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6.5 Results
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immobile phase. Under such conditions, the coefficient of variation of the velocity
distribution increases, and the resulting BTCs can only be described well
by assuming that a large percentage of the water phase is immobile. Thus, the
value of β will decrease with decrease in saturation.
Under low saturation, there is no strongly dominant flow path. Our results
showed that, this regime starts mostly at saturations close to the percolation
threshold, S per . Under this regime, there is less variations in velocity (as shown
in Figure 6.7) and as a result the BTCs can be described well by assuming a
smaller immobile fraction.
6.5.4 Relative permeability
Our results show a relation between dispersivity and variation of the pore-scale
velocity field. The relation was explained using c v of the pore-scale velocity field
(Figure 6.7), as well as the fraction of percolating saturated pores (Figure 6.8).
These observations are pore-scale properties; in practice, it is quite a formidable
job to precisely measure variations of pore-scale velocities throughout a pore
space domain. It would be more practical and useful to relate dispersivity
variations to a macro-scale quantity which is easier to measure. Such a quantity,
under unsaturated conditions, could be relative permeability. Figure (6.12)
shows the relative permeability curves for different networks.
1
var L
var M
var H
Linear plot
1
0.1
k 001 0.01 r
0.001
0.0001
S w
0 0.2 0.4 0.6 0.8 1
0.8
0.6
0.4
0.2
0
Figure 6.12: Relative permeability-saturation (k r − S w) curves shown on the
semi-log scale for the three networks. The k r −S w curve for the network var M is
also shown on the linear scale (corresponding to the secondary axis on the right
side of the figure).
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