A DYNAMIC KINETIC MODEL OF THE ACTIVATED SLUDGE PROCESS
L. M. Chase, Senior Physicist
Central Engineering Laboratories
FMC Corporation
Santa Clara, California 95052
INTRODUCTION
Monod's [ 1 ] formulation of the growth of bacterial cultures has been extensively
applied to the activated sludge process. Under steady conditions the Monod model
has proven to be a reasonably accurate description of the process [2,3].
The growth rate of a bacterial culture is given by
where x is the concentration of organisms and fi is the specific growth rate.
In the case of nutrient-limited cultures the specific growth rate is given by the
expression
""*W^TT (2)
where Mmax is the maximum specific growth rate, Kg is a saturation constant and S is
the substrate concentration.
An additional equation relates growth rate to substrate utilization
« . . Y dS
dt dt w
where Y is the yield coefficient.
Thus, the rate of substrate utilization is given by
« -     »  u        —™- (4)
dt Y Fmax Ks + S y
The Monod model was developed as a description of a steady-state system.   Under
dynamic conditions many investigators have recognized that the specific growth rate
lags behind the values predicted by the Monod model in responding to changes in substrate concentration.   Perret [4] has referred to this phenomenon as "growth-rate
hysteresis."
Several dynamic models which attempt to explain the growth rate lag of biological
cultures have been proposed.   For instance, Young et al. [5] created a model based on
the assumptions that when substrate concentration is increased, the active transport of
nutrients across the cell membrane introduced a time delay, and that there is a pure
time delay between the increase in substrate concentration and the increase in enzymes
required to react the substrate at a higher rate.   Storer and Gaudy [6] constructed a
dynamic model in which they assumed that the growth rate and yield factor vary with
time.   Experiments showed that this view was consistent with observations.   Other
dynamic models have been proposed by Ramkrishna ef al.  [7] and Tanner [8].   Experimental studies of the dynamic response of activated sludge have been conducted
by Adams and Ekenfelder [9] and Sherrard and Lawrence [10].
The kinetic model presented in this report is based on the proposition that the rate
of metabolism is controlled primarily by the concentration of enzymes in the biological
mass.   The enzyme concentration depends on both substrate concentration and time.
Further, for any given substrate concentration there exists an optimum level of enzymes
required to metabolize the substrate efficiently.   In response to changes in substrate
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