Page 233 - Soil and water contamination, 2nd edition

220 Soil and Water Contamination

Relative saturation of non-wetting fluid (NAPL)
1.0 0.5 0.0
1.0

Relative permeability (kr) 0.5 Non-wetting fluid (NAPL) Wetting fluid (water)
Drainage
of water

Imbibition
of water
0.0 6642 6642 6642
0.0 0.5 1.0
Relative saturation of wetting fluid (water)
Figure 11.15 Typical relative permeability curves.

-2
-3
-2
∇P = gradient in pressure head [M L T ], ρ = density of the ith fluid [M L ], and ∇z =
i
gradient of the elevation [-]. The relative permeability to the ith fluid is:
k i
k (11.47)
r, i
k
where k = the relative permeability of the ith fluid [-], which ranges between zero and one,
r,i
2
and k = the intrinsic permeability [L ]. The relative permeability k depends on the relative
ri
saturation, the wettability of the fluid, and whether the fluid is imbibed into or drains from
the aquifer material. Figure 11.15 shows the effect of the relative saturation of the fluids – in
this case an NAPL and water. The relative permeability is equal to one if the porous medium
is fully saturated with one fluid. Note that the relative permeabilities rarely sum to one. This
implies that in the case of multi-fluid flow , the permeability for a fluid depends not only on
the properties of the porous aquifer material, but also on the properties of the other one or
more fluids present in the aquifer. In other words, the medium through which the fluid flows
is comprised of both the aquifer material and the other fluids. If both an NAPL and water are
present in an aquifer, some quantity of either the NAPL or water is not capable of flowing below
a given saturation threshold, since the fluid is not connected across the pore network below this
saturation threshold. This threshold is called a residual saturation , and the residual saturation
of water is typically greater than for the NAPL. At residual saturation of water, the water is
held in the narrowest parts of the pores (pendular saturation ) and at residual saturation of the
NAPL, the NAPL is held as an isolated blob in the centre of the pore (insular saturation ) (see
Figure 11.16). Another feature of the relative permeability curves depicted in Figure 11.14 is the
hysteretic character of the curve for the NAPL. For the same saturation, the relative permeability
for the NAPL when water is displaced by the NAPL (drainage) is greater than when the NAPL
is displaced by water (imbibition). This is because during drainage the NAPL flows mainly
through the larger pores that contribute most to the permeability. In contrast, during imbibition,
water flows through the larger pores, whilst the NAPL occupies the smaller pores.

Example 11.7 Effective hydraulic conductivity

An underground oil storage tank leak has contaminated the shallow, unconfined
groundwater and the oil is floating on top of the water table . After the leak has been
stopped, the oil is contained and recovered by pumping the groundwater. A deeper pump

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