Fixed Outflow Velocity

The bottom boundary may be specified as fixed outflow to represent a base aquifer, where the concentration varies with time as mass is transported into the aquifer from the landfill and transported out from beneath the landfill by the base velocity v_b.

Consideration of the conservation of mass gives the base concentration as:

c(t, z = H_b) = ò [ f(t, z=H_b, c)/n_bh_b - v_b c (t, z=H_b)/n_b L ] dt

where,

  c(t, z=Hb) = the concentration in the base aquifer, averaged over the entire thickness of the base,

  f(t, z=Hb, c) = the mass flux into the aquifer,

  nb = porosity of the base aquifer,

  hb = thickness of the base aquifer,

  vb = Darcy velocity in the aquifer and down-gradient edge of the landfill,

  L = length of the landfill parallel to the velocity vb.

Note that the use of a very large base velocity will give the same results at using a constant base concentration of zero. If the base velocity is zero and the porosity is zero the bottom boundary is effectively a zero flux boundary.