Ind. Eng. Chem. Res. 1998, 37, 253-257
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Study of Nonlinear Wave Propagation Theory. 1. Dye Adsorption by Activated Carbon Jia-Ming Chern* and Shi-Nian Huang Department of Chemical Engineering, Tatung Institute of Technology, 40 Chungshan North Road, 3rd Sector, Taipei, Taiwan 10451, Republic of China
The adsorption of red and yellow dyes by granular activated carbon from aqueous solution was studied. The Langmuir model, Freundlich model, and Redlich-Peterson model were found to fit the adsorption isotherm data well in different dye concentration ranges. Fixed-bed column tests were performed, and the results showed that the activated carbon was very effective in removing the dyes from aqueous solutions at low feed flow rates. The nonlinear wave propagation theory was used to predict the column dynamics, namely, the breakthrough and desorption curves. Without solving the governing equation for column dynamics, the theory used the concept of concentration wave and simple calculations to predict the breakthrough and desorption curves satisfactorily. Introduction Fixed-bed operations are widely used in chemical processes and pollution control processes such as separating ions by an ion-exchange bed or removing toxic organic compounds by a carbon adsorption bed. Traditionally, the design of fixed-bed processes depends upon tedious column tests and sophisticated masstransfer models used to predict the column dynamics. A powerful tool that can be used to predict fixed-bed column dynamics without sophisticated calculations is the nonlinear wave propagation theory (Helfferich and Klein, 1970; Helfferich, 1984, 1993). Two excellent reviews of the nonlinear wave propagation theory are available (Helfferich and Carr, 1993; Hwang, 1995). The first part of this series of experimental studies of the wave theory aimed at environmental applications is dye removal from wastewater by activated carbon adsorption. The textile industry discharges wastewater with high color, high suspended solids, and dissolved organics. Due to its variation in pH, temperature, flow rate, and contained pollutants, the textile wastewater usually requires physicochemical as well as biological treatments to meet the more stringent effluent standards. For example, coagulation is a useful operation for suspended solids removal; the activated sludge process is a commonly used biological process to remove biodegradable soluble organic matters. However, the color in textile wastewater containing dyes is extremely difficult to remove by conventional coagulation and the activated sludge process. A more effective method to remove color is to use an adsorbent such as activated carbon to adsorb the dye molecules and then remove the color from the wastewater (Rodman, 1971; Porter, 1972; Larry and Richard, 1976; McKay et al., 1985; Gupta et al., 1988; Yoshida et al., 1993; Namasivayam et al., 1994; Krupa and Cannon, 1996; Deo and Ali, 1996; Nassar et al., 1996). Powdered activated carbon is directly added to the activated sludge * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: 01188625925252, ext. 3487. Fax: 01188625861939.
process to remove the color from wastewater (Flynnet and Stadnik, 1979). Although this direct addition of powdered activated carbon is quite efficient, the carbon loss as wasted sludge is rather significant. Granular activated carbon is usually used in either a fluidizedbed or fixed-bed adsorption process and is also quite effective. The fixed-bed operation is commonly used because of ease of operation and no carbon loss problem. To design and operate a fixed-bed adsorption process successfully, the column dynamics must be understood; that is, the breakthrough and desorption curves under specific operating conditions must be predictable. This study is therefore focused on understanding the column dynamics of single-component dye adsorption processes that is governed by a partial differential equation coupled with an algebraic equation. Instead of solving the partial differential equation, the nonlinear wave propagation theory is employed to depict the movement of the concentration variation within the column and to predict the breakthrough and desorption curves under various operating conditions. Theory Assuming ideal plug flow, isothermal, constant flow rate, and no chemical reactions in the bed, the column dynamics of a single-component adsorption system can be described by the following differential mass balance equation:
F
∂C ∂q ∂C ∂2 C + + u0 ) De 2 ∂t ∂t ∂z ∂z
(1)
where C is the concentration of the solute in the mobile phase, q the concentration of the adsorbed solute in the stationary phase, F the carbon bed density, the void fraction of the bed, u0 the linear velocity of the carrier fluid, t the operating time, z the distance from the inlet of the mobile phase, and De the axial dispersion coefficient. The adsorption rate can be expressed by the following linear driving-force model (Helfferich and Carr, 1993):
∂q/∂t ) kS(q* - q)
S0888-5885(97)00374-6 CCC: $15.00 © 1998 American Chemical Society Published on Web 01/05/1998
(2)
254 Ind. Eng. Chem. Res., Vol. 37, No. 1, 1998
where kS is the overall stationary-phase mass-transfer coefficient that can be expressed in terms of the external film mass-transfer coefficient and internal diffusion coefficient, and q* is the equilibrium concentration of the adsorbed solute in the stationary phase that is related to the concentration of the solute in the mobile phase by the so-called adsorption isotherm:
q* ) f(C)
(3)
With proper initial and boundary conditions specified, that depend upon operating conditions, the governing equations can be solved for C as a function of z and t by various numerical methods. Instead of directly solving the governing equations, Helfferich and his co-workers used the concept of wave velocity defined as
uc ≡
(∂z∂t)
(4)
c
to describe the column dynamics. Equation 4 defines the velocity at which a given constant concentration C travels through the adsorption column. To utilize the concept of wave velocity, two assumptions are further made: (1) The adsorption reaches local equilibrium, i.e., q ) q* ) f(C). (2) The axial dispersion is negligible. With these two assumptions, eq 1 can be reduced to
F
∂C ∂C ∂q + + u0 )0 ∂t ∂t ∂z
(5)
Using the definition of the concentration wave velocity and chain rule yields
uc ≡
(∂C/∂t)z
(∂z∂t) ) - (∂C/∂z) c
(6)
t
Combining eqs 5 and 6 leads to
uc )
u0 F dq 1+ dC
( )
(7)
Equation 7 is used to calculate the concentration wave velocity of a nonsharpening wave. For a self-sharpening wave, the concentration wave velocity is calculated by the following equation (Helfferich and Klein, 1970; Helfferich, 1984, 1993):
u∆c )
u0 F ∆q 1+ ∆C
( )
(8)
Once the concentration wave velocity is known, the column dynamics can be easily predicted. Experiment The primary purpose of the experimental work in this study was to test if the nonlinear wave propagation theory could be used to predict the column dynamics of dye adsorption by activated carbon. To this end, the batch tests for determining the adsorption isotherms of the yellow and red dye solutions were performed first,
Table 1. Column Test Conditions and Measured Parameters
dye solution used carbon bed void fraction carbon bed density (g/L of bed) carbon bed volume (cm3) presaturation concentration (mg/L) feed concentration (mg/L)
run 1A
run 1B
run 2A
run 2B
red 0.42 303.3 10.7 0 468
red 0.42 303.3 10.7 468 0
yellow 0.38 302.5 10.7 0 500
yellow 0.38 302.5 10.7 500 0
followed by the column tests for measuring the breakthrough and desorption curves. The red and yellow acid dyes (Sumitomo Chemical Corp., Japan) with the main ingredient of triphenylmethane were used to prepare the synthetic wastewater for the tests in this study. The granular activated carbon (Taipei Chemical Corp., Taiwan) with a size range between 30 and 32 mesh was used. The activated carbon was repeatedly washed with deionized water to remove any leachable impurities and adherent powder and then dried to constant weight at 110 °C for 24 h. In determining the adsorption isotherms, various amounts of the washed and dried carbon (0.050-1.000 g) were added to 10 500-mL glass-stoppered flasks, each filled with 250 mL of aqueous red or yellow dye solution. All the flasks were shaken in a temperature-controlled shaker (Hotech Model 706) at a constant shaking speed of 150 rpm for 4 days to reach adsorption equilibrium. After filtration, the solution volumes were measured and the dye concentrations were measured by a UV spectrophotometer (Milton Roy, Spectronic 20D). The adsorbed amounts of the dyes were calculated by mass balance. The column tests were carried out in a water-jacketed glass column with an inside diameter of 1.74 cm. The activated carbon with known dried weight was put into the column randomly, and the bed length was 10 cm. Deionized water was used to wash the carbon in an upflow fashion in order to remove air bubbles and to rinse the carbon. Then, the bed density and void fraction were determined before a column test was begun. In an adsorption column test, an aqueous dye solution was fed to the top of the column by a metering pump (Watson-Marlow, 302S/RL), flowed through the carbon bed, and then exited from the bottom of the column. The feed flow rate was controlled at 1 bed volume/h (23.8 mL/h) with an attempt to satisfy the local equilibrium assumption. After the column was saturated with the feed concentration, deionized water was fed to the top of the column to initiate the desorption cycle. The average temperature during the column test was maintained at 25 ( 2 °C. In all the column tests, the effluent samples were intermittently collected and measured by the UV spectrophotometer. The column test conditions and measured parameters are summarized in Table 1. Results and Discussion The adsorption isotherms of the red and yellow dyes at 25 °C are shown in Figures 1 and 2, respectively. Also shown in the figures are the calculated isotherms whose parameters are listed in Table 2. Three adsorption isotherm models, namely, the Langmuir model, Freundlich model, and the Redlich-Peterson model, were found to give a satisfactory fit to the experimental data. The model parameters were determined from nonlinear regression of the experimental data. As shown in
Ind. Eng. Chem. Res., Vol. 37, No. 1, 1998 255 Table 2. Adsorption Model Parameters for the Red and Yellow Dyes at 25 °C Langmuir model: q ) KCQ/1 + KC
Freundlich model: q )
KCQ 1 + KC
Redlich-Peterson model: q )
AC B + Cm
red dye
yellow dye
K ) 0.045 L/mg Q ) 556 mg/g k ) 243 mg/g/(mg/L)0.13 n ) 0.135 A ) 235 mg/g/(mg/L)0.134 B ) 0.0098 (mg/L)0.866 M ) 0.866
K ) 0.080 L/mg Q ) 1457 mg/g k ) 674 mg/g/(mg/L)0.13 n ) 0.127 A ) 842 mg/g/(mg/L)0.087 B ) 0.266 (mg/L)0.913 M ) 0.913
Figure 1. Adsorption isotherm of red dye on activated carbon at 25 °C.
Figure 3. Experimental and predicted breakthrough curves of red dye at 25 °C.
bed volume can be calculated by the following equation if the dispersion effect is neglected:
(
) (
Vbk F ∆q F qf - qp ) 1+ ) 1+ Vb ∆C Cf - Cp
Figure 2. Adsorption isotherm of yellow dye on activated carbon at 25 °C.
Figures 1 and 2, the Langmuir model fits the experimental data better for higher dye concentrations while the Freundlich model and the Redlich-Peterson model fit the data better for lower dye concentrations. However, none of the three models gives a perfect fit for the whole concentration range. As shown in Figures 1 and 2, the adsorption isotherms for the red dye and the yellow dye are of favorable type. Therefore, the adsorption waves for both dyes are selfsharpening, and the breakthrough volumes in units of
)
(9)
where Vb is the bed volume and the subscripts f and p represent the feed and presaturation conditions, respectively. For all the cumulative effluent volumes less than the breakthrough volume, the effluent dye concentration is theoretically equal to the presaturation dye concentration; at the breakthrough volume, the effluent dye concentration jumps to the feed dye concentration and then stays at that concentration beyond the breakthrough volume. The three adsorption models were used to calculate the adsorbed concentrations of the red and yellow dyes that are used in eq 6 for calculating the breakthrough volumes. The experimental and predicted breakthrough curves for the red and yellow dyes are shown in Figures 3 and 4, respectively. As shown in Figures 3 and 4, the wave propagation theory indeed gives a satisfactory prediction to the experimental breakthrough curves. One key assumption for the wave propagation theory is that there are no chemical reactions involved in the bed. To support this assumption, a series of effluent samples at different times were collected and the absorbance spectra were scanned by the UV spectrophotometer. The scanned results show that the shapes of the absorbance spectra of the red and yellow dye solutions do not change with time. The only change is the peak height corresponding to the dye concentration.
256 Ind. Eng. Chem. Res., Vol. 37, No. 1, 1998
Figure 4. Experimental and predicted breakthrough curves of yellow dye at 25 °C.
Figure 6. Experimental and predicted desorption curves of red dye at 25 °C.
Figure 5. Experimental and predicted breakthrough curves of red dye with varying feed flow rates.
Figure 7. Experimental and predicted desorption curves of yellow dye at 25 °C.
Another important assumption for the nonlinear wave propagation theory is that the adsorption reaches local equilibrium. Preliminary adsorption kinetic studies in the shaker show that the dye adsorption process is quite slow. In the column tests, feed flow rates as low as 1 bed volume/h were used to make the local equilibrium assumption reasonable. If the feed flow rate is slow enough to allow for local adsorption equilibrium, then the breakthrough volume is independent of the feed flow rate according to eq 9. Three additional column tests were performed to study the effects of the feed flow rates on the breakthrough curve of the red dye, and the results are shown in Figure 5. As is clearly shown in Figure 5, the red dye appears earlier than expected, especially for higher feed flow rates. This suggests that the nonlinear wave propagation theory is applicable only for slow feed flow rates. For a column test with a high feed flow rate, the S-shaped breakthrough curve should be predicted by the original model equations (1)-(3).
After the carbon beds were saturated, 50 more bed volumes of the feed dye solutions were pumped through the beds to ensure that all the beds were in equilibrium with the feed solutions before the desorption cycle was begun. According to the wave theory, the desorption wave for a strongly adsorbed solute is a nonsharpening one and the cumulative effluent volume, in the unit of bed volume, for any given effluent concentration can be calculated by the following equation:
F dq V )1+ Vb dC
(
)
(10)
The differential on the right-hand side of eq 10 was evaluated using the three adsorption isotherm models to predict the desorption curves for the red and yellow dyes. Figures 6 and 7 show the experimental and predicted desorption curves for the red and yellow dye, respectively. As shown in Figures 6 and 7, the wave
Ind. Eng. Chem. Res., Vol. 37, No. 1, 1998 257
propagation theory overestimates the effluent concentrations, especially for lower concentration ranges. Moreover, the strongly adsorbed dyes are not easily desorbed by 25 °C deionized water. Even when 400 bed volumes of deionized water flow through the column, the effluent dye concentrations are still high. Obviously cold water is not a good regenerant for the regeneration purpose. In practice, steam or an appropriate solvent should be used to regenerate the exhausted carbon bed because in that case the desorption wave is a selfsharpening one and all the dye can be desorbed by minimal amounts of steam or solvent. Although the wave propagation theory gives correct trends of the breakthrough and desorption curves, it cannot fit the experimental data perfectly. The discrepancy between the theory and the experiment should be stemmed from two unreasonable assumptions, local equilibrium and no axial dispersion in the column. Unlike the ion-exchange rate, the adsorption/desorption rate is relatively slow. External and especially internal mass-transfer steps control the overall adsorption/ desorption rate (McKay, 1983). Moreover, the axial dispersion is usually inevitable. In many industrial applications, macropore adsorbents with sharp breakthrough curves are selected to remove undesired pollutants. The nonlinear wave propagation theory therefore serves as a simple yet useful tool to estimate the volume of wastewater that can be treated by a given fixed bed. In regards to process design, the size of the carbon bed can be estimated by eq 9 with a proper safety factor, provided the adsorption isotherm is obtained by simple batch tests. Conclusions The adsorption of red and yellow dyes by granular activated carbon from an aqueous solution was studied. Three adsorption isotherm models, Langmuir, Freundlich, and Redlich-Peterson, were used to fit the batch isotherm data at 25 °C. The column test results showed that the activated carbon was very effective in removing the dyes from aqueous solutions with a slow feed flow rate; several hundreds of bed volumes of the aqueous solution could be treated before the carbon bed was exhausted. However, desorbing or regenerating the exhausted carbon bed by 25 °C water was not easy. The nonlinear wave propagation theory has been used to predict the column dynamics, namely, the breakthrough and desorption curves. Without solving the governing equation for column dynamics, the theory used the concept of concentration wave and simple calculations to predict the breakthrough and desorption curves satisfactorily. Adsorption isotherm plays a key role on the theoretical calculations. The assumptions of local equilibrium and no axial dispersion are crucial to the theory and may cause deviation from the experimental results.
Acknowledgment This work was supported by the National Science Council of Taiwan, Republic of China (Grant NSC852211-E-036-001). Literature Cited Deo, N.; Ali, M. Dye Removal from Aqueous Solutions by Adsorption on a Low Cost Material. J. Inst. Eng. (India): Environ. Eng. Div. 1996, 76, 48. Flynnet, B. P.; Stadnik, J. G. Start-up of a Powdered Activated Carbon Activated Sludge Treatment System J.sWater Pollut. Control Fed. 1979, 51, 358. Gupta, G. S.; Prasad, G.; Panday, K. K.; Singh, V. N. Removal of Chrome Dye from Aqueous Solutions by Fly Ash. Water Air Soil Pollut. 1988, 37, 13. Helfferich, F. G. Conceptual View of Column Behavior in Multicomponent Adsorption or Ion Exchange Systems. AIChE Symp. Ser. 1984, 80, 1. Helfferich, F. G. Multicomponent Wave Propagation: the Coherence Principle an Introduction. In Migration and Fate of Pollutants in Soil and Subsoils; Petruzzeli, D., Helfferich, F. G., Eds.; NATO Advanced Study Institute Series G32; Springer-Verlag: Berlin, Germany, 1993; p 247. Helfferich, F. G.; Klein, G. Multicomponent Chromatography: Theory of Interference; Marcel Dekker: New York, 1970. Helfferich, F. G.; Carr, P. W. Non-linear Waves in Chromatography: I. Waves, Shocks, and Shapes. J. Chromatogr. 1993, 629, 97. Hwang, Y.-L. Wave Propagation in Mass-Transfer Processes: From Chromatography to Distillation. Ind. Eng. Chem. Res. 1995, 34, 2849. Krupa, N. E.; Cannon, F. S. GAC: Pore structure versus dye adsorption. J.sAm. Water Works Assoc. 1996, 88, 94. Larry, E. S.; Richard, R. D. Textile Dye Process Waste Treatment with Reuse Considerations. Proc. 32nd Ind. Waste Conf. 1977, 581. McKay, G. Adsorption of Dyestuffs from Aqueous Solution Using Activated Carbon: Analytical Solution for Batch Adsorption Based on External Mass Transfer and Pore Diffusion. Chem. Eng. J., Biochem. Eng. J. 1983, 27, 187. McKay, G.; Otterburn, M. S.; Aga, J. A. Fuller’s Earth and Fired Clay as Adsorbents for DyestuffssEquilibrium and Rate Studies. Water Air Soil Pollut. 1985, 24, 307. Namasivayam, C.; Jeyakumar, R.; Yamuna, R. T. Dye Removal from Wastewater by Adsorption on “Waste” Fe(III)/Cr(III) Hydroxide. Waste Manag. 1994, 14, 643. Nassar, M. M.; Hamoda, M. F.; Radwan, G. H. Utilization of PalmFruit Bunch Particles for the Adsorption of Dyestuff Wastes. Adsorpt. Sci. Technol. 1996, 13, 1. Porter, J. J. Treatment of Textile waste with Activated Carbon. Am. Dyest. Rep. 1972, Aug, 24. Rodman, C. A. Removal of Color from Textile Dye Wastes. Text. Chem. Color. 1971, 11, 239. Yoshida, H.; Okamoto, A.; Kataoka, T. Adsorption of Acid Dye on Cross-Linked Chitosan Fibers: Equilibria. Chem. Eng. Sci. 1993, 48, 2267.
Received for review May 27, 1997 Revised manuscript received September 8, 1997 Accepted October 21, 1997X IE970374+
X Abstract published in Advance ACS Abstracts, December 15, 1997.
