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Hall, L. H.; Kier, L. B.; Murray, W. J. J. Pharm. Sei. 1975, 64,1974. Horvath, A. L. Halogenated Hydrocarbons; Marcel Dekker, Inc., New York, 1982. Dietrich, W. S.;Dreyer, N. D.; Hansch, C. J.Med. Chem. 1980,23,120. Cornish-Bowden, A.; Wong, J. T. Biochem. J. 1978,175, 969. Hansch, C.; Quinlan,J. E.; Lawrence, G. L. J. Org. Chem. 1968,33,347. Chiou, C. T.; Schmedding, D. W. Environ. Sei. Technol. 1982,16,4. Opperhulzen, A.; Gobas, F. A. P. C.; Van der Steen, J. M. D.; Hutzinger, 0. Environ. Sei. Technol. 1988, 22, 638. Yalkowski, S.H.; Valvani, S. C.; Mackay, D. Residue Rev. 1983,85,43.
(11) Baker, R. J.;Donelan, B. J.; Peterson, L. J.; Acree, W. E., Jr.; Tsai, C.-c. Phys. Chem. Liq. 1987,16,279. (12) Yalkowski, S. H.; Valvani, S. C. J. Pharm. Sei. 1980,69, 912. (13) Mackay, D.; Shiu, W. Y. J. Chem. Eng. Data 1977,22,399. (14) Miller, M. M.; Wasik, S. P.; Huang, G. L.; Shiu, W. Y.; Mackay, D. Environ. Sei. Technol. 1985,19,522. (15) Water Related Environmental Fate of 129 Priority Pollutants. EPA Report 4401479-0296,1979;Vol. 11. (16) Shiu, W. Y.; Doucette, W.; Gobas, F. A. P. C.; Andren, A.; Mackay, D. Environ. Sci. Technol. 1985,22,651. (17) Tewari, Y. B.; Miller, M. M.; Wasik, S. P.; Martire, D. E. J. Chem. Eng. Data 1982,27,451.
Received July 25, 1988. Accepted February 16,1989.
Evaluation of Mass Transfer Parameters for Adsorption of Organic Compounds from Complex Organic Matrices Edward H. Smith and Waiter J. Weber, Jr."
Environmental and Water Resources Engineering, The University of Michigan, Ann Arbor, Michigan 48109 ~
The short-bed adsorber (SBA) technique has been demonstrated to be an effective method for estimation of maw transport parameters for adsorption of target organic compounds from otherwise organic-free background waters. This work evaluates the procedure for the more pertinent circumstance in which a water or wastewater is not only comprised of target organic species but also contains complex and uncharacterized dissolved organic matter. The SBA is compared with other parameter estimation methods for adsorption of two target compounds from different background waters. A system-specific modeling approach is found to accommodate the variable impacts of different background waters on the equilibrium and kinetic relationships of the target species. Verification studies reveal that mass transfer parameters determined by the SBA technique generally yield more accurate predictions of fixed-bed adsorber breakthrough profiles for target compounds than do those determined by the other methods evaluated.
Introduction Dual resistance rate models have undergone extensive testing and refinement for describing and predicting the adsorption of organic substances by microporous adsorbents in fixed-bed reactor systems (I). The advantages that have been thus gained by refinements in model formulation and numerical solution techniques can potentially be negated, however, by the inaccuracies and uncertainties yet associated with the evaluation of equilibrium and mass transport coefficients required for model simulation and subsequent scale-up. Estimation of reliable mass transfer parameters has been a particular challenge for research aimed at characterizing adsorption processes for such heterogeneous systems as those commonly encountered in environmental field applications. Techniques for evaluating external and intraparticle mass transfer, the two mass transport steps considered important in the development of adsorber models, have, logically, been developed in simple systems of one or more target species in otherwise organic-free background water. It remains to examine the applicability of these parameter estimation techniques for 0013-936X/89/0923-0713$01.50/0
the more pertinent situation of waters and wastewaters containing complex humic and fulvic materials and other uncharacterized dissolved organic matter as well as the particular target organic compounds of interest. External, or film, mass transfer coefficients have often been estimated by using semiempirical correlations developed from experimental data for particle-fluid mass transfer processes measured for specific solutes and solid particulates. A wide range of correlations have been published, each distinguished by an observed functional relationship between the dimensionless Reynolds, Schmidt, and Sherwood numbers. The primary system parameters incorporated into these dimensionless terms are the mass flow rate and void space in the bed. Important solute-solid information includes the free liquid diffusivity of the sorbate and a characteristic length parameter related to the solid particles, usually the equivalent particle diameter, which may be modified by an empirically determined shape factor. Several attempts have been made to deduce a generalized working correlation by nonlinear analysis of all reported film mass transfer data (2,3). The two major advantages of a literature correlation model are that the film diffusion coefficient can be determined without experimental effort and that it provides a means for evaluating external mass transfer independently of other physical and chemical processes in the system. Inherent difficulties in applying these models to granular activated carbon adsorption systems are that (I) nearly all are developed with solids that are different in chemical and physical character than activated carbon and thus ignore potential impacts of surface topography and roughness on film-controlled mass transfer ( 4 , 5 ) ,(2) calculations of free liquid diffusivity and of film diffusion do not incorporate interactions between target contaminants and other background species in solution, and (3) values computed by different correlations vary significantly, and there are no established criteria for determining which correlation may be best suited to a particular system. Film diffusion may also be evaluated by various model calibration techniques by using system-specific experimental data. For example, the film diffusion coefficient, k f ,may be determined from column breakthrough data by
0 1989 American Chemical Society
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using an intraparticle mass transfer rate determined from analysis of batch reactor adsorption data (6). An increasingly popular methodology is to estimate the external diffusion coefficient directly from the initial-time (incipient) breakthrough data of a microcolumn or short-bed adsorber (SBA) (4, 7-10). If the experiments are properly designed, the influence of intraparticle diffusion on the first minutes/ hour of breakthrough is eliminated, validating the assumption of film diffusion control in this region. Because the hydrodynamics of the SBA are similar to those of field-scale fixed-bed adsorbers, the approach more accurately accounts for solid and solution heterogeneities and interactions in the evaluation of kf. Effective internal (surface) diffusion coefficients, denoted here by D,, are normally determined by model calibration of time-concentration rate data measured in systems for which the effects of film mass transfer are either eliminated or quantified. Batch reactors provided with mixing adequate to eliminate the effects of film transport are often employed to estimate D,. Values obtained by this technique are then used in combination with external mass transport coefficients determined by one of the methods discussed above to predict the dynamic behavior of model compounds in fixed-bed adsorbers. Alternatively, the SBA technique can be employed to evaluate D, from the same data set used to estimate kf. The effective intraparticle diffusion rate is searched over the entire breakthrough profile by using the previously determined value for kf. The batch reactor and SBA techniques have both been used to evaluate internal mass transfer coefficients for adsorption of target organics on granular carbon from background waters that contain natural organic matter (10-12). Under certain conditions, significant differences in values of D, obtained from the two experimental systems have been observed, with SBAdetermined values generally resulting in more accurate predictions of fixed-bed breakthrough profiles for both single- and dual-component target solute systems (10). Discrepancies between D,values measured by the two different techniques are assumed to be due largely to differences between the two types of reactors with respect to characteristic hydrodynamic conditions and associated solute removal patterns. For instance, in column-type adsorbers, the concentration gradient at the particle surface is a function of an increasing bulk-phase concentration of adsorbate, approaching a constant value of C,. In a batch reactor, however, the bulk-phase concentration decreases with time, resulting in a different gradient pattern at the carbon surface. The different mixing mechanisms associated with the two reactor systems, and the extent to which these differences are reflected in the corresponding kf values, may contribute to different internal surface concentration gradients and, therefore, variable estimates of D,. In cases of complex mixtures of multiple adsorbing species, it is anticipated that the sequence of loading of individual species onto a given particle of adsorbent will be different for the two reactor configurations. It is also likely that the intricate matrix of solid-olute and solute-solute interactions obtaining in complex mixtures may compound such differences in the intraparticle mass transport step. A differential batch reactor technique employing a microdepth column in combination with a batch recycle tank has been utilized by several investigators to estimate internal diffusion coefficients (8, 13). While this system more accurately approximates the hydrodynamics of a fixed-bed adsorber, it would appear to suffer from the same deficiencies as the batch reactor with respect to simulating 714
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the concentration profiles of adsorbates in flow-through column reactors. In this study, the mass transport parameter calibration procedure pertaining to the SBA is detailed, and the results of the technique are compared with those of other parameter estimation procedures and verified in deeper adsorbers for target compounds in complex background waters comprised of hazardous organics and natural organic matter. A system-specific modeling approach in which equilibrium and mass transfer coefficients are evaluated for the target compound directly in the presence of the background water is employed. This approach has proven useful for descriptive and predictive modeling of single- and dual-component systems of target solutes in uncharacterized organic backgrounds (10-12). A homogeneous surface diffusion version of a dual-resistance mass transfer model, the Michigan Adsorption Design and Applications Model (MADAM),was used to simulate fixedbed adsorber performance (1, 14). The Freundlich isotherm equation was used to describe the equilibrium relationship. Model sensitivity analyses were performed for selected data sets to secure at least a qualitative appreciation for the uncertainties involved in numerical parameter search techniques, and to demonstrate how such analyses can serve as an aid in the optimization of bench-scale experimental design for mass transport parameter determination. Experimental Section Solutes. Trichloroethylene (TCE) and p-dichlorobenzene (p-DCB) were chosen as target solutes. These compounds were selected because they exhibit different adsorption characteristics, have been identified in contaminated surface and ground waters, have been designated as priority pollutants by the U.S.EPA, are relatively straightforward to analyze, and embody a range of solute properties and characteristics. TCE is a straight-chain, unsaturated aliphatic of relatively high volatility and solubility compared to the aromatic p-DCB. Background waters included a field leachate from a hazardous waste landfill cell (HWL, Wayne Disposal, Rawsonville, MI) and a laboratory simulated leachate comprised of a commercial humic acid and a three-solute mixture of known organic contaminants, designated throughout as TRISOL+HA. For purposes of this study, the background waters are characterized according to their total organic carbon (TOC) content only. Raw HWL was prefiltered through a prewashed glassfiber filter prior to use to remove suspended particles that might adsorb pollutants in competition with activated carbon. Appropriate volumes of leachate were diluted with deionized distilled water (DDW) to the desired organic background concentration in terms of TOC. The humic acid in the TRISOL+HA mixture was prepared as a stock solution by dissolving dried Aldrich humic acid (Aldrich Chemical Co., Milwaukee, WI; Lot No. 3061-KE) in DDW at pH 11. Following readjustment of the pH to 7, the solution was filtered through a glass-fiber filter to remove undissolved solids. The TOC of the filtrate was then measured. As with the HWL, humic acid stock was diluted with DDW to the desired TOC concentration. In the experiments described in this study, the humic acid concentration used was 15 ppm as TOC; hence the notation TRISOL+HA(15). The three solutes constituting the TRISOL mixture (lindane,tetrachloroethylene,and carbon tetrachloride) were chosen by selection criteria similar to those for the two target compounds. The concentrations of these solutes used in all studies were approximately 1000,575, and 525 yg/L, respectively. This corresponds
to an equimolar amount of each compound of -3.4 pmol/L and a TOC level of 0.37 pg/L. Working solutions consisted of background water spiked with TCE or p-DCB to the desired concentration. Experiments were conducted at room temperature (22 f 2 "C) at pH 6.5 f 0.2. Mass concentration determinations of TCE, p-DCB, and the TRISOL compounds were by gas chromatography using a liquid-liquid extraction procedure and an external standard calibration. Analysis of other organic materials, humic acid and HWL, was by direct TOC measurement or by ultraviolet spectroscopy correlated with TOC measurements. Adsorbent. The adsorbent used in all experiments was Filtrasorb 400 activated carbon (F-400, Calgon Corp., Pittsburgh, PA), a bituminous coal based carbon consisting of irregularly shaped granules. Powdered carbon was used for the isotherm experiments to minimize equilibrium time. For rate studies, the 30/40U.S. standard sieve size, which corresponds to an arithmetic mean particle radius of 256 pm, was selected. Other physical properties of F-400 are documented elsewhere (15),and the carbon preparation procedure is given in a companion paper (IO). Adsorption Studies. Bottle-point isotherm studies were used to establish the equilibrium relationship required for solution of the dynamic model. Rate experiments were performed both in completely mixed batch reactors (CMBRs) and in SBA systems of 1-2-cm bed depth. Dynamic studies were also conducted using fixed-bed systems that were 4-5 fold deeper for the purpose of parameter and model verification. Although these deeper beds used for model verification are significantly more shallow than fixed-bed adsorbers commonly used in practical applications, they were sufficiently deep to contain the entire adsorption wave front for the target compounds, the critical requirement for this study. The average interstitial velocity was 1.7-1.9 cm/s in both sets of experiments, corresponding to a superficial hydraulic loading rate of approximately 10-11 gal min-I ft-2 (0.4-4.5 m3 m-2 min-') for a bed void ratio range of 0.35-0.4. The details of both equilibrium and kinetic experiments are presented in a companion paper (IO). Parameter Evaluation Procedures SBA Technique. A primary objective of this study was to investigate the application of the SBA technique, developed for simple systems of one and two target compounds in otherwise organic-free water (7,16), to systems containing complex forms of background dissolved organic matter (DOM) in addition to the target compounds. In this approach, the fixed-bed adsorber model was calibrated by using SBA data to simultaneously determine kf and D,. The general procedure is to first estimate kffrom the initial segment of the breakthrough curve followed by a nonlinear regression analysis to search for the value of D, over the entire remaining portion of the data profile. The minimization function used in the fitting exercise for both parameter searches is based on the square of the residuals, or
where FMIN is the value of the minimization function, N is the number of data points, C , , is the dimensionless predicted concentration at time, t (Le., Cp,JC0),and Cd,t is the dimensionless concentration determined experimentally at time, t (cd,t/c,,). More specifically, the calibration procedure involves performing several preliminary computer runs to obtain
. . . . . . . . . . . . . . . . . . . . . . . . . - DATA 1 - MODEL (Ds + 50%) 2 - MODEL (Ds = 4.7~10-'0 c ~ / s ) 5 - MODEL (Ds - 50%)
0
'4
I
Figure 1. Initial segment of SBA breakthrough data and model calibrations to illustrate numerical search for k,. One hour is equivalent to 1125 bed volumes for the data shown.
rough estimates of kfand D,. Coincident with this initial approximation is an examination of the first 2-3 h of model calculations to note at which point (on the throughput scale) substantive changes in D, produce differences in the predicted values of concentration. This is illustrated in Figure 1for the case of TCE in TRISOL+HA(15) background. Because external mass transfer alone controls over the initial portion of the profile, this film region can then be best fit by varying kf until the residuals are minimized for the region. As demonstrated in Figure 1, the film region was typically the first 30-60 min of data, as a f50% alteration in the value of the intraparticle diffusion coefficient produced no shift in the model profile for a fixed value of kf. Once kfis determined, D, is varied by trial and error (or a step-search routine can be implemented) against the fixed value of kf until a minimum value of FMIN is achieved for data covering the entire duration of the experiment. Rate coefficients determined by this procedure were used directly in FBR verification studies employing deeper beds. The effects of dispersion on SBA breakthrough profiles have been examined for systems having Peclet numbers similar to those associated with the SBAs employed in this study (
