Environmental Engineering Reference
In-Depth Information
It should be noted that equations [13.18] and [13.19] combine the pollutant
concentration in mobile water C , immobile water C immobile , and at the surface of the solid
C solid . It must also note the evolution equations for the two last variables of the problem.
13.4. Balance equations
To calculate a field of pollutant concentration, it is necessary to establish constitutive
laws expressing the conditions of movement and retention, and to write balance
equations. The balance equations of pollutant transport in mobile water are similar to
those of single-phase flows. They express that in an elementary volume, the sum of
inputs and outputs of a pollutant is equal to the stored pollutant mass. In other words,
they are conservation equations of pollutant mass, expressed as an average or
homogenized REV value.
n
q p
δ v x
δ x
v x
v + dx
x
S , Q
v
dx
Figure 13.3. Balanced at the surface and in an elementary volume
We write two equations. The first one is relative to the balance at the surface. It
expresses that the imposed flow q p , positive in input, is equal to the component of
the inside flow normal to the boundary:
T
n
v + q
= 0
[13.20]
p
The other balance equation is relative to the volume:
T
Q dV -
n
v dA =
(C + S
) dV
[13.21]
V
p
A
V
p
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