## 3 Results and Discussion  
### Model Application  
Nine sets of kinetics studies were conducted using artificial seawater to calibrate each coefficient. The coefficients, \(d_{1}\), \(p_{s}\), and mf were chosen as important coefficients via sensitivity tests (see Section S1 and Figure S1). The estimation of each coefficient was performed in the order of the sensitivity-test results as shown in Table 1 and Figure 3. The coefficients were carefully estimated to minimize the total root mean square error (RMSE); the condition for model calibration is presented in Section S1. Then, kinetics constants for the parallel first-order decay model are estimated as follows:  
\[k_{s}=1.01\ C_{0}^{-0.005}\ e^{0.02\ TOC} \tag{6}\]  
\[k_{f}=33.7\ C_{0}^{-0.002}\ e^{0.67\ TOC} \tag{7}\]  
\[z=0.355\ C_{0}^{0.11}\ TOC^{-0.10} \tag{8}\]  
Based on Equations (6)-(8), it can be assumed that more chlorine would be consumed by the fast reaction than the slower one, since the fraction of the slow reaction (\(z\)) changes little or remains stable within the range of 0.2-0.5 under typical seawater conditions. The estimated constants and correlation factors for each case are summarized in Table 1, and the fittings are also presented in Figure 3. As shown in Table 1, the slow reaction rate constant varied little compared to that of the fast reaction under the given conditions. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & **TOC Concentration** & **Initial Chlorine** & \multicolumn{3}{c}{**Estimated Constants**} & **R2** & **RMSE** \\  & **(mg L\({}^{-1}\))** & **Dose (mg L\({}^{-1}\))** & **\(k_{s}\) (h\({}^{-1}\))** & **\(k_{f}\) (h\({}^{-1}\))** & **z** & & \\ \hline \multirow{8}{*}{Artificial seawater} & \multirow{4}{*}{1.0} & 1.2 & 1.029 & 65.83 & 0.362 & 0.776 & 0.190 \\  & & 1.8 & 1.027 & 65.78 & 0.379 & 0.880 & 0.134 \\  & & 2.4 & 1.026 & 65.74 & 0.391 & 0.924 & 0.138 \\ \cline{1-1} \cline{2-7}  & & 1.2 & 1.050 & 128.7 & 0.338 & 0.910 & 0.057 \\ \cline{1-1}  & & 1.8 & 1.048 & 128.6 & 0.353 & 0.944 & 0.120 \\ \cline{1-1}  & & 2.4 & 1.047 & 128.5 & 0.365 & 0.943 & 0.090 \\ \cline{1-1}  & & 1.2 & 1.071 & 251.4 & 0.325 & 0.603 & 0.064 \\ \cline{1-1}  & & 1.8 & 1.069 & 251.2 & 0.339 & 0.853 & 0.110 \\ \cline{1-1}  & & 2.4 & 1.068 & 251.1 & 0.350 & 0.809 & 0.154 \\ \hline \multirow{2}{*}{West Sea seawater} & \multirow{4}{*}{1.3} & 1.2 & 1.036 & 80.49 & 0.353 & 0.885 & 0.109 \\ \cline{1-1}  & & 1.8 & 1.034 & 80.43 & 0.369 & 0.941 & 0.194 \\ \cline{1-1}  & & 2.4 & 1.032 & 80.38 & 0.381 & 0.905 & 0.143 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Estimated kinetics parameters depending on total organic carbon (TOC) and initial chlorine dose. RMSE = root mean squared error. Notably, both reaction rate constants were more affected by TOC levels than by initial chlorine concentration. Moreover, the fast reaction rate constant varied considerably according to the TOC level of the seawater. We observed an inverse relationship between the initial chlorine concentration and first-order kinetics coefficient as reported by others [22; 33]; however, the correlation was not strong compared to that between TOC and \(k\). In other words, the rate constants did not change much depending on \(C_{0}\), because the exponential part of \(C_{0}\) in this study was very small. Fortunately, this can be an advantage in determining the rate constants for in-situ electro-chlorination, because there is no \"initial concentration\" in in-situ electro-chlorination. In the simulation, the electrode served as the mass source for chlorine generation, and the chlorine concentration in each cell (control volume) was calculated by the internal solver of Flow-3D in accordance with the surrounding flow. The injected chlorine decayed rapidly within one minute and then decayed more gradually, as shown in Figure 3. Although there are some small variations between the predicted and measured data, the model describes the chlorine decay in seawater well.