Page 103 - Chemical process engineering design and economics

88 Chapter 3

The total mole balance is not an independent equation because by adding the
component balances and then substituting Equations 3.4 to 3.8 into the sum will
yield the total mole balance,

n^ + ms =m 2 +ni4 (3.9)

If you decide to use the total balance, then you must eliminate one of the
equations from 3.4 to 3.8, given above. You may eliminate any one of the equa-
tions. The equation eliminated will depend on the particular problem. Even if the
total balance is not an independent equation, it still must be satisfied and could be
use as a check on your computations.

Energy Balances
The macroscopic energy balance is used whenever energy changes occur, particu-
larly energy exchange with the surroundings. Energy exchange occurs frequently
because of the need to cool or heat process streams and to transfer liquids, gases or
solids from one process unit to another. Energy exchange usually occurs more
frequently than separation and chemical reaction. The energy balance is given by

v 2
Ah + — + gAz = Q-W (3.10)
2g

which states that the change in enthalpy in the process unit must be compensated
for by a change in kinetic energy, potential energy, heat transferred into the sys-
tem, and work done by the system. In many processes, the kinetic and potential
energy changes are small when compared to the magnitude of the other terms and
may be neglected.

Rate Equations
All physical and chemical transformations take time. Some physical phenomena,
such as the vaporization at a boiling liquid surface, occurs very rapidly and for all
practical purposes are instantaneous. Also, some chemical reactions, such as
combustion reactions, are very rapid, but mass transfer and many chemical reac-
tions are very slow by comparison. For such phenomena to occur to the extent
desired requires allowing sufficient time, which is achieved by allowing sufficient
equipment volume or surface area. Rate equations, then, are necessary to deter-
mine equipment sizes. For example, the well-known expression for the rate of
heat transfer,

(3.11)
Q = UA(At) LM

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