Frequency-domain finite-element simulations of 2D sonic wireline borehole measurements acquired in fractured and thinly bedded formations

摘要

We simulated wireline borehole sonic waveforms to appraise modal frequency dispersions across fractured and thinly bedded formations. Simulations included monopole and dipole sources of excitation and explicitly took into account the borehole, the mandrel tool, and casing whenever present. Calculations were performed in the frequency domain with a highly accurate finite-element method that automatically generates optimal grids for each problem/frequency combination. The method guarantees solutions at significantly reduced computational time with relative energy errors below 0.5% (even in the presence of singularities in the solution that can originate from complex geometries, high material contrasts, and simultaneous presence of large and fine structures). Such a high accuracy in the simulation of sonic waveforms is necessary to accurately quantify the effects of fractures and thin beds on acoustic logs. Simulations indicate that fractures mainly influence propagation modes related to the formation shear velocity. In slow thinly bedded formations, effective properties are similar to those of average layer properties, as predicted by the Reuss lower bound. However, presence of intralayer interfaces gives rise to multiple reflections that can deleteriously affect the estimation of elastic properties with dispersion processing. Casing effectively functions as a low-pass frequency filter of sonic waveforms, significantly distorting the original borehole modes, hence the estimation of elastic properties.