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8.4: Untitled Page 193

  • Page ID
    18326
  • Chapter 8

    8.2 Batch Reactor

    In many chemical process industries, the continuous reactor is the most common type of chemical reactor. Petroleum refineries, for example, run day and night and units are shut down on rare occasions. However, small‐scale operations are a different matter and economic considerations often favor batch reactors for small‐scale systems. The fermentation process that occurs during winemaking is an example of a batch reactor, and experimental studies of chemical reaction rates are often carried out in batch systems.

    The analysis of a batch reactor, such as the liquid phase reactor shown in Figure 8‐4, begins with the general form of the species mole balance d

    c dV

    c (v w)  n dA

    R dV

    (8‐22)

    A

    A

    A

    dt

    A

    V ( t)

    A ( t)

    V ( t)

    a

    a

    a

    The batch reactor, by definition, has no entrances or exits, thus this result reduces to

    d

    c dV

    R dV

    (8‐23)

    A

    A

    dt V( t)

    V ( t)

    Here we have replaced V ( t) with V( t) since the control volume is no longer a

    Figure 8‐4. Batch reactor

    arbitrary but is specified by the process under consideration. In terms of the volume averaged values of c and R , we can express our macroscopic balance A

    A

    as

    d

     c V( t)   R V( t)

    A

    (8‐24)

    A

    dt

    index-370_1.png

    Transient Material Balances

    361

    In some batch reactors the control volume is a function of time; however, in this development we assume that variations of the control volume are negligible so that Eq. 8‐24 reduces to

    dc

    A

      R

    (8‐25)

    A

    dt

    The simplicity of this form of the macroscopic species mole balance makes the constant volume batch reactor an especially useful tool for studying the net rate of production of species A. Often it is important that the batch reactor be perfectly mixed; however, we will avoid imposing that condition for the present.

    As an example, we consider the thermal decomposition of dimethyl ether in the constant volume batch reactor illustrated in Figure 8‐5. The chemical species Figure 8‐5. Constant volume batch reactor

    involved are C H O which decomposes to produce CH , H and CO . The 2

    6

    4

    2

    visual representation of the atomic matrix is given by

    Molecular Species  CH

    H

    CO C H O

    4

    2

    2

    6

    carbon

     1

    0

    1

    2

    (8‐26)

    hydrogen

    4

    2

    0

    6

    oxygen

     0

    0

    1

    1

    and Axiom II takes the form

    362