Applications of Chemical Kinetics in Environmental Systems - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 386

y obs
X
1 + k decay θ

y x = . (6.248)

As an illustration of the above equation, we shall choose the special case when
k decay = 0. Other relevant parameters are chosen for a typical bacteria ( E. coli ) found
in wastewater plants: K s = 15 mg/L, μ max = 25 d − 1 , y X = 0.6, and [S] in = 15 mg/L.
Figure 6.68 displays the change in [X] and [S] ∗ as a function of the mean residence
time, θ , in the reactor.
It should be mentioned that the above equations only predict the steady-state behav-
ior. In actual operation, the unsteady state should be considered whenever the system
experiences changes in influent concentrations. There will then exist a lag time before
the substrate consumption and microbial growth approach a steady state. The micro-
bial growth lags by several θ values before it adjusts to a new [S] in . This is called the
hysteresis effect .

It is also useful to consider here the competition for a substrate S between an organ-
ism that utilizes it and other competing complexation processes within the aqueous
phase. Consider Figure 6.69. While an enzymatic reaction of species S (an inorganic
metal, for example) occurs via complexation with a cellular enzyme (denoted E), a
competing ligandY in the aqueous phase may bind species S. The cellular concentra-
tion of species S is determined by a steady state between cell growth (division) and
the rate of uptake of S. If [S] cell denotes the cellular concentration of S (moles/cell)
and is the specific growth rate (d − 1 ) , then the rate of cell growth is r cell = μ [S] cell .

From the reaction scheme in Figure 6.69, the uptake rate of species S is given by
r uptake =

μ

k E [S] tot [E] tot , which is the rate of reaction of species S with the enzyme
ligand E. This necessarily assumes that the enzyme is in excess of the concentration

E

E

Aqueous phase

Cell

E

k -Y
(Fast)

E

SE S SY

k E
(slow)

k Y
(Fast)

k uptake
(Fast)

E

(Quasi-equilibrium)

E

r = k E [S][E]

E

FIGURE 6.69 Kinetics of competing biological uptake and complexation in the aqueous
phase. (Adapted from Morel, F.M.M. and Herring, J.G. 1993. Principles and Applications of
Aquatic Chemistry , NewYork: Wiley.)