Consider an ideal ternary mixture composed of components cis2-butene (
), cis2-hexene (
), and cis2-pentene (
). This mixture is subject to an equilibrium-limited chemical reaction
(metathesis or disproportionation of olefins: 2
cis2-pentene ⇌ cis2-butene + cis2-hexene) with reaction rate
, where the equilibrium constant
cal/(mol K). This mixture is fed to a reactive distillation column operating at a pressure of 3 atmospheres with 13 plates; the feed stage location is stage 5, the reactive stages go from stages 2 to 7, and the feed composition contains 100% mole
or pure cis2-pentene. The feed flow rate is chosen to be 100 kmol/hr. For simplicity, we assume constant molal overflow (CMO) and neglect heat effects.
This Demonstration shows three profiles: (1) the composition versus plate number for components
(in red, blue, and green, respectively) with the reactive zone shown in light blue and (2) a ternary diagram with the composition of
versus the composition of
in % mole, and (3) the temperature profile in the column. In the second profile, the feed composition is shown by a magenta dot and the reactive stages 2 to 7 are displayed in blue.
The molar hold-up (in kmol) in the reactive plates is set by the user. The reboil ratio is chosen so that distillate and bottom flow rates are equal (i.e.,
is the reboil ratio and
is the reflux ratio).
For high hold-up values (i.e., high Damköhler numbers) one recovers the equilibrium case shown by the green curve in the ternary diagram.