Table 6 Analyzed kinetic models.

COD

1st order

\(\frac{{ - {\text{d}}s}}{{{\text{d}}t}} = \frac{Q}{v}\left( {s_{0} - s_{e} } \right) - k_{1} s_{e}\)

\(\frac{{s_{0} }}{{s_{e} }} - 1 = k_{1} HRT\)

K₁ = 1.213

–

0.761

Grau 2nd order Model

\(\frac{{ - {\text{d}}s}}{{{\text{d}}t}} = \frac{{k_{2} xs_{e} 2}}{{s_{0}^{2} }}\)

\(\frac{{s_{0} }}{{s_{0} - s_{e} }}HRT = {\raise0.7ex\hbox{${HRT - S_{0} }$} \!\mathord{\left/ {\vphantom {{HRT - S_{0} } {k_{2} x}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${k_{2} x}$}}\)

–

K_s = 10^–05

0.982

Modified Stover-Kincanna model

\(- \frac{{{\text{d}}s}}{{{\text{d}}t}} = \frac{Q}{v}\left( {\frac{{s_{0} - s_{e} }}{{s_{0} }}} \right) = \frac{{U_{M} \frac{{Qs_{0} }}{v}}}{{k_{B} + \frac{{Qs_{0} }}{v}}}\)

\(\frac{v}{{Q\left( {s_{0} - s_{e} } \right)}} = \frac{{k_{B} v}}{{U_{M} s_{0} Q}} + \frac{v}{{U_{M} }}\)

K_B = 0.35

U_M = 1.73

0.978

Monod Model

\(- \frac{{{\text{d}}s}}{{{\text{d}}t}} = \frac{Q}{v}\left( {\frac{{s_{0} - s_{e} }}{{s_{0} }}} \right) = \frac{{U_{M} \frac{{Qs_{0} }}{v}}}{{k_{B} + \frac{{Qs_{0} }}{v}}}\)

\(\frac{vx}{{Q\left( {s_{0} - s_{e} } \right)}} = \frac{{k_{s} }}{{ks_{e} }} + \frac{1}{k}\)

K = 0.062

K_s = 0.073

0.991