Table 8.

Kinetic models applied for estimation of kinetic parameters and kinetic constants values for butanol production, biomass growth and substrate consumption for scale-up fermentation by 5L bioreactor and flask scale fermentation.

Parameter estimation	Fermentation process		Model
	Bioreactor scale up	Flask scale
Butanol production
P0 (g/L)	0.001	0.009	$P=\frac{P_0{P}_{\mathit{max}}{e}^{P_{t}t}}{P_{\mathit{max}}-P_0+P_0{e}^{P_{t}t}}$
Pmax (g/L)	17.005	13.822
Pt	0.0754	0.068
R2 (regression coefficient)	0.999	0.988
δ (variance)	0.0353	0.412
MSE	0.0413	0.1601
Biomass
X0	0.205	0.303	$X=\frac{X_0{X}_m{e}^{{\mu }_{0}t}}{X_m-X_0+X_0{e}^{{\mu }_{0}t}}$
Xm	1.742	1.710
μ0	0.241	0.189
R2 (regression coefficient)	0.975	0.981
δ (variance)	0.0098	0.0039
MSE	0.0218	0.0156
Glucose consumption
S0	50.80	50.30	$S=S_0-\frac{1}{Y_{p/s}}(P-P_0)+\frac{1}{Y_{x/s}}(X-X_0)$
YP/S	0.363	0.310
R2 (regression coefficient)	0.999	0.999
δ (variance)	0.06826	0.02032
MSE	0.04563	0.00378

Mean squares error (MSE).