Chemical Engineering question. Cumene (C) is made from propylene (P) and Benzene

Question

Chemical Engineering question.

Cumene (C) is made from propylene (P) and Benzene (B). The propylene is contaminated with 5 mol% inert (I). The total flow rate (P+I) in stream 1 is 100 kgmol/h. If the process is at steady state what is the total flow rate (P+I) in purge stream? Give answer in kgmol/h.

Stream 1 (100 kgmol/h) is 95%P, 5% I. Stream 2 is B. Stream 7 is recycled P+I. Stream 1, 2, 7 go into a mixer. From the mixture is stream 3 which includes P, B, I and goes into the reactor. From the reactor is stream 4 with P, I, C and goes into a separator. The separator splits into two streams, stream 5 with C (desired product: stored) and stream 6 with P and I. Stream 6 goes into a splitter which separates into two streams, the purge and the recycle stream. The purge stream is stream 8 and has 50% P, 50% I. Stream 7 is the recycle stream which as mentioned goes into the mixer.

(1)(2)(7)--> MIX --(3)--> RX--(4)--> SEP--(6)---> SPLITTER---(8)>

^^^ --(5)--> ^^^-----(7)-->mix

Explanation / Answer

Under steady state condtions

Entering amount of inerts = leaving inerts amount in the purge

entering inerts =100*5/100 =5 kgmol/hr

leaving stream contains 50%I

let the leaving stream flow rate be X

making inert balance under steady state conditions

x*50/100= 5

x =5*100/50 = 5 kgmol/hr

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