Temperature Effect on Forward Osmosis

2.1. Mechanism

In the FO process, the solvent (water) transport is driven solely by osmotic pressure difference without the need of any external hydrostatic pressure, allowing for lower energy consumption compared to RO. To extract water from the feed solution, the osmotic pressure at the opposite side of the membrane must be higher, which requires a highly concentrated solution; this concentrated solution is typically referred to as the draw solution. Draw solutes need to be inert and easily removable. A semipermeable membrane separates the feed solution and the concentrated draw solution where the chemical potential difference allows the water to flow through the membrane while leaving behind the solutes in the feed stream. Regions of high and low solute concentrations refer to those of low and high solvent chemical potentials, respectively. As the semipermeable membrane restricts the solute transport and maintains chemical potential differences of both solute and solvent, water migrates from its high solvent chemical-potential region (i.e., of low solute concentration) to low solvent chemical-potential region (i.e., of high solute concentration). Such a water transport leads to dilution of the draw solution where the diluted draw solution can be further recycled such that the initial solute concentration is recovered. Particularly for desalination applications, the solutes in the draw solution (osmotic agent or draw solutes) are chosen to be inert, nontoxic, and easily removed to obtain the desalinated water with ease. One example includes NH4CO2_, which can be easily removed by decomposing at a moderately elevated temperature (~60°C) followed by low-temperature distillation [18, 19]. Extra energy is, however, necessary to re-dissolve NH4CO2into the draw solution for a continuous FO operation.

2.2. Concentration polarization

The water flux across the membrane results in concentration of the feed solution and dilution of the draw solution since the membrane mainly allows passage of water molecules. This phenomenon, referred to as concentration polarization (CP), has an adverse impact on the efficacy of the FO process since such an effect reduces the effective osmotic pressure difference across the membrane, thus hindering water transport.

CP is highly influenced by the morphology of the membranes. The membranes used in the FO process consist of a thin, dense layer that rejects the solutes (active layer) followed by a coarse, thick porous layer (support layer or porous substrate) to reinforce the mechanical stability against fluid pressure and shear. This configuration makes the membrane asymmetric in which the orientation of the membrane with respect to the direction of the water flux (i.e., from low to high osmotic pressure) leads to significantly different transport dynamics [20].

Typically in the FO process, the active layer is placed against the feed stream in order to minimize fouling since the support layer is more susceptible to colloidal fouling due to the large pores. This configuration is called FO mode, as shown in Figure 1(a). However, the downside of placing it in this way is that there is a significant dilutive internal concentration polarization (ICP) in the thick porous substrate. This is because the support layer is in contact with the concentrated draw solution hindering the solute diffusion, which significantly reduces the water flux (Figure 1(a)).

In contrast, when the active layer is placed against the draw stream, one can expect a higher water flux since this configuration can avoid the dilutive ICP at the expense of accelerated membrane fouling. This configuration is called the pressure-retarded osmosis (PRO) mode, as shown in Figure 1(b), typically realized in standard PRO systems. To avoid any confusion, we will refer to the membrane configuration in which the active layer is placed against the feed solution as the FO mode, whereas the opposite case is the PRO mode during FO processes.

3.1. Water flux

The most direct consequence of raising the system temperature is the increased water flux across the membrane due to lowered water viscosity and increased water diffusivity, which effectively increases the water permeability across the membrane. Since the transport of water through the active layer of the membrane follows the solution-diffusion mechanism [22], it is commonly believed (and also observed) that the diffusivity Dexhibits an Arrhenius relation, that is, D∼exp−s/T, where sis an empirical constant related to the activation energy [23, 24]. However, we also note a counterexample where Petrotos et al. failed to show such a behavior [25].

On the basis of our survey, the available literature related to the temperature-dependent FO reported increased water flux with temperature. Table 1 provides a summary of experimental conditions and resulting water flux from the available literature [23, 24, 25, 26, 27, 28, 29, 30, 31]. Here, we define a new quantity to indicate how much solvent flux increases with respect to the system temperature, as indicated in the last column of Table 1:

where Jw,Mand Jw,0are the water fluxes at a given maximum system temperature TMand at base temperature T0, respectively. The survey shows that raising the temperature does increase the water flux, but the extent of such an increase varies across the literature, especially depending on the membrane orientation. This observation implies that the CP phenomena are uniquely influenced by the temperature, leading to variations in the water flux.

McCutcheon and Elimelech were the first to study the influence of temperature on the CP phenomena [29]. Raising the temperature increases the water flux because of the decreased water viscosity in solutions (and/or solubility) and increased water solubility and diffusivity within the membrane. At the same time, however, the higher flux also increases both the ICP and ECP, which essentially limit the water flux as a feedback hindrance. Therefore, such a self-limiting behavior driven by two counteracting effects leads to the fact that the temperature has a “modest” effect on the water flux at high water flux conditions [29]. This self-hindering effect of the solvent flux is unavoidable in most membrane separation processes. It is similar to the fact that, in RO, applying high pressure initiates increasing permeate flux, which will eventually bring more solutes from the bulk phase to the membrane surface, enhancing the CP. Therefore, additional gain of the RO permeate flux is not as much as anticipated when the pressure is increased.

The change in the temperature influences the CP phenomena in different ways depending on the orientation of the membrane. This is because the formation of the ICP, which is the most critical factor that limits the driving force, is dependent on the membrane configurations. In the PRO mode, the concentrative ICP is developed in the feed side (see Figure 1(b)). By reducing the ICP using deionized water as the feed, the water flux was shown to be highly dependent on the temperature, confirming the impact of ICP on the FO process [29].

In the presence of solutes in the feed side so that the ICP is present, however, the water flux was shown to be almost insensitive to the temperature, at least in the operating temperature range (20–40°C). This behavior is attributed to the coupled interaction between ICP and ECP. Although the increased solute diffusion at higher temperature mitigates the concentrative ICP in the support layer so that the water flux can be increased, such an increased water flux carries more solutes from the feed bulk phase to the vicinity of the support layer surface and enhances the dilutive ECP, thereby reducing the osmotic driving force. Therefore, the two opposing effects on the water transport effectively limit the enhancement of the water flux such that the temperature has a marginal effect on the overall water flux. If both water and solute diffusivities increase in a similar behavior, the net diffusive transport must be more or less the same.

In the FO mode, however, the water flux was shown to be significantly influenced by the temperature. Overall, the water flux was observed to be lower than the PRO mode due to the presence of the dilutive ICP. This was proven mathematically using the method of proof by contradiction [32]. Such a low water flux effectively suppresses the extent of concentrative ECP in the feed side. Also, the influence of concentrative ECP on the water flux is less important than the dilutive ECP in the draw solution side because the initial solute concentration in the bulk phase is much lower at the feed solution than the draw solution. This implies that the ECP has a minor effect on the driving force in the FO mode. Therefore, when the membrane is placed in the FO mode, the water flux is significantly influenced by the temperature since the ICP is the only major factor that determines the driving force.

One assumption McCutcheon and Elimelech had made while analyzing their data were the insignificant solute diffusion across the membrane [29], which otherwise leads to further ICP. Obviously, commercially available membranes are known to permit diffusion of the solutes, which can impact the formation of the CP effect. Since the solute diffusion is also sensitive to the temperature, the transmembrane solute flux should also lead to a change in the water flux. We discuss the effect of temperature on the solute diffusion and rejection in the following section.

3.2. Diffusion and rejection of solutes

It is of general consensus that the transmembrane solute diffusion increases with temperature. A number of groups have recently investigated experimentally the temperature effect on the transmembrane solute diffusion and the solute rejection [26, 27, 28].

Xie et al. recognized that the effective size of the solute molecules was the most important parameter for the transmembrane solute diffusion [27], which was predicted theoretically using the integral equation theory [33]. Hydration of charged organic solutes results in an increase in the effective solute size, which directly influences the solute diffusion and rejection rate, as it was well understood that the rejection of the charged organic solutes would be much higher than the neutral organic solutes. In this regard, neutral solutes were more likely to diffuse across the pores than the charged solutes in both the cellulose triacetate membranes and polyamide membranes. This implies that increasing the temperature leads to higher solute diffusion due to the increased solute diffusivity. Moreover, increasing the temperature leads to faster dissolution of the solutes into the membrane such that even hydrophobic neutral solutes absorb into the membrane at an order of magnitude higher rate at elevated temperatures.

Notably, the ratio between the water flux Jwand the solute flux Jswas shown to be more or less constant regardless of the system temperature [27]. Such a constant ratio implies that the structural properties may not change, at least in the operating temperature range (20–40°C). In fact, although it is documented in the literature that the RO membrane properties such as pore sizes may change when the temperature is above 40°C[34], it was reported in various FO studies that the membrane structural properties do not change significantly below 45°C[26, 27]. However, it is more reasonable to say that the structural properties of FO membranes change with temperature in a way that the ratio between solvent and solute fluxes remain almost constant. In a solution-diffusion model, permeabilities of solvent and solutes, Aand B, respectively, are believed to increase with membrane temperature. The permeate concentration is controlled by only their ratio, A/B. If Aand Bincrease with Twhile A/Bremains less sensitive to T, then the solute diffusion can be seen phenomenologically insensitive to temperature. This is because although higher Tincreases both the solute and solvent fluxes, it is only the ratio that influences the concentration of solutes passing through the membrane. This topic is discussed theoretically in detail in Section 5.

Meanwhile, You et al. showed that the transmembrane solute diffusion was also shown to be dependent on the membrane orientation regardless of the temperature in which the PRO mode was shown to exhibit higher solute flux across the membrane than the FO mode, which is similar to the behavior of the water flux [28].

3.3. Membrane scaling

Membrane scaling occurs when the solute concentration is high enough to initiate precipitation. This is directly related to solute rejection and the CP phenomena, implying that membrane scaling should also be temperature-dependent.

Zhao and Zou studied how the temperature influences the membrane scaling over time, which is important in long-term operations [24]. Due to the fast water flux at elevated temperature, increase in the final concentration of the feed solution (i.e., concentration after 28 hours of running) was accelerated by more than 100% when the temperature was raised from 25 to 45°C, which led to faster membrane scaling. Concentrative polarization is also enhanced when the water flux is increased, which results in an accelerated membrane scaling. This was confirmed by directly visualizing the fouled membrane by using a scanning electron microscope (Figure 3(a)–(d)) and also by measuring the decrease in flow rate over time (Figure 3(e)), showing faster decline of water flux over time at elevated temperatures due to the scaling. In addition to higher solute concentration near the membrane surface driven by the temperature-enhanced solvent flux, the changes in solubility limits for inorganic species may contribute to the accelerated fouling behavior.

4.1. Water flux

Although the temperature dependence on the water flux shows an agreeable consensus as shown in Table 1, the anisotropic temperature effect is shown to differ largely across various studies. When the temperature on either side of the solutions is increased, the water flux becomes higher than that at the base temperature, but lower than when the temperatures of both sides of the solutions are increased. It is, however, left unclear which side of the solution has more influence on the FO process when heated as this does not have an agreeable consensus. Table 2 provides a summary of the effect of temperature difference on the FO process under various experimental parameters. For simplicity, we define

and

as included on the right-hand side of Table 2. Eqs. (3) and (4) refer to the water flux increase per temperature change when the feed side or the draw side is heated only, respectively. Phuntsho et al. calculated using a commercial software (OLI Stream Analyzer) where the osmotic pressure difference across the membrane can be higher when the draw side is heated in contrast to heating the feed side [26]. However, the temperature difference not only changes the osmotic pressure difference but also gives spatial nonlinearity to other important transport properties such as the solution viscosity as well as solvent/solute diffusivity in bulk phases and their solubilities in the membrane phase, which may impact the CP phenomena in various ways depending on the membrane orientation.

In general, regardless of either the feed or draw, raising the temperature on either side leads to increase in both the water flux and the solute flux. Xie et al. stated that raising the feed solution temperature leads to enhanced diffusivity of the water molecules, whereas raising the draw solution temperature leads to decreased draw solution viscosity and increased draw solute diffusivity, both of which lead to increased water flux and reverse solute flux [27]. However, the degree to which the water flux and solute flux are increased varies across the literature [10, 26, 27, 28, 31, 35, 36] (see Table 2).

Phuntsho et al. showed that increasing the draw solution temperature resulted in more water flux compared to increasing the temperature of the feed solution [26]. Their membrane was oriented in the PRO mode where the active layer was facing the draw solution. They argued that increasing the draw temperature led to reduced solution viscosity and increased draw solute diffusivity. This change resulted in the reduction of dilutive ICP on the draw side, thereby increasing the water flux. Again, such a behavior is attributed to the fact that the dilutive ICP plays a more significant role than the concentrative ECP in determining the water flux [26]. Such a preferential water flux increase due to the increased draw temperature was also observed by Xie et al. [27] and Cath et al. [31].

You et al. showed, however, that regardless of the membrane orientation, the water flux increased more when the feed solution temperature is increased rather than the draw solution [28], which is in a disagreement with the observations made by Phuntsho et al. [26], Xie et al. [27], and Cath et al. [31]. You et al. argued that the water diffusion kinetics is more important than the thermodynamic driving force (i.e., osmotic pressure difference) of the solution in determining the water flux, thus the feed temperature governs the water flux rather than the draw solution temperature [28].

Interestingly, in Nayak and Rastogi’s study [36], the water flux in the FO mode was shown to be higher than the water flux in the PRO mode particularly when the molecular size of the feed solute is large enough such that the external concentration polarization cannot be ignored. They also showed that this is indeed true for concentrating anthocyanin, which is a large sugar molecule. In their work, the water flux in the FO mode was measured to be 260% higher than that in the PRO mode.

4.2. Solute diffusion/rejection

As mentioned in the preceding section, Xie et al. showed that the neutral solutes are more likely to diffuse through the membrane than the charged ones due to their smaller hydrodynamic size [27]. In this sense, transmembrane temperature differences barely influenced the solute rejection rate for the charged solutes, whereas the neutral solutes were significantly influenced by the temperature difference. It was shown that raising the draw temperature (from 20 to 40°C) led to more neutral solute rejection, even more compared to the isothermal condition at base temperature (20°C) [27]. The reason being is that raising the draw temperature leads to increased water flux, which contributes to the increased solute rejection. At the same time, keeping the feed temperature low reduces the deposition of the solutes on to the membrane, thus preventing the neutral feed solutes from dissolving into the membrane and diffusing across the membrane [27].

5.1. Revisit to the solution-diffusion model

The solution-diffusion model is widely used to describe the FO process, which was originally developed by Lonsdale et al. to explain the RO phenomena using isothermal-isobaric ensemble [39]. In the model, the chemical potential of water is represented as a function of temperature, pressure, and solute concentration, i.e. μw=μwTPC, and its transmembrane gradient is

where the integration is over the membrane region. From the basic thermodynamic relationship,

is used where V¯wis the molar volume of water. In the isothermal-isobaric equilibrium Δμw=0, the applied pressure ΔPis balanced with the transmembrane difference of the osmotic pressure, i.e. ΔP=Δπ. This condition gives

and hence we derive Δμw=V¯wΔp−Δπ. It is assumed that the water transport within the membrane is phenomenologically Fickian, having the transmembrane chemical potential difference of water as a net driving force. The water flux is given as

which becomes

where A=DwCw/RTδmis the solvent permeability that can be obtained experimentally. The solute flux is similarly given as

where ΔC′and ΔCare the concentration differences across the interior and exterior of the membrane, respectively, and Km=ΔC'/ΔCis the partition coefficient, which is assumed to be constant, and B=DsK/δmis the solute permeability.

Figure 4(a) shows a schematic representing the PRO and FO modes altogether. Concentrations in the PRO and FO modes are denoted as Cand n, respectively. In the PRO mode, C1and C5are the draw and feed concentrations, and C2, C3, and C4are concentrations at interfaces between the draw solution and the active layer, the active layer and the porous substrate, and the porous substrate and the feed solution, respectively. In the FO mode, n1and n5are the draw and feed concentrations, respectively, and similarly, n2, n3, and n5have the meanings corresponding to those in the PRO mode. To systematically compare the performances of the PRO and FO modes, we set n1=C1and n5=C5,which are the draw (Cd) and feed (Cf) concentrations, respectively. Solvent and solute fluxes in the PRO mode are denoted as JwPROand JsPRO, and those of the FO mode are JwFOand JsFO, respectively. In each mode, solvent and solute fluxes are oriented in opposite directions, influencing each other’s driving forces. The active layer and porous substrate have thicknesses of δmand δs, respectively, as located in regions of −δm<x<0and 0<x<δs, respectively. Solute molecules migrate with molecular diffusivity D0in the porous substrate that is characterized using its thickness δs, porosity ε, and tortuosity τ.

In the PRO mode, the solvent flux (in magnitude) is

where π2and π3are osmotic pressures at concentration C2and C3, respectively. In a steady state, the water flux Jwis constant in both the active and porous regions. The solute flux in the active layer is:

and that in the porous substrate:

In a steady state, Jsof Eqs. (12) and (13) are equal to each other. Flux equations for the FO mode can be easily obtained by replacing subscript 2 by 4 in Eqs. (11) and (12) and replacing Cby nin Eqs. (12), (13). Fluxes of the PRO and FO modes are calculated as

and

respectively, where πdand πfare the osmotic pressure of the draw and feed concentrations, respectively, and

is interpreted as the characteristic mass transfer resistance, proposed by Lee et al. [37]. Following the convention of standard mass transfer theory, K−1can be interpreted as the mass transfer coefficient of FO processes. In Eq. (16), S=δsτ/ϵ, defined as the structural parameter having units in length, represents the actual path length of molecules passing through the tortuous porous substrate, which is by definition longer than the thickness δs. For mathematical simplicity, one can write the flux equation for both modes:

where

is an integer to toggle between the two modes. Any theoretical development can be initiated from Eq. (17) to consider universally both the FO and PRO modes, and then a proper value of φcan be chosen.

5.2. Heat transfer

Figure 4(b) shows an arbitrary temperature profile across the FO membrane, increasing from the active layer side to the porous layer side. In bulk phases of the active and porous sides, temperatures are maintained at T1and T4, respectively. For simplicity, we set T1<T4. Stream temperature on the active side increases to T2, and within the membrane, temperature elevates from T2to T3. Since the active layer is often made thin, a linear variation of temperature can be readily assumed. From the active-porous interface to the porous layer surface to the solution, the temperature increases from T3to T4. A similar external temperature polarization occurs in the PL-side bulk phase, generating the temperature change from T4to T5. The overall temperature profile is conceptually akin to the concentration profile in the FO mode. Having the same bulk temperatures, i.e. T1and T5, the flow direction can noticeably change values from T2to T4. For logical consistency, a steady state is assumed while investigating the heat transfer across the FO membrane in this chapter. Thus, heat fluxes of the four regions are

where subscripts BA and BP indicate bulk phases in the active and porous layer sides, respectively, and AL and PL mean the active layer and porous layer, respectively. The net temperature difference across the membrane is T4−T2, which is to be approximated as T5−T1. In the steady state, the heat flux qshould be equal in each region, that is, q=qBA=qAL=qPL=qBP. Dividing each equation of (20)–(23) by the heat transfer coefficient h′s, one derives

Note that Eq. (24) assumes that the heat transfer is solely based on thermal conduction without thermal convection, that is, transfer rate of heat by solvent flux. In the FO process with the transmembrane thermal gradient, Eqs. (21) and (22) should be revised as

where Hwand Jware the enthalpy and flux of the solvent, respectively, and the sign is plus when the concentration and temperature profiles both increase and decrease together, otherwise it is negative. For example, for the temperature profile shown in Figure 4, the FO concentration profile has the same trend to that of the temperature, and therefore signs in Eqs. (26) and (27) are positive. In this case, Eq. (25) needs to be modified to

where

This heat balance analysis is very similar to that of membrane distillation [43, 44], but the FO process does not have any solvent phase transition so that the latent heat is not considered.

5.3. Mass transfer mechanisms