Analytical Solutions
Confined Aquifer
Multi-well Variable-Rate Pumping-Test Analysis (click on the figure to enlarge)System Geometry
The schematic of system geometry for a confined aquifer (with an overlying and underlying aquitard) pumping test is shown in the adjacent figure.
The pumping well of finite radius r_{w} is partially penetrating the confined aquifer of thickness b between depths l and d below the top impermeable boundary.
The pumping well has wellbore storage coefficient C_{w} (volume of water released from well storage per unit drawdown in it).
The observation well penetrating between depths z_{1} and z_{2} below the top impermeable boundary is located at distance r from the axis of the pumping well.
Analytical solutions for confined aquifers
The following analytical solutions are implemented in WELLS for confined aquifers:
- Theis [1935] Solution : For fully and partially penetrating well ( d=0, l=b ) of zero radius (r_{w} = C_{w} =0 ) in an isotropic (K_{r} = K_{z}) confined aquifer.
- Hantush [1964] Solution : For partially penetrating well (0 ≤ d,l ≤ b ) of zero radius (r_{w} = C_{w} =0 ) in an anisotropic (K_{r} ≠ K_{z}) confined aquifer.
- Papadopulos and Cooper [1967] Solution : For fully penetrating well (d=0, l=b ) of finite radius (r_{w} ≠ 0 ) with a finite wellbore storage capacity (C_{w} ≠ 0 ) in an isotropic (K_{r} = K_{z}) confined aquifer solution :
- Yang et.al. [2006] Solution : For partially penetrating well (0 ≤ d,l ≤ b ) of finite radius (r_{w} ≠ 0 ) with no wellbore storage capacity (C_{w} = 0 ) in an anisotropic (K_{r} ≠ K_{z}) confined aquifer.
- Mishra et.al. [2011] Solution : For partially penetrating well (0 ≤ d,l ≤ b ) of finite radius (r_{w} ≠ 0 ) with a finite wellbore storage capacity (C_{w} ≠ 0 ) in an anisotropic (K_{r} ≠ K_{z}) confined aquifer.
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.
- Hantush, M.S., 1964. Hydraulics of wells, in: Advances in Hydroscience, V.T. Chow (editor), Academic Press, New York, pp. 281-442.
- Papadopulos, I.S. and H.H. Cooper, 1967. Drawdown in a well of large diameter, Water Resources Research, vol. 3, no. 1, pp. 241-244.
- S.‐Y. Yang, H.‐D. Yeh, and P. Chiu (2006), A closed form solution for constant flux pumping in a well under partial penetration condition, Water Resour. Res., 42, W05502, doi:10.1029/2004WR003889.
- Mishra P.K., V Vessilinov, S P Neuman, Radial flow towards large diamter well in a confined aquifer, Water Resources Research, In review.
Download
The WELLS code is available at no cost. Please follow the instructions on "Download" page.
Question/Comments
For questions/comments please fill out the information on the contact us page.