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7.30: Untitled Page 175

  • Page ID
    18308
  • Chapter 7

    nonlinear systems, the use of values of q near one may be necessary to obtain stable convergence.

    Table 7.7b. Convergence for Dimensionless Recycle Flow Rate

    (Wegstein’s Method)

    i

    q

    ( i)

    ( i+1)

    M5

    M5

    0

    – 1.30

    0.000

    1.610

    1

    – 1.30

    1.610

    2.109

    2

    – 1.30

    2.109

    2.264

    3

    – 1.30

    2.264

    2.312

    4

    – 1.30

    2.312

    2.327

    5

    – 1.30

    2.327

    2.331

    6

    – 1.30

    2.331

    2.333

    7

    – 1.30

    2.333

    2.333

    In the next example we return to a more complex problem associated with the production of ethylene oxide that was studied earlier in Example 7.6. In this analysis we will find that a damped successive substitution process is necessary to obtain a converged solution.

    EXAMPLE 7.8. Sequential analysis of the production of ethylene oxide In Figure 7.8 we have illustrated a process in which ethylene oxide ( C H O ) is produced by the oxidation of ethylene ( C H ) over a 2

    4

    2

    4

    catalyst containing silver. In a side reaction, ethylene is oxidized to carbon dioxide ( CO ) and water ( H O ) . The feed stream, Stream #1, 2

    2

    consists of ethylene ( C H ) and air ( N and O ) which is combined 2

    4

    2

    2

    with Stream #5 that contains the unreacted ethylene ( C H ) , carbon 2

    4

    dioxide ( CO ) and nitrogen ( N ) . The mole fraction of ethylene in 2

    2

    Stream #2 entering the reactor must be maintained at 0 . 05 for satisfactory catalyst operation. The conversion of ethylene in the reactor is optimized to be 70% ( C  0 . 70 ) and the yield of ethylene oxide is 50% ( Y  0 . 50 ) .

    All of the oxygen in the feed reacts, thus there is no oxygen in Stream #3

    and we have ( M

    )  0 . The reactor effluent is sent to an absorber where

    O2 3

    index-336_1.png

    index-336_2.png

    index-336_3.png

    index-336_4.png

    Material Balances for Complex Systems

    327

    all the ethylene oxide is absorbed in the water entering in Stream #8.

    Water is fed to the absorber such that ( M

    )  100 ( M

    ) and we

    H2O 8

    C2H O 7

    4

    assume that all the water leaves the absorber in Stream #7. A portion of Stream #4 is recycled in Stream #5 and a portion is purged in Stream #6.

    In this example we want to determine the fraction of M

     that needs to be

    4

    purged in order that 100 mol/h of ethylene oxide are produced by the reactor.

    This problem statement is identical to that given by Example 7.6, and it is only the procedure for solving this problem that will be changed. In this case we assume the values of the flow rates entering the mixer from the tear stream. We then update these assumed values on the basis of the sequential analysis of the four control volumes.

    Figure 7.8. Control volumes for sequential analysis

    Available Data

    The conversion and the yield are key parameters in this problem, and we define these quantities explicitly as

     RC2H4

    C  Conversion of ethylene 

     0 7

    . 0

    (1)

    ( M

    )

    C2H4 2

    328