Question

The following gas-phase reaction takes place in a plug flow reactor (a tubular reactor) that has a diameter of 6 inches and cross-sectional area of 0.0388 ft²: A --> B + C. The reaction rate depends only on the concentration of A, C_A, and has the following form: rate of destruction of A = k * C_A , where k= 0.12 s^-1. The feed consists of pure A, and enters the reactor at a volumetric flowrate of 0.193 ft³/s. Determine the required length of the tubular reactor (in feet, expressed as an integer) if the desired fractional conversion (X) is 0.80. Note that the volume of the reactor is the cross-sectional area * length. You may assume that the reactor operates ideally and isothermally, the pressure drop in the reactor is negligible, and the gas is ideal.

Answer 1

Reaction A = B + C with pure A

Extent of Reaction = (200-100)/100 = 1

Volume V =?

Volumetric flow rate vo = 0.193 ft3/s

Rate constant k = 0.12 s-1

-rA = k*CA = k CA0 (1-X)/(1+X)

= 0.12 * CA0 * (1-X)/(1+X)

= 0.12*CA0(1-X)/(1+X)

PFR design equation

V/FA0 = (dX /-rA)

V/CA0*vo = dX/[0.12*CA0(1-X)/(1+X)]

V*0.12/0.193 = dX(1+X) /(1-X)

0.6217 V = -2- ln(1-X)

V = -0.8-2*ln (1-0.8)/0.6217

V = 3.8907 ft3

volume of the reactor = cross-sectional area * length

3.8907 ft3 = 0.0388 ft2 x L

L = 100.270 ft