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7.25: Untitled Page 170

  • Page ID
    18303
  • Chapter 7

    At this point we make use of Eq. 7‐34 to obtain the standard constraints on mole fractions when only ethylene ( C H ) , carbon dioxide ( CO ) and 2

    4

    2

    nitrogen ( N ) are present. This provides

    2

    ( x

    )

     ( x

    )  ( x

    )

     1

    (37a)

    C2H4 4

    CO2 4

    N2 4

    ( x

    )  ( x

    )  ( x

    )

     1

    (37b)

    C2H4 6

    CO2 6

    N2 6

    and subtracting Eq. 37a from Eq. 37b leads to

    ( x

    )

     ( x

    )

    (38)

    C2H4 6

    C2H4 4

    We now make use of Eq. 7‐45 to represent the constraints on the three mole fractions as

    ( M

    )

    M

    M

    ( M

    )

    (39a)

    CO

    6

     6 4

    2

    CO2 4

    ( M

    )

    M

    M

    ( M

    )

    (39b)

    N

    6

     6 4

    2

    N2 4

    ( M

    )

    M

    M

    ( M

    )

    (39c)

    C H

    6

     6 4

    2

    4

    C2H4 4

    In Eq. 1 note that  is the fraction of Stream #4 that needs to be purged, i.e.,

      MM

    (40)

    6

    4

    thus the molar flow rates in Stream #6 are given by

    ( M

    )

     ( M

    )

    (41a)

    CO2 6

    CO2 4

    ( M

    )

     ( M )

    (41b)

    N2 6

    N2 4

    ( M

    )

     ( M

    )

    (41c)

    C2H4 6

    C2H4 4

    Use of these results with Eqs. 35 leads to

    C H :

    ( M

    )

     (1  )( M

    )

    (42a)

    2

    4

    C2H4 5

    C2H4 4

    CO :

    ( M

    )

     (1  )( M

    )

    (42b)

    2

    CO2 5

    CO2 4

    N :

    ( M

    )

     (1  )( M )

    (42c)

    2

    N2 5

    N2 4

    Material Balances for Complex Systems

    317

    and we can use Eq. 34b to represent the molar flow rate of ethylene in Stream #5 as

    ( 1  )( 1   )

    ( M

    C

    )

    (43)

    C2H4 5

    CY

    At this point we need to return to Control Volume I in order to acquire additional information needed to determine the parameter,  . Beginning with Eq. 30a, we use Eq. 34a and Eq. 43 to obtain

    C H :

    ( M

    )

    1  1 C 1 

    

    (44a)

    C H

    1

    

    2

    4

    2

    4

    CY

    Moving on to Eq. 30b, we use Eq. 32d along with Eq. 34a and Eq. 42b to obtain

    2 1  1  

    CO :

    ( M

    Y

    )

    (44b)

    2

    CO2 2

    Y

    Next we use Eq. 30c along with Eq. 34d to obtain

    O :

    5

    ( M

    )

     ( M )

     (3  Y) Y

    (44c)

    2

    O2 1

    O2 2

    2

    and finally we make use of Eq. 30c along with Eq. 31 to express the molar flow rate of nitrogen entering the system as

    N :

    5

    ( M

    )

     (3  Y) Y

    (44d)

    2

    N2 1

    2

    At this point we are ready to return to Eq. 34g and make use of Eq. 32d and Eq. 33 to obtain

    ( M

    )

     ( M

    )  2  1  Y Y

    (45)

    CO

    4

    CO

    2

    2

    2

    This result can be used with Eq. 44b to provide the molar flow rate of carbon dioxide ( CO ) entering the splitter

    2

    ( M

    )

     2  1  Y Y

    (46)

    CO

    4

    2

    This result can be used with Eq. 34g to determine the molar flow rate of nitrogen ( N ) entering the splitter as

    2

    2  1  

    Y

    1

    ( M

    )

    1   (1  C  CY) 

    (47)

    N2 4

    2

    CY

    Y

    318