7.2. Model Calibration and Parameter Estimation
217
• When the data are classified according to porous versus fractured media,
there does not appear to be any significant difference between these aquifer
types.
7.2.4 Determination of Mean Flow Velocities
The methods of determining the average flow velocities in an advectiondispersion model can be divided into two categories: indirect determination
and direct determination. The indirect determination involves the use of field
data from pumping tests to calibrate the flow model and thus obtain the
hydraulic conductivity K and effective porosity n. Then K and n are substituted into Darcy's law to get the average velocity. As K, n and the hydraulic gradient values may contain large errors, the velocities obtained by using
this method are usuaHy not reliable. This is a difficult problem in groundwater quality modeling.
In order to calibrate a model, it is better to take direct measurement of the
flow velocity in the field, because the transport model is very sensitive to
errors in velocity. In the direct method, values of velocity are determined
through measuring the movement of artificial tracers or environmental isotopes. The artificial tracers include salts, radioactive isotopes, coloring agents
and so On. The single-weH tests done in the past was to put salt into a weH,
measure the changes of the electric resistance from the ground surface
and then determine the velocity and direction of the flow according to the
changes of electric resistance at different distances. The accuracy of this kind
of test is poor. In the multi-weH method, tracer is injected into one weH and
its arrival time is observed in the others. After eliminating the effect of dispersion, the groundwater velocity can be calculated by considering the distance
between the injection weH and an observation weH and the mean arrival
time of the tracer. This kind of test, however, is very difficult to successfuHy
conduct because of the low natural velocity, unclear flow direction and the
mixture of the water from adjacent aquifers.
To determine the velocity near a weH, one can apply a method called
"point dilution." The tracer is injected at a certain depth in the weH is left to
be diluted by the natural flow. It is known that the rate of dilution depends
on the velo city of the groundwater flow. From the records of tracer concentration changes in the weH we can obtain the values of the velocity. Moreover, we can also determine the velocities at different depths in a weH, and
find the layer having a relatively larger velocity. The large velocity layer plays
an important role in the propagation of pollutants.
F or a detailed demonstration of the use of the direct method to measure
the flow velocities, readers may refer to Cherry et al. (1975) and Fried (1975).
Ciccioli et al. (1980) put forward a method which used various tracers to
accurately determine the velocity of groundwater. The discussion of this
method is beyond the scope of this book.
It is quite evident that the various field tests can only give some local
217
• When the data are classified according to porous versus fractured media,
there does not appear to be any significant difference between these aquifer
types.
7.2.4 Determination of Mean Flow Velocities
The methods of determining the average flow velocities in an advectiondispersion model can be divided into two categories: indirect determination
and direct determination. The indirect determination involves the use of field
data from pumping tests to calibrate the flow model and thus obtain the
hydraulic conductivity K and effective porosity n. Then K and n are substituted into Darcy's law to get the average velocity. As K, n and the hydraulic gradient values may contain large errors, the velocities obtained by using
this method are usuaHy not reliable. This is a difficult problem in groundwater quality modeling.
In order to calibrate a model, it is better to take direct measurement of the
flow velocity in the field, because the transport model is very sensitive to
errors in velocity. In the direct method, values of velocity are determined
through measuring the movement of artificial tracers or environmental isotopes. The artificial tracers include salts, radioactive isotopes, coloring agents
and so On. The single-weH tests done in the past was to put salt into a weH,
measure the changes of the electric resistance from the ground surface
and then determine the velocity and direction of the flow according to the
changes of electric resistance at different distances. The accuracy of this kind
of test is poor. In the multi-weH method, tracer is injected into one weH and
its arrival time is observed in the others. After eliminating the effect of dispersion, the groundwater velocity can be calculated by considering the distance
between the injection weH and an observation weH and the mean arrival
time of the tracer. This kind of test, however, is very difficult to successfuHy
conduct because of the low natural velocity, unclear flow direction and the
mixture of the water from adjacent aquifers.
To determine the velocity near a weH, one can apply a method called
"point dilution." The tracer is injected at a certain depth in the weH is left to
be diluted by the natural flow. It is known that the rate of dilution depends
on the velo city of the groundwater flow. From the records of tracer concentration changes in the weH we can obtain the values of the velocity. Moreover, we can also determine the velocities at different depths in a weH, and
find the layer having a relatively larger velocity. The large velocity layer plays
an important role in the propagation of pollutants.
F or a detailed demonstration of the use of the direct method to measure
the flow velocities, readers may refer to Cherry et al. (1975) and Fried (1975).
Ciccioli et al. (1980) put forward a method which used various tracers to
accurately determine the velocity of groundwater. The discussion of this
method is beyond the scope of this book.
It is quite evident that the various field tests can only give some local