Context:

The task is based around the use of a distillation column to separate a binary hydrocarbon

mixture, as shown in Figure $1$

rigure $1-$ Schemat$$c of dist$$llat$$on system and system properties for Task $2$

A mixture of components $1$ & $2$ are fed to the column at $F$ kmol$/$h$,$ with mole fraction $x_{1F}$ and

state $q.$ The column has an internal diameter of $D_{C}m$ and contains $N_R$ plates in the rectifying

section with a plate efficiency of $.$ The column operates at an absolute pressure of $P_C$ bar.

Vapour leaves the top of the column at Vkmo$\frac{l}{h}$ and passes through a partial condenser. The

condenser works by vaporising a propane refrigerant, which is maintained at pressure $P_p$ bar

with resultant temperature $T_{R}C.$ Top product leaves at Dkmo$\frac{l}{h}$ and a composition of $y_{1D},$

whilst the reflux stream is returned as a saturated liquid to the top of the column at Lkmo$\frac{l}{h}.$

The reflux ratio, $R,$ is defined as L$/$D$.$ At the bottom of the column some of the liquid leaving

passes through a reboiler with a duty of $Q_{B}kW,$ giving a saturated vapour flow of $V^{\text{'}}$kmo$\frac{l}{h}$

back into the column. Bottom product passes through a control valve with a flow coefficient

$C_V$ and downstream pressure of $P_0$ bar $($absolute$),$ at a flowrate of Wkmo$\frac{l}{h}$ with a molar

composition of $x_1.$ The primary measured parameters used for process control are $P_p$ at the

top of the column and $T_b$ at the bottom.

The plate efficiency varies with the superficial vapour velocity within the column, $u\frac{m}{s},$ and

can be estimated by:

$=10[e^{-5u}-e^{-6u}]$

Liquid feed and product streams can be assumed to have a latent heat, ${}_{\text{a}\text{v}\text{g}}$ of $12,000k\frac{J}{k}$mol,

a density ${}_{\text{a}\text{v}\text{g}}$ of $700k\frac{g}{m^3}$ and molecular weight, $M_{\text{a}\text{v}\text{g}}$ of $100\frac{g}{m}ol,$ and a viscosity

comparable to water. The flow valve has a maximum flow coefficient $($US$)C_v$ value of $12.$

The Task:

Develop an excel$-$based algorithm that can determine how key process parameters such as

$y_{1D},D_c,T_t,T_b,P_p,W$ and $x_w$ change for changes in $P_{,}{L}_{,}{Q}_B,F,q$ and $x_{1F},$ and the $C_V$ values

required for flow $W$ to be achieved. The number of stages in the rectifying section of the

column $(N_R)=4.$

With your individual data, calculate $T_t,T_b,P_p,T_p$ and $C_V$

Hints and tips:

Calculating $u$ and $-$ You can calculate these parameters based on an average

temperature within the column, taken as the average of the pure component boiling points

at the column pressure.

Calculating $C_v-$ The density of water can be assumed to be $1000k\frac{g}{m^3}$ at the reference

conditions for the flow coefficient equation.

Calculating $T_t$ and $T_b-$ These temperatures can be estimated based on the bubble point of

the liquid at the appropriate stage.

Calculating $T_p$ and $P_p-$ Assume that the propane refrigerant is at the same temperature as

the two$-$phase mixture in the condenser. The Antoine equation constants for propane are:

$A=6\mathrm{.}803,B=804\mathrm{.}0,C=247\mathrm{.}04,(p^{**}inmmHg,TinC)$