The viscosity of a fermentation broth containing exopolysaccharide is about 10 000 cP. The broth is stirred in an aerated 10 m 3 fermenter of diameter 2.3 m using a single 0.78-m diameter turbine impeller. Other properties of the broth are as follows:

 

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= 2 kJ kg-¹°C-1 k=2Wm-1°C-1 = 10³ kg m-3. kfb P The fermenter is equipped with an internal cooling-coil which provides a heat-transfer area of 14 m². Cooling water is pro- vided; the average temperature difference for heat transfer is 20°C. Neglect any variation of viscosity at the wall of the coil. Assume that the power dissipated in aerated broth is 40% lower than in ungassed liquid. (a) Using logarithmic coordinates, plot Q as a function of stirrer speed between 0.5 and 10 s-¹. (b) From equations presented in Section 7.10, calculate W, the power dissipated from the stirrer, as a function of stir- rer speed. Plot these values on the same graph as Q. (c) If evaporation, heat losses and other factors have only a negligible effect on heat load, the difference between Q and W is equal to the rate of metabolic heat removal from the fermenter, AĤn. Plot AĤn as a function of stirrer speed. rxn (d) At what stirrer speed is removal of metabolic heat most rapid? (e) The specific rate of oxygen consumption is 6 mmol g h-1. If the fermenter is operated at the stirrer speed identi- fied in (d), what is the maximum cell concentration? (f) How do you interpret the intersection of the curves for Q and W, at high stirrer speed in terms of the capacity of the system to handle exothermic reactions? = 2 kJ kg-¹°C-1 k=2Wm-1°C-1 = 10³ kg m-3. kfb P The fermenter is equipped with an internal cooling-coil which provides a heat-transfer area of 14 m². Cooling water is pro- vided; the average temperature difference for heat transfer is 20°C. Neglect any variation of viscosity at the wall of the coil. Assume that the power dissipated in aerated broth is 40% lower than in ungassed liquid. (a) Using logarithmic coordinates, plot Q as a function of stirrer speed between 0.5 and 10 s-¹. (b) From equations presented in Section 7.10, calculate W, the power dissipated from the stirrer, as a function of stir- rer speed. Plot these values on the same graph as Q. (c) If evaporation, heat losses and other factors have only a negligible effect on heat load, the difference between Q and W is equal to the rate of metabolic heat removal from the fermenter, AĤn. Plot AĤn as a function of stirrer speed. rxn (d) At what stirrer speed is removal of metabolic heat most rapid? (e) The specific rate of oxygen consumption is 6 mmol g h-1. If the fermenter is operated at the stirrer speed identi- fied in (d), what is the maximum cell concentration? (f) How do you interpret the intersection of the curves for Q and W, at high stirrer speed in terms of the capacity of the system to handle exothermic reactions?

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b 10000 cP From Table A9 Appendix A 1 cP 103 kg m s therefore 10000 103 kg m s 10 kg ms kfb 2 W m C1 ... View the full answer