Stress and strain fields for overdamped slug tests in aquifer materials, and resulting conservation equation

Abstract

Summary Two theories may be used to analyze overdamped variable‐head (slug) tests in aquifer materials. The first theory assumes that the solid matrix strain has a negligible influence. The second theory takes into account some elastic and immediate strain. Something is wrong with these theories because they yield different hydraulic conductivity values. This paper explains what is wrong after establishing the strain‐stress elastic equations for a slug test in 2 ideal conditions: plane strain and spherical symmetry. The equations show that the radial contraction (or elongation) and tangential elongation (or contraction) yield a null volumetric strain. As a result, the conservation is described by the Laplace equation, which is used by the first theory. This first theory is the only one to yield correct solutions. The diffusion equation, with storativity, which is used by the second theory, is physically ill founded for slug tests in aquifers. This new proof scientifically confirms previously raised doubts and experimental proofs that the second theory is ill founded.