A process engineer aims to purify a feedstock containing $90$ wt$\%$ active component $($A$)$ and $10$ wt$\%$ of impurity $($I$).$ A preliminary separator is able to purify the feed to $97$ wt$\%.$ They build a new purification device capable of generating a product stream containing $80\%$ of the active substance A from its input stream and $30\%$ of the impurities from its input stream. An effluent stream out of the purifier carries the rest of A and impurities. They set up the purification process as shown in Figure $2.$ The stream out of the separator is split equally $($in terms of mass flowrate$)$ into two channels. The first channel is sent directly to the purifier while the second stream is mixed with a recycle stream consisting of half the purifier$$s product stream. Both purifier I and purifier II are similar units. Assuming a basis of $100$ kg$/$hr of feedstock and steady state, $($a$)$ Develop a stream table and fill it with known flow rates and compositions $($b$)$ Find the flowrate of streams leaving the initial separator and the amounts of A and I in it$.($c$)$ Calculate the flowrates of streams entering and leaving purifier I. $($d$)$ Calculate the flowrates of streams entering and leaving purifier II$.($e$)$ How does using a recycle stream affect the purity and recovery of component A $($e$)$ How does using a recycle stream affect the purity and recovery of component A$.$ Purity $=($ Amount of A in final product stream $)/($ Total amount of substance in product stream $)$ Recovery $=($ Amount of A in final product stream $)/($ Amount of A in feedstock $)$ Figure $2$: Purification process $[$Caution Remember that the streams leaving the purifier contain $80\%$ of A that was present in the input to the purifier and $30\%$ of I that was in the input to the purifier. Purity and recovery are to be determined based on the final streams leaving the purifier, i$.$e$,$ after the recycle splitters.$]$Problem $2[60$ points$]$

A process engineer aims to purify a feedstock containing $90wt\%$ active component $($A$)$ and $10wt\%$

of impurity $($I$).$ A preliminary separator is able to purify the feed to $97wt\%.$ They build a new

purification device capable of generating a product stream containing $80\%$ of the active substance

A from its input stream and $30\%$ of the impurities from its input stream. An effluent stream out

of the purifier carries the rest of A and impurities. They set up the purification process as shown

in Figure $2.$ The stream out of the separator is split equally $($in terms of mass flowrate$)$ into two

channels. The first channel is sent directly to the purifier while the second stream is mixed with

a recycle stream consisting of half the purifier's product stream. Both purifier I and purifier II are

similar units. Assuming a basis of $100k\frac{g}{h}r$ of feedstock and steady state,

$($a$)$ Develop a stream table and fill it with known flow rates and compositions

$($b$)$ Find the flowrate of streams leaving the initial separator and the amounts of A and I in it$.$

$($c$)$ Calculate the flowrates of streams entering and leaving purifier I.

$($d$)$ Calculate the flowrates of streams entering and leaving purifier II$.$

$($e$)$ How does using a recycle stream affect the purity and recovery of component A$.$

Purity $=\frac{\text{A}\text{m}\text{o}\text{u}\text{n}\text{t}ofAin\text{f}\text{i}\text{n}\text{a}\text{l}\text{p}\text{r}\text{o}\text{d}\text{u}\text{c}\text{t}\text{s}\text{t}\text{r}\text{e}\text{a}\text{m}}{\text{T}\text{o}\text{t}\text{a}\text{l}\text{a}\text{m}\text{o}\text{u}\text{n}\text{t}ofsubstancein\text{p}\text{r}\text{o}\text{d}\text{u}\text{c}\text{t}\text{s}\text{t}\text{r}\text{e}\text{a}\text{m}}$

Recovery $=\frac{\text{A}\text{m}\text{o}\text{u}\text{n}\text{t}ofAin\text{f}\text{i}\text{n}\text{a}\text{l}\text{p}\text{r}\text{o}\text{d}\text{u}\text{c}\text{t}\text{s}\text{t}\text{r}\text{e}\text{a}\text{m}}{\text{A}\text{m}\text{o}\text{u}\text{n}\text{t}ofAin\text{f}\text{e}\text{e}\text{d}\text{s}\text{t}\text{o}\text{c}\text{k}}$

Figure $2$: Purification process

$[$Caution Remember that the streams leaving the purifier contain $80\%$ of A that was present in the

input to the purifier and $30\%$ of I that was in the input to the purifier.

Purity and recovery are to be determined based on the final streams leaving the purifier, i$.$e$,$ after the

recycle splitters.$]$