Taylor’s expansion application in simplifying the groundwater analytical solution equations

Document Type : Research Paper

Authors

1 Faculty of Earth Sciences, Shahrood University of Technology, Shahrood, Iran

2 Faculty of Mechanical engineering, Shahrood University of Technology, Shahrood, Iran

Abstract

The analytical modeling solutions and Taylor's expansion have been applied to various groundwater equations. This study explores the effectiveness of Taylor's expansion in simplifying the capture zone equations for a multi-horizontal well system. The examined well system encompasses a combination of arbitrarily located production and recharge HWs, each with varying discharge or recharge rates and directions of uniform flow. To validate the utility of Taylor's expansion in this context, the velocity potential values from the equations were calculated both before and after applying the expansion. To further confirm the precision of the results, equipotential and flow lines were generated for both the original and simplified equations. The analysis revealed significant findings regarding accuracy: the percentage differences in hydraulic head between the original equations and those derived from Taylor's expansion reached peaks of 59.07% and 68.51% for aquifer thicknesses ranging from 0 to 50 meters. Remarkably, as the aquifer thickness increased, these percentage differences decreased substantially, achieving minimum values at a thickness of 1500 meters. Overall, application of Taylor's expansion proves to be highly effective for aquifer thicknesses approximately 200 meters or greater in terms of hydraulic head and around 400 m or more concerning the corresponding equations. The drawing of equipotential and flow lines reinforces the validity of these findings and demonstrates the practical applicability of the simplified equations. Furthermore, the established thresholds of thicknesses for accurate application provide critical guidance for future hydrological analyses. Future research could expand on these findings by exploring its applications under diverse geological conditions.

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Article Title [Persian]

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History

  • Receive Date: 24 October 2024
  • Revise Date: 14 December 2024
  • Accept Date: 29 December 2024

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