Stability of Sand Arches: A Key to Sand Control
Authors: Hall C.D. , Harrisberger W.H. 
Published: December 2007

Sand production, from a well completed in an incompetent formation without a metal screen, can be attributed to failure of the sand to form a stable arch around the wellbore or over a perforation. This study shows the usefulness of having a sand of high grain strength outside the perforations, and indicates that even a low-strength plastic can provide the restraint necessary to stabilize an arch.

Introduction
The petroleum industry has used both mechanical and chemical methods for controlling the production of sand from wells completed in unconsolidated formations. In developing sand control methods, mechanical studies have dealt mostly with the design of screens and slotted liners and the placement of gravel packs; chemical studies have dealt with the composition and performance of sand consolidation plastic systems, and techniques of applying them.
Little attention has been paid in the literature to the mechanical process of failure of the sand structure around a wellbore and the factors that affect the stability of the formation.
Our laboratory has conducted, in the past several years, both theoretical and experimental studies on the mechanics of sand failure. W.M. Ayers,1 in 1965, presented results of his theoretical studies combined with field experience. He discussed the stress field around a wellbore and its relation to the formation stability in terms of the shear strength properties of the sand. The work being reported here was a laboratory extension of Ayers' studies. It was conducted as a basic study of sand control and was carried out. in two phases:elucidation of the failure mechanisms of unconsolidated sands and of the mechanism of stabilization of sands by consolidating plastics, using triaxial strength tests; anda direct study of the arching behavior of sand, or the manner in which sand can form a stable structure spanning an opening.

Background

Shear Strength of Sand
The study of the strength of bodies of granular materials generally falls within the realm of soil mechanics. A widely used criterion for shear failure of soils is the Mohr-Coulomb theory.2 This states that failure will occur when the major and minor principal stresses s1 and s3 combine to produce a critical and characteristic value of the obliquity, which is the ratio of shear stress t to normal stress s in the plane of shearing. The validity of this criterion, which ignores the intermediate principal stress s2, is supported by experimental evidence cited by Bishop.3 The shear strength of a sand may therefore be described in terms of a Mohr envelope and its slope a, the angle of shearing resistance.

Shear Strength of Sand
The study of the strength of bodies of granular materials generally falls within the realm of soil mechanics. A widely used criterion for shear failure of soils is the Mohr-Coulomb theory.2 This states that failure will occur when the major and minor principal stresses s1 and s3 combine to produce a critical and characteristic value of the obliquity, which is the ratio of shear stress t to normal stress s in the plane of shearing. The validity of this criterion, which ignores the intermediate principal stress s2, is supported by experimental evidence cited by Bishop.3 The shear strength of a sand may therefore be described in terms of a Mohr envelope and its slope a, the angle of shearing resistance.