The capacities of a water‐bearing formation to transmit water under a hydraulic gradient and to yield water from storage when the water table or artesian pressure declines, are generally expressed, respectively, in terms of a coefficient of transmissibility and a coefficient of storage. Determinations of these two constants are almost always involved in quantitative studies of ground‐water problems.
The non‐steady drawdown distribution near a well discharging from an infinite leaky aquifer is presented. Variation of drawdown with time and distance caused by a well of constant discharge in confined sand of uniform thickness and uniform permeability is obtained. The discharge is supplied by the reduction of storage through expansion of the water and the concomitant compression of the sand, and also by leakage through the confining bed. The leakage is assumed to be at a rate proportional to the drawdown at any point. Storage of water in the confining bed is neglected. Two forms of the solution are developed. One is suitable for computation for large values of time and the other suitable for small values of time. This solution is compared with earlier solutions for slightly different boundary conditions.
Slichter showed in 1898 that a solution may be obtained for a given problem in the steady motion of ground‐water by solving the familiar Laplace equation and that therefore in steady‐state conditions a problem in the motion of ground‐water is mathematically analogous to a problem in the steady flow of heat or electricity [see 1 of “References” at end of paper]. More recently it has been recognized that the analogy holds also for the non‐steady‐state flow of compressible liquids, in elastic systems as well as in rigid systems. In studying the effect of the discharge of flowing wells on the head in the Dakota sandstone, Meinzer [2, 3] concluded that the water discharged by the wells had largely been derived locally from storage. It was found that the amount of water withdrawn from storage could not be accounted for on the basis of the compressibility of water alone but that it might be accounted for on the basis of the probable compressibility of the sandstone itself. Prior to that time, estimates of water‐supplies from artesian aquifers had been based upon the assumption that artesian aquifers are perfectly incompressible and inelastic However, as Meinzer states [2, p. 289], “artesian aquifers are apparently all more or less compressible and elastic though they differ widely in the degree and relative importance of these properties. In general, the properties of compressibility and elasticity are of the most consequence in aquifers that have low permeability, slow recharge, and high head.”
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.
A partial differential equation is set up for radial flow in an elastic artesian aquifer into which there is vertical leakage in proportion to the drawdown. This differential equation is integrated to obtain two steady state solutions, one for the case of a well in an infinite aquifer, and the other for the case where the head is maintained constant along an outer boundary concentric with the well. In the second case, the solution of the non‐steady state is also obtained for flow towards a well discharging at a steady rate, the initial state being one of uniform head distribution. A table and some curves are given for one set of assumed values of three of the parameters of the system.
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