Article pubs.acs.org/IECR
Reverse Permeation of Weak Electrolyte Draw Solutes in Forward Osmosis Jui Shan Yong,† William A. Phillip,*,‡ and Menachem Elimelech† †
Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520-8286, United States Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556-5637, United States
‡
ABSTRACT: The successful development of forward osmosis relies on the identification of draw solutes that can be easily regenerated, produce high water fluxes, and minimize leakage into the feed solution. One promising draw solute currently under investigation, ammonia−carbon dioxide, is a weak electrolyte. Therefore, in this work, we report a fundamental study on the reverse permeation of a model weak electrolyte draw solute, propanoic acid/propanoate ion, through a commercial cellulose triacetate forward osmosis membrane. Reverse solute flux and permeate water flux were monitored as the draw solution pH was varied from pH 4−7. Draw solutions with pH < 4.87, the pKa of propanoic acid, exhibited significantly higher reverse draw solute fluxes. However, pH had little effect on the water flux generated by the draw solutions. A mathematical model for the solute and water fluxes, which accounts for the pH-dependent equilibrium of the propanoic acid dissociation reaction, was developed and compared with experimental data. Using independently determined transport coefficients, strong agreement between theory and experiments was observed over the whole pH range examined in this work.
■
INTRODUCTION A rapidly growing global population coupled with a finite number of unimpaired freshwater resources has led to the increased usage of saline, wastewater, and impaired water sources.1,2 As such, seawater desalination and wastewater reuse are becoming a more common method for providing a steady supply of clean water without impairing or straining natural fresh water ecosystems.3 However, despite their widespread adoption, mature desalination technologies, such as reverse osmosis (RO), are still inherently energy intensive.2,4,5 Therefore, there is a critical need for the development of more robust, less energy intensive water reuse and desalination technologies. One group of emerging technologies that have demonstrated the potential to meet this growing demand are collectively known as osmotically driven membrane processes (ODMPs).5−14 ODMPs, which include forward osmosis (FO) and pressure retarded osmosis (PRO), utilize the osmotic pressure difference between a concentrated draw solution and a dilute feed solution to drive the permeation of water across a semipermeable membrane from the feed solution into the draw solution. Using osmotic pressure as the driving force for permeation, instead of an applied hydraulic pressure, provides a range of benefits, including lower energy consumption, lower capital costs, higher water recoveries, and facile foulant removal.15−23 The utility of ODMPs, however, hinges on the identification of suitable draw solutes. Several demands are placed on the “ideal” draw solute. The ideal draw solute should be inexpensive, generate a high osmotic pressure, and, if necessary, be easily and efficiently regenerated. Recent studies have demonstrated the potential of 2-methylimidazole-based compounds,24 magnetic nanoparticles,25,26 and thermolytic inorganic salts (e.g., ammonia−carbon dioxide)15,27 as regenerable draw solutes. Of these, the ammonia carbon dioxide system has been the most developed.27−30 © 2012 American Chemical Society
One research area that is critical to the development and future commercial adoption of draw solutions is the thorough understanding of their reverse permeation. The reverse permeation of the draw solution reduces the effective osmotic pressure difference across the membrane, increases the costs associated with maintaining the draw solution concentration, and could require the feed solution to be treated prior to discharging it into the environment. Previous studies have explored the reverse permeation of draw solutes experimentally and theoretically. Experimental studies have focused on the single and bidirectional permeation of feed and draw solutes in FO24,31−37 and quantifying the rates of reverse permeation for a diverse range of draw solutes, 15,24,26,27,31−35,38−42 while theoretical work developed mathematical models to predict the reverse flux of strong electrolytes and neutral draw solutes.34,35 None of these prior studies have explored the effects of reaction equilibrium on reverse permeation. We anticipate that these effects will be particularly important for the ammonia− carbon dioxide draw solution because it is the ability to shift this equilibrium using temperature that allows for the facile regeneration of the draw solution.27 This equilibrium will also impact the reverse permeation of the draw solute because the dissolved gases (NH3 and CO2) are known to have dramatically different permeabilities than their corresponding ions (NH4+ and HCO3−).19 The objective of this study is to develop a fundamental understanding of the processes that govern the reverse permeation of a weak electrolyte draw solution. To meet this objective, we develop a mathematical model for the pHReceived: Revised: Accepted: Published: 13463
June 21, 2012 September 12, 2012 September 19, 2012 September 19, 2012 dx.doi.org/10.1021/ie3016494 | Ind. Eng. Chem. Res. 2012, 51, 13463−13472
Industrial & Engineering Chemistry Research
Article
weak electrolyte and the other two cases is that the dissociation of a weak electrolyte in an aqueous solution is not always complete. Instead, the degree of dissociation is highly dependent on the solution pH and temperature. The pH dependence can be demonstrated by writing the dissociation as an equilibrium reaction, where the neutral form of the weak electrolyte, which in this study is propanoic acid, dissociates to form the corresponding anion (i.e., propanoate ion) and a proton. Using Le Chatelier’s principle it can be determined that at low pH, propanoic acid will be favored, while at high pH the propanoate ion will be the dominant species. The permeabilities of the charged and uncharged propanoate species are dramatically different. Therefore, in order to accurately model the reverse permeation of a weak electrolyte draw solution, the effects of this dissociation reaction, HP ⇔ P− + H+, need to be taken into account. This can be accomplished by writing a mass balance, which accounts for convection, diffusion, and reaction, on all three species in the porous support layer, followed by doing mass balances on the species in the active layer, where only diffusion occurs. In writing the equations this way, it is assumed that the dissociation reaction only takes place within the water-filled pores of the support layer. This is a reasonable approximation because water has a high dielectric constant, while the polymers used to fabricate the active layer of FO membranes have much lower dielectric constants. Mass Balances in the Support Layer. Three mass balances can be done on a differential volume within the support layer of the membraneone for each of the three components: propanoic acid, propanoate ion, and protons, which will be denoted by the indices 1, 2, and 3, respectively.44 The generalized form of these steady-state mass balances can be written as follows:
dependent transport of a weak electrolyte draw solution and compare the model with experiments that measure the reverse solute flux and water flux as a function of the draw solution pH. Propanoic acid was selected as a model weak electrolyte, because it has a single dissociation constant (pKa = 4.87) that falls within the stable operating range of current commercial membranes designed for ODMPs.19 Additionally, a recent report proposed the use of propanoate containing draw solutions in osmotic membrane bioreactors.43 In contrast, the ammonia−carbon dioxide draw solution has three pKa values over a wider pH range, which significantly complicates the mathematical modeling. The implications of the results for the operation of an ODMP using a weak electrolyte draw solution are discussed, laying the foundation for subsequent studies involving the NH3/CO2 (NH4HCO3) draw solution.
■
THEORY The reverse permeation of a weak electrolyte (shown schematically for a membrane operating in FO mode in Figure 1) is similar to the reverse permeation of strong electrolytes
0=
dJiS dz
+ ri = −Deff
d2ci dz
2
+ Jw
dci + ri dz
(1)
where is the total flux of species i across the support layer, ci is the concentration of species i, Deff is the effective diffusion coefficient in the support layer, Jw is the superficial fluid velocity, which is equivalent to the solvent flux, and ri is the reaction rate. Note that because propanoic acid is being consumed by the reaction, r1 equals −r and r2 = r3 = r because propanoate ions and protons are being produced by the reaction. Equation 1 is subjected to the following boundary conditions: JSi
Figure 1. Schematic of a weak electrolyte draw solute permeating into the feed solution. The high concentrations of solutes in the draw solution, ciD, create a chemical potential gradient that drives both the water flux, Jw, and the reverse flux of the draw solutes, Js. For weak electrolytes, such as propanoic acid, the concentrations of each of the draw solute species are interrelated through an equilibrium dissociation reaction, where propanoic acid dissociates to form propanoate ions and protons. The indices 1, 2, and 3 refer to propanoic acid, propanoate ion, and protons, respectively. For these solutes to permeate across the asymmetric membrane into the bulk feed solution where their concentrations, ciF, are negligible, they must first be transported across the support layer of thickness, ts, followed by the active later of thickness, tA. It is assumed that the dissociation of propanoic acid only occurs within the support layer and is negligible in the active layer. cmiD and cmiF represent the draw solute concentrations on the support layer side and active layer side of the support layer-active layer interface, respectively.
m z = 0 c1 = c1D m c 2 = c 2D m c3 = c3D
z = ts c1 + c 2 = ctotal c3 = c3D
(2a)
(2b)
where cm iD represents the concentration of species i at the interface between the active layer and support layer of the membrane, and ctotal is the total concentration of carbon added to the bulk draw solution. The boundary conditions at z = ts are written in this form because ctotal is known from the draw solution formulations and c3D is directly related to the solution pH, which is easily measured. Furthermore, if the reaction rate is fast relative to convection and diffusion, which is the case for most acid−base reactions, it
and neutral solutes. For example, in all three cases, the draw solute must first diffuse through the support layer, from the bulk draw solution to the active layer, in the opposite direction of the water flux. Once at the active layer, the solute dissolves in the dense polymeric layer, and then diffuses across it. After diffusing across the active layer, the draw solute partitions into the feed solution, which has a negligible concentration of draw solute. The key difference between the reverse permeation of a 13464
dx.doi.org/10.1021/ie3016494 | Ind. Eng. Chem. Res. 2012, 51, 13463−13472
Industrial & Engineering Chemistry Research
Article
⎛ c K ⎞ m m − c 2D = ⎜c3D − total a ⎟ exp( −PeS) = c ̅ c3D K a + c3D ⎠ ⎝
can be assumed that the reaction reaches equilibrium locally throughout the support layer.44 This allows the concentration of the three species to be related through the acid dissociation constant, Ka: cc Ka = 2 3 c1 (3)
where the right-hand side, which is expressed in experimentally accessible quantities, is labeled c.̅ Because we have assumed that the acid dissociation reaction is very fast, and reaches equilibrium everywhere, we can relate m m cm 3D to the interfacial concentrations c1D and c2D using eq 3:
An expression for the total flux of carbon through the support layer, JSC, can be obtained by adding the mass balances for species 1 and 2, and integrating twice to yield: JCS
⎛ ⎛ ⎞ ctotal 1 m m ⎟− )⎜ = ⎜⎜(c1D + c 2D S exp(PeS) − ⎝ exp(Pe ) − 1 ⎠ ⎝
m m m K ac1D = ( c ̅ + c 2D )c 2D
This quadratic equation can be solved for and the physically relevant root (i.e., the one that gives a positive concentration) can be used to develop an expression for the total flux of carbon into the feed solution.
⎞ ⎟⎟J 1⎠ w
m ⎞ 4K ac1D c⎛ m c 2D = ̅ ⎜⎜ ± 1 + − 1⎟⎟ 2 2⎝ c̅ ⎠
where Jw ts Deff
=
Jw tsτ εD
=
Jw S D
Pe is the Peclet number in the support layer, D is the bulk binary diffusion coefficient for the solute in water, and ts,ε, and τ are the thickness, porosity, and tortuosity of the support layer, respectively. Equation 4 demonstrates that the total flux of carbon is constant across the support layer, even though the fluxes of propanoic acid and propanoate ions are not. Mass Balances on the Active Layer. Assuming that the weak electrolyte does not dissociate within the active layer and that there are no other solute−solute interactions, the total flux of carbon across the active layer, JAC, can be written as the sum of the carbon containing species:
m c 2D =
(6)
m c1D =
(12)
m ctotalJw φ − (Jw (φ + 1) + B2 )c 2D
Jw (φ + 1) + B1
(13)
where ⎞ ⎛ 1 φ=⎜ ⎟ s ⎝ exp(Pe ) − 1 ⎠ m Finally, the expressions for cm 1D and c2D, eqs 13 and 12, respectively, can be substituted into eq 6. After some rearrangement, the following expression for the reverse flux of carbon, in the limit that the weak electrolyte draw solution is highly buffered, can be written.
Jc =
(7)
Next, rearranging the equilibrium expression, eq 3, and combining it with the boundary condition, ctotal = c1D + c2D yields c K c 2D = total a K a + c3D
ctotalK a exp( −PeS) K a + c3D
This expression can be substituted into eqs 4 and 6, the total flux of carbon through the support and active layer, respectively. Because there is no reaction occurring at the interface between the two layers, these fluxes are equal. Equating eqs 4 and 6 and solving for the interfacial concentration of propanoic acid gives an equation for cm 1D in terms of experimentally known or measurable quantities.
where B1 and B2 represent the solute permeability coefficients of propanoic acid and sodium propanoate, respectively. Writing the flux in this form assumes that the solution-diffusion model holds and only the diffusive flux contributes to the total flux. m Defining cm 1D and c2D in Experimentally Accessible Quantities. Equations 4 and 6 express the total flux of carbon through the support layer and active layer, respectively. Unfortunately, both are written in terms of the interfacial m concentrations, cm 1D and c2D, which are not easily measured. Therefore, to predict the total flux of carbon from the draw solution into the feed solution, these concentrations must be related to the experimentally known concentrations in the bulk draw solution. We begin doing this by equating dJS2/dz = dJS3/dz, integrating twice, and using the boundary conditions to relate the bulk and interfacial concentrations. m m c3D − c 2D = (c3D − c 2D) exp( −PeS)
(11)
An exact solution can be obtained using this expression (see Appendix 1); however, examining the limit of a highly buffered draw solution provides more insight into the reverse permeation of the weak electrolyte draw solution being studied here. In the limit that the system is highly buffered and c2 ≫ c3, cm 2D is approximately equal to
(5)
s
m m JCA = J1A + J2A = −[B1(c1D − 0) + B2 (c 2D − 0)]
(10)
cm 2D
(4)
PeS =
(9)
Jw ctotal
⎡ 1 + Jw exp(PeS) − 1 ⎤ ⎢ ( B1 ) ⎥ ⎢⎣ (1 − BB2 ) K +Kac − 1 ⎥⎦ 1 a 3D
(14)
There are two interesting limits of eq 14. The first is when the pH is low and c3D ≫ Ka and the second is when the pH is high and c3D ≪ Ka. In the first limit, c3D ≫ Ka, eq 14 can be reduced to
(8)
which is an expression that relates the concentration of the propanoate ion in the draw solution to the proton concentration, and hence the pH. Substituting eq 8 into eq 7 produces the expression below:
Jc =
13465
Jw ctotal
(
1− 1+
Jw B1
) exp(Pe ) S
(15)
dx.doi.org/10.1021/ie3016494 | Ind. Eng. Chem. Res. 2012, 51, 13463−13472
Industrial & Engineering Chemistry Research
Article
Table 1. Composition of the Draw Solution for the Experimentsa amount of NaP (mol amount of HCl (mol L−1) L−1)
amount of HP (mol L−1)
0.2
0
0
0
0
0.2
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
0.001 0.003 0.006 0.0012 0.03 0.05 0.07 0.11 0.15 0.17
0 0 0 0 0 0 0 0 0 0
0.2 0.2 0.2 0.2
0 0 0 0
0.1 0.2 0.3 0.4
total carbon concentration (mol L−1)
average pH
PRO Mode and Diaphragm Cell Experiments Sodium Propanoate 0.2 8.81 Propanoic Acid 0.2 2.50 FO Mode Experiments Sodium Propanoate/Hydrochloric Acid 0.2 6.90 0.2 6.42 0.2 6.22 0.2 5.90 0.2 5.46 0.2 5.24 0.2 5.02 0.2 4.66 0.2 4.20 0.2 3.82 Sodium Propanoate/Propanoic Acid 0.3 5.19 0.4 4.91 0.5 4.67 0.6 4.62
bulk P‑ concentration (mol L−1)
bulk HP concentration (mol L−1)
0.200
0.000
0.001
0.199
0.198 0.194 0.191 0.183 0.159 0.140 0.117 0.076 0.035 0.016
0.002 0.006 0.009 0.017 0.041 0.060 0.083 0.124 0.165 0.184
0.203 0.208 0.193 0.217
0.097 0.192 0.307 0.383
a
The degree of dissociation was shifted by varying the draw solution pH, through the addition of hydrochloric acid or propanoic acid to a 0.2 M sodium propanoate solution. Average draw solution pH and bulk concentrations of the ionized propanoate (P−) and unionized propanoic acid (HP) species are presented. Bulk propanoate and propanoic acid concentrations were calculated using eq 3 and the draw solution pH, the pKa of propanoic acid (4.87), and the total carbon concentration in the draw solution.
which demonstrates that the total carbon flux into the feed is solely dependent on the solute permeability coefficient of the uncharged propanoic acid. This is consistent with our rationalization that the propanoic acid will be the dominant species in solution at low pH. Under the second limit, c3D ≪ Ka, eq 14 can be reduced to Jc =
This was accomplished experimentally by dissolving 0.2 M of analytical grade sodium propanoate (Sigma Aldrich) in deionized water (DI), and adding various amounts of either hydrochloric acid (Fischer Scientific) or propanoic acid (Sigma Aldrich) to the solution so that the final pH fell between 4 and 7. Two different acids are used in the draw solution formulations to explore the influence of solution pH and chemistry on draw solute transport. Adding propanoic acid to the draw solution increases the total concentration of carbon in solution and decreases the pH, while adding hydrochloric acid to the draw solution decreases the solution pH at a constant total carbon concentration. Deionized (DI) water, obtained from a Milli-Q ultrapure water purification system (Millipore, Billerica, MA), was used to prepare the draw solutions. The draw solution formulations for the FO mode experiments as well as the concentration of the various species present in the bulk draw solution are listed in Table 1. For both draw solution systems, as the amount of acid added increased, the pH decreased, and the equilibrium shifted toward the protonated propanoic acid. The experimental conditions of the draw solutions that were used to determine the solute permeability coefficients of sodium propanoate and propanoic acid in the PRO and diaphragm cell are also shown in Table 1. The osmotic pressures of the various draw solutions were calculated using a software package from OLI Systems, Inc. (Morris Plains, NJ). Draw solution pH was measured using a pH meter from Fischer Scientific and the total carbon concentration (i.e., the combined propanoic acid and propanoate ion concentrations) in the feed solution was measured using a total carbon analyzer (Shimazdu). Forward Osmosis and Pressure Retarded Osmosis Crossflow Unit. The experimental system used for FO and PRO testing is similar to that described in our previous
Jw ctotal
(
B1 B2
−
Jw B2
)exp(Pe ) − S
B1 B2
(16)
which demonstrates that the reverse permeation of carbon depends primarily on the solute permeability coefficient of the propanoate anion. Again, this is in line with our intuition that the charged propanoate ion will be the dominant species in solution at pH greater than the pKa of propanoic acid.
■
MATERIALS AND METHODS Forward Osmosis Membrane. A commercial asymmetric cellulose triacetate (CTA) membrane (Hydration Technology Inc., Albany, OR) was used for the FO, PRO, and diaphragm cell experiments. This membrane has been used extensively in previous research exploring osmotically driven membrane processes27,34,35,45,46 and consists of a dense asymmetric polymer layer embedded within a woven fabric mesh. Model Weak Electrolyte. The CTA membrane used in this study is stable within a pH range of 4 to 7.19 Therefore, propanoic acid, which has a single acid dissociation constant, Ka of 10−4.87 (pKa of 4.87) was selected as the model weak electrolyte. By varying the draw solution pH through the addition of different acids to reach predetermined values, the equilibrium of the dissociation reaction could be controlled, and its effects on reverse solute permeation could be explored. 13466
dx.doi.org/10.1021/ie3016494 | Ind. Eng. Chem. Res. 2012, 51, 13463−13472
Industrial & Engineering Chemistry Research
Article
Table 2. Membrane Transport Parametersa solute permeability coefficient, B (m/s) solute propanoic acid sodium chloride sodium propanoate
molecular weight (g/mol) 74.07 58.84 96.07
bulk diffusion coefficientsb, D (m2/s) −10
9.24 × 10 1.61 × −10−9 1.34 × −10−9
mass transfer coefficient, k (m/s) −5
1.18 × 10 1.72 × 10−5 1.53 × 10−5
diaphragm cell −6
2.03 × 10 6.67 × 10−8 1.81 × 10−8
PRO mode 1.44 × 10−6 6.67 × 10−8 1.92 × 10−8
a
Molecular weights and solute permeability coefficients, B, for propanoic acid, sodium chloride, and sodium propanoate are listed. The B values were experimentally determined from diaphragm cell and PRO mode experiments, using methods given in our previous publications.34,35 To convert from units of m s−1 to L m−2 h−1, multiply by 3.60 × 106. Draw solution concentrations of 0.2 M, a crossflow velocity of 21.4 cm/s, and a constant temperature of 20 °C were used for these experiments. The crossflow cell mass transfer coefficients were calculated from correlations for rectangular cell geometry48. bThe bulk diffusion coefficients were obtained using a software package from OLI Systems, Inc. (Morris Plains, NJ).
studies.27,34,35,45,46 The feed and draw solutions, maintained at a constant temperature of 20 °C, were fed cocurrently to the membrane unit at a crossflow velocity of 21.4 cm/s.34,35 By switching the orientation of the membrane, both forward osmosis and pressure retarded osmosis experiments could be run in this system. In FO mode, the active side of the membrane faced the feed solution (i.e., DI), and in PRO mode, the active side of the membrane faced the draw solution. The FO mode experiments were carried out to quantify the reverse solute permeation. These experimentally measured fluxes could be compared to the predicted results from the model presented earlier in the paper. PRO mode experiments were run to measure the solute permeability coefficient of the active layer, B. A slight modification to the experimental system used for FO and PRO testing allowed for diaphragm cell experiments to be run. The draw solution canister and flow connections on the draw side were changed to prevent the permeation of water so that the draw solution had a constant volume of 2.25 L, and only solute diffusion from the draw to the feed could occur. All testing conditions and other aspects of the set up remained the same. This allowed the value of the solute permeability coefficient, B, to be determined in the absence of a water flux. Details regarding both methods of the calculations for the respective B values are given in our previous publications.34,35 Measurement of Water Flux and Reverse Solute Flux. The experimental water flux across the membrane, Jw, was determined from the change in mass of the draw solution reservoir, which rested on a balance (Ohaus, Pine Brook, NJ), as a function of time. The reverse draw solute flux, Js, was determined by measuring the total concentration of carbon in the feed solution at regular intervals. The increase in concentration as a function of time could be used to calculate Js. Details regarding both calculations are given in our previous publications.34,35
propanoate as the representative transport coefficient for the negatively charged propanoate ion because a cation must permeate through the active layer with the propanoate anion to maintain electroneutrality. The experimentally determined solute permeability coefficients are summarized in Table 2. The solute permeability coefficient for sodium propanoate, B2, found from the PRO mode tests, where Jw ≠ 0, and the diaphragm cell experiments, where Jw = 0, are comparable. For propanoic acid, the B values in the PRO and the diaphragm cell experiments consistently differed by approximately 20%. We attribute this difference to the much higher solute permeability coefficient of propanoic acid compared to sodium propanoate. In a previous publication, we demonstrated that for highly permeable draw solutes, solute−solvent interactions arise, and reflection coefficients are needed to accurately predict the water flux generated by these draw solutes.35 The highly permeable propanoic acid may be an extreme example with a reflection coefficient near zero. During the PRO experiments, the propanoic acid draw solution never produced a steady, appreciable water flux. Instead, it produced a sporadic water flux that fluctuated about zero. The inability of propanoic acid to produce reliable water fluxes in PRO mode compromises the accuracy of its solute permeability coefficient measured in this configuration. In our subsequent calculations, we use the average B value of 0.067 L m−2 h−1 (1.87 × 10−8 m/s) for sodium propanoate and the B value found from the diaphragm cell experiments, 7.3 L m−2 h−1 (2.03 × 10−6 m/s), for propanoic acid. Reverse Draw Solute Fluxes as a Function of Draw Solution pH. The reverse flux of carbon (i.e., all propanoatecontaining species) was quantified as a function of draw solution pH using FO mode experiments. As shown in Table 1, either hydrochloric acid or propanoic acid was dosed into a sodium propanoate solution to produce a draw solution adjusted to a predetermined pH. By monitoring the total concentration of carbon in the feed solution over time, the reverse flux of propanoate could be calculated for each draw solution formulation. The results of these experiments are shown in Figure 2. For both systems, as the pH decreases, the reverse flux of carbon dramatically increases. This is a result of the propanoic acid, which has a higher solute permeability coefficient, becoming the dominant species in solution at pH lower than the pKa of propanoic acid (pKa = 4.87). This transition from negatively charged propanoate ion being the majority species in the bulk draw solution at pH > pKa to neutral propanoic acid being the dominant species at pH < pKa is shown in the final two columns of Table 1.
■
RESULTS AND DISCUSSIONS Membrane Performance Characteristics. From previous work, the pure water permeability coefficient, A, and structural parameter, S, of the CTA membrane were found to be equal to 0.44 ± 0.12 L m−2 h−1 bar−1 (1.23 ± 0.33 × 10−12 m s−1 Pa−1) and 481 μm, respectively.34 These average values are used in subsequent calculations. The active layer solute permeability coefficients for propanoic acid and sodium propanoate, B1 and B2, respectively, were determined from diaphragm cell and PRO mode experiments. Experimental conditions are described in Table 1 and the detailed derivation for calculating B from these experiments can be found in our previous publications.34,35 In this work, we use the permeability coefficient of sodium 13467
dx.doi.org/10.1021/ie3016494 | Ind. Eng. Chem. Res. 2012, 51, 13463−13472
Industrial & Engineering Chemistry Research
Article
Figure 4. Water flux as a function of draw solution pH. (a) A comparison of the predicted and experimental water fluxes for the sodium propanoate and hydrochloric acid solutions described in Table 2. (b) A comparison of predicted and experimental results for the water fluxes generated by the sodium propanoate and propanoic acid draw solutions described in Table 2. Predicted water fluxes are represented by a solid line and experimental water fluxes are represented by data points. All water fluxes were measured using DI as a feed solution with a crossflow velocity of 21.4 cm/s and a constant temperature of 20 °C. The predicted water fluxes are calculated from eq 17 for the hydrochloric acid solution and eq 18 for the propanoic acid solution using a pure water permeability coefficient, A, of 0.44 ± 0.12 L m−2 h−1 bar−1 (1.23 ± 0.33 × 10−12 m s−1 Pa−1), the diffusion coefficients from Table 2, and a membrane structural parameter, S, of 481 μm.
Figure 2. Experimental Reverse Carbon Flux as a Function of Draw Solution pH. (a) Total carbon fluxes for the sodium propanoate and hydrochloric acid draw solutions described in Table 2. (b) Total carbon fluxes for the sodium propanoate and propanoic acid draw solutions described in Table 2. For both systems, the total reverse carbon fluxes were measured using DI as the feed solution. All experiments were conducted with a crossflow velocity of 21.4 cm/s at a constant temperature of 20 °C.
Comparison of Model Predictions to Experimental Solute Fluxes. The experimentally measured reverse flux of carbon and the flux predicted by eq 14 are compared on linear−linear plots in Figure 3. The predicted values in Figure 3
Compared to the dramatic increase observed in the reverse solute flux at low pH, the increase in water flux is much more gradual. This more moderate increase in water flux with decreasing draw solution pH can be attributed to several factors. First, the solute permeability coefficient of propanoic acid is large. Prior work has shown that solute−solvent interactions within the membrane active layer, which decrease the water flux generated by a draw solute, are important for highly permeable draw solutes.35 Multiplying the osmotic pressure by a reflection coefficient can account for the effects of these interactions and allows for the accurate prediction of the water flux.35 However, the negligible water fluxes generated by propanoic acid in PRO mode (data not shown) suggest that its reflection coefficient is equal to zero. Therefore, increasing the propanoic acid concentration will not increase the water flux generated. Additionally, the weak electrolyte system studied here could demonstrate nonideal behavior, possibly arising from ion pairing or other solute−solute interactions in solution.31,47 Comparing the osmotic pressure of sodium propanoate solutions calculated using the van’t Hoff equation to those determined by the OLI software supports this hypothesis. The osmotic pressures calculated using the software are consistently lower than those calculated using the van’t Hoff relationship. The ratio of these two values can be used to calculate the osmotic coefficient for sodium propanoate, ϕ, which is about 0.84. Accounting for the inability of propanoic acid to effectively generate an osmotic pressure across the CTA membrane and the nonideal behavior of sodium propanoate leads to the following expression for the water flux generated in FO mode by a weak electrolyte draw solution (Appendix 2). For the sodium propanoate/hydrochloric acid system, the water flux can be estimated from
Figure 3. Predicted versus experimental reverse carbon fluxes. (a) A comparison of model predictions and experimental results for the sodium propanoate and hydrochloric acid system. (b) A comparison of model predictions and experimental results for the sodium propanoate and propanoic acid system. The experimental results are those presented in Figure 2. The predicted solute fluxes are calculated from eq 14 using the corresponding experimental water fluxes, Jw, presented in Figure 4, the solute permeabilities and diffusion coefficients from Table 2, and a membrane structural parameter, S, of 481 μm. The solid line (slope =1) represents perfect agreement between the predictions and experimental data.
were calculated using the B1, B2, and S values determined in the preceding sections and the experimentally measured draw solution pHs and water fluxes. The data points for both systems lie close to the solid line in Figure 3, which has a slope equal to 1, representing perfect agreement between the predicted and experimental values. This strong agreement between experiments and model offers further evidence that it is the pHdependent dissociation of propanoic acid in solution that drives the significant increase in reverse transport. Furthermore, the agreement demonstrates the accuracy of the derived model, and its underlying assumptions (i.e., a single, constant pKa and constant transport coefficients), for the reverse transport of a weak electrolyte draw solution under the experimental conditions tested. Water Fluxes as a Function of Draw Solution pH. In addition to the reverse draw solute flux, the water fluxes generated at each draw solution pH were measured (Figure 4). 13468
dx.doi.org/10.1021/ie3016494 | Ind. Eng. Chem. Res. 2012, 51, 13463−13472
Industrial & Engineering Chemistry Research
Article
⎞ ⎛ ϕ2/5K a + ϕ4/5c3D ⎛ J S⎞ Jw = A⎜ + ϕ4/5⎟ × R gTctotal exp⎜ − w ⎟ ⎝ D ⎠ K a + c3D ⎠ ⎝
decreasing pH, the reverse flux selectivity also decreases significantly with decreasing pH. This highlights the value of understanding how solution conditions such as pH and temperature affect the reverse permeation of weak electrolyte draw solutions and the water flux generated by these draw solutions. Furthermore, the strong agreement between the experimental and predicted reverse flux selectivities demonstrates the value of the theory developed here to understanding these phenomena.
(17)
and for the sodium propanoate/propanoic acid system ⎛ Kc ⎞ ⎛ J S⎞ Jw = 2Aϕ2/5R gT ⎜ a total ⎟ exp⎜ − w ⎟ ⎝ D ⎠ ⎝ K a + c3D ⎠
(18)
■
where n is the number of dissolved species created by the draw solute, Rg is the ideal gas constant, and T is the absolute temperature. The water flux predicted by these equations is shown as a solid line in Figure 4, suggesting a fair agreement between experiment and theory. The average deviation between experiment and theory for the NaP/HCl system is 7%, while that for the NaP/HP system was 31%. Reverse Flux Selectivity as a Function of Draw Solution pH. The reverse flux selectivity, defined as the ratio of the forward water flux to the reverse solute flux, is a measure of the volume of water produced per mole of draw solute lost. Therefore, an FO process should seek to use a membrane-draw solution pair that maximizes the value of the reverse flux selectivity. The experimental reverse flux selectivity for the systems studied here are plotted in Figure 5 as a function of draw
CONCLUDING REMARKS In this work, we focus on elucidating the fundamental phenomena that govern the reverse permeation of weak electrolyte draw solutes in an FO operation. Theoretical work entailed the development of a model for the pH-dependent reverse flux of weak electrolyte draw solutes and the water flux generated by these solutes. Experimental data collected for a model weak electrolyte system (i.e., propanoic acid/propanoate ion) buffered at predetermined pH values were compared to theoretical model predictions. Experimentally, reverse permeation of the draw solute was shown to dramatically increase at pH values below the pKa of propanoic acid, resulting in a large decrease of the reverse flux selectivity. This observation was attributed to the equilibrium of the dissociation reaction shifting toward the uncharged, highly permeable propanoic acid species at low pH. The ability of the model to successfully capture the large changes in the reverse flux of propanoic acid and the reverse flux selectivity validates this hypothesis and demonstrates the accuracy of the model. A variety of phenomena need to be understood as FO operations, and other ODMPs, are developed beyond the bench- and pilot-scales. Among them, understanding the reverse permeation of weak electrolyte draw solutes is key to the development of these emerging technologies. The success of the simple model developed in this work will make it a useful predictive tool as weak electrolyte draw solutes (e.g., sodium propanoate43 and ammonia−carbon dioxide27) are developed for emerging applications of ODMPs.
Figure 5. Flux selectivity as a function of draw solution pH. (a) A comparison of predicted and experimental results for reverse flux selectivities for the sodium propanoate and hydrochloric acid draw solutions as a function of the draw solution pH. (b) A comparison of predicted and experimental results for reverse flux selectivities for the sodium propanoate and propanoic acid draw solutions as a function of the draw solution pH described in Table 2. Predicted reverse flux selectivities are represented by a solid line and experimental values are represented by data points. The reverse fluxes of total carbon and water fluxes in Figures 2 and 4, respectively, were used to calculate the experimental reverse flux selectivity values. The predicted reverse flux selectivities were calculated using the pure water permeability coefficient, A, of 0.44 ± 0.12 L m−2 h−1 bar−1 (1.23 ± 0.33 × 10−12 m s−1 Pa−1) and the solute permeabilities and diffusion coefficients from Table 2.
■
APPENDIX 1 Using eq 11, an exact solution can be derived for the total reverse flux of carbon. To develop this solution eq 4, the flux of carbon through the support layer, is written in a slightly different manner. JCS =
JC
=
(B − B 1
2
−
m m + c 2D ((c1D ) exp(PeS) − ctotal)
(A1)
The flux through the support layer is then set equal to the flux through the active layer, eq 6, and after some algebraic manipulations the following expression is produced. m m B1̅ c1D + B2̅ c 2D − kSctotal = 0
(A2)
where
2Aϕ2/5R gT K +c B1 a K 3D a
exp(PeS) − 1
m m = k S((c1D + c 2D ) exp(PeS) − ctotal)
solution pH. In addition, the theoretical reverse flux selectivity can be calculated using eqs 14, 17, and 18 to yield the following expression: Jw
Jw
)
B1̅ = B1 + k S exp(PeS)
(19)
and
The reverse flux selectivity predicted by eq 19 is plotted as a solid line in Figure 5. Because the water flux generated by the different draw solutions does not vary significantly with pH, while the reverse solute flux increases dramatically with
B2̅ = B2 + kS exp(PeS)
The positive root of eq 11 is then inserted into eq A2. 13469
dx.doi.org/10.1021/ie3016494 | Ind. Eng. Chem. Res. 2012, 51, 13463−13472
Industrial & Engineering Chemistry Research m − B1̅ c1D
Article
For ease, the group of variables in parentheses will be called ψ. Multiplying eq A3 by its complex conjugate, results in a quadratic equation that can be solved for cm 1D.
m ⎛ B̅ c ⎞ 4K ac1D B2̅ c ̅ − ⎜ 2 ̅ + k Sctotal ⎟ = 0 1+ 2 ⎝ 2 ⎠ 2 c̅
(A3)
2ψB1̅ + K aB2̅ 2 m c1D =
B1̅ 2
±
2ψB1̅ + KaB2̅ 2 B1̅ 2
2⎞
B1̅ 2
(A4)
concentration polarization. Additionally, the total molar concentration of the draw solute can be written as the sum of the molar concentration of each species in solution, which produces the following expression that is valid for any membrane draw solution pair. ⎛ J S⎞ n Jw = AR gT exp⎜ − w ⎟ ∑ σϕ i ici D ⎝ D ⎠ i
■
APPENDIX 2 The water flux generated in an osmotically driven membrane process can be expressed as the product of the pure water permeability coefficient, the reflection coefficient, and the osmotic pressure difference across the membrane.
(A7)
In the following paragraphs, we will develop expressions for the two systems studied in this work. For the hydrochloric acid and sodium propanoate system, propanoate, sodium, and chloride ions as well as propanoic acid and protons will be present in the draw solution. Propanoic acid was unable to produce an appreciable water flux in PRO mode. Therefore, we assume its reflection coefficient will be equal to zero. The concentration of propanoate ion will vary depending upon the amount of hydrochloric acid in the draw solution formulation, and can be calculated on the basis of the equilibrium of the acid dissociation reaction. The concentration of protons is easily calculated from the solution pH. However, because the systems studied ranged from pH 4−7, this concentration is considered negligible. The concentration of chloride ions is known because the amount of hydrochloric acid in the draw solution formulation is known, but it is more informative to infer this concentration from the draw solution pH. Lastly, the concentration of sodium ions in solution will be equal to the amount added in the initial draw solution formulation. This information leads to the following equation.
(A5)
The osmotic pressure can be related to the molar concentration of solute using a modified version of the van’t Hoff equation, where an osmotic coefficient, ϕ, accounts for nonideal effects in solution. Jw = AσϕnR gT Δc
B2̅ c ̅ 2
( ) ⎟⎠
2
The physically relevant root of eq A4 (i.e., the one that yields a positive concentration) can be used in conjunction with the physically relevant root of eq 11 and eq 6 to calculate the total reverse flux of carbon. Doing so for the systems studied here gave results that were within 5% of eq 14. Given the relative simplicity of eq 14 and the greater physical insight it provides, we prefer its use.
Jw = Aσ ΔΠ
−
⎛ 4⎜ ψ 2 − ⎝
(A6)
Prior work has shown that it is the solute concentration difference across the membrane active layer that generates the osmotic pressure to drive water permeation.45 For the systems studied here, DI is used as the feed solution, so the solute concentration at the surface of the active layer in the feed solution is assumed to be equal to zero. On the draw side, the total solute concentration at the active layer surface can be written in terms of the bulk concentration by accounting for
⎛ J S⎞ Jw = AR gT exp⎜ − w ⎟(σ1ϕ1c1D + σ2ϕ2c 2D + σ3ϕ3c3D + σ4ϕ4c4D + σ5ϕ5c5D) ⎝ D ⎠ ⎞ ⎛ J S ⎞⎛ c (K + c3D) + c3Dctotal Kc + σ5ϕ5ctotal ⎟ Jw = AR gT exp⎜ − w ⎟⎜0 + σ2ϕ2 a total + 0 + σ4ϕ4 3D a ⎝ D ⎠⎝ K a + c3D K a + c3D ⎠
(A8)
⎛ Kc − K ac3D + c3D2 ⎞ Kc ⎟ Jw = AR gT ⎜σ2ϕ2 a total + σ5ϕ5 a total K a + c3D K a + c3D ⎠ ⎝
Equation A8 can be reduced to eq 17 by ignoring terms of order c3D2 and assuming that all of the reflection coefficients are equal to 1. A similar rationale is used to demonstrate that the water flux generated by the propanoic acid and sodium propanoate system is equal to eq 18. Again, propanoic acid has a reflection coefficient equal to zero and the proton concentration is small. No chloride ions are present because no hydrochloric acid is used in the draw solution formulation. This leaves sodium and propanoate ions to generate the water flux. Both concentrations can be calculated using the known draw solution formulation and the equilibrium of the acid dissociation reaction.
⎛ J S⎞ exp⎜ − w ⎟ ⎝ D ⎠
(A9)
Equation 18, which is capable of predicting the water flux for the propanoic acid and sodium propanoate system, can be derived from eq A9 by assuming that all the reflection coefficients are equal to 1 and terms of order c3D2 are negligible.
■
APPENDIX 3 The reverse flux selectivity for the hydrochloric acid and propanoic acid systems can be derived using eq 14 and either 13470
dx.doi.org/10.1021/ie3016494 | Ind. Eng. Chem. Res. 2012, 51, 13463−13472
Industrial & Engineering Chemistry Research
Article
eq 17 or eq 18, respectively. Because the end result is the same for both systems, and the assumptions used to derive the result are similar, only the derivation for the propanoic acid system is discussed. Taking the ratio of eq 14 to eq 18, rearranging, and canceling common terms gives the following expression. Jw JC
=
⎡ 2Aϕ2/5R gT ⎣⎢1 +
(
Jw 1 −
B2 B1
Jw B1
−
Jw S
■
⎤ ⎦⎥
( )
− exp − Ka + c3D Ka
D
)
(A10)
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Tel.: (574) 631-2708. Notes
The authors declare no competing financial interest.
■
REFERENCES
(1) Shannon, M. A.; Bohn, P. W.; Elimelech, M.; Georgiadis, J. G.; Marinas, B. J.; Mayes, A. M. Science and technology for water purification in the coming decades. Nature 2008, 452 (7185), 301− 310. (2) Aldhous, P. The world’s forgotten crisisOver a billion people cannot get clean water, and things are getting worse. Nature 2003, 422 (6929), 251−251. (3) Elimelech, M.; Phillip, W. A. The Future of Seawater Desalination: Energy, Technology, and the Environment. Science 2011, 333 (6043), 712−717. (4) Greenlee, L. F.; Lawler, D. F.; Freeman, B. D.; Marrot, B.; Moulin, P. Reverse osmosis desalination: Water sources, technology, and today’s challenges. Water Res. 2009, 43 (9), 2317−2348. (5) Hoover, L. A.; Phillip, W. A.; Tiraferri, A.; Yip, N. Y.; Elimelech, M. Forward with osmosis: Emerging applications for greater sustainability. Environ. Sci. Technol. 2011, 45 (23), 9824−9830. (6) Choi, J. S.; Kim, H.; Lee, S.; Hwang, T. M.; Oh, H.; Yang, D. R.; Kim, J. H. Theoretical investigation of hybrid desalination system combining reverse osmosis and forward osmosis. Desalin. Water Treat. 2010, 15 (1−3), 114−120. (7) Khaydarov, R. A.; Khaydarov, R. R. Solar powered direct osmosis desalination. Desalination 2007, 217 (1−3), 225−232. (8) Kravath, R. E.; Davis, J. A. Desalination of sea-water by direct osmosis. Desalination 1975, 16 (2), 151−155. (9) Tan, C. H.; Ng, H. Y. A novel hybrid forward osmosis− nanofiltration (FO−NF) process for seawater desalination: Draw solution selection and system configuration. Desalin. Water Treat. 2010, 13 (1−3), 356−361. (10) Tang, W. L.; Ng, H. Y. Concentration of brine by forward osmosis: Performance and influence of membrane structure. Desalination 2008, 224 (1−3), 143−153. (11) Cath, T. Y.; Adams, D.; Childress, A. E. Membrane contactor processes for wastewater reclamation in space II. Combined direct osmosis, osmotic distillation, and membrane distillation for treatment of metabolic wastewater. J. Membr. Sci. 2005, 257 (1−2), 111−119. (12) Cath, T. Y.; Gormly, S.; Beaudry, E. G.; Flynn, M. T.; Adams, V. D.; Childress, A. E. Membrane contactor processes for wastewater reclamation in space Part I. Direct osmotic concentration as pretreatment for reverse osmosis. J. Membr. Sci. 2005, 257 (1−2), 85−98. (13) Esperanza, M. G. C.; McCutcheon, J. R. Dewatering press liquor derived from orange production by forward osmosis. J. Membr. Sci. 2011, 372 (1−2), 97−101. (14) Martinetti, C. R.; Childress, A. E.; Cath, T. Y. High recovery of concentrated RO brines using forward osmosis and membrane distillation. J. Membr. Sci. 2009, 331 (1−2), 31−39. (15) Cath, T. Y.; Childress, A. E.; Elimelech, M. Forward osmosis: Principles, applications, and recent developments. J. Membr. Sci. 2006, 281 (1−2), 70−87. (16) Holloway, R. W.; Childress, A. E.; Dennett, K. E.; Cath, T. Y. Forward osmosis for concentration of anaerobic digester centrate. Water Res. 2007, 41 (17), 4005−4014. (17) Lay, W. C. L.; Chong, T. H.; Tang, C. Y. Y.; Fane, A. G.; Zhang, J. S.; Liu, Y. Fouling propensity of forward osmosis: investigation of the slower flux decline phenomenon. Water Sci. Technol. 2010, 61 (4), 927−936. (18) Mi, B.; Elimelech, M. Chemical and physical aspects of organic fouling of forward osmosis membranes. J. Membr. Sci. 2008, 320 (1− 2), 292−302. (19) Baker, R. Membrane Technology and Applications, 2nd ed.; Wiley: New York, 2004; p 552.
An osmotically driven membrane process seeks to produce a large water flux. Therefore, the Jw/B1 term in the numerator should dominate the 1 − exp(−JwS/D) term. By making this simplifying assumption, the expression above can be reduced to eq 19.
■
3 = proton 4 = chloride ion 5 = sodium ion
NOMENCLATURE
Latin Letters
A = water permeability coefficient Bi = solute permeability coefficient of species i ci = molar concentration of species i ciD = molar concentration of species i in the bulk draw solution ciF = molar concentration of species i in the bulk feed solution cm iD = molar concentration of species i at the support layeractive layer interface cm iF = molar concentration of species i at the boundary layeractive layer interface ctotal = total molar concentration of carbon in the bulk draw solution D = binary diffusion coefficient of draw solute and water Deff = effective diffusion coefficient of the draw solute in the support layer JAi = total flux of species i across the active layer JSi = total flux of species i across the support layer Jw = water flux Ka = acid dissociation constant n = number of dissolved species created by draw solute PeS = Peclet number in support layer ri = reaction rate Rg = ideal gas constant S = membrane structural parameter t = time tA = active layer thickness tS = support layer thickness T = absolute temperature z = coordinate system Greek Letters
ε = porosity of the support layer ϕ = osmotic coefficient σ = reflection coefficient τ = tortuosity of the support layer
Subscripts
1 = propanoic acid 2 = propanoate ion 13471
dx.doi.org/10.1021/ie3016494 | Ind. Eng. Chem. Res. 2012, 51, 13463−13472
Industrial & Engineering Chemistry Research
Article
compounds rejection by forward osmosis. Environ. Sci. Technol. 2011, 45 (19), 8483−8490. (41) Phuntsho, S.; Shon, H. K.; Majeed, T.; El Saliby, I.; Vigneswaran, S.; Kandasamy, J.; Hong, S.; Lee, S. Blended fertilizers as draw solutions for fertilizer-drawn forward osmosis desalination. Environ. Sci. Technol. 2012, 46 (8), 4567−4575. (42) Chekli, L.; Phuntsho, S.; Shon, H. K.; Vigneswaran, S.; Kandasamy, J.; Chanan, A. A review of draw solutes in forward osmosis process and their use in modern applications. Desain. Water Treat. 2012, 43 (1−3), 167−184. (43) Bowden, K. S.; Achilli, A.; Childress, A. E. Organic ionic salt draw solutions for osmotic membrane bioreactors. Bioresour. Technol. 2012, 122, 207−216. (44) Semmens, M. J.; Foster, D. M.; Cussler, E. L. Ammonia removal from water using microporous hollow fibers. J. Membr. Sci. 1990, 51 (1−2), 127−140. (45) McCutcheon, J. R.; Elimelech, M. Influence of concentrative and dilutive internal concentration polarization on flux behavior in forward osmosis. J. Membr. Sci. 2006, 284 (1−2), 237−247. (46) McCutcheon, J. R.; Elimelech, M. Modeling water flux in forward osmosis: Implications for improved membrane design. AIChE J. 2007, 53 (7), 1736−1744. (47) Cussler, E. L. Multicomponent Diffusion; Elsevier Scientific Pub. Co.: Amsterdam, New York, 1976; p x. (48) Hoek, E. M. V.; Kim, A. S.; Elimelech, M. Influence of crossflow membrane filter geometry and shear rate on colloidal fouling in reverse osmosis and nanofiltration separations. Environ. Eng. Sci. 2002, 19 (6), 357−372.
(20) Achilli, A.; Cath, T. Y.; Marchand, E. A.; Childress, A. E. The forward osmosis membrane bioreactor: A low fouling alternative to MBR processes. Desalination 2009, 239 (1−3), 10−21. (21) Bamaga, O. A.; Yokochi, A.; Beaudry, E. G. Application of forward osmosis in pretreatment of seawater for small reverse osmosis desalination units. Desal. Water Treat. 2009, 5 (1−3), 183−191. (22) Cath, T. Y.; Hancock, N. T.; Lundin, C. D.; Hoppe-Jones, C.; Drewes, J. E. A multi-barrier osmotic dilution process for simultaneous desalination and purification of impaired water. J. Membr. Sci. 2010, 362 (1−2), 417−426. (23) Lee, S.; Boo, C.; Elimelech, M.; Hong, S. Comparison of fouling behavior in forward osmosis (FO) and reverse osmosis (RO). J. Membr. Sci. 2010, 365 (1−2), 34−39. (24) Yen, S. K.; Haja, F. M.; Su, M. L.; Wang, K. Y.; Chung, T. S. Study of draw solutes using 2-methylimidazole-based compounds in forward osmosis. J. Membr. Sci. 2011, 364 (1−2), 242−252. (25) Ge, Q. C.; Su, J. C.; Chung, T. S.; Amy, G. Hydrophilic superparamagnetic nanoparticles: synthesis, characterization, and performance in forward osmosis processes. Ind. Eng. Chem. Res. 2011, 50 (1), 382−388. (26) Ling, M. M.; Wang, K. Y.; Chung, T.-S. Highly water-soluble magnetic nanoparticles as novel draw solutes in forward osmosis for water reuse. Ind. Eng. Chem. Res. 2010, 49 (12), 5869−5876. (27) McCutcheon, J. R.; McGinnis, R. L.; Elimelech, M. A novel ammonia-carbon dioxide forward (direct) osmosis desalination process. Desalination 2005, 174 (1), 1−11. (28) McCutcheon, J. R.; McGinnis, R. L.; Elimelech, M. Desalination by ammonia-carbon dioxide forward osmosis: Influence of draw and feed solution concentrations on process performance. J. Membr. Sci. 2006, 278 (1−2), 114−123. (29) McGinnis, R. L.; Elimelech, M. Energy requirements of ammonia-carbon dioxide forward osmosis desalination. Desalination 2007, 207 (1−3), 370−382. (30) McGinnis, R. L.; McCutcheon, J. R.; Elimelech, M. A novel ammonia−carbon dioxide osmotic heat engine for power generation. J. Membr. Sci. 2007, 305 (1−2), 13−19. (31) Hancock, N. T.; Cath, T. Y. Solute coupled diffusion in osmotically driven membrane processes. Environ. Sci. Technol. 2009, 43 (17), 6769−6775. (32) Hancock, N. T.; Phillip, W. A.; Elimelech, M.; Cath, T. Y. Bidirectional permeation of electrolytes in osmotically driven membrane processes. Environ. Sci. Technol. 2011, 45 (24), 10642− 10651. (33) Jin, X.; Tang, C. Y.; Gu, Y. S.; She, Q. H.; Qi, S. R. Boric acid permeation in forward osmosis membrane processes: modeling, experiments, and implications. Environ. Sci. Technol. 2011, 45 (6), 2323−2330. (34) Phillip, W. A.; Yong, J. S.; Elimelech, M. Reverse draw solute permeation in forward osmosis: Modeling and experiments. Environ. Sci. Technol. 2011, 44 (13), 5170−5176. (35) Yong, J. S.; Phillip, W. A.; Elimelech, M. Coupled reverse draw solute permeation and water flux in forward osmosis with neutral draw solutes. J. Membr. Sci. 2012, 392, 9−17. (36) Lay, W. C. L.; Zhang, J. S.; Tang, C. Y.; Wang, R.; Liu, Y.; Fane, A. G. Factors affecting flux performance of forward osmosis systems. J. Membr. Sci. 2012, 394, 151−168. (37) Xiao, D. Z.; Tang, C. Y. Y.; Zhang, J. S.; Lay, W. C. L.; Wang, R.; Fane, A. G. Modeling salt accumulation in osmotic membrane bioreactors: Implications for FO membrane selection and system operation. J. Membr. Sci. 2011, 366 (1−2), 314−324. (38) Achilli, A.; Cath, T. Y.; Childress, A. E., Selection of inorganicbased draw solutions for forward osmosis applications. J. Membr. Sci. 364, (1−2), 233-241. (39) Garcia-Castello, E. M.; McCutcheon, J. R.; Elimelech, M. Performance evaluation of sucrose concentration using forward osmosis. J. Membr. Sci. 2009, 338 (1−2), 61−66. (40) Hancock, N. T.; Xu, P.; Heil, D. M.; Bellona, C.; Cath, T. Y. Comprehensive bench- and pilot-scale investigation of trace organic 13472
dx.doi.org/10.1021/ie3016494 | Ind. Eng. Chem. Res. 2012, 51, 13463−13472
