**Computational Fluid Dynamics Modeling of the Resistivity and Power Density in Reverse Electrodialysis: A Parametric Study**

#### **Zohreh Jalili 1,2 , Odne Stokke Burheim 1,\* and Kristian Etienne Einarsrud <sup>2</sup>**


Received: 30 June 2020; Accepted: 25 August 2020; Published: 29 August 2020

**Abstract:** Electrodialysis (ED) and reverse electrodialysis (RED) are enabling technologies which can facilitate renewable energy generation, dynamic energy storage, and hydrogen production from low-grade waste heat. This paper presents a computational fluid dynamics (CFD) study for maximizing the net produced power density of RED by coupling the Navier–Stokes and Nernst–Planck equations, using the OpenFOAM software. The relative influences of several parameters, such as flow velocities, membrane topology (i.e., flat or spacer-filled channels with different surface corrugation geometries), and temperature, on the resistivity, electrical potential, and power density are addressed by applying a factorial design and a parametric study. The results demonstrate that temperature is the most influential parameter on the net produced power density, resulting in a 43% increase in the net peak power density compared to the base case, for cylindrical corrugated channels.

**Keywords:** reverse electrodialysis; computational fluid dynamics; power density; factorial design

#### **1. Introduction**

The energy economy is facing its most challenging decade, as it must transcend into a more climate-friendly one, as half of the emitted CO<sup>2</sup> due to energy generation and consumption has been targeted for reduction. To achieve this, the technologies used must be changed from those depending on the burning of fossil fuels into electricity and heat, towards technologies which provide electricity and store it in the form of chemical energy. Striving for renewable energy generation, energy storage systems, and renewable hydrogen production, reverse electrodialysis is one of the few technologies that could address all three of these needs [1–3].

Salinity gradient energy (SGE)—particularly RED, which harvests energy produced by mixing two aqueous solutions with different salinities,—has received great interest in the literature [2–11] since its first use, which was reported by Pattle in 1954 [12]. Concentration batteries have also been recently proposed and discussed, which couple salinity gradient energy (SGE) technologies for energy generation to their corresponding desalination technologies [2,4,13]. Jalili et al. developed mathematical models to compare three types of energy storage systems: electrodialytic, osmotic, and capacitive batteries [2]. Influential parameters, such as temperature and energy consumption of the pump, on the performance of different concentration batteries were also discussed in their work [2] applying a mathematical model. They reported that the peak power densities of the energy storage systems increase at elevated temperature [2].

A schematic of a simple RED stack is shown in Figure 1. In general, a unit cell consists of a dilute solution compartment, a concentrated solution compartment, a cation exchange membrane, and an anion exchange membrane. By repeating unit cells and connecting the end points of the stack to an anode and a cathode compartment (where the electrode rinse solutions are present), a RED stack can be completed for converting an ionic flux into an electrical one [2].

**Figure 1.** Schematic of a simple RED stack, containing (from the left) an anode, an anode electrolyte compartment, a unit cell, an additional membrane, a cathode electrolyte compartment, and a cathode.

The electrical potential of a RED unit cell is always lower than the open-circuit potential, due to the ohmic resistance, concentration changes in the boundary layer, and concentration changes in the bulk solutions. The last two sources can be interpreted as non-ohmic resistances [5,14]. Non-ohmic resistance is mainly controlled by concentration polarization [15], which has been investigated and discussed by several researchers in the literature [15–21].

Although it has been agreed, by some researchers that increasing the flow velocity and the introduction of flow promoters (i.e., spacers) can mitigate the concentration polarization and enhance the mass transfer by disturbing the diffusive boundary layer [16,20,22,23], Vermaas et al. [24] through an experimental work showed that at low Re numbers (less than 100), which are typically used for RED, introducing non-conductive sub-corrugation is not that beneficial to reduce the ohmic losses and increase the power density [24]. They also showed that although the non-ohmic resistance (concentration boundary layer effects) decreases significantly when increasing the Reynolds number; the ohmic resistances are almost independent of the Re number at high Re numbers and dominates the power loss [24]. Pawlowski et al. performed an extensive literature review of the development and application of corrugated membranes in electro-membrane-based processes [25]. They reported the effect of corrugated membranes in the performance of reverse electrodialysis (RED), showing that electrodialysis (ED) is significantly influenced by the shape of the corrugation, Reynolds number, and ion concentrations. For high Reynolds numbers, corrugation creates eddies which lead to enhanced mass transfer, reduced deposition of foulants, and increased diffuse boundary layer thickness. In particular, they highlighted the role of conductive spacers in lowering the resistance of the RED stack, by eliminating spacer shadow effects [25]. They foresaw the rapid progress of the design and manufacturing of corrugated membranes due to advances in CFD simulations and 3D printing technology [25]. Gurreri et al. [26] used CFD modeling to study fluid flow behavior in a reverse electrodialysis stack, aiming to address the effect of the spacer material on the pressure losses along the

channel, evaluating the choice of a fiber-structure porous medium, instead of the commonly adopted net spacers, and investigated the influences of the distributor and channel configurations on fluid dynamics in a RED system [26]. They documented that the total pressure loss in a RED stack is the sum of the pressure drop relevant to the feed distributor, the pressure drop inside the channel, and the pressure drop in the discharging collector [26]. Simulations revealed that the spacer geometry may not necessarily be the main factor controlling the overall pressure drop. In addition, the pressure drop induced by a porous medium made of small fibers is larger than that for a typical net spacer; therefore, they might not be suitable for RED [26]. Pawlowski et al. [27] showed, by CFD modeling, that chevron-corrugated membranes have the highest net produced power density among several investigated profiled membranes, due to increased membrane area, reduction of the concentration polarization, and the proper trade-off between momentum and mass transfer [27]. These results were validated also through experimental comparison [28]. Cerva et al. [29] presented a coupled study of one-dimensional CFD modeling with three-dimensional finite volume modeling for a flat channel, profiled membranes, and different spacer-filled corrugations in a RED stack. Then, they validated the overall model by comparison with experimental data measured in a laboratory [29]. Their results showed that the boundary layer potential drop is significantly lower than the ohmic losses. In addition, woven spacers had the smallest boundary layer potential loss, followed by Overlapped Crossed Filaments (OCF) profiled membranes and then the flat channel, thus indicating that woven spacers provide the most efficient and effective mixing among the considered systems [29]. The highest gross power density and the highest short-circuit current density were reported for OCF profiles, followed by the woven spacers and then the flat channel. However, the highest net power density per cell pair was provided by the flat channel, followed by OCF profiled membranes and then by the woven spacers [29]. Mehdizadeh et al. [30] experimentally studied several non-conductive spacers with different geometries and properties (e.g., different diameters, angles, distances, area fractions, and volume fractions) to understand the spacer shadow effect on the membrane and solution compartment resistances in RED. They reported a correlation between the spacer shadow effect on the membrane resistance and a combined parameter of spacer area fraction and spacer diameter [30]. The spacer shadow effect on the solution compartment resistance was also correlated with the spacer area and volume fraction. They observed that the spacer area fraction had a dominant effect only for less porous spacers [30]. Jalili et al. [31,32] used CFD modeling to examine the influence of flow velocities and spacer topology with respect to the transport of mass and momentum, as well as the flow channel resistivity of a RED unit cell. They reported that the resistivity of the dilute solution channel dominates over the resistivity of the concentrated solution channel and membranes in a RED unit cell [32]. Similar observations have also been reported by Ortiz-Martinez et al. [33]. The electrical potential of a RED unit cell was enhanced by reducing the flow velocity and introducing flow promoters in a dilute solution channel, due to reduced solution resistance [32]. Introducing spacers in a concentrated solution channel or increasing the flow velocity in a dilute solution channel increases the resistivity and has adverse effects on the electrical potential [32]. They also demonstrated that the mass transfer is higher for active membrane-integrated spacers, compared to inactive spacers, under similar flow velocity and spacer topology, due to increased active membrane area [31]. They also concluded that cylindrical membrane-integrated corrugation is an optimum spacer geometry at low flow velocities, while triangular membrane-integrated corrugation is a better geometry at high flow velocities [31]. Recently Dong et al. [34] performed a CFD study of mass and momentum transfer for several types of profiled membrane channels in RED. Their work showed that conductive wavy sub-corrugations improved the mass transfer and reduced the concentration polarization (i.e., non-ohmic losses) [34]. Furthermore, they showed that single-sided wave-profiled membranes had better performance, compared to single-sided pillar-profiled membranes; while single-sided profiled membranes had a smaller impact on the performance, compared to double-sided chevron-profiled membrane and woven spacer-filled channels [34].

Long et al. reported a numerical study matched with experimental data for optimizing channel geometry and flow rate of the concentrated and diluted solutions with non-conductive spacers, to obtain maximum net power output by RED. They reported that the optimal channel thickness and flow rate in the concentrated solution compartment in a RED stack are, respectively, much less than those of the dilute solution compartment [35]. In another work, they revealed that the optimal flow rates in the dilute and concentrated solution channels in an RED stack with varying flow rates along the flow direction to achieve maximum energy efficiency were lower than the optimal flow rates to obtain the maximum net power density. Therefore, an optimization study based on the Non-dominated Sorting Genetic Algorithm II (NSGA-II) was performed, in order to analyze the compromise between the net peak power density and the energy efficiency [36]. Their work showed that the net power density at maximum energy efficiency was less than the peak power density [36].

Several researchers have highlighted the potential use of waste heat in RED systems. Luo et al. [37] reported that by using ammonium bicarbonate as a working fluid in a thermally driven electrochemical generator, waste heat could be converted to electricity [37]. A maximum power density was obtained at an overall energy efficiency of 0.33 W m−<sup>2</sup> , by operating a RED system with a dilute concentration of 0.02 M [37]. Micari et al. [38] reported the conversion of waste heat into electricity by coupling RED with membrane distillation (MD), resulting in considerable system energy efficiency improvement. The construction and operation of the first lab-scale prototype unit of a thermolytic reverse electrodialysis heat engine (t-RED HE) for converting low-temperature waste heat into electricity have been reported by Giacalone et al. [39]. Ortiz-Imedio et al. [33] documented the strong dependence of the performance of RED on temperature. They reported that the membrane resistance increased when reducing the temperature, and that the perm-selectivity reduced when increasing the temperature [33]. Jalili et al. [31] showed that increasing the temperature enhanced the mass transfer of dilute and concentrated solutions, due to higher diffusivity and lower viscosity at increased temperature. In another work, they reported that the open-circuit potential increased with increasing temperature [2]. Contrary to the most of the literature, which has investigated salinity gradient energy at isothermal conditions, Long et al. [40] addressed the asymmetric temperature influence in dilute and concentrated solution channels on the performance of nanofluidic power systems, using numerical simulation by coupling the Poisson–Nernst–Planck equation and the Navier–Stokes equation, as well as the energy-conservation equation. They observed that when the temperature of the concentrated solution channel is lower than the temperature of the dilute solution channel, the ion-concentration polarization is suppressed, ion diffusion along the osmotic direction enhances, and perm-selectivity increases; thus, the membrane potential improves [40]. However when the temperature in the concentrated solution channel is higher than that of the dilute solution channel, the membrane potential reduces; although the diffusion current increases, due to the lower resistance [40]. In another work [41], they reported the influences of heat transfer and the membrane thermal conductivity in the performance of nanofluidic energy conversion systems. They reported that when the temperature of the concentrated solution channel is lower than the temperature of the dilute solution channel, a larger membrane thermal conductivity results, with reduced electrical power improvement; on the other hand, when the temperature of the concentrated solution channel is higher than the temperature of the dilute solution channel, the increased membrane thermal conductivity leads to enhanced power density [41].

Although several studies have reported the application of CFD modeling for investigating momentum and mass transfer in order to determine the trade-off between the pressure loss and mass transfer in an RED channel [16,18,19,22,23,27], there have been limited CFD studies of electrical potential in an RED channel [42,43]. To the best of our knowledge, there have been no parametric studies which assessed the relative effect of relevant parameters on the net power density for a RED cell. In particular, addressing the influence of temperature, as proposed by Jalili et al. [31], was not compared to the other parameters. The current work is an extension of the previously published works [31,32] by the current authors. We demonstrate that the electrical potential changes linearly with the height of the channel for a constant concentration profile, and that it follows a logarithmic

trend with length of the channel height when the concentration profile varies linearly with the channel height [32]. Other interesting observations of this work [32] can be summarized as follows: First, the concentration gradient near the walls of the channel increase, due to reduced boundary layer thickness, with higher Re number. In fact, the concentration at the center of the channel is at its maximum for the concentrated solution channel and is at its minimum for the diluted solution channel [32]. Second, the pressure drop for the dilute solution channel is lower than that in the concentrated solution channel, given similar Re number and channel geometry [32]. This observation was also reported by Zhu et al. [21], when conducting several experiments. Third, the resistance of the dilute solution is more dominant, compared to the resistance of the concentrated solution channel, which can be seen as a limiting factor for the power density of a RED stack. Reducing the Re number (i.e., reducing the velocity at a constant temperature) or introducing corrugation in a dilute solution channel reduces the resistivity of the dilute solution channel by increasing the thickness of the boundary layer, which provides a thicker and more conductive region in the flow channel and results in improved mixing by the developing wakes downstream from the spacers [32]. An opposite trend was observed for the resistivity of the concentrated solution channel [32]. This observation was also supported by Long et al. [35].

This present work describes a numerical framework for simulation of the Navier–Stokes (NS) and Nernst–Planck (NP) system, based on the open source CFD platform OpenFOAM [44], with the aim of predicting the influence of flow velocity, temperature, and geometry on concentration, pressure drop, electrical potential drop, and net power density. Factorial design [45] is applied to address the relative effects of the parameters on the peak power density.

#### **2. Theory and Governing Equations**

The flow in the channel is considered to be two-dimensional, incompressible, steady-state, isothermal, and laminar. Physical properties such as density and viscosity are assumed to be constant. There is charge neutrality in the whole system, where only monovalent ions exist. The Navier–Stokes and Nernst–Plank equations [42,46,47] are presented by Equation (1) and Equation (2), respectively.

$$
\rho \vec{u} \cdot \nabla \vec{u} = -\nabla p + \mu \nabla^2 \vec{u}.\tag{1}
$$

$$\nabla \cdot \left[ \mathcal{D}\_i \nabla \mathcal{C}\_i - \vec{u} \mathcal{C}\_i + \mathcal{C}\_i \mu\_{EP} \nabla \phi \right] = 0,\tag{2}$$

for species *i*, where *C<sup>i</sup>* is the concentration ([mol/m<sup>3</sup> ]), D*<sup>i</sup>* is the diffusivity ([m2/s]), ~*u* is the fluid velocity ([m/s]), and

$$
\mu\_{EPi} = \frac{\mathcal{D}\_i \mathbf{z}\_i \mathbf{F}}{\mathcal{R}T} \tag{3}
$$

is the electrophoretic mobility ([m2/Vs]), where *z<sup>i</sup>* is the valency, *F* = 96485.3 C/mol is the Faraday constant, *R* = 8.314 J/K·mol is the universal gas constant, and *T* is the temperature (in Kelvin), while *φ* is the electrostatic potential ([V]).

Assuming two monovalent ionic species, denoted + and - , and using charge neutrality (i.e., *C*<sup>+</sup> = *C*<sup>−</sup> = *C*), Equation (2) can be written as [31,32]:

$$\mathbb{P}\left(\vec{\boldsymbol{\omega}} \cdot \nabla \, \boldsymbol{\nabla}\right) \mathbb{C} = \frac{\mathsf{2} \cdot \mathcal{D}\_{+} \cdot \mathcal{D}\_{-}}{\mathcal{D}\_{+} + \mathcal{D}\_{-}} \nabla^{2} \mathbb{C} \equiv \mathcal{D} \nabla^{2} \mathbb{C},\tag{4}$$

where D is the effective diffusivity for the salt and *C* is the concentration. The effective diffusivity is assumed to be a function of temperature, using the published data by Bastug and Kuyucak [48].

The electrical potential can be calculated from the conservation of electrical current density~*j* [32],

$$
\nabla \cdot \vec{j} = 0.\tag{5}
$$

The electrical current density is obtained by a weighted sum of the charged species, resulting in

$$\vec{f}\_{-}=\mathcal{F}\left(\mathcal{D}\_{-}-\mathcal{D}\_{+}\right)\nabla\mathcal{C}-\frac{F^{2}\mathcal{C}}{RT}\left(\mathcal{D}\_{+}+\mathcal{D}\_{-}\right)\nabla\phi\_{\prime}\tag{6}$$

where the advective flux cancels out, due to monovalent ions and charge neutrality. Combining Equations (5) and (6), we obtain the following relation [31,32]:

$$\left(\frac{\mathcal{D}\_{+} - \mathcal{D}\_{-}}{\mathcal{D}\_{+} + \mathcal{D}\_{-}}\right) \nabla^{2} \mathcal{C} = \frac{F}{RT} \nabla \cdot \left(\mathcal{C} \nabla \phi \right),\tag{7}$$

from which the electrostatic potential can be calculated, given a known concentration field in Equation (4). The proposed framework essentially consists of four one-way coupled equations—namely the incompressible Navier–Stokes Equations (1) which, together with continuity, determine the pressure and velocity fields; the concentration Equation (4), which essentially is an advection–diffusion equation with a known velocity; and, finally, the equation for the electrostatic potential (7), which is essentially reduced to a Poisson equation with a known source term. Given the domain and boundary conditions described in the following sections, the incompressible Navier–Stokes equations are solved by means of the simpleFoam solver in OpenFOAM, modified to account for concentration and potential following the steps described, for instance, in the openfoamwiki [49].

The trade-off between maximum produced electrical potential and the current density provides the peak power density. The peak power density, *P peak RED* (W/m<sup>2</sup> ), of a RED unit cell, the principal parameter of interest in the current work, can be expressed as follows: [5,11,14]:

$$P\_{RED}^{peak} = \frac{1}{r\_{unit\ cell}} \frac{E\_{OCP}^2}{4} \,\,\,\,\,\tag{8}$$

where *runit cell* and *EOCP* represent the area resistance of the unit cell and the open-circuit potential of the unit cell, correspondingly. The area resistance of the unit cell can be calculated by Equation (9) [5,14]:

$$r\_{\text{unitcell}} = \left(r\_{AEM} + r\_{\text{CEM}} + r\_d + r\_c\right) \,. \tag{9}$$

where *rAEM* and *rCEM* are the area resistances of the AEM and CEM, respectively, and *r<sup>c</sup>* and *r<sup>d</sup>* are the total area resistances for concentrated and dilute solution channels, respectively. The open-circuit potential depends upon the concentrations of dilute and concentrated channels as well as temperature, each of which are assumed fixed for a given setup in the current work. Assuming constant membrane properties, the only remaining variables are the area resistances of the channels. The total area resistance of the channels is calculated by dividing area-weighted average of electrical potential difference across the channel by the current density at the peak power density of RED unit cell, as shown by Equation (10) [14,32]:

$$r\_j = \left| \frac{\Delta \tilde{\Phi}}{j} \right| \,\tag{10}$$

where *r<sup>j</sup>* is the total area resistance (ohmic and non-ohmic) of the concentrated or dilute channels, *j* is the current density, and

$$
\Delta\Phi = \frac{1}{A\_{AEM}} \int\_{AEM} \phi \, dA - \frac{1}{A\_{CEM}} \int\_{CEM} \phi \, dA\_{\prime} \tag{11}
$$

is the difference in area-weighted average of electrical potential Φ, calculated on the active membrane. The electrostatic potential across each channel, and thereby also the resistance, can be calculated based on the coupled Nernst–Planck and Navier–Stokes framework, presented in the theory and governing equations section. The formulation used in the current work accounts for both local values and gradients in concentration, and thus accounts for both ohmic and non-ohmic contributions. It should be noted that when dividing the potential drop by the imposed current, as in the above equation, non-ohmic contributions appear as an ohmic potential drop, although they are not of an ohmic nature [14].

When operating a RED system, the diluted and concentrated solutions are pumped through the compartments between the membranes, which inevitably leads to an energy loss. The required pump power density for each channel can be estimated by Equation (12) [14]:

$$P\_{pump} = \Delta p \frac{Q}{A} = \Delta p \frac{H}{L} u\_{\prime} \tag{12}$$

where *A* is the membrane area, *Q* is the volumetric flow rate through the channel, *H* is the height of the channel, *L* is the length of the channel, *u* is the average velocity in the channel, and ∆*p* is the pressure drop across the channel length which will be estimated through CFD modeling. To reduce ohmic energy losses in RED systems, the channel height should be as thin as possible; however, as this leads to increased pumping losses, there is a need to find an optimum value though. There are several factors affecting the optimal thickness of the inter-membrane distance, dictated by flow velocity, salinity and hydrodynamic pressure drops, but generally 50–300 µm is considered an optimum. This is for sterile particle free systems, but also fouling and other effects in nature can affects this further [2,50].

Given the energy consumption in the pump, the net peak power density can be calculated as:

$$P\_{\text{net}} = P\_{\text{RED}}^{peak} - P\_{\text{pump}}^{total} \tag{13}$$

In summary, the net peak power density can be calculated as follows:


#### **3. Simulation Setup**

Flat and non-conductive spacer-filled channels with cylindrical or triangular corrugation are shown in Figure 2. Jalili et al. [32] reported that introducing flow promoters in a dilute solution channel improves the performance of a RED unit cell, while it has an adverse effect in the concentrated channel. Hence, the corrugated geometries were assumed for the dilute solution compartments, while the flat geometry was considered for concentrated solution compartments in this work.

The inlet concentrations for the channels were considered to be uniform and equal to 0.016 M (close to the salinity of brackish water) for the dilute solution channel and 0.484 M (close to the average salinity of seawater) for the concentrated solution channel.

**Figure 2.** Schematic presentation for sections of the geometry of flat, cylindrical, and triangular corrugated channels with characteristic length scales.

#### *3.1. Boundary Conditions*

A constant molar flux, according to the following equation, was assumed in the current model [16,51]. This molar flux corresponds to a constant current density ~*j*, from which the peak power density of the RED system can be obtained (see Equation (8)):

$$\vec{i\_i}^{\vec{m}} = \frac{\mathbf{t}\_i^{\,0}}{z\_i \mathbf{F}} \vec{j\_i} \tag{14}$$

where ~*i<sup>i</sup> <sup>m</sup>* is the ionic flux of species *i* and *t<sup>i</sup>* 0 is the transport number of species *i*. Assuming an ideal membrane from the perm-selectivity perspective and the transport properties for both cations and anions (of a monovalent binary electrolyte such as NaCl) in the solution for simplicity, we obtain [16,51]:

$$i\_{IEM} = \pm \frac{0.5j}{F} \,\text{\AA} \tag{15}$$

where the sign shows the incoming flux in the dilute channel or outgoing flux in the concentrated channel. Applying Fick's first law of diffusion, as given in Equation (16), and substituting it into Equation (15), we obatin a constant concentration gradient, as shown in Equation (17).

$$i\_{IEM} = \mathcal{D} \frac{\partial \mathcal{C}}{\partial n'} \tag{16}$$

where *n* is the normal direction to the wall, D is the effective diffusivity, and *iIEM* is representative of the ionic flux through the membrane. Equating Equations (15) and (16) provides us with the boundary condition for the concentration at the membranes:

$$\frac{\partial \mathcal{C}}{\partial n} = \pm \frac{0.5j}{\mathcal{F}\mathcal{D}}.\tag{17}$$

The boundary condition for the electrical potential on the top membrane is

$$\nabla \phi\_- = \frac{RT}{F^2 \mathbb{C}} \left[ \frac{F \left( \mathcal{D}\_- - \mathcal{D}\_+ \right) \nabla \mathbb{C} - \vec{f}}{\left( \mathcal{D}\_+ + \mathcal{D}\_- \right)} \right]. \tag{18}$$

Evidently, Equation (7) can be solved using the boundary conditions for the concentration and electrical potential, considering Equations (17) and (18).

The constant flux assumption is an approximation representing the features corresponding to an average concentration difference between the channels. Figure 3 shows the specified boundary conditions for different parts of the channel.

**Figure 3.** The boundary conditions for a section of dilute, non-conductive cylindrical spacer-filled channel. The blue line shows the active membrane section and the arrows show the diffusion direction from the top and bottom wall toward the dilute bulk. The geometry is repeated to build the full length of the compartment.

The value of the velocity at the inlet depends on the sought Reynolds number, and is given as a parabolic profile. The outlet is specified to atmospheric pressure. The membranes and spacers are set to no-slip conditions at the walls, and with zero gradient in pressure. In the case of the spacer-filled channel, the spacers are assumed to be non-ion conductive, with a corresponding zero flux boundary condition. The electric potential at the bottom wall of the channel is set to zero and the electrical potential on the top wall (active membrane) is calculated based on Equation (18).

#### *3.2. Grid Dependence, Verification, and Validation*

A grid dependence study was performed in our previous publication [32]. Local mesh refinement was used for different channel typologies, with extensive refinement near the wall of the channel and spacers, as shown in Figure 4.

Each of the simulations in the current work are based on the finest resolution identified in [32], with an average resolution of 1.13 and 0.25 µm in *x*- and *y*- directions, respectively, resulting in approximately 1 M (hexahedral) cells for the full domain. As shown in [32], this resolution introduces an error of less than 0.5%.

The flow behavior of the proposed framework was validated by comparison with the experimental measurements reported by Da Costa et al. [52] and Haaksman et al. [53]; as presented in [32]. The simulated pressure gradient with cylindrical corrugation was found to be somewhat lower than the pressure gradient for woven spacers, as reported by Gurreri et al. [26] at a given Re number; however, some discrepancies are expected, as Gurreri et al. considered the pressure drop in the collector and distributor of the RED stack, in addition to the main channel. The numerical results for the potential

and concentration have been verified for a flat channel by comparison with the semi-analytical solution proposed by Lacey [43], for both dilute and concentrated channels (see, e.g., [32]), showing good agreement between the concentration profile and the corresponding electrical potential across the height of the dilute compartment and our numerical solution [32].

**Figure 4.** Local grid refinement near the walls of the cylindrical corrugated spacer-filled channel. The coarsest mesh in the local grid refinement process was depicted due to better visibility. The region around the corrugation which goes under local refinement process is confined in a red square.

#### *3.3. Numerical Settings and Configuration*

All simulations presented in the following chapter were performed using the OpenFOAM version 4.1 software [44] on the IDUN cluster [54]. A summary of the numerical settings used in the current work are given in Table 1. The absolute residual for pressure, velocity, concentration, and electrical potential was set to 10−<sup>6</sup> , while the relative residual for the parameters was set to 10−<sup>4</sup> .


**Table 1.** Discretization schemes specified for the case studies.

#### *3.4. Factorial Design and Parametric Study*

The influence of four quantitative parameters—inlet velocity, corrugation density, corrugation height, and temperature—on the resistivity and net peak power density were investigated. In addition to these four quantitative parameters, the effect of corrugation shape (cylindrical versus triangular) was considered to be a qualitative parameter. To determine the relative influence of each parameter on the power density, a parametric study was performed using a factorial design, as described by Montgomery [45]. The various factors and their corresponding levels are given in Table 2.

**Table 2.** Factors and levels used for the 2<sup>4</sup> design for cylindrical and triangular corrugated channels.


The corresponding values of the parameters for each geometry are given in Table 3. Notice that the Re numbers change, based on both the inlet velocity and the temperature, due to the change in viscosity. The pressure drop for Re numbers larger than 10 was so high that it resulted in a negative net peak power density in a unit cell and, therefore, the Re number in this study was limited to less than 10.

**Table 3.** Characteristic parameters of the studied geometries in factorial design and the input parameters. (The values of the current densities are dependent of the available area of the membranes for different topologies).


In the factorial design, each of the parameters (*m* parameters) were investigated at *n* levels, which gave us a set of *n* × *m* simulations, where the influence of each parameter, as well as their combined effect, could be determined. In this factorial design, the parameters were restricted to two levels, designated + and − (i.e., each parameter had a high and low level). Therefore, the results were restricted to a linear response for a given factor. There were 2<sup>4</sup> designs for cylindrical and 2<sup>4</sup> designs for triangular corrugation. Other fluid properties used for the current simulations are summarized in Table 4.

**Table 4.** Transport properties of the fluid at temperatures considered, reported diffusivities by Bastug and Kuyucak [48], and viscosities by Tseng et al. [56].


#### **4. Results and Discussion**

Figure 5 shows the concentration contour for a dilute solution channel with cylindrical spacers. The corrugation height (radius) was 0.1 mm and the distance between two successive corrugation centers was 0.6 mm. The figure also shows the results for two different average inlet velocities (u = 4.5 and 25.8 mm s ) at two different temperatures (T = 25 ◦C and 55 ◦C).

(**d**) Re=10 (u = 25.8 mm s ) and T = 55 ◦C

**Figure 5.** Concentration contour maps for dilute solution in a cylindrical corrugated channel at different Re numbers and temperatures.

Higher velocity and lower temperature resulted in less mixing of solutions and, therefore, lower average bulk concentration (shown by cold blue color in the concentration contour map in Figure 5b); thus, higher resistivities and lower power densities were expected. Enhanced mixing (higher average bulk concentration) was observed at lower velocity and higher temperature (shown by red and warmer blue colors of the concentration contour map in Figure 5c). The concentration profiles versus the height of the channel at the *a* − −*b* cross-section line is shown in Figure 5a, with a distance of X = 10.8 mm from the inlet of the dilute channel. Data sets from this line, for all geometries, are gathered and compared to each other in Figure 6. This was done for two different inlet average velocities (u = 4.5 and 25.8 mm s ) and two different temperatures (T = 25 ◦C and 55 ◦C). Again, this figure confirms that at higher velocities and lower temperatures, the average concentration became lower. For all cases, the current density along the wall of the channel was considered constant (i.e., the current density for the peak power density), while the concentration along the walls was not constant, due to the imposed boundary conditions. Furthermore, the conductivity profiles for four cases versus the height of the channel (the *a* − −*b* cross-section in Figure 5a) are compared in Figure 7. The solution conductivities can be calculated using Equation (19), in which conductivity is a function of the concentration of the solution.

$$\sigma\_{\parallel} = \frac{F^2 \mathcal{C}}{RT} \left( \mathcal{D}\_{+} + \mathcal{D}\_{-} \right). \tag{19}$$

The higher conductivity of the dilute channel agreed with the lower resistivity of the channel and, thus, a higher power density could be achieved. Figure 7 shows that the channel with lower flow velocity (u = 4.5 mm s ) and higher temperature (T = 55 ◦C ) had enhanced mixing, with the highest calculated power density among these four cases.

**Figure 6.** Concentration profiles versus the height of the channel (the *a* − −*b* cross-section in Figure 5a) at X = 0.0108 m from the inlet of the dilute channel at two different inlet average velocities (u = 4.5 and 25.8 mm s ) and T = 25 ◦C and T = 55 ◦C, resulting in four different Re numbers: Re = 1, 1.8, 5.7, and 10.

**Figure 7.** Conductivity versus the height of the channel (the *a* − −*b* cross-section in Figure 5a) at X = 0.0108 m from the inlet of the dilute channel at two different inlet average velocities (u = 4.5 and 25.8 mm s ) and T = 25 ◦C and T = 55 ◦C, resulting in four different Re numbers: Re =1, 1.8, 5.7, and 10.

#### *4.1. Parametric Study*

The performance of reverse electrodialysis is influenced by several parameters. Their single or combined impacts were investigated, using a parametric study and a factorial design. Results for the area resistance and power density are summarized for cylindrical corrugation in Table 5, and for triangular corrugation in Table 6.

The simulated net power densities found in this numerical study were comparable to the maximum power densities for RED reported by the authors in another publication [2], which were calculated by using conceptual analytical models with similar channel dimensions, as well as similar temperature and concentration ranges. In addition, the power densities obtained in this study at 25 ◦C were close to the calculated power densities reported by Long et al. [40], at similar temperature and isothermal conditions, by applying numerical modeling for the investigation of nanofluidic salinity gradient energy harvesting [40]. The simulated net peak power densities were also in the range of the net power densities reported by Vermaas et al. [14], who calculated the theoretical RED net power density for different spacer-filled channels with channel thicknesses between 1–200 µm, and with residence time (defined as the length of the channel divided by the inlet flow velocity) between 0.5–200 s, in addition to changing the channel length and the resistivity of the AEM and the CEM. The residence time in the current work was within 0.2 to 2 s for the high- and low-level cases, respectively. As the resistivity of the channel decreased, the net power density for a RED unit cell increased for all system configurations. This observation was valid both for cylindrical and triangular corrugations, and was due to reduced lower-ohmic and non-ohmic losses. Increasing the temperature had a positive effect on the net peak power density, due to higher open-circuit potential, enhanced diffusivity, and improved mixing of concentrated and dilute solutions, as well as a lower pressure drop due to lower fluid viscosity at elevated temperature. Similar observations were reported experimentally by Luo et al. [37], Benneker et al. [57], and Daniilidis et al. [58]. Increasing the flow velocity had an adverse effect on the net power density, as a result of decreased mass transfer and increased pressure losses.

Vermaas et al. [55] also reported that the RED net power density was reduced for flows with Re numbers larger than 1 in channels with different thicknesses. The corrugation density and corrugation height had both positive and negative effects on the net peak power density. The corrugation height had an adverse effect on net power density, as pressure loss and consumed energy increase with higher corrugation height. This occurs even if the resistivity is lightly reduced, due to the increased corrugation height. In summary, one can conclude that the optimum parameters among the studied cases (i.e., for maximizing the net power density) was when the temperature was 55 ◦C, the flow velocity was 4.5 mm s , the corrugation density was 20, and the corrugation height was 0.05 mm (for both the cylindrical and the triangular corrugation); see Tables 5 and 6.

**Table 5.** Summary of factors, area resistance of the dilute solution compartment, and net peak power densities of the unit cell in the 2D model of a **cylindrical** corrugated channel: A, velocity; B, temperature; C, corrugation density; D, corrugation height. Case 1 is the base case.


**Table 6.** Summary of factors, area resistance of the dilute solution compartment, and net peak power densities of the unit cell in the 2D model of a **triangular** corrugated channel: A, velocity; B, temperature; C, corrugation density; D, corrugation height. Case 1 is the base case.


The triangular spacer corrugation configuration had slightly better performance, compared to the cylindrical one, which was in agreement with the previous studies reported by Ahmad et al. [20] and Jalili et al. [31]. The estimated effect of each factor is shown in Tables 7 and 8. The tables reveal that temperature was the most dominant factor, followed by inlet velocity, corrugation density, and corrugation height, respectively.


**Table 7.** Sign and percent contribution of area resistance and power density for each of the factors in the **cylindrical** corrugated channel shown in Table 5.

**Table 8.** Sign and percent contribution of area resistance and power density for each of the factors in the **triangular** corrugated channel shown in Table 6.


It is worth mentioning that the simulated power densities in this study were larger than the experimentally measured power densities, such as those reported by Zhu et al. [59]. The current mathematical model was developed for incompressible, steady-state, isothermal, and laminar flow with only the presence of monovalent ions. Therefore, the results of the CFD model might not be representative when the flow regime is turbulent, the system is in unsteady state, or if multivalent ions exist. In addition, this CFD model is proposed for a unit cell; thus, it does not represent a full RED stack. The influences of anion and cation exchange membranes or water osmosis of the membranes are ignored in this study. Other sources of energy losses, such as pumping losses through the collector and distributor of the stack, are also neglected, as well as the practical issues relating to 3D flow distribution.

#### *4.2. Concentration Polarization*

The area resistances reported in Tables 5 and 6 were calculated based on the electrical potential drop across the channel height for the whole channel, thereby accounting for both ohmic and non-ohmic contributions. By comparing the corresponding conductivities in Tables 5 and 6 with the conductivities in Figure 7, in which only ohmic contributions are considered, we can obtain the non-ohmic contribution (i.e., the share of polarization in the system), as shown in Table 9. In fact, the resistivity calculated by Equation (10) is the area-weighted total resistivity which depends on the area-weighted electrical potential loss, and is obtained directly from solving Equations (1)–(7), provided the boundary conditions. Equation (19) provides the average conductivity of the channel solution based on the average concentration. The reverse of the average conductivity is the average ohmic resistivity. The difference between the total and the average ohmic resistivity, gives the average non-ohmic resistivity.


**Table 9.** The contribution of ohmic and non-ohmic resistance for Cases 13, 14, 15, and 16 of Table 5 (i.e., with cylindrical corrugation).

By comparing the resistivities in Table 9, three observations can be made: First, the share of non-ohmic losses (i.e., concentration polarization effects) was significantly lower than ohmic losses. Second, by increasing the flow velocity at a constant temperature or reducing the temperature at a constant inlet velocity, the ohmic losses increase. Third, increasing the flow velocity and temperature results in the reduction of the non-ohmic losses share of the total resistivity; that is, increasing the Re number (by enhancing the temperature or increasing the inlet flow velocity) will assist in reducing the concentration polarization effect in RED systems. These are consistent with the experimental observations reported by Vermaas et al. [55].

#### **5. Conclusions**

The effect of flow velocities, temperature, and spacer topology on the resistivity and net peak power density of a reverse electrodialysis (RED) unit cell were explained, based on CFD modeling which enabled the simulation of flow, pressure drop, concentration, electrical potential, and power density. Our parametric study revealed that while increasing the temperature and corrugation density had positive effects on the net produced power density, increasing the flow velocity and corrugation height had adverse effects. Among the studied parameters, temperature was the most dominating factor, followed by inlet velocity, corrugation density, and corrugation height, respectively. Increasing the temperature benefited the system performance by decreasing the non-ohmic resistance and the corresponding energy losses. Increasing the temperature also benefited the system performance by decreasing ohmic resistances. Moreover, elevating the temperature led to a system with a better performance increase than varying the flow velocity. The increase of temperature can be realized by use of low-grade waste heat, as discussed in [1] for instance.

**Author Contributions:** Z.J.'s contribution is developing the idea of the research work, building the models and running the simulations, post-processing and analyzing of the results, and writing the draft of the manuscript, including the literature review, results, and discussions. K.E.E. and O.S.B. contributed to proposing the first idea of the research work and furthermore developing the idea, as well as supervising and revising the manuscript. All authors participated in discussing the results. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by ENERSENSE (Energy and Sensor Systems) group (project number 68024511) at Norwegian University of Science and Technology (NTNU).

**Acknowledgments:** Financial support from ENERSENSE (Energy and Sensor Systems) group at Norwegian University of Science and Technology (NTNU) is greatly acknowledged. NTNU IDUN/EPIC computing cluster was used for performing simulations, which is also highly appreciated. Zohreh Jalili would like to thank Vahid Alipour Tabrizy for all help and support throughout this work, without which this research would not have been made possible.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **A Comprehensive Membrane Process for Preparing Lithium Carbonate from High Mg**/**Li Brine**

**Wenhua Xu, Dongfu Liu, Lihua He \* and Zhongwei Zhao \***

School of Metallurgy and Environment, Central South University, Changsha 410083, China; xuwenhua@csu.edu.cn (W.X.); liudongfu@csu.edu.cn (D.L.)

**\*** Correspondence: helihua@csu.edu.cn (L.H.); zhaozw@csu.edu.cn (Z.Z.)

Received: 21 October 2020; Accepted: 18 November 2020; Published: 26 November 2020

**Abstract:** The preparation of Li2CO<sup>3</sup> from brine with a high mass ratio of Mg/Li is a worldwide technology problem. Membrane separation is considered as a green and efficient method. In this paper, a comprehensive Li2CO<sup>3</sup> preparation process, which involves electrochemical intercalation-deintercalation, nanofiltration, reverse osmosis, evaporation, and precipitation, was constructed. Concretely, the electrochemical intercalation-deintercalation method shows excellent separation performance of lithium and magnesium, and the mass ratio of Mg/Li decreased from the initial 58.5 in the brine to 0.93 in the obtained lithium-containing anolyte. Subsequently, the purification and concentration are performed based on nanofiltration and reverse osmosis technologies, which remove mass magnesium and enrich lithium, respectively. After further evaporation and purification, industrial-grade Li2CO<sup>3</sup> can be prepared directly. The direct recovery of lithium from the high Mg/Li brine to the production of Li2CO<sup>3</sup> can reach 68.7%, considering that most of the solutions are cycled in the system, the total recovery of lithium will be greater than 85%. In general, this new integrated lithium extraction system provides a new perspective for preparing lithium carbonate from high Mg/Li brine.

**Keywords:** membrane process; Li2CO3; electrochemical intercalation deintercalation; high Mg/Li brine

#### **1. Introduction**

The fast development of electric vehicles, storage devices, and hand-held electronic devices has dramatically increased the demands for lithium [1–4]. Lithium carbonate is an important raw material for preparing lithium-ion battery cathode materials [5]. In recent years, global lithium (Li) demand has reached 180,000 tons of lithium carbonate equivalent in 2015, with forecasts as high as 1.6 M tons by 2030 [6,7].

Nowadays, lithium resources mainly exist in solid ore (such as spodumene and lepidolite) and brine, and over 70% of exploitable lithium in the world existed in the brine [8,9]. Compared with the lithium extraction from these two kinds of resources, lithium extraction from brine is more effective, simpler, and cheaper [8]. Most lithium resources in continental brines are found in a small region in South America, often referred to as the "Lithium Triangle" [9,10]. A notable feature of brines in the "Lithium Triangle" region is the low mass ratio of Mg/Li. In contrast, the grade of brine in other regions is much worse. In China, the major lithium-containing brines are located in the Qinghai–Tibet plateau [8,11], and most of the lithium-containing brines in this area are mostly magnesium sulfate subtype [12]. A typical feature of magnesium sulfate subtype brines is the mass ratio of Mg/Li, which has a long span (from tens to hundreds, even more than 1000) [13]. Therefore, how to effectively realize the separation of magnesium and lithium is the key to produce Li2CO<sup>3</sup> from high Mg/Li brines.

Multifarious methods such as solvent extraction [14], membrane separation [15–17], adsorption [18,19], and electrochemical intercalation-deintercalation (EID) method [17,20–23] have been developed for

lithium extraction from high Mg/Li brine. Solvent extraction is an efficient separation technology; both of the separation factors (SFLi–Na, SFLi–Mg) can reach hundreds or even more than one thousand [24,25]. However, the extraction reagent has a slight solubility in aqueous solution [26], which is not suitable for treating brine directly. The ion-sieve absorption method is considered to be an effective approach to extract lithium from the high Mg/Li ratio brines thanks to its low cost, high selectivity, and nontoxicity [27]. However, the ion-sieve absorption method faces the following problems: (1) it is difficult to prepare the high absorption capacity absorbent; and (2) there is a significant loss of capacity in the desorption process when acids or oxidants are used as desorption agents. The above problems seriously restrict its large-scale industrial application [20].

Nanofiltration (NF), as an important membrane separation technology, has been successfully applied for separating lithium and magnesium from a high Mg/Li brine because of its selective rejection of divalent ions and monovalent ions based on Donnan exclusion [28,29]. However, it also suffers from the following problems: (1) This technology can only treat brine with very low sodium and potassium content, and it usually takes 1–2 years to obtain this kind of brine [30–32]. (2) The salinity in the type of brine after potassium removal is too high to meet the operation condition for this purpose, which needs to be diluted with water (the amount of water used for dilution is usually several times than the brine). This process not only needs to consume a large amount of fresh water, but also increases the amount of water to be treated.

In our previous work, we have proved that the EID method shows an excellent lithium extraction properties from the high mass ratio of brine [20,21,33]; the mass ratio of brine can be decreased from the initial 58.5 in the brine to 0.93 in the obtained anolyte. Although the mass ratio of Mg/Li in the anolyte is much lower than the original brine, the lithium concentration in the anolyte is only 1–2 g·L −1 , which is far from the lithium concentration required to precipitate lithium carbonate. For this reason, we need to concentrate the anolyte and remove the residual impurities (e.g., Mg2+, Ca2+, and SO<sup>4</sup> <sup>2</sup>−) in it. Theoretically, all kinds of concentration methods (like reverse osmosis, electrodialysis, evaporation, and so on) [34,35] and impurity removal methods (like nanofiltration, solvent extraction, and so on) [24,28,29] can be used to treat the obtained anolyte. Notably, the total salt concentration of the obtained anolyte is between 20 and 30 g·L −1 , which is an ideal range for NF and reverse osmosis (RO) treatment. Therefore, we proposed an integrated lithium carbonate preparation process combining EID, NF, RO, evaporation, and precipitation processes to prepare Li2CO<sup>3</sup> from a high Mg/Li brine. The aim of the main processes are as follows: (1) the EID method is used to maximize the separation of magnesium and lithium from the brine to obtain a low Mg/Li anolyte; (2) removing the multivalent ions (e.g., Mg2+, Ca2+, and SO<sup>4</sup> <sup>2</sup>−) from the obtained anolyte via the NF method; (3) concentrating the permeate flow produced by NF with the RO method; (4) further increasing the lithium concentration by evaporation; and (5) precipitating Li2CO<sup>3</sup> by adding Na2CO3.

#### **2. Materials and Methods**

#### *2.1. Membranes*

The membrane used in the EID method is a heterogeneous anionic membrane (MA-3475), which was purchased from Beijing Anke Membrane Separation Technology & Engineering Co., LTD. (Beijing, China agent). The heterogeneous anionic membrane selectively allows the anions to pass through and reject the cations. The NF (NF2) and RO (RO5) membranes used for the experiment are disc tube membranes, which were made by RisingSun Membrane Technology Co., Ltd., (Beijing, China). Specifically, the membrane areas of the NF membrane and RO membrane are both 2.2 m<sup>2</sup> , and the operation pH are in the range of 3–11. The permeate flux and desalination rate of NF were 42 L·m−<sup>2</sup> ·h <sup>−</sup><sup>1</sup> and 98%, respectively, which were obtained at 25 ◦C, operating pressure of 0.7 MPa, and test salt concentration of MgSO<sup>4</sup> of 2 g·L −1 . Further, the permeate flux and desalination rate of RO were 42 L·m−<sup>2</sup> ·h <sup>−</sup><sup>1</sup> and 99.5%, respectively, which were obtained at 25 ◦C, operating pressure of 1.55 MPa, and test salt concentration of NaCl of 2 g·L −1 .

#### *2.2. Experimental Illustration*

#### 2.2.1. Methods

LiFePO4/FePO<sup>4</sup> electrodes' preparation: LiFePO<sup>4</sup> electrode was prepared as follows: (1) weighing LiFePO4, polyvinylidene fluoride (PVDF), and acetylene black (C) in a mass ratio of 8:1:1; (2) dissolving PVDF into N-methylpyrrolidone (NMP) and then adding C and LiFePO<sup>4</sup> in order; (3) coating the above-mixed slurry on a carbon fiber sheet; and (4) drying the prepared carbon fiber sheet in a vacuum oven at 95 ◦C for 12 h. The FePO<sup>4</sup> electrode was obtained by deintercalating lithium from the LiFePO<sup>4</sup> electrode. Concretely, an electrolytic cell is divided into an anode chamber and cathode chamber by anion membrane, LiFePO<sup>4</sup> electrode (anode) and nickel foam (cathode) were placed into the anode and cathode chamber, respectively. Both of the chambers were filled with 5 g·L <sup>−</sup><sup>1</sup> NaCl solution and the pH value of the catholyte was controlled to 2–3 using HCl. The voltage used in electrolysis is 1.0 V, and the electrolysis ends until the current density is less than 0.05 mA·cm−<sup>2</sup> .

EID method for lithium extraction: The device for the EID method is shown in our previous work [20]. The device of the EID system was divided into two chambers by the anion membrane, where LiFePO<sup>4</sup> and FePO<sup>4</sup> is used as anode and cathode, respectively. The anode and cathode chambers are filled with supporting electrolyte and brine, respectively. The entire working process is shown below: (1) lithium deintercalated from LiFePO<sup>4</sup> to the supporting electrolyte (LiFePO<sup>4</sup> – e = Li<sup>+</sup> + FePO4); (2) lithium existed in the brine intercalated into FePO<sup>4</sup> (Li<sup>+</sup> + FePO<sup>4</sup> + e = LiFePO4); and (3) the Cl− in the brine diffused into the anode chamber through the anionic membrane to maintain the electroneutrality of the anolyte and brine, and LiCl was obtain in the anolyte.

The brine used for the lithium extraction was from West Taijnar Salt Lake (Golmud, China) with the Mg/Li ratio of 58.8 (Table 1), and the lithium extraction process was carried out via instrument LANHE-CT2001A (Wuhan, China). The effective size of the electrodes was 17 <sup>×</sup> 20 cm<sup>2</sup> , and the electrodes of LiFePO<sup>4</sup> and FePO<sup>4</sup> worked as anode and cathode, respectively. The electrode coating density was about 85 mg (LiFePO4)·cm−<sup>2</sup> . The electrolytic cell was comprised of two chambers, which were separated by an anion exchange membrane (MA-3475, Beijing Anke Membrane Separation Technology Engineering Co. LTD, Beijing, China agent). The anode chamber was filled with 1.5 L of 5 g·L <sup>−</sup><sup>1</sup> NaCl as supporting electrolyte, and the cathode chamber was filled with 1.5 L brine. The entire electrolysis was performed with a constant current of 0.6 A until the voltage reached 0.35 V, and then worked at a constant voltage until the current dropped to 0.1 A to end the electrolysis process.


**Table 1.** The components of the West Taijnar Salt Lake brine (g·L −1 ).

NF for purification: The obtained anolyte was purified by NF, the volume of the feed used in the nanofiltration was 200 L, and the composition of the feed used was configured according to the composition of the anolyte obtained by the EID system. The NF process was carried out at a constant pump power of 2 KW until the operation pressure reached 8 MPa. The total volume of the collected permeate solution was 180 L.

RO for concentration: The collected permeate solution after the NF treatment was concentrated by RO process, and only 175 L feed liquor was used in the process. The whole RO process was performed at the room temperature and ended until the volume of permeate reached 105 L. The RO process was also carried out at a constant pump power of 2 KW.

Evaporation and concentration: The evaporation process was carried out by an electric furnace, and the initial volume of the solution used for the evaporation was 5 L.

Precipitation of Li2CO3: The lithium-containing solution after evaporation process was precipitated by Na2CO<sup>3</sup> (280 g·L −1 ) at 95 ◦C. The addition of sodium carbonate is 1.05 times the dosage of theoretical amount used in the lithium precipitation reaction. When all of the Na2CO<sup>3</sup> wass added into the LiCl solution, the solution was stirred for 1 h to mature the lithium carbonate, and then the Li2CO<sup>3</sup> was filtered out. The obtained lithium carbonate was washed twice with deionized water and dried to obtain the Li2CO<sup>3</sup> product. *Membranes* **2020**, *10*, x FOR PEER REVIEW 4 of 14 Li2CO3 was filtered out. The obtained lithium carbonate was washed twice with deionized water and dried to obtain the Li2CO3 product.

In general, the comprehensive membrane process is shown in Figure 1. In general, the comprehensive membrane process is shown in Figure 1.

**Figure 1.** Schematic diagram of the comprehensive membrane process. EID, electrochemical intercalation-deintercalation; NF, nanofiltration; RO, reverse osmosis. **Figure 1.** Schematic diagram of the comprehensive membrane process. EID, electrochemical intercalation-deintercalation; NF, nanofiltration; RO, reverse osmosis.

#### 2.2.2. Analytical Methods 2.2.2. Analytical Methods

The concentration of Li+, Na+, K+ and Mg2+, and Ca2+ in the solutions was measured by inductively coupled plasma-optical emission spectrometry (ICP-OES, Thermo Scientific iCAP-7200, Shanghai, China agent), and the concentration of SO42− was measured by ion chromatography (ICS-5000/DIONEX, Thermofisher Scientific, Shanghai, China agent). The X-Ray Diffraction (XRD) patterns were measured via a BRUKER D8 ADVANCE using Cu-Kα radiation (λ = 1.54056 Å). The morphology of Li2CO3 was detected by a scanning electron microscope (SEM, JEOL JSM-6490LV, JEOL (BEIJING) CO., LTD., Beijing, China agent). The concentration of Li+, Na+, K<sup>+</sup> and Mg2+, and Ca2<sup>+</sup> in the solutions was measured by inductively coupled plasma-optical emission spectrometry (ICP-OES, Thermo Scientific iCAP-7200, Shanghai, China agent), and the concentration of SO<sup>4</sup> <sup>2</sup><sup>−</sup> was measured by ion chromatography (ICS-5000/DIONEX, Thermofisher Scientific, Shanghai, China agent). The X-ray Diffraction (XRD) patterns were measured via a BRUKER D8 ADVANCE using Cu-Kα radiation (λ = 1.54056 Å). The morphology of Li2CO<sup>3</sup> was detected by a scanning electron microscope (SEM, JEOL JSM-6490LV, JEOL (BEIJING) CO., LTD., Beijing, China agent).

#### 2.2.3. Calculation 2.2.3. Calculation

The separation factor (SF) of lithium and magnesium was calculated as Equation (1): The separation factor (SF) of lithium and magnesium was calculated as Equation (1):

$$\text{SF} = \frac{\text{C}\_{\text{Li}}/\text{C}\_{\text{Mg}}}{\text{C}\_{\text{Li}}^{\prime}/\text{C}\_{\text{Mg}}} \tag{1}$$

where SF is the separation factor of Li+ and Mg2+, *C*Li is the concentration of lithium in the obtained solution (g·L−1), *C*Mg is the concentration of magnesium in the obtained solution (g·L−1), *C*Li' is the concentration of lithium in the feed (g·L−1), and *C*Mg' is the concentration of magnesium retained in the feed (g·L−1). where SF is the separation factor of Li<sup>+</sup> and Mg2+, *C*Li is the concentration of lithium in the obtained solution (g·L −1 ), *C*Mg is the concentration of magnesium in the obtained solution (g·L −1 ), *C* 0 Li is the concentration of lithium in the feed (g·L −1 ), and *C* 0 Mg is the concentration of magnesium retained in the feed (g·L −1 ).

The recovery of lithium (*R*E) for the electrolytic intercalation-deintercalation system was calculated as Equation (2): The recovery of lithium (*R*E) for the electrolytic intercalation-deintercalation system was calculated as Equation (2):

$$R\_{\rm E} = \frac{\mathcal{C}\_0 V\_0 - \int\_0^t \mathcal{C}\_l V\_l}{\mathcal{C}\_0 V\_0} \times 100\% \tag{2}$$

where *R*<sup>E</sup> is the recovery of lithium in the brine, *C*0 is the initial concentration of lithium in the brine

where *R*<sup>E</sup> is the recovery of lithium in the brine, *C*<sup>0</sup> is the initial concentration of lithium in the brine (g·L −1 ), *V*<sup>0</sup> is the initial volume of the brine (L), *t* is the sampling time (h), *C<sup>t</sup>* is the concentration of lithium in brine at *t* (g·L −1 ), and *V<sup>t</sup>* is the volume of brine at *t* (L).

The retention ratio (*R*) refers to the permeability of ions, which is the main index to evaluate the separation performance. The corresponding calculation process is shown in Equation (3).

$$R = \frac{\mathbf{C}\_F V\_F - \mathbf{C}\_P V\_P}{\mathbf{C}\_F V\_F} \times 100\% \tag{3}$$

where *R* represent the retention ratio and *C<sup>F</sup>* and *C<sup>P</sup>* are the concentrations of ions of the feed and permeate solution (g·L −1 ), respectively. *V<sup>F</sup>* and *V<sup>P</sup>* are the volume of the feed and permeate solution (L).

#### 2.2.4. Membrane Cleaning

The membranes need to be washed when the transmembrane pressure difference is greater than 0.35 MPa. For the membrane scaling caused by inorganic salts, 1% (wt) ethylenediamine tetraacetic acid disodium salt (EDTA) + citric acid solution (citric acid is used to adjust the pH of the solution to 3–4) is generally used for cleaning at room temperature for about 1 h.

#### **3. Results and Discussion**

#### *3.1. Lithium Extraction From the Brine*

The primary contents of the West Taijinar used for the lithium extraction are shown in Table 1, and the experimental results are exhibited in Figure 2. From Figure 2a, it can be seen that the concentration of lithium reached 2.1 g·L <sup>−</sup><sup>1</sup> at the end of the second cycle, and the concentration of lithium in the brine decreased from the initial 2.05 g·L −1 to 0.18 g·L −1 , while the total recovery of lithium reached 90.6% at the end of the second cycle. In the same way, the decline rate of lithium in the second cycle is slightly lower than that in the first cycle, which is mainly owing to the continuous decline of lithium concentration in the brine.

Figure 2b shows the voltage and current curves in the first two cycles. It can be seen that the first cycle took 13.5 h, while the second cycle only lasted 10.5 h. In addition, the constant current process in the first cycle lasts longer than in the second cycle. Correspondingly, the voltage growth rate in the first cycle is also slower. The above results are attributed to the fact that the lithium concentration in the second cycle is lower than that in the first cycle, which leads to more serious polarization of lithium extraction in the second cycle.

Figure 2c shows the cyclic voltammetry (CV) curves of LiFePO<sup>4</sup> in the brine; it can be seen that there are a couple of obvious peaks for the deintercalation/intercalation of lithium located at 0.337 V (vs. saturated calomel electrode (SCE)) and 0.178 V (vs. SCE), which correspond to the deintercalation of lithium from LiFePO<sup>4</sup> (LiFePO<sup>4</sup> – e = Li<sup>+</sup> + FePO4) and the intercalation of lithium to FePO<sup>4</sup> (FePO<sup>4</sup> <sup>+</sup> Li<sup>+</sup> <sup>+</sup> <sup>e</sup> <sup>=</sup> LiFePO4), respectively. There also exists a weak reduction peak at <sup>−</sup>0.443 V (vs. SCE), which corresponds to the intercalation of magnesium (FePO<sup>4</sup> + 0.5 Mg2<sup>+</sup> + e = Mg0.5FePO4). Obviously, magnesium is more difficult to insert into FePO<sup>4</sup> than lithium, which means that FePO<sup>4</sup> can selectively extract lithium from a high Mg/Li brine via potential control. In addition, the inset illustration in Figure 2c shows that the mass ratio of Mg/Li in the obtained anolyte is only 0.93, which is far lower than 58.5 in the brine. The above results show that the new EID system has excellent separation performance for lithium and magnesium.

Figure 2d shows the charge/discharge curves of LiFePO<sup>4</sup> in the West Taijinar brine. It can be seen that the charging and discharging curves of the 20 cycles are relatively stable, which means that LiFePO<sup>4</sup> can operate stably in the brine.

*Membranes* **2020**, *10*, x FOR PEER REVIEW 6 of 14

**Figure 2.** The EID system for lithium extraction. (**a**) Li+ concentration and Li+ recovery rate in the first two cycles; (**b**) current and voltage changes in two cycles; (**c**) the cyclic voltammetry (CV) curves of brine and the illustration shows the Mg/Li in the obtained anolyte; (**d**) charge and discharge cycle performance of the brine. SCE, saturated calomel electrode. **Figure 2.** The EID system for lithium extraction. (**a**) Li<sup>+</sup> concentration and Li<sup>+</sup> recovery rate in the first two cycles; (**b**) current and voltage changes in two cycles; (**c**) the cyclic voltammetry (CV) curves of brine and the illustration shows the Mg/Li in the obtained anolyte; (**d**) charge and discharge cycle performance of the brine. SCE, saturated calomel electrode.

Furthermore, the analysis results of the main ions in the produced anolyte are shown in Table 2. From Table 2, it can be seen that the main ions in the anolyte are Li+, Na+, and Mg2+. Compared with the Mg2+ concentration in the brine, the penetration of magnesium into the anolyte is negligible. The rejection rates of the impurities such as K+, Mg2+, and SO42− are 92.2%, 98.5%, and 99.2%, respectively. The retention of cations by the anion membrane is mainly due to the charge repulsion of the fixed cationic groups of the membrane itself to the cations in the solution [36,37]. The interception of divalent sulfate is mainly due to the fact that the ionic radius of sulfate is larger than that of chloride ions, and the concentration of chloride ions is much greater than that of sulfate, which makes the content of sulfate permeable through the membrane very low in the process of lithium extraction. In general, the concentration of the impurities in the obtained anolyte is very low, which is facilitation for the subsequent purification process. Furthermore, the analysis results of the main ions in the produced anolyte are shown in Table 2. From Table 2, it can be seen that the main ions in the anolyte are Li+, Na+, and Mg2+. Compared with the Mg2<sup>+</sup> concentration in the brine, the penetration of magnesium into the anolyte is negligible. The rejection rates of the impurities such as K+, Mg2+, and SO<sup>4</sup> <sup>2</sup><sup>−</sup> are 92.2%, 98.5%, and 99.2%, respectively. The retention of cations by the anion membrane is mainly due to the charge repulsion of the fixed cationic groups of the membrane itself to the cations in the solution [36,37]. The interception of divalent sulfate is mainly due to the fact that the ionic radius of sulfate is larger than that of chloride ions, and the concentration of chloride ions is much greater than that of sulfate, which makes the content of sulfate permeable through the membrane very low in the process of lithium extraction. In general, the concentration of the impurities in the obtained anolyte is very low, which is facilitation for the subsequent purification process.

**Table 2.** The concentration of the main ions in the obtained anolyte (g·L<sup>−</sup>1). **Table 2.** The concentration of the main ions in the obtained anolyte (g·L −1 ).


\* The initial concentration of Na+ added in the form of NaCl is 2.0 g·L−1. \* The initial concentration of Na<sup>+</sup> added in the form of NaCl is 2.0 g·L −1 .

Therefore, the EID system shows excellent separation properties of lithium and magnesium. It is an efficient, environmentally friendly, and stable process without using acid, alkali, or any toxic reagents, nor does it produce any solid waste. The brine after the lithium extraction can be directly discharged back to the salt fields, without affecting the environment. Therefore, the EID system shows excellent separation properties of lithium and magnesium. It is an efficient, environmentally friendly, and stable process without using acid, alkali, or any toxic reagents, nor does it produce any solid waste. The brine after the lithium extraction can be directly discharged back to the salt fields, without affecting the environment.

#### *3.2. NF and RO Processes* retentate solution; (2) the precipitation of the salts on the surface of the NF membrane; and (3) the compaction of the NF membrane.

3.2.1. NF Process

*3.2. NF and RO Processes* 

In order to precipitate lithium carbonate, the lithium-riched anolyte needs to be deeply purified and concentrated. In this paper, NF and RO were used for deep purifying of the divalent ions and concentrating of the penetrating fluid, respectively. Both NF and RO were carried out only once and the corresponding results of the NF and RO processes are shown in below. The concentration of the ions in the permeate flow and collected retentate during the NF process are shown in Table 3 and Figure 3b, respectively. From Table 3, it can be seen that the conductivity increased slowly at the beginning of the initial stage (increased from 37.5 mS·cm−1 to 52.0 mS·cm−1). Subsequently, a significant increase followed after 90 min from the start of the NF, and the conductivity reached 108.2 mS·cm−1. The temperature rose slowly throughout the experiments (from

There are three main reasons for this phenomenon: (1) the increase of the osmotic pressure in the

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the corresponding results of the NF and RO processes are shown in below.

In order to precipitate lithium carbonate, the lithium-riched anolyte needs to be deeply purified and concentrated. In this paper, NF and RO were used for deep purifying of the divalent ions and concentrating of the penetrating fluid, respectively. Both NF and RO were carried out only once and

The corresponding experimental results are shown in Figure 3 and Table 3. As shown in Figure 3a, the initial operation pressure of the nanofiltration was 2.0 MPa. The water flux decreases slowly from the initial 52 L·m−2·h−1 to 50.5 L·m−2·h−1 at first, and then rapidly declines from 50.5 L·m−2·h−1 to

#### 3.2.1. NF Process 24.7 °C to 27.5 °C), and the rise in water temperature comes from two aspects: (1) the mechanical friction of the high pressure pump produce a great deal of heat; and (2) the friction of the fluid and

The corresponding experimental results are shown in Figure 3 and Table 3. As shown in Figure 3a, the initial operation pressure of the nanofiltration was 2.0 MPa. The water flux decreases slowly from the initial 52 L·m−<sup>2</sup> ·h −1 to 50.5 L·m−<sup>2</sup> ·h <sup>−</sup><sup>1</sup> at first, and then rapidly declines from 50.5 L·m−<sup>2</sup> ·h −1 to 31.6 L·m−<sup>2</sup> ·h −1 . Inversely, the operation pressure increases at first and then rapidly reaches 8 MPa. There are three main reasons for this phenomenon: (1) the increase of the osmotic pressure in the retentate solution; (2) the precipitation of the salts on the surface of the NF membrane; and (3) the compaction of the NF membrane. the pipe, which also generates heat. The flow rate of the entire NF process was kept at 16 L·min−1. There was no significant change in the concentration of monovalent ions such as Li+, Na+, and K+, while divalent ions such as Mg2+, Ca2+, and SO42− are abundantly enriched in the retentate solution. Moreover, the concentration of Mg2+, Ca2+, and SO42− at the end of the NF process reached 18.23 g·L−1, 0.02 g·L−1, and 2.41 g·L−1, respectively. It can be found that Mg2+, Ca2+, and SO42− were concentrated 9.3 times, 5 times, and 9.1 times, respectively. The concentrated times of Ca2+ were lower than those of Mg2+ and SO42−. Notably, the main anion in the collected retentate is Cl−, which was rejected to maintain the electrical neutrality of the collected retentate.

**Figure 3.** The NF process for purification. (**a**) The relationship of the operation pressure and the flux of the membrane; (**b**) concentration of Li+, Na+, K+, Mg2+, Ca2+, and SO<sup>4</sup> <sup>2</sup><sup>−</sup> in the permeate flow; (**c**) the rejection rate of Mg2<sup>+</sup> and SO<sup>4</sup> <sup>2</sup>−; (**d**) the recovery of lithium and the separation factor of lithium and magnesium (SFLi-Mg).

**Table 3.** The main analytical results in the collected retentate during the nanofiltration (NF) process.


The concentration of the ions in the permeate flow and collected retentate during the NF process are shown in Table 3 and Figure 3b, respectively. From Table 3, it can be seen that the conductivity increased slowly at the beginning of the initial stage (increased from 37.5 mS·cm−<sup>1</sup> to 52.0 mS·cm−<sup>1</sup> ). Subsequently, a significant increase followed after 90 min from the start of the NF, and the conductivity reached 108.2 mS·cm−<sup>1</sup> . The temperature rose slowly throughout the experiments (from 24.7 ◦C to 27.5 ◦C), and the rise in water temperature comes from two aspects: (1) the mechanical friction of the high pressure pump produce a great deal of heat; and (2) the friction of the fluid and the pipe, which also generates heat. The flow rate of the entire NF process was kept at 16 L·min−<sup>1</sup> . There was no significant change in the concentration of monovalent ions such as Li+, Na+, and K+, while divalent ions such as Mg2+, Ca2+, and SO<sup>4</sup> <sup>2</sup><sup>−</sup> are abundantly enriched in the retentate solution. Moreover, the concentration of Mg2+, Ca2+, and SO<sup>4</sup> <sup>2</sup><sup>−</sup> at the end of the NF process reached 18.23 g·<sup>L</sup> −1 , 0.02 g·L −1 , and 2.41 g·L −1 , respectively. It can be found that Mg2+, Ca2+, and SO<sup>4</sup> <sup>2</sup><sup>−</sup> were concentrated 9.3 times, 5 times, and 9.1 times, respectively. The concentrated times of Ca2<sup>+</sup> were lower than those of Mg2<sup>+</sup> and SO<sup>4</sup> <sup>2</sup>−. Notably, the main anion in the collected retentate is Cl−, which was rejected to maintain the electrical neutrality of the collected retentate.

As shown in Figure 3b, the concentration of Li+, Na+, Mg2+, and K<sup>+</sup> in the permeate flow increased obviously, while the concentration of Ca2+, and SO<sup>4</sup> <sup>2</sup><sup>−</sup> is very low and can almost be ignored (Ca2<sup>+</sup> and SO<sup>4</sup> <sup>2</sup><sup>−</sup> are 3.1 <sup>×</sup> <sup>10</sup>−<sup>4</sup> <sup>g</sup>·<sup>L</sup> <sup>−</sup><sup>1</sup> and 1.07 <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>g</sup>·<sup>L</sup> <sup>−</sup><sup>1</sup> at the end of the NF process). Specifically, the concentration of Li<sup>+</sup> and Na<sup>+</sup> increased from 2 g·L −1 to 2.54 g·L <sup>−</sup><sup>1</sup> and 1.55 g·<sup>L</sup> −1 to 1.97 g·L −1 , respectively. Moreover, the concentration of K<sup>+</sup> also increased slowly from 0.033 g·<sup>L</sup> −1 to 0.041 g·L −1 . In contrast, the concentration of Mg2<sup>+</sup> increased sharply from 0.12 g·<sup>L</sup> −1 to 0.86 g·L −1 . Combining the concentration of ions (Li+, Na+, and Mg2+) in the collected retentate, it can be found that there is basically no interception of monovalent ions, while the interception rate of multivalent ions is very high. The reason for the higher rejection of Mg2<sup>+</sup> can be explained using Donnan exclusion. The concentration of counter ions (ions with charge opposite to the fixed charge in the membrane) in the membrane is higher than that in the bulk solution, while the concentration of homonymous ions in the membrane is lower than that in the bulk solution. The Donnan difference prevents the diffusion of homonymic ions from the bulk solution into the membrane. In order to maintain electrical neutrality, the counter ions are also trapped by the membrane. The coulomb repulsion of the multivalent ions is greater than that of the monovalent ions, which explains why the rejection of Mg2<sup>+</sup> is higher than that of Li<sup>+</sup> and Na+.

The rejection rate of the divalent ions is shown in Figure 3c. It can be seen that the rejection rates of SO<sup>4</sup> <sup>2</sup><sup>−</sup> are higher than 99%, while the retention rates of magnesium gradually drop to 89.9%. Combining the data presented in Figure 3b, it can be found that the concentration of Ca2<sup>+</sup> and SO<sup>4</sup> <sup>2</sup><sup>−</sup> in the permeate flow can almost be ignored, which means that sulfate and calcium ions can hardly pass through the nanofiltration membrane. In order to determine whether there is precipitation in the NF process, the solubility of all chlorides and sulfates in the solution at 20 ◦C is listed, as shown in Table 4.


**Table 4.** The solubility of all the chloride and sulfate exist in the collected retentate.

\* The solubility of calcium chloride and calcium sulfate refers to the solubility of their hydrated salts; they are CaCl2·6H2O and CaSO4·2H2O, respectively.

According to the results provided by Tables 3 and 4, all of the soluble salts that exist in the collected retentate are not saturated. Notably, there is 0.004 g·L <sup>−</sup><sup>1</sup> Ca2<sup>+</sup> and 0.26 g·<sup>L</sup> <sup>−</sup><sup>1</sup> SO<sup>4</sup> <sup>2</sup><sup>−</sup> in the beginning of the NF, which results in 0.04 g·L <sup>−</sup><sup>1</sup> Ca2<sup>+</sup> and 2.6 g·<sup>L</sup> <sup>−</sup><sup>1</sup> SO<sup>4</sup> <sup>2</sup><sup>−</sup> at an assumed retention of 100%, and the concentration of Ca2<sup>+</sup> and SO<sup>4</sup> <sup>2</sup><sup>−</sup> has not reached the *<sup>K</sup>*sp of CaSO4·2H2O (the solubility of CaSO4·2H2O is 0.255 g at 20 ◦C, which means the *<sup>K</sup>*sp of CaSO4·2H2O is 2.2 <sup>×</sup> <sup>10</sup>−<sup>4</sup> ) [38]. Because of the retention of divalent ions by the NF membrane and the influence of the electric double layer, a large amount of divalent ions will be enriched on the surface of the NF membrane. When the sulfate and calcium in the bulk retentate solution have not reached the conditions for CaSO4·H2O precipitation,

there is already CaSO4·H2O precipitation on the surface of the nanofiltration membrane. That is the reason the concentration of Ca2<sup>+</sup> in the bulk collected retentate is only 0.02 g·<sup>L</sup> −1 , as the feed solution has concentrated 10 times. Further, because the total amount of Ca2<sup>+</sup> is much lower than that of SO<sup>4</sup> <sup>2</sup>−, this results in the lower concentrated times of Ca2<sup>+</sup> than SO<sup>4</sup> <sup>2</sup>−. In order to reduce the membrane scaling caused by calcium sulfate precipitation, it is better to wash the membranes after the NF operation. By contrast, Mg2<sup>+</sup> can only be continuously accumulated in the collected retentate without precipitation, resulting in a higher concentration of Mg2<sup>+</sup> in the permeate flow. In other words, the more Mg2<sup>+</sup> that enters the permeate flow, the lower the retention rate of Mg2+. precipitation, there is already CaSO4·H2O precipitation on the surface of the nanofiltration membrane. That is the reason the concentration of Ca2+ in the bulk collected retentate is only 0.02 g·L−1, as the feed solution has concentrated 10 times. Further, because the total amount of Ca2+ is much lower than that of SO42−, this results in the lower concentrated times of Ca2+ than SO42−. In order to reduce the membrane scaling caused by calcium sulfate precipitation, it is better to wash the membranes after the NF operation. By contrast, Mg2+ can only be continuously accumulated in the collected retentate without precipitation, resulting in a higher concentration of Mg2+ in the permeate flow. In other words, the more Mg2+ that enters the permeate flow, the lower the retention rate of Mg2+. The separation factor of lithium and magnesium (SFLi-Mg) and lithium recovery are shown in

The separation factor of lithium and magnesium (SFLi-Mg) and lithium recovery are shown in Figure 3d. It can be seen that the SFLi-Mg rose from 15.4 to 30.1 in the first 30 min, and then gradually decrease from 30.1 to 22.8 in the next 75 min. The increasing concentration of Mg2<sup>+</sup> in the collected retentate is unhelpful for the separation of lithium and magnesium. In addition, the lithium recovery increased almost linearly, and reached 91.6% at the end of the NF process. Noteworthily, the total salinity in the retentate liquid is too high, and the residual lithium cannot be directly recycled by NF, but this retentate liquid can be returned to the EID system to separate lithium and magnesium, which can reduce the waste of lithium. Figure 3d. It can be seen that the SFLi-Mg rose from 15.4 to 30.1 in the first 30 min, and then gradually decrease from 30.1 to 22.8 in the next 75 min. The increasing concentration of Mg2+ in the collected retentate is unhelpful for the separation of lithium and magnesium. In addition, the lithium recovery increased almost linearly, and reached 91.6% at the end of the NF process. Noteworthily, the total salinity in the retentate liquid is too high, and the residual lithium cannot be directly recycled by NF, but this retentate liquid can be returned to the EID system to separate lithium and magnesium, which can reduce the waste of lithium. The final compositions of the permeate flow produced by NF are shown in Table 5. From Table

The final compositions of the permeate flow produced by NF are shown in Table 5. From Table 5, it can be seen that the major cationic ions in the permeate flow are Li+, Na+, and Mg2+, and the main anionic ion is Cl−. The concentration of K<sup>+</sup> is only 0.03 g·L −1 , and other impurities such as Ca2<sup>+</sup> and SO<sup>4</sup> <sup>2</sup><sup>−</sup> can almost be ignored. 5, it can be seen that the major cationic ions in the permeate flow are Li+, Na+, and Mg2+, and the main anionic ion is Cl−. The concentration of K+ is only 0.03 g·L−1, and other impurities such as Ca2+ and SO42− can almost be ignored.

**Table 5.** The compositions of the permeate flow produced by NF (g·L −1 ). **Table 5.** The compositions of the permeate flow produced by NF (g·L-1).


#### 3.2.2. RO Process 3.2.2. RO Process The permeate flow produced by the NF process was treated by the RO process, and the main

The permeate flow produced by the NF process was treated by the RO process, and the main results are shown in Figure 4. Figure 4a has shown that the operation pressure increased from the initial 3 MPa to 5.5 MPa during the RO process, while the flux of the water decreased from 49 L·m−<sup>2</sup> ·h −1 to 21.8 L·m−<sup>2</sup> ·h −1 . Figure 4b shows that the concentration of ions such as Li+, Na+, Mg2+, and K<sup>+</sup> in the collected retentate increased almost linearly. Concretely, Li<sup>+</sup> has increased from 2.2 g·<sup>L</sup> −1 to 5.4 g·L −1 and Mg2<sup>+</sup> increased from 0.21 g·<sup>L</sup> −1 to 0.525 g·L −1 . Figure 4c shows that the concentration of Li+, Na+, and Mg2<sup>+</sup> in the permeate flow increased significantly with the concentration process, but the maximum concentration of lithium is still lower than 0.04 g·L −1 , and the lithium loss is almost negligible. results are shown in Figure 4. Figure 4a has shown that the operation pressure increased from the initial 3 MPa to 5.5 MPa during the RO process, while the flux of the water decreased from 49 L·m−2·h−<sup>1</sup> to 21.8 L·m−2·h−1. Figure 4 b shows that the concentration of ions such as Li+, Na+, Mg2+, and K+ in the collected retentate increased almost linearly. Concretely, Li+ has increased from 2.2 g·L−1 to 5.4 g·L−<sup>1</sup> and Mg2+ increased from 0.21 g·L−1 to 0.525 g·L−1. Figure 4c shows that the concentration of Li+, Na+, and Mg2+ in the permeate flow increased significantly with the concentration process, but the maximum concentration of lithium is still lower than 0.04 g·L−1, and the lithium loss is almost negligible.

**Figure 4.** *Cont.*

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**Figure 4.** The main results in the RO process. (**a**) The relationship of the operation pressure and the flux of the membrane; **(b**) concentration of Li+, Na+, K+, and Mg2+ in the collected retentate; (**c**) concentration of Li+, Na+, K+, and Mg2+ in the permeate flow. **Figure 4.** The main results in the RO process. (**a**) The relationship of the operation pressure and the flux of the membrane; **(b**) concentration of Li+, Na+, K+, and Mg2<sup>+</sup> in the collected retentate; (**c**) concentration of Li+, Na+, K+, and Mg2<sup>+</sup> in the permeate flow.

The final composition of the permeate flow and the collected retentate produced by RO is shown in Table 6. As shown in Table 6, the concentration of ions in the permeate flow is very low, the loss of the lithium in the RO permeate flow almost can be ignored, and the recovery of lithium can reach 99.4%. Moreover, the permeate flow with such a low salinity content can be used to prepare the supporting electrolyte for the EID system. The final composition of the permeate flow and the collected retentate produced by RO is shown in Table 6. As shown in Table 6, the concentration of ions in the permeate flow is very low, the loss of the lithium in the RO permeate flow almost can be ignored, and the recovery of lithium can reach 99.4%. Moreover, the permeate flow with such a low salinity content can be used to prepare the supporting electrolyte for the EID system.

**Table 6.** The final compositions of the permeate flow and collected retentate. **Table 6.** The final compositions of the permeate flow and collected retentate.


#### *3.3. Precipitation of Li2CO3 3.3. Precipitation of Li2CO<sup>3</sup>*

recover the residual lithium.

The concentrations of Li+ and Mg2+ after RO are 5.4 g·L−1 and 0.525 g·L−1, respectively. This solution cannot be used directly for the precipitation of Li2CO3, and generally requires evaporation and impurity removal. Subsequently, we use an electric furnace to evaporate 5 L of solution to 1.2 L, and add NaOH to adjust the pH of the solution to 12.5 for further removal of magnesium (Mg2+ precipitates in the form of Mg(OH)2 when the solution is alkaline). The composition of the solution after magnesium removal is shown in Table 7. The concentrations of Li<sup>+</sup> and Mg2<sup>+</sup> after RO are 5.4 g·<sup>L</sup> <sup>−</sup><sup>1</sup> and 0.525 g·<sup>L</sup> −1 , respectively. This solution cannot be used directly for the precipitation of Li2CO3, and generally requires evaporation and impurity removal. Subsequently, we use an electric furnace to evaporate 5 L of solution to 1.2 L, and add NaOH to adjust the pH of the solution to 12.5 for further removal of magnesium (Mg2<sup>+</sup> precipitates in the form of Mg(OH)<sup>2</sup> when the solution is alkaline). The composition of the solution after magnesium removal is shown in Table 7.

**Table 7.** The composition of the solution after magnesium removal (g·L<sup>−</sup>1). **Table 7.** The composition of the solution after magnesium removal (g·L −1 ).


As shown in Table 7, the concentration of Li+ is enriched to 21.6 g·L−1; the mass ratio of Na/Li is slightly greater than 1; and other ions such as K+, Mg2+, Ca2+, and SO42− are very low. The recovery of lithium in this process can reach 96.1%; such a low lithium loss is attributed to the effective removal of magnesium by the NF, which greatly reduces the generation of Mg(OH)2 and improves the recovery rate of lithium. In the actual production process, the water generated by evaporation can also be returned to the EID system to prepare the supporting electrolyte. As shown in Table 7, the concentration of Li<sup>+</sup> is enriched to 21.6 g·<sup>L</sup> −1 ; the mass ratio of Na/Li is slightly greater than 1; and other ions such as K+, Mg2+, Ca2+, and SO<sup>4</sup> <sup>2</sup><sup>−</sup> are very low. The recovery of lithium in this process can reach 96.1%; such a low lithium loss is attributed to the effective removal of magnesium by the NF, which greatly reduces the generation of Mg(OH)<sup>2</sup> and improves the recovery rate of lithium. In the actual production process, the water generated by evaporation can also be returned to the EID system to prepare the supporting electrolyte.

The solution with 21.6 g·L−1 lithium was used for the precipitation of Li2CO3 with 280 g·L−<sup>1</sup> Na2CO3. Moreover, the concentration of the mother liquor is shown in Table 8. From Table 8, it can be seen that the main ions in the mother liquor are Na+ and Li+. Noteworthily, only 86.7% lithium was precipitated by Na2CO3, and the concentration of lithium in the mother liquor is still 1.8 g·L−1. In the same way, the mother liquor contains a small amount of excess carbonate, which can be neutralized by part of the brine with high Mg2+ ions, and then the mother liquor is returned to the EID system to The solution with 21.6 g·L −1 lithium was used for the precipitation of Li2CO<sup>3</sup> with 280 g·L −1 Na2CO3. Moreover, the concentration of the mother liquor is shown in Table 8. From Table 8, it can be seen that the main ions in the mother liquor are Na<sup>+</sup> and Li+. Noteworthily, only 86.7% lithium was precipitated by Na2CO3, and the concentration of lithium in the mother liquor is still 1.8 g·L −1 . In the same way, the mother liquor contains a small amount of excess carbonate, which can be neutralized by

part of the brine with high Mg2<sup>+</sup> ions, and then the mother liquor is returned to the EID system to recover the residual lithium. it can be seen that the XRD pattern of the obtained powder is indexed to Li2CO3 (JCPDS card 22-1141). Morphology analysis by SEM, as shown in Figure 5b, indicated that the particles were columnar and rod, mostly clusters, and have a relatively flat surface. The chemical composition of the prepared

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**Table 8.** The main parameters of the mother liquor (g·L<sup>−</sup>1). **Element Li+ Na+ K+ Lithium Recovery %** 

Concentration 1.8 90 0.2 86.7


**Table 8.** The main parameters of the mother liquor (g·L −1 ). Li2CO3 is shown in Table 9, and the composition of the obtained Li2CO3 meets the national standard

The phase and morphology analysis of the obtained solid is shown in Figure 5. From Figure 5a, it can be seen that the XRD pattern of the obtained powder is indexed to Li2CO<sup>3</sup> (JCPDS card 22-1141). Morphology analysis by SEM, as shown in Figure 5b, indicated that the particles were columnar and rod, mostly clusters, and have a relatively flat surface. The chemical composition of the prepared Li2CO<sup>3</sup> is shown in Table 9, and the composition of the obtained Li2CO<sup>3</sup> meets the national standard (Li2CO3-0, GB/T 11075-2013). Content (%) 99.6 0.026 0.005 0.0013 0.011 0.007 0.012 In general, the direct recovery of lithium from the high Mg/Li brine to the production of Li2CO3 can reach 68.7%, which was calculated by the product of the recovery of lithium in each process; considering that most of the solutions are cycled in the system (except the lithium loss by the precipitation of Mg(OH)2), the total recovery of lithium will be greater than 85%.

**Figure 5.** (**a**) XRD and (**b**) scanning electron microscope (SEM) of the obtained solid by precipitation. **Figure 5.** (**a**) XRD and (**b**) scanning electron microscope (SEM) of the obtained solid by precipitation.


**Table 9.** The chemical composition of the prepared Li2CO<sup>3</sup> .

**Methods Li+ Concentration in Brine/g·L−<sup>1</sup> Mg/Li in Brine Li+ Recovery Rate % References**  Solvent extraction 2.088 44.06 90.93 \* [39] In general, the direct recovery of lithium from the high Mg/Li brine to the production of Li2CO<sup>3</sup> can reach 68.7%, which was calculated by the product of the recovery of lithium in each process; considering that most of the solutions are cycled in the system (except the lithium loss by the precipitation of Mg(OH)2), the total recovery of lithium will be greater than 85%.

**Table 10.** Comparison of the Li+ recovery between this study and conventional methods.

#### Ion sieve 0.259 95 82.1 \* [40] *3.4. Comparison of Methods for Lithium Extraction from High Mg*/*Li Brine*

Electrodialysis 0.148 60 72.1 \* [41] This study 2.05 58.5 >85 This study Table 10 shows the comparison of methods for lithium extraction from high Mg/Li brine.


\* The asterisk only indicates the recovery rate of the separation of magnesium and lithium from brine. **Table 10.** Comparison of the Li<sup>+</sup> recovery between this study and conventional methods.

\* The asterisk only indicates the recovery rate of the separation of magnesium and lithium from brine.

From Table 10, it can be seen that the total Li<sup>+</sup> recovery rate in this paper is superior to that of ion sieve method and electrolysis method, but slightly lower than that of solvent extraction method. However, the extractant used in the solvent extraction method has a slight dissolution in the brine, which will cause greater environmental pollution. Noteworthily, this comprehensive membrane process has environmental protection significance.

#### **4. Conclusions**

In this paper, we constructed an integrated membrane process combining the EID system and NF and RO processes to prepare Li2CO<sup>3</sup> from a high mass ratio of Mg/Li brine. This method successfully realizes the separation of lithium and magnesium in brine with a high Mg/Li ratio, which relies on the anion membrane to retain cations and the selective characteristics of LiFePO<sup>4</sup> to adsorb lithium. Most of the bivalent ions in the prepared lithium-riched solution were removed by nanofiltration membrane. After concentration, purification, and precipitation, we prepared industrial-grade Li2CO3. Noteworthily, the removal of magnesium by nanofiltration can reduce the amount of alkali and reduce the entrainment loss of lithium caused by the massive production of magnesium hydroxide. In general, this process can efficiently realize the selective separation of magnesium and lithium without pollution to the environment and provide a new perspective for extracting lithium from salt lakes.

**Author Contributions:** Conceptualization and methodology (Z.Z., L.H., W.X.), formal analysis (W.X., L.H., D.L.); original draft preparation (W.X.); writing—review and editing, (W.X., L.H., Z.Z.); supervision (Z.Z.); project administration (Z.Z., L.H.); funding acquisition (Z.Z., L.H.). All authors have read and agreed to the published version of the manuscript.

**Funding:** This study is supported by the Major Program of National Natural Science Foundation of China (51934010), National Science Foundation of Hunan province (Grant No. 2019JJ40377), and Innovation-Driven Project of Central South University (No. 2020CX026).

**Acknowledgments:** The XRD and SEM data were obtained by using the equipment provided by Changsha Research Institute of Mining and Metallurgy Co., Ltd.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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*Perspective*
