Optimization study of the adsorption of malachite green removal by MgO nano-composite, nano-bentonite and fungal immobilization on active carbon using response surface methodology and kinetic study

Environmental Sciences Europe

Table 12 Various kinetic models for effect of substrate on growth rate

Models	Equation	μmax (h^–1)	K_s (mg/L)	K_i	S_m	n	m	RMSE	AICc	AF	R²
Haldane	\(\mu = \frac{\mu \max S}{{\left( {S + KS + \frac{{S^{2} }}{Ki}} \right)}}\)	1.02	70	70	–	–	–	0.05	− 31.8	0.94	0.961
Han and Levenspiel	\(\mu = \frac{{\mu \max S\left[ {1 - \left( \frac{S}{Sm} \right)} \right]n}}{{\left( {S + KS - } \right)\left[ {1 - \left( \frac{S}{Sm} \right)} \right]m}}\)	1.1	100		360	1	1	0.06	− 26.8	0.91	0.922
Luong	\(\mu = \frac{{\mu \max S\left[ {1 - \left( \frac{S}{Sm} \right)} \right]n}}{{\left( {S + KS} \right)}}\)	1.01	140		400	1		0.09	− 20.2	0.88	0.843
Aiba	\(\mu = \frac{{\mu \max S \exp \left( { - S/Ki} \right)}}{{ \left( {S + KS} \right)}}\)	1.6	150	150	–	–	–	0.06	− 27.45	0.91	0.822
Monod	\(\mu \max = \frac{S}{KS}\)	0.9	120		–	–	–	0.3	7.5	0.79	0.69

q_max: maximal reduction rate (h⁻¹); k_s: half saturation constant for maximal reduction (mg/dm³); S_m: maximal concentration of substrate tolerated (mg/dm³); m, n, k: curve parameters; S: substrate concentration (mg/dm³); RMS: residual mean square