Oxygen Response and Aeration in Steams
ROBERT DRESNACK, Assistant Professor
IVAN METZGER, Professor
Department of Civil Engineering
Newark College of Engineering
Newark, New Jersey
INTRODUCTION
The response of oxygen to transient pollutional inputs may be described by a
numerical solution of a partial differential equation describing the basic material
balance. The stability of the method of solution depends on the relative values
of the diffusive and convective fluxes while the actual response is most sensitive
to lower-order terms. Since stability is insured for the range of relative values of
the flux terms which apply to streams, attention is focused on the sensitivity of
response to the lower-order terms such as aeration. A physical model of the
mechanism of aeration is based on the concept that an interfacial liquid film is in
a continuous state of random renewal by turbulent fluid from beneath the surface.
BASIC EQUATIONS
The temporal and spacial distribution of BOD in a stream for one-dimensional
flow is given by
*  9^ = D, 9!k   - H9L   . (K   + K3)L t La (1)
at      LaiF     ax
where L is the BOD concentration at any time, t. at a location x. The first term
in Equation 1 describes the effect of longitudinal dispersion, DL, and the second
term, that of velocity, U. The decay or production represented by the third term
is assumed to follow first order kinetics which is the sum of two distinct processes.
A continuing decay due to oxidation is represented by K,. All other processes,
such as settling or resuspension, are represented by K3 which can be either positive
or negative. The last term, La, describes a uniform addition of BOD along a
stretch.
A similar equation describing the temporal and spacial distribution of dissolved oxygen, C, is
|f   = °L H    -^-K.L.K^-O-DB (2)
where the first three terms are analogous to those in Equation 1. Atmospheric
aeration is described by a first-order reaction with coefficient, K2, and a driving
force equal to the difference between the saturation concentration of oxygen, Cs,
and the concentration C in the stream at any time. The net rate of addition of
oxygen by all other processes is represented by Dg. This term is positive if the
predominant processes are the removal of oxygen by plant respiration and the oxygen demand of the bottom sludge or negative if photosynthetic addition predomi-
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