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

Abstract

When determining the stress state of an elastic hollow ball during liquid filtration through its wall, it is necessary to solve the problem of stresses for the case of liquid filtration towards the center of the ball with a decrease in pressure in its cavity (χ = -1). A change in the sign of the filtration potential leads to a change in the tangential stresses on the borehole wall to a value equal to three times the reservoir pressure drawdown (in this case, the radial stresses are 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 near-wellbore part of the formation, on the stability of the walls of wells, the operation of which is complicated by formation sanding. Thus, the maximum difference in the main normal stresses is observed on the borehole wall, therefore, in order to prevent the destruction of the formation near the bottom, the necessary condition is that the strength properties of the rocks correspond to the stresses acting in this zone. When operating wells prone to plugging, it is necessary to limit the reservoir pressure drawdown to the maximum allowable value, when the material of the near-filter zone is in an elastic state throughout the volume. Keywords: stress; state; casing; string; well; integration; equations.