A hollow-fiber membrane device is operated to achieve the fermentation of glucose to alcohol using yeast cells. Yeast cells are immobilized on the outside walls of the hollow fibers (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 40.0 kg/min. An organic solvent enters the fiber membranes at a mass flow rate of 40.0 kg/min.

The membrane is constructed 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 (i.e., they do not cross the membrane into the solvent). 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.

What is the fractional conversion of glucose?

What is the reaction rate, R, of the system?

Determine the mass flow rate of ethanol across the membrane.

Determine the outlet mass flow rates of glucose in the aqueous stream and of ethanol in the aqueous and solvent streams?

Determine the outlet mass and volumetric flow rates of CO₂.