Analytical Solutions
WELLS computes the drawdown/hydraulic head at one or more predefined locations due to pumping at one or multiple locations in an aquifer. The computation is based on a variety of available analytical solutions.
The analytical solutions implemented in WELLS can be broadly classified in the following categories:
Multi-well Variable-Rate Pumping-Test Analysis
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 rw 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 Cw (volume of water released from well storage per unit drawdown in it).
The observation well penetrating between depths z1 and z2 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 (rw = Cw =0 ) in an isotropic (Kr = Kz) confined aquifer.
- Hantush [1964] Solution : For partially penetrating well (0 ≤ d,l ≤ b ) of zero radius (rw = Cw =0 ) in an anisotropic (Kr ≠ Kz) confined aquifer.
- Papadopulos and Cooper [1967] Solution : For fully penetrating well (d=0, l=b ) of finite radius (rw ≠ 0 ) with a finite wellbore storage capacity (Cw ≠ 0 ) in an isotropic (Kr = Kz) confined aquifer solution :
- Yang et.al. [2006] Solution : For partially penetrating well (0 ≤ d,l ≤ b ) of finite radius (rw ≠ 0 ) with no wellbore storage capacity (Cw = 0 ) in an anisotropic (Kr ≠ Kz) confined aquifer.
- Mishra et.al. [2011] Solution : For partially penetrating well (0 ≤ d,l ≤ b ) of finite radius (rw ≠ 0 ) with a finite wellbore storage capacity (Cw ≠ 0 ) in an anisotropic (Kr ≠ Kz) 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 diameter well in a confined aquifer, Water Resources Research, In review.
Multi-well Variable Rate Pumping Test Analysis
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
- 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
- Mishra, P.K. and S.P. Neuman, 2011. Saturated-unsaturated flow to a well with storage in a compressible unconfined aquifer, Water Resources Research
System Geometry
The schematic of system geometry for leaky confined aquifer pumping test is shown in adjacent figure.
The pumping well of finite radius rw is partially penetrating the leaky confined aquifer of thickness b between depths l and d below the top aquitard.
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 aquitard and is located at distance r from the axis of the pumping well.
Analytical solutions for leaky confined aquifer
The following analytical solutions are implemented in WELLS for leaky confined aquifers:
- Hantush [1960] Solution : For fully and partially penetrating well ( d=0, l=b ) of zero radius (rw = Cw =0 ) in an isotropic (Kr = Kz) confined aquifer.
- Mishra and Vessilinov [2011] Solution : For partially penetrating well (0 ≤ d,l ≤ b ) of finite radius (rw ≠ 0 ) with a finite wellbore storage capacity (Cw ≠ 0 ) in an anisotropic (Kr ≠ Kz) confined aquifer.
References
System Geometry
The schematic of system geometry for leaky unconfined aquifer pumping test is shown in adjacent figure.
The pumping well of finite radius rw is partially penetrating the leaky unconfined aquifer having 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 top boundary of underlying aquitard is located at distance r from the axis of the pumping well.
Analytical solutions for leaky unconfined aquifer
The following analytical solutions are implemented in WELLS for leaky unconfined aquifers:
- Mishra and Vessilinov [2011] Solution : For partially penetrating well of finite radius with wellbore storage
References
- Mishra P.K. and V.V. Vessilinov, 2011. Semi-analytical solution for Radial flow towards large diameter well in a leaky confined aquifer, Journal of Hydrology, In review.
WELLS has been applied to the following studies:
- Identification of Pumping Influences in Long-Term Water Level Fluctuations (Harp and Vesselinov, 2011)
- Accounting for the influence of aquifer heterogeneity on spatial propagation of pumping drawdown (Harp and Vesselinov, 2011)
- On simulation and analysis of variable-rate pumping tests (Mishra et al., 2011)
The code was originaly developed at the University of Mining & Geology, Sofia, Bulgaria in 1992 by Velimir V. Vesselinov (Monty).
