Analysis of Unconfined Flow Induced by Constant Rate Pumping Based on the Lagging Theory

Ye Chen Lin, Ching Sheng Huang, Hund-Der Yeh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


This study proposes a new mathematical model for describing the drawdown distribution due to a constant rate pumping (CRP) in an unconfined aquifer considering the lagging theory. We introduce two lag times in Darcy's law and in turn in a free surface equation to reflect the effects of the capillary fringe and the capillary suction on the water table motion. The present free surface equation can reduce to those used in previous studies. The Laplace and Weber transform methods are used to derive the semianalytical solution to the model including the effect of wellbore storage. The algorithm of numerical Laplace inversion is applied to obtain the transient solution of the model. We find that the delay index, commonly used in the literature, is equivalent to the lag time associated with the effect of the capillary suction. The sensitivity analysis is performed to assess the drawdown behavior in response to the change in each aquifer parameter. The drawdown distributions predicted by the present solution agree fairly well to the field data taken from CRP tests at Cape Cod, Massachusetts; the Canadian Forces Base Borden, Ontario; and Saint Pardon de Conques, Gironde (France). The lag times determined by both CRP tests seem to decrease linearly with increasing distance on the logarithmic scale from the pumping well. The consideration of two lag times considerably improves the accuracy in estimated specific yields.

Original languageEnglish
Pages (from-to)3925-3940
Number of pages16
JournalWater Resources Research
Issue number5
StatePublished - 1 May 2019


  • Darcy's law
  • capillary fringe
  • capillary suction
  • pumping test
  • time lag
  • unconfined aquifer

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