20
2. Hydrodynamic Dispersion in Porous Media
where A o is the area element at the point considered, tlH is the drawdown of
water table, and tlU w is the volume of water releasing from the aquifer with
the bulk of A o as its base and tlH as its height. Generally speaking, Sy is
smaller than porosity n, since capillary water is still retained in the volume
even when the water table is lowered. If this amount of water is negligible, Sy
may be approximated by the effective porosity of the medium.
Some other properties relevant to mass transport in a porous medium,
such as the hydrodynamic dispersion coefficient and molecular diffusion
coefficient, will be introduced later. Appendix A gives a list of symbols
of the parameters mentioned above as weIl as others, along with their
dimensions.
2.2 Phenomena and Mechanism of Hydrodynamic
Dispersion
2.2.1 Hydrodynamic Dispersion Phenomena
Mass transport in a porous medium is carried out in the moving fluid and the
movement of the fluid takes place in a very complicated intersticial system.
These conditions give rise to a very special phenomenon, i.e., hydrodynamic
dispersion. Two examples are given below to show the existence of the hydrodynamic dispersion phenomenon on a macroscopic scale.
Example 1
Consider continuous injection of a tracer into a weIl which is situated in
a uniform one-dimensional flow field in the x direction. We can observe a
gradual spreading of the tracer around the weIl. The extent that the tracer
spreads is larger than the region expected from the average flow alone. It not
only spreads longitudinally along the mean flow direction, but also expands
transversely. There exists a transition zone rather than an abrupt interface
between the tracer-containing solution and the original fluid around the weIl
as shown in Figure 2.4. This is called the hydrodynamic dispersion phenomenon. Without dispersion, the tracer would move in accordance with the mean
flow velocity. There would be no transversal spreading and an abrupt concentration change would be seen.
Example 2
Consider a steady flow in a homogeneous sand column saturated with water.
At a certain time, the water with a tracer concentration Co starts to replace
the original water. The concentration at the other end of the column, C(t),
is monitored, and a curve of relative concentration C(t)/C o versus time t is
drawn. The curve is called the breakthrough curve which is shown in Figure
2.5.
2. Hydrodynamic Dispersion in Porous Media
where A o is the area element at the point considered, tlH is the drawdown of
water table, and tlU w is the volume of water releasing from the aquifer with
the bulk of A o as its base and tlH as its height. Generally speaking, Sy is
smaller than porosity n, since capillary water is still retained in the volume
even when the water table is lowered. If this amount of water is negligible, Sy
may be approximated by the effective porosity of the medium.
Some other properties relevant to mass transport in a porous medium,
such as the hydrodynamic dispersion coefficient and molecular diffusion
coefficient, will be introduced later. Appendix A gives a list of symbols
of the parameters mentioned above as weIl as others, along with their
dimensions.
2.2 Phenomena and Mechanism of Hydrodynamic
Dispersion
2.2.1 Hydrodynamic Dispersion Phenomena
Mass transport in a porous medium is carried out in the moving fluid and the
movement of the fluid takes place in a very complicated intersticial system.
These conditions give rise to a very special phenomenon, i.e., hydrodynamic
dispersion. Two examples are given below to show the existence of the hydrodynamic dispersion phenomenon on a macroscopic scale.
Example 1
Consider continuous injection of a tracer into a weIl which is situated in
a uniform one-dimensional flow field in the x direction. We can observe a
gradual spreading of the tracer around the weIl. The extent that the tracer
spreads is larger than the region expected from the average flow alone. It not
only spreads longitudinally along the mean flow direction, but also expands
transversely. There exists a transition zone rather than an abrupt interface
between the tracer-containing solution and the original fluid around the weIl
as shown in Figure 2.4. This is called the hydrodynamic dispersion phenomenon. Without dispersion, the tracer would move in accordance with the mean
flow velocity. There would be no transversal spreading and an abrupt concentration change would be seen.
Example 2
Consider a steady flow in a homogeneous sand column saturated with water.
At a certain time, the water with a tracer concentration Co starts to replace
the original water. The concentration at the other end of the column, C(t),
is monitored, and a curve of relative concentration C(t)/C o versus time t is
drawn. The curve is called the breakthrough curve which is shown in Figure
2.5.