Radius of Influence Calculator

After aquifer transmissivity and storativity have been determined, the Radius of Influence Calculator can be used to estimate the radius of influence for different scenarios.

The calculator actually estimates the radius to a specified drawdown. For example, to estimate the radius of influence, a negligible drawdown, such as 0.01 should be selected. It may be useful to estimate the radius to other drawdown values such as 1 foot or 1 meter.

Implementation

The user enters transmissivity, storativity, drawdown for which to determine radius, well radius, and pumping rate. The calculator solves the Theis (1935) solution equation consecutively for increasing times until the drawdown stabilizes. The Theis equation is given as:

$image\THEIS.gif$

where:

$image\WU.gif$

and:

$image\U.gif$

The steady state drawdown is then used in the Thiem confined aquifer steady state equation to determine radius for which a user specified drawdown will occur. The Thiem steady-state confined aquifer equation is given as:

$image\THIEMC1.gif$

Five Minute Steady-State Tolerance

The Theis equation describes drawdown that approaches steady-state asymptotically, but never actually reaches a single steady-state value. Therefore some amount of change in drawdown per time must be specified to indicate the well has reached steady state. The value entered here is the amount of drawdown that occurs in five minutes of pumping to define steady-state. By default, this value is 0.001 meters. In other words, when the change in drawdown as described by the Theis equation is less than 0.001 meters in five minutes, it is assumed that steady-state has been reached. A smaller value may be justified in high transmissivity aquifers. Entering a very small value may result in the inability of the algorithm to converge, prompting an error message.

Applicability

Since the calculator uses the Theis and Thiem equations, it is accurate to the extent that these solutions are applicable and accurate. Since steady-state is first determined, the accuracy of the steady state approximation will affect the accuracy of the radius of influence calculator.

The radius-of-influence calculator is intended to estimate actual aquifer conditions. Results should be verified by hand calculations.

Error Messages

Using too small of a pumping rate may result in the inability of the algorithm to converge. This is because the radius of influence is actually smaller than the well radius. If a message is displayed indicating that the algorithm did not converge, try increasing the pumping rate, or decreasing the well radius.