Amplified stress concentration in nonlinear elastic formations: Implications for quantitative stress constraint

Abstract:

Accurate knowledge of the state of stress is key to geomechanical applications, such as development of hydrocarbon, geothermal resources and the disposal of wastewater and greenhouse gases. When in the area lacking seismicity, stress information may be inferred from observations of drilling induced damage in boreholes, the interpretation of which relies largely on Kirsch’s equations that presume the rock is linearly elastic. However, as indicated by experiment studies, the stress-strain curve of rocks is mostly not linear due to the existence of microcracks. Solutions for the concentration of stress in the vicinity of cavities in such nonlinear elastic materials are severely constrained; and numerical approaches must be used. Here, we use finite element modeling to calculate the distribution of stresses near a borehole drilled through a rock mass characterized first by a previously developed simplified stress dependent elasticity and second by considering more properly third-order nonlinear hyperelastic theory. The stress-dependent elasticity solution assumes the Young’s modulus is an exponential function of the mean stress and the Poisson’s ratio remains constant. The hyperelastic model utilizes the third-order Murnaghan parameters (l, m, n). For a vertical borehole subject to an Andersonian stress state, both models indicate that the circumferential hoop stress compression is amplified in the direction of the least horizontal compressive stress. The difference of the circumferential hoop stress between the nonlinear elastic and elastic formations diminishes with increasing mud pressure. For example, in a test case with l=-1850GPa, m=-4200GPa, and n=-5010GPa obtained from experimental measurements, the hoop-stress compression is amplified by 10% relative to a comparable linearly isotropic elasticity. The amplified compressions lead to larger stress deviations with the expectation that borehole breakouts may occur at lower values of in situ stress. The results suggest that nonlinear behavior may need to be included to assist in understanding wellbore stability and to aid in the semi-quantitative constraint of stress magnitudes from borehole breakouts and drilling induced tensile fractures.