Dynamic bulk and shear moduli due to grain-scale local fluid flow in fluid-saturated cracked poroelastic rocks: Theoretical model

Song, Yanping; Hu, Hengshan; Rudnicki, John W.

doi:10.1016/j.jmps.2016.03.019

Cited by 23 publications

(3 citation statements)

References 39 publications

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“…The model can be further extended if the diverse energy loss mechanisms present in the subsurface, which are not explicitly considered in Biot's equations are taken into account. One example of these mechanisms is the so called wave induce fluid flow, studied by several authors [Pride et al, 2004;Rubino et al, 2008;Picotti et al, 2007;Song et al, 2016]. With this goal, instead of considering particular loss processes, we consider that the studied region presents a viscoelastic behaviour, and we use Biot's correspondence principle [Biot, 1956c[Biot, , 1962, replacing the (real) relaxed elastic moduli G and K by complex frequency dependent viscoelastic moduli.…”

Section: Extended Modelsmentioning

confidence: 99%

Finite Element Modeling of Electroseismics and Seismoelectrics

Zyserman

Gauzellino

Jouniaux

2020

Geophysical Monograph Series

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In this chapter we describe a set of finite element formulations employed to approximate the solution to an extension to partially saturated porous media of Pride's equations, which is one of the most widespread theoretical frames that model the coupled electromagnetics and acoustics of saturated porous media. We also show how these numerical algorithms can be implemented on multi-core computers, and analyse their performance, observing that the parallel efficiency of the algorithms decays slower when the resources of each computing core are used as close to their maximum as possible. Further, we perform a study of two dimensional PSVTM electroseismic conversions in a time-lapse carbon dioxide geological deposition monitoring scenario, setting the electromagnetic source in depth, and measuring the seismic responses both in wells and at the surface. We observe that, contrary to what is known from standard field settings, the interface responses play no important role in elucidating the CO 2 plume behaviour, and that the in-depth converted signals convey information about the carbon dioxide saturation in the plume.

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Section: Extended Modelsmentioning

confidence: 99%

Finite Element Modeling of Electroseismics and Seismoelectrics

Zyserman

Gauzellino

Jouniaux

2020

Geophysical Monograph Series

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“…Second, the dynamical moduli caused by pore-scale fluid flow show that the major physical factor in determining the elastic properties is the heterogeneous fluid pressure distribution (Mavko and Jizba, 1991). In fact, Eshelby's solution has been proven to be very useful in studying the pore-scale fluid flow between connected pores (squirt-flow mechanism, see O' Connell and Budiansky, 1977;Chapman et al, 2002;Pride et al, 2004;Gurevich et al, 2010;Tang et al, 2012;Song and Hu, 2013;Song et al, 2016). On the basis of these evidences, we believe that the assumption of homogeneous pore pressure can be used in MT and KT models at low frequencies.…”

Section: Eshelby's Single-inclusion Solutionmentioning

confidence: 99%

“…A potential application of this paper is using the stress-dependent effective modulus expressions 29 and 48 to develop an inclusion-based dynamic modulus model. The application is the subject of another paper (Song et al, 2016).…”

Section: Original Kt Schemementioning

confidence: 99%

Deriving Biot-Gassmann relationship by inclusion-based method

Song

Rudnicki

2016

GEOPHYSICS

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The quasi-static theory of poroelasticity presented by Biot and Gassmann provides a relationship between the drained and undrained elastic constants of an isotropic fluid-saturated porous material in terms of the porosity of the material, bulk modulus of the solid grains, and bulk modulus of the pore fluid. We have developed an alternative approach to derive the Biot-Gassmann (BG) relationship while including the effects of the pore microstructure. First, the Eshelby transformation is used to express the local inclusion/pore strain tensor in terms of the applied strain tensor and reference material elastic properties by the superposition of a void strain and a perturbation term due to induced inclusion stress. Second, the inclusion strain expression and Hill's average principles are combined with the Mori-Tanaka/Kuster-Toksöz scheme to obtain inclusion-stress-dependent effective elastic moduli of porous materials. For an isolated pore system, the effective modulus tensor corresponds to the original Mori-Tanaka/Kuster-Toksöz's expression. Although for communicating pore system, it is proven to satisfy the BG relation. In the second case, the deformation is assumed to occur so slowly that the infiltrating fluid mass has sufficient time to diffuse between material elements and, consequently, the pore fluid pressure is equilibrated within the whole pore system. It is noteworthy that we arrive at a BG relationship without applying reciprocity theorem and that the porous material effective strain is defined from Hill's principles instead of solid phase average strain. A potential application of the stress-independent effective modulus is to help develop a dynamical modulus model of rock physics for a specific pore microstructure.

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