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Permeability scale effect in sandy aquifers: a few case studies
Effet d’échelle et perméabilité des aquifères sableux : quelques études de cas
Chapuis R.P.
École Polytechnique, Montréal, QC, Canada
ABSTRACT: In sandy aquifers, stratification results in a range of values for the hydraulic conductivity
K
, which can be evaluated at
three scales. Since large-scale tests are more likely to meet preferential flow paths, they are also likely to yield larger
K
values than
small-scale tests, which may be viewed as a scale effect. The small scale is that of soil samples: their quality must be assessed and
their grain size distribution analyzed to check for mixes of sub-layers, before using reliable methods to predict the
K
values. The
middle scale is that of field permeability tests for which it is important to respect the standards and perform verifications. The large
scale is that of pumping tests. The paper presents a few case studies of sandy aquifers. Their stratification led to unimodal or
multimodal grain size distributions. For all cases, the
K
distributions provided consistent images of the sandy aquifers. It was then
concluded that, after a quality control of data and interpretations, there was no scale effect in the aquifers.
RÉSUMÉ : Dans les aquifères sableux, la stratification donne une gamme de valeurs pour la conductivité hydraulique
K
qui peut être
évaluée à trois échelles. Les essais à grande échelle ayant plus de chances de tester des zones d’écoulement préférentiel, ils ont aussi
plus de chances de donner des valeurs élevées de
K
que les essais à petite échelle, ce qui peut être vu comme un effet d’échelle. La
petite échelle est celle des échantillons : leur qualité doit être évaluée et leur granulométrie analysée pour détecter les mélanges de
strates, avant d’utiliser des méthodes fiables de prédiction de
K
. L’échelle moyenne est celle des essais de perméabilité in situ pour
lesquels on doit respecter les normes et faire des vérifications. La grande échelle est celle des essais de pompage. L’article présente
des études de cas d’aquifères sableux. Leur stratification a donné des granulométries unimodales ou multimodales. Pour tous les cas,
les distributions de
K
ont fourni des images cohérentes des aquifères sableux. On a conclu, après un contrôle de qualité des données et
des interprétations, qu’il n’y avait pas d’effet d’échelle dans ces aquifères.
KEYWORDS: aquifer, grain size distribution, monitoring well, permeability test, pumping test, scale effect
1 INTRODUCTION
In sandy aquifers, groundwater seepage is controlled by
stratification, with coarse size sediments deposited at high water
velocities and small size sediments settling at low water
velocities, or in temporary ponds. Many methods can be used to
assess the hydraulic conductivity,
K
, which can vary over orders
of magnitude. It is often believed that since large-scale tests
involve large volumes, which are more likely to meet
preferential flow paths, they are likely to yield larger
K
values
than small-scale tests (Bradbury and Muldoon 1990; Rovey
1998; Rovey and Niemman 1998). Thus, there should be a scale
effect for the
K
value, some increase with the tested volume.
There is no consensus about this scale effect. Many studies
tried to check or challenge theoretical opinions. They differed
about testing techniques, investigated scales, and geologic
media. Alas, the quality of each
K
value usually was not
questioned even if poor quality data and interpretation are
known to yield an artificial scale effect. Regrettably, the quality
control of groundwater parameters, which must be methodically
completed for engineered facilities, is not always done (Chapuis
1995). This paper examines quality control issues with data and
interpretation, in order to exclude artificial scale effects.
The idea of scale effect was rejected by Butler and Healey
(1998). They argued that scale effect results from artifacts
linked to incomplete well development and low-
K
skins around
well screens, but they did not study what produce a positive or
negative skin. These skin phenomena and their effects on the
apparent
K
value being related to safety issues, they are more
studied in geotechnique (Chapuis and Chenaf 2010) than in
geosciences.
Moreover, many studies have not examined how incorrect
interpretation methods for slug tests and pumping tests can yield
artificial scale effects. However, the quality control of slug test
methods has been largely investigated in geotechnique (Chapuis
et al. 1981; Chapuis 1988, 1998, 1999, 2001; Chapuis and
Chenaf 2002, 2003). For pumping tests in unconfined aquifers,
the large-scale
K
values obtained were shown to be incorrect if
the interpretation was performed using current methods for
unsteady-state (Akindunni and Gilham 1992).
Therefore, when studying scale effect, some caution must be
observed to avoid using scale effect as a final excuse, or as a
fudge factor, when the heterogeneity of the tested material could
have been more thoroughly investigated and when errors
involved in sampling, testing and interpretation methods could
have been taken into account.
Note that properly taking into account scale effect is
important for numerical analyses, since an aquifer numerical
model cannot be as detailed as the physical reality. Most often,
the grids of numerical models cannot contain enough elements
to model the detail of real features. This is why up-scaling
techniques are needed to define some equivalent
K
value for
grid elements (Renard and de Marsily 1997; Zhang et al. 2011).
In this paper, the results of three sites are briefly examined.
The small scale, about 10
-3
m
3
, is that of samples recovered in
boreholes for which the
K
value was evaluated using predictive
methods. The middle scale, about 1 m
3
, is that of field
permeability tests in monitoring wells. The large scale, about
10
3
m
3
, is that of pumping tests. Now, the problems linked to
the collected data at three scales in sandy aquifers are examined
in detail, starting with the soil samples taken in boreholes.
2 SMALL-SCALE
K
VALUES (SAMPLES)
Many soil samples can be taken in boreholes, usually with a
split spoon. Quality issues relative to soil sampling have been
the topic of many geotechnical researches. Five sample classes
are defined by considering the relationships between sampling
