Kouli_etal_2008_Groundwater modelling_BOOK.pdf - Pantelis ...

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Marek Šváb and Lenka Wimmerová
approach is the fact that there is no limit in terms of complexity of the system to be modeled.
Simply, with increasing complexity of the system, the model semi-empirical parameters can
be modified in order to allow its experimental determination. The other advantage is the
possibility to model dynamic systems as well. The disadvantage of this approach consists of
the necessity to experimentally determine input data, which disables the transfer of the data to
other systems.
For a better explanation of the semi-empirical approach, let us consider the following
example. One of the widely used methods in water treatment is active carbon adsorption,
which can be used for removing various species from water, e.g. metal ions and organic
pollutants [2]. Various curves can be used for quantification of the relation between the
equilibrium concentration of the adsorbate in the solution and its sorbed amount. In most
cases, Freundlich or Langmuir isotherms are applied [3]; however, these isotherms do not
reflect particular sorption mechanisms and reactions that really occur on the sorbent surface.
Active carbon has a very complex structure, with a number of various active surface groups
that are responsible for its sorption properties. If we want to apply the exact approach, it
would be necessary to measure all particular reactions between these various groups and the
adsorbate. Since this task would be very complicated, we can decide not to consider all
particular reactions, but to measure only an equilibrium state in the particular system of active
carbon-pollutant and to characterize it through a suitable curve, e.g. Langmuir, Freundlich or
another mathematical function. The fact should also be considered that the Langmuir model
was prepared especially for the well-defined model adsorbents with one type of a uniform
surface reaction site, and thus its use for description of the sorption equilibrium on activated
carbon is groundless. However, the fact that it often provides good interpolation of measured
data is why the Langmuir curve is so popular. Although the model cannot be used for other
adsorbates and/or adsorbents, we can carry out the equilibrium calculations for various
concentrations, suggest a batch water-treatment system, make the first estimate of a suitable
dynamic system (a sorption filter), and at least partly understand the behavior of the system.
A similar approach represents a distribution coefficient for quantification of the
distribution of species between the solid and liquid phase, which is frequently used in the
description of interactions between soil and groundwater. From the point of view of the solid
phase, soil represents one of the most complex matrixes containing both various types of
inorganic components (clays, sand, silt, etc.) and of organic matter (fulvic acids, humic acid,
etc.). Soil composition results in a number of various possible surface interactions and
reactions, which are almost impossible to define. Furthermore, in the case of toxic metals, a
number of different forms in which the metals can be present in soil are known. Finally,
although the distribution coefficient does not reflect the mechanisms of the interactions
between the phases, it provides relatively reliable data for the particular soil and groundwater.
The third type of modelling approach of the water-solid interactions is the empirical one.
It is typical for this approach that we accept our studied system as a ‘black box’. The
empirical approach needs experimental measuring of the system, observation of its reaction
on modified surrounding conditions, and interpolation of measured data by a suitable
empirical equation. The advantage of the empirical model consists in possibly dealing with
the complex and dynamic systems, although transferability of data is very limited. The data
and results are valid strictly for the same conditions and the range of modified parameters as
those used in the experimental measuring.