A depropanizer has the following feed and constant relative volatilities:

Methane \((M): z_{M}=0.229, \alpha_{M-P}=9.92\)

Propane \((\mathrm{P}): \mathrm{z}_{\mathrm{P}}=0.368, \alpha_{\mathrm{P}-\mathrm{P}}=1.00\)

\(\mathrm{n}\)-Butane \((\mathrm{B}): \mathrm{z}_{\mathrm{B}}=0.322, \alpha_{\mathrm{B}-\mathrm{P}}=0.49\)

\(\mathrm{n}-\) Hexane \((\mathrm{H}): \mathrm{z}_{\mathrm{H}}=0.081, \alpha_{\mathrm{H}-\mathrm{P}}=0.10\)

Reflux is a saturated liquid. The feed is a saturated liquid fed at 1.0 \(\mathrm{kmol} /(\) unit time). Assume CMO.

a. \({ }^{*} \mathrm{~L} / \mathrm{D}=1.5, \mathrm{FR}_{\mathrm{P}, \text { dist }}=0.9854, \mathrm{FR}_{\mathrm{B}, \text { bot }}=0.8791\). Use the FUG method to estimate \(\mathrm{N}\).

b. If \(\mathrm{N}=20, \mathrm{FR}_{\mathrm{P}, \text { dist }}=0.9854\), and \(\mathrm{FR}_{\mathrm{B}, \mathrm{bot}}=0.8791\), estimate the required \(\mathrm{L} / \mathrm{D}\).

c. Find the split of normal hexane at total reflux using \(\mathrm{N}_{\text {min }}\).

d. \(\mathrm{L} / \mathrm{D}=1.5, \mathrm{FR}_{\mathrm{P}, \mathrm{dist}}=0.999, \mathrm{FR}_{\mathrm{B}, \mathrm{bot}}=0.8791\). Use the \(\mathrm{FUG}\) method to estimate \(\mathrm{N}\).

Do part a first. Parts of the solution of part a can be reused for the other parts b to d.