**infinite-acting radial flow**. During infinite-acting radial flow, steady pumping in a nonleaky confined aquifer of infinite extent produces late-time drawdown that changes with the logarithm of time since pumping began. Infinite-acting 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.

A derivative plot is very useful for detecting the infinite-acting radial flow regime under steady pumping conditions. One starts by looking for a

**derivative plateau**(constant derivative) to tentatively identify infinite-acting radial flow. For example, the response data from a constant-rate pumping test shown in Figure 2 suggest that infinite-acting 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 constant-rate pumping test in a nonleaky confined aquifer (Walton 1962). |

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 infinite-acting radial flow conditions. For example, an aquifer limited by a no-flow boundary can produce a constant derivative that is not diagnostic of the infinite-acting radial flow regime. In such a situation, geologic mapping of lithologic contacts, faults and other low-permeability features would be invaluable in making a correct interpretation.

Visit Aquifer Testing 101 for a catalog of derivative plot signatures with more examples of

**infinite-acting radial flow**in pumping tests.

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