**6. Acknowledgments**

198 Mass Transfer in Chemical Engineering Processes

The optimum separation time and separation cycles of the extraction can be estimated. The

Fig. 19 is a plot of the integral concentrations of Cu(II) against time to determine the reaction order (n) and the forward reaction rate constant (kf). The rate of diffusion and/or rates of chemical changes may control the kinetics of transport through liquid membrane depending on transport mechanisms (diffusion or facilitated). The reaction rate constants of first-order

Reaction order (n) Reaction rate constant (kf) R-squared % Deviation First-order 0.393 min-1 0.813 61.233 Second-order 0.708 L/mgmin 0.911 1.453

Table 4. R-squared and percentages of deviation for first-order and second-order reactions The percentage of copper ion extraction is calculated by Eq. (27). The percentage of

> f,in f,out f,in

(27)

(28)

C C % extraction 100 C

<sup>j</sup> Expt. Theo.

 

C C C % deviation 100

function of initial concentration of the target species in feed and also feed flow rate.

experimental data at the average percentage of deviation of 2%.

i 1 Expt. <sup>i</sup>

j

The optimum separation time for the prediction of separation cycles can be estimated by the model based on the optimum conditions from the plot of percentage of extraction as a

In this work, at the legislation of Cu(II) concentration in waste stream of 2 mg/L, the calculated separation time is 10 min for about 15-continuous cycles. The percentage of extraction calculated from this reaction flux model is much higher than the results from other works which applied different extractants and transport mechanisms. Types of extractants and their concentrations are significant to the separation of metal ions. For example, a hard base extractant can extract both dissociated and undissociated forms in a basic or weak acidic condition but dissociated forms are high favorable. While a neutral extractant normally reacts with undissociated forms, but in an acidic condition it can react with dissociated forms. It is noteworthy to be aware that not only types of the extractants (single or synergistic), in this case LIX84I for Cu(II), but also the transport mechanism, e.g., facilitated transport mechanism attributes to the extraction efficiency. The model results are in good agreement with the

Facilitated transport of the solutes or target species benefits the separation process by liquid membrane with a non-equilibrium mass transfer and uphill effect. It is more drastic chemical changes of the target species with the presence of a suitable extractant or carrier (sometimes by synergistic extractant) in liquid membrane to form new complex species

model was verified with the experimental extraction results and other literature.

(n = 1) and second-order (n = 2) are 0.393 min-1 and 0.708 L/mgmin, respectively.

deviation is calculated by Eq. (28).

**5. Conclusions** 

The authors are highly grateful to the Royal Golden Jubilee Ph.D. Program (Grant No. PHD50K0329) under the Thailand Research Fund, the Rare Earth Research and Development Center of the Office of Atoms for Peace (Thailand), Thai Oil Public Co., Ltd., the Separation Laboratory, Department of Chemical Engineering, Chulalongkorn University, Bangkok, Thailand. Kind contributions by our research group are deeply acknowledged.
