Ind. Eng. Chem. Res. 2009, 48, 2125–2128
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Modeling the Adsorption Kinetics of Divalent Metal Ions onto Pyrophyllite Using the Integral Method Neelmani Gupta,† Murari Prasad,*,‡ Nidhi Singhal,† and Vineet Kumar† Department of Chemical Engineering, Thapar UniVersity, Patiala, India, and EnVironmental Chemistry DiVision, AdVanced Materials and Processes Research Institute (C.S.I.R.), Hoshangabad Road, Bhopal, India
The adsorption system was modeled and simulated to predict kinetic parameters for the adsorption of metal cations (lead, copper, and zinc) onto pyrophyllite, a low-cost adsorbent. The developed nonlinear sorption kinetic (NSK) mathematical model was solved using numerical integration (trapezoidal method), the gradient descent method, and least-squares analysis. It was based on application of the Freundlich isotherm to mass transfer across the film surrounding the adsorbent. Batch adsorption experiments were carried out for cation concentrations varying from 5.0 to 100.0 mg L-1. Code was developed in C language both for numerically integrating the model equation and for obtaining the best simulated values of the Freundlich constants, K and N; the order of reaction, n; and the film transfer coefficient, R. The model was sensitive to parameters R, n, and N, whereas it is insensitive to K. The values of parameters N, n, and R lie in the ranges of 0.185-2.06, 0.943-1.341, and 0.009-0.113 [(L/mg)n-1 min-1], respectively, under different experimental conditions. 1. Introduction Environmental pollution due to the discharge of heavy metals from various industries, including metal plating, mining, and painting, and agricultural sources such as fertilizers and fungicidal sprays are causing significant concern1 because of their toxicity and threat to human life, especially when tolerance levels are exceeded.2 In this context, the search for new technologies to remove metals from wastewaters has become a major topic of research. Among the methods commonly used for this purpose, adsorption is considered a better technique for the removal of high volumes/concentrations of toxic metals ions than reverse osmosis, electrodialysis, liquid extraction, precipitation, and others. The most commonly used adsorbent is activated carbon. However, activated carbon is not cost-effective for the removal of metal ions under consideration because of its high price and expensive regeneration. With this in view, a large number of experimental and theoretical studies have been reported on the adsorption of cations, particularly heavy metal ions, on various adsorbents.3-7 Various low-cost adsorbents being used include montmorillonite,8 slag,9 humic acid,10 kaoline,11 peat,12,13 fly ash,14 other carbonaceous substrates,15 and phosphatic minerals.16,17 In the present study, pyrophyllite, found in Jhansi, Uttar Pradesh, India, was used as the adsorbent. Pyrophyllite has a comparatively low (1.238 mequiv g-1) cation-exchange capacity (CEC), but it has been explored and extensively used as an alternative adsorbent by several investigators17-26 (including the authors’ own research work on pyrophyllite) in the recent past. These studies have highlighted the utility of this very lowcost and environmentally friendly mineral as an adsorbent for the removal of divalent cations from aqueous solutions. However, only a limited number of articles have addressed the mathematical modeling of the adsorption of metal ions onto mineral adsorbents. Earlier reported mathematical models for the sorption of heavy metal ion includes surface-complexation,3,5 cation-exchange,4 and triple-layer7 models. * To whom correspondence should be addressed. E-mail:
[email protected]. Tel.: 91-0755-2457105. Fax: 91-07552457042/2488985. † Thapar University. ‡ Advanced Materials and Processing Research Institute (AMPRI).
Because of the complex nature of the adsorption process, several simplifying assumptions have been made by various authors to solve the problem. Lee et al.9 suggested a static, physical, nonequilibrium sorption model (SPNSM) for phosphorus sorption onto slag. This model assumed a first-order rate of reaction (n ) 1) and used the Freundlich isotherm to develop the mathematical expression. It also assumed the Freundlich isotherm constant (N) to be equal to 1, which reduced the isotherm to S ) KC. The mathematical expression obtained for SPNS model is
C ) C0
1+
( mV )K exp[-R(1 + mKV )t] m 1 + ( )K V
(i)
Other simplified approaches include an empirical model based on a cation-exchange equation with scalable selectivity coefficients developed by Voegelin and Kretzschmar.4 Similarly, the homogeneous surface diffusion (HSD) model proposed by Babu and Ramakrishna27 assumed only a film transfer coefficient and diffusivity to be dominant design variable for adsorption. It appears that most of the models available are either empirical or based on greatly simplifying assumptions. With these points in view, the present investigation was undertaken to develop a more rigorous nonlinear sorption kinetic (NSK) model that could be used to predict the kinetic parameters K, N, n, and R. The proposed model was further used to fit the experimentally observed data obtained for the removal of divalent cations (lead, copper, and zinc) using pyrophyllite as the adsorbent. 1.1. Model Development. The model investigated in the present study is based on mass transfer coupled with the Freundlich isotherm. Previous investigators9 have also considered similar approaches, but their models have been limited to first-order (n ) 1) reactions only. The model developed in the present investigation is suitable even for orders of reaction other than unity. The adsorption kinetic behavior for the uptake of divalent metal cations (Pb2+, Cu2+, Zn2+) by an adsorbent as a function of time was studied, and a model for nth-order sorption kinetics
10.1021/ie800975m CCC: $40.75 2009 American Chemical Society Published on Web 01/06/2009
2126 Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009
was developed. The proposed model assumes that an immobile liquid layer surrounds the particles of adsorbent and that the liquid-phase concentration of cations in this layer is in equilibrium with the solid-phase concentration on the adsorbent surface. At any instant, the transfer of cations takes place across the liquid layer (film), and the rate at which sorption takes place is proportional to the concentration gradient of cations in the bulk and in the immobile liquid layer.9,28 If the initial liquid- and solid-phase concentrations are C0 and S0, respectively, then by mass balance, the bulk liquid-phase concentration as a function of the solid-phase concentration can be given by C0 ) C +
( mV )(S - S )
(ii)
0
At any instant, the rate of sorption (milligrams of cation per second per unit volume of solution) can be given by the equation
( mV ) dSdt ) -R(C - C )
n
(iii)
e
where R is the film transfer constant [(L/mg)n-1 min-1] and n is the order of reaction. The adsorption process on pyrophyllite is favorably represented by the Freundlich isotherm as described elsewhere17 S ) KC1/N
(iv)
At equilibrium, concentration C in eq ii becomes Ce. Substituting Ce at equilibrium (C ) Ce) from eq ii into eq iii, we obtain V dS m ) -R C + (S - S0) - C0 dt m V
( )[
n
]
(v)
Differentiating eq iv and substituting in eq v with S0 ) 0, we obtain the following model equation in integral form
tcalc )
∫
C
C0
[
K - C[(1/N)-1] N V m N R C + K√C - C0 m V
(
n
)
]
dC
(vi)
A computer program was developed that evaluates t using numerical integration of the above equation. This program uses the gradient descent method to determine the values of the constants K, N, n, and R by minimizing the least-squares error m
D)
∑ (t
i
- tcalc)2
(vii)
i)1
where D is the overall discrepancy in the observed and calculated values of time to reach a concentration Ci. The observed time in reaching concentration Ci is denoted by ti, and the calculated time to reach this concentration is denoted by tcalc. Thus discrepancy (D) indicates the sum of squares of the error between the observed and calculated time values. The root-mean-square (rms) values of discrepancy D were calculated as follows rms )
D number of data points
(viii)
2. Materials and Experimental Methods 2.1. Adsorbent Materials. Pyrophyllite is an abundant aluminosilicate mineral. The adsorbent properties of pyrophyllite result from its large surface area and negative layer charge when
Table 1. Values of Different Constants for Pb2+ Adsorption onto Pyrophyllite for Different Initial Metal Concentrations initial concentration (mg L-1) constant
5.0
10.0
50.0
100.0
N n R [(L mg-1)n-1 min-1] rms value
1.48 0.943 0.1134 1.06
0.825 1.341 0.0094 1.61
0.185 1.07 0.058 0.945
1.801 0.953 0.031 0.789
in contact with water.22 Adsorption can occur via two different mechanism: (i) cation exchange in the interlayers resulting from interactions between ions and the permanent negative charge and (ii) formation of inner-sphere metal complexes through Si-O- and Al-O- groups at both edge sites of pyrophyllite particles. Representative samples of pyrophyllite were obtained from M/S Eastern Mineral, Jhansi (U.P.), India. The physical properties (surface area ) 1.45 m2/g, CEC ) 1.238 mequiv/g, porosity ) 45.2%, specific gravity ) 2.64, hardness ) 1.35) and chemical analysis (SiO2 ) 53.00%, Al2O3 ) 28.14%, K2O ) 9.21%) of the pyrophyllite sample have been described elsewhere.19 Characterization studies of sericitic pyrophyllite carried out by X-ray diffraction, IR spectrscopy, and scanning electron microscopy (SEM) reported mainly pyrophyllite, R-quartz, kaolinite, and muscovite. Judging from sorption characteristics, the particle size of the powder samples in the -75 + 53 µm size range was used for adsorption studies. The samples (1 kg) were sized and ground separately for the experimental work. Representative ground samples, taken after coning and quartering, were subjected to wet chemical analysis. An electric rotary shaking machine and Systronic digital pH meter were used for equilibration and pH measurement, respectively, of the solutions. For all three heavy metals, a 0.5-g sample of the adsorbent was used. 2.2. Methods. Stock lead, copper, and zinc ion solutions (1000 mg L-1 each) were prepared from analytical-grade lead nitrate, copper nitrate, and zinc nitrate using doubly distilled water and were serially diluted to prepare solutions of varying initial concentration for the experimental work. Pyrophyllite mineral samples were equilibrated separately with 100 mL of solutions of different concentrations of lead, copper, and zinc ions. The suspensions were shaken on a mechanical shaker at 25 °C for 40 min. Samples from the suspensions were collected after 5-min intervals and then filtered through Whatman filter paper (No. 42). The filtrates were analyzed for Pb2+, Cu2+, and Zn2+ concentrations using an atomic absorption spectrophotometer (GBC model 902). To determine the required quiescent time needed to attain adsorption equilibrium, the quiescent time was varied between 10 and 30 min in intervals of 5 min for different initial lead, copper, and zinc concentrations. Equilibrium was observed to be reached within 30 min in each case. Random tests were done for different concentrations to check the reproducibility of the results. For each set of experiments, the pH values of the solution just before addition of the adsorbent and after shaking with the adsorbent were recorded. 3. Results and Discussion The proposed NSK model minimizes the discrepancy (D) by optimizing the values of the four constants K, N, n, and R. As observed from Tables 1 and 2, the model better explains copper and zinc adsorption than lead adsorption, as lead has higher rms values. From Table 1, it can be observed that the model better explains lead adsorption at higher initial metal concentrations. While obtaining the values of these constants using the model, it was observed that the model is sensitive toward N, n, and R
Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 2127
Figure 1. Concentration vs time curves for lead adsorption onto pyrophyllite at an initial lead concentration of 100 mg L-1 for different values of K. Table 2. Values of Different Constants for Cu2+, Zn2+, and Pb2+ Adsorption onto Pyrophyllite for 100 mg L-1 Initial Metal Concentrations metal ion 2+
Cu Zn2+ Pb2+
rms value
N
n
R [(L mg-1)n-1 min-1]
0.455 0.495 0.789
2.06 1.616 1.801
1.03 1.027 0.953
0.0111 0.009 0.031
but the Freundlich constant K has less influence on the curvefitting parameter D. Hence, the discrepancy (D) is a strong function of N, n, and R, but a weak function of K. Figure 1 shows different curves for lead adsorption onto pyrophyllite at an initial lead concentration of 100 mg L-1 for different values of K ranging from 1.0 to 300.0 (mg/g) (mg/L)-1/N. It can be observed that the curves almost overlap despite the large variations in the value of K. Similar large variations (from 0.06 to 727.05) in K values were also observed to have little effect by Babu and Ramakrishna.29 Tables 1 and 2 also list the values of constants N, n, and R. Table 1 shows these values for lead sorption onto pyrophyllite at different initial lead concentrations as obtained by the proposed model. The closeness of the value of n to unity suggests that lead sorption onto pyrophyllite follows a firstorder mechanism irrespective of the initial concentration of the metal ion. It is evident from Table 2 that the values of the reaction order and film transfer coefficient are almost the same for the sorptions of copper and zinc ions onto pyrophyllite, whereas the values of the Freundlich constants N and K are different. Thus, the mechanisms of copper and zinc sorption might be similar with respect to mass transfer and different in terms of the Freundlich isotherm. As suggested in a previous study,28 the value of 1/N should be less than unity for favorable adsorption. The present study thus reveals that pyrophyllite (with N higher than unity, Table 2) is just barely a possible adsorbent for the removal of metal ions. However, because of its low cost and abundant availability, it might prove to be a viable alternative. Plots of concentration vs time for lead adsorption onto pyrophyllite at different initial concentrations (5, 10, 50, and 100 mg L-1) are shown in Figures 2-4. The graphs show the experimental data points and the model curve that corresponds to the simulated values of the kinetic parameters (N, n, and R) as listed in Table 1. It can be observed from these figures that, except for one or two initial experimental data points, the modeled curves provide close approximations to the experimental data. Similar results were also obtained for copper and zinc adsorption, as shown in Figure 4. This figure shows that the model results are in fairly good agreement with the
Figure 2. Concentration vs time graph of lead adsorption onto pyrophyllite at an initial lead concentration of 5 mg L-1. (Points are experimental values, and the line shows the model prediction.)
Figure 3. Concentration vs time graph of lead adsorption onto pyrophyllite at initial lead concentrations of 10 and 50 mg L-1. (Points are experimental values, and the lines show model predictions.)
Figure 4. Concentration vs time graph of lead, copper, and zinc adsorption onto pyrophyllite at an initial concentration of 100 mg L-1. (Smooth curves represent predicted values.)
experimental data used for validation. The deviation of the initial data points might be due to the continued adsorption of metal ions during the filtration process, given that the metal ion concentration is quite high in the solution. Another reason for deviation might be the formation of inner-sphere metal complexes with the pyrophyllite, as described in section 2.1. Thus, excluding the initial phase of adsorption, the developed model accurately estimates the kinetic parameters for the removal of metal ions by adsorption onto pyrophyllite.
2128 Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009
4. Conclusions The study reported herein leads to the following conclusions: (1) The proposed model fits the data satisfactorily. The model is also suitable for the study of reactions with orders other than unity. (2) The model is sensitive to the film transfer coefficient (R), order of reaction (n), and Freundlich constant N, but it is insensitive to the Freundlich constant K. (3) The value of parameters N, n, and R lie in the ranges of 0.185-2.06, 0.943-1.341, and 0.009-0.113 [(L/mg)n-1 min-1], respectively, under different experimental conditions. (4) Copper and zinc adsorption were better explained by the model than lead adsorption. (5) The value of the order of reaction (n) for lead sorption is almost unity for different initial concentrations. Acknowledgment The authors are grateful to Director, AMPRI, Bhopal, India, for his kind permission and encouragement to conduct the present research work and to publish this article. Nomenclature C ) bulk liquid-phase concentration (mg L-1) C0 ) initial cation concentration (mg L-1) Ce ) liquid-phase concentration in equilibrium with the solid-phase concentration (mg L-1) D ) discrepancy, sum of squares of the difference between calculated and observed values of time (min2) K ) Freundlich isotherm constant [(mg/g)(mg L-1)1/N] m ) mass of adsorbent (g) N ) Freundlich isotherm constant n ) order of reaction S ) solid-phase concentration (mg of cation/g of adsorbent) S0 ) initial solid-phase concentration (mg of cation/g of adsorbent) V ) volume of the solution (L) R ) film transfer constant [(L/mg)n-1 min-1]
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ReceiVed for reView June 23, 2008 ReVised manuscript receiVed November 12, 2008 Accepted November 23, 2008 IE800975M
