Effect Of Turbulent Flow In Pores On Elastic Wave Dispersion And Attenuation In Porous Media

Underground rocks can be regarded as porous media containing fluid(oil or water), which are the main research objects in the field of acoustic logging and geological exploration. Biot theory of poroelasticity is widely used to simulate propagation of elastic waves in porous media and investigate dispersion and attenuation characteristics of the elastic waves. However, in high frequencies, the wave attenuation predicted by Biot theory is much lower than that observed by experiments, so the inversion methods based on Biot theory are unable to give precise reservoir parameters in high frequencies. In this paper, it is realized that the high frequency pulse sources in acoustic logging and seismic exploration can cause the turbulent flow of pore fluid, which leads to the dissipation of wave energy, but only laminar flow of pore fluid is considered in Biot theory. Therefore, it is necessary to establish a theoretical model of wave propagation in porous media which includes the turbulent motion effects of pore fluid.Pipe oscillation constant turbulent model is established based on the oscillating viscosity layer thickness and Prandtl pipe constant turbulent model. After that, the velocity distribution of turbulence flow section of cross section of passage, the turbulent drag coefficient, and turbulent viscosity correction coefficient are given.Viscosity correction coefficient is constructed for the full frequency range. When the wave frequency is lower than the flow critical frequency, this coefficient equals Biot viscosity correction coefficient. When the wave frequency is higher than the flow critical frequency, this coefficient equals turbulence viscosity correction coefficient. Then the turbulence correction model of elastic wave propagation in porous media is established, by replacing in Biot theory frame the Biot viscosity correction coefficient by the full frequency viscosity correction coefficient.The numerical algorithm to calculate the flow critical frequency is given using critical oscillation viscosity layer thickness and continuity conditions of wave attenuation. By calculating the wave attenuation curves of Biot viscosity correction coefficient, full frequency viscosity correction coefficient with Biot characteristic frequency to be the flow critical frequency, and turbulent viscosity correction coefficient, it is found that the three curves intersect at a point and are smoothly tangent to each other. This concludes that the flow critical frequency can be approximated to Biot characteristic frequency.Numerical calculations for different formations show that the wave attenuation predicted by the turbulence correction model is greater than that predicted by Biot model when frequency is higher than the threshold frequency, for all the formation models containing water, oil, or gas. Therefore, our turbulence correction model can be used to explain the high wave attenuations observed by experiments. The calculation results of threshold frequency show that oscillation turbulence is most likely to occur in gas-containing formations, less likely in water-containing formations, and least likely in oil-containing formations.