Page 60 - Applied Petroleum Geomechanics

Rock physical and mechanical properties 51

In sedimentary rocks, horizontal permeability usually has a large value
than vertical permeability, depending on porosity, grain size, and grain
packing.
Hydraulic conductivity is a commonly used term (similar to perme-
ability) in hydrogeology and is a measure in how easily a particular fluid
(e.g., water) passes through a particular earth material. It came from Darcy’s
law, i.e., the rate of flow (q) in a porous medium is proportional to the
cross-sectional area (A), proportional to the difference of hydraulic head
(h 1 h 2 ), and inversely proportional to the distance of the two hydraulic
heads (L):

q ¼ KA h 1 h 2 (2.32)
L

where K is the hydraulic conductivity. The following equation gives
permeability and hydraulic conductivity relationship:
r g
f
K ¼ k (2.33)
m
where r f is the fluid density; g is the gravitational acceleration; m is the dy-
namic viscosity of fluid; and k is the permeability.

2.4.2 The relationship of permeability and porosity

The KozenyeCarman equation relates the intrinsic permeability to
porosity, f, and grain size, d, of the rock:
2
d f 3
k ¼ (2.34)
2
180ð1 fÞ
Timur (1968) proposed that permeability and porosity follow the
following relation for clean sandstones, i.e.,
f b
k ¼ a (2.35)
S wirr
c
where S c wirr is irreducible water saturation; a, b, and c are determined from
c
measurements on core samples. In Timur’s relationship, with f and S wirr in
4
units of v/v (fraction) and k in mD, a ¼ 10 ,b ¼ 4.4, and c ¼ 2.
Timur’s equation indicates that a linear relation between log(k) and f
exists. Laboratory core tests in tight gas sandstones in the Green River Basin
and the Haynesville shale gas formation of the United States show that