At the outset of interpreting a pumping test, an important feature to
detect in the response data is
infiniteacting radial flow. During infiniteacting radial flow, steady pumping in a nonleaky
confined aquifer of infinite extent produces latetime drawdown that changes with the logarithm of
time since pumping began. Infiniteacting behavior occurs after wellbore storage effects have dissipated and before the influence of aquifer boundaries. One may observe this flow regime by plotting the familiar
Theis (1935) solution on semilog axes (Figure 1); at late time, a graph of dimensionless drawdown, w(u), versus dimensionless time, 1/u, plots as a straight
line and the
logarithmic derivative is constant.

Figure 1. Infiniteacting radial flow in a nonleaky confined aquifer illustrated with Theis (1935) solution (dimensionless drawdown and dimensionless derivative shown by blue and red curves, respectively). 
This latetime behavior of the Theis model is well known to groundwater hydrologists. The period of infiniteacting radial flow is the basis for the triedandtrue
Cooper and Jacob (1946) method which
one may use to find the transmissivity and storage coefficient of a nonleaky confined aquifer by matching a straight line to latetime drawdown data from a constantrate pumping test plotted on semilog axes.
A
derivative plot is very useful for detecting the infiniteacting radial flow regime under steady pumping conditions. One starts by looking for a
derivative plateau (constant derivative) to tentatively identify infiniteacting radial flow. For example, the response data from a constantrate pumping test shown in Figure 2 suggest that infiniteacting radial flow conditions are present after approximately 30 minutes of pumping once the derivative stabilizes.

Figure 2. Derivative plot of drawdown (squares) and derivative (crosses) measured in an observation well during constantrate pumping test in a nonleaky confined aquifer (Walton 1962). 
Note that the derivative plateau in Figure 2 exhibits some noise; derivative fluctuation at the plateau is common in the
application of derivative analysis, but the presence of a nearconstant derivative in this example is clear and corresponds to the emergence of a welldefined straight line in the drawdown data.
The foregoing results suggest that the derivative plot is an indispensable tool for aquifer test interpretation; however, the mere existence of a derivative plateau does not immediately confirm infiniteacting radial flow conditions. For example, an
aquifer limited by a noflow boundary can produce a constant derivative that is not diagnostic of the infiniteacting radial flow regime. In such a situation, geologic mapping of lithologic contacts, faults and other lowpermeability features would be invaluable in making a correct interpretation.
Visit
Aquifer Testing 101 for a
catalog of derivative plot signatures with more examples of
infiniteacting radial flow in pumping tests.
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