## 4 Discussion
### Efficiency of PAC Utilization  
It is worth comparing the adsorption efficiency for the filter with PAC and a homogeneous system, i.e., a flocculation chamber treating water with both coagulant and PAC. The effect of adsorption on PAC in homogenous system can be determined with a known adsorption isotherm and may exceed real-life effects, because flocculation time does not exceed 1 h, while adsorption isotherms are determined for equilibrium states (e.g., after 24 h) or from equations describing the adsorption kinetics in a homogeneous reactor in steady states [15; 16; 17; 19].  
The adsorption isotherm (Figure 25) of the analyzed PAC is  
\[a=\Gamma\cdot A=0.00167\frac{m^{3}}{\text{g PAC}}\cdot A \tag{20}\]  
where  
\(a\)--adsorption capacity for absorbance (1/m)-m\({}^{3}\)/g PAC:  
\(A\)--absorbance (1/m);  
\(\Gamma\)--[PERSON]'s isotherm coefficient (m\({}^{3}\)/g PAC).  
Table 3 shows the \(D_{h}/D\) ratio, i.e., the ratio of the sorbent doses to the homogeneous reactor \(D_{h}\) vs. the dose \(D\) to the filter. For suitable doses \(D\) and flows Q, the \(D_{h}/D\) ratios are greater than 1 (gray areas). This means that in the filter, the same effects can be achieved at \(D<D_{h}\) and the sorbent efficiency in the filter is higher than in the homogeneous reactor. In practice, lower doses of sorbent would reduce water treatment costs. In experiment No. 16 (Table 3), the ratio \(D_{h}/D\) was 3.0018, so to obtain the same filtration effect, the dose per 1 m\({}^{3}\) of water for the filter was \(D/V=169.5\) g PAC/m\({}^{3}\), while in a homogeneous reactor (flocculator), it was \(D_{h}/V=508.8\) g PAC/m\({}^{3}\).  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{\begin{tabular}{c} **Q** \\ **(m/s)** \\ **Sorbent** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(\Gamma^{*}\)** \\ **(m\({}^{3}\) of** \\ **Water/g** \\ **PAC** \\ **Equation (s)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(\Gamma^{*}\)** \\ **Dose** \\ **D** \\ **PAC** \\ **Equation (s)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(\rho_{p,p}\)** \\ **(m\({}^{3}\) of** \\ **PAC/m\({}^{3}\)** \\ **PAC/m\({}^{3}\)** \\ **of Bed)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(\rho_{p,p}\)** \\ **(m\({}^{3}\) of** \\ **PACS/m\({}^{3}\)** \\ **of Bed)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(\epsilon\)** \\ **(m\({}^{3}\) of** \\ **PACS/m\({}^{3}\)** \\ **of Bed)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Filter** \\ **(m\({}^{3}\) of** \\ **PACS/m\({}^{3}\)** \\ **of Bed)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(A_{p}\)** \\ **(m\({}^{3}\) of** \\ **PACS/m\({}^{3}\)** \\ **of Bed)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(A_{p}\)** \\ **(m\({}^{3}\) of** \\ **PACS/m\({}^{3}\)** \\ **of Bed)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **\(A_{p}\)** \\ **(m\({}^{3}\) of** \\ **PACS/m\({}^{3}\)** \\ **of Bed)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **\(V=Q\)** \\  
It should be noted that even if the effective coefficient \(\Gamma\) for the adsorption column (Table 3, No.: 7, 8, 10 \(\div\) 16) was smaller or equal to \(\Gamma\) (0.00167 m\({}^{3}\)/g PAC) for the adsorption isotherm in bulk adsorption, the ratios \(D_{\rm h}/D\) could exceed 1. Due to the mutual packing of the powdered sorbent in the filter column, the average Henry's coefficient was 0.00158 m\({}^{3}\)/g PAC and was slightly lower than \(\Gamma\) for bulk adsorption (0.00167 m\({}^{3}\)/g PAC).