A hollow-fiber membrane device is operated to achieve the fermentation of glucos

Question

A hollow-fiber membrane device is operated to achieve the fermentation of glucose to ethanol using yeast cells. Yeast cells are immobilized on the outside wall of the hollow-fiber (i.e., the yeast are in the outer, annular space). Once immobilized, the yeast cells cannot reproduce, but they can convert glucose to ethanol according to the equation:

C6H12O6 --> C2H6O + CO2

The aqueous feed stream for the yeast cells contains 10.0 wt% glucose, the rest of the stream can be considered water. The aqueous feed for yeast cells enters the annular space in the reactor at 40 kg/min. An organic solvent enters the fiber membrane lumen space at a mass flow rate of 40 kg/min.

The membrane is constructed of a polymer that repels organic solvents. Thus, the solvent cannot penetrate the membrane, and the yeast cells are relatively unaffected by its toxicity. Glucose and water are insoluble in the solvent, and these compounds remain in the annular space, they do not cross the membrane. On the other hand, ethanol is soluble in the solvent; much of the ethanol passes through the membrane into the solvent and leaves dissolved in the solvent stream in the membrane fibers. The by-product CO2 gas exits from the annular region through an escape valve. The aqueous stream leaving the annular space contains 0.20 wt% glucose and 0.50 wt% ethanol.

(a) What is the fractional conversion of glucose?

(b) What is the reaction rate, R, of the stream?

(c) Determine the mass flow rates of glucose in the aqueous stream and of ethanol in the aqueous and solvent streams.

(d) Determine the mass flow rate of ethanol across the membrane.

(e) Determine the outlet mass and volumetric flow rates of CO2.

Explanation / Answer

(a) the original aqueous stream had 10 wt% glucose the leaving stream had 0.2 wt% glucose so conversion is 98 %.

(b) rate of reaction is conversion /time R = k Ca    since 98% conversion happens and the flow is 40 kg/min. Rate constant depends on volume which we do not have so assuming that the volume is 1 we can write rate to be Fglucose/Fglucose+Fethanol with 98% conversion we see Rate is 0.51.

(c) conversion is 98% concentration of glucose is 10 wt% so flow rate of glucose in aqueous stream is 4Kg/min and flow rate of ethanol in solvent stream is 3.72Kg/min (since 0.5 wt% is still in aqueous phase) and in aqueous stream is 0.2kg/min.

(d) mass flow rate of ethanol across the membrane is 3.72 Kg/min.

(e) 98% conversion means for 10 wt% material at 40 kg/min. Flow of glucose is 4 Kg/min and Molecular weight of glucose is 180 and that of CO2 is 44. CO2 to glucose fraction is 0.24, Thus flow rate of CO2 is 0.958kg/min, by volume it is (ideal gas case) 487L/min.

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