Environmental Engineering Reference
In-Depth Information
The concentration c in this case is defined as mass of solute per unit volume of
solution. When these kinds of sorption models are used, the ADRE in its most
general form can only be solved via numerical techniques [MAN 96]. The sorption
capacity of materials for mineral sealing layers can be assessed by performing batch
tests or from interpretation of simple diffusion tests and column tests [SHA 94b].
However, it is important to stress the fact that the prediction of contaminant
migration based on the adsorption parameters obtained from sorption tests is
different from the prediction obtained from column tests or simple diffusion tests
[RIC 01].
As already mentioned, most of the available ADRE closed-form solutions used
for diffusion and column test interpretation only consider linear isotherms.
Therefore, the interpretation of results should be referred to an average
concentration in the pore liquid of the mineral sample.
In the case of diffusion tests performed on a single reservoir with decreasing
concentration, Manassero
et al
. [MAN 96b, MAN 00] suggest referring to the
average solution concentration in the pore liquid in the soil sample at the end of the
test. In the case of advective-diffusive column tests, the reference concentration can
be taken to be equal to half the source concentration c
0
as a first approximation if c
0
is constant during the test.
16.6.5.
Dispersion-diffusion parameters
It is well known that the effective diffusion coefficients (
D
*
) become significant
for pollutant transport through containment barriers if, and only if, advection
transport is low. The common range of variation in the porosity and diffusion
coefficient of some chemical species (e.g. chloride, ethanol, etc.) for typical
materials used as mineral barriers is indicated in Figure 16.14a. Obviously, the
upper boundary is close to the diffusion coefficients for free solution. The same
range of variation for
D
*
and
n
is reported in Figure 16.14b, where the total
contaminant flux through a 1 m thick mineral barrier is given as a function of Darcy
velocity that, in turn, is proportional to the hydraulic conductivity provided that the
gradient is constant. Diffusion only starts to play a predominant role in the total
contaminant flux when the hydraulic conductivity value (
k
) is lower than 10
-9
m/s
for the common range of hydraulic gradients, as shown in Figure 16.14b.
