### Abstract

This study proposes a generalized Darcy's law with considering phase lags in both the water flux and drawdown gradient to develop a lagging flow model for describing drawdown induced by constant-rate pumping (CRP) in a leaky confined aquifer. The present model has a mathematical formulation similar to the dual-porosity model. The Laplace-domain solution of the model with the effect of wellbore storage is derived by the Laplace transform method. The time-domain solution for the case of neglecting the wellbore storage and well radius is developed by the use of Laplace transform and Weber transform. The results of sensitivity analysis based on the solution indicate that the drawdown is very sensitive to the change in each of the transmissivity and storativity. Also, a study for the lagging effect on the drawdown indicates that its influence is significant associated with the lag times. The present solution is also employed to analyze a data set taken from a CRP test conducted in a fractured aquifer in South Dakota, USA. The results show the prediction of this new solution with considering the phase lags has very good fit to the field data, especially at early pumping time. In addition, the phase lags seem to have a scale effect as indicated in the results. In other words, the lagging behavior is positively correlated with the observed distance in the Madison aquifer.

Original language | English |
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Pages (from-to) | 8500-8511 |

Number of pages | 12 |

Journal | Water Resources Research |

Volume | 53 |

Issue number | 10 |

DOIs | |

State | Published - 1 Oct 2017 |

### Keywords

- Darcy's law
- dual porosity model
- lagging behavior
- leaky aquifer
- pumping test
- scale effect

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## Cite this

*Water Resources Research*,

*53*(10), 8500-8511. https://doi.org/10.1002/2017WR021115