Applications of Chemical Kinetics in Environmental Systems - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 275

Blackburn (1987) reported the determination of the three transport rates for 2,4-
dichlorophenol in an activated sludge process in an impoundment. The impoundment
had a total volume of 10 6 L with a solids (biomass) concentration of 2000 mg/L. The
mean detention time was 1 day. The depth of the impoundment was 1.5 m. The average
biodegradation rate k r was 0.05 h − 1 . The rate constant for settling of the biomass was
estimated to be 2.2 × 10 − 6 h − 1 . The rate constant for volatilization was 2 × 10 − 5 h − 1 .
The overall rate constant k ∗ = 0.05 h − 1 . Therefore, C A /C A0 = ( 1 + 0.05 τ d ) − 1 . This
is shown in Figure 6.5. The contribution of each mechanism toward the loss of DCP
can also be ascertained. For example, the fractional loss from biodegradation is f bio =
k r τ d /( 1 + k r τ d ) .
If the surface impoundment behaves as a PFR, then the steady-state mass balance
will be given by − ( d C A / d V) = (k ∗ /Q 0 )C A , which gives C A / C A0 = exp ( − k ∗ τ d ) =
exp ( − 0.05 τ d ) . This is also shown in Figure 6.5. Note that the decay of DCP is faster
in the PFR than in the CSTR. It is clear that an ideal PFR reactor can achieve the same
removal efficiency as that of a CSTR, but utilizing a much smaller volume of the reactor.

E XAMPLE 6.3 C OMBUSTION I NCINERATOR AS A PFR

Combustion incinerators are used to incinerate municipal and industrial waste. Gener-
allytheyrequirehightemperaturesandanoxygen-richenvironmentwithinthechamber.
Consider a waste containing benzene being incinerated using an air stream at a velocity
of5 m/s.Atypicalinlettemperatureis900 ◦ C(1173 K).Duetoheattransferthetempera-
turechangesalongthechamberlengthfrominlettooutlet.Assumeagradientof10 ◦ C/m.
As a consequence, the rate constant will also vary linearly with length. For benzene the
Arrhenius parameters are activation energy E a = 225 kJ/mol and pre-exponential factor
A = 9 × 10 10 s − 1 .A typical length of the incinerator chamber is − 10 m. Hence the exit
temperature will be 900 800 ◦ C (1073 K). The first-order rate constant for − 10 × 10 =

1s − 1 .As an approximation,
let us consider an average first-order rate constant k = 4s − 1 . The concentration in the
exitstreamcanbeobtainedusingtheequationforaplug-flowreactor: C A /C A0 = e − k τ .
Since τ = 10 m/5 ( m/s ) = 2s, C A /C A0 = 3 × 10 − 4 . Hence the destruction efficiency
is 99.96%.

8s − 1 and k( @1073 K ) = benzene will be k( @1173 K ) =

In many instances in environmental reactors, the reactor (e.g., a CSTR) may not
be at steady state at all times. Examples of these include a waste impoundment and
chemical spills into waterways. In these cases, we need to obtain the solution to the
mass balance equation under non-steady-state conditions. For illustrative purposes
we will use a first-order reaction.
V d C A

d t =

Q 0 (C A0 − C A ) − kC A V . (6.19)

By rearranging, we obtain
d C A
d t +

k C A =

Q 0
V

Q 0
V C A0 .

+ (6.20)