Effect of Scale - Transport and Fate of Chemicals in Soils: Principles and Applications - page 103

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Effect of Sca le
The convection-dispersion equation (CDE) is often used to describe solute
transport in geologic systems under saturated and unsaturated conditions.
Dispersivity, one of the parameters of the CDE, is a measure of the disper-
sive properties of a geologic system. Traditionally, it has been considered as
a characteristic single-valued parameter for an entire medium (Pickens and
Grisak, 1981b). However, a number of studies have shown that a constant
dispersivity is not always adaquate, and a dispersivity that is dependent on
the mean travel distance and/or scale of the geologic system is often needed
(Fried, 1972; Sudicky and Cherry, 1979; Pickens and Grisak, 1981a; Gelhar,
Welty, and Rehfeldt, 1992; Khan and Jury, 1990).
The dependence of dispersivity on the mean travel distance and/or scale
of the geologic system is referred to as the “scale effects.” Pickens and Grisak
(1981a) provided a detailed review of the scale effects in field dispersion
investigations. They summarized results from several computer simula-
tions and laboratory and field transport studies. They found that disper-
sivities obtained from computer modeling studies of contamination zones
ranged from 12 to 61 m and tend to increase with the scale of the contamina-
tion zone (Table 1 in Pickens and Grisak, 1981a). In contrast, dispersivities
obtained from the analysis of laboratory breakthrough curve (BTC) data on
repacked materials were of the order of 0.01 to 1.0 cm, and those obtained
from analysis of various types of field tracer tests ranged between 0.012 and
15.2 m (Table 2 in Pickens and Grisak, 1981a). Gelhar, Welty, and Rehfeldt
(1992) provided a critical review of some 104 dispersivity values determined
from 59 different sites. The longitudinal dispersivities ranged from 10 -2 to
10 4 m for scales ranging from 10 -1 to 10 5 m. Although fairly scattered, the
data indicated a trend of increase in the longitudinal dispersivity with
observation scale.
Case studies conducted by Peaudecerf and Sauty (1978) showed that the
dispersivity changes with distance. From a field transport experiment,
Sudicky and Cherry (1979) found that dispersivity values for chloride based
on analytical solutions increased with mean travel distance in the ground-
water flow domain. Fried (1972) reported longitudinal dispersivities from
several sites. He reported several values ranging from 0.1 to 0.6 m for the
local (aquifer stratum) scale, 5 to 11 m for the global (aquifer thickness) scale,
and 12.2 m for the regional (several kilometers) scale (cited in Pickens and
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