Longitudinal waves in partially saturated porous media: the effect of gas bubbles

Dunin, S. Z.; Mikhailov, D. N.; Nikolayevskii, V.N.

doi:10.1016/j.jappmathmech.2006.06.008

Cited by 12 publications

(7 citation statements)

References 13 publications

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“…Figures 1-3 illustrate the normalized frequency-dependent (Ω = ω/ω c ) dispersion profiles of the phase velocity, damping, and phase lag. As expected, the first wave (see Figure 2) is a slightly decaying high-velocity mode, and the relative motion of fluid and solid phases is the in-phase [26,32,33], exhibiting a pressure-relaxation phenomenon [30], whereas the second wave (see Figure 3) is a strongly damping slow-velocity mode and the movement of fluid and solid phases is the out-of-phase [32,33], showing the feature of diffusion waves [28], in which the pore pressure predominates over the effective stress [26]. As seen in Figure 4, under the condition of λ 1 λ 4 λ 7 = λ 2 λ 5 λ 6 , the properties of the first and second waves coincide.…”

Section: Phase Velocity and Damping Of The First And Secondsupporting

confidence: 78%

“…The coincidence of the properties of Biot waves of the first and second kinds occurs at a characteristic frequency, at which the properties of the first and second waves coincide [25]. Under conditions of two-phase flows, the resonance frequency of the gas is the governing factor for the transition of the wave modes [26]. The strong decay of compressional waves is attributed to the viscous coupling effect [27,28] and the Darcy viscous resistance [29][30][31].…”

Section: Introductionmentioning

confidence: 99%

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Propagation of Pore Pressure and Stress in Saturated Porous Media Based on a Darcy-Brinkman Formulation

Yang

Zhang

2021

Geofluids

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Propagation of pore pressure and stress in water-saturated elastic porous media is theoretically investigated when considering the Darcy-Brinkman law. The wave mode, phase velocity, phase lag, damping factor, and characteristic frequency are found from the updated mathematic model. The Brinkman term describes the fluid viscous shear effects and importantly contributes to the dispersion relation and wave damping. The coincidence of the properties of Biot waves of the first and second kinds occurs at a characteristic frequency, which is remarkably influenced by the Brinkman term. A key finding is that, compared to the Darcy-Brinkman law, Darcy’s law overestimates the phase velocity, damping, and phase lag of the first wave, while underestimates the phase velocity, damping, and phase difference of the second wave. The introduction of the Darcy-Brinkman law yields an improved description of the damping of the compressional wave modes in saturated porous media.

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Section: Phase Velocity and Damping Of The First And Secondsupporting

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Propagation of Pore Pressure and Stress in Saturated Porous Media Based on a Darcy-Brinkman Formulation

Yang

Zhang

2021

Geofluids

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“…Similarly to [15] , we also assume that the pore pressure p is equal to the pressure in the liquid far from the bubble.…”

Section: Dynamics Of Bubblesmentioning

confidence: 99%

“…From [15]- [21], the values of the parameters are: densities, ( [14,16,21,22], the values of the parameters of the rheological scheme in Fig.2 [16,23]. We will also explore the values of E i obtained by a different method, namely by using the formula 2 c  for all three phases, with  being the density of the liquid, solid and gas, respectively,…”

Section: Evaluation Of the Parameters And The Wave Velocitymentioning

confidence: 99%

The Effect of Rheology with Gas Bubbles on Linear Elastic Waves in Fluid-Saturated Granular Media

Ali

Strunin

2018

International Journal of Applied Mechanics and Engineering

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Elastic waves in fluid-saturated granular media depend on the grain rheology, which can be complicated by the presence of gas bubbles. We investigated the effect of the bubble dynamics and their role in rheological scheme, on the linear Frenkel-Biot waves of P1 type. For the wave with the bubbles the scheme consists of three segments representing the solid continuum, fluid continuum and bubbles surrounded by the fluid. We derived the Nikolaevskiy-type equation describing the velocity of the solid matrix in the moving reference system. The equation is linearized to yield the decay rate λ as a function of the wave number k. We compared the λ (k) -dependence for the cases with and without the bubbles, using typical values of the input mechanical parameters. For both the cases, the λ(k) curve lies entirely below zero, which implies a global decay of the wave. We found that the increase of the radius of the bubbles leads to a faster decay, while the increase in the number of the bubbles leads to slower decay of the wave.

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“…The energy transfer between the wave, solid, and fluids when the medium is stimulated near the resonant frequency was analyzed by Frehner et al (2009); the attenuation of wave energy reached its maximum when resonance occurred. In addition, the attenuation and dispersion relation of a compressional wave in partially saturated porous media with gas bubbles were analyzed with the consideration of bubble resonance (Bedford & Stern, 1983; Dunin et al, 2006), and it was concluded that the resonance of nonwetting fluid cannot be ignored in wave attenuation and dispersion analysis. The gas resonance model used in the studies was based on the spherical bubble shape in a simple REV.…”

Section: Introductionmentioning

confidence: 99%

Effect of Subsurface Microseisms on the Motion of Dispersed Droplets in Pores

Zeng

Deng

2020

JGR Solid Earth

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Human-induced seismicity has drawn substantial attention in recent years. The effect of seismicity on subsurface structures has been studied extensively. However, the effect of seismicity, especially microseismicity, on surrounding immiscible fluids is rarely investigated. In porous media with two or more immiscible fluids, different amplitudes of vibration induced by seismicity have distinct effects on the dynamic behavior of the fluids. Three types of pore-scale models are prevalent for analyzing the motion of immiscible droplets. The underlying assumptions and accuracy of these models are compared in this study in both the frequency and time domains. The frequency domain analysis shows that resonance can be addressed in all three of the models; the frequency response curves, however, present significant differences, which are attributed to the missing physics considered in some models. Time domain analysis is performed in both small-amplitude and large-amplitude oscillation. The nonlinearity in large-amplitude oscillation is attributed to the constricted geometry of the capillary tube. Although the term "large-amplitude" is used in this study, the corresponding amplitude is still within the amplitude range of microseisms. The momentum balance model is identified as the most accurate oscillatory model so far in comparison with computational fluid dynamics simulations. In addition, the potential approach to incorporate this pore-scale model in seismic wave attenuation analysis is found to be possible. The frequency correction function and structural factor are calculated to embed the momentum balance model into Biot's poroelastic model. The resonance of the dispersed phase can also be addressed theoretically in porous media of random packed spheres.

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Longitudinal waves in partially saturated porous media: the effect of gas bubbles

Cited by 12 publications

References 13 publications

Propagation of Pore Pressure and Stress in Saturated Porous Media Based on a Darcy-Brinkman Formulation

Propagation of Pore Pressure and Stress in Saturated Porous Media Based on a Darcy-Brinkman Formulation

The Effect of Rheology with Gas Bubbles on Linear Elastic Waves in Fluid-Saturated Granular Media

Effect of Subsurface Microseisms on the Motion of Dispersed Droplets in Pores

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