Page 264 - Soil and water contamination, 2nd edition

Chemical transformation 251

Solution
First, calculate the discharge of the stream just upstream from the effluent outfall (see
Example 11.4):

-1
3 -1
Q = 0.6 m × 5 m × 0.12 m s = 0.36 m s
stream
The ammonium concentration directly downstream from the outfall is (see Equation 11.17):
. 0 22 . 0 36 18 . 0 04 . 0 80 -1
C downstream 0 . 2 mg l
. 0 36 . 0 04 4 . 0
Second, calculate the actual nitrification rate constant corrected for the dissolved oxygen
concentration (see Equation 13.18) and water temperature (see Equation 13.21):
DO T 20 6 4 -1
k k . 1 04 8 . 1 . 0 75 . 0 85 8 . 1 . 1 15 d
n , n max, 20oC
M DO 2 6
n

The time it takes for the water to travel 2.5 km is
2500 1
t . 0 24 d
. 0 12 86400

where 86 400 = the number of seconds per day. The ammonium concentration at 2.5
downstream of the outfall is

C(t) C e k t n 0 . 2 e . 1 15 . 0 24 0 . 2 . 0 76 5 . 1 mg l -1
0
+
The distance downstream from the outfall at which the NH concentration is back to
4
-1
the upstream concentration of 0.22 mg l can be derived as follows:
C(t) 0 . 2 e . 1 15 t . 0 22
t
. 1 15 ln( . 0 22 ) 0 . 2 / . 2 21
t . 1 92 d
The distance that the water travels in 1.92 days is

x . 1 92 86400 . 0 12 19907 m = 19.9 km.

Thus, the influence of the wastewater outfall is discernable up to nearly 20 km
downstream from the outfall.

In rivers and lakes, manifold complex and irreversible biogeochemical reactions that
do not depend on the concentration of the reactant in the overlying surface water occur in
the bed sediments . Therefore, the production and subsequent release of substances to the
overlying water is often modelled using zero-order kinetics , because the release is limited by
physical constraints such as the size of the area over which the release occurs. Examples of
such zero-order reactions are methane production and the release of mineralisation products
3-
(e.g. NH , PO ) from anaerobic sediments. The general differential equation for zero-order
3 4
production or decay is:
dC
w
k 0 (13.22)
dt

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