Tube waves from a horizontal fluid‐filled fracture of a finite radius

Ziatdinov, S. I.; Bakulin, Andrey; Kashtan, Boris

doi:10.1190/1.2370278

Cited by 3 publications

(3 citation statements)

References 3 publications

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“…Fluid-filled fracture waves also have been investigated both numerically and in laboratory studies to explain volcanic tremors and monitoring of hydraulic fracturing (Chouet, 1986(Chouet, , 1988Ferrazzini et al, 1988;Tang and Cheng, 1988;Goloshubin, et al, 1994;Groenenboom and Falk, 2000;Groenenboom and van Dam, 2000;Groenenboom and Fokkema, 1998), Slow fluid waves are essential for generating tube-wave reflections from intersecting fractures (Hornby et al, 1989;Kostek et al, 1998 a, b;Derov et al, 2009;Ziatdinov et al, 2006). The high amplitudes of such waves make the solution of relevant problems rather simple, because we can ignore most other types of waves without compromising the result.…”

Section: Theory For a Fracture Previous Workmentioning

confidence: 99%

Low-frequency fluid waves in fractures and pipes

Korneev

2010

GEOPHYSICS

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Low-frequency analytical solutions have been obtained for phase velocities of symmetrical fluid waves within both an infinite fracture and a pipe filled with a viscous fluid.Three different fluid wave regimes can coexist in such objects, depending on the various combinations of object parameters. These regimes include Biot, Stoneley, and "narrow channel." Equations for velocities of all these regimes have explicit forms and are verified by comparisons with exact solutions. Computations suggest that for pipes, the most common is the Biot regime, while for fractures it is the Stoneley regime. For real rock in fractures, the Biot regime exists only when fluid is in a gaseous state. The dominant role of fractures in rock permeability at field scales and the strong amplitude and frequency effects of Stoneley guided waves suggest the importance of incorporating these effects within poroelastic theories.

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Section: Theory For a Fracture Previous Workmentioning

confidence: 99%

Low-frequency fluid waves in fractures and pipes

Korneev

2010

GEOPHYSICS

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“…Due to their sensitivity to properties of the surrounding formation and fractures intersecting the wellbore, tube waves or water hammer propagating along the well are widely used for formation evaluation and fracture diagnostics (Paillet, 1980;Paillet and White, 1982;Gooch, 1985a, 1985b;Holzhausen and Egan, 1986;Hornby et al, 1989;Tang and Cheng, 1989;Paige et al, 1992Paige et al, , 1995Kostek et al, 1998aKostek et al, , 1998bPatzek and De, 2000;Henry et al, 2002;Ziatdinov et al, 2006;Ionov, 2007;Wang et al, 2008;Derov et al, 2009;Mondal, 2010;Bakku et al, 2013;Carey et al, 2015;Livescu et al, 2016). Here, we are specifically concerned with low-frequency tube waves having wavelengths much greater than the wellbore radius.…”

Section: Introductionmentioning

confidence: 97%

“…By focusing instead on lower frequencies (< 100 Hz) and considering Krauklis waves reflected from the fracture tip, Henry et al (2002) and Henry (2005) argued that reflection/transmission of tube waves is affected by the resonance of the fracture, and this consequently provides sensitivity to fracture length. One approach to account for the finite extent of the fracture is to use the dispersion relation for harmonic Krauklis waves to determine the eigenmodes of a circular disk-shaped fracture of uniform aperture with a zero radial velocity boundary condition at the edge of the disk (Hornby et al, 1989;Henry et al, 2002;Henry, 2005;Ziatdinov et al, 2006;Derov et al, 2009). This treatment fails to account for the decreased aperture near the fracture edge, which decreases the Krauklis-wave phase velocity and increases the viscous dissipation.…”

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confidence: 99%

Hydraulic fracture diagnostics from Krauklis-wave resonance and tube-wave reflections

et al. 2017

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Fluid-filled fractures support guided waves known as Krauklis waves. The resonance of Krauklis waves within fractures occurs at specific frequencies; these frequencies, and the associated attenuation of the resonant modes, can be used to constrain the fracture geometry. We use numerical simulations of wave propagation along fluid-filled fractures to quantify fracture resonance. The simulations involve solution of an approximation to the compressible Navier-Stokes equation for the viscous fluid in the fracture coupled to the elastic-wave equation in the surrounding solid. Variable fracture aperture, narrow viscous boundary layers near the fracture walls, and additional attenuation from seismic radiation are accounted for in the simulations. We then determine how tube waves within a wellbore can be used to excite Krauklis waves within fractures that are hydraulically connected to the wellbore. The simulations provide the frequency-dependent hydraulic impedance of the fracture, which can then be used in a frequency-domain tube-wave code to model tube-wave reflection/ transmission from fractures from a source in the wellbore or at the wellhead (e.g., water hammer from an abrupt shut-in). Tube waves at the resonance frequencies of the fracture can be selectively amplified by proper tuning of the length of a sealed section of the wellbore containing the fracture. The overall methodology presented here provides a framework for determining hydraulic fracture properties via interpretation of tube-wave data.

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Krauklis wave in a stack of alternating fluid-elastic layers

Korneev

2011

GEOPHYSICS

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TitleKrauklis wave in a stack of alternating fluid-elastic layers ABSTRACTThe Krauklis wave is a slow dispersive wave mode that propagates in a fluid layer bounded by elastic media. In a model of alternating fluid and elastic layers, two interface waves can exist at low frequencies: The first wave propagates mostly in the elastic layer and has little dispersion, while the second wave can have strong dispersion and propagates as a Krauklis wave for some parameter combinations. Analytical conditions predict appearance of the Krauklis wave for higher frequencies and low porosities. Interface-wave velocities depend on model porosity, which potentially can be used for fracture mapping.

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Tube waves from a horizontal fluid‐filled fracture of a finite radius

Cited by 3 publications

References 3 publications

Low-frequency fluid waves in fractures and pipes

Low-frequency fluid waves in fractures and pipes

Hydraulic fracture diagnostics from Krauklis-wave resonance and tube-wave reflections

Krauklis wave in a stack of alternating fluid-elastic layers

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