Estimation of long-term losses

This calculation included an estimate of the partition coefficient and retardation

factor for the migration of pyrene through the cap. The partition coefficient and

pore water concentrations were estimated based on the sediment loading (Equa-

tion B5 and the second of Equations B8). The maximum truly dissolved concen-

tration in the pore water is given by the solubility of pyrene in water (150 g/L)

meaning that in the 1-percent organic carbon sediment with a pyrene Koc =

105 L/kg, the sediment loading must be less than 150 mg/kg for this to be true.

At sediment loadings above 150 mg/kg, the pore water concentration in the

contaminated region must be estimated by Equation B7.

Estimation of long-term losses

The simple analytical models presented in this appendix assume that the zone

of contamination is infinitely large and is not depleted by losses through the cap.

Since a groundwater seepage velocity is specified in this example, such an

assumption means that ultimately the flux through the cap is given by the seep-

age velocity times the pore water concentration in the sediment beneath the cap

or 20 mg m-2 year-1. In the absence of any seepage through the cap, the steady-

state diffusive flux would apply, 3.6 mg m-2 year-1. Both estimates overestimate

the actual long-term flux, however, in that they assume that the sediment beneath

the cap exhibits a constant concentration. A numerical calculation of the flux is

provided later to illustrate the degree of conservatism by these calculations, even

if no chemical degradation of the pyrene occurs.

Evaluation of diffusion only mechanism

Using Equations B25 and B26, the breakthrough and steady-state times are

given by 669 and 4,600 years, respectively. These estimates assume only diffu-

sion is applicable and that the concentration is again constant.

At steady-state conditions assuming constant sediment concentrations, the

diffusion model also allows estimation of pore and overlying water concentra-

tions. Although the predominant mass transfer resistance is the undisturbed cap,

the bioturbation zone and the benthic boundary layer resistance influence the

concentrations observed in the bioturbation layer, at the sediment-water inter-

face, and in the overlying water.

Example Calculation of Contaminant Flux-Advection/Diffusion

Mechanism

In this example, flux predictions by the analytical model of capped sediment

are compared with an uncapped case and a numerical model that recognizes the

depletion in the underlying sediment due to transport to the overlying water.

The numerical model is capable of describing arbitrary and heterogeneous initial

conditions and depletion within the sediment. The model is written in

FORTRAN and employs IMSL routines for some calculations. Both the

B22

Appendix B Model for Chemical Containment by a Cap