The bioconversion of glucose to ethanol is carried out in a packed-bed, immobilized cell bioreactor containing yeast cells entrapped in Ca?alginate beads. The rate-Iimiting substrate is glucose, and its concentration in the feed bulk liquid phase is S _0i ,- = 5 g/l. The nutrient flow rate is F = 2 I/min. The particle size of Ca-alginate beads is D _p = 0.5 cm. The surface area of the alginate beads per unit volume of the reactor is a = 25 cm ² /cm ³ , and the cross?sectional area of the bed is A = 100 cm ² .

Following are the rate constants for this conversion:

The following rate expression:

Assuming a first-order reaction-kinetics (e.g., relatively low substrate concentrations), determine the required bed height for 80% conversion of glucose to ethanol at the exit stream.

Where

And

S/cm-h T -100 mg Ks = 10 mg S/cm S " Kg + S n-[n 1 6 tanh 36 1 30 k Ap Ds k: Ks Ds = 10 cm/s