Kicking Off in Large-Diameter Holes
Authors: Durand L.J. , Samhouri F.A. , Barthe D.L. 
Published: December 2007

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.

Introduction

Previous Work
Knowledge of the stress distribution around a drilled hole is of great importance in several situations, such as while drilling, during production or injection, and when calculating, fracturing pressures. One of the early works contributing to this problem is the study by Westergaard. This study was initiated by Karl Terzaghi, who raised the question: What distributions of stress are possible in the soil around an unlined drill hole for a deep well" Westergaard concluded that at great depths a plastic state exists around the hole, which relieves the stresses.
In his work, Westergaard uses the concept of effective stresses. A more detailed discussion of the influence of the pore pressure resulting, from a fluid contained in a porous rock was given by Blot. Blot gave a general theory of 3D consolidation, taking into account also the possibility of a flowing pore fluid. Many of the later works are based on this study.
One of these is the work done by Paslay and Cheatham. They studied rock stresses caused by a fluid flowing into the borehole. In their study, they also considered the case where permeability is reduced in a region adjacent to the wellbore. Paslay and Cheatham assumed that the rock behaved elastically all the way up to the wellbore and thus ignored the effect of a plastic zone around the hole.
Gnirk realized the existence of a plastic zone around the well. He assumed that the rock was situated in a hydrostatic stress field and that it obeyed the Coulomb criterion of plastic yield. Gnirk calculated the wellbore pressures required to prevent plastic yielding of an uncased wellbore, assuming that no fluid flow would be involved.
The same problem was treated later by Geertsma. He studied two specific problems: particle influx in production wells and formation fracturing around injection wells. Geertsma discussed stress and strain solutions and stated that elastic theory is applicable to borehole fracturing, but that sand influx requires accounting for plasticity effects. This study was basically two-dimensional, not taking into consideration the vertical stress. Geertsma discussed the problems in a general way and did not give detailed stress and strain solutions.
In another recent paper, Bradley worked out a semiempirical approach to the wellbore stability problem, discussing, especially inclined boreholes. This approach is useful for predicting the limit of elastic behavior: however, it gives no information on the behavior in the plastic state.
SPEJ
P. 883^