Stability and Failure of Spherical Cavities in Unconsolidated Sand and Weakly Consolidated Rock

Abstract

ABSTRACT The conditions necessary for stability or failure of a spherical cavity in unconsolidated sand or weakly-cemented rocks have been studied. Experiments using physical models have utilized weakly-cemented synthetic, porous rocks. As external confining pressure was applied to the rock, a shear failure region was induced around the cavity. When fluid flowed through this system at increasing rates, the outer boundary of the shear failure zone was calculated to have increased, and a region of disaggregated solids was created adjacent to the cavity. Equations for convergent flow of a fluid towards a cavity predict that tensile stresses tend to be induced near the cavity face. These tensile stresses pull the pack of disaggregated solids apart, causing it to dilate. A region of material at the limit of tensile stability will be formed. The radius of this zone will expand until the system becomes stable with no induced tensile stress being greater than the slight adhesion provided by an immobile phase, if present. As the flow rate is increased, the shear failure zone and the zone of material at the limit of tensile stability propagate farther away from the cavity. To preserve stability, the permeability of the sand at the cavity face must progressively increase by further dilation. When the cavity face porosity has increased to some critical porosity, mechanical interaction of the particles is insufficient to keep the pack from becoming fluid-like and being produced into the cavity. For low permeability models, pressure drop data indicated that average permeabilities in the shear failure zones were greater than the permeabilities of the cemented rock in the surrounding elastic regions. When flow rates increased sufficiently, the shear failure zones expanded to the outer boundary of the models; total collapse of the models ensued and large quantities of sand were produced. Some data for cavity failure in unconsolidated sands, which are available in the literature, as well as the experimental data for weakly-cemented synthetic rocks, have been analyzed using the equations and concepts developed in this paper. For mixtures of fracture proppant sand, for some coarse natural sands, and for disaggregated solids created around a cavity in the weakly-cemented rocks, the critical porosities at the cavity face (when the cavities were barely stable) were estimated to be in the range of 40% to 53%. An apparent unit cohesive strength of a few tenths of a psi was manifested, perhaps due to mechanical interlocking of the individual grains.