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3.4 Slurry Reactors 109

and thus the oerall material balance in the reactor is v
( C B,i C B,G ) b C ( A,i C A,G ) (3.138)

v This oerall material balance is valid only if the reaction is very f i.e. the unreacted ast, A
and B in the liquid phase are in negligible amounts.
v
If the aboe condition is not met, the calculations based solely on oerall material bal- v
ance do not take into account the dissolved unreacted A and B that remain in the liquid
,
phase after the reaction in a batch reactor or which may flow out of the reactor with the
liquid in a continuous-flow system. This w it is assumed that the remoal of a reactant ay , v
is purely a result of the reaction.

The case of the expansion factor
The calculations for the expansion factor in systems involving a gas and a liquid phase are
based solely on the gaseous species. The following cases can be found in practice:

1. The gas phase is dilute, i.e. it contains the reactant A and inerts in great e xcess. The
other reactants and products are nonolatile and are present only in liquid phase. In v
this case, the expansion could be taken as zero .
2. The reaction is very fast in the liquid phase and thus the concentration of A in this
phase is essentially zero. In this case, the expansion can be e aluated as described in v
two-phase systems.
3. All reactants and products are gases. If the limiting reactant, on which the e xpansion
factor is based, is in v i.e. the nonlimiting reactants are in great ery lo w concentration,
excess, then the gas volume cannot be changed considerably . alent v This case is equi
xcess of inerts, to the existence of a great e and the e en as zero. xpansion could be tak
4. The gaseous limiting reactant has a very low solubilityThis means that the moles .
lost by the dissolution of gas in the liquid are very small, and thus the moles that dis-
appear are mainly due to reaction. In this case, the expansion can be ealuated as v
described in two-phase systems.

The first two assumptions as well as the fourth are used by Leenspiel for gas–liquid v
absorption operations.

Example 4
Consider the gas-phase reaction
a A ( g) b B(l) C(l)

which is carried out isothermally and isobaricallyThe gas feed is pure A. The limiting
.
reactant is A. Express the concentration of A as a function of con ersion. v
Solution
The parameter takes into account only the gas-phase species A:

00 a
1
a