Stress-induced anisotropy in Gulf of Mexico sandstones and the prediction of in situ stress

The strong sensitivity of velocity to stress observed in many sandstones originates from the response of stress-sensitive discontinuities such as grain contacts and microcracks to a change in effective stress. If the change in stress is anisotropic, then the change in elastic wave velocities will also be anisotropic. Characterization of stress-induced elastic anisotropy in sandstones may enable estimation of the in situ three dimensional stress tensor with important application in solving problems occurring during drilling, such as borehole instability, and during production, such as sanding and reservoir compaction. Other applications include designing hydraulic fracture stimulations and quantifying production-induced stresses which may lead to rock failure. Current methods for estimating stress anisotropy from acoustic anisotropy rely on third-order elasticity, which ignores rock microstructure and gives elastic moduli that vary linearly with strain. Elastic stiffnesses in sandstones vary non-linearly with stress. Using P- and S-wave velocities measured on Gulf of Mexico sandstones, this non-linearity is found to be consistent with a micromechanical model in which the discontinuities are represented by stress-dependent normal and shear compliances. Stress-induced anisotropy increases with increasing stress anisotropy at small stress but then decreases at larger stresses as the discontinuities close and their compliance decreases. When the ratio of normal-to-shear compliance of the discontinuities is unity, the stress-induced anisotropy is elliptical, but for values different from unity, the stress-induced anisotropy becomes anelliptic. Although vertical stress can be obtained by integrating the formation's bulk density from the surface to the depth of interest, and minimum horizontal stress can be estimated using leak-off tests or hydraulic fracture data, maximum horizontal stress is more difficult to estimate. Maximum horizontal stress is overpredicted based on third-order elasticity using measured shear moduli, with estimates of pore pressure, vertical stress and minimum horizontal stress as input. The non-linear response of grain contacts and microcracks to stress must be considered to improve such estimates.