Very Urgent! A distillation column is a process unit in which a feed mixture is

Question

Very Urgent!

A distillation column is a process unit in which a feed mixture is separated by multiple partial vaporizations and condensations to form two or more product streams. The overhead product stream is rich in the most volatile components of the feed mixture, and the bottom product stream is rich in the least volatile components How many independent material balances may be written for this system, if the total mass balance has been used? How many of the unknown flow rates and/or mole fractions must be specified before the others may be calculated? Suppose values are given for m_1 and x_2. Give a series of equations, each involving only a single unknown, for the remaining variables. Circle the variable for which you would solve.

Explanation / Answer

5300*x2= m3+1200*0.70 = m3+840 ( component A balance)   (1)

0.03*m1+5300*y2= 1200*y4+m5*0.6 ( Component B balance) (2)

0.97*m1=m5*0.4+1200*z4 ( component C balance) (3)

0.7+y4+z4= 1 (4), x2+y2= 1 (5).         

Hence we can write 5 independent equations. Since there are 7 unkowns, m1, x2,y2, m3, y4,z4 and m5, five independent equations.

Degress of freedome= number of variables – number of independent equations =7-5= 2

Two of the variables ifspecified can be used to calcualte the rest.

Given m1 and x2, y2= 1-x2

Hence from Eq.1, 5300*x2-840 = m3      from Eq.1

  , m5 = m1+5300-(1200+m3) ( overall balance)

Component B balance, 1200*y4= 0,03*m1+5300*y2-m5*0.06,

And z4= 1-0.7-y4

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