Environmental Engineering Reference
In-Depth Information
D
∂
c
θ
x
=
0
(18.49)
∂
Most applications require a Cauchy boundary condition rather than Dirichlet
(or concentration) boundary condition. Since Cauchy boundary conditions define
the contaminant flux across a boundary, the contaminant flux entering the trans-
port domain will be known exactly (as specified). This specified contaminant flux
is then in the transport domain divided into advective and dispersive components.
On the other hand, a Dirichlet boundary condition controls only the concentration
on the boundary, but not the contaminant flux into the domain, which because of
its advective and dispersive contributions will be larger than for a Cauchy boundary
condition. The incorrect use of Dirichlet rather than Cauchy boundary conditions
may lead to significant mass balance errors at early times, especially for relative
short transport domains (Van Genuchten and Parker
1984
).
18.3.3 Nonequilibrium Transport
Because equilibrium contaminant transport models have frequently been unable
to describe experimental data accurately, a large number of diffusion-controlled
physical nonequilibrium and chemical-kinetic models have been developed and
used to describe the transport of both non-adsorbing and adsorbing contaminants
(Šimunek and Van Genuchten
2008
). Efforts to model nonequilibrium transport usu-
ally involve relatively simple first-order rate equations. Nonequilibriummodels have
used the assumptions of two-region (dual-porosity) type transport involving contam-
inant exchange between mobile and immobile liquid phase transport regions, and/or
one-, two- or multi-site sorption formulations (e.g., Brusseau
1999
; Nielsen et al.
1986
). Models simulating the transport of particle-type contaminants, such as col-
loids, viruses, and bacteria, often also use first-order rate equations to describe such
processes as attachment, detachment, and straining. In many cases nonequilibrium
models have resulted in better descriptions of measured laboratory and field contam-
inant transport data, in part by providing additional degrees of freedom for fitting
measured concentration distributions.
18.3.3.1 Physical Nonequilibrium
Dual-Porosity and Mobile-Immobile Water Models
Two-region transport models (Fig.
18.14b
and
c
) assume that the liquid phase
can be partitioned into distinct mobile (flowing) and immobile (stagnant) liquid
pore regions, and that contaminant exchange between the two liquid regions can
be modeled as a first-order exchange process. Using the same notation as before,
the two-region contaminant transport model is given by (Toride et al.
1993
;Van
Genuchten and Wagenet
1989
):
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