In hydraulic-fracturing design and oil-recovery efficiency prediction, quantitative evaluation of perforation and its penetration depth is often desired, for which an effective method needs to be developed. We have developed a perforated cased-borehole model for the field test configuration and simulated the elastic wave propagation in the model excited by a borehole monopole source using the finite-difference method. After a multivariate regression analysis, the simulation results yield a relationship for the perforation penetration depth versus the induced P-wave traveltime change and formation slowness. For field application purposes, borehole array acoustic logging with a perforated borehole model is simulated. The calculated waveform data, in conjunction with the above-mentioned relationship, yield an accurate estimate of the perforation penetration depth. A field perforation test is used to develop application of our method.

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