Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer
An aquifer consisting of a skin zone and a formation zone is considered as a two-zone aquifer. Existing solutions for the problem of constant-flux pumping in a two-zone confined aquifer involve laborious calculation. This study develops a new approximate solution for the problem based on a mathemati...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2015-06-01
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| Series: | Hydrology and Earth System Sciences |
| Online Access: | http://www.hydrol-earth-syst-sci.net/19/2639/2015/hess-19-2639-2015.pdf |
| _version_ | 1819274693918588928 |
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| author | C.-S. Huang S.-Y. Yang H.-D. Yeh |
| author_facet | C.-S. Huang S.-Y. Yang H.-D. Yeh |
| author_sort | C.-S. Huang |
| collection | DOAJ |
| description | An aquifer consisting of a skin zone and a formation zone is considered as a
two-zone aquifer. Existing solutions for the problem of constant-flux
pumping in a two-zone confined aquifer involve laborious calculation. This
study develops a new approximate solution for the problem based on a
mathematical model describing steady-state radial and vertical flows in a
two-zone aquifer. Hydraulic parameters in these two zones can be different
but are assumed homogeneous in each zone. A partially penetrating well may
be treated as the Neumann condition with a known flux along the screened
part and zero flux along the unscreened part. The aquifer domain is finite
with an outer circle boundary treated as the Dirichlet condition. The
steady-state drawdown solution of the model is derived by the finite Fourier
cosine transform. Then, an approximate transient solution is developed by
replacing the radius of the aquifer domain in the steady-state solution with
an analytical expression for a dimensionless time-dependent radius of
influence. The approximate solution is capable of predicting good temporal
drawdown distributions over the whole pumping period except at the early
stage. A quantitative criterion for the validity of neglecting the vertical
flow due to a partially penetrating well is also provided. Conventional
models considering radial flow without the vertical component for the
constant-flux pumping have good accuracy if satisfying the criterion. |
| first_indexed | 2024-12-23T23:12:30Z |
| format | Article |
| id | doaj.art-a30c956e6a694623a23460e2b3da2030 |
| institution | Directory Open Access Journal |
| issn | 1027-5606 1607-7938 |
| language | English |
| last_indexed | 2024-12-23T23:12:30Z |
| publishDate | 2015-06-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Hydrology and Earth System Sciences |
| spelling | doaj.art-a30c956e6a694623a23460e2b3da20302022-12-21T17:26:38ZengCopernicus PublicationsHydrology and Earth System Sciences1027-56061607-79382015-06-011962639264710.5194/hess-19-2639-2015Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquiferC.-S. Huang0S.-Y. Yang1H.-D. Yeh2Institute of Environmental Engineering, National Chiao Tung University, Hsinchu, TaiwanDepartment of Civil Engineering, Vanung University, Chungli, TaiwanInstitute of Environmental Engineering, National Chiao Tung University, Hsinchu, TaiwanAn aquifer consisting of a skin zone and a formation zone is considered as a two-zone aquifer. Existing solutions for the problem of constant-flux pumping in a two-zone confined aquifer involve laborious calculation. This study develops a new approximate solution for the problem based on a mathematical model describing steady-state radial and vertical flows in a two-zone aquifer. Hydraulic parameters in these two zones can be different but are assumed homogeneous in each zone. A partially penetrating well may be treated as the Neumann condition with a known flux along the screened part and zero flux along the unscreened part. The aquifer domain is finite with an outer circle boundary treated as the Dirichlet condition. The steady-state drawdown solution of the model is derived by the finite Fourier cosine transform. Then, an approximate transient solution is developed by replacing the radius of the aquifer domain in the steady-state solution with an analytical expression for a dimensionless time-dependent radius of influence. The approximate solution is capable of predicting good temporal drawdown distributions over the whole pumping period except at the early stage. A quantitative criterion for the validity of neglecting the vertical flow due to a partially penetrating well is also provided. Conventional models considering radial flow without the vertical component for the constant-flux pumping have good accuracy if satisfying the criterion.http://www.hydrol-earth-syst-sci.net/19/2639/2015/hess-19-2639-2015.pdf |
| spellingShingle | C.-S. Huang S.-Y. Yang H.-D. Yeh Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer Hydrology and Earth System Sciences |
| title | Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer |
| title_full | Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer |
| title_fullStr | Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer |
| title_full_unstemmed | Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer |
| title_short | Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer |
| title_sort | technical note approximate solution of transient drawdown for constant flux pumping at a partially penetrating well in a radial two zone confined aquifer |
| url | http://www.hydrol-earth-syst-sci.net/19/2639/2015/hess-19-2639-2015.pdf |
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