Hydraulic Parameter Identification

Nowadays, it is becoming common practice to apply mathematical models to simulate groundwater flow, solute and heat transport and subsidence. The present-day problem is not gaining access to computers or obtaining computer codes but the acquisition of numerical values for the different hydraulic parameters to be used in these mathematical models. Other problems on the order of the day are: how to calibrate the mathematical model; what is the reliability of the results of a calibrated mathematical model; and which data should be gathered to have a sufficiently precise simulation of the problem under consideration? It is one of the additional aims of this book to contribute to the solution of all these problems.

In the framework of pumping test analysis two groups of hydraulic parameters are important. The first group of hydraulic parameters describes the water conducting properties of the porous medium and the second group describes the water storing properties of the porous medium. The first group is described in the first section of this part, the second in the second section.

A large number of analytical models was developed. Here only a few steps in the evolution of these models are treated. The steps are first selected to give the reader an idea about the historical evolution of the analytical models so that it becomes clear that the first models deal exclusively with flow in the directly pumped pervious layer. In the following developed models the flow from the adjacent layers to directly pumped layer is incorporated with increasing accuracy. The application frequency of the interpretation methods that are derived from these models was another criterion for the selection of the treated models.

In this chapter a two-dimensional axi-symmetric model is described which allows the simulation of a pumping test in a layered groundwater reservoir. In the axi-symmetric model the layers are subdivided in rings of which the inner and outer radii form a logarithmic series. This allows the calculation of the drawdowns with a same order of accuracy at distances from the pumped well which are in the order of centimeters, decimeters, meters, decameters and hectometers. The points of time for which the drawdowns are calculated also form a logarithmic series so that it is also possible to calculate the drawdowns with the same accuracies after secondes, minutes, hours, days, weeks and months after starting the pump.

With the numerical model the evolution of the drawdown can be calculated in a layered groundwater reservoir for a constant discharge rate. The layers of the groundwater reservoir are supposed to be laterally homogeneous, isotropic and of an infinite lateral extension. When pumping tests are performed in practice, the above mentioned constraints of the numerical axi-symmetric model often limit the possibility to compare the observed and the calculated drawdown. These constrains limit the use of the numerical model as a base for an inverse model which allows the interpretation of a wide range of pumping tests.

In this chapter a number of pumping tests are interpreted with the help of the inverse numerical model. In Sect. 6.5.1 it is already shown that it is possible to interpret pumping tests in groundwater reservoirs in which the flow can be conceptualized according to one of the classical analytical models (Theis, Jacob, Hantush-Jacob, Boulton, etc.). With most of these models, the interpreted drawdown is measured in the directly pumped layer. The hydraulic parameters of the directly pumped layer are derived with a rather high level of accuracy, at least when the used conceptual model is close enough to the actual flow and the schematization of the groundwater reservoir approximates enough the assumed one. Mostly, drawdown observed in the layers adjacent to the directly pumped layers are not involved in those interpretations. Consequently, the accuracies of the derived hydraulic parameters of these indirectly pumped layers are far below the accuracies of the hydraulic parameters of the directly pumped layer. Interpretations following a classical analytical model will not further be treated in this chapter. In the given examples, observed drawdowns in pumped layers are simultaneously interpreted with drawdowns observed in adjacent layer. Not only drawdowns of single pumping tests can be interpreted simultaneously but also all drawdowns of a multiple pumping tests.