The Theis equation gives drawdown at any distance and time around a well pumping a confined aquifer at a constant rate.
The Theis equation, published by Charles Vernon Theis in 1935, describes how drawdown changes with distance and time around a well pumping at a constant rate. It was the first solution to account for water being taken from storage, so it can describe the changing, unsteady conditions of real pumping. In the equation, s is drawdown, Q is the pumping rate, T is transmissivity and W(u) is the well function, an integral read from tables or computed. The term u equals r²S / (4Tt), where r is distance from the well, S is storativity and t is time since pumping began. It can be used two ways: to predict drawdown from known aquifer properties, or to estimate T and S by matching test data against a type curve. When u is small, the equation simplifies to the straight-line Cooper-Jacob method. Its assumptions are strict. The aquifer is confined, uniform and very wide, the well fully penetrates it and has negligible storage, the pumping rate is constant and water release is instant. Departures from the curve often reveal real conditions, such as leakage, a recharge boundary or a barrier.