Comparative Analysis of Various Failure Theories for Borehole Breakout Predictions

Abstract

Abstract Numerous papers have been published for predicting the borehole breakout problems (McLean 1990; Zoback 2007; Ewy 1999). The original theory proposed by Zoback (Zoback 2007) used the Mohr-Coulomb failure theory with a linear elastic stress strain relation. Initially, it was applied to igneous rocks and large diameter boreholes. With these original applications, the linear Mohr-Coulomb theory predicted the breakout width within a reasonable accuracy. Recently, the applications have been expanded to breakout problems for shales, mudstones and sandstones. However, there are some drawbacks. For sedimentary rock applications, the Mohr-Coulomb failure theory significantly over-predicts the breakout width. In addition, strong rocks show significant non-linearity before failure, hence, we need to artificially increase unconfined rock strength (UCS) and friction angle. The theoretical breakout width cannot be matched with the breakout width observed from the image logs unless these adjustments are made. Using the image logs and the rock strength measurements obtained from several fields, comparative analyses were conducted for various failure theories with linear and non-linear stress strains. These failure theories include Mohr-Coulomb, Drucker-Prager, Lade, Modified-Lade, Mogi and critical plastic strain. The authors also compared linear and non-linear stress strain theories. The authors estimated the increase in UCS necessary to match the breakout widths observed from the image logs obtained from several fields. The authors utilized caliper logs to compare the breakout depths as well. The results show that if a linear stress strain relation is used, UCS must be increased artificially by 1.09-2.25 times. This increase is as much as 2.25 times for the Mohr-Coulomb failure theory. On the other hand, if a non-linear stress strain relation is used, no artificial increase is necessary except for the Mohr-Coulomb failure theory. In addition, the effects of temperature change and shale swelling are varied depending on the failure theories. These effects are supposed to de-stabilize the boreholes. Interestingly, the borehole stability differs depending on the failure theory used. Moreover, the actual breakout depths are always deeper than those predicted with a linear stress strain theory while they are shallower than those predicted by a slip line failure theory. This paper compares the merits and demerits of each failure theory when applied to borehole breakout problems. Many triaxial tests were conducted to determine the stress strain and failure envelopes. The predicted breakout widths were compared with the measured breakout widths from the image logs. This kind of comprehensive evaluation (theoretical, experimental and field analyses) has not been performed in previous studies.