1. A mixer applying 150 kW to the mixer shaft is operating in a batch fermentation at a cell concentration of 20gII. Associated with the mixer is a blower, which is providing air at a total expansion horsepower of 37 kW leaving the sparge ring. The cost of power is 0.50/MJ. Use an overall energy efficiency for the equipment of 0.9.
The cost of the mixer plus the associated blower required, plus installation of both is $900/kW with an impeller diameter to tank diameter ratio of 0.35.
By using large diameter impellers at slower speeds, the maximum impeller zone fluid shear rate can be changed, and the cost of the mixer/kW must be changed accordingly. The cost of the mixer can be approximated to change inversely proportional to the maximum impeller zone fluid shear rate to the 2.3 exponent
The particular antibiotic requires 200 mols of oxygen for each kg of product produced. The total production cost of the antibiotic is estimated as $60/kg, of which $30 is a fixed cost, independent of productivity of the fermenter, and $30 is the cost associated with the actual fermentation tank itself.
At 20 g// cell concentration, the mixer is capable of transferring 6.4 mols of oxygen per MJ.
It is proposed to increase the solids concentration in the system to 40 gII, which will effectively double the productivity of the fermentation tank itself. The oxygen transfer activity of the mixer is lowered, due to the increased viscosity, to 4 mol of oxygen per MJ.
Assuming that the mixer is operated for 250 days per year, and using a 5-year evaluation period, calculate the cost of mixing, capital and operating, in this process, and the percentage cost of mixing under the present operation.
At 40 g// of cells, the process horsepower required may be estimated as being proportional to the cell concentration to the 1.4 exponent
(Process mixer hp) oc (cell concentration)1-4
This takes into account the transfer rate due to the change in viscosity and the additional transfer rate needed because of the increase in total biomass in the system.
Calculate the cost of mixing in the new revised system at 40 g//, the total mixer horsepower (air horsepower is in the same proportion as at 20 g//), and reduction in antibiotic production cost.
2. The new larger mixer has a higher maximum impeller zone shear rate, which is estimated at 1.4 times as high as a small unit at the same D/T ratio. Assume that this higher shear rate has cut the productivity of the increased cell concentration to 90% of its normal value. In this case, assuming that the mixer is not changed, calculate the cost of mixing and the percent mixing cost/total product cost, and the savings compared to the original 150 kW mixer.
3. A new mixer has been designed at the same total horsepower, but with a shear rate 1.2 times as high as the previous 150 kW unit.
Calculate the new capital cost of mixing and calculate the total mixing cost and increase in productivity over the original smaller unit.
4. A large diameter impeller at a slower speed would require a larger mixer drive, to reduce the shear rate to the same as it was in the original 150 kW unit. Again calculate the cost of the mixer, mixing cost per MJ and calculate the percent mixing cost/total product cost, as well as the percent savings over the original 150 kW mixer.
238 Fermentation and Biochemical Engineering Handbook 11.0 SOLUTION—FERMENTATION PROBLEMS
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