Simulating elastic wave propagation in boreholes: Fundamentals of seismic response and quantitative interpretation of well log data

Abstract

An analytic formulation oriented to understand the diffraction, dispersion and attenuation of borehole propagation modes is presented. The main aim of this article is to report to the scientific community the fundamentals of the seismic response at the well neighborhood, excited by an internal point source and present novelty simulation results compared against real data. An important, but not widely exploited technique to carefully investigate the elastic wave propagation in petroleum wells is the logging of sonic waveforms. The appropriate treatment and adequate processing of such microseismograms allow the extraction of useful information to characterize and understand the rock formation and is crucial on taking of decisions in the hydrocarbon production chain. In this work, the study of borehole wave propagation is based in the performing numerical simulations with the so–called Discrete Wave–number method applied to various cases of representative wells in Mexican reservoirs. The contributions of this investigation are: (1) to evince in the seismograms the strong effect of diffraction and dispersion of elastic waves, even working with the homogeneous isotropic case, (2) to describe in frequency and time domains, the propagation of waves generated by a point source in a cylindrical borehole filled with fluid, and 3) to compare controlled simulation results versus real data from geophysical logs. To validate our computations, time histories and dispersion curves are compared with down–hole sonic waveforms for several types of lithologies. The set of results reported here may be helpful for understanding and predicting the effects produced by the presence of fractures and heterogeneities over the wave propagation. It is expected that in the near future, mathematical modeling of sonic waveform logs can be established as a trustworthy technique.