Abstract:
The problem of numerical modeling of wave reflections that occur during localization of
natural and hydraulic fractures using acoustic logging methods is considered. For numerical calculations, we use the spectral element method implemented in the SPECFEM3D
software library. An analysis of the accuracy of numerical solutions for problems of wave
propagation from a point source in inhomogeneous anisotropic media is carried out. An
implementation of the Schoenberg fracture linear slip model was added to SPECFEM3D.
In calculations for the model scenario of hydraulic fracture identification problem, practically identical responses in the borehole for reflected waves from fractures are obtained
with the Schoenberg model and with an explicit internal structure specification by a fine
grid. A significant reduction in the required computational resources is achieved, since explicit fracture calculations require several times the number of time steps and a larger number of grid points due to the very small transverse cells sizes near and inside the fracture. It
can be stated that the use of the spectral element method in combination with the Schoenberg fracture model is one of the promising approaches for modeling the process of borehole studies of acoustic reflections from hydraulic fractures.
Keywords:numerical modeling, borehole acoustic reflection survey, hydraulic fracture, Schoenberg linear slip model, spectral element method.
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