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<p>This study examines a&#xa0;finite fractured aquifer that is bordered on one side by an impermeable rock and on the other by a&#xa0;stream. It investigates how a&#xa0;continuous discharge pumped from a&#xa0;stream can cause one-dimensional unsteady flow in a&#xa0;fractured aquifer. The time-dependent governing ordinary differential equation is modified using the Caputo–Fabrizio fractional derivative operator, incorporating the dual porosity model under the assumption of pseudo-steady-state flow from fractures to matrix blocks. The use of the Caputo–Fabrizio derivative, which features a&#xa0;non-singular kernel, allows for more accurate modeling of memory effects and delayed responses in aquifer systems-characteristics commonly observed in fractured and karstic media. Laplace and finite Fourier cosine transformations with respect to time and spatial variables are used to generate the new transient solution, and the drain function is plotted. The aquifer’s drawdowns can be predicted using the resulting solutions, which can also be used to numerically validate an aquifer model.</p>

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Dual permeability fractional model for flow in the karstic aquifer

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • Pravindra Kumar,
  • Mahaveer Prasad Yadav,
  • Ravi Shanker Dubey

摘要

This study examines a finite fractured aquifer that is bordered on one side by an impermeable rock and on the other by a stream. It investigates how a continuous discharge pumped from a stream can cause one-dimensional unsteady flow in a fractured aquifer. The time-dependent governing ordinary differential equation is modified using the Caputo–Fabrizio fractional derivative operator, incorporating the dual porosity model under the assumption of pseudo-steady-state flow from fractures to matrix blocks. The use of the Caputo–Fabrizio derivative, which features a non-singular kernel, allows for more accurate modeling of memory effects and delayed responses in aquifer systems-characteristics commonly observed in fractured and karstic media. Laplace and finite Fourier cosine transformations with respect to time and spatial variables are used to generate the new transient solution, and the drain function is plotted. The aquifer’s drawdowns can be predicted using the resulting solutions, which can also be used to numerically validate an aquifer model.