Advective-dispersive models (Cont.)

should first consider the long-time behavior of Equation B27 when the sediment

originally exhibits a contaminant pore water concentration C0. If the contami-

nant is not subject to significant depletion by either degradation or migration

through the cap, the flux through the cap ultimately reaches that given by

Cw)

Fadv

as t

U (C0

(B29)

That is, the contaminant flux due to advection approaches that which would be

observed if no cap were placed over the sediment. In such a situation, the cap

can be viewed only as a temporary confinement measure until the sediment is

removed or depletion renders the contaminant harmless. It should be empha-

sized, however, that this will only occur when depletion of contaminant in the

capped sediment is negligible, a conservative assumption that may significantly

overestimate the flux of contaminant through the cap. This assumption is com-

pared with more realistic approaches in an example below.

In the advection-dominated case, it is important to examine the transient

release of the contaminant. The conditions on Equation B27 that are appropriate

for a cap include

cap sediment interface (z 0)

Cpw

cap water interface (z Leff)

Cpw

(Generally Cw

0) (B30)

initial cap concentration

Cpw

Available analytical solutions describe only homogeneous cap properties and do

not satisfy the cap-water interface condition of Equation B30. Instead there are

two approximate conditions that are commonly applied instead of the cap-water

interface condition.

Cpw

(finite cap)

at z

Leff

(B31)

Cpw

as z

(infinite cap)

The first explicitly recognizes the finite thickness of the cap, while the second

assumes that it is infinitely thick. The solution subject to the finite boundary

condition is given by Cleary and Adrian (1973), while the solution subject to the

infinite boundary condition can be found in Carslaw and Jaeger (1959). For

Pe > 1, however, the concentration and flux predictions of either model are

essentially identical. Moreover, for Pe < 1 when diffusion dominates, the given

finite cap condition is inappropriate and causes the solution to underpredict the

contaminant flux through the cap. The solution for the infinite cap is also

simpler to use. For these reasons, only the infinite cap model will be described

in this section. However, the full boundary conditions of Equation B30 or

heterogeneous sediment properties can be described using numerical solvers as

illustrated in the example.

B15

Appendix B Model for Chemical Containment by a Cap