220
7. Mathematical Models of Groundwater Quality
7.2.7 Computer Aided Design Jor Field Experiments
It is more difficult to design a tracer experiment for determining the parameters relevant to dispersion (average velocity, dispersivity, distribution coefficient, etc.) than to design a pumping test for determining parameters relevant
to water flow (hydraulic conductivity, porosity, etc.). Some problems that
may be encountered in the tracer tests include: the peak value of concentration fails to be caught in observation weHs, the testing period lasts too long,
the observed values of concentration are not accurate, and so on.
The use of the mathematical model in the eady stage of designing a tracer
test will help to make the field experiment as reasonable as possible, and will
enable one to predict the probable consequences. As a result, the expected
goal of the test can be achieved. This is the basis for applying computer aided
design (CAD) to hydrogeology. We shaH explain, through a concrete design
of a tracer experiment, the application of the CAD approach to hydrogeology as foHows.
Suppose that we want to design a tracer test by the dual-weH injectionextraction method to determine the dispersivity of an aquifer. The foHowing
problems may be raised:
1. What is the suitable rate of injection (or extraction)?
2. Wh at is the suitable distance between the two weHs?
3. What depth should the weH be driHed to? Should the vertical flow be
taken into account if the weH is partiaHy penetrated?
4. How long should the experiment last?
In practice, we may have some prior information before the design. Some
useful data in geology and hydrogeology may be obtained through field
investigations. The problem is how to transfer this information into a quantitative basis for experimental design. In the case given by Mercer and Faust
(1980), the aquifer being considered is formed by limestone with a thickness
of 200 m to 500 m. From experience, its permeability coefficient can be
assessed as 10- 4 to 10- 6 m/s, porosity 0.08 to 0.32, the ratio ofhorizontal and
vertical permeabilities (K,/K z ) ranged from 1 to 100, and the longitudinal
dispersivity 5 to 40 m. Suppose we already have a general program for water
quality simulation, then a sensitivity analysis can be carried out by the
computer for every design parameter. That is, let a parameter vary within the
possible range, while the others are fixed, then output the results of the
corresponding changes (i.e., the concentration curve of a pumping weH). It is
just like doing a number of"experiments," but completed on a computer. The
cost is low and the time is saved. During this process, the designer can
quantitative1y understand the effects of different parameters on the observed
concentration, and can compare the results generated from different schemes.
There are some examples of sensitivity analyses in Figures 7.13 to 7.16.
Figure 7.13 shows the concentration-time curves changing with longitudinal
dispersivity rl.L. The other parameters are fixed as foHows: the transverse
7. Mathematical Models of Groundwater Quality
7.2.7 Computer Aided Design Jor Field Experiments
It is more difficult to design a tracer experiment for determining the parameters relevant to dispersion (average velocity, dispersivity, distribution coefficient, etc.) than to design a pumping test for determining parameters relevant
to water flow (hydraulic conductivity, porosity, etc.). Some problems that
may be encountered in the tracer tests include: the peak value of concentration fails to be caught in observation weHs, the testing period lasts too long,
the observed values of concentration are not accurate, and so on.
The use of the mathematical model in the eady stage of designing a tracer
test will help to make the field experiment as reasonable as possible, and will
enable one to predict the probable consequences. As a result, the expected
goal of the test can be achieved. This is the basis for applying computer aided
design (CAD) to hydrogeology. We shaH explain, through a concrete design
of a tracer experiment, the application of the CAD approach to hydrogeology as foHows.
Suppose that we want to design a tracer test by the dual-weH injectionextraction method to determine the dispersivity of an aquifer. The foHowing
problems may be raised:
1. What is the suitable rate of injection (or extraction)?
2. Wh at is the suitable distance between the two weHs?
3. What depth should the weH be driHed to? Should the vertical flow be
taken into account if the weH is partiaHy penetrated?
4. How long should the experiment last?
In practice, we may have some prior information before the design. Some
useful data in geology and hydrogeology may be obtained through field
investigations. The problem is how to transfer this information into a quantitative basis for experimental design. In the case given by Mercer and Faust
(1980), the aquifer being considered is formed by limestone with a thickness
of 200 m to 500 m. From experience, its permeability coefficient can be
assessed as 10- 4 to 10- 6 m/s, porosity 0.08 to 0.32, the ratio ofhorizontal and
vertical permeabilities (K,/K z ) ranged from 1 to 100, and the longitudinal
dispersivity 5 to 40 m. Suppose we already have a general program for water
quality simulation, then a sensitivity analysis can be carried out by the
computer for every design parameter. That is, let a parameter vary within the
possible range, while the others are fixed, then output the results of the
corresponding changes (i.e., the concentration curve of a pumping weH). It is
just like doing a number of"experiments," but completed on a computer. The
cost is low and the time is saved. During this process, the designer can
quantitative1y understand the effects of different parameters on the observed
concentration, and can compare the results generated from different schemes.
There are some examples of sensitivity analyses in Figures 7.13 to 7.16.
Figure 7.13 shows the concentration-time curves changing with longitudinal
dispersivity rl.L. The other parameters are fixed as foHows: the transverse