## 3 Results
### Adsorption in an Anthracite-Sand Filter with PAC
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{\begin{tabular}{c} **Q** \\ **(m/s)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(\Gamma^{\star}\)** \\ **(1/m\({}^{3}\)** \\ **Sorbent**) \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **PAC** \\ **(g PAC/m\({}^{3}\)** \\ **of Bed)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} \(\rho_{p,sorb}\) \\ **(m\({}^{3}\) of** \\ **Pores/m\({}^{3}\)** \\ **of Bed)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} \(\varepsilon\) \\ **(m/s)** \\ **(m/s)** \\ **(m/s)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} \(k\cdot a_{m}\) \\ **(m/s)** \\ **PAC)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(k\cdot a_{m}\) \\ **(m/s)** \\ **PAC)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **\(Nu\)** \\ **PAC)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Re** \\ **(m/s)** \\ **PAC)** \\ \end{tabular} } \\ \hline
1 & 2.2 & 5.58 & 1 & 3143.80 & 0.47 & 3.251\(\cdot 10^{-3}\) & 4.123\(\cdot 10^{-7}\) & 2.489 & 4.380 \\ \hline
2 & 2.2 & 12.00 & 2 & 6287.60 & 0.465 & 3.362\(\cdot 10^{-3}\) & 6.754\(\cdot 10^{-7}\) & 8.243 & 4.579 \\ \hline
3 & 2.2 & 43.78 & 3 & 9431.40 & 0.46 & 3.251\(\cdot 10^{-3}\) & 9.591\(\cdot 10^{-7}\) & 17.747 & 4.476 \\ \hline
4 & 2.2 & 44.20 & 4 & 12,575.21 & 0.45 & 3.251\(\cdot 10^{-3}\) & 1.703\(\cdot 10^{-6}\) & 42.938 & 4.575 \\ \hline
5 & 1.5 & 13.05 & 1 & 3010.02 & 0.47 & 2.212\(\cdot 10^{-3}\) & 2.597\(\cdot 10^{-7}\) & 1.501 & 2.981 \\ \hline
6 & 1.5 & 8.65 & 2 & 6020.05 & 0.465 & 2.341\(\cdot 10^{-3}\) & 7.457\(\cdot 10^{-7}\) & 8.713 & 3.188 \\ \hline
7 & 1.5 & 27.92 & 3 & 9030.07 & 0.46 & 1.910\(\cdot 10^{-3}\) & 1.092\(\cdot 10^{-6}\) & 19.341 & 2.630 \\ \hline
8 & 1.5 & 33.15 & 4 & 12,040.09 & 0.45 & 2.054\(\cdot 10^{-3}\) & 6.598\(\cdot 10^{-7}\) & 15.932 & 2.891 \\ \hline
9 & 1 & 9.03 & 1 & 3042.39 & 0.47 & 1.226\(\cdot 10^{-3}\) & 6.107\(\cdot 10^{-7}\) & 3.567 & 1.651 \\ \hline
10 & 1 & 16.24 & 2 & 6084.78 & 0.465 & 1.175\(\cdot 10^{-3}\) & 5.848\(\cdot 10^{-7}\) & 6.907 & 1.600 \\ \hline
11 & 1 & 34.95 & 3 & 8841.94 & 0.46 & 1.045\(\cdot 10^{-3}\) & 1.713\(\cdot 10^{-6}\) & 29.722 & 1.439 \\ \hline
12 & 1 & 36.94 & 4 & 12,040.09 & 0.45 & 9.403\(\cdot 10^{-4}\) & 7.569\(\cdot 10^{-7}\) & 18.277 & 1.323 \\ \hline
13 & 0.8 & 7.24 & 1 & 3109.25 & 0.47 & 7.004\(\cdot 10^{-4}\) & 2.229\(\cdot 10^{-7}\) & 1.331 & 0.944 \\ \hline
14 & 0.8 & 18.55 & 2 & 6218.51 & 0.465 & 7.959\(\cdot 10^{-4}\) & 6.234\(\cdot 10^{-7}\) & 7.524 & 1.084 \\ \hline
15 & 0.8 & 25.47 & 3 & 9327.76 & 0.46 & 6.310\(\cdot 10^{-4}\) & 4.770\(\cdot 10^{-7}\) & 8.730 & 0.869 \\ \hline
16 & 0.8 & 32.89 & 4 & 12,437.02 & 0.45 & 5.876\(\cdot 10^{-4}\) & 5.774\(\cdot 10^{-7}\) & 14.402 & 0.827 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Data for the adsorption model (2), (3), (4) and the calculated model parameters \(\Gamma^{\star}\), \(k\cdot a_{m}\) (numerical values refer to the anthracite layer). \(R_{it}\)--hydraulic radius (m);  
\(N\)--number of particles in a bed;  
\(D\)--outer diameter of the filter column (m);  
\(D_{m}\)--molecular diffusion coefficient (m\({}^{2}\)/s), assumed \(D_{m}=10^{-9}\) m\({}^{2}\)/s;  
\(h\)--height of the bed (m);  
\(V_{z}\)--volume of the bed (m\({}^{3}\));  
\(V_{p}\)--volume of the tube dosing the PAC suspension (m\({}^{3}\));  
\(A_{z}\)--wetted surface area of the bed particles (m\({}^{2}\));  
\(d_{50}\)--average diameter of the bed particle (m), \(d_{50}=0.00095\) m;  
\(\rho_{p,sorb}\)--apparent sorbent density (g PAC/m\({}^{3}\) of bed);  
\(\rho_{0,p,sorb}\)--standard apparent sorbent density (g PAC/m\({}^{3}\) of bed), assumed as \(\rho_{0,p,sorb}=1000\) g PAC/m\({}^{3}\) of the bed  
\(v_{w}\)--kinematic water viscosity (m\({}^{2}\)/s), assumed \(v_{w}=10^{-6}\) m\({}^{2}\)/s;  
\(\epsilon\)--porosity (m\({}^{3}\) of pores/m\({}^{3}\) of bed).