A Five Minute Solution for Stream
Assimilative Capacity
ARTHUR W. BUSCH, Professor
Department of Environmental Engineering
Rice University
Houston, Texas
INTRODUCTION
One of the cornerstones of environmental management is the use of the
maximum capacity of our natural waters to assimilate organic wastes. This capacity is
called the stream assimilative or stream purification capacity. As was pointed out
recently (1), discharging as much waste as possible to our natural waters is a policy of
intentional pollution. Much work and many hundreds of thousands of dollars have
gone into studies whose objective is to maximize intentional pollution. The intent of
this paper is to show that if we insist on intentionally polluting our natural waters,
the minimum capacity for assimilation, without lowering oxygen content below a
pre-determined value, is the significant capacity and becomes the maximum available
for intentional pollution. Discharge of any wastes in excess of this minimum capacity
must involve a probabilistic analysis. The minimum assimilative capacity is set by the
minimum reaeration capacity because reaeration is the only source of continuous
oxygen supply. The minimum reaeration capacity thus is the maximum usable
assimilative capacity for uniformly applied and distributed wastes.
CONCEPTS
Last year at this conference, a paper on aeration and oxygen transfer pointed
out that in waste treatment aeration the effectiveness of esternal energy input is
constrained by the biological reaction (2). In other words, we can not transfer
oxygen faster than we use it. Natural reaeration of streams is exactly the opposite. In
this case we can not count on using oxygen unless it is transferred into the water by
natural phenomena or unless instream aeration is practiced. See Figure 1.
This means that the assimulative or purification capacity of a body of water is
set by the product of the minimum surface (mass) transfer coefficient, the maximum
dissolved oxygen deficit and the surface area under consideration.
The general expression for gas transfer to a liquid is
dM = KLA(Cs-C) (1)
dt
Where Kj_ is the mass transfer coefficient, A is the interfacial surface area and Cs and
C are  saturation  and ambient  dissolved  oxygen concentrations.  For the worst
condition   in  a  natural body  of water; i.e.  no  surface  turbulence  and  highest
temperature:
151