Project Description
Persons
have complained that their drinking water has had a
slight “disinfectant” taste to it. Samples indicate
that a trace amount of phenol has indeed entered the
treatment complex and that as little as 1 ppb can be
detected by taste. The State Department of
Environmental Quality [SDEQ], in cooperation with three
plants whose discharges contain phenol-type compounds
which might cause the problem, conducted three surveys
along the stream course; one before and two just after
two separate modifications at Plant 2.
The
results of these surveys are shown in
Table 1. The plant locations, relative to the
drinking water intake, are shown in
Figure 1. A segmented creek/river model is proposed
to analyze this system. The segments used are also
depicted in Figure 1.
In
order to simulate chemical transport and fate in this
stream course, a mathematical model is developed having
the form of a partial differential equation:
[dC/dt]
= - U [dC/dx] +
R (1)
where
C is the concentration of chemical (phenol), M/L3
t is time, t
x is distance or stream mile, L
U is the stream velocity, L/t
R is the rate of disappearance of chemical
from the stream, M/tL3
In
words, this equation states that the rate of change of
chemical concentration with time is proportional to the
rate of physical transport down the river course as
measured at some location plus the rate of disappearance
by reaction
If the
flow rates and plant discharges remain relatively
constant over a given time frame, then equation (1) can
be simplified to a steady state (time invariant) form
expressed as an ordinary differential equation:
U [dC/dx] =
R
(2)
In
words, this equation states that the change in
concentration of a chemical as a function of stream
distance is proportional to the rate of disappearance by
reaction. In such streams the rate of disappearance by
reaction can occur by either chemical or biological
mechanisms.
Therefore, the value for R
can be expressed as:
R = - (Ke + Kb)
C (3)
where Ke
is a rate constant controlled by biophysical extraction,
(1/t), and
Kb is the rate constant
associated with BOD satisfaction, (1/t)
In the
absence of detailed stream data that would allow
separating these mechanisms, it is often necessary to
treat them as a lumped or overall rate constant, K, such
that equation (3) simplifies to:
R = - K
C
(4)
Substitution into equation (2) results in:
U [dC/dx] = - K
C
(5)
This
equation can be integrated between the limits x = 0, C =
Co and x =
¥,
C = 0 resulting in the following:
C = Co exp[-Kx/U]
(6)
where
Co is the initial concentration of chemical
entering a segment, M/L3.
When
there is merging of two (or more) streams in a segment,
Co can be calculated as the average of the
chemical composition after the streams merge:
Co
= [QrCr + QtCt]/[Qr
+ Qt]
(7)
where
Cr is the concentration of chemical in the
main stream, M/L3
Qr is the volumetric flow rate in
the main str
Qt is the volumetric flow rate of
the tributary or the plant discharge, L3/t
Therefore, using equations (6) and (7), and data (See
Table 2) that allows one to calculate the rate
constants (usually from stream survey and laboratory
analysis plans), the concentration of chemical in the
stream at any location can be found.
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