Problem:

A feed mixture with a flow rate of $2000$kmo$\frac{l}{h},$ containing components $A,B,C,$ and $D,$ is provided. The objective for the selected system is to achieve a minimum recovery of $90\%$ of the most volatile component from the feed in the top product. The composition of the mixture, in order of decreasing volatility, is $x_A=0\mathrm{.}40,x_B=0\mathrm{.}25,x_C=0\mathrm{.}20,$ and $x_D=0\mathrm{.}15.$

$*$In the case where the proposed mixture could not lead to the desired minimum recovery of $90\%,$ you may adjust the value$($s$)$ accordingly.

The column operates under a pressure of $1$ atm absolute$,$ and the feed is in a liquid state at its boiling point at this pressure. Your task is to determine the appropriate operating reflux ratio for the column and provide a justification for your choice.

Assigned alcohol mixture $-3,7,11$ and $12$

$\backslash$table$[[$I$,$Component,Boiling point $)],[$A$,2-$methyl$-2-$propanol,$82\mathrm{.}0],[$B$,$n$-$Butanol,$117\mathrm{.}7],[$C$,$Hexanol,$157\mathrm{.}0],[$D$,1-$Heptanol,$175\mathrm{.}8]]$Part A $(60$ marks$)$

a$)$ Determine the flow rates and compositions of the distillate and bottoms product, indicating the selection of the light key and heavy key components. Specify the source of the utilized $K$ values. $(8$ marks$)$

b$)$ Determine the temperatures at the top $($dew point$)$ and bottoms product $($boiling point$).$

marks$)$

c$)$ Calculate the minimum number of stages required. $(5$ marks$)$

d$)$ Validate the component distribution using the minimum number of stages obtained in part c$).(7$ marks$)$

e$)$ Assess if the obtained dew point, boiling point, and minimum number of stages from part b$)$ need to be revised based on the composition obtained in part d$).(7$ marks$)$

f$)$ Calculate the minimum reflux ratio. $(5$ marks$)$

g$)$ Determine the operating reflux ratio and justify the chosen value. $(8$ marks$)$

h$)$ Calculate the number of theoretical stages and indicate the method used $($e$.$g$.,$ ErbarMaddox, Gilliland, or Molokanov$).(5$ marks$)$

i$)$ Determine the location of the feed tray. $(5$ marks$)$

Part B $(40$ marks$)$

To propose a preliminary design of the distillation column, the following elements should be considered:

a$)$ Estimate the column efficiency by taking into account the fluid viscosity and the selected tray type. Provide a justification for the chosen tray type. $(6$ marks$)$

b$)$ Calculate the actual number of trays based on the theoretical number of trays and the overall column efficiency. $(3$ marks$)$

c$)$ Determine the precise location of the feed tray. $(4$ marks$)$

d$)$ Estimate the height of the column. $(5$ marks$)$

e$)$ Calculate the diameter of the column based on the ratio of vapor to liquid flow rates. Use a design velocity for the vapor phase that is within the range of $75-85\%$ of the flooding velocity. $(10$ marks$)$

$2$

f$)$ Check for the possibility of weeping. $(6$ marks$)$

g$)$ Verify the ratio of column height to diameter. $(3$ marks$)$

h$)$ Propose the suitable material for constructing the column and trays, providing a justification for the selection. $(3$ marks$)$

Optional $($for bonus points$)$:

a$)$ Calculate the reboiler duty and the flow rate of heating element required. Propose the heating element and the condition at which it will be supplied. $(10$ marks$)$

b$)$ Calculate the condenser duty and the flow rate of cooling element required. Propose the cooling element and the condition at which it will be supplied. $(10$ marks$)$