Simplification of the IAST for activated carbon adsorption of trace organic compounds from natural water

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41 (2007) 440– 448

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Simplification of the IAST for activated carbon adsorption of trace organic compounds from natural water Shaoying Qia, Lance Schidemana, Benito J. Marin˜asa,, Vernon L. Snoeyinka, Carlos Camposb a

Department of Civil and Environmental Engineering, and Center of Advanced Materials for the Purification of Water with Systems University of Illinois at Urbana-Champaign, 205 N. Mathews Avenue, Urbana, IL 61801, USA b Suez Environment-CIRSEE, France

ar t ic l e i n f o

A B S T R A C T

Article history:

Recent studies have shown that the ideal adsorbed solution theory (IAST) coupled with the

Received 24 September 2005

concept of equivalent background compound (EBC) can be simplified for describing trace

Received in revised form

organic compound adsorption from natural water, provided that the adsorbent surface

11 September 2006

loading is dominated by competing natural organic matter. The resulting simplified IAST

Accepted 16 October 2006

has been used to reduce the complexity of kinetic models for various dynamic adsorption

Available online 29 November 2006

processes. In order to be correctly applied, however, the simplified IAST requires some

Keywords:

additional clarification and a quantitative evaluation of the deviation caused by the

Activated carbon

simplifying assumption. In this study, we derive a simple equation that relates the relative

Competitive adsorption

deviation of the simplified IAST directly to the molar ratio of EBC and trace organic

IAST

compound surface loadings and their Freundlich isotherm exponents. We then verify the

Organic compound

simplified IAST using the original IAST and experimental isotherm data from the literature

Natural water

for trace organic compounds at various initial concentrations in natural water. By further assuming that the adsorbed amount of the EBC is substantially greater than what remains in solution, a new pseudo single-solute isotherm equation is derived and a simple relation is subsequently established between the carbon dose and the remaining trace compound concentration. The results show that the adsorption capacity and relative removal of a trace organic compound at any carbon dose can be estimated directly with the simple equations developed here and data from a single isotherm experiment for the target compound conducted in the natural water of interest. & 2006 Elsevier Ltd. All rights reserved.

1.

Introduction

Activated carbon, in both granular and powdered forms, has been widely used to control trace organic contaminants in drinking water. Its effectiveness, however, depends not only on the trace compounds of concern but also on dissolved naturally occurring organic matter (NOM) present in any natural water. A major effect of NOM is its direct competition for the available adsorption surface/sites according to the Corresponding author. Tel.: +1 217 333 6961; fax: +1 217 333 6968.

E-mail address: [email protected] (B.J. Marin˜as). 0043-1354/$ - see front matter & 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.watres.2006.10.018

thermodynamics of adsorption. NOM is typically present at a concentration that is orders of magnitude higher than those of trace organic contaminants of interest and can thus result in a strong competition that significantly lowers the adsorption capacity for target trace compounds. Competitive adsorption equilibrium is usually described by the ideal adsorbed solution theory (IAST) of Radke and Prausnitz (1972). When the Freundlich equation is used for single solute isotherms, the IAST can be expressed in a

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41 (20 07) 44 0 – 448

Nomenclature

f

C1

K1

C2 C1,0 C2,0

aqueous phase concentration of trace organic compound, mM aqueous phase concentration of equivalent background compound (EBC), mM initial aqueous-phase concentration of trace organic compound, mM initial aqueous-phase concentration of the EBC, mM concentration of activated carbon, mg/L

CC hC1 iIAST aqueous-phase concentration of trace organic

compound predicted using the IAST, mM hC1 iSimplified IAST aqueous-phase concentration of trace organic compound predicted using the simplified IAST, mM

system of algebraic equations (Crittenden et al., 1985; Sontheimer et al., 1988). The IAST, however, cannot be applied directly to the natural water adsorption since competing NOM is a complex mixture of many poorly defined natural compounds. Overcoming this obstacle has been attempted by representing NOM with one or more fictive or equivalent background compounds (EBCs) (Crittenden et al., 1985; Graham et al., 2000; Knappe et al., 1998; Najm et al., 1991; Newcombe et al., 2002; Qi et al., 1992, 1994; Speth and Adams, 1993). Although the EBC-IAST method provides good representation of experimental isotherm data, its parameterization is a cumbersome process and the resulting EBC parameters are generally not unique (Najm et al., 1991; Knappe et al., 1998; Graham et al., 2000). Taking into the consideration that trace organic contaminants are present at much lower concentrations than NOM may make it possible to simplify the IAST equations, streamline the parameterization procedures and promote a better understanding of the relative significance and mathematical correlation of the EBC parameters. For a trace organic contaminant in natural water, the adsorbent surface loading can be dominated by competing NOM and the IAST can then be simplified (Graham et al., 2000; Knappe et al., 1998; Matsui et al., 2003). The resulting simplified IAST has been used to reduce the complexity of kinetic models (based on surface or pore diffusion mechanisms) for trace compound adsorption from natural water (Ding et al., 2006; Li et al., 2003; Matsui et al., 2003). These IAST simplifications make it possible to partially decouple the competitive interactions between NOM and a trace compound, which significantly increases modeling efficiency. However, the simplified IAST itself has not been compared systematically with the original IAST and past work has relied on empirical determination of when the NOM is sufficiently dominant. To ensure the proper use of simplified IAST approaches, a theoretical basis for calculating the level of approximation introduced by the underlying assumption was thus developed in this study. Another recent achievement in quantifying the NOM competition is the experimental demonstration of a direct

K2 Ka(q2) 1/n1 1/n2 RD1 q1 q2

441

molar ratio of EBC and target organic compound surface loadings Freundlich isotherm capacity parameter of trace organic compound, (mmol/mg)/(mM)1/n Freundlich isotherm capacity parameter of the EBC, (mmol/mg)/(mM)1/n partition coefficient for trace organic compound, (mmol/mg)/mM Freundlich isotherm exponent of trace organic compound Freundlich isotherm exponent of the EBC relative deviation of the simplified IAST from the IAST solid-phase concentration of trace organic compound, mmol/mg solid-phase concentration of the EBC, mmol/mg

link between the carbon dose and the relative removal of a trace organic compound (Campos et al., 2000; Cook et al., 2001; Gillogly et al., 1998; Graham et al., 2000; Knappe et al., 1998; Matsui et al., 2003; Newcombe et al., 2002; Quinlivan et al., 2005; Westerhoff et al., 2005). This important finding has been confirmed by calculations using the IAST coupled with the EBC concept. Additionally, a simple equation derived from the IAST has partially established the direct link between the carbon dose and the relative removal (Knappe et al., 1998; Matsui et al., 2003). This simple equation of practical significance, however, is limited to relatively high carbon dose applications, in which the amounts of both the EBC and the trace compound remaining in the solution are negligible compared to their respective adsorbed concentrations. A more general (but still simple) equation relating the relative removal of a trace organic compound directly to the carbon dose for the full range of carbon doses was also developed in this study.

2.

Development of IAST simplifications

2.1.

IAST coupled with EBC concept

Following Najm et al. (1991), the complex mixture of NOM that competes with the adsorption of a target organic compound from natural water is represented by a single hypothetical compound, referred to as the EBC. The EBC, characterized by its Freundlich isotherm parameters (K2, 1/n2) and initial concentration (C2,0), is assumed to impose adsorption competition to the target compound that is equivalent to the effect of background NOM. Applying the IAST to the twocomponent adsorption system at equilibrium then gives (Crittenden et al., 1985; Sontheimer et al., 1988)   q1 n1 q1 þ n2 q2 n1 , (1) C1 ¼ q1 þ q2 n1 K1 C2 ¼

  q2 n1 q1 þ n2 q2 n2 , q1 þ q2 n2 K2

(2)

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where subscripts 1 and 2 represent the target organic compound and the EBC, respectively, and the single solute isotherm for the target compound is described by the Freundlich equation (with parameters K1 and 1/n1) as well. According to Eqs. (1) and (2), adsorption competition between the EBC and the target compound is a direct result of the nonlinearity of their single solute isotherms. The EBC parameters are determined by solving Eqs. (1) and (2) as an inverse problem using isotherm data for a target organic compound in natural water (Knappe et al., 1998). As a result, the hypothetical EBC represents the fraction of NOM that competes directly with the target compound for the available adsorption surface.

2.2.

IAST simplification

If the adsorbent surface loading is dominated by the competing EBC (q2bq1) and n2 of the EBC is comparable with n1 of the target trace compound, then (n1q1) is negligible in comparison with (n2q2) and Eqs. (1) and (2) can be simplified to (Graham et al., 2000; Knappe et al., 1998; Matsui et al., 2003) 1n1 C1

q1 ¼ ðK1 n1 =n2 Þn1 q2

¼ Ka ðq2 ÞC1 ,

1=n2 ,

q2 ¼ K2 C2

(3) (4)

where Ka ðq2 Þ ¼ K1 n1 =n2


n 1

1n1 .

q2

(5)

Eqs. (4) and (3) show, respectively, that the adsorption isotherm for the EBC is the same as its single solute isotherm and adsorption capacity q1 of the trace compound linearly depends on its aqueous concentration C1 at a given q2 of the EBC. The simplified IAST of Eqs. (3) and (4) may be used conveniently to reduce the complexity of a kinetic model for trace compound adsorption from natural water because the model can be solved for the EBC independently. For a trace organic compound with linear single solute isotherm (n1 ¼ 1), Eq. (3) reduces to q1 ¼

K1 C1 , n2

(6)

where K1 is referred to as the limiting partition coefficient. Eq. (6) shows that the adsorption isotherm for the trace compound remains linear provided that the adsorbent surface loading is dominated by the EBC (q2/q1b1). This linear isotherm has a partition coefficient reduced by a factor of n2 (for n241) and is independent of K2 and C2,0 of the EBC. Blum et al. (1994) and Luehrs et al. (1996) developed simple correlations for predicting the limiting partition coefficient of a trace organic compound as single solute. Eq. (6) derived here from the IAST provides a theoretical basis for describing its linear adsorption behavior in the presence of strongly competing background compounds.

2.3.

Relative deviation of simplified IAST

The above simplification of the IAST for trace compound adsorption from natural water is based on the assumptions that the adsorbent surface loading is dominated by the EBC (q2bq1) and n1 of the trace compound and n2 of the EBC are

41 (2007) 440– 448

comparable. It is important to understand the degree of deviation from the original IAST resulting from these assumptions so that the simplified IAST equations can be properly applied. Using the molar ratio (f ¼ q2 =q1 ) of the EBC and trace compound surface loadings, Eqs. (1) and (3) are rewritten, and then the relative deviation (RD1) can be expressed as RD1 ¼ 1 

hC1 iSimplified hC1 iIAST

IAST

¼1

1 þ ð1=f Þ 1 þ ðn1 =n2 Þð1=f Þ


n1 ,

(7)

where hC1 iIAST and hC1 iSimplified IAST are predicted by the original and the simplified IAST, respectively. Eq. (7) shows that the relative deviation of the simplified IAST for predicting the trace compound aqueous phase concentration depends on molar ratio f ¼ q2 =q1 as well as n2 of the EBC and n1 of the trace compound. With Eq. (7), different levels of approximation can be considered such that the accuracy requirements for the simplified IAST can be tailored to the particular needs of different applications. In Section 4, we will examine the minimum molar ratio of surface loadings that allows the simplified IAST to satisfy a given (acceptable) deviation from the IAST at various n1 and n2 values.

2.4.

Pseudo-single solute isotherm

When the adsorbed amount of the competing EBC is much greater than what remains in solution, the mass balance for the EBC (CCq2 ¼ C2,0C2, where C2,0 is the initial concentration) over a batch isotherm bottle may be approximated by (Knappe et al., 1998) q2 

C2;0 CC

(8)

ðCC 40Þ.

Given that the EBC dominates the surface loading (q2bq1) and n1 and n2 are comparable, Eq. (3) can be combined with the mass balance for the trace compound (q1CC ¼ C1,0C1, where C1,0 is the initial concentration) so that the adsorption capacity for the trace compound can be related to the carbon dose applied q1 ¼

C1;0 n 1

CC þ ½n2 =ðn1 K1 Þn1 q21

.

(9)

Eq. (8) overestimates the surface loading (q2) for the EBC at a given carbon dose CC. If q2 in Eq. (9) is replaced with Eq. (8), then the EBC competition on trace compound adsorption will be overestimated, and consequently the adsorption capacity for the trace compound will be underestimated (which can be readily shown by differentiating Eq. (9) with respect to q2 at a given CC). Substituting Eq. (8) into (9), and subsequently eliminating CC using the mass balance for the trace compound yields the pseudo-single solute isotherm ð1n1 Þ=n1 ðC

q1 ¼ K1 ðn1 =n2 ÞC2;0

1;0

1=n1

 C1 Þðn1 1Þ=n1 C1

(10)

which establishes a direct link between the adsorbed and aqueous-phase concentrations for a trace organic compound in natural water. Eq. (10) shows that the strongly competing EBC influences the trace compound adsorption through the collective effect of its C2,0 and 1/n2. At C1ooC1,0, Eq. (10)

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reduces to a form similar to the Freundlich equation   C2;0 ð1n1 Þ=n1 1=n1 C1 ðC1 5C1;0 Þ. q1 ¼ K1 ðn1 =n2 Þ C1;0

2.5.

(11)

Direct link between relative removal and carbon dose

For an ideal batch reactor or a continuous stirred tank reactor (CSTR) at adsorption equilibrium, combining the pseudosingle solute isotherm of Eq. (10) with the trace compound mass balance relates the relative remaining concentration directly to the carbon dose applied n 1

1 ½n2 =ðn1 K1 Þn1 C2;0 C1 ¼ n . n C1;0 C 1 þ ½n2 =ðn1 K1 Þ 1 Cn1 1 C 2;0

(12)

Eq. (12) shows that for a trace compound with Freundlich 1/ n1o1, an increase in initial concentration of the EBC (C2,0) always results in a decrease in the trace compound removal (1C1/C1,0); and when comparing two EBCs with different Freundlich-1/n2 values at a given C2,0, the one with a smaller 1/n2 value always has a more negative impact on the trace compound removal. If a desirable treatment objective (C1/C1,0) is set, then Eq. (12) can be rearranged to calculate the required carbon dose as CC ¼

n2 ð11=n1 Þ C ðC1;0 =C1  1Þ1=n1 . n1 K1 2;0

(13)

Since the kinetic effects have been ignored, the carbon dose calculated with Eq. (13) is the minimum amount needed to achieve the given treatment (C1/C1,0). As the carbon dose (CC) goes to zero and infinity, Eq. (12) approaches the correct physical limits of 1 and zero, n respectively. Additionally, if CC is sufficiently large that CC1 b n1 n1 1 ½n2 =ðn1 K1 Þ C2;0 , then Eq. (12) reduces to the result of Knappe et al. (1998) n1

½n2 =ðn1 K1 Þ C1 ¼ n C1;0 CC1

n1 1 C2;0

(14)

which is a special case of Eq. (11). Isotherm data for a trace organic compound in natural water may be fitted to the following logarithmic form of Eq. (12): ð11=n1 Þ 

ln½ðC1;0 =C1 Þ  1 ¼ n1 ln CC  n1 ln½n2 =ðn1 K1 ÞC2;0

(15)

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which gives a straight line with a slope of n1 and an intercept ð11=n Þ of n1 ln½n2 =ðn1 K1 ÞC2;0 1 . In Eq. (15), the two EBC parameters ð11=n Þ (C2,0 and 1/n2) are correlated by the quantity of n2 C2;0 1 and therefore, their individual values could not be resolved independently. Once the two parameters, n1 and ð11=n Þ n2 =ðn1 K1 ÞC2;0 1 are known, Eq. (12) or (13) can be readily used to calculate the relative removal of the trace compound from natural water at any carbon dose.

3.

Data sources used for verifications

Adsorption isotherm data selected from several literature sources cover four trace organic contaminants of environmental relevance: atrazine, methylisoborneol (MIB), estrone and simazine at typical initial concentrations. The atrazine (Campos et al., 2000) and the MIB (Gillogly et al., 1998) data sets were used to verify both the simplified IAST and the pseudo-single solute isotherm equations on the same basis. The estrone data (Chang et al., 2004) were used to show that the adsorption isotherm for a trace compound with a linear single solute isotherm remains linear in the presence of strongly competing background compounds. Finally, the simazine data (Matsui et al., 2003) were used to demonstrate how to determine the parameters and predict the equilibrium removal from a single isotherm experiment conducted for the trace compound in natural water. Table 1 summarizes the single solute isotherm parameters and the EBC parameters determined by Campos et al. (2000), Gillogly et al. (1998), and Matsui et al. (2003). Concentration parameters are expressed in molar units, as required by the IAST and simplified IAST equations.

4.

Results and discussion

4.1.

Deviation analysis for the simplified IAST

Eq. (7) can be used to determine the relative deviation of the simplified IAST from the original IAST caused by the underlying assumptions. The analysis here is focused on determining the minimum surface loading ratio, fmin ¼ (q2/q1)min that allows the simplified IAST to satisfy a given (acceptable) deviation for trace organic compounds with different n1 at

Table 1 – Isotherm parameters of trace organic compounds and competing EBCs Parameters

Initial concentration (mM) Freundlich-K (mmol/mg)/(mM)1/n Freundlich-1/n

1

2

3

Atrazine

EBC

MIB

EBC

Simazine

EBC

N/A 0.56 0.44

1.07 1.23 0.53

N/A 2.1  102 0.49

3.4  102 5.3  102 0.49

N/A 0.64 0.41

3.5 1.39 0.61

1. WPH carbon; Central Illinois ground water (Campos, 1999). 2. Watercarb carbon; Lake Michigan Water (Gillogly et al., 1998). 3. Coal-based carbon; River water (Matsui et al., 2003).

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100 (n1/n2)= 3

(n1/n2)= 2

fmin

(n1/n2)= 1

(n1/n2)= 0.5

10

(n1/n2)= 0.1

(n1/n2)= 0.2

(n1/n2)= 0.5 1 1

2

3 n1

4

5

Fig. 1 – Minimum molar ratio of EBC and trace compound surface loadings that allows the simplified IAST to satisfy a 10% deviation from the original IAST.

various (n1/n2). Typical 1/n1 values are in the range of 0.2–1 (n1 ¼ 125) (Snoeyink and Summers, 1999; Speth and Adams, 1993). To examine the effect of assuming that n1 and n2 are comparable, (n1/n2) is allowed to vary from 0.1 to 3. Past research has shown that when comparing experimental isotherm data with predictions based on the original IAST coupled with the EBC concept, typical values for the average error can be expected to exceed 10%. For example, Crittenden et al. (1985) used one or two theoretical (fictive) components to represent three ‘‘unknown’’ composition mixtures that actually consisted of known organic compounds with known single solute isotherm parameters. The average errors of fits and predictions by the IAST for the aqueous phase concentrations of different target organic compounds were found to be in the range of 3.7–80.7%, and over 20% for half of the 18 cases investigated. Recognizing the typical errors inherent in comparing the original IAST with experimental results, a maximum deviation criterion of 10% was targeted for the allowable difference between trace compound aqueous-phase concentrations predicted using the simplified IAST and the original IAST, which was on the low end of the range of experimentally observed IAST relative errors. However, Eq. (7) is quite general and can be used to determine the minimum molar ratio (fmin) that allows the simplified IAST to satisfy other deviation criterion for different applications. Note that according to Eq. (7), positive (+) and negative () relative deviations correspond to underestimation and overestimation of /C1SIAST by the simplified IAST, respectively. Accordingly, the maximum deviation criterion used in this paper was 710%. Fig. 1 shows the minimum surface loading ratio, fmin ¼ (q2/q1)min that allows the simplified IAST of Eq. (3) to satisfy a 10% deviation for predicting aqueous phase concentrations of trace organic compounds with different n1 values and at various (n1/n2) ratios. For n1 and (n1/n2) in the ranges of 1–5

and 0.1–3, respectively, fmin varies within the range of 1–130. In other words, as long as the NOM or EBC dominates over the trace compound by a factor of 130 or more on the adsorbent surface, then the simplified IAST introduces an error of less than 10% for the full range of expected n1 and n2 values. However, the required level of EBC predominance is much lower for more typical n1 and n2 values. For instance, in the range of n1 ¼ 1–3, fmin required to satisfy a 10% deviation is less than 50 if (n1/n2)p2 and less than 20 if (n1/n2)p1. The dependence of fmin ¼ (q2/q1)min on n1 and (n1/n2) can follow three distinct trends as shown in Fig. 1. When (n1/n2) is relatively low, such as 0.1 or 0.2, fmin decreases with increasing n1 and (n1/n2). When (n1/n2) is high, such as above 1, fmin increases with increasing n1 and (n1/n2). In between these two opposite trends, such as at (n1/n2) ¼ 0.5, changes in fmin with increasing n1 switches from decreasing at low n1 values to increasing at high n1 values. At a given (n1/n2), a decreasing fmin with increasing n1 is accompanied by a negative () relative deviation while an increasing fmin with increasing n1 is accompanied by a positive (+) relative deviation. To further examine the relation between the relative deviation and the molar ratio of surface loadings (f ¼ q2/q1) at various n1 and (n1/n2) values, the term ½1 þ ðn1 =n2 Þð1=f Þn1 in Eq. (7) can be expanded at ðn1 =n2 Þð1=f Þ ¼ 0 using a Taylor’s series. Given that f ¼ q2/q1b1 and n1on2 or n1 and n2 are comparable, then (n1/n2)(1/f)51. Truncating terms higher than the first-order derivative in the Taylor’s expansion gives ½1 þ ðn1 =n2 Þð1=f Þn1  1 þ ðn21 =n2 Þð1=f Þ.

(16)

Subsequently, substituting the above result into Eq. (7) yields RD1 

½ðn21 =n2 Þ  1ð1=f Þ 1 þ ðn21 =n2 Þð1=f Þ

(17)

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445

Fig. 2 – Adsorption isotherms for atrazine in Central Illinois groundwater. (Data shown in symbols and the IAST predictions are from Campos et al., 2000).

Fig. 3 – Adsorption isotherms for MIB in Lake Michigan water. (Data shown in symbols and the IAST predictions are from Gillogly et al., 1998).

which shows that RD1 is positive (+) when ðn21 =n2 Þ41 and negative () when ðn21 =n2 Þo1. As mentioned before, positive (+) and negative () relative deviations correspond to underestimates and overestimates by the simplified IAST, respectively. The value of ðn21 =n2 Þ is typically greater than 1 and the simplified IAST then predicts an aqueous concentration for the trace compound that is lower than that by the original IAST. Eq. (7) also shows that RD1 is inversely proportional to f ¼ q2 =q1 when ðn21 =n2 Þð1=f Þ51, which is true in most practical applications. In these situations, if the acceptable deviation is increased (relaxed) by a factor of 2, then the required f ¼ q2 =q1 can be reduced by approximately half.

4.2.

Verification of simplified IAST

Figs. 2 and 3 present natural water isotherm data for atrazine and MIB, respectively, and a comparison of the simplified IAST of Eq. (3) to the original IAST of Eq. (1). The parameters in Table 1, optimized for the original IAST, were used as input data for both Eqs. (1) and (3). As shown in the two figures, the simplified IAST predictions follow reasonably close to those of the original IAST for both atrazine and MIB at different initial concentrations. The degree of deviation between the two IAST equations decreases with decreasing initial concentration of the trace compound because the assumption that the

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20 q1= 1.10C1 (r2= 0.96; Single Solute) q1= 0.27C1 (r2= 0.68; Simplified IAST of Eq. (6))

15

q1 (ng/mg)

Single Solute

10

5

Secondary Effluent 0 0

5

10 C1 (ng/L)

15

20

Fig. 4 – Adsorption isotherms for estrone as single solute and in secondary effluent. (Data shown in symbols and the single solute isotherm fit are from Chang et al., 2004).

EBC dominates the surface loading is more valid. In certain cases, the two models agree almost exactly (i.e., initial concentrations, C1,0, of 2.0 mg/L for atrazine and 149 ng/L for MIB) and the broken-dashed lines of Eq. (3) fall on top of the solid lines of Eq. (1). In comparison to the experimental isotherm data, the average relative errors of the simplified IAST are 20% and 26% for atrazine at C0,1 ¼ 2.0 and 54.7 mg/L and 15% and 18% for MIB at C0,1 ¼ 149 and 1245 ng/L. These relative errors are higher than but comparable with those of the original IAST, which equaled 20% and 10% for atrazine at C0,1 ¼ 2.0 and 54.7 mg/L and 15% and 11% for MIB at C0,1 ¼ 149 and 1245 ng/L. Consistent with Eq. (17), the relative deviation of the simplified IAST is positive, or in other words, the simplified IAST underestimated aqueous phase C1 in comparison to the original IAST for both atrazine and MIB in Figs. 2 and 3. The average relative deviations between the simplified and the original IAST increase from 0.9% to 25% for atrazine and from 2% to 8% for MIB as their initial concentrations increase from 2.0 to 54.7 mg/L and from 149 to 1245 ng/L, respectively. The relative deviation is thus the main contributing factor for the increasing errors of the simplified IAST with increasing initial concentration of a target trace compound. Another factor that might contribute to the relative higher errors is that the EBC parameters used as input data by the simplified IAST were optimized for the original IAST itself. If a trace organic compound has a linear single solute isotherm, Eq. (6) predicts that the adsorption isotherm for the trace compound remains linear when the adsorbent surface loading is dominated by competing background compounds. Fig. 4 shows an example of this special situation using the data of Chang et al. (2004) for estrone adsorption from a secondary effluent. At the extremely low equilibrium concentrations of less than 20 ng/L, the single solute isotherm of

estrone is apparently linear with limiting partition coefficient K1 ¼ 1.10 L/mg and the isotherm for estrone in the secondary effluent with initial concentrations C1,0 ¼ 18–22.2 ng/L is also apparently linear. The high concentration of competing background compounds (13.2 mg total organic carbon/L), however, reduces the partition coefficient for estrone from 1.10 to 0.27 L/mg. These results are consistent with Eq. (6), which can be used to calculate a 1/n2 value of 0.25 for the EBC of the secondary effluent. This 1/n2 value falls in the typical range of 0.2–0.6 obtained by the conventional EBC procedure (Campos, 1999; Gillogly et al., 1998; Graham et al., 2000; Qi et al., 1992, 1994; Quinlivan et al., 2005; Speth and Adams, 1993). Eq. (6) provides a simple means for determining a Freundlich-1/n2 value of the EBC when the adsorption isotherms of a trace organic compound are linear both as single solute and in the presence of competing background compounds. The 1/n2 value from Eq. (6) is uniquely determined because it is no longer correlated with initial concentration C2,0 and Freundlich K2 of the EBC.

4.3.

Verification of pseudo-single solute isotherm

Predictions for atrazine and MIB with the pseudo-single solute isotherm of Eq. (10) are also shown in Figs. 2 and 3, respectively. Again, the EBC parameters in Table 1, optimized for the original IAST itself, were used with Eq. (10). As shown in the two figures, Eq. (10), using only two EBC parameters (1/n2 and C2,0), is able to approximate the original IAST of Eq. (1) as well as the isotherm data for both atrazine and MIB at different initial concentrations in natural water. The two assumptions: q2/q1b1 and q2EC2,0/CC cause Eq. (10) to deviate from the original IAST in opposite directions. As discussed earlier on Eq. (3), assuming q2/q1b1 will typically

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41 (20 07) 44 0 – 448

1

C1/C1,0

0.8

0.6 Data (C1,0=94 µg/L) 0.4

Data (C1,0=29 µg/L) Eq. (12) with best-fit parameters Eq. (12) with calculated parameters Eq. (14) of Knappe et al. (1998) IAST (C1,0=94 µg/L)

0.2

0 0.1

1 CC (mg/L)

10

Fig. 5 – Relative removal of simazine from river water. (Data shown in symbols and the IAST prediction are from Matsui et al., 2003).

overestimate q1 for a trace compound, with the effect being more pronounced at higher C1,0. In contrast, assuming q2EC2,0/CC will underestimate q1, especially at C1 near C1,0. For MIB in Fig. 3, Eqs. (10) and (3) give almost identical predictions, even at C1 near C1,0. The lack of impact by assuming q2EC2,0/CC agrees with the IAST in that MIB competes poorly with the EBC near C1,0 (shown by a sharp drop in q1 to the right of the maximum in Fig. 3). For atrazine in Fig. 2, the effect of assuming q2EC2,0/CC is more visible as Eq. (10) deviates from Eq. (3) with C1 approaching C1,0, especially at low C1,0 ¼ 2.0 mg/L. This result coincides with the IAST in that atrazine competes well with the EBC near C1,0 (as shown by the lack of a sharp drop in q1 to the right of the maximum in Fig. 2). The ability of Eq. (10) with two well-defined parameters: 11=n 1/n1 and ½n2 =ðn1 K1 ÞC2;0 1 ] to approximate the original IAST, as demonstrated in Figs. 2 and 3, suggests that K2 of the EBC plays a much less important role than C2,0 and 1/n2, and also shows that C2,0 and 1/n2 can be correlated for describing trace compound adsorption from natural water. Isotherm data with both low and high initial trace compound concentrations (C1,0 ) as well as C1 close to C1,0 (using low carbon doses) are needed to reveal the possible contribution of K2 and to determine the actual individual values of C2,0 and 1/n2 by the EBC method. Eq. (12) or (13) establishes a direct link between the carbon dose (CC) and the relative remaining concentration (C1/C1,0) of a trace organic compound in natural water. This carbon dose defines the minimum adsorbent usage rate for achieving a given treatment objective (C1/C1,0) in a batch reactor or a CSTR. Fig. 5 shows an example for simazine adsorption from river water (Matsui et al., 2003). Using Eq. (15) to fit the isotherm data for an initial simazine concentration, C1,0 ¼ 11=n 29 mg/L, the two parameters, n1 and ½n2 =ðn1 K1 ÞC2;0 1 were determined at 2.17 and 1.84 mg/L (r2 ¼ 0:997), respectively.

Those values are smaller but comparable with n1 ¼ 2:44 and 11=n ½n2 =ðn1 K1 ÞC2;0 1 ¼ 2:20 mg=L calculated using the isotherm parameters of Matsui et al. (2003) in Table 1. With the best-fit 11=n values of n1 ¼ 2:17 and ½n2 =ðn1 K1 ÞC2;0 1 ¼ 1:84 mg=L, Eq. (12) describes the simazine removal at all carbon doses, even when C1,0 increases from 29 to 94 mg/L, as shown in Fig. 5. In contrast, the existing model of Eq. (14) (Knappe et al., 1998) describes the simazine removal only at higher carbon doses. As also depicted in Fig. 5, Eq. (12) with the calculated values of 11=n ½n2 =ðn1 K1 ÞC2;0 1 ¼ 2:20 mg=L and n1 ¼ 2:44 agrees well with the original IAST at C1/C1,0o0.5 and then consistently predicts higher remaining concentrations than the IAST at C1/C1,0X0.5. This occurs because of the assumption q2EC2,0/CC that overestimates the EBC competition. However, the maximum difference between Eq. (12) and the original IAST is less than 15% and the predictions by Eq. (12) are actually closer to the experimental data than to the original IAST predictions at C1/C1,0X0.5. Both Eq. (12) and the IAST approach the correct limit of C1/C1,0 ¼ 1 as CC goes to zero. The ability of Eq. (12) to approximate the IAST for simazine removal supports the previous conclusions that K2 of the EBC is much less important than C2,0 and 1/n2 and that C2,0 and 1/n2 can be correlated parameters that are difficult to determine independently.

5.

Conclusions

In this study, we presented a unified analysis and application of the IAST simplifications for describing trace compound adsorption from natural water onto activated carbon. The underlying simplifying assumptions were quantitatively examined and the resulting simplified IAST equations were verified using the original IAST and isotherm data in the literature.

ARTICLE IN PRESS 448

WA T E R R E S E A R C H

To ensure the proper use of the simplified IAST, an analytical expression was derived for determining its relative deviation (RD) from the original IAST. For a target trace compound with n1 in the typical range of 1–3, the minimum molar ratio of f ¼ q2 =q1 needed to satisfy a 10% RD criterion is less 50 if n1/n2p2 and less than 20 if n1/n2p1. If the acceptable deviation is relaxed (increased) by a factor of 2, then the required f ¼ q2 =q1 can be reduced by approximately half (1/n2 and 1/n1 are the Freundlich isotherm exponents and q2 and q1 are the surface loadings of the EBC and the target compound, respectively). A pseudo single-solute isotherm equation was derived from the simplified IAST and an explicit relation was subsequently established between the carbon dose and equilibrium removal. The results showed that Freundlich K2 of the EBC is much less important than initial concentration C2,0 and 1/n2 of the EBC and also showed that C2,0 and 1/n2 could be correlated for describing trace compound adsorption from natural water. Additionally, the adsorption capacity and minimum adsorbent usage rate can be estimated directly with the simple equations developed here and data from a single isotherm experiment for the trace compound conducted in the natural water of interest.

Acknowledgments This work was partially supported by Suez Environment and by The WaterCAMPWS, a Science and Technology Center of Advanced Materials for the Purification of Water with Systems under the National Science Foundation agreement number CTS-0120978. Valuable comments by the three anonymous reviewers are also greatly appreciated. R E F E R E N C E S

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