Page 216 - Soil and water contamination, 2nd edition

Substance transport 203

11.2.2 Load calculation and mixing
In Section 11.1 we saw that the load of a substance in a river is defined as the product
of its concentration and the water discharge (see Equation 11.1), and thus represents the
amount of substance transported by advection . Actually, this calculation is only valid for a
momentaneous load. The average load that has passed a point over a longer period of time
can be defined as:
1 t
C (t ) Q (t ) dt
0 (11.16)
L
t 1 t 0
-1
where L = Load that passes a point in the time interval from t=0 to t=t [M T ]. Because
1
concentration and discharge are usually correlated, the average load over a long period, say
a year, is not equal to the annual average concentration times the annual average discharge.
If there is a positive correlation between discharge and concentration due to increased
substance inputs during high flow conditions, for instance as a result of soil erosion , the
simple product of annual average concentration and discharge underestimates the annual
load. If there is a negative correlation due to dilution during high flow conditions, the simple
product of annual average concentration and discharge overestimates the annual load.
The load calculation also enables us to calculate concentrations downstream from a point
source , e.g. an effluent discharge or a tributary river. In contrast to concentrations, loads
may be added up. If we assume instantaneous mixing of two converging streams, the load
downstream of the confluence (C Q ) is the sum of the loads from both streams (C Q and
3 3 1 1
C Q , respectively). The concentration downstream is:
2 2
C Q C Q
C 1 1 2 2 (11.17)

3
Q Q
1 2
In reality, it takes a certain distance downstream of a confluence to complete mixing over
the entire cross-section of the river. This mixing length is treated in more detail in Section
11.3.4.
Advection is one of the most important modes for substance transport in both
groundwater and surface water. Note that in all the equations related to advective transport
presented in this chapter, the concentration is calculated using water discharge. This
emphasises the importance of an accurate water balance, because without a balanced water
budget it is impossible to obtain an accurate mass balance for advective transport.

Example 11.4 Load calculation and mixing

A wastewater treatment plant discharges its effluent in a stream at a constant rate
-1
of 40 l s . The stream has a depth of 0.6 m, a width of 5.0 m, and a flow velocity of
-1
12 cm s . The chloride concentration in the stream just upstream from the effluent
-1
-1
outfall is 20 mg l and the chloride concentration of the effluent water is 180 mg l .
Calculate the chloride concentration directly downstream from the effluent outfall,
assuming instantaneous mixing.
Solution
This is a rather straightforward application of Equation (11.17): First, calculate the
discharge of the stream just upstream from the effluent outfall:
3 -1
-1
Q = 0.6 m × 5 m × 0.12 m s = 0.36 m s
stream

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