Modeling of Fixed Bed Adsorption: Application to the Adsorption of an Organic Dye

MATERIALS AND METHODS

The adsorbent: In this study, the adsorbent used is natural clay. The used clay is of smectite type. The minerals of this group are characterized by a structure of the interlayer type 2:1 of distance equal to 14 Å.

Table 1:	Chemical composition of natural clay

Table 2:	Characteristics of Rhodamine B

Table 3:	Properties of the column

The smectite is a consistent mineral, very soft, which is generally presented in compact mass, the stacking of the layers is disordered. This disorder and the weak load of the layers facilitates their spacing from where the adsorption of varied molecules. The analysis of our clay by the method of x-ray fluorescence gave the following results concerning their characterizing chemical compounds (Table 1).

The adsorbate: The dye used during our work is the Rhodamine B (CI No. 45170). It is an organic compound whose physicochemical properties are grouped in Table 2.

Fixed bed experiments and mathematical models: In this study, an adsorber, whose dimensions are shown in Table 3, was used. The dye is aspired from the dye tank by means of a feed pump. Then, it crosses the bed of the column filled with burnt clay mass. At the exit of the column, the solution is recovered with intervals of 15 min time to determine its concentration. Before carrying out discoloration, the clay bed was percolated by the distilled water instead of the dye during 2 to 3 h to ensure the damping and the swelling of clay.

Model of clark: Clark proposed a new simulation of the breakthrough curves (Clark, 1987). The model developed by Clark is based on the following hypotheses:

By using the laws of mass transfer and by neglecting the phenomenon of dispersion, Clark solved the system of equations of mass transfer and obtained the following relation (Sahel and Ferrandon-Dusart, 1993).

(1)

(2)

Where:

n = Freundlich parameter

A and r are the constants of the model and are obtained starting from the following equation:

(3)

(4)

When linearizing this equation, we obtain:

(5)

Model of thomas: The Thomas model is one of the most general and widely used theoretical methods to describe column performance (Rozada et al., 2007). This model can be described by the following expression:

(6)

where, C₀ and C_t are respectively the influent and effluent concentrations (mg L^-1), K_th is the Thomas rate constant (mL/mg/min), q∞ is maximum capacity of adsorption (mg g^-1), X quantity of adsorbent in the column (g), V_ef is volume of solution (mL) and F is the feed flow (mL mn^-1).

The Thomas model which assumes Langmuir kinetics of adsorption-desorption and no axial dispersion is derived with the assumption that the rate driving force obeys second-order reversible reaction kinetics (Thomas, 1944; Wu and Yu, 2008; Ayoob and Gupta, 2007; Rozada et al., 2007).

Model of Yoon-Nelson: The Yoon-Nelson model is not only less complicated than other models, but also requires no detailed data concerning the characteristics of adsorbate, the type of adsorbent and the physical properties of the adsorption bed (Aksu and Gonen, 2004). This model assumes that (Yoon and Nelson, 1984):

The Yoon-Nelson equation for a single component system is expressed as (Yoon and Nelson, 1984):

(7)

where, K_YN is the rate constant (mn^-1), τ is time required for 50 % adsorbate breakthrough (mn) and t is time (mn).

Model of Adams-Bohart: To account for the adsorption of chlorine on a fixed bed activated carbon in a dynamic model, Bohart and Adams established the fundamental equation describing the relationship between C/C₀ and time. The modeling conceived by these authors was in the beginning planned for gases and it was transposed later to the liquids by quite simply replacing the terms in pressure by terms of concentration, since it is the same definition even of the chemical activity of an aqueous solution in solution in a diluted medium (Sahel and Ferrandon-Dusart, 1993; Bohart and Adams, 1920).

To solve the equations of the model, certain assumptions were put forth:

The resolution of the conservation equations of the matter leads to:

(8)

where, C₀ and C: are, respectively the concentrations initial and instantaneous aqueous solution in the solution (g L^-1), K is the kinetic constant (L/g/min), N₀ is capacity of adsorption (g L^-1), Z is the bed depth in the column (m), t is time (mn) and U and the speed of gas out (m sec^-1).

Error analysis: The squares of the differences between the experimental data and the data obtained by calculating from the models can be obtained as the following formula:

(9)

where, (C/C₀)_cal is the ratio of effluent and influent RB concentrations obtained from calculation according to dynamic models and(C/C₀)_exp is the ratio of effluent and influent RB concentrations obtained from experiment.

RESULTS AND DISCUSSION

Choice of models: The dynamic behavior of the column is approached by the following models: Bohart and Adams, Thomas, Yoon-Nelson and Clark (Fig. 1).

We deduce from this first comparison that the models of Clark, Thomas and Yoon-Nelson correctly smooth the experimental curve of opening, whereas the model of Bohart and Adams describes only the initial part of the curve of opening, in accordance with the made approximation (C<< C₀).

The method of least square confirms this conclusion by the absolute error analysis carried in Table 4.

Fig. 1:	Comparison between the curve of experimental opening and the curves predicted by the models

Table 4:	The error analysis

Fig. 2:	Breakthrough curves : the effect of different bed depths on RB adsorption (C0 = 80 mg L-1, Q = 0,18 L mn-1)

According to this table, one finds that the model of Clark gives the best result. Several studies found the same result (Bohart and Adams, 1920; Han et al., 2009).

Fixed bed adsorption experimental results and modeling
Effect of different bed depths on breakthrough curve: The sorption performance of natural clay was tested at various bed heights bed depths, 16, 8 and 4 cm at flow rate of 0,18 l mn^-1 and initial concentration of 80 mg L^-1. The breakthrough curves at different bed depths are shown in Fig. 2.

Effect of initial concentration on breakthrough curve: The experiments of two different initial concentration, 50 and 20 mg L^-1, were operated at the same bed depth (8 cm) and flow rate (0, 18 L mn^-1), respectively. The results are shown in Fig. 3.

Effect of flow rate on breakthrough curve: The experimental conditions chosen to study the effect of the flow rate were : inlet concentration of RB 80 mg L^-1 ; bed depth, 8 cm and feed flow rates 0, 06, 0,18 and 0,3 L mn^-1. The breakthrough curves at various flow rates are shown in Fig. 4.

Estimation of breakthrough curves
Model of clark: The adsorption isotherm of clay can be described by the Freundlich isotherm. The Freundlich constant (n) was used to calculate the parameters in the Clark model. The values of A and r in the Clark model are shown in Table 5. As seen in this later as both flow rate and influent dye concentration increased, the values of r increased. From the experimental results and data regression, the model proposed by the Clark model provided good correlation on the effects of influent RB concentration, flow rate and bed depth.

These results are similar to those found by other researchers working on different sorbate-sorbent systems (Ayoob and Gupta, 2007; Han et al., 2009; Ayoob et al., 2007).

Fig. 3:	Breakthrough curve : the effect of influent concentration on RB adsorption (H = 8 cm, Q = 0,18 l mn-1)

Fig. 4:	Breakthrough curves : the effect of flow rate on RB adsorption (C0 = 80 mg L-1, H = 8 cm)

Model of Yoon-Nelson: This model is very simple and does not require any data concerning the characteristics of the adsorbent and the bed. The parameters of this model are gathered in Table 6.

From Table 6, the rate constant K_YN increased with increasing both flow rate and RB influent concentration (Ayoob and Gupta, 2007; Han et al., 2009). The data in Table 6 also indicate that values of τ are similar to the experimental results.

Model of thomas: The Thomas model is one of the most general and widely used methods in column performance theory. The parameters of the model of Thomas are also listed in Table 7. It is shown in Table 7 that as the influent concentration increased, the value of q_e increased but the value of Kth decreased. With flow rate increasing, the value of q_e decreased while the value of Kth increased. As the bed depth increased, the value of q_e increased significantly but the value of Kth decreased significantly (Han et al., 2009; Aksu and Gonen, 2004).

Table 5:	Parameters of the Clark model at different conditions

Table 6:	Parameters of the model of Yoon-Nelson

Table 7:	Parameters of the model of Thomas

Evaluation of basic design parameters of adsorption column: The formation and movement of adsorption zone can be mathematically described and evaluated (Ayoob et al., 2007; Bhakat et al., 2007).

Partial capacity of the adsorbent bed: The partial capacity of the adsorbent bed determines the adsorbent’s removal efficiency, denoted F, it is defined as the amount actually involved in adsorption phenomenon compared to the total amount of adsorbent. It can also be defined as the amount of adsorbate actually eliminated from the potential disposal of the adsorbent inside the zone transfer. It is calculated by the ratio:

(10)

where, C₀ is the initial concentration of RB in water (mg L^-1); C is the concentration of solute RB at any instant in the effluent (mg L^-1); Az is the amount of RB that has been removed by the adsorption zone from breakthrough to exhaustion (mg) and Amax is the amount of RB removed by adsorption zone if completely exhausted (mg), t_s is the saturation time and t_b: the breakthrough time.

Table 8:	Parameters for the fixed bed clay column

The height of the mass transfer zone: It is in this portion of the bed, practically, that most of the transfer phenomenon. Take place it determines the rate of removal of adsorbate by the adsorbent. It is an effective parameter to quantify the overall rate of exchange which is calculated by the equation below:

(11)

where, H_b is the height of the adsorbent bed

The speed of the mass transfer zone: The speed of the mass transfer zone depends on the capacity of the adsorbent and allows us to calculate the velocity saturation of the bed. It is directly related to the height of the mass transfer zone. It is given by:

(12)

where, t_z is the time required for the adsorption zone to travel its own length when established, t_f is The time required for the formation of the transfer zone.

The value of t_f can be calculated as:

(13)

The percentage of saturation of the column to the breakthrough: Fix a breakthrough concentration C_b = 0.2C₀ and a saturation concentration Cs and C₀ = 0.9, than calculate all parameters at different initial concentrations for a bed height H = 8 cm and a flow rate Q = 0.18 L min^-1. The calculation results are given in Table 8.

We note that the speed of the mass transfer area increases with the initial concentration after increasing the driving force that controls the adsorption process. The rate of saturation and the partial capacity of the bed do not depend on operating conditions.

CONCLUSIONS

On the basis of the experimental results of this investigation, the following conclusion can be drawn: