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Abstract <p>The propagation of harmonic plane waves in a fractured porous medium saturated with two immiscible viscous fluids is important to be studied for modelling complex subsurface wave phenomena. Such multiphase fractured systems are commonly present in sedimentary rock formations, where the coexistence of immiscible fluids and fractures challenges conventional modelling approaches. Despite its relevance to geophysics, reservoir engineering, and environmental applications, studies in this area are limited. Traditional single-porosity models often fail to capture the coupled fluid–solid interactions and the added complexity introduced by fractures. The present study is motivated by the need to develop a more comprehensive understanding of wave propagation under these realistic conditions. The volume average approach is used to model the poroelastic solid in this study. Double porosity and double permeability are incorporated in the mathematical formulation. Analytical results yield complex wave velocities for five types of waves in the fractured porous solid saturated with two immiscible fluids. The interface between water and the fractured porous solid is considered as permeable, with both closed-pore and open-pore boundary conditions as particular cases of this realistic interface. The amplitude and energy ratios of the reflected and refracted waves are derived by hybrid numerical and analytical methods. Numerical computations are done to examine the phase velocity and attenuation of plane waves as a function of frequency. The effects of volume fractions, matrix and fracture permeabilities, and fluid saturation on phase velocities are also examined. The influence of incidence angle, frequency, fracture volume fraction, and partially opened surface pores significantly affects the energy partition. A comparison of Biot’s theory and volume average theory is also done to assess their relative merits in simulating the behaviour of porous media. The outcomes of this study provide useful insights into energy distribution in complex porous structures and have potential applications in subsurface imaging, reservoir characterisation, and underwater sound propagation. Further, results from earlier studies are reached as limiting cases for model validation.</p>

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Binary Poroelastic Model with Duality in Porosity and Permeability: Wave Propagation and Reflection-Refraction Phenomena

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Anil K. Vashishth,
  • Vishakha Gupta,
  • Sourab Kamboj

摘要

Abstract

The propagation of harmonic plane waves in a fractured porous medium saturated with two immiscible viscous fluids is important to be studied for modelling complex subsurface wave phenomena. Such multiphase fractured systems are commonly present in sedimentary rock formations, where the coexistence of immiscible fluids and fractures challenges conventional modelling approaches. Despite its relevance to geophysics, reservoir engineering, and environmental applications, studies in this area are limited. Traditional single-porosity models often fail to capture the coupled fluid–solid interactions and the added complexity introduced by fractures. The present study is motivated by the need to develop a more comprehensive understanding of wave propagation under these realistic conditions. The volume average approach is used to model the poroelastic solid in this study. Double porosity and double permeability are incorporated in the mathematical formulation. Analytical results yield complex wave velocities for five types of waves in the fractured porous solid saturated with two immiscible fluids. The interface between water and the fractured porous solid is considered as permeable, with both closed-pore and open-pore boundary conditions as particular cases of this realistic interface. The amplitude and energy ratios of the reflected and refracted waves are derived by hybrid numerical and analytical methods. Numerical computations are done to examine the phase velocity and attenuation of plane waves as a function of frequency. The effects of volume fractions, matrix and fracture permeabilities, and fluid saturation on phase velocities are also examined. The influence of incidence angle, frequency, fracture volume fraction, and partially opened surface pores significantly affects the energy partition. A comparison of Biot’s theory and volume average theory is also done to assess their relative merits in simulating the behaviour of porous media. The outcomes of this study provide useful insights into energy distribution in complex porous structures and have potential applications in subsurface imaging, reservoir characterisation, and underwater sound propagation. Further, results from earlier studies are reached as limiting cases for model validation.