Full-Range Solution for the Theis Well Function
Publication: Journal of Hydrologic Engineering
Volume 19, Issue 3
Abstract
Pumping tests are used to determine the transmissivities and storage coefficients of aquifers. For nonleaky aquifers, the solution reduces to the exponential integral, which is also called the Theis well function. It is beneficial to have a simple and handy approximation for the Theis well function. A simple (minimum number of terms) and reliable approximation that is efficient, yet sufficiently accurate, is preferable. This research provides a simple and accurate approximation to the Theis well function valid for all values of its arguments. The approximation is constructed by a combination of two solutions that are valid for small and large arguments. The approximation contains unknown coefficients, which are determined by using an optimization procedure. An accurate approximation to the well function should also be able to accurately compute the derivative of the well function. The proposed approximation minimizes errors in both the well function and its derivative. The maximum relative error in the proposed approximation and its derivative are less than 0.2% and 0.22%, respectively, making it useful for routine groundwater applications.
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Published In
Journal of Hydrologic Engineering
Volume 19 • Issue 3 • March 2014
Pages: 649 - 653
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Aug 14, 2012
Accepted: Apr 18, 2013
Published online: Apr 20, 2013
Discussion open until: Sep 20, 2013
Published in print: Mar 1, 2014
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