Sand Stresses Around a Wellbore

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Abstract
We have studied theoretically the stresses in a poorly consolidated sand around a cylindrical well, assuming axial symmetry. Applying theories of elasticity and plasticity on this three-dimensional (3D) model, analytical solutions for all three stress components have been worked out. The existence of a plastic zone around an uncased wellbore is confirmed, and the size of the zone is determined. When allowing an incompressible fluid to flow radially into the wellbore, a stability criterion describing the failure of the sand is found to exist. This criterion relates fluid flow forces to rock strength properties. Consideration also has been given to the stress distribution around a cased hole. It is shown that a decrease in the size of the plastic zone relative to an uncased hole occurs.

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