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2. Hydrodynamic Dispersion in Porous Media
FIGURE 2.6. Non-uniformity of the microseopie flow velocity due to the existence of
solid matrices.
transport processes in porous media: mechanical dispersion and molecular
diffusion.
Mechanical Dispersion
When fluid flows in a porous medium, there exist very complex interactions
between the liquid and solid phases, such as adsorption, precipitation, dissolution, ion exchange, chemical reaction, and even biological processes. The
main interaction, however, is mechanical in nature. As a result of the microstructure of the medium, the fluid velo city varies both in magnitude and in
direction inside the pore system. The velocity distribution can roughly be
divided into three categories. First, as a result of the fluid viscosity, the
velocity in a small channel is at its maximum along the axis, and its minimum
near the walls of the channel, as shown in Figure 2.6a. Second, because of the
variation in size ofthe pore space, the maximum velocities along the axis also
vary, as shown in Figure 2.6b. Third, the actual movement of fluid particles
is on a zigzag path, because of the resistance of the solid matrices and the
microscopic stream line fluctuations along the mean flow direction. This is
shown in Figure 2.6c.
Because of the stochastic nature of the pore space in porous media and the
nonhomogeneity of the microscopic velocity distribution, the tracer particle
groups are being separated continuously during the flow process, flowing
into finer and more closely woven channels, and occupying ever-increasing
space. The result is that the tracer spreads out more than what is expected
from just the mean flow velocity. This mass transport phenomenon, resulting
from the heterogeneity of the microscopic velocity distribution, is called the
mechanical dispersion.
Molecular Diffusion
Molecular diffusion is caused by the nonhomogeneous distribution of tracer
in a fluid. The tracer molecules in high concentration will move to the low
2. Hydrodynamic Dispersion in Porous Media
FIGURE 2.6. Non-uniformity of the microseopie flow velocity due to the existence of
solid matrices.
transport processes in porous media: mechanical dispersion and molecular
diffusion.
Mechanical Dispersion
When fluid flows in a porous medium, there exist very complex interactions
between the liquid and solid phases, such as adsorption, precipitation, dissolution, ion exchange, chemical reaction, and even biological processes. The
main interaction, however, is mechanical in nature. As a result of the microstructure of the medium, the fluid velo city varies both in magnitude and in
direction inside the pore system. The velocity distribution can roughly be
divided into three categories. First, as a result of the fluid viscosity, the
velocity in a small channel is at its maximum along the axis, and its minimum
near the walls of the channel, as shown in Figure 2.6a. Second, because of the
variation in size ofthe pore space, the maximum velocities along the axis also
vary, as shown in Figure 2.6b. Third, the actual movement of fluid particles
is on a zigzag path, because of the resistance of the solid matrices and the
microscopic stream line fluctuations along the mean flow direction. This is
shown in Figure 2.6c.
Because of the stochastic nature of the pore space in porous media and the
nonhomogeneity of the microscopic velocity distribution, the tracer particle
groups are being separated continuously during the flow process, flowing
into finer and more closely woven channels, and occupying ever-increasing
space. The result is that the tracer spreads out more than what is expected
from just the mean flow velocity. This mass transport phenomenon, resulting
from the heterogeneity of the microscopic velocity distribution, is called the
mechanical dispersion.
Molecular Diffusion
Molecular diffusion is caused by the nonhomogeneous distribution of tracer
in a fluid. The tracer molecules in high concentration will move to the low