Environ. Sci. Technol. 2003, 37, 2997-3004
Three-Component Competitive Adsorption Model for Flow-Through PAC Systems. 1. Model Development and Verification with a PAC/Membrane System Q I L I N L I , †,‡ B E N I T O J . M A R I N ˜ A S , * ,† VERNON L. SNOEYINK,† AND CARLOS CAMPOS§ Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 North Mathews Avenue, Urbana, Illinois 61801, and Suez Environment-CIRSEE, 38 Rue du President Wilson, 78230 Le Pecq, France
Natural organic matter (NOM) interferes with the adsorption of trace organic compounds on porous adsorbents such as powdered activated carbon (PAC) by pore blockage and direct competition for adsorption sites. The competitive effect of NOM in flow-through systems in which the retention time of the PAC is greater than the hydraulic retention time of the system can be magnified because NOM from the influent water can continue to adsorb on the PAC retained in the system. As a result, the adsorption capacity and the diffusion coefficient of trace compounds can decrease as NOM from the influent water accumulates. In this study, a dynamic three-component adsorption model was developed to quantitatively describe the removal of a trace compound from water in flowthrough PAC processes. The system was simplified by using p-dichlorobenzene (p-DCB) to represent the NOM fraction that competes directly with the target trace organic atrazine for adsorption sites and by using poly(styrene sulfonate) (PSS-1.8k) to represent large, pore-blocking NOM. The model was based on the homogeneous surface diffusion assumption with the adsorption capacity of atrazine being gradually adjusted using a simplified version of the ideal adsorbed solution theory model developed in this study. The surface diffusion coefficients of atrazine and p-DCB were modeled as a function of the surface concentration of the pore-blocking compound, PSS-1.8k. The model was verified experimentally with a PAC/ microfiltration (MF) system. The use of single-solute adsorption parameters obtained from batch isotherm and kinetic tests resulted in good model predictions for the adsorption of atrazine and the two model compounds under operating conditions typical of PAC/MF systems. The model will be applied to study various operating conditions and other system parameters of PAC/membrane systems in part 2 of this study. * Corresponding author e-mail:
[email protected]; phone: (217)333-6961; fax: (217)333-6968. † University of Illinois at Urbana-Champaign. ‡ Present address: Department of Chemical Engineering, Yale University, P.O. Box 208286, New Haven, CT 06510. § Suez Environment-CIRSEE. 10.1021/es020989k CCC: $25.00 Published on Web 05/30/2003
2003 American Chemical Society
Introduction Activated carbon adsorption processes have been used by the drinking water industry for decades. Compared to other treatment processes, adsorption has the advantages of (i) removing a wide variety of dissolved organic compounds and (ii) not producing any harmful byproducts. Activated carbon adsorption is especially efficient for the removal of contaminants such as pesticides and odor-causing compounds present in water at trace concentration levels. Despite its wide application, the adsorption process is not well understood at the quantitative level, especially for the removal of trace organic compounds from natural water. Good predictive tools are not currently available because of two major reasons: (i) the complexity of natural organic matter (NOM) and corresponding competitive effects on the adsorption of trace organic contaminants and (ii) an insufficient understanding of competitive adsorption reactions in multi-solute dynamic systems. The adsorption equilibrium and kinetics of NOM itself as well as its competitive effect on the adsorption equilibrium and kinetics of trace organic contaminants remain to be fully described. Many past studies of this phenomenon were conducted in batch systems, while adsorption processes in water treatment usually take place in continuous-flow, dynamic systems. A commonly used approach for kinetic models of competitive adsorption is the pseudo-single-solute method (1, 2), in which the target trace organic compound is considered to be the only adsorbate in the system and its adsorption parameters were those determined from competitive adsorption experiments in batch systems. It assumes that the adsorption parameters of the target trace organic compound are constant through the adsorption process and that they are the same as those obtained in batch experiments. However, it was found that NOM can cause a more serious impact on trace organic compound adsorption in flowthrough systems that retain the carbon for a time longer than the hydraulic residence time of the process as compared to batch systems (3-5). Because of the continuous accumulation of NOM on the carbon surface in such processes, the adsorption capacity and the diffusion coefficient of the trace organic compound decrease with time. Therefore, the assumption made in the pseudo-single-solute approach that the competitive effect of NOM is constant through the adsorption process often is not valid for flow-through systems. The determination of the necessary adsorption equilibrium and kinetic parameters for such systems presents a major challenge, however. A commonly used approach to predict adsorption equilibrium of trace organic contaminants in natural water involves the Equivalent Background Compound (EBC)-Ideal Adsorbed Solution Theory (IAST) method (6, 7). This method considers NOM as a single background compound that has the same competitive effects as the entire mixture of NOM itself. The adsorption equilibrium of the target trace compound is then predicted by the IAST assuming that the natural water system is a bi-solute system consisting of the EBC and the target trace compound. This approach accurately predicted adsorption equilibrium of trace organic contaminants in different natural waters in batch reactors (3, 4, 7, 8). A critical feature of the EBC-IAST approach is that it treats all NOM compounds as if they have the same adsorption properties and competitive effects. In contrast, several researchers have found that NOM of different molecular sizes affects trace organic compound adsorption through different mechanisms that are determined by the VOL. 37, NO. 13, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Important Characteristics of PACs A and B (9)
FIGURE 1. Molecular structures of the adsorbates: (a) atrazine; (b) PSS-1.8k (average n ) 7); (c) p-DCB. size of NOM relative to the pore size distribution of the carbon (9-15). Most trace organic compounds preferably adsorb in small pores that are similar to their molecular size. For example, atrazine, a herbicide commonly found in surface water, has molecular dimensions of 9.6 Å × 8.4 Å × ∼3 Å (11) and preferably adsorbs in micropores between 7.5 and 10 Å in width (12). Therefore, its adsorption capacity can be greatly impacted through direct site competition by NOM molecules that adsorb in the same pores. Because of size exclusion, large NOM molecules are less likely to compete with atrazine for adsorption sites. However, adsorption of the large NOM molecules in larger carbon pores can constrict or even block the openings of the small pores and cause slower adsorption kinetics of trace organic compounds. It has been shown that the surface coverage of large NOM or other large competing molecules determines the surface diffusion rate of the trace organic compound (5, 9). These two mechanisms, direct competition for sites and pore blockage, have been reported as the two major mechanisms of competitive adsorption. An accurate description of competitive adsorption can only be achieved by properly taking into account both of these mechanisms. In this study, a competitive adsorption model was developed to describe trace organic compound adsorption in flow-through powdered activated carbon (PAC) systems. The two mechanisms, direct competition for sites and pore blockage, were included in the model by varying adsorption equilibrium and kinetic parameters of the trace organic compound based on the surface concentrations of the trace organic compound and the competing compounds. The model was validated with experimental data obtained with a PAC/microfiltration (MF) system. In part 2 of this study, the model will be applied to investigate the role of various operating conditions and other system parameters of PAC/ membrane systems (16).
Materials and Methods Water. All experiments were conducted in organic-free water buffered with 10-3 M NaH2PO4 at a pH of 7. The organic-free water was obtained by passing deionized water through a Nanopure ultrapure water system (Barnstead, Dubuque, IA). The dissolved organic carbon (DOC) concentration of the organic-free water was lower than 0.3 mg/L. Adsorbents. Two types of commercial PAC, WPH (referred to as PAC A, Calgon Carbon Corp., Pittsburgh, PA) and SAUF (referred as PAC B, NORIT France, S.a.r.l., Le Blanc Mesnil Cedex, France), were used to demonstrate the effect of pore size distribution on competitive adsorption mechanisms. Important characteristics of these carbons are presented in Table 1. The PAC was oven-dried at 105 °C and kept in a desiccator prior to use. Adsorbates. Atrazine was used as the target adsorbate. The stock solution was prepared by mixing 14C-labeled atrazine (Sigma, St. Louis, MO) and nonlabeled atrazine (Chem Service, Chester, PA). The specific radioactivity of the mixture was 22.6 µCi/mg. The solution was refrigerated until 2998
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parameter
PAC A
PAC B
BET surface area (m2/g) primary micropore ( qcr Ds0
(17)
The solution to the HSDM equation and the system mass balance for both step and pulse PAC addition as well as assumptions regarding system condition and mass transfer in the adsorption process are described in a previous study by Li et al. (21). In the three-component model COMPSORB, developed in this study, effluent concentrations for all the three compounds are calculated. The adsorption of the poreblocking compound is calculated first as if it was the only solute in the system because it adsorbs in different pores than the other compounds. The surface diffusion coefficients of the strongly competing and the target trace organic compound at any given time are then calculated from the solid-phase concentration of the pore-blocking compound at this time point using eq 17. The liquid- and solid-phase concentrations of the strongly competing compound are then obtained using the calculated surface diffusion coefficient. With eq 16, the adsorption capacity of the target trace organic compound at any given time can be determined from the calculated concentrations of the strongly competing compound and the trace compound at the previous time point. The numerical methods used to solve the model equations are generally the same as those described previously (21).
Results and Discussion Adsorption Equilibrium and Kinetic Parameters. Singlesolute adsorption equilibrium and kinetic parameters were obtained from batch isotherm and kinetic tests conducted in organic-free water. Table 2 summarizes the single-solute adsorption parameters used in this study. The adsorption parameters of atrazine and PSS-1.8k and the adsorption equilibrium parameters of p-DCB were determined in previous studies (4, 9, 19). Figure 3 shows the single-solute adsorption isotherms of p-DCB obtained in organic-free water using both PAC A and PAC B. As shown in Table 2, PAC A and PAC B had similar adsorption capacities for p-DCB and atrazine. This could be explained by the similarity in micropore surface area of the two PACs (see Table 1). Both atrazine (MW of 215.7 Da) and p-DCB (MW of 147.1 Da) are small molecules, which will mainly adsorb in micropores. Pelekani and Snoeyink (12)
TABLE 2. Single-Solute Adsorption Parameters of the Three Adsorbates adsorbate PAC K (µg/mg)(L/µg)1/n 1/n Ds (cm2/min)
atrazine (4) A 12.1 0.41 6.2 × 10-11
B 13.8 0.44 6.3 × 10-11
FIGURE 3. p-DCB adsorption isotherms obtained in organic-free water with PAC A and PAC B.
p-DCB A 20.2 (9) 0.39 (9) 2.6 × 10-10
PSS-1.8k (19) B 26.3 (9) 0.37 (9) 2.8 × 10-10
A 0.13 0.72 3.5 × 10-11
B 116 0.07 5.0 × 10-11
FIGURE 5. Atrazine adsorption isotherms obtained with PAC B in the presence of p-DCB (C0,DCB ) 2 mg/L).
TABLE 3. EBC Parameters of p-DCB Fraction That Competes with Atrazine EBC parameters
PAC A
PAC B
(µg/mg)(L/µg)1/n
2.11 0.703 1210
10.1 0.380 477
K 1/n C0 (µg/L)
FIGURE 4. Atrazine adsorption isotherms obtained with PAC A in the presence of p-DCB (C0,DCB ) 2 mg/L). reported very good correlation between atrazine adsorption capacity and surface area in pores between 7.5 and 10 Å in width. Therefore, the micropore surface area is the most important factor that determines the adsorption capacities of these two compounds. Competitive adsorption isotherm tests were conducted for both PACs with atrazine and p-DCB using two different initial concentrations of atrazine: 5 and 100 µg/L. The p-DCB concentration used in all the competitive adsorption isotherm tests was 2 mg/L, a value that should be in the concentration range of the strongly competing fraction of NOM. The competitive adsorption isotherms for atrazine are presented in Figures 4 and 5 for PAC A and B, respectively. Also shown in Figures 4 and 5 are atrazine adsorption isotherms predicted by an IAST model based on eq 3 (22) using the single-solute adsorption equilibrium parameters of atrazine and p-DCB. As depicted in the figures, the IAST model predicted much less atrazine adsorption than was observed in the presence of p-DCB for both PACs. A plausible explanation for this difference is that p-DCB and atrazine do not have equal access to the same adsorption sites as the IAST model assumes. Since p-DCB is smaller, it is reasonable that some of it adsorbs in pores that are too small for atrazine to access. Only the fraction of p-DCB that adsorbs in pores where atrazine adsorbs will compete with atrazine for adsorption sites, resulting in an actual adsorption capacity for atrazine higher than that predicted by the IAST model. To estimate the Freundlich coefficient of the p-DCB fraction that competes with atrazine, the Equivalent Back-
ground Compound (EBC) method was used (7). The EBC method is usually used to evaluate the competitive effect of an unknown background matrix. It was used here to evaluate the competitive effect of p-DCB on atrazine because the fraction of p-DCB that competes with atrazine was unknown. The atrazine isotherms obtained with the initial concentrations of 5 and 100 µg/L were simultaneous fit with the IAST model using the program developed by Knappe (22) to determine the EBC parameters for p-DCB (K and 1/n) and the concentration of the p-DCB fraction that competes with atrazine. The results are summarized in Table 3. The EBC parameters were then used in the IAST model as the p-DCB single-solute adsorption parameters to predict atrazine adsorption isotherms at different initial concentrations. The atrazine isotherms that resulted from the EBC-IAST calculation are shown in Figures 4 and 5. The EBC-IAST model fitted the experimental data well, showing that the EBC parameters were a good measure of the competitive effect of p-DCB on atrazine within the range of PAC doses used. These EBC parameters were then used as the p-DCB input parameters in the three-component dynamic model. Adsorption kinetic parameters for p-DCB were obtained from a batch adsorption kinetic test with an initial concentration of p-DCB of 2.0 mg/L in organic-free water. The kinetic data for both PACs are presented in Figure 6 together with the HSDM fit of the data. The standard errors of the data fit were 0.05 and 0.03 for PACs A and B, respectively. The surface diffusion coefficients obtained (2.6 × 10-10 cm2/min for PAC A and 2.8 × 10-10 cm2/min for PAC B) are 1 order of magnitude higher than those of atrazine, consistent with its smaller molecular size. A comparison of these values and the lower Ds values for PSS-1.8k also presented in Table 2 demonstrates the effect of molecular size on surface diffusion coefficient. Effect of Initial Concentration on Competitive Adsorption Capacity in Batch Systems: Demonstration of the VOL. 37, NO. 13, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 6. p-DCB adsorption kinetic curves obtained with PAC A and PAC B.
FIGURE 8. Normalized atrazine and p-DCB concentrations in the effluent from the PAC/MF system operated with PAC B (Cinf,ATR ) 117 µg/L, Cinf,DCB ) 2 mg/L, PAC dose ) 20.2 mg).
FIGURE 7. Normalized atrazine and p-DCB concentrations in the effluent from the PAC/MF system operated with PAC A (Cinf,ATR ) 117 µg/L, Cinf,DCB ) 2 mg/L, PAC dose ) 20.2 mg).
FIGURE 9. Change of competitive adsorption Freundlich coefficient of atrazine during the continuous-flow PAC/MF experiment.
Simplified IAST Equation. Adsorption capacity of a trace organic compound in natural water is a function of its initial concentration in batch systems (1, 4, 7, 8, 23). In a continuousflow system, the concentration of the trace organic compound relative to the concentration of NOM in the system changes with time when it and NOM continuously accumulate on PAC. Although the IAST model can predict competitive adsorption equilibrium for different initial concentration ratios, incorporating it into a dynamic model makes the model very complex. It was shown in the Mathematical Modeling section that the competitive adsorption Freundlich coefficient of a trace organic compound could be calculated using a simplified IAST equation for a batch system (eq 12) and a continuous-flow system (eq 13). The validity of the simplification was verified by comparing the results using eq 12 with those using the IAST model (eq 3). The error was found to be less than 3% for a wide range of initial concentrations. When the IAST model was used to predict atrazine adsorption isotherms, the K values were determined using only the linear part of the predicted isotherms. This is in agreement with the assumption that Ceq , qCc, which was made when developing eq 12. Continuous-Flow Experiments. Continuous-flow experiments were conducted with a PAC/MF system using both PAC A and PAC B. The flow rate used in all experiments was 10 mL/min, resulting in a hydraulic retention time of 40 min. Analysis of atrazine and p-DCB adsorption by the membrane reactor itself when no PAC was added showed negligible adsorption of atrazine by the polycarbonate membrane and viton O-ring used. Experiments with Atrazine and p-DCB. Continuous-flow experiments were conducted to demonstrate the effect of p-DCB on atrazine adsorption capacity. The influent solution contained 117 µg/L of atrazine and 2.0 mg/L of p-DCB. The PAC dose was 20.2 mg for both carbons. Figures 7 and 8 present effluent concentrations (normalized by the influent concentrations) of atrazine and p-DCB from the PAC/MF
system for PAC A and PAC B, respectively. The COMPSORB model was used to predict atrazine and p-DCB effluent concentrations by setting the influent concentrations of the pore-blocking compound equal to zero. The single-solute p-DCB adsorption equilibrium and kinetic parameters were used to calculate p-DCB effluent concentration. The assumption was made that the effect of atrazine on p-DCB adsorption was negligible because atrazine was present at a much lower concentration and was more weakly adsorbed as shown by the K values in Table 2. When the atrazine effluent concentration was calculated, the single-solute atrazine adsorption parameters and the EBC parameters of p-DCB as given in Table 3 were used considering that only a fraction of p-DCB competes with atrazine. As shown in the figures, the model predictions for both p-DCB and atrazine concentrations agreed very well with the corresponding experimental data. Figure 9 presents the change of the equivalent Freundlich coefficient, K′, of atrazine during the adsorption process for both PACs. As discussed in the Mathematical Modeling section, the adsorption capacity of atrazine changes with the change of atrazine/p-DCB mass ratio in the system, and K′ can be calculated using eq 13. As shown in Figure 9, the predicted atrazine K′ of PAC A decreased continuously during the experiment by a total of 9% after 900 min of operation. For PAC B, however, the K′ of atrazine decreased slightly at the beginning but increased thereafter. By the end of the simulated experiment, the atrazine K′ of PAC B increased by 6%. The difference is a result of the different adsorption capacities of the two PACs for p-DCB (see the EBC parameters in Table 3), which in turn is related to their different pore size distributions. As shown in Table 1, PAC B has more micropore volume but less micropore surface area than PAC A, indicating that PAC A has more small micropores than PAC B, presumably in the size range where p-DCB and atrazine adsorb. At low concentrations of p-DCB, the competitive effect of p-DCB is smaller for PAC A than for
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FIGURE 10. Measured and model-predicted normalized concentrations in the effluent from the PAC/MF system operated with PAC A (Cinf,ATR ) 5.04 µg/L, Cinf,DCB ) 1.1 mg/L, Cinf,PSS ) 9.84 mg/L, PAC dose ) 10.1 mg).
FIGURE 11. Measured and model-predicted normalized concentrations in the effluent from the PAC/MF system operated with PAC A (Cinf,ATR ) 98.4 µg/L, Cinf,DCB ) 1.2 mg/L, Cinf,PSS ) 10.1 mg/L, PAC dose ) 20.8 mg). PAC B, as shown by the K values in Table 3, since there are more small pores that are accessible to p-DCB but not to atrazine. At higher concentrations, the competitive effect of p-DCB is greater for PAC A, indicated by the larger 1/n value shown in Table 3 since it also has more pores in the size range where both p-DCB and atrazine adsorb. Therefore, during the adsorption process in the continuous-flow experiment, the total amount of p-DCB in the reactor kept increasing relative to atrazine when PAC A was used, resulting in a continuous decrease in atrazine K′. For PAC B, the rate of accumulation of p-DCB on the carbon surface became slower than that of atrazine in the later phase of the experiment, leading to a decrease in the p-DCB/atrazine mass ratio in the system and an increase in atrazine K′. Experiments with Atrazine, p-DCB, and PSS-1.8k. Continuous-flow experiments were also conducted with influent solutions that contained all three model compounds (atrazine, p-DCB, and PSS-1.8k) using different influent concentrations and PAC doses for both PACs. Figures 10-13 present the effluent concentrations (normalized by the influent concentrations) of the three adsorbates for the four experiments performed. The three-component model developed in this study, COMPSORB, was used to predict effluent concentrations of the three adsorbates. The single-solute adsorption parameters shown in Table 2 and the EBC parameters for p-DCB shown in Table 3 were used as the input parameters for the model. When effluent concentration of p-DCB was calculated, its single-solute adsorption parameters were used. However, when the effluent atrazine concentration was calculated, the EBC parameters for p-DCB were used as if they were the single-solute equilibrium parameters for p-DCB in order to calculate competitive adsorption capacity of atrazine. Since the EBC initial concentrations of p-DCB listed in Table 2 were obtained for the actual p-DCB initial concentration of 2 mg/L, the EBC initial concentrations for other p-DCB initial concentrations
FIGURE 12. Measured and model-predicted normalized concentration in the effluent from the PAC/MF system operated with PAC B (Cinf,ATR ) 5.04 µg/L, Cinf,DCB ) 1.1 mg/L, Cinf,PSS ) 9.84 mg/L, PAC dose ) 10.1 mg).
FIGURE 13. Measured and model-predicted normalized concentrations in the effluent from the PAC/MF system operated with PAC B (Cinf,ATR ) 98.4 µg/L, Cinf,DCB ) 1.2 mg/L, Cinf,PSS ) 10.1 mg/L, PAC dose ) 20 mg). were calculated assuming that the fraction of the total p-DCB that competes with atrazine was constant. The two parameters in eq 17 (β and qcr) were determined by Li et al. (19) for atrazine on both PAC A and PAC B. Since both atrazine and p-DCB adsorb in small pores, PSS-1.8k was assumed to have the same pore-blockage effect on both p-DCB and atrazine. Therefore, the same β and qcr values were used for p-DCB. The model predictions are presented in Figures 10-13. As shown in the figures, the COMPSORB model prediction agrees very well with the experimental data. The experimental data for p-DCB have more scatter due to the higher standard deviation of the analytical method used. The good agreement between the model prediction and the experimental data demonstrates that the COMPSORB model is able to describe competitive adsorption of the three model compounds in the continuous-flow PAC/MF system by taking into account the competitive mechanisms of direct site competition and pore blockage. The implication is that if NOM can be categorized into two groups based on its molecular weight and relative adsorbability, the same modeling approach can be used for competitive adsorption of trace organic compound in natural water. The COMPSORB model will be applied in part 2 of this study (16) to investigate the effect of various operating conditions and other system parameters on trace organic compound removal in PAC/membrane systems.
Acknowledgments The authors thank L. Ding for her assistance with sample analysis and L. C. Schideman for many helpful discussions concerning this work. This research was supported by the University of Illinois, the National Science Foundation under Grant 0123281, and Suez Environment-CIRSEE (Paris, France). The opinions in this paper are not necessarily those of the sponsors. VOL. 37, NO. 13, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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Nomenclature
l
large, pore-blocking compound
C
s
small, strongly competing compound
t
target trace organic compound
liquid-phase concentration of adsorbate (µmol/ L, µg/L, or mg/L)
C0
initial liquid-phase concentration of adsorbate (µmol/L, µg/L, or mg/L)
Cc
carbon dose (mg/L)
Literature Cited
Ceff
effluent concentration of adsorbate (µg/L or mg/ L)
Ceq
equilibrium liquid-phase concentration of adsorbate (µmol/L, µg/L or mg/L)
Cinf
influent concentration of adsorbate (µg/L or mg/ L)
Ds
surface diffusion coefficient of adsorbate (cm2/ min)
Ds0
surface diffusion coefficient of adsorbate in organic-free water (cm2/min)
K
Freundlich coefficient ((µmol/mg)(L/µmol)1/n or (µg/mg)(L/µg)1/n)
K′
equivalent Freundlich coefficient for competitive adsorption ((µmol/mg)(L/µmol)1/n or (µg/ mg)(L/µg)1/n)
MPAC
total amount of adsorbent in the system (mg)
MS
total amount of adsorbate adsorbed (µmol or µg)
MT
total amount of adsorbate in the system (µmol or µg)
1/n
Freundlich exponent
q
equilibrium solid-phase concentration of adsorbate (µmol/mg, µg/mg, or mg/g)
qcr
pore-blockage parameter, critical surface concentration of PSS-1.8k at which pore blockage takes place (mg/g)
qavg
average solid-phase concentration of adsorbate (µmol/mg, µg/mg, or mg/g)
t
time (min)
V
volume of reactor (L)
(1) Qi, S.; Adham, S. S.; Snoeyink, V. L. J. Environ. Eng. (Reston, Va) 1994, 120, 202-218. (2) Campos, C.; Marin ˜ as, B. J.; Snoeyink, V. L.; Baudin, I.; Laine´, J. M. J. Environ. Eng. (Reston, Va) 2000, 126, 97-103. (3) Campos, C.; Snoeyink, V. L.; Marin ˜ as, B. J.; Baudin, I.; Laine´, J. M. Water Res. 2000, 34, 4070-4080. (4) Li, Q.; Snoeyink, V. L.; Campos, C.; Marin ˜ as, B. J. Environ. Sci. Technol. 2002, 36, 1510-1515. (5) Li, Q.; Snoeyink, V. L.; Marin ˜ as, B. J.; Campos, C. Submitted for publication in Water Res. (6) Radke, C. J.; Prausnitz, J. M. J. Am. Inst. Chem. Eng. 1972, 18, 761-768. (7) Najm, I.; Snoeyink, V. L.; Richard, Y. J. Am. Water Works Assoc. 1991, 83, 57-63. (8) Knappe, D. R. U.; Matsui, Y.; Snoeyink, V. L.; Roche, P.; Prados, M. J.; Bourbigot, M. M. Environ. Sci. Technol. 1998, 32, 16941698. (9) Li, Q.; Snoeyink, V. L.; Marin ˜ as, B. J.; Campos, C. Water Res. 2003, 37, 773-784. (10) Pelekani, C.; Snoeyink, V. L. Water Res. 1999, 33, 1209-1219. (11) Pelekani, C.; Snoeyink, V. L. Carbon. 2001, 39, 25-37. (12) Pelekani, C.; Snoeyink, V. L. Carbon. 2000, 38, 1423-1436. (13) Ebie, K.; Li, F.; Azuma, Y. Water Res. 2001, 35, 167-179. (14) Kilduff, J. E.; Karanfil, T.; Weber, W. J., Jr. J. Colloid Interface Sci. 1998, 205, 271-279. (15) Kilduff, J. E.; Karanfil, T.; Weber, W. J., Jr. J. Colloid Interface Sci. 1998, 205, 280-289. (16) Li, Q.; Marin ˜ as, B. J.; Snoeyink, V. L.; Campos, C. Environ. Sci. Technol. 2003, 37, 3003-3009. (17) Randtke, S. J.; Snoeyink, V. L. J. Am. Water Works Assoc. 1983, 75, 406-413. (18) Hand, D. W.; Crittenden, J. C.; Thacker, W. E. J. Environ. Eng. (Reston, Va) 1983, 109, 82-101. (19) Li, Q.; Marin ˜ as, B. J.; Snoeyink, V. L.; Campos, C. Submitted for publication in J. Environ. Eng. (Reston, Va). (20) Crittenden, J.; Luft, P.; Hand, D. W.; Oravltz, J. L.; Loper, S. W.; Ari, M. Environ. Sci. Technol. 1985, 19, 1037-1043. (21) Li, Q.; Marin ˜ as, B. J.; Snoeyink, V. L.; Campos, C. Submitted for publication in J. Environ. Eng. (Reston, Va). (22) Knappe, D. R. U. Ph.D. Thesis, Department of Civil Engineering, University of Illinois at Urbana-Champaign, 1996. (23) Gillogly, T. E. T.; Snoeyink, V. L.; Elarde, J. R.; Wilson, C. M.; Royal, E. P. J. Am. Water Works Assoc. 1998, 90, 98-108.
β
pore-blockage parameter (g/mg) Received for review October 16, 2002. Revised manuscript received March 29, 2003. Accepted April 23, 2003.
Subscripts i/j
3004
ith/jth adsorbate in a multi-solute system
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ES020989K
