2.5.2. Kinetic Studies

Many studies have shown that the removal process of nitrate from solution by ZVI composites conforms to first-order or second-order kinetics [47]. The removal process of NO<sup>3</sup> −-N from the solution by the ZB12-500 composite can be divided into two stages: the fast removal stage and the slow removal stage. Therefore, the first-order kinetic model, second-order kinetic model, and two-compartment first-order kinetic model were used for analysis and fitting in this experiment, and the fitting equations were as follows:

$$\frac{\mathbf{C}\_{\mathbf{t}}}{\mathbf{C}\_{0}} = \mathbf{e}^{-\mathbf{k}\_{1}\mathbf{t}} \tag{16}$$

$$\frac{1}{\mathbf{C}\_{\text{t}}} - \frac{1}{\mathbf{C}\_{0}} = \mathbf{k}\_{2}\mathbf{t} \tag{17}$$

$$\frac{\mathbf{C\_{f}}}{\mathbf{C\_{0}}} = \mathbf{f\_{f}} \ast \mathbf{e^{-k\_{f} \ast t}} + \mathbf{f\_{s}} \ast \mathbf{e^{-k\_{s} \ast t}} \tag{18}$$

where C<sup>t</sup> (mg/L) is the residual concentration of nitrate, C<sup>0</sup> (mg/L) is the initial concentrations of nitrate; k<sup>1</sup> and k<sup>2</sup> (1/h) are the reaction rate constants of first and second order reaction kinetics, respectively; f<sup>f</sup> and f<sup>s</sup> are the proportion of fast and slow compartment removal in the total removal, respectively, and f<sup>f</sup> + f<sup>s</sup> = 1; k<sup>f</sup> and k<sup>s</sup> (1/h) are the fast and slow compartment reaction rate constants, respectively.
