A 10-m stirred fermenter with liquid height 2.3 m is used to culture Trichoderma reesei for production of cellulase. The density of the culture fluid is 1000 kg m3. An equation for the oxygen transfer coefficient as a function of operating variables has been developed for T reesei broth kLa=2.5 × 10^-3(Pt/vL)^0.7 u0.3G
where kLa has units of s1, Pr is the total power input in W, Vi is the liquid volume in m3, and ug is the superficial gas velocity in m s The fermenter is sparged using a gas flow rate of 0.6 vvm (vvm means volume of gas per volume of liquid per minute). The vessel is stirred with a single impeller but two alternative impeller designs, a Rushton turbine and a curved-blade disc turbine, are available. Both impellers are sized and operated so that heir ungassed power draw is 9 kW
(a) If the power loss with gassing is 50% for the Rushton and 5% for the curved-blade turbine, compare the kia values achieved using each impeller.
(b) What is the percentage contribution to PT from gassing with the two different impellers?
(c) If the cell concentration is limited to 15g1 using the Rushton turbine because of mass transfer effects, estimate the maximum possible cell concentration with the curved-blade disc turbine It is decided to install the Rushton turbine, but to compensate for the effect on kia of its loss of power with gassing by increasing the gas flow rate
(d) Estimate the gas flow rate required to obtain the same maximum cell concentration using the Rushton turbine as that achieved with the curved-blade disc turbine. Express your answer in vvm. What are your assumptions? (Iterative solution may be required.)