Adsorption on Powdered Activated Carbon (PAC) Dosed into an Anthracite-Sand Filter in Water Treatment—Model and Criterion Equations

This paper presents research on the mass dispersion and adsorption of organics present in tap water on powdered activated carbon (PAC) in a two-layer filter column. The adsorption rate depends on the difference between the concentration of organics and the equilibrium concentration. In homogeneous flocculators with simultaneous adsorption on PAC, the concentration difference is lower than in a filter column with PAC. Therefore, the utilization of the PAC’s adsorption capacity in filters is higher than in homogeneous flocculators. PAC is introduced into the upper anthracite layer of a filter bed, while the bottom layer is a sand layer, which protects the underdrain system from becoming clogged with PAC particles. The sorbent wis introduced into the bed in the final phase of filter backwashing. The authors present a model of adsorption on PAC in a filter column. Both experiments and calculations confirmed a better utilization of PAC’s adsorption capacity in the filter column compared to its utilization in a homogeneous flocculator. Three criterion equations were developed using dimensionless numbers, Re, <i>Pe</i> and <i>Nu</i>, as well as two similarity moduli related to a sorbent apparent density and an adsorption coefficient. Additionally, a relationship between the Peclet number (<i>Pe</i>) and the Reynolds number (Re) as well as the similarity modulus for the sorbent apparent density were determined for the mass dispersion process. The relationship between the diffusive Nuselt number (<i>Nu</i>) and the Re number as well as the similarity modulus for the sorbent apparent density were determined for the parameter describing an adsorbate permeation rate across a water–sorbent interface. The impact of the Re number and the similarity modulus for the sorbent apparent density on the Henry constant was also investigated. The criterion equations can be used to determine the adsorption model parameters; they may be helpful in designing a filtration system supplemented with PAC. In the capillary velocity range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>V</mi><mi>x</mi><mo>*</mo></msubsup></mrow></semantics></math></inline-formula> ∈ ⟨0.15·10⁻²; 0.72·10⁻²⟩ m/s and with a change in the apparent density of the sorbent <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ρ</mi><mrow><mi>p</mi><mo>,</mo><mi>s</mi><mi>o</mi><mi>r</mi><mi>b</mi></mrow></msub></mrow></semantics></math></inline-formula> from 3000 to 12,000 g PAC/m³ of the bed, as a result of the experimental tests carried out, it was established that the actual coefficient of longitudinal dispersion <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>D</mi><mi>x</mi><mo>*</mo></msubsup></mrow></semantics></math></inline-formula> varied in the range of 0.16·10⁻⁴ to 2.03·10⁻⁴ m²/s, the product of the constant mass transfer rate and the specific outer surface of sorbent <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>⋅</mo><msub><mi>a</mi><mi>m</mi></msub></mrow></semantics></math></inline-formula> varied in the range of 2.23·10⁻⁷ to 1.70·10⁻⁶ (m/s)·(m²/g PAC), while the Henry constant Γ* varied in the range of 7.24 to 44.20 1/m³ of sorbent and the Henry constant Γ varied in the range of 0.0012 to 0.0019 m³ of water/g PAC.