Environmental Engineering Reference
In-Depth Information
gradient and pressure drop were in the same direction, the oil flow rate was
increased.
If the direction of the hydraulic pressure gradient coincides with the
direction of DC electric field current, i.e., Darcy's flow and the electro-
kinetic transport occur in the same direction, a one-dimensional math-
ematical model can be used to show the main mechanisms of the species'
transport. In this case, redistribution of the species concentration in space
can be described as a result of the combined influence of three mecha-
nisms: Darcy flow, electrokinetics and diffusion. The first two relate to the
contaminants' solution flow with respect to the solid soil matrix, whereas
the last redistributes the species inside the flowing fluids (Chilingar et al.,
1997).
For the purpose of simplified analysis, it is reasonable to consider a
one-dimensional fluid flow in the direction from anode to cathode. The
total fluid flow rate can be obtained by adding the electroosmotic relation
to the Darcy equation (Chilingar et al., 1968):
)
+
)
=Δ
(
(
(1.9)
q
kp L
/
m
kE L
/
m
t
e
where
A
is the cross-sectional area;
k
is the Darcy permeability;
L
is
the length of the core;
k
e
is the electrokinetic permeability and
E
is the
imposed electrical potential gradient. This equation can be presented in a
dimensionless form by normalizing the flow rates and, thus, eliminating
the viscosity, area and length terms:
(1.10)
qq
/
=+
1
kEkp
/
Δ
t
i
e
and
(
)
(1.11)
qqq kEkp
t
−
/
=
/
Δ
i
i
e
where
q
i
is the initial hydrodynamic stabilized flow rate.
Equation (1.10) shows that an increase in flow rate is dependent upon
the zeta potential, dielectric constant, brine concentration, Darcy perme-
ability, and pressure drop. If the dependence of
k
e
on
k
is not considered,
then Eq. (1.11) would suggest that as the hydrodynamic permeability
decreases, the percent increase in flow rate caused by electrical potential
would become more significant. This means the electrokinetic technique
is especially effective in cases when hydraulic permeability
k
is very small,
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