Table 2 Geometrical details of reactors and parameters used for scale-up experiments

Reactor configurations

 Filling volume [m³]

\({V}_{L}\)

0.001

0.004

0.04

0.2

 Reactor diameter [m]

\({D}_{R}\)

0.11

0.16

0.3

0.6

 Stirrer diameter [m]

\({d}_{r}\)

0.044

0.064

0.135

0.196

 Stirrer height [m]

\({h}_{r}\)

0.009

0.015

0.027

0.04

 Number of stirrers

\({S}_{N}\)

2

2

2

2

Scale-up parameters (Eqs. 1–6)

 Maximum local energy dissipation rate [W/kg]

\({\varepsilon }_{max}\)

3.92

3.92

3.92

3.92

 Ratio of maximum to specific energy dissipation rate (aerated)

\({\Phi }_{g}\)

2.36

3.02

4.58

7.83

 Ratio of maximum to specific energy dissipation rate (unaerated)

\(\Phi\)

36.54

41.45

51.75

82.86

 Estimated volumetric gas transfer coefficient [1/h] [25]

\({k}_{L}a\)

41.7

57.6

74.3

74.1

 Volumetric power input (aerated) [kW/m³]

\({P}_{g}\)

1.66

1.3

0.86

0.50

 Gas velocity [m/s]

\({u}_{g}\)

5.26 × 10^–4

9.95 × 10^–4

2.83 × 10^–3

3.54 × 10^–3

 Power number

\({P}_{O}\)

8.26

7.6

6.5

5.56

 Stirring rate [1/s]

\({n}_{r}\)

10.83

8.88

5.41

4.29