Nonsteady flow to a well of constant drawdown in an extensive aquifer

Abstract

A mathematical theory is given for the discharge of a well of constant drawdown, discharging as by natural flow from an effectively infinite aquifer of uniform transmissibility and uniform compressibility. This theory is based on the solution by L. P. Smith of the analogous problem in heat conduction. The mathematical function involved in the solution, which cannot be integrated directly, is evaluated by numerical integration. A table of its values is given for a wide range of its argument. This function is compared with other,asymptotic solutions, and simple, useful approximations are given. Two graphical methods are outlined for determining the coefficients of storage and transmissibility from variations in the rate of discharge of wells flowing at constant drawdown. Data from the Grand Junction, Colo., artesian basin are treated by these methods. In the Grand Junction artesian basin there are about 25 flowing wells ranging in depth from 600 to 1600 ft, most of which obtain water from the Entrada sandstone. A few of the wells obtain water from a sandstone in the overlying Morrison formation and a few tap the underlying Wingate sandstone. The procedure of the tests is outlined, and the “ink‐well” mercury gage used to measure the artesian pressures is described. Recovery tests were run on the same wells after the discharge tests. Values of transmissibility obtained from the recovery tests check those obtained by means of the discharge tests.

Borehole geophysical methods for analyzing specific capacity of multiaquifer wells : ground-water hydraulics

“…After a sufficient time has passed, however, the changes in specific capacity per unit change in time become quite small, so that considerable differences in the time of pumping at the various discharge rates can often be tolerated. Jacob and Lohman (1952) have demonstrated that, after a reasonable time of pumping, discharge-drawdown points determined by pumping a well at a variable rate so as to maintain a constant drawdown value approach very closely those determined by discharging the well at a constant rate. and that the specific-capacity ratio calculated from equation 8 will therefore approach the specific capacity calculated from equation 5.…”

Potential effects of surface coal mining on the hydrology of the West Otter area, Ashland and Birney-Broadus coal fields, southeastern Montana

“…The flow from the fully saturated Knobloch coal bed would be about 14,000 ft^/d along a 1,000-foot-wide mine face, as determined by calculations using the constant drawdown formula of Jacob and Lohman (1952). In solving the formula, the values used were: an average transmissivity of 60 ft^/d, a time of 100 days, an area of 250,000 ft^, an assumed coefficient of storage of 0.01, and a drawdown of 60 feet.…”

“…Based on information from nearby areas, the hydraulic conductivity of the sandstone aquifer in the potential north mine area may be about 10 ft/d. The flow of water from a 10-foot-thick saturated sandstone bed along a 1,000-foot-wide face would be about 15,000 ft-Vd, as determined from the constant drawdown formula of Jacob and Lohman (1952). The values used to solve the formula were: an average transmissivity of 100 ft^/d, a time of 100 days, an area of 100,000 ft2, an assumed storage coefficient of 0.01, and a drawdown of 40 feet.…”

“…10). The volume of water flowing downvalley through alluvium can be calculated using Darcy's law, Q = KIA (as explained in Jacob and Lohman, 1952). The volume entering the study area near wells 0-26 and 0-30 through 0-33 is about 16,000 ft"Vd, as determined using the values of 100 ft/d for an average hydraulic conductivity (K), 0.004 for the gradient (I), and 40,000 ft2 for an approximate area (A).…”

Preliminary report of the geohydrology near Cypress Creek and Richton salt domes, Perry County, Mississippi

“…Flowing wells were tested by holding drawdown constant and decreasing the discharge during the testing period. Equations by Jacob and Lohman (1952) were used to analyze the data from tests of flowing wells.…”