Waste injected in deep geologic formations mixes with
formation fluids. This results in a plume defined by lines of equal
concentration. The size of the plume depends on the injection rate,
duration of injection, height of the receiving formation, formation porosity and
coeffcient of dispersivity. In the form
below, enter values for the calculation and the analytical solution are
presented. We use the Hoopes and Harleman solution for radial dispersion.
This page
allows evaluation to concentrations down to 1 x 1030. The solution include a
Fortran program to evaluate the Error Function. Other solutions such as Excel are limited to 1. x 1015.
The model for fluid displacement without
dispersion is defined as:
_{
}
where:
r_{o} = advective radius to position of undispersed injectate
front (ft),
V = cumulative injectate volume (ft^{3}),
H = injection interval thickness (ft), and
f
= formation porosity.
The
effect of dispersion are added to the advective displacement and calculated
using the approximate solution provide by Bear, 1972 and Hoopes and Harleman,
1967 as:
_{}
where:
C = dimensionless concentration,
r =
radial distance from well (ft),
α
= dispersivity (ft), and
erfc =
complementary error function.
References:
Hoopes,
J. A. and D. R. F. Harleman, 1967. Dispersion in radial flow from a recharge
well, Journal of Geophysical Research, 72(14), 35953607.
Bear,
J., 1972. Dynamics of Fluids in Porous Media, American Elsevier, New
York.
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Additional Deep Well References
