Computational Fluid Dynamics Modeling of Acoustics Generated by Fluid Flow Through a Perforation

Abstract

Abstract Fiber optic sensing technology is a useful tool in diagnosing fracture generation during hydraulic fracturing. Distributed acoustic sensing (DAS) monitors the local acoustic vibrations around the fiber optic cable in real time. In particular, the audible frequency range of DAS is sensitive to the sound induced by fluid flow through perforations and can be used to estimate fluid distribution through each cluster of a multiple stage fracture treatment. As perforations erode during fracture pumping, the acoustic signals decay rapidly, and the DAS waterfall plot used in the field may result in misleading interpretation. To understand the relationship between flow path geometries and flow rates to acoustic responses, a theoretical model was built in this study. Computational fluid dynamics (CFD) was used to calculate the acoustic waves generated by fluid flow through a perforation with defined geometry. The model investigates the relationships of perforation diameters and flow rates. The acoustic model in CFD consists of two steps: solving the pressure profile due to fluid flow in the corresponding geometry; and calculating the acoustic pressure at the specified receiver locations. After time-domain acoustic pressure is transformed into frequency-domain by using Fast Fourier Transform (FFT), the sound pressure level is calculated and evaluated. For computational efficiency, a small-scaled CFD model with a single perforation and 2 in I.D. casing size was built and used to determine the appropriate sampling frequency and mesh size. The result was upscaled in the CFD model to a single perforation and 4.77 in I.D. casing. The impact of important parameters on the fluid flow-induced acoustics around the perforation was evaluated. The parameters included the perforation diameter, fluid flow rate, fluid flow energy, roundness of the perforation entrance and perforation shape. The results are compared with experimental observations. From a sensitivity study, it was observed that small sampling frequencies caused aliasing errors which results in the formation of incorrect frequency peaks. The energy of the fluid flow through a perforation, expressed as the multiple of perforation pressure drop and flow rate, correlates with the sound pressure level. It was also noticed that the roundness of perforation entrances significantly reduces the sound pressure level. As the perforation size increases because of erosion, the characteristics of acoustic signals change, clearly indicating the enlargement of the perforation hole. The findings of this study help to understand DAS measurements and its interpretation for perforation performance and fluid distribution in fracture stimulation.