Numerical Simulation of Filtration Noise
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Radiophysics and Quantum Electronics, Vol. 63, No. 2, July, 2020 (Russian Original Vol. 63, No. 2, February, 2020)
NUMERICAL SIMULATION OF FILTRATION NOISE A. V. Lebedev∗
UDC 534.131.1+532.685
We numerically simulate filtration noise within the framework of the earlier proposed model for the generation of acoustic noise as a result of excitation of relaxation self-oscillations. The simulation is performed for typical parameters of reservoir rocks. As a result, appearance of the radiation frequencies observed in the experiment is demonstrated. It is also shown that due to the nonlinear interaction between elementary sources of the acoustic radiation, its spectrum is enriched with combination frequencies. In the case where the ratios of the frequencies of the interacting oscillators are fractional, the acoustic interaction can lead to nonlinear synchronization of elementary radiation sources.
1.
INTRODUCTION AND STATEMENT OF THE PROBLEM
The authors of work [1] published in 1973 discussed the information content of amplitude-frequency spectra of acoustic noise in studies of the characteristics of turbulent flows of fluids in production wells and the borehole annuB A lus. The results obtained in [1] served as an impetus for the development of fluid flow diagnostics for the oil and gas industry. Analysis of low-frequency acoustic noise in the band from fractions of a hertz to several kilohertz was used to diagnose the rate of fluid influx from the formation to the zone adjacent to the well. Analysis of noise in Fig. 1. Operation of the injection (A) and devel- the 5–100 kHz band, which is reasonably related to the opment (B) wells. flow of the fluid in pores, allows one to perform passive acoustic diagnostics of fluid influx from the zones farther from the well. Up to now, the mechanism of radiation of acoustic waves by the turbulent flows in pores, which was proposed in [2], has been regarded as the source of noise in these zones [3–6]. We believe that this idea is not right, since the Reynolds number of the corresponding flows is small. Note that the flow in the well, which was studied in [1], is characterized by great values of the Reynolds number, and the generation of noise by such a flow is actually determined by turbulent pulsations of the fluid flow. The scheme of operation of the injection and development wells in a homogeneous porous medium (top view) is shown in Fig. 1, which is an adaptation of Fig. 40 from [7]. The solid lines with arrows indicate the flow paths, and the dashed lines show the isobars. The pressure at the point A (source) exceeds the pressure at the point B (sink). This makes the fluid in the pores move in the required direction, e.g., push the oil to the top of the development well (point B). The flow path shown by the straight line connecting the points A and B corresponds to the experiments with samples of porous rocks [3, 4]. ∗
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Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radio
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