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    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

    Source: Journal of Hydraulic Engineering:;2014:;Volume ( 140 ):;issue: 007
    Author:
    Shaw-Yang Yang
    ,
    Ching-Sheng Huang
    ,
    Chih-Hsuan Liu
    ,
    Hund-Der Yeh
    DOI: 10.1061/(ASCE)HY.1943-7900.0000884
    Publisher: American Society of Civil Engineers
    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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      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

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    contributor authorShaw-Yang Yang
    contributor authorChing-Sheng Huang
    contributor authorChih-Hsuan Liu
    contributor authorHund-Der Yeh
    date accessioned2017-05-08T22:06:18Z
    date available2017-05-08T22:06:18Z
    date copyrightJuly 2014
    date issued2014
    identifier other28178689.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/71424
    description abstractA 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.
    publisherAmerican Society of Civil Engineers
    titleApproximate Solution for a Transient Hydraulic Head Distribution Induced by a Constant-Head Test at a Partially Penetrating Well in a Two-Zone Confined Aquifer
    typeJournal Paper
    journal volume140
    journal issue7
    journal titleJournal of Hydraulic Engineering
    identifier doi10.1061/(ASCE)HY.1943-7900.0000884
    treeJournal of Hydraulic Engineering:;2014:;Volume ( 140 ):;issue: 007
    contenttypeFulltext
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