Skip to main content
Engineering LibreTexts

7.27: Untitled Page 172

  • Page ID
    18305
  • Chapter 7

    The engineer or operator in charge of a specific unit will be thinking about a single control volume around that unit, and this motivates the sequential problem solving approach that we describe in this section. The sequential approach naturally leads to many redundant cuts; however, the advantage of this approach is that concepts associated with the analysis are simple and straightforward. We will use the pyrolysis of dichloroethane studied earlier in Example 7.5 to illustrate the sequential analysis of a simple recycle system.

    EXAMPLE 7.7. Sequential analysis of the pyrolysis of dichloroethane.

    In this example we re‐consider the pyrolysis of dichloroethane ( C H Cl ) to produce vinyl chloride ( C H Cl) and hydrochloric acid 2

    4

    2

    2

    3

    ( HCl ) using a sequential analysis. The conversion of dichloroethane is given by

     RC H Cl

    2

    4

    2

    C  Conversion of C H Cl

     0 . 30

    (1)

    2

    4

    2

    ( M

    )

    C2H4Cl2 2

    and the unreacted dichloroethane is separated from the reaction products and recycled back to the reactor as indicated in Figure 7.7.

    Figure 7.7. Control volumes for sequential analysis of a recycle system The composition of Stream #1 is 98% dichloroethane ( C H Cl ) and 2%

    2

    4

    2

    ethane ( C H ) on a molar basis, and the total molar flow rate is M

     . We

    2

    6

    1

    assume that the separation column produces a sharp separation meaning

    Material Balances for Complex Systems

    321

    that all the dichloroethane leaves in Stream #5 and the remaining components (ethane, hydrochloric acid and vinyl chloride) leave in Stream #4. Our objective in this example is to determine the recycle flow rate in Stream #5 along with the composition and flow rate of Stream #4 in terms of the molar flow rate of Stream #1. Since our calculation is sequential, we require the three control volumes illustrated in Figure 7.7

    instead of the two control volumes that were used in Example 7.5. In the sequential approach we enclose each unit in a control volume and we assume that the input conditions to each control volume are known. For Control Volume I in Figure 7.7 this means that we must assume the molar flow rate of Stream #5. This process is referred to as tearing the cycle and Stream #5 is referred to as the tear stream.

    Given the input conditions for the mixer, we can easily calculate the output conditions, i.e., the conditions associated with Stream #2. This means that we know the input conditions for the reactor and we can calculate the output conditions in Stream #3. Moving on to the separator, we use the conditions in Stream #3 to determine the conditions in Stream #4 and Stream #5. The calculated conditions in Stream #5 provide the new assumed value for the molar flow rate entering the mixer, and a sequential computational procedure can be repeated until a converged solution is obtained. For linear systems, convergence is assured; however, the matter is more complex for the non‐linear system studied in Example 7.8.

    Since the input information for each control volume is known, the structure for all the material balances has the form

    ( M

     )

     ( M )  R ,

    A  C H , HCl , C H Cl , C H Cl (2) A out

    A in

    A

    2

    6

    2

    3

    2

    4

    2

    Here the unknown quantities are on the left hand side and the known quantities are on the right hand side. Directing our attention to the first control volume illustrated in Figure 7.7 we find

    Control Volume I

    C H :

    ( M

    )

     ( M

    )

    (3a)

    2

    6

    C2H6 2

    C2H6 1

    C H Cl :

    (o)

    ( M

    )

     ( M

    )  ( M

    )

    (3b)

    2

    4

    2

    C2H4Cl2 2

    C2H4Cl2 1

    C2H4Cl2 5

    HCl :

    ( M

    )

     0

    (3c)

    HCl 2

    C H Cl :

    ( M

    )

     0

    (3d)

    2

    3

    C H Cl 2

    2

    3

    322