Applications of Chemical Kinetics in Environmental Systems - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 271

Δ z

F j 0

F j

F j ( z )

F j ( z + Δ z )

FIGURE 6.3 Schematic of a tubular or plug-flow reactor.

Taking the limit as Δ z → 0 and rewriting, we obtain

1
A c

d F j
d z =

v j r (6.11)

or

d F j
d V =

v j r . (6.12)

It can be shown that the above equation also applies to the case where the cross-
sectional area varies along the length of the reactor. This is the case of a river going
through several narrow channels along its path.
If the reaction is first order, namely, A → B, the rate of disappearance of A is

r = kC A . The stoichiometry of the reaction is such that ν A =− 1. If we consider a

constant-density reactor, and note that F A = Q 0 C A with Q 0 being the volumetric flow

rate, we have

d C A
d V =

k
Q 0

− C A . (6.13)

Integrating with the initial condition, C A = C A0 at 0, we obtain

k ln C A0

Q 0

V = (6.14)

C A

If 50% of C A0 has to be converted into products, then V = 0.693 Q 0 /k is the reactor

volume required.

6.1.1.4 Design Equations for CSTR and PFR

For any general stoichiometric equation of the form a A + b B → c C + d D, we can

write the following equation on a per mole of A basis:

b
a B

c
a C

d
a D.

A + −→ + (6.15)