A Thermodynamical Approach for Evaluating Energy Consumption of the Nanofiltration-Crystallization Process on Selective Separation of Chloride and Sulfate

Abstract

Nanofiltration (NF) coupling processes have been applied to treat high salinity wastewater in many studies. The main reason that affects the industrialization of the wastewater treatment is the high cost, which is mainly caused by the energy consumption of the entire system. Therefore, how to evaluate the energy consumption of different process configurations is an important issue. In this work, a thermodynamical approach was explained in detail, which could be used for evaluating energy consumption for pressure-driven membrane processes (e.g., NF and reverse osmosis) and osmotically driven membrane processes (e.g., forward osmosis). The coupling process configurations of NF, reverse osmosis (RO) and crystallization (Cryst) were selected to evaluate the energy consumption for high NaCl and Na₂SO₄ concentration wastewater in this paper. Four different process configurations (NF-Cryst, RO-Cryst, RO-NF-Cryst, NF-RO-Cryst) were simulated using Aspen Plus. The processes were discussed using a thermodynamical approach with a customized NF model. The electrolyte Non-Random Two-Liquid (electrolyte-NRTL) model was employed to calculate the thermodynamic properties of the solutions. The simulation results showed that the energy consumption per cubic meter of treated water (E_water) in NF-Cryst and NF-RO-Cryst processes were lower than that of RO-Cryst and RO-NF-Cryst. When $c_{f,N{a}_{2}S{O}_4}$ was low (e.g., 15 g·L⁻¹), there was not much difference in energy consumption between NF-Cryst and NF-RO-Cryst processes. Moreover, the high efficiency of NF was revealed in the separation of salt and decrease in the energy consumption of the whole process.

1. Introduction

Among the wastewaters, high salinity wastewater is one of the most difficult to recycle due to its high salinity [1,2]. The main components are NaCl and Na₂SO₄ [3,4]. Treatment technology for high salinity water is still immature and energy consumption is relatively high [5]. Membrane technology is advantageous, with its low energy consumption and stable operation, and it is easy to scale up. The molecular weight cutoff (MWCO) of nanofiltration (NF) membrane is between the ultrafiltration (UF) membrane and the reverse osmosis (RO) membrane, about 200~2000 Da, and the active separation layer of NF membrane is charged. Hence, NF has a unique advantage in treating wastewater containing divalent and monovalent ions [6,7,8,9,10]. Recent treatment processes under development are coupled with NF, such as RO, FO, electrodialysis (ED), multistage flash (MS), multieffect distillation (MED), and ion exchange (IX), to decrease the overall energy consumption [11].

In order to recover salts from high salinity wastewater, it is common to adopt an integrated process to achieve salt separation and production. For example, NF is used to separate and concentrate the NaCl and Na₂SO₄ in high salinity wastewater, and afterwards the crystallization unit is used to produce sulfate. The concept of integrating membrane separation technologies with other unit operations was first proposed by Drioli et al. [12,13]. Drioli [14] utilized an UF-NF integrated membrane process for recovering CaCO₃, NaCl and MgSO₄·7H₂O from NF retentate. It presented that seawater was first pretreated by UF and then concentrated by NF. The desired salts were finally obtained from the retentate by reaction crystallization or membrane crystallization. Curcio et al. [15] established a nanofiltration-membrane crystallization system for the recovery of sulphate from wastewater, which was generated by the production of nickel-metal hydride batteries. After pre-concentration by NF, a membrane crystallizer was used to produce Na₂SO₄ crystals of uniform size distribution. Wei et al. [16] used ED stacks consisting of monovalent selective ion-exchange membranes to treat seawater concentrate. Integrating with NF was, and would be a key strategy to lower the cost of current desalination processes [11]. Moreover, under different conditions, NF might be used to remove natural organic matter (NOM) [17,18], and recycle water from organized industrial zones (OIZ) [19]. Therefore, it is very important to evaluate different integrated membrane processes under certain criteria. Based on previous work reported, four different process configurations (NF-Cryst, RO-Cryst, RO-NF-Cryst, NF-RO-Cryst) were designed for separation and concentration, followed by the traditional crystallization operation to recover the sulfate from the wastewater in this paper.

To optimize the energy cost of RO, Zhu et al. [20] calculated the thermodynamic properties of the solutions based on thermodynamic restrictions. In the development of membrane integration processes, process simulation softwares like Aspen Plus [21] are powerful tools to help develop, design, analyze, and optimize a new industrial process. However, compared to other traditional unit operations, membrane separation technology is a relatively new separation operation, resulting in the lack of membrane process simulation. Customized membrane distillation unit models with Aspen Plus software were applied by Chang et al. [22]. Sharifian used a similar approach to simulate the gas separation process using hollow fiber membranes [23]. In both cases, the unit operation models for the membrane separation process were designed using the Formula Translation (FORTRAN) interface provided by Aspen Plus. Up to now, no work has been done on the simulation calculation of the membrane integration process for treating high salinity wastewater.

In the preceding paper [24], a thermodynamical approach for evaluating energy consumption of the FO process has been proposed. Zeng compared FO process performance using different draw solutes. In this paper, a much detailed approach was discussed and adopted to evaluate energy consumption of NF or RO integrated with crystallization. The process was employed to recover sulfate from high salinity wastewater containing mainly NaCl and Na₂SO₄. Meanwhile, relatively pure by-product NaCl solution obtained as permeate through the membrane separation process could be used as the feed of chlor-alkali industry. For this purpose, an operation model describing the membrane separation process was developed. Thermodynamic data such as salt solubility and osmotic pressure involved in the simulation, was calculated by the electrolyte Non-Random Two-Liquid model (electrolyte NRTL). The influence of concentration and concentration ratio of NaCl to Na₂SO₄ ($c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$) on the membrane integration process was investigated. Meanwhile, different process configurations were designed and energy consumption was evaluated under different circumstances.

2. Materials and Methods

2.1. Thermodynamical Approach for Membrane Process

The main task of this study was to evaluate energy consumption under ideal conditions. Hence, membranes are assumed to be perfect, and processes are operated close to thermodynamic equilibrium. Consequently, the concentration polarization effect and the pressure drop effect were not considered for simplicity. For the FO process, membranes were considered perfect so that salt could be fully rejected.

For pressure-driven membrane processes and osmotically driven membrane processes, the mass transfer stopped when osmotic equilibrium is reached. The process is shown in Figure 1.

The model for the membrane process was built with the FORTRAN programming interface from the Aspen Plus software. The initial concentrations were known and given by the simulation flowsheet. The permeate and retentate (or draw and feed solution) concentrations were determined when the pressure difference was zero, as shown by Equation (1):

$$\Delta P=\Delta \pi =\left({\pi }_1-{\pi }_2\right)$$

(1)

where ΔP is the applied pressure difference, and Δπ is the osmotic pressure difference which is the difference between π₁ (feed solution or retentate) and π₂ (draw solution or permeate).

By changing the amount of water migrating from the retentate (or feed solution) to permeate (or draw solution), osmotic pressure equilibrium is reached. The osmotic pressure is expressed as a function of the activity of water, which could be obtained by the following equation:

$$\pi =-\frac{RT}{\overline{V_A}}\ln a_A$$

(2)

where R is the gas constant which is 8.314 J·mol⁻¹·K⁻¹, and T is the temperature (K). $\overline{V_A}$ is the partial molar volume of water and a_A represents the activity of water, which is calculated by the electrolyte NRTL model. In the model, binary parameters are a and τ. a is set to 0.2 while τ is calculated by the following equation:

$$\tau =C+\frac{D}{T}+E\left[\frac{T_0-T}{T}+\ln (\frac{T}{T_0})\right]$$

(3)

where T₀ is 273.15 K. C, D, and E are adjustable parameters which could be regressed by experimental thermodynamic data.

2.1.1. FO Unit Model

When the membrane process is osmotically driven, take FO for example, which is proposed in the preceding paper [24]. There is no applied pressure, and a high concentration of draw solution is used to obtain water from the feed solution. Therefore, for the FO process, ΔP = 0, the thermodynamical equilibrium is reached when Δπ = π₁ − π₂ = π_feed − π_draw = 0.

2.1.2. NF Unit Model

When the process is pressure-driven, take NF for example, water migrates through a membrane from the retentate to the permeate under applied pressure. Therefore, the thermodynamical equilibrium is reached when ΔP = Δπ = π_r − π_p. Where ΔP represents the transmembrane pressure difference, π_r is the osmotic pressure of the retentate while π_p is the osmotic pressure of the permeate.

The NF unit model has three parameters: operating pressure (P), Cl⁻ rejection (${\mathrm{R}}_{{\mathrm{Cl}}^{-}}$), SO₄²⁻ rejection (${\mathrm{R}}_{{\mathrm{SO}}_4{}^{2-}}$). NF membranes have a low ${\mathrm{R}}_{{\mathrm{Cl}}^{-}}$ and a high ${\mathrm{R}}_{{\mathrm{SO}}_4{}^{2-}}$ for single salt solutions [25]. For binary salt solutions, NF membranes present slightly higher ${\mathrm{R}}_{{\mathrm{SO}}_4{}^{2-}}$ and much lower ${\mathrm{R}}_{{\mathrm{Cl}}^{-}}$ [26]. When the Na₂SO₄ concentration ($c_{N{a}_{2}S{O}_4}$) was over a certain value, a negative ${\mathrm{R}}_{{\mathrm{Cl}}^{-}}$ is even observed [27]. Hence, under different total salt concentrations and different concentration ratios of NaCl over Na₂SO₄ ($c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$), the NF membrane might present a different ${\mathrm{R}}_{{\mathrm{SO}}_4{}^{2-}}$ and ${\mathrm{R}}_{{\mathrm{Cl}}^{-}}$. In this study, the ${\mathrm{R}}_{{\mathrm{SO}}_4{}^{2-}}$ and ${\mathrm{R}}_{{\mathrm{Cl}}^{-}}$ of the simulation NF process were set based on experimental data according to a previous study [28].

The RO unit operation also used the customized NF model to simulate the energy consumption, while only changing the three main parameters. The operating pressure and rejection were set higher.

2.2. Thermodynamic Model

In the simulation process, the thermodynamic model was used to calculate physical properties such as osmotic pressure and solubility. Because the parameters of Aspen on the solubility calculation have a large deviation, the model parameters of NaCl-Na₂SO₄ system were regressed using the solubility data in the literature [29,30]. Regression parameters included the NRTL model interaction parameters of electrolytes between Na⁺, Cl⁻–H₂O; Na⁺, SO₄²⁻–H₂O; Na⁺, Cl⁻–Na⁺, and SO₄²⁻ ions, and the solubility products of Na₂SO₄·10H₂O, Na₂SO₄ and NaCl. The solubility product (K_sp) is a function of temperature (T) [29,30]:

$$\ln \left(K_{sp}\right)=A+B/T+C\times \ln \left(T\right)+D\times T$$

(4)

The calculated solubilities using the new model parameters were compared with the experimental data in Figure 2. Based on the reported results in the literature, it could be seen that sulfate existed in the form of sodium sulfate decahydrate (Na₂SO₄·10H₂O) at a low temperature. As the temperature or NaCl concentration increased, sulfate existed in Na₂SO₄. At low temperature, the Na₂SO₄·10H₂O solubility decreased with increasing NaCl concentration due to the common ion effect. Except for the case when the NaCl concentration was particularly high (over 6 mol·kg⁻¹), Na₂SO₄·10H₂O could be recovered from NaCl–Na₂SO₄ system by freeze-crystallization. In addition, the calculated results of the model were in good agreement with the experimental data, which also showed that it is feasible to use the electrolyte NRTL model to calculate the thermodynamic properties of the system.

2.3. Process Design

For a given feed concentration, the max retentate concentration is reached when the process is operated close to the thermodynamic limit. Assuming that the concentration process is a batch operation, the component rejection remains constant. Wang [31] used an equation to calculate the final concentration multiple:

$$c_f=c_0{\left(V_0/V_f\right)}^R$$

(5)

where c_f is the final feed concentration, and c₀ is the initial feed concentration. V₀ is the initial volume of the feed and V_f is the final volume of the feed. R is the rejection and V₀/V_f is the concentration multiple.

For the treatment of wastewater, besides the use of NF for concentration and separation, RO is commonly used for concentration. Therefore, NF, RO, Cryst were combined to design a proper process configuration. Figure 3a shows the most classical type of process configuration, which is wastewater treated by NF, and retentate further treated by crystallization (the NF-Cryst process) [13]. This process is simple and efficient, through which NF can separate chloride and sulfate and concentrate feed, while crystallization isolates Na₂SO₄·10H₂O from the retentate. The RO-Cryst process (Figure 3b) was designed to highlight the difference between using NF and RO as the first membrane unit for concentration. The RO-NF-Cryst (Figure 3c) and NF-RO-Cryst (Figure 3d) processes were employed to discuss how additional membrane unit (NF or RO) affects the whole process. The influence of different process configurations on system energy consumption, salt production and other factors are explored in Figure 3a–d.

Figure 3a shows the NF-Cryst process configuration. After the wastewater was concentrated and separated by NF, the NF retentate was imported to the crystallization unit to produce sulfate. In Figure 3b, the NF unit in the previous configuration was replaced by RO, and the crystallizer was treated on the RO retentate. RO is very commonly used in wastewater treatment due to its lower cost and higher operating pressure, without selective separation on ions of different valence. Thus, RO and NF were compared to determine whether higher operating pressure could achieve higher V₀/V_f. The third configuration (RO-NF-Cryst) is shown in Figure 3c. The wastewater was firstly preconcentrated by RO, and then the RO retentate was further concentrated by NF, lastly being treated by the crystallization unit. For the fourth configuration (NF-RO-Cryst) shown in Figure 3d, the NF retentate was further concentrated by RO and finally crystallized. Compared with the former two configurations, the latter two mainly highlighted the influence of more complex process configuration on total energy consumption.

In the simulation process, the membrane unit operation consumed electrical energy to drive the high-pressure pump, and the crystallization unit used the electric energy to cool the solution down. In addition, low-pressure pumps were also required to transport the solution in the process. However, the energy consumption of the low-pressure pumps was not considered in this study. The energy consumption of a low-pressure pump is much lower than that of a high-pressure pump or a crystallizer, and the energy consumption of the low-pressure pump of each process is generally similar. Hence, neglecting the energy consumption of the low-pressure pump did not have a great impact on the result. For the operation of the membrane unit, the energy recovery procedure was not considered, and the operating pressure was maintained at a fixed pressure. The high-pressure pump worked on the whole feed; this part of the energy consumption could be calculated using the following formula:

$$W_{mem}=P\times V_0$$

(6)

where P is the system pressure and V₀ is the initial volume of the feed. For the energy consumed by the crystallizer, the following formula was used:

$$W_{cryst}=\frac{Q_d}{COP}$$

(7)

where Q_d is the heat transferred for cooling and the Coefficient of Performance (COP) is set constantly as 4.5. The energy of the whole process containing high-pressure pump and crystallizer is expressed as:

$$W_{total}=W_{mem}+W_{cryst}$$

(8)

3. Results

3.1. Effect of the Feed Concentration on NF-Cryst Process

Firstly, the NF-Cryst process configuration was discussed. The operating pressure of NF was set at 4 MPa. Rejection towards a certain ion depends on the flux and each component concentration. The Cl⁻ and SO₄²⁻ ion rejections were estimated based on experiment data. Assuming that the flux was 50 L·m⁻²·h⁻¹, the relevant rejections used in the simulation are given in

Table 1. Feed concentrations and NF rejections.

${\mathit{c}}_{\mathit{f}\mathbf{,}\mathit{N}\mathit{a}\mathit{C}\mathit{l}}$ (g·L−1)	${\mathit{c}}_{\mathit{f}\mathbf{,}\mathit{N}{\mathit{a}}_{\mathbf{2}}\mathit{S}{\mathit{O}}_{\mathbf{4}}}$ (g·L−1)	${\mathbf{R}}_{{\mathbf{Cl}}^{\mathbf{-}}}$	${\mathbf{R}}_{{\mathbf{SO}}_{\mathbf{4}}{}^{\mathbf{2}\mathbf{-}}}$
4	4	0.288	0.996
8	8	0.224	0.993
16	16	0.125	0.986
32	32	0.000	0.974
32	6.4	0.155	0.978
32	16	0.097	0.979
32	32	0.000	0.974
32	64	−0.189	0.960

. The table shows the apparent rejection. During the concentration process, the salt concentration was constantly changing, and the flux of the permeate decreased as the concentration proceeded. All of these factors resulted in varieties in the actual rejection. For simplicity, the rejections set in the simulation process did not change.

3.1.1. NF-Cryst Process Configuration Results under Different Total Salt Concentrations

Figure 4a shows the max V₀/V_f and retentate concentration of NaCl ($c_{r,NaCl}$) and Na₂SO₄ $c_{r,N{a}_{2}S{O}_4}$) as a function of the feed concentration at a fixed $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$. It could be seen that V₀/V_f decreased as $c_{f,N{a}_{2}S{O}_4}$ increased, which was caused by the higher osmotic pressure of the feed solution at high salt concentrations. Although $c_{f,N{a}_{2}S{O}_4}$ increased from 4 to 32 g·L⁻¹, $c_{r,N{a}_{2}S{O}_4}$ changed slightly and only increased from 92.1 to 96.6 g·L⁻¹. When $c_{f,NaCl}$ increased from 4 to 32 g·L⁻¹, the concentration difference of NaCl on both sides did not change much, therefore $c_{r,N{a}_{2}S{O}_4}$ reached the osmotic pressure balance under identical operating pressure. For NaCl concentration process, the salt concentration in the feed solution increased continuously. In terms of the ratio of Na₂SO₄ and NaCl concentration in the final retentate, when $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$ was fixed, the separation efficiency of the two salts gradually became worse as the salt concentration increased.

Figure 4b shows the salt production per ton of wastewater treated by NF-Cryst at different feed concentrations, as well as the E_water and energy consumption per ton of salt production (E_salt) under fixed $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$. With the increase of $c_{f,N{a}_{2}S{O}_4}$, the amount of obtained Na₂SO₄·10H₂O crystal also increased. Although $c_{r,N{a}_{2}S{O}_4}$ was similar at different concentrations before crystallization, the amount of retentate was more with higher $c_{f,N{a}_{2}S{O}_4}$, resulting in a larger amount of salt production. The crystallization energy consumptions resulted in higher E_water. However, from the point of salt production energy consumption, the energy consumption of NF per ton of salt became lower, and hence E_salt decreased.

3.1.2. NF-Cryst Simulation Results under Different $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$

As shown in Figure 5a, $c_{r,N{a}_{2}S{O}_4}$ decreased rapidly from 12.7 times of the initial concentration to 1.8 when $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$ was changed under fixed $c_{f,NaCl}$. $c_{r,N{a}_{2}S{O}_4}$ increased, while $c_{r,NaCl}$ decreased. As can be seen from Table 1, ${\mathrm{R}}_{{\mathrm{Cl}}^{-}}$ decreased with the increase of $c_{f,N{a}_{2}S{O}_4}$, and even negative rejection was achieved, which led to the decrease of $c_{r,NaCl}$ with the increase of $c_{f,N{a}_{2}S{O}_4}$. In general, at a fixed $c_{f,NaCl}$, the separation efficiency was better when $c_{f,N{a}_{2}S{O}_4}$ was higher.

From the perspective of energy consumption, as shown in Figure 5b, the increase of $c_{f,N{a}_{2}S{O}_4}$ resulted in the increase of E_water and the decrease of E_salt. Under the condition of high Na₂SO₄ concentration, $c_{r,N{a}_{2}S{O}_4}$ increased and the amount of retentate increased. As a result, the salt production increased with the increase of $c_{f,N{a}_{2}S{O}_4}$. In the feed containing 32 g·L⁻¹ NaCl and 64 g·L⁻¹ Na₂SO₄, up to 0.112 tons of Na₂SO₄·10H₂O could be produced from one ton of feed with E_salt at 55.7 kWh/ton or E_water 6.24 kWh/m³.

3.2. Comparison between Different Process Configurations

The process configurations of NF-Cryst, RO-Cryst, RO-NF-Cryst and NF-RO-Cryst under different feed concentrations were simulated and the results were discussed. For the NF-RO-Cryst process, since the feed concentration entering the NF operation unit was identical with that of the NF-Cryst, the rejection of the NF model also used the values shown in Table 1. However, for the RO-NF-Cryst process, since the NF unit was used to treat RO retentate, the rejection was re-evaluated according to Table 1. Because of the pre-concentration by RO, $c_{f,N{a}_{2}S{O}_4}$ increased compared with that of the feed, therefore the rejections all decreased to a certain extent.

3.2.1. Comparison of Simulation Results under Different Total Salt Concentrations

The simulation results for different process configurations are shown in Figure 6a–f when $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$ (1:1) is fixed. Among them, the retentate in RO-NF-Cryst and NF-RO-Cryst processes referred to the final retentate obtained after the feed was treated by a two-stage membrane unit and then entered the into the crystallizer. V₀/V_f was the ratio between the retentate before entering the crystallizer and the feed, which was the concentration multiple achieved by the whole membrane process. From the comparison of the V₀/V_f shown in Figure 6a, it can be seen that the NF-RO-Cryst process had the highest V₀/V_f among the four investigated process configurations. The NF-RO-Cryst process achieved a maximum V₀/V_f of 43.1 when the feed concentration of NaCl and Na₂SO₄ were both 4 g·L⁻¹. The RO-NF-Cryst process had a lower V₀/V_f than the NF-RO-Cryst process while it was higher than the NF-Cryst and RO-Cryst processes. Although NF-RO-Cryst and RO-NF-Cryst processes had higher V₀/V_f, these two types of much complex process configurations required more initial investment and operating costs. It is interesting to notice from Figure 6a that although the RO operation in the RO-Cryst process was at a higher pressure (8 vs. 4 MPa), the achievable V₀/V_f was still lower than that of NF-Cryst operated at a lower pressure. This was due to the high rejection towards NaCl and Na₂SO₄ in the feed during RO operation, resulting in a larger osmotic pressure that should be overcome, offsetting the effect of increased operating pressure. In addition, there was a tendency for V₀/V_f to decrease with increasing concentrations in all four processes.

It can be noticed from Figure 6b that the RO-Cryst process concentrated directly through RO and had the highest concentrated NaCl concentration. In the RO-NF-Cryst process where the NF continued after the RO operation, $c_{r,NaCl}$ decreased due to the separation effect of the NF on the divalent salt. When the total concentration increased under fixed $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$, $c_{r,NaCl}$ in the RO-Cryst and RO-NF-Cryst processes remained almost constant. When rejections towards NaCl and Na₂SO₄ were close, the final concentration of NaCl to Na₂SO₄ was close to that of the feed. Hence, for the process started with RO, the final concentration was also close when $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$ was fixed. For the NF-Cryst and NF-RO-Cryst processes, $c_{r,NaCl}$ also increased as the salt concentration in the feed increased due to the NF separation effect. Due to the subsequent RO concentration, $c_{r,NaCl}$ of the NF-RO-Cryst process was slightly higher than that of the NF-Cryst process.

In Figure 6c, the RO-Cryst process had the lowest $c_{r,N{a}_{2}S{O}_4}$ when $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$ was fixed, even lower than that of the NF-Cryst process. The $c_{r,N{a}_{2}S{O}_4}$ of RO-NF-Cryst was slightly higher than that of NF-Cryst. However, $c_{r,N{a}_{2}S{O}_4}$ in NF-RO-Cryst was the highest, and reached 169.3 g·L⁻¹ when $c_{f,NaCl}$ and $c_{f,N{a}_{2}S{O}_4}$ were both 4 g·L⁻¹. $c_{r,N{a}_{2}S{O}_4}$ in the other three process configurations did not change much with the increase of total salt concentration. However, for the NF-RO-Cryst process, $c_{r,N{a}_{2}S{O}_4}$ decreased as the total salt concentration increased. In the NF-RO-Cryst process, Na₂SO₄ concentration in the NF retentate treated by RO did not change much. However, the NaCl concentration increased with the increase of the total salt concentration, resulting in a decrease in the concentration multiple of the RO and $c_{r,N{a}_{2}S{O}_4}$.

Figure 6d,e show the comparison of energy consumption for different process configurations when $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$ was fixed. Figure 6f compares the amount of salt that was produced by different processes. The RO-Cryst process had the highest E_water and E_salt. This suggests that only using RO for the treatment of wastewater containing NaCl and Na₂SO₄ might not be economically viable. The NF-Cryst process had the lowest E_water. This was due to the fact that it decreased the consumption of RO by contrasting the RO-NF-Cryst and NF-RO-Cryst processes. In particular, the RO should be operated at a higher pressure so that the energy consumption of the high-pressure pump can also increase. The NF-RO-Cryst process had lower E_salt and E_water than that of the RO-NF-Cryst process. Compared NF-RO-Cryst process with NF-Cryst process, RO operation required additional energy consumption. Indicating further concentration of the NF retentate allowed salt production to increase, offsetting the increased RO energy consumption. The RO-NF-Cryst and NF-RO-Cryst processes were similar in salt production, both being higher than that of the NF-Cryst and RO-Cryst processes. The NF-RO-Cryst and RO-NF-Cryst process were both two-step membrane operations, and NF-RO decreased the concentration required for the next step, therefore there would be a higher V₀/V_f. Without considering the initial investment of RO and NF, the simulation results showed that the RO arranged at the back of NF was economically beneficial.

3.2.2. Comparison of Simulation Results under Different $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$

The comparison of simulation results of different processes under the fixed $c_{f,NaCl}$ of 32 g·L⁻¹ and changing $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$ is shown in Figure 7a–f. From Figure 7a, it can be seen that the RO-Cryst process had the lowest V₀/V_f. Even when the feed concentrations of NaCl and Na₂SO₄ were 32 and 6.4 g·L⁻¹, respectively, the V₀/V_f was about 2.6. The NF-Cryst process, operating at a pressure of 4 MPa, achieved a concentration multiple of 12.7 for identical feed concentration. The concentration multiples of the NF-RO-Cryst and RO-NF-Cryst processes were higher than that of NF-Cryst process. However, the difference was not obvious when Na₂SO₄ concentration was high. As the Na₂SO₄ concentration increased, the osmotic pressure also increased significantly, therefore the concentration multiple of the process configuration containing NF unit decreased significantly.

Figure 7b,c show that the retentate concentrations of NaCl and Na₂SO₄ in different processes under different $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$ are similar to the results at different total salt concentrations. The NF-Cryst process also had the lowest NaCl concentration, while $c_{r,NaCl}$ in the RO-Cryst process was the highest. For the Na₂SO₄ concentration, the highest $c_{r,N{a}_{2}S{O}_4}$ was obtained by the NF-RO-Cryst process. With the increase of $c_{f,N{a}_{2}S{O}_4}$, V₀/V_f decreased. When $c_{f,NaCl}$ was fixed, $c_{f,NaCl}$ of all process decreased. For $c_{r,N{a}_{2}S{O}_4}$, all processes showed an increasing trend with the increase of $c_{f,N{a}_{2}S{O}_4}$, while the increase rate slowed down. The Na₂SO₄ concentration could be doubled in the NF-RO-Cryst process even when $c_{f,N{a}_{2}S{O}_4}$ increased to 64 g·L⁻¹.

As can be seen from Figure 7d,e, as $c_{f,N{a}_{2}S{O}_4}$ increased, E_water increased and E_salt decreased. The NF-Cryst progress had the lowest energy consumption under different $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$. E_water of NF-RO-Cryst was higher than that of NF-Cryst process, while E_salt was basically identical. This showed that for the NF-RO-Cryst process, the increase in the amount of salt produced offset the increase in total energy consumption, despite the increase in overall process energy consumption due to the addition of a RO unit. When $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$ was high and $c_{f,N{a}_{2}S{O}_4}$ was low, $c_{r,N{a}_{2}S{O}_4}$ might not have reached the saturation concentration when the Na₂SO₄ concentration in the RO-Cryst process was low. For example, as can be seen from Figure 7f, when ${\mathrm{c}}_{{\mathrm{r},\mathrm{Na}}_2{\mathrm{SO}}_4}$ was 6.4 g·L⁻¹, the amount of salt produced in the RO-Cryst process was close to zero, resulting in enormous values of E_salt by this process. Moreover, it showed that the salt production was close, mainly because $c_{p,N{a}_{2}S{O}_4}$ was low in all four processes. Therefore, the mass of Na₂SO₄ in retentate was similar, and so was the salt production after the crystallization unit. In general, compared to a simple NF-Cryst process, as a much more complex process, the NF-RO-Cryst process increased the amount of produced salt as $c_{f,N{a}_{2}S{O}_4}$ increased while E_salt remained constant.

3.3. Effect of NF Operating Pressure

NF is sometimes referred to as low pressure RO, which traditionally has lower operating pressures [32]. For example, General Electric Company’s (GE) DL series of NF membranes, the operating pressure is usually limited to 4 MPa or less [33]. For the treatment of high salinity wastewater, there are commercialized high-pressure NF membranes. In order to investigate the influence of NF operation under high pressure on the membrane integration process, the NF operation pressure in NF-Cryst process was set at 4–8 MPa for simulation. The feed was a high salinity solution containing 32 g·L⁻¹ NaCl and 64 g·L⁻¹ Na₂SO₄. The rejection assumed identical values under different operating pressures, and Cl⁻ and SO₄²⁻ rejection were set as −0.189 and 0.960, respectively. The results are shown in Figure 8a,b below.

As can be seen from Figure 8a, V₀/V_f and $c_{r,N{a}_{2}S{O}_4}$ grew linearly as the operating pressure increased. At an operating pressure of 8 MPa, Na₂SO₄ could be concentrated up to 217.4 g·L⁻¹. Since ${\mathrm{R}}_{{\mathrm{Cl}}^{-}}$ was negative, as the operating pressure increased, V₀/V_f increased and $c_{r,NaCl}$ decreased slightly. Above all, high pressure NF operation is beneficial to improve the divalent salt separation efficiency and concentration multiple.

As the operating pressure increased, Figure 8b showed that E_water decreased in the range of 4–7 MPa. At 8 MPa, further increasing the operating pressure would increase energy consumption. The concentration multiple in the higher operating pressure was higher; the amount of water which treated by the crystallizer would also be decreased. Although energy consumption of the high-pressure pump increased, the energy consumption of the crystallizer decreased, and the total energy consumption of the process decreased. Increasing the operating pressure could recover more sulfate from the wastewater and lower E_salt. Furthermore, it can be concluded that the use of NF membranes which could operate at higher pressures is beneficial for improving the efficiency of NF-crystallization integration processes.

4. Conclusions

A thermodynamical approach was described in detail, and was used for energy consumption evaluation. The performances of the nanofiltration-crystallization process on selective separation of chloride and sulfate were compared with four different process configurations. Moreover, the effect of the feed concentration and the operating pressure was discussed.

For concentration multiples at different salt concentrations under fixed $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$, when $c_{f,N{a}_{2}S{O}_4}$ was low (e.g., 5 g·L⁻¹), the results of four processes were appreciably different while the concentration multiple of NF-RO-Cryst was the highest. However, when $c_{f,N{a}_{2}S{O}_4}$ was high (e.g., 30 g·L⁻¹), the results of the four processes were similar.

The value of E_water of the NF-Cryst and NF-RO-Cryst processes were lower than that of RO-Cryst and RO-NF-Cryst. Under fixed $c_{f,NaCl}$/$c_{f,N{a}_{2}S{O}_4}$, when $c_{f,N{a}_{2}S{O}_4}$ was low (e.g., 15 g·L⁻¹), there was not much difference in energy consumption between the NF-Cryst and NF-RO-Cryst processes, therefore considering the fixed investment, NF-Cryst might be the proper choice. However, when $c_{f,N{a}_{2}S{O}_4}$ was high (e.g., 30 g·L⁻¹), compared to NF-Cryst, NF-RO-Cryst had an obvious advantage.

The high efficiency of NF was revealed in the separation of salt and the decrease in the energy consumption for the whole process. Although RO could be operated under higher pressure, the concentration multiple and other indicators were lower than NF. For an integrated process design, it was advantageous to arrange RO after NF. The development of NF membranes with higher operating pressures could increase the concentration ratio while decreasing the volume of the retentate, therefore decreasing the crystallizer treated water volume, and finally decreasing the total energy consumption of the process.