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Volume 69, Issue 3
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Stress, rock microstructure and frequency are the three key factors that influence the velocities of elastic waves and, hence, are sensitive to the Biot effective stress parameter (α) in porous rocks. The effective stress in an isotropic poroelastic medium relates to applied pressure and pore pressure, with the Biot parameter (α) as a scaling factor of the pore pressure. This paper provides an independent derivation of the tensor characteristics of α through elastic moduli, a microscopic effective medium derivation, and frequency‐dependent behaviour of α for an anisotropic medium. We provide an explicit expression, especially for isotropic rock under uniaxial stress, considering the nonlinear part of elastic constants. In the effective medium derivation, we assumed that the rock contained both isolated pores and connected pores saturated with liquid. To support our theoretical formulation, we calculated the Biot tensor of sandstone and shale by inverting the ultrasonic velocities of transversely isotropic rock under uniaxial stress where mineralogical composition and porosity are known. Even though porosity and rock microstructure play significant roles in α as stress varies, we also see as much as a 21% difference between horizontal and vertical components of α for rocks with transversely isotropic symmetry. We then estimated the frequency‐dependent Biot tensor for transversely isotropic models using numerical calculations. We noticed significant differences between vertical (α) and horizontal (α) components of α, especially at the surface seismic frequency band. However, uniaxial stress and horizontally aligned microstructure influence the elastic moduli and Biot tensor contrarily. In general, anisotropy due to uniaxial stress shows lower α and higher α. The proposed method shows an excellent prediction of α and α for given data of uniaxial stress and vice versa.

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2021-02-12
2024-04-26

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Biot effective stress parameter in poroelastic anisotropic media: Static and dynamic case
Geophysical Prospecting 69, 530 (2021); https://doi.org/10.1111/1365-2478.13046
/content/journals/10.1111/1365-2478.13046
/content/journals/10.1111/1365-2478.13046
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  • Article Type: Research Article
Keyword(s): Anisotropy; Mathematical formulation; Rock physics; Theory; Time lapse

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