Applications of Chemical Kinetics in Environmental Systems - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 384

E XAMPLE 6.35 M ICROBIAL G ROWTH AND S UBSTRATE K INETICS IN A CSTR

A microbial culture in a CSTR is a very efficient method for degrading substrates.
The technique has been widely employed in the biotechnology field. It has also been
employed in activated sludge wastewater treatment process. Indigenous bacteria are
grown in a reactor that is fed with the substrate (nutrients) at a specified rate. The
operating conditions (pH, dissolved oxygen, and temperature) are maintained constant
within the reactor. The effluent is monitored for both microbial population and substrate
concentration. Figure 6.67 represents the CSTR.
The seed culture of microbes is placed within the reactor and nutrients provided to it
in the influent stream that contains the substrate. The submerged bubble generators that
are used to introduce oxygen into the reactor provide mixing. Paddle mixers are also
used to gently mix the constituents. The biomass in the reactor is uniformly distributed
with no clumping at the vessel wall and the yield factor, y X , is assumed to be constant.
A mass balance on the microbial concentration, [X], should include its growth and its
loss via overflow into the effluent and decay within the reactor. We have

V d [ X ]

d t = μ [X] V − F [X] − k decay [X] V .

(6.241)

At steady state, d[X]/d t = 0, and hence

F
V + k decay .

μ = (6.242)

This is called the dilutionrate (time − 1 ) of the microbe.The reciprocal V / F = θ is called
the meancellresidencetime . Note that θ is the same as the specific growth rate discussed
earlier. Thus, in a CSTR it is an important parameter in understanding microbial growth

Q
[X]
[S] *

Q
[S] in

V

[X]
[S] *

FIGURE 6.67 Schematic of a CSTR for microbial and substrate kinetics.