Environ. Sci. Technol. 2001, 35, 3008-3018
Membrane Rejection of Nitrogen Compounds SANGHO LEE AND RICHARD M. LUEPTOW* Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208
Rejection characteristics of nitrogen compounds were examined for reverse osmosis, nanofiltration, and lowpressure reverse osmosis membranes. The rejection of nitrogen compounds is explained by integrating experimental results with calculations using the extended NernstPlanck model coupled with a steric hindrance model. The molecular weight and chemical structure of nitrogen compounds appear to be less important in determining rejection than electrostatic properties. The rejection is greatest when the Donnan potential exceeds 0.05 V or when the ratio of the solute radius to the pore radius is greater than 0.8. The transport of solute in the pore is dominated by diffusion, although convective transport is significant for organic nitrogen compounds. Electromigration contributes negligibly to the overall solute transport in the membrane. Urea, a small organic compound, has lower rejection than ionic compounds such as ammonium, nitrate, and nitrite, indicating the critical role of electrostatic interaction in rejection. This suggests that better treatment efficiency for organic nitrogen compounds can be obtained after ammonification of urea.
Introduction Nitrogen in water and wastewater is one of the major pollutants to water resources (1, 2). Nitrogen exists in various chemical forms including inorganics such as ammonia (NH3), nitrate (NO3-), and nitrite (NO2-) as well as organic nitrogen compounds (3). Although nitrogen is an essential element for all living matter, nitrogen compounds in groundwater and wastewater cause harmful effects on human health as well as deterioration of water quality. Thus, environmental legislation requires the removal of nitrogen compounds from most wastewater (1, 4). Furthermore, water reuse necessitates the removal of nitrogen compounds (5-7). Different approaches have been proposed and used to remove nitrogen compounds from groundwater and reclaimed wastewater. The classical means for nitrogen control include biological treatment, ion exchange, and catalytic oxidation. Recently, technologies using nanofiltration (NF) and reverse osmosis (RO) membranes have drawn attention as treatment options for nitrogen compounds (4). Membrane filtration generally results in higher rejection efficiency of ionic nitrogen compounds than other methods. The membrane also simultaneously removes other pollutants such as organic carbon and hazardous chemicals. Moreover, membrane treatment is an absolute filtration method, so its efficiency and performance are stable and predictable. Recent * Corresponding author telephone: (847)491-4265; fax: (847)4914180; e-mail:
[email protected]. 3008
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developments of high-performance membranes such as lowpressure reverse osmosis (LPRO) membranes have broadened the applications for membrane technology from water treatment to wastewater treatment (8-10). However, the physicochemical basis for RO and NF is quite complex. In addition to rejection at the membrane based on physical size, the rejection depends on the physical chemistry of the solvent, the solute, and the membrane. For ionic solutes, the degree of separation depends not only on the hydrated size of the ion but also on its ionic charge. For organic solutes, the chemical affinity of the solute for the membrane material is as important as the molecular weight of the solute. Therefore, a fundamental understanding of the chemical and physical mechanisms governing the rejection by RO membranes is of practical significance. Thus, the transport mechanisms of ions and organics through NF or RO membranes have been widely studied in recent years (11-14). The objective of this paper is to provide insight into the nature of rejection characteristics of RO, NF, and LPRO membranes for nitrogen compounds. Our interest is in establishing a technique for combining experiments with computation to provide fundamental insight into separation processes and membrane characteristics not otherwise available. We focus on analysis of experimental rejection data using the extended Nernst-Planck equation combined with film theory. In addition, the separation behavior for a variety of organic and inorganic nitrogen compounds is established.
Experimental Methods Flat sheet samples of three commercially available thin film composite-type membranes listed in Table 1 were used for the filtration experiments. These membranes were selected because they represent typical RO, LPRO, and NF membranes. RO and LPRO membranes have similar high rejection of both monovalent and divalent ions. LPRO membranes have a greater water permeability than the RO or NF membranes. NF membranes typically have low rejection for monovalent ions and high rejection for divalent ions. Except for NF-45, which is made of poly(piperazine amide), the manufacturers did not provide the polymer makeup of their membranes. We examined the stability of the membranes, and we could not observe any significant change in flux and rejection over several hours of testing. Experiments were performed in batch mode using a stirred cell similar to those which have been widely used for the study of the rejection by RO membranes (11, 13). The stirred cell shown in Figure 1 was made of aluminum and coated with Teflon to improve chemical stability. The diameter of the stirred cell was 54 mm, and the working volume was 50 mL. A magnetic stirrer (Stirrer Assembly 8200, Millipore, USA) was positioned just above the membrane. The length of the stirring bar was 52 mm. The working pressure was provided by a high-pressure nitrogen cylinder with a gas pressure regulator. The stirring speed was controlled by a magnetic stirrer plate. The permeate flux was measured using a graduated cylinder. The permeate flux was monitored in terms of concentration factor ( fc). The concentration factor, defined as a ratio of the feed volume to concentrate volume, indicates the extent of concentration:
fc )
Vf Vp )1+ Vc Vc
10.1021/es0018724 CCC: $20.00
(1)
2001 American Chemical Society Published on Web 06/07/2001
TABLE 1. Membranes and Their Characteristics membrane type
type
manufacturer
pH range
NaCl rejection (catalog)
measd pure water flux at 8 atm (L m-2 h-1)
low-pressure RO brackish water RO nanofiltration
ESPA ATFRO-HR NF-45
Hydranautics AMT Filmtec
3-10 3-10 2-11
0.99a 0.99b 0.58c
68 32 35
a Test condition: 2000 mg/L NaCl solution, 1530 kPa, 15% recovery. b Test condition: 1500 mg/L NaCl solution, 1040 kPa, 15% recovery. c Test condition: 1240 mg/L NaCl solution, 1380 kPa, 15% recovery.
FIGURE 1. Schematic diagram of stirred cell RO device.
TABLE 2. List of Nitrogen Compounds Used in This Study (15, 16)
FIGURE 2. Rejection of salts. Operating condition: ∆P, 800 kPa; stirring speed, 400 rpm. (O, sodium chloride; 3, calcium chloride; 0, sodium sulfate).
where Vf, Vc, and Vp are defined as the volumes of feed, concentrate, and permeate, respectively. The solute concentrations of the permeate were measured at different fc. Before an experiment, a fresh membrane was rinsed by letting it float skin-side down in distilled water for 30 min. Then it was placed in the stirred cell. The stability of the membrane permeability during the experiment was checked by comparing the pure water flux before and after the experiment. Only those membranes for which permeability changes were low (less than 5-10%) were used. Even though there were minor differences in pure water and solute permeability between different samples of the same membrane, the reproducibility error between samples of same membrane was less than 10%. For each membrane, the rejection was measured for the eight nitrogen compounds listed in Table 2, including organic
compounds and inorganic ions. Two classes of nitrogen compounds were considered. The first class includes nitrogen compounds that are typical in wastewater (6, 7). These include organic creatine and urea as well as ionic ammonium (NH4Cl), nitrate (NaNO3), and nitrite (NaNO2). The second class of nitrogen compounds was considered in order to examine the rejection of urea in depth. Nitrogen compounds with similar molecular structures to urea (H2NCONH2) include ammonium carbonate ((NH4)2CO3), ammonium carbamate (NH2CO2NH4), and ammonium formate (HCO2NH4). The concentrations of nitrogen compounds were set to maintain the net nitrogen concentration at 250 mg/L for all solutions. In all of the experiments, the feed solution contained only a single compound. The rejection for species i was calculated as
(
Ri ) 1 -
)
Ci,p Ci,b
(2)
where Ci,p is the permeate concentration and Ci,b is the concentration in the bulk solution. The concentration in VOL. 35, NO. 14, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. Rejection of different salts for various RO membranes. Operating condition: ∆P, 800 kPa; stirring, 400 rpm; feed concentration: 250 mg N/L. (a) LPRO, (b) RO, and (c) NF (b, creatine; 9, urea; O, ammonium carbonate; 0, ammonium carbamate; ], ammonium formate; ", ammonium chloride; 4, sodium nitrate; 3, sodium nitrite) Filled symbols are organic compounds; open symbols are monovalent compounds; gray symbol is a divalent compound. permeate was measured several times until f ) 2.5 (60% recovery). Rejection was measured at a transmembrane pressure of 8 atm and a stirring speed of 400 rpm. After filtration tests, all samples containing organic nitrogen were acidified below a pH of 2.0 by adding 10% sulfuric acid to prevent the loss of nitrogen compounds for analysis. All experiments were performed at room temperature (20 °C), and the change in temperature during the experiments was less 1 °C. Analyses of free ammonium ions and total nitrogen were conducted using the procedures described in Standard Methods (17). The spectrophotometric method of Hach (18) was adapted to measure the total nitrogen concentration and the ammonium ion concentration in the feed and the permeate. The concentrations of other ionic compounds were determined by conductivity measurements and were automatically corrected for temperature influence. The physical structures of the membranes were analyzed using scanning electron microscopy (SEM). The conditions for sample preparation were carefully selected in order to minimize the damage to the membrane structure. The specimens were dried under a vacuum at 30 °C, mounted on 3010
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specimen studs sputter-coated with silver (Cressington highresolution sputter coater, USA), and viewed using a SEM (Hitachi S4500FE, Hitachi, Japan) operating at 5 kV.
Experimental Results and Discussion To initially characterize the rejection behavior of the three membranes, single salt rejection measurements based on electrical conductivity were performed for several concentrations of CaCl2, NaCl, and Na2SO4. As shown in Figure 2, the RO and LPRO membranes showed no clear difference for the rejection of the three compounds as expected for RO membranes. The NF membrane had much lower rejection for NaCl than the other membranes, typical of NF membranes where ion valence is important for selectivity. The rejection of nitrogen compounds for the three membranes is shown in Figure 3 as a function of the molecular weight of the rejected species. The rejection of creatine was over 0.97 for the RO and LPRO membranes because the creatine molecule (MW 131.15) is large enough to be rejected via size exclusion. The rejection of creatine is also relatively high (nearly 0.9) for the NF membrane. The rejection of ionic compounds is also high for both RO membranes, even though
the molecular weights of the ionic compounds range from 53.5 to 96. The NF membrane had substantially lower rejections for ionic compounds than the RO membranes, and the rejection is roughly proportional to the molecular weight. Urea rejection was substantially lower than all other compounds ranging from 0.19 (NF) to 0.52 (LPRO). Urea is small and uncharged, so it is difficult to reject by size exclusion or by charge repulsion for all of the membranes. The rejection is substantially greater for compounds such as ammonium carbonate, ammonium carbamate, and ammonium formate that are structurally similar to urea except for their ionic character. For RO and LPRO membranes, those compounds have similar rejection, most likely due to their charge. The rejection characteristics of the NF membrane are more complex since the rejection is affected not only by size exclusion but also by the valency of the ions. The rejection is higher for ammonium carbonate than for ammonium chloride, sodium nitrate, and sodium nitrite because it contains a divalent anion. The rejection of ammonium carbamate and ammonium formate differs because of their size. The two RO membranes have similar rejection patterns despite their large difference in water permeability. Thus, it appears that the RO and LPRO membranes have similar pore size and surface charge characteristics but different effective membrane area. SEMs of the membrane surfaces are shown in Figure 4. The LPRO membrane (Figure 4a,b) has a rough surface that could result in a large effective membrane area (Ak) and consequently a small effective thickness ∆x/Ak. The RO membrane (Figure 4c,d) also has rough surface but not as rough as the LPRO membrane. The surface of the NF membrane (Figure 4e,f) is relatively smooth. It is possible that the difference in surface roughness is related to greater effective membrane area, as suggested by Sakka (9).
tion, and convection. Although this approach has been described in some detail elsewhere (11, 19, 20), we briefly review its application to the rejection of nitrogen compounds. Since the membrane pore radius and the charge density ratio are not known for the membranes, experimental data are used to determine these values. This is accomplished by solving the transport equations for values of the pore radius and charge density ratio until the calculated permeate concentration matches the measured permeate concentration. The transport model for the solutes in the membrane is based on the extended Nernst-Planck equation:
dci ziKi,dDiF dΨm - ci + Ki,cJvci Ji ) -Ki,dDi dx RT dx
(3)
where Ji is the solute flux, Di is the diffusion coefficient of solute i, ci is its concentration in membrane phase, x is the coordinate in the flow direction through the membrane, z is the valency, F is the Faraday constant, ∆Ψm is the membrane potential, R is the gas constant, T is the temperature, Jv is the solvent flux, Ki,d is the hindrance factor for diffusion, and Ki,c is the hindrance factor for convection. The terms on the right-hand side represent transport due to diffusion, the electric field gradient, and convection, respectively. In the case of uncharged solutes, the membrane potential gradient related to uncharged solute transport is of no consequence. Using Ji ) JvCi,p/Ak, eq 3 can be rewritten in the form of a concentration gradient as indicated in eq 4, given in Table 3. The electric potential gradient and other supporting equations are also shown in Table 3 (eqs 5-12). In these equations for solute transport in the membrane, the ratio of effective charge density per solute concentration, ξ, and the pore radius, rp, are unknown parameters for any particular membrane. In eq 6, activity coefficients have not been included as they are assumed to be accounted for by the effective charge density (ξ) (11). Moreover, only dilute solutions are considered in this work, so the activity coefficients are near 1. The charge density of the membrane increases with bulk solute concentration in eqn 11 due to co-ion adsorption on the membrane (11, 13, 16). Thus, the
Model for Analysis of Solute Rejection Mechanism Using a transport model based on the extended NernstPlanck Equation with a concentration polarization model makes it possible to determine the significance of the various membrane transport mechanismssdiffusion, electromigra-
TABLE 3. Equations for the Extended Nernst-Planck Model (16, 20) meaning concentration gradient in the membrane
equation d ci Jv ziFci dΨm ) (K c - Ci,p) dx Ki,dDi i,c i RT dx n
potential gradient in the membrane
dΨm
)
i)1
dx
Donnan-steric partitioning hindrance factor
ziJv
∑K
i,dDi
F
(Ki,cci - Ci,p) (5) n
∑
RT i)1
()
(4)
(z2i ci)
(
)
(6)
Ki,d ) 1.0 - 2.30λi + 1.154λi2 + 0.224λi3 Ki,c ) (1.0 + 0.054λi - 0.988λi2 + 0.441λi3)(2 - Φi)
(7) (8)
ci ziF ) φi exp ∆Ψd Ci RT
φi )
{
(1 - λi)2 λi < 1 λi g 1 0
λi ) ri,s/rp
(9) (10)
n
electroneutrality conditions
∑ z c + ξC i i
avg
) 0 (in membrane)
(11)
i)1 n
∑z C ) 0 (in concentrate or permeate) i i
(12)
i)1
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FIGURE 4. Scanning electron micrographs of membrane surfaces. (a) LPRO membrane (×5000), (b) LPRO membrane (×25 000), (c) RO membrane (×5000), (d) RO membrane (×25 000), (e) NF membrane (×5000), and (f) NF membrane (×25 000). charge density is proportional to the amount of ions adsorbed on the membrane phase. The rejection data for uncharged molecules (urea and creatine) are used to calculate rp for each membrane. For these nonionic molecules, z is zero so that the potential driven migration of solute is zero. In this case, rejection only depends on the pore radius for the membrane (rp). The equations in Table 3 can be solved analytically (20): 3012
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Cp )
CmKcφ Kc Jv∆x 1 - exp (1 - φKc) Kd DAk
(
c(x) ) φCm -
(
) (
)
)
Cp K c Jv x Cp exp + Kc KdDAk Kc
(13)
(14)
TABLE 4. Membrane Properties Obtained from Eqs 13 and 14 for Urea and Creatine LPRO
RO
NF
meaning concn polarization
Ci,m - Ci,p ) eJv/k Ci,b - Ci,p
mass transfer coeff
k ) 0.104
effective diffusion coeff
Deff )
effective pore size, rp (nm)
urea creatine average
0.351 0.353 0.352
0.352 0.347 0.350
0.439 0.457 0.448
effective membrane thickness, ∆x/Ak (µm)
urea creatine average
0.62 0.60 0.61
1.20 1.23 1.22
1.94 1.80 1.87
In these equations, the pore radius is hidden in the factors φ, Kc, and Kd, which are functions of rp according to eqs 7-10 in Table 3. The calculated values for rp are provided in Table 4 based on solving eqs 13 and 14 using the experimental parameters. The average effective pore radius rp of the membranes ranged from 0.350 nm (RO) to 0.448 nm (NF). The value of rp for the NF membrane (NF-45) obtained in this analysis is similar to previous reports [0.45 nm by Wang et al. (21); 0.48 nm by Bowen and Mohammad (16); 0.42 nm by Schaep et al. (20)]. For RO and LPRO membranes, there is no data available for comparison. The solvent transport in the membrane is based on the Hagen-Poiseuille equation, which relates the water flux and the applied pressure across the membrane:
Jv )
rp2∆P 8µ(∆x/Ak)
TABLE 5. Equations for Concentration Polarization Effect (22-24)
(15)
where rp is the pore radius of the membrane, ∆P is the effective transmembrane pressure, µ is solvent viscosity, ∆x is the membrane thickness, and Ak is the porosity (the fraction of effective filtration area) of the membrane. In this equation, the pore radius and membrane thickness divided by the porosity (∆x/Ak) are unknown parameters for any particular membrane. However, the pore radius was determined as described above. Given the pore radius, ∆x/Ak is readily obtained from the measurements of the pure water flux. The results are shown in Table 4. The effective thickness ∆x/Ak of the LPRO membrane is significantly less than the effective thickness of RO and NF membranes. This small value along with a pore size similar to RO membranes explains the high rejection along with the high water permeability of LPRO membranes. The order of ∆x/Ak is NF > RO > LPRO, which is the inverse of the surface roughness order shown in Figure 4. This suggests that the difference in ∆x/Ak may be due to the difference in surface structure and effective membrane area. With the pore radius (rp) and effective thickness (∆x/Ak) known, the rejection for ionic nitrogen compounds can be estimated. For these calculations, only the charge density (ξ) can be changed to adjust the calculations to match the experimental results. In the case of ionic compounds, the exact solutions (eqs 13 and 14) cannot be used, because the membrane potential term in eq 3 is nonzero. Thus, a numerical method was used to find the proper value of ξ based on the experimental results. In addition, the solute concentration on the concentrate side of the membrane was modeled based on concentration polarization using film theory and Fick’s law for diffusion. Using eqs 16-18 in Table 5, the solute concentration profiles on the concentrate side of the membrane can be calculated from experimental results. The numerical technique is fairly involved, so it is briefly described here. To begin, the solute concentration at the membrane surface (Ci,m) was calculated from the experimental values of Ci,b, Ci,p, and Jv using the concentration
equation (16)
( )( ) ( ) Deff ωr 2F r µ
2/3
µ FDeff
1/3
(17)
D1D2(|z1| + |z2|) |z1|D1 + |z2|D2
(18)
polarization model of eqs 16-18. Next, the rp based on measurements with uncharged compounds was used to calculate φi from eqs 9 and 10. The values for the solute mass transfer coefficient (k) and solute radius (ri,s) are from the literature (15, 16). ∆Ψd|x)0 was more difficult to obtain. It was determined from the Donnan equilibrium relationship (eq 6) and the electroneutrality conditions in the membrane (eq 11) using an initial guess for ξ. To calculate ∆Ψd|x)0, Ci,m was substituted for ci in eq 6 for both positive ions and negative ions, resulting in two equations. These two equations (eq 6) along with the electroneutrality condition in the membrane (eq 11), provided three equations with four unknowns (c1, c2, ∆Ψd|x)0, and ξ). Combining the equations and using a guess for ξ provided a (|z1 + z2|)-th order polynomial equation for ∆Ψd|x)0, which could be solved either analytically or numerically. Next φi and ∆Ψd|x)0 were used to calculate ci|x)0 (the solute concentration in the membrane at the concentrate side interface) using eq 6. Then, the differential eqs 4 and 5 were solved numerically using a fourth order Runge-Kutta method with the initial value of ci|x)0. This step yielded ci|x)∆x (the solute concentration in the membrane at the permeate side interface). Again, ∆Ψd|x)∆x (the Donnan potential at the permeate side) was required to obtain Ci,p. The values of ci|x)∆x for both the positive and negative ions were substituted into eq 6 for ci. These two equations along with the electroneutrality condition in the solution (eq 12) provided three equations for three unknowns (C1,p, C2,p, and ∆Ψd|x)∆x). The model result for Ci,p was compared to the experimental value. This process was repeated using a new guess for ξ until the relative difference between the calculated and experimental Ci,p was less than 1%. The corresponding Donnan potential describes the electronic partitioning characteristics of the solute/membrane combination.
Theoretical Analysis Using the Model Rejection Mechanisms. The differences in characteristics of RO, LPRO, and NF membranes are clearly demonstrated in Figure 5. The rejection and solvent flux for urea were calculated using eqs 13 and 14 as a function of ∆x/Ak and rp. Figure 5a shows that the rejection is independent of ∆x/ Ak as expected but is strongly dependent on rp. The experimental rejection of urea by RO and LPRO membranes is similar given similar rp. The only difference between the two types of membranes is ∆x/Ak, which plays no role in the rejection. The model also provides an estimate of the urea rejection as the pore size is reduced. A pore size of about 0.27 nm would be needed for 90% urea rejection. But the solvent flux decreases as pore size decreases and effective thickness increases, as shown in Figure 5b. The superior flux of the LPRO membrane is a result of its small effective thickness as compared to the RO membrane and its small thickness as compared to the NF membrane. Figure 6 shows the ratios of solute concentration on membrane surface to bulk concentration for the membranes. The LPRO membrane has VOL. 35, NO. 14, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 5. Calculated rejection of urea and solvent flux as a function of ∆x/Ak and rp. The symbols correspond to data from the experiments (0, LPRO; O, RO; 3, NF). (a) Rejection and (b) solvent flux (×10-6 m/s at 8 bar).
FIGURE 6. Ratio of the solute concentration on the membrane surface to bulk concentration for RO membranes (b, creatine; 9, urea; O, ammonium carbonate; 0, ammonium carbamate; ], ammonium formate; ", ammonium chloride; 4, sodium nitrate; 3, sodium nitrite). Filled symbols are organic compounds; open symbols are monovalent compounds; gray symbol is a divalent compound. a higher ratio because of its higher flux. The NF membrane exhibits the lower ratio than the RO membrane due to its lower rejection. The lower ratios for urea are also a result of rejection. The partitioning of solute in the membrane is determined by the relative sizes of the pore and the ion as well as the electrical characteristics of the solutes and membranes. In the model, the relative size effect is represented by the ratio of the solute size to the pore size, λavg (or the average steric factor, φavg). The average ratio of solute size to pore size, λavg, is λ for uncharged compounds and (λ1 + λ2)/2 for ionic compounds. Solute sizes are included in Table 2. The electrical interaction effect is expressed as the Donnan potential between the concentrate and the permeate sides of the membrane, ∆Ψd,∆() |∆Ψd|x)0 - ∆Ψd|x)∆x|). The Donnan potential is induced by the charge balances (eqs 11 and 12) 3014
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FIGURE 7. Effect of solute radius/pore radius and Donnan potential on rejection for various membranes and solutes (0, LPRO; O, RO; 3, NF). in bulk and membrane phase. Using the theory described in the previous section along with the experimental results provides the Donnan potential for a particular solute/ membrane combination. Since the combined effects of size exclusion and electrical characteristics determine the rejection for a particular combination of solute and membrane, it is useful to consider the dependence of rejection on the solute to pore size ratio and the Donnan potential. Figure 7 shows the experimentally measured rejection as a function of these two parameters as estimated from the theory. The symbols correspond to the characteristics for all of the solutes and membranes considered experimentally. The surface plot was obtained from the interpolation of the points using the inverse distance method.
TABLE 6. Equations for the Contribution of Transport Mechanisms Using a Central Difference Approximation (16) meaning
equation
( ( (
)
contribution of transport by diffusion (%)
ci|x)∆x - ci|x)0 100 -Ki,dDi Ji ∆x
contribution of transport by electrostatic interaction (%)
ci|x)0 + ci|x)∆x ziKi,dDiF Ψm|x)∆x - Ψm|x)0 100 Ji 2 RT ∆x
(20)
contribution of transport by convection (%)
ci|x)0 + ci|x)∆x 100 Ki,cJv Ji 2
(21)
In the case of noncharged molecules such as urea and creatine, the Donnan potential induced by the solute transport is zero, so rejection is based on size exclusion. For ionic compounds, the Donnan potential plays a key role in rejection. Figure 7 indicates that, unless λavg is quite near 1 (steric partitioning is near zero), the Donnan potential must be significant to obtain high rejection. This makes the rejection of small uncharged molecules such as urea quite difficult. Likewise, solutes with small λavg (high values of steric partitioning) do not have high rejection unless the Donnan potential is substantial. Solutes are most easily rejected when the ratio of the solute radius to pore size is greater than about 0.8 and the Donnan potential is greater than 0.05 V.
)
(19)
)
However, if neither of these conditions is met, the rejection is quite poor. Figure 7 suggests the possibility of “engineered membranes” in which the pore size and the charge density are designed into the membrane to provide an adequate Donnan potential and solute-to-pore size ratio to ensure high rejection. To better understand the nature of solute transport in the membrane, the contribution of each transport mechanism in the membrane can be approximated as suggested by Bowen and Mohammad (16) using a one-step central difference estimate of the gradient. These equations reflect the percentage contribution of each transport mechanism in eq 3 to the total and are summarized in Table 6. The
FIGURE 8. Result of the analysis of transport mechanisms with different membranes and solutes (0, LPRO; O, RO; ∇, NF). (a) Diffusion, (b) convection, and (c) electromigration. VOL. 35, NO. 14, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 9. Effect of nitrogen form on experimentally measured rejection (NH4+, ammonium carbonate; NO2-, sodium nitrite; NO3-, sodium nitrate). Operating condition: ∆P, 800 kPa; stirring speed, 400 rpm; feed concentration: 250 mg of N/L (0, LPRO; O, RO; 3, NF). membrane potential is a key property related to transport due to the electrical field gradient, the second term on the right side of eq 3. The ratio of pore size to solute size plays a role in the hindrance factor for all three transport terms on the right side of eq 3. The contributions of diffusion, electromigration, and convection are shown in Figure 8 as a function of the membrane potential (∆Ψm) and the ratio of solute size to pore size (λavg). For ionic compounds, only the solute flux for anion is shown. For all but the uncharged molecules, the transport is controlled largely by diffusion. The contribution of convection is also important for uncharged molecules. Electromigration appears to be of minimal importance in all cases. The importance of electrical effects in rejection seems at odds with the minimal importance of electromigration. Electrical effects in membrane separation can be expressed as two potential terms: the Donnan potential, ∆Ψd,∆() |∆Ψd|x)0 - ∆Ψd|x)∆x|), and the membrane potential |Ψm|x)0 - Ψm|x)∆x|. The Donnan potential decreases the partitioning coefficient of ions (Donnan equilibrium) while the membrane potential retards the ion transport in the membrane. In Figure 7, the rejection increases with an increase in Donnan potential for charged ions. However, Figure 8 indicates that diffusion is the most important transport mechanism for the charged ions that are not rejected, independent of the membrane potential. Thus, the electrical interaction related to the Donnan potential is crucial for rejection, but the membrane potential has little effect on the subsequent transport of ions through the membrane. Dependence of Rejection on the Chemical Form of Nitrogen. As a result of biological reactions, various nitrogen compounds including organic nitrogens, ammonium, nitrite, and nitrate exist in wastewater. Thus, the biological conversion of nitrogen compounds from one form to another should be considered for RO treatment of wastewater. In particular, the effect of biological degradation of urea to ammonium ions is an especially important issue for the use of RO in wastewater recycling for manned space missions (25, 26). In a biological system, a urea molecule is converted to ammonium (oxidation state: -3), nitrite (oxidation state: +3), and nitrate (oxidation state: +5). Figure 9 compares the experimentally measured rejection of urea, ammonium, nitrite, and nitrate. For RO and LPRO membranes, the rejection of ionic nitrogen compounds is better than that for 3016
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FIGURE 10. Theoretical estimate of the dependence of rejection on the ratio of ammonium carbonate to urea. Theoretical operating condition: ∆P, 800 kPa; stirring speed, 400 rpm; feed concentration: 250 mg of N/L.
FIGURE 11. Theoretical estimate of rejection for a LPRO membrane as a function of the ratio of charge density (ξ) for urea and ammonium carbonate. The filled symbols correspond to the conditions for experimental measurements. urea because of the Donnan partitioning effect in addition to size exclusion. This suggests that the conversion of organic nitrogen to an inorganic form should be carried out before membrane treatment. In case of NF, the rejection of ammonium ions is much higher than nitrite and nitrate because the carbonate counterion is divalent for the ammonium compound that was tested. The difference in rejection might be insignificant if the counterions of nitrite and nitrate were divalent rather than monovalent. As urea in wastewater naturally decomposes to ammonium carbonate, the ratio of the two compounds varies. Figure 10 illustrates the dependence of the overall nitrogen rejection as the urea decomposition reaction progresses and the ratio of ammonium carbonate to total nitrogen changes from 0 to 100% based on the model for rejection. The overall
of ammonium carbonate occurs at a much lower solvent flux, 4.5 × 10-6 m/s (∆P ) 7 atm). Thus, the transmembrane pressure for rejecting urea must be higher than that for ammonium carbonate to obtain maximum rejection. Even so, the rejection is higher, and the optimal transmembrane pressure is lower for ammonium carbonate than for urea, further supporting Lee and Lueptow’s suggestion that urea hydrolysis enhances rejection of nitrogen compounds in wastewater (25).
Acknowledgments This work was supported by NASA. We thank Karen Pickering for her support and advice regarding the experiments. We also thank Hydranautics Inc. and Advanced Membrane Technology, Inc. for their donation of membrane samples.
Nomenclatures
FIGURE 12. Effect of solvent flux on rejection of urea and ammonium carbonate by LPRO. The filled symbols correspond to the conditions for the experiments. rejection of nitrogen compounds increases significantly as the ratio of ammonium carbonate to total nitrogen increases, indicating that the complete conversion of urea to ammonium carbonate is optimal for the highest rejection of nitrogen. The linear increase in overall rejection results because the rejections for urea and ammonium carbonate are independent. Similar results were obtained experimentally (25). In that case, the total nitrogen rejection measured for an LPRO membrane was 97% for ammonium carbonate but only 68% for urea. The importance of the electrical interaction in the rejection of urea and ammonium carbonate can be clearly demonstrated by varying the electrical characteristic of the membrane using the theoretical model. In Figure 11, the calculated rejections of urea and ammonium carbonate are shown as a function of the ratio of charge density (ξ) for the LPRO membrane. The filled symbols are the actual ξ value calculated from the experiments. If the electrostatic interaction did not occur (ξ ) 0), the rejection of ammonium carbonate would be lower than that of urea. This is a result of steric partitioning of urea since urea is a large molecule as compared to the average size of the ammonium and carbonate ions. As ξ increases, the rejection of ammonium carbonate is enhanced by the electrical interaction. This result also suggests that the rejection of ammonium carbonate can be improved by using a membrane with an even larger ξ. Since the rejection mechanisms of urea and ammonium carbonate are different, the operating conditions for optimum rejection may also be different. Figure 12 shows the dependence of the rejection of urea and ammonium carbonate on the solvent flux or, equivalently, transmembrane pressure estimated using the model. At low transmembrane pressure, the rejection increases as the solvent flux increases. However, above a particular transmembrane pressure, the rejection decreases. This decrease in rejection can be attributed to increased concentration polarization resulting from the higher solvent flux. The overall dependence of rejection on solvent flux is different for urea and ammonium carbonate. The optimal rejection of urea is obtained at a solvent flux of 8.75 × 10-6 m/s (∆P ) 12.5 atm), while the highest rejection
Ak
effective porosity of the membrane (-)
ci
solute concn inside membrane phase (mol/m3)
Cavg
average solute concn in liquid phase (mol/m3) ) Ci/|zi| (salts) or Ci (noncharged molecule)
Ci
solute concn in liquid phase (mol/m3)
Cm
solute concn at membrane surface (mol/m3)
Cp
solute concn at permeate side (mol/m3)
Di
diffusion coeff of solute i (m2/s); subscript 1 and 2 implies cation and anion, respectively, for single salt
Deff
effective diffusion coeff of solute defined by eq 18 (m2/s)
F
Faraday constant () 96485 C/mol)
Ji
solute flux through membrane (m/s)
Jv
solvent flux through membrane (m/s)
k
mass-transfer coeff on high-pressure side of membrane (m/s)
Ki,d
hindrance factor for diffusion (-)
Ki,c
hindrance factor for convection (-)
n
number of ion species in solution (-)
∆P
transmembrane pressure (Pa)
r
radius of stirred cell (m)
rp
effective pore radius of membrane (m)
ri,s
radius of solute i (m)
R
gas constant ()8.314 J mol-1 K-1)
Ri
rejection for compound i (-)
T
temperature (K)
x
coordinate in flow direction (m)
zi
valency of ion i (-)
∆Ψd
Donnan electrical potential (V)
∆Ψd,∆
Donnan electrical potential between concentrate and permeate side (V) () |∆Ψd|x)0 - ∆Ψd|x)∆x|)
Ψm
electrical potential in membrane phase (V)
F
solution density (kg/m3)
µ
solvent viscosity (kg m-1 s-1)
ω
stirring velocity (rad/s)
φi
steric partitioning term (-)
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λi
ratio of solute radius/pore radius (-)
ξ
ratio of charge density (charge density/solute concn) (-)
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(15) Lide, D. R. CRC Handbook of Chemistry and Physics: CRC Press: Boca Raton, FL, 2000. (16) Bowen, W. R.; Mohammad, A. W. Trans. Inst. Chem. Eng. 1998, 76, 885-893. (17) APHA; AWWA; WEF. Standard Methods for the Examination of Water and Wastewater, 18th ed.; American Public Health Association: Washington, DC, 1992. (18) Hach Company. Hach Water Analysis Handbook, 2nd ed.; Hach: Colorado, 1992. (19) Ratanatamskul, C.; Urase, T.; Yamamoto, K. Water Sci. Technol. 1998, 38, 453-462. (20) Schaep, J.; Vandecasteele, C.; Mohammad, A. W.; Bowen, R Sep. Sci. Technol. 1999, 34 (15), 3009-3030. (21) Wang, X. L.; Tsuru, T.; Togoh, M.; Nakao, S.; Kimura, S. J. Chem. Eng. Jpn. 1995, 28, 186-192. (22) Cherayan, M. Ultrafiltration and Microfiltration Handbook; Technomic Publishing: Lancaster, Basel, 1998. (23) Nicolas, S.; Balannec, B.; Beline, F.; Bariou, B. J. Membr. Sci. 2000, 164, 141-155. (24) Newman, J. S. Electrochemical Systems, 2nd ed.; Prentice-Hall: Englewood Cliffs, NJ, 1991. (25) Lee, S.; Lueptow, R. M. Int. J. Life Support Biosphere Sci. 2001, 7/3, 151-161. (26) Lee, S.; Lueptow, R. M. J. Membr. Sci. 2001, 182/1-2, 77-90.
Received for review November 13, 2000. Revised manuscript received April 6, 2001. Accepted April 17, 2001. ES0018724
