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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Aquifer thickness, H		ft
Transmissivity, K		gal/ft-day
Storativity, S
Well flow rate, Q		gpm
Distance from well, r		ft
Time, t		days

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OUTPUT   VARIABLES   &   GRAPHS

Variables	Values	Units
♦  Well function parameter, u			Graphs:  Drawdown vs Distance
♦  Well function, W(u)
♦  Drawdown, s		ft

Unsteady State Flow Into Water Wells

Water is pumped out of wells for drinking, irrigation, etc. Also water is pumped into wells for waste disposal, oil reservoir pressurization, etc. It is often necessary to determine the yield, drawdown around a well and the impact on neighboring wells.
Theis has developed an analytical solution for the drawdown of non-steady state flow in confined homogeneous isotropic aquifer. The Theis equation has become the most widely used equation in transient groundwater hydraulics:

where
     s = drawdown at distance r at time t
     Q = constant water pumping (discharge) rate
     W(u) = Well Function of Theis
     r = radial distance from well
     t = time after the start of pumping
     S = storativity of the elastic infinite aquifer
     K = transmissivity of aquifer
     γ = Euler's constant = 0.577215665

In the implementation here, the infinite series is approximated by summation from m=1 => 20, with insignificant loss of accuracy.

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point

BIBLIOGRAPHY

• Lindeburg MR; 101 Solved Civil Engineering problems; Professional Publications, Inc., Belmot, CA, USA, 2001.
• Warner DD, Clemson University, SC, USA; http://www.math.clemson.edu/faculty/Warner/Projects/GroundWater/node8.html
• Hicks TG; Civil Engineering Formulas, Pocket Guide; McGraw Hill, New York, 2002.