Applications of Chemical Kinetics in Environmental Systems - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 272

For continuous systems (CSTR and PFR), it is convenient to express the change in
terms of conversion of A, , which is defined as the fractional conversion of A at

steady state. Then the mass balance can be written as follows: molar rate ofA leaving
the reactor, F A =

χ

molar rate ofA fed into the reactor, F A0 − molar rate of consumption

of A in the reactor, F A0 χ .

Therefore,

F A = F A0 ( 1 − χ ) . (6.16)

For a CSTR, the reactor volume is given by

F A0 χ
r

V = . (6.17)

For a PFR, we have

d (F A0 χ )

= r . (6.18)

d V

Since F A0 is a constant, we can integrate the above to obtain V .

E XAMPLE 6.1 C OMPARISON OF R EACTOR V OLUMES FOR A CSTR AND A PFR

In both a CSTR and a PFR, r A can be expressed as a function of the conversion x A .A
most frequently observed relationship between r A and χ (for a first-order reaction) in
environmental engineering is r A = kC A0 ( 1 − χ ) . Using this relationship for a CSTR,
we have

V CSTR
F A0

χ
kC A0 ( 1 − χ ) .

=

For a PFR we obtain the following:

χ

V PFR
F A0 =

1
kC A0

χ
( 1 − χ ) .

0

If the molar feed rate F A0 and initial feed concentration C A0 are the same in both cases,
we have

V CSTR

V PFR = χ ( 1 − χ ) ln ( 1 /( 1 − χ )) .

If the desired conversion is χ = 0.6, then the ratio of volumes is 1.63. Thus, a 63%
larger volume of the CSTR than that of a PFR is required to achieve a 60% conversion.

E XAMPLE 6.2 A CSTR M ODEL FOR A S URFACE I MPOUNDMENT

Surface impoundments are used at many industrial sites for the treatment of wastewater.
It is generally a holding tank where water is continuously fed for treatment.