An Advanced Elasto-plastic Model For Borehole Stability Analysis of Horizontal Wells In Unconsolidated Formation
Authors: Fung L.S.K. , Wan R.G. , Rodriguez H. , Silva Bellorin R. , Zerpa L. 
Published: March 2010

Abstract
Borehole stability problems can dramatically increase the cost of drilling and completing wells. For example, sand failure and production may lead to costly well shut-in and workover, as well as equipment failure. Wellbore instability is particularly important when operating in deep unconsolidated formations or when horizontal wells are planned. Also, stability requirements increase when drilling into producing formations. Drilling problems such as stuck drillstring, caving, logging difficulties, well enlargement, inadvertent side tracking, and stuck casing can be costly to remediate. Traditionally, analytical methods are used to predict required mud weights. However, they are typically too conservative and are unsuitable for applications to horizontal wells in unconsolidated formations.
In order to analyse horizontal drilling in an unconsolidated formation, a wellbore stability model has been developed. The model uses a robust finite element elasto-plastic code as a tool to perform effective stress analysis of the near-wellbore tensile and shear failure. The code is capable of handling extremely low confining stresses (near tensile regime) in unconsolidated formations. It is considered that plastic yielding, occurring at relatively low deviatoric stresses under low confining stress conditions, is not a good indicator of wellbore failure in terms of loss of service. Therefore, a more realistic criterion based on the accumulated plastic strain is applied. The model has been used successfully to analyse the stability of a horizontal well with open-hole completion in unconsolidated oil sand. The results show reasonable agreement with field observations.

Introduction
Formations at depth exist under a state of compressive in situ stress. When a well is drilled, the rock adjacent to the wellbore must now carry the load that was once supported by the removed material. This alteration in stress state adjacent to the wellbore wall can exceed the strength of the material leading to some form of failure. As drilling costs are expensive, particularly with horizontal wells, it is imperative that the possibility of well failure be minimized.
Borehole failure can be broadly classified as being either tensile or compressive. Tensile failure occurs when the wellbore pressure increases so as to exceed the tensile strength of the rock. On the other hand, compressive failure occurs when there is insufficient wellbore pressure support. This can lead to rubbling (sloughing) in brittle formation, resulting in wellbore enlargement. On the other hand, if the formation behaves plastically, it will flow in the hole resulting into hole tightening. Since rock behaves differently in tension than in compression, a separate failure criterion is required to describe each type of failure mechanism.

Tensile Failure
Rocks generally have low tensile strength. Bradley(l) suggested that rock strength usually is less than 1,000 psi and seldom more than 3,000 psi. For unconsolidated sands, the tensile strength is zero. Using continuum mechanics sign convention in the sense that tensile stresses are positive and compressive stresses are negative, the tensile strength criterion is generally given as Equation 1 (available in full paper)