Analytical Solutions

Unconfined Aquifer

Multi-well Variable Rate Pumping Test Analysis (click on the figure to enlarge)
Schematic of unconfined Aquifer

System Geometry

The schematic of system geometry for unconfined aquifer pumping test is shown in adjacent figure.

The pumping well of finite radius rw is partially penetrating the confined aquifer of initial saturated thickness b between depths l and d below the initial water table.

The pumping well has wellbore storage coefficient Cw (volume of water released from well storage per unit drawdown in it).

The observation well penetrating between depths z1 and z2 above the bottom impermeable boundary is located at distance r from the axis of the pumping well.

Analytical solutions for unconfined aquifer

The following analytical solutions are implemented in WELLS for unconfined aquifers:

  • Transformed Theis [1935] Solution for unconfined aquifer : For fully penetrating well of zero radius
  • Tartakovsky and Neuman [2007] solution : For partially penetrating well of zero radius in unconfined aquifer having infinitely thick unsaturated zone (L → ∞).
  • Mishra and Neuman [2010] solution : For partially penetrating well of zero radius in unconfined aquifer having finitely thick unsaturated zone.
  • Mishra and Neuman [2011] solution : For partially penetrating well of finite radius in unconfined aquifer having finitely thick unsaturated zone.

References

  • Theis, C.V., 1935. The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using groundwater storage, Am. Geophys. Union Trans., vol. 16, pp. 519-524.
  • Tartakovsky, G.D. and S.P. Neuman, 2007. Three-dimensional saturated-unsaturated flow with axial symmetry to a partially penetrating well in a compressible unconfined aquifer, Water Resources Research, 43, W01410, doi:1029/2006WR005153.
  • Mishra, P.K. and S.P. Neuman, 2010. Improved forward and inverse analyses of saturated-unsaturated flow toward a well in a compressible unconfined aquifer, Water Resources Research, 46, W07508, doi:10.1029/2009WR008899.
  • Mishra, P.K. and S.P. Neuman, 2011. Saturated-unsaturated flow to a well with storage in a compressible unconfined aquifer, Water Resources Research, 2010WR010177.

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