## 3 Model Development  
### Model Establishment  
Odorous substances were absorbed by the aqueous solution from the gas through mass transfer. The absorbed odorous substances were then oxidized by electrochemical oxidation reactions. In this study, we established a model composed of mass transfer and oxidation terms, which are the main mechanisms of EWS, based on zero-order reactions. The concentration changes in the aqueous and gaseous H\({}_{2}\)S are calculated as follows:  
\[\frac{\mathrm{dC}_{\mathrm{LS}}}{\mathrm{dt}}=\mathrm{K}_{\mathrm{L}}\mathrm{ as}\left(\frac{\mathrm{C}_{\mathrm{GS,in}}}{\mathrm{H}_{\mathrm{S}}}-\mathrm{C}_{ \mathrm{LS}}\right)-\mathrm{k}_{\mathrm{s}} \tag{1}\]  
\[\frac{\mathrm{dC}_{\mathrm{GS,out}}}{\mathrm{dt}}=\frac{\mathrm{Q}_{\mathrm{G} }}{\mathrm{V}_{\mathrm{G}}}(\mathrm{C}_{\mathrm{GS,in}}-\mathrm{C}_{\mathrm{ GS,out}})-\frac{\mathrm{V}_{\mathrm{L}}}{\mathrm{V}_{\mathrm{G}}}\mathrm{K}_{ \mathrm{L}}\mathrm{aS}\left(\frac{\mathrm{C}_{\mathrm{GS,in}}}{\mathrm{H}_{ \mathrm{S}}}-\mathrm{C}_{\mathrm{LS}}\right) \tag{2}\]  
where C\({}_{\mathrm{LS}}\) is the liquid-phase concentration (mg dm\({}^{-3}\)), K\({}_{\mathrm{L}}\)aS is the mass transfer coefficient (min\({}^{-1}\)), C\({}_{\mathrm{GS,in}}\) is the gas inlet concentration (mg dm\({}^{-3}\)), H\({}_{\mathrm{S}}\) is the Henry's law constant (dimensionless), C\({}_{\mathrm{LS}}\) is the aqueous concentration (mg dm\({}^{-3}\)), k\({}_{\mathrm{S}}\) is the zero-order kinetic constant (mg dm\({}^{-3}\) min\({}^{-1}\)), C\({}_{\mathrm{GS,out}}\) is the gas outlet concentration (mg dm\({}^{-3}\)), Q\({}_{\mathrm{G}}\) is the gas flow rate (dm\({}^{3}\) min\({}^{-1}\)), V\({}_{\mathrm{G}}\) is the volume of gas present in the liquid phase as the form of bubbles (dm\({}^{3}\)), and V\({}_{\mathrm{L}}\) is the volume of the aqueous solution (dm\({}^{3}\)).  
The concentration changes in aqueous and gaseous NH\({}_{3}\) are calculated as follows:  
\[\frac{\mathrm{dC}_{\mathrm{LN}}}{\mathrm{dt}}=\mathrm{K}_{\mathrm{L}}\mathrm{ a}_{\mathrm{NH_{3}}}\left(\frac{\mathrm{C}_{\mathrm{GN,in}}}{\mathrm{H}_{ \mathrm{N}}}-\mathrm{C}_{\mathrm{LN}}\right)-\mathrm{k}_{\mathrm{N}}\left(1- \frac{\mathrm{C}_{\mathrm{LS}}}{\mathrm{K}_{\mathrm{I}}+\mathrm{C}_{\mathrm{ LS}}}\right) \tag{3}\]  
\[\frac{\mathrm{dC}_{\mathrm{GN,out}}}{\mathrm{dt}}=\frac{\mathrm{Q}_{\mathrm{G} }}{\mathrm{V}_{\mathrm{G}}}(\mathrm{C}_{\mathrm{GN,in}}-\mathrm{C}_{\mathrm{ GN,out}})-\frac{\mathrm{V}_{\mathrm{L}}}{\mathrm{V}_{\mathrm{G}}}\mathrm{K}_{ \mathrm{L}}\mathrm{a}_{\mathrm{NH_{3}}}\left(\frac{\mathrm{C}_{\mathrm{GN,in}} }{\mathrm{H}_{\mathrm{N}}}-\mathrm{C}_{\mathrm{LN}}\right) \tag{4}\]  
where the subscript N represents the value of NH\({}_{3}\) and K\({}_{\mathrm{I}}\) is the retardation constant (mg dm\({}^{-3}\)). K\({}_{\mathrm{I}}\) illustrates the phenomenon of H\({}_{2}\)S oxidation before NH\({}_{3}\) when H\({}_{2}\)S and NH\({}_{3}\) coexist in an aqueous solution. Using the numerical model, EWS performance was predicted with respect to the H\({}_{2}\)S inlet concentration. The values obtained from the experimental results for each reactor was used [6]. Table 1 summarizes the values of the model parameters predicted in this study.