Why does the Theis equation for well flow assume the water-bearing layer is very big and goes on forever?

The Theis equation assumes the water-bearing layer, known as an aquifer, is infinite in extent primarily for mathematical tractability. This assumption simplifies the complex partial differential equation (PDE) that describes the transient, or time-dependent, flow of groundwater to a pumping well, allowing for an analytical solution. An analytical solution is a precise mathematical formula that provides an exact answer, rather than a numerical approximation.

By assuming an infinite aquifer, the model postulates that the cone of depression—the localized lowering of the water table in an unconfined aquifer, or the potentiometric surface in a confined aquifer, around a pumping well—will never encounter any physical boundaries within the duration of the analysis or pumping test. Physical boundaries include features like rivers, lakes, impermeable faults, or changes in aquifer material. If boundaries were present, they would affect the propagation and shape of the cone of depression, either by providing recharge (constant head boundary) or by preventing flow (no-flow boundary). These interactions would introduce additional complexities into the PDE, making it significantly harder, if not impossible, to solve analytically using the methods Theis employed.

This simplification allows the Theis equation to model purely radial flow toward the well, where water moves uniformly from all directions towards the pumping point. Coupled with other key assumptions like a homogeneous (uniform properties throughout) and isotropic (properties are the same in all directions) aquifer, the infinite extent ensures that the drawdown propagates outward predictably and symmetrically. In practical hydrogeology, an aquifer is considered effectively infinite if the pumping duration is short enough that the cone of depression has not yet reached any physical boundaries, meaning the aquifer behaves as if it were infinite for the purpose of the analysis, enabling the estimation of important aquifer properties like transmissivity and storativity.