Applications of Chemical Kinetics in Environmental Systems - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 274

The rate of settling of A on solids in the water column is given by

r set = k s C A .

The chemical reaction rate is given by

r react = k r C A .

The total rate of loss of A from the surface impoundment is given by

r tot = r react + r voln + r set = (k r + k v + k s )C A = k ∗ C A .
The overall first-order rate constant is k ∗ . For a first-order loss process, ν A =− 1. For
a constant-density reactor, N A = VC A . If the influent and effluent feed rates are same
( = Q 0 ) , we have the following mass balance equation:

V d C A

d t = Q 0 C A0 − Q 0 C A − k ∗ C A V .

Assuming steady state,

1
1 + (k ∗ (V/Q 0 )) ,
where C A0 is the concentration of A in the influent. The quantity V/Q 0 has units of
time and is called the meandetentiontime , residencetime ,or contacttime in the reactor
for the aqueous phase and is designated τ d .

C A
C A0 =

1

0.8

0.6

0.4

CSTR

0.2

PFR

0

0 20 40 60 80 100

t d /h

FIGURE 6.5 Comparison of exit to inlet concentration ratio in a surface impound-
ment modeled as a CSTR and a PFR.