4764
Ind. Eng. Chem. Res. 2007, 46, 4764-4771
Kinetic Modeling of the Adsorption of Basic Dyes onto Steam-Activated Bituminous Coal Emad N. El Qada,* Stephen J. Allen, and Gavin M. Walker School of Chemistry and Chemical Engineering, Queen’s UniVersity of Belfast, Belfast BT9 5AG, United Kingdom
The principal aim of this work is to investigate the mechanism of basic dye (methylene blue (MB) and basic red (BR)) adsorption onto activated carbons produced from steam-activated bituminous coal. The rate of adsorption onto various activated carbons, produced in small laboratory-scale and pilot-industrial-scale processes, was investigated under a variety of conditions. The kinetic data from these investigations were correlated to a number of adsorption models in an attempt to elucidate the mechanism of the adsorption processes. The adsorption mechanism was found to follow pseudo-second-order and intraparticle-diffusion models, with external mass transfer predominating in the first 5 min of the experiment. Filtrasorb 400 (Chemviron Carbon) exhibited the highest adsorption rate for the removal of basic dyes followed by activated carbons produced by our research group: PAC1 (activated carbon produced from Venezuelan bituminous coal in small laboratory scale using physical activation technique) and PAC2 (activated carbon produced by the steam activation of New Zealand bituminous coal on a pilot-industrial scale). 1. Introduction
2. Mathematical Modeling
The removal of dye from industrial effluent is a major concern for the textiles industry worldwide. Recently, a number of successful systems have been developed using adsorption techniques to remove dye from industrial wastewater.1,2 Moreover, adsorption using activated carbon has been used extensively for wastewater-treatment processes.1,2 Although equilibrium studies are important in determining the effectiveness of adsorption, it is also important to determine the type of adsorption mechanism within a given system.3 The study of adsorption kinetics in wastewater treatment is essential as it provides understanding of the reaction pathways and the mechanisms of adsorption reactions.4 Furthermore, identifying the rate-determining step in adsorption processes is important as it provides information on rate parameters for design purposes.5-7 Specifically, the kinetics of adsorption processes is concerned with intermolecular forces between adsorption sites and adsorbate molecules and forms an important area of surface chemistry.8 This work is aimed at the understanding of the rate of adsorbent transport processes of basic dyes onto PAC1, PAC2, and F400 activated carbons. Batch contact time experiments are usually undertaken to provide information on the rate processes governing the adsorption process. Therefore, the dynamic adsorption behavior of basic dyes using activated carbon and the adsorption rate were determined. Theses were further correlated to process parameters such as initial dye concentration, solution pH, agitation rate, adsorbent mass, and adsorbent particle size. Because modeling of adsorption kinetics is important for simulation, scaling-up, and control purposes,9 the rate and mechanism of dye removal have been determined from the application of several kinetic models. The pseudosecond-order kinetic model, intraparticle-diffusion model, and external mass-transfer model were used to describe the kinetic data, and the rate constants were evaluated.
In general, the adsorption mass-transfer model requires: (i) a series of rate equations to describe the adsorption masstransfer rates; (ii) a mass balance equation; and (iii) a coupling equation connecting the equilibrium condition with the rate equations.10-13 2.1. External Mass-Transfer Model. The importance of mass transfer or boundary layer effects can be analyzed using an appropriate boundary-layer model, which assumed that the surface concentration of the adsorbate is negligible at time t ) 0.14,15 Consequently, intraparticle diffusion in this scenario would be negligible. In a well-agitated system, mixing in the liquid phase is rapid and, as a result, the concentrations of both the adsorbent particle and the adsorbate molecules within the liquid phase are assumed to be uniform. The Furusawa-Smith model relates change in the fluid-phase concentration with respect to time to mass-transfer coefficient according to the following equation:14,15
* To whom correspondence should be addressed. Tel.: 00962795354480, 00442890974172. Fax: 00442890974627. Email:
[email protected].
[
mskL 1 + mskL Ct 1 ) + exp ‚kfSst Co 1 + mskL 1 + mskL mskL
]
(1)
Hence,
ln
(
) (
) (
)
Ct mskL 1 + mskL 1 ) ln ‚kfSst Co 1 + mskL 1 + mskL mskL
(2)
where Ct is the liquid-phase concentration at time t (mg/dm3); Co is the initial phase concentration (mg/dm3); kL is the equilibrium constant in the Langmuir isotherm (dm3/g); ms is the concentration of adsorbent (g/dm3); Ss is the specific surface area (m-1); t is the time (min); and kf is the external mass transfer coefficient (m‚min-1). A more rapid method of determining kf is possible using the relation below15
[
]
d(Ct/Co) dt
10.1021/ie0701165 CCC: $37.00 © 2007 American Chemical Society Published on Web 06/15/2007
tf0
) -kfSs
(3)
Ind. Eng. Chem. Res., Vol. 46, No. 14, 2007 4765
Thus, simply by drawing a tangent to the curve of Ct/Co versus t, kf could be obtained. According to McKay et al.,16 such a plot is difficult to interpret, particularly if the decay curve is steep. 2.2. Intraparticle Diffusion Model. Weber et al., while studying the phenomena of mass transport within porous carbon adsorbent, observed that the adsorption data were well-fitted by plotting Ct/Co or Ct versus t0.5.17 Kannan and Sundaram18 considered that the adsorbate species are most probably transferred from the exterior to the interior surface of the solid through an intraparticle diffusion/transport process, which is often the rate-limiting step in many adsorption processes, especially in a rapidly stirred batch reactor. According to Guibal et al.,19 a plot of fraction of solute adsorbed against t0.5 can be used to estimate the intraparticle diffusion rate in the linear range. This mathematical dependence of concentration in the solid on t0.5 has been deduced by considering the adsorption mechanism to be controlled by diffusion in the adsorbent (as spherical particles) and by convective diffusion in the solution. Solving the diffusion equation leads to a relationship between the concentration in the solid and the parameter (Dt/r2)0.5. Since D and r are constant during the experiment, the concentration varies as a function of t0.5.20 Equation 4 below describes the mathematical expression for the intraparticle-diffusion model:21
qt ) kpt0.5
(4)
where qt is the adsorption capacity (mg/g) and kp is the intraparticle-diffusion rate constant (mg/g‚min1/2). The effective diffusion coefficient for the adsorption process in porous adsorbents can be determined from the fractional approach to the equilibrium, F(t), which depends on the dimensionless time parameter, Dt/r.3,22,23
(
[
F(t) ) 1 - exp -
(8)
where (P)t is the number of active sites occupied on the adsorbent at time, t, and (P)o is the number of equilibrium sites available on the adsorbent. Equation 8 can be rewritten as follows,26
dqt ) k2(qe - qt)2 dt
(9)
(5)
π2D t r2
(6)
3. Experimental Section
0.5
where F(t) represents the ratio (Co - Ct)/(Co - Ce); Co is the initial dye concentration (mg/dm3); Ct is the dye concentration at time, t (mg/dm3); Ce is the dye equilibrium concentration (mg/dm3); D is the intraparticle-diffusion coefficient (m2/s); and r is the particle size radius assuming spherical geometry (m). The overall rate constant is
π2D r2
d(P)t ) k[(P)o - (P)t]2 dt
)]
and
kÅ )
the adsorbent and expressed the kinetic rate equation accordingly:
where k2 is the adsorption rate constant (g/mg‚min); and qt (mg/ g) and qe (mg/g) are the amount of dye adsorbed at time t and at equilibrium, respectively. If chemical adsorption is the ratecontrolling step, the pseudo-second-order model is more likely to predict the behavior over the entire concentration range of the adsorption process.20,26
π2Dt r2
ln[1 - F(t)2] ) -
Figure 1. Chemical structure of adsorbates (a) basic red 22 and (b) methylene blue.
(7)
Theoretical equations for intraparticle diffusion indicate that the concentration dependence of a diffusion-adsorption process will vary depending on the characteristics of the adsorption system and on the fraction of solute adsorbed at equilibrium.24 2.3. Pseudo-Second-Order Kinetic Model. The pseudosecond-order model assumes that the adsorption process is a pseudo-chemical reaction process with the driving force being the difference between the average solid concentration and the equilibrium concentration with the overall adsorption rate proportional to the square of the driving force.21 Ho and McKay25 assumed that the adsorption capacity is proportional to the number of active sites occupied in
3.1. Materials. Two basic dyes were chosen as principal adsorbates: methylene blue C.I. 52015 (MB), supplied by ACROS Organics, U.S.A., and basic red C.I. 22 (BR) (supplied by Dyestar, GmbH & Co., Frankfurt, Germany). Both dyes were commercial samples and were used without further purification. Figure 1 depicts the chemical structures for both dyes. The main focus of the study was MB adsorption, with the red dye data used for comparison. Three activated carbons, namely, PAC1, PAC2, and F400, were used for the removal of basic dyes from aqueous solution. The three activated carbons were produced from bituminous coal using a steam-activation process. PAC2 was produced by the steam activation of New Zealand bituminous coal on a pilotindustrial scale. A detailed description of the production process can be found elsewhere.27 Filtrasorb 400 supplied by Chemviron Carbon (U.K.) is one of the most widely used grades of activated carbon in the wastewater-treatment industry. It is produced by the gas activation of bituminous coal, and it has a high surface area (1050-1200 m2/g) and good mechanical hardness.28 PAC1 refers to activated carbon produced from Venezuelan bituminous coal in a small laboratory scale using a physical activation technique. The adsorbents were washed and sieved into the desired particle size before coming in contact with the dye
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Ind. Eng. Chem. Res., Vol. 46, No. 14, 2007
Table 1. Physical and Chemical Characteristics of Activated Carbons total surface area (BET) (m2 g-1) micropore surface area (m2 g-1) total pore volume × 101 (cm3 g-1) micropore volume (cm3 g-1) average pore radius (nm) surface aciditya (meq g-1) surface basicitya (meq g-1) pHsolution (10 wt %) pHzpcb
F400
PAC1
PAC2
1216.4 918.70 8.211 0.456 1.124 0.408 0.610 8.30 7.80
863.50 783.58 4.695 0.380 1.233 0.389 0.482 7.95 8.30
857.14 801.83 4.467 0.389 1.210 0.462 0.560 8.20 6.30
a Both the surface acidity and basicity of the activated carbons were determined by using titration methods as reported by Al-Degs et al.48 b Alkalimetric titration technique recommended by Al-Ghouti et al.49 was adopted to measure surface charge density of activated carbons and to determine pHzpc.
Figure 3. Prediction of Furusawa-Smith model to the experimental data of adsorption of MB onto PAC2: temperature ) 20 °C, size < 106 µm, agitation ) 400 rpm, pH ) 7, volume ) 1.7 dm3, and concentration ) 100 ppm.
4. Results and Discussion
Figure 2. Plot of pseudo-second-order model for the adsorption of MB onto PAC1: temperature ) 20 °C, agitation ) 400 rpm, size < 106 µm, mass ) 0.85 g, pH ) 7, and volume ) 1.7 dm3; concentration in ppm.
aqueous solution. Table 1 shows the physical and chemical characteristics for activated carbons. 3.2. Procedure. A series of contact-time experiments were undertaken in an agitated batch adsorber to assess the effect of the system variables such as concentration and pH of dye solution, mass and particle size of adsorbent, and agitation speed. Kinetic experiments were performed in glass beakers with an internal diameter of 0.13 m, holding a volume of 2 dm3 of solution. To prevent vortex formation and ensure complete mixing, four baffles of width 0.013 m were fixed evenly around the circumference of the adsorption vessel at 45°. Mixing was provided by a four-blade glass impeller using a Heidolph variable-speed motor (RZR1). The progress of the adsorption process was determined by measuring the absorbance of the dye at different time intervals. Samples of 4-5 mL (( 0.5 mL) were withdrawn and filtered through 0.45 µm cellulose nitrate membrane and analyzed using a Perkin-Elmer UV/vis spectrometer (Lambda 12 model, Germany). The first part of the filtrate was discharged to avoid the effects of dye adsorption on the filter paper. Analysis was made at the wavelength corresponding to the maximum absorbance of 663 and 533 nm for MB and BR, respectively. Duplicate samples were measured, and the average was used in subsequent analysis. The dye uptake by the adsorbent was calculated by the following equation:
qt )
(Co - Ct)V m
(10)
where qt is the amount of dye adsorbed (mg/g); Co is the initial dye concentration (mg/dm3); Ct is the concentration of dye solution at time, t (mg/ dm3); m is mass of the adsorbent (g); and V is the volume of dye solution (dm3).
4.1. Modeling of Adsorption Kinetics. In general, adsorption theory is based on the principle that three steps are involved in the process, any of which could be the rate-controlling factor. The three steps are as follows: external mass transport across the external boundary layer, internal mass transport within the particle by pore and/or surface diffusion, and adsorption at a site.29,30 The final step is assumed to be rapid with respect to the first two steps and is, thus, not considered in kinetic analysis. 4.1.1. Pseudo-Second-Order Kinetic Model. In order to quantify the extent of uptake in adsorption kinetics and investigate the mechanism of the adsorption of basic dyes onto the activated carbons, the pseudo-second-order model was applied to the experimental data. A plot of t/qt versus t was used to calculate the second-order rate constant k2, the initial adsorption rate, h, and qe. The results of this analysis for adsorption of MB onto PAC2 are shown in Table 2. The results show that the MB adsorption rate constant decreased from 289 × 10-4 to 5.422 × 10-4 (g/mg‚min) as the initial dye concentration increased from 25 to 150 ppm. Increasing adsorbent mass served to increase the adsorption rate constant because of the increased of the number of active sites that are available for adsorption. Bouberka et al.31 reported similar influences of adsorbent mass and initial dye concentration on the second-order rate constant k2. Chu32 ascribed the effect of initial adsorbate concentration to heterogeneous binding and adsorbate loading on the adsorbent. At low initial adsorbate concentration, the adsorbate will bind preferentially to highenergy sites. This is due to the fact that sites of higher energy are usually taken up by adsorbate molecules first, with sites of lower energy progressively filled as adsorbate loading is increased. It follows that the adsorbate bond in low adsorbate loading situations will result in faster reaction kinetics, as reflected by high values of k2. Adsorption on sites of lower energy, as in the case of high loading, will subsequently result in a decrease in the k2 value.32 The initial adsorption rate was also found to increase with the increase in solution pH. The increase can be attributed to the effect of pH on the charge of the adsorbent surface. As pH increases, the surface charge density of the adsorbent decreases, which results in a decrease in the electrostatic repulsion forces between the positively charged dye and the negatively charged adsorbent surface, thus increasing the rate of adsorption.33 It is also noticed that the second-order correlation coefficient decreased as the particle size of the adsorbent increased. This might be due to the fact that, by increasing particle size, the external surface area available for rapid reaction decreases. Therefore, the pseudo-reaction is diffusionally controlled as the
Ind. Eng. Chem. Res., Vol. 46, No. 14, 2007 4767 Table 2. Pseudo-Second-Order Rate Constants for Adsorption of MB onto PAC2, PAC1, and F400 PAC 2 variable
k2×104 a qe(Pred) (g/mg‚min) (mg/g)
PAC 1
qe(Expt) hb (mg/g) (mg/g‚min)
k2×104 qe(Pred) (g/mg‚min) (mg/g)
r2
F40 0
qe(Expt) hb (mg/g) (mg/g‚min)
r2
k2×104 qe(Pred) (g/mg‚min) (mg/g)
qe(Expt) hb (mg/g) (mg/g‚min)
r2
pH 4 7a 9 11 Conc (ppm) 25 50 150 Mass (g) 0.425 0.600 1.700 Agitation (rpm) 200 300 500 Size (µm) 106-1 80 180-2 50 250-5 00 a
6.74 4 10.6 6 10.9 3 10.7 66
178. 57 178. 57 188. 67 204. 08
164. 68 168. 01 185. 30 197. 04
289. 0 50.2 50 49.8 80 97.0 3 101. 01 99.4 00 5.42 2 243. 90 244. 02
21.5 04 34.0 10 38.9 10 44.8 38
0.99 05 0.99 75 0.99 78 0.99 82
72.9 74 98.9 99 32.2 53
0.99 99 264. 0 50.2 50 49.7 00 0.99 99 84.4 9 101. 01 99.6 00 0.99 02 6.67 8 270. 27 244. 90
3.85 3 196. 07 174. 87 14.8 12 9.86 3 166. 66 159. 20 27.3 95 208. 3 100. 00 99.8 00 208. 33 7.82 6 166. 66 156. 50 10.5 8 169. 49 165. 00 15.3 9 175. 43 170. 70
21.7 37 30.3 93 47.3 63
5.53 5 175. 43 169. 42 4.30 1 166. 66 156. 00 3.40 4 161. 29 144. 90
5.67 5 16.4 9 19.2 3 21.6 3
181. 81 192. 30 200. 00 204. 08
174. 40 188. 40 193. 90 198. 00
18.7 58 60.9 78 76.9 20 90.0 86
0.99 61 0.99 98 0.99 98 0.99 99
19.8 00 24.7 50 28.2 40 36.7 60
204. 08 204. 08 204. 08 200. 00
191. 90 194. 08 195. 22 196. 50
82.4 64 103. 08 117. 61 147. 00
0.99 95 0.99 97 0.99 97 0.99 98
66.6 61 0.99 90 430. 80 50.2 50 49.9 00 108. 77 0.99 99 86.2 05 0.99 80 144. 13 101. 01 98.4 00 147. 05 0.99 98 48.7 80 0.99 88 6.00 00 270. 27 252. 87 43.8 27 0.99 70
0.99 01 2.90 2 285. 71 265. 40 23.8 90 0.99 08 4.49 00 322. 58 282. 90 46.7 21 0.99 56 0.99 70 6.04 6 243. 90 232. 60 35.9 65 0.99 85 6.84 00 277. 77 246. 90 52.7 74 0.99 10 0.99 99 256. 4 100. 00 99.8 00 256. 40 1.00 00 625. 00 100. 00 99.2 00 625. 00 1.00 00 0.99 58 0.99 75 0.99 78
17.0 34 0.99 06 11.9 46 0.99 00 8.85 53 0.99 13
11.7 5 13.1 2 40.9 8
185. 18 180. 00 192. 30 188. 80 200. 00 199. 10
40.2 92 0.99 93 48.5 16 0.99 95 163. 92 0.99 99
10.3 2 188. 67 180. 80 6.16 6 181. 18 166. 90 3.80 0 175. 43 158. 30
36.7 35 0.99 90 20.2 40 0.99 80 11.6 94 0.99 42
12.0 60 19.5 20 39.0 60
204. 08 193. 70 204. 08 194. 65 200. 00 196. 30
50.2 28 0.99 87 81.2 98 0.99 95 156. 24 0.99 97
12.6 70 185. 18 169. 40 9.25 00 178. 57 164. 8 5.85 00 178. 57 153. 20
43.4 49 0.99 87 29.4 95 0.99 70 18.6 54 0.99 17
Standard experimental conditions, pH ) 7, agitation ) 400 rpm, particle size < 106 µm, concentration ) 100 ppm, and mass ) 0.85 g. b h ) k2qt2.
Table 3. External Mass-Transfer Coefficient for the Adsorption of MB onto PAC2, PAC1, and F400 PAC2 variable pH 4 7c 9 11 Conc (ppm) 25 50 150 Mass (g) 0.425 0.600 1.700 Agitation (rpm) 200 300 500 Size (µm) 106-1 80 180-2 50 250-5 00
a
PAC1
r2
kf×10 (m‚min-1)
r2
kf×10 (m‚min-1)
r2
kf×10 (m‚min-1)
r2
kf×10 (m‚min-1)
r2
kf×104 b (m‚min-1)
r2
15.59 16.74 18.66 20.94
0.994 2 0.973 9 0.976 0 0.977 8
11.88 12.58 13.49 14.69
0.977 8 0.946 2 0.937 8 0.935 6
17.06 38.66 42.16 47.54
0.9574 0.9839 0.9801 0.9822
13.75 24.21 25.30 27.14
0.930 5 0.928 6 0.913 3 0.908 5
67.00 69.40 76.48 79.31
0.981 8 0.979 8 0.984 8 0.982 4
37.16 38.08 39.87 39.93
0.9219 0.9028 0.9011 0.8826
66.86 51.52 12.42
0.989 2 0.969 5 0.975 7
24.36 22.55 9.930
0.827 5 0.829 8 0.952 3
107.1 80.91 30.35
0.9547 0.9976 0.9913
36.65 34.39 21.66
0.907 2 0.931 4 0.979 7
254.3 136.1 30.16
0.980 6 0.977 2 0.987 1
55.08 49.55 23.01
0.8770 0.8803 0.9908
9.670 10.70 37.59
0.973 4 0.962 6 0.989 5
8.900 9.300 12.79
0.979 5 0.945 7 0.829 0
35.61 29.56 74.19
0.9669 0.9960 0.9940
29.49 22.90 19.69
0.969 5 0.980 6 0.838 4
48.13 44.84 150.8
0.980 0 0.969 5 0.985 5
38.68 33.21 24.57
0.9785 0.9361 0.7173
12.51 16.20 22.61
0.978 9 0.987 9 0.994 9
10.12 12.36 15.55
0.986 7 0.970 1 0.973 7
26.68 33.84 63.26
0.9808 0.9835 0.9906
19.14 22.45 30.69
0.944 5 0.938 9 0.911 7
39.16 67.20 80.27
0.941 2 0.998 4 0.986 7
27.28 38.39 39.98
0.9097 0.9625 0.9010
14.36 14.75 21.25
0.973 3 0.988 9 0.984 6
11.99 13.06 19.37
0.960 5 0.984 1 0.984 7
34.34 35.44 40.21
0.9595 0.9907 0.9924
24.85 28.84 35.03
0.913 8 0.988 4 0.995 2
53.14 62.86 83.29
0.995 9 0.995 7 0.994 7
37.00 47.25 66.60
0.9761 0.9797 0.9919
4
b
4
a
F400
kf×10 (m‚min-1) 4
4
b
4
a
a Using Furasawa-Smith model, eq 2. b Using simple graphical method, eq 3. c Standard experimental conditions, pH ) 7, agitation ) 400 rpm, particle size < 106 µm, concentration ) 100 ppm, and mass ) 0.85 g.
particle size increases.34 Increasing the rate of agitation was found to increase the reaction rate constant, caused by a decrease in the resistance to adsorption attributed to the hydrodynamic boundary between the adsorbent particle and the dye solution. The correlation coefficients for the pseudo-second-order model were >0.99. It was also found that the calculated values of the equilibrium adsorption capacity qe show good agreement with the experimental data. These analyses suggest that the model adequately describes the experimental data, which may indicate that the pseudo-second-order adsorption mechanism is predominant and the rate-limiting step may be chemisorption involving valency forces through the sharing or exchange of electrons between the active sites of activated carbon and polar dye ions.35 Similar phenomena were obtained with PAC1 and F400, as illustrated in Table 2. The data in Table 2 indicate that adsorption of MB onto F400 is the most rapid as shown
by high values of k2. This can be correlated to the relative physical characteristics of the activated carbons. Figure 2 illustrates the application of the pseudo-second-order model to the experimental data for the adsorption of MB onto PAC1 at different initial dye concentrations and shows reasonable fit between the calculated and experimental concentration decay curves. BR dye adsorption onto PAC2 exhibits a similar behavior but with a higher rate constant than that for MB. 4.1.2. External Mass-Transfer Coefficient. Two methods were adopted to determine the external mass-transfer coefficient: the Furusawa-Smith method and the simple graphical method. Table 3 lists the values of the external mass transfer coefficient, kf, for the adsorption of MB onto PAC2. Similar trends were obtained for the adsorption of MB onto F400 and PAC1, as shown in Table 3. It is evident from Table 3 that increasing the initial dye concentration served to decrease the
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Ind. Eng. Chem. Res., Vol. 46, No. 14, 2007
Table 4. Intraparticle-Diffusion Rate Constant, kp, for the Adsorption of MB onto PAC2 variable pH 4 7a 9 11 Conc (ppm) 25 50 150 Mass (g) 0.425 0.600 1.700 Agitation (rpm) 200 300 500 Size (µm) 106-180 180-250 250-500
kp1 (mg‚g-1‚ in-0.5)
r2
kp2 (mg‚g-1‚ min-0.5)
r2
14.199 25.077 22.568 25.468
0.999 4 0.980 4 0.980 6 0.921 0
11.563 6.7955 4.2732 11.925
0.956 8 0.999 9 0.964 3 0.999 0
2.6162 7.4390 26.160
0.864 6 0.953 6 0.984 4
0.1454 0.3759 13.497
0.971 8 0.985 5 0.999 5
39.647 27.784 4.4816
0.962 1 0.973 4 0.785 5
4.5561 6.7193 0.0058
0.987 0 0.999 0 0.943 8
21.137 20.676 18.329
0.995 9 0.994 0 0.986 1
5.9803 6.7577 5.9863
0.991 9 0.999 5 0.947 4
19.991 23.006 22.620
0.967 1 0.988 5 0.999 0
13.950 10.210 10.913
Figure 4. Amount adsorbed of MB per unit weight of PAC1 against t0.5: temperature ) 20 °C, mass ) 0.8 g, pH ) 7, volume ) 1.7 dm,3 size < 106 µm, and concentration ) 100 ppm.
0.999 8 0.996 2 0.994 8
a Standard experimental conditions, pH ) 7, agitation ) 400 rpm, particle size < 106 µm, concentration ) 100 ppm, and mass ) 0.85 g.
initial rate of adsorption. This can be attributed to the interactions between solute molecules in solution and to increased competition for the available adsorption sites, overriding the increased driving force found at higher dye concentrations.36 Increasing adsorbent mass served to decrease external mass-transfer resistance, and hence, an increase in the external mass transfer coefficient was observed. McKay et al.16 reported that increasing the mass of the adsorbent increased the surface area available for adsorption and increased the rate of adsorption and, subsequently, increased the external mass-transfer coefficient. Increasing agitation speed causes a decrease in the thickness of Nernst layer resistance surrounding the adsorbent particles, and consequently, an increase in the external mass-transfer coefficient was observed.37 Increasing pH and adsorbent particle size caused a decrease in the external mass-transfer resistance, as can be seen from the increases in the kf values. The effect of particle size can be explained in terms of momentum, since under well-agitated conditions, larger particles have a higher momentum and, therefore, thinner boundary layers.38 Figure 3 shows the ability of the Furusawa-Smith model to predict the experimental data for the adsorption of MB onto PAC2 at different particle sizes, illustrating good agreement between the experimental and predicted data in the first 5 min of the experiment, after which a noticeable deviation was evident. This illustrates the importance of the surface mass transfer of dye from the bulk liquid across the boundary layer to the surface of the adsorbent particle during the initial stages of the adsorption process. The deviation of experimental and predicted data after 5 min indicates that external mass transfer is no longer controlling the process with intraparticle mass transfer, now likely to be rate-controlling. It is also evident from Figure 3 that the predicted curves simulate the experimental data well at higher loadings of PAC2, indicating that external mass transfer controlled the adsorption process over the whole time interval. Consequently, resistance due to the intraparticle diffusion can be considered as negligible when high adsorbent masses are used. The results in the following section confirm this assumption since the kp value is very low (Table 4) at an adsorbent loading ) 1.7 g/1.7 L, and this may indicate the occurrence of the adsorption process on the external surface. A similar behavior was found for the adsorption of BR onto PAC2.
Figure 5. Simulation of the intraparticle-diffusion model to the experimental data of the adsorption of MB onto PAC2: temperature ) 20 °C, mass ) 0.85 g, agitation ) 400 rpm, pH ) 7, volume ) 1.7 dm3, and concentration ) 100 ppm; size in µm.
It is noted that the two different methods used in calculating the external mass-transfer coefficient, kf, showed variation in the numerical values but showed similar trends. This can be attributed to the accuracy and sophistication of each model. Since the graphical method depends on the determination of the slope at t ) 0 for the plot of Ct/Co versus time, the possibility of the errors in determining the plot gradients is high, especially in the case of very steep curves, and this is clear from the low value of r2 in the case of applying the graphical method. As a result, there is more accuracy in applying the Furusawa-Smith model than the graphical method. The data in Table 3 show that the calculated values of kf increased in the order PAC2 < PAC1 < F400. This indicates that less resistance to the external mass transfer was experienced by adsorbate molecules in the case of F400. The heterogeneity of the adsorbent surface may play a significant role in controlling the resistance to the external mass-transfer process.39 4.1.3. Internal Mass-Transfer Coefficient. Intrapaticle diffusion plays a significant role in many adsorption processes and assumes that diffusion of adsorbate occurs within the pore structure of the adsorbent. Equations 4, 5, and 6 were used to determine the intraparticle-diffusion rate constant, kp, the intraparticle-diffusion coefficient, D, and the overall rate constant, kÅ , respectively. The kp values were calculated from the slope of the plot of qt versus t0.5. A plot of qt versus t0.5 for the adsorption of MB onto PAC1 is shown in Figure 4 for variation in system agitation speeds. It is evident from Figure 4 that each curve consists of three regions: an initial curved section representing external mass transfer followed by two linear sections representing intraparticle diffusion in the macroand mesopores.40 The existence, on the same experimental data curve, of a linear region of different gradient suggests that
Ind. Eng. Chem. Res., Vol. 46, No. 14, 2007 4769 Table 5. Intraparticle-Diffusion Coefficient and over Rate Constant for the Adsorption of MB onto PAC2, PAC1, and F400 PAC2 variable pH 4 7a 9 11 Conc (ppm) 25 50 150 Mass (g) 0.425 0.600 1.700 Agitation (rpm) 200 300 500 Size (µm) 106-180 180-250 250-500 a
PAC1
F400
D× (m2/min)
kÅ × (min-1)
r2
D× (m2/min)
kÅ × (min-1)
r2
D× (m2/min)
kÅ × 102 (min-1)
r2
5.8914 12.636 13.661 10.929
2.0699 4.4390 4.7999 3.8390
0.9933 0.9436 0.9850 0.9430
6.4606 16.535 16.991 21.658
2.2660 5.8090 5.9690 7.6090
0.9973 0.9811 0.9642 0.9924
41.837 33.641 29.790 41.524
14.699 11.819 10.469 14.589
0.9678 0.9841 0.9814 0.9913
32.274 39.504 6.1476
11.3390 13.8790 2.1599
0.9101 0.9960 0.9809
66.912 40.914 14.173
23.509 14.199 4.9790
0.9590 0.9831 0.9934
21.602 83.021 15.283
7.5890 29.169 5.3690
0.9723 0.9937 0.9511
15.795 14.999 76.560
5.5499 5.2699 26.899
0.9596 0.9958 0.7512
10.274 8.7091 30.567
3.6090 3.0590 10.733
0.9902 0.9458 0.8034
13.433 8.6522 22.854
4.7340 3.0390 8.0290
0.9715 0.9908 0.9135
11.469 10.929 11.526
4.0299 3.8394 4.0499
0.9982 0.9964 0.9384
14.002 13.319 40.500
4.9190 4.6790 1.4290
0.9924 0.9863 0.9595
15.654 22.996 62.045
5.4990 8.0790 21.799
0.9376 0.9762 0.9765
9.0128 24.705 74.091
1.7399 2.1099 2.0799
0.9507 0.9857 0.9770
22.065 38.756 84.064
4.2590 3.3090 2.3540
0.9964 0.9843 0.9906
39.780 55.266 109.35
7.6790 4.7190 3.0690
0.9873 0.9887 0.9902
1012
102
1012
102
1012
Standard experimental conditions, pH ) 7, agitation ) 400 rpm, particle size < 106 µm, concentration ) 100 ppm, and mass ) 0.85 g.
variation in intraparticle-diffusion coefficients can be attributed to a large distribution of the pore size.41 It also suggests that two or more steps may influence the sorption process.2 Tseng et al.42 referred to the last stage as the final equilibrium stage where intraparticle diffusion starts to slow down because of extremely low solute concentration, whereas Lazaridis and Asouhidou29 attributed the last stages to an adsorption/chemical reaction and further illustrated that the multiple nature of the relationship between qt and t0.5 confirms that intraparticle diffusion is not the sole adsorption mechanism. In this study, similar behavior was obtained for F400 and PAC1 as for PAC2. Figure 5 shows the predicted and experimental data for the adsorption of MB onto PAC2 for variation in adsorbent particle sizes. Table 4 summarizes the results for the determination of intraparticle-diffusion rate constant, kp. The results in Table 4 indicate that, for MB and PAC2, the value of kp increased from 2.616 to 26.160 (mg‚ g-1‚min-0.5) as the initial dye concentration increased from 25 to 150 (mg/dm3) (attributed to the increase in driving force of diffusion), and decreased from 39.64 to 4.48 (mg‚g-1‚min-0.5) as the adsorbent mass increased from 0.425 to 1.7 (g). This latter result was due to an increase in the overall rate of the dye adsorption, which resulted in a rapid decrease in the dye concentration and, thus, the driving force for intraparticle diffusion.43 Moreover, this can also be attributed to the significance of the external diffusion and the reduction in the effect of intraparticle diffusion as the ratio of the adsorbent/adsorbate in the system increased.16 Increasing agitation rate resulted in a slight reduction in the value of kp. Increasing agitation rate reduces external film resistance, allowing more dye uptake, with the data showing good correlation to previous studies.44 No common trends were noticed for pH. This can be attributed to the effect of pH on the overall adsorption rate, as increasing pH would increase attraction forces between the dye and the adsorbent surface and result in a slight increase in the dye uptake (and rate constant). The effect of the particle size on the diffusion rate was irregular, which could be related to the structure of the adsorbent. Increasing adsorbent particle size resulted in a decrease in the intraparticle-diffusion rate constant. If surface mass transfer is a significant resistance in the adsorption process, then kp should vary with the reciprocal of particle diameter.45 In this work, it
Table 6. Values of the Constants A and B for Correlation of Intraparticle-Diffusion Coefficient with Experimental Variables PAC1
PAC2
F400
variable
A
B
A
B
A
B
pH concentration mass agitation size
1.645 0.026 9.384 44.56 16.43
0.127 1.410 -1.963 -0.119 0.063
7.006 0.034 12.68 28.75 25.89
0.564 1.369 -1.566 -0.051 -0.025
32.48 0.004 4.495 271.0 32.58
-0.245 2.271 -3.271 -0.432 -0.087
was found that kp varied with the reciprocal of particle diameter raised to the power of 0.025, which is an indication of the significance of intraparticle diffusion within this adsorption process. The data in Table 4 show that the correlation coefficient for kp increases as the particle size increases, indicating a trend toward diffusion control with increasing particle size. Table 5 displays the calculated values of the intraparticlediffusion coefficient, D, and the overall rate constant, kÅ , for the adsorption of MB onto PAC2, PAC1, and F400. It is clear from the data that, as the initial concentration increased from 25 to 50 ppm, the intraparticle-diffusion coefficient, D, increased from 32.3 × 10-12 to 39.5 × 10-12 (m2/min) and then decreased to 6.146 × 10-12 (m2/min) as concentration increased to 150 ppm. Allen et al.39 reported a decrease in D with increasing initial adsorbate concentration and attributed this behavior to the capability of dye to form micelles at higher concentration. Walker and Weatherley46 attributed the decrease in diffusivity, D, with increased dye concentration to dye agglomeration at high bulk liquid concentrations, which would increase the diffusional resistance. Al-Duri and McKay47 explained the increase in D with initial dye concentration to a decrease in bonding energies. As surface coverage increases, bonding energy decreases due to the progressive filling of adsorption sites of decreasing energy. A similar behavior for the adsorption of BR onto PAC2 was obtained with higher values of D in the case of BR. It is reported in the literature that the values of the intraparticle-diffusion coefficient are in the range of 10-11 to 10-13 (m2/ min), which are in good agreement to the data obtained in this work. The relatively low value of D in this work indicates the role of intraparticle diffusion in the adsorption of basic dyes onto PAC1, PAC2, and F400.
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Ind. Eng. Chem. Res., Vol. 46, No. 14, 2007
The relative effect of intraparticle diffusion on the overall rate of the adsorption process can be correlated with each of the system variables according to the following equation:
kp ) A(variable)B
(11)
log kp ) log A + B log(variable)
(12)
and
Table 6 lists the calculated values of A and B for each variable and for each activated carbon. The low values of B indicate that intraparticle diffusion is not the sole rate-controlling step. The theoretical equations for intraparticle diffusion indicate that the concentration dependence of a diffusion-adsorption process will vary depending on the characteristics of the adsorption isotherm and the fraction of solute adsorbed at equilibrium. In the case of intraparticle diffusion being the only rate-determining step, it was found that kp varied with the square root of the initial concentration.45 The magnitude of B (Table 6) indicated that kp varied with initial concentration raised to the power of 1.41, 1.369, and 2.27 for PAC1, PAC2, and F400, respectively, confirming that intraparticle diffusion was a prominent factor in the adsorption process but not the sole rate-determining step. 5. Conclusions Kinetics of the transport processes accompanying the adsorption process were investigated, and the rate and mechanism of dye adsorption onto activated carbons were determined. F400 exhibited the highest adsorption rate for the removal of basic dyes followed by PAC1 and PAC2, because of its highest surface area and well-developed pore structure. This indicates the significant influence of the physical characteristics of the adsorbent on the adsorption process. Kinetic analyses showed that the mechanism of the adsorption of basic dyes on PAC1, PAC2, and F400 was quite complex. During the first few minutes of the experiment, it was found that boundary-layer processes controlled the rate, after which internal diffusion became the predominant rate-controlling factor with the possibility of chemical reaction mechanism. Literature Cited (1) Poots, V. J.; McKay, G.; Healy, J. J. Removal of Basic Dye from Effluent Using Wood as an Adsorbent. J.sWater Pollut. Control Fed. 1978, 18, 426. (2) Srivastava, V. C.; Mall, I. D.; Mishra, I. M. Characterization of Mesoporous Rice Husk Ash (RHA) and Adsorption Kinetics of Metal Ions from Aqueous Solution onto RHA. J. Hazard. Mater. 2006, B134, 257. (3) Khraisheh, M.; Al-Degs, Y.; Allen, S.; Ahmad, M. Elucidation of Controlling Steps of Reactive Dye Adsorption on Activated Carbon. Ind. Eng. Chem. Res. 2002, 41, 1651. (4) Sag, Y.; Aktay, Y. Kinetic Studies on Sorption of Cr(VI) and Cu(II) Ions by Chitin, Chitosan and Rhizopus Arrhizus. Biochem. Eng. J. 2002, 12, 143. (5) Faust, S. D.; Aly, O. M. Chemistry of Water Treatment, 2nd ed.; Ann Arbor Press, Inc.: Ann Arbor, MI, 1998. (6) Lee, C. K.; Low, K. S.; Chung, L. C. Removal of Some Organic Dyes by Hexane-Extracted Spent Bleaching Earth. J. Chem. Technol. Biotechnol. 1997, 69, 93. (7) Dabrowski, A. AdsorptionsFrom Theory to Practice. AdV. Colloid Interface Sci. 2001, 93, 135. (8) McKay, G.; El Guendi, M.; Nassar, M. External Mass Transport Processes during the Adsorption of Dyes onto Bagasse Pith. Water Res. 1988, 22 (12), 1527. (9) Polat, M. Kinetic Estimation of the Adsorbate Distribution on the Surface from Adsorbed Amounts. J. Colloid Interface Sci. 2006, 298, 593.
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ReceiVed for reView January 18, 2007 ReVised manuscript receiVed April 20, 2007 Accepted April 25, 2007 IE0701165
