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8.8: Untitled Page 197

  • Page ID
    18330
  • Chapter 8

    Here it should be clear that R is not defined by dc / dt ; rather R is an intrinsic A

    A

    A

    property of the system that represents the net molar rate of production of species A per unit volume. This is the sense in which the net rate of production was introduced in Chapter 4.

    8.4 Biomass Production

    Biological compounds are produced by living cells, and the design and analysis of biological reactors requires both macroscopic balance analysis and kinetic studies of the complex reactions that occur within the cells. Given essential nutrients and a suitable temperature and pH, living cells will grow and divide to increase the cell mass. Cell mass production can be achieved in a chemostat where nutrients and oxygen are supplied as illustrated in Figure 8‐8.

    Figure 8‐8. Cell growth in a chemostat

    Normally the system is charged with cells, and a start‐up period occurs during which the cells become accustomed to the nutrients supplied in the inlet stream.

    Oxygen and nutrients pass through the cell walls, and biological reactions within the cells lead to cell growth and the creation of new cells. In Figure 8‐8 we have illustrated the process of cell division in which a single cell (called a mother cell) divides into two daughter cells. In Figure 8‐9 we have identified species A and B

    index-378_1.png

    index-378_2.png

    Transient Material Balances

    369

    as substrates, which is just another word for nutrients and oxygen. Species C

    represents all the species that leave the cell, while species D represents all the species that remain in the cell and create cell growth. The details of the enzyme-catalyzed reactions that occur within the cells are discussed in Sec. 9.2.

    Figure 8‐9. Mass transfer and reaction in a cell

    To analyze cell growth in a chemostat, we need to know the rate at which species D is produced (Rodgers and Gibon, 2009). In reality, species D represents many chemical species which we identify explicitly as F, G, H, etc. The appropriate mass balances for these species are given by

    d

    dV

     (v w) n dA

    (8‐36a)

    dt

    r dV

    F

    F F

    F

    V ( t)

    A( t)

    V ( t)

    d

    dV

     (v w) n dA

    (8‐36b)

    dt

    r dV

    G

    G G

    G

    V ( t)

    A( t)

    V ( t)

    d

    dV

     (v w) n dA

    (8‐36c)

    dt

    r dV

    H

    H H

    H

    V ( t)

    A( t)

    V ( t)

    etc.

    (8‐36d)

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    index-379_2.png

    index-379_3.png

    index-379_4.png

    index-379_5.png

    index-379_6.png

    370