Page 266 - Soil and water contamination, 2nd edition

Chemical transformation 253

(e.g. Van der Perk, 1996). The value of the equilibrium concentration depends on the
sediment composition with respect to grain size distribution and organic matter content ,
and phosphorus /nitrogen loading of the river or lake. Table 13.5 lists some literature values
of the first-order constant k and the equilibrium concentration for ammonium (EAC) and
phosphate (EPC) in selected rivers (see Equation 13.25).

Example 13.4 Phosphate release

3-
In a 75 cm deep channel draining a Dutch polder, the equilibrium phosphate (PO )
4
-1
3-
concentration EPC and the PO fixation rate constant were measured to be 0.6 mg l
4
3-
-1
and 0.4 d , respectively. Assuming that the PO fixation process can be entirely
4
attributed to exchange between the bed sediments and the overlying water, calculate the
3-
corresponding zero-order PO release rate from the bed sediments.
4
Solution
From Equation (13.25), it can be seen that the EPC equals
J
EPC
H k
Thus,
J -1 -3
6 . 0 mg l (= g m )
. 0 75 4 . 0
-1
3-
-2
3-
-2
J = 0.18 g PO m d = 180 mg PO m d -1
4 4
EXERCISES
1. Derive the analytical solution of the following differential equations (hint: compare Box
11.I)
dC
a. kC
dt
dC
b. k C C eq
dt
2. The mass balance of a biodegradable substance in a small well-mixed lake is:
dM
Q C in - Q C k V C
dt
where M = mass of biodegradable substance [M], Q = discharge through lake
3
-3
-1
[L T ], C = concentration of biodegradable substance in inflowing stream [M L ],
in
-3
C = concentration of biodegradable substance in lake [M L ], k = biodegradation rate
-1
constant [T ], V= lake volume. The steady state solution of the concentration is
C in
C
1 kT
where T = residence time of water in lake [T].
Derive this steady state solution from the differential equation given above.

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