Page 90 - Materials Chemistry, Second Edition

Plume Migration in Aquifer and Soil 73

These two terms, permeability and hydraulic conductivity, are sometimes
used interchangeably. However, they do have different meanings. The
intrinsic permeability of a porous medium (e.g., subsurface soil or an
aquifer) defines its ability to transmit a fluid. It is a property of the medium
only and is independent of the properties of the transmitting fluid. That
is probably the reason why it is called the “intrinsic” permeability. On the
other hand, the hydraulic conductivity of a porous medium depends on the
properties of the fluid flowing through it and those of the medium itself.
Hydraulic conductivity is conveniently used to describe the ability of an
aquifer to transmit groundwater. A porous medium has a unit hydraulic
conductivity if it will transmit a unit volume of groundwater through a unit
cross-sectional area (perpendicular to the direction of flow) in a unit time at
the prevailing kinematic viscosity and under a unit hydraulic gradient.
The relationship between the intrinsic permeability and hydraulic conduc-
tivity is

kρg Kµ
K = or k = (3.4)
µ ρg

where K is the hydraulic conductivity, k is the intrinsic permeability, μ is the
fluid viscosity, ρ is the fluid density, and g is the gravitational constant (Note:
kinematic viscosity = μ/ρ). The intrinsic permeability has a unit of area as
shown in Equation (3.5):

⋅
Kµ  (m/s)(kg/ms) 
k = =  3 2  =[m] (3.5)
2
ρ g  (kg/m )(m/s ) 
In petroleum industries, the intrinsic permeability of a formation is often
expressed in the units of darcy. A formation has an intrinsic permeability of
1 darcy, if it can transmit a flow of 1 cm /s with a viscosity of 1 centipoise
3
(1 mPa∙s) under a pressure gradient of 1 atmosphere/cm acting across an area
of 1 cm (note: 1 Pa = 1 N/m ). That is,
2
2
⋅
−3
3
(1 cm /s)(10Pas)
1darcy = 2 (3.6)
(1 atm/cm)(1 cm )
By substitution of appropriate units for atmosphere (i.e., 1 atm = 1.013 × 10
5
Pa), it can be shown that
1 darcy = 0.987 × 10 cm 2 (3.7)
-8
Table 3.2 lists the mass density and viscosity of water under 1 atmo-
sphere. As shown in the table, the density of water from 0°C to 40°C is