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Table 1 Reaction kinetic models

From: Novel pre-treatment of zeolite materials for the removal of sodium ions: potential materials for coal seam gas co-produced wastewater

Model Non-linear equation Linear equation Model parameters  
Pseudo-first order \( q_{t} = q_{e} (1 - e^{{ - k_{1} t}} ) \) \( \log (q_{e} - q_{t} ) = \log (q_{e} ) - k_{1} t \) \( q_{e} ,K_{1} \) Equation 2
Pseudo-second order \( q_{t} = \frac{{q_{e}^{2} k_{2} t}}{{(1 + q_{e} k_{2} t)}} \) \( \frac{t}{{q_{t} }} = \frac{1}{{k_{2} q_{e}^{2} }} + \left( {\frac{1}{{q_{e} }}} \right)t \) \( q_{e} ,K_{2} \) Equation 3
Elovich \( q_{t} = \left( {\frac{1}{b}} \right)\ln (abt + 1) \) \( q_{t} = \frac{\ln (ab)}{b} + \frac{\ln (t)}{b} \) a, b Equation 4