Derive an expression for concentration of substrate versus

Question

1. You are using a packed bed reactor to perform an enzymolysis step (S ® P). The catalyst particles are non-porous and spherical, and the enzyme is bound to the external surface. The particles are 6 um in diameter, and the void spacing of the packed bed is 0.8. If the cylinder housing is 2 inches in diameter, determine how long the reactor needs to be for 80% of the substrate to be converted to product at a flowrate through the column of 500 ml/min. Note: assume the mass transfer coefficient for the column at 500 ml/min is 5 x 10^-8 m/s.

2. In working with the packed bed reactor in problem 1 above, you notice that the reactor behaves the same (i.e. product concentration leaving the reactor) regardless of the viscosity of the fluid flowing through it.

a.) Does equation 10-64 from your class notes accurately describe the reactor performance? Why or Why not.

b.) Assume that the kinetics for the immbolized enzyme in this reactor limit the production of P (not mass transfer, as in question 1 above), and that the kinetics take on the standard Michaelis-Menton form:

(V (mol/m²s) = Vm"[S] / Km + [S]

With V_m" defined per unit of catalyst surface area

Derive an expression for Concentration of substrate versus the length of the packed bed reactor as a function of (V_m", K_m, ε_b, a, U, d_p and C_A0).

c.) Use the values given in problem 1 above. Assume that the reactor is NOT limited by mass transfer. Assume that K_m = 0.001 mol/l, that C_A0 = 1 mol/l. Using the reactor length calculated in problem 1, determine the V_m" (mol/m²s) value necessary to convert 80% of the substrate to product in the reactor.