## 6 Conclusions  
Powdered activated carbon can be used in water treatment during both coagulation and filtration processes. If a homogeneous or batch reactor is used, lower adsorption effects are observed than in a filter bed to which PAC is introduced. The filter with PAC works as an advection-dispersion reactor in which adsorption process proceeds faster than in other types of reactors. In such a reactor, the average difference between the concentration of contaminants in water and the equilibrium concentration is larger than in other types of reactors. In particular:  
1. At a low velocity, doubling \(V_{x}^{*}\) increases the capillary turbulent diffusion coefficient \(D_{x}^{*}\) by 3.5 times; in the medium range, doubling \(V_{x}^{*}\) increases \(D_{x}^{*}\) by 3.1 times; and in the high velocity range, such an increase results in an increase in \(D_{x}^{*}\) by 3.0 times. 2. In the velocity range \(V_{x}^{*}\in\langle 0.1\cdot 10^{-2}\); \(1.06\cdot 10^{-2}\rangle\) m/s and with the density \(\rho_{p,sorb}\) changing from 3000 to 12,000 g PAC/m\({}^{3}\) of bed, the coefficient \(D_{x}^{*}\) changes by 1.34 times. 3. In the capillary velocity range \(V_{x}^{*}\in\langle 0.15\cdot 10^{-2}\); \(0.72\cdot 10^{-2}\rangle\) m/s and with a change in the apparent density of the sorbent \(\rho_{p,sorb}\) from 3000 to 12,000 g PAC/m\({}^{3}\) of the bed, it was established that the actual coefficient of longitudinal dispersion \(D_{x}^{*}\) varies in the range of \(0.16\cdot 10^{-4}\) to \(2.03\cdot 10^{-4}\) m\({}^{2}\)/s. 4. When changing the apparent density of the sorbent from 3000 to 12,000 g PAC/m\({}^{3}\) of the bed, the \(k\cdot a_{m}\) value changes by 3.2 times; this change is slightly smaller than for the sorbent apparent density. 5. In the capillary velocity range \(V_{x}^{*}\in\langle 0.15\cdot 10^{-2}\); \(0.72\cdot 10^{-2}\rangle\) m/s and with a change in the apparent density of the sorbent \(\rho_{p,sorb}\) from 3000 to 12,000 g PAC/m\({}^{3}\) of the bed, the product of the constant mass transfer rate and the specific outer surface of sorbent \(k\cdot a_{m}\) varies in the range of \(2.23\cdot 10^{-7}\) to \(1.70\cdot 10^{-6}\) (m/s)-(m\({}^{2}\)/g PAC). 6. Doubling the filtration velocity \(V_{x}^{*}\) increases the \(k\cdot a_{m}\) value by approximately 1.5 times, while quadrupling it increases the \(k\cdot a_{m}\) value approximately by 2.4 times. 7. An increase in the apparent density of the sorbent \(\rho_{p,sorb}\) from 3000 to 12,000 g PAC/m\({}^{3}\) of the bed may increase the adsorption coefficient \(\Gamma^{*}\) by about 5.1 times and \(\Gamma\) by about 1.2 times. 8. The Re number affects the adsorption equilibrium constant and can cause changes in \(\Gamma^{*}\) by about 1.23 times for \(\rho_{p,sorb}\in\langle 3000\); 12,000) g PAC/m\({}^{3}\) of bed and changes of \(\Gamma\) by approximately 1.2 times. This means that turbulent diffusion affects the adsorption isotherm coefficient of the powdered sorbent; the particles of sorbent may partially overlap each other. A turbulent motion may promote the transport of adsorbate into the aggregated particles, increasing the adsorption capacity. 9. In the capillary velocity range \(V_{x}^{*}\in\langle 0.15\cdot 10^{-2}\); \(0.72\cdot 10^{-2}\rangle\) m/s and with a change in the apparent density of the sorbent \(\rho_{p,sorb}\) from 3000 to 12,000 g PAC/m\({}^{3}\) of the bed, the [PERSON] constant \(\Gamma^{*}\) varies in the range of 7.24 to 44.20 1/m\({}^{3}\) of sorbent and the Henry constant \(\Gamma\) varies in the range of 0.0012 to 0.0019 m\({}^{3}\) of water/g PAC. 10. Equations comprising dimensionless criterion numbers (Re, _Pe, Nu_) and similarity moduli can be used to determine the parameters of the adsorption model that facilitate the design of filters with PAC. 11. The high organic removal observed in a filter with PAC means that the PAC dose per unit volume of treated water may be several times lower than such a dose in a homogeneous flocculator at the same average effluent adsorbate concentration. 12.