Investigation of the stress state of an elastic hollow ball during filtration of liquid through its wall

Abstract

When determining the stress state of an elastic hollow ball when filtering liquid through its wall, it is necessary to solve the stress problem for the case of liquid filtration to the center of the ball with a decrease in pressure in its cavity. This case represents for us an element of the general problem of the stressed state of the annular filter behind the casing during well operation. First, the problem of liquid filtration is solved -pressure changes in the body under study are determined during liquid filtration. Then the equilibrium equation with respect to radial deformation is solved. A change in the sign of the filtration potential leads to a change in the tangential stresses on the well wall to a value equal to a tripled depression of reservoir pressure (with radial stresses equal to zero). This explains the negative effect of well shutdowns, and even more so the change in the direction of the filtration flow in the downhole part of the formation on the stability of the walls of wells, the operation of which is complicated by sand formation. The maximum difference of the main normal stresses is observed on the well wall, therefore, in order to prevent formation destruction near the bottom, a necessary condition is that the strength properties of rocks correspond to the stresses acting in this zone. When operating wells prone to plugging, it is necessary to limit the depression of reservoir pressure to the maximum permissible value when the material of the filter zone is in an elastic state throughout the volume.