Problem $4(50\%)$: The feed is $60$ mol$\%$ dimethyl ether $($DME$)$

and $40$mol$\%$ methanol. Assume that the equilibrium data

provided are correct.

a$)$ A feed of $200$kmo$\frac{l}{h}$ is flashed at $5$ bar and $50C.$ What are

the liquid and vapor flowrates and the mole fractions in the vapor

and liquid exit streams?

A feed of $200$kmo$\frac{l}{h}$ is to be fractionated to give a distillate

containing $98$mol$\%$ DME and a bottoms product containing $98$

mol $\%$ methanol. The feed is $20\%$ vapor and $80\%$ liquid. There is

a total condenser and a partial reboiler.

b$)$ Determine the molar flowrates of the distillate and bottoms.

c$)$ Calculate all internal flows for operation at a reflux ratio of

$0\mathrm{.}1$

d$)$ In order to use cooling water in the condenser, assume that

the DME must condense no lower than $55C.$ Estimate the top

pressure for this column.

e$)$ In order to use low$-$pressure steam in the reboiler, the

bottom temperature must be no higher than $148C.$ Estimate the

bottom pressure for this column.

f$)$ Assume that the tray efficiency is $42\%.$ Estimate the maximum

weir height for which trays can be designed to meet the pressure

specifications.

g$)$ Determine the diameter of a packed tower to operate at $70\%$

of flooding using I$\mathrm{.}5-$in$,$ ceramic Berl saddles. Determine the

diameter both above and below the feed.