Kinetics-based development of two-stage continuous fermentation of 1,3-propanediol from crude glycerol by Clostridium butyricum

Table 7 Kinetics-based design of two-stage continuous fermentations and their experimental verification

Conditions	C_f (g/L)	\(D_{1}\)	\(D^{\prime}_{1}\)	Groups	\(C_{S}\)	Biomass	1,3-PDO	Butyrate	Q_PDO	Q_Biomass	MRE (%)	\(V_{2}\)/\(V_{1}\)
Conditions	C_f (g/L)	(h⁻¹)		Groups	(g/L)				(g/(L·h))		MRE (%)	\(V_{2}\)/\(V_{1}\)
No constraint	92	0.341	0.358	PV	30.12	3.38	31.45	4.50	11.26	1.12	4.2	11.9
No constraint	92	0.341	0.358	EV	28.28	3.60	31.72	4.93	11.36	1.29	4.2	–
\({8 } \le C_{{\text{S}}}\) ≤ 20 g/L \(C_{{{\text{PDO}}}}\) ≥ 45 g/L	102	0.200	0.214	PV	10.11	4.09	45.49	7.34	9.73	0.88	12.5	6.9
	102	0.200	0.214	EV	7.04	3.95	44.62	7.42	9.55	0.85	12.5	–
\({8 } \le C_{{\text{S}}}\) ≤ 20 g/L \(C_{{{\text{PDO}}}}\) ≥ 55 g/L	126	0.131	0.142	PV	9.21	4.16	55.06	10.00	7.82	0.59	10.7	4.4
	126	0.131	0.142	EV	7.64	4.24	54.27	12.34	7.71	0.60	10.7	–

PV: the predicted values; EV: the experimental values; V₂/V₁: the predicted volume ratio of two reactors in a two-stage fermentation to achieve 80 g/L 1,3-PDO at the second stage

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