Page 63 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 22 Design Equations 35

The number of moles of A in the reactor after a conversion X has been
achieved is

NA = NAO - NAOX = NAo (1 - X) (2-4)

'When no spatial variations in reaction rate exist, the mole balance on
species A for a batch system reduces to the following equation:

This equation is valid whether or not the reactor volume is constant. In the
general reaction
A+ - B ----+ -C+-D l(2-2)
d
b
c
a a a
reactant A is disappearing; therefore, we multiply both sides of Equation i(2-5)
by -1 to obtain the mole balance for the batch reactor in the form

The rate of disappearance of A, -rA, in this reaction might be given by a rate
law similar to Equation (1 -2), such as - rA = kCACB.
For batch reactors we are interested in determining how long to leavle the
reactants in the reactor to achieve a certain conversion X. To determine this
length of time, we transform the mole balance, Equation (2-5), in terms of
Conversion by differentiating Equation (2-4),
NA = NAO - NAOX I(2-4)

with rlespect to time, while remembering that NAO is the number of moles of A
initially present and is therefore a constant with. respect to time.

- dX
dNA = 0- NAO -
dt dt
Combining the above with Equation (2-5) yields

For a batch reactor, the design equation in differential form is

Batch reactor
design equation (2-6)
,
The differential forms of the design equations often appear in reactor
analysis and are particularly useful in the interpretation of reaction rate data.