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Fixed-bed adsorption of chlorinated hydrocarbons from multicomponent aqueous solution onto activated carbon: Equilibrium column model
Journal of Colloid and Interface Science 296 (2006) 458–464 www.elsevier.com/locate/jcis
Fixed-bed adsorption of chlorinated hydrocarbons from multicomponent aqueous solution onto activated carbon: Equilibrium column model Robert Pełech ∗ , Eugeniusz Milchert, Marcin Bartkowiak Department of Organic Technology, Szczecin University of Technology, Pułaskiego 10, PL 70-322 Szczecin, Poland Received 20 July 2005; accepted 10 September 2005 Available online 10 October 2005
Abstract The results of studies on the adsorption dynamics of light chlorinated hydrocarbons, 1,2-dichloroethane, 1,1,2,2-tetrachloroethane, chloroform, carbon tetrachloride, 1,1-dichloroethene, perchloroethylene and 1,1,2-trichloroethene, from a seven-component solution on to activated carbon are presented. The experimental results were described using the equilibrium model. The application of this model allows to determine the location of the midpoint of the breakthrough profile. © 2005 Elsevier Inc. All rights reserved. Keywords: Activated carbon; Adsorption; Chlorinated hydrocarbons; Fixed bed; Wastewater
1. Introduction Growing interest in the application of adsorption processes for the treatment of industrial wastewater, as well for the recovery of organic compounds from aqueous solution, has been observed. These processes are used particularly in the case where impurities did not undergo biological degradation and their concentration is very low. In general, the adsorption methods are used as the final stage in industrial wastewater treatment [1–6]. The fundamental design solution of the adsorbers comprises an apparatus with a fixed-bed adsorbent. The removal of organic compounds from wastewater is most often performed using carbon adsorbents [7,8], in particular activated carbons. The calculations of the adsorption process on a fixed bed are restricted to the determination of the cause of the breakthrough curve. Despite its apparent simplicity, the problem of optimal design of such absorbers is extremely complicated [9]. The majority of existing adsorption models under the dynamic conditions concern the removal of a single component from a treated solution. The prediction of the course of the breakthrough curves for multicomponent systems was solved in several particular cases. However, a universal method has not yet * Corresponding author. Fax: +48 91 449 43 65.
E-mail addresses: [email protected], [email protected] (R. Pełech). 0021-9797/$ – see front matter © 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2005.09.020
been proposed; thus the problem is solved for the specific case [10,11]. The physical phenomena occurring in adsorption columns operating by elution chromatography under isothermal conditions are typical examples of a nonstationary process. The general mathematical model is impossible to solve by known methods. For this reason, several simplifications are incorporated into modeling [12]. An approximate distribution of the concentration in an adsorption column makes it possible to determine an equilibrium model. Paderewski et al. [13] have determined the concentration distribution in a bed based on the equilibrium model during the adsorption of a three-component mixture of acetone, methanol, and benzene vapors. They calculated the adsorption equilibrium for the particular components from the Markham– Benton equation (extended Langmuir equation), whereas Crittenden et al. [14] applied the equilibrium model to the determination of the concentration distribution in a bed in the case of adsorption from a six-component aqueous solution. The adsorption equilibrium was calculated from the developed model IAS (ideal adsorbed solution) in relation to the Freundlich equation for the single-component solution. In this work, the experimental results and a description of multicomponent adsorption under dynamic conditions using the equilibrium model are presented.
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2. Experimental: materials and methods 2.1. Materials 2.1.1. Sorbent The adsorbent used in these studies was activated carbon of the DTO type, supplied by GRYFSKAND SA (Poland). According to the manufacturer’s specifications, this adsorbent is generally suitable for water treatment with activated carbon. Adsorbent was sieved into several discrete particle size ranges. The size range of activated carbon 0.4–0.63 mm was used in these studies. The sieved activated carbon was washed by distilled water to remove fines and then dried at 110 ◦ C in an oven for 24 h. The carbon particles were assumed to be spheres having a diameter given by arithmetic mean value between respective mesh sizes (average particle diameter dz was 0.53 mm). Their properties are presented in Table 1. The surface area, pore size distribution, and pore diameter were measured with N2 (g) adsorption (ASAP 2010 pore structure analyzer, Micromeritics, USA) at 77 K with liquid N2 ; the remaining values were taken on the basis of data given by the manufacturer. The pore volume distribution is presented in Fig. 1 [1,4,6]. 2.1.2. Sorbates Seven chlorinated hydrocarbons, namely 1,2-dichloroethane (12DCE), 1,1,2,2-tetrachloroethane (S-TET), chloroform (CHCl3 ), carbon tetrachloride (CCl4 ), 1,1-dichloroethene (VDC), perchloroethylene (PER) and 1,1,2-trichloroethene (TRI) (Fluka, A.G.), were used in these studies. Table 1 Physical properties of DTO activated carbon Bulk density (g/dm3 ) Apparent density (g/dm3 ) Total surface (N2 BET method) (m2 /g) Pore volume (cm3 /g) Pore volume <1.5 nm (cm3 /g) Porosity Average particle diameter (mm)
400 860 943 0.53 0.25 0.45 0.53
Fig. 2. Schematic diagram of the experimental system: (1) glass adsorption column, (2) peristaltic pump, (3) solution reservoir, (4) damper, (5) sampling of eluate, (6) thermostat.
2.2. Experimental methods The studies were carried out under isothermal conditions at 30 ± 0.5 ◦ C. The experimental setup is shown in Fig. 2. An aqueous solution of chlorinated hydrocarbons was passed through a glass column with diameter 0.24 dm and height 1.5 dm, which was packed with DTO activated carbon. The composition of the feed solution was as follows: CCl4 , 12DCE, S-TET, VDC, TRI, and PER with concentration 5 µmol/dm3 and CHCl3 with 15 µmol/dm3 . This composition corresponds to the average concentration of these compounds in wastewater from a plant manufacturing vinyl chloride by the dichloroethane method with the chlorine balance [15]. A seven-component solution was supplied to the bottom of the column by a peristaltic pump at a flow rate of 0.067 dm3 /min. Linear velocity recalculated on an empty adsorber amounted to 1.5 dm/min. For such established hydrodynamic conditions the Reynolds number was Re = 1.3. Samples of solution were collected at three heights of 0.4, 0.8, and 1.2 dm and were analyzed for chlorinated hydrocarbons content. During the process the inlet concentration was also controlled. In order to maintain constant concentration it was necessary to supplement the loss of a given chlorinated hydrocarbon due to its evaporation. For this purpose methanol solutions of the respective components with a concentration of 50 mmol/dm3 were used, which were added progressively as the concentration decreased, so that a required initial concentration Ci0 of a given component was maintained. 2.3. Analytical method The determination of the chlorinated hydrocarbon concentrations was performed by gas chromatography. A detailed description of this method is provided in [4,6,16,17]. 3. Theoretical background In equilibrium adsorption theory it is assumed that the adsorption equilibrium between the solid and mobile phases is established instantly at each point of the bed. Thereby all the mass transfer resistances are ignored. The principles that determine the equilibrium distribution of adsorbed substances in a column were given by DeVault [18]. The equations used for the description of this phenomenon are derived based on the following assumptions:
Fig. 1. Pore size distribution for DTO activated carbon.
• process proceeds isothermally,
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• axial diffusion and radial mass transfer are negligible, • pressure drop in a bed is insignificant. The mass balance equations have the form ∂Ci ρa ∂ai ∂Ci + + = 0, ∂x ∂t ε ∂t
(1)
ai = fi (C1 , C2 , . . . , Cn ),
(2)
with the initial and boundary conditions Ci (0, x) = ai (0, x) = 0,
Ci (t, 0) = Ci0 ,
i = 1,2, . . . .
(3)
It is assumed that the substances have different sorption affinities with respect to a given adsorbent and they form the adsorption series A1 > A2 > · · · > Ai ,
(4)
where A is adsorption affinity [10,12–14]. The equilibrium model was solved, describing the adsorption in the multicomponent system by the equation ai = f (Ce,i )Θi , where Θi =
amax − i−1 1 ai . amax
(5)
(6)
A function f (Cei ) corresponds to the adsorption isotherm in the single-component system. The adsorption equilibrium in such a system was described by the Langmuir equation [16,19] bCe,i . f (Ce,i ) = am 1 + bCe,i
(7)
The total adsorption of component i in the band with width xi can be expressed by ai0 =
qtCi0 , xi ρ b F
where xi = Ui dt and q = w. F Than Eq. (8) takes the form ai0 =
wtCi0 . xi ρ b
(8)
(10)
(11)
(12)
whereas the adsorption magnitude of any component in band 1 amounts ai,1 = f C10 , C20 , . . . , Ci0 , . . . , Cn0 . (13)
a20 x2 − a2,1 x1 Θ2,2 . x 2 − x1
a2,2 =
(15)
Since the remaining components do not influence the adsorption of component 2 in band 2, the concentration in this band can be directly calculated from the adsorption isotherm equation in the single-component system. The component i = 3 is located in the three bands k = 1, 2, 3, thus its mass balance can be presented as a3,1 = f C30 Θ3,1 , (16) a30 x3 − a3,1 x1 Θ3,2 , x 3 − x1
a3,2 =
C3,2 = f (a2,2 , a3,2 , . . . , an,2 ),
(17) (18)
where the first character of the index denotes the component number and the second one the band number. The adsorption of component 3 in band 2 is affected by component 2; hence the concentration in this band should be calculated taking into consideration the parameter Θ. After the rearrangement of the Langmuir equation, the concentration is calculated from the equation C3,2 =
a3,2 , b3 (am Θ3,2 − a3 )
(19)
a3,3 =
a30 x3 − a3,1 x1 − a3,2 (x2 − x1 ) Θ3,3 . x 3 − x2
(20)
(9)
The adsorption magnitude of component i in any band k is equal to ai,k = f (C1,k , C2,k , . . . , Ci,k , . . . , Cn,k ),
All the n components occur in band 1, whereas in each subsequent band there will be n − k components, where k denotes the band number. In accordance with the assumption of the equilibrium model and designation of the components in the sequence of decreasing adsorption affinity, for the component i, i adsorption bands will be formed. The component i = 1 is located in one band k = 1, i = 2 in two bands k = 1 and k = 2, for which the mass balance is expressed by the equations a2,1 = f C20 Θ2,1 , (14)
The concentration of component 3 in band 3 is calculated in the same manner as component 2 in band 2. The adsorption of component i in band k can be written by the recurrent balance equation ai,k =
ai0 xi −ai,1 (x1 −x0 )−ai,2 (x2 −x1 )−···−ai,k−1 (xi−1 −xi−2 ) Θi,k xi −xk
(21)
and the concentration of component i in band k as Ci,k =
ai,k . bi (am Θi,k − ai,k )
(22)
According to the statement that components with lower sorption affinity do not influence on adsorption of components with higher affinity [16], the velocity of the concentration wave front of component i will be determined by the adsorption isotherms
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Table 2 The velocities of the concentration wavefronts of particular components Compound
PER
S-TET
TRI
CCl4
VDC
CHCl3
12DCE
U (dm/min·103 )
0.11
0.27
0.49
0.66
0.82
1.05
2.51
in a single-component system. The velocities of the concentration wave fronts are determined from the relationship [20,21] w . Ui = (23) 1 + ρb (dai /dCi ) To calculate the velocity of the concentration wave front of band k, the knowledge of the component concentrations at the front of this band is required. The concentrations at the sorption fronts undergo constant changes from a value Ci0 at the column inlet to a value Ci (x). However, the analytical solution of this problem is impossible because the concentration is a function of velocity. A method of successive approximations was utilized for the calculation of velocity of the concentration wave front. In the first step, the value of the velocity for the conditions existing at the column inlet was calculated from the equation [13,22] w . Ui = (24) 1 + (ai0 ρb )/Ci0 The obtained value was substituted into Eq. (21), and after the substitution, xi = Ui t,
(25)
this equation takes the form ai,k =
ai0 Ui −ai,1 (U1 −U0 )−ai,2 (U2 −U1 )−···−ai,k−1 (Ui−1 −Ui−2 ) Θi,k . Ui −Uk
(26) The calculated value Ci from Eq. (22) allows the calculation of a new value Ui from Eq. (23). Subsequently, after the determination of the average value of velocity of the concentration p−1 p and Ui , wave front between the iterated values Ui p−1
p
+ Ui (27) , 2 the consecutive iteration step was calculated. The average difference between the values in the first iteration step and the twentieth step was found to amount to 0.08%. This allows the assumption of practically constant velocity of concentration wave front along the column in relation to the initial values, which is equal to the value obtained from Eq. (23). This results from the fact that the adsorption isotherms in the studied concentration range possess a shape close to linear. This allows assuming da/dC = const and as a consequence, constant velocity of the concentration wave front. Their values are compiled in Table 2. Ui =
Ui
4. Results and discussion The calculated distribution of concentration (Eqs. (22)–(25)) in the bed during the process of chlorinated hydrocarbon adsorption from seven-component aqueous solution is shown in
Fig. 3. Distribution of adsorptive components concentration calculated from equilibrium column model.
Fig. 3, whereas the distribution of adsorptive components along the bed depth is presented in Fig. 4. Figs. 3 and 4 correspond to the moment of equilibrium breakthrough of a bed layer with height of 12 cm by 12DCE. The calculated profiles of these concentrations at the bed outlet as a function of time are presented in Fig. 5. To show more distinctly the eluent concentration, the concentration profiles in Figs. 3–5 are presented in the range of relative concentrations Ci /Ci0 = 0.95–1.07. The obtained model indicates that the concentration profile of 12DCE considerably overtakes the profiles of the remaining components. At the moment of the equilibrium breakthrough of the bed by 12DCE, the CHCl3 profile will be located at a height of 5.0 cm, whereas VDC, CCl4 , TRI, S-TET, and PER are at the heights 3.9, 3.2, 2.4, 1.3, and 0.5 cm, respectively. In the zone x7 = 6.96 cm there is only 12DCE, the concentration of which in the liquid phase amounted to 1.031C 0 . In the zone x6 = 1.12 cm there are 12DCE and CHCl3 with the concentrations 1.027 and 1.06C 0 ; in x5 = 0.75 cm there are 12DCE, CHCl3 and VDC with concentrations 1.024, 1.055, and 1.069C 0 ; and successively, x4 = 0.82 cm, 12DCE, CHCl3 , VDC and CCl4 at 1.020, 1.045, 1.056, and 1.063C 0 ; x3 = 1.06 cm, 12DCE, CHCl3 , VDC, CCl4 , and TRI at 1.014, 1.014, 1.036, 1.042, and 1.051C 0 ; x2 = 0.75 cm, 12DCE, CHCl3 , VDC, CCl4 , TRI, and S-TET at 1.007, 1.016, 1.020, 1.023, 1.029, and 1.050C 0 . For the zone x1 = 0.54 cm there are all the components supplied to the bed with concentrations equal to the inlet ones. The presence of 12DCE considerably decreases the effectiveness of column performance. If the working time the bed will be limited to the moment of the appearance of this component at the outlet, then more than 50% of the adsorption zone will be not available for remaining adsorbates. Obviously such a distribution will be possible only in the case of lack of any kinetic effects of the adsorption process. However, this allows the determination of the sequence of appearance and the degrees of overshoot concentrations of the particular components at the outlet of the adsorption column. The course of the breakthrough curves obtained experimentally (points) and calculated from the equilibrium model (bro-
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Fig. 5. Breakthrough curves calculated from equilibrium column model.
Fig. 6. Experimental breakthrough curves and curves calculated from equilibrium column model, bed depth 1.2 dm.
ken line) as a function of time at the bed depth of 1.2 dm is shown in Fig. 6. Exemplary courses of the breakthrough curves of component as a function of the relative volume of treated solution V /Vads are shown in Fig. 7. The changes of the total concentration of chlorinated hydrocarbons Ci / Ci0 (sum) at the column outlet are also shown in Fig. 7. The breakthrough curves calculated from the equilibrium model determine the surroundings of the central point (∼0.5Cmax /C 0 ) for the individual experimental curves. The breakthrough curve calculated in relation to the sum of concentrations of the column outlet Ci / Ci0 = f (V /Vads ) precisely reflects the experimental data. The experimental breakthrough curves for each component were constricted with increased bed depth. The difference decreases as Fig. 4. Distribution of adsorptive components concentration calculated from equilibrium column model along a bed.
(t0.1 − t0.95 )q V = , Vads Vads
(28)
where tbi = t0.1 and t0.95 denotes the moment of reaching the concentration 0.1Ci0 and 0.95Ci0 at the column outlet.
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463
Fig. 7. Breakthrough curves, experimental and calculated from equilibrium column model.
This indicates that for H → ∞ the experimental breakthrough curve will approach a shape obtained from the equilibrium model. This also results from an increase of the relative volume of the treated solution with increasing height of bed for the particular components. The relative amount of treated solution was defined as qtbi wF tbi tbi Ψi = (29) = = . Vads FH tc The dependence of relative volume of solution as a function of the bed depth was shown in Fig. 8. Extrapolation of the courses beyond the measurement range was performed with the assumption that at H → ∞ this value is equal to that calculated from the equilibrium model. For a bed depth of about 10 dm, the volume of treated solution per unit of adsorbent volume—Ψ —increases distinctly. Above this height the increment volume dΨ/dH is already insignificant. An increase of bed depth above 10 dm should not cause a pronounced chanse of the effective utilization of the adsorbent. However, it only allows prolonging the time of the adsorption cycle. This operation, however, may unfavorably influence the process due to an increase of the flow resistance. The application of too high an
adsorption bed causes a large part of it not to participate in the process of mass transfer. A dead layer of adsorbent is formed, which only causes flow resistances. 5. Conclusion The presented solution of the equilibrium model allows determining the midpoint of the breakthrough curve of adsorption of chlorinated hydrocarbons from multicomponent aqueous solutions and the degree of overshoot concentrations of the particular components at the column outlet. The changes of velocity of the equilibrium profile moving along the bed are negligible. They can be omitted in practical calculations and the constant value of front migration resulting from Eq. (24) and the inlet conditions can be assumed. It was found that a profile of the experimental curve approaches the equilibrium shape with increasing bed depth. Appendix A. Nomenclature A
adsorption affinity
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Fig. 8. Relative volume of treated solution as a function of bed depth.
a amax C Ci0 Ce,i Cmax F H q Re t tb tc U V Vads w x
adsorptivity (mmol/g) maximum molar adsorptivity (mmol/g) concentration (mmol/dm3 ) initial concentration of component i (mmol/dm3 ) equilibrium concentration of component i (mmol/dm3 ) degree of overshoot concentration (mmol/dm3 ) cross-section of the bed (dm2 ) bed depth (dm) flow rate (dm3 /min) Reynolds number Re = wdμz ρ time (min) throughput time (min) contact time (min) velocity of the concentrate wave front (dm/min) volume of liquid phase (dm3 ) volume of adsorbent (dm3 ) interstitial velocity (dm/min) axial coordinate (dm)
Greek letters ε Θ μ ρ ρb ρa Ψ
porosity adsorption free space fraction dynamic viscosity (Pa s) liquid density (g/dm3 ) bulk density (g/dm3 ) apparent density (g/dm3 ) relative amount of treated solution
Subscripts i k
component adsorption band
References [1] R. Pełech, A. Bembnowska, E. Milchert, Pol. J. Chem. Technol. 3 (2001) 17–19. [2] C. Moreno-Castilla, Carbon 42 (2004) 83–94. [3] B. Singh, S. Madhusudhanan, V. Dubey, R. Nath, N. Rao, Carbon 34 (1996) 327–330. [4] A. Bembnowska, R. Pełech, E. Milchert, J. Colloid Interface Sci. 256 (2003) 276–282. [5] R. Suri, J. Crittenden, D. Hand, J. Environ. Eng. 125 (1999) 897–905. [6] E. Milchert, W. Goc, R. Pełech, Adsorpt. Sci. Technol. 18 (2000) 823–837. [7] K. Urano, Y. Koichi, Y. Nakazawa, J. Colloid Interface Sci. 81 (1981) 477–485. [8] M. Uchida, S. Ito, N. Kawasaki, T. Nakamura, S. Kanada, J. Colloid Interface Sci. 220 (1999) 406–409. [9] H. Błasi´nski, S. Krauze, In˙z. Chem. Proc. 3 (1982) 3–20. [10] M. Paderewski, Adsorption Processes in a Chemical Engineering, WNT, Warszaw, 1999. [11] A. Tyczkowski, In˙z. Chem. 8 (1978) 763–771. [12] W. Raczy´nski, Theory of the Dynamic Sorption and Chromatography, WNT, Warszaw, 1966. [13] M. Paderewski, M. Jabło´nski, A. J˛edrzejak, In˙z. Chem. Proc. 1 (1980) 795–804. [14] J. Crittenden, T. Speth, D. Hand, P. Luft, B. Lykins, J. Environ. Eng. ASCE 113 (1987) 1363–1375. [15] E. Milchert, Technology Production of Chloroorganic Compounds. Waste Utilization, Technical University of Szczecin, Szczecin, 1997. [16] R. Pełech, A. Bembnowska, E. Milchert, Adsorpt. Sci. Technol. 21 (2003) 707–720. [17] R. Pełech, E. Milchert, A. Wróblebska, J. Colloid Interface Sci. 285 (2005) 518–524. [18] D. DeVault, J. Am. Chem. Soc. 65 (1943) 532–540. [19] N. Vahdat, Carbon 35 (1997) 1554–1557. [20] O. Lisec, P. Hugo, A. Seidel-Morgenstern, J. Chromatogr. A 908 (2001) 19–34. [21] D. Basmadjian, P. Coroyannakis, Chem. Eng. Sci. 42 (1987) 1723–1735. [22] M. Paderewski, A. J˛edrzejak, Wiad. Chem. 34 (1980) 313–327.
Fixed-bed adsorption of chlorinated hydrocarbons from multicomponent aqueous solution onto activated carbon: Equilibrium column model Robert Pełech ∗ , Eugeniusz Milchert, Marcin Bartkowiak Department of Organic Technology, Szczecin University of Technology, Pułaskiego 10, PL 70-322 Szczecin, Poland Received 20 July 2005; accepted 10 September 2005 Available online 10 October 2005
Abstract The results of studies on the adsorption dynamics of light chlorinated hydrocarbons, 1,2-dichloroethane, 1,1,2,2-tetrachloroethane, chloroform, carbon tetrachloride, 1,1-dichloroethene, perchloroethylene and 1,1,2-trichloroethene, from a seven-component solution on to activated carbon are presented. The experimental results were described using the equilibrium model. The application of this model allows to determine the location of the midpoint of the breakthrough profile. © 2005 Elsevier Inc. All rights reserved. Keywords: Activated carbon; Adsorption; Chlorinated hydrocarbons; Fixed bed; Wastewater
1. Introduction Growing interest in the application of adsorption processes for the treatment of industrial wastewater, as well for the recovery of organic compounds from aqueous solution, has been observed. These processes are used particularly in the case where impurities did not undergo biological degradation and their concentration is very low. In general, the adsorption methods are used as the final stage in industrial wastewater treatment [1–6]. The fundamental design solution of the adsorbers comprises an apparatus with a fixed-bed adsorbent. The removal of organic compounds from wastewater is most often performed using carbon adsorbents [7,8], in particular activated carbons. The calculations of the adsorption process on a fixed bed are restricted to the determination of the cause of the breakthrough curve. Despite its apparent simplicity, the problem of optimal design of such absorbers is extremely complicated [9]. The majority of existing adsorption models under the dynamic conditions concern the removal of a single component from a treated solution. The prediction of the course of the breakthrough curves for multicomponent systems was solved in several particular cases. However, a universal method has not yet * Corresponding author. Fax: +48 91 449 43 65.
E-mail addresses: [email protected], [email protected] (R. Pełech). 0021-9797/$ – see front matter © 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2005.09.020
been proposed; thus the problem is solved for the specific case [10,11]. The physical phenomena occurring in adsorption columns operating by elution chromatography under isothermal conditions are typical examples of a nonstationary process. The general mathematical model is impossible to solve by known methods. For this reason, several simplifications are incorporated into modeling [12]. An approximate distribution of the concentration in an adsorption column makes it possible to determine an equilibrium model. Paderewski et al. [13] have determined the concentration distribution in a bed based on the equilibrium model during the adsorption of a three-component mixture of acetone, methanol, and benzene vapors. They calculated the adsorption equilibrium for the particular components from the Markham– Benton equation (extended Langmuir equation), whereas Crittenden et al. [14] applied the equilibrium model to the determination of the concentration distribution in a bed in the case of adsorption from a six-component aqueous solution. The adsorption equilibrium was calculated from the developed model IAS (ideal adsorbed solution) in relation to the Freundlich equation for the single-component solution. In this work, the experimental results and a description of multicomponent adsorption under dynamic conditions using the equilibrium model are presented.
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2. Experimental: materials and methods 2.1. Materials 2.1.1. Sorbent The adsorbent used in these studies was activated carbon of the DTO type, supplied by GRYFSKAND SA (Poland). According to the manufacturer’s specifications, this adsorbent is generally suitable for water treatment with activated carbon. Adsorbent was sieved into several discrete particle size ranges. The size range of activated carbon 0.4–0.63 mm was used in these studies. The sieved activated carbon was washed by distilled water to remove fines and then dried at 110 ◦ C in an oven for 24 h. The carbon particles were assumed to be spheres having a diameter given by arithmetic mean value between respective mesh sizes (average particle diameter dz was 0.53 mm). Their properties are presented in Table 1. The surface area, pore size distribution, and pore diameter were measured with N2 (g) adsorption (ASAP 2010 pore structure analyzer, Micromeritics, USA) at 77 K with liquid N2 ; the remaining values were taken on the basis of data given by the manufacturer. The pore volume distribution is presented in Fig. 1 [1,4,6]. 2.1.2. Sorbates Seven chlorinated hydrocarbons, namely 1,2-dichloroethane (12DCE), 1,1,2,2-tetrachloroethane (S-TET), chloroform (CHCl3 ), carbon tetrachloride (CCl4 ), 1,1-dichloroethene (VDC), perchloroethylene (PER) and 1,1,2-trichloroethene (TRI) (Fluka, A.G.), were used in these studies. Table 1 Physical properties of DTO activated carbon Bulk density (g/dm3 ) Apparent density (g/dm3 ) Total surface (N2 BET method) (m2 /g) Pore volume (cm3 /g) Pore volume <1.5 nm (cm3 /g) Porosity Average particle diameter (mm)
400 860 943 0.53 0.25 0.45 0.53
Fig. 2. Schematic diagram of the experimental system: (1) glass adsorption column, (2) peristaltic pump, (3) solution reservoir, (4) damper, (5) sampling of eluate, (6) thermostat.
2.2. Experimental methods The studies were carried out under isothermal conditions at 30 ± 0.5 ◦ C. The experimental setup is shown in Fig. 2. An aqueous solution of chlorinated hydrocarbons was passed through a glass column with diameter 0.24 dm and height 1.5 dm, which was packed with DTO activated carbon. The composition of the feed solution was as follows: CCl4 , 12DCE, S-TET, VDC, TRI, and PER with concentration 5 µmol/dm3 and CHCl3 with 15 µmol/dm3 . This composition corresponds to the average concentration of these compounds in wastewater from a plant manufacturing vinyl chloride by the dichloroethane method with the chlorine balance [15]. A seven-component solution was supplied to the bottom of the column by a peristaltic pump at a flow rate of 0.067 dm3 /min. Linear velocity recalculated on an empty adsorber amounted to 1.5 dm/min. For such established hydrodynamic conditions the Reynolds number was Re = 1.3. Samples of solution were collected at three heights of 0.4, 0.8, and 1.2 dm and were analyzed for chlorinated hydrocarbons content. During the process the inlet concentration was also controlled. In order to maintain constant concentration it was necessary to supplement the loss of a given chlorinated hydrocarbon due to its evaporation. For this purpose methanol solutions of the respective components with a concentration of 50 mmol/dm3 were used, which were added progressively as the concentration decreased, so that a required initial concentration Ci0 of a given component was maintained. 2.3. Analytical method The determination of the chlorinated hydrocarbon concentrations was performed by gas chromatography. A detailed description of this method is provided in [4,6,16,17]. 3. Theoretical background In equilibrium adsorption theory it is assumed that the adsorption equilibrium between the solid and mobile phases is established instantly at each point of the bed. Thereby all the mass transfer resistances are ignored. The principles that determine the equilibrium distribution of adsorbed substances in a column were given by DeVault [18]. The equations used for the description of this phenomenon are derived based on the following assumptions:
Fig. 1. Pore size distribution for DTO activated carbon.
• process proceeds isothermally,
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• axial diffusion and radial mass transfer are negligible, • pressure drop in a bed is insignificant. The mass balance equations have the form ∂Ci ρa ∂ai ∂Ci + + = 0, ∂x ∂t ε ∂t
(1)
ai = fi (C1 , C2 , . . . , Cn ),
(2)
with the initial and boundary conditions Ci (0, x) = ai (0, x) = 0,
Ci (t, 0) = Ci0 ,
i = 1,2, . . . .
(3)
It is assumed that the substances have different sorption affinities with respect to a given adsorbent and they form the adsorption series A1 > A2 > · · · > Ai ,
(4)
where A is adsorption affinity [10,12–14]. The equilibrium model was solved, describing the adsorption in the multicomponent system by the equation ai = f (Ce,i )Θi , where Θi =
amax − i−1 1 ai . amax
(5)
(6)
A function f (Cei ) corresponds to the adsorption isotherm in the single-component system. The adsorption equilibrium in such a system was described by the Langmuir equation [16,19] bCe,i . f (Ce,i ) = am 1 + bCe,i
(7)
The total adsorption of component i in the band with width xi can be expressed by ai0 =
qtCi0 , xi ρ b F
where xi = Ui dt and q = w. F Than Eq. (8) takes the form ai0 =
wtCi0 . xi ρ b
(8)
(10)
(11)
(12)
whereas the adsorption magnitude of any component in band 1 amounts ai,1 = f C10 , C20 , . . . , Ci0 , . . . , Cn0 . (13)
a20 x2 − a2,1 x1 Θ2,2 . x 2 − x1
a2,2 =
(15)
Since the remaining components do not influence the adsorption of component 2 in band 2, the concentration in this band can be directly calculated from the adsorption isotherm equation in the single-component system. The component i = 3 is located in the three bands k = 1, 2, 3, thus its mass balance can be presented as a3,1 = f C30 Θ3,1 , (16) a30 x3 − a3,1 x1 Θ3,2 , x 3 − x1
a3,2 =
C3,2 = f (a2,2 , a3,2 , . . . , an,2 ),
(17) (18)
where the first character of the index denotes the component number and the second one the band number. The adsorption of component 3 in band 2 is affected by component 2; hence the concentration in this band should be calculated taking into consideration the parameter Θ. After the rearrangement of the Langmuir equation, the concentration is calculated from the equation C3,2 =
a3,2 , b3 (am Θ3,2 − a3 )
(19)
a3,3 =
a30 x3 − a3,1 x1 − a3,2 (x2 − x1 ) Θ3,3 . x 3 − x2
(20)
(9)
The adsorption magnitude of component i in any band k is equal to ai,k = f (C1,k , C2,k , . . . , Ci,k , . . . , Cn,k ),
All the n components occur in band 1, whereas in each subsequent band there will be n − k components, where k denotes the band number. In accordance with the assumption of the equilibrium model and designation of the components in the sequence of decreasing adsorption affinity, for the component i, i adsorption bands will be formed. The component i = 1 is located in one band k = 1, i = 2 in two bands k = 1 and k = 2, for which the mass balance is expressed by the equations a2,1 = f C20 Θ2,1 , (14)
The concentration of component 3 in band 3 is calculated in the same manner as component 2 in band 2. The adsorption of component i in band k can be written by the recurrent balance equation ai,k =
ai0 xi −ai,1 (x1 −x0 )−ai,2 (x2 −x1 )−···−ai,k−1 (xi−1 −xi−2 ) Θi,k xi −xk
(21)
and the concentration of component i in band k as Ci,k =
ai,k . bi (am Θi,k − ai,k )
(22)
According to the statement that components with lower sorption affinity do not influence on adsorption of components with higher affinity [16], the velocity of the concentration wave front of component i will be determined by the adsorption isotherms
R. Pełech et al. / Journal of Colloid and Interface Science 296 (2006) 458–464
461
Table 2 The velocities of the concentration wavefronts of particular components Compound
PER
S-TET
TRI
CCl4
VDC
CHCl3
12DCE
U (dm/min·103 )
0.11
0.27
0.49
0.66
0.82
1.05
2.51
in a single-component system. The velocities of the concentration wave fronts are determined from the relationship [20,21] w . Ui = (23) 1 + ρb (dai /dCi ) To calculate the velocity of the concentration wave front of band k, the knowledge of the component concentrations at the front of this band is required. The concentrations at the sorption fronts undergo constant changes from a value Ci0 at the column inlet to a value Ci (x). However, the analytical solution of this problem is impossible because the concentration is a function of velocity. A method of successive approximations was utilized for the calculation of velocity of the concentration wave front. In the first step, the value of the velocity for the conditions existing at the column inlet was calculated from the equation [13,22] w . Ui = (24) 1 + (ai0 ρb )/Ci0 The obtained value was substituted into Eq. (21), and after the substitution, xi = Ui t,
(25)
this equation takes the form ai,k =
ai0 Ui −ai,1 (U1 −U0 )−ai,2 (U2 −U1 )−···−ai,k−1 (Ui−1 −Ui−2 ) Θi,k . Ui −Uk
(26) The calculated value Ci from Eq. (22) allows the calculation of a new value Ui from Eq. (23). Subsequently, after the determination of the average value of velocity of the concentration p−1 p and Ui , wave front between the iterated values Ui p−1
p
+ Ui (27) , 2 the consecutive iteration step was calculated. The average difference between the values in the first iteration step and the twentieth step was found to amount to 0.08%. This allows the assumption of practically constant velocity of concentration wave front along the column in relation to the initial values, which is equal to the value obtained from Eq. (23). This results from the fact that the adsorption isotherms in the studied concentration range possess a shape close to linear. This allows assuming da/dC = const and as a consequence, constant velocity of the concentration wave front. Their values are compiled in Table 2. Ui =
Ui
4. Results and discussion The calculated distribution of concentration (Eqs. (22)–(25)) in the bed during the process of chlorinated hydrocarbon adsorption from seven-component aqueous solution is shown in
Fig. 3. Distribution of adsorptive components concentration calculated from equilibrium column model.
Fig. 3, whereas the distribution of adsorptive components along the bed depth is presented in Fig. 4. Figs. 3 and 4 correspond to the moment of equilibrium breakthrough of a bed layer with height of 12 cm by 12DCE. The calculated profiles of these concentrations at the bed outlet as a function of time are presented in Fig. 5. To show more distinctly the eluent concentration, the concentration profiles in Figs. 3–5 are presented in the range of relative concentrations Ci /Ci0 = 0.95–1.07. The obtained model indicates that the concentration profile of 12DCE considerably overtakes the profiles of the remaining components. At the moment of the equilibrium breakthrough of the bed by 12DCE, the CHCl3 profile will be located at a height of 5.0 cm, whereas VDC, CCl4 , TRI, S-TET, and PER are at the heights 3.9, 3.2, 2.4, 1.3, and 0.5 cm, respectively. In the zone x7 = 6.96 cm there is only 12DCE, the concentration of which in the liquid phase amounted to 1.031C 0 . In the zone x6 = 1.12 cm there are 12DCE and CHCl3 with the concentrations 1.027 and 1.06C 0 ; in x5 = 0.75 cm there are 12DCE, CHCl3 and VDC with concentrations 1.024, 1.055, and 1.069C 0 ; and successively, x4 = 0.82 cm, 12DCE, CHCl3 , VDC and CCl4 at 1.020, 1.045, 1.056, and 1.063C 0 ; x3 = 1.06 cm, 12DCE, CHCl3 , VDC, CCl4 , and TRI at 1.014, 1.014, 1.036, 1.042, and 1.051C 0 ; x2 = 0.75 cm, 12DCE, CHCl3 , VDC, CCl4 , TRI, and S-TET at 1.007, 1.016, 1.020, 1.023, 1.029, and 1.050C 0 . For the zone x1 = 0.54 cm there are all the components supplied to the bed with concentrations equal to the inlet ones. The presence of 12DCE considerably decreases the effectiveness of column performance. If the working time the bed will be limited to the moment of the appearance of this component at the outlet, then more than 50% of the adsorption zone will be not available for remaining adsorbates. Obviously such a distribution will be possible only in the case of lack of any kinetic effects of the adsorption process. However, this allows the determination of the sequence of appearance and the degrees of overshoot concentrations of the particular components at the outlet of the adsorption column. The course of the breakthrough curves obtained experimentally (points) and calculated from the equilibrium model (bro-
462
R. Pełech et al. / Journal of Colloid and Interface Science 296 (2006) 458–464
Fig. 5. Breakthrough curves calculated from equilibrium column model.
Fig. 6. Experimental breakthrough curves and curves calculated from equilibrium column model, bed depth 1.2 dm.
ken line) as a function of time at the bed depth of 1.2 dm is shown in Fig. 6. Exemplary courses of the breakthrough curves of component as a function of the relative volume of treated solution V /Vads are shown in Fig. 7. The changes of the total concentration of chlorinated hydrocarbons Ci / Ci0 (sum) at the column outlet are also shown in Fig. 7. The breakthrough curves calculated from the equilibrium model determine the surroundings of the central point (∼0.5Cmax /C 0 ) for the individual experimental curves. The breakthrough curve calculated in relation to the sum of concentrations of the column outlet Ci / Ci0 = f (V /Vads ) precisely reflects the experimental data. The experimental breakthrough curves for each component were constricted with increased bed depth. The difference decreases as Fig. 4. Distribution of adsorptive components concentration calculated from equilibrium column model along a bed.
(t0.1 − t0.95 )q V = , Vads Vads
(28)
where tbi = t0.1 and t0.95 denotes the moment of reaching the concentration 0.1Ci0 and 0.95Ci0 at the column outlet.
R. Pełech et al. / Journal of Colloid and Interface Science 296 (2006) 458–464
463
Fig. 7. Breakthrough curves, experimental and calculated from equilibrium column model.
This indicates that for H → ∞ the experimental breakthrough curve will approach a shape obtained from the equilibrium model. This also results from an increase of the relative volume of the treated solution with increasing height of bed for the particular components. The relative amount of treated solution was defined as qtbi wF tbi tbi Ψi = (29) = = . Vads FH tc The dependence of relative volume of solution as a function of the bed depth was shown in Fig. 8. Extrapolation of the courses beyond the measurement range was performed with the assumption that at H → ∞ this value is equal to that calculated from the equilibrium model. For a bed depth of about 10 dm, the volume of treated solution per unit of adsorbent volume—Ψ —increases distinctly. Above this height the increment volume dΨ/dH is already insignificant. An increase of bed depth above 10 dm should not cause a pronounced chanse of the effective utilization of the adsorbent. However, it only allows prolonging the time of the adsorption cycle. This operation, however, may unfavorably influence the process due to an increase of the flow resistance. The application of too high an
adsorption bed causes a large part of it not to participate in the process of mass transfer. A dead layer of adsorbent is formed, which only causes flow resistances. 5. Conclusion The presented solution of the equilibrium model allows determining the midpoint of the breakthrough curve of adsorption of chlorinated hydrocarbons from multicomponent aqueous solutions and the degree of overshoot concentrations of the particular components at the column outlet. The changes of velocity of the equilibrium profile moving along the bed are negligible. They can be omitted in practical calculations and the constant value of front migration resulting from Eq. (24) and the inlet conditions can be assumed. It was found that a profile of the experimental curve approaches the equilibrium shape with increasing bed depth. Appendix A. Nomenclature A
adsorption affinity
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R. Pełech et al. / Journal of Colloid and Interface Science 296 (2006) 458–464
Fig. 8. Relative volume of treated solution as a function of bed depth.
a amax C Ci0 Ce,i Cmax F H q Re t tb tc U V Vads w x
adsorptivity (mmol/g) maximum molar adsorptivity (mmol/g) concentration (mmol/dm3 ) initial concentration of component i (mmol/dm3 ) equilibrium concentration of component i (mmol/dm3 ) degree of overshoot concentration (mmol/dm3 ) cross-section of the bed (dm2 ) bed depth (dm) flow rate (dm3 /min) Reynolds number Re = wdμz ρ time (min) throughput time (min) contact time (min) velocity of the concentrate wave front (dm/min) volume of liquid phase (dm3 ) volume of adsorbent (dm3 ) interstitial velocity (dm/min) axial coordinate (dm)
Greek letters ε Θ μ ρ ρb ρa Ψ
porosity adsorption free space fraction dynamic viscosity (Pa s) liquid density (g/dm3 ) bulk density (g/dm3 ) apparent density (g/dm3 ) relative amount of treated solution
Subscripts i k
component adsorption band
References [1] R. Pełech, A. Bembnowska, E. Milchert, Pol. J. Chem. Technol. 3 (2001) 17–19. [2] C. Moreno-Castilla, Carbon 42 (2004) 83–94. [3] B. Singh, S. Madhusudhanan, V. Dubey, R. Nath, N. Rao, Carbon 34 (1996) 327–330. [4] A. Bembnowska, R. Pełech, E. Milchert, J. Colloid Interface Sci. 256 (2003) 276–282. [5] R. Suri, J. Crittenden, D. Hand, J. Environ. Eng. 125 (1999) 897–905. [6] E. Milchert, W. Goc, R. Pełech, Adsorpt. Sci. Technol. 18 (2000) 823–837. [7] K. Urano, Y. Koichi, Y. Nakazawa, J. Colloid Interface Sci. 81 (1981) 477–485. [8] M. Uchida, S. Ito, N. Kawasaki, T. Nakamura, S. Kanada, J. Colloid Interface Sci. 220 (1999) 406–409. [9] H. Błasi´nski, S. Krauze, In˙z. Chem. Proc. 3 (1982) 3–20. [10] M. Paderewski, Adsorption Processes in a Chemical Engineering, WNT, Warszaw, 1999. [11] A. Tyczkowski, In˙z. Chem. 8 (1978) 763–771. [12] W. Raczy´nski, Theory of the Dynamic Sorption and Chromatography, WNT, Warszaw, 1966. [13] M. Paderewski, M. Jabło´nski, A. J˛edrzejak, In˙z. Chem. Proc. 1 (1980) 795–804. [14] J. Crittenden, T. Speth, D. Hand, P. Luft, B. Lykins, J. Environ. Eng. ASCE 113 (1987) 1363–1375. [15] E. Milchert, Technology Production of Chloroorganic Compounds. Waste Utilization, Technical University of Szczecin, Szczecin, 1997. [16] R. Pełech, A. Bembnowska, E. Milchert, Adsorpt. Sci. Technol. 21 (2003) 707–720. [17] R. Pełech, E. Milchert, A. Wróblebska, J. Colloid Interface Sci. 285 (2005) 518–524. [18] D. DeVault, J. Am. Chem. Soc. 65 (1943) 532–540. [19] N. Vahdat, Carbon 35 (1997) 1554–1557. [20] O. Lisec, P. Hugo, A. Seidel-Morgenstern, J. Chromatogr. A 908 (2001) 19–34. [21] D. Basmadjian, P. Coroyannakis, Chem. Eng. Sci. 42 (1987) 1723–1735. [22] M. Paderewski, A. J˛edrzejak, Wiad. Chem. 34 (1980) 313–327.