$(30$ points$)$ In the production of a bean oil, beans containing $13\mathrm{.}0wt\%$ oil and $87\mathrm{.}0wt\%$ solids are ground and fed to a stirred tank $($extractor$)$ along with a stream of liquid n$-$hexane composed of fresh and recycled hexane. The feed ratio is $3kg$ hexane $\frac{?}{kg}$ beans. The ground beans are suspended in the liquid, and essentially all of the oil in the beans is extracted into the hexane. The extractor effluent passes to a filter. The filter cake contains $75\mathrm{.}0wt\%$ bean solids and the balance bean oil and hexane, the latter two $($i$.$e$.$ oil and hexane$)$ in the same mass ratio in which they emerge from the extractor. The filter cake is discarded and the liquid filtrate is fed to a heated evaporator in which the hexane is vaporized and the oil remains as a liquid. The oil is stored in drums and shipped. The hexane vapor is subsequently cooled and condensed, and the liquid hexane condensate is recycled where it is combined with fresh hexane feed prior to entering the extractor.

a$.$ Draw a process flow diagram depicting this process.

b$.$ Do a degree$-$of$-$freedom analysis on the overall process and EACH of the single units. Where should you start the analysis of this problem?

c$.$ Calculate the following:

Percent yield of bean oil product $(kg$ oil$/kg$ beans fed$)[$Ans: $11\mathrm{.}8\%]$

The recycle to the fresh feed ratio $(kg$ hexane recycled $\frac{?}{kg}$ fresh hexane feed$)$