Wave propagation in double-porosity dual-permeability materials: Velocity and attenuation

Sharma, M. D.

doi:10.1016/j.advwatres.2017.02.016

Cited by 15 publications

(22 citation statements)

References 23 publications

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“…Consequently, while looking at the plots for phase velocities of P 2 and P 3 waves, it may be noted that these velocities surpass the velocity of P 1 wave as the frequency increases beyond 1 MHz. A similar situation is faced in the propagation of attenuated waves in double-porosity dual-permeability materials (Sharma 2017). This clearly issues an alert that something is not good in the mathematical model, which is being solved to calculate these propagation characteristics.…”

Section: N U M E R I C a L E X A M P L Ementioning

confidence: 87%

“…Host to both pore-fluids is a porous skeleton with uniform bulk modulus (K), rigidity modulus (G) and a compressibility parameter α (Biot and Willis 1957). Following Sharma (2017), the constitutive relations for confining pressure averaged over isotropic porous aggregate ( p c ) and fluid pressures in porous phases ( p f 1 , p f 2 ) are expressed as follows:…”

Section: Constitutive Relationsmentioning

confidence: 99%

“…The equations of motion are considered for the time harmonic (∼ e −ıωt ) small vibrations of constituent particles in isotropic PSP media. Following Pride et al (2004) and Sharma (2017), these equations, in the absence of body forces, are written as follows:…”

Section: Equations Of Motionmentioning

confidence: 99%

“…Following the procedure of Sharma (2017), three complex velocities represent the propagation of three compressional waves in PSP solid. These velocities are obtained from the roots of a cubic equation, given by…”

Section: Velocitiesmentioning

confidence: 99%

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Propagation of seismic waves in patchy‐saturated porous media: double‐porosity representation

Sharma

2019

Geophysical Prospecting

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Propagation of harmonic plane waves is studied in a patchy‐saturated porous medium. Patchy distribution of the two immiscible fluids is considered in a porous frame with uniform skeletal properties. A composition of two types of patches, connected through continuous paths, constitutes a double‐porosity medium. Different compressibilities of pore‐fluids in two porous phases facilitate the wave‐induced fluid‐flow in this composite material. Constitutive relations are considered with frequency‐dependent complex elastic coefficients, which define the dissipative behaviour of porous aggregate due to the flow of viscous fluid in connected patches. Relevant equations of motion are solved to explain the propagation of three compressional waves and one shear wave in patchy‐saturated porous solids. A numerical example is solved to illustrate dispersion in phase velocity and quality factor of attenuated waves in patchy‐saturated porous materials. Role of fluid–solid inertial coupling in Darcy's law is emphasized to keep a check on the dispersion of wave velocities in the porous composite. Effects of patchy saturation on phase velocities and quality factors of attenuation are analysed using the double‐porosity formulation as well as the reduced single‐porosity equivalents.

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Section: N U M E R I C a L E X A M P L Ementioning

confidence: 87%

Section: Constitutive Relationsmentioning

confidence: 99%

Section: Equations Of Motionmentioning

confidence: 99%

Section: Velocitiesmentioning

confidence: 99%

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Propagation of seismic waves in patchy‐saturated porous media: double‐porosity representation

Sharma

2019

Geophysical Prospecting

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“…Those newly introduced parameters are difficult to measure in practice. Sharma () questioned a disadvantage of such models that at high frequencies, the predicted velocity of slow P wave can exceed that of fast P wave.…”

Section: Introductionmentioning

confidence: 99%

S wave attenuation based on Stokes boundary layer

2019

Geophysical Prospecting

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Biot theory was based on two ideas: the coupling factor to quantify the kinetic energy of fluid and Darcy permeability to quantify the dissipation function. As Biot theory did not well predict attenuation of ultrasonic S wave, we modify the theory to better characterize the S wave attenuation. The range of the coupling factor is at first estimated in view of fluid mechanics. Application of the original theory to water‐saturated Boise sandstone and brine‐saturated Berea sandstone shows that the model prediction significantly underestimates the S wave attenuation ultrasonically measured. For this reason, we replace Darcy permeability with variable permeability to improve the fluid momentum equation. The new model yields predictions of phase velocity and the quality factor both close to the ultrasonic measurements. The reason why the improved model is superior to Biot theory is that variable permeability is based on the Stokes boundary layer at the fluid–solid interface, thus accurately quantifying the viscous stress between the two phases. Finally, the length scale of the viscous stress is calculated in the mesoscopic sense.

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Reflection of plane seismic waves at the surface of double-porosity dual-permeability materials

2018

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The present work deals with the reflection of plane seismic waves at the stress-free plane surface of double-porosity dualpermeability material. The incidence of two main waves (i.e., P 1 and SV) is considered. As a result of the incident waves, four reflected (three longitudinal and one shear) waves are found in the medium. The expressions of reflection coefficients for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy for fully closed as well as perfectly open pores. Effect of incident direction on the partition of the incident energy is analyzed with the change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure. It has been confirmed from the numerical interpretation that during the reflection process, conservation of incident energy is obtained at each angle of incidence.

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Wave propagation in double-porosity dual-permeability materials: Velocity and attenuation

Cited by 15 publications

References 23 publications

Propagation of seismic waves in patchy‐saturated porous media: double‐porosity representation

Propagation of seismic waves in patchy‐saturated porous media: double‐porosity representation

S wave attenuation based on Stokes boundary layer

Reflection of plane seismic waves at the surface of double-porosity dual-permeability materials

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