Frequency Domain Characteristic of Acoustic Signals Generated by Proppant Slurry Flow Through Perforations

Abstract This study focused on the frequency domain characteristics of acoustic signals generated from sand-perforation interaction. The effects of parameters on the spectrum of sand-related signals were discussed in detail. The goal is to predict the frequency range of sand-perforation interaction with given operation parameters. The predicted frequency range can serve as a reference when locating the sand-related signals from distributed acoustic sensors (DAS) data. With the frequency range determined, sand-related signals can be isolated at each cluster location and utilized to estimate sand distribution among clusters for each fracturing stage. To determine the frequency domain characteristics of the sand-related signals, our approach combined the excitation frequencies and natural frequencies of a system to estimate the excited natural frequencies. We used the contact mechanics to estimate the contact time of sand and casing. With the contact time signal in the time domain, we used the Fourier transform to estimate the range of excitation frequency. The natural frequencies of a system can be determined from hammer tap tests and modal analysis with the finite element method. To estimate the natural frequencies of the system we used, both methods were conducted to the experimental apparatus. The estimated excited natural frequencies were compared to the sand-related frequencies determined in the slurry injection experiment to validate the approach. The comparison between excited natural frequencies from the two methods and sand-generated frequencies from experiments shows that the spectra had a good agreement on the peak frequency location. Indicating that the approach developed can estimate the sand-related frequencies well. Based on the model of excitation frequency, sand sizes from 50 to 100 meshes have a minor effect on the sand-related frequency peak location but result in different excitation amplitudes. Parameters including impact velocity, sand density, sand radius, Young's modulus, and Poisson's ratio of both sand and casing determine the excitation frequency range. Casing material properties and corresponding boundary conditions (constraint and stress) determine the natural frequencies of the system. To apply this approach to the field DAS data interpretation, since hammer impact cannot be applied to the casing buried underground, a high-speed jet generated by a perforating gun was selected as the excitation source. By analyzing the DAS signal right after the perforating, when the casing still vibrates, the damped natural frequency can be captured from the frequency domain. The captured damped natural frequency had an agreement with the sand-related signal determined during sand injection, which shows the possibility of estimating the range of the sand-related signal before sand injection. This study provides a novel approach to predicting the sand-related frequency range resulting from sand-casing collision. This approach can be further applied to the field high-frequency DAS data to improve the interpretation result for sand distribution among clusters.