Theis Solution for Confined Aquifers

Theis Solution for Confined Aquifers

Theis (1935) derived an analytical solution for flow to a well in a confined aquifer under the following set of assumptions:

- Aquifer is infinite in extent, homogeneous, and isotropic
- Aquifer has a uniform thickness and is horizontal
- Aquifer is fully confined and discharge is derived exclusively from storage in the aquifer.
- The potentiometric surface is initially horizontal
- The well fully penetrates the confined aquifer
- The pumping rate is constant
- The resulting flow to the well is horizontal and laminar

The equation for predicting drawdown, s (or h₀ - h) is:

where h₀ is the initial water level; h is the head at some radial distance, r, and at some time, t; T is the transmissivity; Q is the pumping rate; W(u) is the well function, which is the infinite series part of the analytical solution to nonsteady, radial groundwater flow; and u = r²S/(4Tt).

In AQtestNET, an analytical approximation developed by Barry, Parlange and Li (1999) is used to estimate the well function for all values of its argument.

Barry, D.A., Parlange, J.Y. and Li, L., 2000. Approximation for the exponential integral (Theis well function). Journal of Hydrology, 227(1-4), pp.287-291.

Aquifer Properties

Hydraulic Conductivity

Use the default value or assign a different value for hydraulic conductivity in the text field next to 'Conductivity'. (Hydraulic conductivity is needed for computing aquifer transmissivity (T=Kb), a direct input to the Theis solution.)

Aquifer Elevations / Thickness

Use the default value or assign a different value for aquifer thickness in the text field next to 'Thickness'.

Storage Coefficient

A known or assumed storage coefficient is needed to calculate theoretical drawdown. Specific storage is defined as the volume of water that a unite volume of a confined aquifer releases from storage under a unit decline in head, produced by compactions of the aquifer and the expansion of water caused by decreasing pressure.

Use the default value or assign a different value for the storage coefficient in the text field next to 'Storage Coefficient'.

Test Parameters

Pumping Rate

A steady (time-independent) pumping rate input is needed for the Theis solution. Use the default value or assign a different value for the pumping rate in the text field next to 'Pumping Rate'.

Distance from well

The represents the radial distance from the well to the point of drawdown observation. Use the default value or assign a different value for distance in the text field next to 'Distance from well'.

Add Observation Data

Use the large text field to enter drawdown (in feet) and time of observation (days snice the start of the test). Please one line for each data point, with a comma separating drawdown from the time observation.