In the Name of God

Bioreactor Design Homework 2 Due Date :93.3.21 1-The power consumption by an agitator in an unbaffled vessel can be expressed as

Can you determine the power consumption and impeller speed of a l000-gallon fermenter based on findings of the optimum condition from a one-gallon vessel by using the same fluid system? Is your conclusion reasonable? Why or why not? 2- A fermenter containing 10 m3 of medium (25°C) is going to be sterilized by passing saturated steam(500 kPa, gage pressure) through the coil in the fermenter. The typical bacterial count of the medium is about 3x1012 m-3, which needs to be reduced to such an extent that the chance for a contaminant surviving the sterilization is 1 in 100. The fermenter will be heated until the medium reaches 115°C. During the holding time, the heat loss through the vessel is assumed to be negligible. After the proper holding time, the fermenter will be cooled by passing 20 m /hr of 25°C water through the coil in the fermenter until the medium reaches 40°C. The coils have a heat-transfer area of 40 m and for this operation the average overall heat-transfer coefficient for heating and cooling are 5,500 and 2,500 kJ /hr m K, respectively. The heat resistant bacterial spores in the medium can be characterized by an Arrhenius coefficient( kd ) of 5.7 x 1039 hr-1 and an activation energy(Ed) of 2.834 x 105 kJ/kmol. The heat capacity and density of the medium are 4.187 kJ /kgK and 1,000 kg/m3 ,respectively. Estimate the required holding time.