![]() ![]() In the above equation s is drawdown (L), Q is the discharge (L 3/T), T is the transmissivity (L 2/T), t is the time (T), S is the dimensionless storage coefficient, and r is the radial observation distance from the pumped well (L). The derivation and solution is documented many places (Jacob, 1940) and will not be discussed further here. The radius of the pumped well is assumed negligible (line source or sink approximation). The Theis equation (Theis, 1935) describes radial confined groundwater flow in a uniformly thick horizontal, homogeneous, isotropic aquifer of infinite areal extent. The automated method has the advantage of always being objective and always indicating its error by calculating the rms error in drawdown. The automated method is simply, quick, and inexpensive. These sensitivity coefficients are used in the section on least squares fitting to develop an algorithm for fitting the Theis equation to experimental pumptest data. After the Theis equation has been evaluated, the sensitivity coefficients can be obtained with little additional work. Evaluation of this integral is considered in the section on numerical approximation. The Theis equation involves an integral whose upper limit is infinity. For a more detailed discussion of sensitivity coefficients and their uses, see McElwee and Yukler (1973). The purpose of this paper is to present techniques and computer programs to evaluate the Theis equation to evaluate the sensitivity with respect to transmissivity and storage and to automatically fit experimental pumptest data to the Theis equation, obtaining the "best" transmissivity and storage in the least squares sense. Comparison of experimental pumptest data with this theoretical curve by graphical means has been a standard method of determining aquifer transmissivity and storage (Jacob, 1940). Through the years, the Theis equation has played an important role in groundwater hydrology (Theis, 1935). As a measure of the error in fitting, the rms error in drawdown is calculated for the "best" transmissivity and storage. The automated fit has the advantage that it is always objective. It is simple to use, quick and inexpensive. The automated fit for pumptest data developed in this work should be a useful tool for the groundwater hydrologist. The purpose of this paper is to present techniques and computer programs to evaluate the Theis equation, to evaluate the sensitivity with respect to transmissivity and storage, and to automatically fit experimental pumptest data to the Theis equation obtaining the "best" transmissivity and storage in the least squares sense. Comparison of experimental pumptest data with this theoretical curve by graphical means has been a standard method of determining aquifer transmissivity and storage. Through the years, the Theis equation has played an important role in groundwater hydrology. The method is not universally applicable to all pumping tests, but has been designed to analyze data conforming to assumptions implicit in the Theis equation. The method also gives an indication of how well it could analyze the data. The automated analysis has the advantage that it is always objective and cannot consider any personal bias. However, access to a computer capable of using the FORTRAN language is necessary. The method is simple, quick, and inexpensive. Some means of automating the analysis of these pumping tests would be desirable. Undoubtedly, many more pumping tests will be made in the future. Many pumping tests have been made through the years to help determine the aquifer transmissivity and storage coefficient (transmissivity is a measure of how easily water flows through the earth and the storage coefficient is a measure of how much water is stored per unit volume). It is clear that computer storage and manipulation are necessary to make full use of the data. ![]() The data base is massive and still is not complete. Much money and effort are expended each year to collect various kinds of data. Water is a valuable resource of the State of Kansas. This is, in general, the original text as published. Originally published in 1980 as Kansas Geological Survey Ground Water Series 3. Prepared by the Kansas Geological Survey in cooperation with the U.S. The Theis Equation: Evaluation, Sensitivity to Storage and Transmissivity, and Automated Fit of Pumptest Data by Carl D. ![]() Kansas Geological Survey, Ground Water Series 3, originally published in 1980 KGS-Ground Water Series 3-The Theis Equation ![]()
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