Page 261 - Formation Damage during Improved Oil Recovery Fundamentals and Applications
P. 261
232 Xingru Wu
r
r
Figure 5.8 Porous medium with cylindrical tubes after scale formation.
The corresponding porosity ratio as follows:
φ 1 2
φ 2 5 X (5.12)
Assuming two cases for the Carman-Kozeny equation: before scale
formation shown by K 1; and, after scale formation shown by K 2 , then:
3
1 φ D 2
K 1 5 1 s (5.13)
72τ 12φ 1 2
3
1 φ D 2
K 2 5 2 s (5.14)
72τ 12φ 2
2
where τ is tortuosity, D s is the representative diameter of rock, and φ 1
and φ are porosities before and after scale deposition. Assuming that the
2
characteristic diameter and tortuosity remain the same, the ratio of per-
meability contrast gives:
φ 3
2
2
K 2 ð 12φ 2Þ
5 (5.15)
K 1 φ 3 1
2
ð 12φ 1Þ
2
Substituting φ with φ x to get Eq. (5.16):
1
2
12φ
2
K 2 6 1
5 X (5.16)
K 1 12φ X 2
1