Analytical investigations of in situ stress inversion from borehole breakout geometries

Abstract

This study aims to investigate the feasibility of deriving in situ horizontal stresses from the breakout width and depth using the analytical method. Twenty-three breakout data with different borehole sizes were collected and three failure criteria were studied. Based on the Kirsch equations, relatively accurate major horizontal stress (σH) estimations from known minor horizontal stress (σh) were achieved with percentage errors ranging from 0.33% to 44.08% using the breakout width. The Mogi-Coulomb failure criterion (average error: 13.1%) outperformed modified Wiebols-Cook (average error: 19.09%) and modified Lade (average error: 18.09%) failure criteria. However, none of the tested constitutive models could yield reasonable σh predictions from known σH using the same approach due to the analytical expression of the redistributed stress and the nature of the constitutive models. In consideration of this issue, the horizontal stress ratio (σH/σh) is suggested as an alternative input, which could estimate both σH and σh with the same level of accuracy. Moreover, the estimation accuracies for both large-scale and laboratory-scale breakouts are comparable, suggesting the applicability of this approach across different breakout sizes. For breakout depth, conformal mapping and complex variable method were used to calculate the stress concentration around the breakout tip, allowing the expression of redistributed stresses using binomials composed of σH and σh. Nevertheless, analysis of the breakout depth stabilisation mechanism indicates that additional parameters are required to utilise normalised breakout depth for stress estimation compared to breakout width. These parameters are challenging to obtain, especially under field conditions, meaning utilising normalised breakout depth analytically in practical applications faces significant challenges and remains infeasible at this stage. Nonetheless, the normalised breakout depth should still be considered a critical input for any empirical and statistical stress estimation method given its significant correlation with horizontal stresses. The outcome of this paper is expected to contribute valuable insights into the breakout stabilisation mechanisms and estimation of in situ stress magnitudes based on borehole breakout geometries.