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Cross-sectional plot of transient Theis solution for radial distance vs drawdown over time. The Theis equation was created by Charles Vernon Theis (working for the US Geological Survey) in 1935, [1] from heat transfer literature (with the mathematical help of C.I. Lubin), for two-dimensional radial flow to a point sink in an infinite ...
where s is drawdown (units of length e.g., m), is the pumping rate (units of volume flowrate e.g., m³/day), is the aquifer loss coefficient (which increases with time — as predicted by the Theis solution) and is the well loss coefficient (which is constant for a given flow rate).
In hydrology, there are two similar but distinct definitions in use for the word drawdown: In subsurface hydrogeology , drawdown is the reduction in hydraulic head observed at a well in an aquifer , typically due to pumping a well as part of an aquifer test or well test .
The Theis equation is one of the most commonly used and fundamental solutions to the groundwater flow equation; it can be used to predict the transient evolution of head due to the effects of pumping one or a number of pumping wells. The Thiem equation is a solution to the steady state groundwater flow equation (Laplace's Equation) for flow to ...
The above groundwater flow equations are valid for three dimensional flow. In unconfined aquifers, the solution to the 3D form of the equation is complicated by the presence of a free surface water table boundary condition: in addition to solving for the spatial distribution of heads, the location of this surface is also an unknown. This is a ...
These equations relate a change in total or water volume (or ) per change in applied stress (effective stress — or pore pressure — ) per unit volume. The compressibilities (and therefore also S s ) can be estimated from laboratory consolidation tests (in an apparatus called a consolidometer), using the consolidation theory of soil mechanics ...
Because the flow rate into or out of the well is not constant, as is the case in a typical aquifer test, the standard Theis solution does not work. Mathematically , the Theis equation is the solution of the groundwater flow equation for a step increase in discharge rate at the pumping well; a slug test is instead an instantaneous pulse at the ...
It was formulated by Jules Dupuit and Philipp Forchheimer in the late 1800s to simplify groundwater flow equations for analytical solutions. The Dupuit–Forchheimer assumption requires that the water table be relatively flat and that the groundwater be hydrostatic (that is, that the equipotential lines are vertical):