Prediction of the Adsorption Capacity for Volatile Organic Compounds Onto Activated Carbons By the Dubinin-Radushkevich-Langmuir Model

By Hung, Hsu-Wen; Lin, Tsair-Fuh

ABSTRACT

Prediction of the adsorption capacity for volatile organic compounds (VOCs) onto activated carbons is elucidated in this study. The Dubinin-Radushkevich (D-R) equation was first used to predict the adsorption capacity of nine aromatic and chlorinated VOCs onto two different activated carbons. The two key parameters of the D-R equation were estimated simply from the properties of the VOCs using quantitative structure-activity relationship and from the pore size distribution of the adsorbent. The approach based on the D-R equation predicted well the adsorption capacity at high relative pressures. However, at the relative pressures lower than ~1.5 10^sup -3^, the D-R approach may significantly overestimate adsorption capacity. To extrapolate the approach to lower relative pressures, the integration of the D-R equation and the Langmuir isotherm, called the D-R-L model, was proposed to predict adsorption capacity over a wide range of relative pressures of VOCs. In this model, the Langmuir isotherm parameters were extracted from the predicted D-R isotherm at high relative pressures. Therefore, no experimental effort was needed to obtain the parameters of the D-R- L model. The model successfully predicted the adsorption capacity of aromatic and chlorinated hydrocarbons tested onto BPL and Sorbonorit B carbons over relative pressures ranging from 7.4 10^sup -5^ to 0.03, suggesting that the model is applicable at the low relative pressures of VOCs often observed in many environmental systems. In addition, the molecular size of organic compounds may be an important factor affecting the adsorption capacity of activated carbons. For BPL carbon, an ultramicroporous adsorbent, the limiting pore volume W^sub o^ of the D-R equation decreased when the kinetic diameter of the adsorbate was larger than 6 . However, for Sorbonorit B carbon, no reduction of W^sub o^ was found, suggesting that the W^sub o^ may be related to the pore size distribution of the adsorbents, as well as to their molecular size. This size exclusion effect may play an important role in predicting the adsorption capacity of VOCs onto microporous adsorbents in the D-R- L model and in the corresponding D-R equation.

(ProQuest-CSA LLC: … denotes formulae omitted.)

INTRODUCTION

Volatile organic compounds (VOCs) are often present in many industrial and environmental systems. The emission of VOCs into the environment must be controlled, because many organic chemicals are toxic and/or carcinogenic. Activated carbon adsorption is one of the most commonly used processes, and it processes the advantages of high removal efficiency at low concentrations, entailing low energy costs, being reusable, and offering the possibility of product recovery.1,2 To design a costeffective adsorption device, the adsorption capacity for target compounds must be understood in advance, because it is one of the most important factors governing the service life of the device. The effort required to obtain the adsorption capacity through experiments may be markedly high, because these are costly and time consuming. The cost may largely increase while the organic vapors treated are at low concentrations, because the time needed to reach equilibrium would increase substantially, 3 and it may become more difficult to analyze low concentrations of VOCs. Environmental systems with a low concentration of organic vapors, such as air purifiers in indoor air control systems, air stripping towers in drinking water treatment systems, and in situ sparging devices in groundwater remediation systems, are widespread. Other than cost considerations, because there exist many VOCs and a variety of activated carbons, it may be impractical to measure for all combinations of VOC/ carbon systems. Therefore, a reliable prediction model of equilibrium capacity based on minimal or even no experimental work is always of interest in designing activated carbon adsorption devices.

The Dubinin-Radushkevich (D-R) equation is based on well-known Polanyi’s potential and has been widely used to estimate the adsorption capacity for VOCs onto microporous adsorbents, such as activated carbon.1,2,4-7 The D-R equation requires only two parameters to predict the adsorption capacity, and when used with other estimation methods for the parameters, no experimental inputs are required for the prediction. According to the D-R equation, the adsorption capacity (W), expressed as the adsorbed liquid volume per unit mass of adsorbent, is related to the adsorption potential (A) as given by:4

W = W^sub o^ exp(-kA^sup 2^) (1)

and

A = RT ln(P^sub o^/P) (2)

where W is the volumetric adsorption capacity; W^sub o^ is the limiting pore volume; k is the D-R equation parameter for the target adsorbate; R is the universal gas constant; T is the absolute temperature; P^sub o^ is the saturated vapor pressure at temperature T; and P is the partial pressure of the adsorbate. By selecting a reference adsorbate, the adsorption capacity of a target compound onto an adsorbent can be estimated by means of the following equation:

… (3)

where k^sub s^ is the value of k for the reference adsorbate, and β is the affinity coefficient for the target adsorbate. The affinity coefficient is obtained by calculating the ratio of a specific property value, such as molar volume, for the target adsorbate to that of the reference compound.

To apply the D-R equation to the prediction of the adsorption capacity, the parameters W^sub o^ and k (or k^sub s^ and β) must be obtained in advance. W^sub o^ has been shown to relate to the microporous structure of the adsorbent and is generally assumed to be a constant for a given type of activated carbon regardless of which adsorbates are used.6-8 The value of W^sub o^ can be obtained using one reference adsorbate such as benzene, and it can be applied to the same adsorbent.6 Urano et al.6 developed an approach to predict W^sub o^ from the pore size distribution (PSD) of different activated carbons. It was found that the PSD-estimated W^sub o^ is equal to a volume of pores of <32 plus 0.055 (in cubic centimeters per gram unit) for the activated carbons studied.6 Based on this approach, the W^sub o^ may be estimated based merely on the PSD data for the activated carbon. Although this approach is simple and no experimentation is required, it has not been used to any great extent in the study of the D-R equation.

Unlike W^sub o^, the k value is independent of the type of activated carbons and is only a function of the adsorbate. 6,9,10 As shown in eq 3, the k (= k^sub s^/β^sup 2^) value can be estimated on the basis of the parameters k^sub s^ and β. In determining the k^sub s^ value, a reference adsorbate and experimentation are generally required.5 For the estimation of β values, three approaches have been proposed, including the methods of the molar volume, the molecular parachor, and the electronic polarization.5 Although these three values may be estimated and/or experimentally measured, the selection of an appropriate reference adsorbate and the estimation of β may prove to be an arbitrary choice.5,6

To avoid the choice of the reference adsorbate and to reduce efforts in experimentation, several estimation methods, such as the quantitative structure-activity relationship (QSAR), have been proposed to predict the k value for VOC/carbon systems.9,10 Nirmalakhandan and Speece9 have developed a simple equation to estimate k values using the QSAR model, in which no reference adsorbates and experimental inputs are required. In their study, a modified, first-order molecular connectivity index (MCI),^sup 1^x^sup v^, was used to correct the QSAR-based k values for different chemicals adsorbed onto six activated carbons. The fitted equation can be expressed as follows9:

logk ~ 1.585 0.442^sup 1^x^sup v^ (4)

where a unit of k is equal to 10^sup -8^ mol^sup 2^/cal^sup 2^. Similar approach using ^sup 1^x^sup v^ and the affinity coefficient was also proposed in the studies of Qi et al.11 and Ramirez et al.12 The MCI can be estimated on the basis of the number of chemical bonds and valance values of the organic chemicals. A detailed description of MCI calculation procedures can be found in Nirmalakhandan and Speece.9

Although W^sub o^ and k may be successfully estimated by means of the PSD of the adsorbents and the QSAR model, respectively, the possibility of using a combination of the D-R equation and the PSD- estimated W^sub o^ and QSAR-based k has scarcely been investigated. In addition, the application of the QSAR/D-R model has been limited to the conditions of relatively high VOC relative pressures. At lower VOC pressures, the D-R equation may need to be modified, and the model may not describe the adsorption capacity well.8,13-16 To our knowledge, no reports have extensively discussed the pressure range applicable to the QSAR/D-R model, and none have extrapolated the model for use in conditions of lower pressure ranges in environmental systems. In this study, a modified version of the QSAR/ D-R model is proposed to predict the adsorption capacity of VOC/ activated \carbon systems at a wide range of vapor pressures. The model is a combination of the D-R equation and the Langmuir isotherm, called the D-R-L model, and is used to amend the inadequacies of the D-R equation at low pressures. The QSAR-based k and the PSD-estimated W^sub o^ are incorporated into the model for the purpose of predicting the adsorption capacity of nine aromatic and chlorinated VOCs onto two different activated carbons. In addition, the effects of the molecular sizes of the VOCs tested on the precision of the model are also discussed.

EXPERIMENTAL WORK

Adsorbents and Adsorbates

The granular activated carbons used in this study were BPL from Calgon Carbon Corp. and Sorbonorit B from Norit Activated Carbon Co. The virgin samples of bituminous coal-based BPL activated carbon were of 4 10 U.S. mesh size, whereas those of Sorbonorit B were activated extruded carbon with a particle diameter of 4 mm. The virgin samples were crushed and sieved to the desired particle size of between 1.40 and 1.70 mm (12 14 U.S. mesh size). The surface area and PSD of the two carbons were measured using the nitrogen adsorption method at 77 K (ASAP 2010, Micromeritics Inc.). The Brunauer-Emmett- Teller (BET) surface areas of BPL and Sorbonorit B carbons were 1051 and 1131 m2/g, respectively. The volumes of the micropore (pore width [w] < 20 ), mesopore (20 < w < 500 ), and macropore (w > 500 ) were 0.349, 0.129, and 0.003 cm^sup 3^/g, respectively, for BPL carbon, and 0.377, 0.155, and 0.004 cm^sup 3^/ g, respectively, for Sorbonorit B carbon. It must be noted that the micropore, mesopore, and macropore volumes were calculated by using the Micropore (MP) method17 and the Barret-Joyner- Halenda method18 from nitrogen desorption isotherm at 77 K. Figure 1,a and b, displays the PSDs of the two carbons, indicating that the pores of both the BPL and Sorbonorit B carbons are mainly of the microporous adsorbents, among which BPL carbon contains a higher proportion of ultramicropores (w < 7 ) than that of Sorbonorit B carbon. The sizes of micropores of BPL carbon are mainly from less than ~6 to 10 , and a large portion of the pores are <6 . Sorbonorit B possesses a wider ranging PSD, from 6 to 10 , of which the major portion is nearly at 7 . For pore sizes <10 , the pore volume of BPL carbon (0.240 cm^sup 3^/g) is slightly smaller than that of Sorbonorit B carbon (0.270 cm^sup 3^/g).

Two groups of VOCs, aromatic and chlorinated hydrocarbons, were selected as representative organic compounds and include benzene, toluene, p-xylene, o-xylene, methyl tert-butyl ether (MTBE), 1,3,5- trimethylbenzene (mesitylene), trichloroethene (TCE), tetrachloroethane (PCE), and 1,1,2,2-tetrachloroethane (1,1,2,2- TCA). These compounds are highly toxic and commonly found in many environmental systems. Mesitylene and 1,1,2,2-TCA of reagent grade were purchased from Tokyo Chemical Industry Co. and Showa Chemicals Inc., Japan, respectively. The other seven chemicals were of analytical grade and purchased from Merck Ltd., Germany. All of the chemicals were used in the experiments without further purification.

Procedures

Adsorption capacity for organic compounds onto activated carbons was measured either by an electrobalance apparatus with a precision of 1 g (D200, Cahn Inc.) or by differential adsorption bed (DAB). A more detailed description of experimental concepts and procedures similar to those used in this study may be found elsewhere. 3,19 The adsorption capacities were tested using both the electrobalance and DAB methods for several VOCs at the same concentration. The adsorption capacities obtained from both methods were almost the same for the same VOC at the same concentration, indicating a consistency between the two techniques used. The electrobalance and DAB were placed into a temperature-controlled chamber. The temperature of the chamber was maintained at 25 1 C for all of the experiments. The oven-dried carbon of ~0.02 g was placed on a stainless steel basket of the electrobalance, whereas ~0.0035 g was put within a bed of glass beads inside the DAB. The VOC-loaded air was prepared by passing high purity, hydrocarbon- free (HC-free) air through a diffusion vial or bubbler containing a pure chemical. The total hydrocarbon content (as methane) in the HC-free air is <0.1 ppmv, whereas that of water vapor is <0.1% relative humidity. The saturated vapor pressure at operational temperatures was estimated using the Wagner equation20:

… (5)

where P^sub o^ is the saturated pressure (bar); Pc is the critical pressure (bar); a, b, c, and d are the constants; x is 1 – T/Tc; T is the temperature (K); and Tc is the critical temperature (K). The physical constants and corresponding coeffi- cients in eq 5 were obtained from the study by Reid et al.20 The VOC concentration was analyzed by means of a gas chromatograph (HP-6890, Hewlett Packard) equipped with a flame-ionization detector, an electronic capture detector, and a DB-624 capillary column (0.32 mm 30 m, 1.8 m in film thickness). The oven temperature was held at 38 C for 2 min, followed by an increase to 90 C at a rate of 10 C/min; it was held at 90 C for 2 min, and then increased to 200 C at a rate of 30 C/min, at which it was held for 2 min. The adsorption capacity of activated carbons for the compounds tested was calculated on the basis of either weight measurements in the case of the electrobalance method or the desorbed VOC mass in the case of the DAB method.

RESULTS AND DISCUSSION

Adsorption Isotherms

The Langmuir isotherm … and the Freundlich isotherm (q = KP^sup 1/n^) are first used to simulate the experimental adsorption capacities for different adsorbates onto the activated carbons, where q is the adsorption capacity; q^sub mo^ is the maximum adsorption capacity; b is the Langmuir isotherm constant; K and n are the Freundlich isotherm constants; and P is P/P^sub o^, which represents the equilibrium relative pressure at operational temperature. The Langmuir and Freundlich isotherms have been widely used to describe adsorption capacity over a limited range of pressures in environmental systems. Figure 2a exhibits the isotherm fits of the experimental data for benzene onto BPL carbon. As shown in the figure, the Langmuir isotherm agreed well with the experimental data, indicating that the Langmuir isotherm is appropriate for describing the adsorption of benzene onto BPL activated carbon. Unlike the Langmuir isotherm, the Freundlich isotherm had a poor fit to the experimental data, especially at low pressures. Similar degrees of fitting for both the Langmuir and Freundlich isotherms were also found in other adsorbates onto BPL and Sorbonorit B carbons. The limitations of the applicability of the Freundlich isotherm in the low-pressure range are similar to those of the D-R equation, which will be discussed in the next section.

D-R Equation

Other than the Langmuir and Freundlich isotherms, the experimental data were also depicted by the D-R equation using characteristic curves. A characteristic curve was plotted as lnW versus A2 for a given adsorbent, where W is the adsorbed volume and A is the adsorption potential. The D-R equation would be applicable to the description of the adsorption capacity of the system, provided that the isotherm data are linearly simulated by the characteristic curve. To test the applicability of the D-R equation to different adsorbate/activated carbon systems, an independent study by Yun et al.21 was also explored in this study. Yun et al.21 studied the equilibrium and dynamic adsorption of benzene, toluene, and p-xylene in a carbon bed of Sorbonorit B at 30 C.

The characteristic curves of benzene, toluene, TCE, PCE, p- xylene, o-xylene, MTBE, mesitylene, and 1,1,2,2- TCA onto BPL carbon are shown in Figure 3, a and b. As shown in the figure, the characteristic curves for all nine of the compounds are simulated linearly at a lower A2 range (and also at higher relative pressures). However, the isotherm data of benzene, toluene, TCE, and PCE cannot be linearly fitted over the entire range of abscissa. An obvious transition was observed at ~26 10^sup 7^ J^sup 2^/mol^sup 2^ of A^sup 2^, which is equivalent to a relative pressure (P/P^sub o^) of 1.5 10^sup -3^ for the adsorbates. Similar patterns of a good fit at lower levels of A^sup 2^ (high P/P^sub o^) and of a big discrepancy at high A^sup 2^ (low P/P^sub o^) were also observed in Sorbonorit B carbon conducted both in this study and Yun et al.,21 as shown in Figure 3c. The results reveal that the D-R equation is able to simulate the experimental adsorption data except very low relative pressures. In the case of relative pressures lower than ~1.5 10^sup -3^, the D-R equation may be difficult to apply to the simulation of the adsorption capacity for the adsorption systems tested. The observed discrepancy is attributed to the fact that the D-R equation fails to describe a low relative pressure system at Henry’s law regime, in which the adsorption capacity is supposed to be proportional to the equilibrium relative pressure as P/P^sub o^ 3 0. Consequently, the isotherms simulated by the D-R equation are not thermodynamically consistent with the adsorption capacity data at low pressures. 8,15,16 Such limitations at low pressures are also observed in the Freundlich isotherm, as shown in the previous section. Based on the experimental results, the D-R equation may only be applicable for VOCs adsorbed onto the two activated carbons at a P/P^sub o^ >1.5 10^sup -3^ at room temperature. It should be noted that the P/P^sub o^ range at which the D-R equation is applicable was obtained from the VOCs tested onto the BPL and Sorbonorit B carbons. Further studies may be needed to verify the P/ P^sub o^ range at which can be applied to different adsorbates and activated carbons.

Although limitations in the applicability of the D-R equation at low pressures havebeen suggested, the upper boundary of this low pressure range has seldom been elucidated. Dubinin22 pointed out that the validity of the theory of volume filling of micropores (and also of the D-R equation) is restricted to a level of micropore filling ( = W/W^sub o^) >0.1-0.2. Micropore filling ( ) is defined as the degree of filling of the micropores. The lower limit of micropore filling, which permits the applicability of the D-R equation, is ~0.45 for the VOCs/activated carbon systems tested, which is equivalent to a P/P^sub o^ of 1.5 10^sup -3^ at room temperature. Note that using P/P^sub o^ as an indicator of the lower boundary at which the D-R equation is better than , because the VOC pressure is one of the operational factors of a system, and it can be known in advanced. The limited micropore filling obtained in this study is almost twice that reported in the study of Dubinin.22 This may be explained by the fact that different types of adsorbents were used in Dubinin22 (activated carbons, zeolites, and amorphous mineral adsorbents) compared with this study.

Prediction of D-R Equation

To obtain the D-R parameters of k and W^sub o^, the isotherm data with equilibrium relative pressures >1.5 10^sup -3^ were fitted. Table 1 presents both the fitted values of k and W^sub o^ for different adsorbates tested onto BPL and Sorbonorit B carbons. Figure 2a exhibits the fitted results of adsorbing benzene onto BPL carbon, suggesting that the fitted values of k and W^sub o^ are in good agreement with the experimental data at high relative pressures. The QSAR-based k values calculated from MCI using eq 4 are also listed in Table 1. It is shown that the QSAR-based k values of different adsorbates are comparable with those fitted from experimental data. The average error for all of the compounds tested onto the BPL and Sorbonorit B carbons were 13.4% and 9.7%, respectively. As shown in Table 1, nearly identical W^sub o^ values were found, on the one hand, for benzene, toluene, p-xylene, TCE, and PCE adsorbed onto BPL carbon and, on the other, for toluene, o- xylene, and TCE tested onto Sorbonorit B carbon. The average W^sub o^ values for these adsorbates tested onto the BPL and Sorbonorit B carbons were 0.448 and 0.504 cm^sup 3^/g, respectively. These W^sub o^ values were further compared with those based on the estimation of the PSD proposed by Urano et al.6 The PSD-estimated W^sub o^, based on pore volumes of sizes <32 , was obtained from the PSD of the carbons as shown in Figure 1. It is found that the PSD- estimated W^sub o^ values are 0.449 and 0.518 cm^sup 3^/g for the two carbons, which are almost the same as those obtained from experiments. This may indicate that the PSD-based estimation of W^sub o^ is appropriate for the VOC/carbon systems explored. Additionally, as seen in Table 1, a subgroup of VOCs, including o- xylene, MTBE, mesitylene, and 1,1,2,2- TCA, possesses smaller W^sub o^ values when adsorbing onto BPL carbon. This result is contrary to those of benzene, toluene, p-xylene, TCE, and PCE tested onto BPL carbon, as well as those of toluene, o-xylene, and TCE adsorbed onto Sorbonorit B carbon. These discrepancies in the values of W^sub o^ for different adsorbates tested onto BPL and Sorbonorit B carbons will be discussed in the section of size exclusion effect.

Figure 2b displays the predictive isotherm of benzene adsorbed onto BPL carbon using the D-R equation with the QSAR-based k (2.87 10^sup 9^ mol^sup 2^/J^sup 2^) and the PSD-estimated W^sub o^ (0.449 cm^sup 3^/g). Although excellent prediction is observed, a significant discrepancy is discerned at low equilibrium relative pressures (P/P^sub o^ < 1.5 10^sup -3^). Similar results were also found in the adsorbate/adsorbent systems with low relative pressures, such as toluene, TCE, and PCE, onto BPL carbon and toluene onto Sorbonorit B carbon. These results reveal that a marked deviation may be found when applying the D-R equation in the region of low pressures. The advantage of the D-R equation is its ability to predict the adsorption capacity of VOCs onto activated carbons after combining it with the QSAR and PSD for the estimation of k and W^sub o^. However, the D-R equation substantially overestimates the adsorption capacity at lower VOC pressures. On the other hand, the Langmuir isotherm is able to describe the adsorption systems at lower pressures as shown in Figure 2. Because the parameters of the Langmuir isotherm must be fitted by experimental data, and the isotherm parameters are specific to the adsorbate/adsorbent system tested, the isotherm is difficult to use for the prediction of the adsorption capacity of different VOCs. Therefore, a model integrating the D-R equation and the Langmuir isotherm was developed to predict the adsorption capacity at a wider range of VOC pressures.

D-R-L Model

To overcome the limitations of the D-R equation at low pressures, the equation is combined with the Langmuir isotherm (here called the D-R-L model) to simulate the VOC adsorption capacity at a wider range of pressures. The D-R-L model includes two approaches to the prediction of the adsorption capacity of VOCs onto activated carbons at two different ranges of equilibrium relative pressures. For relative pressures >1.5 10^sup -3^, the D-R equation with the QSAR- based k and PSD-estimated W^sub o^ is used to predict the adsorption isotherm for the adsorbate, because the equation provides good predictability in this pressure range. The D-R equation-based isotherm is then fitted with the Langmuir isotherm to obtain the Langmuir isotherm parameters. The extracted Langmuir isotherm is used to predict the adsorption capacity of VOCs at lower relative pressures, that is, P/P^sub o^ <1.5 10^sup -3^.

Two aspects of this approach need to be qualified. The first one is that if both the D-R equation and the Langmuir isotherm generate equivalent isotherm results in the relative pressure range of interest, this is 1.5 10^sup -3^ to 0.01 in this study. The second aspect needing clarification is the reasons for choosing the Langmuir isotherm to describe the equilibrium at lower pressures. As shown in Figure 2a, the model fits of the D-R equation and the Langmuir isotherm are almost the same at relative pressures between 1.5 10^sup -3^ and 0.01, indicating that both equations may generate similar isotherms over a limited pressure range. Similar results were also observed for other VOC/carbon systems tested in this study. This may justify that the Langmuir isotherm parameters can be determined by fitting the isotherms obtained from the D-R equation. The first reason for choosing the Langmuir isotherm to describe adsorption at lower pressures is that a better model fit was observed, as shown in Figure 2a. In addition, unlike the D-R equation and the Freundlich isotherm, the Langmuir isotherm reduces to a linear form at low pressures and is in accordance with Henry’s law. With this kind of approach, a purely predictive isotherm over a wide range of equilibrium relative pressures may be obtained. The only parameters required to generate the predictive isotherms are similar to those of the D-R equation and include the MCI of the adsorbate for determining k from QSAR and PSD of the adsorbent for estimating W^sub o^.

The isotherm of benzene adsorbed onto BPL carbon was first applied to validate the D-R-L model proposed in this study. As shown in Figure 2b, the isotherm of the D-R equation with the QSAR-based k and PSD-estimated W^sub o^ is in good agreement with the experimental data at relative pressures >1.5 10^sup -3^, suggesting the adequacy of the model at high relative pressures. Then, the Langmuir isotherm parameters were determined by fitting with the D- R equation over relative pressures ranging from 1.5 10^sup -3^ to 0.01. The fitted Langmuir isotherm parameters are listed in Table 2. The model prediction, based on the fitted Langmuir isotherm, and the experimental data at P/P^sub o^ < 1.5 10^sup -3^ are shown in Figure 2b. It is found that the predictions follow the experimental data closely. The good agreement between the model and experimental data over a wide range of relative pressures suggests that the D-R- L model is appropriate for predicting the adsorption capacity for benzene onto BPL carbon. In fact, average discrepancies of only 9.7% and 2.5% are observed between the model predictions and experimental data for benzene tested onto BPL carbon at low and high relative pressures, respectively. Similar results are found for different adsorbates onto BPL and Sorbonorit B carbons. The D-R-L model predictions and their corresponding experimental data for the adsorption of toluene, TCE, and PCE onto BPL carbon and for that of toluene, TCE, and o-xylene onto Sorbonorit B carbon are displayed in Figure 4. Again, the fitted and estimated parameters are listed in Table 2. It is shown that the predictions of the D-R-L model agree well with the isotherm data for the VOCs used on BPL and Sorbonorit B carbons over relative pressures ranging from 7.4 10^sup -5^ to 0.03. The D-R-L model not only improves the deficiencies of the D-R equation but also successfully predicts the adsorption capacity of the organic compounds at low pressures. The average discrepancies between the model prediction and experimental data for adsorption of benzene, toluene, p-xylene (figure not shown), TCE, and PCE onto BPL carbon and that of toluene, TCE, and o-xylene onto Sorbonorit B carbon is only 3.7% and 5.6%, respectively. A large deviation in the model is found for VOCs at extremely low relative pressures (P/ P^sub o^ = ~ 1 10^sup -4^). The model deviations of PCE and TCE adsorbed onto BPL and Sorbonorit B carbons are 41% and 31%, respectively. This may be attributed to the different experimental techniques used and the heterogeneity of the activated carbon pellets tested. Similar observations have also been found in the predicti\ons of the data obtained by Yun et al.21 Figure 5 exhibits the predictions of the D-R-L model and the experimental data from Yun et al.21 for the adsorption of benzene, toluene, and p-xylene onto Sorbonorit B carbon. The model predictions for toluene and p- xylene are in good agreement with the experimental data, because the average discrepancies are only 8.7% and 6%, respectively. For benzene, the model seems to overestimate the adsorption capacity onto Sorbonorit B carbon, ranging from 40% to 56%, with an average of 43.2%. Although the deviation of these predictions is high, the model does capture the trend of the adsorption behavior. To find out the reasons for the deviations of different adsorbates, the experimental data of Yun et al.21 were fitted into the D-R equation. It was found that the D-R equation can be applied to the benzene/ Sorbonorit B adsorption system; however, the fitted W^sub o^ (0.368 cm^sup 3^/g in average) is obviously lower than that of toluene and p-xylene (0.479 and 0.481 cm^sup 3^/g, respectively). We are not sure what causes such differences; nevertheless, one of the reasons may be the heterogeneity of the activated carbon pellets tested.

Size Exclusion Effect

As shown in Table 1, nearly identical W^sub o^ values are obtained in experiments for the adsorption of benzene, toluene, p- xylene, TCE, and PCE onto BPL carbon, and these W^sub o^ values are almost the same as the PSD-estimated W^sub o^ (0.449 cm^sup 3^/g). This is in accordance with the general consensus that the W^sub o^ for a specific activated carbon is almost constant.6-10 However, as also listed in Table 1, the W^sub o^ values of o-xylene, MTBE, mesitylene, and 1,1,2,2- TCA tested onto BPL carbon are significantly smaller than those of other adsorbates. The average W^sub o^ for these four compounds was only 0.395 cm^sup 3^/g based on experimental interpretation (here denoted as modified W^sub o^ for the four compounds). The predictions of the D-R-L model for the adsorption of o-xylene, MTBE, mesitylene, and 1,1,2,2- TCA onto BPL carbon using both the PSD-estimated W^sub o^ (0.449 cm^sup 3^/g) and the modified W^sub o^ (0.395 cm^sup 3^/g) are listed in Table 3. Obviously, the model with the modified W^sub o^ has a much better predictability than that with the PSD-estimated W^sub o^ for the compounds, in which the average error decreased from 8.2% to only 4.2%.

To explore the deviation of W^sub o^ for different adsorbates onto BPL carbon, the kinetic diameter (σ) of the tested VOC molecules was collected and is shown in Figure 6a.20,23-27 To expand the spectrum of compounds tested, the W^sub o^ values of BPL carbon from independent studies by Reucroft et al.5 and Barton et al.28 are also included in Figure 6b. In the figure, the W^sub o^ of cyclohexane comes from Barton et al.,28 whereas those of the other compounds are from Reucroft et al.5 It is presumed that the kinetic diameters of benzene, toluene, and p-xylene are identical.23 The kinetic diameters of all of the adsorbates, except o-xylene, MTBE, TCE, 1,1,2,2-TCA, and mesitylene, come directly from the study by Reid et al.20 For o-xylene, the diameter is from Berck,23 whereas those of MTBE and TCE were collected from Anderson,24 Chintawar and Greene,25 and Li et al.26 The kinetic diameters of 1,1,2,2-TCA and mesitylene are regarded as the same as those of CCl4 20 and 1,3,5- triethylbenzene.27

Figure 6, a and b, displays the W^sub o^ values of BPL carbon calculated in this study and in the two studies of Reucroft et al.5 and Barton et al.,28 respectively. The dashed line in Figure 6a represents the PSD-estimated W^sub o^, and in Figure 6b it is the average W^sub o^ value of acetone, ethyl acetate, benzene, chloroform, hexane, and CCl4. The results reveal that the W^sub o^ of small molecules (σ < ~6 ), such as benzene, toluene, p- xylene, TCE, and PCE, is nearly constant. In this study, the average W^sub o^ for these VOCs is 0.448 cm^sup 3^/g, which is similar to that presented in Figure 6b (0.431 cm^sup 3^/g) based on the results of Reucroft et al.5 However, for adsorbates of which the diameters are >6 , the W^sub o^ is found to decrease as the kinetic diameter increases (see Figure 6, a and b). For example, the W^sub o^ of benzene (5.35 ) is 0.442 cm^sup 3^/g and that of o-xylene (6.8 ) is 0.398 cm^sup 3^/g. This size exclusion effect, however, is not found in the case of Sorbonorit B carbon adsorbing the larger molecules of o-xylene, as shown in Figure 6c. Again, the dashed line in Figure 6c represents the PSDestimated W^sub o^. Unlike the results for BPL carbon, the W^sub o^ values obtained in the adsorption of smaller compounds (toluene and TCE) and a larger compound (o-xylene) onto Sorbonorit B carbon are almost the same. This result may be attributed to the different micro-PSDs of BPL and Sorbonorit B carbons.25 As presented in Figure 1a, the sizes of the micropores of BPL carbon are mainly from less than ~6-10 , and a large portion of the pores are <6 . However, Sorbonorit B possesses a wider PSD, from 6 to 10 , the major portion of which is ~7 . Consequently, the micropore space of BPL carbon may not be large enough to adsorb larger adsorbates (such as o-xylene) and, thus, may not be able to complete pore filling, as in the case of smaller molecules. This effect may cause a reduction of the adsorption capacity for larger adsorbate molecules onto BPL carbon. Therefore, the W^sub o^ of BPL carbon can only be considered constant for adsorbates with smaller kinetic diameters. On the contrary, larger adsorbates may be able to fully enter and fill the micropores of Sorbonorit B carbon because of the wider micropore distribution of the adsorbent. The results reveal that the W^sub o^ is related not only to the size distribution of the micropores of the adsorbents but also to the molecular size of the adsorbate. This size exclusion effect may play an important role in the adsorption of larger organic compounds onto an ultramicropore adsorbent in terms of both the D-R equation and the D-R-L model. In this case, both the equation and model should be adjusted to account for this effect.

CONCLUSIONS

The D-R equation with the QSAR-based k and the PSDestimated W^sub o^ successfully predicted the equilibrium capacity of VOCs onto activated carbons at high relative pressures. The overestimation of adsorption capacity was observed when attempting to predict the VOC adsorption capacity at relative pressures <1.5 10^sup -3^. This may be attributed to the fact that the D-R equation deviates from Henry's law at low pressures. The integration of the D-R equation and the Langmuir isotherm, the D-R-L model, was proposed to predict the VOC adsorption capacity over a wide range of relative pressures. Without requiring that any adsorption experiments be conducted in advance, the D-R-L model successfully predicted the equilibrium capacity of almost all of the VOCs tested onto BPL and Sorbonorit B carbons over a variety of relative pressures ranging from 7.4 10^sup -5^ to 0.03. This may indicate the potential applicability of the model. In the case of larger VOC molecules adsorbed onto activated carbons, a size exclusion effect was observed. The effect was only significant for the adsorption of large VOCs onto ultramicroporous BPL carbon and was not observed in the case of Sorbonorit B carbon, which possesses a wider PSD. Under this effect, the W^sub o^ of the D-R equation may become smaller, because the large VOC molecules may be excluded from adsorption by the small- sized pores of the adsorbent. This would cause an overestimation of the adsorption capacity for the VOCs when using the D-R equation or the D-R-L model for the predictions. Therefore, it is necessary to consider the PSD of the adsorbent and the molecular size of the target VOC before applying both the D-R equation and the D-R-L model.

ACKNOWLEDGMENTS

This work was supported by the National Science Council, Taiwan, under grant number NSC89-2211-E-006-013.

IMPLICATIONS

Although the D-R equation has an excellent predictive ability of the adsorption capacity for VOCs onto activated carbons, it may fail to describe the equilibrium capacity of VOCs at low relative pressures. To extend the predictability of the equilibrium capacity to lower VOC concentrations, the D-R-L model was proposed and verified for nine aromatic and chlorinated hydrocarbons onto two activated carbons. The results revealed that capacity predictions are possible only with knowledge of the physicochemical properties of the adsorbate and the pore size distribution of the carbon. This approach may simplify the prediction of VOC adsorption onto activated carbons and may be used in many environmental systems with low VOC concentrations, such as indoor air control devices, air stripping towers, and off-gas treatment systems.

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Hsu-Wen Hung

Sustainable Environment Research Center, National Cheng Kung University, Tainan City, Taiwan, Republic of China

Tsair-Fuh Lin

Department of Environmental Engineering, National Cheng Kung University, Tainan City, Taiwan, Republic of China

About the Authors

Hsu-Wen Hung is an assistant researcher at the Sustainable Environment Research Center, National Cheng Kung University. Tsair- Fuh Lin is a professor in the Department of Environmental Engineering, National Cheng Kung University. Address correspondence to Tsair-Fuh Lin, Department of Environmental Engineering, National Cheng Kung University, No. 1, University Rd., Tainan City 70101, Taiwan, Republic of China; phone: +886-6-2364455; fax: +886-6- 2752790; e-mail: tflin@mail.ncku.edu.tw.

Copyright Air and Waste Management Association Apr 2007

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