IV. Wastewater Treatment Technologies
Topic IV. 8. Biological Processes of Wastewater
Treatment: Fazes, Kinetics - Monod’s Equations
Basic Fazes of Biological Processes
General mechanism of substances micro-biological transfer:
 Extracellular substrate degradation by external enzymes
 Substrate particles attachment at the cells walls
 Substrate diffusion into the cells through the cells membranes
 Cell metabolism (biochemical transformations)
 Metabolism products diffusion out of the cells
1
Basic Fazes of Biological Processes
General mechanism of substances micro-biological transfer:
 Substrate necessary composition
BOD20 : N : P  100: 5 : 1
 Processes of substrate dissimilation (breathing)
C x H y Oz N  ( x  0,25y  0,33z  0,75)O2  enzymes
 xCO2  (0,5 y  1,5) H 2 O  NH 3  Energy
 Processes of substrate assimilation (cell growth)
C x H y Oz N  NH 3  O2  enzymes
 C5 H 7 NO2  H 2 O  CO2  Energy
 Processes of the cells substances dissimilation (endogenous respiration)
C5 H 7 NO2  5O2  enzymes
NH 3  O2  enzymes HNO2 
 5CO2  NH 3  2H 2 O  Energy ;
 O2  enzymes HNO3
2
Basic Fazes of Biological Processes
Biological Processes Kinetics
Biomass Growth Kinetics
1 - lag-faze; 2 - exponential growth faze; 3 - steady-state faze; 4 - endogenous respiration faze
3
Biological Processes Kinetics
Equations of Monod
 Rate of biomass growth
S
  m.
Ks  S
dX / dt  X  k d X
X - biomass concentration, g/m3
 - coefficient of specific biomass growth rate, d-1
kd - coefficient of endogenous respiration, d-1
m - maximal value of the coefficient  , d-1
S - substrate concentration, g/m3
Ks - half-saturation constant, g/m3
 Rate of substrate utilisation
 dS / dt  X / Y 
m
Y
.
S. X
Ks  S
Y - biomass yeld coefficient, gX/gS
4
Biological Processes Kinetics
Transformations of Monod’s
Equations
 Substrate utilisation specific rate - U
1 dS 
 .
  U , gS/gX.d
X dt Y
 Biomass age - x
X
x 
dX / dt
,d
 Biomass growth rate
1 /  x  Y .U  k d
, d-1
5
Biological Processes Kinetics
Kinetic Parameters Use
in the Practice
 In the bioreactors design
1 dS
 .
U
X dt
S
t
S0
0
  dS  U . X  dt
S0  S
t
X .U
t - necessary design hydraulic
retention time to achieve S
6
Biological Processes Kinetics
Kinetic Parameters Use in the Practice
 In the real process regulation
S0  S

S0
 - necessary degree of purification in respect to S
S0 - substrate concentration at the influent
S - substrate concentration at the effluent
U

Y

 m .S
Y .(K s  S )
Then S 
and U 
1 1
(  kd )
Y x
U .K s
K s (1 /  x  k d )
K s  Y .S



, or x
 m  U .Y Y ( m  1 /  x  k d )
Y .S.( m  k d )  K s .k d
Therefore, the necessary effluent concentration S can be maintenance
by maintenance of the relevant values of U and x. The value of the 7
later can be achieved by the excess biomass regulation.