Ideal Flow Reactors - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 180

the reactor. Our interest is in maintaining the same level of catalyst. Therefore, the rate of
reactor contents being replaced by the feed stream is defined as the dilution rate. Therefore,
dilution rate and space velocity are two identical quantities. In this text, we shall not differ-
entiate dilution rate from space velocity.
The space velocity or dilution rate is simply defined as the inlet flow rate divided by the
reactor volume. That is

Q 0
V

D ¼ (5.4)

where D stands for dilution rate that is commonly used associated with chemostats. For
chemical reactors, the quantity defined in Eqn (5.4) is commonly referred to as the space
velocity .

5.2. PLUG FLOW REACTOR

PFR is an idealized flow reactor such that along the direction of the flow all the reaction
mixture are moving along with the same speed, there is no mixing or back flow. The
contents in the PFR flow like plugs, from inlet to outlet. On the other hand, the reaction
mixture is well mixed, just like that in a batch reactor, within each plug or on the cross-
section plane of the PFR. This idealization makes the flow reactor analysis simplified
extremely as now one can treat the PFR as a one-dimensional flow reactor.
Figure 5.1 shows a schematic of PFR. Mole balance for a given species j over a differential
volume between V and V þ d V leads to

F j V F j Vþ d V þ r j d V ¼ vðC j d VÞ (5.5)

vt

which leads to

d F j þ r j d V ¼ vðC j d VÞ

(5.6)

vt

or

v C j

vt ¼ r j vð QC j Þ

(5.7)

vV

which is the general mole balance equation for a PFR.
Since the total amount of mass cannot be created or destroyed during chemical and bio-
reactions, we obtain through mass balance over the differential volume as shown in Fig. 5.3 ,

DðrQÞ¼ vðrD V Þ
vt

(5.8)

which is reduced to

vr

vt ¼ vðrQÞ

(5.9)

vV