Estimation of Formation Stresses Using Radial Variation of Three Shear Moduli— A Case Study From a High-Pressure and High-Temperature Reservoir in a Norwegian Continental Shelf

摘要

Formation stresses and rock strength together with wellbore and pore pressures are important inputs to failure models whose predictions help in well planning, wellbore stability and production. A complete characterization of formation stresses requires estimation of the overburden, maximum and minimum horizontal stresses together with pore pressure as a function of depth. The overburden stress is reliably estimated by integrating with depth the formation bulk density, and pore pressure is directly measured in a permeable reservoir interval. The maximum and minimum horizontal stresses can be estimated from borehole sonic data in the presence of crossing dipole dispersions. A new stress magnitude estimation algorithm inverts radial variation of the three shear moduli together with the overburden stress and pore pressure at a given depth for the maximum and minimum horizontal stress magnitudes and formation nonlinear constants referred to a local reference state. The algorithm uses equations relating differences in the dipole shear moduli at two radial positions and corresponding differences in the principal stresses obtained from near-wellbore stress concentrations using the Kirsch’s equations. Radial positions in the plastically yielded region close to the borehole surface are excluded from the inversion algorithm. Processing of sonic data yields crossing dipole dispersions in three sand intervals in a development well drilled in a high pressure (770 bars) gas condensate field operated by Statoil in the Norwegian continental shelf. Results for both the maximum and minimum horizontal stress magnitudes are consistent in the three sand intervals in the Bent reservoir of the Kvitebjorn field. Estimated minimum horizontal stress magnitude is in good agreement with the mini-frac test conducted at a nearby depth. The maximum horizontal stress direction coincides with the fast-shear azimuth obtained from the Alford rotation of cross-dipole waveforms. Horizontal stress magnitude results have helped in refining the mechanical earth model and in subsequent drilling of development wells in this field.