226
B. Nilkens et al.
ac
at
--storage
U. ac +~~(& ac)+
ax
Aax xax
'-.r-'
'------v------'
advection
dispersion
!(&-O')
h
'----v-----'
erosion,
se dim entation
+ qzu (C zu -c)± r.
~ transformation
side flows
(1)
can be simplified by neglecting the time derivative. Beyond this the dispersion
term can be discarded, if flow is dominated by advection (Fischer et al. 1979).
Static and steady - state simulations have shown that even if assuming low flow
velocities and large dispersion coefficients, the error, which is caused by neglecting dispersion, is minimal. Moreover, this error can partly be absorbed by calibrating the decay terms (Schlaeger et al. 2000). After simplifying Eq. 1, the analytical
solution can be determined easily. This solution is implemented into the quality
module. By solution of analytical equations instead of a system of equations to
solve the complex advection-diffusion equation, running time can be reduced.
Interaction between the simulated parameters is normally considered by time -
consuming iterations. To take these interactions into account without applying iterations, on the one hand, the sequence of parameters is chosen in such a manner
that first conservative substances and finally most reactive parameters are calculated. On the other hand, distances between river profiles at which parameters are
calculated are decreased. In this way, the error caused by abandonment of iterations can be reduced. Test simulations have proved that a distance of 25 m yields
the pareto-optimum of run time and accuracy.
The next step was to determine the relevant transformation processes. Exemplarily, this procedure is clarified by means of the parameter total iron. As described
above, high concentrations of iron are typical for mining - affected rivers. In general, iron exists as a sensitive reacting redox couple, ferrous iron Fe(II) and ferric
iron Fe(III). Depending on pH and DO concentration, Fe(II) is oxidised into
Fe(III) hydroxide, which covers the river bed with a red-brown, hardly soluble
precipitation [Fe(OHh(s)] (Stumm et al. 1996). Under anaerobic conditions, by a
decrease of pH value, or by erosion processes during flood events, precipitated
iron is resuspended.
Sedimentation and resolution, as well as resuspension caused by erosion and
chemical processes, should be considered as the relevant transformation processes
of iron. Hence, the concentration of total iron, Fetot. shall be described by the following equation:
B. Nilkens et al.
ac
at
--storage
U. ac +~~(& ac)+
ax
Aax xax
'-.r-'
'------v------'
advection
dispersion
!(&-O')
h
'----v-----'
erosion,
se dim entation
+ qzu (C zu -c)± r.
~ transformation
side flows
(1)
can be simplified by neglecting the time derivative. Beyond this the dispersion
term can be discarded, if flow is dominated by advection (Fischer et al. 1979).
Static and steady - state simulations have shown that even if assuming low flow
velocities and large dispersion coefficients, the error, which is caused by neglecting dispersion, is minimal. Moreover, this error can partly be absorbed by calibrating the decay terms (Schlaeger et al. 2000). After simplifying Eq. 1, the analytical
solution can be determined easily. This solution is implemented into the quality
module. By solution of analytical equations instead of a system of equations to
solve the complex advection-diffusion equation, running time can be reduced.
Interaction between the simulated parameters is normally considered by time -
consuming iterations. To take these interactions into account without applying iterations, on the one hand, the sequence of parameters is chosen in such a manner
that first conservative substances and finally most reactive parameters are calculated. On the other hand, distances between river profiles at which parameters are
calculated are decreased. In this way, the error caused by abandonment of iterations can be reduced. Test simulations have proved that a distance of 25 m yields
the pareto-optimum of run time and accuracy.
The next step was to determine the relevant transformation processes. Exemplarily, this procedure is clarified by means of the parameter total iron. As described
above, high concentrations of iron are typical for mining - affected rivers. In general, iron exists as a sensitive reacting redox couple, ferrous iron Fe(II) and ferric
iron Fe(III). Depending on pH and DO concentration, Fe(II) is oxidised into
Fe(III) hydroxide, which covers the river bed with a red-brown, hardly soluble
precipitation [Fe(OHh(s)] (Stumm et al. 1996). Under anaerobic conditions, by a
decrease of pH value, or by erosion processes during flood events, precipitated
iron is resuspended.
Sedimentation and resolution, as well as resuspension caused by erosion and
chemical processes, should be considered as the relevant transformation processes
of iron. Hence, the concentration of total iron, Fetot. shall be described by the following equation: