3033
Simultaneous estimation of transverse and longitudinal dispersion in unsaturated
soils using spatial moments and image processing
Estimation simultanée de la dispersion transversale et longitudinale dans des sols insaturés au
moyen de la méthode des moments pour l’analyse des données spatiales et du traitement
d’images
Inoue K., Shimada H., Tanaka T.
Graduate School of Agricultural Science, Kobe University, Japan
ABSTRACT: A new methodology using spatial moment analysis linked with image processing of a dye tracer behavior in porous
media was developed to estimate dispersivities not only in longitudinal but in transverse directions. Laboratory and field tracer
experiments using a relatively mobile dye tracer Brilliant Blue FCF were conducted under saturated and unsaturated flow conditions.
Dye tracer in field moved through the soils in a preferential path pattern, which induced higher dispersivities in more irregular pore
patterns as compared with those in laboratory. Experimental results demonstrated the effectiveness of the developed methodology for
simultaneous assessment of transverse and longitudinal dispersion in unsaturated soils.
RÉSUMÉ : Nous avons développé une nouvelle méthodologie utilisant l’analyse par la méthode des moments associée au traitement
d’images pour suivre le comportement d’un traceur colorant en milieu poreux afin d’estimer les dispersivités, aussi bien dans la
direction longitudinale que transversale. Nous avons mené des expériences de traçage en laboratoire et sur le terrain au moyen d’un
traceur colorant bleu brillant FCF relativement mobile dans des conditions de flux saturé et insaturé. Sur le terrain, le traceur colorant
s’est déplacé dans les sols suivant un modèle de trajet préférentiel et, comparé à celles constatées en laboratoire, a présenté des
dispersivités induites plus élevées dans les profils d’interstices plus irréguliers. Les résultats de ces expériences ont démontré
l’efficacité de la méthodologie que nous avons mise au point pour évaluer simultanément la dispersion transversale et longitudinale
dans des sols insaturés.
KEYWORDS: longitudinal and transverse dispersion, dye tracer, image processing, spatial moment, unsaturated soils.
1 INTRODUCTION
The movement of groundwater in porous media is subject to
convection and dispersion, independently of any material being
transported (Vanderborght and Vereecken, 2007). Dispersion
results from the irregular movement of water in porous
formations where tortuosity of flow paths is induced. The
importance of local transverse dispersion is now identified as a
key factor in the smoothing of concentration fluctuations and
controlling the rate of dilution of conservative and non-
conservative solutes. Despite the importance of transverse
dispersion, transverse dispersivity is rarely determined due to
the lack of data in the experimental and quantitative difficulties
associated with such determinations. Recently, a few of the dye
tracer experiments combined with image analysis techniques
have been conducted to quantify the behavior of dye tracers
(McNeil et al., 2006).
The popularity of dyes is attributable to their low detection
limits, visualization potential and ease of quantification by
chemical analysis (Flury and Flühler, 1995). Application of
image analysis has shown that a time series of digitized images
reflecting the movement of dye tracer could be successfully
used to monitor solute transport in porous media as well as to
estimate transport parameters such as dispersion coefficient,
dispersivity (Forrer et al., 1999) and retardation factor (Flury
and Flühler, 1995). However, there are many aspects of solute
dispersion in unsaturated porous media that still be poorly
understood. In the present study, a new methodology using
spatial moment analysis linked with image processing of a dye
tracer behavior was developed to estimate dispersivities not
only in longitudinal but in transverse directions. This technique
was applied to dye tracer experiments both in laboratory and
field.
2 DYE TRACER EXPERIMENTS
2.1 Materials and method
Dye tracing has been widely used to characterize water flow and
solute transport behavior in porous media. Previous work
demonstrated that colored dye tracers could be successfully
used to visualize and monitor solute transport in a porous
medium confined in a transparent container (Flury and Flühler,
1995). In this study, one of the soluble dyes, Brilliant Blue FCF,
was employed as a dye tracer with the initial concentration of
1.0 mg/cm
3
. Although the initial concentration of dye tracer was
determined to be low enough to avoid density-induced flow
effects, there was no denying the effect of gravity on solute
transport during the course of movement.
Tracer experiments were carried out in a two-dimensional
and vertically placed water tank with the dimensions of 100 cm
width, 100 cm height and 3 cm thickness. The water flow tank
allowed to contain soils in order to form transparent quasi two-
dimensional solute transport phenomena and consisted of two
glass plates with 2 cm thickness. Schematic diagram of
experimental apparatus is shown in Figure 1.
In dye tracer experiments, silica sand with a low uniformity
coefficient was selected in order to simulate a sandy aquifer. In
addition, Andisols, which are volcanic ash soils and have
unique properties such as a low bulk density, were taken from a
maize field, dried at 110ºC and passed through a 2-mm sieve.
Grain sizes less than 0.2 mm were excluded to avoid the
adsorption of dye onto the surface of silt or clay. Physical
properties for both soils (silica sand and Andisol) are listed in
Table 1. In Figure 2, the relationship between suction and
volumetric water content for the drying process is plotted with
fitting curves based on van Genuchten’s formula (van
Genuchten, 1980).
