Geotechnical News • September 2016
29
GROUNDWATER
Tracer tests: Experimental verification of a new predictive
equation for effective porosity in stratified alluvial aquifers
Robert P. Chapuis
Abstract
Tracer tests in aquifers involve effec-
tive porosity,
n
e
, and longitudinal
dispersivity, α
L
, which are known to
depend upon the aquifer heterogeneity.
There is no reliable method to predict
n
e
, which is extracted by fitting the
test data of a breakthrough curve to a
theoretical curve. Chapuis (2015) used
physical principles to derive a new
predictive equation for
n
e
in stratified
alluvial aquifers. The new equation is
verified experimentally in this paper,
using laboratory and field data for
tracer tests.
Introduction
Large populations depend upon
groundwater and wells. Starting in the
1980s, many countries have developed
protection plans against the risks of
contamination. Current bylaws require
to delineate the total area from which
groundwater is captured (the catch-
ment), and a few capture zones which
define protection perimeters. For
example, a capture zone of 200 days
is the area from which groundwater
is captured by the well within 200
days. Several delineation methods are
available. They range from the simple
arbitrary fixed-radius to complex
numerical modelling. A few analyti-
cal solutions have been developed for
capture zones, but always for idealized
conditions (Bear and Jacobs 1965;
Grubb 1993; Chapuis and Chesnaux
2006; Chapuis, 2011).
Protecting water supplies involves
predicting the fate of pollutants in
groundwater. This is a difficult and
uncertain exercise using solute trans-
port theory, which involves effective
porosity
n
e
, and longitudinal disper-
sivity,
α
L
. Laboratory reduced-scale
models have verified that the theory is
realistic for homogeneous materials.
In nature, however, most aquifers are
heterogeneous, and have to be studied
using more complex theories and
numerical models.
Effective porosity,
n
e
, denotes the
fraction of the total volume of a
saturated porous material that is used
for movement of water. It excludes
unconnected and dead-end pores and
thus, is smaller than total porosity,
n
. Also called kinematic porosity, it
differs from “specific yield”,
S
y
, which
depends upon length of specimen,
duration and type of drainage test,
final suction, etc.
Some papers still confuse
n
e
and
S
y
despite the warning by Bear (1972).
This confusion may come with the
belief that a soil has a single
n
value,
thus ignoring the concept of compac-
tion. Let us consider two uniform
soils, coarse sand and non-plastic silt:
they may be tested at the same
n
=
0.40 and yield
n
e
≈ 0.39 for two labo-
ratory column tracer tests. However,
some drainage test may yield
S
y
=
32% for coarse sand and less than 5%
for non plastic silt, which confirms
that
n
e
and
S
y
are different physical
parameters. Another type of confusion
appeared in Riva et al. (2006) who
proposed a linear correlation between
ln (
n
e
) and
ln
(
K
),
K
being hydraulic
conductivity. For the two soils, both
may have
n
= 0.40 and
n
e
≈ 0.39, but
their
K
values differ by a ratio of 10
3
to 10
4
. Therefore,
ln
(
n
e
) and
ln
(
K
)
cannot be linearly related.
Dispersivity is used to describe the
dispersion of tracer mass. It has been
studied in statistically correlated per-
meability fields, which have confirmed
that dispersivity and heterogeneity are
related. Gelhar and Axness (1984),
Schwarze et al. (2001) and Dentz et
al. (2011) proposed to correlate
α
L
and
the variance,
σ
2
, of the
K
distribution
when
σ
2
< 1,
K
being the hydraulic
conductivity.
A recent research with the Web of
Science and three key words (aquifer
tracer dispersivity) brought back 215
papers. Adding “effective porosity”
gave only 22 of the 215 papers. This
means that 90% of the 215 papers
had no information on
n
e
, which is
surprising. Another research with
key words (aquifer tracer “effective
porosity”) brought back 45 papers. A
few had information for
n
e
, but most
of these simply used
n
e
as an input for
their numerical models. This confirms
that
n
e
is not known a priori and has
to be extracted from breakthrough
curves (BTCs) by fitting data with
1D, 2D or 3D solutions with more or
less parameters (Ptak et al. 2004). In
laboratory tests (homogenized soils),
n
e
is lower than
n
but very close. In
field tests,
n
e
is also lower than
n
, but
by how much?
While
α
L
can be predicted by rough
correlations (Chin 1986; Gelhar et al.
1992; Xu and Eckstein 1995, 1997) or
scaling methods (Frippiat and Holey-
man 2008), there is no reliable method
