On the flow of water in an elastic artesian aquifer

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 It was found that the amount of water withdrawn from storage could not be accounted for on the basis of the compressibility of water alone but that it might be accounted for on the basis of the probable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.”