Uncertainties in the estimation of in situ stresses: effects of heterogeneity and thermal perturbation

In situ stress directions and magnitudes in subsurface are commonly estimated using two different methods: (1) borehole break-out—drilling-induced fracture interpretation complemented by extended leak-off tests; (2) stress estimation from acoustic measurements using advanced wireline tools. Both methods use stress perturbations around boreholes to estimate far field stresses employing Kirsch’s equations, which are only valid for boreholes aligned with one of the principal stresses, linear elastic deformation and homogeneous isotropic materials. Furthermore, the original stress state may have been altered by drilling-mud-circulation induced temperature changes. Using heuristic models including heterogeneity, this study investigates potential errors in the estimation of far-field stress due to (a) the generalisation of Kirsch’s equations to heterogeneous media and (b) plausible temperature perturbations. First, errors due to uncertainties in measuring wave slowness are analysed for an idealised homogeneous material. Second, errors due to application of Kirsch’s equations are investigated considering potential effects of frictional interfaces between layers, pore pressure in the rock matrix and thermal perturbations induced by drilling for example cases. To analyse stress in these complex scenarios finite element analysis was used, revealing strong effects of lithological and thermal variations. Stress magnitude was amplified by stiff layers and was attenuated by soft ones. At layer interfaces, substantial changes in stress orientation occurred. Kirsch’s equations for the considered cases resulted in errors in far field stresses as large as 44% in the magnitude and 90° in orientations. An uncertainty propagation analysis indicated a high accuracy of acoustic estimates for homogenous materials. However, a dramatic impact of small-scale heterogeneity may not be resolved by the logging process.