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Sustainable water recovery and reuse are critical yet challenging, especially from industrial effluents in cold regions. This work presents a robust numerical model of the transport phenomena in a hybrid two-step forward osmosis (FO)-directional freeze crystallization (DFC) desalination process, whose application in areas with cold climates is advantageous. Deionized (DI) water and a hydrometallurgical effluent were considered as the feed solution in the FO step, while three aqueous solutions of inorganic salts were considered as the draw solutions (DS): NaCl, CaCl2, and MgCl2. The effects of temperature and initial DS concentration were investigated on water flux, reverse solute flux, and specific water flux using computational fluid dynamics (CFD). Based on the simulation results, the highest water flux (18 L/m2/h for DI water and 5 L/m2/h for the hydrometallurgical effluent) and lowest reverse solute flux (consistently below 0.3 mol/m2/h) were obtained when MgCl2 was used as the DS. The effect of solute type in the DS on both water recovery yield and purity was in turn studied in the subsequent DFC step, allowing to visualize the solute distribution during the freezing process.

  • Model development and validation of a forward osmosis-directional freeze crystallization (FO-DFC) desalination process.

  • MgCl2 exhibited the highest water flux and lowest reverse solute flux in FO.

  • MgCl2 showed the highest rejection flux among the inorganic salts tested during DFC.

  • The highest impurity rejection flux rate during ice growth occurred at the solid–liquid interface.

computational fluid dynamics, desalination, directional freeze crystallization, forward osmosis, sustainable processing, water recovery

Water is an extremely valuable resource, but its global supply is limited, so it is up to the scientific community to use and reuse it responsibly and intelligently. A significant threat to the sustainability of industrial operations is the disposal of contaminated wastewater, typically for a processing fee from industrial activities, such as mining and mineral and metal processing. Several desalination processes have been developed to overcome water scarcity by producing clean water from brine water and wastewater, including reverse osmosis (RO), evaporation, electrodialysis, electrocoagulation, nanofiltration (NF), ultrafiltration (UF), and forward osmosis (FO) (Chung et al. 2012; Goh et al. 2019; Mohammadifakhr et al. 2020; Liu et al. 2021). Among these approaches, FO has attracted the attention of many researchers, primarily due to its low energy consumption (Blandin et al. 2016; Goh et al. 2019; Toh et al. 2020). Its energy-efficiency arises from the fact that no external energy input, such as hydraulic pressure, is required: FO and RO consume 5 and 8.2 kWh/m3, respectively (Youssef et al. 2014). Osmosis refers to the spontaneous movement of solvent molecules, namely water, from a solution of the high chemical potential of water (i.e., a feed solution, FS) into one of the lower chemical potential of water (i.e., a draw solution, DS) through a semi-permeable membrane (Cath et al. 2006; Kolliopoulos et al. 2017). This movement is bound to continue until the chemical potential of water becomes equal across the membrane separating the two solutions. Therefore, during FO, the DS gets diluted, while the FS gets concentrated over time.

A significant challenge associated with FO is the recovery of water from the resulting diluted DS (DDS) and the subsequent regeneration of the concentrated DS (CDS), which requires energy. Many studies have tested, among other techniques, membrane-based separation methods, precipitation, thermal recovery, and freeze concentration, as means to regenerate the CDS (Ling & Chung 2012; Ge et al. 2013; Kolliopoulos et al. 2018, 2022; Chaoui et al. 2019; Le et al. 2020). Freeze crystallization (FC) has been acknowledged as a cost-effective and environmentally friendly water recovery technology (Youssef et al. 2014; Kolliopoulos et al. 2018). FC is a separation process that recovers water from saline solutions in the form of ice, regardless of their composition, without the addition of new chemicals. The driving force for water separation and recovery in FC is the difference between the freezing point of water and that of other compounds in aqueous solutions (Adeniyi et al. 2014). From an energy consumption point of view, since the heat of fusion is seven times less than the heat of evaporation of water, FC becomes fundamentally more economical than evaporation in the regeneration of the CDS from the DDS (Williams et al. 2015; Jayakody et al. 2018). For example, the operating cost to produce water by FC has been estimated to 0.34 vs. 3.9 $/m3 by solar distillation (Youssef et al. 2014).

Computational fluid dynamics (CFD) is a powerful numerical modeling tool that can be used to model fluid flow, heat transfer, mass transport, and chemical reactions, based on a set of governing equations. CFD models can numerically simulate the fluid flow inside complex geometries and couple the hydrodynamic properties with chemical reactions that might occur during processing (Amani & Jalilnejad 2017). Several CFD modeling studies have been carried out on both FO and DFC processes separately; however, to the best of our knowledge, there are no studies that numerically model FO and DFC together with the intention of using DFC as a CDS regeneration method after FO (Gruber et al. 2012; Sagiv et al. 2014; Akther et al. 2019; Jayakody et al. 2020; El Kadi et al. 2021; Shabani et al. 2021).

The main objective of this study is to develop a numerical model of both FO and DFC, that could be used in a hybrid FO-DFC process, with consideration of both external and internal concentration polarization (ICP) effects in the FO process. In the FO section, deionized (DI) water and a hydrometallurgical effluent were studied as the FS, while three aqueous solutions of inorganic salts were considered as the DS. The impact of operational parameters, such as the type of draw solution, initial concentration of draw solution, and temperature on water flux, reverse solute flux, and specific water flux was investigated. The study of a hydrometallurgical effluent as the FS in FO constitutes a departure from conventional FO modeling, which typically employs deionized water as the FS, thus representing a noteworthy advancement. An additional novelty of this research work is the formulation of a mathematical model that accounts for the regeneration of the CDS via DFC. DFC was modeled numerically as a means to regenerate the draw solution by recovering water as ice, which could be particularly promising in cold regions. The effects of the initial concentration and type of the solute on both water recovery and ice purity were studied alongside the transport phenomena in the phase layer interface (solid and liquid) and the impurity rejection rate during the phase change (i.e., solidification). The results obtained from this modeling work of both FO and DFC processes were validated against experimental results reported in the literature (Kolliopoulos et al. 2022).

A CFD model was developed using COMSOL Multiphysics (Version 5.6, COMSOL Inc.) and used in the numerical modeling of the FO-DFC process. COMSOL Multiphysics is based on the finite element method (FEM) to solve nonlinear equations using the Newton–Raphson method. In our model, for both FO and DFC, the convergence criterion was 10−4. Two different types of equations were considered with different boundary and initial conditions to model the FO and the DFC parts, as explained in the following sections. A conceptual representation of the FO-DFC process is presented in Figure 1.
Figure 1
A conceptual flowchart of a forward osmosis-directional freeze crystallization (FO-DFC) process. Water first permeates through a semi-permeable membrane from a FS into a concentrated draw solution (CDS). The resulting diluted draw solution (DDS) is then exposed to low temperatures to recover water as ice and regenerate the CDS, which is recycled in the FO process.
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A conceptual flowchart of a forward osmosis-directional freeze crystallization (FO-DFC) process. Water first permeates through a semi-permeable membrane from a FS into a concentrated draw solution (CDS). The resulting diluted draw solution (DDS) is then exposed to low temperatures to recover water as ice and regenerate the CDS, which is recycled in the FO process.

Figure 1
A conceptual flowchart of a forward osmosis-directional freeze crystallization (FO-DFC) process. Water first permeates through a semi-permeable membrane from a FS into a concentrated draw solution (CDS). The resulting diluted draw solution (DDS) is then exposed to low temperatures to recover water as ice and regenerate the CDS, which is recycled in the FO process.
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A conceptual flowchart of a forward osmosis-directional freeze crystallization (FO-DFC) process. Water first permeates through a semi-permeable membrane from a FS into a concentrated draw solution (CDS). The resulting diluted draw solution (DDS) is then exposed to low temperatures to recover water as ice and regenerate the CDS, which is recycled in the FO process.

Close modal

Numerical methodology for FO modeling

A rectangular FO cell with an active membrane area of 42 cm2 was used in our CFD model. A 2D axisymmetric domain, which corresponds to the geometry described above, was designed using COMSOL Multiphysics (Version 5.6, COMSOL Inc.). This domain includes an FS channel, active layer, membrane support, and a DS channel. This setup is similar to the one used in the experimental work by Martin et al. (2020) and Kolliopoulos et al. (2022), whereby a stainless steel CF042-FO cell and asymmetric cellulose triacetate (CTA) membranes were used. Counter-current flow was studied for the FS and DS at a crossflow velocity of 2.1 cm/s to emulate the experimental conditions studied by Martin et al. (2020). Three salts, namely NaCl, CaCl2, and MgCl2, were studied as draw solutes. DI water and a hydrometallurgical effluent containing Al = 34 ppm, As = 7,700 ppm, Ca = 21 ppm, Cl = 46,000 ppm, Cu = 88 ppm, K = 44 ppm, Mg = 2,000 ppm, Na = 65,000 ppm, and S = 22,000 ppm, were simulated as the FS.

The osmotic pressure and physical parameters reported by Martin et al. (2020) and Kolliopoulos et al. (2022) were used in the FO modeling section. Both the FS and DS streams were considered incompressible, as the Reynolds number is 1 < Re < 100, the fluid flow at both sides of the membrane was assumed to be laminar flow, the support layer in the membrane was considered homogeneous and isotropic, and the process was at steady state. No slip (walls), inlet flow rates, outlet pressure, water flux rate, no-flux, and reverse solute flux rate were selected as boundary conditions. Molality units (m) were used for the concentration of the DS streams.

Governing equations

Momentum transport equations
Navier–Stokes equation (Equation (1)) was used to predict fluid flows inside both compartments of the FO cell (i.e., FS and DS) (Kahrizi et al. 2020):
formula
(1)
where u (m/s) denotes the velocity field, p (Pa) the pressure field, ρ (kg/m3) the constant density, μ (Pa.s) the dynamic viscosity coefficient, and f (N) the external body forces imposing on the domain (i.e., gravity and electrical field). For flow inside porous media (i.e., to predict fluid flow inside the membrane), resistance parameters need to be considered in Equation (1), which reduces Equation (1) to the Brinkman equation (Equation (2)):
formula
(2)
where ρ (kg/m3) is the density; κ and εp indicate the permeability (d) and porosity of the support layer of the CTA membrane, respectively; F (N) refers to external forces that can be exerted on the system, such as electric or magnetic field; μ (Pa s) is the dynamic viscosity; and βF (m−1) is the Forchheimer coefficient, which shows friction forces in porous media, and can be calculated by Equation (3) (Ruth & Ma 1992):
formula
(3)
where L (m) is the length of porous media and K refers to the pressure resistance factor that can be calculated using Equation (4) (Gruber et al. 2011):
formula
(4)
where ϕ is the porosity of the membrane.
Mass transfer equations
There are two main mass transport mechanisms in the FS and DS compartments: convection and diffusion. Equation (5) was used to describe the mass transport phenomena on both sides of the membrane at a steady state (Ren et al. 2020):
formula
(5)
where D (m2/s) refers to the diffusion coefficient and c refers to the solute concentration. To calculate the mass transfer of solute in the porous support layer of the membrane, convection and diffusion terms were considered using Equation (6) (Ren et al. 2020):
formula
(6)
where c is the solute concentration (m), ɛ is the bed porosity, and τ is the tortuosity of the support layer.
Osmosis governing equations

Membrane selection is a key element in FO, especially with regard to ICP, external concentration polarization (ECP), and fouling. These issues are associated with a reduction in water flux that is rooted from a decrease of driving force, which in turn has a negative impact on the overall FO performance. ICP corresponds to the accumulation of solutes inside the FO membrane, whereas ECP refers to the accumulation of solutes at the active layer surface (Kim et al. 2017; Martin et al. 2020). Embedded spacers at the surface of the active layer (Zhang et al. 2014) as well as the effect of turbulent flow by increasing the FS and DS flowrates (Akther et al. 2019) have been tested to overcome this issue.

Considering both ICP and ECP in numerical modeling is essential to achieve accurate FO performance predictions with regards to water flux, salt rejection, and the overall FO system performance. Equations (7) and (8), which consider both ICP and ECP, were used to estimate water flux (Jw) and reverse solute flux (Js), respectively (Tiraferri et al. 2013):
formula
(7)
formula
(8)
where πdb (Pa) and πfb (Pa) represent the bulk osmotic pressure in the draw solution and the FS, respectively; Ds (m2/s) is the bulk solute diffusion coefficient in the membrane support layer interface; cs,db (m) and cs,fb (m) refer to the solute concentration in draw and feed bulk solutions, respectively; kf (m/s) refers to the mass transport coefficient in the FS; A (m/s Pa), B (m/s), and S (m) represent water permeability across the membrane, solute permeability, and a membrane structural parameter, respectively. In Equations (7) and (8), the terms exp(JW/kf) and exp(JW(S/DS)) correspond to ECP and ICP, respectively (Tiraferri et al. 2013). The methodology to estimate πdb, πfb, A, B, and S has been presented elsewhere (Martin et al. 2020).

Numerical methodology for DFC modeling

The concentrated draw solution (CDS) regeneration via water recovery was achieved by DFC. The experimental setup modeled has been presented by Shum & Papangelakis (2019): a silicone container insulated on the sides and bottom that exposes only the surface of the solution to the cold air. In our simulation work, the DFC setup was considered insulated on the sides and bottom to present only the solution surface to the cold air.

Governing equations

In the DFC section, whereby all equations are time-dependent, a time step of 0.01 s was considered.

Species transport equations
When an aqueous solution starts freezing, solutes are rejected from the forming solid phase into the aqueous phase. A mushy freeze/melt zone (interface between solid and liquid) was considered between a low-temperature solidus (Tsolidus, °C) (Equation (9)) and a high-temperature liquidus (Tliquidus, °C) (Equation (10)) and in a single component mixture (Jayakody et al. 2017):
formula
(9)
formula
(10)
where Yi refers to the solute mass fraction, Ki to the partition coefficient of the solute (the ratio of the mass fraction in the solid to that in the liquid), Tmelt (°C) to the melting point temperature, and mi to the slope of the liquidus surface as regards to Yi. The temperature at the interface can be estimated by the following equation (Jayakody et al. 2017):
formula
(11)
where Ni refers to the number of species and β to the liquid volume fraction. Species transport was modeled by the following equation (Jayakody et al. 2017):
formula
(12)
where ρ (kg/m3) refers to the density of the fluid, Yi, liq and Yi, sol refer to the liquid and solid mass fractions, respectively, vliq (m2/s) refers to the liquid velocity, and Di,m (m/s) refers to the mass diffusion coefficient for species. Yi, liq and Yi, sol are related by the partition coefficient Ki as shown in the following equation (Eghtesad et al. 2020):
formula
(13)
Heat transfer equation
Equation (14) was used as the heat transfer equation, considering species transport, for the solidification process.
formula
(14)
where T (°C) denotes the temperature, k (m/s) the mass transfer coefficient, H the enthalpy (J), β the liquid volume fraction, v (m2/s) the velocity, and Amush the mushy zone constant. To prevent the last fraction of Equation (14) from being undefined when β = 0, a small number (ε = 0.001) was added to this.
Continuity and momentum equations
The calculation of the concentration gradient and the local mass fraction of individual species in DFC was carried out in COMSOL Multiphysics using Equations (15) (mass transport equation) and Equation (16) (momentum equation).
formula
(15)
where Ji (mol/m2 s) is the diffusion flux of the species.
formula
(16)
where μ is the viscosity of the fluid and p is the pressure.
Thermal and solutal buoyancy equation
As there are more than one species in the mixture, variations in temperature and concentration result in buoyancy forces (Jayakody et al. 2017): when the concentration and temperature of the solution change, the density changes, and consequently, a buoyancy force appears. Buoyancy forces in our model were solved as in the following equation:
formula
(17)
where ρref (kg/m3) is the reference density, g (m/s2) is the gravity, Ns is the total number of solute species, βs,i is the solutal expansion coefficient, and Yl,i and Yref,i are the mass fraction of the liquid phase and the reference mass fraction, respectively.

Mesh and grid independency

The FO and DFC setups were meshed using free triangular, quad, edge, and vertex unstructured meshes. The grid independency check was done by testing the effect of mesh density on water flux using a 1 m NaCl CDS in FO. According to the results presented in Table 1, water flux in FO reaches a plateau at 3.9 × 104 number of cells. Similarly, Table 2 presents the results obtained in our grid independency test for DFC. According to the volume fraction of ice in 0.5 m NaCl at −15 °C, 3.3 × 104 was selected as optimum number of cells, as an increase in the number of cells did not lead to a decrease in the simulated ice volume fraction.

Table 1

Grid independency check for the FO setup

Number of cellsWater flux (L/m2/h) using a 1 m NaCl CDS
2.0104 8.3 
2.5104 8.65 
3.5104 9.0 
4.0104 9.02 
4.5104 9.02 
Number of cellsWater flux (L/m2/h) using a 1 m NaCl CDS
2.0104 8.3 
2.5104 8.65 
3.5104 9.0 
4.0104 9.02 
4.5104 9.02 
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Table 2

Grid independency check for the DFC process using the volume fraction of ice in 0.5 m NaCl at −15 °C as the criterion

Number of cellsVolume fraction of ice in 0.5 m NaCl at −15 °C
1.7104 0.35 
2.4104 0.33 
2.9104 0.31 
3.3104 0.30 
3.7104 0.30 
Number of cellsVolume fraction of ice in 0.5 m NaCl at −15 °C
1.7104 0.35 
2.4104 0.33 
2.9104 0.31 
3.3104 0.30 
3.7104 0.30 
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Validation of developed CFD model

To validate the developed CFD model, our simulated CFD results were compared with experimental data from Kolliopoulos et al. (2022). The comparison of FO simulation results was done for all DSs at 25 °C and at four initial DS concentration levels (0.5, 1, 2, and 3.5 m) with experimental results at the same conditions when the FS was DI water. A good agreement with a relative error of less than 3% was found (Figure 2). Similarly, regarding the DFC data, the predicted volume fraction of ice in 0.5 m DDS at three different temperatures (−10 °C, −15 °C, and −20 °C) was found to be within 6% of the experimentally obtained values (Figure 3). Therefore, our CFD model, based on the governing equations described in Section 2, is valid and capable to predict both FO and DFC accurately.
Figure 2
Validation of the forward osmosis simulation results with experimental data at four draw solution concentration levels: 0.5, 1, 2, and 3.5 m at 25 °C using (a) NaCl, (b) CaCl2, and (c) MgCl2 and DI water as the feed solution.
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Validation of the forward osmosis simulation results with experimental data at four draw solution concentration levels: 0.5, 1, 2, and 3.5 m at 25 °C using (a) NaCl, (b) CaCl2, and (c) MgCl2 and DI water as the feed solution.

Figure 2
Validation of the forward osmosis simulation results with experimental data at four draw solution concentration levels: 0.5, 1, 2, and 3.5 m at 25 °C using (a) NaCl, (b) CaCl2, and (c) MgCl2 and DI water as the feed solution.
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Validation of the forward osmosis simulation results with experimental data at four draw solution concentration levels: 0.5, 1, 2, and 3.5 m at 25 °C using (a) NaCl, (b) CaCl2, and (c) MgCl2 and DI water as the feed solution.

Close modal
Figure 3
Validation of the directional freeze crystallization simulation results with experimental data from 0.5 m diluted draw solutions at three different temperatures: −10, −15, and −20 °C: (a) NaCl, (b) CaCl2, and (c) MgCl2 and DI water as the feed solution.
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Validation of the directional freeze crystallization simulation results with experimental data from 0.5 m diluted draw solutions at three different temperatures: −10, −15, and −20 °C: (a) NaCl, (b) CaCl2, and (c) MgCl2 and DI water as the feed solution.

Figure 3
Validation of the directional freeze crystallization simulation results with experimental data from 0.5 m diluted draw solutions at three different temperatures: −10, −15, and −20 °C: (a) NaCl, (b) CaCl2, and (c) MgCl2 and DI water as the feed solution.
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Validation of the directional freeze crystallization simulation results with experimental data from 0.5 m diluted draw solutions at three different temperatures: −10, −15, and −20 °C: (a) NaCl, (b) CaCl2, and (c) MgCl2 and DI water as the feed solution.

Close modal

Impact of operating parameters on FO performance

Effect of operating parameters on the water flux

Water flux was studied as a function of the initial DS concentration and temperature. Figure 4(a) and 4(b) present the relationship between water flux and DS concentration at 25 °C, while Figure 4(c) and 4(d) present the relationship between water flux and temperature. Three inorganic solutes, namely NaCl, CaCl2, and MgCl2, were tested as the DS and DI water as well as a hydrometallurgical effluent (Al = 34 ppm, As = 7,700 ppm, Ca = 21 ppm, Cl = 46,000 ppm, Cu = 88 ppm, K = 44 ppm, Mg = 2,000 ppm, Na = 65,000 ppm, and S = 22,000 ppm) were chosen as the FS.
Figure 4
Water flux (L/m2/h) at 25 °C using NaCl, CaCl2, and MgCl2 as the DS (from 1–3.5 m) and (a) DI water as the FS and (b) the hydrometallurgical effluent as the FS. The effect of temperature on water flux (L/m2/h) is shown in (c) when DI water was used as the FS and in (d) when the hydrometallurgical effluent was used as the FS; NaCl, CaCl2, and MgCl2 at an initial concentration of 1 m were used as the DS.
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Water flux (L/m2/h) at 25 °C using NaCl, CaCl2, and MgCl2 as the DS (from 1–3.5 m) and (a) DI water as the FS and (b) the hydrometallurgical effluent as the FS. The effect of temperature on water flux (L/m2/h) is shown in (c) when DI water was used as the FS and in (d) when the hydrometallurgical effluent was used as the FS; NaCl, CaCl2, and MgCl2 at an initial concentration of 1 m were used as the DS.

Figure 4
Water flux (L/m2/h) at 25 °C using NaCl, CaCl2, and MgCl2 as the DS (from 1–3.5 m) and (a) DI water as the FS and (b) the hydrometallurgical effluent as the FS. The effect of temperature on water flux (L/m2/h) is shown in (c) when DI water was used as the FS and in (d) when the hydrometallurgical effluent was used as the FS; NaCl, CaCl2, and MgCl2 at an initial concentration of 1 m were used as the DS.
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Water flux (L/m2/h) at 25 °C using NaCl, CaCl2, and MgCl2 as the DS (from 1–3.5 m) and (a) DI water as the FS and (b) the hydrometallurgical effluent as the FS. The effect of temperature on water flux (L/m2/h) is shown in (c) when DI water was used as the FS and in (d) when the hydrometallurgical effluent was used as the FS; NaCl, CaCl2, and MgCl2 at an initial concentration of 1 m were used as the DS.

Close modal

Based on Figure 4(a) and 4(b), by increasing the NaCl concentration (from 1 to 3.5 m), the water flux increased from 6 to 14 L/m2/h when DI water was used as the FS and from 2 to 3.5 L/m2/h when the hydrometallurgical effluent was used as the FS. This change in water flux was consistent for all DS studied and may be attributed to the higher osmotic pressures exhibited when the concentration of the DS increases. However, when the initial concentration of DS was set at 3.5 m, the highest water flux was obtained for magnesium chloride (MgCl2) DS at 17 L/m2/h when DI water was used as the FS and at 5 L/m2/h when the hydrometallurgical effluent was used as the FS, while it was estimated at 14 and 3.5 L/m2/h for NaCl, and at 16 and 4 L/m2/h CaCl2, for DI water and the hydrometallurgical effluent, respectively. This difference may be attributed to the higher osmotic pressures generated by divalent electrolytes when compared to the monovalent NaCl and ionic size of cations (Johnson et al. 2018).

The impact of temperature on the water flux was also investigated: three temperatures (5, 15, and 25 °C) and an initial DS concentration of 1 m were studied, and the water flux results are presented in Figure 4(c) and 4(d), respectively. Water flux increases with increasing temperature from 5 to 25 °C for all DS. This increase can be attributed to the decrease in viscosity and the increased draw solute diffusivity at higher temperatures (Kolliopoulos et al. 2022), meaning that, as the temperature of FO setup increases, the osmotic pressure (driving force) increases across the membrane and consequently the water flux increases.

Effect of operating parameters on the reverse solute flux

Figure 5(a) and 5(b) present the relationship between reverse solute flux and DS concentration, using the same inorganic DSs. The reverse solute flux decreases with decreasing DS concentration. The reverse solute flux decreased from circa 0.6 to 0.3 mol/m2/h when NaCl concentration was decreased from 3.5 to 1 m and DI water was used as the FS, while from 0.57 to 0.22 mol/m2/h when the hydrometallurgical effluent was used as the FS. The use of divalent salts also increased the ability of salt rejection during FO with both CaCl2 and MgCl2 reverse solute flux values being consistently less than 0.3 mol/m2/h for both feed solutions (DI water and hydrometallurgical effluent). This behavior can be attributed to their bigger ionic size (larger radii of hydration) and, in the case of MgCl2, its lower solute permeability (B) compared to NaCl and CaCl2 (Johnson et al. 2018). Based on Figure 5, the reverse solute flux decreased when the hydrometallurgical effluent was used as the FS instead of DI water. This decrease in reverse solute flux can be attributed to the lower chemical potential when the hydrometallurgical effluent is used as the FS.
Figure 5
Reverse solute flux (mol/m2/h) at 25 °C using NaCl, CaCl2, and MgCl2 as the DS (from 1 to 3.5 m) for (a) DI water as the FS and (b) the hydrometallurgical effluent as the FS. The effect of temperature on reverse solute flux (mol/m2/h) is shown in (c) when DI water was used as the FS and in (d) when the hydrometallurgical effluent was used as the FS; NaCl, CaCl2, MgCl2 at an initial concentration of 1 m were used as the DS.
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Reverse solute flux (mol/m2/h) at 25 °C using NaCl, CaCl2, and MgCl2 as the DS (from 1 to 3.5 m) for (a) DI water as the FS and (b) the hydrometallurgical effluent as the FS. The effect of temperature on reverse solute flux (mol/m2/h) is shown in (c) when DI water was used as the FS and in (d) when the hydrometallurgical effluent was used as the FS; NaCl, CaCl2, MgCl2 at an initial concentration of 1 m were used as the DS.

Figure 5
Reverse solute flux (mol/m2/h) at 25 °C using NaCl, CaCl2, and MgCl2 as the DS (from 1 to 3.5 m) for (a) DI water as the FS and (b) the hydrometallurgical effluent as the FS. The effect of temperature on reverse solute flux (mol/m2/h) is shown in (c) when DI water was used as the FS and in (d) when the hydrometallurgical effluent was used as the FS; NaCl, CaCl2, MgCl2 at an initial concentration of 1 m were used as the DS.
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Reverse solute flux (mol/m2/h) at 25 °C using NaCl, CaCl2, and MgCl2 as the DS (from 1 to 3.5 m) for (a) DI water as the FS and (b) the hydrometallurgical effluent as the FS. The effect of temperature on reverse solute flux (mol/m2/h) is shown in (c) when DI water was used as the FS and in (d) when the hydrometallurgical effluent was used as the FS; NaCl, CaCl2, MgCl2 at an initial concentration of 1 m were used as the DS.

Close modal
In addition, the impact of temperature on the reverse solute flux was also investigated: three temperatures (5, 15, and 25 °C) and an initial DS concentration of 1 m were studied. The reverse solute flux results are presented in Figure 5(c) and 5(d). The reverse solute flux results increase with increasing temperature from 5 to 25 °C for all CDS solutions. Further, according to Figure 6, the specific water flux increases indicating a higher selectivity for water at lower temperatures.
Figure 6
Specific water flux vs. temperature for the three aqueous DSs of 1 m (NaCl, CaCl2, and MgCl2) when: (a) DI water and (b) the hydrometallurgical effluent are used as the FS.
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Specific water flux vs. temperature for the three aqueous DSs of 1 m (NaCl, CaCl2, and MgCl2) when: (a) DI water and (b) the hydrometallurgical effluent are used as the FS.

Figure 6
Specific water flux vs. temperature for the three aqueous DSs of 1 m (NaCl, CaCl2, and MgCl2) when: (a) DI water and (b) the hydrometallurgical effluent are used as the FS.
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Specific water flux vs. temperature for the three aqueous DSs of 1 m (NaCl, CaCl2, and MgCl2) when: (a) DI water and (b) the hydrometallurgical effluent are used as the FS.

Close modal

Selecting the optimum DS in FO requires a careful balance between generation of osmotic pressure, reverse solute flux, molecular size of the solutes, solubility and concentration, and environmental and economic factors. It often involves experimental evaluation and simulation studies to determine the most suitable draw solute for a specific separation application, considering the desired separation flux, environmental impact, toxicity, availability, cost, and overall process efficiency. Table 3 summarizes the water flux, the reverse solute flux, and the cost of each DS studied in this work. MgCl2 resulted in the highest water flux and lowest reverse solute flux, while NaCl was found to be the optimum option from an economic point of view.

Table 3

Water flux, reverse solute flux, and cost ($/kg) of each DS studied in this work

Type of DS (3.5 m)Water flux (L/m2/h)Reverse solute flux (mol/m2/h)Cost ($/kg) (Achilli et al. 2010)
NaCl 3.5 0.57 15 
CaCl2 4.0 0.27 35 
MgCl2 5.0 0.25 28 
Type of DS (3.5 m)Water flux (L/m2/h)Reverse solute flux (mol/m2/h)Cost ($/kg) (Achilli et al. 2010)
NaCl 3.5 0.57 15 
CaCl2 4.0 0.27 35 
MgCl2 5.0 0.25 28 

The hydrometallurgical effluent was used as the FS in FO alongside a CTA membrane at 25 °C.

View Large

Regeneration of the CDS using DFC

In an energy-conscious society, the use of low-temperature water separation processes is increasingly desirable because of advancements in refrigeration technology. FC has been acknowledged as a cost-effective and environmentally friendly technology to regenerate the draw solution used in FO, especially in cold regions, where the energy of cooling is free for extended periods of time per year. A directional FC unit, as described in Section 2.2, was used in our CFD modeling. The effects of freezing time, initial DDS concentration, and DS type on water recovery yield and purity were investigated. The eutectic composition and temperature of the DSs studied have been determined by Kolliopoulos et al. (2022).

Purity of produced water and temperature profile

In this work, the purity of the recovered water in the DFC process was assessed using the final concentration of dissolved ions in the recovered water as the basic water quality parameter. The effect of freezing time on water recovery as ice was studied to identify the optimum operating for the DS regeneration. The concentration distribution of the draw solutes alongside the freezing setup at an initial concentration of 0.5 m and at −20 °C is depicted in Figure 7. An upward trend in trapped solutes inside ice was observed when the freezing time of the DFC unit increased from 180 to 1,800 s: the concentration of the impurities in the recovered water was 0.010, 0.007, and 0.005 m at 180 s and reached 0.42, 0.40, and 0.35 m after 1,800s when 0.5 m NaCl, CaCl2, and MgCl2 were chosen as the DDSs, respectively. Based on Figure 7, the purity of recovered ice is decreasing over time. This impurity increase may be attributed to the dendritic growth of ice crystals, which has been observed by researchers (Shum & Papangelakis 2019). During FC of brine solutions of high salinity, the exclusion of salt ions at high rates accelerates the growth of dendritic ice (Shum & Papangelakis 2019). Furthermore, the structural transition of ice from a planar sheet to a three-dimensional ice matrix (or spongy ice) over time is thought to be a contributing cause to the increased salt content in ice (Barma et al. 2021). Therefore, during FC, pockets of liquid solution are entrapped within the growing ice layer due to the dendritic growth of ice, decreasing its final purity (Shum & Papangelakis 2019).
Figure 7
Draw solute concentration distribution versus z-coordinate (height of the freezing container) at −20 °C and different freezing times for NaCl, CaCl2, and MgCl2.
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Draw solute concentration distribution versus z-coordinate (height of the freezing container) at −20 °C and different freezing times for NaCl, CaCl2, and MgCl2.

Figure 7
Draw solute concentration distribution versus z-coordinate (height of the freezing container) at −20 °C and different freezing times for NaCl, CaCl2, and MgCl2.
View largeDownload slide

Draw solute concentration distribution versus z-coordinate (height of the freezing container) at −20 °C and different freezing times for NaCl, CaCl2, and MgCl2.

Close modal
The temperature gradient (°C/cm) inside the DFC setup is shown in Figure 8. The maximum temperature gradient occurred at the middle and bottom of the setup and based on the results, the minimum temperatures (blue area) occurred at the top of the setup where the solution was exposed to cool air. Pure ice was produced at this area, and since the process of ice formation is exothermic with ice acting as a thermal insulation, the maximum temperature occurred at the interface of ice and rejected solution towards the bottom of the simulated DFC setup (Shum & Papangelakis 2019). It is generally known that, in DFC, a slower growth rate is frequently recommended to increase the process' salinity reduction performance, as ice crystallisation at a lower growth rate provides the required time to the diffusion-driven transfer of salt ions from the ice-solution interface to the bulk solution (Shum & Papangelakis 2019).
Figure 8
Temperature gradient (°C/cm) of the directional freeze crystallization (DFC) unit for NaCl, CaCl2, and MgCl2 at 0.5 m and −10 °C.
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Temperature gradient (°C/cm) of the directional freeze crystallization (DFC) unit for NaCl, CaCl2, and MgCl2 at 0.5 m and −10 °C.

Figure 8
Temperature gradient (°C/cm) of the directional freeze crystallization (DFC) unit for NaCl, CaCl2, and MgCl2 at 0.5 m and −10 °C.
View largeDownload slide

Temperature gradient (°C/cm) of the directional freeze crystallization (DFC) unit for NaCl, CaCl2, and MgCl2 at 0.5 m and −10 °C.

Close modal

Mass transport study of DS recovery

Figure 9 presents the ice and solute distribution in the DFC unit as blue and red areas, respectively. The bulk temperature was set at −10 °C and the DDS concentration was 0.5 m. The main problem of water recovery by natural freezing is the entrapment of liquid pockets, namely impurities, inside and interface of formed ice due to dendritic ice growth (Shum & Papangelakis 2019). For instance, in Figure 10, as the hydrated ion size and hydration enthalpy are higher for MgCl2 compared to NaCl and CaCl2, the resulting solute concentration is higher for MgCl2 towards the middle and the bottom of the DFC unit (red areas), and consequently, the recovered ice is purer when the solution is MgCl2.
Figure 9
Concentration distribution of NaCl, CaCl2, and MgCl2 in the DFC unit. The bulk temperature was set at −10 °C and the initial DS concentration was 0.5 m.
View largeDownload slide

Concentration distribution of NaCl, CaCl2, and MgCl2 in the DFC unit. The bulk temperature was set at −10 °C and the initial DS concentration was 0.5 m.

Figure 9
Concentration distribution of NaCl, CaCl2, and MgCl2 in the DFC unit. The bulk temperature was set at −10 °C and the initial DS concentration was 0.5 m.
View largeDownload slide

Concentration distribution of NaCl, CaCl2, and MgCl2 in the DFC unit. The bulk temperature was set at −10 °C and the initial DS concentration was 0.5 m.

Close modal
Figure 10
Iso surface of diffusive flux magnitude (mol/m2s) of NaCl, CaCl2, and MgCl2 at an initial concentration of 0.5 m and temperature of −5 °C. This figure shows the rejection flux of salt compounds from the ice formed during the DFC process.
View largeDownload slide

Iso surface of diffusive flux magnitude (mol/m2s) of NaCl, CaCl2, and MgCl2 at an initial concentration of 0.5 m and temperature of −5 °C. This figure shows the rejection flux of salt compounds from the ice formed during the DFC process.

Figure 10
Iso surface of diffusive flux magnitude (mol/m2s) of NaCl, CaCl2, and MgCl2 at an initial concentration of 0.5 m and temperature of −5 °C. This figure shows the rejection flux of salt compounds from the ice formed during the DFC process.
View largeDownload slide

Iso surface of diffusive flux magnitude (mol/m2s) of NaCl, CaCl2, and MgCl2 at an initial concentration of 0.5 m and temperature of −5 °C. This figure shows the rejection flux of salt compounds from the ice formed during the DFC process.

Close modal

The iso surface of the diffusive flux magnitude inside of DFC setup for the inorganic salt solutions is shown in Figure 10. The maximum diffusive flux or solute rejection from the ice formed during the DFC process occurred at the interface between the solid (i.e., ice) and the rejected brine solution, which is consistent with Shum & Papangelakis (2019). This can be explained by the temperature at the interface of the ice formed and the rejected brine solution, which is higher than the other areas of the DFC setup since ice acts as a heat insulator. Based on this phenomenon, namely the diffusion of solutes away from the advancing ice front, the ice formed has a lower concentration of salt than the resulting brine (Shum & Papangelakis 2019; Xu et al. 2022).

This study focused on developing a comprehensive CFD model for the integral parts of the newly proposed forward osmosis-directional freeze crystallization (FO-DFC) process. Validation of the model was done by comparing the modeling results with experimental data from literature studies. The outcome of this comparison validated our CFD model with an error of less than 6%. Three aqueous solutions, namely of NaCl, CaCl2, and MgCl2, were chosen and simulated as the draw solution (DS) in FO. CFD modeling revealed that the MgCl2 solution imposed a higher osmotic pressure difference across the FO cell and resulted in higher water permeation. Further, since Mg is a divalent element with a larger hydrated radius, it resulted in lower reverse solute flux in comparison with two other salts tested. DFC simulations showed that the separation of MgCl2 and water resulted in higher purity water, recovered as ice, compared to NaCl and CaCl2 solutions. The operating temperature and the initial DS concentration play a key role in DS recovery. These findings demonstrate that CFD modeling is essential to improve the membrane performance upon a proper selection of both the draw solution and the FO process conditions, as well as to develop a better fundamental understanding of DFC as a promising CDS regeneration and water recovery process. Regarding the potential and forthcoming avenues in numerical modeling for the hybrid FO-DFC process, it is noteworthy to highlight the ample room for investigating diverse mining and hydrometallurgical effluents, alongside various types of DS in FO. Moreover, there is significant merit in delving into the realm of regeneration techniques.

The authors would like to acknowledge the Natural Sciences and Engineering Research Council of Canada (NSERC) (Grant No. RGPIN-2020-04262) and the Fonds de recherche du Québec–Nature et technologies (ERA-MIN 2 Grant; Project acronym: nanoBT) for the financial support of this research. Further, the authors acknowledge CMC Microsystems and Canada's National Design Network (CNDN) for the provision of products and services that facilitated this research, including access to COMSOL Multiphysics. The graphical abstract and Figure 1 were created with BioRender.com.

A. A. contributed to the methodology, model development, formal analysis, visualization, and writing of the original draft. G. K. contributed to the writing of this work via review and editing, visualization, supervision, and funding acquisition.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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© 2023 The Authors
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