Page 36 - Percolation Models for Transport in Porous Media With

2.2 "PERMEABILITY- POROSITY" CORRELATION 27

/

TOO

!0 I I
I I
/B

I
41~~~~~~~~
Q 41 42 D.J m
Figure 6: Plot of the coefficient of permeability for a grained medium against
porosity

of permeability of the medium near the percolation threshold in the interval
P: ~ pa < P: + !l.P is determined from the relationship (1.4)
8
(2.8)

Outside this interval, the conductivity of the medium can be adequately de-
scribed by a linear relation between the conductivity and the quantity ps. More-
over when all pores are open (P 8 = 1) the permeability of the medium is deter-
mined from Causeni's formula [44]

(2.9)

Hence the coefficient in the formula (2.8) can be found approximately by match-
ing the relations (2.8) and (2.9) for ps > P: + !l.P 8 • In this case, the formula for
the coefficient of permeabiltiy becomes

3
-
K = 7 ·10- (l ~::)2 ( : 0 - P:) d 11 ( : P:). (2.10)
0
Formula (2.10) describes the permeability of the medium in the interval P: ~
ps < ps + !l.P 8 adequately and in the region ps ~ P: + !l.P 8 , approximately.
The following important fact is implied in by the formula (2.10). The value of
the porosity at the point of the IC formation depends on \l>o, a parameter which
characterizes the structure of pore space. Structural porosity \1> 0 , in its turn,
depends on the density of packing of the grains and thus can vary within the
following limits, 0.26 ~ \1>0 ~ 0.48. So the value of the porosity of a grained
medium when an IC is formed in it is \l>c = \l>oP: and can vary within the interval
3.9% ~ \l>c ~ 7.2%. This range defines the lower bound of the permeability for the
grained reservoirs, a result that agrees with experimental data [45]. The dotted line
in fig. 6 reflects the relation between the coefficient of permeability of a medium