A mixture (A) in a continuous pharmaceutical manufacturing

Chapter 4, Problem 4.55

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A mixture (A) in a continuous pharmaceutical manufacturing process contains up to 10 wt% of an ingredient R [mass fraction XRA(g Rig A)]. The mixture is subjected to a reaction step in which the conversion of R is 99%. The final product (P) must contain 0.75 wt% R. To achieve this goal, a fraction f of the A fed to the process bypasses the reactor and combines with the product stream leaving the reactor to produce P. A second feed stream (B), which contains no R, enters the reactor along with the A not bypassed. The mass flow rates of A and B entering the reactor (not the process) are equal. *Computer problem. 177 1 (8) mso(kg B/h) 1 kg B/kg A fed to reactor .----- (A) mAo(kg Alhl xRA(kg R/kg A) (Pl mp(kg P/h) 0.0075 kg R/kg P (a) Without taking a basis of calculation, draw and label a flowchart. Then list the equations you are allowed to write for the stream splitting and mixing points and the reactor, and prove that the process has two degrees of freedom. (Be careful when counting allowable balances on the pre-reactor stream splitting point.) (b) Suppose the production rate of the final product. mp, and the mass fraction of R in the process feed. XRA, are kno\\"I1. Write a set of equations that may be solved for the rates, mAo(kg/h) and mBo(kg/h), at which A and B must be fed to the process (not the reactor), and for the fraction of the process feed, f(kg bypass/kg fresh feed), that must be bypassed to achieve the desired mass fraction of R in the final product (0.0075 kg Rlkg P). Do not perform any numerical calculations. (c) Suppose mp = 4850 kg Pih and XRA = 0.0500 kg R/kg A. Calculate mAO, mBO, and f. *(d) The desired production rate (mp) and the mass fraction of R in the feed (XRA) both vary from day to day. Use an E-Z Solve parameter sweep to to generate a plot of f versus XRA for mp = 4850 kg/h and XR...>,. varying between 0.02 and 0.10. Prove that you would get the same curve regardless of the value of mp.