Forced oscillation measurements of seismic wave attenuation and stiffness moduli dispersion in glycerine‐saturated Berea sandstone

Chapman, Samuel; Borgomano, Jan V. M.; Yin, Hanjun; Fortin, Jérôme; Quintal, Beatriz

doi:10.1111/1365-2478.12710

Cited by 41 publications

(33 citation statements)

References 38 publications

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“…Indeed, strong and frequency-dependent attenuation has been observed in fluidsaturated rocks, mostly through laboratory experiments, and has been interpreted as a result of wave-induced fluid pressure diffusion (FPD), often denoted wave-induced fluid flow, at the microscopic or mesoscopic scales (e.g. Best, McCann and Sothcott 1994;Sams et al 1997;Batzle, Han and Hofmann 2006;Adelinet et al 2010;Tisato and Quintal 2013;Pimienta, Fortin and Guéguen 2015;Subramaniyan et al 2015;Chapman et al 2016Chapman et al , 2019.…”

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confidence: 99%

Numerically quantifying energy loss caused by squirt flow

Quintal

Caspari

Holliger

et al. 2019

Geophysical Prospecting

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In interconnected microcracks, or in microcracks connected to spherical pores, the deformation associated with the passage of mechanical waves can induce fluid flow parallel to the crack walls, which is known as squirt flow. This phenomenon can also occur at larger scales in hydraulically interconnected mesoscopic cracks or fractures. The associated viscous friction causes the waves to experience attenuation and velocity dispersion. We present a simple hydromechanical numerical scheme, based on the interface‐coupled Lamé–Navier and Navier–Stokes equations, to simulate squirt flow in the frequency domain. The linearized, quasi‐static Navier–Stokes equations describe the laminar flow of a compressible viscous fluid in conduits embedded in a linear elastic solid background described by the quasi‐static Lamé–Navier equations. Assuming that the heterogeneous model behaves effectively like a homogeneous viscoelastic medium at a larger spatial scale, the resulting attenuation and stiffness modulus dispersion are computed from spatial averages of the complex‐valued, frequency‐dependent stress and strain fields. An energy‐based approach is implemented to calculate the local contributions to attenuation that, when integrated over the entire model, yield results that are identical to those based on the viscoelastic assumption. In addition to thus validating this assumption, the energy‐based approach allows for analyses of the spatial dissipation patterns in squirt flow models. We perform simulations for a series of numerical models to illustrate the viability and versatility of the proposed method. For a 3D model consisting of a spherical crack embedded in a solid background, the characteristic frequency of the resulting P‐wave attenuation agrees with that of a corresponding analytical solution, indicating that the dissipative viscous flow problem is appropriately handled in our numerical solution of the linearized, quasi‐static Navier–Stokes equations. For 2D models containing either interconnected cracks or cracks connected to a circular pore, the results are compared with those based on Biot's poroelastic equations of consolidation, which are solved through an equivalent approach. Overall, our numerical simulations and the associated analyses demonstrate the suitability of the coupled Lamé–Navier and Navier–Stokes equations and of Biot's equations for quantifying attenuation and dispersion for a range of squirt flow scenarios. These analyses also allow for delineating numerical and physical limitations associated with each set of equations.

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Numerically quantifying energy loss caused by squirt flow

Quintal

Caspari

Holliger

et al. 2019

Geophysical Prospecting

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“…Laboratory measurements of seismic attenuation on fluid‐saturated rock samples are usually obtained under variable confining pressure at ranges affecting the rocks in subsurface (e.g., Chapman et al, ; Pimienta et al, ; Subramaniyan et al, ). The increase of confining pressure on cracked rock samples produces the occurrence of contact areas between crack walls or compliant pores, which in turns increases the overall stiffness of the rock (Shapiro, ).…”

Section: Resultsmentioning

confidence: 99%

“…The consequent friction between particles of the viscous fluid dissipates energy. Squirt flow evidence at seismic and sonic frequencies were shown in laboratory experiments in which glycerine‐saturated samples of Fontainebleau and Berea sandstones, as well as of limestones, were submitted to forced oscillations by Pimienta et al (), Subramaniyan et al (), Borgomano et al (), and Chapman et al ().…”

Section: Introductionmentioning

confidence: 97%

Squirt Flow in Cracks with Rough Walls

et al. 2020

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We explore the impact of roughness in crack walls on the P wave modulus dispersion and attenuation caused by squirt flow. For that, we numerically simulate oscillatory relaxation tests on models having interconnected cracks with both simple and intricate aperture distributions. Their viscoelastic responses are compared with those of models containing planar cracks but having the same hydraulic aperture as the rough wall cracks. In the absence of contact areas between crack walls, we found that three apertures affect the P wave modulus dispersion and attenuation: the arithmetic mean, minimum aperture, and hydraulic aperture. We show that the arithmetic mean of the crack apertures controls the effective P wave modulus at the low-and high-frequency limits, thus representing the mechanical aperture. The minimum aperture of the cracks tends to dominate the energy dissipation process and, consequently, the characteristic frequency. An increase in the confining pressure is emulated by uniformly reducing the crack apertures, which allows for the occurrence of contact areas. The contact area density and distribution play a dominant role in the stiffness of the model, and in this scenario, the arithmetic mean is not representative of the mechanical aperture. On the other hand, for a low percentage of minimum aperture or in the presence of contact areas, the hydraulic aperture tends to control the characteristic frequency. Analyzing the local energy dissipation, we can more specifically visualize that a different aperture controls the energy dissipation process at each frequency, which means that a frequency-dependent hydraulic aperture might describe the squirt flow process in cracks with rough walls. Key Points:• We solve the quasi-static linearised Navier-Stokes equations coupled to elasticity equations • Seismic attenuation due to squirt-flow is strongly affected by the roughness of the crack walls • The minimum and the hydraulic apertures significantly affect the energy dissipation process presented a comparison between numerical results and an analytical model for squirt flow. In general, accepted analytical models should reproduce the equations of Gassmann (1951) in the low-frequency limit (Chapman et al., 2002). The reason is that at the relaxed state for undrained boundary conditions (low-frequency limit), the time of a half period of a passing wave allows for fluid pressure to equilibrate through FPD. At the unrelaxed state (high-frequency limit), the fluid pressure has no time to equilibrate during a half period of a passing wave and the elastic properties of the saturated material are predicted by the formulation of Mavko and Jizba (1991), which assumes that no FPD occurs during the passage of the wave. At intermediate frequencies, FPD occurs inside the cracks during the passage of the wave and part of its energy is dissipated. Nevertheless, all analytical solutions assume smooth walls for the cracks despite the fact that crack walls in rocks have been observed to present complex profiles including wall roughnes...

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“…Seismic properties of the glass specimen FDL2 of Li et al () were measured with the low‐frequency apparatus at the Laboratoire de Géologie, of ENS Paris. A more detailed description of the setup has been provided elsewhere (e.g., Borgomano et al, ; Chapman, Borgomano et al, and recently in Yin et al, ). Here, only a summary of the essential components is provided for completeness.…”

Section: Experimental Methodsmentioning

confidence: 99%

Poroelastic Relaxation in Thermally Cracked and Fluid‐Saturated Glass

et al. 2020

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To test theoretical models of modulus dispersion and dissipation in fluid‐saturated rocks, we have investigated the broadband mechanical properties of four thermally cracked glass specimens of simple microstructure with complementary forced‐oscillation (0.004–100 Hz) and ultrasonic techniques (~1 MHz). Strong pressure dependence of moduli (bulk, Young's, and shear), axial strain, and ultrasonic wave speeds for dry conditions attests to essentially complete crack closure at a confining pressure of 15 MPa—consistent with ambient‐pressure crack aspect ratios ≤2 × 10−4. Oscillation of the confining pressure reveals bulk modulus dispersion and a corresponding dissipation peak, near 0.002 Hz only at the lowest effective pressure (2.5 MPa)—attributed to the transition with increasing frequency from the drained to saturated‐isobaric regime. The observations are consistent with Biot‐Gassmann's theory, with dispersion and dissipation adequately represented by Zener model. Above the draining frequency, axial forced‐oscillation tests show dispersion relatively low differential press's modulus and Poisson's ratio, and an associated broad dissipation peak centered near 0.3 Hz, thought to reflect local “squirt” flow and adequately modeled with a continuous distribution of relaxation times over two decades. Observations of Young's and shear moduli dispersion and dissipation from complementary flexural and torsional oscillation measurements for differential pressure ≤10 MPa provide supporting evidence of the transition with increasing frequency from the saturated‐isobaric to the saturated‐isolated regime—also probed by ultrasonic technique. These findings validate predictions from theoretical models of dispersion in cracked media and emphasize need for caution in the seismological application of laboratory ultrasonic data for cracked media.

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Forced oscillation measurements of seismic wave attenuation and stiffness moduli dispersion in glycerine‐saturated Berea sandstone

Cited by 41 publications

References 38 publications

Numerically quantifying energy loss caused by squirt flow

Numerically quantifying energy loss caused by squirt flow

Squirt Flow in Cracks with Rough Walls

Poroelastic Relaxation in Thermally Cracked and Fluid‐Saturated Glass

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