Abstract
This note develops a general mathematical model for describing the transient hydraulic head response for constant-head test, constant-flux test, and slug test in a radial confined aquifer system with a partially penetrating well. The Laplace-domain solution for the model is derived by applying the Laplace transform with respect to time and finite Fourier cosine transform with respect to the z-direction. This new solution has been shown to reduce to the constant-head test when discounting the wellbore storage and maintaining a constant well water level. This solution can also be reduced to the constant-flux test solution when discounting the wellbore storage and keeping a constant pumping rate in the well. Moreover, the solution becomes the slug test solution when there is no pumping in the well. This general solution can be used to develop a single computer code to estimate aquifer parameters if coupled with an optimization algorithm or to assess the effect of well partial penetration on hydraulic head distribution for three types of aquifer tests.
Highlights
The constant-head and constant-flux tests are two typical aquifer tests in site characterization
The purpose of this paper is to develop a general mathematical model for describing the hydraulic head as a result of the constant-head, constant-flux, and slug tests at a partially penetrating well in a radial confined aquifer
For the constant-flux test, the pumping rate is maintained at a constant and the effect of wellbore storage on the hydraulic head, which occurs at early time of pumping, is generally negligible
Summary
The constant-head and constant-flux tests are two typical aquifer tests in site characterization. Perina and Lee (2006) presented a general well function for pumping from a confined, leaky, or unconfined aquifer as well as considering the effects of finite-thickness skin and well partial penetration Their semi-analytical solution was derived via Laplace and generalized finite Fourier transforms and allowed for non-uniform radial flux distribution along the well screen using a dsicrization approach which is essentially to divide the screen into several segments. The solution of the model is developed by utilizing Laplace and finite Fourier cosine transforms This new general solution can be used to predict the hydraulic head distribution for one of the constant-head test, constant-flux test, and slug test performed at a partially penetrating well in a radial confined aquifer system. This general solution can further be simplified for the case that the aquifer system has a fully penetrating well
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