212
7. Mathematical Models of Groundwater Quality
have as = XS/a.L , hence
(7.2.30)
By correlating the observed curve of N4 with the typical curves, we can
identify another value of a, marked as a4. Let the coordinates of N 4 be
(X 4 , Y4), then from Eq. (7.2.26) we have
a4 = [xl/a.I + Yl/a.La.Tr/ 2 ,
and consequently
(7.2.31)
The Regional Scale (Average Distance of Propagation Is over 100 m)
On this scale, if the above-mentioned tests are conducted, many wells must
be drilled and a large amount of tracer should be injected. As a result, the test
period must be very long and the test cost must be very high. When the
distance ofpropagation ranges from 100 to 300 m, a possible alternative is to
use the geophysical technique. The application of geophysical prospecting
to hydrogeological research can provide the estimates of flow velocity and
flow direction, as weIl as hydrogeological parameters such as porosity and
transmissivity. The increase of salinity in water causes its resistance to decrease, so the salinity changes in groundwater can be observed from resistance measurements. During the experiment, an electrolyte solution, for example, saline water, is injected into a weIl, and transported by the natural
flow. Then, electrical resistance changes are measured at some points in the
region being considered. The resistance changes may be interpreted as the
changes of flow velocity field and concentration field by the geophysical
approach. A mathematical model can then be established based on site
conditions and the procedure of test. A geophysical survey conducted before
the injection may provide necessary initial and boundary conditions for
the model. With the mathematical model, as weIl as observations of the
flow velocity field and concentration field, dispersivities a.L and a.T can be
identified by a model calibration procedure demonstrated in Section 7.2.1.
The defect of this method is that it may cause man-made local groundwater
pollution.
The study of groundwater quality in practice should not be limited to the
vicinity of a weIl. We are unable to use the injection tests to affect the
overall region when the study area reaches more than ten or tens of square
kilometers. The calibration of the model in this scale must rely on historical
observations of the pollution or environmental tracer. Concentration contours at each known time are drawn, and then, using the common program
of water quality model, the parameters are modified so that the model outputs
coincide with these curves. Because of the larger area, the non-homogeneity
of porous media should be taken into account. Different values of a.L and a.T
7. Mathematical Models of Groundwater Quality
have as = XS/a.L , hence
(7.2.30)
By correlating the observed curve of N4 with the typical curves, we can
identify another value of a, marked as a4. Let the coordinates of N 4 be
(X 4 , Y4), then from Eq. (7.2.26) we have
a4 = [xl/a.I + Yl/a.La.Tr/ 2 ,
and consequently
(7.2.31)
The Regional Scale (Average Distance of Propagation Is over 100 m)
On this scale, if the above-mentioned tests are conducted, many wells must
be drilled and a large amount of tracer should be injected. As a result, the test
period must be very long and the test cost must be very high. When the
distance ofpropagation ranges from 100 to 300 m, a possible alternative is to
use the geophysical technique. The application of geophysical prospecting
to hydrogeological research can provide the estimates of flow velocity and
flow direction, as weIl as hydrogeological parameters such as porosity and
transmissivity. The increase of salinity in water causes its resistance to decrease, so the salinity changes in groundwater can be observed from resistance measurements. During the experiment, an electrolyte solution, for example, saline water, is injected into a weIl, and transported by the natural
flow. Then, electrical resistance changes are measured at some points in the
region being considered. The resistance changes may be interpreted as the
changes of flow velocity field and concentration field by the geophysical
approach. A mathematical model can then be established based on site
conditions and the procedure of test. A geophysical survey conducted before
the injection may provide necessary initial and boundary conditions for
the model. With the mathematical model, as weIl as observations of the
flow velocity field and concentration field, dispersivities a.L and a.T can be
identified by a model calibration procedure demonstrated in Section 7.2.1.
The defect of this method is that it may cause man-made local groundwater
pollution.
The study of groundwater quality in practice should not be limited to the
vicinity of a weIl. We are unable to use the injection tests to affect the
overall region when the study area reaches more than ten or tens of square
kilometers. The calibration of the model in this scale must rely on historical
observations of the pollution or environmental tracer. Concentration contours at each known time are drawn, and then, using the common program
of water quality model, the parameters are modified so that the model outputs
coincide with these curves. Because of the larger area, the non-homogeneity
of porous media should be taken into account. Different values of a.L and a.T