Pumping Well Drawdown Thiem Theis Calculator

The Theis solution describes transient radial flow toward a fully penetrating well in a confined aquifer. Drawdown scales with Q divided by 4 pi T, and the dimensionless group u = r squared times S divided by 4 T t compresses distance, time, and aquifer properties into one argument of the well function W(u), which is the exponential integral. Transmissivity T equals hydraulic conductivity K times saturated thickness b and measures how much water the full thickness can transmit; storativity S is the volume released per unit plan area per unit head decline. When u falls below about 0.01, at large times or short distances, the series truncates to the Cooper-Jacob form in which drawdown plots as a straight line against the logarithm of time, so T comes from the slope and S from the intercept. The Thiem equation is the steady-state limit, s1 - s2 = Q/(2 pi T) x ln(r2/r1), requiring neither S nor time. Transmissivity spans roughly 10^-5 m2/s in silty aquitards to 10^-1 m2/s in productive karst, with sand and gravel aquifers commonly between 10^-4 and 10^-2 m2/s. Storativity runs about 5 x 10^-5 to 5 x 10^-3 for confined systems, while unconfined specific yield is 0.01 to 0.30. The assumptions are demanding: an infinite, homogeneous, isotropic aquifer, constant pumping rate, negligible wellbore storage, and no leakage or boundaries. Real drawdown records deviate at early time from wellbore storage and at late time from leakage, recharge boundaries, or delayed yield. Applied to an unconfined aquifer, drawdown must be corrected using Jacob's expression s' = s - s squared divided by 2b, because pumping itself thins the saturated section.

The steady-state case came first. The German engineer G. Thiem published in 1906 the equilibrium method for deriving hydraulic conductivity from drawdown measured at two observation wells around a pumped well, building on well tests his father Adolph Thiem had conducted for municipal water supplies. Its weakness is that it requires the cone of depression to stop expanding, a condition many aquifers never truly reach. The transient problem was solved by Charles Vernon Theis (1900-1987), a US Geological Survey hydrologist based in Albuquerque, New Mexico. Theis recognised that drawdown spreading around a well is mathematically the same problem as temperature spreading around a line heat sink in a solid, and asked the mathematician Clarence Lubin of the University of Cincinnati for the corresponding solution; Lubin supplied it but declined to be listed as an author. The result was published in 1935 in the Transactions of the American Geophysical Union and for the first time allowed both transmissivity and storativity to be estimated from a single pumping test and future drawdown to be predicted. Extensions followed steadily: Cooper and Jacob's logarithmic approximation in 1946 made graphical hand analysis routine and is still what students learn first; Hantush and Jacob published a leaky-aquifer solution in 1955; Papadopulos and Cooper added a wellbore-storage correction in 1967; and Neuman produced the delayed-yield solution for unconfined aquifers in 1972.