In situ calibrated velocity-to-stress transforms using shear sonic radial profiles for time-lapse production analysis

Abstract

Borehole acoustic waves are affected by near- and far-field stresses within rocks that exhibit stress sensitivity, typically in medium- to high-porosity formations. Nonlinear, or third-order, elastic constants are obtained from the inversion of borehole sonic shear radial profiles with an elastic wellbore stress model. The stress-to-velocity relationship determined from these profiles in the elastic region surrounding the wellbore is used for calibration to compare with empirical laboratory data traditionally used in time-lapse seismic-feasibility studies to assess simulated production. This analysis enables rock physicists to use the wellbore as a laboratory and to examine the stress dependence of the acoustic velocities from in situ field data in their zone of interest. Laboratory experiments on core samples can yield both empirical and mathematical rock-physics models to describe the relationship between stress and velocity to link rock properties to in situ measurements of acoustic data (seismic and sonic). In an example from offshore Malaysia, full-waveform borehole sonic data are processed to produce shear radial profiles in a deepwater environment. The compressional velocities are mainly sensitive to stress in the polarization-propagation direction, and shear velocities are mainly sensitive to stresses in propagation and polarization directions, as expected from nonlinear elasticity. The three compressional and shear velocities vary greatly with vertical stress depending on the stress path because they depend on the three principal stress magnitudes. In contrast, a classical empirical model that depends on porosity, clay content, and effective stress cannot capture differences caused by stress path because it relies on only one stress. Results show that stress sensitivities are significantly stronger with borehole radial profiles than the empirical model for all considered stress paths (K = −0.5, 0, 0.5, and 1).

Stress impact on elastic anisotropy of triclinic porous and fractured rocks

“…Many experimental works implementing this theory into geophysical measurements have been directly or implicitly based on this assumption. For example, works on estimating third‐order elastic constants and using the nonlinear elasticity theory by accounting for stress‐dependencies of seismic velocities imply isotropy of this tensor [ Winkler and Liu , ; Johnson and Rasolofosaon , ; Rasolofosaon , ; Sarkar et al , ; Prioul et al , ; Donald and Prioul , ]. These works demonstrate indirectly that the isotropic approximation of the third‐order elasticity tensors is sufficient for explaining corresponding observations.…”

“…Both compliance tensors possess the same permutation symmetries with respect to their index pairs and inside the index pairs as the corresponding stiffness tensors. From , two mutual relationships follow: The formalism of nonlinear elasticity theory as briefly summarized above, is frequently applied in order to explain the stress dependencies of rock elasticity, e.g., [ Mavko et al , ; Prioul et al , ; Donald and Prioul , ; Sarkar et al , ; Johnson and Rasolofosaon , ; Winkler and Liu , ; Rasolofosaon , ]. However, because it is based on the linear expansion of the strain energy as a function of strain and linear relations and , these models are restricted to quite limited ranges of load variations.…”

Probabilistic analysis and comparison of stress-dependent rock physics models

“…This is further compounded since the definitive segment divisions may not be appropriate for all samples given different shape/curvature of the stress-velocity relationship. Furthermore, by subdividing the data into m regimes, the number of model coefficients is increased to n × m. Regardless, the TOE model is still widely used due to its flexibility of allowing general anisotropy (e.g., Herwanger and Koutsabeloulis, 2011 ) and has been adapted to in situ well log measurements (e.g., Donald and Prioul, 2015 ). The TOE-2 model on the other hand, shows a relatively good fit to velocity depth trends and stacking velocities (e.g., Korneev & Glubokovskikh, 2013 ).…”

“…A similar limitation is seen in the TOE-2 equations where, a lack of multi-directional data, causes an ill-posed inversion for the individual third order coefficients A, B and C (e.g., Figure 6). Therefore it appears for TOE models to be better constrained multi-directional data is required (e.g., Donald and Prioul, 2015 ).…”

Third‐order elasticity of transversely isotropic field shales

“…This model has been cali-brated to ultrasonic data obtained from different lithologies (Prioul & Lebrat, 2004; and has been utilized to predict the seismic response (Asaka, 2023;Herwanger & Koutsabeloulis, 2011;MacBeth et al, 2018). Apart from Duda et al (2020) and Bakk, Holt, Duda et al (2020), who studied a model with hexagonal symmetry of the TOE tensor, restricted to isotropic horizontal strains, only isotropic TOE tensors have been employed in the modelling of sedimentary rocks (Asaka, 2023;Donald & Prioul, 2015;Prioul & Lebrat, 2004;Rasolofosaon, 1998;Sarkar et al, 2003;Sinha & Kostek, 1996;Winkler & Liu, 1996). To our knowledge, a transversely isotropic (TI) symmetric TOE tensor has not been previously proposed for any application.…”