Leaching of Contaminants to Groundwater - Dealing with Contaminated Sites: From Theory Towards Practical Application - page 815

+ ρ b K d +

aK H

R = 1

θ

(18.45)

aD g K H
θ

D E = D h +

Jury et al. ( 1983b , 1984 ) provided for many organic contaminants their distribu-
tion coefficients K d and Henry's constants K H , from which calculated percent mass
present in each phase may be obtained.

18.3.2.4 Initial and Boundary Conditions

Initial Conditions

The governing equations for one-dimensional contaminant transport can be solved
analytically or numerically if the initial and boundary conditions for the prob-
lem being considered are specified. Initial conditions need to be provided for one
equilibrium phase concentration, i.e.,

=

c ( z , t ) c i ( z , 0) (18.46)

where c i is the initial concentration [ML − 3 ], as well as for all non-equilibrium
phases if nonequilibrium transport is to be considered (see further).

Boundary Conditions

Complex interactions between the transport domain and its environment often must
be considered for the water flow part of the problem at hand since these interactions
determine the magnitude of water fluxes across the domain boundaries. By compari-
son, the contaminant transport part of most analytical and numerical models usually
considers only three types of boundary conditions. When the concentration at the
boundary is known, one can use a first-type (or Dirichlet type) boundary condition
of the form:

c ( z , t ) = c 0 ( z , t ) (18.47)

where c 0 is a prescribed concentration [ML − 3 ] at the top or bottom of the soil
profile. This boundary condition is often referred to as a concentration boundary
condition. A third-type (Cauchy type) boundary condition may be used to prescribe
the concentration flux at the boundary as follows:

D ∂

c

− θ

x +

qc = qc 0 (18.48)

∂

in which q represents the boundary fluid flux [LT − 1 ], and c 0 is the concentration
of the incoming fluid [ML − 3 ]. In some cases, for example when a boundary is
impermeable ( q 0) or when water flow is directed out of the region, the Cauchy

boundary condition reduces to a second-type (Neumann type) boundary condition of
the form:

=