2.6	1.88	7.05 × 10−3	0.593	Usami and Yamakado [32]
3	1.07	Bentonite	2.6	2.62	2.75	0.152	Shimizu and Takagi [34]
4	1.065	Bentonite	2.6	3.17	4.68	0.156	Shimizu and Takagi [34]

show the model dimensions and material properties for calculation based on the parameters of the related previous experiments, respectively. The lifting characteristics of slurry are similar to those of water. That is, when the input air increases, the lifted slurry increases, and the curves have a convex upward shape. Similar tendencies are observed in the calculations compared with the experimental data. In Case 2, the lifted slurry flow rate of the calculation is larger than that of the experiment under the same air flow rate. The dashed line shows the results of changing the flow consistency index $K$ to 10 times the original value. The calculated results are sensitive to this parameter in this case.

3.3. Lifting Characteristics of Gravel

Figure 7, Figure 8 and Figure 9 show the lifting characteristics of gravels, i.e., water and solid flux versus the mass flow rate of lifted solids by plotting the experimental data from previous studies [9,30,33] and the calculated results. The solid, the dashed and the dashed-dotted lines represent the related calculations. The dotted lines represent $C_S\left(\equiv J_S/\left(J_L+J_S\right)\right)$.

Table 5. Model dimensions used for calculations (gravel). Abbreviations are defined in Table 2 (see also Figure 6).

Case	HW	L	LE	LO	LU	RS	D	Previous Studies
	[m]	[m]	[m]	[m]	[m]	[-]	[m]
1	279	286	178	7	101	0.962	0.3	Weber and Dedegil [30]
2	321	328	220	7	101	0.969	0.3	Weber and Dedegil [30]
3	443	450	246	7	197	0.972	0.3	Weber and Dedegil [30]
4	48.2	55.4	42	7.2	6.2	0.854	0.3	Weber and Dedegil [30]
5	200	212.6	184	12.6	16	0.936	0.102	Shimizu et al. [9]
6	200	212.6	150	12.6	50	0.923	0.102	Shimizu et al. [9]
7	200	212.6	117	12.6	83	0.903	0.102	Shimizu et al. [9]
8	200	212.6	71	12.6	129	0.849	0.102	Shimizu et al. [9]
9	200	212.6	184	12.6	16	0.936	0.151	Saito et al. [33]

The variables representing the dimensions of the pipe are the same as those shown in Figure 5 and Figure 6.

and

Table 6. Material properties used for calculations (gravel).

Case	Gravel			Previous Studies
	Particle Dia. DP	Drag Coef. CD	Density
	[mm]	[-]	[g/cm3]
1–4	5	1.21	2.575	Weber and Dedegil [30]
5–8	15	1.17	2.65	Shimizu et al. [9]
9	15.6	1.34	2.65	Saito et al. [33]

, respectively, show the model dimensions and material properties used for the calculations based on the parameters of the related previous experiments. Note that the drag coefficient $C_D$ in the case of Weber and Dedegil [30] and Shimizu et al. [9] is evaluated by the method of Sato et al. [35]. For all cases, when the mass flow rate of lifted solids increases, the water and solid flux gradually decrease. The calculated results in Cases 1–4 show better performance compared with that of experiments. On the other hand, in Case 9, the calculated result shows lower performance compared with that of experiments.

4. Simulations

4.1. Models and Conditions

Figure 10 shows the model dimensions and conditions used in the simulation. The lifting pipe is set up vertically relative to the sea surface. The total length of the lifting pipe; L is 5640 m, of which 5600m are under the sea surface; H_W and 40m are above the sea surface; L_O. The pipe is divided into equal lengths of 20m, creating 282 elements. The diameter of the lifting pipe is 0.212 m below the air injection point and 0.283 m above the air injection point. The pipe increases to 0.354 m in diameter starting at a 500 m water depth. The air is injected into the lifting pipe at a water depth of 2800 m, i.e., the middle of the lifting pipe under the sea surface, and air flow rates are 6, 12, and 18 kg/s. The pressure boundary is set at the bottom and top of the lifting pipe. The hydrostatic pressure at a 5600 m water depth is specified at the bottom. A pressure of 0.5 MPa(G), which corresponds to the back pressure, is specified at the top.

Table 7. Material properties used for the calculations (air and water).

Material	Density	Viscosity	Surface Tension	Molecular Mass
	[kg/m3]	[Pa·s]	[N/m]	[kg/mol]
Air	Equation (20)	1.76 × 10−5	7.4 × 10−2	2.88 × 10−2
Water	1.02 × 103	1.3 × 10−3	-	-

shows the material properties of air and water used for the simulation. The properties of seawater are used for the liquid phase. The density is 1.02 g/cm³, and the viscosity is 1.3 mPa·s. The density of air is calculated by Equation (20) based on the pressure in the lifting pipe.

Table 8. Material properties used for the calculations (REE-rich mud and polymetallic nodules).

Material	Density	K	n	Particle Dia. DP	Drag Coef. CD	Case
	[kg/m3]	[Pa·sn]	[-]	[mm]	[-]
REE-rich mud	2.8 × 103	Equation (15)	Equation (16)	-	-	1
		Equation (17)	Equation (18)	-	-	2
Polymetallic nodules	2.0 × 103 (wetted)	-	-	60	0.78	A
		-	-	20	1.17	B

shows the material properties of REE-rich mud and polymetallic nodules used for the simulation. The density of REE-rich mud is 2.8 g/cm³. For the flow consistency index $K$ and the flow behavior index $n$ in the pseudo-plastic fluid, Equations (15) and (16) are used for original REE-rich mud, i.e., without a hydrocyclone. Equations (17) and (18) are used for the UF slurry including highly REE-rich mud classified by the hydrocyclone. The density (wetted) of polymetallic nodules is 2.0 g/cm³. As shown in Table 8, two types of polymetallic nodules are modeled. One is the diameter is 60 mm, and the drag coefficient is 0.78. The other is the diameter is 20 mm, and the drag coefficient is 1.17. The latter one represents the case that polymetallic nodules are crushed before being fed into the lifting pipe, or that they are crushed during moving upward in the lifting pipe. The crushed small-sized polymetallic nodules are unlikely to cause blockage in the lifting pipe. The drag coefficient of crushed polymetallic nodules is calculated by the method of Sato et al. [35].

$${\rho }_G={\displaystyle \frac{M}{R}}{\displaystyle \frac{\left(P_M+P_{at}\right)}{\left(T+273.15\right)}}$$

(20)

where $T$: temperature [celsius], $P_{at}$: atmospheric pressure, 1.01 × 10⁵ [Pa], $M$: molecular weight, in case of air: 2.88 × 10⁻² [kg/mol], $R$: gas constant, 8.3145 [J/(mol·K)].

The time proceeding scheme is adopted in the simulation, which mimics the actual operations. The starting up process is as follows. After initial conditions have been established, a source term of gas-phase, which is related to a specified air flow rate, 6, 12, and 18 kg/s is added in the element, whose level corresponds to that of the air injection point. To minimize unwarranted transient phenomena by sudden air injection, the air flow rate is increased linearly up to the specified air flow rate over 360 s, and then the simulation continues until reaching the steady-state condition at 5400 s. The pressure at the top boundary is then specified at 0.5 MPa, which is related to the back pressure. The pressure is increased linearly up to 0.5 MPa over 360 s and then the simulation continues until reaching the steady-state condition at 10,800 s. The next step is to feed REE-rich mud and polymetallic nodules into the lifting pipe. In the case of REE-rich mud, a constant volume concentration of mud is specified at the bottom boundary. In the case of polymetallic nodules, a constant volume fraction of the solid phase is specified at bottom boundary, based on the flow rate of the solid phase. The simulation continues for 5400 s in each of the feeding conditions. This process is repeated by increasing the feeding rate gradually until reaching the maximum flow rate of REE-rich mud or polymetallic nodules. The time-step of calculation is 4 s, and required data are recorded every 20 s.

4.2. Results and Discussion

4.2.1. Operations, Time Transient

Figure 11 shows the time transient of the air flow rate (the first), and water flow rate (the second) when beginning to input air in the lifting pipe from the air injection point at a specified air flow rate of 12 kg/s. In the first graph, the solid line shows the flow rate at the top of the lifting pipe, and the dashed line: at the air injection point; i.e., the specified air flow rate. In the second graph, the solid line shows the flow rate at the top of the lifting pipe, and the dashed line: at the bottom of the lifting pipe. When beginning to input air, water is sucked in from the bottom of the lifting pipe, and the water level in the lifting pipe rises. After 240 s from the beginning to input air, water discharges at the top of the lifting pipe. Temporarily, a substantial amount of water, which is preserved initially in the lifting pipe is discharged. The water flow rate is 4.3 times that of the steady-state condition. Subsequently, a substantial amount of air, which is used for lifting preserved water is discharged. The air flow rate is 4.0 times that of the steady-state condition. The system reaches a steady-state condition after 1800 s.

Figure 12 shows the time transient of air flow rate (the first), slurry flow rate (the second), mass flow rate of REE-rich mud (the third), and mass flow rate of polymetallic nodules (the fourth) when polymetallic nodules begin to be fed at 2 kg/s in the lifting pipe while the volume concentration of REE-rich mud is kept at 5%. The air flow rate is 12 kg/s, and the back pressure is 0.5 MPa. In the first graph, the solid line shows the flow rate at the top of the lifting pipe, and the dashed line: at the air injection point. In the second to the fourth graphs, the solid line shows the flow rate at the top of the lifting pipe, and the dashed line: at the bottom of the lifting pipe. The slurry flow rate at the bottom, and then at the top gradually decreases after the feeding of polymetallic nodules begins. The mass flow rate of REE-rich mud also gradually decreases. It takes about 900 s to lift polymetallic nodules from the bottom to the top in the lifting pipe. The mass flow rate of polymetallic nodules at the top increases more slowly, i.e., it takes about 500 s to reach the steady-state condition. Similar tendencies were observed in the cases of feeding REE-rich mud and polymetallic nodules separately.

4.2.2. Lifting Characteristics

Figure 13 shows the lifting characteristics of REE-rich mud; slurry flux versus the mass flow rate of REE-rich mud for two cases. The air flow rate is 6, 12, and 18 kg/s. The solid lines show the case using empirical equations by Hanamura et al., Equations (15) and (16) [20] (Case 1), the dashed lines: empirical equations of the UF; the underflow slurry after classification by the hydrocyclone, Equations (17) and (18) (Case 2). Slurry flux gradually decreases when the mass flow rate of REE-rich mud increases. The maximum mass flow rate of REE-rich mud of Case 2 is larger than that of Case 1, though the lifting characteristics of both cases are almost the same except for around the maximum mass flow rate. The maximum mass flow rates of REE-rich mud of Case 1 in each air flow rate are 1470, 2460, and 3050 t/d, respectively. Those of Case 2 are 1480 (101%), 2770 (113%), and 3590 t/d (118%), with the ratio of Case 2 to Case 1 in parentheses.

Figure 14 shows the lifting characteristics of polymetallic nodules; water plus solid flux versus mass flow rate of polymetallic nodules for two cases. The air flow rate is 6, 12, and 18 kg/s. The solid lines show the case of D_P; 60 mm, C_D; 0.78 (Case A), and the dashed lines; D_P; 20 mm, C_D; 1.17 (Case B). Similar tendencies, but better performances are observed compared with the case of REE-rich mud as shown in Figure 13. Water plus solid flux gradually decreases when the mass flow rate of polymetallic nodules increases. Compared with Case A, Case B exhibits better performance, i.e., the mass flow rate of the polymetallic nodules of Case B is larger than that of Case A under the same water plus solid flux. This is because the relative velocity of polymetallic nodules to seawater is small for smaller particle sizes and larger drag coefficients. The maximum mass flow rates of polymetallic nodules of Case A in each air flow rate are 1770, 3760, and 5240 t/d, respectively. Those of Case B are 1980 (112%), 4120 (110%), and 5620 t/d (107%), with the ratio Case B to Case A in parentheses.

Figure 15 shows the lifting characteristics of REE-rich mud and polymetallic nodules at the same time; slurry plus solid flux versus mass flow rate of REE-rich mud and polymetallic nodules. Empirical equations by Hanamura et al., Equations (15) and (16) [20] for REE-rich mud (Case 1), and D_P; 20 mm, C_D; 1.17 for polymetallic nodules (Case B) are adopted. The air flow rate is 12 kg/s. The solid lines show the case of lifting each of REE-rich mud and polymetallic nodules only. Two cases are shown in the case of hybrid mining. One is the case that the mass flow rate of polymetallic nodules increases while the volume concentration of REE-rich mud is kept at 3% (Case I, the dashed line). The other is the case of keeping the 5% volume concentration of REE-rich mud (Case II, the dashed-dotted line). Because the slurry flux decreases when the mass flow rate of polymetallic nodules increases, the mass flow rate of REE-rich mud also decreases. At a slurry plus solid flux of 4.5 m/s, the mass flow rates of REE-rich mud and polymetallic nodules in Case I are 1060 and 2300 t/d, (total: 3360 t/d) respectively. In Case II, they are 1840 and 1110 t/d, (total: 2950 t/d) respectively. The mass flow rate of REE-rich mud only (Case 1) is 2440 t/d, and that of polymetallic nodules only (Case B) is 3770 t/d as shown in

Table 9. Lifting performance at slurry plus solid flux of 4.5 m/s with M_G = 12 kg/s.

Case	MX + MS	MX	MS	CX	CS	JM exit	Npower	η
	[t/d]	[t/d]	[t/d]	[%]	[%]	[m/s]	[kW]	[-]
1	2440	2440	0	6.34	0	18.1	3230	0.310
II	2950	1840	1110	5.00	4.04	18.1	3220	0.345
I	3360	1060	2300	3.00	8.40	18.1	3220	0.362
B	3770	0	3770	0	13.7	18.1	3220	0.372

. The total amount of REE-rich mud and polymetallic nodules increases if the ratio of polymetallic nodules increases under the same slurry plus solid flux.

Figure 16 shows mixture velocities at the exit of the lifting pipe $J_{M exit}$ versus back pressure in the case of adopting empirical equations by Hanamura et al., Equations (15) and (16) [20] for REE-rich mud (Case 1) and D_P; 20 mm, C_D; 1.17 for polymetallic nodules (Case B). The air flow rates are 6, 12, and 18 kg/s. By specifying the back pressure at the exit, the mixture velocities decrease compared with the case of zero pressure (G). The mixture velocities at the exit under a back pressure; 0.5 MPa(G), and an air flow rate of 12 kg/s in Cases 1 and B are 18.0 and 17.8 m/s, respectively.

Figure 17 shows the required power of an air compressor $N_{power}$ and the efficiency of the air-lift system $\eta$, when the air flow rate is 12 kg/s in the case of adopting empirical equations by Hanamura et al., Equations (15) and (16) [20] for REE-rich mud (Case 1) and D_P; 20 mm, C_D; 1.17 for polymetallic nodules (Case B). The efficiency is defined by Equation (21); the numerator is the power to lift REE-rich mud and polymetallic nodules, and the denominator is the required power for the air compressor. The required power is calculated by Equation (22). In Equation (22), $P_{out}$ is evaluated by Equation (23) assuming an isothermal change in the air pipe. The required power decreases when the back pressure increases. The required power under a back pressure of 0.5 MPa(G) in Cases 1 and B are 3220 and 3190 kW, respectively. Applying pressure at the exit of the lifting pipe as a back pressure is efficient in terms of reducing the amount of required power. And the efficiency increases as the back pressure increases. The efficiency under a back pressure of 0.5 MPa(G) in Cases 1 and B are 0.313 (136%) and 0.411 (129%), respectively with the ratio of the efficiency compared with the case of zero pressure(G) is in parentheses.

$$\eta ={\displaystyle \frac{\left({\rho }_X{C}_X{Q}_L+{\rho }_S{Q}_S\right)g{L}_O+\left(\left({\rho }_X-{\rho }_{L0}\right)C_X{Q}_L+\left({\rho }_S-{\rho }_{L0}\right)Q_S\right)g\left(L_U+L_E\right)}{N_{power}}}$$

(21)

where

$$N_{power}={\displaystyle \frac{R}{M}}\left(T+273.15\right)\ln {\displaystyle \frac{P_{out}}{P_{in}}}{M}_G$$

(22)

$$P_{out}={\displaystyle \frac{P_{M\_apt}}{\exp \left(L_{A}Mg/\left(R\left(T+273.15\right)\right)\right)}}$$

(23)

where $P_{in}$: pressure at the inlet of the air compressor [Pa], $P_{out}$: pressure at the outlet of the air compressor [Pa], $P_{M\_apt}$: pressure at the air injection point [Pa], $M_G$: air flow rate [kg/s], $L_A(=L_E+L_O)$: length of air pipe [m].

5. Conclusions

A numerical study using a one-dimensional drift–flux model for gas–liquid–solid three-phase flow and gas–liquid two-phase flow was conducted to examine the characteristics of an air-lift pumping system for mining REE-rich mud and polymetallic nodules under the seabed at a 5500–5700 m water depth around Minamitorishima island. Empirical equations of REE-rich mud, which represent relations between the flow characteristics of pseudo-plastic fluid versus volume concentration of the slurry, and the physical properties of polymetallic nodules around Minamitorishima island were utilized in the analysis.

As a result, the characteristics and the performance of the system were clarified in the case of lifting REE-rich mud only, polymetallic nodules only, and hybrid mining. Under the condition that the total length of the lifting pipe is 5640 m, of which 5600 m is under the sea surface, the diameter is 0.212 m below the air injection point, 0.283 m over the air injection point, and 0.354 m from a 500 m water depth, and the water depth of air injection point is 2800 m, in addition to an operational condition of air flow rate of 12 kg/s and back pressure of 0.5 MPa(G), the following performances in each case were derived.

In the case of lifting REE-rich mud, adopting empirical equations by Hanamura et al., Equations (15) and (16) [20], the maximum mass flow rate of REE-rich mud is 2460 t/d at a volume concentration of 6.9%, where the slurry flux below the air injection point is 4.18 m/s, the mixture velocity at the exit of the lifting pipe is 18.0 m/s, and the required power is 3220 kW.

In the case of lifting polymetallic nodules, adopting a D_P of 20 mm and a C_D of 1.17, the maximum mass flow rate of polymetallic nodules is 4120 t/d at a volume concentration of 18.9%, where the water plus solid flux below the air injection point is 2.89 m/s, the mixture velocity at the exit of the lifting pipe is 17.8 m/s, and the required power is 3190 kW.

In the case of hybrid mining, lifting REE-rich mud, adopting empirical equations by Hanamura et al., Equations (15) and (16) [20]) and polymetallic nodules, adopting a D_P of 20 mm and C_D of 1.17 at the same time by keeping the volume concentration of REE-rich mud at 5%, the mass flow rate of REE-rich mud and polymetallic nodules are 1840 and 1110 t/d (volume concentration of polymetallic nodules: 4.0%), respectively, the mixture velocity at the exit of the lifting pipe is 18.1 m/s, the required power is 3220 kW at the slurry plus solid flux below the air injection point of 4.5 m/s.

Further, the following results were derived from the parametric experiments.

(1). Regarding lifting characteristics of REE-rich mud, the maximum mass flow rate of REE-rich mud of Case 2 using empirical equations of the UF; the underflow slurry after classification by the hydrocyclone is larger than that of Case 1 using empirical equations by Hanamura et al. [20]; slurry is without classification, though the lifting characteristics of both cases are almost the same except for the condition around the maximum mass flow rate.

(2). Regarding lifting characteristics of polymetallic nodules, Case B; D_P; 20 mm, C_D; 1.17 exhibits better performance compared with Case A; D_P; 60 mm, C_D; 0.78, i.e., the mass flow rate of polymetallic nodules of Case B is larger than that of Case A under the same water plus solid flux. This is because the relative velocity of polymetallic nodules to seawater is small for smaller particle sizes and larger drag coefficients. The crushed small-sized polymetallic nodules are also unlikely to cause blockage in the lifting pipe.

(3). By specifying the back pressure at exit, the mixture velocities decrease compared with the case of zero gage pressure. The mixture velocities at exit under the back pressure of 0.5 MPa(G), and the air flow rate of 12 kg/s are 18.0 and 17.8 m/s for Cases 1 and B. Also, the efficiencies increase compared with the case of zero gage pressure. They are 0.313 and 0.411 for Case 1 and B, respectively.

The time transient, i.e., the unsteady characteristics of the air-lift pumping system were also clarified as well as the lifting characteristics, such as at start-up, and beginning to feed slurry with REE-rich mud and polymetallic nodules. The findings from the unsteady characteristics are also useful to consider the operation on the real project or the commercial system in the future.

In this study, the mechanical characteristics of the air-lift pumping system were clarified for mining REE-rich mud and polymetallic nodules from the deep seabed around Minamitorishima island. The program and the schemes used in the study could derive useful information not only in the case of Minamitorishima island but also in other applications, in which mineral resources such as REE-rich mud and polymetallic nodules are transported from the deep seabed.