15 Conceptual Models and Computer Models
526
if the appropriate Excel
®
setting (‘Iterative Calculation’) should not be selected. The diffusive O 2
flux is calculated by employing Fick’s First Law
of Diffusion (Equation 3.2 in Chapter 3),
whereby the gradient obtained from the concentrations in column (F) is used. The concentrations in column (F) are calculated stepwise for
each time interval from the preceding value, from
the material flux in and out of the cell, and from
the decomposition activity listed in column (D).
Hence, the result in cell D11 reads in Excel
®
notation:
D11=B11*C11*((F11-F12)/$A$6)
D11 consequently contains the flux rate of material directed from the bottom water into the
sediment. The cells D12 to D60 will be accordingly
copied from this cell. Cell D61 remains empty.
The decomposition of organic substance in the
uppermost sediment zone is written in the cell E12;
cell E11 (bottom water) remains empty. In the
example shown the decomposition of organic
substance mediated by oxygen in a reaction
following first order kinetics was still bound to the
Table 15.5 Worksheet (excerpts) from modeling the decomposition of organic substance by dissolved oxygen and
dissolved nitrate in a diffusion controlled pore water profile. The model procedure was performed according to the ‘PressF9-method’ with an Excel
® . worksheet The columns are marked in the uppermost row with alphabetical characters, the
rows are numbered in the first column. Details pertaining to the model are further explained in the text.
A
B
C
D
E
F
G
H
I
1
2 M odel oxidation C org with oxygen and nitrate
switc h
C:N
k(O2)
3
0
3.0
7.9E-09
4
---------------------- mmol l
-1 = mol m
-3 -----------------------5
dx(m)
dt(sec)
C0(O2)
C0(NO3
- )
Cb(O2)
Cb(NO3
- )
k ( N O 3
- )
6
0.001
1.0E+06
0.2
0.03
0.0
0.0
3.2E-09
7
8
9
Depth
φ
Ds
O2-Flux
O2-Red.
O2
NO3
- -Flux NO3
- -Red.
NO3
-
10
m
m
2 sec
-1 --------- mol m
-2 s
-1 ----- mmol l
-1
--------- mol m
-2 s
-1 ----- mmol l
-1
11
0.000 0.60 5.4E-10 9.36E-09
2.00E-01 -2.11E-09
3.00E-02
12
0.001 0.60 5.4E-10 8.01E-09 1.35E-09 1.71E-01 -1.66E-09 0.00E+00 3.65E-02
13
0.002 0.60 5.4E-10 6.85E-09 1.16E-09 1.46E-01 -1.27E-09 0.00E+00 4.16E-02
14
0.003 0.60 5.4E-10 5.86E-09 9.90E-10 1.25E-01 -9.40E-10 0.00E+00 4.55E-02
:
continued
:
29
0.018 0.60 5.4E-10 5.65E-10 9.53E-11 1.21E-02 8.27E-10 0.00E+00 3.63E-02
30
0.019 0.60 5.4E-10 4.83E-10 8.16E-11 1.03E-02 8.55E-10 0.00E+00 3.37E-02
31
0.020 0.60 5.4E-10 4.13E-10 6.98E-11 8.83E-03 8.78E-10 0.00E+00 3.11E-02
32
0.021 0.60 5.4E-10 3.54E-10 5.97E-11 7.56E-03 8.07E-10 9.09E-11 2.84E-02
33
0.022 0.60 5.4E-10 3.03E-10 5.11E-11 6.46E-03 7.42E-10 8.29E-11 2.59E-02
34
0.023 0.60 5.4E-10 2.59E-10 4.37E-11 5.53E-03 6.81E-10 7.56E-11 2.36E-02
:
continued
:
55
0.044 0.60 5.4E-10 1.15E-11 1.40E-12 1.77E-04 1.30E-10 7.13E-12 2.23E-03
56
0.045 0.60 5.4E-10 1.04E-11 1.12E-12 1.41E-04 1.25E-10 5.84E-12 1.83E-03
57
0.046 0.60 5.4E-10 9.56E-12 8.62E-13 1.09E-04 1.20E-10 4.61E-12 1.44E-03
58
0.047 0.60 5.4E-10 8.93E-12 6.29E-13 7.96E-05 1.17E-10 3.42E-12 1.07E-03
59
0.048 0.60 5.4E-10 8.52E-12 4.11E-13 5.20E-05 1.15E-10 2.26E-12 7.07E-04
60
0.049 0.60 5.4E-10 8.32E-12 2.03E-13 2.57E-05 1.14E-10 1.13E-12 3.52E-04
61
0.050
0.00E+00
0.00E+00