8 Transient Analytical Model for Pumping of a Fully Confined Aquifer

A hydrogeologic unit is considered confined when the heads in tightly cased wells are higher than the top of the unit. The surface defining the head distribution is referred to as the potentiometric surface (Woessner & Poeter, 2020, Figure 46). The pressure in confined systems exceeds the hydrostatic pressure.

C. V. Theis (1935), with the assistance of C. I. Lubin, applied the mathematics that describe a “…continuous point source for a heat conduction problem” (Lohman, 1972), to formulate an analytical solution for flow to a well in a confined aquifer under transient conditions. Transient conditions are non‑equilibrium conditions. The Theis solution (1935) describes how a confined groundwater system would react to pumping over time. This was the first transient model available for analyzing non‑steady time‑drawdown data sets. Prior to his work, wells would be pumped for long periods until drawdown reached steady‑state or pseudo‑steady‑state conditions (as described in Section 7). Then drawdown versus distance data would be analyzed using the Thiem steady‑state equations. Theis’s non‑equilibrium analyses resulted in shorter hydraulic tests in which time‑drawdown data are used to derive hydraulic properties of confined systems.