Criteria for Scaling-Up Fermentors

Few steps are available for the so-called scale-up of fermentors, starting from the glass apparatus used in fundamental research investigations. Usually, chemical 

For anaerobic fermentation, the unaerated stirred tank discussed in Section 7.4 is used almost exclusively. One criterion for scaling-up this type of bioreactor is the power input per unit liquid volume of geometrically similar vessels, which should be proportional to N3 L2 for the turbulent range and to N2 for the laminar range, where N is the rotational stirrer speed and I is the representative length of the vessel. 

In order to minimize any physical damage to the cells, the product of the diameter d and the rotational speed N of the impeller - which should be proportional to the tip speed of the impeller and hence to the shear rate at the impeller tip -becomes an important criterion for scale-up. 

If the rate of heat transfer to or from the broth is important, then the heat transfer area per unit volume of broth should be considered. As the surface area and the liquid volume will vary in proportion to the square and cube of the representative length of vessels, respectively, the heat transfer area of jacketed vessels may become insufficient with larger vessels. Thus, the use of internal coils, or perhaps an external heat-exchanger, may become necessary with larger fermentors. 

Aerated stirred tanks, bubble columns and airlifts are normally used for aerobic fermentations. One criterion of scaling-up an aerated stirred tank fermentor is kLa, an approximate value of which can be estimated using Equations 7.36 or 7.36a. For the turbulent range, a general correlation for kLa in aerated stirred fermentors is of the following type [3]  

For a range of gas rates, the sum of gas compressor power plus agitator power becomes almost minimal [12]. 

---

When the fermentor in Problem 7.8 is scaled up to a geometrically similar tank of 1.8 m diameter, show the criteria for scale-up and determine the aeration rate and rotational stirrer speed. 

---