Mixing Model for Activated Sludge
R. B. GRIEVES, Assistant Professor of Sanitary Engineering
W. F. MILBURY, Graduate Student
W. O. PIPES, Associate Professor of Civil Engineering
The Technological Institute
Northwestern University
Evanston, Illinois
INTRODUCTION
Methods of increasing the efficiency of biological waste treatment processes
are currently receiving much attention. One of the most important considerations
in improving the activated sludge process is a description of the mixing regime
which may exist within the system. Two basic classifications for activated sludge
systems are presently accepted: conventional activated sludge which involves plug
or piston flow with some back-mixing; and complete-mixing activated sludge.
These systems have traditionally been treated as two separate cases, and little
consideration has been given to the possible existence of combinations of plug flow
and complete mixing within a given unit. Two arrangements which could occur
would be plug flow and complete mixing in series or in parallel. In addition, the
presence of short-circuiting a portion of the feed directly to the outlet and of stagnant zones within the unit have not been included in mathematical descriptions of
the two basic classifications.
The overall objective of this study was the development of a mixing model
to describe intermediate situations between plug flow and complete mixing and to
include such effects as short-circuiting and stagnant zones. In particular this included the selection of a technique which could be used to analyze mixing patterns in activated sludge units and the combination of the resulting hydraulic
model with equations describing biological growth and metabolism. The resulting
hydraulic and kinetic description can be used to enable the prediction of the performance of an activated sludge unit with respect to nutrient utilization and
growth of active mass of organisms. The description presented includes both aeration with sludge recycle and separate wasting, and aeration only; the latter case
may be applied to oxidation ponds.
HYDRAULIC MODEL
Many approaches have been presented in the literature by chemical and hydraulic engineers to describe the flow regime in chemical reactors; the method of
Cholette and Cloutier (1) was adopted for this study. The choice was based upon
the simplicity and ease of physical application of their mixing convention which,
at the same time, provides a rigorous analysis of the hydraulic regime. A volume
apportionment method is employed to divide the system into different mixing patterns. Relations may be derived which consider an effective volume of complete
mixing, stagnant zones, and short-circuit and plug-flow conditions. In studying a
continuous flow system, the tank or vessel is considered to act as a damper to
variations in the composition of the feed. Ihus, the mathematical treatment becomes similar to that performed on a capacity in a servo-mechanism circuit where
a transfer function exists and transient or permanent responses are obtained.
Figure 1 presents an analysis for a completely-mixed system.   The vessel of
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