7 Thiem Steady-State Analytical Models for Pumping Confined and Unconfined Aquifers

Steady‑state conditions occur when water levels stop changing within the cone of depression during a pumping test. Steady state is an equilibrium condition. Steady state occurs when the expansion of the cone of depression is limited by a recharge boundary condition that provides a source of water to the pumping well other than water stored in the aquifer and creates a steady condition when the inflow rate is equal to the extraction rate of the well (Figures 8 and 9). When steady‑state conditions occur, water is not being released from storage in the unit being pumped. Thiem (1906) developed equations that describe steady‑state conditions during pumping confined and unconfined units. These are known as the Thiem equations.

A well may need to be pumped for a long period before the cone of depression expands sufficiently to capture recharge sources that equal the well discharge rate and thus stabilize the heads. Tests may require pumping over several days or weeks before reaching a steady state. When recharge sources are not encountered pseudo‑steady‑state conditions may be observed. This refers to conditions where drawdown rates become minimal with long pumping times. Steady‑state equations are often applied to these conditions to estimate hydraulic conductivity and transmissivity.