Environmental Engineering Reference
In-Depth Information
As the main part of the M-file and the function calls coincide with the previous
example, the explanation of the code is restricted to the function section. Note that
in this example there are six unknown functions, which are the concentrations of the
three redox species that are included in the model with their derivatives. All
functions are included in the vector
y
.
y(1)
is the oxygen concentration,
y(4)
its
derivative,
y(2)
is the nitrate concentration,
y(5)
its derivative,
y(3)
is the manga-
nese concentration and
y(5)
its derivative.
In the variable
c0
the analytical solution for organic matter is implemented. The
lambda
value used here coincides with the ratio
l=w
of formula (
9.14
). In the
monod
vector three Monod terms are calculated and in the
inhib
vector the two inhibition
factors for the two redox processes with higher preference.
The derivative specifications for the first three components of
y
are the defining
formulae for the derivatives of the concentrations. The other three specifications
represent the differential equations in the following form:
@
@z
c
O
2
0
¼
1
D
u
@
k
O
2
c
O
2
K
O
2
þc
O
2
@z
c
O
2
0
þc
org;s
k
O
2
k
O
2
þc
O
2
@
@z
c
NO
2
0
¼
1
D
u
@
k
NO
2
c
NO
2
K
NO
2
þc
NO
2
@z
c
NO
2
0
þc
org;s
k
O
2
k
O
2
þc
O
2
k
NO
2
k
NO
2
þc
NO
2
@
@z
c
Mn
0
¼
1
D
u
@
k
Mn
c
MnO
2
K
Mn
þc
MnO
2
@z
c
Mn
0
c
org;s
(9.21)
The degradation of oxygen is given by the product of organic matter concentra-
tion with the Monod term:
c0*monod(1)
. The coefficients
k
O
2
; k
NO
2
and
k
Mn
are
stored in the
k1
vector, the parameters
K
O
2
; K
NO
2
and
K
Mn
in the
k2
vector and the
inhibition parameters
k
O
2
and
k
NO
2
in the
k3
vector. The degradation term for nitrate
in addition to the Monod term includes the inhibition term for oxygen
inhib(1)
.
The corresponding term for manganese has another additional term:
inhib(2)
, the
inhibition term for nitrate. Note that the sign of the reaction term in the equation for
manganese is opposite to that of the other two substances, as free manganese ions
are produced in the redox reaction, while oxygen and nitrate are consumed. That is
the reason why the Monod-term for the manganese redox reaction is different.
Equations (
9.21
) also contain the concentration of the reaction product MnO
2
.In
order to keep the number of parameters small, it is assumed that the manganese
pool in the porous matrix remains at a constant high level for this model.
For
c
MnO
2
>>K
Mn
the Monod term can be approximated by
k
Mn
(Fig.
9.6
).
Biochemical redox reactions, which are strongly coupled with the degradation of
organic matter, are taken into account by the formulation:
q
i
¼l
org
c
org
f
i
(9.22)
with concentration of organic matter
c
org
and degradation constant
l
org
. The factor
f
i
is a measure for the relative share of the
i
th redox process on the total degradation
