14
then if we define k1 by
(l.40)
we get
(1.41 )
On the other hand we suppose pointwise discharges of BOD at points Pj which are
included in the model by taking
No
S1 = L q{lr,/5(Pj).
(1.42)
j=l
By integrating in depth we get the corresponding terms in ( 1.33)
(1.43)
No
81 = Lqt~j5(Pj).
(1.44)
i=1
The parameter kl depends of several factors as type of organic matter, water temperature,
etc. At 20°C typical values are between 0.2 and 0.5 d- 1 .
Dependency on temperature is given by the formula
(1.45)
where usually the constant (} is between 1.03 and 1.05.
Now we are concerned with the dissolved oxygen (DO). We refer to this species by
subscript 2. The main factors for changes in DO are the following:
1. Consumption by BOD.
In equation ( 1.33) the consumption of dissolved oxygen due to the BOD is taken
into account by defining the term R2 by
(1.46)
2. Reaeration. Absorption of oxygen from the atmosphere depends on its saturation
concentration in water. As a source term it is included in 82 as follows
s~ = k2( d. - P2) on the water surface
(1.47)
where
• k2 is the interface transfer rate for oxygen,
• d. is the saturation density of oxygen in water depending on temperature.