Theis Step-Drawdown Test Solution for Nonleaky Confined Aquifers
- Data requirements
- Solution options
- Estimated parameters
- Curve matching tips
Related Solution Methods
Theis (1935) developed a mathematical solution for determining the hydraulic properties (transmissivity and storativity) of nonleaky confined aquifers from pumping tests. Hantush (1961a, b; 1964) later introduced equations for partially penetrating wells.
For step-drawdown tests, the Theis/Hantush solution can be easily modified to include linear and nonlinear well losses occurring at the pumping well (Jacob 1947; Rorabaugh 1953; Ramey 1982). Analysis involves matching a curve to drawdown data collected during a step-drawdown test.
- aquifer has infinite areal extent
- aquifer is homogeneous and of uniform thickness
- control well is fully or partially penetrating
- aquifer is nonleaky confined
- flow is unsteady
- water is released instantaneously from storage with decline of hydraulic head
- diameter of pumping well is very small so that storage in the well can be neglected
The Theis/Hantush model for a partially penetrating pumping well in an infinite anisotropic nonleaky confined aquifer and adapted for step-drawdown tests to include linear and nonlinear well loss is given by the following equation:
- is aquifer thickness [L]
- is nonlinear well loss coefficient [TP/L3P-1]
- is the depth to the top of pumping well screen [L]
- is the radial (horizontal) hydraulic conductivity [L/T]
- is the vertical hydraulic conductivity [L/T]
- is the depth to the bottom of pumping well screen [L]
- is pumping rate [L³/T]
- is well radius [L]
- is drawdown in the pumped well [L]
- is storativity [dimensionless]
- is wellbore skin factor [dimensionless]
- is elapsed time since start of pumping [T]
- is transmissivity [L²/T]
- is the Theis well function for nonleaky confined aquifers [dimensionless]
- is the Hantush and Jacob well function for leaky confined aquifers [dimensionless]
- pumping and observation well locations
- pumping rate(s)
- observation well measurements (time and displacement)
- partial penetration depths (optional)
- saturated thickness (for partially penetrating wells)
- hydraulic conductivity anisotropy ratio (for partially penetrating wells)
- variable pumping rates
- multiple pumping wells
- multiple observation wells
- partially penetrating pumping and observation wells
AQTESOLV provides visual and automatic methods for matching the Theis nonequilibrium step-drawdown test method to data from step-drawdown tests. The estimated aquifer properties and well-loss parameters are as follows:
- (wellbore skin factor)
- (nonlinear well loss coefficient)
- (nonlinear well loss exponent)
Curve Matching Tips
- Use the Cooper and Jacob (1946) solution to obtain preliminary estimates of aquifer properties.
- Choose Match>Visual to perform visual curve matching using the procedure for type curve solutions.
- Use active type curves for more effective visual matching with variable-rate pumping tests.
- Use parameter tweaking to perform visual curve matching and sensitivity analysis.
- Perform visual curve matching prior to automatic estimation to obtain reasonable starting values for the aquifer properties.
- Due to correlation in the equations between (storativity) and (wellbore skin factor), estimate either or for a single-well test but not both as the same time.
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.
Jacob, C.E., 1947. Drawdown test to determine effective radius of artesian well, Trans. Amer. Soc. of Civil Engrs., vol. 112, paper 2321, pp. 1047-1064.
Ramey, H.J., 1982. Well-loss function and the skin effect: A review. In: Narasimhan, T.N. (ed.) Recent trends in hydrogeology, Geol. Soc. Am., special paper 189, pp. 265-271.
Rorabaugh, M.J., 1953. Graphical and theoretical analysis of step-drawdown test of artesian well, Proc. Amer. Soc. Civil Engrs., vol. 79, separate no. 362, 23 pp.