16
2. Hydrodynamic Dispersion in Porous Media
is also called water content. Another variable, water saturation, is defined as
S =
Volume of water in REV
w
Volume of pore space in REV
Obviously, the two variables (}w and Sw are interrelated by the equation
(2.1.27)
Specific Surface
The specific surface, Mo, is defined as the ratio ofthe interfacial area betweell
the solid matrix and pores, So, to the bulk volume, U o , of the REV in a
porous medium, that is,
So
Mo = - ·
U o
(2.1.28)
Obviously, the smaller the solid particle size, the larger the specific surface
area. The magnitude of Mo is dependent on the porosity, particle-size distribution, and the shape and configuration of the particles. Since adsorption,
desorption, and ion exchange all occur at the solid-liquid boundary interface,
the specific surface area plays an important role in the study of solute
transport.
U there are multiple phases in the REV of a porous medium, the specific
surface of phase y can be defined as
S
M=~
y
U o '
(2.1.29)
where So, y is the total area of interfaces between phase y and other phases.
Tortuosity
At the microscopic level, the fluid flow within a porous medium is actually a
movement along the tortuous three-dimensional passages in voids, as shown
in Figure 2.2. The local velocities in the passages are different from their
macroscopic average values, both in magnitude and in direction. In a physical model, the void space of a porous medium may be regarded as a network
of curved channels. One of the channels is shown schematically in Figure 2.3.
It is so placed that the axis of the channel is on the same plane as the mean
flow direction (x). Its length is L e and its projection on axis x has a length
of L.
U the me an flow velocity along the channel axis is V, and its projection on
axis x is U, then from Le/V = L/u, we have
(2.1.30)
Let Ah be the water head difference between the two ends of the channel.
The mean velocity along the channel, V, is proportional to the me an hydraulic gradient Ah/L e , i.e.,
2. Hydrodynamic Dispersion in Porous Media
is also called water content. Another variable, water saturation, is defined as
S =
Volume of water in REV
w
Volume of pore space in REV
Obviously, the two variables (}w and Sw are interrelated by the equation
(2.1.27)
Specific Surface
The specific surface, Mo, is defined as the ratio ofthe interfacial area betweell
the solid matrix and pores, So, to the bulk volume, U o , of the REV in a
porous medium, that is,
So
Mo = - ·
U o
(2.1.28)
Obviously, the smaller the solid particle size, the larger the specific surface
area. The magnitude of Mo is dependent on the porosity, particle-size distribution, and the shape and configuration of the particles. Since adsorption,
desorption, and ion exchange all occur at the solid-liquid boundary interface,
the specific surface area plays an important role in the study of solute
transport.
U there are multiple phases in the REV of a porous medium, the specific
surface of phase y can be defined as
S
M=~
y
U o '
(2.1.29)
where So, y is the total area of interfaces between phase y and other phases.
Tortuosity
At the microscopic level, the fluid flow within a porous medium is actually a
movement along the tortuous three-dimensional passages in voids, as shown
in Figure 2.2. The local velocities in the passages are different from their
macroscopic average values, both in magnitude and in direction. In a physical model, the void space of a porous medium may be regarded as a network
of curved channels. One of the channels is shown schematically in Figure 2.3.
It is so placed that the axis of the channel is on the same plane as the mean
flow direction (x). Its length is L e and its projection on axis x has a length
of L.
U the me an flow velocity along the channel axis is V, and its projection on
axis x is U, then from Le/V = L/u, we have
(2.1.30)
Let Ah be the water head difference between the two ends of the channel.
The mean velocity along the channel, V, is proportional to the me an hydraulic gradient Ah/L e , i.e.,