Leaching of Contaminants to Groundwater - Dealing with Contaminated Sites: From Theory Towards Practical Application - page 820

balance equations for both water flow and colloid transport, and in addition for
the total contaminant, for contaminants sorbed kinetically or instantaneously to the
solid phase, and for contaminants sorbed to mobile colloids, to colloids attached
to the soil solid phase, and to colloids accumulating at the air-water interface.
Development of such a model is beyond the scope of this chapter. The interested
reader will find additional documentation from de Jonge et al. ( 2004 ), Flury and
Qiu ( 2008 ), Massoudieh and Ginn ( 2009 ), Šimunek et al. ( 2006a ), and Totsche and
Kögel-Knabner ( 2004 ).
18.3.4 Stochastic Models
Several studies have demonstrated that solutions of classical contaminant trans-
port models often fail to accurately describe transport processes in most field soils.
A major reason for the inability to capture field-scale contaminant transport is the
fact that the subsurface environment is very heterogeneous. Heterogeneity occurs
at different levels of spatial and time scales (Wheatcraft and Cushman 1991 ),
ranging from microscopic scales involving time-dependent chemical sorption and
precipitation/dissolution reactions, to intermediate scales involving the preferential
movement of water and contaminants through macropores or fractures, and further
to large scales involving the spatial variability of soils across the landscape. Soil het-
erogeneity can be addressed in terms of process-based descriptions which attempt
to consider the effects of heterogeneity at one or several scales. It can also be tack-
led using stochastic approaches which incorporate certain assumptions about the
transport process in the heterogeneous system (e.g., Dagan 1989 ; Sposito and Barry
1987 ). In this Section we briefly review flow and transport parameter heterogeneity
and discuss several stochastic transport approaches, notably those using stream tube
models and the transfer function approach.
18.3.4.1 Flow and Transport Parameter Heterogeneity
Spatial Variation of Physical and Chemical Properties
Hydrological and geological processes are known to vary in space (Delhomme
1979 ; Nielsen et al. 1973 ). This is due to the natural evolution of the subsurface
over geological time scales and anthropogenic activities in recent times. Knowledge
of spatial variability of physical and chemical properties is of utmost importance
not only from the point of view of characterisation of the heterogeneous subsur-
face, but also in the context of long term prediction of water flow and contaminant
transport in the subsurface. In this context, the last four decades has seen significant
number of studies carried out in order to comprehend the spatial variability of phys-
ical and chemical properties of soil with the help of both conventional statistics and
geostatistics.
From the vast body of literature, a wealth of data have been meticulously com-
piledbyJury( 1985 ) and Thibault et al. ( 1990 ) on the spatial variability of physical
and chemical properties respectively; salient data from these compilations are pre-
sented in Tables 18.2 and 18.3 . Note that the properties which are treated statistically