The bacteria acetobacter aceti convert ethanol to acetic acid in the presence of oxygen according to the reaction

In a continuous fermentation process, ethanol enters the top of the fermenter at a rate of 145 kg/h, and the air fed to the bottom of the fermenter is 25% in excess of the amount required to consume all of the ethanol. A gas stream containing nitrogen and unreacted oxygen leaves the top of the fermenter, and a liquid stream containing acetic acid, water, and 10% of the entering ethanol leaves the bottom.
Assume that none of the ethanol, water, and acetic acid in the reactor is vaporized. The fermenter operates at 30°C, maintains a liquid (SG = 0:95) height of 4.5 m, and is open to the atmosphere (i.e., the pressure at the top of the fermenter is 1 atm).
(a) What is the volumetric flow rate of air as it enters the bottom of the fermenter? What is the volumetric flow rate of gas leaving the top of the fermenter?
(b) Assume a linear relationship between the fraction of oxygen reacted and the position of gas bubbles rising through the liquid in the fermenter: for example, half of the oxygen reacted is consumed in the bottomhalf of the fermenter. At the vertical midpoint of the fermenter, the average bubble diameter is 1.5mm. What is the average bubble diameter at the entry point of the air and as the gas leaves the liquid at the top of the fermenter?
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(c) What difference does the bubble size make in the design and operation of the fermenter?

Transcribed Image Text:

С,НОН + 0, — CҢ, СООН + Н,0