Dilatational and Compacting Behavior around a Cylindrical Cavern Leached Out in a Solid–Fluid Elastic Rock Salt

Abstract

A fluid-filled cylindrical cavern of circular cross section in a homogeneous infinite fluid-saturated polycristalline (salt) formation subjected to isotropic stress is set under internal pressure that differs from the confining pressure. The fluid in the cavern and in the mixture is treated as ideal and the solid as elastic. The state of stress that is established as a consequence of an outside pressure and a cavern pressure serves as the reference state. Perturbing the cavern pressure induces small changes in the solid and fluid densities and in the solid displacements. We compute these and other fields as functions of the radial distance from the cavern center and show that, depending on the relative stress levels, the (salt) formation experiences either a dilatation or a compaction that is highly concentrated in a thin boundary layer near the cavern wall and tapers off as one moves away from it. The amount of dilatation/compaction of the cylindrical wall and the thickness of the boundary layer grow with an increase in the difference between the referential confining pressure and the pressure in the cavern.