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RESERVOIR HETEROGENEITY AND PERMEABILITY 77
q 1
k 1 , h 1
q 2
k 2 , h 2
Length L
Inlet Outlet
FIguRE 4.4 Flow through two layers of porous material.
Thickness, h
q k 1 , L 1 k 2 , L 2
Length L
Inlet Outlet
FIguRE 4.5 Serial flow through two adjacent beds of porous material.
drop for each segment. Using Darcy’s law, it can be shown that the average
permeability is
L + L
k ave = 1 2 (4.20)
/
/
Lk + Lk 2
1
1
2
Generalizing to multiple segments in series gives
∑ L
k ave = i i (4.21)
Lk
∑ i i / i
In the case of radial flow, beds in series are concentric rings around a wellbore
with radius r . The average permeability for a series of three beds is
w
e (
ln rr / )
k = w (4.22)
rr )
e (
ave
ln rr ) + ln ( 2 / 1 + ln rr )
/
/ ( 1
w
2
k 3 k 2 k 1
4.3.3 Dykstra–Parsons Coefficient
The Dykstra–Parsons coefficient is one of several ways to characterize the heterogeneity
of permeability with a single number. Having a single number allows simple compari-
sons of permeability data from different wells, reservoirs, and even numerical models.
