Page 212 - gas transport in porous media

Chapter 11: Scaling Issues in Porous and Fractured Media
(a)
Digital image 0.31 cm tip seal 1.27 cm tip seal 207
20 20 20
Z-axis (cm) 10 10 10

0 0
0
0 10 20
0 10 20 0 10 20
(b) –30.5 –30.0 –29.5 –29.0 –28.5
ln(k)
30 30
30
Y-axis (cm) 20 20 20

10
10
10
0 0
0
0 10 20 30 0 10 20 30 0 10 20 30
X-axis (cm) Y-axis (cm) Z-axis (cm)
-36 -32 -28 -24
(c)
(d) ln(k)
-28 10

-29
Berea sandstone Topopah tuff
1
-30
E[ln(k)] Var[ln(k)]
-31
0.1
-32 Berea sandstone
0.6
Topopah tuff
-33 0.01
0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4
Inner tip seal radius (cm) Inner tip seal radius (cm)
Figure 11.1. Permeability scaling measured on a block of Berea Sandstone and Topopah Spring Tuff. (a)
Digital image of the Berea Sandstone sample and corresponding natural log permeability fields measured
with two different size tip seals. (b) Same as (a) but for a block of Topopah Spring Tuff. (c) Scaling of
the mean of the natural log permeability as measured on the two rock samples shown above (note that
permeability maps for two of the tip seals are not shown). (d) Scaling of the variance of the natural log
permeability