Three-Component Competitive Adsorption Model for Fixed-Bed and

Sep 22, 2006 - Heterogeneous natural organic matter (NOM) present in all natural waters impedes trace organic contaminant adsorption, and predictive ...
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Environ. Sci. Technol. 2006, 40, 6805-6811

Three-Component Competitive Adsorption Model for Fixed-Bed and Moving-Bed Granular Activated Carbon Adsorbers. Part I. Model Development LANCE C. SCHIDEMAN, BENITO J. MARIN ˜ AS, AND VERNON L. SNOEYINK* Department of Civil & Environmental Engineering and Center of Advanced Materials for the Purification of Water with Systems, University of Illinois, Urbana, Illinois 61801 CARLOS CAMPOS Suez Environment, 75009 Paris, France

Heterogeneous natural organic matter (NOM) present in all natural waters impedes trace organic contaminant adsorption, and predictive modeling of granular activated carbon (GAC) adsorber performance is often compromised by inadequate accounting for these competitive effects. Thus, a 3-component adsorption model, COMPSORB-GAC, is developed that separately tracks NOM adsorption and its competitive effects as a function of NOM surface loading. In this model, NOM is simplified into two fictive fractions with distinct competitive effects on trace compound adsorption: a smaller, strongly competing fraction that reduces equilibrium capacity and a larger pore-blocking fraction that reduces adsorption kinetics (both external film mass transfer and surface diffusion). COMPSORB-GAC tracks these two NOM fractions, along with the trace compound, and changes adsorption parameters according to the local surface loading of the two NOM fractions. Model parameters are allowed to vary both temporally and spatially to reflect differences in the NOM preloading conditions that occur in GAC columns. This dual-resistance model is based on homogeneous surface diffusion with external film masstransfer limitations. The governing equations are expressed in a moving-grid finite-difference formulation to accommodate the modeling of spatially varying parameters and moving-bed reactors with counter-current adsorbent flow. A series of short-term adsorption tests with fresh and preloaded GAC is proposed to determine the necessary model input parameters. The accompanying manuscript demonstrates the parameterization procedure and verifies the model with experimental data.

Introduction Granular activated carbon (GAC) adsorbers have proven to be effective and economically viable water purification systems for removing a wide variety of trace organic contaminants. Applications are expected to increase as many emerging contaminants are amenable to removal by GAC * Corresponding author phone: +1 217 333 4700; fax: 1 217 333 6968; e-mail: [email protected]. 10.1021/es060590m CCC: $33.50 Published on Web 09/22/2006

 2006 American Chemical Society

(1) and because granular adsorbents can be recovered for regeneration and reuse, which fosters more environmentally sustainable engineering practices. However, accurate longterm prediction of adsorption performance in GAC columns is hampered by difficulties in accounting for the dynamic competitive effects of the natural organic matter (NOM) present in all natural waters. NOM profoundly affects both the equilibrium capacity and the kinetics of trace compound adsorption because NOM is present at significantly higher concentrations and has a much longer mass-transfer zone (2-9). These characteristics usually cause most GAC in a column to be exposed to NOM before trace compound adsorption ensues: a phenomenon called NOM preloading that significantly complicates trace compound adsorption modeling. One important effect of NOM is a reduction in trace compound equilibrium capacity because of competition for adsorption sites, which is referred to as direct site competition, or strong competition (3, 9-13). This effect was successfully modeled in GAC columns using the homogeneous surface diffusion model (HSDM) and a single reduced value of the Freundlich isotherm capacity parameter, K, derived using natural water isotherms and the ideal adsorbed solution theory (IAST) (14). Others found that the trace compound equilibrium capacity can continue to decline for years and instead used a kinetic model with a dynamic Freundlich K value that was an empirical function of preloading time (6, 13, 15). While this approach improved predictions, it also has some critical limitations. Most importantly, this approach ignores the NOM mass-transfer zone and the resulting impact of design parameters like column depth and influent flow rate on the extent of NOM preloading. At a given preloading time, a column with greater depth or lower influent flow rate experiences less NOM preloading on average because it is exposed to less NOM per unit mass of GAC. However, this modeling approach assumes uniform preloading effects that are only a function of preloading time, and thus, it is not expected to yield good predictions for GAC systems with NOM preloading conditions that vary significantly from those used to determine the empirical model parameters. Another shortcoming is that tests for parameter determination need to have long durations. Since model parameters are functions of preloading time, the parameter tests need to have the same duration as the desired simulation period or at least until plateau parameter values are achieved, which can take years. A second major effect of NOM preloading is a reduction in adsorption kinetics that is best described by reducing the rate of external film mass transfer through the boundary layer around GAC particles (5, 6, 13, 14, 16). There has not been a consistent nomenclature for this competitive effect of NOM, but herein, it is referred to as external surface pore blockage or surface blockage for short. This effect was incorporated into a GAC kinetic model by making the external film mass transfer coefficient, kf, an empirical function of preloading time (6). Such an approach yielded good predictions for the 1 month of breakthrough data reported, but it also shared the same shortcomings noted earlier for relating parameters to preloading time. In particular, the inability to account for spatial variations conflicts with the findings of Speth (5), who observed that GAC from a reactor outlet had a kf value that was significantly higher than GAC from the reactor inlet. A third competitive effect of NOM is a reduction in the intraparticle kinetics of trace compound adsorption, which is often referred to as pore blockage or pore constriction (6, VOL. 40, NO. 21, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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13, 17-20). Several studies have successfully incorporated this effect into GAC kinetic models by varying the intraparticle pore diffusion coefficient as an empirical function of preloading time (3, 6, 13, 15), but once again, this approach suffers several previously noted disadvantages. Li et al. (2) proposed a novel modeling approach to quantify the competitive effects of direct site competition and intraparticle pore blockage as functions of the NOM surface loading by separately tracking the adsorption of three components: the trace (TR) compound, a strongly competing (SC) fraction of NOM that is similar is size to the TR compound and reduces equilibrium capacity, and a larger-sized poreblocking (PB) fraction of NOM that affects adsorption kinetics. Direct competition for sites was described as a function of the SC fraction using the IAST, and intraparticle pore-blockage effects were described by varying the surface diffusion coefficient as an empirical function of the PB compound surface loading. Because the adsorption parameters were related to NOM surface loading instead of preloading time, the parameters were not specific to reactor operating conditions and could be determined independently. This model was validated experimentally for different adsorbents and operating conditions using a powdered activated carbon ultrafiltration (PAC-UF) reactor and a synthetic water with known surrogate compounds corresponding to the smaller SC fraction and the larger PB fraction of NOM. Ding et al. (21) extended the 3-component modeling approach to the PAC-UF treatment of natural waters by developing a procedure using independent batch tests to characterize the relevant adsorption parameters for the SC and PB fractions of NOM, which were represented as fictive compounds that caused the equivalent competitive effects as the heterogeneous NOM mixture. These authors showed that the 3-component model provided reasonable predictions that were a significant improvement over previous approaches. NOM preloading effects on trace compound adsorption in GAC adsorbers can be reduced by using a moving-bed reactor with counter-current adsorbent flow or by adding layers of fresh GAC periodically at the outlet of an upflow adsorber. In either case, fresh GAC is introduced only when needed for trace compound removal, which reduces NOM preloading and has been shown to reduce carbon usage rates by up to 60% (3, 5, 22-24). Despite better efficiency, layered and counter-current adsorption systems have not been used extensively because of concerns with liberating carbon fines and higher reactor capital costs. However, applications are expected to increase because of increasing attention on NOM preloading effects and some recently developed processes that address the practical concerns (25, 26). Predictive mathematical adsorption models for non-fixed-bed systems have not been adequately developed, but they are needed to better understand and optimize GAC adsorption processes. The main goal of this study is to further extend the 3-component adsorption modeling approach to various GAC column systems including a parameter determination procedure for natural water applications. To accomplish this goal, the specific objectives were to (i) develop a dualresistance HSDM model that tracks three components and allows equilibrium and kinetic parameters to vary in time and space, (ii) investigate the effect of NOM preloading on external film mass-transfer coefficient and define a mathematical relationship between the two for use in the model, and (iii) provide a model with the ability to simulate a movingbed reactor with counter-current adsorbent flow. This paper presents the needed developments to realize a 3-component GAC adsorption model and an independent parameterization procedure for natural water applications. The accompanying paper demonstrates the parameter determination procedure for a natural water application and provides model verification by comparing predictions with experi6806

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mental breakthrough curves for fixed-bed and moving-bed configurations.

Materials and Methods Water. Groundwater from a well at the Newmark Civil Engineering Laboratory (NCEL) of the University of Illinois was used for natural water experiments. NCEL water was filtered through greensand to remove iron and particulate matter and then stored at 4 °C in a stainless steel barrel with 100 mg/L of sodium azide to arrest biological activity. The dissolved organic carbon (DOC) concentration of NCEL water was 2.4 mg/L. Just prior to experimental use, the NCEL water was spiked with radio-labeled atrazine, which served as the trace compound for this study. NCEL water has a distribution of molecular weights of qcr Ds,0

(6)

where Ds,0 is the initial surface diffusion coefficient without NOM preloading, qcr is the critical PB surface loading at which pore blockage ensues, and β quantifies the rate of exponential decay. Our 3-component GAC modeling approach also assumes that the pore-blockage mechanism is applicable to both the TR and SC compounds because the compounds are assumed to be of similar size and to compete for the same adsorption sites. Direct Competition For Adsorption Sites. The competitive effect of the SC fraction of NOM on TR compound adsorption capacity was quantified using the IAST with the assumption that the PB fraction has a negligible effect on the equilibrium adsorption capacity of the other two components. The IAST uses the single-solute adsorption relationship of each component without competition, which was described using the Freundlich isotherm model (eq 1). The IAST equations for a bisolute system of the SC and TR compounds with single-solute Freundlich isotherm parameters can be expressed as follows (3)

)[ )[

( (

] ]

qSC nTRqTR + nSCqSC qTR + qSC nSCKSC

n

qTR nTRqTR + nSCqSC Ce,TR ) qTR + qSC nTRKTR

n

Ce,SC )

SC

(7) TR

(8)

Assuming that the surface loading of the SC compound dominates over the TR compound (i.e., qSC . qTR) and nTR is comparable to or lower than nSC, then these equations can be simplified and rearranged to the following form (34)

qTR )

[

1/nSC qSC ) KSCCe,SC

]

KTRnTR nSC

nTR

[qSC(z,t)](1-nTR)Ce,TR

(9) (10)

Equation 9 shows that the SC compound equilibrium surface loading can be determined independently from its single-solute Freundlich parameters. Equation 10 shows that the TR compound equilibrium surface loading can then be determined explicitly from its Freundlich parameters as well as nSC and qSC. Therefore, the simplified IAST of eqs 9 and 10 allow the bisolute system to be decoupled and analyzed as two sequential pseudo-single-solute applications of the HSDM, which is not possible with eqs 7 and 8. Qi et al. (34) showed that eq 10 provided predictions that were a very good approximation of those by the unsimplified IAST (eqs 7 and 8) for a variety of trace compounds over a wide range of concentrations. The HSDM assumes instantaneous equilibrium at the outer surface of the adsorbent as a boundary condition for eq 3. Thus, eqs 9 and 10 were simply used to define the equilibrium relationship between liquid and solidphase concentrations at the outer surface of the adsorbent particle. The simplified IAST approach and equations presented here differ from the ones used to quantify direct competition in the original 3-component modeling approach developed for completely mixed PAC-UF systems by Li et al. (2); these authors developed a different simplified IAST equation for the TR compound surface loading that was a function of the total mass (liquid and solid phase) of SC compound in the reactor and that required assuming complete reactor mixing, which is not valid for most GAC adsorbers. Equation 10 is more general in that no particular reactor configuration or

mixing condition is required and the equilibrium relationship is only applied instantaneously at the outer surface of the particle, which is an assumption already embedded in the HSDM. It is also important to note that the IAST was developed on the basis of molar concentrations rather than mass concentrations. In developing the parameters for the SC compound as described in the accompanying paper, the SC and TR compounds are assumed to have the same molecular weight, which makes it possible to use either mass or molar concentrations with eqs 9 and 10 that are derived from the IAST. Moving-Grid Finite-Difference Numerical Solution. The numerical solution procedure selected for the 3-component GAC model was a finite-difference approach that provided a convenient way to incorporate spatial variations in the adsorption parameters. The numerical formulation followed the approach of Yuasa (35), which utilized the Crank-Nicolson implicit method (36) to transform the governing partial differential equations (eqs 2-4) and corresponding initial/ boundary conditions into a system of finite-difference equations. Newton’s method was used to approximate the nonlinear isotherm relationship (eqs 1, 9, or 10). Yuasa’s original approach was modified to allow for transient equilibrium and kinetic parameters (Freundlich K, kf, and Ds) that can vary in time and space according to eqs 5, 6, and 10, which satisfies the first objective of this study. The transient parameters are updated at each time step and axial finite-difference node before the resulting system of linear equations are solved by Gauss-Seidel elimination (37). Yuasa (35) also proposed the use of a moving grid of finitedifference nodes that was integrated into the 3-component GAC model. With this approach, the grid of finite-difference nodes in the axial (z) and radial (r) directions is adjusted over time as the mass-transfer zone changes, which increases the speed and accuracy of the numerical solution. New finitedifference nodes are added whenever breakthrough occurs above some threshold level at the last grid node (unless the end of the column or the center of the adsorbent particle is reached). Conversely, a finite-difference node is subtracted from the grid when it becomes saturated above a threshold surface loading. Also, the spacing of the finite-difference nodes changes to keep the total number of bed sections between 10 and 20 in each direction (z and r). Since each component can have a different mass-transfer zone, the grid nodes can also be different for each component. Thus, it was necessary to add linear interpolation routines that computed the surface loading of previously determined components at the particular grid nodes of the component currently being analyzed. Modeling Counter-Current Adsorbent Flow. The moving-grid finite-difference approach also provided a convenient opportunity to model counter-current adsorbent flow, which is of interest as a method for reducing NOM preloading effects and satisfies the third major objective of this study. Counter-current adsorbent flow was incorporated into the model by adding some additional criteria that trigger a shift in the moving grid. The model input file allows the user to specify specific times and carbon amounts to be added or removed from the reactor. When the model reaches one of the specified times that GAC is to be removed, the finitedifference nodes associated with the specified amount of GAC are considered saturated and are shifted out of the moving-grid. To simulate the addition of new GAC layers at a specified time, the reactor length is simply increased corresponding to the amount of new GAC. The model then automatically adds new finite-difference nodes as breakthrough occurs into the added GAC layers. When this approach is used, it is necessary to coordinate the locations of the finite-difference nodes with the amounts of carbon to VOL. 40, NO. 21, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 1. Summary of Parameterization Procedure for the 3-Component COMPSORB-GAC Adsorption Modela parameters determined

model or equation used for parameterization via data fitting

experiment or data source for parameterization

key assumptions and comments on parameterization procedure

trace compound: K, 1/n SC fraction of NOM: K, 1/n

isotherm for trace compound in organic-free water using pulverized GAC (PGAC)

Freundlich isotherm equation qe ) KCe1/n

assume SC fraction has the same single-solute isotherm params as trace compound

SC fraction of NOM: C0

isotherms for trace compound in natural water using PGAC

equivalent background compound-ideal adsorbed solution theory (EBC-IAST)

molecular weight (MW) of SC fraction equals that of trace compound, assume DOC equals 50% of NOM mass

PB fraction of NOM: C0, K, 1/n natural water DOC isotherm DOC mass balance (can be obtained simultaneously C0,PB ) C0,NOM - C0,SC with trace compound isotherm) Freundlich isotherm equation

calculate SC fraction using already determined equilibrium params and subtract from total DOC for PB fraction

trace compound: Ds,0, kf,0 SC fraction of NOM: Ds,0, kf,0

short-bed adsorber (SBA) for conventional dual-resistance trace compound in natural water homogeneous surface using GAC diffusion model (HSDM)

use only early and late data for independent fittings of kf and Ds, assume SC fraction has the same kinetic params as the trace compound

PB fraction of NOM: Ds,0, kf,0

SBA test for DOC of natural water using GAC

DOC mass balance HSDM

calculate SC fraction removal using HSDM with already determined params and subtract from DOC for PB fraction

params describing external surface pore blockage for trace compound and SC fraction: R, kxf,min

SBA tests for trace compound using GAC preloaded with NOM (4-6 preloading conditions needed)

HSDM empirical fit of film mass-transfer coefficient vs PB fraction surface loading kf/kf,0 ) kxf,min + (1 - kxf,min) exp(-RqPB)

calculate SC fraction using HSDM with already determined params and subtract from DOC for PB fraction, assume PB effect on trace compound and SC fraction kinetics are the same

params describing intraparticle pore blockage for trace compound and SC fraction: β, qcr

batch kinetic tests of trace compound with PGAC preloaded with NOM (4-6 preloading conditions needed)

HSDM empirical fit of surface diffusion coefficient vs PB fraction surface loading Ds/Ds,0 ) exp[-β(q - qcr)]

calculate SC fraction using HSDM with already determined params and subtract from DOC for PB fraction, assume PB effect on trace compound and SC fraction kinetics are the same

average GAC particle diameter and density, bulk density of GAC bed trace compound, C0 GAC mass, influent flow rate, column run time

GAC characteristics that are usually available from the supplier reactor operational conditions selected by system designer

a

NOM) natural organic matter; SC) strongly competing fraction of NOM; PB ) pore-blocking fraction of NOM.

be shifted into and out of the reactor. Otherwise, the process can introduce errors associated with discrete boundaries of the finite-difference nodes that do not align with the GAC layers being added or removed.

Determination Of Model Parameters The 3-component COMPSORB-GAC modeling approach described above represents a significant advancement by integrating spatial variability in the competitive phenomena of NOM preloading into GAC kinetic models while balancing the needs for model simplicity and a practical parameter determination effort. COMPSORB-GAC requires all the typical parameters associated with HSDM mathematical adsorption modeling, and these must be defined for each component. There are also a four additional empirical parameters from eqs 5 and 6 that are needed to characterize the magnitude and rate of the external and intraparticle pore blockage. The parameters are specific to the combination of trace compound, source water, and GAC because their particular physicochemical characteristics influence the competitive adsorption interactions. Table 1 provides a summary of the model parameters, experimental data sources, key assumptions and data analysis procedures that are needed. All of the proposed experiments are relatively short-term and can be 6810

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conducted independently of the desired prediction interval. The accompanying manuscript illustrates this parameterization procedure and provides model verification by comparing experimental breakthrough data at multiple EBCTs to predictions with the independently determined parameter set.

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Received for review March 13, 2006. Revised manuscript received July 28, 2006. Accepted August 2, 2006. ES060590M

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