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3.3 T o-Phase Agitated Reactors w 87

then

r V )
Fx ( (3.79)
iA u L

Variable-volume systems
ariable-v
A volume batch reactor is a constant-pressure (piston-like) closed tank. On the
other hand, a variable-pressure tank is a constant-volume batch reactor (F 1999). ogler ,
Thus, in batch reactors, the e actor is used only in the case of a constant-pressure xpansion f
v
tank whereas and not in a constant-volume tank, een if the reaction is realized with a
v
er
change in the total moles. Ho in continuous-flow reactors, the expansion f actor
,
we
should be alays considered. In the following section and for the continuous-flow reac-
w
tors, the v olume V can be replaced by the volumetric flow rate Q , and the moles N by the
molar flow rate F in all equations.
Change in the total moles in gas–solid r eactions Consider a reaction of the form
a A b B cC D d
where all the reactants and products are gases and A is the limiting reactant. Then, based
v on the conersion level of A,
initial moles,
N tot,i N A,i N N C,i N D,i (3.80)
B,i
v el ersion le final moles after a con v x of A,
N A N A,i x N A,i (3.81)
A
b
N B N B,i A xN (3.82)
A,i
a
c
N C N C,i A xN (3.83)
A,i
a
d
N D N D,i A xN (3.84)
A,i
a
and thus,
N t to N t to,i x N A,i (3.85)
A

where x A is the conersion of the limiting reactant v A,

N A,i N A,o
x (3.86)
A
N
A,i