Horizontal Stress Magnitude Estimation Using the Three Shear Moduli—A Norwegian Sea Case Study

Abstract

Abstract Formation stresses play an important role in geophysical prospecting and development of oil and gas reservoirs. A reliable in-situ stress determination is a premise for all geomechanical evaluations of a reservoir including initial drilling, infill drilling, sand prediction, stimulation and fracturing, well integrity evaluation, coupling with reservoir flow analyses, fault reactivation and environmental aspects particularly related to injection. The underlying theory behind the estimation of formation stresses using borehole sonic data is based on acoustoelastic effects in rocks. Acoustoelasticity in rocks refers to changes in elastic wave velocities caused by changes in pre-stress in the propagating medium. Elastic wave propagation in a pre-stressed material is described by equations of motion for small dynamic fields superposed on a statically deformed state of the material. These equations are derived from the rotationally invariant equations of nonlinear elasticity. However, shear wave propagation in a triaxially stressed rock can also be expressed in terms of the stress-dependent shear moduli. A new Stress Magnitude Estimation (SME) algorithm yields the maximum horizontal stress magnitude using the three shear moduli outside the near-wellbore altered annulus together with the Mechanical Earth Model that provides the overburden stress, pore pressure, and minimum horizontal stress as a function of depth. The maximum and minimum horizontal stresses can also be obtained from a multi-frequency inversion of cross-dipole dispersions in the presence of stress-induced crossovers. Inversion results for the stress magnitudes are obtained together with the stress coefficients of velocities in terms of the formation nonlinear constants referred to a local reference state. Formation stress magnitudes together with stress coefficients of velocities help in distinguishing radial alteration of shear slownesses caused by near-wellbore stress concentrations from those resulting from plastic yielding of rock. The methodology used in the two Norwegian Sea wells, operated by Statoil, successfully estimated the horizontal stress magnitudes. Results for the minimum horizontal stress corroborate well with the stress magnitude estimated from extended leak-off test in one of the wells.