Ind. Eng. Chem. Res. 2008, 47, 7019–7026
7019
Adsorption Equilibrium and Kinetics of Water Vapor on Different Adsorbents Ana M. Ribeiro,† Ticiane P. Sauer,†,‡ Carlos A. Grande,† Regina F. P. M. Moreira,‡ Jose´ M. Loureiro,† and Alı´rio E. Rodrigues*,†
Ind. Eng. Chem. Res. 2008.47:7019-7026. Downloaded from pubs.acs.org by UNIV OF KANSAS on 01/19/19. For personal use only.
Laboratory of Separation and Reaction Engineering (LSRE), Department of Chemical Engineering, Faculty of Engineering, UniVersity of Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal, and Laboratory of Energy and EnVironment (LEMA), Department of Chemical Engineering and Food Engineering, Federal UniVersity of Santa Catarina, Campus UniVersita´rio, 88040-900 Floriano´polis, SC, Brazil
Water vapor needs to be removed from many industrial streams using, for example, adsorption processes. Equilibrium and kinetic data are essential for the design of these adsorption processes. In this work, the adsorption equilibrium isotherms of water vapor were measured at 303 K by a gravimetric system on three commercial adsorbents, an activated carbon, an activated alumina, and a zeolite. The zeolite sample presented the highest capacity at low relative pressures, while at pressures near saturation the higher amount adsorbed was obtained on the alumina sample. The experimental points obtained for the activated carbon and the zeolite were fitted with the Virial isotherm while the n-layer BET equation was used in the fitting of the alumina data. The adsorption kinetics was evaluated through the analysis of breakthrough curves obtained at the same temperature for different feed humidity values. The fixed bed behavior was described using an isothermal model that includes axial dispersion and external (film model) and internal (homogeneous LDF model) mass transfer resistances. The homogeneous diffusivity values were determined by adjusting the model to the experimental data. 1. Introduction Water is present in several gaseous industrial streams: natural gas and hydrogen production from steam methane reforming are two examples. Normally these products are pressurized either to be packed or to be transported. Specifications of usage and transport require the removal of water to a few parts per million to avoid condensation or corrosion problems. This specification leads to specialized units for water removal from gaseous streams.1 The techniques applied for gas drying are diverse: removal with glycol,2,3 condensation either by reducing temperature or by sudden depressurization, and adsorption.4,5 The design of the particular water removal process to be employed depends on the gas where drying is required and also on the volume of the stream to be treated. In general, adsorption can be employed in large plants for natural gas drying6 and also for water removal in He purification.7 When an adsorption-based process is employed to remove water, a cyclic scheme should be designed to regenerate the adsorbent and to operate continuously, requiring a multicolumn array. The regeneration of the adsorbent can be done by increasing the temperature in a process termed temperature swing adsorption (TSA) or by reducing the pressure in a pressure swing adsorption (PSA) unit. The design of any of TSA or PSA processes requires the determination of adsorption equilibrium and kinetics of the contaminant to be removed in the material (adsorbent) to be employed. The most common adsorbents for water vapor removal are activated carbon and activated alumina for bulk removal to a few percent and silica gel and zeolites to reduce the amount of water significantly from some percent to the parts per million level. Numerous studies of water vapor adsorption on different adsorbents can be found in the literature.8-12 On the other hand, the published results on the * To whom correspondence should be addressed. Phone + 351 22 508 1671. Fax: + 351 22 508 1674. E-mail:
[email protected]. † University of Porto. ‡ Federal University of Santa Catarina.
dynamic adsorption of water vapor on fixed beds are scarce. Qi et al.13 presented some results for activated carbon, Desai et al.14 for activated alumina, and Gorbach et al.15 for zeolite 4A. In this work, we evaluated the performance of three different adsorbents to remove water from a gaseous stream at ambient temperature. The objective of the work is to obtain fundamental data of water adsorption necessary for the design of an adsorption based process for gas dehydration. The adsorbents tested are commercial samples of activated carbon, activated alumina, and zeolite. Adsorption equilibria of water vapor on the different adsorbents was determined at 303 K covering the whole range of humidity until saturation. Adsorption equilibrium on the activated carbon and the zeolite samples were analyzed with the Virial model while the equilibrium data on the alumina sample was fitted with the n-layer BET model. The determination of adsorption kinetics was performed by measuring breakthrough curves of water at different feed partial pressures. The experimental breakthrough curves were analyzed using a mathematical model that takes into account axial dispersion and external (film) and internal (linear driving force, LDF) mass transfer resistances. In the case of the activated carbon, the effect of the nonlinearity of the adsorption isotherm on the LDF coefficients was considered in the model by the calculation of a homogeneous diffusivity that varies locally with derivative of the isotherm. 2. Experimental Section 2.1. Materials. The adsorption equilibrium and kinetics of water vapor were studied on three commercial adsorbents: activated carbon Norit R2030, basic activated alumina Norton, and zeolite. The textural properties of the activated carbon and activated alumina were evaluated using two techniques, nitrogen adsorption at 77 K and mercury porosimetry. The nitrogen isotherms at 77 K were measured using an automatic volumetric sorption analyzer (Micromeritics, ASAP 2000) while the mercury intrusion was determined on a Poresizer 9320 (Micromeritics).
10.1021/ie701732x CCC: $40.75 2008 American Chemical Society Published on Web 08/13/2008
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Figure 1. Nitrogen adsorption isotherms at 77 K for the (a) activated carbon and (b) alumina.
The determined nitrogen adsorption isotherms at 77 K are shown in Figure 1. It can be seen that the isotherm obtained for the activated carbon rises sharply at low relative pressures reaching an almost constant plateau, which is indicative of a microporous material.16 The alumina isotherm also presents an initial raise at low relative pressures, but the amount adsorbed keeps increasing at higher relative pressures, suggesting the formation of adsorbed layers with a progressively growing global thickness; that is, it indicates the presence of larger pores, namely, the presence of mesoporosity.16 Figure 2 shows the pore size frequency distribution function of the adsorbents obtained from mercury intrusion, that is, for pore diameters greater than 6 nm. In the case of activated carbon, it has a large peak in the macropore region with the highest incidence at approximately 2 µm and also some mesoporosity. A small peak with a highest incidence at approximately 10 µm is also observed which is probably due to interparticle space. On the other hand, the alumina sample has some macropores, with an average pore width of approximately 1 µm, but exhibits a large peak in the mesopore region which is consistent with that observed in the nitrogen adsorption results. Some physical properties of the three adsorbents are summarized in Table 1. 2.2. Adsorption Equilibrium. The adsorption isotherms were obtained at 303 K on a gravimetric system operated in open mode. A schematic representation of the experimental setup employed can be seen in Figure 3. A magnetic suspension
Figure 2. Pore size frequency distribution function of the (a) activated carbon and (b) alumina obtained from mercury intrusion. Table 1. Physical Properties of the Adsorbents
form average pellet radius (m) BET surface area (m2/g) pellet density (kg/m3) pellet porosity
activated carbon
alumina
zeolite
cylindrical 1.45 × 10-3 688 874 0.60
spherical 1.80 × 10-3 216 875 0.60
cylindrical 8.50 × 10-4 434 1126 0.50
balance (Rubotherm, Germany), with a 0.01 mg precision, was used for the measurements. For each isotherm, approximately 2 g of adsorbent were placed in a basket suspended by the permanent magnet of the balance. The balance was then closed with a jacketed cell, and the temperature inside this cell was controlled by a thermostatic circulating bath (Lauda, Germany). Prior to the equilibrium measurements, the residual humidity adsorbed during the setup assembling was removed by flowing dry helium through the samples overnight at 180 °C. The adsorbate vapors were generated by flowing dry helium through glass bubblers filled with distilled water. Before entering the balance, this water vapor “saturated” stream was diluted by a second stream of dry helium to reach the desired humidity values. The composition of the resulting stream was regulated by balancing the flow rates of the two helium streams using two mass flow controllers (Hastings, U.S.A.). To avoid condensation, all the tubes in the setup were covered by a heating
Ind. Eng. Chem. Res., Vol. 47, No. 18, 2008 7021 Table 2. Conditions for the Breakthrough Experiments parameters
activated carbon
mass of adsorbent (g) bed diameter (cm) bed length (cm) bed porosity inlet humidity (%) flow ratea (cm3/min) temperature (K)
2.2008 0.87 8.5 0.50 59 97 102.3 109.3 303
a
Figure 3. Experimental setup used in the determination of the adsorption isotherms.
alumina
zeolite
2.3703 1.7571 0.87 0.87 8.5 4.5 0.46 0.42 14 69 84 6.3 116.0 111.2 110.9 112.8 303 303
Measured at 303 K.
values of 59 and 97%, respectively. In the case of the alumina sample three breakthrough curves were determined using inlet humidity values of 14, 69, and 84% respectively. With the zeolite sample only one experiment was performed at 6.3% humidity. 3. Theoretical Section 3.1. Adsorption Equilibrium. The Virial isotherm17,18 was chosen to fit the experimental data obtained in this work for the activated carbon and the zeolite samples. This equation is given by 3 q exp 2A1q + A2q2 + . . . (1) H 2 where P is the adsorbate partial pressure, q is the amount adsorbed, H is the Henry constant, and A1 and A2 are the Virial coefficients. This isotherm presents several advantages; namely, it has correct thermodynamic limits both at low and high coverage, and it is very flexible to fit isotherms with different degrees of steepness and enables the prediction of multicomponent adsorption by using analytic expressions for the calculation of the mixing Virial coefficients.19,20 For the fitting of the experimental adsorption data the Virial isotherm was truncated at the second Virial coefficient. In the case of the water vapor/alumina system, as it presents a type II isotherm, the n-layer BET equation (eq 2), frequently employed in the correlation of this type of isotherm,21 was used.
(
P)
Figure 4. Experimental setup used in the determination of the water vapor breakthrough curves.
tape kept 2-4 °C above the desired experimental temperature. During adsorption, the temperature and pressure inside the balance were monitored by a thermocouple and a pressure transducer (Sensortechnics, Germany) connected to the balance exit. When the sample mass reached a constant value, the balance outlet stream composition was determined by a thermohygrometer model T605-H1 (Testo, Germany). In the case of the activated carbon and the alumina some desorption equilibrium points were also determined. 2.3. Adsorption Kinetics. The adsorption kinetics of water vapor on the three adsorbents were evaluated through the analysis of breakthrough curves. The breakthrough curves were determined on an experimental setup schematically represented in Figure 4. The experiments were performed using a stainless steel column, containing the adsorbent samples, placed inside a convective oven to control the adsorption temperature. As in the case of the equilibrium determinations, the residual humidity adsorbed during the setup assembling was removed by flowing dry helium at 180 °C through the column overnight, and the adsorbate streams entering the bed were also generated by adjusting a desired ratio between a saturated helium stream and a dry helium stream. In this setup all the tubes were once again covered by heating tape kept 2-4 °C above the experimental temperature to avoid condensation. The water compositions of the inlet and outlet gases were measured respectively by a thermo-hygrometer model T605-H1 (Testo, Germany) and a humidity sensor model SHT71 (Sensirion, Switzerland). The bed dimensions as well as the experimental conditions employed in the experiments are given in Table 2. For the activated carbon sample two experiments were preformed with inlet humidity
)
( ) ( ) ( )
P P n P (n+1) 1 - (n + 1) +n P0 P0 P0 q ) qm P P (n+1) P 11 + (CBET - 1) - CBET P0 P0 P0 CBET
(2)
In this equation, P0 is the water vapor saturation pressure and CBET, qm, and n are the isotherm fitting parameters. The parameter qm is related to the monolayer coverage and CBET to the convexity of the isotherm at the low partial pressures. As for the parameter n, when it is equal to 1, the n-layer BET equation reduces to the Langmuir equation, while as it approaches infinite the classical BET equation is obtained.21 All the fitting parameters were obtained by the minimization of an error function using a program developed in MATLAB (The MathWorks, Inc.). The error function employed took into account both the absolute and the relative errors weighted by the parameter w (0 e w e 1) and is given by Error ) w
∑ (p
2 ( ) cak - pexp) + 1 - w
q
∑ q
(
pcal - pexp pcal
)
2
(3)
3.2. Adsorption Kinetics. Breakthrough experiments were performed to evaluate the adsorption kinetics of water vapor on the three adsorbents. These breakthrough experiments were analyzed with a mathematical model that considers isothermal behavior, axial dispersed plug flow, external mass transfer resistance expressed with the film model, internal mass transfer
7022 Ind. Eng. Chem. Res., Vol. 47, No. 18, 2008
resistance expressed with the linear driving force (LDF) model, constant velocity, and porosity along the bed. The following material balances were written for the fluid (eq 4) and solid (eq 5), phases respectively. εDax
∂C ( ∂2C ∂C -ε - 1 - ε)kfap(C - C*) ) 0 - u0 ∂x ∂t ∂x2 ∂q ΩLDFDh ( ) q* - q) ∂t R2
(4)
(5)
p
In these equations, x is the axial position, t is time, ε is the bed porosity, u0 is the superficial velocity, C is the gas phase concentration of the adsorbate, C* is the adsorbate concentration at the solid interface, qj is the particle averaged adsorbed concentration, and q* is the adsorbed concentration in equilibrium with C*. The mass axial dispersion coefficient is represented by Dax, the film mass transfer coefficient by kf, and the homogeneous diffusivity in the particle pores by Dh. The particle radius, specific area, and LDF geometric factor are given by Rp, ap, and ΩLDF, respectively. The LDF geometric factor is equal to 15 in the case of spherical particles and 8 in the case of cylindrical particles. This system of partial differential equations, coupled with the appropriate boundary and initial conditions given respectively by eqs 6a6b and 7, was numerically solved by the method of orthogonal collocation in finite elements using gPROMS environment (PSE Enterprise, U.K.). x ) 0 u0Cinlet ) u0C - εDax x)L t)0
∂C ∂x
(6a)
∂C )0 ∂x
(6b)
C)q)0
(7)
The transport parameters needed in the model were calculated from the relations presented below. The axial dispersion and the film mass transfer coefficients were calculated according to the following equations:22 Dax ) (0.45 + 0.55εp)Dmol + 0.35Rp Sh )
1.09 0.33 0.33 Re Sc ε
Figure 5. Amount of water vapor adsorbed on the activated carbon sample at 303 K: closed circles, adsorption; open circles, desorption; gray triangles, obtained from the analysis of the fixed bed experiment; line, virial isotherm fitting of the adsorption branch.
u0 ε
Figure 6. Amount of water vapor adsorbed on the alumina sample at 303 K: closed symbols, adsorption; open circles, desorption; gray triangles, obtained from the analysis of the fixed bed experiment; line, n-layer BET isotherm fitting.
(8) (9)
where Sh () 2Rpkf/Dmol) is the Sherwood number, Re () 2Fgu0Rp/ µg) is the Reynolds number, and Sc () µg/FgDmol) is the Schmidt number. Dmol represents the molecular diffusivity for the mixture helium/water vapor and was approximated with Dmol )
1 - yi n
∑ j)1 j*i
yi Dij
(10)
where the binary molecular diffusivity Dij was calculated with the Chapman-Enskog equation.23 The homogeneous diffusivity in the particle pores was obtained by adjusting the model to the experimental data. Previous studies reported in the literature revealed experimental evidence that the adsorption kinetics of water vapor on activated carbon strongly depends on the water loading value.13,24-26 In this study, this variation was accounted for through the dependence of the homogeneous diffusivity on the
Figure 7. Amount of water vapor adsorbed on the zeolite sample at 303 K: circles, adsorption branch; gray triangle, obtained from the analysis of the fixed bed experiment; line, virial isotherm fitting.
nonlinearity of the adsorption isotherm, that is, the homogeneous diffusivity value is a function of the local value of the isotherm derivative (Dh ∝ (∂qj/∂C)-1).
Ind. Eng. Chem. Res., Vol. 47, No. 18, 2008 7023 Table 3. Isotherm Fitting Parameters at 303 K virial isotherm parameters adsorbent
H (mol/(kg · bar))
A1 (kg/mol)
A2 (kg2/mol2)
activated carbon zeolite
77.711 2.85 × 1012
-0.125 1.754
5.550 × 10-3 -8.460 × 10-2
BET isotherm parameters adsorbent alumina
qm (mol/kg)
n
CBET
1.75
74.7
200
4. Results and Discussion 4.1. Adsorption Equilibrium. The adsorption equilibrium points measured at 303 K are shown for the activated carbon, the alumina, and the zeolite samples in Figures 5-7, respectively. The fitted isotherms are shown in the same figures as lines, and the corresponding parameters are given in Table 3. The three adsorbents present significantly different behaviors concerning their affinity to water vapor. It is known that water vapor has low affinity toward the surface of graphite, that its adsorption mechanism on activated carbons is initially due to the interaction between water and specific surface functional groups, and that these adsorbed molecules act afterward as secondary sites for further water adsorption.21 As a result of this adsorption mechanism, the water adsorption isotherm on activated carbons is usually either of type IV, for highly oxidized carbons, or of type V, for hydrophobic carbons. In several studies reported in the literature,9,27-29 type V isotherms were obtained for several activated carbon/water systems, and this type of isotherm was also observed in this work (Figure 5). In what concerns the adsorption capacity, a wide range of values can be found; for this sample a capacity of 18.8 mol/kg was obtained at 97% humidity. Another typical characteristic of these systems is the presence of hysteresis which was also observed in this study by the determination of some desorption equilibrium points (open symbols in Figure 5). In the case of alumina, a type II isotherm was obtained (Figure 6). This is due to the fact that three distinct mechanisms contribute to the adsorption of water vapor on alumina.8 At low partial pressures, water molecules chemisorb to the surface of the adsorbent. At intermediate partial pressures, water molecules physisorb on the already chemisorbed molecules, and at higher partial pressures, capillary condensation occurs within the mesopores and the smaller macropores.8,30 Desai et al.,8 Kotoh et al.,31 and Serbezov12 reported isotherms for water vapor on several aluminas, all of which present a resembling type II behavior, although comparing the different sample capacities, a generally higher value was obtained for this particular sample at pressures near saturation but a similar, or even smaller, capacity was obtained at low and intermediate partial pressures. That is, this sample presents a very pronounced increase in capacity for relative pressures higher than 0.8, not observed in the other studies. The adsorption isotherm determined for the zeolite sample is presented in Figure 7. For this adsorbent, a type I isotherm was obtained with a high adsorption capacity even at very low relative pressures, reflected in the value of the Henry constant obtained in the isotherm fitting. 4.2. Adsorption Kinetics. As mentioned before, the adsorption kinetics of water vapor on the three adsorbents was evaluated through the analysis of several breakthrough experiments. The results obtained for the activated carbon are presented in Figures 8 and 9 as the water vapor partial pressure history at the column exit. In these figures the model predictions, using
Figure 8. Breakthrough curve obtained with activated carbon for inlet humidity value of 59% at 303 K (points, experimental; solid line, model; dashed line, equilibrium model).
Figure 9. Breakthrough curve obtained with activated carbon for inlet humidity value of 97% at 303 K (points, experimental; solid line, model; dashed line, equilibrium model).
the transport parameter values given in Table 4, are shown as solid lines. In addition, the predictions of the equilibrium theory are also shown in the same figures as dashed lines. As it was seen in the previous section, the adsorption isotherm of water vapor on activated carbon is unfavorable at low partial pressures and then favorable at the higher humidity region. This isotherm shape is reflected on the breakthrough curves obtained for this system. That is, if the inlet concentration is smaller than the one corresponding to the point of inflection in the isotherm, an entirely dispersive breakthrough curve is obtained. For feed concentrations beyond this point the obtained breakthrough curve is composed of two parts. The first part is dispersive, and the second is a compressive front or shock. The concentration at which this discontinuity occurs is determined by the point in the isotherm for which a straight line drawn from the inlet concentration point is tangent to the isotherm.32 The experimental results shown in Figures 8 and 9 correspond to this last case, and in both a dispersive part followed by a compressive wave are observed and predicted by the model. As mentioned in the theoretical section, it was considered that the homogeneous diffusivity value depends on the water vapor adsorbed concentration, such that its value is inversely proportional to the local value of the isotherm derivative. This dependence is shown graphically in Figure 10. Notice should be given to the fact that for the experiment of Figure 9 the model predicts very well the experimental results while for the experiment of Figure 8 a slightly larger concentration is predicted for the discontinuity.
7024 Ind. Eng. Chem. Res., Vol. 47, No. 18, 2008 Table 4. Transport Parameter Values Used in the Simulations of the Fixed Bed Experiments parameters
carbon
inlet humidity (%) Dax (m2/s) kf (m/s) Dh (m2/s)
59 97 9.25 × 10-5 9.45 × 10-5 -2 6.43 × 10 6.75 × 10-2 2.98 × 10-9a
a
alumina 14 1.06 × 10-4 6.27 × 10-2
69 1.04 × 10-4 6.19 × 10-2 2.40 × 10-10
zeolite 84 1.04 × 10-4 6.18 × 10-2
6.3 8.18 × 10-5 1.14 × 10-2 5.53 × 10-11
Value at zero loading.
Figure 10. Dependence of the homogeneous diffusivity value of water vapor on the activated carbon with the adsorbed concentration considered in the model solution.
Figure 11. Breakthrough curve obtained with alumina for inlet humidity value of 14% at 303 K (points, experimental; solid line, model; dashed line, equilibrium model).
This is due to the difference between the experimental and fitted isotherm and affects the prediction of the time at which the shock occurs (displaced in time in the simulation results). Also notice that an unexpected and strange change of shape is observed in the simulation results of Figure 9 sometime after 5 h (P ≈ 0.023). This occurs due to numerical problems caused by the abrupt change in the adsorption capacity and consequently in the homogeneous diffusivity around that pressure. In contrast, the alumina isotherm is somehow opposite to that of activated carbon. That is, it presents first a favorable behavior at low relative pressures and then an unfavorable region. The experimental results for this adsorbent are shown in Figures 11-13. Comparing these results, it is seen that for the first experiment (Figure 11), an inlet concentration within the favorable region of the isotherm was used and a compressive wave is observed and predicted. For the other two experiments (Figures 12 and 13), the feed concentration is beyond the tangency point of the isotherm, resulting in a breakthrough curve
Figure 12. Breakthrough curve obtained with alumina for inlet humidity value of 69% at 303 K (points, experimental; solid line, model; dashed line, equilibrium model).
Figure 13. Breakthrough curve obtained with alumina for inlet humidity value of 84% at 303 K (points, experimental; solid line, model; dashed line, equilibrium model).
composed of two parts: a compressive shock followed by a dispersive wave. Note that for these two breakthrough curves, the shock velocity is the same, corresponding to the velocity of the concentration of the tangency point,32 and it is larger than that of the shock of the experiment of Figure 11. The experimental breakthrough curve obtained for the zeolite sample is shown in Figure 14. As the adsorption isotherm of this system is favorable, a compressive front is observed with a good model prediction. The homogeneous diffusivity values determined in this study are given in Table 4, and it can be seen that the zeolite sample presents the highest mass transfer resistance. In the case of the activated carbon, the value given in Table 4 corresponds to the value at zero loading. The results presented in this study show that the accurate description of the adsorption equilibrium assumes special importance in systems with isotherms containing different
Ind. Eng. Chem. Res., Vol. 47, No. 18, 2008 7025
HY2SEPS (SES6-019887) and additional funding from CAPES/ GRICES and POCI/EQU/59330/2004. Literature Cited
Figure 14. Breakthrough curve obtained with zeolite for inlet humidity value of 6.3% at 303 K (points, experimental; solid line, model; dashed line, equilibrium model).
regions, that is, favorable and unfavorable. For systems with only a favorable region (as type I isotherms) the equilibrium information until the inlet concentration is lost in the discontinuity (shock). On the other hand, when multiple regions are present a slight error in the isotherm fitting can cause significant errors in the breakthrough curve predictions. 5. Conclusions In this work the adsorption equilibrium of water vapor was measured at 303 K on three commercial adsorbents: activated carbon, activated alumina, and zeolite. The three isotherms obtained are respectively of type V, type II, and type I, according to the IUPAC classification. The zeolite sample presented the highest capacity at low relative pressures with an adsorbed amount of near 11 mol/kg at higher relative pressures. On the other hand, at high relative humidity values, the alumina samples had the largest adsorption capacity with an adsorbed amount of near 35 mol/kg at 95% relative humidity. The Virial isotherm was used to fit the experimental data on the activated carbon and the zeolite while the n-layer BET isotherm was employed for the fitting of the water vapor adsorption on the alumina sample. The adsorption kinetics of water vapor on the three adsorbents was assessed through the analysis of fixed bed breakthrough experiments. The description of the fixed bed behavior was done with an isothermal mathematical model that considers axial dispersed plug flow, external (film) mass transfer resistance, and internal (homogeneous LDF) mass transfer resistance. In the case of the activated carbon sample the dependence of the homogeneous diffusivity on the adsorbate concentration was accounted for through the local isotherm derivative. A good agreement between the experimental data and the model predictions was obtained. The homogeneous diffusivity values determined from the analysis of the breakthrough experiments were 2.98 × 10-9, 2.40 × 10-10, and 5.53 × 10-11 m2/s respectively for the activated carbon (at zero loading), activated alumina, and zeolite. It was shown that in systems for which the adsorption isotherm contains favorable/unfavorable regions the accurate description of the adsorption equilibrium assumes special importance, since small differences in the equilibrium can be reflected as large errors in the breakthrough curve predictions. Acknowledgment The authors would like to acknowledge the financial support from European Commission through the FP6 funded project
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ReceiVed for reView December 20, 2007 ReVised manuscript receiVed May 14, 2008 Accepted June 24, 2008 IE701732X
