Theis Equation Calculator
Compute drawdown for unsteady groundwater flow to a pumping well in a confined aquifer
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Units in Theis unsteady groundwater flow to a well calculator: cm=centimeter, ft=foot, gal=gallon (U.S.), hr=hour, km=kilometer, m=meter, min=minute, s=second.
Diagrams of Groundwater Flow to a Pumping Well (Wells Screened in Confined Aquifer)
Unsteady Groundwater Flow to a Pumping Well in a Confined Aquifer
Equation - Conservation of Mass
The equation describes mass conservation of groundwater flow in the radial direction allowing for change in storage volume (expansion or contraction of the confined water due to change in pressure).
s(r=0,t=0) = 0 s(r=∞,t) = 0
The goal is to solve for drawdown as a function of radial distance r from the pumping well at time t since pumping started. The solution is commonly called the Theis solution, after Charles Theis who developed the solution in 1935 (Bear, 1979, p. 321):
Our calculation carries out the series to the u100 term which is sufficient for convergence to machine precision for u up to 9.5.
The LMNO Engineering unsteady groundwater flow calculation allows entry of either a positive or negative value for the pumping rate Q. A positive Q simulates pumping, and drawdown s will be positive since the piezometric surface drops. If a negative value is entered for Q, water injection is simulated. In that case drawdown is negative since the piezometric surface rises.
The groundwater flow program checks that r, t, T, and Sc are positive inputs. It also checks to make sure u ≤ 9.5 which is the maximum value printed in many texts (e.g. Bear, 1979, pp. 320-321). All input variables are converted to SI units prior to calculations.
The groundwater calculation does not check if the input values are physically reasonable and does not check if Reynolds number Re is less than or equal to 1.0. Darcy's law for groundwater flow (expressed in the boundary condition above that has "-Q" in it) is only valid for Re ≤ 1. Darcy's law is typically valid in groundwater flow since water velocities are very low through porous subsurface formations.
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