Wellbore Stability
Authors: Cheatham J.B. 
Published: December 2007

Distinguished Author Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized as experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: to informthe general readership of recent advances in various areas of petroleum engineering.

Introduction
Maintaining a stable wellbore is of primary importance during drilling and production of oil and gas wells. The shape and direction of the hole must becontrolled during drilling, and hole collapse and solid particle influx must be prevented during production. Wellbore stability requires a proper balance between production. Wellbore stability requires a proper balance between the uncontrollable factors of earth stresses, rock strength, and pore pressure, andthe controllable factors of wellbore fluid pore pressure, and the controllable factors of wellbore fluid pressure and mud chemical composition. pressure andmud chemical composition. Wellbore instabilities can take several forms (Fig.1). Hole size reduction can occur when plastic rock is squeezed into the hole, and hole enlargement can be caused by caving shales or hard rock spalling. If the wellbore fluid pressure is too high, lost circulation can occur as a resultof unintentional hydraulic fracturing of the formation; if it is too low, the hole may collapse. Excessive production rates can lead to solid particlein flux. Hole instabilities can cause stuck drill pipe as well as casing or liner collapse. These problems can result in side tracked holes and abandoned wells. Since 1940 considerable effort has been directed toward solving rock mechanics problems associated with wellbore instabilities, and much progress has beenmade during the past 10 years toward providing predictive analytical methods. Some of the literature representative of this work is discussed in thisarticle. Emphasis here is on understanding factors that influence wellbore stability in open holes, prediction of wellbore failures, and applications of rock mechanics concepts to control wellbore stability, A brief historical overview is followed by discussion of various types of wellbore instabilities and descriptions of studies of field wellbore stability problems.

Stresses Around Wellbores
H.M. Westergaard published a paper entitled "Plastic State of Stress Arounda Deep Well" in 1940. This now-classic paper defined the wellbore stability problem as follows.
The analysis that follows is a result of conversations with Dr. KarlTerzaghi who raised this question: What distributions of stress are possible inthe soil around an unlined drill hole for a deep well? What distributions of stress make it possible for the hole not to collapse but remain stable for sometime, either with no lining or with a thin "stove pipe" lining of small structural strength?
Westergaard uses stress functions in cylindrical coordinates to solve the elastic-plastic wellbore problem for zero pressure in the hole and all normal stress components equal to the overburden far from the hole. Hooke's law was applied for the elastic region and a Coulomb yield condition* where "the limiting curve for Mohr's circle is a straight line" was assumed for the plastic region. His conclusions were:
The plastic action makes it possible for the great circumferential pressures that are necessary for stability to occur not at the cylindrical surface of the hole but at some distance behind the surface, where they may be combined with sufficiently great radial pressures. The formulas that have been derived serveto explain the circumstances under which the drill hole for a deep well may remain stable.
Westergaard's elasticity solution agrees with the Lame solution for a thick-walled cylinder subjected to the same boundary conditions. Hubbert and Willis (1957) demonstrated how earth stresses can vary from regions of normal faulting to those with thrust faulting. On the basis of a Coulomb failure model, they suggest that the maximum value of the ratio of the maximum to the minimum principal stress in the earth's crust should be about 3:1.
JPT
P. 889