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108 3. Heterogeneous Processes and Reactor Analysis

r
Then, the oerall rate of the reaction ( v ) per unit volume of liquid is
u
1d N m 1
( r u ) s ( r vs ) m s ( r m ) ( R ) (3.133)
V d t h
L p L
These relationships can be used along with the material balances and rate expressions, and
the solutions can be expressed in various forms of the rate coeficient in conjunction with f
different variables.

3.4.5 Expansion of gas phase in three-phase systems

To follow the same analysis as in two-phase systems, the stoichiometry of the reaction
should be used for the determination of the final moles in the gas phase after the reaction.
However, in slurry reactors, a liquid phase is ined and the reactants are dissolved and olv v
react in the liquid phase. In this case, the moles remaining in the gas phase after the reac-
.
tion are not only determined from the reaction stoichiometryThis is why a part of the
moles that disappear from the gas phase is unreacted and dissolved in the liquid. This sit-
uation introduces some complications in the determination of the expansion f . actor
At this point, there is an opportunity to analyze the effect of dissolution of reacting
v
species in a second fluid in the oerall material balance in a reactorThe oerall mate- . v
rial balance is conenient in the case where the conersion of one species is known and v
v
we want to estimate the conersion of the other species without solving the reactor
v
models.
However, as will be analyzed, this approach should be followed with great attention as
it can lead to erroneous results and conclusions.
The case of the oall material balance ver
Consider the reaction

d
A( s) ga B( s) ga products (dissolve in liquid) b

where A is the limiting reactant. The final concentration of reactants is

C B,G C B,i C b A x (3.134)
A, i
C A,G C A,i A x (1 ) (3.135)

ference is Then the concentration dif

C B,i B,G b x C (3.136)
C
A,i A

C C C x
A,i A,G A,i A (3.137)