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Kinetics of Salicylic Acid Adsorption on Activated Carbon Milan Polakovic,*,† Tatiana Gorner,‡ Fre´de´ric Villie´ras,‡ Philippe de Donato,‡ and Jean Luc Bersillon‡ Department of Chemical and Biochemical Engineering, Faculty of Chemical and Food Technology, Slovak University of Technology, Radlinske´ ho 9, 812 37 Bratislava, Slovak Republic, and Laboratoire Environnement et Mine´ ralurgie, Ecole Nationale Supe´ rieure de Ge´ ologie, UMR 7569 Institut National Polytechnique de Lorraine & CNRS, 15, av. du Charmois, BP 40, 54501 Vandoeuvre-le` s-Nancy Cedex, France Received November 21, 2004. In Final Form: January 7, 2005 The adsorption and desorption of salicylic acid from water solutions was investigated in HPLC microcolumns packed with activated carbon. The adsorption isotherm was obtained by the step-up frontal analysis method in a concentration range of 0-400 mg/L and was well fitted with the Langmuir equation. The investigation of rate aspects of salicylic acid adsorption was based on adsorption/desorption column experiments where different inlet concentrations of salicylic acid were applied in the adsorption phase and desorption was conducted with pure water. The concentration profiles of individual adsorption/desorption cycles data were fitted using several single-parameter models of the fixed-bed adsorption to assess the influence of different phenomena on the column behavior. It was found that the effects of axial dispersion and extraparticle mass transfer were negligible. A rate-determining factor of fixed-bed column dynamics was the kinetics of pore surface adsorption. A bimodal kinetic model reflecting the heterogeneous character of adsorbent pores was verified by a simultaneous fit of the column outlet concentration in four adsorption/ desorption cycles. The fitted parameters were the fraction of mesopores and the adsorption rate constants in micropores and mesopores, respectively. It was shown that the former rate constant was an intrinsic one whereas the latter one was an apparent value due to the effects of pore blocking and diffusional hindrances in the micropores.
Introduction The capacity and rate factors are key quantities in the fixed-bed adsorption. In different application areas including the removal of organic compounds from drinking water or wastewater, they constitute the basis for the selection of suitable adsorbents, design, and process optimization of plant adsorption units and for the analysis of their economical, long-term operation. High capacities of activated carbon for adsorption of organic molecules and low pollutant concentrations result in a long duration of column experiments. For that reason, the experiments aimed at obtaining equilibrium and mass transport properties of adsorption systems have mostly been conducted in separate batch studies; the bottle point technique has traditionally been used for the determination of adsorption isotherm parameters, and the pore or surface diffusivities have been estimated from stirred batch experiments. Fixed-bed experiments are then conducted for the verification of models.1-3 The so-called homogeneous surface diffusion model (HSDM) has been predominantly used for the modeling of fixed-bed adsorption of organic water pollutants on activated carbon.1,4-9 HSDM incorporates two phenomena responsible for spreading of breakthrough curves: the * Corresponding author. E-mail:
[email protected] † Slovak University of Technology. ‡ Institut National Polytechnique de Lorraine. (1) Van Vliet, B. M.; Weber, W. J. J.; Hozumi, H. Water Res. 1980, 14, 1719-1728. (2) Crittenden, J. C.; Hand, D. W. In Fundamentals of adsorption; Myers, A. L., Belfort, G., Eds.; Engineering Foundation: New York, 1984; p 185. (3) Smith, E. H.; Weber, W. J. J. Environ. Sci. Technol. 1989, 23, 713-722. (4) Weber, W. J. J.; Liu, K. T. Chem. Eng. Commun. 1980, 6, 49-60. (5) Thacker, W. E.; Snoeyink, V. L.; Crittenden, J. C. J. Am. Water Works Assoc. 1983, 75, 144-149.
liquid-phase mass transport to the adsorbent particle outer surface and the mass transport inside the particles by surface diffusion. Only seldom the mass-transfer of organic pollutants in the activated carbon particles was characterized by a model with the parallel pore and surface diffusion10,11 or with a pure pore diffusion.11 HSDM was successfully applied in rare cases of modeling of aqueous phase desorption processes.8,9,12,13 Using the same model parameter values for adsorption and desorption, a good agreement was achieved only in a batch process12 but not in a fixed-bed process.8 At a Langmuirian isotherm, the typical demonstration of the surface diffusion control of the dynamics of fixedbed adsorption is an asymmetrical shape of the breakthrough curve.14 The flexibility of the fixed-bed models using the surface diffusion can be further enhanced by incorporating a concentration dependence of the surface diffusivity.8,9,15 It should be however noted that although an exponential increase of surface diffusivity with concentration can be theoretically substantiated,8,16,17 this (6) Weber, W. J. J.; Wang, C. K. Environ. Sci. Technol. 1987, 21, 1096-1102. (7) Crittenden, J. C.; Reddy, P. S.; Arora, H.; Trynoski, J.; Hand, D. W.; Perram, D. L.; Summers, R. S. J. Am. Water Works Assoc. 1991, 83, 77-87. (8) Chatzopoulos, D.; Varma, A. Chem. Eng. Sci. 1995, 50, 127-141. (9) Mollah, A. H.; Robinson, C. W. Water Res. 1996, 30, 2907-2913. (10) Fritz, W.; Merk, W.; Schlu¨nder, E. U.; Sontheimer, H. In Activated carbon adsorption of organics from the aqueous phase; Suffet, I. H., McGuire, M. J., Eds.; Ann Arbor Science Publishers: Ann Arbor, 1980; Vol. 1, p 193. (11) Matsui, Y.; Yuasa, A.; Ariga, K. Water Res. 2001, 35, 455-463. (12) Chatzopoulos, D.; Varma, A.; Irvine, R. L. AIChE J. 1993, 39, 2027-2041. (13) Karimi-Jashni, A.; Narbaitz, R. M. Water Res. 1997, 31, 30393044. (14) Ma, Z.; Whitley, R. D.; Wang, N. H. L. AIChE J. 1996, 42, 12441262. (15) Li, Q.; Marinas, B. J.; Snoeyink, V. L.; Campos, C. Environ. Sci. Technol. 2003, 37, 2997-3004.
10.1021/la047143+ CCC: $30.25 © 2005 American Chemical Society Published on Web 02/17/2005
Salicylic Acid Adsorption Kinetics
dependence can sometimes be caused by using a model with the single transport mechanism instead of parallel pore and surface diffusion.14,18 On the other hand, a concentration-dependent decrease of surface diffusivity of some organic pollutants in activated carbons was interpreted by a pore blocking mechanism.15,19 Pore blocking is one of the phenomena that can be manifested at adsorption processes in the complex pore structure of activated carbon.20 Peel et al. designed the first rational mathematical model, the branched pore model, for liquid-solid systems that incorporated the slow transfer of organics from macropores to micropores.21 The intraparticle mass transfer was characterized in this model by three adjustable parameters: the surface diffusivity in macropores, volumetric fraction of micropores, and interpore mass transfer coefficient. (It should be noted that macropores and micropores were not understood here in a strict, conventional way.) Ko et al. improved the branched pore model by correcting the boundary condition on the particle surface.17 Two alternative approaches to the modeling of adsorption in bimodal structures of activated carbon were suggested recently although not for aqueous solutions of organics.22,23 Both used the kinetic form of the Langmuir equation for the characterization of the effect of micropore mouth barrier and micropore blocking on the overall kinetics of adsorption in activated carbon. Bhatia et al. applied the Langmuirian kinetics only for the surface adsorption in mesopores where they assumed a negligible mass transfer resistance.23 The subsequent transport of adsorbed molecules into the micropores with the specific grain size was expressed by the second Fick’s law. The adjustable parameters of this model are the grain size, adsorption (desorption) rate constant and effective micropore diffusivity. The model of Nguyen and Do was exclusively kinetic one.22 It was based on a two-step sequential reversible mechanism of the binding where the fluid phase molecules first reversibly bind in mesopores and only these adsorbed molecules can be reversibly bound in micropores. As has been mentioned above, the fixed-bed technique has relatively seldom been used for the determination of equilibrium or kinetic parameters in the field of water pollutant adsorption. It is surprising in the case of adsorption equilibria since this methodology is well established in the field of adsorption chromatography.24-26 We have recently employed two methods of frontal analysis in the investigation of equilibrium of adsorption and desorption of phenylalanine on activated carbon.27 Using an HPLC microcolumn, a reasonable duration of adsorp(16) Suzuki, M. Adsorption Engineering; Kodansha: Tokyo, 1990. (17) Ko, D. C. K.; Tsang, D. H. K.; Porter, J. F.; McKay, G. Langmuir 2003, 19, 722-730. (18) Yoshida, H.; Yoshikawa, M.; Kataoka, T. AIChE J. 1994, 40, 2034-2044. (19) Petersen, F. W.; Vandeventer, J. S. J. Chem. Eng. Sci. 1991, 46, 3053-3065. (20) Bhatia, S. K. AIChE J. 1987, 33, 1707-1718. (21) Peel, R. G.; Benedek, A.; Crowe, C. M. AIChE J. 1981, 27, 2632. (22) Nguyen, C.; Do, D. D. Langmuir 2000, 16, 1868-1873. (23) Bhatia, S. K.; Liu, F.; Arvind, G. Langmuir 2000, 16, 40014008. (24) Guiochon, G.; Shirazi, S. G.; Katti, A. M. Fundamentals of preparative and nonlinear chromatography; Academic Press: Boston, 1994. (25) Tondeur, D.; Kabir, H.; Luo, L. A.; Granger, J. Chem. Eng. Sci. 1996, 51, 3781-3799. (26) Tondeur, D.; Luo, L.; Kabir, H. In Proceedings of International Symposium on Preparative and Industrial Chromatography and Allied Techniques (SPICA 98); Strasbourg, 1998; p 3.1. (27) Go¨rner, T.; Villieras, F.; Polakovic, M.; de Donato, P.; Garnier, C.; Bersillon, J. L. Langmuir 2002, 18, 8546-8552.
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tion/desorption experiments could be achieved and the thermodynamics of the interaction of phenylalanine molecules on the activated carbon surface could efficiently be analyzed. The determination of kinetic parameters from column experiments faces the problem of sensitivity of concentration signals toward kinetic parameters and of a need of a good match of the adsorbed amount obtained from the adsorption isotherm and by the integration of concentration signal.28 Nevertheless, several studies reported fitting of breakthrough curves for obtaining a transport parameter.4,6,8,9 In this paper, we report the results of experiments and modeling designed to study the mechanisms governing the rate of adsorption and desorption of salicylic acid, on activated carbon particles of micrometer dimensions. The adsorption equilibrium of salicylic acid was determined by the step-up method of frontal analysis from the measurements in an HPLC microcolumn. The modeling of adsorption/desorption cycles at different inlet concentrations of salicylic acid that were conducted in the same HPLC setup with the on-line measurement of the column outlet concentration allowed the analysis of the kinetic aspects adsorption/desorption process. Theoretical Section The quantitative description of a liquid-solid adsorption process in the fixed-bed column is based on the material balances of species in the liquid and solid phases. A general liquid-phase balance (eq 1) was expressed in a form where the intraparticle liquid was grouped with the bulk liquid phase.29
∂c ∂c ∂cj ∂q j ∂2c + p(1 - ) + Fb ) -u + DL 2 (1a) ∂t ∂t ∂t ∂z ∂z
t)0 z)0 z)L
c ) cj ) q j)0
(1b)
∂c u(c - ci) ) DL ∂z
(1c)
∂c )0 ∂z
(1d)
The symbols in eq 1 as well as in the following equations are defined in the Nomenclature. Individual terms in eq 1 represent (from left to right) the rate of accumulation in the interstitial voids, in the liquid filling particle pores, and in the adsorbed phase and the convective transport and axial dispersion of species. Solid-phase mass balances were obtained using different assumptions about the rate-controlling step and the linear driving force approximation for mass transfer.30 In combination with the additivity principle of zone-spreading phenomena,29,31 the models could be simplified to contain a single, total or apparent transport coefficient. (The word apparent is usually omitted in the further text.) The comparison of such apparent coefficient with the independently obtained true transport parameters was used for the evaluation of the significance of the effect of particular transport phenomena on the column adsorption of salicylic acid. (28) Tata´rova´, I.; Polakovic, M. Chemical Papers 2004, 58, in press. (29) LeVan, M. D.; Carta, G.; Yon, C. M. In Perry’s Chemical Engineers' Handbook, 7th ed.; Perry, R. H., Green, D. W., Maloney, J. O., Eds.; McGraw-Hill: New York, 1997; p 16.1. (30) Glueckauf, E. Trans. Faraday Soc. 1955, 51, 1540-1551. (31) van Deemter, J. J.; Zuiderweg, F. J.; Klinkenberg, A. Chem. Eng. Sci. 1956, 5, 271-289.
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Table 1. Summary of the Models Used in This Studya model
equation
dispersive-equilibrium (DE) liquid-phase linear driving force (LLDF) solid-phase linear driving force (SLDF) unimodal kinetic (UK) bimodal kinetic (BK)
assumption
1, 2
c ) cj, q ) q j
1, 3, 4
DL ≈ 0
1, 5, 2
DL ≈ 0, c ) cj
1, 9
DL ≈ 0, c ) cj, q ) q j
1, 10, 11
DL ≈ 0, c ) cj, q ) q j
qi qmK Λi ) Fb ) Fb ci 1 + Kci
a D ≈ 0 means that D ) 1 × 10-9 m2/s. The true plug flow (D L L L ) 0) was not used but only approximated for the purpose of a better numerical stability.
The first group of the models applied in this study were the equilibrium-transport models where the surface adsorption was described by an adsorption isotherm and transport processes were represented by a single coefficient. The simplest single-parameter model used was the dispersive-equilibrium (DE) model (Table 1). Since this model assumes the absence of mass-transfer limitations, the liquid-phase concentrations c and cj are equal. The solid-phase concentration q was expressed through the Langmuir isotherm,
q)
qmcK 1 + cK
(2)
The liquid-phase linear driving force (LLDF) model (Table 1) defined that the total rate of intraparticle accumulation in the pore liquid and adsorbate layer was equal to the mass flux through the external particle surface,
∂cj ∂q j + Fb ) klap(1 - )(c - cj) ∂t ∂t
p(1 - )
(3)
where the liquid-phase mass transfer coefficient, kl, was the key parameter. The relationship between the intraparticle concentrations cj and q j was given by the adsorption isotherm
q j)
qmcjK 1 + cjK
(4)
The solid-phase linear driving force (SLDF) model (Table 1) assumed that the total rate of intraparticle accumulation was given by the mass transfer rate inside the particles,
∂q j ∂cj j) p(1 - ) + Fb ) ksapFb(q - q ∂t ∂t
(5)
If the solid-phase mass transfer occurs by a single diffusion mechanism, the mass transfer coefficient, ks, can be used to calculate the surface, Ds, or pore, Dp, diffusion coefficients, respectively29
Dp )
ksapdp2Λi 60ΨP(1 - )p Ds )
)
ksapdp2Λi 1 - 0.225xr 0.775 60(1 - )p
ksapdp2 ksapdp2 1 - 0.106xr ) 60Ψs 60 0.894
nonlinearity and Λi is the partition coefficient defined by eq 7
(6a)
(6b)
where ψs and ψp are the correction factors for isotherm
(7)
For the Langmuir isotherm, the separation factor r had the following form
r)
1 1 + ciK
(8)
The second group of models considered the surface kinetics as the sole adsorption zone spreading phenomenon and thus assumed the absence of mass transfer limitations. The simplest model of surface kinetics is the kinetic form of the Langmuir equation on which the unimodal kinetic (UK) model was based. The solid-phase mass balance of UK model had the form
ka ∂q ) kac(qm - q) - q ∂t K
(9)
To express the effect of pore size distribution of activated carbon on the rate of adsorption, the porous structure was characterized by two distinct pore types loosely termed mesopores (labeled with the subscript 1) and micropores (subscript 2). The bimodal kinetic (BK) model (Table 1) assumed independent kinetic binding on the surfaces of mesopores and micropores. The mass balances in these two parts of the solid phase were as follows
ka1 ∂q1 ) ka1c(qm1 - q1) q ∂t K 1
(10a)
ka2 ∂q2 ) ka2c(qm2 - q2) q ∂t K 2
(10b)
The total adsorbate concentration q was obtained as a sum of the adsorbate concentrations in mesopores, q1, and micropores, q2. Likewise, the maximum monolayer adsorbate concentration qm was distributed between these two structures using an adjustable parameter x1 that will be called the fraction of mesopores,
qm1 ) qmx1
(11a)
qm2 ) qm(1 - x1)
(11b)
It should be however noted that this parameter characterizes the accessibility and binding capacity of these pore structures to salicylic acid so it should not be interpreted in terms of volumetric fractions or relative surface areas. Experimental Section Activated Carbon. The adsorbent used in this study was a granular activated carbon Filtrasorb F400 (Calgon Carbon Co., Pittsburgh, PA). Prior to use the adsorbent was gently ground in an agate mortar. Its particle size distribution was measured by the Mastesizer χ from Malvern Instruments Ltd. (Malvern, U.K.). The particle mean diameter was 8.8 µm and the Sauter mean diameter was 7.5 µm. This value was used to calculate the specific surface area ap ) 6/dp ) 8000 cm-1. The Pore Sizer 9310 mercury porosimeter (Micromeritics, U.S.A.) was used to measure the volume of macropores. The maximum pressure that could be developed by the device was about 200 MPa, which corresponded to the minimum detected pore radius of 3.6 nm. The total specific pore volume and surface area determined by the mercury porosimetry method were 0.36 cm3/g and 37 m2/g. After detracting
Salicylic Acid Adsorption Kinetics the volume of pores with the calculated diameter below 50 nm, the specific macropore volume of 0.19 cm3/g was obtained. The determined specific surface area corresponded exclusively to the part of detected mesopores; the contribution of the surface area of macropores was negligible. The BET specific surface area, derived from nitrogen adsorption at 77 K (lab-built set up), was 1200 m2/g, corresponding mainly to adsorption in micropores (equivalent micropore surface area around 1000 m2/g). The cumulative specific volume of micropores determined by t-plot method was 0.47 cm3/g. The specific volume of micropores and mesopores determined from nitrogen adsorbed amount at p/p0 ) 0.98 was 0.69 cm3/g. It means that, taking into account the macropores, the total specific pore volume, vp, was 0.88 cm3/g when the calculated fraction of micropore volume was 53%. Using the value of the structural density of solid carbon (Fs ) 2.0 g/cm3),32 the particle density Fp ) 1/(vp + 1/Fs) ) 0.72 g/cm3, and the porosity p ) vpFp ) 0.64, were obtained. All the reported values are in a good agreement with literature data. Adsorption Experiments. Equipment. Chromatographic experiments were performed on a HP 1081B liquid chromatograph equipped with UV-vis HP 1040A detection system (2 nm resolution) and with a computer data acquisition system HP ChemStation (Hewlett-Packard, Palo Alto, CA). Columns. The stainless steel chromatographic microcolumns from Upchurch Scientific Inc. (Washington, U.S.A.) used had a length of 20 mm and the inner diameter of 2 mm, so the volume of empty column was 63 µL. The columns were packed manually with the activated carbon powder by shaking the column against its bottom. The average mass of dry carbon in the column was ma ) 33.7 ( 0.2 mg. From the known column volume and adsorbent mass, the bed density Fb ) 0.54 g/cm3 was calculated. The bed voidage could then be calculated from the formula ) (Fp - Fb)/Fp. A somewhat lower value of 0.26 can be attributed to the polydispersity of adsorbent particles. After the column packing was completed, the column was flushed overnight with ultrapure water [checked by a UV-vis table spectrophotometer (Shimadzu 2100) for absence of any UVvis absorption bands]. The dead retention volume of the system was measured 20 times with KNO3 (10 g/L) solutions at 0.5 and 1.0 mL/min flow rates and was 0.077 mL. Mobile Phase. Solutions of salicylic acid (molecular weight of 138.12, Merck, Darmstadt, Germany), highly pure of DAB quality, in ultrapure water of 18 MΩ (station Millipore Milli-Q Plus) were used in different concentrations to feed the columns in the adsorption phase. Ultrapure water was used as the desorbent. Experimental Procedures. The column flushed with ultrapure water was fed with a 10 mg/L salicylic acid solution until equilibrium was reached. For desorption, it was fed with ultrapure water for a sufficiently long time so that all reversibly bound solute was removed. About 5% of adsorption capacity of virgin activated carbon was lost by irreversible adsorption, but the same quality of the adsorbent was observed during successive adsorption/desorption steps similarly as in previous studies.12,27 All adsorption/desorption experiments were carried out at 24 °C. Two different flow rates were used: 1.5 mL/min in the step-up frontal analysis equilibrium experiments and 0.5 mL/min in the adsorption/desorption cycles aimed at the investigation of kinetic and mass transfer phenomena. The latter value of the flow rate corresponded to the superficial flow velocity w ) 0.265 cm/s. The calculated interstitial velocity was then u ) 1.02 cm/s. The liquid mean residence time in the column was, ht ) L/u ) 1.96 s. The values of Reynolds and Schmidt numbers, needed for the estimation of DL and kl were calculated as follows: Re ) dpw/ν ) 2.2 × 10-2 where ν was the kinematical viscosity of water 9.2 × 10-3 cm2/s; Sc ) ν/D ) 9.2 × 10-3/8.4 × 10-6 ) 1090 where the diffusion coefficient of salicylic acid in water D was approximated from the Wilke-Chang equation.33 The column outlet concentration was measured with the UV detector at 257 nm. The raw data were acquired with the HP ChemStation program using the frequency of one point per 3.5 s. To avoid processing of extremely large data sets in the modeling study, only about twothree data points per hour were taken for parameter estimation. (32) Keltsev, N. V., Osnovy adsorbciyonnoy tekhniki (Fundamentals of adsorption technology); Khimiya: Moskva, 1976. (33) Wilke, C. R.; Chang, P. AIChE J. 1955, 1, 264-270.
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Figure 1. Adsorption isotherm of salicylic acid on activated carbon F400. The circles are the equilibrium values obtained by the step-up frontal analysis method, and the solid line represents their fit with the Langmuir equation (eq 2). Frontal Analysis (FA). The principle of determination of equilibrium data by frontal analysis is based on feeding the column with the stream with an inlet solute concentration ci until equilibrium is reached in the whole column, which is indicated by the outlet concentration equal to ci. In the simple one-step FA method, a column initially free of adsorbate was used and the equilibrium adsorbate concentration q was calculated from the breakthrough curve, the dependence of the outlet column concentration on time. The same principle was applied in one-step desorption and step-up adsorption methods. The details of the calculation using these methods were published previously.27 Modeling. A commercial process engineering software, Athena Visual Workbench34 (Stewart & Associates Engineering Software, Madison, WI; www.athenavisual.com), was used for all simulation and parameter estimation tasks in this study. The models were in the form of mixed (partial and ordinary) differential and algebraic equations with time discontinuities and were written in the user-friendly source code of the software. The details of numerical procedures incorporated in the Athena Visual Workbench can be found in original research papers.35,36 The main options available to the user were the choice of the discretization of space coordinate (finite difference, global orthogonal collocation, and orthogonal collocation on finite elements techniques) and the choice of the parameter estimation procedure (least squares or Bayesian methods). We used exclusively uni-response absolute least-squares and mostly finite difference technique with 100 space points.
Results and Discussion Salicylic Acid Adsorption Equilibrium. The adsorption equilibrium of salicylic acid on activated carbon F400 was determined by the step-up method of frontal analysis. The inlet concentrations of salicylic acid were successively increased from 10 mg/L to 400 mg/L. At the flow rate of 1.5 mL/min in the bed containing 33.7 mg of activated carbon, it took from about 30 min to 3 h in individual steps to reach the outlet concentration equal to the inlet one. The column was further fed for at least twice as long time to guarantee that the equilibrium was reached in the bed. The experimental equilibrium data obtained were fitted using the Langmuir isotherm (Figure 1). The mean square error of approximation was 0.003 mg/mg and the 95% confidence intervals of the parameters were as follows: qm ) 0.296 ( 0.07 mg/mg and K ) (2.26 ( 0.15) × 10-2 L/mg. (34) Athena Visual Workbench. Technical Manual; Stewart & Associates Engineering Software Inc.: Madison, WI, 2001. (35) Stewart, W. E.; Caracotsios, M.; Sorensen, J. P. AIChE J. 1992, 38, 641-650. (36) Caracotsios, M.; Stewart, W. E. Comput. Chem. Eng. 1995, 19, 1019-1030.
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Table 2. Comparison of Adsorbed and Desorbed Amounts at One-Step and Step-Up Methods of Frontal Analysis adsorbed or desorbed mass per mass of activated carbon (mg/mg) concentration (mg/L)
one-step adsorption
one-step desorption
step-up adsorption
30 40 50 60
0.120 0.138 0.155 0.177
0.122 0.139 0.152 0.171
0.123 0.142 0.158 0.167
A well-known weakness of FA step-up method is that a gross error in a certain step distorts further measurements and that systematic errors are cumulative. The check of the correctness of the adsorption equilibrium data obtained was based on a series of four one-step adsorption/ desorption experiments that were carried out in the column of the same dimensions but with a newly filled bed and at the liquid flow rate of 0.5 mL/min. Table 2 shows the comparison of equilibrium adsorbed amounts determined by three different procedures. All the values were within 3% from the mean value at the given concentration, which means that the step-up method measurements were free of gross or systematic errors. Furthermore, no significant differences were found between the adsorbed and the desorbed masses, respectively. The salicylic acid adsorption on a solvent-regenerated activated carbon F400 was thus fully reversible. Comparison of Adsorption and Desorption Rates. One-step adsorption/desorption cycles, introduced in the previous subsection, were primarily conducted to perform the analysis of rate aspects of salicylic acid adsorption. The experimental outlet concentration profiles are shown in Figure 2. It is well-known that an ideal course of equilibrium adsorption free of zone-broadening effects has a shock-wave form, which is an abrupt change of the outlet solute concentration from zero to the value of the inlet concentrations, for favorable isotherms such as the Langmuir equation. The results presented in Figure 2 clearly demonstrate a significant influence of zonebroadening phenomena. The first step in the rate analysis was to compare the dynamics of adsorption and desorption. For that purpose, the adsorption and desorption phases of the results presented in Figure 2 were fitted separately and the whole adsorption/desorption cycles were fitted at once using all equilibrium-transport models from Table 1. Minimal differences were found between the fits of the whole cycle or its parts at any concentration using a single model. The predicted courses were almost identical. The differences among the estimated parameter values (data not shown) were in all cases smaller than the parameter uncertainties represented by the 95% confidence intervals. Owing to the compatibility of adsorption and desorption experiments, we used the fits of whole cycles in further modeling. Such a good correspondence between the quantitative description of adsorption and desorption of organic compounds in liquid phase was achieved only in a batch study of Chatzopoulos et al.12 In not so frequent quantitative studies of column adsorption/desorption, smaller or larger discrepancies were observed.8,9,13 Equilibrium-Dispersive and Liquid-Phase Linear Driving Force Models. The next step was to assess a possible impact of different transport phenomena on the dynamics of the process of adsorption and desorption of salicylic acid. Table 3 summarizes the results of modeling of adsorption/desorption fixed-bed experiments using the individual equilibrium-transport models. In these single-
parameter models, the spreading of the adsorption zone was assigned to a single phenomenon that was characterized by an apparent transport parameter. Although there was a slight dependence of transport parameters, DL and kl, on the concentration, the values of the estimated transport coefficients were of the same order of magnitude in the investigated concentration range. The analysis of the effect of individual transport phenomena was based on the comparison of the apparent values of transport parameters with the independently calculated values from correlations between dimensionless criteria. The axial dispersion coefficient was calculated for our experimental conditions from different correlations for liquid/solid systems available in the literature.37-40 Very similar values of DL, ranging from 0.9 × 10-7 m2/s to 1.1 × 10-7 m2/s, were provided by all equations. (For details see Supporting Information.) These theoretical values were about 200-800 times smaller than the apparent DL values estimated from the breakthrough curves using the DE model (Table 3). This implies that the contribution of axial dispersion to the spread of adsorption/desorption zones was negligible in our experiments. The effect of the extraparticle liquid mass transfer coefficient, kl, to the performance of fixed-bed was treated analogously as that of DL. Using four different correlations,41-44 the obtained kl values were in the range of 0.5-1.4 × 10-3 m/s. (For details see Supporting Information). The values of apparent kl obtained by modeling were 200-1400 times smaller (Table 3). This was again strong evidence that extraparticle mass transfer could not have a significant influence on the dynamics of column performance. The same observation of the elimination of extraparticle mass transfer resistance for the activated carbon particles of reduced size was made by several other authors.45-47 Solid-Phase Linear Driving Force Model. The assessment of estimated values of the solid-phase mass transfer coefficient, ks, was based on the proportionality between ks and the effective diffusion coefficient. Since the total intraparticle mass flux could be formed by the contributions of pore and surface diffusion fluxes, which are not easy to discriminate,14,16,48 the apparent rather than the effective diffusion coefficients were evaluated in the first step. The apparent diffusion coefficients are based on the simplification of the intraparticle mass transport to a single mechanism, either pore or surface diffusion. The equations for the calculation of Dp and Ds at adsorption equilibrium described by the Langmuir isotherm were given in Theoretical Section (eq 6a,b). Table 4 presents the calculation of the values of Ds and Dp. The values of the separation factor r demonstrate a moderate nonlinearity of the adsorption isotherm sug(37) Chung, S. F.; Wen, C. Y. AIChE J. 1968, 14, 857-866. (38) Wakao, N.; Funazkri, T. Chem. Eng. Sci. 1978, 33, 1375-1384. (39) Hejtma´nek, V.; Schneider, P. Chem. Eng. Sci. 1993, 48, 11631168. (40) Koch, D. L.; Brady, J. F. J. Fluid Mech. 1985, 154, 399-427. (41) Wilson, E. J.; Geankoplis, C. J. Ind. Eng. Chem. Fundam. 1966, 5, 9-14. (42) Dwivedi, P. N.; Upadhyay, S. N. Ind. Eng. Chem. Proc. Des. Dev. 1977, 16, 157-165. (43) Kataoka, T.; Yoshida, H.; Ueyama, K. J. J. Chem. Eng. Jpn. 1972, 5, 132. (44) Ohashi, H.; Sugawara, T.; Kikuchi, K. I.; Konno, H. J. J. Chem. Eng. Jpn. 1981, 14, 433. (45) Summers, R. S.; Roberts, P. V. J. Environ. Eng. 1987, 113, 1333. (46) Najm, I. J. Am. Water Works Assoc. 1996, 88, 79-89. (47) Lebeau, T.; Lelievre, C.; Woplbert, D.; Laplanche, A. Water Res. 1999, 33, 1695-1705. (48) Merk, W.; Fritz, W.; Schlu¨nder, E. U. Chem. Eng. Sci. 1980, 36, 743-757.
Salicylic Acid Adsorption Kinetics
Langmuir, Vol. 21, No. 7, 2005 2993
Figure 2. Fixed-bed experiments of adsorption/desorption cycles of salicylic acid on activated carbon F400. The plots a, c, e, and g represent the adsorption phases at different inlet concentrations, (a) 30 mg/L, (c) 40 mg/L, (e) 50 mg/L, and (g) 60 mg/L. The plots b, d, f, and h are the corresponding desorption phases. The circles are the measured values of concentrations of salicylic acid at the column outlet. The solid lines are the predicted time-concentration dependencies using the BK model obtained by a simultaneous fit of all data. The dashed and dotted-dashed lines were obtained by the fitting of individual cycles or simultaneously all data, respectively, with the UK model.
gesting that the principle of additivity of the resistances of individual transport phenomena to the overall resistance is valid here.29 The partition coefficients Λi were
rather high which implied that a value of Dp larger than the salicylic acid diffusion coefficient in water, D ) 8.4 × 10-10 m2/s, could be expected in the case of strong surface
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Polakovic et al.
Table 3. Results of Modeling of Salicylic Acid Adsorption/Desorption Experiments in an HPLC Microcolumn Using Equilibrium-Transport and Unimodal Kinetics Models DE model LLDF model SLDF model ci (mg/L)
DL × 105 (m2/s)
kl × 106 (m/s)
ks × 1010 (m/s)
30 40 50 60
2.18 4.36 5.70 7.67
2.57 1.58 1.37 1.08
9.33 6.03 5.92 5.59
UK model ka × 1010 MSEa [L/(mg‚s)] (mg/L) 12.5 8.20 7.24 5.67
1.31 1.16 3.04 2.90
a MSE: the mean square error of outlet concentration of salicylic acid in the UK model.
Table 4. Calculation of Pore and Surface Diffusivities, Dp and Ds, from the Solid-Phase Mass Transfer Coefficient, ks (eq 6a,b) ci
Λi
r
ψp
ψs
30 40 50 60
2141 1887 1687 1525
0.600 0.525 0.469 0.424
0.938 0.926 0.916 0.908
0.974 0.968 0.964 0.960
Dp × 1012 (m2/s) Ds × 1016 (m2/s) 3.37 1.95 1.73 1.49
7.19 4.67 4.61 4.37
diffusion.3,16 Table 4 shows that both pore and surface diffusivities were however much lower than D. The Dp values were about 200-500 times smaller than D. If the conventional correlation, Dp ) Dp/τ, and typical values of the tortuosity (τ ) 2-6),29 were used, the pore diffusivity of salicylic acid in the activated carbon would be 3-10 times smaller than the diffusivity in water. The observed discrepancy implies that the rate of adsorption process was controlled by another mechanism than by pore diffusion. The assessment of the possible control of the rate of adsorption/desorption process by the mechanism of surface diffusion is somewhat more complicated. One should first emphasize that pore diffusion in the pores with a large pore-to-solute size ratio must be always considered as a parallel transport mechanism to surface diffusion. Surface diffusion increases the intraparticle diffusional flux compared to that one that would be achieved by sole pore diffusion. As follows from eq 6a,b, the pore and surface diffusivities essentially differ by the factor of partition coefficient. The typical values of surface diffusivities of organics in the adsorption from aqueous phase on the granular activated carbon were reported to be of the order of magnitude (10-12 m2/s)4,8,10,12,17,21,48 where the total flux was 10-100 higher than the one obtainable by pore diffusion. Table 4 shows that the apparent surface diffusivities, Ds, of salicylic acid were of the order of magnitude 10-16 m2/s. It should be noted that the values of surface diffusivities as low as 10-15 to 10-17 m2/s that could be justified were reported for powdered activated carbons having almost no mesopores and micropores.9,15,46,47 The absence of mesopore transport and surface adsorption is however not a sound conclusion for the activated carbon used in this study where the mesopores and macropores formed about 50% of total pore volume and about 20% of their surface area. Furthermore, it has already been mentioned in the Introduction that the micropore surface diffusion model was only an interpretation of pore blocking mechanism in one of the cited studies.15 All the above arguments indicated that surface diffusion could not be a ratecontrolling mechanism in the process of salicylic acid adsorption. Unimodal Kinetic Model. Since no transport mechanism assessed in the previous subsection occurred to be rate-controlling in the salicylic acid adsorption process,
a further analysis was focused on the models that assumed that the binding of the solute on the adsorbent surface was not instantaneous but it had a kinetic character. The concentration profiles of individual adsorption/ desorption cycles were fitted using the unimodal kinetic (UK) model, based on the simple Langmuir kinetics, with one adjustable parameter, the adsorption rate constant, ka. The results are presented in Table 3 and Figure 2. Table 3 shows that the estimated values of ka varied by a factor of 2 with the inlet concentration of salicylic acid. It was not so much therefore an attempt was made if all experimental results could be fitted simultaneously with the UK model. The estimated value of ka and its 95% confidence interval was (7.39 ( 0.45) × 10-6 L/(mg‚s). The mean square error (MSE) of the fit was 2.40 mg/L. The average of MSE of individual experiments from Table 3 is 2.10 mg/L. This is a quite good match which is also confirmed by the coincidence of most curves in Figure 2. Minor differences can be observed only at 30 mg/L, and a very small difference is at the adsorption phase at 60 mg/L. The corresponding desorption rate constant ka/K was 3.3 × 10-4 s-1. There are not enough references so that it could be judged a plausibility if this value could be an intrinsic rate constant. In previous works using activated carbons, the values ranging in the orders of magnitude from 10-1 s-1 to 10-6 s-1 were reported.22,23 This is one factor that raises the question of a need of a more complex model. The second, critical factor in this respect was the agreement of the model and experiments. At the first glance, a coincidence of the model and experiments could be alleged and the deviations dismissed as artifacts. A careful assessment however shows that the adsorption curves had an asymmetric shape with the inflection point at low concentrations whereas the model curves are symmetric. Although the second phase of adsorption process proceeds at a lower rate, the adsorption curves are however not as elongated as those of typical dual-rate models.21 Further systematic deviations can be observed at both adsorption and desorption curves. The model curves predict an earlier breakthrough at adsorption and almost immediate decrease of outlet concentration at desorption. Bimodal Kinetic Model. Following the above-mentioned arguments, the discussion at the evaluation by equilibrium-transport models and the theoretical overview made in the Introduction, it was meaningful to test a dualrate model. We suggested the bimodal kinetic (BK) model described in the Theoretical Section (Table 1). It contained a meaningful number (three) adjusted parameters and best suited our knowledge on the pore distribution of activated carbon and analysis of transport phenomena made above. We tested by simulations if the equilibrium models of adsorption could describe at least the first part of the adsorption/desorption curves using feasible values of pore diffusivity. No good match was however achieved. We thus accepted that the adsorption in mesopores should be of kinetic nature similarly as in the model of Nguyen and Do.22 The principle difference between these two models is that our model is exclusively parallel whereas Ngueyn-Do model is exclusively sequential. It means that in the former model, the adsorption in mesopores and micropores can proceed independently. In the latter model, only molecules adsorbed in the mesopores can be further bound in micropores. We assumed equal affinity of salicylic acid to adsorbent surface in mesopores and micropores. This is a requirement if both partial isotherms and summed isotherm should have the form of the Langmuir equation. Without this assumption, the model should
Salicylic Acid Adsorption Kinetics Table 5. Results of Parameter Estimation Using the BK Model (Table 1) Obtained by the Simultaneous Fit of All Data Presented in Figure 2a parameter
optimal estimate ( maximum error
x1 ka1 × 104 [L/(mg‚s)] ka2 × 106 [L/(mg‚s)]
0.495 ( 0.027 1.43 ( 0.86 3.54 ( 0.26
a The maximum errors delimit the 95% confidence intervals of the parameters calculated from the variance-covariance matrix. The mean square error of the fitted column output concentration was 1.47 mg/L.
contain three more parameters without a better description of experimental data, since the suitability of the Langmuir isotherm for the total adsorbed amount was evidently proved. The BK model was used to fit all experimental results simultaneously. The results are presented in Figure 2 and Table 5. The mean square error of the fitted concentration was 1.47 mg/L which is a significant improvement compared to its value of 2.40 mg/L at UK model. The markedly better description of experimental results is visible in Figure 2. Two adsorption curves (Figure 2c,e) and three desorption curves (Figure 2d,f,h) exhibited an excellent match with the experiments. The slight deviations at the boundary concentrations could be attributed to two aspects that were not incorporated in the model. First, the maximum adsorption capacity of micropores was considered independent of liquid-phase concentration which was experimentally shown not to be true at pore blocking mechanism.49 Second, the salicylic acid concentrations in the liquid filling mesopores and micropores were considered equal. The estimated parameters and their confidence intervals are given in Table 5. The fraction of mesopores x1 was estimated to be about 50%, which is in compliance with the porosity measurements. The adsorption rate constants in mesopores and micropores were 1.43 × 10-4 L/(mg‚s) and 3.54 × 10-6 L/(mg‚s), respectively. As the adsorbent sites in mesopores and micropores were considered chemically equal, the lower value of the adsorption and consequently also the desorption rate constants in micropores can be attributed to the pore blocking at the pore aperture and diffusional hindrances in micropores that decrease the effective concentrations inside micropores. The adsorption rate constant in mesopores is 1 order of magnitude higher than in the UK model. The discussion if this could be an intrinsic rate constant can be made on the basis of the initial rates of surface reaction and mesopore diffusional flux. Using a conservative estimate of pore diffusivity value of salicylic acid, Dp ) D/τ ) 8.4 × 10-10 × 0.64/4 ) 1.3 × 10-10 m2 s-1, the characteristic volumetric rate constant of mass transport of solute through the adsorbent particle surface was 3Dp/rp2 ) 28.7 s-1. The initial rate constant of adsorption in respect to the liquid-phase salicylic acid concentration was calculated as ka1qmx1Fb/(1 - ) ) 1.43 × 10-4 × 0.294 × 0.495 × 5.37 × 105/(1 - 0.26) ) 15.1 s-1. The higher diffusion rate constant means that the reaction would not be limited by diffusion, and the calculated adsorption rate constant could indeed be an intrinsic one. It is worth mentioning that if granular activated carbon particles of ordinary size of about 0.5-1 mm were used, the characteristic diffusion rate constant would be by 4 orders of magnitude lower and the process would be much more limited by intraparticle diffusion. As the local rate (49) Michot, L.; Francois, M.; Cases, J. M. Langmuir 1990, 6, 677681.
Langmuir, Vol. 21, No. 7, 2005 2995
of intraparticle reversible surface adsorption would be controlled by diffusion in that case, the local adsorption equilibrium would be achieved more easily and the overall process would appear as an equilibrium one. According to our opinion, this explains why the kinetic character of surface adsorption of organic compounds on the activated carbon was seldom reported. Conclusions The Langmuir equation has described the adsorption equilibrium of dilute aqueous solutions of salicylic acid on an activated carbon. The adsorption has been fully reversible, and no hysteresis has occurred in adsorption/ desorption cycles. A regime analysis of fixed-bed adsorption/desorption experiments in an HPLC microcolumn has revealed that the spreading of adsorption and desorption fronts has not been affected by axial dispersion and extraparticle mass transfer. This is not an unexpected result for the particles with the mean diameter close to 10 µm. A further analysis has pointed out surprisingly low mass transfer rates between the flowing liquid and the adsorbent microparticles. This has been demonstrated by very low values of apparent pore or surface diffusivities estimated from the adsorption/desorption cycles. They are by several orders of magnitude lower than the common values. This has led to the conclusion that the adsorption of salicylic acid on the pore surface of activated carbon is not an infinitely fast equilibrium interaction but it has a kinetic character. A kinetic form of the Langmuir equation has been a logical choice to describe the surface kinetics. A good match between the model and the experiments can be achieved when the heterogeneous character of adsorbent pores is considered. A very simple representation of the heterogeneity is the distribution of pores into two fractions, loosely termed mesopores and micropores, that have different adsorption rate constants. The good fit can be further supported by the meaningful values of estimated parameters. The values of the fractions of mesopores and micropores being each 50% correspond well with the results of standard porosimetric methods. The adsorption rate constant in mesopores is lower than the potential diffusion rate constant which means that the mesopore adsorption is not limited by diffusion. On the contrary, the micropore adsorption has been affected by the effects of pore blocking and diffusional hindrances in micropores. Nomenclature A ap c cj ci DL Dp Ds dp F K ka kl ks L
column cross-section area (m2) ) 6/dp, particle specific surface (m-1) extraparticle liquid-phase concentration (kg m-3) mean intraparticle liquid-phase concentration (kg m-3) column inlet concentration (kg m-3) axial dispersion coefficient (m2 s-1) pore diffusion coefficient, pore diffusivity (m2 s-1) surface diffusion coefficient, surface diffusivity (m2 s-1) particle diameter (m) volumetric flow rate (m3 s-1) adsorption equilibrium constant (m3 kg-1) adsorption rate constant (m3 kg-1 s-1) liquid-phase mass transfer coefficient (m s-1) solid-phase mass transfer coefficient (m s-1) bed length (m)
2996 ma q q j qi qm p p0 Pe r Re Sc Sh t ht t0 u vp w x z
Langmuir, Vol. 21, No. 7, 2005 adsorbent mass (kg) adsorbate concentration per mass of adsorbent (kg kg-1) mean adsorbate concentration per mass of adsorbent (kg kg-1) equilibrium adsorbate concentration to ci (kg kg-1) maximum monolayer adsorbate concentration (kg kg-1) pressure (Pa) saturation pressure (Pa) ) udp/DL, Pe´clet number separation factor ) dpw/ν, Reynolds number ) ν/D, Schmidt number ) kldp/D, Sherwood number time (s) mean residence time (s) dead retention time (s) ) w/, interstitial velocity (m s-1) specific pore volume (m3 kg-1) ) F/A, superficial velocity (m s-1) fraction of adsorption sites axial distance (m)
Greek Letters γ1, γ2 p
coefficients in the correlation of Pe´clet number bed voidage particle porosity
Polakovic et al. Λi ν Fb Fp Fs ψp ψs
partition coefficient kinematical viscosity (m2 s-1) bed density (mass of dry adsorbent per bed volume; kg m-3) particle density (mass of dry adsorbent per particle volume; kg m-3) structural density of carbon (kg m-3) correction factor for isotherm nonlinearity in eq 6a correction factor for isotherm nonlinearity in eq 6b
Subscripts 1 2
mesopores micropores
Acknowledgment. This work was supported by grants from Lyonnaise des Eaux, CIRSEE, 78230 Le Pecq, France, and Slovak-French scientific cooperation programme Sˇ tefa´nik. M.P. acknowledges INPL for a visiting professor grant and Dr. Daniel Bobok from SUT for useful advice. Supporting Information Available: Two tables that give the details of the calculation of the axial dispersion coefficient and the liquid-film mass transfer coefficient. This material is available free of charge via the Internet at http://pubs.acs.org. LA047143+
