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5.12: Untitled Page 110

  • Page ID
    18243
  • Chapter 5

    In this case we are given the inlet mole fractions, ( x )  0 and A o

    ( y )

    0 . 010 , and the system parameters, K

     2 5

    . 3 , M

    90 kmol/h

    A N 

    1

    eq,A

     

    and M

    30 kmol/h . For these particular values, we want to know how

     

    Figure 5.9. Multi‐stage gas‐liquid contacting device

    many stages, N, are required to reduce the exit mole fraction of acetone to ( y )  0 001

    .

    . In this case we express Eq. 5‐91 as

    A 1

    ( y )

    N

    A N

    0 010

    .

    2

    3

    1

    1  A A A .... A

     10 . 0

    (1)

    ( y )

    0 . 001

    A 1

    Two‐Phase Systems & Equilibrium Stages 201

    in which the value of the absorption coefficient is given by A M

    M

    K

     1 186

    .

    . This leads to the values listed in Table 5.9

    eq,A

    where we see that 5 stages are insufficient to achieve the desired result, ( y )  0 001

    .

    . In addition, the use of 6 stages reduces the exit mole A 1

    fraction of acetone in the air stream to ( y )  0 00081

    .

    which is less than

    A 1

    the desired result. For this type of situation, it is the responsibility of the chemical engineer to make a judgment based on safety considerations, environmental constraints, requirements for other processing units, and economic optimization. Such matters are covered in a future course on process design, and we have alluded to some of these concerns in Sec. 1.1.

    Table 5.9. Number of stages, N, versus ( y )

    ( y )

    A N

    1

    A 1

    Number of stages, N

    1 + A + A 2 + A 3 +….+ AN

    1

    2.186

    2

    3.592

    3

    5.260

    4

    7.238

    5

    9.584

    6

    12.366

    Type II: Given the inlet mole fractions, ( x ) and ( y )

    , the

    A o

    A N1

    system parameters, and the number of stages, N, we would like to determine the value of ( y ) .

    A 1

    In this case we consider an existing unit in which there are 7 stages. The inlet mole fractions are given by ( x )  0 and ( y )  0 . 010 , and the A o

    A 8

    parameters associated with the system are specified as K

     2 5

    . 3 ,

    eq,A

    M

    90 kmol/h and M

    30 kmol/h . In order to determine the mole

     

     

    fraction in the  ‐phase (air) leaving the cascade, we make use of Eq. 5‐91

    to express ( y ) as

    A 1

    ( y )

    A 8

    ( y )

    (2)

    A 1

    2

    3

    4

    5

    6

    1

    7

    A A A A A A A This leads to the following value of the mole fraction of acetone leaving the top of the cascade illustrated in Figure 5.9:

    202