One-Dimensional Contaminant Migration

The theory implemented by the POLLUTEv7 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 - r K_d dc/dt - n l 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,

  r = dry density of the soil at depth z,

  Kd = distribution/partitioning (sorption) coefficient 

       at depth z,

  va = nv = Darcy velocity,

  l = 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):

n_f dc_f/dt = n_f D_f d²c_f/dz² - n_f v_f dc_f/dz - D K_f dc_f/dt - q - n_f l c_f

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,

  D = 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,

  l = decay constant of the contaminant species.

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