Approximate Solution for a Transient Hydraulic Head Distribution Induced by a Constant-Head Test at a Partially Penetrating Well in a Two-Zone Confined Aquifer
Publication: Journal of Hydraulic Engineering
Volume 140, Issue 7
Abstract
A mathematical model describing the transient hydraulic head distribution induced by constant-head pumping/injection at a partially penetrating well in a radial two-zone confined aquifer is a mixed-type boundary value problem. The analytical solution of the model is in terms of an improper integral with an integrand having a singularity at the origin. The solution should rely on numerical methods to evaluate the integral and handle the problems of convergence and singularity. This study aims at developing a new approximate solution describing the transient hydraulic head distribution for a constant-head test (CHT) at a partially penetrating well in the aquifer. This approximate solution is acquired based on a time-dependent diffusion layer approximation proposed in the field of electrochemistry. The diffusion layer can be analogous to the radius of influence in the area of well hydraulics. The approximate solution is in terms of modified Bessel functions for aquifers with a partially penetrating well and can reduce to a simpler form in terms of a natural logarithmic function for the case of well full penetration. The predicted hydraulic heads from the present approximate solution are compared with those estimated by the Laplace-domain solution of the model. The result shows that the predicted spatial head distributions are accurate in the formation zone and fairly good in the skin zone. In addition, the present solution gives an accurate temporal head distribution at a specific location when the radius of influence is far away from the observation wells. This newly developed approximate solution has advantages of easy computing and good accuracy from practical viewpoint, and thus is a handy tool to evaluate temporal and spatial hydraulic head distributions for the CHT.
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Acknowledgments
Research leading to this paper has been partially supported by the grants from Taiwan National Science Council under the contract numbers NSC 101-2221-E-009-105-MY2 and 102-2221-E-009-072-MY2.
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Information & Authors
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Published In
Journal of Hydraulic Engineering
Volume 140 • Issue 7 • July 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Aug 11, 2013
Accepted: Feb 7, 2014
Published online: Mar 26, 2014
Published in print: Jul 1, 2014
Discussion open until: Aug 26, 2014
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