Environ. Sci. Technol. 1994, 28, 614-623
Modeling Adsorption of TCE by Activated Carbon Preloaded by Background Organic Matter Margaret C. Cartert and Walter J. Weber, Jr.
Environmental and Water Resources Engineering, The University of Michigan, Ann Arbor, Michigan 48109-2 125 Experiments with a natural water and a synthetic water were conducted to investigate systematically the effects of preloading of activated carbon by background organic matter on the subsequent adsorption of trichloroethylene (TCE). Equilibrium capacities and rates of adsorption were both found to decrease with increased periods of continuous preloading by both background waters. The effect of preloading by the natural water was observed to level off after several weeks. A pore diffusion model calibrated with adsorption parameters measured under different controlled conditions was used to predict fixedbed adsorber breakthrough behavior. The modeling results indicated that equilibrium and rate parameters may need to be varied with preloading time to accurately predict target compound breakthrough for systems which undergo extensive preloading. A constant parameter approach appears adequate if preloading effects are small, or if the operating time of an adsorber is very long.
intraparticle pore diffusion is considered negligible compared to surface diffusion. Similarly, the pore diffusion model neglects the mechanism of surface diffusion. An adsorption isotherm equation is used to quantify equilibria in the models. The rate mechanisms of film diffusion, surface diffusion,and pore diffusion are quantified through parameters typically designated by kf,D,, and D,, respectively. The Freundlich isotherm is the most commonly used single-solute equilibrium expression in fixed-bed adsorber modeling. It has been found to describe experimental equilibrium data well over the concentration ranges of interest in drinking water treatment, and its simple form allows for facile implementation in the computer algorithms necessary for solution of the pore-surface diffusion model. This isotherm has the form q e = KFc,”
t Present address: Amoco Chemical Co., 150 West Warrenville Rd., D-3, Naperville, IL 60563.
(1) where q e is the solid-phase equilibrium concentration of solute and Ce is the solution-phase equilibrium concentration. The preexponential Freundlich coefficient, KF, provides a measure of overall adsorption capacity, while the exponential parameter, n, relates to the intensity of adsorption and the heterogeneity of adsorption site energies (11). Use of the pore-surface diffusion model and its derivatives is usually predicated on the assumption that simultaneous adsorption of background organic matter and target contaminants is the dominant competitive effect and has thus employed isotherm and rate parameters which remain constant over the entire simulation period (1-3). An overview of the most common constant parameter modeling approaches for predicting fixed-bed adsorption phenomena has been presented by Weber and Smith ( 4 ) . Recent work indicates that under conditions typically present in drinking water treatment applications, preloading of background organic matter rather than simultaneous competition may exert the greatest impact on target compound adsorption capacities and rates (5-9,12). Nonetheless, constant parameter modeling approaches have yielded reasonable simulations of breakthrough behavior in some studies even though there was evidence of significant preloading. Researchers in Germany found that despite significant losses of adsorption capacity for TCE of GAC preloaded with the organic matter in Rhine River water, constant parameter simulations by the homogeneous surface diffusion model and pore diffusion model captured pilot-column breakthrough data well using “average” isotherm parameters and after adjusting D, or D,, respectively (6). Similarly, investigators examining adsorption of cis-1,2-dichloroethenefrom Ohio River water were able to obtain adequate constant parameter poresurface diffusion model predictions of pilot-column breakthrough despite evidence of significant decreases in FreundlichKF with preloading (7).In a subsequent study of the same solute/background water system, the rate parameters kf and D, were also found to be significantly
614 Envlron. Sci. Technoi., Voi. 28, No. 4, 1994
0013-936X/94/0928-0614$04.50/0
Introduction Treatment of drinking water sources by granular activated carbon for the removal of synthetic organic chemicals is a proven decontamination technology. Granular carbon is typically applied in fixed-bed reactors, for which predictive mathematical models can provide accurate descriptions of breakthrough phenomena and, thus, serve as useful design tools. The phenomenon of “preloading” of carbon by background organic matter has been observed to significantly impact contaminant adsorption and thereby complicate accurate estimation of model parameters. Preloading occurs when the wavefront of more weakly and slowly adsorbing background organic matter moves ahead of those of target compounds in fixed-bed adsorbers, causing reductions in equilibrium capacity and rates for subsequent target compound adsorption in downstream sections of the adsorbers. The validity of properly calibrated mathematical models for predicting or simulating fixed-bed adsorber performance in natural water systems has been demonstrated in a number of investigations (1-10). The most commonly applied models are the pore-surface diffusion model and its two major derivatives, the pore diffusion model and the homogeneous surface diffusion model. The poresurface diffusion model incorporates mathematical description of the major physicochemical mechanisms recognized to occur in FBR systems: namely, axial flow with dispersion, local equilibrium at the particle surface, mass transfer resistance across a hydrodynamic boundary (film) layer surrounding the particle, and intraparticle diffusion along pore surfaces and through pore liquid within the particle. The homogeneous surface diffusion model is identical to the pore-surface diffusion model except that
0 1994 American Chemical Society
reduced with advancing preloading (9). Incorporation of the reduced values of isotherm and rate parameters into the pore-surface diffusion model resulted in reasonable simulations of pilot-column breakthrough data. In a study employing pilot-scale fixed-bed adsorbers, reductions in KFandD, were found for TCE in a Wisconsin groundwater, although these variations were not incorporated into the modeling scheme (10). Other research has indicated that adequate simulation of breakthrough behavior in preloading systems must be obtained through variation of some isotherm and rate parameters with time to simulate reductions in adsorption due to preloading. An equation for KF reduction with preloading time was determined by fitting fieldequilibrium data for several synthetic organic chemicals in natural waters. This expression was used along with an assumed time-variable reduction in D, in the pore diffusion model to yield adequate simulations of tetrachloroethylene and TCE breakthrough in a full-scale municipal adsorber (5). In a related study, the Freundlich KF was varied in the homogeneous surface diffusion model to simulate simultaneous breakthrough of tetrachloroethylene and TCE from a pilot-column. This study also found a 10-fold decrease in D, with preloading time, but this change was not used in the modeling procedure (8). While application of mathematical models using timevariable parameters shows substantial promise for predicting adsorption behavior in preloaded systems, a consistent approach for the prediction of preloading phenomena has yet to be developed. Previous studies have been limited to the use of either a constant parameter or a time-variable parameter modeling protocol, with no comparison of the two methods for the same data. Moreover,the time-variable parameter methods that have been employed have varied only KFor KFand D,. There is strong evidence that all isotherm and rate parameters of the pore-surface diffusion model may be altered by preloading. This work thus undertook a systematic comparison of constant parameter and time-variable parameter modeling approaches for the prediction of performance of two different preloaded systems to better define conditions under which each of these approaches may be most appropriate and to provide insight into the mechanistic basis of the preloading process. The specific objectives of the research were (i) to examine equilibria and rates of contaminant adsorption for systems in which competitive and time-variable preloading effects from background organic matter exist; (ii) to refine an existing mathematical model to incorporate parameters which account for temporal variations in adsorption equilibria and rates caused by preloading phenomena; and (iii) to investigate and compare constant and time-variable parameter model formulations for predicting fixed-bed adsorber performance.
Experimental Section Granular activated carbon was preloaded for varying times with two background waters of differing composition and used in experiments that evaluated equilibrium capacity and rates of adsorption for TCE. To the extent possible, the time-variable impact of preloading on the adsorption of the target compound was isolated by preloading carbon for use in subsequent studies in relatively short beds. A separate, bench-scale fixed-bed
system that fed the background waters spiked with TCE was run in tandem with the carbon preloading system for comparison of the different modeling protocols. Background Waters. A natural and a synthetic background water were employed. Water from the Huron River, which serves as a raw water source for the city of Ann Arbor, MI, was chosen to represent a natural source of background organic matter. The synthetic water incorporated polymaleic acid (PMA) as the background organic matter. PMA is a polyelectrolytic macromolecule containing aliphatic, olefinic, and aromatic components. I t was selected for several reasons: (i) it exhibits elemental analyses, infrared spectra, and numerous acid hydrolysis products similar to those of naturally occurring soil fulvic acids (13,14); (ii) screening studies indicated its potential for adsorbing onto carbon and exerting a preloading effect similar to natural background organic matter; and (iii) it is readily synthesized in the laboratory using the method of Spiteller and Schnitzer (14)to yield the large quantities required for fixed-bed adsorber preloading experiments. Huron River water was stored, refrigerated, in 55-gal stainless-steel drums until use. Prior to use, the Huron River water was filtered through a 1.0-pm filter (polypure capsule, Gelman Science, Ann Arbor, MI) to remove particulate matter and to help prevent column plugging. PMA background water was made by diluting aqueous stock solutions of polymaleic acid, reagent-grade sodium bicarbonate, reagent-grade calcium chloride, and reagentgrade sodium chloride with ultrapure water (Millipore Corp., Bedford, MA) to yield the chosen solution levels for total organic carbon (TOC), alkalinity, hardness, and ionic strength, respectively. Approximately 100 mg/L sodium azide was added to retard bacterial growth and the degradation of organic matter in the background waters. Batch reactor isotherm studies were conducted to determine that the sodium azide did not affect the adsorption of TCE. During the course of all experiments, pH (Model 240, Corning Co., Corning, NY), ionic strength (Model CDM 83 conductivity meter, Radiometer Co., Copenhagen, Denmark, calibrated to NaCl standards),hardness (ref 15,Method 2340), calcium (ref 15, Method 3500), alkalinity ( ref 15, Method 2320), and TOC (Model TOC-500, Shimadzu Corp., Japan) were monitored daily to provide information about the variability of water composition. The range of molecular weight of organic matter in the background waters was determined using size exclusion chromatography (SynChropak GPClOO column, SynChrom Corp., Lafayette, IN, calibrated with random-coil polystyrene sulfonate standards). The molecular weight range of the synthetic background, PMA, was measured to be 1000-9000, which falls within the typical range for natural background organic matter found in surface water (16). The compositional properties of the background waters are given in Table 1. Solute. Trichloroethylene (Mallinckrodt Corp., Paris, KY) was selected as the target compound in this work for several reasons: (i) it has been designated as a priority pollutant by t h e U.S. Environmental Protection Agency; (ii) it has been identified in contaminated surface waters and groundwaters; (iii) it is straightforward to analyze; and (iv) it represents a broad class of mobile halogenated organic contaminants commonly found in the environment. For all fixed-bed adsorber experiments, the influent concentration of TCE was approximately 50 pg/ Envlron. Sci. Technol.. Vol. 28, No. 4. 1994 615
Table 1. Compositions of Background Waters and Adsorption of Background Organic Matter during Preloading compositional parameter total organic carbon (mg/L) PH alkalinity (mg/L as CaC03) calcium (mg/L as CaC03) hardness (mg/L as CaC03) ionic strength (mM as NaCl) mol w t of organic matter (amu) (peak weight) mg of TOC/g of carbon adsorbed during 4 weeks of preloading
L, a concentration selected because it was high enough to permit accurate analyses of samples, yet still low enough to fall within the range of contamination levels commonly found in contaminated surface and subsurface water supply sources. Feed solutions for the experiments were prepared by direct injection into the bulk background water of a stock solution containing a high-concentration of TCE dissolved in methanol. Studies have shown that micromolar amounts of methanol in aqueous systems do not alter the adsorption properties of synthetic organic chemicals (17). Experiments were conducted at temperatures of 23" f 2 "C. Samples were extracted immediately into hexane and analyzed by capillary column gas chromatography utilizing an electron capture detection method [Model 5890 with HP-5 (cross-linked 5% Ph Me silicone) column, HewlettPackard Co., Palo Alto, CAI. The method had aminimum detection limit of 0.1 pg/L and an analytical error of less than 3 % . Activated Carbon. The general physical properties of the activated carbon (F-400, Calgon Corp., Pittsburgh, PA) used in all the experiments are given elsewhere (11). Two fractions of U. S. Standard Sieve Sizes 801100 (0.162 mm arithmetic mean diameter) and 30/40 (0.512 mm arithmetic mean diameter) were obtained by crushing and sieving carbon samples obtained from one lot of carbon. The resulting fractions were washed in ultrapure water to remove fines, dried overnight at 105 "C, and transferred to air-tight containers for storage. Carbon for immediate use was dried again to remove any adsorbed moisture and stored in a desiccator. Activated carbon was preloaded with each of the background waters for periods of 1, 2,3, and 4 weeks in a column-based system. Four parallel 1.27-cm i.d. Plexiglass columns were fed background water containing no TCE using a multichannel peristaltic pump (Masterflex, Cole-Parmer Co., Chicago, IL). Each column was packed with two layers of carbon particles of size SO/lOO and 301 40, respectively, separated by a layer of glass beads and glass wool. Glass beads and glass wool were also packed at the inlet and outlet ends of the column to support the bed. A nominal surface loading of 10.7 cm/min was maintained throughout the preloading process, the same as that used in other fixed-bed column systems in this study. Breakthrough of the organic matter in the columns was monitored during the preloading process. The mass of background organic matter as TOC loaded onto the carbon after 4 weeks of preloading is reported in Table 1. At the conclusion of the designated period, the preloaded carbon was dried at room temperature in a vacuum desiccator to less than 1% moisture content to facilitate accurate measurement of carbon masses in subsequent 616
Environ. Sci.
Technol.. Vol.
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mean concn *95 % confidence limits Huron River water polymaleic acid background water 7.37 f 0.80 8.28 f 0.03 248 f 2 178 f 2 260 f 5 6.85 0.06 1000-5000 (1860)
*
26.6
7.43 f 0.06 7.82 0.03 231 f 1 50.7 0.3 53.0 f 0.2 8.70 0.05 1000-9o0O (3900)
* * *
25.1
experiments. All carbons were stored in a desiccator until use. Mathematical Model. The pore diffusion version of a pore-surface diffusion model was used for the calibration of rate data and the simulation of fixed-bed adsorber breakthrough data. A pore diffusion model was selected because it gave fits superior to those of a homogeneous surface diffusion model to all data collected in this study. This is in accordance with the findings of other researchers for adsorption modeling of preloading systems (8,10).The model equations and solutions are based upon the formulation of Crittenden et al. (18). The model was reduced to a set of simultaneous ordinary differential equations (ODES)in time using the method of orthogonal collocation. The coefficients of the ODES encapsulated the isotherm and rate information provided by the parameters KF,n, kfandD,. The breakthrough simulation was then obtained by callingageneral ODE solver for stiff equations (LSODE) to solve the ODESthrough a series of time steps until the total run time was met. The validity of this approach and the ability of the pore diffusion model to describe adsorption in fixed beds have been widely demonstrated (5, 7, 10, 18, 19). The conventional constant parameter version of the pore diffusion model was used for calibration of short-bed adsorber rate data and for simulation of fixedbed adsorber data. In these cases, the coefficients of the ODESremained unchanged over the entire model run time. A second version of the pore diffusion model, referred to here as the time-variable parameter model, was developed for this research. In this model, each of the isotherm and rate parameters was input as a function of model run time, e.g., KF = f (time). The isotherm and rate parameters were then updated at each time step, resulting in ODE coefficients that changed over the model run time according to the parametric input expressions. Isotherm Studies. Isotherm studies in completely mixed batch reactors (CMBFb)were conducted to establish equilibrium relationships between TCE and the preloaded carbons in the two background waters. Additionally, selected isotherms in Huron River water were determined using a column-based approach, the micro-diameter-depth adsorption system, or MIDDAS method (20). The CMBR method, also known as the bottle-point technique, used 30140 carbon, the same size as was employed in the benchscale fixed-bed adsorber studies. The MIDDAS approach employs smaller (80/lOO) carbon. Details of both techniques have been described by Carter et al. (12). The Freundlich isotherm model was employed in this work. The parameters KF and n were determined by linear geometric mean functional regression of log-transformed experimental data. The geometric functional regression algorithm accounts for errors incurred in measurement
Table 2. Isotherm Parameters Obtained under Varying Conditions*
Huron River water system [CMBR] KF~ nb __... ~.~ _.. .~
preload time (wk)
background water [reactor type1 Huron River water system [MIDDAS (co1umn)l KF n
unpreloaded
1.39 (1.21-1.58)
0.542 (0.515-0.569)
0.400 (0.352-0.455)
0.703 (0.673-0.734)
1
NDc
ND
ND
ND
2
0.487 (0.428-0.554) 0.407 (0.344-0.480) 0.287 (0.224-0.367)
0.634 (0.606-0.663) 0.667 (0.631-0.703) 0.713 (0.659-0.767)
0.178 (0.109-0.291) 0.183 (0.120-0.279)
0.762 (0.643-0.881) 0.723 (0.622-0.824)
ND
ND
3 4
uolymaleic acid background water system [CMBR] KF n 1.75 (1.58-1.93) 1.23 (1.08-1.40)
1.08 (1.00-1.16) 0.948 (0.832-1.08) 0.778 (0.696-0.868)
0.516 (0.495-0.537) 0.563 (0.535-0.591) 0.577 (0.560.594) 0.577 (0.547-0.606) 0.599 (0.575-0.623)
*
a Numbers in parentheses are 95% confidence limits on the parameter. Based on Freundlich isotherm, qe = KFC,", with q, in Ng/mg and C, in pg/L. ND = not determined.
and calculation of both liquid- and solid-phase equilibrium concentrations (21-23). Confidence intervals of 95 % on the regression parameters were determined for all experiments using standard statistical methods (24). Fixed-Bed Adsorber Studies. A bench-scale fixedbed column system was used to obtain breakthrough data for both short-bed rate experiments, which were designed to give immediate TCE breakthrough, and deep-bed adsorption studies, which used sufficient carbon to initially contain the TCE wavefront. The bench-scale fixed-bed column system consisted of a 25.4-cm or 50.8-cm long stainless steel column of 1.4-cm id for the short-bed and deep-bed studies, respectively. The ratio of column diameter to particle size was approximately 25, sufficient to eliminate wall effects (25). Each column apparatus was packed with successive layers of 30/40 size glass beads at the inlet to establish uniform flow, a measured mass of 30140 carbon, and more 30140 glass beads from the top of carbon bed to the outlet of the column. A dual pump system was used to feed the bench-scalefixed-bed adsorber system at a surface loading of 10.7 cmlmin. The main flow through the system was provided by pumping the appropriate background water from a 45-L glass reservoir using a peristaltic pump (Masterflex, Cole-Parmer Co., Chicago, IL). TCE was introduced to the feed water in a concentrated methanol-based stock from a syringe inserted into the feed stream. Stock infusion was controlled by a syringe pump (Harvard Apparatus, South Natick, MA). The resulting solution was then passed through a mixing chamber prior to introduction to the column. Sampling ports located both before and after the column were used to monitor influent and effluent concentrations of TCE throughout the experiment. Model simulations indicated that dispersion effects were not negligible under the conditions tested. Dispersion coefficients for use in computer modeling were estimated using the particle Peclet number, Dh/uid, where Dh is the mechanical or hydrodynamic dispersion coefficient, ui is the interstitial velocity, and d is the adsorbent particle diameter. Over the range of flow rates commonly encountered in fixed-bed systems (8.1-40.8 cmlmin), the particle Peclet number is approximately constant, and equal to 2 (26,27). The Dh value of 5.2 X cm2/swas computed for the bench-scale fixed-bed adsorber system. This value was similar to those reported by others for fixed-bed reactors (7, 28, 29). The short-bed adsorber (SBA) technique (27, 30) was utilized for the calibration of data to obtain values for
mass transport parameters required for model predictions of adsorber performance. In the pore diffusion model, the relevant rate parameters are kf,the film transfer coefficient which characterizes mass-transfer resistance across a hydrodynamic boundary layer surrounding the carbon particle, and D,, the intraparticle pore diffusion coefficient which quantifies TCE diffusion through the liquid-contained internal particle pores. Using the SBA method, the carbon bed was made sufficiently short so that virtually immediate breakthrough of TCE occurred. For early time data, before significant intraparticle mass transport occurred, simulations of the data by the pore diffusion model were only sensitive to changes in the film transfer coefficient,kf. By calibrating only early time data, an explicit determination of kfwas made by finding that value which minimized the mean sum of squared residuals between model simulation and experimental data. Once kf was determined, it was held constant and the entire SBA breakthrough data set was then calibrated with the model by varying D, until a best fit of the model simulation to the experimental data was obtained. D, has been reported in terms of an impedance factor, 7 , using the , D1 is the free liquid diffusivity relationship D, = D ~ Twhere of the solute. For TCE, D1 was calculated to be 9.15 X lo4 cm2/s using the correlation presented by Hayduk and Laudie (31). Confidence limit estimation techniques applicable for nonlinear models such as the pore diffusion model were used in the analysis of all rate parameter calibrations (23).
Results and Discussion
Equilibrium Studies. Isotherms for adsorption of TCE from Huron River water in CMBR systems for the cases of no preloading and preloading for 2,3, and 4 weeks are presented in column 1of Table 2. The data indicate significant loss of equilibrium capacity with increased preloading time with the biggest drop occurring by the end of the second week. KFvalues dropped from 1.39 to 0.287 over 4 weeks of preloading. Correspondingly, Freundlich n values increased from 0.542 to 0.713. TCE isotherm data obtained by the column-based MIDDAS method for Huron River water are presented in column 2 of Table 2. These data also show that the most dramatic decrease in capacity occurs within the first two weeks of preloading, with KF dropping from an already low value of 0.400 to 0.178 in that time period. In contrast to the data obtained by the CMBR method, however, the Environ. Scl. Technol., Vol. 28, No. 4, 1994 617
Table 3. Physical Parameters Used for Short-Bed Adsorber Rate Studies
background water Huron River water
preloading level (wk) influent TCE (rgiL) carbon dose (g) bed length (cm) flow rate (mL/min) unpreloaded 2 3 4
polymaleic acid background water
unpreloaded 1 2 3 4
MIDDAS isotherms did not exhibit any clear statistically significant differences in Freundlich n values, regardless of the extent of preloading. The n values for all of the MIDDAS isotherms are quite high, on the order of 0.7 and statistically indistinguishable from that of the CMBR isotherm for the most extensively preloaded carbon. A complete analysis of these equilibrium results has been presented elsewhere (12). In brief, the high TCE capacity of unpreloaded carbon relative to that in the column-based MIDDAS system was attributed to the large initial driving force afforded by the high solute starting concentrations inherent in the CMBR methodology. However, convergence of the CMBR and MIDDAS isotherms to similar capacities after several weeks of carbon preloading suggests that preloading eventually levels differences in isotherm capacity due to differencesin solute driving force. The low equilibrium capacities of the MIDDAS isotherms observed over all levels of preloading were attributed to the fact MIDDAS is a column-based system and, therefore, subject to preloading during the isotherm measurement itself, regardless of any external preloading. The isotherms for TCE in the polymaleic acid system also indicated a loss of equilibrium capacity with increased preloading time, although the changes were not as extensive as those for Huron River water. KFvalues dropped from 1.75 to 0.778 over 4 weeks of preloading with Freundlich n values increasing from 0.516 to 0.599. It is interesting to note that the amount of TOC adsorbed during the carbon preloading was essentially the same for the two background waters: 26.6 mg of TOC/g of carbon for Huron River water and 25.1 mg of TOC/g of carbon for the PMA background water (Table 1). However, the TCE adsorption capacity of the PMA-preloaded carbon was affected to a much lesser extent by the adsorbed background organic matter than that preloaded by the Huron River water organic matter. This observation suggests that TOC loading, which is a lumped-parameter measurement of a complicated process, is not a good indicator of how extensively preloading by a particular background may impact adsorption of a target solute. Rate Studies. Rate parameters were gathered in the two background waters for various levels of preloading using the short-bed adsorber technique. Conditions for the SBA experiments are given in Table 3. Because the SBA method uses equilibrium isotherm data as input to the fitting model, SBA data for the Huron River water were calibrated with both CMBR and MIDDAS isotherms. Representative graphical data and SBA calibrations using both the CMBR and the MIDDAS isotherm for the unpreloaded carbon data for TCE and Huron River water are given in Figure 1. For the PMA background water, only CMBR isotherm data were available for calibration. 618
Envlron. Scl. Technol., Vol. 28, No. 4, 1994
51.2 49.7 52.9 53.2 54.8 55.5 54.7 53.8 54.6
0.6113 0.7826 0.7997 0.8018 0.4334 0.5103 0.5378 0.5729 0.5902
0.77 0.95 0.90 0.93 0.50 0.62 0.68 0.69 0.71
16.6 16.8 16.6 16.6 16.8 16.8 16.7 16.6 16.6
40 Y
2 dm3
30 20
10
CMBR calibration MIDDAS calibration
0
I
0
10
*
I
20
.
l
.
30
40
50
60
70
t h e (hr)
Figure 1. Short-bed adsorber data and model calibrations for unpreloaded carbon in Huron River water uslng CMBR and MIDDAS isotherm parameters.
There was some variation in influent concentrations during the SBA studies due to difficulties in TCE stock solution mixing. However, these variations were accounted for during the calibration process by using a variable influent concentration input in the pore diffusion model. For the Huron River water data, a distinguishing feature of each of the SBA model fits calibrated with the CMBR isotherms was an overprediction of TCE removal through intermediate portions of the breakthrough curve. This behavior was particularly notable for the calibrations of unpreloaded carbon data shown in Figure 1. In contrast, the MIDDAS-based calibrations of the unpreloaded SBA data captured the trend in the data quite well. With increased preloading, deviations between data and calibration curves due to the calibrating isotherm decreased substantially. The MIDDAS-based calibrations of the 3-week preloaded SBA data were very similar to the CMBR-based fits (11). These results are in accord with the equilibrium data gathered using the two experimental methods (12). The column-based isotherm better captured early time behavior of a column system when deviations between the MIDDAS and CMBR isotherms were the greatest. A t extended preloading times, as equilibrium measurements from the different methods converged, both isotherms calibrated SBA data equally well. External Film Transfer. The parameter values resulting from model calibrations of SBA data are presented in Table 4. A statistically significant decrease in the external film transfer coefficient with increasing preloading was observed for all background waters. For Huron River water, kfvalues based on the CMBR isotherm calibrations dropped from 3.5 x 10-3 to 1.0 X cm/s over 4 weeks of preloading. Values of kf from the MIDDAS isotherm
Table 4. Rate Parameters Obtained under Varying Conditions.
preload time (wk) unpreloaded 1
Huron River water system [CMBRI k f (cm/s x 103) (dimensionless) 3.5 (3.2-3.8) NDc
1.2 (0.7-2.1) ND
3.7 (3.4-4.1) ND
0.6 (0.5-0.9) ND
1.4 (1.3-1.6) 1.2 (1.1-1.4)
5 (1-30+) 8 (2-30+) 6 (2-30+)
1.5 (1.3-1.7) 1.3 (1.1-1.4) ND
3 (1.5-6) 3 (1.5-7) ND
1.0
(0.8-1.1) a
background water [calibrating isotherm] Huron River polymaleic acid background water system [CMBRI water system [MIDDAS (column)] kf (cm/s X 103) 7 (dimensionless) kf (cm/s X lo3) T (dimensionless) 4.3 (3.9-4.7) 3.1 (2.9-3.3) 2.4 (2.2-2.6) 1.9 (1.7-2.1) 1.5 (01.4-1.6)
0.6 (0.3-1.0) 0.9 (0.5-1.5) 0.6 (0.4-1.1) 0.5 (0.2-1.1) 0.6 (0.3-1.0)
Numbers in parentheses are 95% confidence limits on the parameter. b Impedance, 7, as defined by Dp = D1/7.c ND = not determined.
calibrations agreed with the CMBR-based kfvalues within the limits of statistical significance for the data. This is expected since solute loading on the carbon over early time data, when kf is the controlling parameter, is essentially negligible and, therefore, nearly independent of the isotherm expression (32). Results from the calibration of SBA data gathered in the PMA background water with their respective CMBR isotherms yielded kf data similar to that for the Huron River water. For this water, kfdecreased from 4.3 X to 1.5 X cm/s over 4 weeks of preloading. These findings suggest that preloading may impact diffusion processes on the surfaces of GAC particles. Similar results were found by Speth (9). One possible explanation may be that the local fluid viscosity of the film surrounding a particle is increased by the presence of the relatively large molecular weight background organic matter preloaded on the particle surface, resulting in decreased rates of diffusion of TCE across the hydrodynamic boundary layer (11,33,34). Another possibility is that some effective area for TCE mass-transfer flux into the carbon particle is lost due to a partial blockage of external pores by preloaded background organic matter. Intraparticle Diffusion. The values measured for the pore diffusion impedance factor, T , can be related to changes in resistance to TCE diffusion with preloading. Impedances near unity imply that the total mass diffusion is on the order of that given by the free liquid diffusivity of the solute, Le., the carbon pore spaces are relatively open and free of obstruction. Impedances several factors greater than unity indicate that intraparticle diffusion of TCE is greatly restricted by the presence of preloaded background organic matter in the carbon pores. The impedance data prekented in Table 4 for the Huron River and PMA background water rate studies can be interpreted within the above framework. For unpreloaded carbon in Huron River water, the T value was 1.2. This indicates that significant intraparticle transport of TCE occurred in the unpreloaded carbon. For all of the Huron River water preloaded carbons, however, the impedance factors were found to be significantly greater than unity. Values of 7 between 5 and 10 indicate that intraparticle diffusion was 5-10 times slower than that for TCE in pure water. This suggests that preloaded background organic matter posed a significant resistance to TCE diffusion within the carbon pores. Impedance values from the MIDDAS-based calibrations showed a similar increase in 7 between unpreloaded and preloaded carbons. The high
upper confidence limits of r values greater than 3 was caused by an increasing insensitivity of the model to this parameter as intraparticle resistance became large. In contrast to the Huron River system, which showed significant pore diffusional resistance, impedance values for the carbons preloaded with PMA background were near unity for all levels of preloading. This suggests that preloading by the PMA left pore diffusion paths relatively open to the adsorbing TCE. These findings are consistent with the isotherm studies, in which preloading by PMA background was observed to exert the lesser effect of the two background organic systems studied. Time-Variable-Parameter Model Sensitivity. To assess the relative contribution of each isotherm and rate parameter to the overall shape of the breakthrough profile in the time-variable-parameter modeling method, each parameter was varied individually from a constant baseline condition. The baseline case was produced by simulating breakthrough in the bench-scale fixed-bed adsorber using unpreloaded carbon isotherm and rate parameters based on the CMBR isotherms and corresponding rate parameters for Huron River water over a period typical of the run times used in this research. For the time-variable parameter simulations, a nonlinear regression software package (SYSTAT, Systat, Inc., Evanston, IL) was used to obtain continuous functions of the isotherm and rate parameter values with preloading time that were incorporated into the model. Exponential and linear expressions, which give parameter values as functions of preloading time, were fitted to the isotherm and rate data given in Tables 2 and 4, respectively, for the Huron River and the PMA background water data. The resulting equations are presented in Table 5. In the sensitivity analysis, parameter expressions for the Huron River water CMBR-based system were varied one at a time from the baseline condition, and the resulting simulations are plotted in Figure 2. Examination of the breakthrough curves presented in Figure 2 reveals that the greatest impact on this profile was caused by changes in Freundlich KFand impedance factor values. Decreases in the Freundlich KFvalue caused a very sharp rise in the latter portion of the breakthrough profile. This rapid rise was probably due to the coupled effect of an accelerated approach to equilibrium as the carbon became loaded with solute and a simultaneous lowering of capacity as KF values declined. The effect produced by the increasing impedance largely impacted intermediate time data. The decreasing rate of uptake of Envlron. Scl. Technol., Vol. 28, No. 4, 1994 618
Table 5. Mathematical Expressions Used in Time-Variable-ParameterModeling Approach (with Variable t in wk)
modeling parameter
Huron River water CMBR
Freundlich KF = f ( t ) Freundlich n = n(t) film transfer, kf = g(t) impedance, T = h(t)
Huron River water MIDDAS (column) 0.18 + 0.22e2.0t 0.0040t .t 0.72 0.0037e-0.37t 4.8 - 4.2e-0.36t
1.4e0.44t 0.042t + 0.54 0.0034e-0.3It 7.2 - 6.1e-0.70t
1.0-
................
0
,..’
KF varying tau varying
5
10
,/’
15
20
25
30
time (days)
Figure 2. Sensitivity of time variable modeling approach to individual parameters.
Table 6. Physical Parameters Used for Bench-Scale Fixed-Bed Adsorber Studies
background water Huron River water polymaleic acid background water
influent TCE carbon bed flow rate (FglL) dose (g) length (cm) (mLimin) 51.2 53.4
4.465 6.007
5.57 7.44
16.7 16.6
solute by the carbon as r increased promoted faster breakthrough of solute. Smaller impacts were noted for variations in Freundlich n and film transfer coefficient (kf)values. Increases in n actually produced a decrease in the breakthrough profile in the sensitivity analysis. This result is an artifact arising from changing n while holding KFconstant which,in effect, results in an apparent increase in isotherm capacity. In actuality, increases inn are always accompanied by decreases in KF. The notable feature of the curve resulting from the n variation is that the effect is relatively small, although it still would provide some offset to the impacts of declining KF values. The range of impact of decreasing film-transfer coefficient (kf)values is surprising; changes in this parameter are significant over the entire period simulated. The mechanistic nature of this parameter would suggest that kfvariations would primarily impact early time data and diminish thereafter (3, 27, 30). This behavior may be due to the relatively large drop in kf (-70 % ) that was seen with these data. It may also relate to the portion of the breakthrough curve simulated, which reflected only about 50 ’?6 breakthrough. As breakthrough approaches completion, the impact of changes in kf may very well decrease. Fixed-Bed Adsorber Experimental Data and Modeling Results. Breakthrough data were obtained for TCE in the two background waters over a period of 4 weeks using the bench-scalefixed-bed adsorber system. Physical specifications for the adsorber runs are given in Table 6. For each set of fixed-bed breakthrough data, both constant 620
Envlron. Scl. Technol., Vol. 28, No. 4, 1994
polymaleic acid water CMBR 1.7e-0.20t 0.59 - 0.08e-0,78t 0.0042e4.27t 0.020t + 0.66
parameter and time-variable parameter simulations were made using the pore diffusion model. For the constant parameter simulations, parameter sets obtained at each of the individual preloading levels were used in the pore diffusion model to simulate bench-scale fixed-bed adsorber TCE breakthrough behavior. The time-variable-parameter pore diffusion model was used to ascertain whether better predictive capability could be achieved if equilibrium and rate parameters are made to vary with time of operation. In the case of the Huron River water, MIDDAS isotherm data were available only up to 3 weeks of preloading, and parameters for the fourth week were therefore estimated. Due to the tendency of the isotherm parameters to go toward limiting values, 4-week isotherm parameters were taken to be identical to those measured from the 3-week data. For film transfer, the kffrom the 4-week preloaded CMBR measurement was used due to this parameter’s insensitivity to isotherm data. Lastly, impedance was estimated by extrapolating the existing data for the earlier weeks in a manner similar to that seen for the CMBRbased impedance data. Huron River Water System. The data and the constant parameter predictions using the CMBR isotherm set for TCE breakthrough in the Huron River system are presented in Figure 3a. The data are bracketed by predictions from the unpreloaded carbon and 2-week preloaded parameters, with the unpreloaded carbon set overpredicting removal and the 2-week set underpredicting removal. The close proximity of the 4-week CMBR set to the 2-week set prediction in Figure 3a suggests that preloading by the Huron River water was beginning to level off. Similar bracketing behavior was observed for the individual MIDDAS-based parameter set predictions. Predictions resulting from use of the CMBR- and MIDDAS-based time-variable parameter expressions are shown in Figure 3b. The CMBR-based curve exhibited a sharper breakthrough profile than that from the MIDDAS-based set. The CMBR-based curve predicted more removal of TCE at early times. The faster breakthrough over this same time period predicted by the MIDDAS-based parameters better captured the actual breakthrough behavior, probably as a result of the decreased capacity afforded by the MIDDAS isotherms relative to the CMBR isotherms over this early time period, as well as better characterization of actual contaminant removal patterns and background organic matter competitive effects prevailing in the fixed-bed system. Similarly, at later times, the CMBR-isotherm parameter set predicted more removal than did the MIDDAS set, but unlike early time data, the CMBR-based set better reflected actual column behavior at this breakthrough stage. The sensitivity analysis presented earlier can provide insight into the reasons why a time-variable-parameter approach better fits the data. Intraparticle pore diffusion resistance was shown to primarily influence intermediate
1.o
El
,
1.0
1
a
S data
- unprld. parameters
........ 2-week parameters
____----.......................
_*-----
,.‘
0.6
...................
0
@
EIEI
0.4
0.2
........ 2-week parameters ---. 4-week parameters
0.0
0.0 0
5
10
15
20
25
30
time (days) 1.o
1 .o
0.8
b
-
0.6
-
0.4
-
0
0, 0
0.2
0
data
-CMBA prediction 5
10
15
20
25
30
time (days)
0
7
14
21
28
time (days)
Figure 3. Constant-parameter (a) and time-variable-parameter (b) model predictions for TCE breakthrough in a bench-scale fixed-bed adsorber preloaded by Huron River water.
Flgure 4. Constant-parameter (a) and time-variable-parameter (b) model predictions for TCE breakthrough in a bench-scale fixed-bed adsorber preloaded by polymaleic acid background water.
time data, causing a rapid breakthrough over this region, while decreasing capacity (as measured by&) significantly impacted later time data. Individually, the unpreloaded carbon parameters estimated too much capacity and intraparticle mass transport,while the 2-week parameters gave levels that were too much reduced. With the timevariable parameter model, the impacts due to preloading appear to be apportioned over the run time in a manner representative of the changes in equilibrium capacity and rates of adsorption that occurred in the bed. Thus, the transition from low to high values for T caused an acceleration of breakthrough due to slower mass-transfer resistances when capacity was high over intermediate time data. At later times, when intraparticle resistance reached a limiting value, the enhanced upward trend of the breakthrough data was continued as the& capacity effects became more significant. Polymaleic Acid Background Water System. The data and three constant parameter predictions for the fixedbed adsorber experiments with PMA preloaded carbon are presented in Figure 4a. The low level of breakthrough shown by the data is a reflection of the diminished impact of preloading in the PMA system relative to the Huron River background water. The 0- and 4-week predictions bracket the experimental breakthrough data. The 2-week simulation fits the data quite well until about 3 weeks of breakthrough, at which point the curve begins to overpredict removal slightly. Unlike the Huron River water predictions shown in Figure 3a, those for the PMA
background water system in Figure 4a do not indicate any slowdown in preloading over the time frame of this study. The time-variable-parameter prediction of PMA background fixed-bed adsorber data is plotted in Figure 4b. The time-variable-parameter model provided an adequate characterization of the observed breakthrough behavior, although it tended to underpredict removal slightly after about 3 weeks of run time. Overall, isotherm and rate parameters determined for the PMA background water did not change greatly over the course of this study and both time-variable and 2-week constant parameter simulations were quite similar. Given the limited range of the fixed-bed adsorber PMA background water data, it is difficult to determine which is the superior modeling approach in this case. The similar predictions of the two modeling approaches suggest that for waters which do not preload extensively,i.e., for systems in which parameters do not change markedly over run time, fixed-bed adsorber breakthrough data may be adequately simulated using a constant-parameter modeling approach and some representative “average” parameter set. Indeed, fixed-bed adsorber removal of target organic compounds in a background organic matter matrix has been successfully modeled using a single set of isotherm and rate parameters obtained on unpreloaded carbons (3, 6, 7). These studies either used concentrations of target compounds at least an order of magnitude higher than Envlron. Scl. Technol., Vol. 28, No. 4, 1094 621
those used in this work or were conducted over significantly shorter periods of time (a few days). Enhanced target compound adsorption rates from higher concentrations or a reduced time for preloading from the shorter run times would reduce the scope of any parameter changes which might occur, resulting in reasonably accurate fixedbed adsorber modeling with a single parameter set. Conversely, in the time-variable-parameter modeling approach necessary for accurate predictions of TCE breakthrough data for the Huron River water, parameters varied a great deal over the period of study. Thus, a timevariable-parameter modeling approach may be best suited when target compound concentrations are low relative to background organic matter and to fixed-bed adsorber run times long enough for significant preloading to occur. Practical Implications
For both background waters, experimental breakthrough data were found to lie between model simulations based on parameters derived from unpreloaded carbon data and those based on preloaded carbons. This finding suggests that, in practice, competitive sorption posed by background organic matter to a target solute will not be strictly simultaneous or strictly preloading in nature. Nonetheless, the bench-scale fixed bed adsorber data do define two modeling regimes for the prediction of preloading system behavior. For background waters that do not cause extensive changes in parameter values with preloading, the use of parameters obtained on unpreloaded or an intermediately preloaded carbon may reasonably simulate fixed-bed adsorber behavior. One indication of this state may be that intraparticle diffusion in a preloaded carbon is not yet substantially diminished from the free liquid diffusion of the target solute. In the case where isotherm and rate parameters are observed to change with preloading over the time period of interest, the time-variableparameter approach is the likely candidate for accurate predictions. An intraparticle diffusion coefficient several factors less than free liquid diffusion of the target solute may be a sign for this condition. It is clear that any pretreatment options or system design features implemented to reduce preloading effects would also facilitate a constant parameter modeling approach. One design feature that may reduce the impacts of preloading is the selection of carbons with very small pore size distributions to enhance size exclusion of relatively large molecular weight background organic matter. Another is to optimize pretreatment options to remove as much background organic material as possible prior to treatment by activated carbon. Unfortunately, it is not possible to know a priori how standard pretreatment options such as coagulation and flocculation will alter the adsorbability of any particular background organic matter (35, 36), so the expected effectiveness of these process steps in reducing adverse preloading effects would have to be critically evaluated on a case-by-case basis. The tendency observed in the Huron River water data for preloading effects to approach limiting values suggests a third modeling regime: use one set of constant parameters representative of a highly preloaded state in the model. This approach was investigated by simulating breakthrough from a 1-meter long column over a period of 1 year by both time-variable and constant parameter 622
Environ. Sci. Technol., Vol. 28, No. 4, 1994
methods, using parameters representative of the preloading effects found in the Huron River treatment system. In the time-variable simulation, parameters were allowed to vary over the first 4 weeks of preloading in the same fashion as for the shorter time predictions discussedearlier. After 4 weeks of simulation, the values were fixed at those levels. In the constant parameter approach, the parameters were set at the 4-week preloading level over the entire simulation time. A breakpoint of 10% of influent concentration was chosen for comparison purposes. The constant parameter modeling approach gave a time to breakpoint of 107 days while the time-variable parameter simulation predicted 143 days. The "extra" capacity afforded by the time-variable parameter simulation over the first 4 weeks of preloading, i.e., before the model parameters became equivalent, is surprisingly large given the 1-year simulated run time. Nonetheless, use of a constant parameter approach with parameters representative of an extensively preloaded state would, in practice, provide a conservativeestimate of overall adsorber capacity that would be acceptable for preliminary design calculations. While three possible modeling regimes have been proposed, the uniqueness of each adsorption system precludes determination of which predictive approach is most appropriate without performing some isotherm and rate parameter measurements. Because of the heterogeneous characteristics of background organic matter, the amount of TOC preloaded onto a given mass of carbon is not a reliable indicator of the resulting preloading effect on adsorption of a target compound. Moreover, characteristics of the solute itself will influence the impact of preloading on its adsorption equilibria and rates. The impact of preloading may be more severe for a weakly hydrophobic compound such as TCE than for a highly hydrophobic solute that would tend to sorb to preloaded organic matter. Exact identification of the mechanisms of the preloading process, assessment of key properties that can be used to quantify the preloading potential of a background organic material, and an understanding of how solutes interact with preloaded organic matter in the preloaded state are areas requiring further research. Acknowledgments Partial support for this research was provided through Research Grant CES-8702786 from the National Science Foundation (Environmental and Ocean Systems Program), by a Department of Education award, and by an Abel Wolman Fellowship (American Water Works Association) to M.C.C. The authors express appreciation to Gina Saginor, Kerry Larson, and Nefise Karanfil for indispensable assistance with the experimental aspects of this work. Literature Cited Summers, R. S.; Roberta, P. V. In Treatment of Water by Granular Activated Carbon; McGuire, M. J., Suffet, I. H., Eds.; Advances in Chemistry 202; American Chemical Society: Washington, DC, 1983; pp 503-524. Crittenden,J. C.;Luft, P.; Hand. D. W.;Friedman, G. Water Res. 1985,19, 1537-1548. Weber, W. J., Jr. Environ. Sci. Technol. 1989, Smith, E.H.; 23, 713-722. Weber, W. J.,Jr.; Smith, E. H. Environ. Sci. Technol. 1987, 21, 1040-1050. Zimmer, G.; Crittenden, J. C.; Sontheimer, H.;Hand, D. W. In Proceedings ofthe A WWAAnnual Conference;Orlando, FL; AWWA: Denver, CO, 1988, pp 211-220.
(6) Summers, R. S.; Haist, B.; Koehler, J.; Ritz, J.; Zimmer, G.; Sontheimer, H. J.-Am. Water Works Assoc. 1989,81 (51, 66-74. (7) Speth, T. F.; Miltner, R. J. J.-Am. Water Works Assoc. 1989,81 (4), 141-148. ( 8 ) Sontheimer, H.; Crittenden, J. C.; Summers, R. S. Activated Carbon for Water Treatment. 2nd ed.: DVGWForschungsstelle: Karlsruhe, Germany,’l989. ’ Speth, T. F. J. Environ. Eng. Diu. (Am. SOC.Civ. Eng.) 1991, 117,66-79. Hand, D. W.; Crittenden, J. C.; Arora, H; Miller, J. M.; Lykins, B. W., Jr. J.-Am. Water Works Assoc. 1989,81 (l), 67-77. Carter, M. C. Analysis and Modeling of the Impacts of Background Organic Matter on TCE Adsorption by Activated Carbon. Doctoral Thesis, The University of Michigan, 1993. Carter, M. C.; Weber, W. J., Jr.; Olmstead, K. P. J.-Am. Water Works Assoc. 1992, 84 (8), 81-91. Anderson, H. A,; Russell, J. D. Nature 1976, 260, 597. Spiteller, M.; Schnitzer, M. J. Soil Sci. 1983, 34, 525-535.
Standard Methods for the Analysis of Water and Wastewater, 20th ed.; American Public Health Association: Washington, DC, 1989. Reid, P. M.; Wilkinson, A. E.; Tipping, E.; Jones, M. N. Geochim. Cosmochim. Acta 1990,54, 131-138. Nkedi-Kizza, P.; Rao, P. S. C.; Hornsby, A. G. Environ. Sci. Technol. 1985,19, 975-982. Crittenden, J. C.; Hutzler, N. J.; Geyer, D. G.; Oravitz, J. L.; Friedman, G. Water Resour. Res. 1986,22, 271-284. Oravitz, J. L. Transport of Trace Organics with OneDimensional Saturated Flow: Mathematical Modeling and Parameter Sensitivity Analysis. Master’s Thesis, Michigan Technological University, 1984.
(20) Weber, W. J., Jr.; Wang, C. K. Environ. Sci. Technol. 1987, 21, 1096-1102. (21) Halfon, E. Environ. Sci. Technol. 1985, 19, 147-753. (22) Smith, E. H.; Weber, W. J., Jr. Environ. Sci. Technol. 1988, 22,313-321. (23) Olmstead, K. P.; Weber, W. J., Jr. Environ. Sci. Technol. 1990,24, 1693-1700. (24) Draper, N. R.; Smith, H. Applied RegressionAnalysis, 2nd ed.; Wiley: New York, 1981. (25) Chu, C. F.; Ng, K. M. AIChE J. 1989, 35, 148-158. (26) Levenspiel, 0. Chemical Reaction Engineering, 2nd ed.; Wiley: New York, 1972. (27) Liu, K. T.;Weber, W. J., Jr. J.-Water Pollut. ControlFed. 1981,53, 1541-1550. (28) Langer, G.; Roethe, A.; Roethe, K.-P.; Gelbin, D. Znt. J. Heat Mass Transfer 1978, 21, 751-759. (29) Cooney, D. 0. Chem. Eng. Commun. 1991,110, 217-231. (30) Weber, W. J., Jr.; Liu, K. T. Chem. Eng. Commun. 1980, 6, 49-60. (31) Hayduk, W.; Laudie, H. AIChE J. 1974,20,611-619. (32) Roberts, P. V.; Cornel, P.; Summers, R. S. J. Environ. Eng. Diu. (Am. SOC.Civ. Eng.) 1986, 111, 891-905. (33) Ghosh, K.; Schnitzer, M. Soil Sci. 1980, 129, 266-276. (34) Atkins, P. W. Physical Chemistry, 4th ed.; Freeman: New York, 1990. (35) Randtke, S. J.; Jepsen, C. P. J.-Am. Water Works Assoc. 1981, 73 (8), 411-419. (36) El-Rehaili, A. M.; Weber, W. J., Jr. Water Res. 1987,21, 573-582.
Received for review May 27,1993. Revised manuscript received November 17. 1993. Accewted Januarv 10. 1994.” Abstract published in Advance ACS Abstracts, February 15, 1994. @
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