When the pump is shut down after a pumping test, the water level inside the pumping and observation wells will start to rise. This rise in water level is known as residual drawdown (s'). Recovery-test measurements allow the transmissivity of the aquifer to be calculated, thereby providing an independent check on the results of the pumping test.
Residual drawdown data can be more reliable than drawdown data because the recovery occurs at a constant rate, whereas constant discharge pumping is often difficult to achieve in the field. Residual drawdown data can be collected from both the pumping and observation wells.
Strictly applied, this solution is appropriate for the conditions shown in the figure below. However, if additional limiting conditions are satisfied, the Theis recovery solution method can also be used for leaky, unconfined aquifers and aquifers with partially penetrating wells (Kruseman and de Ridder, 1991, p. 183).
According to Theis (1935), the residual drawdown, after pumping has ceased, is:
is the residual drawdown at a point [L]
is the discharge from the well [L3/T]
is the transmissivity of the aquifer [L2/T]
is the well function [-]
is the distance from the well to the observation point [L]
and are the elapsed times since the start and cessation of pumping, respectively [T]
and are the storativity values during pumping and recovery, respectively [-]
Using the approximation for the well function, , shown in the Cooper-Jacob method, this equation becomes:
When and are constant and equal and is constant, this equation can be reduced to:
To analyze the data, s' is plotted on the logarithmic Y axis and time is plotted on the linear X axis as the ratio of t/t' (total time since pumping began divided by the time since the pumping ceased).
An example of a Theis Recovery analysis graph has been included below:
An example of a Theis Recovery analysis is available in the project:
The Theis Recovery Solution assumes the following:
•The aquifer is confined and has an “apparent” infinite extent
•The aquifer is homogeneous, isotropic, and of uniform thickness over the area influenced by pumping
•The piezometric surface was horizontal prior to pumping
•The well is fully penetrating and pumped at a constant rate
•Water removed from storage is discharged instantaneously with decline in head
•The well diameter is small, so well storage is negligible
The data requirements for the Theis Recovery Solution are:
•Recovery vs. time data at a pumping or observation well
•Distance from the pumping well to the observation well
•Pumping rate and duration