Chapter 1 Introduction > Theory > One-Dimensional Contaminant Migration

The theory implemented by the POLLUTEv8 program, in its basic mode of operation, is described in detail by Rowe and Booker [1985, 1987, 1991b] and Rowe et al [1994]. According to this theory contaminant migration in one-dimension, for an intact material, is governed by:

n dc/dt = n D d2c/dz2 - n v dc/dz - ρ Kd dc/dt - n λ c

where,

c = concentration of contaminant at depth z at time t,

D = coefficient of hydrodynamic dispersion at depth z,

v = groundwater (seepage) velocity at depth z,

n = porosity of the soil at depth z,

ρ = dry density of the soil at depth z,

Kd = distribution/partitioning (sorption) coefficient at depth z,

va = n v = Darcy velocity,

λ = decay constant of the contaminant species (i.e., the reciprocal of the species mean half life times ln 2).

Contaminant migration in a fractured layer is primarily in one direction along the fracture (e.g. either horizontally or vertically), but contaminants can migrate from the fractures into the intact material in all three co-ordinate directions. Thus contaminant migration along the fractures is governed by [Rowe et al, 2004]:

nf dcf/dt = nf Df d2cf/dz2 - nf vf dcf/dz - ∆ Kf dcf/dt - q - nf λ cf

where,

cf = concentration in a fracture at depth z and time t,

Df = coefficient of hydrodynamic dispersion of the fractures,

vf = fracture (groundwater) velocity in the fractures,

nf = fracture porosity in the plane of flow = h1/H1+h2/H2,

∆ = surface area of fractures per unit volume of soil/rock,

Kf = fracture distribution coef. [Freeze and Cherry, 1979],

q = contaminant transported into the intact matrix material, from the fractures, by matrix diffusion,

λ = decay constant of the contaminant species.

Note: the program automatically calculates nf, vf, and q from other information provided by the user.