ABSTRACT
The hold-up or void fraction, E (-), is the volume of gas, V g (m3), present in a fermentation broth, expressed as a fraction of the total volume, V g + V I (m3).
(-) 10.1
If v bw (m s-1) is defined as the velocity of the bubbles relative to the vessel wall, the hold-up can be derived as
pressure-corrected gas superficial velocity
(-) 10.2
The gas superficial velocity is corrected for the local pressure as this determines the actual gas volume in the reactor. U bw is the sum of U bs (m S-l), the bubble rise velocity, or "slip" velocity, relative to the surrounding liquid, and v lw (m S-l), the velocity of the liquid relative to the vessel wall. Eq. (10.2) can then be rewritten as
(-) 10.3
The liquid velocities are strongly dependent on reactor type and process conditions as shown in Chapter 9. The bubble slip velocity is related to the
single bubble rise velocity v br in an infinite medium. This velocity is given in Fig. 10.1.
